METAL OXIDATION By M. WYN ROBERTS (DEPARTMENT OF CHEMISTRY THE QUEEN’S UNIVERSITY OF BELFAST) IT is not intended to give an exhaustive survey of metal-oxygen reactions but to discuss some properties of the metal and oxide oxygen chemisorption and the metal-oxide and oxide-oxygen interfaces and to show how these considerations are relevant to mechanistic studies of oxidation. There is a trend towards treating surface reactions quantitatively before they are completely understood qualitatively and therefore certain aspects will be considered which at first sight seem to bear little relation to metal oxidation but which must with more detailed studies become important factors in the interpretation of such reactions. The formation of an oxide layer may be tentatively considered to take place as follows Oxygen molecules adsorbed on the metal surface are dissociated and ionised incorporation then occurs in which the oxide is formed with the simultaneous formation of cation or anion vacancies.It is therefore necessary to consider the properties of the metal its ability to chemisorb oxygen the subsequent oxide growth and the properties of that oxide. The standard free energy change for the oxidation of all metals except gold is negative thus a chemisorbed layer should be formed spontaneously on exposing a metal to oxygen even at verylow pressures (e.g. - 10-6mm.). Further oxide growth usually requires an appreciable activation energy so that the chemisorbed layer remains in a metastable state at much higher oxygen pressures. Reaction beyond the monolayer stage or incor- poration is therefore kinetically controlled and will be dependent on the characteristics of a diffusion process viz the diffusion of cations out through the oxide the diffusion of oxygen inwards (possibly a contribu- tion of both) or electron transport.Since diffusion is synonymous with the inherent defective character of the system then it is essential to consider first the existence of defects in metals and oxides. 1. Defects in Metals and Oxides The perfect solid can be regarded as an aggregate of atoms arranged in unbroken lattice array each cell of the lattice having an identical arrange- ment of the chemical constituents so that the internal structure is flawless. Solids do however exhibit a number of imperfections the primary ones being vacant lattice sites interstitial atoms positive holes and dislocations.The ratio of the number of defects to lattice atoms is given by eqn. (l) C = exp [- ( AHf - TdSf)/kT] (1) where AHf is the heat of formation of the defect and OSf is the entropy 71 72 QUARTERLY REVIEWS change associated with the defect. On the assumption that d&/k is of the order of unity and by using theoretical estimates of AHf Broom and Ham1 have derived the concentrations of vacancy vacancy pair and interstitial atom defects in copper at 300" 800" and 1300"~ (Table 1). TABLE 1. AHf Number of defects per lattice atom (kcal. mole-') 3 0 0 " ~ 800"~ 1300"~ Vacancy 22 10-17 loaa2 103.9 vacancyair 35 10-27 10-l0 10-6.2 Interstitial atom 88 1047 10-25 10-15 Thus the vacant lattice site may be present in appreciable concentration in thermodynamic equilibrium in metals since with rapid quenching as is the case during the preparation of metal films the concentration may be as high as 1 in lo4.The most mobile of these defects is the interstitial type; interstitial atoms produced by irradiation may become mobile at tempera- tures as low as 4 0 " ~ the activation energy for movement being about 2 kca1.mo1e-1.2 Single vacancies in copper and gold become mobile only above 240"~ and have an activation energy of - 20 kcal.mole-l. If the vacancies exist as clusters which they may well do with evaporated metal fihs the activation energy for vacancy-cluster movement is much smaller than for single vacancies being about 8 kcal.mole-l for a di-vacancy in copper. A value of approximately 4 kcal.mole-l for the activation energy of the sintering of iron films suggests the participation of vacancy-cluster movement in the sintering proce~s.~ Few crystals have been prepared with a dislocation density of less than lo4 per cm.2.This is probably due to vacancies present at the melting point coalescing and finally collapsing to form dislocations. Etching techniques have enabled individual dislocations to be revealed and have also demonstrated the existence of spiral growths on surfaces. The latter have been reported by Forty4 for the growth of small magnesium crystals from the vapour and also on titanium prepared by fused-salt electrolysis. Measurements of the average step height by the Tolansky multiple-beam interference techniques have a value of about 200 A. The unique properties of dislocations are of considerable significance in oxidation processes.Their r81e as paths for easy diffusion has been emphasised by Hofman and Turnbulls who showed that the rate of silver self-diffusion along sub- boundaries was a million times faster than that of lattice diffusion. The sensitivity of dislocation lines to etching is also evidence of a greater chemical reactivity along such a disarray of atoms. Since atoms associated Broom and Ham Institute of Metals Monograph 1957 No. 23. Seitz Adv. Phys. 1952 1 43. Roberts Trans. Faraday Soc. 1960 56 128. Forty Phil. Mag. 1952 43 949. Hofman and Turnbull Acta Metallurgica 1954 2 419. WYN ROBERTS METAL OXIDATION 73 with steps are less tightly bound to a surface than others then such energy differences would be expected to lead to differences in the tendency for surface atoms to react depending on their geometrical arrangement.The r61e of surface kink sites in the oxidation of metals has been discussed by Vermilyeas especially in relation to possible stresses that develop at the metal-oxide and oxide-gas interfaces. The process of self-diffusion in metals most probably occurs by a vacancy mechanism. This requires normal lattice sites from which the atom is missing to receive atoms from neighbouring sites leaving vacant the site from which the atom jumped. The vacancies may cluster in groups of two or more and therefore remain associated through many unit jumps. Two other mechanisms are possible for self-diffusion ; they involve either rotation of a coplanar group of atoms which form a closed ring (diffusion therefore occurring by rotation of the ring) or an interstitial mechanism the diffusing atoms moving through the interstitial spaces between the atoms occupying normal lattice points.For the rotation mechanism the energy barrier to self-diffusion consists of the energy to squeeze the rotating groups of atoms past the interfering atoms. In the interstitial and vacancy mechanisms the activation energy consists of the energy to form the defect plus the energy to move it from one equilibrium site to another. In oxides the exchange mechanism is less likely owing to the large repulsion energy associated with the interchange of two ions of opposite sign. If the initial oxide layer is amorphous as Eley and Wilkinson7 have suggested for aluminium oxide then electrostatic repulsion will not be an important factor and the exchange mechanism is feasible.Diffusion in oxides is however more likely to occur as a consequence of the existence of Frenkel and Schottky defects; the basic principles of such a mechanism have been developed by Wagner and his co-workers.8 Since the concen- tration of lattice defects is relatively low the laws of ideal dilute solutions can be applied although deviations mainly because of the electrostatic forces between the imperfections can occur. The two main classes of defect oxides are those involving excess of metal (n-type) and metal de- ficiency (p-type). The former include zinc and aluminium oxide in which the excess of metal is located at interstitial positions while in the latter examples of which are nickel oxide cuprous oxide and cobalt oxide there occur cation vacancies.Electrical neutrality is maintained in n- and p-type oxides by quasi-free electrons and positive holes respectively. 2. The Metal and Oxide Surfaces The most serious difficulty in the study of the early stages of oxidation is to define the metal surface. Not only do uncertainties arise from surface Vermilyea General Electric Research Laboratory Report No. 57-RL-1704 1957. Eley and Wilkinson Pvoc. Roy. SOC. 1960 A 254 327. cf. Wagner Z. phys. Chern. 1933 B 21 25. 74 QUARTERLY REVIEWS contamination but also from structural imperfections. A perfect free metal surface i.e. one containing an ideal arrangement of atoms in itself represents a defect since at the surface the continuity of the bulk atoms is absent. Owing to the high chemical activity of the surface atoms oxide is inevitably present unless special techniques have been used in surface preparation.It is only since the advent of ultra-high vacuum methods that the surface contamination factor has been minimised. A number of techniques are now available for the preparation of metal surfaces which are substantially free from presorbed gas. These include the use of flashed metal filaments metal films deposited from the vapour phase and the positive-ion bombardment of filaments. Metal filaments are usually no greater than 1 cm.2 in area and since a monolayer of oxygen could be adsorbed on a metal filament of this area in 100 sec. at a pressure of - mm. is necessary. Metal films are prepared by the thermal evaporation of a well-outgassed metal usually in the form of a filament and subsequent condensation on a cooled substrate.Such films usually have a high surface area to weight ratio and are intrinsically unstable. Atoms present in the surface of a metal will tend to rearrange in such a manner that the total free energy is a minimum. The r6le of the surface energy of solids and the consequent surface mobility of atoms has been particularly well demonstrated by Chalmers King and Shuttleworthg with silver surfaces. When heated to above 500" silver surfaces in the presence of oxygen developed a striated appearance which is attributed to the preferential exposure of (1 11) planes; heating in nitrogen caused the striations to disappear. Because of the instability of silver oxide it was not considered that an oxidation reaction supplied the motivation for the change and it was concluded that in the presence of nitrogen a smooth silver surface of any orientation is thermodynamically more stable than a stepped surface of (111) planes and that with oxygen the situation is reversed.Johnsonlo has shown that tungsten filaments heated electrically in an inert gas develop plane facets normal to the <loo> and <110> directions ; similar facets have been observed with tantalum. The migration of surface atoms has been suggested by Beckerll to occur only at tempera- tures above Tm/3 where Tm is the melting point of the metal in OK. Investigations of reaction rates as a function of crystal orientation indicate that certain crystal planes are more stable than others. Tragert and Robertson12 have used electrochemical techniques in an attempt to define the stable planes of copper.They conclude that the (1 11) plane is the only stable one and that all other planes approach the (1 11) configuration with time the process being considered to involve an etch-type mechanism. mm. a background pressure of < Chalmers King and Shuttleworth Proc. Roy. SOC. 1948 A 193 465. lo Johnson PhjJs. Rev. 1938 54 549. l1 Becker Adv. Catalysis 1955 6 135. l2 Tragert and Robertson Trans. Electrochem. SOC. 1955 102 86. WYN ROBERTS METAL OXIDATION 75 Young Cathcart and Cunningham13 have emphasised the dynamic nature of surfaces especially when used as catalysts. The faces which are stable vary markedly with the reacting gases and the experimental condi- tions the surface rearranging to expose these faces. Thus the nature and structure of a metal surface during reaction may be different from the nature and structure during adsorption although the distinction between adsorption and reaction may be difficult.Interference patterns produced by the oxidation of a copper crystal at 250” show clearly the different crystal regions. Large differences in oxidation rate with crystallographic region have been observed; for example after 50 min. at 178” the thickness of oxide on the (100) plane was 10o0 A while that on the (31 1) face was about 60 A. It is usual to regard the oxide lattice as a rigid immobile structure and this may possibly be correct at low temperature (< O”) but there is now considerable evidence from the use of isotopic and other techniques that at higher temperatures ready transfer of lattice oxygen and chemisorbed oxygen will occur.Winter14 has discussed the experimental evidence for the mobility of lattice oxygen in chemisorption and catalytic studies and there appears to be no doubt that surface oxygen is extremely mobile in oxide catalysts such as manganese dioxide cupric oxide and ferric oxide at temperatures of about 200”. Topographically the oxide surface may vary from being atomically uneven to grossly rough. In the latter instance protrusions a few hundred A in length may be observed. Even the formation of the first few oxide layers may disrupt appreciably the surface contour of the metal substrate and it could conceivably be regarded as a “surface corrosion” process. 3. Oxygen Chemisorption The precursor of oxidation is the chemisorption of oxygen. A detailed discussion will not be given of the mechanism of oxygen chemisorption.It will suffice to consider only the possible final states. If in the adsorbed oxygen a vacant energy level is present which is below the Fermi level of the metal an electron can be transferred from the metal to the oxygen. This is the case when oxygen is chemisorbed with a negative dipole pointing away from the surface. There is no unambiguous evidence for the reverse process i.e. the formation of a positive dipole during oxygen chemisorption. Suhrmann15 has suggested that the change in the resistance of a bismuth film at 77°K during the adsorption of oxygen can be attributed to the formation of Oz+. Such a conclusion may not be correct since if the bismuth film is an intrinsic semiconductor the de- crease in resistance may reflect the formation of positive holes; on the other hand surface contamination could account for the phenomenon.In l3 Young Cathcart and Cunningham Acta Metallurgica 1946,4 145. 14 Winter Adv. Catalysis 1958 10 196. l5 Suhrmann “Chemisorption” ed. Garner Butterworths London 1957. 76 QUARTERLY REVIEWS covalent bonding the chemisorbed layer is stabilised by electron exchange rather than by electrostatic forces. Such bonds would nevertheless be partially ionic as revealed by the presence of a surface dipole layer al- though the latter may only correspond to about 0.5 D. This would suggest that the metal-oxygen bond is predominantly covalent but with a small electron surfeit on the adsorbed oxygen atom. Tompkins16 concludes that transition metals exhibit definite covalent bonding with both hydrogen and carbon monoxide when these gases are adsorbed at -195” whereas with sp metals a predominantly “electrostatic” bond is formed the dipole moment of which is mainly controlled by the first ionisation potential of the adsorbate.Since the oxygen molecule has a positive electron affinity of 2-3 kcal.mole-l it is feasible that 02- ions could be formed. There is neverthe- less much speculation regarding the exact nature of a chemisorbed ion Le, whether it exists as 02- 0- or 02-. On the basis of the properties of zinc oxide surfaces Barry and Stone1’ suggest that at room temperature either 0- or 02- is prevalent but between 100” and 400” the 02- species predominates. Experiments with oxygen isotopes at low temperature strongly suggest that dissociative adsorption occurs on the oxide surface so that 0- is the more likely.The formation of the 02- species at high temperature is in agreement with the conductivity data of von Baumach and Wagner1* and of Bevan and Ander~0n.l~ As a consequence of the surface dipole at the metal-oxygen interface the apparent work function # of the metal is altered. The change in # corresponding to a surface coverage 8 is given by eqn. (2) where o m is the total number of sites available and M is the dipole moment of the adsorbed molecule. The values for the surface potentials of oxygen on metals are all negative; the only system for which there is good agreement between different workers is tungsten-oxygen. In this case values of about -1.8 v have been obtained by various investigators using different techniques and this is particularly strong evidence that the value refers to a “clean” surface.20$21 In general the variations in the surface potential can be ascribed to the use of contaminated surfaces although crystal orientation may also be a contributing factor.The presence of a potential Vat the gas-metal interface implies that a field Fexists such that F = V / X where Xis the adsorbate thickness. With a value of 1 v for V and 3 for X the field approaches 108 v/cm. Such a field would on general grounds l6 Tompkins Diskussionbeitrag Bunsengesellschaft Bad Homburg 1958. l7 Barry and Stone Proc. Roy. SOC. 1960 A 255 124. l8 von Baumach and Wagner Zphys. Cheni. 1933 B 22 199. l9 Bevan and Anderson Discuss. Furuduy Soc. 1950 8. 238. 2o Gomer and Hulm J . Chem. Phys. 1957 27 1363 21 Mignolet Rec.Trav. chim. 1955 74 685. WYN ROBERTS METAL OXIDATION 77 be expected to have a profound influence on the kinetics of the initial oxidation of metals. The formation of a chemisorbed oxide layer is usually difficult to separate and distinguish kinetically from second- or third-layer formation. In general the primary oxide layer is formed at an immeasurably fast rate at temperatures as low as -195" with a high heat of adsorption (> 50 kcal.mole-1). Oxygen chemisorption occurs with all metals; the only possible exception is with gold but Daglish and Eley22 have recently suggested that even with gold some sites possibly gold atoms at disloca- tion sites are active in chemisorption. Lanyon and T r a ~ n e l l ~ ~ measured the extent of oxygen chemisorption by comparing the volume of oxygen adsorp- tion with the uptake of gases such as hydrogen and carbon monoxide.By making assumptions concerning the nature of the chemisorbed gases the extent of the oxygen uptake could be estimated i.e. whether it involved only the formation of the first layer or whether it involved appreciable incorporation. Making use of physical adsorption techniques in conjunc- tion with chemisorption and Brennan Hayward and Trap- nel12j have estimated the extent of oxygen incorporation. The use of physical adsorption as a complementary measurement is of particular significance especially as chemisorbed gases may induce surface sintering. Table 2 summarises the extent of incorporation using various criteria of coverage and the maximum heat of adsorption for a number of metal-oxygen systems the oxygen pressure usually not exceeding 10-1 mm.It had been expected that a correlation between the d-band structure of metals and chemisorption is a means of systematising adsorption pheno- mena. Nitrogen carbon monoxide ethylene and acetylene were considered to require d-band vacancies i.e. covalent linkages are formed between the adsorbed molecule and the partly filled d-band. This fact was considered to be a distinguishing feature since oxygen chemisorption occurred on both transition and non-transition metals. There is now evidence38 that the adsorption of hydrogen atoms occurs on metals in which d-bands do not contribute significantly to the electronic structure namely on copper silver and gold. This seems to invalidate any simple correlation between d-band structure of the metal and adsorption.There may not be any simple relation between band structure and the formation of surface bonds since the mere presence of an interface may considerably alter the electrdnic distribution in its vicinity. That the surface states of metals can sometimes approximate to those of free atoms was suggested by G o ~ d w i n ; ~ ~ this would imply that activity in chemisorption will be more closely related to the properties of atoms rather than to bulk crystals. In fact 22 Daglish and Hey Preprint lliternational Congress Catalysis Paris 1960. 23 Lanyon and Trapnell Proc. Roy. SOC. 1955 A 227 387. 24 Roberts Trans. Faraday SOC. 1961 57 99. 25 Brennan Hayward and Trapnell Proc. Roy. Suc. 1960 A 256 81. 38 Pritchard and Tompkins Trans. Faraday SOC. 1960 56 540. 5 9 Goodwin Proc.Canzb. Phil. SOC. 1939 35 221. 78 Metal A1 Rh Rh Mo Mo Ta Ta Fe Fe Fe Fe Fe Fe Fe Fe Ca Ba Na Si QUARTERLY REVIEWS TABLE 2. Metal-oxygen systems. Temp. of oxidn. ("a 23 * 23 23 - 183 -183 - 183 23 23 23 23 0 - 195 - 183 - 78 - 195 23 35 23 23 Cu (100 face) 23 c u 23 c u 20 c u - 183 Ni 23 Ni 23 Ni 23 c o 25 No. of layers formed 4-5 1.0 1.0 1.5 1.0 1-0 3.0 1.5 5.0 9.0 up to 10 5-10 10.0 6.0 - -50 >200 a0 1.5 4.0 up to 6 6.0 1.0 2.5 4.0 1.0 6-0 Max. heatof adsorption (kcal. mole-l) 210 110 1 70 - - - 220 100 130 - - - 1 20 - - - - - - - - - - 105 120 and 130 150 115 Criteria for coverage b a b b a a b a b b a b b b b b b b a d d b b b b - C Ref. 25 23 25 25 23 23 25 26 25 24 23 27 28 29 24 30 31 30 32 33 23 34 34 25 35 36 37 * The temperature 23" is used for data determined at room temperature if it is not stated precisely.aSurface coverage estimated by use of chemisorption. bSurface coverage estimated by use of physical adsorption. Coverage calculated from the assumption that 4 8 of oxide is equivalent to one oxide layer. dBased on the number of molecules re- quired to form a single layer on a (1 11) copper surface. 26 Bagg and Tompkins Trans. Faraday SOC. 1955 51 1071. 27 Emmett "Structure and Properties of Solid Surfaces," ed. Gomer and Smith 28 Beebe and Stevens J. Amer. Chem. SOC. 1940 62 2134. 29 Kummer and Emmett J. Arner. Chem. SOC. 1951 73 2886. 30 Roberts and Tompkins unpublished data. 31 Bloomer Nature 1957 179 493. 32 Green and Maxwell J. Phys. and Chem. Solids 1960 13 145. 33 Rhodin J. Amer. Chem. SOC. 1951 73 3143. 34 Allen and Mitchell Discuss.Faraduy SOC. 1950 8 309. 35 Beeck Adv. Catalysis 1950 1 150. 36 Klemperer and Stone Proc. Roy. Soc. 1957 A 243 375. 37 Rudham and Stone Trans. Faraduy Soc. 1958 54 420. University of Chicago Press 1953. WYN ROBERTS METAL OXIDATION 79 Pickup and Trapnel140 have correlated the apparent inactivity of mercury and gold in oxygen chemisorption with the high ionisation potentials of the atoms rather than with the work function of the crystals. Some correlation does exist between the number of electronic states near the Fermi level and the susceptibility to oxygen chemisorption of the metalloid elements arsenic antimony bismuth selenium and tellurium. Apker Taft and Dickey41 have derived the following order of electron densities Bi>Sb>As>Se>Te. This sequence agrees with the observed order of activity in oxygen chemisorption.Such a correlation is compatible with the fact that for oxygen to be adsorbed as negative ions a large electron con- centration in the higher occupied states is probably necessary. It is never- theless a very tentative correlation since the activity of the metals was not strictly defined. Subsequent to the formation of the first oxide layer oxygen interaction will occur with a surface oxide. Although there is evidence for the occur- rence of 0- and 02- species on an oxide surface the use of such symbols to describe the surface species is undoubtedly an over simplification since the interaction of a gas with an adsorbate will rarely result in complete electron transfer. Grimley and T r a ~ n e l l ~ ~ have suggested that neutral pairs may exist on the oxide surface.These could arise from the attraction of positive holes eu and adsorbed oxygen ions their formation taking place as shown by eqn. (3) where 0- e n is the neutral pair and (US) is +02 + (US) + 0- eO (3) a possible site for adsorption on the oxide surface. 4. Oxygen Incorporation It is convenient to discuss the mechanism of oxygen incorporation in terms of the possible rate-controlling processes. Subsequent to the chemi- sorption of oxygen and by this is meant the fast initial oxygen uptake at low temperature and which may therefore include multilayer formation further oxide growth will only occur as a result of the movement of cations outwards through the oxide oxygen inwards or possibly a contribution from both processes.Electrochemical and diffusion experiments with oxides sulphides or halides have shown that in these phases cations anions and electrons are mobile but their mobilities may differ widely. It would be expected that in general owing to the smaller ionic radii of cations cation diffusion would be energetically more favourable than anion diffusion. Complications arising from the breakdown of a compact oxide lattice may however enable direct access of oxygen to the metal covered by a relatively thin oxide layer 100 8 thick. On the other hand it is possible 4 0 Pickup and Trapnell J. Chem. Phts. 1956 25 182. 41 Apker Taft and Dickey Phys. Rev. 1949 76 270. 4 2 Grimley and Trapnell Proc. Roy. SOC. 1956 A 234 405. 80 QUARTERLY REVIEWS that the flow of electrons through the oxide to the oxide-gas interface is the rate-controlling process.(a) The metal-oxide interface. Cabrera and M ~ t t ~ ~ suggested that the initial energy barrier to be surmounted by a cation entering the oxide lattice was greater than any subsequent barrier so that cation entry is rate-controlling during the formation of thin oxide films. The situation at the metal-oxide interface may be represented as in Fig. 1 which shows the change in potential energy of a cation as it leaves the metal enters the oxide and then diffuses through the oxide. The rate of oxidation at temperature T would therefore be expected to be given in the form of eqn. (4) where Xis the oxide thickness at time t E the activation energy - _ - c exp(-E/RT) dX dt (4) and c a constant. According to the theory of E ~ r i n g ~ ~ the rate of reaction is given by eqn.(9 r = (kT/h) exp( AS*/R). exp(- AH*/RT) (5) where AS* is the entropy of activation AH* the heat of activation and the other terms have their usual significance. Since the difference between the activation energy and the heat of activation is insignificant then the general expression for the activation energy of an oxidation process the rate of which is controlled by the barrier to cationic movement at the metal-oxide interface is given by eqn. (6) where W is the entry barrier E = AH* = W - AH + c‘ - qa‘FN (6) (Fig. l) AHis the heat of oxygen chemisorption c’ is the heat of formation of an anion vacancy (the site for oxygen chemisorption) the lowering of the energy barrier W by the superimposed I X I I I * I I M e t a l ! O x i d e I Oxygen I I I I I and qa‘FN is field F arising FIG.1. The potential energy of a cation on moving from a metal into the oxide. from the surface potential of the adsorbed oxygen. a’ is the jump distance for the cation N is Avogadro’s number and q is the charge on the cation. There are very few data relating to the heat of oxygen chemisorption on 43 Cabrera and Mott Reports Progr. Phys. 1948 12 163. 44 Glasstone Laidler and Eyring “The Theory of Rate Processes,” McGraw Hill New York 1941. WYN ROBERTS METAL OXIDATION 81 oxides i.e. the value of AH beyond the monolayer. In for example the oxidation of nickel oxide the slow incorporation process occurs with a heat of about 25 k ~ a l . m o l e - ~ . ~ ~ ~ ~ ~ Since the value of c’ is about 1 ev then AH - c’ beyond the monolayer and therefore E = AH* = W - qa’FN.And so eqn. (4) leads to eqn. (7). Cabrera and Mott suggested that (W - qa’FN) RT = c exp __- d X dt - (7) the constant c be given by N’Qv where N’ is the number of special sites from which a cation may enter the oxide (i-e. position S of Fig. l) Q is the volume of oxide per cation and v is the frequency of vibration of the cations in the lattice. The field 4; may be replaced by V / X where V is the surface potential of the chemisorbed oxygen on the oxide and X i s the oxide thickness. The variation of the term qa’ VN/X with oxide thickness X assuming q = 3e a’ = 2.5 A and V = 2 v is shown in Fig. 2. Thus up to an oxide thickness of approximately 30-40 A the presence of the superimposed field is likely to have a very marked influence on the ob- served kinetics.The only known attempt to detect any influence of an external field on oxidation behaviour is that of Uhlig and B~enner.*~ An electric field of 15,500 v cm.? was applied across a copper surface covered by approximately 700 A in an oxygen environment. No noticeable effect on the oxidation rate was observed which is in agreement with considera- tions similar to those of Fig. 2 the lowering of the energy barrier for cation entry being about 1 kcal.mole-I. Such a field would also be insufficient to create defects in the oxide; its r61e would therefore be merely to direct the random movement of ions already taking place in the absence of the field. 2 30 4 .& 2o 10 FIG. 2. The ‘tfield eflect” as a function of oxide thickness. The following would now appear to be relevant to the formation of thin oxide films on metals (i) The structural characteristics of the metal surface since N’ is related to surface defects.(ii) The surface potential V of the chemisorbed gas since this controls the field F ; the larger the surface potential the more extensive should be the incorporation. In the theory of 45 Uhlig and Brenner Actu Metallurgica 1955 3 108. 82 QUARTERLY REVIEWS Cabrera and Mott V is assumed to be independent of both temperature and pressure. (iii) Since W = U + H where U is the activation energy for cation diffusion through the oxide and H i s the heat of solution of the cation in the oxide then the value of W will be least for a metal-oxide system where both the heat of solution and the energy for cation diffusion are a minimum. Thus an open type oxide structure involving a cation of small ionic radius should result in a minimum of the activation energy.(iv) Electrons are able to establish an equilibrium between metal and adsorbed oxygen on the oxide in a time small with respect to that re- quired for a cation to diffuse through the oxide. That the above considerations are applicable to the initial interaction of gases with metals has been shown by a number of investigators. Bloomer,J6 studying the oxidation of barium films at pressures of about mm. showed that the initial reaction was an acceleratory one which suggests that a nucleation process was occurring which involved specific sites on the barrier surface. Above 35" oxidation continued until the metal had completely oxidised but below this critical temperature the oxide thickness approached a limiting value.Such a critical temperature is understandable since on rearranging equation (7) and substituting F = V/XL eqn. (8) is 1 W(1 - at) _ - - XL Va'qN obtained where 01 = -(R/W) In [(dXL/dt)(l/vL?n")] and dXL/dt is the experimentally defined limiting rate. Therefore when the temperature is l/a the limiting oxide thickness XL is infinite. Critical temperatures of approximately 160" and 400" have been estimated for the nitridation of calcium47 and the oxidation of iron films24 respectively. Since the field is given by F = 4vne/K where n is the number of adsorbed species per unit area e is the electronic charge and K is the dielectric constant of the oxide it would be expected that the contact potential V is a function of the oxide thickness. The assumption of Cabrera and Mott that V is constant during oxide growth implies that n varies inversely as the oxide thickness X.Since n is in general temperature-dependent then V should vary with temperature. A recent approach to gas-metal intera~tion~~ considers the electric field to be confined to narrow tubes these tubes being associated with field-creating species. Thus although the number of tubes n is temperature dependent n cc exp(- AHIRT) where AH is the heat of formation of a field-creating species; the field across any one tube is temperature independent and varies only as the inverse of the oxide thickness. The anodic oxidation experiments of Vermilyea show that with tantalum the oxide grows at the electrolyte- oxide interface. This means that the mobile entities are cations which was a priori most likely owing to the difference between the ionic radii of 46 Bloomer Nature 1957 179 173.47 Roberts and Tompkins Proc. Roy. SOC. 1959 A 251 369. WYN ROBERTS METAL OXIDATION 83 Ta5+ and 02-. The mechanism of cation transport has been recently investigated by Verkerk Wenkel and de G r ~ o t * ~ and they concluded that the mechanism was neither pure vacancy nor pure interstitial. A process termed “place exchange” was suggested by Lanyon and TrapnellZ3 to account for the initial oxidation of metals. The adsorbed oxygen is considered to change places with an underlying metal atom and this process is subsequently repeated further oxide layers being formed. Similarly it has been suggested that the initial oxidation of germanium49 occurs by a “switching” process; this is illustrated in Fig.3. 0 FIG. 3. Place-exchange mechanism. The motivation of the exchange was considered to be derived from the liberated heat of adsorption. Both nickel films and reduced nickel powder exhibit surface regeneration after oxygen chemisorption when kept in vacuo (< mm.) at room t e m p e r a t ~ r e ; ~ ~ ~ ~ ~ 1 ~ ~ whatever the detailed mechanism of the regeneration process it must involve the re-creation of surface cations. Similarly Law,53 and Eley and Wilkin~on~~ observed regeneration during the oxidation of silicon and aluminium respectively. It therefore seems unlikely that surface regeneration requires that heat be liberated during chemisorption. In the initial oxidation of aluminium place-exchange is thought only to apply during the formation of the first 6 A of oxide after which recrystallisation of the initially amorphous oxide results in a change-over of the rate-controlling process to electron transport.A recent in~estigation~~ of the amorphous oxide present on aluminium foil has shown that crystallisation is not observable with the electron microscope until a temperature of about 500” is attained. The process of place-exchange was probably first recognised by de who used photoelectric sensitivity techniques. When oxygen reacts with casium the czsium oxide becomes “buried” in the metal and the mobility of the czesium atoms is so high that the photoelectric sensitivity remains essentially unaltered until almost all the caesium is converted into oxide. This would 48 Verkerk Wenkel and de Groot Philips Res. Repts.1958 13 506. 49 Green Progr. in Semiconductors 1959 4 37. j0 Roberts and Sykes unpublished data. 61 Oda Bull. Chem. Soc. Japan 1954 27 465. 52 Anderson and Klemperer Nature 1959 183 899. j3 Law J . Phys. and Chem. Solids 1958 4 91. 64 Eley and Wilkinson Proc. Roy. Soc. 1960 A 254 327. j5 Thomas and Roberts J . Appl. Phys. accepted for publication. 56 De Boer “Electron Emission and Adsorption Phenomena,” Cambridge New York 1935. 84 QUARTERLY REVIEWS indicate that either a layer of czesium atoms remains on the oxide surface even after extensive oxidation had occurred or that the czesium surface was initially oxide and the photoelectric measurements thus referred to an oxide layer rather than to the metal. Although place-exchange suggests a process quite distinct from cation- diffusion controlled by a superimposed field the two are at least pheno- menologically identical.The place-exchange mechanism has been suggested to involve an activation energy Eexp. that increases linearly with oxide thickness X so that eqn. (9) holds. This equation clearly has only sig- nificance for small values of X . Oxidation controlled by cation diffusion in the presence of a superimposed field implies a limiting value for the activation energy since eqn. (10) is obtained from equation (7). A E = W - (qa‘VN/X) (10) distinction between two mechanisms the activation energies of which vary according to equations (9) and (lo) is not easy since the term qa‘VN/X decreases almost linearly with X . Now the kinetic equations which follow from equations (9) and (10) are (11) and (12) respectively x K log t and 1/X cc log t X being the oxide thickness at time t Over restricted ranges of oxide thicknesses both equations (1 1) and (12) may be found to describe the results equally well and a distinction is only possible if constants derived from them are shown to have a reasonable physical significance.(b) Electron transport and the logarithmic law. Electron availability and transport is an essential prerequisite for the occurrence of oxidation. According to wave mechanics a small proportion of the electrons which are incident on a potential barrier will penetrate it. This phenomenon called “the tunnel effect” is responsible for the flow of electrons between two metals the surfaces of which are inevitably covered by oxide. Up to an oxide thickness of 30 8 or so electrons are therefore considered to move through the oxide from the metal by a tunnelling process and it was Mott5’ who first suggested that the slow step in oxidation was electron transport to the oxide-gas interface by this mechanism.He later abandoned this concept for control by ionic transport. More recently Hauffe and I l ~ c h n e r ~ ~ have revived the electron transport rate-controlling process to explain the results of Scheuble for the oxidation of nickel. It is relevant to consider the possible mechanisms by which electrons may be made available. 57 Mott J . Inst. Metals 1939 65 333. 58 Hauffe and Ilschner 2. Elektrochem. 1954 58 382. WYN ROBERTS METAL OXIDATION 85 Subsequent to the formation of the initial oxide layer the energy re- quired to remove an electron from the metal is no longer related to the work function of the clean metal.The system is now a composite one involving a metal-semiconductor interface with the possibility of oxygen adsorbed on the semiconducting oxide surface resulting in electron acceptor levels being made available. The potential-energy diagrams shown in Figs. 4 5 and 6 may therefore be considered to represent the conditions for a FIG. 4. Clean metal in a vacuum. FIG. 5. “Clean” metal and chemisorbed oxygen. CONDUCT1 ON BAND ~-IFER%~;~~EL OF M E T A L ADSORBED OXYGEN LEVEL t VALENCE BAND N - O X I D E FIG. 6. Possible non-eqdlibriim electron energy levels in a metal-oxide-oxygen system. “clean” metal a “clean” metal on which oxygen has been chemisorbed and a metal in contact with oxide on which oxygen is chemisorbed.In the case of metal + chemisorbed oxygen electrons may penetrate the potential barrier #+ the work function of the metal by the tunnelling mechanism 0- ions being formed on the surface. If chemisorption and subsequent incorporation result in the formation of an n-type oxide of low work function electron transfer may occur from the oxide to the metal and if a simultaneous movement of cations in the opposite direction does not occur a space charge normally called the Schottky depletion layer is formed. Fig. 6 illustrates a possible non-equilibrium state Fig. 7 the equilibrium attained between oxide and metal and Fig. 8 the equilibrium between oxide metal and chemisorbed oxygen. The depth of the space- charge layer is related to the density of the donor states in the oxide by 86 QUARTERLY REVIEWS eqn.(13) where xo is the depth of the Schottky barrier E is the dielectric constant of the oxide e is the electronic charge and A+ is the height of Ad the barrier. In the case of a low density of donor states say 1015 per ~ r n . ~ then with E = 10 and A$ = 1 ev the space charge region is approximately lo-* cm. deep whereas for a site density of 1019 per ~111.~ the depth is only cm. Equilibrium is established when the Fermi levels in the metal and the oxide are the same. OXYGEN LEVEL N OXIDE I FIG. 7. Electron transfer from oxide to metal resulting in an energy barrier to further transfer and a space-charge layer of depth x,,. O X I D E FIG. 8. Electronic equilibrium established between metal oxide and adsorbed oxygen. Oxygen chemisorbed on an oxide surface generally results in electron levels being made available which are much lower than the conduction band of the oxide (Fig.6). At equilibrium the highest filled oxygen level will be at the height of the Fermi level in the semiconductoi (Fig. 8). If the semiconductor is an intrinsic semiconductor the effect of the positive space-charge could result in the filled band's being raised sufficiently to donate electrons to the adsorbed oxygen thus creating holes in the filled band. The latter process could continue until the top of the filled band is at the same height as the Fermi level so that the height of the barrier is restricted to Q (Fig. 8) the difference in energy between the conduction and filled bands. Oxygen-ion formation is therefore possible either by electron tunnelling from the metal into the conduction band of the oxide provided the width of the energy barrier is not prohibitive or in special circumstances from the filled band of the oxide.WYN ROBERTS METAL OXIDATION 87 Garner Gray and Stone59 have suggested that with an oxide capable of exhibiting variable valency bonding of oxygen to surface cations may take place with an attendant valency change e.g. 2Cu+ + QO + 2Cu2+ + 02-. That shallow electron-emitting centres do exist on metal surfaces un- doubtedly covered by an oxide layer is borne out by the ability of certain metals to initiate free-radical reactions at room temperature. This pheno- menon termed exoelectron emission,60 is thought to account for the forma- tion of hydrogen peroxide from water in the presence of abraded metal and illustrates the capacity of “freshly prepared” surfaces to act as an electron source.The boundary layer theory of chemisorption which is based on the presence of a surface barrier to electron transport has been applied by HauffeG1 to derive the kinetics of the uptake of oxygen by oxides. Since oxygen chemisorption increases the work function of the adsorbent the rate of oxygen chemisorption by the oxide surface is given by eqn. (14) where Xis the concentration of surface atoms at time t po is the height of the energy barrier at the beginning of chemisorption (Le. X = 0) A$ is the change of the work function of the surface as a consequence of adsorption e is the electronic charge T is the temperature and k is the Boltzmann constant. By expressing A$ in terms of the concentration of chemisorbed oxygen the concentration of holes in the oxide and the potential difference between the interior of the oxide and the surface Hauffe derived the logarithmic eqn.(15) where b = 47rea/~ E is the dielectric constant of the oxide and a is the distance between the surface of the oxide and the centres of charge of the chemisorbed atoms. Engel and Hauffe62 find that eqn. (15) is valid for the first 10 min. of the oxidation of nickel oxide at 25” after which there is a marked deviation. This logarithmic expression sometimes referred to as the Elovich or Roginski- Zeldovitch equation has been shown to be applicable to a large number of systems involving an activated process. Taylor and ThorP3 suggested that the prime function of the adsorbed gas is to create sites which over the course of the activated process decay at a bimolecular rate.A similar equation has been derived by Porter and TompkinsG4 and by Jennings and jg Garner Gray and Stone Proc. Roy. SOC. 1949 A 197 294. 6 o Grunberg Proc. Pliys. SOC. 1953 66 153. 61 Hauffe Adv. Catalysis 1955 7 213. 62 Engel and Hauffe quoted in ref. 61. 63 Taylor and Thon J . Amer. Chem. SOC. 1952 74 4169. 64 Porter and Tompkins Proc. Roy. SOC. 1953 A 217 529. 88 QUARTERLY REVIEWS Stone65 who assumed a linear increase in activation energy with surface coverage. More recently Gundry and TompkinP have invoked the presence of an intermediate chemisorbed state which must be passed through before the adsorbed molecule attains its final equilibrium state. The initial bonding to the surface is thought to involve d-orbitals only; this then transforms to a stronger hybridised dsp final state.So long as the free energy of adsorption decreases linearly with coverage the Elovich equation can be deduced. The changing hybridisation of surface bonds may play an important r81e in many slow oxidation phenomena. The Elovich type equation is however so frequently obeyed by gas- solid reactions that to invoke a particular mechanistic model merely on the basis of linearity of plots is not a satisfactory criterion of validity. There is also the difficulty of obtaining a unique value for the constant to. Landsberg6' has suggested that the ubiquitous nature of the logarithmic equation in chemisorption reflects the same basic mechanism. He derived the equation (16) where t o = l/mNapS, m is a constant 18 is the efkctive area over which the sites become invalidated by the adsorption of a single molecule N is the number of impacts of the gas molecules with the surface per unit area per unit time a is the effective contact area between a mole- cule and the surface and So is the number of sites per unit area at the commencement of the reaction.This is a denial of the Langmuir hypo- thesis that the total number of adsorption sites is constant. to would be expected to be inversely dependent on pressure. Another interpretation of the logarithmic equation is that due to Uhlig68 who considers electron flow to be controlled by a space-charge. The space-charge is envisaged as being composed of two parts (1) a uniform charge-density layer next to the metal and (2) a diffuse-charge layer beyond the uniform layer the latter arising from the presence of electrons trapped at lattice imperfections within the oxide.5. Dependence of Oxygen Uptake on Pressure The process of metal oxidation may be considered as three concurrently operating processes adsorption desorption and incorporation. The rates of these processes can be expressed by the following equations Vads. = klcxacs (17) where a is the pressure dependence of the adsorption process cs is the number of bare sites per cm.2 and k = (W,/h) (f*/fc,"fe> exp( -E,/RT) 65 Jennings and Stone Adv. Catalysis 1957 9 441. 66 Gundry and Tompkins Trans. Faruduy Sac. 1956 52 1609. 67 Landsberg J. Chem. Phys. 1955,23 1079. 68 Uhlig Actu Met. 1956 4 541. WYN ROBERTS METAL OXIDATION 89 where c is the gas phase concentration and E the activation energy for adsorption.Vdes. == k2Ca (18) where k2= (kT/h) (f+Ka) exp( -E,/RT) Ca is the concentration of adsorbed species and E the activation energy for desorption; Vim. = kinc.ca (19) where kine. is the rate constant of the incorporation process. A steady state will be established in the adsorbed layer so that lilcxacs - k2ca - ki,,.ca = 0 (20) Since c6 + Ca = N the total number of surface sites then Thus the rate of gas uptake V is given by V = Vads. - I/dea. = klcxacs - k2cs = nTklkinc.Cra/klCxa + k2 + kine. If kine. 9 k2 + klcXa then V = NklcXa which means that the rate-deter- mining step is that of adsorption. However if k,cXaBk2 + kine. then Y = khc.N and incorporation is rate controlling. On this basis alone we would expect the slow step to be adsorption at low pressures and in- corporation at high pressures.The influence of phase-boundary equilibria the nature of the adsorbed layer etc. complicate these conclusions and are discussed further. Wagner first directed attention to the pressure-dependence of the chemical composition of the oxide and according to von Baunach and Wagner18 interstitial zinc ions are formed in zinc oxide according to the equation (21) Zn2+ + 02- + Zni2+ + 2e + +O,(g) (21) where Zni2f represents an interstitial ion formed from a lattice ion Zn2+. It being assumed that the defects are in dilute solution and do not interact the equilibrium constant for the formation of interstitial ions is [Zni2+] [e-I2 p o .+ [Zn2+] [02-] K = Within the range of composition possible for the zinc oxide phase [Zn2+] and [02-] do not change appreciably so the equation can be put in the form Kl = [Zni2+] [e-]po2+ 90 QUARTERLY REVIEWS Since electrical neutrality requires that [Zni2+] = +[e-] the change in the concentration of interstitial zinc ions with oxygen pressure should be given by [Zni2+ J = (K,/4)5 po2-i Thus if incorporation proceeds by the diffusion of Zni2+ the expected pressure dependence is - 116.GrimleyGg and Grimley and T r a ~ n e l l ~ ~ have derived growth laws for oxide films by considering the equilibria that may be set up at the metal- oxide and oxide-gas interface. n- and p-type oxides with rates controlled either by cation transport or by surface reactions have been examined for two general cases (a) Surface saturated by field-creating ions. The dependence of the deiived rate laws on pressure is particularly significant.Linear laws are derived for p-type oxides when surface reaction is rate- determining similarly for an n-type oxide when the transport of interstitial cations is rate-determining. A logarithmic equation with a pressure de- pendence of 0.25 is predicted for a p-type oxide when movement of cation vacancies is rate-controlling. (b) Neutral pairs in the adsorbed layer. An equilibrium is considered to exist between neutral pairs and field-creating ions. Neutral pairs are considered to arise from the attraction of positive holes and adsorbed oxygen ions their formation taking place as follows where 0- e n is the neutral pair and (0s) is a possible site for adsorption on the oxide surface. The neutral pair may subsequently dissociate to form field-creating species,O-/ads.The position of equilibrium in the above equation is important since although the oxide surface may be apparently saturated not all the species need be of the field-creating kind. The derived pressure dependences are shown to be a function of the nature of the adsorbed species; values of -0-75 0.25 and 0 are calculated for a system where the surface species are assumed to be 02- 0- and 02- respectively. With n-type oxides the growth law is insensitive to the nature of the surface layer. thick) has been suggested to be controlled in certain cases by electron transport;58 if tunnelling is the mechanism then the oxygen uptake should be independent of pressure. If tunnelling is not feasibke and the electrons have to surmount an energy barrier E the rate of electron transport is of the form Rate cx exp(-E/RT) where E is related to the space charge at the surface.Since the space charge is a function of the concentration of adsorbed species for an unsaturated The Formation of thin oxide layers (< 50 6 9 Grimley “Chemistry of the Solid State,” ed. Garner Butterworths London 1957 336. WYN ROBERTS METAL OXIDATION 91 adsorbed layer the rate of electron tiansport will be some function of the oxygen pressure although the exact form of the pressure dependence may be difficult to predict. If the concentration q of adsorbed species is related to the pressure by q cc p n and the rate of electron trans- port is some linear function of q then the value of rz also gives the dependence of oxygen rate on pressure. Similarly in rate control by cationic diffusion in the presence of a superimposed field F the magnitude of which is a linear function of the concentration of chemi- sorbed species the oxidation rate will be related to pressure.If a saturated adsorbed layer is formed the rate will be pressure independent but if an equilibrium is set up between oxygen molecules at a pressure p and oxygen atoms the surface concentration of atoms and similarly the rate will be proportional to poe5. Table 3 gives values of n for a number of TABLE 3. Gas-metal systems. Metal Gas Temp. dependence Ref. Pressure Ca Fe Fe Fe A1 c u Mg Si U ("a 23 - 80 22 to 95 0 20 0 23 25 180 (4 1.0 0 0.28 0.2 0.6 0.75 0.8 0.52 0.15 47 24 24 23 7 23 70 71 72 gas-metal systems. There is the general difficulty of formulating a mechan- ism for a gas-metal reaction which is compatible with the dependence of rate on pressure.Eley and Wilkin~on,~ for example suggested that in the oxidation of aluminium the value 0-6 is evidence for a dilute ideal film of oxygen atoms but that owing to interaction within the monolayer there is a small increase in the value of rz over that predicted theoretically. At -80" the oxidation of iron films is independent of pressure and this has been ascribed to a saturated surface layer of some kind; in the tem- perature range 0-100" the mean values of 0.2 and 0.28 are compatible with a surface equilibrium involving species which influence cationic diffusion. 6. Nucleation and Anisotropic Oxidation The realisation that nucleation is an important factor in oxide formation stems from the work of B~5nard~~ and his collaborators.As a consequence of the microtopology of metal surfaces it would be expected that pre- 70 Sack Diskussionbeitrag Bunsengesellschaft Bad Homburg 1958. 71 Law J. Phys. and Chem. Solids 1958 4 91. 72 Anderson and Roberts J. Chem. SOC. 1955 3946. 73 Bardolle and BCnard Rev. met. 1952 49 613. 92 QUARTERLY REVIEWS ferential reaction sites exist on the surface resulting in the initiation of oxide growth at isolated points on the surface. The number of nuclei formed will depend on the activation energy for surface nucleation which may vary over the metal surface; whether nucleation is initiated as a two- dimensional monolayer or whether three-dimensional nuclei are formed is not known. Bloomer74 suggested that since the initial oxidation of barium appeared to start from a fixed number of nuclei the rate of oxygen uptake up to the commencement of the second layer would be expressed by eqn.(22) where Xis the volume of oxygen adsorbed at time t k is a constant dX/dt = ktn* (22) and n* is a non-dimensional parameter. The value of n* is considered to reflect the geometry of the nucleus and its mode of growth. For flat circular nuclei n* has the value 0-5 whereas if the oxide grows into hemi- spherical caps i.e. a second-layer process commences before the comple- tion of the monolayer a value of 0.66 would be expected. Sack70 has reported values between 0.2 and 0.7 for the oxidation of magnesium at 27" and Roberts and Tompkins4' a value of 0.19 for the nitridation of calcium films at 23". Although a small value of n* implies a large con- centration of nucleating centres it is difficult to give n* an exact physical meaning.The orientation of alien crystals by an anisotropic substrate surface termed epitaxy is important in relation to the occurrence of anisotropic oxidation and the possibility of stresses that arise in oxide films sub- sequently leading to cracking. van der M e r ~ e ' ~ developed a theory of epitaxy that involved as a necessary prerequisite the formation of a pseudomorphic layer. According to this theory such an oriented layer will occur provided the misfit is not greater than about 14%; it also predicts increasing instability of strained layers with increasing thickness. Rhodin explains the anisotropic behaviour of thin oxide layers on copper in terms of the van der M e r ~ e ~ ~ model of epitaxial growth. Oxidation is undoubtedly dependent on the crystallographic plane being oxidised.R h ~ d i n ~ ~ Gwathmey and B e n t ~ n ~ ~ and Lustman and Mehl" showed that of the most commonly occurring planes in a copper surface the (1 10) is the most readily oxidised and the (1 11) plane the least. Young Cathcart and G~athrney'~ found that at 150" the rate of oxidation of the (100) plane is four times that of the (311) although the limiting oxide thickness on the former is ten times that on the latter. Bhard and T a l b ~ t ' ~ observed at 900" that the oxidation rates for different planes of copper decreased in the following order (210~ (211) (110) ( l l l ) (loo) (123). 74 Bloomer Brit. J . App. Phys. 1957 8 321. 75 van der Merwe Discuss. Faraday SOC. 1949 5 208. 76 Gwathmey and Benton J. Phys.Chem. 1941 46 969. i i Lustman and Mehl Trans. Amer. Inst. Mining Met. Engrs. 1941 143 1. Young Cathcart and Gwathmey Acta Metallurgica 1946 4 145. BCnard and Talbot Compt. rend. 1948 225 41 1. WYN ROBERTS METAL OXIDATION 93 Such a sequence was similarly reported earlier by Gwathmey and Benton at 1OOO". The difference in behaviour at low and high temperatures suggests that different mechanisms are operating. The concept of metal atoms entering the oxide lattice only at kink sites possibly accounts for the anisotropic behaviour; a surface with a large number would be expected to oxidise faster than one with fewer. This is implicit in the theory of Cabrera and Mott. Anisotropic behaviour may in some cases be complicated by the crystallisation of an initially amorphous layer or of recrystallisa- iion.Such processes have recently been observed with copper at 150". Crystallisation of an amorphous film could result in the oxide's becoming less protective since movement can occur more easily along grain bound- aries chan within grains. Gulbransen and Coplanso have used electron optical techniques to investigate the possible influence of disloca tions defects and internal stress on the chemical reactivity of the metal surface. Thin oxide whiskers 100-150 A in diameter occur when pure iron reacts with oxygen at 400"; these whiskers may grow to a length of lo5 A. With water vapour at 400" oxide platelets are formed. These observations together with those of Pfefferkorn,81 strongly suggest a growth mechanism in which the metal structure itself determines the progress of growth the growth of a whisker taking place only at the tip where one or more screw dislocations emerge.Bknard Grarnlund Oudar and Durets2 have studied the formation of oxide and sulphide nuclei on copper. A rather surprising feature is the constant rate of formation of nuclei at 550" and an oxygen pressure of 6 x mm. With aluminium Roberts and Thomass3 have observed the formation of nuclei at temperatures around 550" the geometrical form of the nuclei being dependent on the pressure conditions. At a pressure less than mm. needle-shaped nuclei appear and at atmospheric pressure an oxide layer composed of contiguous crystals of diameter - 0-2 p are formed. Recrystallisation of the initial amorphous film is suggested since electron diffraction shows that crystalline aluminium oxide of lattice parameter 7.9 A is formed.7. Thick Oxide Films Although the general practice of discussing oxidation regions in terms of kinetic laws is an ambiguous one the parabolic growth law is correctly associated with oxidation occurring in the presence of a thick oxide layer usually 1000 A or more deep. The oxide layer must be coherent and yore- free and above about 300" the kinetics should conform to eqn. (23) dx/dt = k1/x (23) Gulbransen and Coplan Discuss. Faraday Soc. 1960 28 229. Pfefferkorn Naturwiss. 1953 40 551. 82 Benard Grmlund Oudar and Duret Diskussionbeitrag Bunsengesellschaft 83 Thomas and Roberts J. Appl. Phys. accepted for publication. Bad Homburg 1958. 94 QUARTERLY REVIEWS where x is the oxide thickness at time t and kl is a constant. If x = x, at t = 0 then This is probably the best way to express the law as it enables the initial uptake to be discarded since the origin of time may be set at any desired oxide thickness.Thus a plot of t/x against x gives a straight line of slope 2k1. It may well be that the value of y o from the intercept has little quantitative significance in view of uncertainties regarding non-isothermal conditions and departures from parabolic behaviour at small times. Wagner suggested that diffusion in oxide (or sulphide) phases may in general be interpreted as migration processes of ions and electrons whereas the migration of electrically neutral atoms or molecules can be neglected. There are therefore two limiting cases which are illustrated in Fig. 9 (1) Positively charged cations and electrons may migrate in the same direction from the metal-oxide interface to the outer surface.(2) Negatively charged anions migrate inwards and electron movement oc- curs in the opposite direction. x - XO = x = 2kl(t/x) - 2x0 C A T I O N ELECTRON P (1) ______L (2) ANION ELECTRON - FIG. 9. Diflusion in oxide phases. Wagner applied the model of a compact oxide layer with lattice defects to the derivation of the parabolic rate law assuming that cation diffusion within the oxide is rate controlling so that a concentration gradient exists between the metal-oxide and oxide-oxygen interfaces. The concentration of defects is generally so low that analytical procedures are of little value. Engel,s4 using an electrochemical method has succeeded in measuring the defect variation in an iron(@ oxide layer.He has shown a linear increase of defect concentration from the metal-oxide to the oxide-gas interface. It is significant that the defect concentration at the metal interface was not in fact 0 but at 900" amounted to 6%. Such a gradient of defect concen- tration apparently exists only when the iron(I1) oxide layer is in intimate contact with the metal phase; poor adhesion results in equilibrium being established with the Fe,O phase which leads to a constant defect con- centration in these positions of the iron@) oxide layer. If transport processes (electron cation or anion movement) within the oxide are more rapid than any of the possible phase boundary equilibria 84 Engel 2. Elektrochem. 1959 63 835. WYN ROBERTS METAL OXIDATION 95 non-equilibrium conditions then exist at the interface.The oxidation of iron under different conditions demonstrates clearly the influence of phase- boundary conditions. In oxygen at high temperature a number of oxide phases are formed and the parabolic law is obeyed; in carbon monoxide- carbon dioxide mixtures above 900" a linear rate law with only iron(I1) oxide occurs while in a hydrogen-water environment above 950" para- bolic dependence with iron@) oxide formation takes place. Evidently the high defect concentration in iron(1r) oxide ensures a high diffusion velocity compared with the surface equilibria existing in a carbon monoxide- carbon dioxide environment whereas in a water-hydrogen atmosphere the surface equilibrium proceeds sufficiently rapidly so that the diffusion of cations through the iron(I1) oxide layer represents the slower process.That diffusion through an oxide film was not solely responsible for the oxidation rate was first emphasised by Evans85 who obtained a more general equation by solving the simultaneous equations which represented the law of mass action at the boundary and transport across the film. The mixed parabolic equation (24) which expresses a reaction influenced by both diffusion and boundary processes has two obvious limiting cases the simple parabolic law and the rectilinear law. The occurrence of the latter would suggest that the replenishing of the oxidising gas cannot keep up with the rate at which oxide growth occurs so the oxygen-replenish- ment rate takes over control. GulbransensG has recently developed Wagner's diffusion picture of oxidation by combining it with the transition-state theory.This development gives an expression for the parabolic rate con- stant involving absolute physical constants two entropy and two heat of activation terms. In the case of the formation of nickel oxide a p-type oxide vacancies are formed according to equation (25); one cation vacancy n c is formed together with two positive holes and one oxygen ion 0,-. The concentration of vacancies is therefore given by where AH" and AS" are the standard heat and entropy of formation respectively N is Avogadro's number R the gas constant T the tempera- ture and po the oxygen pressure. Since the parabolic rate constant is according to Mott given by kl = 2QD(n - n,) where nl and I t 2 are the number of vacancies per ~ m . ~ at the oxide-gas and oxide-metal interfaces respectively and L2 is the volume of the oxide per cation then where AGO is the standard free energy of formation of vacancies.ay2 + py = kt (24) +O,(g) + 02- + U C + 2 0 (25) nc = (N/49)(p0,)* exp(- dH0/3RT) exp( dS0/3R) kl = [2i2DN(p0)i exp( - d G"/3RT)] /49 85 Evans Trans. Electrochem. SOC. 1924 46 247. 86 Gulbransen Proc. Gothenburg Conference on Solid State Reactions 1952. 96 QUARTERLY REVIEWS From Zener’ss7 theory of diffusion the diffusion coefficient D is related to the vibration frequency V of the lattice the free energy dG* of the diffusion process and the distance a between the jumps by D = ya2vexp(- AG*/RI’) where y is a constant characterising the nature of the jumps. Thus the rate constant is given by equation (26) k = 2ya2DvN(p,,)* exp[( AS0/3 + dS*)/R] exp[- AH0/3 + AH*/RT] Two metal-oxide systems have been considered in the light of the above theory.For nickel the agreement between the experimentally determined AS* the entropy of activation of diffusion and the calculated value is good. With cobalt the agreement is poor which possibly suggests that the assumed mechanism is not the correct one. A second model for an oxide assumes it to be composed of macroscopic as well as lattice defects. These macroscopic defects are considered to be pores cracks or blisters formed as a consequence of internal stresses in the oxide film. Pilling and Bedworth’s rule,8s which still arouses much discussion is a consequence of such considerations. It states that an oxidation process will obey a linear law if the oxide occupies a smaller volume than that of the consumed metal.A linear law can also occur if the metal forms an oxide of larger volume than that of the consumed metal but stress relief results in breakdown of the oxide film. This breakdown may be complete or partial and in the latter case a porous oxide would be formed over a compact oxide film with the result that the rate will be controlled by ionic diffusion which occurs by a defect mechanism in a com- pact oxide film of constant thickness; hence the linear law. Aylmore Gregg and Jepsonsg have recently investigated the porosity of a number of oxides. Metals such as calcium magnesium tungsten and uranium form porous oxides which oxidise at a linear rate while cobalt and copper form coherent non-porous oxides and obey the parabolic law. A phenomenon which has as yet no unambiguous explanation is that of breakaway.This has been observed during extensive studiesg0 of the high-temperature oxidation of magnesium in which a rate process which has been constant for maybe 10 hours or more suddenly accelerates. Cracking and re- crystallisation of the oxide and stress relief have been suggested as the cause. The exact origin of the stress is uncertain but factors such as thermal gradients phase changes at the metal-oxide interface and diff- erences in thermal expansion of oxide and metal may be important. Evansg1 considers that “breakdown” of an oxide scale can occur in one (26) Zener J. Appl. Phys. 1951 22 372. Pilling and Bedworth J . Inst. Metals 1923 29 529. Gregg and Jepson J. Inst. Metals. 1958 87 187. 1 3 ~ Aylmore Gregg and Jepson J. Electrochem.Soc. 1959 106 1010. 91 Evans Trans. Electrochem. SOC. 1947 91 547. WYN ROBERTS METAL OXIDATION 97 of three ways (a) Blistering which involves detachment of the oxide but no real breakage may be expected where adhesion is poor and cohesion good. Rectilinear thickening should occur dX/dt = Kl if the cracks in the blister wall admit oxygen to the cavities so that new oxidation starts at the base of each blister ; but otherwise it should obey a logarithmic growth law since the outward movement of cations although aided by rifts normal to the surface is interrupted by cavity barriers parallel to the surface. (b) Shear cracking involving breakage but no detachment which may be expected where adhesion is good and cohesion poor. This should lead to a rectilinear a parabolic or an intermediate growth law.(c) Flaking is probably rare and may be considered to be that process likely subsequent to blistering. It involves the separation of the oxide as a flap so that the oxidation should resume at the initial rate. If the assumption is made that an expression of the form of (27) de- dx - cc f(x)exp(-E/RT) dt scribes the rate of cracking at an oxide thickness x where E is the activation energy of the cracking process then for a linear growth law the rate of oxide cracking and formation must be equal. By comparing equations (27) and (7) it is seen that the experimentally determined activation energy is a composite quantity involving the terms F W and E. The ideas of Evans on scaling have been extended and equation (28) has been derived by Haycockg2 to describe the kinetics of a scaling process k k P x = - l n k1 kp - kl(x - kit) where kp and kl are the parabolic and interface reaction rate constants.The interface reaction which depletes the barrier layer may be either vaporisation of the primary reaction product or the formation of a porous scale possibly by crystallisation grain growth or mechanical cracking. If vacancies remain at the metal-oxide interface they may coalesce and fonn cavities; this would ultimately lead to considerable porosity at the interface which in turn would lead to considerable decrease in contact area. These irregularities should affect the kinetics of the reaction and Birchenallg3 has developed a number of kinetic equations based on simple models of pore growth at the interface. The ability of porosity to form is thought to be related closely to the plastic properties of both metal and oxide.A minor constituent present in the metallic phase may influence oxida- tion in the following possible ways (1) A new oxide of the minor com- ponent is formed on the outer surface and if cation diffusion is rate 92 Haycock J. Electrochem. Soc. 1959 106 771. 93 Birchenall J. Electrochem. SOC. 1956 103 619. 98 QUARTERLY REVIEWS controlling the new oxide layer will influence the oxidation rate. Quarrelg4 has suggested that the oxidation resistance of heat-resisting steels is due to the formation of a stable surface spinel. On the other hand Wagnerg5 has recently shown that if an alloy consisting of two metals A and B is oxidised one oxide only may be formed; with alloys rich in A only A 0 is formed and with alloys rich in B only BO occurs.At intermediate com- positions of the alloy the formation of an oxide does not correspond to a stable state and therefore the two oxides A 0 and BO are formed simul- taneously. Under these conditions diffusion and hence oxidation rates will depend on the spatial distribution of the two oxides in the scale. (2) The effect of substituting ions OF valency different from the cations of the parent oxide is to change the cation vacancy and positive-hole concentra- tion and hence the reaction rate. In an oxide containing cation vacancies the introduction of a minor constituent of higher valency than the parent metal will increase the number of vacancies and hence the oxidation rate (Fig. 10). Conversely in an n-type oxide a minor constituent of lower FIG.10. The influence of the addition of Cr3+ on the defect structure of nickel@) oxide. valency will increase the oxidation rate and one of higher valency will diminish it. The predicted influence of alloying elements on the concen- tration of vacancies and hence the rate of oxidation is due to Hauffeg6 and js known as the “Valency Rule”. Wagner and Ziemensg7 have shown that the addition of chromium to nickel alloys in small concentrations in- creases the oxidation rate presumably by increasing the cation vacancy Concentration in nickel oxide when some Ni“ ions are replaced by Crw. Alloying elements may decrease the oxidation rate of iron above 700” by lowering the composition range of wustite which constitutes 95% of the oxide scale and therefore most probably is the phase with the greatest natural groivth rate.Additional protection could be observed if the alloy- ing element lowers the range of defect concentration in the spinel phase or decreases the ion mobilities. If the mobilities of the cations are sufficiently 94 Quarrel Nature 1940 145 821. y5 Wagner J . Electrochem. SOC. 1952 99 369. 9G Hauffe Prog. Metnl Phjssics. 1952 4 71. 9i Wagner and Ziemens Acrn Chem. Scand. 1947 1 547. WYN ROBERTS METAL OXIDATION 99 decreased a changeover to anion control could occur. (3) If the minor component oxide is incompatible with the parent oxide embrittlement with subsequent cracking can occur thus leading to a possible “breakaway” reaction. (4) If the alloying element has a greater affinity for oxygen than the solvent metal the minor element may oxidise below the surface oxide in an area where the partial oxygen pressure is too low to cause oxidation of the parent metal. This phenomenon termed internal ~ x i d a t i o n ~ ~ has been suggested to occur when (a) oxygen is soluble in the alloy and is able to diffuse fairly rapidly within the alloy and (b) the minor constituent forms an oxide which is thermodynamically more stable than the parent metal. It is a pleasure to acknowledge many stimulating discussions with Professor F. C. Tompkins F.R.S. Rhines Trans. Amer. Inst. Min. Met. Engrs. 1940 137 246. 4*