摘要:

GENERAL DISCUSSIONS OF THE FARADAY SOCIETY Date 1907 1907 1910 191 1 1912 1913 1913 1913 1914 1914 1915 1916 1916 1917 1917 1917 1918 1918 1918 1918 1919 1919 1920 1920 1920 1920 1921 1921 1921 1921 1922 1922 1923 1923 1923 1923 1923 1924 1924 1924 1924 1924 1925 1925 1926 1926 1927 1927 1927 Subject Osmotic Pressure Hydrates in Solution The Constitution of Water High Temperature Work Magnetic Properties of Alloys Colloids and their Viscosity The Corrosion of Iron and Steel The Passivity of Metals Optical Rotary Power The Hardening of Metals The Transformation of Pure Iron Methods and Appliances for the Attainment of High Temperatures in a Refractory Materials Training and Work of the Chemical Engineer Osmotic Pressure Pyrometers and Pyrometry The Setting of Cements and Plasters Electrical Furnaces Co-ordination of Scientific Publication The Occlusion of Gases by Metals The Present Position of the Theory of Ionization The Examination of Materials by X-Rays The Microscope : Its Design, Construction and Applications Basic Slags : Their Production and Utilization in Agriculture Physics and Chemistry of Colloids Electrodeposition and Electroplating Capillarity The Failure of Metals under Internal and Prolonged Stress Physico-Chemical Problems Relating to the Soil Catalysis with special reference to Newer Theories of Chemical Action Some Properties of Powders with special reference to Grading by The Generation and Utilization of Cold Alloys Resistant to Corrosion The Physical Chemistry of the Photographic Process The Electronic Theory of Valency Electrode Reactions and Equilibria Atmospheric Corrosion.First Report Investigation on Oppau Ammonium Sulphate-Nitrate Fluxes and Slags in Metal Melting and Working Physical and Physico-Chemical Problems relating to Textile Fibres The Physical Chemistry of Igneous Rock Formation Base Exchange in Soils The Physical Chemistry of Steel-Making Processes Photochemical Reactions in Liquids and Gases Explosive Reactions in Gaseous Media Physical Phenomena at Interfaces, with special reference to Molecular Atmospheric Corrosion. Second Report The Theory of Strong Electrolytes Cohesion and Related Problems Laboratory Elutriation Orientation Volume Trans. 3 3 6 7 8 9 9 9 10 10 11 12 12 13 13 13 14 14 14 14 15 15 16 16 16 16 17 17 17 17 18 18 19 19 19 19 19 20 20 20 20 20 21 21 22 22 23 23 24GENERAL DISCUSSIONS OF THE FARADAY SOCIETY Date 1928 1929 1929 1929 1930 1930 1931 1932 1932 1933 1933 1934 1934 1935 1935 1936 1936 1937 1937 1938 1938 1939 1939 1940 1941 1941 1942 1943 1944 1945 1945 1946 1946 1947 1947 1947 1947 1948 1948 1949 1949 1949 1950 1950 1950 1950 1951 1951 1952 1952 1952 1953 1953 1954 1954 Subject jomogeneous Catalysis Zrystal Structure and Chemical Constitution itmospheric Corrosion of Metals.Third Report vlolecular Spectra and Molecular Structure Iptical Rotatory Power Zolloid Science Applied to Biology 'hotochemical Processes The Adsorption of Gases by Solids The Colloid Aspects of Textile Materials iquid Crystals and Anisotropic Melts lree Radicals 3ipole Moments 2olloidal Electrolytes The Structure of Metallic Coatings, Films and Surfaces The Phenomena pf Polymerization and Condensation Disperse Systems in Gases : Dust, Smoke and Fog Structure and Molecular Forces in (a) Pure Liquids, and (b) Solutions The Properties and Functions of Membranes, Natural and Artificial Reaction Kinetics Chemical Reactions Involving Solids Luminescence Hydrocarbon Chemistry The Electrical Double Layer (owing to the outbreak of war the meeting The Hydrogen Bond The Oil-Water Interface The Mechanism and Chemical Kinetics of Organic Reactions in Liquid The Structure and Reactions of Rubber was abandoned, but the papers were printed in the Transactions Systems Volume 24 25 25 25 26 26 27 28 29 29 30 30 31 31 32 32 33 33 34 34 35 35 35 36 37 37 38 39 Modes of Drug Action Molecular Weight and Molecular Weight Distribution in High'Polymers.(Joint Meeting with the Plastics Group, Society of Chemical Industry) The Application of Infra-red Spectra to Chemical Problems Oxidation Dielectrics Swelling and Shrinking Electrode Processes Disc. 1 The Labile Molecule Surface Chemistry. (Jointly with the Socikt6 de Chimie Physique at Colloidal Electrolytes and Solutions Trans. 43 The Interaction of Water and Porous Materials Disc. 3 4 The Physical Chemistry of Process Metallurgy 5 Crystal Growth 6 Lipo-Proteins 7 Chromatographic Analysis 0 40 41 42 42 A 42 B 2 Bordeaux.) Published by Butterworths Scientific Publications, Ltd. Heterogeneous Catalysis Physico-chemical Properties and Behaviour of Nuclear Acids Spectroscopy and Molecular Structure and Optical Methods of In- Electrical Double Layer Hydrocarbons The Size and Shape Factor in Colloidal Systems Radiation Chemistry The Physical Chemistry of Proteins The Reactivity of Free Radicals The Equilibrium Properties of Solutions of Non-Electrolytes The Physical Chemistry of Dyeing and Tanning The Study of Fast Reactions Coagulation and Flocculation vestigating Cell Structure 6 Trans.46 Disc. 9 Trans. 47 Disc. 10 11 12 13 14 15 16 17 18GENERAL DISCUSSIONS OF THE FARADAY SOCIETY Date Subject Volume 1955 I955 1956 1956 1957 1957 1958 1958 1959 1959 1960 Microwave and Radio-Frequency Spectroscopy 19 Physical Chemistry of Enzymes 20 Membrane Phenomena 21 Physical Chemistry of Processes at High Pressures 22 Molecular Mechanism of Rate Processes in Solids 23 Interactions in Ionic Solutions 24 Configurations and Interactions of Macromolecules and Liquid Crystals 25 Ions of the Transition Elements 26 Energy Transfer with special reference to Biological Systems 27 Crystal Imperfections and the Chemical Reactivity of Solids 28 Oxidation Reduction Reactions in Ionizing Solvents 29 For current availability of Discussion volumes, see inside of back cover.

ISSN:0366-9033    

DOI:10.1039/DF959280X001

出版商:RSC    

年代:1959

数据来源: RSC

摘要:

I ELECTRON OPTICAL STUDIES OF IMPERFECT CRYSTALS AND THEIR SURFACES BY G. A. BASSETT J. W. MENTER AND D. W. PASHLEY Tube Investments Research Lab. Hinxton Hall Cambridge Received 20th May 1959 The preparation of simple reproducible single-crystal surfaces by direct growth, electropolishing vacuum evaporation and cleavage is first considered. It is shown that the step structure of some cleavage surfaces may be studied by a " decoration replica " technique which reveals all steps down to those of unit atomic height. Singlecrystal cleavage-surfaces may be used as substrates on which to grow thin single-crystal metal-films. After detaching from the substrate these films may be studied in the transmission electron microscope. Their defect structure (dislocations etc.) may be characterized either by diffraction contrast effects or by means of rnoh-6 patterns formed by superposing two films.These films may be used as starting materials for studies of a variety of nucleation and growth phenomena occurring at surfaces in order to determine for example whether the termination of a dislocation line is a preferred site. Preliminary results on the very early stages of the electrodeposition of nickel on gold and the oxidation of copper are described. 1. INTRODUC~ON In chemical reactions between a solid and a liquid or gaseous phase the reaction proceeds at the solid interface. It is important to know as much as possible about the detailed geometry of this interface since it is well known that the binding energy of an atom in the surface depends strongly upon its local environment.Thus atoms are more readily removed from step edges corners or kink sites on steps than they are from a site within a close packed face. These energy differ-ences may be expected to lead to differences in the tendency for atoms to react in these different sites so that surface geometry is an important consideration in solid/gas and solid/liquid reactions. In addition to step edges kink sites and vacant sites on the surface of a perfect crystal there are other types of site on the surface of imperfect crystals associated with emergent dislocation lines. Near the core of the dislocation the lattice is severely strained and depending upon the Burgers vector of the dislocation there may be a step tied to the end of the dislocation.If the Burgers vector of the dis-location lies in the plane of the surface no trailing step is associated with the point of emergence but if the dislocation is extended into two partials then there will still be a short length of step joining the two partial dislocations. It is well known that specific etchants will attack certain crystals along dislocation lines the termination of the dislocation at the surface being rendered visible by means of the etch pit formed. Although this specific attack frequently depends additionally upon the segregation of impurities at the dislocation it appears that there are situations in which the termination of the " pure " dislocation is sufficient to make it a favoured reaction site. Thus many lines of evidence lead to the conclusion that the nucleation of reactions involving solid surfaces may well be affected by surface and lattice singularities at the atomic level.It is therefore profitable to consider what 8 ELECTRON OPTICAL STUDIES relevant information may be obtained by studying crystal lattices and surfaces at maximum resolution using the electron microscope supported by electron-diffraction techniques. In this paper we first review methods for obtaining simple reproducible crystal surfaces and show how in the particular case of the cleavage surface of some ionic crystals the step structure may be revealed right down to atomic dimensions. We then show how suitable single-crystal surfaces may be used as substrates for growing single-crystal metal-films the defect structure of which may be examined in great detail by high-resolution transmission electron microscopy.Finally we consider a number of ways in which these films may be used to study nucleation phenomena including nucleation of electrodeposits and chemical overgrowths. 2. PREPARATION OF SURFACES In all surface studies it is of the utmost importance to prepare the surface in a simple and reproducible form. Techniques likely to cause any surface con-tamination or damage in the form of severe working are to be avoided and in order to simplify the situation further it is advisable to work with single crystals. Good single crystal surfaces are best prepared by one of four techniques viz. (i) direct growth from the vapour or from solution (ii) electropolishing (iii) vacuum evaporation or (iv) cleavage.(i) DIRECT GROWTH The growth of whisker-like crystals has received considerable attention in recent years (see for example review by Jackson and Nabarro 1) and in some cases it appears that both the surfaces and interior of these crystals may be free of singularities. This perfection has been inferred in some instances by indirect methods. Vermilyea 2 inferred the absence of surface steps on copper whiskers from observations on the overpotential for electrodeposition upon them and the exceptional mechanical properties observed by several workers (see for example, review by Brenner 3) have been taken to imply an extremely low or even zero dislocation density. We have been able to confirm this directly in a number of cases by direct observation in the electron microscope.Needle-like crystals of copper and platinum phthalocyanine are frequently found with molecularly straight edges and the extreme uniformity of the resolved lattice image over large areas comparable with the size of the crystal together with the absence of " wedge-fringe '' effects suggest extreme interior perfection and the absence of steps on the faces normal to the electron beam (fig. 1). We have recently examined ribbon-like crystals of silicon prepared by Dr. C. C. Evans in our laboratory by the reduction of silicon tetrachloride with zinc vapour. Moirk patterns (see $4) have been obtained from overlapped crystals which show large areas of crystal to be quite free from any imperfection. We may deduce that surface singularities associated with interior imperfections will be completely absent over an area such as that illustrated in fig.2. A different type of growth habit in the form of platy crystals grown by the spiral mechanism of Frank 4 leads again to crystals with a low dislocation density and a simple predictable surface geometry. This may take the form of spiral terraces terminating at the edge of the crystal and an emergent dislocation generally near the centre of the face. -Alternatively closed concentric growth layers are formed around a pair of dislocations. The presence of steps of molecular height of this type have been confirmed by many electron microscope observations on long chain hydrocarbon compounds (e.g. Dawson and Vand,s etc.). Thus growth from the vapour or from solution often leads to the production of single crystals with a simple surface and interior geometry.As substrates for reactions however their use is somewhat limited on account of their rather small size G . A. BASSETT J . W. MENTER AND D . W. PASHLEY 9 (ii) ELECTROPOLISHING Electropolishing has frequently been used in the past for preparing " smooth " metal surfaces. The pronounced refraction effect frequently observed in re-flection electron diffraction patterns from such surfaces has led to their character-ization as " atomically smooth ". However this evidence should be interpreted conservatively. The refraction effect only sets an upper limit to the mean angles of the slope between the entry and exit surfaces of the electrons and it is quite likely that such surfaces are covered by terraces of steps with a very small angle of inclination to the mean direction of the surface.Although it has been suggested that there are frequently residual films on the surface from the electropolishing bath it appears that in some circumstances at least this is not so. Brame and Evans 6 found for example that epitaxial films of gold could be readily grown upon an electropolished silver surface. However for general use such surfaces are not ideal. Although they are substantially free of singularities arising from cold work their surface geometry is not predictable or readily observable in detail. (iii) VACUUM EVAPORATION The phenomenon of oriented overgrowth (epitaxy) of one crystal upon another has been well known for many years and has been extensively studied (for review, see Pashley7).This technique has been used by Pashley 8 to produce highly reproducible silver substrates by vacuum evaporation on to a freshly cleaved mica surface at - 270°C. If the deposit is thickened to 1500-20o0 A reflection diffrac-tion examination of the outer surface shows a pronounced refraction effect in-dicating a high degree of smoothness and an absence of any orientations other than that corresponding to [ l l l ] normal to the surface and [lTO] Ag parallel to [OlO] mica in the plane of the surface. These substrates have proved exceedingly useful as starting material for a whole range of investigations including surface reactions and film growth some of which will be described in more detail in $ 4 and 3 5.Silver surfaces of good quality in [loo] orientation may be prepared on rocksalt as a substrate and there are undoubtedly a number of other combinations which could be exploited. (iv) CLEAVAGE Some crystals may be cleaved to molecular smoothness over areas of the order of mm2. This has been demonstrated both by optical interferometry and by reflection electron microscopy. The main source of such steps as are observed are probably dislocation lines with Burgers vector components normal to the cleavage surface intersecting the latter. These will be associated with trailing steps as pointed out by Pratt.9 In materials which show appreciable plastic deformation there is another source of steps arising from dislocations nucleated in the vicinity of the crack during cleavage.The extent to which plastic deformation occurs depends upon the speed of propagation of the crack as shown by Gilman 10 and Forty 11 in studies of the lithium fluoride and rocksalt cleavage. If the crack is slowed down during propagation then appreciable plastic deformation occurs in the region of maximum strain in the vicinity of the crack tip dislocation loops with Burgers vectors 14 3 01 [&% 01 [+ 0 31 [+ O-+] are nucleated (cleavage plane (100)) leading to steps of height ($00). Examples of this are shown below. If the cleaved crystal is exceptionally soft as with zinc. there is frequently severe local deformation of the surface manifested by a general surface rumpling (basal plane kinking) and twinning. These surface markings have been studied in detail by Jillson,l2 Moore 13 and Pratt and Pugh 14 using sensitive optical techniques.The electron microscope has been used in a number of ways to study the microstructure of cleavage surfaces. Fig. 3 shows a zinc single-crystal cleavage 10 ELECTRON OPTICAL STUDIES surface viewed at a low glancing angle in the reflection electron microscope (Menter 15). Changes in surface slope associated with twins and their accom-modation kinks are revealed together with surface undulations arising from the kinking and bending of the basal plane. In favourable circumstances using exceedingly small glancing angles of the electron beam on to the surface this tech-nique is capable of revealing surface steps down to about 20 A in height (Menter 16), but it suffers from the serious disadvantage of lacking resolution in the plane of the surface.This shortcoming is overcome using a technique developed by Bassett.17 While at the moment this seems to be restricted to the study of a limited class of cleavage surfaces it is the only method known to us giving simultaneously high resolution in three dimensions i.e. high resolution in the cleavage plane together with a step height sensitivity capable of revealing unit atomic steps. Some recent results relating to the microstructure of the rocksalt cleavage surface are given below. 3. CHARACTERIZATION OF SURFACE STRUCTURE OF ALKALI HALIDE CLEAVAGE SURFACES A very small quantity of gold is evaporated from a hot tungsten filament at normal incidence on to a freshly cleaved surface of rocksalt.If spread as a layer of uniform thickness over the surface of the crystal the gold would form a film - 5 in thickness. After the gold evaporation the surface is covered with a thin (100A) carbon film which together with the gold is detached from the crystal surface by immersion in water and acts as a supporting film for examining the gold deposit in the transmission electron microscope. It is found that the gold is deposited in the form of very small separated nuclei which are of two types. The first type appear to be deposited at random over the surface with a density of 2.5 x 10ll/cm2 whereas the second type are formed along the step edges with a linear density along the step of - 13 x 104/cm. A typical area of a cleaved surface decorated at room temperature is shown in fig.4. The steps appear to be of two types the first curvilinear or wavy and the second straight. Unit glide on (Oll) (Oil) (101) or (101) leads to the formation of surface steps on the (001) cleavage surface the change in surface level across the step being a/2 = 2.8 A where a is the unit-cell dimension. Thus dislocation half-loops initiated from the cleavage surface spread into the crystal leaving a straight step at the surface. Fig. 5 shows a situation in which two " staircases " of cleavage steps are crossed orthogonally by a slip step. Since the glide plane is inclined at 45" to the free surface the trace of its intersection with the latter is displaced sideways by a distance t on crossing a terrace of height t as illustrated in fig.6. From measurements of t on the electron micrograph and a count of the number of steps in the terrace it has been deduced that the majority of the steps in such terraces are of monatomic height i.e. half the unit-cell dimension = 2.8 A. From this we may deduce that every step on the surface is susceptible of decoration by this technique so that all of the step structure is made visible. If slip has not extended across the full width of the crystal then it is possible to find a terminating step which must be associated with the end of a dislocation passing into the interior of the crystal. An example of this effect is shown in If the temperature of the rocksalt is raised after cleavage it appears that con-siderable movement of the surface steps occurs.Appreciable changes may be observed after 1 h at 250°C. Some of this change may be associated with the movement of dislocation lines terminating at the surface but undoubtedly extensive migration of individual NaCl molecules occurs also. Interactions between inter-secting steps are observed (fig. 8) and sometimes small isolated circles (diameter - lOOOA) of nuclei (fig. 9) appear and in one case an arrangement of nuclei in the form of rectangles approximately 2508 square has been observed (fig. 10.) fig. 7 (6) FIG. 1 .-(u) Copper phthalocyanine crystal showing molecularly smooth edge ; (6) shows an enlargement of part of the edge together with the 201 spacing resolved within the crystal. The grey region AB is carbon contamination formed during examination in the electron microscope.Magnification (a) 160,000 ; (b) 1,000,000. FIG. 2.-Rotation moir6 pattern formed by two overlapping Si whiskers. The extreme uniformity of this pattern with a spacing of - 200 A shows both crystals to be free of [To face page 10. dislocation lines over the area illustrated. Magnification 60,000 FIG. 3.-Reflection electron micrograph from cleavage surface of zinc single crystal showing twins op cd efand rumpling of surface due to basal plane bending and kinking. (a and b are dust particles.) Magnification 1250. FIG. 4.-Decoration replica of rocksalt cleavage surface showing " staircases " of steps and individual steps breaking away from them. Magnification 32,000 FIG. 5.-Decoration replica of rocksalt cleavage surface. The slip step ABCD is formed by slip on one of the (110) planes inclined at 45” to the cleavage surface.Viewed in projection it is displaced sideways first to the left and then to the right as it crosses a rising and descending staircase (see fig. 6). Magnification 80,000. FIG. 6.-Schematic representation of surface geometry on rocksalt cleavage surface revealed by fig. 5. ABCD is the slip step formed by glide in the direction indicated on a (1 lo} plane. From a measurement of the sideways displacement of the step on crossing the elevated region EFGH together with a count of the number of steps in the staircase, it has been deduced that most of the steps in the latter have a height equal to half the unit-cell dimension i.e. 2.8 A FIG. 7.-Decoration replica of rocksalt cleavage surface.Step AB associated with dis-location line terminating at the surface at A. Magnification 140,000 FIG. 8.-Rocksalt cleavage surface heated at 250°C for 1 h. Decoration replica shows a number of examples of interactions between migrating steps leading to rounded corners Magnification 56,000. where initially there must have been linear intersections. FIG. 9.-Rocksalt cleavage surface heated at 250°C for 1 h. Decoration replica shows closed rounded steps which may be monatomic islands or depressions. Magnification, 40,000 FIG. 10.-Rectangular and square groups of nuclei of gold formed by vacuum deposition on to rocksalt cleavage surface after heating at 250’C for 1 h. Each gold crystal in a group may be nucleated in the corner of a rectangular depression formed by the aggrega-tion of vacancies at the surface.Magnification 240,000. FIG. 11 (a).-Transmission electron diffraction pattern from (100) gold single crystal grown by vacuum evaporation. FIG. 11 (b).-Transmission electron diffraction pattern from (1 11) gold single crysta! grown by vacuum evaporation FIG. 12.-Electron micrograph of (100) gold film showing dislocations (for example A.) as dark lines passing from one surface of the specimen to the other. Numerous twins (for example B) are also visible. Magnification 130,000. FIG. 13.-Electron micrograph of (I 1 I) gold film. Dislocation lines are steeply inclined to the plane of the specimen and are generally visible only as a result of black-white dot contrast as shown in the encircled areas. Magnification 500,000 FIG.l4.-Rotation moire pattern formed by superposition of two ( I 11) single crystal ‘gold films with relative rotation of - 2” about (1 11). The spacing of the moire pattern is - 40 A. Magnification 500,000. FIG. 15.-Parallel moire pattern from (1 11) copper single crystal grown epitaxially upon (1 1 1) gold single crystal film. Magnification 1,750,OOO FIG. 16.-Dislocation in (111) parallel moire pattern from Au + Pd specimen. The dislocation passes from one surface to the other of one of the crystals. The direction of the Burgers vector is indicated by the arrow. Magnification 1,5OO,OOO FIG. 17.-Moir6 pattern formed between gold single crystal film and very thin nickel electrodeposit formed directly upon it. The nickel is not deposited uniformly and the prescnce of " dislocations " in the moire pattern shows that the defect structure of the nickel is different from that of the gold.Magnification 1,000,000 FIG. 18.-Transmission electron micrograph of thin (100) Cu single crystal after heating in air at 1 mm Hg at 250°C showing island nucleation of Cu20. Magnification 160,000 FIG. 19.-Transmission electron micrograph of thin ( I 00) Cu single crystal after oxidation. Moire patterns are formed between the Cu20 nuclei and the Cu. At A and B Cu20 nuclei appear to be associated with the ends of dislocation lines but there are many other places e.g C. where no such correlation is observed. Magnification 1,000,000 G . A . BASSETT J . W. MENTER AND D. W . PASHLEY 11 These may represent either islands of sodium-chloride molecules formed as a result of the aggregation of migrating molecules or possibly monatomic depres-sions in the surface.The latter is more likely in the case of the rectangles since one would not expect preferential nucleation to occur at a corner of an island on the surface. Such depressions might well be formed by the aggregation of vacant lattice sites. In addition to the evidence concerning surface step configurations obtained from these studies the micrographs contain important information relating to the mobility of gold atoms on the surface. The quantity of gold per unit pro-jected area of the surface is constant but in places where the steps are closely packed together the nuclei are considerably smaller than at points far from steps presumably because the density of nuclei at step edges is much higher and for these nuclei to grow they can only draw on gold atoms deposited on the terraces immediately above and below them.It appears that when the steps are closer than about 150-200 A all the gold atoms deposited upon the terraces migrate to the steps. As the terrace width increases above this value then nuclei of the “random” type begin to appear on the terraces. To what extent the latter are truly random we do not know at the moment. Careful experiments on the dependence of the distribution of these nuclei on the rate of evaporation might decide whether they result from a homogeneous nucleation process or whether their distribution is determined by the presence of surface singularities in the form of point defects in the rocksalt surface or adsorbed gas molecules.For reasons not fully understood the system gold + ionic crystal appears at present to be in some way unique. Gold has been used successfully to decorate steps on NaCl KBr and LiF. Other noble metals do not show similar effects nor does gold decorate steps on metal surfaces. However gold + NaCl is useful as a model system and much more work should be carried out to investigate both changes in step structure with changing conditions e.g. temperature bulk plastic deformation (Bassett 32) etc. and the more fundamental aspects of surface nucle-ation and migration in terms of substrate temperature rate of evaporation surface cleanliness etc. 4. GROWTH AND MICROSTRUCTURE OF THIN SINGLE CRYSTAL METAL FILMS (i) GROWTH We now turn to a consideration of the manner in which single crystals may be grown reproducibly in a form suitable for studying their internal defects in the transmission electron microscope.For some materials it is possible to rely on exaggerated habits arising from growth conditions to produce crystals of the required thickness. This is 100-2000 A for materials of average atomic number. Examples of this type of growth were referred to in § 2(i). In our laboratory we have been particularly interested over the last few years in the properties of thin metallic films. A number of techniques are available for thinning-down bulk material to the form of thin films but in order to obtain reproducible pro-perties we have preferred a technique of building-up films by vacuum evaporation on to single-crystal substrates.We wish to indicate briefly here the technique of preparation the micro-structural features we have observed in them and later the way in which they may be used to study chemical reactions in great detail. Much of our work has been concerned with the properties of gold films with either [l 1 13 or [lo01 normal to the film. The former are prepared by evaporation of gold on to a single-crystal silver substrate which is itself prepared by evaporation on to a mica cleavage surface as described in FJ 2(iii). Films of gold up to - 2000 in thickness may usefully be examined in the transmission electron microscope at 1 0 0 kV. The films are obtained in a form suitable for transmission examin-ation by detaching from the silver substrate with HNO3 and are mounted across a platinum aperture.Apart from its use as a “parting” layer from the mica 12 ELECTRON OPTICAL STUDIES the silver interlayer between the gold and mica has other advantages discussed by Pashley.18 A similar technique has been used for preparing the (100) films using the rocksalt cleavage surface as the initial substrate. (ii) DEFECT STRUCTURE It has been demonstrated in a series of papers (Hirsch Horne and Whelan,lg Whelan Hirsch Horne and Bollmann,20 Whelan and Hirsch,21 Whelan and Hirsch,22 Hirsch Silcox Smallman and Westmacott 23) that lattice imper-fections may be made visible in transmission electron microscope images of thin crystals by contrast effects arising from the modified scattering of electrons in the vicinity of the imperfection.Thus dislocation lines generally appear as black lines on a white background (print) and stacking faults may be recognized by a characteristic interference pattern of lines parallel to the plane of the specimen across the stacking fault. Using these effects it has been possible to characterize many of the imperfections in the metal single-crystal films described above. In the first place it should be noted that the films are continuous and relatively free from holes except when very thin (< 200 A) and the single-crystal orientation indicated by the diffraction patterns (fig. lla b) is maintained over the whole area of the specimen (- 1 cm2). Fig. 12 13 show typical micrographs of the (100) and (111) films respectively. In the former dislocation lines passing from one surface of the film to the other and lying on the (111) slip planes inclined at 55" to the surface are visible.The lines are not so readily seen on (111) specimens since here the slip plane is steeply inclined (70") to the specimen surface and the line tends to degenerate into a black-white dot contrast as shown in the figure. In addition it is found particularly in the (100) films that there are a number of twins grown into the film (By for example fig. 12) which have complex contrast effects associated with the interface between them and the matrix. The third main feature observed is in the form of small dislocation loops up to 100A in diameter thought to arise from collapsed vacancy aggregates. (iii) HIGH-RESOLUTION STUDY OF DEFECTS BY MEANS OF MOIF& PATTERNS Some aspects of these imperfections have been studied by a quite different technique involving the formation of periodic images intimately related to the fundamental lattice periodicities of the crystal.Menter 24 showed that it was possible to resolve lattice periodicities directly in the electron microscope by transmission through thin crystals and further to detect disturbances of the perfect periodicity associated with lattice imperfections. The aberrations of the image, however set a lower limit to the resolvable distance and so far the smallest lattice periodicity directly resolved is 6-9 A in Moo3 (Bassett and Menter25). This diffi-culty has to a large extent been overcome by adopting the technique of moirk patterns.In applying this technique to the study of thin metal films two distinct methods may be used (Bassett Menter and Pashley 26). In the first a " rotation " moirk pattern is formed by superposing two identical films with a small relative rotation E . This gives rise to a moire pattern with spacing D = d/E where d is the spacing of the lattice planes in the two crystals giving rise to the pattern. Thus the irre-solvable periodicity d appears magnified in the moire pattern the so-called miore magnification M being 1 / ~ . Fig. 14 shows a typical example of a pattern formed in this way from two overlapped gold crystals. The lattice periodicity is d220 = 1-44 A E - 2" giving a moire pattern spacing of - 40 A. Rotation patterns may of course also be formed by two dissimilar crystals but in this case the spacing of the pattern is given by D = Qd2(d12 + d22 - 2dld2 cos E)-*.In the second method a " parallel " moirk pattern is formed by growing a different single crystal metal film epitaxially upon the first to give a pattern with a spacing Dp = d1d2/(dl - d2) where d l d2 are the spacings of the lattice planes in the tw G. A . BASSETT J . W. MENTER AND D. W. PASHLEY 13 crystals giving rise to the pattern. Here the moirk magnification of d2 is dl/(dl- d2). A typical example of a parallel pattern formed by an Au + Cu combination is shown in fig. 15. For simple lattices such as those of metals the geometry of the pattern formed is similar to that of the lattices of the metal films viewed in the same direction so that the patterns may be used to study the atomic arrangement.In particular it has been shown (Pashley Menter and Bassett,27 Hashimoto and Uyeda 28) that a dislocation line in either crystal passing from one surface to the other gives rise to " extra " terminating half-lines in the moirk pattern leading to a disturbance in the pattern remarkably similar to the disturbance of the lattice of the dislocated crystal. In this way it is possible to study in great detail the configuration of crystal lattices in the vicinity of dislocation lines (fig. 16). The surface structure of these metal films has not been investigated in any detail but indirect evidence from their mechanical properties suggests that they must be substantially free from gross irregularities. Having established a consistent preparation technique and methods of examin-ing microstructure at very high resolution we now turn to consider how we may utilize these films in studying nucleation and growth processes at their surfaces.5. ELECTRON MICROSCOPY AND DIFFRACTION APPLIED TO THE STUDY OF NUCLEATION AND GROWTH PHENOMENA AT SURFACES Although the emphasis of our discussion so far has been on observations by electron microscopy detailed information can also be obtained by reflection electron diffraction. A number of workers have studied the growth of tarnish layers on single-crystal surfaces in this way. The technique is particularly useful because it can be used to analyze the structure of films at very early stages of growth when the average thickness is only about one atomic thickness.In this way Newman and Pashley 29 showed that the earliest stages of growth of silver bromide on silver involve the formation of isolated three-dimensional nuclei. The orientation can readily be determined and the way in which the chemical growth is influenced by more gross features of the substrate surface topography can be examined. By making use of secondary diffraction effects it is possible (Pashley,30 Lucas 31) to determine how the orientation of the tarnish layer varies from one crystallo-graphic facet to another where a substrate surface is covered by sub-microscopic facets of several different kinds. For example on an etched (31 1) surface of silver, silver bromide orients in a number of different ways which can be attributed to two basic orientations occurring on a number of different facets parallel to (100) and (110) planes (Pashley 30).However this kind of investigation is very tedious and requires great care in interpretation and it is clear that a combined electron-microscope electron-diffraction attack on the problem is highly desirable. Using as substrates the thin single-crystal metal-films described in 9 4 it is possible to follow various nucleation phenomena in great detail. Two short illustrations of our approach to these problems are given here to demonstrate the scope of the method. Fig. 17 shows an example due to T. Evans and D. Schwarzen-berger of the initial stages of formation of a nickel electrodeposit upon a single crystal (111) gold substrate. Since the nickel grows in parallel orientation with the gold a parallel type (220) moire pattern with a spacing of - 9 8 is formed in the regions where nickel has been deposited.Under the plating conditions used here it appears that the nickel has not deposited uniformly. In some areas there appear to be isolated nuclei whereas in others the nuclei appear to have already joined together to form a continuous deposit. Many dislocations are seen in the moire pattern indicating that the distribution of imperfections in the nickel is different from that in the gold. Much more work needs to be done in order to discover possible interrelations between the substrate and deposit micro-structures. 14 ELECTRON OPTICAL STUDIES In another investigation undertaken in collaboration with Dr. L. N.D. Lucas, we have been examining the growth of copper oxide on copper. The substrate consists of a (100) single-crystal film of copper a few hundred A in thickness grown by evaporation on to rocksalt. The copper film is detached by dissolving the rocksalt in water and after annealing is oxidized by heating to about 250°C in air at a pressure of about 1 mm Hg. The oxidation is carried out inside an electron-diffraction camera so that the growth can be controlled by examination of the difraction pattern after various intervals of time. The oxidized film is then examined in the transmission electron microscope. There is a strong prefer-ence for the oxide to grow in parallel orientation on the copper. Since Cu20 is cubic in structure with a0 = 4.26 A and the f.c.c. copper has a0 = 3.61 A this is an ideal system with which to obtain moirt patterns; the moirC magnification M is 5.6.The { 11 l} (200) and (220) moirt spacings are 13.6 11.8 and 8.4 A respectively. So far the specimens have been prepared so that the copper surface is covered by a number of isolated crystallites usually about 100-500 8 across and certainly thinner than this. Fig. 18 shows at relatively low magnification the general distribution of square and rectangular oxide nuclei upon the copper. A large number of oxide nuclei show moirk patterns (see fig. 19) due to their mis-matching with the copper lattice ; in some cases complications arise because oxide nuclei on one side of the film overlap nuclei on the other side. It is clear that the oxidation proceeds at least in the early stages by the growth of these isolated nuclei rather than by the growth of a uniform continuous surface film.The orientation of the moird pattern is sensitive to the relative orientations of copper and oxide. If the oxide is rotated through a small angle a (from the exact parallel setting) with respect to the copper the moirC pattern is rotated by Ma. Small misorientations are therefore easily detected and when a range of relative orientations occurs as in this case this range of orientation is magnified in the distribution of orientations of the moire patterns from the oxide nuclei (see fig. 19). Since dislocations in the copper are visible by diffraction contrast it is possible to investigate whether there is any correlation between the sites at which copper-oxide nuclei appear and the points at which dislocation lines emerge on the copper surface.The evidence on this is by no means clear at the moment. There are certainly many dislocations which do not have oxide nuclei associated with their ends. A few examples suggesting a correlation have however been observed (A B in fig. 19). It is possible that these may be selected because they have a favourable Burgers vector. It is interesting to note at A that the dislocation in the metal does not apparently extend into the oxide since there is a terminating half-line in the moire pattern. Had the dislocation extended into the oxide with the same Burgers vector then no such extra half-line would be seen (see ref. (26)). It is clear that many questions remain unanswered since we are now only at the beginning of this investigation.The next stage is to carry out the oxidation in situ inside the electron microscope. In this way it will be possible to follow the nucleation and growth of the oxide continuously both by transmission diffrac-tion and microscopy. Our main purpose here has been to demonstrate that useful advances have been made over the last few years in physical techniques for studying the microstructure of solids. These techniques should find many useful applica-tions in fields of interest to the physical chemist. This paper is published by permission of the Chairman of Tube Investments, Ltd. 1 Nabarro and Jackson ed. Doremus Roberts and Turnbull Growth and Perfection 2 Verrnilyea J. Chem. Physics 1958 28 717.3 Brenner ed. Doremus Roberts and Turn'ull Growth and Perfection of Crystals of Crystals (John Wiley and Sons New York 1958) p. 11. (John Wiley and Sons New York 1958) p. 157 G . A . BASSETT J. W. MENTER AND D . W . PASHLEY 4 Frank Faraday SOC. Discussions 1949,5 48. 5 Dawson and Vand Proc. Roy. SUC. A. 1951,206 555. 6 Brame and Evans Phil. Mag. 1958 3 971. 7 Pashley Adw. Physics 1956 5 173. 8 Pashley Phil. Mag. 1959 4 316. 9 Pratt unpublished work quoted in Prugr. Metal Physics 1956 6 268. 10 Gilman J. Appl. Physics 1956 27 1262. 11 Forty Proc. Roy. SOC. A 1957 242 392. 12 Jillson Trans. Amer. Inst. Min. (Met.) Eltg. 1950 188 1009. 13 Moore Acta Met. 1955 3 163. 14 Pratt and Pugh Acta Met. 1953 1 218. 15 Menter J. Inst. Metals 1952 81 163. 16 Menter J. Photo. Science 1953 1 12. 17 Bassett Phil. Mag. 1958 3 1042. 18 Pashley Phil. Mag. 1959 4 324. 19 Hirsch Horne and Whelan Phil. Mag. 1956 1 677. 20 Whelan Hirsch Horne and Bollmann Pruc. Roy. SOC. A 1957 240 524. 21 Whelan and Hirsch Phil. Mag. 1957 2 1121. 22 Whelan and Hirsch Phil. Mag. 1957 2 1303. 23 Hirsch Silcox Smallman and Westmacott Phil. Mag. 1958 3 897. 24 Menter Pruc. Roy. SOC. A 1956 236 119. 25 Bassett and Menter Phil. Mag. 1957 2 1482. 26 Bassett Menter and Pashley Pruc. Roy. SOC. A 1958 246 345. 27 Pashley Menter and Bassett Nature 1957 179 752. 28 Hashimoto and Uyeda Acta Cryst. 1957 10 143. 29 Newman and Pashley Phil. Mag. 1955 46 927. 30 Pashley Proc. Roy. SUC. A 1952 210 355. 31 Lucas Pruc. Roy. SOC. A 1952 215 162. 32 Bassett Acta Mat. 1959,7,753. 15 C

ISSN:0366-9033    

DOI:10.1039/DF9592800007

出版商:RSC    

年代:1959

数据来源: RSC

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THE STRUCTURE OF CRYSTAL SURFACES* BY N. CABRERA Dept. of Physics University of Virginia Charlottesville Virginia U.S.A. Received 19th June 1959 1. INTRODUCTION The purpose in writing this paper is both to attempt a summary of the main, well-established ideas on the structure of surfaces as well as to bring up some points which still require further consideration. Accordingly the paper is divided into three sections. (i) In 0 2 a distinction is made between singular interfaces (including in many respects vicinal interfaces) and non-singular ones. This distinction is well known, the nomenclature being due to F. C. Frank; but its full implications are perhaps summarized here for the first time. (ii) The atomic structure of singular crystal-fluid surfaces is discussed in 3 3.First it is suggested that the distortions inherent in the surface layers even at very low temperature required to diminish as much as possible surface stresses, are probably always taken care of without the need of introducing “defects” (point defects or dislocations); more work should be done however in order to decide definitely this point. The concentrations of surface point defects appearing at higher temperatures are then discussed as well as their mobility and lifetime on the surface. The role of these three parameters in kinetic processes is then emphasized particularly the lifetime which has been very often overlooked. (iii) At the basis of most of the theories on the role of point defects in kinetic processes (diffusion and so forth) the assumption is made that an excited point defect (e.g.an absorbed atom on a crystal surface) can lose very rapidly this extra energy by the spontaneous emission of phonons into the crystal. It is shown that according to classical mechanics this should be definitely so but it is however, emphasized that the problem requires more careful consideration on the basis of quantum mechanics before it is fully understood. 2. CLASSIFICATION OF INTERFACES Interfaces between two different phases can be classified into three types ac-cording to their thermodynamical properties their atomic structure as well as their behaviour during kinetic processes. These three types are (a) singular surfaces (b) vicinal surfaces and (c) non-singular surfaces. From the thermodynamical point of view singular surfaces are those cor-responding to a cusped minimum in Wulf’s plot giving the surface free energy as a function of orientation.The orientations immediately around a singular one correspond to vicinal surfaces and for them the surface free energy increases linearly for all orientations away from the singular one. All other orientations can be included in the non-singular type of surfaces their free energy being roughly independent of orientation. From the definition of the different types of inter-faces it is obvious that singulaL and vicinal surfaces only occur when at least one phase is crystalline. * This work has been supported by the Office of Naval Research United States Department of the Navy. 1 N. B. CABRERA 17 An analysis of the atomic structure of the different types can only be deduced from statistical mechanics.To my knowledge the first attempt to do so was carried out by Burton and Cabrera.1 They justified in their analysis the as-sumption that singuZar surfaces are atomically flat except for the presence at high temperatures of point defects (see 0 3). Furthermore they showed that the surface disorder increases with the temperature and that there must be a more or less critical temperature beyond which the cusped minimum disappears. The actual value of this critical temperature is very sensitive to composition ; roughly speaking however its value is of the order y&/k (ya2 = surface energy per surface atom). This estimate shows of course that only when the corresponding y is in the range 10-100 erg/cm2 is the critical temperature likely to be below melting for most crystals.We conclude therefore that singular interfaces are eliminated only when y is particularly small and the range of temperatures within which equilibrium between the two phases occurs sufficiently high. Crystal-fluid inter-faces far below the melting point of the crystal as well as crystal-crystal interfaces, are likely to have singular surfaces for certain orientations. On the other hand, the surface of a solid in equilibrium with its melt is very likely not to show any singular surfaces.2 The statistical analysis 1 shows also that as the temperature increases the thickness of the interface increases from two atomic layers to many atomic layers when the singular character disappears.When the transition be-tween the two phases becomes really diffuse it is then better to deal with the problem on a thermodynamical basis following the treatment by Cahn and Hilliard.3 Regarding vicinal surfaces the only difference with respect to the corresponding singular surface is that they further contain steps producing the extra surface energy linearly dependent on orientation. Burton and Cabreral also showed in their statistical analysis that the atomic structure of the steps is at any reasonable tem-perature and for all orientations of the step non-singular. (This is because of the one-dimensional character of the step in contrast to the two-dimensional character of a surface.) The non-singular character of the steps is represented by the presence of a great number of kinks along them.Finally regarding the third type of surfaces it was noticed by Herring 1 that every orientation would be either a singular or a vicinal surface at sufficiently low temperature. However the corresponding critical temperatures for most surfaces are so low that for all practical purposes they can be considered as non-singular. As mentioned before Cahn and Hilliard,3 extending an old method of van der Waals have put forward a thermodynamical treatment which assumes the density of free energy to be not only a function of the particle density n but also of the gradient v n of that density. Accordingly a system composed of two phases 1,2 occupying respectively x > 0 and x < 0 is assumed to have a free energy per unit surface f= Ja EFOW + ~(dn/dx)Wx, where Fo(n) is the density of free energy (for dn/dx = 0) at the point x where n(x) is between the two extreme values nl(x -+ 00) and nz(x +- a).Also K (assumed independent of n) is an unknown phenomenological parameter. The density n(x) in the transitional layer its thickness and the actual value of the surface free energy are obtained by minimizing f. This description has un-doubtedly great merits in eliminating the many assumptions necessary for the development of a complete statistical treatment ; but of course it is only applic-able for small values of dn/dx. In particular it has not been possible as yet to show the existence of a critical temperature below which the diffuse surface layer does not occur. To terminate this paragraph we should consider the different behaviour of the three kinds of surfaces during kinetic processes.Considerable work has -18 STRUCTURE OF SURFACES been and is being carried out in this respect.4 However we wish only to show how the classification put forward here is also useful in this connection. Singular surfaces lose their importance during kinetic processes as they auto-matically become a composite of vicinal faces. The rates of kinetic processes on vicinal faces are definitely orientation dependent much as the surface energies are. This similarity is however still a common source of misunderstanding; in fact the orientation dependence of the surface energy has at most an indirect effect on the orientation dependence of the kinetic rates. In attempting to obtain quantitative expressions for kinetic rates on a particular vicinal surface it is usually sufficient to assume equilibrium in the proximity of the steps.4 This of course, implies that equilibrium is nut maintained all over the surface.Finally the rates of kinetic processes become orientation independent to some degree of approximation when non-singular surfaces are considered. Then the assumption of equilibrium all over the surface (Nernst hypothesis) is a good ap-proximation. One should however point out that very likely a non-singular surface will tend to approach a singular surface (e.g. the thickness of the transition layer will tend to decrease) if the rate is made sufficiently high. It is probable that the methods of irreversible thermodynamics might clarify this point when applied to Calm and Hilliard’s type of treatment.3. DEFECTS ON SINGULAR SURFACES Let us now consider more in detail the structure of singular (as well as vicinal) interfaces limiting ourselves to crystal-fluid interfaces. The knowledge of the nature and the concentration of surface defects is of course necessary for the under-standing of kinetic processes. Usually the word defect refers to a more or less localized imperfection in the perfect lattice requiring a certain amount of energy to produce it. When we consider the surface layers of the crystal however we must take account of the fact that the continuation of the perfect lattice up to the interface is not necessarily the configuration with lowest energy; in fact several people have suggested that a configuration containing a certain con-centration of ‘‘ defects ” might correspond to a lower energy.Before making some comments about whether or not this might be so I would like to discuss the concept of surface stress, which is very much related to the same problem. This has been exhaustively considered by Herring 1 ~ 5 but being a rather elusive concept it might be useful to consider here a simplified version of as a function of strain e. it. Fig. 1 represents as a function of one of the macroscopic strains e both the free energy per unit volume F and the free energy unit per surface f due to the presence of the interface. Both curves will have a minimum but there is clearly no reason for both minima to correspond to the same strain.The ordinate of the surface energy curve at the strain (which is usually chosen as zero) for which F is a minimum is called surface energy y =f(O). Its derivative f’(0) not being zero it is clear that stresses must exist near the surface even when no stresses exist in the bulk. Consequently one would be tempted to callf’(0) the surface stress, y’ = f ’ ( O ) corresponding to the particular strain component. This is perfectly correct as long as one only considers changes in the energy of the body which both strains the volume and the surface. At sufficiently high temperature however, F e FIG. 1 .-volume F and surface fenergie N. B . CABRERA 19 there is also the possibility of changing the energy of a body without altering its volume energy at all namely by changing the amount of surface keeping both volume and strain constant.These changes can be produced by external forces that can only be compensated by surface forces namely y. All together the usual name of surface stress is reserved for the expression g = y + y‘. For thermo-dynamical reasons y must always be positive but y’ (as well as g ) can be positive or negative according to whether the minimum inf(e) is at the right or the left of e = 0. Nobody really knows what f(e) looks like in the case of crystalline interfaces. From an experimental point of view one can assume f(e> = y + y’e + &e2, and then determine y’ and c from the changes in lattice parameters and elastic constants of very thin films. It appears that y’ < lO3erg/cm2 and c < 105 erg/cmZ as both the changes mentioned above only begin to show perhaps at thicknesses below 10-5 cm.Experiments along these lines should be very welcome, particularly as a function of composition which is suspected to alter considerably the values of all these parameters. Returning now to the atomic structure of the surface layers of a crystal-fluid interface let us first consider the situation at low temperatures. Of course the actual atomic structure will minimize f(e) for every value of e ; and this might be expected to occur by making y’ as small as possible. For crystal-fluid interfaces, it is our belief that this is achieved by suitable displacements from the lattice points of the bulk crystal of all the surface atoms. However it is intuitively very tempting to assume that the introduction of defects (vacancies interstitials dislocations) in the surface layers would further reduce f(e) by changing the average lattice parameter at the surface and reducing the surface stress.As the relaxation of stress introduced by point defects is more concentrated than that introduced by an equivalent number of dislocations it is expected that dislocations will be pre-ferred. Herring,s who suggested first this possibility estimated that a grid of dislocations will be present at an interface crystal-fluid if y’ > 103 erg/cm2 where y’ is our surface stress of the surface before the dislocations are introduced. At the present time it appears unlikely that such a high value of y’ will in fact occur, particularly if one remembers that impurities are capable of reducing y’ consider-ably.However it should be important to decide this point as it might be a simple way of explaining the introduction of large numbers of dislocations during growth from vapour or solution as compared to the small numbers that can be introduced during growth from the melt. In conclusion it is not likely that point defects at any rate will appear in the surface layers of any kind of singular interface at low temperatures. At reason-able higher temperatures however surface vacancies or interstitials (adsorbed) atoms or both will appear as is well known. Unfortunately not much is known about their concentration n,. Regarding their relative concentrations it is likely that vacancy concentration is always sometimes considerably higher.Besides their concentration two more physical parameters are of importance namely, their surface diffusion coefficient D or mobility and their lifetime T on the sur-face. Both combine into another important parameter x = (D,r,)+ representing the average displacement of a surface point defect. In kinetic processes in which interfaces are involved these three parameters play an important role. When both volume and surface currents are important, the parameter 7 plays a role which has been very often overlooked. To illustrate this point consider the simple problem of diffusion along a cylindrical volume of radius R surrounded by an interface. The volume diffusion is characterized by a coefficient D and a mean free path L’I ; the surface diffusion by D and 7,.In steady state it is easy to prove that the ratio of the surface concentration gradient to the volume concentration gradient is D,rS/A and consequently the ratio of For fluid interfaces of course y’ = 0 and g = y 20 STRUCTURE OF SURFACES surface current to volume current is given by which shows that even if A/R < 1 the surface contribution is larger than the volume one if x? < AR which implies a large lifetime 7,. To terminate this paragraph let us write down the usual temperature dependent expressions for the three parameters. n = no exp (- W,/kT) ; &pRY (1) D = Azv exp (- UJkT) ; r;1 = v exp (- A,/kT). The activation energies W, Us A are very poorly known. These expressions make definite assumptions concerning the possible interchange of energy between the point defect and the crystal which deserves more close consideration.This point will be discussed in the following paragraph as applied to the adsorbed atoms on a crystal surface. 4. ENERGY EXCHANGE BETWEEN ADSORBED ATOMS AND CRYSTAL SURFACES As mentioned before expressions like (1) for the parameters D and 7 make specific assumptions for the exchange of energy between adsorbed atoms and the crystal. First an excited adsorbed atom is assumed to lose its extra energy very rapidly by spontaneous emission of phonons into the crystal in a way practically independent of the temperature. This implies that an atom reaching the surface wlll be captured by it unless its energy is larger than a certain critical value well above kT (condensation coefficient very nearly one).It also implies that in the process of surface diffusion the jumping distance of the adsorbed atom can be safely assumed to be the smallest distance between equilibrium positions on the surface. Secondly an adsorbed atom can be excited only by the absorption of phonons from the crystal which implies an exponential dependence with tem-perature. There is no quarrel with the latter conclusion but the former one appears to leave room for argument. Indeed the experimental evidence regarding con-densation coefficients accommodation coefficients and so forth appear to yield values much smaller than one would expect.6 Secondly when energy is locally available as during catalytic processes on crystal surfaces,7 or when atoms impinge on the surface with a sufficiently high energy,8 the mobility of the surface layer seems to be considerably increased.This implies perhaps that adsorbed atoms moving parallel to the crystal surface have some difficulty in losing their extra energy. Lennard-Jones and his collaborators 9 studied these problems theoretically from a quantum-mechanical point of view. They considered one-phonon transi-tions but they did not treat the difficult problem of a cascade of onsphonon transitions which has to occur during the condensation of one atom. It is possible, on the other hand to consider the corresponding classical problem and to show on that basis that the loss of energy by the atom in the form of lattice waves is extremely rapid. To illustrate this let us consider a semi-infinite chain of particles of mass m occupying the positions, xn = (n + n = 0 1 2 .. ., a being the distance between particles when at equilibrium. Suppose that the particles interact only by harmonic forces of strength K = mu2 between nearest neighbours; then the equations of motion ar N. B. CABRERA 21 Now let us assume that the particle n = 0 only interacts with the particle n = 1 for distances XI - xo < (1 + a)a otherwise the binding energy between 0 - 1 is E = ($)mw2a2a2. The condensation of an atom coming from infinity with an incident normal velocity XO = 2wajS (p arbitrary) can be analyzed completely if we can solve the system (2) with the boundary conditions : 50(0) = - a loco> = 2wps (3) t n ( 0 ) = &do> = 0 n = 1 2 .. . . The extra energy that has to be dissipated is 3(4p + a2)rnwW = [(2/9/a)2 + 1 ] € . (4) The eqn. (2) corresponding to the semi-infinite chain can be solved if we replace (5) them by the equations corresponding to an infinite chain. C = w2(tn+l - 2tn + tn-l) n = 0 A 1 f 2 . . ., with the extra condition t O ( 0 = t-dt). Indeed eqn. (5) have the general solution 4 = AvJ2(,+v) (7.1 7- = 2wt; where J,(T) is the ordinary Bessel function of order n and A and v are completely arbitrary. Then the extra condition (6) and the particular boundary conditions of our problem (3) are all satisfied by the solution, co 5 n = - d J 2 n + J2(n+l)l + 215CJ2n+l + 2 2 J2(n+v)+ll, v = 1 where the argument is always r = 2wt. J 0 A -/ -2 -3 -4 FIG.2.-Relative position x1 - xo = a(1 + an) of incoming atom (0) and surface atom (1) as a function of time 7 = h t for several values of the initial velocity (2/3/cr = 0, 2,5) of the incoming atom. Let us consider particularly the relative position x1 - xo = a (1 + CCA) where A = ( 2 / W 1 - 3J3) - (2P/CC)(Jl + J3). A is plotted in fig. 2 as a function of T = 2wt and for various values of 2p/cc = 0, 2 5. We see there that as long as 2p/a < 5 the incoming particle will be trapped by the crystal having lost all his initial kinetic energy during his first swing. This means that a particle coming with a normal kinetic energy smaller than 256 will be trapped in the attractive field of the crystal (binding energy E). Of course 22 STRUCTURE OF SURFACES this calculation gives an upper limit to the critical kinetic energy particularly be-cause the harmonic approximation makes the atoms too soft.According to fig. 2 the minimum value of x1 - xo is a(1 - 4a) ; furthermore x2 - x1 also has a minimum value of the order a(l - 3a). Choosing X - 8 shows that the particles are able to approach each other at distances for which the harmonic approximation is obviously wrong. However it is difficult to imagine that a harder core would decrease the factor 25 below say 10. We conclude therefore that according to classical physics and neglecting anharmonic effects the condensation coefficient should always be very nearly one. IBurton Cabrera and Frank Phil. Trans. 1951 243 299. Cabrera 2. Elektro-See also Herring Surface Energy Problem in Solid Surfaces chem. 1952,56 294. ed. by Gomer and Smith 1953 p. 5. 2 see e.g. Hilliard and Cahn Acta Met. 1958 6 772. 3 Cahn and Hilliard J. Chem. Physics 1958 28 258 ; and also in press. 4 Frank Kinematic theory of crystal growth in Growth and Perfeciion of Crystals, ed. by Doremus Roberts and Turnbull 1958 p. 411. Cabrera and Vermilyea ibid., p . 393. 5 Herring Surface tension in sintering in The Physics of Powder Metallurgy ed. Kingston 1951 p. 143. 6 e.g. Thomas and Schofield J. Chem. Physics 1955,23 861. 7 Cunningham and Gwathmey Adw. Catalysis 1958 10 57. 8 Gomer Field emission from mercury whiskers in Growth and Perfection of Crystals, 9 Lennard-Jones Proc. Roy. SOC. A 1937 163 127 where other references are given. M. J. Ives Thesis (Univ. of Bristol 1950). ed. Doremus et al. 1958 p. 126

ISSN:0366-9033    

DOI:10.1039/DF9592800016

出版商:RSC    

年代:1959

数据来源: RSC

摘要:

SURFACE STRUCTURE AND DIFFUSION BY ROBERT Gem* Dept. of Chemistry and Institute for the Study of Metals, University of Chicago, 5640 Ellis Avenue, Chicago 37, Ill. Received 6th May, 1959 Field emission studies of surface diffusion on clean single crystals of known orientation and structure have shown the existence of several modes of surface diffusion for chemisorbed gases. It is found that there is a definite correlation between activation energy and entropy for diffusion on the one hand and surface structure (on the atomic scale) on the other. The ratio of activation energy to heat of binding shows similar behaviour, increasing with increasing roughness. In addition the size and binding mode of the adsorbate plays an important role. These studies illuminate also the well-known changes in heats of adsorption with coverage and indicate that a large fraction of the effect can be attributed to the inherent atomistic inhomogeneity of metal surfaces.Some detailed correlation can be made. Similar results for physical adsorption and multilayer formation will be discussed. A study of diffusion processes on metal surfaces is not only of intrinsic interest but sheds considerable light on the relations between adsorption energy and surface structure. The paper contains a brief summary of the method 1 and the results obtained to date, and a discussion of their meaning. METHOD The field emission microscope, invented by Muller,2 is a device particularly suited for the study of adsorption phenomena, since the adsorbent consists of a single crystal of known orientation, surface condition, and a high degree of perfection.Since all adsorbates including Ne) change its electron emission, surface diffusion can be studied if a portion of the emitter can be kept clean while another receives a gas deposit. This is accomplished as follows. A sealed-off field emission tube is immersed in a bath of liquid He or H2. The vapour pressure of all gases except He (viz., H2 at 20°K) is < 10-15 mm at these tempera- tures so that high vacuum is automatically attained and the tip can be cleaned by electric heating of a supporting loop. Evaporation from a gas source after the tip has cooled produces a deposit only on that part of it which " sees " the former. This results from the high sticking coefficients of all gases on very cold walls, and the high ratio of wall to tip area.Gas sources either utilize the thermal decomposition of such compounds as CuO or ZrH2 (formed in situ) 1 or depend on the sublimation of gas selectively precondensed on a heatable Pt sleeve.3 In this way the adsorption and diffusion of almost all gases on field emitters can be studied. RESULTS AND DISCUSSION At least three types of diffusion are encountered with chemisorbed gases. (i) Diffusion occurs with a sharp boundary a t very low temperature (2 > T > 70"K, depending on the gas) for initial deposits in excess of a monolayer.l.3-5 The layer formed in this way is not itself mobile ; if the initial deposit is insufficient for complete spreading the sharp boundary at first advances and then stops.If more gas is deposited, movement is resumed at low temperature. There is also an upper temperature limit above which no amount of deposition will advance the boundary. These facts indicate that diffusion occurs in a second (and possibly higher 6s 7) physically adsorbed layer, on top of an immobile chemisorbed one. Physically * Alfred P. Sloan Fellow. 2324 SURFACE DIFFUSION adsorbed molecules are mobile at low temperature, can wander to the edge of the chemisorbate, become incorporated into the latter and thus extend it, thereby permitting further diffusion over the newly covered region. Since there is a sharp discontinuity at the adsorbate-clean substrate edge, a moving boundary will be observed. The upper temperature limit corresponds to desorption of physically held molecules before their migration to the edge of the monolayer and chemisorp- tion on the bare surface can occur.It is possible to estimate the diffusion coefficient of the migration, its activation energy, and the heat of desorption from the relations - X Z dot, (1) D a2vexp [- Edlkq, (2) (3) which are all approximately valid. x represents the linear distance advanced by the boundary, X the average distance traversed before evaporation, D the diffusion coefficient, a the jump length, - 3 A, v a jump frequency, - 1012 sec-1, and Edes and Ed the activation energies for desorption and diffusion respectively. Eqn. (3) can be derived by assuming that the same frequency applies to diffusion and desorption. It is interesting that the coverage after type- 1 spreading is - 80 % of the maximum attainable by prolonged exposure of H and 0 on W.194 This suggests that only - 20 % of all sites require any activation for adsorption.(ii) For initial deposits of - 0.3 to - 1.0 monolayers diffusion with a sharp boundary is observed at temperatures ranging from 180°K for H on W1 to 750°K for CO on W.3~8 The activation energy of these processes varies from 6 to > 40 kcal, depending on the system, so that the phenomenon must involve the chemisorbate. With hydrogen1 and oxygen4 on tungsten a boundary moves radially outward from the central (011) face of the tip, if the initial coverage is 8 0.8. Diffusion occurs at 1 80"-220" and 500"-550"K respectively, and advances most rapidly along zones like (01 1)-(121)-(110) which consist of terraces and steps of 1 10 orientation. For 0 on W, 4 a boundary spreading outward from the cube faces, is also observed at - 400°K.For CO on W 3 . 8 boundaries advance from the centre of the tip in such a way as to close in on the cube faces, so that the CO-free portions of the tip appear convex with the cube faces at the centre of curvature. (iii) For deposits insufficient to permit type-2 migration, or after its cessation, diffusion occurs without a boundary at higher temperatures and with higher activa- tion energies than the corresponding type-2 processes. With the exception of CO,398 diffusion occurs in a temperature range where desorption is slow at the coverages involved. Reasonably accurate values of the activation energies of most type-2 and -3 processes can therefore be obtained from semi-logarithmic plots of the rate against 1/T.Comparison of these values with D, obtained approximately from eqn. (1) and (2) permits an estimate of the activation entropy. The results obtained to date for chemically and physically adsorbed gases are summarized in table 1. The mechanism for H on W serves as a convenient starting point for other cases and will be examined first. It is reasonable to assume that atoms will be least tightly bound and also most mobile on the closest-packed regions of the substrate, i.e. the (011) face for b.c.c. crystals. Atoms migrating over it will reach the edges rapidly but will be precipitated there since this face is surrounded by atomically rough surfaces everywhere except along the directions corresponding to the zones 112-011-121 and 112-01 1-121.These also provide low impedance paths of ingress into the central (01 1) face. This can be demonstrated experimentally by arranging the tip-source geometry to exclude the former from the initial deposit. Although the regions surrounding 01 1 are atomically rough, local saturation of trap sites leaves 01 1-like diffusion paths open to permit further migration if adsorbate E b = Ed + 9-2 Tlogl&/a), This process occurs for initial coverages as low as 6 = 0-3.R . GOMER 25 is available. Consequently diffusion with an activation energy corresponding to that on 011 will occur if there are enough adatoms to saturate traps. A boundary will result if the average precipitation distance is less than the resolution 6 of the field emission microscope (20-30 A).It is easy to show 1 that the trapping distance xt is given by (4) where a is the jump length, Nt and Nd the number of trap and diffusion sites per unit surface area and y a trapping coefficient of the order of unity. A sharp boundary will therefore be observed if Furthermore the coverage so that estimates of the number of trapping sites are possible. Eqn. (6) shows that - 40 % of all sites on atomically rough regions of tungsten emitters are trap sites for H atoms. Eqn. (4) then indicates values of the order of - 3 A for xt, so that eqn. ( 5 ) predicts a boundary. If this mechanism is correct, boundary-free diffusion with increased activation energy, Corresponding to migration from trap to trap, should become rate controlling when there are no mobile ad-particles left.This is the case. With Ni as substrate, type-2 diffusion is not observed for hydrogen3 except vestigially near the (1 10) faces, although the values of the activation entropy, energy, and its ratio to the energy of adsory’ion are very similar to those found for type-2 diffusion of H on W. Examination of a lattice model shows that the surface of an Ni emitter consists almost entirely of slabs and terraces of 100 and 11 1 orientation. In a face-centred structure these are the most closely packed faces, so that almost all portions of the Ni emitter are atomically smoother than the closest packed face of tungsten. A quasi type-2 diffusion can occur, but without a boundary, since the number of traps to be saturated is too small.Eqn. (2) indicates that NJN < 0.01, except in the immediate vicinity ofthe (1 10) faces. where the lattice is somewhat less closely packed. These observations do not conflict with the fact that the activation energy of the desorptiong of H2 from Ni shows a “tail” of 45 kcal at very low average 8, probably corresponding to tight binding sites near 110. It is also interesting to note that there is some evidence for equilibrium between adsorbed H and H2 at very high coverage and low temperature.9 This could easily result from the close proximity of ad-sites on this surface. The mechanism just presented assumes that sites of different binding, or at least activation energy for place change, are built into all but the closest-packed faces of a b.c.c.crystal and correspond to the various atomic surface configurations of the substrate. While there is no question that these occur, some care must be exercised in associating them with adsorption and diffusion sites. It is clear that the effects of this structure must disappear in the limit of very small ad-particles, since it is always possible to pick three surface atoms whose relation to each other corresponds to that of atoms in the (1 10) face. Hydrogen on W begins to approach this situation, although the variation in electronic configuration of the surface on the (110) compared with the (1 11) or (100) face is sufficient to bind hydrogen more tightly on the latter two and to increase the value of Ed/Edes there. However, H is sufficiently small so that it cannot differentiate between the configurations occurring on (1 11) or (100).The situation for 0 on W bears out this argument. The general mechanism seems similar to that for H on W, but the larger size of 0 atoms enables these to “ feel ” variations in the surface structure that are not apparent to H. Thus, after type-2 spreading must be Of Nt/(Nt -/- Nd)r (6)26 SURFACE DIFFUSION type-2 diffusion from the (100) face has a slightly lower activation energy than that from the (110) face. The reason is probably connected with the fact that there are two distinct types of sites for 0 atoms on the former. The first, very strongly binding, corresponds to a position in the interstice between four corner atoms of a face of the unit cell where simultaneous contact with at least four (possibly five) W atoms is possible because of the large size of 0.The second corresponds to contact with only two W atoms, once the interstice is filled. On the other hand, an 0 atom makes simultaneous contact with three W atoms on the smoother (1 10) face and must break one of these " bonds " in the process of changing sites. Diffusion from a " two-atom " site on the (100) face may or may not involve a larger fraction of the corresponding binding energy ; the latter will be considerably lower than on 011 so that the net result is a slightly decreased activation energy. The fairly low coverage at which the process occurs is in accord with the loose spacing of atoms on 100 and the large size and relatively low concentration of interstices, i.e.trap-sites. The case of CO on W is particularly interesting for two reasons. First, CO is non-dissociatively adsorbed under most conditions 8810 and secondly, its very large size provides a useful variation in that parameter from the other cases. Examination of a marble model of the emitter surface indicates that binding will be tightest on the cube faces, a site corresponding to the entire interstice between four W atoms of a unit cell face. Diffusion over a filled row of such sites cannot occur. Tight binding can also take place on 11 1 configurations, but place change there involves almost no relinquishing of contacts with substrate atoms. These facts explain the observed behaviour very well. Migration proceeds rapidly and without a boundary over 0 1 1 and its vicinals and also into 11 1.Along the approaches to the cube faces, 001 traps appear with increasing frequency among the micro-configurations so that the precipitation distance becomes small and a boundary appears around 001, but not around 111, where diffusion occurs relatively easily. When the boundary around 001 has advanced to the point where 001 sites predominate almost completely, the temperature must be increased to the point where diffusion out of 001 trap sites can occur, since filled sites block diffusion past them. The rate of this migration will be slow relative to equilibration of the adsorbate behind the diffusion front and consequently a sharp boundary will still be maintained almost until the (001) face itself is reached. It is interesting to examine the ratio of the activation energy for diffusion to the energy of binding, Table 1 shows that (&/Edes) (where known) increases with Ed in a given system and that it is least for H and greatest for CO on tungsten.TABLE 1 .-SUMMARY OF SURFACE DIFFUSION RESULTS type of diffusion a+exp(AS+lR)cm2lsec Ed(kca1) AS*(cal/mole deg.) Edes (kcal) Ed/Edes - [go]* [0*66] - 52 [70] 0 on W boundary free 4 82 30% 1.5 13 f 5 130 0.24 0 on W 110 boundary 4 3 X 10-2 24.8 & 1 7 & 5 125 0.2 0 on W 100 boundary 4 1 22.7 f 1 13 f 5 125 0.18 H on W boundary free 1 3-2 x 10-4 9.6 - 16 i 3 [- 2 rt 51 65-82 0.20 H on W 110 boundary1 1.8 x 10-5 5.9 f 1 [- 8 f 51 60 0.1 H on Ni boundary free9 3.2 x 10-5 7 i 1 - 7 f 5 68-72 0.1 COZ on C02/W 5 [lo-31 2.4 - 5.5 0.43 - [2*3] 0.39 - 2.3 0.39 CO on CO/W 8 [0.91 0.9 0 2 on O/W 4 - 5.9 [Om181 - 1.9 0.3 KronW8 110-31 [0*91 A o n W 7 [lo-31 0 6 Column 2 gives the pre-exponential part of the diffusion coefficient. Column 4 lists activation entropies.Values in brackets are preliminary or represent only rough estimates. CO on W boundary free (1 10) 8 CO on W boundary (110) 8 - 160 f 51 36 - - 9-10 0.3 [ 10-31 Xe on W 8,11 [lo-31 [3 1 The symbols X/W refer to an X-covered W surface. * for 8 - 0.06 monolayerR. GOMER 27 The first observation can be explained by assuming that the corrugation of the potential structure imitates that of the physical surface. Consequently diffusion on a (subatomically) smooth surface would require no activation energy whatever, regardless of the heat of binding.However, the discreteness of atomic surfaces insures that diffusion out of the tightest binding sites requires the greatest amount of partial desorption. The second observation supports the previous arguments regarding the impor- tance of adsorbate size. Thus the place change of a CO molecule from one interstice of the cube face of a unit cell to another requires that contact be reduced from five to two W atoms, during the process. The large size of CO precludes any squeezing between W atoms and consequently the activation energy approaches > 50 % of the heat of binding. On the (I 10) face, diffusion of CO should similarly require - 33 % of the binding energy there. The small size of H permits a certain amount of squeezing between, rather than over, the substrate atoms during place change, and thus results in a much lower ratio for &/Edes.0 as one might expect lies between these extremes. This confirms that &/&s cannot be predicted from nearest-neighbour arguments except perhaps with very large ad-particles, although such considerations are extremely useful in predicting and corroborating qualitative behaviour. Similar arguments hold for the entropy of activation, although the very great uncertainties in the experimental values make a detailed discussion unwarranted. The adsorption and diffusion of inert gases on field emitters have been studied by Ehrlich 11 and by the author.69 7 The results, although incomplete, can be explained along very similar lines. A detailed correlation was made by Ehrlich 11 for Xe on W and seems to apply also to the other cases.12 CONCLUSIONS These results indicate that a certain amount of heterogeneity is built into all but the most closely-packed faces of any crystal.Since the microstructure consists of various combinations of a very small number of different building units, the same types of sites can appear on many different faces, the variation being chiefly in number. Thus macro-orientation is much less important (in many cases) than one might at first suppose. The extent to which a given adsorbate notices variations in structure depends among other things on size, since this determines both the number and position of the substrate atoms an ad-particle can interact with simultaneously. This picture verges dangerously close on a rather naive pairwise-interaction model. The results for hydrogen adsorption indicate that this would be an over- simplification. However, an increase in adsorption energy with the number of participating substrate atoms can be justified quantum mechanically : either by invoking resonance, or equivalently, the uncertainty principle. If these arguments are correct, it must be concluded that variations in heats of adsorption with coverage and orientation can arise without the need of invoking ad-ad interactions until the coverage becomes quite high. It is a pleasure to acknowledge stimulating discussions with many of my colleagues, particularly Dr. A J. Melmed and Dr. D. 0. Hayward. 1 Gomer, Wortman and Lundy, J. Chem. Physics., 1957, 26, 1147. 2 for a summary and references, see Good and Miiller, Handbuch d. Physik, 1956, vol. 4 Gomer and Hulm, J. Chem. Physics, 1957, 27, 1363. 6 Gomer, J. Physic. Chem., 1959, 63, 468. 7 Gomer, J. Chem. Physics, 1958, 29, 441. 9 Wortman, Gomer and Lundy, J. Chem. Physics, 1957,27, 1099. 10 Ehrlich, Hickmott and Hudda, J. Cheni. Physics, 1958, 28, 506. l 1 Ehrlich and Hudda, J. Chem. Physics, 1959, 30, 493. l 2 Klein, J. Chem. Physics, 1959, 31, 1305. XXI, p. 176. Hayward and Gomer, J. Chem. Physics, 1959, 30, 1617. 3 Gomer, J. Chem. Physics, 1958, 28, 168. 8 unpublished results.

ISSN:0366-9033    

DOI:10.1039/DF9592800023

出版商:RSC    

年代:1959

数据来源: RSC

摘要:

ACTION OF LIGHT ON THE GAS ADSORPTION BY SOLIDS BY A. TERENIN AND Yu. SOLONITZIN Physical Institute, The University, Leningrad B-164, U.S.S.R. Received 22nd May, 1959 Specific photodesorption effects, not due to heating by light, have been previously observed for CO adsorbed on Ni and for H20 on Cd and Zn, but not on Bi and Sb (Valnev). Oxygen is photodesorbed from ZnO with Zn excess. Photosorption of 0 2 and of CO takes place on ZnO with oxygen excess. A strong photosorption of oxygen by well- degassed silica gel was found, and interpreted as due to the splitting-off of surface hydroxyls by the ultra-violet light. In a previous review of this field,l four kinds of processes occurring at the boundary gas/solid under illumination were described, viz., (a) a photodesorption of unchanged gas molecules, (b) a photosorption of gases under the influence of light, absorbed by the solid, (c) a photo-decomposition of the adsorbed gas molecules, or the surface compounds, (d) a photoreaction of the illuminated surface with the adsorbed molecules.In some cases it is impossible to separate the elementary processes here enumerated, which can take place simultaneously, or consecutively. We limit this contribution to the presentation of the results obtained for the photodesorption and the photosorption of gases at low pressures of the order of 10-2 to lO-5mm Hg, which have been partially described in previous papers.1-5 EXPERIMENTAL From the start of this line of research in the thirties,l we used in our laboratory various set-ups, the principle of which is shown in fig.1. The cell 1 was of Uviol glass, or quartz, joined to the rest of the apparatus by graded seals ; the Pirani gauge 2 had a tungsten filament 200 mm long and ca. 10 p thick, which formed a branch of the resistance bridge, and was immersed during the measurements into a constant temperature bath. Various cut-offs 3 have been tried, viz., with mercury,* melted tin and, in the last model, a metal valve. In the control experiments the cell with the gauge has been sealed-off from the vacuum line. The trap 4 was used to test the condensability of the desorbed gas, that at 5 was cooled by liquid-nitrogen or -air for a final elimination of condensable gases and vapours. For the solids in the form of powders the cell was shaped as shown in fig.1, the powder being kept between the semi-spherical surfaces and the light incident from the concave side. For sublimed metal layers a rectangular or cylindrical cell was used, the metal being sublimed on one side of the wall. The closed volume of the cell, the trap 4 and the gauge was, in the latter experiments, 10-15 cm3. Samples of the powdered solids, after being heated in air at 600°C in order to burn out organic contaminations, were subjected to a degassing in the cell for many hours at 300-400°C until there was no further gas desorption. The layers of the volatile metals Zn, Cd, Sb, Bi, investigated by Valnev,3 were obtained by evaporation of a small bead of the metal from an appendix of the cell into it, after careful degassing of both ; the metal layer was sublimed several times from one wall to another in a vacuum of 10-6 mm Hg.The pressures in the gauge, previously calibrated for various gases, were recorded on photosensitive paper using the spot of the galvanometer, and later with a pen recorder. The barograms in the figures are reproductions of the actually recorded curves. The * Control experiments showed that the presence of mercury vapour did not influence the results. 28A. TERENIN AND YU. SOLONITZIN 29 sensitivity of the gauge was 1.5 x 10-5 mm Hg per mm of the scale on the paper ; in the latest set-up the sensitivity was 6 x 10-7 mm Hg per mm. The sources of light were: (a) a condensed 200-W spark with Al, Zn, Cd or Fe-Ni electrodes, (b) a quartz high-pressure mercury 250-W lamp, (c) an incandescent projection 300-W lamp. The small magnitude of the effects observed did not permit the use of monochromators, therefore the active range of the ultra-violet light was roughly deter- mined with the following light-filters having absorption limits at the wavelengths given in brackets : glass 1-5 mm thick (330 mp), mica (310 mp), organic film (290 mp), gelatine film (240 mp), calcite 9 mm thick (225 mp), Cellophane film (210 mp).FIG. 1 .-Experimental set-up. 1, the cell ; 2, the Pirani gauge; 3, a mercury cut-off; 4 and 5 , traps. 4 2 5 The gases required were obtained in small quantities by the following procedures : oxygen by heating KMn04 crystals in vacuo; CO by heating a mixture of CaC03 and Zn powder; 6 hydrogen by electrolysis ; nitrogen from NaN3. These gases were passed through traps cooled by liquid-air.Water vapour was obtained at its saturation pressure from copper sulphate hydrate crystals. Ammonia was produced by heating in vacuo its complex salt with silver chloride : before admission the gas was purified by freezing it at - 78°C. For photodesorption experiments, the preliminary adsorption was carried out at pressures of 10-1 to 10-2 mm Hg, but in some cases a pressure of 10 mm was used. After introducing the gas to the solid, the latter was pumped off and the evacuation repeated until the thermal desorption of the gas stopped or was substantially reduced in the dark. For the photosorption experiments the degassed sample was put into contact with the gas studied at a pressure of 10-2-10-3 mm Hg. RESULTS AND DISCUSSION PHOTODESORPTION FROM METALS Fig.2, taken from Valnev’s paper,3 shows a typical barogram for the action of u.-v. light on Ni which has adsorbed CO.* From the experiments, it can be * The disperse nickel used in the experiments was obtained by thermal decomposition of NiN03 to the oxide state and subsequent reduction with hydrogen at 250-300°C. The degassing in vacuo of the metal layer was carried out at 300°C for many hours.30 ACTION OF LIGHT ON ADSORPTION inferred that an irreversible desorption of a gas non-condensable at - 18O"C, takes place under the action of wavelengths shorter than ca. 240mp. Water and ammonia vapours, adsorbed on a similar Ni sample, exhibit likewise an enhanced degassing under illumination, but in contrast to CO, the rate of this desorption does not depend on the light-filters used ; moreover, a slight desorption is observed under illumination by low intensity infra-red radiation.The gas desorbed in these cases condensed at - 180°C. This points, for H20 and NH3, to a purely thermal action of the light, absorbed by the disperse Ni. 0 3 rA 2 a FIG. 2.-Photodesorption of CO from disperse nickel. 1, unfiltered light of a zinc spark ; sX104 rnm "9 I I I 2, light filtered through a gelatin film 111 I I transmitting only wavelengths longer I 1 than 240 mp. I I < I I I I I I I I 0 10 min In contrast to this behaviour on Ni, water vapour adsorbed on sublimed laycrs of Cd and Zn, gives photodesorption of a gas which is 50 % condensable at - 180°C, but only under the action of wavelengths shorter than ca.250 mp. Moreover, the spectral threshold for Cd was obtained somewhat to the red as compared with Zn. No photodesorption from sublimed layers of Bi and Sb was observed after H20 adsorption. Likewise, no enhancing action of light could be found on the slow thermal desorption at 20°C of CO, CO2, 02, H2 from sublimed Cd, Sb and Bi layers, although the latter was black and absorbed practically all the incident energy. The presence of a sufficient concentration of the adsorbed gases with the sublimed layers was proved by their appearance on raising the temperature. A photodesorption of hydrogen from the Ni sample was also absent. From the desorption rate from the sublimed layers it could be inferred that the coverage was approximately monomolecular on the geometric area of the layer.For H20 adsorbed on Cd, Valnev2~ 3 ascertained that the photoelectronic emission from the metal produced by the u.-v. light simultaneously with the desorption, had nothing to do with it. With a potential difference of 15 V applied between the metal and a wire, the sign of the potential on the metal did not affect the photo- desorption rate, whereas the photocurrent increases 5-10 times when the metal is made negative. The specificity of the photodesorption by short u.-v. light limited to CO on Ni and to H20 on Cd and Zn, for which the purely thermal desorption in the dark is relatively slow, indicates a primary quantum origin of the phenomenon. For desorption caused by the thermal action of the light, the liberated gas is re- adsorbed.1 The presence in the case of H20 on Cd, or Zn of a high percentage of a non- condensable gas at - 1 80"C, indicates that a photodissociation of chemisorbed water molecules is taking place simultaneously.The active wavelengths are considerably shifted (by about 2 eV) towards the red as compared with the threshold of photodissociation of water vapour. It is strange that a photo-A. TERENIN AND YU. SOLONITZIN 31 dissociation of ammonia adsorbed on Cd could not be obtained, although such a process has been observed for NH3 adsorbed on alumina, MgO and Cu sulphate.7~ 8 There are no grounds for ascribing the photodesorption of CO from Ni to a similar photodissociation of nickel tetracarbonyl formed at the surface of the disperse metal upon CO adsorption.First, nickel tetracarbonyl is not known to be produced by simple contact of Ni with CO gas at room temperature. Secondly, Tagantzev 1 has shown that when nickel tetracarbonyl is formed on the surface of the metal by heating a layer of Ni in CO, the u.-v. irradiation produces a gas which is condensable at - 180°C, in contrast to the experiment described above. In this case, evidently nickel tetracarbonyl molecules were photodesorbed. The experiments on photodesorption described above indicate that the electronic energy of excitation imparted to adsorbed molecules by light is dissipated by the solid at a slower rate, than the rupture of a covalent, or adsorption bond. It can be presumed for metals that the electronic excitation energy of a chemisorbed species on them will be dissipated by the metal in a time of the order of 10-15 sec. The transition of the electronic excitation energy into the kinetic energy of the disrupted bond with a co-ordinate perpendicular to the surface would require ca.10-12 sec. This gives approximately 10-3 for the probability that a sufficient energy will remain in the bond, to disrupt it. This estimation, if correct, means that a photodesorption of an entire molecule or a photodissociation of an ad- sorbed molecule should be of observable magnitude, as is the case. In the paper,l potential curves were drawn for the photodesorption process of CO on the as- sumption that CO is chemisorbed as a carbonyl diradical =C=O. It was ten- tatively presumed that the absorption of a large u.-v. quantum would lead from the deep potential minimum of the chemisorbed state directly to the repulsion branch of the potential curve depicting the physical adsorption of the CO molecule.Thus, for the possibility of a photodesorption, the minimum on the chemisorption curve should not lie too deep, otherwise much shorter wavelengths would be required. Besides, a strong chemisorption should lead to a more efficient dis- sipation of any excess of vibrational, or kinetic energy in an adsorption bond. The chemisorption of H20 molecules on metals occurs probably through the oxygen atom.9 An alternative explanation of the relatively slow dissipation of the excitation energy of the adsorbed molecules on metals would be the assumption that the surface is in our samples a very irregular one, and therefore the centres on which the adsorbed molecules are attached, are feebly interacting with the bulk of the metal.PHOTODESORPTION AND PHOTOSORPTION OF GASES ON SEMICONDUCTORS The desorption of oxygen from ZnO under the action of light absorbed by the semiconductor, has been observed by Miassnikov,lol 11 Heiland 12 and Melnick 13 by the changes of the electrical conduction, by Putzeiko and Terenin14 by the changes of the e.m.f. under intermittent illumination, and by Tagantzev and Terenin 15 by the luminescence of ZnO. Direct manometric measurements have been carried out by one of the authors.4~ 1 * One of the barograms obtained by him is shown in fig. 3 ~ . The first experiments were unsuccessful ; this is explained by the fact that the effect is clearly observed only for ZnO with excess metal.The photodesorption can be observed even with metallic Zn, evidently covered with a thin oxide coating. If Zn metal remains in contact with oxygen several hours at 20°C, the photodesorption disappears and neither admission of fresh oxygen, nor a heating of the sample up to complete oxidation, renewed the photo- desorption. This explains why in the experiments of Valnev 3 a photodesorption * In a recent paper by Medved 11 the photodesorption of 0 2 from ZnO has been meas- ured with an ionization gauge'in a flow system. Such dynamic conditions do not always allow unambiguous conclusions.32 ACTION OF LIGHT ON ADSORPTION of 0 2 from Zn has not been observed, since in all these experiments the adsorption of oxygen took a long time.In the experiments with ZnO, samples of different origin have been used. The preliminary thermal degassing was such, that before the oxygen adsorption, no gas was evolved on illumination. 0 5 10 0 3 6 A B min FIG. 3.-A photodesorption of oxygen from ZnO under u.-v. light in the range 366 mp; (B) photosorption at 90°C of oxygen on ZnO, enriched by 0 2 . Some oxygen desorption from ZnO could be produced not only by light of wavelengths shorter than 400 mp, but to a much smaller extent by infra-red radi- ation in the range from 1 to 2p. The non-thermal origin of the photodesorption by the near u.-v. is also shown by the behaviour of CO in contact with ZnO : the illumination in the near u.-v. gives a photosorption, whereas the infra-red radiation always leads to a pressure increase (fig.4), the desorbed gas being adsorbed again after the end of the E? a k ) I 1.0 I 1 I. 0 5 10 I 5 time, min FIG. 4.-(a) Thermal desorption of CO from ZnO under infra-red illumination (filter 1 to 2 p) ; (b) photosorption of CO by ZnO under near u.-v. irradiation by 366 mp. illumination. It may be that the irreversible photosorption of CO on ZnO is in reality due to its oxidation, sensitized by the semiconductor. This effect is being studied further. As shown in fig. 3A, the continuation of the illumination leads to a pressure decrease of the initially photodesorbed gas. This photosorption cannot be ex- plained by the adsorption of the gas on sites of the surface kept in the dark, sinceA . TERENIN AND YU. SOLONITZIN 33 on raising the oxygen pressure to 1 x 10-2 mm Hg the photosorption increases.On ZnO enriched by oxygen, the photosorption is very striking (fig. 3 ~ ) . The wavelengths most effective for the photosorption are shorter than 400 mp, but a decreasing activity can be followed down to 500mp. The rate of photo- sorption sharply decreases on rise of temperature; * at 150°C, no photosorption of 0 2 on ZnO could be observed. We have, first, supposed that this photosorption is due to traces of water, since it became larger after ZnO has been in contact with water vapour. Under such conditions, a well-known oxidation of water by oxygen can occur, photosensitized by ZnO, with the formation of hydrogen peroxide. However, Fujita and Kwan 17 have recently found an irreversible photosorption of oxygen on oxidized ZnO; the active wavelengths were likewise shorter than 450mp.If, under their con- ditions, traces of water were definitely excluded, this would mean that in the experi- ment of one of US,^ reproduced in fig. 3 ~ , the same true photosorption was present. Kobajashi and Kawaji 18 have recently found a photosorption of oxygen on ZnS containing a trace of Cu (10-2mole %) and followed it by measurements of the contact potential of the surface. Some cases of photodesorption and photosorption of hydrogen on Tho3 have been mentioned by Luycks, Bodart and Rens (cf. ref. (1)) and by Duval (cf. ref. (2)), but the limitation of the active range to the Hg line 254 mp raises some questions about the possible participation of the excited mercury atoms present as traces in the gas phase.An explanation of the photosorption of oxygen on the electronic semi- conductors ZnO and ZnS should be sought in the accumulation of electrons in surface traps, according to the theoretical presentation of Kobayashi and Kawaji,lg or the theory of Volkenstein,lg implying an adsorption of molecular radicals on electrons at the surface. Oxygen can be regarded as a biradical. The photodesorption of oxygen from ZnO does not present theoretical diffi- culties. It is now generally admitted20~21 that 0 2 molecules, adsorbed on an electron-excess semiconductor, like ZnO, do act as electron traps producing a negative surface layer. Strongly held 02- molecules cannot leave the surface, unless they lose their electron when an exciton reaches the surface of ZnO.The direct experimental proof of the existence of such a negatively-charged layer has been given recently in this laboratory by measurements of the exit work of photo- electrons from ZnO.22 Moreover it has been shown in this laboratory 23 that for ZnO, and also for Ti02 and WO3, specific wide unselective absorption ranges are present in the infra-red between the wavelengths 4 and 14 ,u which are to be ascribed to electrons in donor surface levels.? In fact, this absorption spectrum dis- appears when oxygen, or NO, or quinone vapour, is in contact with the semi- conductor in powdered form. Under illumination in vacuo by near u.-v. wave- lengths in the range of the absorption of the semiconductor, the infra-red absorp- tion spectrum re-appears and the experiment can be reversibly repeated many times.A thermal degassing is less effective. We thus have here another inde- pendent evidence of a photodesorption process. The results for Ti02 and WO3 are corroborated by measurements of changes of the conductivity under illumin- ation.25 The fluorescence of ZnO equally experiences changes attributed to photo- desorption of NO and quinone.15 PHOTOSORPTION OF OXYGEN ON SILICA GEL One of the authors 5 has found that silica gel, or aerogel thoroughly degassed (5 h a . 600°C in vacuo) brought in contact with dry oxygen at a pressure of 10-2 mm Hg, exhibit a rapid irreversible photosorption on illumination by u.-v. * The decrease is exponential with a thermal deactivation energy of 0-7 eV. f For ZnO the same unselective absorption in the infra-red has been independently found in the work.24 D34 ACTION OF LIaHT ON ADSORPTION light in the range of wavelengths shorter than 250mp.A typical barogram is reproduced in fig. 5. No such effect is observed with nitrogen, hydrogen, CO and 4 liqht k- E 0 5 10 I 5 2 0 min FIG. 5.-Sorption of oxygen by silica gel : (a) under illumination by short u.-v. (Fe spark, wavelengths shorter than 250mp active); (b) after preliminary illumination. C02. The capacity of rapid sorption of oxygen is retained by the gel even after a preliminary illumination in vacuo (cf. fig. 5). In the presence of water vapour (5 x 10-2 mm Hg), the photosorption of 0 2 disappears, but after the removal of adsorbed water by evacuation at 20°C, the photosorption increases in magnitude somewhat.Although the gel was subjected, before de- gassing, to a heat treatment in air at 600°C to burn out possible organic contaminations, to disprove the possibility of a photo-oxidation of traces of organic compounds the following experiment has been performed. Acetone vapour (20mmHg) was adsorbed on the gel, then pumped off to a pressure of 10-2 to lO-3mmHg and the gel illuminated in the presence of oxygen. It was found that the adsorption of acetone entirely suppressed the oxygen photosorption. Evidently H20 and acetone molecules are blocking the surface centres of the gel which are responsible for the photosorption. It proves, in addition, that no photo-oxidation of acetone is taking place at the surface. The phenomen cannot be explained by a thermal action of the u.-v.light since : (a) heating of the gel for a long time in oxygen does not suppress the photo- sorption, (b) on samples exhibiting a marked photosorption, a comparable thermal sorption in the dark begins at 400-450°C only, (c) the photosorption rate'is pro- portional to the light intensity. On crushed and degassed crystalline quartz, photosorption of oxygen is also observed, although, however, to a much lesser The most plausible explanation of the photosorption of oxygen on silica gel is that the u.-v. light splits off OH radicals of the silanol Si-OH groups from the surface. These latter are easily observed and their behaviour studied with the help of infra-red spectra.26-29 The free valencies freed at the Si atoms can function as adsorption centres for 0 2 molecules, leading to the formation of peroxide radicals of the kind Si--O-O*.It has been shown recently that silica gel heated under high vacuum acquires the property of strong oxygen sorption.30 The OH radicals split off by the u.-v. light give subsequently H202 on the surface. This follows from the fact that, after the irreversible photosorption, a gas can be desorbed thermally at 100°C which partially condenses at - 180°C. A slow pressure increase observed during long periods of u.-v. illumination can be ascribed to the photolysis of H202. extent. pq 1 Terenin, Problems of Kinetics mtd Catalysis (ed. Acad. Sci. U.S.S.R.), 1955, 8, 17 ; J. Physic. Chem. (U.S.S.R.), 1935, 6, 189 ; 1940, 14, 1362 ; Heterogeneous Catalysis in the Chemical Industry (Moscow, 1956), p.197. 2 Terenin, J. Chim. physique, 1957,54, 114. 3 Valnev, J. Physic. Chem. (U.S.S.R.), 1956, 30, 1308 ; Sc. Bull. Leningrad University, 4 Solonitzin, J. Physic. Chem. (U.S.S.R.), 1958, 32, 2142. 5 Solonitzin, J. Physic. Chem. (U.S.S.R.), 1958, 32, 1241. 6 Weinhouse, J. Amer. Chem. Soc., 1948, 70, 442. 7 Kassparov and Terenin, Acta physicochim., 1941, 15, 343. 8 Belosselsky, J. Physic. Chem. (U.S.S.R.), 1939, 13, 586. 9 Suhrmann and Schulz, 2. Elektrochem., 1952,56, 351 ; Naturwiss., 1953,40,139. 1949,23, 10.A. TERENIN AND YU. SOLONITZIN 35 10 Miassnikov and Pshezhetzki, Doklady Akad. Sci. U.S.S.R., 1954,99, 125 ; Problems of Kinetics and Catalysis (ed. Acad. Sc. U.S.S.R.), 1955, 8, 34. 11 Miassnikov, J. Physic. Chem. (U.S.S.R.), 1957, 31, 1721, 2005 ; Izvest. (Bull.) Akad. Sci. U.S.S.R., ser.phys., 1957, 21, 192. 12 Heiland, 2. Physik, 1957, 142, 415. 13 Melnick, J. Chem. Physics, 1957, 26, 1136. 14 Putzeiko and Terenin, Doklady Akad. Sci. U.S.S.R., 1955, 101, 645 ; Problems of Kinetics and Catalysis (ed. Acad. Sc. U.S.S.R.), 1955, 8, 53 ; J. Physique Rad., 1956, 17, 650. 15 Tagantzev and Terenin, Doklady Acad. Sci. U.S.S.R., 1957, 112, 251 ; Optika Spektroskopia, 1957, 2, 356 ; J. Physique Rad., 1956, 17, 650. 16 Medved, J. Chem. Physics, 1958, 28, 870. 17 Fujita and Kwan, Bull. Chem. SOC. Japan, 1958, 31, 379. 18 Kobajashi and Kawaji, J. Physic. SOC. Japan, 1955, 10, 270 ; J. Chem. Physics, 1956, 19 Volkenstein and Kogan, J. Chim. physique, 1958,55,483. 20 Bevan and Anderson, Faraday SOC. Discussions, 1950,8,246. 21 Hauffe, Angew. Chem., 1955,67, 189. 22 Wilessov and Terenin, Naturwiss., 1959, 46, 167 ; Doklady Acad. Sci. U.S.S.R., 23 Filimonov, Optika Spektroskopia, 1958, 5, 709. 24 Milosslavsky and Kovalenko, Optika Spektroskopia, 1958,5, 61 3. 25 Korssunovsky, Problems of Kinetics and Catalysis (ed. Acad. Sci. U.S.S.R.), 1960, 26 Yarosslavsky and Terenin, Doklady Acad. Sci. U.S.S.R., 1949, 66, 885. 27 Kurbatov and Neuimin, Doklady Acad. Sci. U.S.S.R., 1949, 68, 341. 28 Sidorov, J. Physic. Chem. (U.S.S.R.), 1956, 30, 995. 29 Terenin and Filimonov, Hydrogen Bonding Symposium (Lubljana, 1957, Pergamon 30 Krassilnikov, Kisselev and Sysoev, Doklady Acad. Sci. U.S.S.R., 1957, 116, 990. 24, 907. 1959,125, 1053. 10, in press; J, Physic. Chem. (U.S.S.R.), 1960, 34, in press. Press, 1959).

ISSN:0366-9033    

DOI:10.1039/DF9592800028

出版商:RSC    

年代:1959

数据来源: RSC

摘要:

THE PHOTOCONDUCTIVITY OF MOLECULAR CRYSTALS BY J. N. MURRELL Dept. of Theoretical Chemistry, University Chemical Laboratory, Lensfield Road, Cambridge Received 14th May, 1959 Theoretical expressions are derived for the photocurrent of a molecular crystal in the form of a power series in the light intensity, which includes the first- and second-order terms. The current depends in the first instance on the relative values of the potential difference across the crystal, the extinction coefficient of the crystal, and the rate at which free carriers are trapped. It is shown that the experimental results can only be under- stood if one assumes that the trapping of charge carriers is more important in limiting the carrier concentration than the discharge of the carriers at the electrodes.From the sign of the rectifying effect it is deduced that the positive carriers are the more mobile. 1. INTRODUCMON Although the phenomenon of photoconduction in molecular crystals has been known since the beginning of the century,l-3 it is only in the last decade that sufficient care has been taken over the experimental procedure to obtain repro- ducible results. Chynoweth and Schneider,4 and later Goldsmith,s and Compton, Schneider and Waddington,6 have shown the existence of a true bulk conductivity, which, unlike the surface conductivity, is not influenced by the presence of ab- sorbed gases. It is with this bulk conductivity that I shall concern myself in this paper. The steady-state photoconductivity of a pure single crystal depends on the temperature, the wavelength and intensity of the incident light, and on the direc- tion (relative to the direction of the light) and strength of the applied field.I shall attempt to explain these experimental facts by assuming that the charge carriers can be treated as classical particles having characteristic diffusion constants and mobilities. Several earlier papers deal with the " kinetics " of photoconduction with an emphasis on inorganic semi-conductors.7-9 However, the solution of the equa- tions presented in this paper is somewhat different from that presented hitherto, and emphasis is laid on the interpretation of the photoconductive properties of organic crystals. 2. GENERAL THEORY: LOW LIGHT INTENSITIES We shall consider a plate-like crystal of thickness r (along the x-co-ordinate) and of infinite extension in the yz-plane.The face Oyz is uniformly illuminated by monochromatic light, normal to the surface, and the crystal is sandwiched between infinitely conducting electrodes. Under these conditions we can assume that the concentration of positive and negative charge carriers is only a function of the x-co-ordinate. Since the photocurrents obtained in the experiments we shall consider are about 103-104 times larger than the dark currents obtained for the same voltage, we can assume that the charge carriers arise solely from the absorption of photons by the crystal. In addition we shall assume that there is no injection of carriers from the electrodes (since the dark current is negligible), and that the carriers are discharged immediately on reaching the electrodes (since the electrodes are 36J .N. MURRELL 37 infinitely conducting). With these assumptions we can assume that the con- centration of positive and negative carriers drops to zero at the boundaries x = 0 and x = Y. We shall assume that there are no free charge carriers produced in the dark, but that there is an equilibrium concentration of trapped charges produced by thermal processes. The absorption of a photon may produce two free charge carriers, or one free and one trapped carrier, depending on the nature of the site which absorbs the photon. If no andpo are the concentrations of trapped carriers, and n and p that of the free charges, then we can distinguish the following processes : rate of rate of formation recombination X -k kT + no +PO F(T) ZnoPo X + h v + n + p I X knp X + hv + no + p 9; g+nop X i- Av + n +po 9; g-npo Any other process, such as the production of a free carrier arising from the ab- sorption of a photon by a trapped carrier, can be obtained by taking suitable combinations of these equations.If we assume that the concentration of carriers is small compared with the number of lattice sites (X is constant), then in a steady state we can write the following equations : dn/dt = (Ix - knp) + (3 i- g-npo) + dj-/dx = 0, dpldt = (I, - knp) + (9; - g+pno) - dj+/dx = 0, (2.1) (2.2) (2.3) (2.4) (2.5) (2.6) dnoldt = - (9; - g+pno) + (F(T) - Znopo) + djcldx = 0, dpoldt =- (9; - g-npo) + (F(T) - Znopo) - dji/dx = 0, j - = p-gn + ap-dnldx, j + = p+gp - ap+dp/dx, where thejs are the current densities of charge carriers given by (and similarly f o r j i andji).In defining these current densities we have made use of the Einstein relationship 10 between the mobility p and diffusion constant 8 of a charge carrier, (4, the electronic charge; k, Boltzmann's constant ; T, the absolute temperature). 8 = ap, a = kT/q, (2.7) The electrostatic field is given by Poisson's equation, d8'1d.x = 47rq(p - n + PO - no), (2.8) 8 being finally determined by the potential difference across the crystal v = Jr8'd.x. 0 (2.9) The net current flowing in the crystal is j = 40'- +i+ + jti +$I, (2.10) djldx = 0: (2.11) and satisfies the conservation law as is seen by combining eqn. (2.1) to (2.4). We now make the assumption that the current density of trapped carriers can be neglected by comparison with that of free carriers.If one writes j6 = j ; = 0,38 PHOTOCONDUCTIVITY OF CRYSTALS then dji/dx = dji/dx = 0, (j- + j + ) is a constant, and by integrating expressions (2.5) and (2.6) from x = 0 to Y, and applying the boundary conditions, we have (2.12) Also from (2.3) and (2.4) we have (3; - g+Pno> = (3; - g-npo), (2.13) but since the rate of formation of carriers must be independent of the concentra- tion of carriers in the crystal (providing it is not too large) this can be satisfied only if Jq!= 9; (2.14) and g+pno = g-npo. (2.15) In the dark the steady-state concentrations of trapped carriers must be equal to one another, hence we can write no = po = N. It follows from (2.14) that to the first order in the light intensity p / n = g-/g+ (a constant).(2.16) This can obviously not be true in general, since the application of an electric field to the crystal will tend to build up the positive-carrier concentration near the negative electrode and the negative-carrier concentration near the positive electrode. The anomaly is due to the fact that if one puts do-/dx = djG/dx = 0 in eqn. (2.1) to (2.4) and assumes that the rate of formation of carriers is inde- pendent of the number of carriers in the crystal, then it is not possible in general to reach a steady state. One is left with two alternatives, either to make the problem more complicated by allowing for the current of trapped carriers, and/or for the number of lattices sites to be depleted by the process of carrier formation, or to ignore these complications and choose the constants which enter into the equations in such a way that expression (2.16) is in fact true.It is this latter approach that will be adopted in this paper. In short, I shall assume that 3: = Yi, and that j ; = j , = 0, and that the current is given by (2.12). If our solutions do not represent a steady state then j defined in this way can be considered to be the average value of the current due to the free carriers in the crystal. By Lambert’s law the ratio of the light intensity at a depth x in the crystal to that on the surface is proportional to exp (- EX), where E is the extinction co- efficient. It follows that the rate of formation of free charge-carriers can be expressed in the form (2.17) where I0 is proportional to the incident light intensity, but will also contain some constant which is determined by the efficiency of the formation process: not every photon absorbed may give rise to charge carriers, since an excited molecule in the lattice may return to its ground state before the carriers have been formed, emitting either a photon or thermal energy in the process.To the first-order in the light intensity the steady-state concentrations of charge carriers are then determined by the equations, (2.18) (2.19) The first-order current is given 1, + Yx = I0 E exp (-- EX), I O E exp (- EX) - g+Np + ap+dZp/dx2 - (Vp+/u)(dp/dx) = 0, IOE exp (- EX) - g-Nn + ap-dzn/dxZ + (Vp-/r)(dn/dx) = 0, in which the zeroth-order field is taken as V/r.by (2.12) as r r j = qV/r (p+p + p-n)dx. (2.20) JoJ . N. MURRELL 39 Writing eqn. (2.18) in symbolic form, where D = d/dx, we can obtain the solution (02 - (V/ar)D - g+N/ap+)p = - I0 E exp (- EX), (2.21) P = ap+[(A+)2 - lopr Vp/a - ,021 (-.. (- Ex) - exp (g) [cosh (F) + sinh ($)I}, (2.22) (exp (- p - V/2a) - cosh a+)) sinh a+ + where we have defined p = Er; A+ = @y; a+ = [g + (A.2.J (2.23) as dimensionless constants (as is V/a). By similar analysis the concentration of negative charge carriers is given by sinh ‘“I>. (2.24) It is seen that the concentration of carriers in the crystal depends on the There are six CASE A, V/2a > A*-Under these conditions o( = V/2a, and the concentration (exp (- p + V/2a) - cosh a-) sinh a- + where the constants A- and a- are defined as in (2.22).relative values of the three dimensionless constants V/a, p and A. simple cases to be considered. of positive carriers can be written in the form exp (- a)(exp (V/a) - 1) - Iopr ap+[(A+)2 - Vp/a - p2](exp (V/a) - 1) P = > - exp-(Vx/ar) (e-P - 1) + (e-p - ev/7). (2.25) The concentration of negative carriers is obtained by replacing p+ byp-, A+ by A- and Vby - V. The current is then obtained from (2.20) as CASE Al, V/2a > X and p > A. j = v 2 d o - v p2a2fil - e-’) coth V/2a - (ap/V)(l:+ It is seen that under these conditions the current is an odd function of V, that is, there can be no rectifying effect. Under the conditions Al, the trapping of charge carriers can be neglected, and the carrier concentration is limited solely by the rate of migration to the electrodes.The concentration of carriers is found to be inversely proportional to their mobilities, and since we have to multiply the carrier concentration by their mobility to obtain the current, we obtain the rather surprising result that the current is independent of the carrier mobilities. * The “greater than” symbol, > , will be taken in this paper to mean appreeiably greater than.40 PHOTOCONDUCTIVITY OF CRYSTALS CASE Al,.-If p > V/A > A, then (V/pa)(e-p - 1) coth V/2a + (e-” + 1) (2.28) and we have the two limiting cases j @ -+a) = dovla, (2.29) (2.30) j<V/a -+ 0) = (d0V/ap2) [(e-” + 1)(2 + p) + 2pl. In both cases, j is proportional to the first power of the potential. CASE Alb.-If V/a > p > A, then j = qIO[(l - e-”) coth V/2a - (ap/V)(l + evP)], (2.31) and we have the two limiting cases j ( V/a + CO) = qIo(1 - e-p), (2.32) (2.33) It is seen that the current approaches a limiting value for large values of the potential : under these conditions the current is limited by the rate of formation of charge carriers in the crystal. The current given by (2.33) is always positive since coth x > l/x for positive x .Moreover we can expand j ( p -+ 0) = qIop (coth V/2a - 2a/V). where the Bs are Bernoulli numbers, this series converging for x < 7r. It follows that for small values of p, j is linear in the potential only when V/a < 27r. Writing V/a = tp, expression (2.26) becomes (2.35) Fig. 1 shows the behaviour of j/qIo as a function of t for various values of p. We can only observe an ohmic current when t < 1, or for small p when t < 2r/p.CASE A2.-V/2a > h > p. CASE A2,.-1f A < Vp/a, the current is given by Alb. CASE A26.-If A > Vp/a, then assuming V/a > 1, we have (2.36) The current is again found to be ohmic. From the definition of A [(2.23),] the current is seen to be favoured by carriers of high mobility, and by a small proba- bility of the carriers being trapped. It can be seen that as p -+ 0 the current is of order p2. CASE B.-A > V/2a.-Under these conditions cc = A, the reduced equation of (2.21) has roots 5 A+/r, and the concentration of positive carriers is given by Iopr = ap+[(A+)2,- vp/a-pz] The concentration of negative carriers is again obtained by replacing A+ and p+ by A- and p-, and V by - V in this equation. The current is determined as before :J .N . MURRELL 41 CASE B 1 . A > V/2a; A > p . (2.39) The current is again ohmic, and is favoured by high mobilities of the carriers and a small trapping rate. In the limit p -+ 0, j is proportional to p (cf. (2.35)). When p -+ a the current becomes independent of p . f FIG. 1 . T h e first-order current as given by (2.35) as a function of p and f = pV/a. CASE B2. p > A > V/2a.-We again have an ohmic current : j = qLv(l + e-') af (2.40) The following limits are of interest : Our analysis of the above cases is summarized in table 1. p + GO, j EP-1; X + O , j E A ; A + GO, j E A-1. (2.41) TABLE 1.-A SUMMARY OF THE LIMITING CASES FOR THE FIRST-ORDER CURRENT CASE A, V/2a > A Ala, p > V/2a > A, ohmic current ; p -+ co , j = qV/a.Alb, V/2a > p > A, ohmic only if V/a < 2n, saturation above that ; P -+ 0, i a p . CASE By A > V/2a CASE B1, A > p , ohmic current, p --f 0, ja: p. CASE B2, p > A, ohmic current, p -+ co , j a p-1. A --f 0, j c c x . A-+- co , j a A-1.42 PHOTOCONDUCTIVITY OF CRYSTALS The cases Ala, Alb and Aza can be shown to be true stationary states corresponding to the situation in which there is no trapping of charge carriers. By examining the ratio p / n as given by (2.25) or (2.37), and comparing it with the steady-state condition (2.16), it can be shown that A26 does not represent a steady state unless V,a is very small, and that B1 and B2 represent steady states only if A+ = A-, that is, if g+/v+ = g;/p-.It is interesting to note that in none of these limiting cases should one observe a rectifying effect, that is, contributions to the current which are of even power in the applied potential. However, it is possible that in intermediate cases such an effect would be observed, since neither (2.26) nor (2.38) are strictly odd functions of V (but neither do they strictly represent stationary states). We can now compare theory with experiment. Unless otherwise stated the experimental data will be taken from a thesis by Kommandeur,11 who has studied the bulk photocurrent of anthracene (using a guard ring to remove surface currents) induced by monochromatic light, as a function of the intensity and wavelength of the light, and the strength of the applied field.If anthracene is illuminated with light of wavelength greater than 4350 8, (the first absorption band of anthracene has a maximum at about 39408,), the photo- current is found to be proportional to the light intensity (over a range of 20 to 240 pW cm-2) and the applied voltage (through a range 0 to 3500 V in either direction). At these wavelengths, the extinction coefficient is too small to be measured experimentally because of the relatively large amount of scattered and reflected light. However, it is probably safe to say that for crystals 1 mm thick p will be less than one. At 300"C, the Einstein constant a has the value a = 0.026 V, hence in the experiments we are considering the current is found to be ohmic up to a value V/a = 1-4 x 105. There are two situations which could lead to these results : case A2b in which Vp/a < A < V/2a, or case B1 in which X > V/2a.However, the first case will only hold over a range of voltages such that p > V/aA > 1 , and this range will be small since it is unlikely that p is very much less than one. We therefore conclude that for the crystals used in Kommandeur's experiments, case B1 is applicable and that A > 1.4 x 105. From the definition of A [(2.22)], it is seen that r2/@ is proportional to the product of the diffusion constant (ap), and the lifetime (gN-1 of the carrier before it is trapped. It follows that the diffusion length r/A is less than 70 A : this is the root-mean-square of the distance that a carrier travels before it is trapped. From (2.38) we predict that the current should vary as ( 1 - e-p), which is proportional to p for small values of p, and quickly reaches a saturation value when p becomes greater than one.Because of experimental difficulties this prediction has not been confirmed experimentally. For light of wavelength greater than 4000 A, the extinction coefficient is about 104 cm-1, hence p is about 1000. The current should still then be determined by the condition B1. However, experiments in this region of the spectrum have shown that the current deviates significantly from a first-order dependence on the light intensity, Kommandeur finds that j cc 10.5 when the illuminated elec- trode is positive, and j cc ZO.7 t o j cc 11.0 when the illuminated electrode is negative. The exact behaviour depends somewhat on the field strength.No detailed experi- ments at low light intensity have been carried out in this region, although Kommandeur has reported to me privately that a linear dependence is found for low illumination of the crystal. We shall consider in the next section the situation in which the photocurrent deviates from a linear dependence on the light intensity. Before discussing the case of high light intensities, however, it is interesting to consider the approximation in which we ignore the diffusion of the charge carriers. This would at first sight appear to be a valid approximation, since by the Einstein relationship the diffusion constant is only about one-fortieth of the mobility of a carrier. If we drop the diffusion term in (2.18) and (2.19), theJ .N . MURRELL 43 steady-state concentrations of the charge carriers are determined by the equations IOP VP+ ( D + = - exp (--- ex), (2.42) (2.43) These are now first-order differential equations and only one boundary condition is needed for each carrier. It can be shown that the conditions n = 0 when x = Y, and p = 0 when x = 0, give sensible solutions. That is, there is zero concentration of charge carriers at the electrode from which they are moving. (The boundary conditions It = 0, x = 0, and p = 0, x = Y, give solutions of (2.42) and (2.43) corresponding to negative concentrations of carriers.) Solving eqn. (2.42) and (2.43), we have from which we can evaluate the current by (2.20), We now have the following limiting cases : (1) Vp/a > X2. j = ‘3h2[ 1 - exp (- ‘F)] - g2[ 1 - exp (- ‘?)I}.(2.47) If Via > h2, j = qIO(1 - e-”), which corresponds to the limit Via +cO in case Alb. If Via < M, (2.48) (2.49) and this has no counterpart among the solutions obtained when diffusion was included. (2.50) This is the solution B1 in table 1. We note, however, the more restrictive con- ditions which are contained in B1, namely, h > V/a and h > p. This result leads us to hope that the experimental features of the photoconduction of anthracene can be interpreted without including the diffusion term in the transport equations, and it is this approximation that we shall adopt in examining the contributions to the current which are non-linear in the light intensity. 3. HIGH LIGHT INTENSITIES I shall first list the effects which have to be aIlowed for in cakulating the current when the concentration of charge carriers in the crystal becomes large.(1) The concentration of trapped charges may differ appreciably from the level (no = po = N ) reached at thermal equilibrium in the dark. It follows that44 PHOTOCONDUCTIVITY OF CRYSTALS the life-time of a free carrier may increase in some parts of the crystal where the the concentration of trapped charges has dropped below N, and decrease in others, where the concentration of trapped carriers is greater than N. (2) The diffusion of the positive and negative carriers to opposite electrodes, and the accompanying change in the concentration of trapped charges, will give a contribution to the electric field according to Poisson's eqn. (2.8).(3) The recombination of free carriers : this will lead to a sub-linear dependence of the carrier concentration on the light intensity. It can be seen that an exact solution, even in the form of a power-series expan- sion in the light intensity would be extremely complicated. I shall present two solutions for the contribution to the current of order I& both of which involve considerable approximations. For the first of these solutions, I assume that there is no trapping of the charge carriers in the crystal, so that the concentration of carriers is limited either by their discharge at the electrodes, or by their recom- bination with a carrier of opposite sign. The solution is presented as a power series in the applied potential, and is probably only valid when V/a is small.For the second solution, I drop the diffusion term in the transport equations, and assume that the concentration of trapped carriers remains the same as in the dark. With this last assumption, I can take the lifetime of the carriers to be independent of the light intensity, and neglect the effect of the trapped carriers on the electric field. NO TRAPS The equations are solved using a double series expansion in I0 and V. The final solutions involve products of exponentials and power series in p, but in the limit of p tending to infinity, the solution has the following form : V2 a2 + 2 (p+ - p--) - + higher powers of It is seen that a current flows even when there is no potential difference across the electrodes. This can be considered to be a diffusion current since it only occurs when the charge carriers are formed non-uniformly through the crystal, and when the positive and negative carriers have different mobilities : the more mobile carrier diffuses the more rapidly down the concentration gradient.The term linear in V contains contributions from the recombination effect, and from the back e.m.f. which arises from the displacement of the two types of carrier relative to one another. The term in V2, which gives rise to the rectifying effect, also depends on the difference in mobility of the two carriers. It is smaller than the diffusion current unless V/a > 412- Expression (3.1) is the second-order current for the conditions which give (2.29) as the first-order term. As such it is not expected to apply to the molecular crystals we are considering in this paper.NO DIFFUSION, AND THE CONCENTRATION OF TRAPPED CARRIERS EQUAL TO THEIR DARK VALUE. The second-order concentration of positive charge carriers ( p 2 ) is given by the solution of the differential equation, where nl andpl are the first-order concentrations, and 81 is defined by the equations d & / h = 4 d m - nl), (3.3)J . N. MURRELL 45 Likewise the concentration of negative carriers is given by (3.5) and the boundary conditions are taken as in § 2 to bep = 0, x = 0 ; n = 0, x = r. 1 have put A+ = A- in accordance with the steady-state condition. The second-order contribution to the current is then given from (2.12) as The resulting expression for the current, under the condition that both p and aA2/ V are considerably greater than one, is as follows : - %'+ higher powers of In the limit, A2 < Vpla, ka PV "4 [(p+ - p-) - (p+ + p-)] - -- + higher powers of V-1 For small values of p it can be shown that j2 cc p2, which if we compare with j p for the first-order current, explains why the photocurrent in anthracene induced by 4350A light shows no tendency to deviate from a linear dependence on the light intensity.Expressions (3.7) to (3.9) represent the current obtained when the positive electrode is illuminated. To obtain the current when it is the negative electrode that is illuminated, we interchange p+ and p-: this gives the current flowing in the direction of the applied potential, that is, against the light flux. The solution of the equations that we have obtained is evidently not valid in the limit of V tending to zero.Since we have neglected the diffusion term there should be no current when V = 0. In addition, for the current to be continuous through V = 0, the terms of odd power in V should be symmetric in p+ and p-, whereas the terms of even power should be antisymmetric. Looking back at our original equations it can be seen that the source of error lies in our choosing unsymmetric boundary conditions. If we had included the diffusion term in our equations and retained the symmetric boundary conditions n = p = 0 when x = 0 and x = Y, then we should have obtained the correct behaviour for small values of V. It requires further investigation before we can be certain that our equations are valid at high voltages.The rectifying current is given by the term in (p+ - p-) in expressions (3.7) to (3.9). Since p, V/a and X are all positive quantities, the rectifying current has the same sign as (p+ - p-). Experimentally it is found that the current obtained when the positive electrode is illuminated is greater than that obtained when the negative electrode is illuminated. We conclude that p+ > p-, or the positive carriers are the more mobile. This is the conclusion reached by other workers in this field on the basis of direct experimental measurements.46 PHOTOCONDUCTIVITY OF CRYSTALS If the current is to vary sub-linearly with the light intensity, then the negative terms in j 2 must predominate. It follows that the recombination term propor- tional to k must be the most important.Fig. 2 indicates the variation of the photocurrent with the applied voltage obtained by Kommandeur for anthracene illuminated by 3650A light. It is seen that the rectifying current, indicated by +(j(+) - j(-)), follows almost exactly a V2-dependence, whilst even the non-rectifying part deviates considerably from Ohm’s law. Our expressions for the second-order current only show some tendency towards a V2 variation over a small range of voltages such that Vp/a is less than A2 but is still of the same order of magnitude as h2. However, perhaps we should not look too closely at the experimental data which are available. 0 0 0 I /‘ negative /’ e I e ct ro d e il I uminated j(-1 -I 2 - 2 -3 Our solution is after all only valid under conditions in which the current only deviates slightly from the linear dependence on the light intensity.Kommandeur’s experiments shown in fig. 2 were in fact carried out using such high light intensities that a j ot I* relationship was observed. Experimental data are needed under conditions for which p is large, but the light intensity is low enough for only small deviations from the linear law to be observed. 4. DISCUSSION It must be emphasized that it is not possible to obtain an exact algebraic solution of the photoconduction problem since the differential equations involved are non-linear. A power series expansion in the light intensity gives a solution which is valid only under conditions in which the current does not deviate ap- preciably from a linear dependence.There are two main points in which the basic equations presented in this paper differ from those usually adopted. First, I have assumed that the con- centration of charge carriers goes to zero at the boundaries, whereas it is more usual to assume that there is a given rate of destruction at the electrodes. My assumption essentially implies that the rate constant for this destruction is infinite, so that every carrier that reaches the electrodes is immediately swept away or neutralized. There are two main advantages to be gained by this choice of boundary condition: it introduces a few less parameters into the final solution, and it enables one to deduce expression (2.12) for the current.J . N. MURRELL 47 The second point of difference lies in the use of two different rate constants for the trapping process, that is, different lifetimes for the carriers.The more usual approach is to put the net formation of positive and negative carriers equal as follows : (T being the lifetime of the positive carrier), and whilst this has the advantage of insuring that divj = 0, it implies that the rate of trapping of negative carriers depends not on the concentration of negative carriers but on the concentration of positive carriers. As I have shown in the preliminary analysis one cannot in general obtain a steady state unless one takes into account the current of trapped carriers, or allows for the number of lattice sites (probably imperfections) to be depleted by the process of carrier formation. To get over this difficulty I have had to restrict the values of my parameters in such a way that my solutions do represent a steady state (for example, by putting A+ = A- in case B1).This is certainly a limitation of the theory, but it has the advantage over the approach which leads to eqn. (4.1) in that there is some symmetry between the transport equations for the positive and negative carriers and this leads to expressions for the concentrations of p and n which have the same form. I have shown that the experimental features of the anthracene photo-conduction cannot be understood on the basis of a perfect crystal containing no trapping centres. If this were the case then the current should reach a saturation value at not-too-high voltages. From the fact that one observes an ohmic current to field strengths of about 104 V cm-1, one can deduce that the diffusion length for free carriers is less than 70A. I have derived two expressions for the second-order current ; one for no traps. which cannot apply to anthracene; and one by ignoring the diffusion term in the transport equations and assuming that the concentration of trapped carriers is not appreciably affected by the light. It requires further study to show whether this last approach gives a sensible solution to the problem: it is certainly not valid for small voltages. Lastly, I have assumed that there is no injection of carriers from the electrodes -that is, there is no secondary current. The appearance of secondary currents in organic photoconductors is usually suggested by a calculated efficiency of more than one pair of charge carriers produced for each photon absorbed. This is certainly not the case in anthracene. Lyons and Morris 12 from their experi- ments estimate that only one photon in 107 that is absorbed produces carriers. For this reason I think it is a valid assumption to neglect secondary currents, although it must be admitted that the experimental results in which we have been interested may be interpretable by allowing for secondary currents and omitting the traps. dj+/dx = - dj-/dx = I, - P/T (4.1) I wish to thank Prof. H. C. Longuet-Higgins for valuable discussions on this topic. 1 Volmer, Ann. Physik, 1913, 40, 775. 2 Byk and Borck, Ber. Deut. physik. Ges., 1910, 8, 621. 3 Gudden and Pohl, 2. Physik., 1921, 7, 65. 4 Chynoweth and Schneider, J. Chem. Physics, 1954,22, 1021. 5 Goldsmith, Ph.D. Thesis (Purdue University, 1955). 6 Compton, Schneider and Waddington, J. Chem. Physics, 1957,27, 160. 7 Aigrain and Bulliard, Compt. rend., 1953, 236, 595, 672. 8 Moss, Pincherle and Woodward, Proc. Physic. Soc. B, 1953, 66, 743. 9 GrosvaIet, Ann. Radioelect., 1954, 9, 360. 10 Einstein, Ann. Physik, 1905, 17, 549. 11 Kommandeur, Ph.D. Thesis (University of Amsterdam, 1958). 12 Lyons and Morris, J. Chem. Soc., 1957, 3648, 3661.

ISSN:0366-9033    

DOI:10.1039/DF9592800036

出版商:RSC    

年代:1959

数据来源: RSC

摘要:

TRAPPING CENTRES IN ANTHRACENE CRYSTALS BY F. 3. BRYANT,* A. BREE,* P. E. FIELDING* AND W. G. SCHNEIDER Division of Pure Chemistry, National Research Council, Ottawa Received 25th September, 1959 Discrete trapping centres in anthracene single crystals have been established by the conductivity glow-curve method. Evidence is presented for the existence of three separate levels having trap depths of approximately 0 6 , 0 7 and 0.8 eV. The centres at 0.8 eV give rise to the most prominent peak in the glow-curve. Doping with tetracene eliminates this peak leaving a small but broad peak due to trapping centres in the region of 0.7 eV. Irradiation of the crystals with X-rays also causes the main glow peak to disappear. The nature of semiconduction and photoconduction in crystals of organic compounds, such as the aromatic hydrocarbons, as yet has not been satisfactorily interpreted.The basic questions of whether these materials are intrinsic semi- conductors, and what role, if any, is played by impurities or crystal imperfections, have not been settled. The present paper reports an attempt to investigate some of these questions. To date, most of the experimental work on organic crystals has been carried out with anthracene, which has also been used in the present study. While it is clearly an advantage to have a detailed knowledge of one substance, which may be regarded as typical of the whole class of such materials there are also certain practical aspects to consider. Good single crystals of anthracene are readily obtained and anthracene is more easily purified than the more complex organic compounds.In addition, information is available on the crystal structure and on a variety of pertinent molecular properties. Previous work has shown that both the dark conductivity and photocon- ductivity currents are space-charge limited.lS2, 3 When the applied field is re- moved, the back-e.m.f. due to the space charge causes a flow of current in the reverse direction which decays exponentially with a relatively long time constant (about 20 min and frequently much longer). These effects together with the field and light intensity dependence 39 4 and the effects of infra-red illumination 2 can be satisfactorily accounted for in terms of a high density of trapping levels in anthracene crystals. The depth of these levels as well as the question of whether they are to be associated with impurity centres or crystal imperfections, and whether they may also function as recombination centres are clearly of funda- mental importance to an understanding of the conduction process.In the present work the glow-curve method has been used to obtain information about trapping centres. The conductivity glow-curve technique 59 6 has proved to be the most useful although some measurements of thermoluminescent glow- curves were also carried out. Various methods were attempted to introduce imperfections into the crystal but the majority of these proved unsuccessful. One method involved the compression of polycrystalline anthracene to very high pressures with the hope that an essentially single crystal with controllable im- perfections might thereby be produced, If successful, such a method would also provide a simple way of introducing known amounts of impurities into anthracene, which is generally not possible by ordinary crystal growing techniques.However, even at pressures up to 100,OOO atm and elevated temperatures it was * National Research Council of Canada Post-doctorate Fellow. 48F. J. BRYANT, A. BREE, P. E. FIELDING AND W. G. SCHNEIDER 49 not possible to obtain optically clear crystals. An attempt was also made to introduce small amounts of the free radical diphenyl-picryl-hydrazyl by co- crystallization with anthracene. The picryl group may be expected to complex with anthracene as in the anthracene-picric acid complex.This experiment also proved unsuccessful. Of a variety of impurity substances tried to date, tetracene has been the only one which could be incorporated in the crystal. EXPERIMENTAL The glow-curve method consists of cooling the crystal to low temperature and sub- sequently, with or without illumination at the low temperature, heating at a uniform rate in the dark. On cooling the crystal, carriers become localized in trapping centres, from which they are subsequently ejected on heating. The released carriers can be detected optically, if they give rise to luminescence (thermo-luminescent glow-curve), or electrically due to an enhanced conductivity (conductivity glow-curve). In the simplest case of a crystal having a single set of trapping levels at a uniform depth E, the rate of carrier release is given by ns exp (- E/AT), where n is the number of trapped carriers and s is a frequency factor.Thus, on heating at a uniform rate, the glow curve will rise exponentially at first, but because of the rapid depletion of the number n of trapped carriers, the glow intensity, after having passed through a maximum, will again approach zero. Detailed analyses of glow- curves based on several kinetic models have been given in the literature.6-9 It follows that, in general, the glow curve maximum occurs at higher temperatures for deeper traps, and that more than one glow peak may be observed if there are several discrete trapping levels of different depth. The apparatus used to observe con- ductivity glow-curves is shown schematic- ally in fig.1. It consists of a silvered- glass dewar vessel with a quartz window. A copper cylinder containing a heater was joined to the lower end of the inner glass vessel. The crystal was mounted on the flat end of the copper cylinder. Two types of crystal electrodes were employed, viz., evaporated silver or blocking elec- trodes. With the evaporated electrodes, the crystal was mounted directly on the copper support with silver paste. The lower electrode was semitransparent and occupied a small central portion of the crystal surface. A “ guard ” electrode was painted on with silver paste around the outer edge. This electrode was grounded. To measure the crystal tem- perature a thermocouple was soldered to FIG. 1 .-Schematic diagram of glow-curve apparatus. A-glass dewar, B-copper cylinder, C-crystal, D-heater, E-dummy crystal, F-conducting glass plate, G-Teflon ring, H-quartz window, K-electrometer lead, L-battery lead, T.C.-thermocouples.the copper support and a second thermocouple was attached to the guard electrode. Blocking electrodes were obtained by placing a thin (0*003 in.) sheet of Mylar between the crystal and the copper support and using a conducting glass plate on the opposite side of the crystal as shown in fig. 1. The crystal temperature in this arrangement was measured by two thermocouples on either side of a second “dummy” anthracene crystal placed adjacent to the measuring crystal and having the same thickness. Ex- perience showed that with the metallic electrodes and the rigid mounting of the crystal50 TRAPPING CENTRES I N ANTHRACENE to the copper support, repeated heating and cooling eventually caused cracks to develop in the crystal and at the crystal-electrode contact leading to erratic and non-reproducible results.Blocking electrodes largely avoided this difficulty. In later experiments a further arrangement, which proved equally successful consisted of mounting the anthracene crystal directly on the copper support and placing conducting glass above it, the assembly being held together with a brass strip in the form of a spring. This arrangement may be regarded as intermediate to that with ohmic electrodes and to that with blocking elec- trodes. With blocking electrodes the temperature on the two sides of the crystal differed by at most 10°C over the temperature range of interest.In the other arrangements this difference was substantially less, and of course depended somewhat on the heating rate. The crystal temperature was taken as the mean of the two thermocouple readings. The heating rates used were within the range 1 deg./sec to 0.05 deg./sec. The anthracene crystals employed, 0.5 to 1 mm thick and 8 mm in diameter, were grown from the melt in a Bridgeman furnace from commercial " scintillation " grade material (Reilly Tar and Chemical Co.) purified by elution through a chromatographic column charged with aluminium oxide. RESULTS AND DISCUSSION Preliminary measurements of conductivity glow-curves of single anthracene crystals tended to give well-defined glow peaks in some crystals and not in others, and frequently the crystal gave rise to excessive noise.Much of this behaviour was due to the measuring techniques rather than a characteristic of the crystals themselves, and was largely overcome in later measurements by using a faster heating rate and extreme care in mounting the crystal-electrode assembly and the thermocouples. After evacuating the cell an inert gas (argon or helium) was added to a pressure of about 0.1 rnm to reduce sublimation of the crystal and to improve the thermal connection of the sample to the copper block. One other serious difficulty encountered was a tendency of the conduction current to become reversed in the neighbourhood of a glow peak. This was undoubtedly due to space charges which develop in the crystal under the influence of the d.c.measuring field (- 3000 V/cm). It was found that the space charge could be removed by u.-v. illumination at room temperature with an a.c., 110 V field applied. The a.c. field was left on during the subsequent illumination at liquid nitrogen tem- peratures. The crystal was then warmed up in the dark and the d.c. conductivity was recorded in the usual manner. Fig. 2 shows a series of typical conductivity glow-curves for a pure anthracene crystal in the temperature range - 150°C to + 50°C. The upper curve (a) was obtained without illumination of the crystal at low temperature. It shows a small glow peak at about - 40°C together with a noticeable " noise " signal in this region. At higher temperatures there is a slow exponential increase of current corresponding to the normal semiconduction current.Curves (b) and (c) are from successive runs on the same crystal as that of curve (a), but with u.-v. illumin- ation at liquid-nitrogen temperature. There is a large glow-peak at - 1O"C, a smaller and somewhat broader peak at - 70"C, and an additional, but somewhat less reproducible, peak of intermediate intensity around - 40°C. The latter is again " noisy " and is no doubt related to that shown in curve (a), but its intensity is enhanced by illumination. Curve ( d ) was obtained under similar conditions to those for curves (b) an? (c) except that the u.-v. illumination at - 180°C was followed by a 1Zmin irradiation with an infra-red lamp. The resulting glow curve closely resembles (b) and 'c) but the noise on the middle peak has disappeared. Illumination with infra-red might be expected to eject the trapped carriers and yield a glow-curve with reduced intensity.However, the infra-red source also emitted visible light, which is known to produce charge carriers in anthracene.4 In a later experiment, a monochromator was used to select desired wavelengths from the spectrum of a 50 W tungsten lamp. Glow peaks were found following low- temperature irradiation only at wavelengths less than 40oO A, i.e., at wavelengths within the strongly absorbing, low energy singlet-singlet band of the crystal. AnF . J . BRYANT, A. BREE, P . E. FIELDING AND w. G. SCHNEIDER 51 attempt was made to depopulate the trapping levels by following the irradiation at 3850 A by an approximately equal dose (in terms of photons/sec cm2) at 15,000 A.The half-intensity band pass at 15,000 8, was 0.1 eV. No diminution in the height of the glow peak was observed. A search was made for an optical absorption corresponding to a discrete level at 0.8 eV after an anthracene crystal had been cooled to low temperature and illuminated with u.-v. light. Although a rather strong vibrational band appeared at 0.73 eV (optical density D = 1.0 at the crystal thickness of about 2 mm) there was no evidence for the presence of any new ab- sorption with D > 0 -01 at 0.8 eV. These experiments demonstrate that the process of optical de-trapping is very inefficient. FIG. 2.--Typical conductivity glow- curves of pure anthracene crystal. Heating rate, 0.7 deg./sec, applied field, 3000 V/cm.(a) No illumina- tion, (b) and (c) u.-v. illurnintion at - 180°C, ( d ) u.-v. illumination at - 180°C, followed by infra-red illumination. temp., "C Fig. 3 shows the behaviour of the main glow peak at - 10 to - 20°C at three different heating rates. This peak was quite reproducible and appeared only when the crystal was illuminated at low temperatures. The behaviour shownin fig. 3 is typical of that for a discrete trap level. The current increase on the low- temperature side of the peak is very nearly exponential and the peak becomes higher and shifts to higher temperature as the heating rate is increased. The trap depth was evaluated from the temperature of the maximurn and the tem- perature of half-height according to the method of Grossweiner.7 The results are summarized in table 1.The mean trap depth, close to 0.8 eV, was confirmed heating rate deg.C/sec 0.083 0.168 0.370 Ttnax. ("K) 249-5 253-3 262.5 TABLE 1 (A x 1013) (ev) (OK) 240.2 1-30 0.71 243.4 4-95 0.8 1 253-8 6.40 0.77 peak conductivity trap depth T+52 TRAPPING CENTRES IN ANTHRACENE from an analysis of the exponential rise of the glow peaks 6 and from the variation of the peak temperature and peak height with heating rate.8 The additional glow peaks near - 40" and - 70"C, correspond to trap depths in the region of 0.7 and 0.6 eV. The glow-curve response of a crystal strongly doped with tetracene (- 10-3 mole/mole) was investigated. One rather broad and unresolved glow peak centred around - 40°C was observed together with a weak, very broad peak near - 140°C.The glow peak structure observed in pure anthracene was no longer discernible in this crystal and the large peak in the region - 10 to - 20°C I I I I I I I 220 230 240 250 260 270 280 temp., "K FIG. 3.-Glow-curve peak of anthracene at three different heating rates. was absent. This behaviour can be understood if the optical excitation energy is transferred with high efficiency to the tetracene impurity, where it is trapped and subsequently emitted as fluorescence. Under these conditions it would be difficult to populate the anthracene metastable levels or to form charge carriers which could be trapped. The glow-curve response characteristic of pure anthracene crystals was also destroyed by irradiation with X-rays. Several crystals with a radiation dose of 1.3 x 1 0 5 roentgen from a 1oOkV source, and after standing for 6 days, gave but a single small glow peak in the region of - 30" to - 40°C.There was a close resemblance in the crystals doped with tetracene and those irradiated with X-rays in that one relatively broad glow peak appeared in the region of - 40°C, and the large glow peak at - 10" to - 20°, characteristic of pure anthracene crystals, was absent. To confirm the above results, a further crystal of pure anthracene, free of cracks and visible surface imperfections, was measured for glow-peak response in the usual manner. The normal, well-defined glow peaks appeared near - 10°C and - 70°C. This crystal was then given the same X-ray radiation dose as above and remeasured about an hour later. Again the characteristic large peaks at - 10" and - 70" were completely absent and only a very smallF .J . BRYANT, A . BREE, P . E . FIELDING A N D W . G . SCHNEIDER 53 peak near - 40°C was observed. Visually the irradiated crystals were not dis- coloured and the fluorescence emission appeared unaltered. The effect of smaller X-ray dosages has not been studied. The question of whether electrons or holes are being trapped in these experi- ments cannot as yet be decided. It is known that in the conduction process in anthracene crystals positive holes are the majority carriers. It appears reasonable to assume that this is a result of electron trapping, although hole trapping cannot be excluded. Further experimental studies are needed to establish the nature of the trapping levels, and meanwhile one can only offer some speculative suggestions.Because of the marked alteration (or quenching) of the trapping levels of anthracene on the addition of tetracene, it is unlikely that small amounts of tetracene in the " purified " anthracene crystals * could be responsible for the trapping centres observed in the latter. On this basis, crystal imperfections, either in the bulk or on the surface of the crystal, appear as a more likely possibility. It may be noted here that while there may be differences in the intensities of the glow-curve peaks, the general pattern for the pure anthracene crystals appears to be similar from crystal to crystal and largely independent of surface roughness or internal cracks in the crystal. This would seem to indicate the trapping sites are bulk imper- fections.The discrete nature of the trapping centre may be taken to indicate some kind of bound state of the electron at the trapping centre. One possibility is that of an anthracene molecule capturing an electron to form the negative ion, A+e-+A-. The electron affinity of an isolated molecule of anthracene has been quoted 10 as 1.19 eV, and the polarographic value for anthracene in solution as 1.38 eV.11 Assuming the trapping molecule to be located at a crystal imperfection, the ob- served trap depth near 0.8 eV may be regarded as being consistent with the above values. However, the only conclusion that can be drawn with certainty from the experiments is that illumination of the crystal at low temperatures causes discrete metastable states in the crystal to become populated and that these states are subsequently depopulated on heating the crystal. The possibility that the meta- stable states may be ionized exciton states cannot be overlooked. Dissociation of the exciton to form free charge carriers when the crystal is heated could con- ceivably give rise to the observed glow peaks. Preliminary experiments t designed to observe thermoluminescence in anthra- cene crystals were unsuccessful. *Because of the difficulty of removing small traces of tetracene, this is usually re- These experiments were conducted in collaboration with Dr. F. Lipsett to whom we garded as the most likely impurity in anthracene. are also indebted for providing the anthracene crystals. 1 Chynoweth and Schneider, J. Chem. Physics, 1954, 22, 1021. 2 Goldsmith, Ph.D. Thesis (Purdue Univ., 1955). 3 Kommandeur and Schneider, J. Chem. Physics, 1958,28, 590. 4 Compton, Schneider and Waddington, J. Chem. Physics, 1957, 27, 160. 5 Herman and Hofstadter, Physic. Rev., 1940, 57, 936. Randall and Wilkins, Proc. Roy, SOC. A, 1945, 184, 366. Grossweiner, J. Appl. Physics, 1953, 24, 1306. 8 Boer, Oberlander and Voigt, Ann. Physik, 1958, 2, 130. 9 Hoogenstraaten, Thesis (Univ. of Amsterdam, 1958). 10 Hush and Pople, Trans. Faraday Soc., 1955, 51, 600. 11 Lyons, Nature, 1950, 166, 193.

ISSN:0366-9033    

DOI:10.1039/DF9592800048

出版商:RSC    

年代:1959

数据来源: RSC

摘要:

THE SEMI-CONDUCTIVITY OF ORGANIC SUBSTANCES PART 4.-*SEMI-QUINONE TYPE MOLECULAR COMPLEXES BY D. D. ELEY, H. INOKUCHI~ AND M. R. WILLIS University of Nottingham, Nottingham, England Received 14th May, 1959 The electrical conductivities of some molecular complexes of the donor-acceptor type between aromatic amines and halogenated p-benzo-quinones have been examined by both a.c. and d.c. methods. The complexes were found to behave as semiconductors with an energy gap of approximately 0 5 eV. Complexes with a stronger electron donor show a much enhanced conductance and marked deviation from Ohm’s law. These results are discussed in relation to the optical and magnetic properties of these compounds. The semiconducting properties of organic molecular crystals have been ex- tensively studied in the last decade.In resonating aromatic systems the conduction has been attributed to activated rr electrons.1 The electrons and/or positive holes have been considered as moving in energy bands common to the whole crystal, on tunnelling through the potential barriers between molecules.2s The inter- molecular forces in this type of crystal are of the van der Waals type and result in intermolecular distances of about 3.5 A. Molecular complexes, on the other hand, are substances in which the bonding is frequently stronger than pure van der Waals forces. Such interaction has been treated quantum mechanically by Mulliken.4 Complexes between halogen molecules and polycyclic hydrocarbons show a very high electronic conductivity and semi-conduct with very low 59 6 activation energies (A€ = 0.1-0.2 eV).The formation of these complexes is accompanied by changes in magnetic properties.7~ 8 Analogous results for complexes between anthracene and alkali metals and for sodium and bromine with nitrogen heterocyclic compounds have been obtained by Ubbelohde.9~ 10 Weiss 11 has considered the possibility of ionization in complexes between quinones or nitro compounds and aromatic hydrocarbons. The magnetic im- plications of such bonding have been investigated by paramagnetic resonance methods 12 and by the magnetic balance.13 These findings are in accordance with a low energy ionic state in favourable cases. This paper describes an investigation into the energetics and mobility of elec- trons in charge transfer complexes between halogenated quinones (acceptors) and aromatic amines (donors), by electrical methods. The effect of the strong inter- molecular (or ionic) forces and the crystal structure 14 are discussed in relation to the electron mobility.It is hoped that investigations of this kind will lead to a better understanding of the mobility and spin-resonance of electrons in organic crystals and their bearing on catalytic activity.15 In addition, the mobility of electrons resulting from the charge transfer process has been suggested as one of the processes of energy transfer in living organisms.16 A preliminary publication of some of the work reported in this paper has been made elsewhere.17 * part 1 : ref. (1) ; part 2 : ref. (2) ; part 3 in Faraday SOC. Discussions on “ Energy transfer with special reference to Biological Systems ”, Nottingham, April, 1959.-f present address : Department of Chemistry, University of Tokyo, Japan. 54D . D . ELEY, H. INOKUCHI AND M. R. WILLIS EXPERIMENTAL RESISTANCE/TEMPERATURE MEASUREMENTS BY THE D.C. METHOD 55 Preliminary experiments showed that the solid complexes decomposed rapidly under vacuum due to the evaporation of the more volatile component (the base). The effect was also very marked in air, as shown by a rapid increase in resistance, and a change of colour to that of the quinone. To obviate this effect, the freshly prepared crystals A (fig. 1) were compressed in a tube of insulating material B between two tightly fitting electrodes C. The sample was then effectively in a closed system in which it can reach equilibrium with its vapour.The sample attained a constant resistance in 4-2 h. Measurements on the NN-dimethyl aniline complexes were made in the cell described by Inokuchi.5 Measurements on the NNN’N’-tetramethyl p-phenylene diamine complexes were made in a slightly modified cell, as shown in fig. 1. A pressure of 80 kg cm-2 was appiied by means of a nickel Monk spring D to minimize intercrystalline resistances. The cell, together with a thermometer, was placed in a screened glass tube and surrounded by a Dewar vessel. Owing to the low melt- ing points and instability of the complexes, resistance measurements were made as the samples were cooled below room temperature with solid C02. The resist- ance was measured using a valve voltmeter whilst the specimen was cooled at the rate of approximately 1 deg./min.The specimen was recovered in the form of a tablet and its dimensions determined with a micrometer. RESISTIVITY BY THE A.C. METHOD The method used was that described by Eley and Parfitt 2 using a Marconi Q-meter. This depends on the fact that the equivalent circuit of a powder may be regarded as a resistance p3 (of the crystals themselves) in series with a parallel arrangement of a condenser C2 and a resistance p2 (typical of the intercrystalline gaps). A measurement of the full and empty cells was taken at a range of frequencies between 50 kc/sec and 20 Mc/sec. The calculated resistance of the powder itself was then found to fall to a constant value p3, at high frequencies, characteristic of the crystal.A typical result is shown in fig. 2 Owing to the gradual decomposition of the samples and to the difficulty of maintaining specimens at constant temperatures below room temperature, it was not found possible to do temperature/resistance measurements. However, as a comparison with the d.c. results, resistivities at room temperature were measured. The complex between iodanil and NNN’N’-tetramethyl p-phenylene diamine was unstable at room temperature and so the measurement was made at a lower temperature (7°C) and the value corrected to room temperature. The cell shown in fig. 1 was again used. For the run on the empty cell, the electrodes were separated by a tablet of Perspex of the same dimensions as the sample. This Perspex disc had a resistance some 106 times that of the specimen.l--The conductivity Cell for a.c- and d-c. measurements on molecular complexes. PREPARATION OF MATERIALS CHLoRANIL.-The commercial product was recrystallized twice from benzene. BROMAN1L.-The commercial product was recrystallized twice from benzene. IoDANrL.-Prepared by the method of Jackson and Bolton 18 and recrystallized twice NN-DIMETHYL ANILINE (DMA).-The commercial product was distilled twice under NNN’N’-TETRAMETHYL p-PHENYLENE DIAMINE (TMPD).-The dihydrochloride was The free base was obtained by treating an aqueous solution of from benzene and once from acetone. reduced pressure to give a colourless liquid. obtained from B.D.H.56 SEMICONDUCTIVITY OF ORGANIC SUBSTANCES dihydrochloride with dilute NH40H. The white precipitate was filtered, washed with distilled water and dried overnight in a vacuum desiccator.The white powder was then dissolved in ether, filtered and distilled in ‘uacuo. COMPLEXES OF “-DIMETHYL ANILINE.-The quinone was dissolved in dimethyl aniline and one-fifth of its volume of alcohol added to precipitate the crystals. The product was dried at room temperature. loglo frequency FIG. 2.-A.c. measurements on the TMPD-bromanil complex. (a) corresponds to measurements on the empty cell, (6) to the cell plus sample, and (c) to the sample alone. COMPLEXES OF NNN”’-TETRMTHYL p-PHENYLENE DImIm.-The base was dis- solved in benzene and a solution of the quinone in benzene added.27 The crystals were filtered and washed with benzene and ether. With the iodailil complex, the low solubility of it in benzene made this method unsuitable and acetone was used.All the complexes were shown by analysis to contain a 1 : 1 ratio of components. RESULTS RESISTIVITES AT ROOM TEMPERATURE BY THE A.C. METHOD COMPARED WITH THOSE BY D.C. Both measurements were made on the same specimen in order to provide the most direct comparison. The resistivities include a packing factor of 0.5 to correct approx- imately for the volume fraction of voids in the packed polycrystalline samples.15 RESISTANCE/TEMPERATTJRE MEASUREMENTS for intrinsic semiconductors, The variation of resistance with temperature was found to obey the usual equation p = po exp (Ac/2kT). Typical runs are shown in fig. 3 and 4. DEVIATIONS FROM OHM’S LAW Fig. 5 and 6 show the variation of current with potential gradient for one complex from each series, namely, bromanil-NN-dimethyl aniline and bromanil-NN”N-tetra- methyl p-phenylene diamine.Owing to the low resistances of the samples, high potential- gradients were not employed as they would lead to heating effects. To minimize thermalD. D. ELEY, H . INOKUCHI AND M. R . WILLIS 57 1/T ( x lO4), Tin O K dimethyl aniline, (c) iodanil-dimethyl aniline. FIG. 3.-The d.c. conductivity of complexes. (a) chloranil-dimethyl aniline, (b) bromanil- 8 p! Y 9 6 .- rn 4 FIG. 4.-The d.c. 38 39 4 0 41 33 34 35 36 104/T, Tin O K TMPD, (c) iodanil-TMPD. conductivity of [complexes. (a) chloranil-TMPD, (b) bromanil-9 8 7 6 5 4 3 2 I 0 I f 1'1 10 I 1 L I ~ 100 200 300 400 500 600 700 000 - - potential gradient, V/cm FIG.5.-Variation of current with potential gradient for bromanil-DMA. Curve (b) shows the effect of reaching electrical and thermal equilibrium at each point. W 2 s X n U / / V I I I I 0 100 200 300 400 500 600 potential gradient, V/cm bromanil-TMPD. FIG. 6.-Variation of current with potential gradient forD . D . ELEY, H. INOKUCHI AND M. R. WILLIS 59 effects, the sample was allowed to reach equilibrium at the highest voltage used. The complete run was then rapidly performed. Polarization was quite marked, and the effect of allowing the resistance to reach equilibrium at each potential is shown in fig. 5. Me-N-Me A II I \/ Me-N-Me I I Me-N-Me TABLE SP SPECIFIC RESISTANCE OF THE COMPLEXES c1- Cl Br -FBr 5 x 107 9 x 107 3 x 107 8.1 x 108 1.5 x 109 1.7 x 108 1.3 x 104 4 2 x 104 1.1 x 105 2.0 x 104 1.3 x 105 1.5 x 106 parameter resistivity p a.c., l2 cm at 22°C resistivity p d.c., Q cm at 22°C resistivity p ax., f2 cm at 22°C resistivity p d.c., L2 cm at 22°C TABLE 2.-ENERGY GAP, AND PRE-EXPONENTIAL FACTOR Me-N-Me 1 0.47 0-45 0.43 AE, eV (1 0-93 X 104 2.1 x 105 2-9 x 104 PO, Q Cm \ Me-N-Me 0-5 3 0.59 0.56 2-21 0.59 14.15 DISCUSSION The complexes have been shown to be relatively good organic semiconductors. Complexes of this type have been investigated by X-ray diffraction and shown to have crystal lattices built up of stacks of alternate D and A molecules.~4~ 19 Here the electron donor D is the amine, the acceptor A the quinone.A rough relation- ship between energy gap and number of 7~ electrons allows us to predict a A€ of about 5 eV for crystalline benzene, the resistivity being immeasurably large.;! By contrast, the alternate arrangement of aromatic quinone and halogenated quinone molecules have energy gaps of about 0.5 eV and resistivities at 22°C (measured by ax.) of 104 to 107 i2 cm.The complexes must therefore fall into a different class of semiconductors from the aromatic molecules. In fact, their energy gap and resistivity approach that of the solid monoradical, diphenyl picryl hydrazy1,Z. 15 which has h e = 0.16-0-26 eV and p 15°C = 1.7 x 108 L? cm and it seems probable60 SEMICONDUCTIVITY OF ORGANIC SUBSTANCES that the conduction mechanisms are similar. The hydrocarbon + halogen com- plexes are even better conductors, e.g. violanthrene-iodine 5.6 has A6 = 0.14 eV and resistivity at room temperature 45 i2 cm.Both the amine-quinone and the hydrocarbon-halogen complexes fall into the class of charge transfer complexes recently investigated in detail by Mulliken.20~ 21 This author describes these complexes (in solution) in term of a ground state, wave function $p~, largely made up of the van der Waals complex # (A,D) but with a small amount of ionic resonance hybrid # (A-D+), i.e., $N = a#(A,D) + b$(A-D+), a > b. The characteristic colour is attributed to excitation to the first excited state of the complex, $E, mainly the ionic state, plus a small amount of van der Waals resonance hybrid. $IZ = a*$(A-D+) - b*#(A,B), a* > b*. This description may apply to the three dimethylaniline complexes in solution, and possibly in the solid state, since the crystals have been shown to be non- paramagnetic in a sensitive electron-resonance spectrometer.22 On the other hand, the three tetramethyl p-phenylene diamine solid complexes show a strong electron resonance, the percentage free radical content being 0.2 % for the chlor- anil, 2.0 % for the bromanil and 20 % for the iodanil complex.12922 This corresponds to a high degree of stability of the ionic state, which has been stated to predominate in certain complexes.13'23 These results may be explained in terms of two completely independent ions, behaving as a diradical (A-224, D+ 2,&), or in terms of a certain overlap of electronic wave functions giving rise to a triplet state (A-D+3&).However, the population of the triplet state should depend upon temperature, while the percentage of diradicals has been found independent of temperature 22 (by comparison of the electron-resonance signal with that from a stable solid monoradical).The Mulliken theory has been developed for DA pairs in solution, and the extension to the crystalline state is not obvious. It is possible that increased neighbour contacts will favour Coulombic interactions and tend to stabilize the ionic diradical state. We note that in going from the van der Waals type dimethyl- aniline complexes to the ionic diradical type tetramethyl-p-phenylene diamine type there is a 102-104 times decrease in resistivity, in spite of a small increase in A€, That is to say, changing to the stronger donor molecule increases the conductance at the same time as the fraction of diradicals present.It is interesting that Matsunaga 8 has recently reported 14 % of free radical character for the violanthrene-iodine complex, with similar results for related systems. This supports our suggestion to associate free radical character of the crystal with the observed high conductivity. However, this model alone cannot account for differences between the specific complexes; thus the order of in- creasing conductivity, namely, TMPD-iodanil (20), < TMPD-bromanil (2), < TMPD-chloranil (0.2), < violanthrene-iodine (1 4) clearly does not correspond to the percentage free-radical character, given in the brackets. THE FREE ELECTRON MODEL We shall now adapt the model already used to explain conductivity in aromatic molecules and D.P.P.H.2 to charge transfer complexes.In this model the con- ductance process is separated into 2 stages. (a) A molecule containing n r electrons possesses on molecular orbital theory n energy levels, the lower n/2 levels being filled each with 2 electrons with paired spins. An electron is first excited from the highest filled ( 4 2 ) level to the lowest unfilled ( 4 2 + 1) level, and the excitation energy AE is equated to the observed energy gap. Considering 4 adjacent molecules, only, for simplicity, AAAA -+ AA*AA.D . D. ELEY, H. INOKUCHI AND M. R. WILLIS 61 (b) From this level, the electron may tunnel through the intermolecular potential barrier to the corresponding level in the crystal. The tunnelling process determines the electron mobility, and hence the pre-exponential resistivity factor PO.AA*AA -+ AA+A-A -+ AA+AA-. Charge separation may occur against the Coulomb attractive energy, since the charges will be stabilized by polarization of the surrounding T electrons, the 7-r electrons effectively screening the positive and negative changes from each other. Where there is a single unpaired electron in the uppermost filled level, as in the solid monoradical DPPH, tunnelling occurs without the need for excitation energy At-, which in fact is very small. D+ A- (4 FIG. 7.-The free electron model for molecular complexes. This model is adapted to crystalline donor-acceptor complexes in fig. 7. This gives a diagrammatic representation of adjacent donor and acceptor molecules, treated as one-dimensional potential energy boxes, the T electron energy levels for simplicity being drawn as equally spaced although this is never actually the case (cf.a treatment of complex formation by Shuler25). In (a) we show the van der Waals D,A molecule pair. The zero of energy is taken as the electron at infinity and the two boxes are placed side by side in accordance with this convention. Let us now imagine an electron transferred from D to A, to give a D+A- pair (b). The lowering of energy due to Coulombic interaction e2/r is expressed by lowering the energy box corresponding to A. Taking I D for the ionization potential of the donor, and EA for the electron affinity of the acceptor, and r as the separation of the molecules, we have : DMA acceptor, I,, - EA - e2/r = 7.2 - 1.0 - 4.1 = 2.1 eV, (r = 3-40A); TMPD acceptor, ID - EA - e2/r = 6.7 - 1-0 - 4.5 = 1.2 eV, (r = 3*26&.The ID values are from Foster 26 and the Y values from Wallwork.14 On this62 SEMICONDUCTIVITY OF ORGANIC SUBSTANCES view there will be a greater tendency for the TMPD-complexes to be ionic. We have assumed an electron affinity of 1.0 eV for the halogenated quinones, but this will of course vary over the series. If we knew the Madelung constant 2, we could estimate the Coulombic energies in the lattice. A value of 1.75 as for the ordinary rock salt lattice would give Coulombic energies of 7.2 eV for the DMA complex and 7.9 eV for the TMPD complex, giving overall energies of formation of - 1.0 eV and - 2.2 eV respec- tively, and making the acceptor level lower than the donor level in both cases.In fact, it must remain higher than the donor level to explain the diamagnetism of the DMA complexes. The situation for the two types of complex is shown in (c) and (d). For the DMA complexes (c), the electrons remain paired in the highest level of the donor and the energy gap A€ for semiconductivity is the energy to raise the electron to the lowest unfilled acceptor level. In the TMPD complexes (d), one electron may pass over the higher D level to the lower A level and in fact one has stacks of ion radicals, all in 2 2 states. Departures from 100 % radical character may be associated with a small degree of overlap of wave functions, and a certain degree of electron pairing as a result. rhe electronic conduction in this system should be analogous to that in the solid monoradical DPPH.One may visualize electron transfer at the highest filled levels, for example, The energy gap should be related to AE'. On this picture, the energy gaps A€ and A& are really determined by the degree of matching of the levels in donor and acceptor which result from Coulombic interaction. A more significant factor for the conductance increase on passing from DMA to TMPD complexes may be the decrease in intermolecular spacing, estimated as from 3.40A to 3.26A. This should result in a more transparent barrier to electron tunnelling, and the marked decrease in po observed should result from this. It is possible also that the more marked non-ohmic behaviour of the TMPD complexes is to be associated with differences in barrier dimension, from-the DMA complexes. D+A-D+A- --f D+ADA- -+ D+AD+A".SURPACB PARAMAGNETISM In our preliminary publication 17 we gave rate constants for the ortho-para H2 conversion on the dimethylaniline complexes at - 183°C which were definitely indicative of surface paramagnetism. Thus, translating these figures into absolute rates, of molecules cm-2 catalyst sec-1, we have the figures DMA-chloranil 0.64 x 1010, DMA-bromanil 1.29 x 1010 and DMA-iodanil 1-61 x 1011. The corresponding figure 15 for DPPH is 6-47 x 1010 at - 183°C. (An error in the ref. (15) quoted is noted : the first-order constant for the conversion on DPPH at 17°C of 2.58 x 10-3 min-1 in fact should correspond to an absolute rate of 8.2 x 109 molecules cm-2 catalyst sec-1 and a collision efficiency of 1.14 x 10-12, not 3.3 x 1012 and 4-6 x 10-10,) Thus within the experimental error associated with estimation of surface areas, the DMA-iodanil surface is a 100 % free radical surface, although no bulk paramagnetism was detectable in electron resonance.In further work we have found these complexes and also the TMPD complexes (which latter do show bulk paramagnetism) ineffective in converting ortho to para hydrogen. We have concluded that the surface paramagnetism must be deter- mined by the conditions of preparation, and the matter is still under investigation. There is published evidence 3 for a variable degree of bulk paramagnetism depending on preparative conditions, so this suggestion is not unreasonable.The authors' best thanks are due to the Ramsay Memorial Fellowships Trust for the award of a Japanese Fellowship to H. Inokuchi, and to the British Petroleum Ltd., for a studentship awarded to M. R. Willis and for a grant for purchase of apparatus.D. D. ELEY, H. INOKUCHI AND M. R. WILLIS 1 Eley, Parfitt, Perry and Taysum, Trans. Faraday SOC., 1953, 49, 79. 2 Eley and Parfitt, Trans. Furuduy SOC., 1955,51, 152. 3 Mette and Pick, 2. Physik, 1953, 134, 566. 4 Mulliken, Rec. truv. chim., 1956, 75, 845. 5 Akamatu, Inokuchi and Matsunaga, Nature, 1954, 173, 168. 6 Akamatu, Inokuchi and Matsunaga, Bull. Chem. SOC. Jupan, 1956,29,213. 7 Matsunaga, Bull. Chem. SOC. Jupan, 1955, 28,473. 8 Matsunaga, J. Chem. Physics, 1959, 30, 856. 9 Holmes-Walker and Ubbelohde, J . Chem. Soc., 1954, 720. 10 Slough and Ubbelohde, J. Chem. SOC., 1957, 982. 11 Weiss, J. Chem. SOC., 1942, 245. 12 Kainer, Bijl and Rose-Innes, Naturwiss., 1954, 41, 303. 13 Kainer and Uberle, Ber., 1955, 8, 1147. 14 Wallwork, lecture to X-ray Analysis group (Inst. of Physics, Spring, 1958). 15 Eley and Inokuchi, 2. Electrochem., 1959, 63, 29. 16 Szent-Gyorgyi, Introductory lecture : Faraday SOC. Discussion on " Energy Transfer 17Eley and Inokuchi, 3rd Biennial Carbon Conference Bufalo (N.Y., 1957), to be 18 Jackson and Bolton, J. Amer. Chem. Soc., 1914, 36, 301. 19 Harding and Wallwork, Acta Cryst., 1955, 8, 787. 20 Mulliken, J. Amer. Chem. SOC., 1952, 64, 811. 21 Mulliken, J. Physic. Chem., 1952, 56, 801. 22 BijI, Kainer and Rose-Inns, J. Chem. Physics, 1959, 30, 765. 23 Kainer and Otting, Ber., 1955, 12, 1921. 24 Schneider, Radiospectroscopy Group Meeting (Southampton Univ., 1957). 25 Shuler, J. Chem. Physics, 1952, 20, 1865. 26 Foster, Nature, 1959, 183, 1253. 27 Schlenk and Knorr, Annalen, 1909, 368,277 63 with Special Reference to Biological Systems " (Nottingham, 1959). published by the Pergamon Press.

ISSN:0366-9033    

DOI:10.1039/DF9592800054

出版商:RSC    

年代:1959

数据来源: RSC

摘要:

DIFFUSION PROCESSES AT LOW TEMPERATURES BY A. B. LIDIARD AND K. THARMALINGAM Dept. of Physics, University of Reading, Berkshire Received 13th May, 1959 Existing knowledge of defects in alkali and silver halide crystals is used to predict the influence of impurity concentration and temperature upon their anion diffusion properties. The free anion-vacancy concentration is depressed by the presence of multivalent cations in substitutional solution, especially at low temperatures. Dislocations and vacancy pairs are therefore likely to be important in anion diffusion. The principles of the determination of anion diffusion coefficients by exchange experiments are discussed. General features of our discussion apply to other ionic systems. Existing experimental data on alkali and silver halides are discussed.1. INTRODUCTION Our basic understanding of mobile lattice defects in crystals is now at a very interesting stage. Soundly based information about types of lattice disorder, heats of formation and movement of defects, and interactions between defects is now available in a number of systems, and on this basis we can make theoretical predictions which can be tested experimentally. In this paper we shall be largely concerned with the study of lattice imperfections as related to the study of diffusion in ionic crystals. Much of what we have to say is stated in terms of the alkali halides but applies with only trivial changes to other ionic systems (e.g. oxides, doped and non-stoichiometric) and to AgBr and AgCl. We shall be particularly concerned with anion diffusion in alkali halides (and AgBr and AgCl).In the next section we shall discuss some implications of our present understanding of imperfections in these crystals for their anion diffusion properties at " low " tem- peratures, i.e. at temperatures below the intrinsic range. Existing experimental results are briefly reviewed, but it is shown that further experimental work would be very illuminating. In 5 3 we give a brief survey of the principles involved in the, very convenient, exchange technique for measuring anion diffusion coefficients. Apart from its intrinsic interest, a better knowledge of anion defects is relevant to our understanding of irradiation effects and colour-centre reactions.1 2. ANION DIFFUSION (SINGLE CRYSTALS) Let us summarize the picture as follows.The intrinsic defects, dominant at high temperatures, are Schottky defects in the alkali halides and principally cationic Frenkel defects in AgBr and AgCl; at lower temperatures the presence of unavoidable cation impurities of higher valency leads to approximately con- stant concentrations of cation vacancies in all cases. Multivalent cations can also be introduced deliberately (doping) to extend and control the impurity-domin- ated range. Multivalent anion impurities seem always to be present in much smaller concentrations, and their deliberate addition is difficult. This picture provides a quantitative account of ionic conductivity and diffusion properties 2 and ties in closely with other properties determined by lattice im- perfections, e.g.thermoelectric power,3 dielectric loss and paramagnetic resonance.4 A little reflection shows that it has been largely built up on the basis of cation studies, e.g. cation diffusion or properties of cation-doped crystals. It does nevertheless carry quite definite implications for anion properties. These we shall now consider. 64A . B . LIDIARD AND K . THARMALINGAM 65 (i) FREE ANION VACANCIES Our discussion embodies two assumptions, (1) thermodynamic equilibrium and (2) the usual electrical neutrality condition. Clearly at sufficiently low tem- peratures assumption (1) will become inapplicable, but there seems no reason to reject it at the temperatures of interest here. Dislocations act as sources and sinks of vacancies 5 and thus preserve thermal equilibrium concentrations, so that assumption (1) is always applicable when the diffusion times are greater than the average time for a vacancy to migrate across unit distance of the dislocation network.If x+ and x- are the molar fractions of cation and anion vacancies, then application of the condition of thermodynamic equilibrium leads to in which gs is the free energy of formation of a Schottky pair. This " solubility- product " relation is always true provided interactions among the vacancies can be neglected.6 The second assumption says the crystal must be electrically neutral in the bulk. Hence -e(x+ - x-) should equal the sum of the molar effective charges on the other imperfections present. This provides a second equation in x+ and x- which may therefore be calculated as functions of temperature, impurity concentration, etc.We have performed this simple computation for NaCl. Etzel and Maurer7 determined exp (- gs/kT) by studying the conductivity of NaCl doped with CdC12. Their results give exp (- gs/kT) = 28 exp (- 23,40O/T). (2.2) FIG. 1 is obtained from (2.1) and (2.2). Below a temperature Tk - gs/2 k In c, x+ is practically constant and equal to the cation-impurity concentration, c. But if x+ = c, then (2.1) shows that x- must decrease rapidly as T decreases ; this is shown by fig. 1. In specimens of high purity, x- becomes depressed below Tk. At high impurity concentrations, for which no real intrinsic range appears below the melting point, x- is substantially depressed at all temperatures. Similar conclusions apply to AgC1; and to ionic semiconductors when the electrons (or holes) accompanying departure from perfect stoichiometric composition remain free and do not become localized on the vacancies introduced.Vacancies which have trapped electrons are not to be included in (2.1) ; they are a different species not represented in the quasi-chemical reaction leading to (2.1). It is clearly of interest to have quantitative tests of these simple conclusions at temperatures where well-tried techniques are applicable. Laurent and BCnard 9 have recently made a number of studies of anion diffusion in pure alkali halides, but the only experiments in which conventional techniques have been applied to doped crystals are those of Tannhauserlo who studied Br self-diffusion in AgBr and AgBr containing 1-27 mole % CdBr2 (see below), Considerable interest must also be attached to measurements at " low " temperatures where foreign cations depress the free anion vacancy concentration very much below the intrinsic value.(Exchange experiments by Morrison et al.11 in this range are discussed in $ 3 . ) The consequent rapid drop in diffusion coefficient suggests that we may expect other diffusion mechanisms to become evident. General knowledge of imperfections in crystals suggests vacancy pairs and/or dislocation paths. (ii) VACANCY PAIRS Vacancy pairs are electrically neutral and are unaffected by the presence of impurity ions. (There is no mass-conservation requirement, as in real chemical reactions, and the concentration of vacancy pairs is not affected by the decrease in free anion-vacancies.) In fig.1 we have plotted two different estimates of the concentration of vacancy pairs in NaCl. It is seen that at low enough tem- peratures the concentration of vacancy pairs exceeds that of free anion vacancies, E66 DIFFUSION PROCESSES AT LOW TEMPERATURES and in this region we must expect them to make a large contribution to the diffusion coefficient. If the vacancy pair mobility is appreciably greater than that of free anion vacancies they will make a significant contribution at high temperatures also. In his study of AgBr, Tannhauserlo did, in fact, find that the influence of CdBr2 on anion diffusion coefficient was much less than was compatible with any reasonable degree of Schottky disorder.In addition, the slope of the In D ld4 4 ' .........._.._........,....._........,.................,..,..........................,...,.................._......................... - c NaC L 1.0 1.5 103/~ 20 FIG. 1.-The concentrations of cation and anion vacancies (x+ . . . and x- ) as a function of temperature for NaCl containing various concentrations c of divalent cations as indicated. The lines I and I1 represent two different estimates of the concentration of vacancy pairs, both based on a theoretical calculation of the heat of association 8 (0.6eV). Curve I also uses a theoretical calculation for the heat of formation of the separated Schottky pair and neglects any entropy terms; it should represent a lower limit. Curve I1 uses eqn. (2.2) and neglects the entropy of association; by the same standard it should be an upper limit.against T-1 plots decreased with decreasing temperature in such a way that they could be represented as the sum of two separate exponential contributions. It is reasonable to assign these effects to the presence of vacancy pairs. It will be interesting to have such measurements over a range of impurity concentrations and on other systems. (iii) DISLOCATIONS Despite the interest of vacancy-pair diffusion we should also consider the possibility of accelerated diffusion via dislocations. If the scale of the dislocation distribution, or network, is small compared with the diffusion length (-Z/E)A . B . LIDIARD AND K . THARMALINGAM 67 the system will be effectively homogeneous and will obey the appropriate macro- scopic bulk diffusion laws.For part of their time, however, the diffusing atoms will be in the immediate neighbourhood of dislocations where they will move more quickly; this leads to an enhanced diffusion coefficient of lower apparent activation energy. This possibility, which is quite distinct from the grain-boundary diffusion problem analyzed by Fisher and Whipple 12 and studied experimentally by several workers,l3 was pointed out by Hart.14 If this effect occurs in connection with anion diffusion at low temperatures it may be sought in a dependence of diffusion coefficient on dislocation density. Increased mobility of atoms in dislocations has been demonstrated 15 already in Ag. 3. EXCHANGE EXPERIMENTS OF MORRISON et aZ.16 In view of the possibilities discussed in the last section the attempts recently made by Morrison and co-workers to measure C1 diffusion coefficients in NaCl and KC1 at low temperatures using an exchange technique merit attention.The original results were discussed elsewhere by one of us in terms of the vacancy pair model.16 However, it now seems that the results are more involved than appeared originally and it is appropriate at this stage to review the principles of the determination of diffusion coefficients by this new technique. We refer the reader to the original papers for experimental details but the underlying principle is as follows : the diffusing species (Cl36) initially present in uniform concentration CO, escapes into the surroundings at the surface, the rate of escape being limited only by diffusion to the surface.If the system is homo- geneous the diffusion is described by Fick’s law with a single parameter D : Solution of this equation 17 shows that after time t the amount rz which has escaped is given by provided the diffusion length .\/ot is much smaller than the crystal dimensions. Here A is the area of the specimen. Eqn. (3.2) is characteristic of bulk diffusion (which may include dislocation contributions, cf. $2(iii)). The law appropriate to grain-boundary diffusion may be obtained by integrating the solutions of Fisher and Whipple.12 The result we obtain is (cf. (3.2)). However, more than the difference of (3.2) and (3.3) is involved in the differ- ence between homogeneous and inhomogeneous systems. At t = 0 the concen- tration is co everywhere; now suppose that a diffusion run is made for time tl at a temperature TI at which the diffusion coefficient is D1.If a second run is made at new temperature T2 for time t 2 the total amount of material to escape may be shown to be (3.4) This has an obvious generalization to further runs. Hence a plot of n2 against the time of a run is always linear. This fact, which is part of the convenience of an exchange method (and also of autoradiographic methods), has its origin in the single-parameter form of eqn. (3. l), whose sohtions can clearly always be written c(r, Dt). The distribution at the end of the first run, c(r, Dltl), can be written as c(r, D27) where T = Dltl/D2. Diffusion in the second run at T2 now proceeds as though it had already gone on for time T at D2; from which (3.4) follows.The above argument clearly fails for inhomogeneous systems characterized by more than a single diffusion coefficient. The solutions in this case form at least a two-parameter family and the solution after the first run tl at temperature 3c/3t = D ~ J ~ c . (3.1) n2 = (2Ac#Dt/n, (3.2) n2 = const. tz, (3.3) n:, + t 2 = (2AC0>2(Dltl + &t2)/77.68 DIFFUSION PROCESSES AT LOW TEMPERATURES TI cannot in general be expressed as a solution for temperature TI after any time T. The basic equation must be solved anew, taking the distribution at the end of the first run as the new initial condition. The major difference between bulk diffusion and grain-boundary diffusion in exchange experiments is then the absence of any simple law like (3.4) in grain-boundary diffusion.Conversely the observation of linear n2 against t plots in a succession of runs is good evidence for bulk diffusion. There is one situation apparently of practical importance in which inhomo- geneous systems may give a simple addition law for successive runs. Imagine that in regions of internal or external surfaces the diffusion coefficient D' is much greater than in the bulk D, and suppose that diffusion to the surroundings is via these regions. Initially diffusion will be largely out of these regions them- selves and only when they are depleted will appreciable diffusion out of the bulk occur. Under these conditions we expect (3 * 5 ) in which no is the material initially in the high diffusivity regions.A plot of n2 against t will then be parabolic in its early stages. Such plots, closely parabolic, have in fact been observed by Morrison under certain conditions. n = no + const. (Dltl + D2t2 + . . .)*, 4. SUMMARY In this paper we have pointed to the interesting conclusions which we expect to flow from studies of anion diffusion in alkali and silver halide crystals. Existing knowledge, based on cation studies, enables definite predictions to be made of the role of free vacancies in anion diffusion. At low temperatures and high con- centrations of multivalent cation impurities the concentration of free anion vacancies is depressed and we expect to see other factors entering the diffusion (vacancy pairs, dislocations). General implications of this apply also to ionic semiconductors (doped and non-stoichiometric).Exchange techniques are con- venient for low-temperature anion-diffusion studies provided conditions for bulk diffusion are satisfied (n2 linear in t). We are indebted to Dr. J. A. Morrison for stimulating correspondence. of us (K. T.) wishes to acknowledge a research grant from A.E.R.E., Harwell. One 1 Seitz, Rev. Mod. Physics, 1946, 18, 384 ; 1954, 26, 7. 2 see, e.g., the review by Lidiard, Handbuch der Physik, vol. 20 (Springer-Verlag, 1956). 3 Christy, Fukishima and Li, J. Chem. Physics, 1959, 30, 136; also Naga, J. Physic. 4 Watkins, Physic. Rev., 1959, 113, 79, 91. Hayes, Faraday SOC. Discussions, 5 see, e.g., Amelinckx, Suppl. Nuovo Cimento, 1958, 7, 569. 6 Lidiard, Physic. Rev., 1958, 112, 54. 7 Etzel and Maurer, J. Chem. Physics, 1950, 18, 1003. 8 Tosi and Fumi, Nuovo Cimento, 1958, 7 , 95. 9 Laurent and Benard, J. Physics Chem. Solids, 1957, 3, 7 ; 7, 218. 10 Tannhauser, J. Physics Chem. Solids, 1958, 5, 224. 11 Patterson, Rose and Morrison, Phil. Mag., 1956, 1, 393. Harrison, Morrison and 12 Fisher, J. Appl. Physics, 1951, 22, 74. Whipple, Phil. Mag., 1954, 45, 1225. 13 see, for example, the review by Lacombe in La Difusion dans les Mitaux (Biblio- 14 Hart, Acta Met., 1957, 5, 597. 15 Turnbull and Hoffman, Acta Met., 1954, 2, 419. Hoffman, Acta Met., 1956, 4, 97. 16 Lidiard, J. Physics Chem. Solids, 1958, 6, 298. 17 Carslaw and Jaeger, Conduction of Heat in Solids (Oxford University Press, 2nd edn., Soc. Japan, 1958, 13, 1090. 1958, 26, 58. Rudham, Trans. Furaday Soc., 1958, 54, 106 ; and further unpublished work. thbque Technique Philips, Eindhoven, 1957), p. 23. 1959).

ISSN:0366-9033    

DOI:10.1039/DF9592800064

出版商:RSC    

年代:1959

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GENERAL DISCUSSION Dr. W. J. Dunning (Bristd University) said: Dr. Menter has mentioned the desirability of preparing crystal surfaces of predetermined structure ; we have recently discovered a method of doing this in the case of sucrose. We frequently obtain surfaces on sucrose crystals on which the step systems are simple (fig. la). If the solution from which the crystal is growing has been in contact with silicone grease, this solution can be removed and it is then found that a drop of solution replaced on the surface does not spread. When the drop is supersaturated, the growth steps beneath it grow to the edge of the drop, leaving a smooth patch which is stepless and apparently smooth (fig. lb). At present, areas a few square millimetres in extent can be prepared in this way, but we con- sider that areas up to a square centimetre could be obtained without undue difficulty.FIG. l(a). FIG. l(b). Further to the problems considered by Dr. Menter, I should like to mention some studies we are undertaking on the epitaxial overgrowth from solution of ammonium iodide on cleaved surfaces of mica. It is found that the nucleation of the NH4I crystals is not random but takes place at preferred sites on the mica surface. Under the microscope, the first thing to be observed is the appearance of an ill-defined layer. This layer thickens slowly and this fact suggests that it may be a perfect crystal growing in a direction normal to the mica surface by Volmer two-dimensional nucleation. As this thin layer spreads over the surface, it meets a cleavage step on the mica and there, at definite points on the step, it very rapidly transforms into and develops as a triangular pyramidal crystal.The preferred site where this occurs is where the staircase of steps forming the cleavage step becomes steep and this suggests that the transformation from layer to rapidly growing pyramids is brought about by dislocation loops pulled out of the mica during cleavage; these loops introduce screw dislocations into the hitherto perfect crystal layers. We have studied the kinetics of formation of the layers by determining the time of appearance r as a function of the supercooling AT. Plotting logr against the reciprocal of AT, smooth curved lines are obtained. These lines are different 6970 GENERAL DISCUSSION for different patches on the mica and this implies that the structure of the mica surface in these patches is significant.Dr. F. S. Stone (Bristol University) (communicated): Dr. Menter and his co- workers have provided us with a very clear illustration of the occurrence of localized oxide growths on copper. One is left wondering how early in the process of oxidation these effects begin to occur. Granted that dislocations may confer on localized areas an enhanced activity in oxidation, it nevertheless seems extremely unlikely that the remainder of the surface stays absolutely bare. Yet one of the striking things which calorimetric studies of the initial stages of the oxidation of metals has revealed is the constancy of the heat of reaction after only sufficient oxygen to cover about 10 or 20 % of the total available surface has been fixed on the metal.Moreover, it is sometimes found (with copper,l for instance) that this plateau is at a level very close to the heat of formation of the bulk oxide. A priori, one would not expect a correspondence of this kind, if only because of strain in the oxide film. Now it is true that this type of experiment as hitherto performed leads to ambiguities in interpretation because of the possibility of preferential uptake on the most accessible surface, but it is possible that this could be overcome by a modification in the technique of admitting oxygen to the calori- meters. A heat of reaction constant at the heat of oxidation after only a fraction of the surface was covered would strongly support the concept of localized oxidation.The regeneration of oxidation activity at low temperatures which can be produced by treatment in vaczio at elevated temperatures also bears on this question of preferential growth of oxide at localized sites. The position as it affects the initial oxidation of copper, nickel and cobalt has been well summarized by Dell.2 Dr. G. A. H. Elton (B.B.I.R.A., Herts.) said: During the discussion of Dr. Cabrera's paper, Dr. Spinks mentioned that if a saturated solution of a tagged strontium salt is percolated through a column of the solid salt, then the isotopic ratio in the emerging eluate is considerably different from the isotopic ratio in the original solution. He claimed that this observation tended to invalidate Dr. Cabrera's conclusions concerning the magnitude of condensation coefficients, since different isotopes were being adsorbed to differing extents.It should be pointed out that there is no reason to expect that Dr. Cabrera's theory should be applicable to a case such as this, and I am sure that it was never intended to be so. The system which Dr. Spinks mentioned is far more complicated than the simple vapour-solid system considered in the theory. In the former case, we have an ionic crystal in contact with an ionic solution, and both interphase potentials and electrokinetic potentials (in the double layer) will exist ; further- more, ion-exchange and counter-ion adsorption will have to be taken into account before a quantitative theory to account for the ionic system can be worked out.Sir Hugh Taylor (Princeton, N.J.) said: Langmuir showed some thirty years ago that cadmium metal condensed readily on cadmium but less readily on glass. He showed that a beam of cadmium vapour atoms did not condense on the wall of an evacuated glass vessel, although the vapour was supersaturated, until the area of glass where the atom beam was striking was cooled sufficiently for deposi- tion of cadmium film to occur. Further condensation took place with an ac- commodation coefficient of the order of unity. The beautiful work of Estermann on the growth of mercury platelets on a sur- face cooled with liquid air, the vapour pressure of the mercury corresponding to a saturation pressure at - 78"C, should be recalled. Hexagonal platelets many- fold in length and breadth without marked growth in thickness were formed.Nevertheless it was shown that the accommodation coefficient was approximately unity. It was concluded that condensation on the face of the platelet did not immobilize the condensed atoms which accordingly moved over to the edges, 1 Dell, Stone and Tiley, Trans. Faraday Soc., 1953, 49, 195. 2Del1, J . Physic. Chern., 1958, 62, 1139.GENERAL DISCUSSION 71 there to add to the crystal and increase two of the dimensions. Only when the size of the platelet became large did the mobile condensed atoms start the growth of additional layers. Dr. T. Hickmott (G. E., Schenectady) said: The value of the heat of desorption of hydrogen from tungsten used by Prof. Gomer, 60 kcal/mole, is incompatible with his observation that hydrogen evaporates from tungsten in a few seconds at 600°K.Adsorbed hydrogen evaporates as molecules below 1050°K. We have examined the kinetics of evaporation of hydrogen from tungsten by flash-filament methods and find that for surface concentrations, n < 25 x 1012 molecules/cmz, the rate of evaporation may be expressed as = (5 x lO-3)n2 exp (- 31,000/RT) molecules/cm2 sec. For an ideal hard-sphere two-dimensional gas of hydrogen ad- atoms at 600”K, one calculates a pre-exponential factor for molecular desorption of 4 x 10-3, in good agreement with the experimental value. Using a model of an ideal two-dimensional gas, for n - 1 x 1013 molecules/cm2 and a heat of desorption of 60 kcal/mole, the rate of evaporation of hydrogen of - 60 molecules/cm2 sec would be much too small to produce noticeable evaporation of adsorbed hydrogen at 600°K.With Edes = 30 kcal/mole, Ed/&eS - 0.2 for hydrogen, in agreement with the value for oxygen, as has been pointed out by Ehrlich.1 Dr. D. Brennan (Liverpool University) said: Dr. Gomer finds a heat of ap- proximately 90 kcal mole-1 for the heat of desorption of carbon monoxide from tungsten. The heat of adsorption of carbon monoxide on iron is 32 kcal mole-1,2 and on nickel it is 35 kcal mole-l,3 which values are comparable in magnitude to the heats of adsorption of hydrogen on these surfaces. By analogy, one might have expected the heat of adsorption of carbon monoxide on tungsten to have been less than say 50 kcal mole-1. Would Dr. Gomer like to comment further on his value of 90 kcal mole-1 and perhaps give additional information about the determination, particularly with reference to the coverage? Mr.H. D. C. Rapson (Beecham Research Lab. Ltd.) (communicated): It is generally assumed that the activation energy for surface diffusion (Ed) is related to that for desorption (Edes). Dr. Gomer accepts the presence of heterogeneous surfaces. It follows that the apparent “ mean ” activation energy for surface diffusion becomes, in part, a function of coverage. It would therefore be desirable to compare activation energies at similar coverages. However, it is not clear that Dr. Gomer has done this for the data in table 1. It is appreciated that the tech- nique is experimentally difKcult. However, for diffusion that is not boundary free could not this be effected by following boundary movement over a limited region at similar coverage? The precise physical meaning of the ratio Ed/Edes is not clear, even assuming E d and Ed- to have been measured at similar coverage.Some workers seem to regard E d and Edes as though they refer to the same group of sites (cf. eqn. (3)), here used approximately. In fact, as coverage increases Edes refers essentially to a collection of the most recently occupied sites ; these exhibit a range of site energies, whereas E d refers to a collection of those sites whose energy barriers permit surface diffusion. It does not follow that both collections involve the same sites. Dr. Gomer’s assumption that “ the corrugation of the potential surface imitates that of the physical surface” is therefore thought to require further examination. It is suggested that both site energy and barrier energy distribution functions are required for proper consideration of adsorption and diffusion.Finally, the assumption, that binding is at a minimum on the surface having the closest packing, is thought to be questionable. Is this not the surface capable of exhibiting highest dispersion force interactions ? The data of table 1 for oxygen on W, incidentally shows no great difference between the (110) and (100) faces. 1 Ehrlich, J. Chem. Physics, 1959, in press. 2 Bagg and Tompkins, Trans. Faraday SOC., 1955, 51, 1071. 3 Baker and Rideal, Trans. Faraday SOC., 1955, 51, 1957. This value is unexpectedly high.72 GENERAL DISCUSSION Prof.R. Comer (University of Chicago) (communicated) : Dr. Hickmotts’s point is well taken. I can think of no artifact that would vitiate our measurement, which I still believe to be good, per se. It is possible that it refers to desorytion from a very small group of sites near the (211) faces, where the local coverage was much lllgher and the mobility much lower than the average, so that the perfect (two-dimensional) gas approximation breaks down. However, even with this scheme the rate would be extremely low. It is conceivable that hydrogen ad- sorption caused a slight amount of rearrangement of the W lattice and that the measurement which is after all based on visual changes, refers to the annealing of these. However, all this is purely conjectural and I have no really good answer at present.Dr. Brennan is correct in expecting much lower values for the heat of ad- sorption of CO at moderate coverages. There is in fact an energy spectrum as is also indicated by Klein’s work.1 The high value of 90 kcal refers to very low coverage, probably below 0.1 of maximum coverage, and to desorption temper- atures near 1300°K. However, the fact that activation energies for diffusion start at 36 kcal and go up, indicates that energies of adsorption may well be high. In reply to Mr. Rapson, I wish to say that the data of table 1 enable one to compare activation energies under physically similar situations. It would be meaningless to attempt a comparison at nominally identical coverages because the effective surface heterogeneity depends also on the adsorbate, as the results dis- cussed in my paper indicate rather clearly.Thus the coverages at which boundary migrations (by essentially similar mechanisms) just occur with hydrogen differ from those with oxygen or COY largely because the nature of the “ traps ” varies with the adsorbate. The comparison of Ed and Edes is based on coverages in such a way that diffusion could most plausibly be associated with those sites whose Edes is used. While it is strictly true that one should use differential values, the best one can do in practice is to use groups of values. However, the spectrum both of Ed and Edes varies sufficiently slowly to make this reasonable. I see no reason to doubt the assumption that minimum binding occurs on the most close-packed planes, either from the experimental point of view, or theoretic- ally, as briefly indicated in my paper. The work of Ehrlich 2 and of Gomer 3 also indicates that this conclusion is correct in physical adsorption.I believe the basic reason is that interaction with nearest neighbours is much more important than with next nearest, etc., ones, so that surfaces offering the smallest number of nearest neighbours will always be least effective in binding, regardless of how many longer range interactions they may be able to offer. Prof. D. D. Eley (Nottingham) said: Dr. D. Shooter at Nottingham has recently completed a study of the activity of conversion (k20) of pH2 -+ oH2 at 20°C on evaporated films of metals of the first transition series, Ti to Zn. The activity closely parallels the cohesive energy of the metal E(M-M), which suggests to us that the conversion occurs preferentially for each metal on its plane of highest work function, i.e.its most close-packed plane. The argument is that one would expect a priori a correlation between k20 and E(M-H) the strength of the surface M-H bond. This is given by +{E(M-M) + E(H-H)) + 23(XM-XH)2, and the second or ionic term will be small on planes of highest electronegativity X , (therefore highest work function) in which case the theoretically expected correla- tion of k20 with E(M-H) would lead the experimentally observed correlation of k20 with E(M-M). A preliminary account is in course of publication in Proc. Chem. SOC. Dr. F. S. Stone (Bristol University) said: The paper by Terenin and Solonitzin raises the interesting question as to why zinc oxide sometimes shows the property of photodesorption of oxygen, whilst under other conditions it shows photo- 1 Klein, J.Chem. Physics, 1959, 31, 1306. 2 Ehrlich, Hickmott and Hudda, J . Chem. Physics, 1958, 28, 977. 3 Gomer, J . Physic. Chem., 1959, 63, 468. J. Chem. Physics, 1958, 29, 441.GENERAL DISCUSSION 73 adsorption. Dr. T. I. Barry and I 1 have recently been studying these same pro- cesses. I should like to mention, first, the conditions under which we have ob- served photodesorption and photoadsorption respectively, and then say a few words about the mechanisms which we think are responsible for photoadsorption. Like Dr. Solonitzin we have studied it manometrically, using in our case zinc oxide prepared by decomposition of the carbonate in air.This oxide can be expected to possess a low degree of non-stoichiometry. When outgassed specimens of this oxide were exposed to oxygen at room temperature and then, after removal of the residue of gaseous oxygen, exposed to ultra-violet light, photodesorption was readily ob- served. If, on the other hand, a similar experiment was carried out on a zinc oxide which had been prepared by decomposition of the carbonate in wacuo (and which possessed a much higher degree of non-stoichiometry), the characteristic reaction was photoadsorption of oxygen. The difference in behaviour of the two oxides could also be shown up in studies of the photocatalysis of the oxygen equilibration reaction 1802 + 1602 -+ 2 1 8 0 1 6 0 over zinc oxide.Finally, the reversal of the photo-property from oxygen desorption to oxygen adsorption could be demonstrated with one and the same specimen by treating an oxide specimen of the first type with hydrogen at 500°C. The conclusion which one is inclined to draw from these results is that there is a correlation between high non-stoichiometry and the property of photoadsorption of oxygen. There is, however, another important factor to consider. We find that the nature of the oxygen chemisorption is different under different conditions of stoichiometry and of temperature (speaking now of the dark reaction). On zinc oxide with high interstitial zinc content much of the adsorbed oxygen is held very strongly and coverages are high. On the more nearly stoichiometric zinc oxide, coverages are very low and the oxygen is much more readily desorbed.We incline to the view that over all ranges of temperature oxygen is chemisorbed on the highly non-stoichiometric zinc oxide primarily as 0 2 - (perhaps being partially embedded in the surface), and it also seems likely to us that the field of these oxygen ions draws interstitial zinc towards the surface, as Thomas 2 and Roberts 3 have suggested. On the more nearly stoichiometric zinc oxide, however, we consider that the stable form of adsorbed oxygen provided the adsorption is carried out below 300°C is 0-. If, on the other hand, the adsorption of oxygen is carried out on this oxide at 300°C or above, studies of the kinetics of adsorption and de- sorption over a range of temperature have led us to the conclusion that the more tightly bound species O,”& is formed.Thus we believe that photodesorption of oxygen is linked with the presence on the surface of O& ions, whilst photo- adsorption of oxygen is coupled with O:gs ions and perhaps also with high sub- surface concentrations of interstitial zinc. Two mechanisms for photoadsorption follow from this. We visualize in the first that the positive holes generated in the photo-process are trapped at the sur- face by o,”& ions, converting them to O&, viz. O& f p -+ O&. No change in pressure will follow from this reaction. The electrons simultaneously pro- duced, however, will lead to adsorption by the reaction : e + 3 0 2 -+ O& The second mechanism invokes the conclusion drawn by Mollwo 4 from his photo- conductivity work that interstitial zinc is a trap for holes.If there is a high con- centration of sub-surface interstitial zinc we then have the important reaction Zn+ 4- p --f Zn2+ alongside the above reaction, which again leads to photo- adsorption. The first of these mechanisms could account for the photoadsorption observed by Terenin and Solonitzin, and also by Fujita and Kwan,S if we infer The phenomenon of photodesorption is already well documented. 1 Barry and Stone, Proc. Roy. SOC. A , 1960, 255, 124. 2 Thomas, J. Physics Chem. Solids, 1957, 3, 229. 3 Roberts et al., Trans. Faraday SOC., 1959, 55, 1386, 1394. 4 Mollwo, Ann. Physik. (6), 1948, 3, 230. 5 Fujita and Kwan, Bull. Chem. Soc. Japan, 1958, 31, 379.74 GENERAL DISCUSSION that their so-called “ enriched ” or “ oxidized ” oxides were obtained by exposure to oxygen at high temperatures (300°C or above) and then quenched.As regards CO adsorption, which we have also studied, we find in agreement with Terenin and Solonitzin that specimens of zinc oxide which show photo- adsorption of oxygen show photodesorption of carbon monoxide, and vice versa. One would expect this if CO were chemisorbed as CO+. The high activity of zinc- rich ZnO for the photocatalysis of CO oxidation at low temperatures, which we briefly reported elsewhere,l is evidently due to photoadsorption of oxygen. The apparent decay in the photo-effect in the range of temperature between 50°C and 100°C in that work we now attribute to the purely thermal desorption of CO accentuated by photodesorption.Dr. G. A. H. Elton (B.B.I.R.A., Herts.) said: Dr. Terenin and Dr. Solonitzin give no discussion of their remarkable experimental observations on the “ photo- dissociation” of water chemisorbed on cadmium or zinc surfaces. If, as they suggest, water molecules are chemisorbed through the oxygen atom, the shift in the energy of the active wavelength by 2eV towards the red (as compared with the threshold for the photodissociation of water vapour) seems rather large. I t seems more likely that some, at least, of the water molecules are chemi- sorbed in a dissociated state, as radicals. The function of the illumination energy would them be simply to desorb these radicals, thus giving an apparent photo- dissociation.If the dissociation of the adsorbed water is not complete, de- sorption of the radicals would tend to disturb the surface equilibrium with the result that further dissociation would occur. This theory could be verified or refuted by simple isotope-exchange experiments. Dr. G. Heiland (University of Erlangen) said: Terenin and Solonitzin report in their interesting review, that photosorption occurred on “ ZnO enriched by oxygen”. I would like to know more precisely the previous treatment of the specimens. At Erlangen we have used thin layers prepared by oxidation of evaporated zinc coating in air for similar experiments. Observed was not the oxygen pressure but the conductivity of the layers. Irradiation in the funda- mental absorption region produced a slow and steady increase of the conductivity.The slope was independent of oxygen pressure, but the saturation value decreased with increasing oxygen pressure. In every case an increase of conductivity was observed, corresponding to photodesorption of oxygen. The conductivity de- creased after the irradiation was turned off, initially fast and then more slowly, still decreasing in air after months according to a power law of time.2 Two reasons have been discussed for this : a very low rate of chemisorption caused by exhaustion of electrons at the surface or a sluggish diffusion of donors towards the surface allowing still more oxygen to be adsorbed. For ZnO specimens Prof. Terenin reports a wide non-selective absorption in the infra-red region. This absorption disappeared on oxygen adsorption and re- appeared on photodesorption.At Erlangen, we have observed a similar absorption for single crystals covering the same spectral range, but this was definitely a volume effect. If the conductivity is increased by doping with different kinds of donors, this absorption increases, but it does not follow the changes of conductivity produced by variation of temperature. There- fore this absorption is attributed mainly not to free carriers but to occupied im- purity levels. These levels can be emptied by prolonged heating in oxygen or by additions of copper. The continuous absorption in this spectral region then becomes very low. From these results for single crystals one may also conclude that the surface donors mentioned above may not be located at the outer surface but in the interior of the crystallites within range of the depletion layer produced by the adsorbed oxygen.1 Stone, Admnces in Catalysis, 1957, 9, 270. 2 Mahr, Diss. (University of Erlangen, 1957). 3 Ameth, 2. Physik, 1959, 155, 595. It was attributed to surface donors.GENERAL DISCUSSION 75 Prof. A. Terenin (Leningrad University) (communicated): In reply to the com- ment by Dr. Heiland, I should remark that we used mainly polycrystalline ZnO powder, obtained by thermal decomposition of the oxalate, and not oxidized evaporated zinc coatings. The sample was degassed at 400°C for ca. 8 h and then brought in contact for a few minutes with oxygen at 10-2 mm Hg, the excess gas being afterwards removed by evacuation to lO-5mm Hg.It is the remaining adsorbed gas which is photodesorbed in our experiments, the necessary require- ment being that the ZnO sample should contain excess metal. Now, when the metal stays in oxygen of 10-2mm Hg at 20°C, the illumination in its presence invariably produces the irreversible photosorption, likewise described by Fujita and Kwan (ref. (17) in our paper). This latter is due to some photochemical pro- cess not involving the conductivity. It may be mentioned than an irreversible photosorption and surface reaction of 0 2 and NO has been described for Ti02 by Kennedy, Ritchie and Mackenzie.1 In respect to the second remark by Dr. Heiland, we agree that the oxygen- sensitive infra-red absorption spectrum in ZnO (and other oxides) can belong to volume donor levels, provided there is an easy electron interchange between them and the surface.In fact, the rapid action of the admitted gas is inconsistent with a volume diffusion. Dr. A. D. Buckingham (N.R.C., Ottawa and Oxford University) said: I should like to ask Dr. Murrell three questions. (i) Could the presence of light lead to the injection of charge carriers from the electrodes? (ii) Is not the rather sur- prising result that the rates of formation of free positive and trapped negative, and free negative and trapped positive carriers are equal (eqn. (2.14)), only applicable in the limit of very weak light intensities? (iii) Is it possible that the rates of formation of charge carriers are significantly dependent upon the applied potential difference? The positive and negative ions of an ion-pair in an anthracene crystal need about ten neutral molecules between them before the energy change in transferring the charge to the next molecule becomes equal to kT at room tem- perature, and at these separations the energy of the ion pair in a field of 104 volts cm-1 is about 15 % of kT.This effect would presumably lead to a photocurrent proportional to Y2 at low voltages. Dr. J. N. Murrell (Cambridge University) said: I agree that the three points raised by Dr. Buckingham have to be considered in an exact mathematical treat- ment of photoconduction. I shall comment on them in turn. (i) I have assumed that there is no injection of free carriers from the electrodes on the evidence that the dark current is small compared with the photocurrent.I agree that this is not conclusive. A more important reason for my assumption is that it leads to a great simplification of the mathematics, allowing us to deduce eqn. (2.12) for the photocurrent. (ii) The rate of formation of positive and negative carriers will be equal pro- vided that the number of lattice sites which can give rise to carriers is not ap- preciably depleted by the number of carriers in the crystal. (iii) Although the field strengths used in the experiments on anthracene are small (104 V cm-1) in comparison with the internal fields in the crystal, it is possible at first sight that the formation process is field dependent to a significant extent, since the production of free carriers from an exciton appears to be a highly in- efficient process.However, the fact that a strictly ohmic current is observed for light of wavelength h 4350 A, would appear to eliminate this possibility. It would be an extreme coincidence if the saturation effect (case Alb in my paper) was counterbalanced by the effect of a field dependent formation process so as to give an ohmic current, A conclusive answer to this question could be given by examin- ing the effect on the photocurrent of an electric field applied at right-angles to the normal direction of current flow. If this increased the current to any large extent then it could be deduced that the formation process was field dependent. 1 Kennedy, Ritchie and Mackenzie, Trans. Furaday SOC., 1958, 54, 119.76 GENERAL DISCUSSION Prof. D. D. Eley (Nottingham University) said: Dr.Inokuchi's thermal energy gap of 2.7eV for anthracenel would fit in better with the photochemical value of 3-0 eV, than the lower values mentioned by Dr. Schneider. Dr. J. N. Murrell (Cambridge University) said: The energy required to form a positive ion and a negative ion in gaseous anthracene, and separate them by an infinite distance is 5.8 eV. In the crystal this energy is reduced by two effects: first, the electrostatic field of the ion will polarize the surrounding molecules, and secondly there will be some overlap of the wave function of the ion with those of the surrounding molecules, so that the electron (or positive hole) will be partly delocalized. Lyons 2 has estimated the polarization energy to be 2.0 eV. How- ever, we can obtain the combined polarization and delocalization energy ( W ) by comparing the energy required to produce photoemission from an anthracene crystal 3 (5.7 eV) with the ionization potential in the gas phase (7.2 eV), The difference between these two energies is equal to the stabilization of the positive ion in the crystal (1.5 ev).If we now assume that the positive and negative ions are equally stabilized, we conclude W = 3.0eV. It follows that the energy required to produce a free positive and negative ion in the crystal is 2.8 eV, and this is about equal to the energy of the longest wavelength light which is found to produce a photocurrent. Dr. W. G. Schneider (N.R.C., Ottawa) said: The crystals of the charge-transfer complexes described by Prof. Eley are of considerable interest, both from the point of view of semiconduction and of electron spin resonance. Crystal analyses by Harding and Wallwork4 have shown that in these complexes the aromatic rings of the donor and acceptor molecules are alternately superimposed with the planes of the rings parallel.There is thus a large n-electron overlap along the columns so formed. One would therefore expect the conduction along the column direction in the crystal to be almost metallic and to be very small normal to this direction. With polycrystalline samples one is presumably measuring some mean conductivity of the crystals averaged over all directions, together with the conductivity across grain boundaries. For this reason it would be extremely interesting to have conductivity data on single crystals and specifically to measure the conductivity along different crystal axes. I would also like to ask Prof.Eley if he attempted any photoconduction measure- ments. Some years ago we examined single crystals of the chloranil-hexamethyl- benzene complex. The photoconductivity appeared disappointingly small. Fluorescence also appeared to be absent, from which it was assumed that the excitation energy was effectively quenched thus limiting charge-carrier formation. However, measuring techniques have improved considerably since the time these measurements were made so I think they may bear repeating. Recently in our laboratory Dr. Danyluk has prepared a 1 : 1 charge-transfer complex of azulene and iodine. Azulene, a non-alternant hydrocarbon isomeric with naphthalene, has a dipole moment of about 1 D as a result of a piling-up of charge in the 5-membered ring.This ring should therefore be an excellent T- electron donor. In the crystal one might therefore expect the 12 molecule to have its axis centred on the 5-membered ring and normal to the place of the latter, with columns built up of alternating donor and acceptor molecules. The solid complex gives rise to an electron spin resonance which consists of a rather strong, somewhat broadened, signal. No hyperfine splitting could be resolved. The density of free electron spins has not yet been determined. Dr. E. E. Schneider (Durham University) said: The model of electronic levels may provide an understanding of the semiconducting properties of solid molecular compounds, but it does not solve the great puzzles of their magnetic behaviour.1 Inokuchi, Bull. Chem. Soc., 1956,29, 131. 2 Lyons, J. Chem. Soc., 1957, 5001. 3 Casswell and Isedale, J . Appl. Sci. Austral., 1953, 4, 329. 4 Harding and Wallwork, Actu Cryst., 1955, 8, 787.GENERAL DISCUSSION 77 The problem is accentuated by Dr. Matsunaga’s interesting identification of the two superimposed magnetic resonance lines of one of the solid molecular com- pounds with the resonances of the component mono-radicals. A similarly in- dependent behaviour of the components of some molecular compounds in solution, as shown by a strictly additive optical absorption spectrum (1 1, 13”) may possibly be related to a spatial separation of the component radical molecules by molecules of solvation.As regards the solid of the strongly magnetic molecular compounds, further theoretical and experimental work is required to reconcile the apparent magnetic isolation of the radical components with a closely-stacked structure of neighbouring acceptor and donor molecules. The situation in the weakly paramagnetic molecular compounds is equally obscure. The authors’ explanation of a deviation from 100 % radical character by a small degree of overlap of the wave functions appears questionable. Over- lapping would lead to exchange phenomena, which would affect the shape of the paramagnetic resonance spectrum, but would not reduce the number of effective spins and hence not alter the integrated intensity of the resonance line. It should be noted that the fraction of magnetic molecules (percentage free radicals) is in some cases less than 1/100.This could possibly be ascribed to crystalline im- perfections or impurities, near or through which a fraction of the radical com- ponents may become sufficiently separated. Prof. D. D. Eley (Nottingharn University) said: In reply to Dr. Chromey, there was no visual evidence for decomposition in our charge-transfer complexes during the course of our experiments. With reference to the failure of the solid free radical mentioned by Dr. Chromey to conduct, Mr. M. R. Willis has carried out experiments on a similar substance and also found a low conductance, but there was an incertainty on the purity of the specimen. I would emphasize the need to recrystallize diphenyl picryl hydrazyl several times from a suitable solvent, to secure the low energy gap of 0.26 eV.l Dr.G. D. Parfitt found diethyl ether the best solvent for this purpose, and recently we have tested again that no complex is formed with this solvent,2 unlike chloroform and benzene.3 In reply to Dr. E. E. Schneider, an attempt to correlate electron resonance signal and conductivity is given in the paper. I should prefer to reserve any further comments until we have completed a study of the effect of preparative conditions on the electron resonance signal of the solid complexes, as we have some evidence that there is an important connection between the two. In reply to Dr. W. G. Schneider, we hope to examine the photoconductivity of the complexes and experiments are planned along these lines.On his point about single crystals. also referred to by Prof. MacDowell, many substances, particularly molecular complexes, do not yield suitable single crystals. A certain amount of semiconductivity work has been done on single crystals of pure sub- stances, for example, phthalocyanines 4 and recently Cardew and I have reported on the semi-conductivity of a glycine single crystal.5 I have no immediate com- ments to make on Dr. Le Blanc’s interesting point. Prof. D. D. EIey (Nottingham University) (communicated): Some time ago Mr. M. R. Willis at Nottingham examined the semiconductivity of Coppinger’s radical, 2-, 6-, 31-, 5’-tetra tert.-butyl41-phenoxy-4 methylene-2, 5-cyclohexadiene- 1-one radical,6 provided by Dr. G. E. Bennett of Shell Research Laboratories * Numbers refer to references in papers. 1 Eley and Parfitt, Trans.Furaduy Soc., 1955,51, 1529. 2 Eley and Inokuchi, Z. Elektrochem., 1959, 63, 29. 3 Lyons and Watson, J. Polymer Sci., 1955, 16, 141. 4 Fielding and Gutmann, J . Chem. Physics, 1957, 26, 41 1. Cardew and Eley, Energy Transfer with Special Reference to Biological Systems (Faraday Soc. Discussions, Nottingham, April, 1959). Coppinger, J. Amer. Chem. Soc., 1957, 79, 541.78 GENERAL DISCUSSION (Thornton, Cheshire), who also warned us about a possible instability of the radical to oxygen. Willis found = 1.34eV for this radical. Subsequent to the Kingston discussion, Dr. St. Pierre of the G. E. Laboratories (Schenectady) gave me a sample of galvinoxyl (the same substance) and we have measured a A€ of 1-45 eV for this.We tentatively conclude that A, w 1.4 eV is characteristic of Coppinger’s radical but we are continuing to study conductivity and electron resonance of this substance and hope to publish a paper soon. The present results do not allow us to conclude whether the partial localization of the free radical electron in Coppinger’s radical is intramolecular or intermolecular. It is always possible that the relatively high conductivity of DPPH is exceptional for solid free radicals and is associated with a molecular stacking in the crystal specially favourable to electron transfer. If so, then we were lucky to choose DPPH for our first experiments. The question can only be decided after further experiments have been made on other solid free radicals.Referring to Dr. Le Blanc’s comment, if the organic semiconductor is an in- trinsic semiconductor with equal numbers of electrons and holes it is surely difficult to predict the Schottky barrier layer width, which might be relatively small compared to semiconductors of the donor or acceptor atom types. An upper value can be calculated using the usual equation 1 but ignoring one type of charge carrier in the intrinsic semiconductor; orders of magnitude of the thickness in cm are given for the energy gaps in eV in brackets, 10-4 (0.5), 10-2 (1-0), 1 (1.5), 102 (2.0) and 106 (3-0). Since typical specimens have a thickness of 0-2 cm, this suggests barrier layer effects may be neglected for semiconductors with energy gaps of less than 1-0eV.In practice, the evaluation of “ energy-gaps” for a given organic substance with different electrode spacings is clearly desirable. On the theoretical side, it may be that the potential-well model used in our discussion will lead to thinner barrier-layers than the band model, but this is pure speculation at present. Dr. L. G. Harrison (University of Britidz Columbia) said : Lidiard and Thar- malingam have mentioned two possible ways in which accelerated diffusion via dislocations could occur while the observed rate laws remain those of simple bulk diffusion. I should like to add some further clarification of these situations, particularly in regard to the conditions required for each of them. A full dis- cussion will be submitted for publication shortly.It is convenient to consider principally the case in which the regions of rapid diffusion are grain boundaries ; for mathematical investigations, I have used a spherical assembly of spherical grains. I shall use the following notation : D,, D,, diffusion coefficient in grain boundaries and bulk respectively ; D,, observed diffusion coefficient ; a,, grain size (radius, in the simple model) ; and 1, thickness of boundary region to which D, applies. In general, three types of behaviour appear to be possible when D, > D,. (a) The case treated by Hart,2 in which the overall diffusion coefficient is enhanced (D, > Dg), but no large concentration differences develop between the bulk and the dislocations, so that even examination of concentration distributions on a microscopic scale would fail to reveal the role of the dislocations.Lidiard and Tharmalingam give the condition (Dct)* > ag, or &/D, (< t. Mart also states that the time of migration of a particle between dislocations must be much less than t, i.e. ai/D, < t. The distinction is important, since D, could con- ceivably be orders of magnitude smaller than &. Using a different approach from Hart, based on solutions of the diffusion equation in the spherical model, I obtain a more quantitative expression : a ; p g 5 10-5 t. (1) 1 Kittel, Introduction to Solid State Physics (New York, 1956), p. 389. 2 Hart, Acta Met., 1957, 5, 597.GENERAL DISCUSSION 79 This excludes the complete range of experimental observations of Morrison 1 and co-workers ; for t - 105 sec, D, < D, < 10-8 cm2 sec-1, ag must be as small as 1 p.This derivation appears to contradict Hart’s requirement that the array of dislocations should not be orderly. (6) The more complicated concentration distribution treated by Whipple 2 will arise at greater ratios DJD, than case (a). Lidiard and Tharmalingam state that this will give a tQ law in place of the usual ta ; this is not general, but is a limiting form, subject to DJD, > (D,t)$/Z 1. (2) (c) For even larger D,/D,, diffusion will at first occur in the boundaries only, obeying a simple rate law. The condition (another limit of Whipple’s expression) is (Dgt)$ < 1. (3) This is most likely to be satisfied if 1 greatly exceeds the core size of a dislocation, e.g. in ionic crystals, if there is a “space charge” of point defects.D, will be sensitive to grain size in an exchange experiment, but not in the more conventional sectioning experiment, for which D, = D, in this case. Both types of experiment have been reported for sodium chloride ; 1, 3 and since D, is sensitive to grain size in both, and type (a) diffusion appears to be excluded for exchange, it seems likely that the experimental conditions are sufficiently different for case (a) to be observed in sectioning and case (c) in exchange. It should be noted that all these situations can arise in one system at one tem- perature. The above discussion is in terms of a variable DJD,; but if D,/D, is fixed, in a semi-infinite medium with a wide range of sensitivity of measurement, all the situations described should be observed, in reverse order, as the diffusion proceeds.Dr. J. A. Morrison (N.R.C., Ottawa), said: I should like to mention briefly results of measurements of anion diffusion in NaCl which are relevant to the paper by Lidiard and Tharmalingam. The experiments have been done over the past two years by Dr. Hoodless and Rudham in our laboratory; a full account will be submitted for publication shortly. Previous results 1 for anion diffusion in NaCl showed two ranges of diffusion, with the transition occurring in the vicinity of 500°C. It is important to note, however, that in the experiments at higher temperatures ( t > 500°C) single crystals were used while at the lower temperatures the specimens consisted of lightly crushed crystals.When experiments were tried to explore the transition region i n detail it was found that the magnitudes of the diffusion coefficient and of the apparent activation energy depended markedly on the previous mechanical and thermal treatment of the crystals. In particular, prior annealing of the crystal specimens in general reduced the diffusion coefficients and increased the apparent activation energy. Typical results are shown in fig. 1 and 2. The solid lines in the figures indicate the results obtained previously4 for unannealed crystals. The significant feature of the new results is that sufficient annealing removes the low temperature range of diffusion. Dr. Barr in our laboratory has made estimates of the densities of dislocations in the larger crystal specimens used in the diffusion experiments.For the examples illustrated in fig. 1 the dislocation density changes from about 1 x 106/cm2 for unannealed plates to about 5 x 10q/cm2 for the single crystal annealed at 740’C. From a number of such experiments a reasonable correlation between the magnitude of I) and the dislocation density has been established. Harrison, Morrison and Rudham, Trans. Faraday Soc., 1958, 54, 106 ; and further unpublished work. 2 Whipple, Phil. Mag., 1954, 45, 1225. 3 Laurent and Benard, Compt. rend., 1955,241, 1204. 4 Harrison, Morrison and Rudham, Trans. Faraday SOC., 1958, 54, 106.GENERAL DZSCUSSLON FIG. 1 .-Chloride ion diffusion in singie crystals of NaQ. Single crystal plates of NaCl: 0 A A unanneded ; 0 annealed 2 h at 580°C; '\\ %\ \\\ " \ \ 'e, 'O \ \ \ \ \ \ \ 1 I 1 I I I I ' 1.0 I-2 1.4 1.6 103 x i p FIG.2.-Chloride ion dif- fusion in crushed crystals of NaCI. Crushed crystals of NaCI; A-A- unanneded; 0 annealed 4 h at 575°C; 0 annealed 50 h at 585°C. 4 2 ba 3GENERAL DISCUSSION 81 The simple kinetics of bulk diffusion was not always observed but it has not been possible to relate the departures quantitatively to the examples discussed in 5 3 of the paper by Lidiard and Tharmalingam. Prof. T. J. Gray and Dr. P. G. Harrison (Alfred University) said: Diffusion studies made on alkali halide crystals grown from solution at room temperature have been shown to exhibit significantly different characteristics in the low-tem- perature region than do crystals grown from the melt.1 It has been demonstrated that the predominant feature is the initial random distribution of impurities (even in extremely pure specimens) achieved during growth from solution.However, heating the crystals to a temperature corresponding to the “ knee ” in the classic - I 2 n a, v1 . 3 2 -13 25 GI - -14 -14.5 reciprocal temperature (1031°K) FIG. 1 .-Ionic diffusion in solution-grown NaCl illustrating the characteristic shift observed after precipitation has occurred at dislocations. diffusion relationship leads to aggregation of impurities at dislocations as is clearly seen in the etch patterns. This aggregation is invariably present in all melt-grown crystals and cannot be removed. When the characteristic diffusion relationships are examined for the solution-grown crystals, it is immediately observed that the relationship is contiguous with the classical curve for high temperatures during the heating process.The curve is reversible providing the temperature character- istic of the normal “knee” is not too closely approached, but once this tem- perature is exceeded the curve is virtually identical with that obtained for melt- prepared specimens and is no longer reversible. This is illustrated in fig. 1 and the etch pit patterns before and after heating are shown in fig. 2 and 3. From this evidence it seems certain that the low-temperature process is definitely associated with the aggregation of impurities and vacancies at dislocations. 1 Gray and Giess, Int. Con$ High-Temperature Kinetics, M.I.T., 1958.82 GENERAL DISCUSSION An additional point of significance is derived from a detailed infra-red study of the different crystals from which it has been established that the solution-grown crystals contain some two orders of magnitude less hydroxyl ion than do typical melt-grown crystals (Harshaw samples).This is of very great significance in diffusion studies as the majority of investigations have ignored the presence of these ions, as also the lead ions normally present in commercial crystals, being added to develop " optical " quality. Two other important characteristics have been observed during a continuing study of a variety of alkali halides with numerous controlled impurities. No dielectric relaxation phenomena have yet been observed in any soh tion-grown I x-rays FIG. 4.-Apparatus.A, crystal in irradiation position ; A', crystal in measuring position ; B and B', reference slit ; C, photomultiplier tube ; D, interference filters (445-480 mp) ; E, tungsten filament lamp ; F, balanced filters ; G, recorder. crystal until after heating to above the " knee " temperature corresponding to the aggregation of impurities at dislocations. This is in agreement with the work of Breckenridge who found the same to be true for natural halide. The evidence strongly suggests that the relaxation phenomenon is intimately related to aggregated impurities and vacancies in the vicinity of dislocations rather than associated with randomly distributed defect centres. The second observation related to the increase in rate of formation of F-centres observed after heat treatment has occasioned aggregation.The rate of formation of F-centres as measured in equipment described in fig. 4 increase by 30 to 50 %. These characteristics are currently under investiga- tion and preliminary rate expressions have been developed which establish a double exponential function, one portion referring to the formation of F-centres at sites randomly distributed in a homogeneous matrix, while the other applies to the dis- location phenomenon. Typical curves are illustrated in fig. 5-8. ConsiderableFIG. 2. PIG. 3. Photographs of etch pit display on solution-grown sodium chloride crystals before (fig. 2) and after (fig. 3) annealing at a temperature higher than the " knee " temperature. [To fuce page 82.GENERAL DISCUSSION I 83 2Y W r( I X 0, $ I / ,/’/ Y O 10 2 0 3 0 4 0 5 0 6 0 7 0 time FIG. 5.-Artificial halide crystals ; A, pretreated at 700°C ; B, untreated crystal. time FIG. 6.-Manganese-doped NaCl ; A, pretreated at 700°C ; B, untreated crystal.84 GENERAL DISCUSSION additional information is currently being derived from this study of rate pro- cesses. By extrapolation of the curves relating the number of F-centres with time back to zero time and plotting the intercepts thus obtained for a range of b - 5 - 4 - 3 - time FIG. 7.-Magnesium-doped NaCl ; A, pretreated at 700°C ; B, untreated crystal. time FIG. 8.-Sulphate-doped NaCl ; A, pretreated at 700°C ; B, untreated crystal.GENERAL DISCUSSION 85 temperatures, it is possible to derive the activation energy of the process associated with the dislocation phenomenon. The activation energy for the lattice formation of F-centres is derived by classical means varying the energy of the incident X-ray beam. By this approach, it is possible to achieve a relatively complete quanti- tative model for the system. A wide variety of impurities of both anion and cation character are under study at varying concentrations. Provision is made for the application of mechanical stimulus while classical measurements of conductivity, dielectric relaxation and dislocation studies are conducted on each individual specimen in clear, coloured and bleached condition. One practical point worthy of comment is the natural rejection by the crystals during growth of impurities exceeding about 0.01 %. Even from solutions con- taining several percent of the controlled impurity it is rarely possible to introduce more than 0.001 % impurity and the level is frequently considerably less. This is hardly surprising and emphasizes the possibility that even this amount may be associated with the dislocations. It is believed that this evidence precludes the acceptance of any oversimplified theoretical treatment which ignores the complexity introduced by aggregation at dislocations. Full consideration should and actually can be given to this important aspect which in the low temperature region would appear on the basis of evidence to be of paramount importance.* *Grateful acknowledgment is made for the experimental work of P. G. Harrison and R. Pettigrew and for the continuing support of the Air Force Office of Scientific Research (Contract AF 18(600)1448.

ISSN:0366-9033    

DOI:10.1039/DF9592800069

出版商:RSC    

年代:1959

数据来源: RSC