摘要:

Theoretical Studies of Phase Transitions in Tetr acyanoethylene BY ROBERT W. MUNN Department of Chemistry, University of Manchester Institute of Science and Technology, Manchester M60 1QD AND TADEUSZ LUTY * Institute of Organic and Physical Chemistry, Technical University, 50-370 Wroc€aw, Poland Received 15th November, 1979 The equilibrium structure and harmonic lattice dynamics of monoclinic tetracyanoethylene under imposed symmetry-preserving strains are calculated from a 6-exp atom-atom potential function. Some lattice frequencies become imaginary for extensions and shears above E 10%. Calculations of the eigenvalues of the dielectric function for the strained structures show the absence of dielectric singularities, but a dielectric mechanism for the observed transitions is not completely excluded.1. INTRODUCTION Theories of molecular crystals seek to explain the crystal properties in terms of the properties of the molecules and their arrangement in the crystal structure. To explain the temperature and pressure dependence of the crystal properties, the corresponding dependence of the crystal structure must be known. For the unit cell parameters, such information is fairly readily obtainable, but for the arrangement of molecules within the unit cell it is not. One may be able to deduce changes of molecular ar- rangement from crystal properties or from the unit cell parameters through empirical rules,2 but in general another source of structural information is needed. If an intermolecular potential is available, the molecular arrangement can be determined from the condition that it must minimize an appropriate energy function for given lattice parameters3 In this paper, we first report calculations of the equilibrium structure of the tetracyanoethylene (TCNE) crystal under imposed external symmetry-preserving strains.An improved 6-exp potential function derived from lattice-dynamical calculations4 is used, with the molecules treated as rigid. TCNE is of interest because under atmospheric pressure it forms monoclinic crystals above 292 K5 and cubic crystals below.6 The monoclinic phase is readily supercooled, and appears to trans- form to another monoclinic phase around 280 K.7 Secondly we report calculations of the lattice dynamics in the harmonic approxima- tion for the strained structures.For sufficiently large strains, certain frequencies become imaginary, indicating a possible lattice instability. TCNE acts as the acceptor in many donor-acceptor complexes, and is highly * Work performed while on leave of absence at Institute of Theoretical Chemistry, University of Nijmegen, The Netherlands.108 STUDIES ON TCNE polarizable. We have shown elsewhere’ that for crystals composed of molecules with a sufficiently high and anisotropic polarizability, the inverse dielectric function can become singular for some wavevector. This causes the polarization energy to diverge, leading to static and dynamic instabilities. In the third part of this paper we therefore report calculations of the dielectric function for the strained structures to investigate whether there are any singularities which can be related to the in- stabilities given by the empirical potential.Finally we discuss our results, their inter-relation and possible extensions. Our treatment concentrates on dynamic instabilities and so is better suited to elucidating the smooth transition to the other monoclinic phase of TCNE than that to the cubic phase. We do not consider thermodynamic stability. 2. STRUCTURE OF STRAINED CRYSTAL In a homogeneous deformation, a point x in the reference configuration is dis- placed by u to x‘. The strain can be described by the symmetric tensor with Cartesian components za/3 = +(auu/ ax, + au,/axu>, (2.1) although for finite strains this may include a contribution from r ~ t a t i o n . ~ We take the reference configuration as the unstrained monoclinic structure with lattice para- meters a, b, c and p.Under symmetry-preserving strains, the lattice parameters become a’, b’, c’ and p’ and the strain components arelo Zll = a’/a - 1, ZS3 = c‘ sinp’lc sinp - 1, Z13 = +(c’ cosp’/c sinp - a’ cospla sinp). 122 = b’/b - 1, In the monoclinic TCNE structure there are two molecules in the unit cell at centres of symmetry,’ so that under symmetry-preserving strains the molecular arrangement can be specified by three Euler angles, 9, w and 8. t -0104 -0.02 d (4) 0102 0104 w‘iiR. W. MUNN AND T. LUTY 109 -0.64 -0.'02 b Of02 0104 .lij ic 1 FIG. 1 .-Variation with strain of the Euler angles (degrees) describing the molecular orientation in TCNE: (a) q, zero-strain value 5.53"; (b) y, zero-strain value 22.60'; (c) 0, zero-strain value 28.36": The crystal potential energy is calculated from an improved parameter set for the 6-exp atom-atom potential function for crystals containing cyano group^.^ De- formed lattice parameters corresponding to a single non-zero strain component are imposed, and the potential energy is then minimised with respect to changes in the three Euler angles.The results are shown in fig. 1. The diagonal strain components represent compression for negative values and expansion for positive values. As can be seen, the orientations change very differently110 STUDIES ON TCNE with different strains, though the effect of Z,, is never large. These differences reflect the molecular packing, and give some insight into the crystal potential.Some of the graphs curve for strains as little as 1 %, indicating a marked curvature in the potential. The initial slopes of the graphs give the derivatives of the internal strains with respect to external strain ; these are important parameters in theories of elasto-optic proper- ties,2 generalized thermodynamics l3 (where they correspond to the bridging matrix &A) and elasticity'' (where they correspond to the internal strain tensor AE;). 3. DYNAMICS OF STRAINED CRYSTAL Minimisation of the crystal potential energy is a necessary standard first step in lattice dynamical calculations. The lattice dynamics is calculated as for the un- strained s t r u c t ~ r e . ~ The strain dependence of the lowest optic mode frequencies at the centre of the Brillouin zone is shown in fig.2. Under compression, the frequencies all increase as expected and are not shown. Under extension, more complicated behaviour is observed. Some modes are relatively unaffected while others soften markedly, becoming unstable for strains of the order of 12%. w /cm -1 t / * * 1 ' I , , 0.15 0.10 0.05 0 0.05 0.10 0.15 133+ C + 1.15 0.10 0.05 0 0.05 0.10 &I13 0.15 FIG. 2.-Variation with strain of the lowest zone-centre optic mode frequencies in TCNE. (a) Strains Zz2 (left-hand side) and l , , (right-hand side); (6) strains 133 (left-hand side) and ZI3 (right-hand side). The modes Qre labelled by their symmetry species.R. W. MUNN AND T. LUTY 1 1 1 The dispersion curves for modes propagating along high-symmetry directions have also been calculated.The most strongly strain-dependent dispersion curves are shown in fig. 3, again only for positive strains but this time including acoustic modes. Y w /cm-l 122 4 I 3 3 x Y Y FIG. 3.-Variation with strain of selected dispersion curves along high-symmetry directions in TCNE. The point r is the Brillouin zone centre (0, 0, 0), X is (0.5, 0, 0) and Y is (0,0.5,0). (a) Strains lZ2 (left-hand side) and l,, (right-hand side); (b) strains Il3. The value of the strain is marked on each curve. Broken lines indicate unstable regions corresponding to imaginary frequencies. Various instabilities are seen: with respect to longitudinal acoustic modes in the Y direction for the strain Z22; with respect to transverse acoustic and translational optic modes in the X direction for the strain ZS3; and with respect to librational optic modes at the zone centre and in the X and Y directions for the strain Z13.4. DIELECTRIC FUNCTION OF STRAINED CRYSTAL The dielectric function relates the electric field applied to a crystal to the local field it produces. In a molecular crystal containing 2 molecules labelled k in the primitive unit cell, it is convenient to describe the applied and local fields by their Fourier transforms ei(k) and f,(k), where q is the wavevector. The molecules are viewed as being polarized by the local fields, which are given bys h ( k ) = 2 eql(kk’) ei(k‘). E,(kk‘) = 16kk. - t,(kk‘) p(k’), (4.1) k’ Here the dielectric function eq is a 3 2 x 3 2 matrix with elements given by (4.2) where t,(kk’) is a modulated lattice dipole sum and p(k’) is a dimensionless reduced polarizability .If the molecular polarizability is sufficiently large and anisotropic, an eigenvalue of E~ may become zero so that is singular. The inverse dielectric function deter- mines the crystal polarization energys*12 and through it a mechanism of electron- phonon coupling.A singularity in ~ q l thus implies an instability of the electronic system of the molecular crystal against dipole fluctuations induced by a phonon of the appropriate wavevector. TCNE offers the opportunity to examine this prediction in a case where the conventional alternative calculations in section 3 indicate an instability . They are The eigenvalues of eq for the unstrained structure are shown in fig. 4.r x 9+ 1.7 1.5 1 . 3 NO : . 1 . 1 8 0.9 0.7 0.5 r Y 9+ 1.7 c 0.51- r Z q-+ FIG. 4.-Eigenvalues of the dielectric function in TCNE as a function of wavevector at zero strain. Symmetric and antisymmetric branches are labelled S and A. Points r, X and Yare as in fig. 3, and Z is (0, 0,0.5). expressed in the usual way as the square of a frequency scaled relative to the corre- sponding frequency for the free molecule. The curves are labelled as symmetric or antisymmetric as for phonon dispersion curves.13 Some of the eingenvalues depend quite markedly on q, but none falls below ~ 0 . 6 . The lowest pair of symmetric and antisymmetric eigenvalues of E~ for positive and negative strains (Zll and Z22, as an illustration) are shown in fig. 5. For the diagonal strain components, compression lowers the lowest eigenvalue and extension raises it.Thus extension tends to stabilize the crystal against dielectric singularities, and al- though compression tends to destabilize the crystal the eigenvalues remain above 0.5. This weak tendency towards dielectric instability on compression contrasts with the dynamic instability on extension. 5. DISCUSSION The results presented here fall into two distinct groups which must be compared The results in Sections 2 and 3 explore the detailed consequences of the 6-ex- cautiously.R. W . MUNN AND -1. L U - - - T Y 113 - 0.9 NO 8 $ 0 . 7 0. 5 0 . 9 ..................... ...... $ 0.7 0.5 r X 4-+ 1 I 1 I r X q-, 1 0.9 -0 8 NO $ 0.7 0.9 t 0.9 .................. ................... NO .... 8 ................... 0 .7 --- 0 . 5 0 . 5 FIG. 5.-Variation with strain of the lowest pair of eigenvalues of the dielectric function in TCNE. ( a ) Strains Ill; (b) strains Iz2. The solid lines denote a strain of -0.10, the broken lines 0, and the dotted lines +0.15. potential function and parameters for molecules containing cyano groups. The structural changes under strain are of use in theoretical treatments of the various experiments carried out on TCNE [see references in ref. (4)]. The dynamical in- stabilities under strain imply a phase transition like that predicted l4 and observed 's in HCN. However, the HCN calculations did take explicit account of electrostatic interactions not treated in section 3. The predicted instabilities in TCNE should therefore be regarded with some scepticism. In any case, it is unlikely that the re- quired extension could be applied mechanically in order to seek the instabilities, although the thermal expansion is markedly and increasingly anisotropic above room temperature.'The results in Section 4 show that there is no dielectric singularity in TCNE. These calculations treat the molecular polarizability as located at a point. Such an approximation is known to exaggerate the anisotropy of dielectric propertiesI6 and when the polarizability is treated as a Gaussian distribution the eigenvalues of E~ do increase as the distribution broadens, in accordance with the observation that high anisotropy tends to produce a singularity.However, the absence of a dielectric singularity does not exclude the possibility of a soft mode.The dynamic multipoles model1’ provides a method of treating the lattice dynamics of molecular crystals in which the dielectric properties are incor- porated naturally.1s In this model, the phonon frequencies can be expressed as Q 2 q j = m* q.i - E . a E-~*ET,~. (5.1) where Eqj gives the electric field induced by the mode q j and a(&’) = a(k)Skkf is a polarizability. The frequencies coqj are those given by the forces between non- polarizable molecules ; the electron-phonon coupling arising from the vibrational dependence of the polarization energy reduces these frequencies to Qqj through the last term in eqn (5.1). As can be seen, a soft mode is produced if c-ql is large enough for the polarization term to cancel m i j .Unfortunately, calculations within the dynamic multipoles model have not yet been performed for TCNE. One problem is that the 6-exp intermolecular potential is partly fitted to observed librational frequencies which must incorporate a polariza- tion contribution. The frequencies reported in Section 3 are therefore not simply the mqj, but neither are they the proper Qqj. An internally consistent treatment requires potential parameters fitted to experimental data through a model which incorporates dielectric effects explicitly. It will then be possible to examine more thoroughly the dielectric mechanism for phase transitions in molecular crystals. J. W. Rohleder, Kristall. Technik, 1978,13, 517; W. J. Kusto and J. W. Rohleder, Mol. Cryst. Liq. Cryst., 1979, 51, 215; 1979, 55, 151. P. J. Bounds and R. W. Munn, Mol. Cryst. Liq. Cryst., 1978,44,301; Chem. Phys., 1979, 39, 165. T. H. K. Barron, T. G. Gibbons and R. W. Munn, J. Phys. C, 1971,4,2805. T. Luty, A. van der Avoird and A. Mierzejewski, Chem. Phys. Letters, 1979, 61, 10. D. A. Bekoe and K. N. Trueblood, 2. Krist., 1960,1,113. R. G. Little, D. Pautler and P. Coppens, Acta Cryst., 1971, B27, 1493. J. Swiqtkiewicz, Sci. Papers Inst. Org. Phys. Chem. Technical Univ. Wroclaw, 1978, 16, 305. R. W. Munn and T. Luty, Chem. Phys., 1979, 38,413. R. W. Munn, J. Phys. C , 1978, 11, L61. lo J. L. Schlenker, G. V. Gibbs and M. B. Boisen, Acta Cryst., 1978, 34A, 52. l1 C. S. G. Cousins, J. Phys. C, 1978, 11, 4867. l2 P. J. Bounds and R. W. Munn, Chem. Phys., 1979,44, 103. l3 G. S. Pawley, Acta Cryst, 1974, ,430, 585. l4 A. I. M. Rae, J. Phys. C , 1972, 5, 3309. l5 0. W. Dietrich, G. A. Mackenzie and G. S. Pawley, J. Phys. C, 1975,8, L98; G. A. Mackenzie l6 P. J. Bounds and R. W. Munn, Chenz. Phys., 1977, 24,343; J. H. Meyling, P. J. Bounds and l7 T. Luty, J. Chem. Phys., 1977, 66, 1231. and G. S. Pawley, J. Phys. C, 1979, 12, 2717. R. W. Munn, Chem. Phys. Letters, 1977, 51, 234. T. Luty and R. W. Munn, Chem. Phys., 1979, 43.295.

ISSN:0301-7249    

DOI:10.1039/DC9806900107

出版商:RSC    

年代:1980

数据来源: RSC

摘要:

Some Novel Symmetry Aspects of Phase Transitions BY L. L. BOYLE, J. R. WALKER? AND ANNE C. WANJIEJ: University Chemical Laboratory, Canterbury, Kent Received 1 1 th January, 1980 Two aspects of phase transitions in the solid state are discussed, namely the structure of the sym- metry group of a plastic crystal and the prediction of plausible pathways for first-order phase transi- tions. It is explained how group extension theory may be used for the former and how space group representation theory is an essential adjunct of crystallographic considerations in the latter. T H E SYMMETRY OF PLASTIC CRYSTALS It is the authors' contention that the description of the symmetry properties of the plastic phases of crystalline solids may well be improved by the use of symmetry groups which are rather more complicated in structure than the familiar Federov space groups.The case for a new group-theoretical description depends on how one regards the relative motions of the molecules in the plastic phase. If one accepts the conclusion of Finbak' that in the high-temperature cubic phases of CBr,, CzCls and camphor, the rotation of the molecules is a co-operative phenomenon since the sphere of rotation of any one molecule penetrates those of its neighbours, one can describe the rotational motion of the molecules as a lattice vibration of a non-plastic phase. In molecules such as tin tetraethyl, however, two or three polymorphs can co-exist,2 and a new model should at least be able to cater for the case where different polymorphic forms can be interconverted by the rotational motion.To achieve this one has to get away from the idea of treating the lattice vibration as spanning an irre- ducible representation of a space group, which is really only valid for small amplitudes of vibration, and to find a description in which the reorientational motion is an integral part of the description. The symmetry elements of a group corresponding to such a description would not only contain the translations (which interrelate the co-ordinate axes of different unit cells) and the point group operations (which interrelate equiva- lent settings, relative to the lattice vectors, of the co-ordinate axes of a given unit cell) but also the molecular rotations (which interrelate equivalent settings of the molecular axes relative to the co-ordinate axes in a given unit cell.) By not requiring the molecu- lar rotations to conserve the periodicity of the original lattice one can include the orientationally-disordered structures as well as those highly ordered structures which actually correspond to non-plastic solid phases.Thus the enlarged symmetry group can have more than one classical space group as a subgroup: further, librational and translational motions can be included by use of the irreducible representations of this group. The problem now arises as to how one might construct such a group: extensive details may be found in Dr. Walker's t h e s i ~ , ~ but an attempt will be made here to t Present address: Chemistry Laboratory, University College, 20 Gordon Street, London W.C.I . t ne'e Philpot.116 SYMMETRY ASPECTS OF PHASE TRANSITIONS summarize the structure of the solution. The mathematical technique needed is group extension theory, a formal technique developed by Schur in 1907 and especially by Schreier in 19245 and 1926.6 (An account for chemists has recently been published by Boyle and Walker.)' Group extension theory uses two ingredients: an invariant (or normal) subgroup and a factor group. The invariant subgroup is a genuine sub- group of the extension and in physical terms we might regard it as a subgroup which is unaffected by all the permutations due to the other elements of the group. Thus, the point group D,, is an invariant subgroup of Oh because, as a group, it is unaltered by permutations caused by other elements of Oh such as C3.In rigorous mathematical terms, an invariant subgroup is invariant to all the inner automorphisms of the group, i.e., if we choose to permute the elements Ni of the invariant subgroup by conjuga- tion with an operation G j of the group, then, whichever element Gj is chosen, the set of permuted elements {Gj-'NiGj) is in 1 : 1 correspondence with the set {Ni). In other words the conjugation just changes the order in which we write the elements down. The factor group is a little more difficult to explain because it is not a subgroup of the original group, although it may be isomorphic to one. Its elements are cosets of the original group and their multiplication law simply states that the product of two representative elements is an element representative of the product coset. A familiar example may help: a space group is an extension of the lattice (ie., translation group) by the point group.The lattice is the invariant subgroup because, as a group, it is unchanged by the point operations. The point group is not a genuine subgroup, because the space group elements act on the lattice as well as on the co-ordinate axes while the point group operations act on co-ordinate axes alone. The coset of space group operations corresponding to a point group operation will contain all those space group operations having the same rotational part, but differing in translational element. Such cosets are therefore infinite, although the point group itself is finite. The multiplication law of the cosets defines a group which is isomorphic to the point group. In mathematical terms, one says that the point group is the quotient of the space group with the translational group and is hence called the factor group or quoti- ent group.TABLE 1 .-SOME EXAMPLES OF GROUP EXTENSIONS Some familiar examples of group extensions are listed in table 1. invariant isomorph of subgroup factor group lattice point group C;" point group torsional symmetry frame symmetry reorientations space group non-magnet ic time-reversal Schur multiplicator point group - group extension space group double group non-rigid molecule symmetry group plastic crystal magnetic symmetry representation group OC; is the group consisting of the identity and R, the element which reverses the signs of one-electron spin functions.It should be noted that since the factor group is actually a group of cosets, the point group, where quoted in the preceding description, is only isomorphic to the factor group. In cases where the groups concerned all act on the same basis func- tions, e.g., the resolution of point groups as direct or semi-direct product^,^*^ this distinction becomes unimportant but in solid-state problems it is essential to bear it in mind. The final stage in setting up the mathematical machinery to establish these group extensions is to decide exactly what permutations of the invariant subgroup areL . L . BOYLE, J . R . WALKER A N D A . C . WANJIE 117 induced by the various elements of the factor group. This may not be easy for various reasons. On the mathematical side, one must be sure that the " extension " really is a group and know whether it is or is not isomorphic to any other extensions obtained by this process.On the physical side, one must know what the physical consequences are of any proposed extension, i.e., is the specification of the action of the generators of the factor group on the generators of the invariant subgroup in accordance with experiment and geometric considerations ? In the case of the plastic-crystal problem this is not a simple question to answer. Recognizing the rotations of the molecules as generating the invariant subgroup and the space group (or something closely related to it) as generating the factor group, the problem boils down to asking us to specify in advance how the rotations are correlated in the " unit cell ", however big this may be, of the plastic crystal.Once one has agreed on this the group can be produced by computation. In such a problem it is always useful to know what are the possible mathematically meaningful ways of permuting the elements of a group. These ways form a group called the outer automorphism group of the group being permuted. Dr. Walker's thesis contains both the elegant mathematical and computational derivations of the outer automorphism groups of all point groups as well as an indication of the possible automorphisms of the molecular rotational groups required in the plastic-crystal problem. SYMMETRY PROPERTIES OF FIRST-ORDER PHASE TRANSlTIONS To contribute a new approach to the elucidation of the mechanism of first-order phase transitions necessarily involves various assumptions which of their essence will rule out its application to numerous observed systems, at least in so far as they are presently understood.Following the definition of Ehrenfest," second-order phase transitions are those involving continuous changes of thermodynamic variables with temperature while first-order phase transitions are those involving discontinuity. From the group-theoretical point of view, second-order phase transitions have been successfully interpreted as involving a reduction in space-group symmetry as one cools the crystal through the transition point. Second-order transitions usually involve a zeZZengZeich reduction in symmetry, i.e., the translational elements are unaffected by the change and the volume of the primitive unit cells remains constant.By contrast, we have been able to propose mechanisms for numerous first-order phase transitions on the basis of a multi-stage process which involves an intermediate space group which is a subgroup (or, occasionally, a supergroup) of the space groups of both high- and low-temperature phases. First-order phase transitions often involve changes in the volume of the primitive unit cell. Our interest, then, has been to find feasible pathways which the atoms would fol- low in the transition from one structure to another. The existence of such a pathway is difficult to justify in the all-too-frequent case where there is no " crystallographic continuity", i.e., the crystal breaks up into a powder on being taken through the transition.It may well be that the kinetics of the transition are so sluggish that taking the crystal through the transition temperature at an experimentally reasonable speed sets up stresses within the crystal which disrupt its macroscopic form. Certainly the reproducibility of phase transitions argues in favour of the idea that the atoms know where they are going, at least within a given grain. To produce an absolutely random arrangement of the atoms at the point of transition is probably more difficult energetically than to allow them to follow rather more symmetrical pathways. Even in a theory which depends implicitly on the use of symmetry, the r d e of dislocations118 SYMMETRY ASPECTS OF PHASE TRANSITIONS and defects in providing the " breathing space " which catalyses the transition is clearly recognized.Such features, however, only need to be taken into account when comparing the relative energetics of different plausible pathways. One of the key requirements of the present theory for predicting plausible path- ways is that the motion of the atoms is determined by lattice vibrations and that there is a continuity between the lattice vibrations in both phases and through the inter- mediate space groups postulated. This is essentially an extension of one of Landau's criteria concerning which space-group representations were allowed to generate a given distorted structure. Its consequences, however, were more far-reaching than were expected as far as the actual prediction of plausible pathways was con- cerned.Rather than work out the symmetries of the lattice modes at all the possible different types of special points in the Brillouin zone of the high-symmetry phase and then examine the distortions to which they corresponded, it seemed a very much sim- pler task to use some extremely reliable tables of maximal subgroups of the space groups which had been produced in 1969 by Neubiiser and Wondratschek,12 and which will be incorporated in the forthcoming Volume A of the International Tables for Crystallography. Coupled with some other tables of Ascher', and Boyle and L a ~ r e n s o n , ' ~ ? ' ~ it is a relatively simple matter to find chains of space groups which link the two structures involved in a phase transition. However, the application of the extended Landau criterion mentioned above really highlights the need for these crystallographic tables to be supplemented by some indication of which space-group representation is capable of generating the distortion.One of the simplest examples of this difficulty arises in the attempt to switch from a face-centred cubic (Fm3m, O;, no. 225) structure to a simple cubic structure (Pm3m, Oi, no. 221). According to the Neubuser-Wondratschek tables, Pm3m is a maximal subgroup (of index 4) of Fm3m. One can draw this rather easily by colouring the atoms on the centres of the faces of a conventional unit cell a different colour from those at the apices of the cube. However, there is no space-group representation which would allow this process which we can draw so readily! To confirm this, one merely has to glance at the list of symmetries of the special points of the Brillouin zone of the face-centred cubic lattice which may be conveniently found in Bradley and Cracknell's book.16 This list shows that at no point outside the centre of the Brillouin zone can a vibration produce a cubic structure; whilst at the centre, no change of lattice type is possible.Another pitfall encountered in the use of maximal subgroups is that one may well insert intermediate space groups into a pathway which are such that they do not correspond to the instantaneous positions of the atoms at any given moment. An example of this is the cubic (Pm3m, Ok, no, 221) to tetragonal (14/mcm, Dii, no. 140) phase transition17 which is found in various perovskites, e.g., in SrTiO, at 110 K and in KMnF, at 184 K.Now 0:; happens to be a subgroup of Oi, but is of the allgemein or general type, and hence according to a theorem of Hermann," is non-maximal and can be reached in stages from 0; which are either purely zellengleich (cell-preserving) or klnssengleich (crystal class-preserving). A possible route is therefore i. e. and the Wyckoff positions of the atoms correlate between the different phases.19 However, the perovskite is incapable of undergoing a zellengleich distortion to the primitive tetragonal structure since the atoms involved cannot generate an &-type lattice mode at the centre of the Brillouin zone. Indeed, since all of the atoms are onL . L . BOYLE, J . R . WALKER AND A . C. WANJIE 119 centrosymmetric sites at room temperature all of the zero wave-vector vibrations are anticentrosymmetric and hence would lead to polar structures.It is, of course, possible for those simple cubic, Oi, crystals having atoms occupying Wyckoff’s e , f , g, h, i, j , k, I or rn sites20y21 to undergo an E,-distortion and produce a D&-structure. The mode which is thought22 to be responsible for the phase transition in the perovskites is a triply-degenerate mode at the R-point of the Brillouin zone. On descent to Dii symmetry, this yields a totally symmetric r-point mode in accordance with the Landau theory. It is interesting to note that it correlates with A-point modes in D:,, which in turn correlate with the same r-point modes in 0::: this is, however, no indication that the D& step has any real existence.Once a set of lattice modes capable of producing the transition has been identified, taking full account of these representation-theoretic restrictions, one must decide whether there are alternative plausible routes and, if so, how one should choose between them. In principle some spectroscopic or other criterion (e.g., measurement of certain components of a physical property tensor) should be suggested which is capable of diagnosing the intermediate steps in a phase transition. In practice, there is remarkably little choice of routes for many substances: it would therefore lend added credibility to a proposed pathway if the crystal could be pumped with radiation of the soft-mode frequency near the transition temperature to see if the crystal could be taken through the transition (and perhaps back) with less physical damage.This would lend support to the damage being caused by the simultaneous thermal excita- tion of other lattice modes, rather than by the soft mode, and hence strengthen the case for considering preferred pathways. The authors thank the S.R.C. for the award of a research studentship to J. R. W. for his work on plastic crystals and the University of Kent Graduate Studies Support Fund for the award of a research studentship to A. C . W. for her work on phase transitions. C. Finbak, Arch. Math. Naturvidenskab, 1938, (B), 42, 71. L. A. K. Staveley, J. B. Warren, H. P. Paget and D. J. Dowrick, J. Chem. Soc., 1954, 1992. J. R. Walker, Automorphisms and Extensions in Chemical Physics, Ph.D. Thesis (University of Kent at Canterbury, 1977), chap. 5. I. Schur, J . reine angew. Math., 1907, 132, 85. 0. Schreier, Abh. math. Sem. Hamburg. Univ., 1924, 3. 0. Schreier, hlonatsh. Math. Phjs., 1926, 34, 165. S. L. Altmann, Phil. Trans., A, 1963, 255,216. S. L. Altmann, Rev. Mod. Phys., 1963, 35, 641. lo P. Ehrenfest, Proc. Acad. Sci. (Amsterdam), 1933, 36, 153. L. D. Landau, Phys. 2. Sowjetunion, 1937, 11, 26 and 545. l2 J. Neubuser and H. Wondratschek, Maximal Subgroups of’ the Space-groups (privately pub- lished, Kiel and Karlsruhe, 2nd edn, 1969). l3 E. Ascher, Lattices of Equi-translation Slrbgroups of the Space Groups (Internal report, Battelle Institute Advanced Studies Centre, Geneva, 2nd edn, 1968). l4 L. L. Boyle and J. E. Lawrenson, Acta Cryst, 1972,28A, 485. l5 L. L. Boyle and J. E. Lawrenson, Acta Cryst, 1972, 28A, 489. l6 C. J. Bradley and A. P. Cracknell, The Mathematical Theory ofSyrnmetry in Solids (Clarendon l7 H. Unoki and T. Sakudo, J . Phys. Soc. Japan, 1967,23, 546. l9 J. E. Lawrenson, Theoretical Studies in Crystallography, Ph.D. Thesis (University of Kent at 2o L. L. Boyle, Acta Cryst, 1972, 28A, 172. 21 L. L. Boyle, Spectrochimica Acta 1972, 28A, 1355. 22 P. A. Fleury, J. F. Scott and J. M. Worlock, Phys. Rev. Letters, 1968, 21, 16. ’ L. L. Boyle and J. R. Walker, Int. J . Quantum Chem., 1977, 12, 157. Press, Oxford, 1972), p. 118. C. Hermann, Z . Krist., 1929, 69, 533. Canterbury, 1973).

ISSN:0301-7249    

DOI:10.1039/DC9806900115

出版商:RSC    

年代:1980

数据来源: RSC

摘要:

GENERAL DISCUSSION Prof. G. M. Schneider (University of Bochum) said : The phase diagram of deuter- atedp-terphenyl (fig. 4 of the paper of Cailleau et al.) is remarkable in two respects: (1) The T(p) transition curve has a negative slope; that would mean that AV is negative (since AH is positive; see page 11). This is an unusual pressure dependence since normally T(p) transition curves with positive slopes are found in similar cases. The behaviour shown is unlikely in the context of phase theory. (2) No break in the transition line is found at the triple point. Mr. H. Cailleau (University of Rennes) said: Concerning point (l), the negative slope of the T(p) transition curve appears as a confirmation of the proposed transition mechanism in polyphenyls (competing intramolecular and intermolecular forces).This mechanism is different from the orientational ordering of numerous rigid molecules where T(p) transition curves with positive slopes are found. With respect to point (2), within the precision of our measurements we cannot say that no break in the transition line is found at the triple point. Above the triple point the shift of the transition temperature with pressure is clearly not linear, but below this, the shift is closely linear. Prof. R. M. Pick (Universite' Pierre et Marie Curie, Paris) said: In an order- disorder phase transition, the ordering temperature is not related to the height of the energy barrier separating the various minima, but to the difference of interaction energy between molecules when they are in different relative positions.The value of T, in para-terphenyl is thus entirely related to intermolecular interactions. Further- more, the low-temperature structure may result from a balance of the interactions between different pairs of molecules; the effect of pressure on the strength of these various interactions may differ from one to another. It is thus not clear that the sign of the change in the ordering temperature with pressure may be easily predictable. Prof. A. J. Leadbetter (University of Exeter) said: Can Mr. Cailleau tell us some- thing about the phase transition in quaterphenyl ? Mr. H. Cailleau (University of Rennes) said : In p-quaterphenyl, superlattice reflections appear at the C(+, $, 0) reciprocal point of the high-temperature phase as in p-terphenyl, and the two low-temperature structures are similar.The average torsion angles are 17.1 O between an external and an internal ring and 22.7' between two internal rings. These torsion angles, like the thermal motion in the high- temperature phase, lead us to suppose that the phase transition is order-disorder as in p-terphenyl, although no inelastic neutron scattering investigations have been performed. Dr. G. S. Pawley (University of Edinburgh) said: We have recently discovered what we believe to be similar incommensurate behaviour in p-dibromotetrafluoro- benzene. The space group is the same as that for biphenyl and superlattice reflec- tions are observed at points associated with a wave-vector (0, q, 0) for q 21 0.45.GENERAL DISCUSSION 121 I Does Mr.Cailleau think that in biphenyl the incommensurate phase transition is in any way related to the easy torsion about the central C-C bond? Mr. H. Cailleau (University of Rennes) said: The possibility of incommensurate phases is related to the occurrence of a minimum in the soft-phonon branch away from a high-symmetry point in the Brillouin zone. In biphenyl, this is realized with the existence of a Lifshitz invariant at the B (O,+, 0) zone boundary point. The easy torsion about the central C-C bond is only related to the mechanism of the soft mode and numerous different mechanisms have been observed in numerous organic and inorganic compounds. Dr. N. Boden (University of Leeds) said: Ewen et al. state in their paper that " phase transitions can generally be regarded as reactions of the crystal lattice to the onset of specific types of molecular motion ".The results presented for n-C&68 certainly seem to substantiate this assertion. However, 1 wonder whether this is really true in general ? My reason for asking this question is based upon some recent n.m.r. measurements of ours (measurements made by Mr. Gene Peterson) on the neighbouring homologue n-C3,Hb6. The different relative orientations of the terminal CH, groups of the two molecules impart different crystal structures and sequences of phase transitions on the two solids. Thus, n-C&66 exhibits a monoclinic structure at low temperatures and undergoes a transition to a rotor phase at 339 K before finally melting at 343 K. Yet measurements of the contribution of the proton second moment M2 from the intra-CH, interaction (fig.1) reveal four distinct temperature intervals I-IV for motion, I I 1 ' O L 8 4 L I 2 c 4 I I I I I I A A I I I "k pi I I I I I I I1 I I ; with 1-111 corresponding to the monoclinic phase. In interval I, M , ( i n t ~ a ) ~ ~ z changes very little with temperature, whilst the total M2 (not shown) exhibits a more marked decrease due to a reduction in the extramolecular interaction caused by lattice ex- pansion. In the interval 11, M,(int~a)~~'2 decreases more rapidly with temperature due to more extensive intramolecular oscillations. M,- (intra)CHZ is constant whilst M , ( e ~ t r a ) ~ ~ ~ decreases smoothly up to the transition to the rotor phase. This requires 180" reorientational jumps of the molecules about their long axes and is the " a-process " region as described by Olf and Peterlin I.Here, the onset of the a-process is not accompanied by a phase transition as for n-C,3H68. The value of M,(intra)C"2 implies 25" angular oscillations. The behaviour in interval I11 is more exciting.122 GENERAL DISCUSSION Our measurements suggest that the fraction of molecules undergoing such jumps increases linearly from 0 at 290 K to 0.5 at 339 K, the temperature of transition to the rotor phase. Thus, the %-process in n-C32H66 seems to involve a translational defect mechanism ; the defect is thermally generated and its concentration increases strongly with temperature. Interval IV is the rotor phase: two types of molecules are again identified, one undergoing reorientational motion similar to the molecules in the rotor phase of n-C,,H,, and the other reorientational and translational diffusion.To conclude, it appears that n-C32H66 exhibits similar though not exactly corre- sponding motional processes as Ewen et al. have so elegantly demonstrated for n-C33H68, but without undergoing a parallel sequence of phase transitions. It is, of course, possible, though unlikely, that the difference in the behaviour of these two molecular solids could originate from impurities in the former case. H. G. Olf and A. Peterlin, J. Polymer Sci., 1970, 8, 791. Prof. G. Chapuis (University of Lausanne) said : In their model Ewen et aZ. assume that phase B is accompanied by a pure 180" rotational jump. From geometrical considera- tions, one sees also that a 90" rotational jump leaves the cell dimensions and symmetry invariant.Such a motion has been observed in, e.g., (C10H21NH3)2CdC14 (paper by Blinc et al., this Discussion). Is there any evidence suggesting that a 90" rotational jump can be excluded from the model? Prof. A. J. Leadbetter (University of Exeter) said: I wish to draw attention to similarities and differences between the behaviour of the long-chain paraffin systems and that of smectic liquid crystals. It seems to me that it might be fruitful to pursue this comparison more deeply and I would be interested to have comments from the authors. The first point of similarity is that many substances exhibit a number of different smectic phases (up to five) with change of temperature but the chemical constitution is much more complex than that of the simple alkanes.Liquid crystals very often have the general formula, It seems inevitable that some differences in detailed behaviour must arise from the loss of the simple chain structure of the alkanes. However, a major difference is in the crystallinity: the transitions A -+ B -+ C --+ D all have lower entropy than D --+ Liquid whereas for the smectic phases the first transition from ordered crystal (equivalent to the A phase) to the lowest-temperature (most ordered) smectic phase generally has a greater entropy than that of all the other transitions combined. Nevertheless, the more ordered smectic phases (below) are now generally considered to be true 3-dimensional crystals, although the diffraction spots, while sharp, are confined to relatively low scattering vectors and there is very strong diffuse scattering : both indicate considerable disorder.For example, the reciprocal lattice of the ordered smectic phases generally shows hkl or hkO reflections only for h or k 7 2 and notGENERAL DISCUSSION 123 usually more than 5 orders of the 001 layer reflections. How does this compare with diffraction patterns of phases B-D of the alkanes? A brief summary of the main smectic phases is given in table 1. The molecular long axes may be tilted or orthogonal to the smectic layer planes and the symmetry is given of the molecular packing in planes perpendicular to the molecular long axes and of the lattice. TABLE 1.-sUMMARY OF THE MAIN SMECTIC TYPES orthogonal molecular lattice tilted (tilt angle name packing tY Pe name typically ca. 25") SmA liquid liquid SmC ? hexagonal hexagonal SmF (short range order) SmB hexagonal hexagonal - SmE chevron orthorhombic - - hexagonal monoclinic SmG - chevron monoclinic SmH In addition to the structural similarities there are remarkable similarities in the dynamic behaviour, except for the special effects arising from chain kinking.The observations with a particular technique depend on the relation of the time-scale of the motion to that of the experiment but, as for the alkanes, the molecular dynamics in the smectic phases are dominated by reorientation about the long axis together with a longitudinal motion of this axis. In the most ordered smectic phases E and H the orientational motion on a time-scale of ca.1 0 - l ' ~ or less is restricted with, respectively, bipolar and polar distribution functions. This motion becomes less restricted in the smectic B and H phases, tending toward a random 6-fold distribution, which tends to a uniform distribution in smectic A and C phases. In all phases there exists a restricted longitudinal motion of the molecules which in the E and H phases is of amplitude ca. 1 8, (on a time-scale of 7 10-l' s) and not strongly coupled to the reorientations. In the B (G) and A (C) phases the amplitude increases to <' 2 A and the strength of the coupling also increases. Except that the amplitude of the longitudinal motion is not related to the > CH2 repeat unit as for the alkanes, the existence of this motion seems to be a characteristic feature of all the disordered phases of long rod-like molecules. Dr.A. Huller (KFA Jiilich) said: Prof. Leadbetter says that he cannot explain his EISF data with just one type of motion of the molecules. Even if one has only one type of motion, say a rotation around the threefold symmetry axis of the molecules, one may observe more than one correlation time. The rapidly rotating molecules will feel a much lower frictional force than the slowly rotating molecules.' This leads to long relaxation times for the rapidly rotating molecules and to short relaxation times for the slow molecules.2 I want to demonstrate this by using a model contributed by Werner Press and myself. It consists of magnetic quadrupoles sitting on pins which allow a rotation of the magnets around a vertical axis.If I set one of them into rapid rotation the neighbours cannot respond to the high-frequency a.c. field which results. Therefore the rotation is almost undamped. The small friction one sees is due to the bearing. As the magnet gradually slows down its neighbours begin to respond. The energy is dissipated over the whole system, the rotating particle now loses its kinetic124 GENERAL DISCUSSION energy very quickly and the rotation comes to an end. Slowly rotating molecules feel much higher frictional forces. R. Gerling and A. Huller, to be published. R. G. Gordon, J . Chem. Phys., 1965, 43, 1307. Prof. A. J. Leadbetter (University of Exeter) said: 1 agree with Dr. Huller’s remarks to the effect that rotational motion about even a single axis might have complex dynamics and I congratulate him on his beautiful model demonstration.However, the EISF gives direct geometric information on the average proton trajectory in space, and this shows that the protons do more than simply move in a circle, irrespective of the dynamical details. In other words there are certainly at least two types of motion occurring and the overall dynamics (as revealed by the quasielastic scattering com- ponent) are indeed quite complex. We have proposed in the paper an interpretation in terms of a centre-of-mass relaxation triggered by simultaneous rotations of adjacent molecules and have modelled this assuming a superposition of local structures similar to that of the low-temperature modification, such as to give the correct high-tempera- ture symmetry.This is the most novel aspect of our work and I wonder if anyone has any comments on this model: I know that Prof. Pick for example has thought about this kind of problem. Dr. D. N. Batchelder (Queen Mary College, London) said: In our paper we have suggested that the asymmetry in the intensities of certain Friedel pairs, as illustrated in the Bijvoet ratio A, could be due to anomalous scattering. We have now used a simple model to estimate the maximum possible value of A for the (5,0,1)-(~,O,T) pair which could result from anomalous scattering and found it to be an order of magnitude smaller than the experimental result. The model assumed that only the sulphur atoms contribute to the anomalous scattering and that the structure factor FhkI can be separated into two parts, F s h k [ due to sulphur atoms in the unit cell and Fohk[ due to the rest.F o h k [ is real while FShkl has an imaginary component which, in a vector diagram, is anti-parallel to the imaginary component of Fsi,z,j. By adjusting the real and imaginary components in the vector diagram one can obtain a non- centrosymmetric ‘‘ structure ” which maximizes the difference between the structure factors of the (5,0,1) and (5,O,T) reflections. Since anomalous scattering thus appears to be ruled out as the cause of the asymmetry of the intensities of Friedel pairs, we are now investigating the possibility that there is a variation of transition temperature throughout the sample. With an absorption coefficient of 3 mm-I for Cu Kct radiation, different parts of the crystal could contribute more to the intensity of one reflection than its reciprocal.It is unlikely that the asymmetry is due to residual strain resulting from the solid- state polymerization in the crystal. Although the initial polymer which forms in the crystal is under strain, with the completion of polymerization all that strain should be relieved. The only residual strain should be that due to lattice defects present in the starting monomer crystal. Indeed these defects must be very important as the transition temperature appears to vary considerably from one crystal to another. We accept that any order parameters obtained for this phase transition must be treated with caution. It is certainly not yet possible to say that the transition has no first-order component and, in addition, it is still far from clear what the behaviour of a ‘‘ perfect ” crystal would be.Prof. A. J. Leadbetter (University of Exeter) said: Would Prof. Blinc expand a little on just what he means by the “ melting of chains”?GENERAL DISCUSSION 125 Prof. R. Blinc (University of Ljubljana) said: In the low-temperature phase the chains are rigid, well ordered and parallel to a given preferred direction. In the high- temperature phase, on the other hand, a chain may have several kinks which can be created and annihilated and which can move up and down the chain. Each con- figuration of kinks (defined as a series of gauche configurations of C-C bonds between which an odd number of trans C-C bonds must be present) decreases the overall chain length by an integer multiple of I .26 A.Taking into account the increase in the c lattice constant by 3 8, and a reorientation of the chains from an initially tilted position with respect to the layer normal, to a position parallel to this normal one finds that the average number of gtg kinks per chain is 1.5/1.26 = 1.2 in the high-temperature phase. The chains thus retain a significant amount of " nematic " order in the high-temperature phase above the " melting " transitions. Prof. R. M. Pick (Uniuersite' Pierre et Marie Curie, Paris) said : Other transitions take place with the same type of material CdC14(C,H2,+1NH3)2 for n < 10. Is it possible to relate, at least partly, the transitions with n z 10, with those with n = 1, 2 or 3? Prof.R. Blinc (University of Ljubljana) said : In layer-structure perovskites there are two driving mechanisms which induce the transitions: the melting of the chains and the disordering of the keys, i.e. the NH3 groups in the cavities formed by the CdC16 octahedra. In long-chain compounds the melting of the chains is dominant, whereas in compounds with n = 1, 2 or 3 it is the disordering of the keys and the transitions between the various NH-C1 hydrogen-bonding schemes which are responsible for the observed phase transitions. Dr. A. Novak (CNRS, Thiais, France) said: The compound of the general formula (NH3(CH2)3NH3)MnC14 shows four different phases in the temperature range 10- 350 K. The phase below 110 K is completely ordered while the three high-temperature phases are more or less disordered.Infrared and Raman spectra show discontinuities in the vicinity of T, in frequency, intensity and half-width for several bands due to internal and lattice vibrations, NH3 torsional motion in particular. The mechanism of the phase transitions is believed to be due mainly to rotational jumps of NH3 groups which couple with the librational motions of the (NH3(CH2)3NH3)2+ ion about its long axis when the temperature is raised.' C . Sourisseau and G . Lucazeau, J . Raman Spectrosc., 1979, 8, 311. Dr. D. N. Batchelder (Queen Mary College, London) said: A number of di- acetylenes also form lipid bilayers in a crystalline matrix which exhibit phase transi- tions. These materials have the general chemical formula CmH2, + l-C=C-C=C- (CH,),-COOH and they have been prepared as polycrystalline samples and, in a few cases, as multilayers using a Langmuir trough. Samples which contain ca.1% diacetylene polymer show optical and Raman spectra which are very sensitive to phase transitions which are dominated by the lipid bilayer. The lithium salt of tricosa- 10,12-diynoic acid is particularly convenient to study as there is a wide temperature range between the onset of the phase transition and the melting point. In this salt the optical and Raman spectra begin to shift and broaden above 50 "C indicating the onset of disorder. Provided the temperature is kept below 120 "C the changes are reversible. Research into these materials has been carried out by Prof. G. Wegner and Dr.B. Tieke at the University of Freiburg and Dr D. Bloor and Mr. C. Hubble at Queen Mary College.126 GENERAL DISCUSSION Prof. R. M. J. Cotterill (Technical University of Denmark, Lyngby) said: 1 am currently carrying out a Monte Carlo study of the gel-fluid transition in a lipid mono- layer, the preliminary results of which appear to endorse those obtained by Prof. Blinc. Each molecule in the computational model has two fully-saturated acyl chains, each having sixteen carbon and thirty-three hydrogen atoms. Rotation is possible about each carbon-carbon bond, the angular potential being taken to be the same as that for the central bond in n-butane. This has a barrier of 3.5 kcal mol-' between the trans and gauche positions, and the gauche and cis angular energies are 0.6 and 5.8 kcal mol-l, respectively, relative to the trans state.Intra- and inter-molecular poten- tials for all carbon-carbon, hydrogen-hydrogen, and carbon-hydrogen non-bonding interactions are assumed to have the Lennard-Jones form, Y(r) = ~ { ( a / r ) ' ~ -2(0/r)~}, and the individual parameters are occ = 0.51 nm, CTHH = 0.36 nm, oCH = 0.44 nm, cCC = 0.120 kcal mol-l, eHH = 0.123 kcal mol-' and cCH = 0.107 kcal mo1-I. The first carbon atoms of pairs of chains are at fixed separation distances, simulating the glycerol backbones of (dipalmitoyl) phospholipid molecules. Periodic boundaries are used and the irreducible cell contains 24 (= 6 x 4) molecules, i.e., 48 paired acyl chains. A typical elevational view of the model, during the order-disorder process, at 40 "C, is given in fig.2. FIG. 2.-Typical elevational view of the model, during the order-disorder process, at 40 "C.GENERAL DISCUSSION 127 An interesting feature of such an intermediate stage of the disordering process is the fact that the disorder increases with increasing proximity to the CH, terminal ends (seen at the bottom of fig. 2). This is in agreement with what has been found by Prof. Blinc. A particularly significant difference between his system and my own lies in the constraints imposed on the other ends of the acyl chains: these ends are fixed in his case but relatively free in my own. In his system the disorder might lead to chain-chain interdigitation, while in mine the most important effect is probably the increase in free volume, which promotes the transition.Dr. A. Dworkin (Uniuersite' Paris Sud, Orsay) said : I wish to emphasize the conclu- sions of Dr. Huller about using heat capacity measurements on molecular crystals in order to get evidence for second-order (continuous) phase transitions and conse- quently to determine their critical exponents. First, I draw attention to the paramount importance of the resolution in tempera- ture, by giving the example of SnC1,.2H20, whose transition appears continuous when looked at with temperature increments of 0.15 K' but shows a discontinuity when studied at 0.02 K intervals by the same authors., The very popular a.c. calorimetry works with such small temperature interval^,^ but this method does not give absolute values and its results should always be suspected, because of a lack of thermal equilibrium.Secondly the critical exponent a is obtained when plotting lnAC, against In (T - T,)/T,, which implies that a " normal " heat capacity has to be determined in order to get ACp. This is done either by a phenomenological treatment, by a com- parison with a similar substance without phase transition,' or by an extrapolation of the results obtained at lower or higher temperatures. Therefore it is clear that the critical exponent depends sensitively on the choice of the base line, as was shown previ~usly.~ Many other criteria are nevertheless discussed by Kornblit and Ahlers on this ~ubject.~ ' T. Matsuo, M. Oguni, H. Suga and S. Seki, Bull. Chem. Soc. Jpn, 1974, 47, 57. * T. Matsuo, M. Tatsumi, H.Suga and S. Seki, Solid State Comm., 1973, 13, 1829. F. L. Lederman, M. B. Salamon and L. W. Shacklette, Phys. Rev B, 1974,9, 2981. A. Kornblit and G. Ahlers, Phys. Rev. B, 1973, 8, 5163. H. Cailleau and A. Dworkin, Mol. Cryst. Liq. Cryst., 1979, 50, 217. Dr. A. Huller (KFA Jiilich) said: I agree with your comment-one has to be very careful with published critical exponents on apparently second-order phase transi- tions. In many cases a close look reveals a small discontinuity. One of the best safe- guards against a misinterpretation of experimental data is to see if the order parameter extrapolates to zero at the same temperature where the susceptibility extrapolates to infinity. If they do not, then the transition is discontinuous. Prof. G. M. Schneider (University ofBochum) said: With respect to fig.1 of Huller's paper, from which the existence of a phase transition at negative pressures can be deduced, I would like to mention a similar phenomenon found for the phase separa- tion in liquid binary mixtures in spite of the fact that there is no perfect analogy with respect to generalized theory. In some binary liquid mixtures, e.g., 2-methylpyridine + H20, closed immiscibility loops have been found to exist at negative pressures that can be shifted to positive pressures by the substitution of H20 by D20 or by adding outsalting salts to the 2-methylpyridine + water mixture.' G. M. Schneider, in Chemical Thermodynamics, ed. M. L. McGlashan (Specialist Periodical Report, The Chemical Society, London, 1978), vol. 2, chap.4.128 GENERAL DISCUSSION Prof. J. S. Rowlinson (University of Oxford) said : Prof. Schneider has suggested an analogy between the pressure maximum in Stevenson’s generalised phase diagram for the ammonium halides, which can lie at positive or negative pressures according to the composition, and the pressure extrema in liquid-liquid immiscibility curves which can also be changed from positive to negative pressures by changes of composition. There is, however, an important difference between the two phenomena; in his repre- sentation of the second, Schneider used mole fraction (a generalised density) as his independent variable and so it follows that the extrema are always (ordinary) critical points. In contrast, the extremum in Stevenson’s diagram, as drawn in Huller’s paper, is merely a turning point on a line of first-order transitions-there is no critical point.Dr. A. Huller (KFA Jiilich) said) : I thank Prof. Rowlinson for his comment, but I would like to remark that one can really do something to NH,Cl which has the same effect as applying negative pressures. If you replace some of the ammonium ions by Cs ions the lattice constant becomes larger (as with negative pressure) and the triple point is reached-l P. Brauer and A. BuBmann, 2. Nuturforsch. Teil A , 1976, 31, 213. Prof. H. Suga (Osaka University) said: I also would like to make a comment on the generalized phase diagram of ammonium halide crystals reported by Dr. Steven- son that Dr. Huller cited as fig. 1 in his paper. The phase diagram led us to suppose that we have an interesting sequence of phase transitions at constant high pressure just above the triple point.We questioned this interesting idea and studied the equi- librium coexistence curves by use of a high-pressure calorimeter recently constructed in our laboratory. Fig. 3 shows the heat capacities and molar volumes of ND,Br measured at 0.1, 50 and 1 11 MPa. These data were obtained along the constant pressure in the appro- priate temperature range. At low pressures, the transition takes place in two stages; from ordered cubic to tetragonal, and then to disordered cubic. At 111 MPa, the transition proceeds in a single step; from ordered cubic to disordered cubic. Fig. 4 gives the entropy of transition as a function of temperature and pressure around the triple point.The total entropy change is ca. Rln2 irrespective of pressure, and corresponds to the two possible orientations of NH; ion in the disordered cubic phase. Fig. 5 is the phase diagram obtained by plotting the temperature of the heat capacity peak as a function of pressure. There is a complicated situation around the triple point owing to the extremely slow rate of the lower phase transition, but the triple point is represented essentially by an intersection of the three coexisting lines. There seems to be no maximum in one branch of the coexisting curves. The dotted line in fig. 5 corresponds to that given by Dr. Stevenson. Although the present result is only for ND,Br crystals, we believe that it is generally true for the other ammonium halides. Dr.A. Huller (KFA Jiilich) said: I fully agree with Dr. Suga’s valuable comment on the shape of the Stevenson plot. On heating, the phase diagram of NH4Cl is exactly as represented in fig. 5 shown by Dr. Suga. I have shown the generalized Stevenson plot including the deuterated species which has first been published by Press et al. [ref. (14) of my paper]. It was my intention to stress the effect of deuteration and I was not so much interested in the detailed shape of the diagram in the vicinity of the triple point. I would like to remark, however, that all the transition lines shown in Dr. Suga’sGENERAL DISCUSSION 129 180 140 ,-I + 100 2 G E - c, --- 60 r( I - E “E 40.5 2 40.0 39.5 I I . 1 I I I 130 170 21 0 2 50 TIK FIG. 3.-Heat capacities and molar volumes of ND4Br measured at 0.1, 50 and 111 MPa.plot represent first-order phase transitions. There is an appreciable hysteresis for the 6 to y transition and the transition temperature is ill defined. Extensive measurements by Jahn’ on mixtures of NH,Br and NHjCl confirm Dr. Suga’s point on heating. On cooling the shape of the diagram is rather close to Stevenson’s original suggestion. I. R. Jahn, personal communication and to be published. Prof. G. M. Schneider (University of Bochurn) said: With respect to fig. 1 of Huller’s paper I would like to mention that the literature values of temperature and pressure for the tricritical point of NH,C1 differ considerably. Weiner and Garland1 found 255.95 K and 1492 bar from capacitance measure- ments of the change in length of a single crystal. Trappeniers and Mandema’ deter- mined 251.3 K and ca.950 bar from spin-lattice relaxation time experiments; older d.t.a. measurements of this group3 are probably erroneous since no corrections for the pressure dependence of the heat conductivity of the pressurizing gas were made. From preliminary d.s.c. experiments of M. Wirths in our Institute at Bochum a tri-130 GENERAL DISCUSSION critical pressure of ca. 1.5 kbar can be estimated. For additional citations see e.g., ref. (4). B. B. Weiner and C. W. Garland, Phys. Rev. B, 1971, 3, 1634; J. Chern. Phys., 1972, 56, 155. N. J. Trappeniers and W. Mandema, Physica, 1966,32, 1170; 1974,76, 123. N. J. Trappeniers et al., Physica, 1966, 32, 1161 ; Ber Bunsenges. Phys. Chem., 1966, 70, 1080.N. G. Parsonage and L. A. K. Staveley, Disorder in Crystals (Clarendon Press, Oxford, 1978). T / K FIG. 4.-Entropy of transition as a function of temperature and pressure around the triple point. Pressures are as follows: (a) 57.0, (6) 62.0, (c) 63.5, (d) 65.0, (e) 66.0 and (f) 67.0 MPa. Mr. M. Sprik (Uniuersity of Amsterdam) said: I would like to make a comment to support the point of view that the reversed isotope effect in ammonium bromide may be understood without the introduction of a pseudo spin-phonon coupling or an isotope-dependent hydrogen bonding. In a first approximation, the stress induced in the lattice by the orientational system can be represented by an isotropic contribution to the total pressure, the so-called orientational pressure. In an ordered phase, the orientational pressure is generally lower than in a disordered phase because of the negative anisotropic interaction energy due to the ordering.On the other hand, the rotational kinetic energy will, in general, be larger in an ordered phase as a consequence of the confinement of rotational or librational motion by the molecular field. For dis- continuous phase transformations these general considerations may be applied in approximate Clausius-Clapeyron relations for the derivatives of transition tempera- ture and pressure with respect to the inverse inertial moment.'GENERAL DISCUSSION 131 where p o is the orientational pressure; KO is the rotational kinetic energy; B; is the isothermal bulk modulus of the stable lattice and B = h2/I is a rotational parameter.120 100 80 a" 60 c --- 4 40 20 0 160 180 200 220 T/K FIG. 5.-Phase diagram obtained by plotting the temperature of the heat-capacity peak as a function of pressure: (-0-) present data, (- - -) R. Stevenson (1961). The first relation implies that, in general, the heavier isotope has the higher transition temperature. The 11-IV phase transition in ammonium bromide shows this common behaviour, as is summarized in table 2. The second relation predicts that the transition pressure is reduced by deuteration. The resulting slope of the transition line in the p T phase diagram of a particular isotope is given by the third relation. These values for the signs of the derivatives are not a thermodynamic necessity. I would like to propose that an interaction competing with the ordering interaction [for ammonium bromide, see ref.(2)] may be able to decrease the kinetic energy in the ordered phase with respect to the disordered phase and raise the orientational pressure, while at the same time the total Gibbs free energy is still reduced by the ordering. One may imagine that the competing interaction, by opposing the ordering potential, renders the angular dependence of the potential well more square in comparison to the simple crystal-field potential, confining the librational motion in the disordered phase. This allows the potential well in the ordered phase to be both deeper and wider. A similar argument can be given for the change in orientational pressure [see ref. (l)]. In this case, the Clausius-Clapeyron relations yield signs for the derivatives as is observed for the I1 + I11 transition (see table 2).132 GENERAL DISCUSSION TABLE 2.-sUMMARY OF THE II-IV PHASE TRANSITION IN AMMONIUM BROMIDE AKo AP” The relation for the isotope effect on the transition pressure also suggests an explanation for the fact that the difference in transition pressure between two isotopes (ca.1.3 kbar) is much larger than expected from the effect of deuteration in a stable phase, say the disordered phase (ca. 250 bar). The 1.3 kbar difference in transition pressure contains the thermodynamic change in the orientational system pertaining to the ordering, while the 250 bar does not. It is, therefore, my opinion that the re- normalization parameter r, correcting for the kinetic effect in eqn (2.7), is confusing because the kinetic effect also depends on the thermodynamic state of the orientational system itself.M. Sprik, A. J. Nijman and N. J. Trappeniers, Physicu, 1979, 98A, 231. A. Huller and J. W. Kane, J. Chem. Phys., 1974, 61, 3599; A. Huller, 2. Phys., 1974,270, 343. Dr. A. Huller (KFA Jiilich) said: Mr. Sprik develops his ideas about the negative isotope effect in the II-IV phase transition of NH,Br in two stages. The first one is based on thermodynamics. He concludes that the trend of the “orientational pressure ” at the transition must be anomalous. In a second step he proposes that competing interactions could be the reason for such behaviour. The first conclusion is true, if deuteration does not change the interactions. If it does, as Garland has proposed, the thermodynamic arguments are not conclusive. With respect to the second step I find it hard to imagine that the potential well simultaneously becomes deeper and wider at the phase transition.Prof. G. M. Schneider (Uniuersity of Bochum) said: I would like to present some results on mesomorphic phase transitions in liquid crystals at normal and high pressures that are related to the general scope of this Discussion. Phase-transition temperatures T,, and phase-transition enthalpies AHtr were determined up to 3 kbar using differen- tial thermal analysls (d.t.a.) and differential scanning calorimetry (d.s.c.) as experi- mental methods. Measurements were performed especially on some nematic liquid crystals (e.g., MBBA, EBBA) and on some homologues of the bis(4,4’-n-alkoxybenzyl- idene)-1,4-~henylenediamine series with 4 to 13 carbon atoms in the n-alkoxy chains where up to six smectic phases exist and triple points involving smectic phases only are found.Some results have already been published.’ Most of the T&) transition curves measured run essentially parallel, thus exhibiting rather similar slopes for very different phase transitions (solid-solid, solid-smectic, smectic-smectic, smectic- nematic, smectic-liquid isotropic, nematic-liquid isotropic). This fact provides evi- dence that the ratio AV/AS (or to a better degree of approximation AVIAH) is nearly constant for all these very different phase transitions, whereas the absolute values of AV and AS or AH, respectively, vary over orders of magnitude, AV/AH being ca.0.0013 cm3 J”. Approximately the same numerical value of AV/AH has been found in our paper of this Discussion for 1,3-dimethyladamantane. W. Spratte and G. M. Schneider, Ber. Bunsenges. Phys. Chem., 1976, 80, 886; W. Spratte and G. M. Schneider, Mol. Cryst. Liq. Cryst., 1979, 51, 101; J. Hermann, J. Quednau and G. M. Schneider, Mol. Cryst. Liq. Cryst., submitted for publication.GENERAL DISCUSSION 133 Prof. A. J. Leadbetter (University of Exeter) said: Can Dr. More say whether there is any relationship between the short-range structural correlations observed in the high-temperature disordered phase and structure of the low-temperature ordered phase? Dr. M. More (University of Lille) said: There is no direct relation between the two phases in CBr,.In the high-temperature phase, the observed diffuse scattering has been attributed to the effect of correlations via a hard-core potential but no critical effect has been observed when lowering the temperature. However, the low-tempera- ture phase shows a small distortion from a pseudo-cubic lattice with parameter equal to the high-temperature lattice parameter. Then one can distinguish between " centre- of-mass reflections " and the other ones which are characteristic of long-range orientational order. Because of the translation rotation coupling in phase I, the orientational order is coupled with the lattice distortion in a complicated way, leading through a first-order transition to a new phase where the translation-rotation coupling vanishes.Prof. R. M. Pick (Universite' Pierre et Marie Curie, Paris) said: Concerning the problem of linewidths in neutron scattering, I would like to mention that in our laboratory, we have performed Raman scattering experiments on the internal lines of CBr, in its plastic phase. For the vz and v4 lines, which are affected by molecular reorientations but not by induced-dipole-induced-dipole interactions, the half-width at half-maximum is ca. 3 cm-l (i.e., 0.1 THz), out of which 0.5 or 1 cm-l might be related to a vibrational lifetime, and these lines stand on a rather flat background. This 0.1 THz value is within a factor of 2 that obtained for r2 (cf. fig. 2 of More's paper); it is also in the same frequency range as the one at which the longitudinal sound velocities saturate (cf.fig. 6). It seems reasonable to relate this 0.2 THz value to the reorientational motion of a CBr, molecule from one potential well to another. Indeed (a) in a plastic crystal, the saturation of the sound velocity should be related to the quenching of the coupling between a macroscopic distortion and a molecular reorientation. (b) If the reorientations represent 90" rotations [as may be suggested by the p.d.f. Po (a)] and if they occur with an angular velocity of the order of the free- rotation angular velocity C O ~ = (kT'/I)* one also obtains a half-width at half-maximum of ca. 0.1 THz. If this interpretation is correct, the difficulty is transferred to the explanation of the r3 value of 0.5 THz obtained in the neutron coherent scattering experiments throughout the entire Brillouin zone.In this respect one can note that, as far as librations are concerned, the disordered nature of a plastic crystal also affects strongly the force constants (and the eigenvectors which are no longer plane waves) as the detection mechanism, which takes place only through the disordered Br atoms. The difference between a collective (or extended) librational mode and an individual (or local) one might then be difficult to detect even in a coherent scattering experiment: the presence of a given peak in the whole Brillouin zone could not be a decisive argument against its assignment to collective librational modes. Dr. G. S. Pawley (Uniuersity of Edinburgh) said : The dynamic aspects of the plastic phase with translation rotation coupling included can be attacked by computer simulations, always providing that a good potential function is available. Such a function exists for SF6 which gives instabilities for the lattice dynamics in the cubic phase but which gives a stable model in the simulation. In this model the molecules are oriented on average in the way X-ray diffraction suggests, but the molecules undergo occasional reorientational jumps.These jumps are about the (100) axes, and134 GENERAL DISCUSSION a jump by one molecule is usually followed by a jump of a neighbouring molecule about a different (100) axis. As yet insufficient calculations have been done to know whether there is any cooperative motion which localizes the excess jump energy for greater than a few picoseconds.The model used for the calculation was oversimpli- fied as translational motions were not included. Mr. M. Sprik (University of Amsterdam) (communicated): Prof. Michel’s choice of the operators in eqn (3.12) as the set of dynamical variables in the Mori formalism is, in my opinion, justified, provided the orientational system behaves classically. If quantum mechanics is no longer negligible in the dynamics of the orientational system, additional quasiconstants of motion have to be taken into account. This makes the validity of the expressions (4.1) and (4.2) in the NH,Br case questionable since, if the damping parameter II for NH,Br is still given by the expression (4.4), it may be expected that A is of the order of a typical phonon frequency instead of being smaller, as is stated on page 94.Unless the coupling coefficient p’ is extremely large, expression (4.4) implies that 3, will be comparable with the square root of the second moment of the spectral density of a second-order irreducible tensor [Raman spectrum, see eqn (3.18) and (3.19)]. The latter quantity is approximately equal to the librational frequency of the NHZ ions in the crystal field potential and, hence, of the order of an optical phonon frequency. On the other hand, NH4Br is certainly an instance of the slow relaxation case 3, < mi. But instead of identifying the damping parameter A with expression (4.4), it should, in my opinion, be interpreted as the rate of re- orientation between the two available orientations with respect to the cubic lattice.Prof. K. H. Michel (University of the Saar) (communicated): Our first aim in the present approach is to get a microscopic expression of the transport coefficient A, based on the Hamiltonian (2.1). The calculation is indeed classical and the choice of variables is the most simple non-trivial one. As a major approximation, the second moments (4.5a) and (4.5b) are calculated with a single-particle potential in the classical limit. As has not been mentioned explicitly in the present paper, subsequent. investi- gations show that the present theory enables us to understand the temperature dependence of the phonon linewidth measured by Brillouin scattering in KCN.l In addition, for KCN we understand from eqn (4.4) why the 3, measured by neutron coherent scattering [ref.(6)] has about the same value as the single-particle relaxation frequency measured by Raman scattering.2 As far as NH,Br is concerned, the Hamiltonian (2.1) with the coupling to acoustic phonons is not relevant. Consequently the calculation of the moments (A;, A:), eqn (3.13a)-(3.13~) would give different results. Nevertheless I believe that a calculation according to the lines of the present approach, eventually with consideration of additional dynamic variables, would also be of great interest in the case of Nl3,Br. M. Boissier, R. Vacher, D. Fontaine and R. M. Pick, J. Physique, 1978, 39, 205. * D. Fontaine and R. M. Pick, J. Physique, 1979, 40, 1105. Dr. A. I. M. Rae (University of Birmingham) said: Since submitting our paper, we have collected single-crystal X-ray data from the h0Z zone of malononitrile at a temperature of ca. 100 K, from which we have confirmed that the space-group of the a phase is P21/n identical with that of the y phase.We have also collected X-ray powder data at a temperature of ca. 85 K and have refined this using Dr. Pawley’s EDINP program with rigid-body constraints. The resulting structure of the a phase is very similar toethat of the y phase and will be reported in detail elsewhere.GENERAL DISCUSSION 135 We have given some further consideration to the implications of the Landau theory discussed in our paper [eqn (1)-(4)] which describes the temperature variation of the free energy and order parameter in an cc-/?-cc series of phase transitions. The resulting contributions to the entropy and heat capacity are : A ‘‘2 s = - (:$) = -- (2T - Tl - T2) (T - TJ (T - TJ P 2c and c = T%= [(T - Q2 + 4(T - Tl) (T - T2) + (T - TJ2].dT 2C (Note: P is the order parameter not the pressure.) It follows that C = 0 when T = $[(Tl + T2) & (Tl - T2)/v’3] and is negative between these two temperatures. Such a negative contribution to the specific heat is a necessary consequence of the assumption that the entropies of the high- and low- temperature phases are identical, and does not depend on the details of the model used. In practice other contributions (e.g., vibrational) are positive and much larger than this and the total heat capacity is therefore always positive. However, this property is not an intrinsic requirement of the model and it would appear to be possible to imagine a hypothetical ensemble of oscillators whose coupling coefficients were such that the ratio A”2/2C was very large and the total heat capacity consequent- ly negative over some temperature range.Prof. G. J. Hills (University of Southampton) said : In his verbal introduction of his paper, Dr. Rae touched on the possibility of systems exhibiting negative heat capaci- ties. Quite apart from any ensuing damage that such a possibility might inflict on the laws of thermodynamics it needs to be restated (with surprising regularity) that isobaric enthalpy changes in condensed media always contain a temperature- dependent-density-dependent contribution which is invariably large because the internal pressure of condensed phases is high. Moreover, the contribution to the specific heat may be positive or negative depending on the sign of the volume change.Thus, UT (AH), = ( W V + p ( A v ) ’ and \ J Y necessarily positive possibly negative where the terms have their usual thermodynamic meaning ( p is the pressure, cc the molar expansivity and p the molar compressibility). The question of apparently negative specific heats therefore needs to be examined in a wide framework of related quantities. Dr. R. M. Lynden-Bell (University of Cambridge) said: In introducing this paper Dr. Rae remarked that his model gives a negative contribution to the specific heat and that he sees no reason to stop such a model from having a total heat capacity that is negative.136 GENERAL DISCUSSION There is no theoretical reason why an isolated system should not show such behaviour.Systems with negative specific heat are well known in astrophysics; both self-gravitating gas spheres’ and black holes’ can show this phenomenon. We can see the reason for this from the Virial theorem for an r-I potential: E+T=O where T is the kinetic energy. As the temperature is proportional to the kinetic energy, an increase in energy, E , leads to a decrease in temperature, Although systems with negative specific heats can exist in microcanonical en- sembles (that is when isolated), they are unstable in contact with a heat bath or with a number of duplicate systems. The specific heat of a Gibbs canonical ensemble is always positive as it depends on the square of the energy fluctuations C, = kp’ (E - E)’.A system which has a negative specific heat when isolated shows a first-order phase transition in a canonical en~emble.~ Thus the negative specific heat regions of Dr. Rae’s models might be difficult to observe. D. Lynden-Bell and R. Wood, Mon. Not. R. Astr. Suc., 1967, 136, 101. S. W. Hawking, Phys. Rev. D, 1976, 13, 191. D. Lynden-Bell and R. M. Lynden-Bell, Mon. Not. R. Astr. Soc., 1977,181,405; P. Hertel and W. Thirring, Comm. Math. Phys., 1972, 28, 159. Dr. A. Novak (CNRS, Thiais, France) said: I have three comments on phase transi- tions in malononitrile. They are based mainly on an infrared and Raman study of this compound. The first one concerns the space-group symmetries of a, p, y phases. The infrared and Raman spectra of a and y phases are very similar and consistent with C2, factor group symmetries and four molecules in the unit cell.In the spectral region corresponding to internal vibrations we observe mainly doublets and their infrared and Raman frequencies generally do not coincide. The spectra of the inter- mediate phase /?, on the other hand, are different. Triplets and even quadruplets are frequently observed in both Raman and infrared. We would thus prefer a non- centrosymmetric space group such as P21 = C? as initially suggested by Nakamura et aZ.l in order to interpret our spectra. Some dielectric or other measurements of the phase /? would be useful. The second comment is about the soft mode which has been observed in the Raman spectra as the lowest lattice frequency at 12 cm-’ at 15 K. It has been assigned to a predominantly 3; libration, i.e., to a rotational vibration about the C2 molecular axis which is in very good agreement with the X-ray diffrac- tion work given in the discussed paper (Dove and Rae).The most remarkable feature of the soft mode, however, is its behaviour with temperature: its frequency decreases continuously to zero at the a -+ p transition temperature (T, = 141 K) and then increases to a maximum at 16 cm-I in phase /? at 21 5 K, i.e., zero frequency is reached when T, is approached from above and below. When the temperature is raised above 215 K the frequency decreases again to zero at T, = 296 K corresponding to /? --f y transition. No equivalent of this mode has been observed in the y phase and there is no anomalous broadening of the Rayleigh line either.The soft-mode behaviour is strikingly similar to the 14N n.q.r. results of Zussman and Alexander2 and reminds one of that of the Rochelle salt.3 The vibrational data confirm thus the suggestion that the u 3 p -+ y transitions are of second order and of the displacive type. The p exponent can be extracted from a log v against T plot and its value amounts to 1/2. The last comment deals with the 6 phase which is quite different in many aspects. The low- temperature 6 phase is stable with respect to /? phase below 260 K. It contains, unlikeGENERAL DISCUSSION 137 a, p, y phases, intermolecular C-N * - N hydrogen bonds as indicated by a low- frequency shift (ca. 60cm-I) of CH stretching bands and by a high-frequency shift of CN stretching and CH, scissoring bands in going from a~ to 6 phase at 90 K.There are fewer Raman lattice bands with respect to any of u, p, y phases, showing a higher symmetry and/or smaller 2 of the 6 phase crystal in agreement with the n.q.r. results. Finally, the lowest two Raman lattice frequencies at 95.5 and 59.6 cm-I (1 10 K) decrease strongly with increasing temperature but they never reach zero. This shows that the 6 -+ /3 transition is a first-order one which is consistent with the normal specific-heat a n ~ r n a l y . ~ The fact that there is a considerable volume change during the transformation and that the 6 phase alone contains hydrogen bonds would suggest that 6 -+ /3 phase change is of reconstructive type. N. Nakamura and K. Obatake, Phys. Letters, A, 1971, 34, 3721.A. Zussman and S. Alexander, J. Chem. Phys., 1968, 49, 372. J. Habluetzel, Helu. Phys. Acta, 1939, 12, 489. H. L. Girdhar, E. F. Westrum, and C. A. Wulf, J. Chem. Eng. Data, 1968, 13, 239. Dr. A. I. M. Rae (University of Birmingham) said: The X-ray evidence for the p- phase of malononitrile being triclinic is set out in our paper and is, we believe, in- controvertible. If the structure were also to be non-centrosymmetric, the space group would have to be PI rather than Pi as assumed by us. However, this is highly im- probable, both because our structure refinement assuming Pi was quite successful and also because a continuous transition from P2Jn to PI is forbidden by the Landau rules. We believe that the multiplet structures of the Raman and infrared spectra reported by Dr.Novak and also by Savoie et al.' are in fact consistent with the structure of the p phase reported in our paper, when it is remembered that this con- tains two independent malononitrile molecules in the asymmetric unit. The temperature dependence of the soft mode reported by Dr. Novak is in good agreement with what would be expected, both from our experimental results and from the extended form of Landau theory reported in our paper. The spectroscopic evidence concerning the nature of the 6 phase is also very interesting and we are currently carrying out experimental and theoretical investiga- tions into the structure of this modification. R. Savoie et al., Can. J. Chem., 1976, 54, 3293. Prof. R. M. Pick (Universite' Pierre et Marie Curie, Paris) said: The Raman scattering experiments by Le Calve and Novak presented at the poster session on malononitrile, show the existence of a soft mode both above and below the a-p transition.As the Dove and Rae experiments show that the a phase has a higher symmetry than the p one, the existence of a Raman active soft mode in the a phase implies a coupling of this mode with an elastic constant, and it is this latter quantity which should go to zero at the a-/3 transition.' The same effect should also exist at the /3-y transition as the a and y phases are identical. It would be interesting to look for those elastic constant softenings. It also means that the thermodynamics of these phase transitions has to be partly remodelled to take into account these effects which are required by symmetry considerations. Axe-Miller theorem: see P. B. Miller and J. Axe, Phys. Rev., 1967, 163, 924. Dr. R. W. Mum (UMIST, Manchester) and Dr. T. Luty (Technical University, Wroclaw) (partly communicated): Prof. Strobl asked whether from the calcula- tions of the lattice dynamics under different strains one could calculate microscopic138 GENERAL DISCUSSION Gruneisen parameters and hence the equation of state in the quasiharmonic approximation. The microscopic Gruneisen parameters are defined as where is the frequency of mode Y, lij is a strain component and I' denotes that other strain components are held constant. These quantities are simply related to the slopes of the curves in fig. 2 of our paper. We have calculated Gruneisen parameters for the zone-centre optic modes under symmetry-preserving strains in the limit of zero strain. The results are given in table 3. TABLE 3 .-MICROSCOPIC ZERO-STRAIN GRUNEISEN PARAMETERS CALCULATED FOR ZONE-CENTRE OPTIC MODES IN TETRACYANOETHYLENE 54.8 77.5 100.8 29.1 91.8 105.7 25.3 89.4 73.3 3.72 3.81 4.05 0.34 2.76 4.05 5.27 6.23 1.93 6.79 1.16 3.02 4.00 3.07 0.40 1.80 5.04 -0.68 1.84 -0.36 4.22 -1.66 2.00 1.10 11.26 -2.71 2.65 1.76 1.91 0.85 8.66 -5.38 1.69 1 .so 1.51 1.37 Calculation of the equation of state would require Gruneisen parameters at points throughout the Brillouin zone for all strains, including those which lower the crystal symmetry. Macroscopic Gruneisen functions could then be obtained in the quasi- harmonic approximation as averages of the microscopic Gruneisen parameters weighted with the heat capacity contribution c(') of the corresponding mode: yij = (l/C,)(aS/aIij)Tl', (2) where Cl is the heat capacity at constant strain.' With the elastic constants, derived from the slopes of the dispersion curves for the acoustic modes at the zone centre, the Gruneisen functions yield the thermal expansion. In this way the equation of state could be obtained for arbitrary strain (ignoring constant-strain anharmonicity). However, we have not attempted this rather complicated procedure. T. H. K. Barron and R. W. Munn, Philos. Mag., 1967, 15, 85.

ISSN:0301-7249    

DOI:10.1039/DC9806900120

出版商:RSC    

年代:1980

数据来源: RSC

摘要:

Calorimetric Investigations of Plastic Crystais at Low Temperatures and High Pressures with Differential Scanning Calorimetry BY HORST ARNTZ AND GERHARD M. SCHNEIDER Department of Chemistry, University of Bochum, 4630 Bochum, West Germany Received 3rd December, 1979 A new high-pressure low-temperature differential scanning calorimeter (d.s.c.) has been developed. The calorimeter has been designed for the investigation of some plastic crystals over wide ranges of temperature and pressure, e.g., between 100 and 450 K at normal pressure and 100 and 300 K at 4 kbar. This d.s.c. apparatus has been applied to the determination of transition temperatures and transition enthalpies of cyclohexane, 1 ,3-dimethyladamantaneY and 1,3,5-trimethyIadamantane at normal and elevated pressures from which the transition entropies were also determined.By means of these values and the slopes of the T(p) transition curves transition volumes could be additionally calculated. Quantitative determinations of enthalpies of transformation at high pressures were recently performed by Kamphausen lV3 using the d.s.c. principle. The high-pressure microcalorimeter developed was also applied to the investigation of phase transitions of some liquid crystals up to 2.5 kbar.4 The results show that the d.s.c. technique is capable of yielding accurate values, e.g., of the enthalpy changes for solid-solid and solid-liquid transitions at high pressures. Since the use of this microcalorimeter was limited to temperatures above 250 K a new high-pressure low-temperature d.s.c. microcalorimeter has been developed t o make possible high-pressure investigations in the low-temperature region down t o 100 K.EXPERIMENTAL The main parts of the high-pressure low-temperature d.s.c. microcalorimeter are two iden- tical cylindrical autoclaves, each of them closed by two Bridgman pistons. They are in- stalled in a thermostatted jacket that can be cooled with liquid nitrogen and also heated with linear heating rates from 0.1 to 2.5 K min-'. The sample and reference holders of the high-pressure d.s.c. measuring head are mounted in the vessels on the top of the lower piston, respectively; the control unit is a Perkin-Elmer DSC-2 regulator. In order to get quantitative values for the transition enthalpies one has to prevent heat transport by convection.Therefore both holders are carefully insulated with glass fibre, Teflon, and steatite. The pressure is transmitted by highly purified helium and measured with a Heise bourdon gauge and a strain gauge. The substances are enclosed into a capsule made of indium or stainless steel in order to prevent the pressure-transmitting gas from being dissolved in the samples. The temperature was calibrated with the melting point of indium (99.999%) and the transition points of highly purified cyclopentane. Energy calibrations were based on the fusion of indium and the transitions of cyclopentane. At high pressures mercury was used as an internal standard.1 40 CALORIMETRIC INVESTIGATIONS AT HIGH PRESSURES SUBSTANCES Cyclohexane was obtained from Merck AG, Darmstadt, with a purity of 99.7%.1,3- Dimethyladamantane ( > 99%) was obtained from EGA-Chemie, Steinheim/Albuch. 1,3,5-TrimethyIadamantane was prepared from the appropriate bromide using the Grignard coupling procedure described by E. Osawa et al.’ Both adamantanes were purified by pre- parative gas chromatography; the final purity was found to be better than 99.8%. RESULTS AND DISCUSSION CYCLOHEXANE In fig. 1 five original d.s.c. traces obtained experimentally are presented for cyclo- hexane at 1,270, 500, 1000 and 1300 bar; only the peaks of the solid-solid transitions are plotted. The plastic crystalline phase sI is face-centred cubic6 and stable between 279.8 and 186.2 K; phase s I I is monoclinic and stable below 186.2 K. At elevated pressures a new solid At normal pressure cyclohexane exhibits a solid-solid transition at 186.2 K.I I 186 190 t 1 I 192 197 I I I 196 200 205 * 1 I I 200 205 210 21 5 T K FIG. 1.-D.s.c. peaks of cyclohexane at different pressures (see text), ( a ) 1 , (6) 270, (c) 500,(d) 1000, ( e ) 1300 bar. phase, sIl1, which has been reported by Wurflinger,’ was confirmed; its structure is not yet known. Fig. 2 shows the T(p) phase diagram of cyclohexane (without the melting curve) obtained from measurements of this work; it is in good agreement with the values found by Wii~-flinger.~ The triple point where the three solid phases sI, sII and s l I I coexist is at ca. 200 bar and 191 K.230 220 g 210 &- 2.00 190 H . ARNTZ AND G . M. SCHNEIDER I I I 1 141 I I 1 500 1000 1 500 2 000 p I bar FIG.2.--T(p) phase diagram of cyclohexane (without the melting curve). In fig. 3 the enthalpies of the solid-solid transitions AH(sI1 --f sII1) and AH(sIIl --+ sI) of cyclohexane along the coexistence lines as well as the sum AH(s,, -+ sIII) + AH(sIII -+ s,) of both transitions are plotted as a function of pressure. The enthalpy of melting of mercury (internal standard substance) AH(s -+ 1) is additionally given. TABLE 1 .-PHASE TRANSFORMATIONS OF CYCLOHEXANE AS A FUNCTION OF PRESSURE. TRANSI- TION TEMPERATURES, T, ENTHALPY CHANGES, AH, ENTROPY CHANGES, AS, AND VOLUME CHANGES, Av, ALONG THE COEXISTENCE LINES. SII + SI SII -+ SIII SIII -+ SI SII + SI SII + SIII SIII + SI - 6.72 - - 1 186.2 - 500 - 195.6 198.7 - 1.18 5.76 1000 - 202.7 210.2 - 1.21 5.85 1500 - 209.4 221.2 - 1.25 6.00 p/bar A V/cm3 mol - AS/J K-l mol-' - - 1 9.7 - 36.1 - 500 - 0.87 7.1 - 6.03 29.0 1000 - 0.81 6.3 - 5.97 27.8 1500 - 0.77 5.8 - 5.97 27.1142 CALORIMETRIC INVESTIGATIONS AT HIGH PRESSURES This enthalpy change is nearly independent of pressure,* whereas the values for the solid-solid transition of cyclohexane increase slightly with pressure.From the T(p) and AH(p) diagrams in fig. 2 and 3, respectively, the data compiled in table 1 were obtained by interpolation. The value of the transition enthalpy AH(sI1 --f s,,,) is about one fifth of the transition enthalpy AH(s,II --f s,). From the transition enthalpies and the transition temperatures the entropy changes AS along the coexistence lines were calculated from eqn (1) AS = AHIT. I ,-x-x-x-x- I 500 1000 1500 plbar FIG.3.-Transition enthalpies AH of cyclohexane and mercury (standard substance) as a function of pressure along the coexistence lines [I, AH(sII -+ s d ; 11, AH(s111 -+ sJ; 111, AH(s.11 -+ s.111) + AH(sII1 --+ sI); IV, AH(s -+ 1) of Hg]. The corresponding volume changes A V could be calculated using Clapeyron’s equa- tion, eqn (2) (dPldT)coex = AHITAV - (2) The data for the entropy changes and the volume changes accompanying the phase transformations are also summarized in table 1. It follows that AV(SII -+ s,,,) is only z 13% of AV(~111 -+ s,).H . ARNTZ AND G . M. SCHNEIDER 143 From the precision of the transition enthalpies (better than 3 %) and the transition temperatures ( z & 1 K) and taking into account the error of (dp/dT),,,, ; an error of The precision of the results can be tested by the condition that at the triple point the sum of the corresponding transition enthalpies AH(s11 +.sIII) and AH(s111 -+ sI) must be equal to AH(sI1 + sI) [see eqn (3a)l. The corresponding condition also holds for the transition volumes [see eqn (3b)l 10% for the A V values was estimated. m s 1 1 + SIII) + AH(SII1 +. SI) = AWSII -+ SI) AV(S1, +. S I I I ) + m s 1 1 1 +. SI) = AVSII +. SI) (34 (3b) These equations only hold at the triple point. volume changes and enthalpy changes, respectively. According to eqn (3a) and (3b) deviations of <5% result from the sums of the 1,3-D I METH Y LA D A MA N T AN E 1,3-Dimethyladarnantane (Cl2HZO) consists of three condensed cyclohexane rings in the chair configuration with two methyl groups.It has a high melting point ( T = 244 K) and a low entropy of melting (AS = 2.85 J K-' mol-I) at normal pressure. The plastic crystal undergoes a solid-solid phase transition at 221 K with a high value TABLE 2.-PHASE TRANSFORMATIONS OF 1,3-DIMETHYLADAMANTANE AS A FUNCTION OF PRESSURE. CHANGES A Y ALONG THE COEXISTENCE LINES. TRANSITION TEMPERATURES T, ENTHALPY CHANGES AH, ENTROPY CHANGES A S AND VOLUME 1 2 2 1 .o 244.0 7.65 0.94 500 2 3 5 . 0 258.9 7 . 2 3 1.01 800 2 4 3 . 6 268.0 7.08 1 . 1 0 - 6.76 - 1 2 0 0 255.4 p/bar AV/cm3 mol-' AS/J K-' mol-' 1 9.9 1 . 2 34.6 3.85 500 8.8 1 . 2 30.8 3 . 9 800 8.3 1 . 2 29.1 4.1 - 26.5 - 1 2 0 0 7.6 of the entropy of transition AS = 34.6 J K-l mol-l. The phase transition enthalpies AH(s, -+ 1) = 0.94 kJ mol-I and AH(s11 -+ s,) = 7.65 kJ mol-' and the above mentioned temperatures determined in this work at atmospheric pressure are in good agreement with those reported by T.Clark et aL9 In fig. 4(a) the T(p) phase diagram and in fig. 4b the enthalpies of melting and of the solid-solid transition of 1,3-dimethyladarnantane are shown as a function of pressure along the coexistence lines ; whereas the values for the solid-solid transition144 CALORIMETRIC INVESTIGATIONS A T HIGH PRESSURES enthalpy decrease slightly with increasing pressure, the enthalpy change on melting increases by z 16% between 1 and 800 bar. The slopes of both T(p) transition curves are nearly equal implying that the quotient AV/AS is essentially constant. Nevertheless at atmospheric pressure AS(s11 --f s,) is about nine times as large as AS(SI -+ 1) and AV(s11 --f s,) about eight times as large as AV(s, -+ 1) giving evidence for a correlation between AVand A S or AH, respectively.The same has also been observed for liquid crystals lo where similar AV/AH values plbar plbar FIG. 4.-Phase transitions of 1,3-dirnethyladamantane. (a) T(p) phase diagram. (b) Transition enthalpies AH as a function of pressure along the coexistence lines [I, AH(sI -+ 1); 11, AH(s1I -+ s')]. have been found for some mesomorphic transformations as for the solid-solid transitions of the plastic crystals studied in this work. I ,3,5-TR I M E T H Y L A D A MANTA N E The investigation of 1,3,5-trimethyladarnantane showed that the solid-solid transition behaviour depends strongly on thermal pretreatment of the sample whereas melting temperature (255 & 1) K and melting enthalpy (1.92 & 0.05) kJ mol-1 were found to be independent of the pretreatment.Because of large supercooling effects transition temperatures and transition en- thalpies have been determined from heating runs. From heating the solid starting at 180 K a solid-solid transition enthalpy of (4.38 0.06) kJ mol-' at 210.5 K is obtained. When 1,3,5-trimethyladarnantane, however, is tempered at 100 K, the solid- solid transition occurs at 2 3 4 . 7 K on heating, the transition enthalpy being ( 7 . 7 5 * 0.12) kJ mol-l, and sometimes even an exothermic transition is found in the region of 180 K. The transition temperatures and the transition enthalpies obtained experimentally in this work differ from the values reported by Clark et ~ 1 .~ At high pressures only the second transition is found. Some results for 1,3,5- trimethyladamantane at elevated pressures are given in Table 3.H . ARNTZ AND G . M . SCHNEIDER 145 TABLE 3.-PHASE TRANSFORMATIONS OF 1,3,5-TRIMETHYLADAMANTANE AS A FUNCTION OF AND VOLUME CHANGES, A v , ALONG THE COEXISTENCE LINES. PRESSURE. TRANSITION TEMPERATURES, T, ENTHALPY CHANGES, AH, ENTROPY CHANGES, AS, SII+SI s,+l SII+SI s p l 200 241.2 263.1 7.62 1.94 300 244.4 267.1 7.56 1.95 400 247.6 271.1 7.49 1.96 500 250.9 7.43 800 260.6 7.23 1100 270.3 7.04 plbar AV/cm3 mol-' AS/J K-' mol-I SII-tSI SI+l SII-+SI SI+1 200 10.2 3.0 31.6 7.4 300 10.0 2.9 30.9 7.3 400 9.8 2.9 30.3 7.2 500 9.6 29.6 800 9.0 27.7 1100 8.4 26.1 There is only a small temperature range (ca.20 K) for the orientationally disordered phase of 1,3,5trimethyladamantane. Whereas the melting enthalpy is essentially constant, the solid-solid transition enthalpy decreases with increasing pressure in analogy with the results on 1,3-dimethyladamantanee Accordingly the transition entropy also decreases with pressure here by ca. 17% up to 1 kbar. The authors thank Dr. G. Klaerner for his help in the preparation and purifica- Financial support of the Deutsche Forschungsgemeinschaft tion of the adamantanes. (D.F.G.) is gratefully acknowledged. M. Kamphausen and G. M. Schneider, Thermochim. Acta, 1978,22, 371. M. Kamphausen Dissertation (University of Bochum W. Germany, 1976). E. Osawa, Z. Majerski and P. von R. Schleyer, J . Org. Chem., 1971, 36, 205. R. Kahn, R. Fourme, D. Andri and M. Renaud, Acta Cryst. B, 1973,29, 131. A. Wiirfiinger, Ber. Bunsenges. phys. Chem., 1975, 39, 1195. 112a. T. Clark, T. Mc. 0. Knox, H. Mackle, M. A. McKervey. J.C.S. Faraday I, 1977,73,1224. Crysf., 1979, 51, 101. ' M. Kamphausen, Rev. Sci. Instr., 1975, 46, 668. * R. Sandrock, M. Kamphausen and G. M. Schneider, Mol. Cryst. Liq. Cryst., 1978,45, 257. * Landolt-Bornstein, Zuhlenwerte und Funktionen (Springer-Verlag, Berlin, 6th edn, 1960), vol lo W. Spratte and G . M. Schneider, Ber. Bunsenges. phys. Chem., 1976, 80, 886; Mol. Cryst. Liq.

ISSN:0301-7249    

DOI:10.1039/DC9806900139

出版商:RSC    

年代:1980

数据来源: RSC

摘要:

High-pressure Phase Transitions in Molecular and Plastic Crystals BY ALBERT WURFLINGER University of Bochum, Institute of Physical Chemistry, 4630 Bochum, West Germany Received 3rd December, 1979 The phase transitions of some molecular and plastic crystals have been studied byp Wand dielectric constant measurements up to 3000 bar. The pVT data show that the density of solid dodecane immediately below the freezing point is comparable with the density of solid undecane immediately below the rotational transition temperature. The phase diagram of acetonitrile exhibits a solid- solid transition (denoted as an a-B solid-solid transition at atmospheric pressure), the pressure de- pendence of which has not yet been reported. Also cyclohexanone has been studied; it exhibits three solid phases (I, I1 and 111), one of which (11) is only observed at elevated pressures.The dielectric results for cyclohexanone are discussed in terms of the Kirkwood-Frohlich-Onsager theory. The Kirkwood correlation g-factor is about unity both for liquid and solid (I) cyclohexanone. How- ever, a small increase in the g-factor is observed at the freezing point and a considerable decrease at the 1-11 solid-solid transition. In recent years the high-pressure phase behaviour of molecular and plastic crystals has been studied by different experimental methods, e.g., differential thermal analysis,l4 dielectric c o n ~ t a n t , ~ * ~ and p VT measurement^.^-^^ Plastic crystals exhibit at least one solid-solid transition, accompanied by a large enthalpy and volume change. This phase transition is associated with the loss of orientational freedom, leading to a distinct break in the permittivity insofar as polar compounds are considered.Some plastic crystals, moreover, have an intermediate phase transition for which the orien- tational order is partially l o ~ t . ~ p ~ ~ * ~ ~ In some cases the intermediate solid-solid transi- tion is only observed at elevated pressure^.^*^ This paper gives new experimental results for the p VT data of undecane and dode- cane, the phase behaviour of which has been studied in earlier investigations.' Also the phase behaviour of acetonitrile is studied with p VT and dielectric measurements. New dielectric results of cyclohexanone are discussed, together with recently de- termined p VT data,l' in terms of the Kirkwood-Frohlich-Onsager theory.This theory has been widely used for the discussion of polar fluids,14*15 but should also be applicable to the plastic phases of polar compounds, where the high value of the dielectric constant is maintained or even increased. Bottcher et aZ.16 have shown that the Kirkwood-Frohlich equation is also valid in the case of molecules with isotropic polarizabilities on a cubic lattice, and Hassel and Sommerfeldt l7 found cyclohexanone to have a face-centred cubic lattice in the high-temperature solid phase (denoted here as solid I). EXPERIMENTAL The pVTmeasurements were carried out with a new high-pressure apparatus developed by Landau Two high-pressure devices have been used for the differential thermalA . WURFLINGER 147 and described in detail el~ewhere.~*’O The substance under investigation is enclosed within a steel capsule that is closed by a special moving piston.The piston consists of two parts, separated by an indium seal. A hollow space between these works like a Bridgman’s un- supported area yielding a very good sealing of the piston, even after solidification of the substance. The displacement of this moving piston is recorded inductively allowing the calculation of volume changes. The high-pressure equipment for the dielectric measurements has been described in ref. (7) where details of the experimental procedure and instruments used are also given. Prelimin- ary results on cyclohexanone were obtained with an open capacitor that consisted of two cylinders.’ A remarkable improvement was achieved in transmitting the pressure with a moving piston similar to that mentioned above for the p VT measurements.The improved capacitor was first applied to the dielectric investigation of acetonitrile and will be described elsewhere. Commercial cyclohexanone (Merck, Darmstadt) was purified as described in ref. (6) and re-examined with the improved capacitor. The frequency used was 1 MHz. No significant frequency dependence or dielectric relaxation was observed. The accuracy in E (dielectric constant) is believed to be between 0.5 and 1%. RESULTS THERMODYNAMIC MEASUREMENTS Fig. 1 shows former results of the phase behaviour of some even (on the left) and odd (on the right) n-alkanes.’” Most of them exhibit a solid-solid transition 403 383 k4 L.363 3 4 3 323 303 I 1 2 233LJ+’*- 213b 1 2 3 plkbar FIG. 1 .-Phase diagrams of several even (left-hand) and odd (right-hand) n-alkanes. The hatched areas are confined above by the melting curve and below by the rotational transition line.148 HIGH-PRESSURE PHASE TRANSITIONS (rotational transition) immediately below the melting curve. The high-temperature solid phase is to a certain degree plastic and marked as a hatched area in fig. 1. The rotational transition is observed between nonane and henicosane only for the odd n-alkanes and between docosane and about C40 also for the even n-alkanes. A detailed discussion for the odd n-alkanes has already been given in ref. (1). The even n-alkanes reported by Koppitz et al.' were partially re-examined by Josefiak et aL3 The plot of C36H74 is missing from fig.1 (because it has not yet been redeter- mined), but is most probably similar to the phase behaviour of the adjacent n-alkanes. In all cases the experimentally observed plastic phase of the alkanes is restricted to a limited pressure range. Fig. 2 shows recently determined pVT data of undecane and d ~ d e c a n e . ~ The 1 . 4 1.2 4 I M % . a 1 . 2 1.1 plkbar FIG. 2.-Specific volume as a function of pressure for undecane (left-hand) and dodecane (right-hand) at different constant temperatures (in K). specific volume is plotted against pressure for different constant temperatures. Two distinct steps are observed in the volume against pressure plot of undecane, corre- sponding to the melting (larger step) and the rotational transition (lower step), whereas dodecane shows only one step corresponding to the volume change of melting. The distance between the two steps of undecane diminishes with increasing pressure, indicating the convergence of the transition lines which intersect at the triple point liquid-solid-I-solid-I1 (cf.fig. 1). Above the triple point there is only one step, due to the melting. The volume change of the rotational transition is nearly pressure-independent, but the volume changes of melting decrease considerably with increasing pressure as has also been found by other authors.'* Furthermore the volume change of melting of dodecane (which exhibits no rotational transition) is approximately the sum of the volume changes of melting and the rotational transition of undecane.It seems as if the rotational transition anticipates part of the melting process of the n-alkanes. Fig. 2 shows further that the rotational transition line runs fairly parallelA . WURFLINGER 1 49 to an isochore, a statement that had already been suggested in earlier investiga- tions.' p VT data of acetonitrile (Landa~),~.'~ cyclohexane and cyclohexanone (Wisotzki) have also been determined, both for the liquid and solid states. Fig. 3 shows the 0 1 2 3 plkbar x , pVTmeasurements ; FIG. 3.-Phase diagram of acetonitrile. 0, dielectric constant measurements;6 A, ref. (19); 0, ref. (20). phase diagram of acetonitrile in comparison with literature data. The melting curve has already been reported by other author^,^^,^^ but the pressure dependence of the a-/3 solid-solid transition has not been found in the literature.However, there is an additional paper of interest by Jakobsen and Mikawa21 who believe they have found a third solid phase y, using high-pressure infrared spectroscopy. They report a transition at 30 kbar and room temperature which most probably does not belong to the a-p transition. The volume changes accompanying the phase transitions allow the calculation of the associated enthalpy changes using the Clausius-Clapeyron equation: Melting of dodecane: 35.4 kJ mol-' at I bar rising to 41.4 at 2600 bar. Melting of undecane: 21.5 kJ mol-l, nearly pressure-independent ; rotational transition: 6 kJ mol" at 1 bar rising almost linearly to 12 kJ rno1-I at the triple point (2300 bar).Melting of acetonitrile: 8 kJ mol-' at 1 bar rising to 9.5 kJ mol-' at 3000 bar; or-p solid-solid transition: 0.87 kJ mol-I at 1 bar increasing to z 1 kJ mo1-I at 2700 bar. In the case of the n-alkanes the pressure dependence of the enthalpy changes has been determined for related compounds by Kamphausen et aZ.22 using high-pressure d.s.c. calorimetry. The reported pressure dependence 22 agrees qualitatively with the calculations in this paper.150 HIGH-PRESSURE PHASE TRANSITIONS DIELECTRIC MEASUREMENTS Fig. 4 shows the dielectric constant as a function of temperature for various sub- stances. Liquid acetonitrile has a large value of the permittivity, which decreases by an order of magnitude at the freezing temperature. There is a further small change (A& N" 0.05) at the cc-p solid-solid transition (see arrow) corresponding to the small volume change.On the other hand cyclohexanone shows only a small dielectric step at the freezing point, but a considerable decrease in the dielectric constant at a lower 50 I I I I I I I I I I I I I x-. I - x 20 - 10 - C T K FIG. 4.-Dielectric constant as a function of temperature at different pressures (in bar): cyclo- hexanone (-), acetonitrile (- - - -), and cyclohexane (- - - - - - -). AB = liquid-solid I, CD, 1-11 solid-solid and EF, 11-111 solid-solid transition of cyclohexanone. 0, Corfield and Davies." solid-solid transition. The completely different dielectric behaviour of these two substances indicates clearly that cyclohexanone must possess orientational freedom within the high temperature solid phase, whereas acetonitrile obviously does not belong to the class of " reorientational solids ".Cyclohexanone is a typical represen- tative of the " plastic crystals " which usually have low enthalpy- and volume-changes of melting, as has been confirmed in high pressure calorimetric6 and volumetric" measurements. Fig. 4 also shows atmospheric pressure data of Corfield and Davies" for comparison. The agreement is good at room temperature and a t w -50 "C, but some deviations occur near the melting temperature. Even low concentrations of water impurities cause a sluggish melting transition and values of E that are too low in solid phase I, which might perhaps be the reason for the deviations.A . WURFLINGER 151 Furthermore fig. 4 shows that cyclohexanone has an additional dielectric step at 2000 bar, due to a second solid-solid transition recently found by differential thermal analysk6 Preliminary dielectric measurements of cyclohexanone7 have now been extended to 3000 bar and are summarized in table 1.The dielectric results of aceto- nitrile will be discussed in detail elsewhere.8 TABLE STATIC DIELECTRIC CONSTANT, E, OF CYCLOHEXANONE AS A FUNCTION OF PRESSURE AND TEMPERATURE. THE COLUMNS ARE SUBDIVIDED, REFERRING TO THE LIQUID, SOLID I AND SOLID 11, RESPECTIVELY. THE DATA WERE SMOOTHED USING A POLYNOMIAL E = a + bp 3. cpz AT CONSTANT TEMPERATURE FOR EACH PHASE SEPARATELY. T/K plbar 303 293 283 273 263 253 243 233 223 1 250 500 750 1000 1250 1500 1750 2000 2000 2250 15.54 15.77 16.00 16.20 16.40 16.59 16.76 16.92 17.07 17.21 16.17 16.85 17.57 18.35 19.16 20.00 22.10 23.1 16.35 17.05 17.79 18.52 19.32 21.10 22.20 16.53 17.26 18.00 18.70 20.40 21.30 20.86 16.72 17.46 18.19 19.78 20.60 21.50 16.91 17.65 18.37 19.96 20.80 20.38 17.10 17.83 19.30 20.15 19.75 20.5 17.29 18.68 19.50 20.34 19.87 17.48 18.87 19.68 19.33 20.0 18.30 19.04 19.87" 18.84" 19.44 18.47 19.22 18.94 19.54 2500 17.94 18.65 18.40 19.05 19.65 2750 18.15 18.80 18.50 19.15 3000 18.22 18.03 18.60 19.25 * Both values refer to the 1-11 solid-solid transition which takes place at 2000 bar.Cyclohexane is a further representative of the " plastic crystals " and has also been studied by calorimetri~~*~~ and pYT measurements.11 However, this compound does not possess a permanent dielectric dipole moment ; therefore, its dielectric constant is small and does not change much (A& x 0.05) at the phase transitions (see arrows).The temperature dependence of E agrees on the whole with the literature data of Chew and Chan.24 Fig. 5 shows another representation of the dielectric results of cyclohexanone. The dielectric constant is plotted as a function of pressure along the phase transition lines of cyclohexanone. The curves A, B, C . . . correspond to the edges A, B, C . . . of fig. 4. The distance AB shows the increase in E at the freezing temperature and the distance CD refers to the decrease in E at the solid-I-solid-I1 transition, respectively. The low value of E in the solid phase I11 (edge F) is not shown in fig. 5, because it was152 HIGH-PRESSURE PHASE TRANSITIONS rather difficult to perform dielectric measurements in that brittle and hard solid phase.The value at atmospheric pressure is ~ 2 . 8 , in accordance with data of Corfield and Davies.12 At higher pressures the accuracy of E in the solid phase I11 is less, but E does seem to be below 3.0. Fig. 5 further shows that the transition lines E and D diverge with increasing pres- sure according to the increasing solid phase I1 region. They intersect at atmospheric w I I I I I I 0 . 5 1 1.5 2 2 . 5 3 I plkbar FIG. 5.-Dielectric constant of cyclohexanone as a function of pressure along the phase transition lines. The letters A, B, C . . .refer to fig. 4. 0, smoothed values according to a polynomial E = a + bp + cp’; A and +, experimental points except curve E which was also smoothed. pressure at the triple point solid-I-solid-11-solid-I11 ; for details of the phase diagram see ref.(6), where the phase-transition temperatures as a function of pressure are also given. DISCUSSION n-A L KANES One of the striking features of the n-alkanes of higher chain length is the occurrence of the “rotational transition”. The nature of this phase transition has been in- vestigated i n t e n s i ~ e l y , ~ ~ - ~ ~ and will certainly be discussed by Ewen et aZ.29 Apart from the difficulties of explaining the mechanism of the rotational transition the question arises: why does this phase transition occur at all? Bople and Karasz3’ have suggested a model that allows one to a certain extent to predict the existence of plastic phase transitions.A good review of this model is given by Findenegg31 The essen- tial parameters of the model are two energy barriers w and w’, concerning the repulsion of a positionally disordered molecule in the lattice and the energy of an orientationally disordered molecule, respectively. Then the ratio w’/w is a measure of the anisotropy of the non-spherical molecule. Assuming a certain volume de- pendence of w and w’ (but such that the ratio w ’ / ~ is independent of temperature and pressure) it is possible to predict the pressure dependence of the phase transitions. The main result is that the high-temperature solid phase region should be increased with increasing pressure. This is indeed true for many plastic ~ r y s t a l s , ~ , ~ but is not observed in the case of the n-alkanes (see fig.l), as has already been pointed out by KO hler .32 This different high-pressure phase behaviour of the n-alkanes may perhaps be qualitatively understood if a pressure dependence of w’/w is assumed. According to early X-ray results of Muller 33 the compressibility of tricosane is anisotropic. There-A . WURFLINGER 153 fore the ratio w’/w is most probably pressure-dependent and should increase with increasing pressure. However, an increasing ratio of w’/w is unfavourable for the existence of a plastic phase. According to Karasz and Pople3’ a plastic phase does not occur for w’/w > 0.66, occurs only at elevated pressures for 0.325 < w’/w < 0.66, and at atmospheric pressure for W’/W < 0.325. It is possible that, in the case of the n-alkanes, the ratio w’/w is considerably enlarged with increasing pressure and leads to a disappearance of the plastic phase region (hatched areas in fig.1) for a sufficiently high pressure (triple-point pressure). However, the theory of Pople and Karasz should not be taken too seriously in the case of the n-alkanes, because certainly more than two orientations, as well as more than two energy barriers, are involved with these comparatively long chain molecules, not to mention that more than one solid-solid transition is observed in some case^.^^^^ CYCLOHEXAN ONE Fig. 4 shows that the dielectric constant of cyclohexanone increases with de- creasing temperature. There is a further increase at the freezing point, probably caused by the increase in the density.It is the main purpose of this section to discuss whether the changes in E with temperature and pressure correspond exactly to changes in the density. An eventual deviation may be caused by the interaction of the individual molecular dipoles which is often described in terms of the Kirkwood- Frohlich-Onsager theory using the well-known Kirkwood g-factor : 34 ( E - EW)(~E + ~m)9kTM = E ( E ~ + 2)24~N0pp2 ’ E is the measured static dielectric constant and ,ndex (n, = 1.451 at 20 “C and 1 atm)35 according to the relation36 is calculated from the refractive E , = 1.05 n2. The change in with temperature and pressure was calculated with the help of the Lorenz-Lorentz equation. The necessary density data, p, have been taken from Wisotzki.’l p is the permanent electric dipole moment of an individual molecule that is usually obtained from dielectric measurements of dilute gases.However, most of the reported literature data refer to dilute solutions of cyclohexanone, p being 2.8,37 2.9,38*39 2.9540 and 3.01 D.41*42 Another value of 2.87 D has been obtained from microwave spectros~opy.~~ A mean value of 2.9 D is used for the calculation of the Kirkwood g-factor. Also Corfield and Davies” report 2.9 D calculated from Onsager’s equation; but of course this cannot be taken into account, because the application of Onsager’s equation would mean g = 1. On the other hand the results of Corfield and Davies show that the g-factor of cyclohexanone must be about unity, provided that the mean value of p = 2.9 D37-43 truly refers to an individual molecular dipole.The latter statement is supported by the close value of 2.87 D43 obtained without using any of the assumptions of the Kirkwood-Frohlish-Onsager theory. The other constants of the Kirkwood-Frohlich equation are explained in ref. (34); very similar calculations have also been done by F r a n ~ k . ’ ~ . ~ ~ Fig. 6 shows the Kirkwood g-factor as a function of pressure at three different temperatures in comparison with three isotherms of acetonitrile.* Whereas the g- factor of acetonitrile is distinctly less than 1, indicating preferred antiparallel correla- tion, the g-factor of cyclohexanone is very close to unity, in accordance with the above remarks concerning the results o f Corfield and Davies.12 The pressure and temperature dependences of g are similar for liquid cyclohexanone and liquid aceto-1 54 HIGH-PRESSURE PHASE TRANSITIONS nitrile.At the freezing point of cyclohexanone (2360 bar at 30 "C, 1080 bar at 0 "C, 360 bar at -20 "C), however, a small increase in the g-factor is observed which means that the increase in E at the freezing temperature does not exactly correspond to the increase in the density on freezing. Although this small change in g ( z 1.5%) during the melting transition is comparable with the sum of the relative uncertainties of the measured quantities involved, the increase in g was observed in all cases, also at atmospheric pressure: g = 0.99 in solid cyclohexanone at -35 "C, compared with g = 0.97 in liquid cyclohexanone at -20 "C. The higher value of the g-factor in the solid phase I is perhaps caused by the greater ease of molecular rotation of the cyclo- hexanone molecules compared with the liquid state.This assumption is supported plkbar FIG. 6.-Kirkwood g-factor of cyclohexanone (liquid, solid I, and solid 11) as a function of pressure for 3 different temperatures (in K) in comparison with 3 isotherms of liquid acetonitrile. by Corfield and Davies12 who have shown that the solid rotator phase has an even lower activation energy for dipole relaxation than the liquid. Furthermore Bottcher et aZ.44 report g = 0.66 for solid cyclohexanone at -40 "C, in considerable disagreement with the present paper. The discrepancy arises from the different quantities used, for example p = 1.12 instead of 1.03 g cm-3 [ref.(45)], p = 3.08 instead of 2.9 D, etc. As far as the solid phase I1 which exists only at elevated pressures is concerned, no structural information is available. If solid I1 is also characterized by a cubic lattice the Kirkwood-Frohlich equation may be applied to this phase as well. Reserv- ing this limitation, the calculations have been extended to the solid phase 11. Fig. 6 shows that the g-factor decreases considerably at the 1-11 solid-solid transition (2000 bar at 0 "C, 1240 bar at -20 "C), demonstrating that some part of the reorientational freedom must be frozen in. It does not seem reasonable to describe the lower g-value of the solid phase I1 in terms of antiparallel oriented dipoles or dimers, as has been done with certain success in the case of liquid acetonitrile and related com- poUnd~.8,15,46.47A .WURFLINGER 155 Fig. 6 further shows that the steps of the Kirkwood g-factor are nearly independent of temperature and pressure. Obviously the change in g along a phase transition line is much less (almost negligible) than along an isotherm: g being about 0.95 (A), 0.965 (B), 0.955 (C), 0.89 (D), and 0.88 (E), respectively, the letters A-D referring to fig. 4 and 5. Similar behaviour was found with liquid acetonitrile, which has an approximately constant value of g z 0.7 at the melting curve.' The author thanks the Deutsche Forschungsgemeinschaft for financial support. A. Wiirflinger and G. M. Schneider, Ber. Bunsenges. phys. Chem., 1973,77, 121. B. Koppitz and A. Wiirflinger, Colloid Polymer Sci., 1974, 252, 999.C. Josefiak, A. Wiirflinger and G. M. Schneider, Colloid Polymer Sci., 1977, 255, 170. A. Wiirflinger, Ber. Bunsenges. phys. Chem., 1975, 79, 1195. A. Wiirflinger and J. Kreutzenbeck, J . Phys. Chem. Solids, 1978,39, 193. A. Wurflinger, Ber. Bunsenges. phys. Chem., 1978, 82, 1080. A. Wurflinger, Ber. Bunsenges. phys. Chem., 1980, submitted. R. Landau, Doctoral Thesis (University of Bochum, 1980). lo R. Landau and A. Wiirflinger, Rev. Sci. Instr., submitted. K. D. Wisotzki, Diplom. Thesis (University of Bochum, 1980). l2 G. Corfield and M. Davies, Trans. Faraday Soc., 1964, 60, 10. I3 D. N. Glidden, Thesis (University of New Mexico, 1972). l4 E. U. Franck and R. Deul, Faraday Disc. Chem. Soc., 1978, 66, 191. l5 E. U. Franck, in Organic Liqltids, ed. A. D.Buckingham, E. Lippert and S. Bratos (John Wiley, London, 1978), p. 181. I6 C. J. F. Bottcher and P. Bordewijk, Theory of Electric Polarization (Elsevier, Amsterdam, 1978), vol. IT, p. 445. l7 0. Hassel and A. M. Sommerfeldt, Z. phys. Chem. (Leipzig), 1938, 40, 391. R. R. Nelson, W. Webb and J. A. Dixon, J. Chem. Phys., 1960,33, 1756. l9 J. Timmermans and M. Kasanin, Bull. Soc. Chim. Belg., 1959, 68, 527. 2o G. M. Schneider, 2. phys. Chem. (Leipzig), 1964, 41, 327. 21 R. J. Jakobsen and Y. Mikawa, Appl. Optics, 1970, 9, 17. 22 M. Kamphausen and G. M. Schneider, Thermochim. Acta, 1978,22, 371. 23 H. Arntz and G. M. Schneider, Faraday Disc. Chem. Soc., 1980,69, 139. 24 H. A. Chew and R. K. Chan, Canad. J. Chem., 1973,51,2141. 25 G . Strobl, B. Ewen, E. W. Fischer, and W.Piesczek, J . Chem. Phys., 1974,61,5257 and 5265. 27 W. Pechhold, W. Dollhopf, and A. Engel, Acoustica, 1966, 17, 61; S. Blasenbrey and W. 28 D. H. Bonsor and D. Bloor, J. Marer. Sci., 1977, 12, 1552. 29 B. Ewen, G. R. Strobl and D. Richter, Fmaday Disc. Chem. SOC., 1980, 69, 19. 30 J. A. Pople and F. E. Karasz, J. Phys. Chem. Solids, 1961,18,28 and 20,294. 31 G. H. Findenegg in The Liquid State, ed. F. Kohler (Verlag Chemie, Weinheim, 1972), p. 194. 32 F. Kohler, in Organic Liquids, ed. A. D. Buckingham, E. Lippert and S. Bratos (John Wiley, 33 A. Miiller, Proc. Roy. SOC., 1941, 178, 227, and earlier papers. 34 C. J. F. Bottcher, Theory of Electric Polarization (Elsevier, Amsterdam, 1973), vol. I, p. 258. 35 J. A. Riddick and W. B. Bunger, Techniques of Chemistry, vol. 11, Organic Solvents, ed. A. 36 C. J. F. Bottcher, Theory of Electric Polarization (Elsevier, Amsterdam, 1972), vol. I, pp. 180 37 S. 0. Morgan and W. A. Yager, Ind. Eng. Chem., 1940,32, 1519. 38 J. W. Williams, J . Amer. Chem. Soc., 1930, 52, 1831. 39 I. F. Halverstadt and W. D. Kumler, J. Amer. Chem. Soc., 1942, 64, 1982. 40 W. Holzmiiller, Z. phys. Chem. (Leipzig), 1937, 38, 574. 41 J. B. Bentley, K. B. Everard, R. J. B. Marsden and L. E. Sutton, J. Chem. Soc., 1949,2957 and 42 K. HOUSSOU, A. Proutiere, A. Caristan, and H. Bodot, J. Chim. phys., Phys. biol., 1977,74,499. ' R. Landau, A. Wiirflinger and G. M. Schneider, Z. analyt. Chem., 1977,286,216. Ishinabe, Takao, J. Phys. Soc. Japan, 1974, 37, 31 5. Pechhold, Rheologica Acta, 1967, 6, 174. London, 1978), p. 260. Weissberger, (Wiley-Interscience, New York, 3rd edn, 1970), p. 246. and 272. 2963.156 HIGH-PRESSURE PHASE TRANSITIONS 43 Y . Ohnishi and K. Kozima, Bull. Chem. SOC. Japan, 1968,41, 1323. 44 C. J. F. Bottcher and P. Bordewijk, Theory of Electric Polarization (Elsevier, Amsterdam, 1978), 4s R. J. Meakins, Trans. Faraday SOC., 1962, 58, 1962. 46 W. Dannhauser and A. F. Fluckinger, J . Phys. Chem., 1964, 68, 1814; G. P. Johari and W. 47 K. R. Srinivasan and R. L. Kay, J . Solution Chem., 1977, 6 , 357. vol. 11, p. 451. Dannhauser, J . Chem. Phys., 1968, 48, 51 14.

ISSN:0301-7249    

DOI:10.1039/DC9806900146

出版商:RSC    

年代:1980

数据来源: RSC

摘要:

The Use of Powder Diffraction in the Study of Molecular Phase Transitions BY G. STUART PAWLEY Physics Department, University of Edinburgh, Kings Buildings, Edinburgh EH9 352 Received 7th January, 1980 An outline is given of the experimental techniques available for studying the structure of molecular systems through powder diffraction. A wide range of physical environments is possible with this technique making it appropriate for the study of phase transitions by means of structure. The difficulties encountered in the data analysis are enumerated and the limitations imposed by resolution are discussed. The state of the art is not yet fine enough for us to be able to put a high probability of success on neutron diffraction studies, though this is possible in practice. A new program to help in the search for unknown unit cells is described.The advantages of the fully operational program EDINP for the study of molecular phase transitions through the use of constrained refinements are stressed. A typical example of the type of system which can be studied in this way is presented, namely C6D6.CaF6, where the powder diffraction scans for the two phases are given for comparison. The purpose of the present paper is to focus attention on a technique which is very rapidly developing and is outstripping the expertise needed for its analysis. Powder diffraction has been understood from the earliest days of crystallography, but has remained neglected until recently because of the unquestionable success of single-crystal diffraction work. Considerable stimulus was given to neutron powder diffraction by the work of Rietveld' and this field has flowered with the study of magnetic systems and with phase transitions in such systems as the perovskites, where small distortions of the unit cell usually occur.Success in these fields has depended in large measure on the approximate foreknowledge of the structure of the unknown phase. It is a very big step therefore to move to systems where phase changes occur between structures which are so unrelated that there can be no assistance in deter- mining the structure of one phase simply by knowing the structure of the other. Such phase transitions are common in the molecular solid state, and it behoves us to develop the techniques to be able to attempt the analysis of such unknown phases.EXPERIMENTAL TECHNIQUES In neutron scattering the technique of high resolution multicounter diffractometry is well developed, but there is still a possibility of further progress, increasing the resolution on even the best instruments such as D1A at I.L.L. Grenoble. Soller systems can now be made so that the ultimate possible resolution is achievable, this being governed only by the crystallite particle size. It appears, after considerable effort, that the resolution of D1A at present is not quite enough for us to put a high probability of success on a structure determination - we had hopes of presenting a success at this meeting, but will have to be satisfied in outlining the difficulties faced in such tasks. With increased resolution there comes a loss in intensity, but as few powder diffraction analyses are statistics-limited, this should not unduly concern us.Clearly structures with We should convince ourselves a t the outset that the prize is worth the effort.158 DIFFRACTION STUDIES OF PHASE TRANSITIONS supercells and therefore weak superlattice reflections will need higher count rates, but in these cases it often happens that a knowledge of the pseudocell is sufficient to enable the structure determination without the higher resolution. One difficulty with neutron powder diffraction which has been almost totally neglected is the correct procedure for accounting for thermal scattering. It is not inconceivable that this problem be circumvented by the inclusion on a high resolution single counter diffractometer of a spin-echo device which would reject all those neutrons which were scattered with an energy change.This is possible to some extent by using a conventional analyser, but even then most of the troublesome scattering from the acoustic phonons is still not eliminated. A spin-echo powder diffractometer is technically possible, and simply needs the demand of the scientific community for it to be constructed. But we should not restrict ourselves to considering only conventional neutron diffracto- metry. Pulsed source diffractometry is now possible on instruments such as the back- scattering apparatus on the Harwell LINAC, and in the early 1980s this will be possible on the higher flux spallation neutron source, SNS. The back-scattering technique is not limited in its resolution by sample particle size, and could well prove to be the superior technique. The difficulties with this technique lie in the diffraction peak shape which is very asymmetric and varies widely over one measurement set.However, it appears to the writer that a greater problem exists, and that concerns the range of measurements permitted. If a structure is known to some extent, then the improvement in knowledge of the structure lies in the measurement of the higher order reflections, at which this technique is undeniably successful. But for an unknown structure it is essential to measure the first-order lines, and these are produced by neutrons of, e.g., 40 8, wavelength if back-scattered from a unit cell of 20 A. Such cell edges are not rare.Although the neutron flux at 40 A will be very weak, the prob- lem of measurement is exacerbated by the fact that the long-wavelength neutrons travel so slowly that they are overtaken by faster neutrons from later pulses. It will be essential in our work to be able to reduce the pulse rate by a large factor, otherwise we will be denied these all-important reflections. Another experimental source which should not be overlooked is the synchrotron X-ray source. Here again there are problems with the diffraction peak shape, but these are general problems which will be surmounted. These X-ray sources promise to be so powerful, as does the SNS, that full diffraction data from one sample can be collected in minutes or even in seconds. As a comparison, the conventional neutron diffractometer DlB at I.L.L.gives a respectable scan in about five minutes, though the resolution is not high. Neutrons have the advantage over X-rays that they are not highly absorbed by the sample or its container. Thus it is possible to have quite a large specimen with a carefully controlled temperature environment and also with controlled pressures up to 35 kbar. The specimen size required restricts the pressure range possible, but most molecular transitions occur within this range. Thus the techniques are possible for studying molecular systems over a wide range of conditions, but the analysis of the results now presents the most difficult problems. STRUCTURE REFINEMENT Logically it would be better to discuss the solving of structures before their refinement, but as the solution stage is the main stumbling block it will be left to last.One aspect of such refinements must be made quite clear, and that is that the powder technique cannot rival accurate single-crystal work in the precision of the final result. A number of papers have appeared (uncited) in which unreasonably small standard deviations are quoted without qualification. The fallacy which leads to these results has recently been analysed.2 The information content of a powder scan is necessarily very limited, and therefore our scientific objectives will be limited. A very effective way of working within such limits is to employ constrained refinements3 whereby use can be made of additional information. This is particularly advantageous for molecular systems.G .S . PAWLEY 159 If a molecular system undergoes a phase transition, it is to be expected that there is no change in the basic molecular structure, but that a rearrangement of the mole- cules takes place. The molecules retain their integrity. This is considerable informa- tion, and if it can be used in the data refinement it will improve the reliability of the other parameters being determined. Thus we are not concerned with the relative positions of the atoms in the molecules, these we know, but do want to know how the molecules rearrange themselves. The orientation is most usually determined by three parameters, such as Euler angles, and the structure can be described by a molecule of predetermined shape positioned through the use of these variable parameters.The first molecular system to be studied by powder diffraction in this way was perfl~orobiphenyl,~ using Rietveld's pr0gramme.l In this example a molecule of 22 atoms was oriented by one Euler angle, but two other parameters were needed: the angle between the two ring systems and the length of the bond connecting them. The constraints necessary to retain the shape of the ring systems taxed the programme to the full, and were only possible because of the symmetry of the particular problem. However, the analysis showed that the technique is feasible and that it was worth- while developing a programme that could cope with constraints of any complexity. Such a programme has now been written and tested4v5 and is now available for general distribution.The first tests of the programme were done on two unknown structure^,^ p-C6F,Br2 and p-C6F412, though in these cases the unit cells were deter- mined by single-crystal studies. The systems are isostructural, except that the latter has a transition to a higher-temperature phase at about 80 "C. D.t.a. studies show this transition only on warming, and therefore a sample frozen from the melt was ground up and studied by powder diffraction, but it would seem that the grinding process precipitated the transition as the resulting diffraction pattern was consistent with the lower phase. A feeling for the capacity of the method can be gained from these examples. The unit cells have monoclinic angles very close to 90", and such occurrences always lead to ambiguities. These ambiguities were, however, easily resolved by this technique. A number of false structural minima occur in these structures because the neutron scattering cross-sections for F, Br and I do not differ greatly.The false minima occur when the molecules are oriented wrongly by 60 and 120" in the molecular plane, but the true minimum was clearly indicated by the method. EXAMPLES SHOWING THE SCOPE OF THE METHOD The examples mentioned so far in this paper could have been studied just as successfully with single crystals, but there are many cases where single-crystal work is impossible and the powder technique comes into its own. This is true of perbromobenzene, where the original attempts at single-crystal study were frustrated by the lack of good crystals, as this substance forms over- growths even in the most favourable growing condition^.^ The interest in this system is to know the molecular orientation in order to understand the cause for the overgrowing, and we therefore need to determine only the three Euler angles.A refinement of atomic coordinates is counter-productive as the information in a powder diffraction scan is insufficient to be able to improve on a molecule of predicted shape, and therefore only two molecule structure parameters were investigated, the C-C and C-Br bond lengths. The resulting structure was well-determined, but unfortunately no clear reason for the overgrowing emerged.8 There are many transitions of the order-disorder type, and the study of these will be greatly facilitated by the ability to collect full structural data at a given temperature in a small time.This was attempted on the system C214 using the instrument D1B160 DIFFRACTION STUDIES OF PHASE TRANSITIONS at I.L.L. Earlier results examined by unconstrained refinement9 did not give a clear picture of disorder, but when reexamined with EDINP (Edinburgh Powder Pro- gramme5p6) the disordering was significantly determined.1° We hoped to be able to follow the change in disorder as a function of temperature, but now think that for such a study the information content of a low-resolution diffraction scan is insufficient. In octafluoronaphthalene there is at least one pressure-induced phase transition at ~ 0 . 8 kbar and probably a further transition at higher pressures." The first transition has been elucidated through neutron powder diffractometry, but the prob- lems outlined in the following section were avoided by the fact that the high-pressure phase was identical to the low-temperature phase, which had already been solved. One problem with the study of pressure-induced phase transitions is that a given sam- ple may not experience an even pressure throughout its bulk.We have an example (pyrene, unpublished) where the diffraction scan appears to be the superposition of two diffraction patterns from two phases. As each pattern consists of many over- lapping lines it is impossible to discard some data leaving a scan for just one phase. Consequently both phases must be refined together, and for such cases a special version of EDINP has been produced which will simultaneously refine any number of structures.This programme is not quite ready for general distribution. Certain transitions may be caused by an instability against a mode of vibration. When this occurs, the mode frequency approaches zero and the amplitude increases, and it is possible that this manifests itself through the Debye-Waller factor. In molecular systems the type of the motion concerned is most likely to be of the rigid- body type, and the rigid-body Debye-Waller factors are therefore of interest. We have examined whether it is possible to determine these by constrained powder refinernent,12 and it is clear that the very best data are necessary if any reliance is to be put on such a result. Bearing in mind that the new techniques may well improve on those existing now, such studies are worth undertaking.Many molecular systems undergo phase transitions to plastic phases, phases in which there is some degree of dynamic disorder. It is often not possible to grow single crystals in the crystalline phase, once more making powder diffraction the obvious tool. An example is given by pivalonitrile, as presented by one of the papers at this Discussion.13 The tertiary butyl group consists of three methyl groups, each of which has considerable orientational freedom about the C-C bond. A special subroutine for EDINP was written for this case, in which each methyl group is oriented independently about its C-C bond. Many problems require the pro- gramming of a special constraint, but this is usually a simple procedure for anyone acquainted with FORTRAN.STRUCTURE SOLUTION In most of the examples quoted above, the unit cell or the structure was approxi- mately known before the powder analysis was done. However, many cases exist where this is not so, and it is essential for us to develop the methods necessary to enable the solving of a structure without any crystallographic information. There are essentially three steps in this process, that of finding the unit cell, then the space group and then the full structure. The first step is undoubtedly the most difficult, and has received some attention over the last decade or so. For a review of the present state of the art the reader is referred to the work of Shirley.14 Procedures do exist for suggesting possible unit cells, and these have to be examined with the knowledge of the probable volume occupied by a molecule in mind.It is essential for any hopes of success in such aG . S . PAWLEY 161 venture to have a very accurate knowledge of the zero scattering angle for a scan, for if this is just slightly wrong the correct solution may slip through the computa- tional net, whereupon any subsequent work is entirely wasted. Next in importance is the resolution of the scan, as poor resolution results in close reflections being thought of as just one reflection, and when this happens the position of the average reflection does not correspond to any actual reflection, and false suggestions are supported. Finding the appropriate unit cell becomes increasingly difficult if the low-order reflections are missing, and for this reason it becomes important to insist on having the ability to measure these reflections when pulsed-source diffraction is used.As all unit-cell solution techniques rest heavily on the lowest-order reflections, it is very important that these be resolved. This is probably the most limiting factor with conventional neutron techniques. A typical example of a neutron powder diffraction scan is given in fig. 1, from which one can see that the peak half-width at 30" is 0.3". It is unusual for the indexing programme to result in a clear correct solution for the unit cell. We have to be prepared to investigate a number of different possible solutions before choosing one in which to invest the effort of structure solution.To aid in this step we have recently produced a version of EDINP which does not require a trial structure before it can be run. The programme aims to fit the whole scan profile while refining the unit cell. Other parameters refinable if desired are the scan zero angle and the peak shape parameters. All this is exactly as in EDINP which, in this respect, is the same as Rietveld's programme. The alteration in the functioning of the new programme concerns the crystallo- graphic structure factors, which are replaced by independent intensities. By allowing these intensities to refine at the same time as the unit cell is refined, we are able to change the indexing of the scan in a smooth fashion, making allowances for the frequent occurrences of more than one reflection in one resolved peak.It is planned that each highly probable unit cell suggested by the indexing programme will receive some refinement by the new programme before a final assessment is made. Because this is a total profile fitting the result has to be very good before a solution is accepted for further study. Only one scan has been examined by the programme to date, cyclohexene-F,,, and only one unit cell, which may be incorrect, has been investi- gated. This cell fits the first 100 reflections except for two very small shoulders, but these discrepancies may well prove to be crucial and the result may have to be rejected. One problem with this new programme has not been mentioned, and that is that two very close reflections cannot take on independent variable reflection intensities without enormous correlation.This correlation can be partially suppressed by con- straining close reflections to have intensities which are nearly the same. The amount of correlation suppression can be controlled by the user. At the end of a refinement a set of reflection intensities is produced, with indices and correlations, and this data set may well be the best input for the next two stages of analysis. If the unit cell is correct, the second stage, that of determining the actual space group, must be tackled. Either the list of reflection indices has to be scrutinised for possible systematic absences, or possible space group symmetries should be applied to the unit cell used with the programme just described. By either of these methods, or even by intuition, a space group must be proposed before the third stage can be at tempted .Possibilities can be postulated through packing arguments or calculations or through more sophisticated potential function lattice statics calculations. Probably the quickest way to test any proposed structure is to compare calculated intensities with the intensity set just mentioned, tak- This third stage is a search for a possible structure.162 DIFFRACTION STUDIES OF PHASE TRANSITIONS ing due care of the correlations. When a good trial structure is thus obtained, refinement with EDINP should be straightforward. AN EXAMPLE In conclusion an example will be described which has not yet been solved success- fully. Two of the diffraction scans, obtained recently on DlA at I.L.L.are shown in fig. 1 . The system under investigation is C6D6.C6F6, being a 1 : 1 complex between 10 20 30 40 50 60 l b I 0 20 30 40 50 60 scattering angle/deg cooling, upper phase; (6) at 195 K on warming, lower phase. FIG. 1.-Neutron powder diffraction scans of C6D6.C6F6 taken on D1A at I.L.L.: (a) at 180 K onG . S. PAWLEY 163 benzene and perfluorobenzene. This has been studied most recently by Raman ~cattering,'~ and a transition was observed on cooling at 170 K which was not reversed on warming until 210 K. The first scan shows the result on cooling below 210 K, but still in the upper phase, while the second scan shows the result at a higher tempera- ture in a warming sequence and therefore in the lower phase. These scans are con- sistent with others taken well away from the transition temperature.These scans are clearly distinct, but have a number of features in common. The common features probably indicate a relationship between the structure in the two phases. We surmise that the phase change in akin to a crystal-to-plastic phase, but the orientational disorder in the plastic phase could take on many forms, reorientation of individual molecules or reorientation of close pairs of dissimilar molecules which are rather more tightly bound together than the overall intermolecular binding. We hope to make progress on this system by searching for the unit cell of the upper phase structure by single-crystal X-ray methods, but our long-term objective is to be able to solve such structural probems entirely through the use of powder diffraction methods. H. M. Rietveld, J . Appl. Cryst., 1969, 2, 65. M. Sakata and M. J. Cooper, J. Appi. Crysf., 1979, 12, 554. G. S. Pawley, Aduances in Structure Research by Diffraction Methods, ed. W. Hoppe and R. Mason (Pergamon Press, Oxford, 1972), vol. 4, pp. 1-64. G. A. Mackenzie, 0. W. Dietrich and G. S. Pawley, Acfa Cryst. A , 1975, 31, 851. G. S. Pawley, G. A. Mackenzie and 0. W. Dietrich, Acfa Cryst. A, 1977, 33, 142. G. S. Pawley, J . Appl. Cryst., submitted. E. G. Boonstra and F. H. Herbstein, Acta Crysf., 1963, 16, 252. B. C. Haywood and R. Shirley, Acfa Crysf. B, 1977, 33, 1765. G. A. Mackenzie, B. Buras and G. S. Pawley, Acta Crysf. B, 1978, 34, 1918. G. E. Bacon, E. J. Lisher and G. S. Pawley, Acta Cryst. B, 1979, 35, 1400. * E. Baharie and G. S. Pawley, Acfa Cryst. A , 1979, 35, 233. lo G. S. Pawley, Acta Cryst. B, 1978, 34, 523. l3 J. C. Frost, A. J. Leadbetter and R. M. Richardson, Faraday Disc. Chem. Soc., 1980, 69, 32. l4 R. Shirley, Crystallographic Computing, Proc. 1978 Sumrizer School (Delft University Press and Oosthoeks, 1978). G. A. Mackenzie, J. S. Overell and G . S . Pawley, Solid State Comm., 1979, 31, 431.

ISSN:0301-7249    

DOI:10.1039/DC9806900157

出版商:RSC    

年代:1980

数据来源: RSC

摘要:

Thermoluminescence in Solid Methane BY MARY ANNE WHITE,? THOMAS G. RYAN* AND JAMES A. MORRISON Department of Chemistry and Institute for Materials Research, McMaster University, Hamilton, Canada Received 29th November, 1979 Thermoluminescence from both CH4 and CD4 doped with benzene or toluene ( d 0.5 mol %) has been measured in the temperature region 10 < T/K < 40. The methane was deposited from the vapour on a rotatable copper target. usually held at T z 10 K, and irradiated with ultraviolet light (predominantly of wavelength 2537 A). Before the glow curves (emitted light intensity as a function of temperature) were recorded, phosphorescence and recombination luminescence from the specimens were allowed to decay isothermally. Certain sharp peaks in the thermoluminescence spectrum can be correlated with the known phase transitions in CH4 and CD4.Under appropriate conditions, thermally-activated recombination of radiation- induced charged species in solids can give rise to luminescence. This thermolumines- cence has been studied in both inorganic and organic solids and some correlation has been claimed to exist between peaks in the luminescence spectrum and solid- solid phase transitions.' More recently, the results of an investigation of radiothermo- luminescence in eleven doped solid hydrocarbons, including methane, have been re- ported.2 Some experimental factors such as sample size, glass-transition temperature and prior thermal treatment appeared to be important. Experimental and theoretical study of solid isotopic methanes (CH,D4- ,) has become rather extensive during the past few yeam3 In part, this is because of a range of interesting phenomena that the solids exhibit: orientational ordering of the mole- cules ; quantum crystal behaviour ; conversion between nuclear spin symmetry species ; negative thermal expansion and other lattice dynamical oddities.The current state of understanding of solid CH4 is well-summarized in a recent article., Under its own vapour pressure, CH, forms two phases, the structures of which are, known : phase I, T > 20.4 K, space group Fm3m, 4 molecules per unit cell; phase 11, T < 20.4 K, space group Fm3c, 32 molecules per unit cell. The deuterated methanes (and CH, under pressure) form a third solid phase, phase 111, but its struc- ture has not been fully established as yet.Theoretical calculations suggest7 the space group P4,lrnbc with 16 molecules per unit cell but this is not completely consistent with thermodynamic data obtained for phase 111.' The essential point is that, for the solid methanes, the changes in molecular arrangements that occur via the phase transitions are now reasonably well understood. In phase I, the molecules are orientationally disordered although there is some evidence9 that some orientational correlations persist in the temperature region a few degrees above the phase I1 -+ I transition point. In phase 11, molecules on six of eight sub-lattices become orientationally ordered. Further ordering must occur in 7 Natural Sciences and Engineering Research Council (Canada) 1967 Science Scholar, 1975-79.Present address : Inorganic Chemistry Laboratory, South Parks Road, Oxford. $ Present address : Research Division, Sherritt-Gordon Mines, Fort Saskatchewan, Alberta, Canada.M. A . WHITE, T. G . RYAN AND J . A . MORRISON 165 the formation of phase 111 but, as has been indicated, its exact nature is not yet completely established. Nevertheless, enough structural information is available overall so that it seemed appropriate to try to use it at this time to connect changes in thermoluminescence spectra with phase transitions in solid methane. EXPERIMENTAL CRYOSTAT The cryostat, shown schematically in fig. 1 was a modified MD4A model made by Oxford Instruments. The flow of liquid helium from the main reservoir to a smaller pot beneath it could be controlled through a needle valve operated from the top of the cryostat.A copper plate of dimensions 20 x 20 x 2 mm, on which the samples were vapour-deposited, was connected to the lower helium reservoir by a copper rod which provided good thermal contact. A c B 1 C D F--h ;I G H J 0- 10 cm FIG. 1 .-Schematic representation of the cryostat in cross-section. A, vacuum space; B, liquid nitrogen; C liquid helium; D, rotatable shaft; E, helium flow tube; F, optical window; G, Speer resistance thermometer; H, sample block; J, copper-constantan thermocouple; K, liquid helium ; L, sample inlet tube.166 THERMOLUMINESCENCE I N SOLID METHANE The principal modification to the basic MD4A cryostat was the introduction of a rotatable shaft through the main helium reservoir.This insert carried the lower helium pot and the sample block, and was installed to allow the rotation of the sample block to face either the sample deposition port or the irradiation/light detection window without loss of vacuum or refrigerant. (O-ring seals at the top and bottom of the shaft made this possible.) The sample block was rotated with a screw mechanism at the top of the cryostat, and its position, as determined on a goniometer, was reproducible within 1" of arc. A carbon resistance thermometer (Speer Carbon Co, St. Marys, Pennsylvania) was at- tached to the back side of the sample block, and was used to determine the sample tem- perature during the thermoluminescence measurements. The thermometer was first com- pared with a copper-constantan thermocouple that was attached to the bottom of the block.The thermocouple had previously been calibrated at 4.2 and 77 K, which was sufficient to fix the deviation of the e.m.f., characteristic of the particular constantan wire used, from a stand- ard table. The thermocouple and the thermometer were intercompared over the region 13 < T/K < 38, and gave absolute values of the temperature to within 0.5 K or better. At lower temperatures, copper<onstantan thermocouples are rather insensitive and the resistance of the carbon thermometer was used in the well-known lo resistance-temperature relationship : where R is the resistance, T is the temperature in K and A and B are constants of the par- ticular Speer thermometer. Eqn (1) was fitted to data for 13 < T/K < 20, and gave the correct temperature down to 4.2 K to within 0.5 K, or better.The resistance-temperature relationship was reproducible over many cooling and heating cycles of the thermometer. The lower reservoir was usually kept full of liquid helium during the sample deposition and irradiation procedures in order to maintain the sample block at its lowest temperature, which was 9.5 K because of the large heat input to the block. (The major source of this energy seemed to be radiation from the relatively warm sample inlet tube which was <2 cm away from the sample block.) To allow the temperature to rise during the thermoluminescence measurements, the needle valve to the lower helium pot was closed. When the liquid helium in the pot had evaporated, the temperature of the sample block rose in a smooth and reproducible fashion, as shown in fig.2. A heater was wound around both the lower helium pot and the copper rod connecting the pot to the sample block and, after a thermoluminescence experiment, it was used to heat the block so that the sample could be pumped away. In addition, the heating rate for seme experiments was changed by balancing the current through the heater and the flow of helium into the smaller pot. In R = A + BIT (1) SPECIMEN PREPARATION AND DEPOSITION The CH4 used was ultra-high purity grade (Matheson Gas, Whitby, Ontario), with a stated chemical purity of 299.97%. The principal impurities were N2 and C2H6; no purifi- cation was performed. The CD, (Merck, Sharp and Dohme, Montreal) was only >99% chemically pure, and ca.97% isotopically pure. It was not purified isotopically since the phase transition tempera- ture in CD, does not critically depend on small amounts of CHD3. In some experiments, the cylinder containing the CD, was cooled to -78 "C (dry ice + acetone) while a sample was removed. The experiments in which the CD4 specimens were treated in this manner will be identified in the results section. Reagent grade benzene and toluene, the doping agents, were dried over anhydrous CaCl, and fractionally distilled before being subjected to several freeze-pump-melt cycles on a high vacuum line to remove traces of dissolved gases. The methane and the aromatic impurity, at pressures P1 and P2, respectively, where PI > P2, were allowed to mix for a few minutes in the gas phase, before the homogeneous sample was deposited onto the sample block.The spray-deposition of the sample took place through the tube that is shown in fig. 1. The wide-mouthed stainless steel tube was con-M . A . WHITE, T. G . RYAN A N D J . A . MORRISON 167 nected via copper tubing to the sample reservoir on the outside of the cryostat and the flow of vapour into the cryostat was controlled by a needle valve. As the sample was deposited, the temperature of the sample block rose to z 10 K or more, depending on the deposition rate (usually 2-20 mg min-1), due to the energy released on solidification. The specimens contained up to 0.5 mol % of aromatic impurity, and ranged in size from M 5 to 300 mg. t/min FIG. 2.-Typical heating curve for a thermoluminescence sample.A freshly-deposited sample at its lowest temperature (T M 9.5 K) was a white translucent film but, as the temperature was increased during a thermoluminescence experiment, the sample took on a layered or flaky appearance. IRRADIATION A N D MEASUREMENT OF LIGHT EMISSION A mercury pencil lamp (Spectronics Corp., Westbury, New York) of principal wavelength 2537 A, and with an intensity of 2 x W cm-2 at a distance of 2.5 cm, was placed at the same optical window which was used for light detection, approximately 6 cm from the sample block. When the sample had been irradiated, the light was removed and the light detector immediately placed in position. (The delay between the end of the u.v.-irradiation and the detection of the emitted light was usually (30 s.) An RCA 6199 head-on photomultiplier tube was used to detect the light from the sample.The tube had its maximum sensitivity in the range 3000 s l / A -5 6000, with an absolute maximum at ;1 = 4400 A. The tube output ( z A) was amplified and recorded on a chart recorder. To monitor the background response of the photomultiplier tube, a mechanical shutter mounted between the cryostat and the detector was closed and opened intermittently during the luminescence measurements. RESULTS GENERAL ASPECTS OF THE LUMINESCENCE It has been postulated l1 that the mechanism responsible for photothermolumines- cence is as follows. Photoionization of a species, A, in the solid takes place such that A is excited by a two-photon process:168 THERMOLUMINESCENCE I N SOLID METHANE A + hv + A* + 3A, 3A + hv -+ A** + A+ + e-, (2) (3) and an electron is produced.(Similarly, in radiothermoluminescence, X-rays, electrons or prays bombard A to produce A+ and electrons.) The electron that is produced can be trapped either at impurity centres (to form anions) or at lattice defects in the solid so as to lower the overall energy. This can take place either by changing the orientation of the neighbouring molecules (in the case of a polar medium), or by the induction of multipole moments in them (in the case of a non-polar medium). The electron is trapped at a distance <lo0 A from the parent cation' and, if addi- tional energy is supplied, the two may recombine. In thermoluminescence, the electron may be detrapped by thermal energy, e- + kT+ e- (mobile), (4) e- (mobile) + A+ + A* -+ A + { :::, ( 5 ) and the result will be recombination of the mobile electron with the cation, A+, and fluorescence or phosphorescence that is characteristic of species A.Because of the high ionization energy of pure alkanes, a small amount of aromatic impurity must be added for photothermoluminescence to be detected in these matrices; the aromatic compound then serves as species A in the above sequence. The presence of an aro- matic impurity (benzene or toluene) was found to be essential to the observation of luminescence in the present experiments, and the so-called isothermoluminescence or ITL results support the above mechanism. The luminescence of benzene in various matrices at low temperatures has recently been characterized.l2 Immediately following the deposition and irradiation of a methane + aromatic specimen, and before the temperature was allowed to increase, luminescence was observed. The light given off was of purple colour; a typical decay of the ITL is illustrated in fig. 3. Clearly, two processes are taking place, one short-lived and one long-lived. Within z 2 min after irradiation, the ITL decay is exponential with lifetimes con- sistent with those of solute phosphorescence (z = 15 s for benzene and 12 s for toluene, in either CH4 or CD,). As has been demonstrated,12*13 the phosphorescence lifetimes for benzene in CH4, N2 and Ar are very similar. Although the spectrum of the emitted light was not determined in the present experiments, similar studies on other systems have shown it to be consistent with phosphorescence of the solute m01ecules.l~ After the solute phosphorescence has decayed sufficiently, the ITL decay follows the relationship where k is a scaling parameter, and rn z 1.A similar decay of the long-lived isothermal luminescence has been observed in many other solute + solvent systems, and is generally accepted to be due to the slow recombination of trapped electrons with cations .15-18 Whether the recombination takes place by diffusion or by electron tunnelling is a subject of much discussion; some other results aimed at elucidating the recombination mechanism will be discussed in detail e1~ewhere.l~ I = kt-", (6) THERMOLUMINESCENCE Many factors, such as the sample size, heating rate and specimen preparation, have been reported to influence the glow curves of molecular solids, but they have notM.A . WHITE, T. G . RYAN AND J . A . MORRISON 169 always been studied systematically. The reproducibility of many of the earlier results can therefore be questioned. An attempt was made here to investigate these factors thoroughly; the present results will illustrate the limitations placed on the absolute determinations of a glow curve for a particular matrix + solute system. Sugawara and Tabata reported grossly different thermoluminescence curves for alkane + toluene samples when the size was varied from 5 to 30 mg. In the present experiments, the shapes of the glow curves for methane + aromatic mixtures were found to be independent of the sample size from 2 to 200 mg. (Representative glow curves for CH4 + toluene are shown in fig.4.) In other experiments that are not illustrated, heating rates were varied from those given in fig. 2 to a constant 0.14 K min-'; the shapes of the glow curves remained unchanged although the positions 10 + c - 5 I I I 500 1000 1500 tls FIG. 3.-Decay of the isothermal luminescence. The results shown are for CH4 + benzene at T = 10 K; the luminescence intensity is in arbitrary units. of peaks shifted by as much as &l K from one experiment to another. A possible source of the irreproducibility in the earlier work2 may have been the extremely rapid heating rate used at low temperatures (as high as ~ 2 0 K min-l at the start of the determination of a glow curve).As illustrated in fig. 4, the shape of the glow curve of CH4 + toluene was also independent of the solute concentration. This was true for all methane + aromatic samples used, over a solute concentration range 0.001-0.5 mol %. In fact, it can be seen from fig. 4 that the luminescence intensities are proportional to the total number of moles of solute present. Although the vapour deposition method has been used to prepare glassy or non- crystalline samples of CHJOH and H20,20 it is improbable that glassy methane was formed here because extremely slow deposition rates were not used. (If the deposition is carried out rapidly, the heat released on solidification should provide sufficient energy to crystallize the sample.) In the present experiments, the deposition rate was varied by more than a factor of 10 without any change in the main features of the glow curves.This result indicated that the samples used were probably crystalline170 THERMOLUMINESCENCE IN SOLID METHANE and this was confirmed by the lack of dependence of the results on thermal treatment of the samples. (In solids which are known to form glasses, such as C2H50H and CH,OH + H20, thermoluminescence is strongly dependent on whether or not the samples were annea1ed.)21p22 Variation of the solute, although not often considered in thermoluminescence studies, has been shown to have little effect on the shape of the glow curves of qual lane*^ and polystyrene,24 as well as of many other organic matrices.l The prevailing view appears to be that the presence of the solute only serves to increase the luminescence, but some specific effects were found in the present experiments.For example, we may contrast fig. 4 which shows the thermoiuminescence glow curve for CH4 + toluene, with fig. 5,6 and 7 which illustrate curves for CH, + benzene, CD4 + toluene and CD, + benzene, respectively. It is not surprising to see some dissimilarities between the glow curves for CH, + aromatic and CD, + aromatic because of the differences between the CH, and CD, phase diagrams, but the change of the thermo- luminescence on substitution of benzene for toluene is remarkable. The results for CH, indicate that more types of trapping sites are available in 30 20 n m E: Y .* -!i W cr 10 0 T/K FIG. 4.-Effect of sample size and solute concentration on the glow curve.0,54 mg of CH, + 0.008 mol % toluene; x , 12 mg of CH, + 0.008 mol % toluene; 0 , 5 4 mgof CH4 + 0.0009 moly(, toluene. CH, + toluene than in CH, + benzene. This can perhaps be reconciled with the possibility that the methyl group of toluene produces extra distortion of the matrix. It can be seen from the results for CD, that extremely small amounts of extraneous impurities can also greatly influence the thermoluminescence profile. CD, untreated in any way and mixed with benzene always gave the glow curve displayed in fig. 7(a). On the other hand, when the cylinder containing the CD, was cooled in dry ice, the glow curve shown in fig. 7(b) was observed for 10 of 20 experiments; the other experiments yielded curves such as the one given in fig.7(a). It is difficult to see thatM. A . WHITE, T . G . R Y A N A N D J . A . MORRISON 171 the cooling procedure could have had any effect other than to promote preferential adsorption of an impurity (or impurities) on the cylinder wall. DISCUSSION The presence of both sharp and broad peaks in the glow curves indicates that two processes give rise to electron detrapping. Each of the broad peaks are attributable to one or more Randall-Wilkins processes,25 i.e., thermally activated recombination of electrons and cations. Our results illustrate that the distribution of the electron trap depths and the distance from the trapped electron to the parent cation depend n c) ." a T/K FIG. 5.-Glow curve of CH4 + benzene. on both the solute (benzene or toluene) and the matrix (CH, or CD,) which were used.However, Randall-Wilkins peaks generally have widths which are z 10% of the peak temperatures (i.e., AT/T, w 0.1),25 and peaks which were much narrower than that were also observed. As noted in the introduction, CH, undergoes a transition from phase I1 -+ I at T = 20.4 K. Similarly, CD, transforms from phase I11 -+ I1 at T = 22.0 K and from phase I1 -+ I at T = 26.9 K. From the results with benzene as additive, we see a clear correlation between thermoluminescerice peaks and the solid-solid phase transitions: the sharp peak at T = 20 K in CH, + benzene and the shoulder and sharp peak at T = 22 K and T = 27 K, respectively, in CD, + benzene coincide with the transitions. It is possible that the luminescence from accelerated recombination at the phase I I j I transition in CH, + toluene is masked by processes that are associated with the thermally activated electron-cation recombination, i.e., with the Randall-Wilkins process.Sharp peaks from the phase-transition-induced recornbination appear to be also absent in CD4 + toluene. This system was not investigated in more detail because of the occurrence of Randall-Wilkins peaks in the regions where effects of the phase transitions would be expected to be seen. Since it seems probable that the methane samples were crystalline, it must be It is these sharp peaks which are of most interest here.I 72 THERMOLUMINESCENCE IN SOLID METHANE assumed that the phase transitions still take place in impure CD,; perhaps the im- purities bind tightly electrons that would otherwise be detrapped at the phase transi- tions.At this time, we can only speculate about the microscopic processes that are re- sponsible for the lowering of the barrier to electron-cation recombination at the phase transitions. Two obvious ones are changes in the arrangement of the centres of mass or in the orientational order of the molecules. Since the volume changes at the transitions are very small (x 1 %)26 and since the basic crystal structure remains f.c.c. in the phase I1 -+ I transition, it seems improbable that displacements of the centres TIK FIG. 6.-Glow curve of CD4 + toluene. of mass play a role. If orientational ordering/disordering of the molecules provides the basic release mechanism, it is then not surprising that extraneous impurity traps are so important.The energy changes corresponding to shifts of orientational order are very small (< 100 J mol-I). In principle, the shapes and positions of the sharp peaks in the glow curves should provide information about the kinetics of the phase transitions. However, as noted earlier, the precise peak temperature varied by as much as 1 K from sample to sample. In addition, the peak width at half height ranged from 0.3 to 1 K for the phase I1 --+ I transition in both CH, and CD,. These variations were probably caused by the exist- ence of domain-type sub-structures in the samples with a resulting distribution of phase-transition temperatures. If the glow curve of a sample at a uniform temperature and in perfect thermal contact with the thermometer could be realized, a correlation between the peak widths and the two-phase coexistence region ought to be expected.(An X-ray diffraction study of CH, shows no appreciable temperature range of co- existence between phases I and II.26 Similar experiments show a range of coexistence of 0.10 K for the phase I11 -+ I1 and I1 -+ I transitions in CD4.)6M. A . WHITE, T . G . R Y A N A N D J . A . MORRISON 173 CONCLUSIONS This experimental study of thermoluminescence in solid CH4 and CD4 doped with benzene or toluene has established that the phenomenon is independent of factors such as sample size, solute concentration and prior thermal treatment. In these respects, the results differ from those of a prior study2 of thermoluminescence in CH, + toluene.On the other hand, glow curves are found to be strongly dependent on the nature of the solute and on small amounts of extraneous impurities. The technique of specimen preparation by vapour deposition was satisfactory for an exploratory type of investigation. The absence of a dependence of the shapes of cn c .I !3 - C .I C 4 1 ° 1 0 T K FIG. 'I.-Glow curve of CD, + benzene: (a) untreated CD,: (b) CD4 cooled in dry ice. glow curves on solute concentration indicates that the specimens had a uniform com- position. To study peak shapes and positions more quantitatively, larger specimens whose temperatures could be controlled more accurately would be desirable. How- ever, it would probably be very difficult to produce bulk specimens (even single crystals) of uniform solute distribution.174 THERMOLUMINESCENCE I N SOLID METHANE The results support the general proposition' that phase transitions can and do produce particular features such as sharp peaks in therrnoluminescent spectra.But the recombination processes that lead to the abrupt light emission are strongly affected by traces of impurities. To extend the investigation, more attention would need to be paid to the purification of the materials. We thank Drs. E. A. Ballik, M. L. Klein and Z. Racz for much helpful discussion and Mr. W. Scott for supplying liquid helium very efficiently. The financial support of the Natural Sciences and Engineering Research Council (Canada) is gratefully acknowledged. F. Kieffer and M. Magat, Actions Chimiques et Biologiques des Radiations, ed.M. Haissinsky (Masson, Paris, 1970), vol. 14, p. 135. M. Bloom and J. A. Morrison, Surface and Defect Properties of Solids, ed. M. W. Roberts and J. M. Thomas (The Chemical Society, London, 1973), vol. 2, p. 140. T. Yamamoto, Y. Kataoka and K. Okada, J. Chem. Phys., 1977,66,2701. W. Press, J. Chem. Phys., 1972, 56, 2597. D. R. Baer, D. A. Fraass, D. H. Riehl and R. 0. Simmons, J. Chem. Phys., 1978,68,1411. M. A. White and J. A. Morrison, J. Chem. Phys., 1979, 70, 5384. W. Press, A. Huller, H. Stiller, W. Stirling and R. Currat, Phys. Rev. Letters, 1974,32, 1354. lo G. K. White, Experimental Techniques in Low Temperature Physics (Oxford University Press, Oxford, 2nd edn, 1968). l1 W. A. Gibbons, G. Porter and M. I. Savadatti, Nature, 1965,206, 1355. E. P. Gibson, G. R. Mant, R. Narayanaswamy, A. J. Rest, S. Romano, K. Salisbury and J. R. Sodeau, J.C.S. Faraday 11, 1979, 75, 1 179. ' I. Sugawara and Y. Tabata, Chem. Phys. Letters, 1976,41, 357. ' K. Maki, Y. Kataoka and T. Yamamoto, J. Chem. Phys., 1979, 70, 655. l3 M. R. Wright, R. P. Frosch and G. W. Robinson, J. Chem. Phys., 1960,33,934. l4 W. M. McClain and A. C. Albrecht, J. Chem. Phys., 1965,43, 465. P. Debye and J. 0. Edwards, J . Chem. Phys., 1952, 20, 236. l6 J. Bullot and A. C. Albrecht, J. Chem. Phys., 1969, 51, 2220. l7 J. Kroh and J. Mayer, Int. J. Radiat. Phys. Chem., 1973, 5, 59. l9 M. A. White, T. G. Ryan and J. A. Morrison, to be published. 'O 0. Haida, H. Suga and S. Seki, Thermochim. Acta, 1972, 3, 177. 22 J. Kroh, J. Mayer, W. Roszak, Z. Galdecki, Z . Gorkiewicz and B. Ptaszysnki, Int. J. Radiat. 23 I. Boustead and A. Charlesby, Proc. Roy. SOC. A , 1970, 315, 271. 24 L. F. Pender and R. J. Fleming, J . Phys. C, 1977, 10, 1571. 25 J. T. Randall and M. H. F. Wilkins, Proc. Roy. SOC. A, 1945, 184, 366. 26 D. R. Aadsen, Ph.D. Thesis (University of Illinois, 1975). F. Kieffer, N. V. Klassen and C. Lapersonne-Meyer, J. Luminescence, 1979, 20, 17. J. Bullot A. DCroulede and F. Kieffer, J. Chim. phj's., 1966, 63, 150. Phys. Chem., 1974, 6, 423.

ISSN:0301-7249    

DOI:10.1039/DC9806900164

出版商:RSC    

年代:1980

数据来源: RSC

摘要:

Studies of Phase Transformations in Molecular Crystals Using the Positron Annihilation Technique BY MORTEN ELDRUP Chemistry Department, Risar National Laboratory, 4000 Roskilde, Denmark AND DAVID LIGHTBODY AND JOHN N. SHERWOOD Department of Pure and Applied Chemistry, University of Strathclyde, Glasgow G1 1XL Received 10th December, 1979 An examination has been made of the brittle/plustic phase transformation in the molecular crystals cyclohexane, DL-camphene and succinonitrile using the positron annihilation technique. In each material, the transition is characterized by a distinct increase in ortho-positronium lifetime. The influence of impurities on the transition was examined for DL-camphene. Addition of the impurity tricylene in concentrations in the range 0.14-4.0 mol "/b resulted in a lowering of the transition tem- perature from 176 to 167 K and a broadening of the transition region.Following emission from a nucleus a positron will annihilate with an electron of the environment with the emission of gamma quanta.l Annihilation may occur directly from the free state with the emission of two 0.51 MeV quanta or via the formation of the electron-positron bound state, positronium (Ps). Positronium can exist in two forms : para-positronium (p-Ps) with the electron and positron having spins anti-parallel or ortho-positronium (0-Ps) ; spins parallel. In free space, p-Ps annihilates via a two-gamma decay with a mean lifetime z1 = 0.125 ns whereas o-Ps undergoes a three-gamma annihilation, mean lifetime 140 ns. In condensed matter, there is a high probability of interaction between o-Ps and the electrons in the surrounding molecules.The positron may then annihilate with an electron of the opposite spin with the emission of two gamma quanta. This pick-off annihilation process dominates and reduces the o-Ps lifetime to the order of a few nanoseconds. Free annihilation of the positron in molecular solids is characterized by a lifetime r2 w 0.3-0.5 ns. The 0-Ps annihilation process is sensitive to small variations in the electron density and hence molecular density of its environment. This renders it a potentially useful probe for the examination of small-scale structural processes such as vacancy and void formation and phase transformations in molecular solids. All of the materials studied belong to that state of matter usually described as Plastic Cry~tals.~ At low temperatures they exist as brittle solid phases of low crystallographic symmetry, with little or no re-orientational molecular disorder.With increasing temperature, they undergo a lambda-type transition,- to yield a re- orientationally disordered form of higher symmetry (f.c.c. or b.c.c.). This latter form176 PHASE TRANSITIONS STUDIED BY PAT usually persists to the melting point. This change of state results in a significant change in molar volume' which should be reflected by a change in o-Ps lifetimes. Although the phase behaviour of certain liquid-crystal systems have been in- vestigated in detail using the positron annihilation technique,s the study of poly- morphism in molecular solids has only been noted in a limited number of cases, e.g., tri~almitin,~ tristearin," CH30H, CD30D and CG2SH." Only cyclohexane,12 2c n &? ,h 16 8 v .I c, *- 12 a 2.4 2 .o 3 3 3 1.6 \ .- 2 Y 1.2 0.0 100 150 20 0 250 300 temperature/K FIG.1.-Succinonitrile. The temperature dependence of the average 0-Ps lifetime, z3, and its in- tensity, &. The phase transition takes place at 234 31 1 K. In all figures open symbols are for increasing, closed ones for decreasing, temperatures. cyclo-octanone l3 and DL-camphor,14 of the plastic crystal class have received previous mention. The present study illustrates the degrees of sensitivity available to the technique in the region of the transition, where hysteresis and impurity effects are observed. No detailed examinations have been reported.EXPERIMENTAL All materials were purified by fractional sublimation, distillation or zone refining l5 and analysed using gas-liquid chromatography. Single crystals of succinonitrile (< 1 p.p.m. total impurity content) prepared in uacuu by a Bridgman technique were sectioned into 1 cm diameter x 0.5 cm discs. The cyclohexane ((100 p.p.m. total impurity) and doped DL- camphene (0.14, 1.3 and 4 mol yo tricylene) samples were prepared by freezing the degassed liquid and sectioning the resulting polycrystal as noted above. The samples were mounted on either side of the positron source which consisted of 20M . ELDRUP, D . LIGHTBODY AND J . N . SHERWOOD 177 pCi 22NaCl contained in an envelope of Kapton foil. This sample/source arrangement was mounted in a liquid nitrogen cryostat with a temperature control of i0.5 K.Lifetime measurements were made using a conventional fast-slow or a novel fast-fast lifetime spectrometer l6 with time resolutions of 0.35-0.4 ns full width at half maximum. Zero time is marked by the prompt 1.28 MeV gamma which accompanies the positron emis- sion and subsequent annihilations by the 0.51 MeV annihilation gammas. Accumulation Lot-, , , , , , , , , [ I , , , [ [ , , I ,A 100 150 200 250 300 temperature/K FIG. 2.-Camphene with 1.3% tricyclene. The temperature dependence of the average 0-Ps lifetime, T ~ , and its intensity, 4. The phase transition for material of this purity is defined at 173 k 1 K (see also fig. 4). of data was carried out over periods of 12-15 h to produce spectra containing z lo6 counts.All spectra were analysed using the computer programme POSITRONFIT.” RESULTS The spectra were resolved into three lifetimes, zl, z2 and z3, associated with p-Ps, free positrons and o-Ps, respectively. It is, however, the o-Ps lifetime which is of the greatest interest in this study since the others show little or no detectable change in value across the phase transition. The values of 0.05-0.25 ns determined in the present experiments are in satisfactory agree- ment with the theoretical value of 0.125 ns. The shortlived p-Ps component is often experimentally difficult to resolve.178 PHASE TRANSITIONS STUDIED BY PAT The variations of z3 and Z3 (the 0-Ps yield) with temperature, for the materials studied, are illustrated in fig.1-3. In all cases the lifetime increases almost linearly with temperature in the low-temperature phase. The phase transition is clearly identified by an abrupt change in z3. In succinonitrile and camphene a behaviour characteristic of 0-Ps trapping at thermally generated defects is noted in the plastic phase. This sigmoidal variation of z3 and its interpretation has been discussed in detail elsewhere.2 It would seem rational to define the phase transition temperature as that tempera- ture at which z3 has the mean value of the lifetimes directly before and after the transition; the assessment being made on increasing the temperature. On this basis, 30 15 10 2.5 c 1 1.0' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' J 180 185 190 195 temperature/K FIG. 3.-Cyclohexane with 100 p.p.m.impurities. The temperature dependence of the average o-Ps lifetime, t3, and its intensity, I,, around the phase transition. The transition is found at 188 & 0.5 K. the phase transition from the low-temperature monoclinic phase to the high-tempera- ture b.c.c. phase in succinonitrile occurs at 234 I K with an associated hysteresis of ~ 2 5 K. Cyclohexane exhibits its transition from the low-temperature phase to the high-temperature f.c.c. phase at a temperature of 188 & 0.5 K with z 2 K hysteresis. Fig. 4 and 5 illustrate the influence of the impurity, tricyclene on the characteris- tics of the phase transition in the camphene system. The transition from the low- temperature phase to the high-temperature b.c.c. phase at temperatures of 176, 173, 167 K (all with an uncertainty of I K) correspond to samples of 0.14, 1.3, 4.0% tricyclene concentration, respectively.The effect of dopant concentration seems also to be reffected in the width of the transition which increases with increasing concentra- tion as illustrated in fig. 5(b).M . ELDRUP, D. LIGHTBODY AND J . N . SHERWOOD 179 DISCUSSION In all three materials examined, the variation of 0-Ps lifetime with temperature shows a significant change in the vicinity of the phase transformation. These changes can be roughly correlated with the change in free volume in the system.18 The frac- tional increases in the densities of camphene and cyclohexane are 2.7 and 9.4%, respectively,’ compared with lifetime increases of 0.52 and 1.0 ns. Within the limitations of the definition of purity of the specimens used in previous studies, the present estimates of the transition temperatures correlate well with the values previ- ously quoted and probably provide a better estimate of these temperatures.For succinonitrile, heat capacity4 and n.m.r. studies l9 define the transition tem- perature as 233 and 236 K, respectively. The quoted purification schemes suggest a 1.8 1.6 1.2 160 165 170 175 180 185 temperature/# FIG. 4.-Camphene with (a) 0.14, (6) 1.3 and (c) 4.0% tricyclene. The shift in phase transition tem- perature as detected by the 0-Ps lifetime, 73. The arrows show the temperature at which t3 = 1.55 ns, taken to be the transition temperature. similar purity of material in both cases. The present value of 234 K for potentially purer material is in adequate agreement with these values.The purity of one previously studied sample of cyclohexane is better defined. Here assessments have been made using heat capacity measurements6 (186.1 K) infrared absorption spectroscopy” (187 0.5 K), n.rn.r.” (186 K) and positron180 PHASE TRANSITIONS STUDIED BY PAT annihilationI2 (187 & 4 K). A sample purity of 950 p.p.m. was noted for the material used in the heat capacity measurements. The present value is in good agreement with the above and is in the correct relationship to that obtained from the latter measurements allowing for the ten-fold improvement in purity (see below). The values obtained for DL-camphene show the largest discrepancy with previous data. The previously published value of 153 K5 is 24 K lower than that estimated for the present sample of highest purity.This difference probably arises from the presence of impurities in the original sample. Reagent grade DL-camphene can be extremely impure (4-15% of tricyclene and L -I 0 1 2 3 L 5 ct c I c . ( %) 10 8 2 1 2 3 4 5 ct r Ic . ( %I FIG. 5.-~~-Camphene (a). tricyclene concentration. The phase transition temperature as defined in fig. 4 as a function of the (6) The width of the phase transition (defined as the temperature range over which r3 changes from 1.35 to 1.75 ns) as a function of the tricyclene concentration. lesser amounts of other impurities).22 The influence of increasing tricyclene content on the phase transition temperature confirms this speculation (fig. 5).Further confirmation of the present value has been obtained from n.m.r. studies23 of DL-camphene of similar quality to that of the most pure sample (175 K). This experiment, and to a lesser extent that on cyclohexane, demonstrates the considerable influence of included impurities on the transformation process. It confirms the view that experiments should be performed with samples of the highest purity obtainable. It is also notoriously difficult to purify.M. ELDRUP, D . LIGHTBODY AND J . N. SHERWOOD 181 The basic reason for the noted influence probably resides in the ease with which tricyclene forms solid solutions with DL-camphene.22 Since the impurity molecule is more symmetrical than the host, its substitutional inclusion could lead to a lower- ing of the potential barriers opposing the orientational disordering.This in turn will lower the transition temperature. A similar effect has been noted previously in heat capacity studies of methane containing krypton as A systematic lowering of the phase transformation temperature was found to accompany the progressive temperature/K FIG. 6.-Camphene with 4% tricyclene. Intensities of 0-Ps lifetime components with lifetimes characteristic of the low-temperature and the high-temperature phases, 1 . 3 ns (IA) and 1.8 ns (IB), respectively. addition of the more symmetrical krypton atoms. A parallel broadening of the transition region was also noted in this case. Above and below the phase transformations specific values of the o-Ps yields and lifetimes can be assigned to the separate phases.If we make the reasonable assump- tion that the gradual change observed in the 0-Ps yield arises from the temporary coexistence of the two phases in the region of the transition, then we can attempt to estimate the relative concentrations of each. At the present time sufficient data for such an analysis only exist for the least pure camphene sample. The results are shown in fig. 6. With improved accuracy, it should be possible to extend this kind of analysis to the more pure systems. The positron annihilation technique is presently suitable for the accurate definition of the phase transition temperature and potentially useful for the analysis of composi- tion in the vicinity of the transition. More detailed structural interpretations derived from the nature of the annihilation process must await further work on this topic using a wider variety of materials.The degree with which the o-Ps lifetimes can be associated with density changes is noted above. A relationship exists here which can be developed. The formation of Ps takes place between the injected positron and one of the elec- The variations in o-Ps yield (I,) are more difficult to explain.182 PHASE TRANSITIONS STUDIED BY PAT trons created by the positron during the ionisation of the medium as it loses energy. The yield is thus dependent on the physical and chemical properties of the Similar processes are studied in radiation chemistry and, potentially, Ps yields could be correlated with those results. The current lack of such investigations in molecular crystals limits immediate progress.The potential of the positron annihilation tech- nique for the study of solid-solid phase transformations is, however, clearly illustrated. We thank 0. E. Mogensen for discussions, S. J. Lund for his work on the lifetime spectrometry, H. Egsgaard Pedersen for supplementary impurity analyses and A. Blanke-Nielsen and N. J. Pedersen for their technical assistance. The financial support of the S.R.C. and NATO is most gratefully acknowledged. Positrons in Solids, ed. P. Hautojarvi (Springer, Berlin, 1979). M. Eldrup, N. J. Pedersen and J. N. Sherwood, Phys. Rev. Letters, 1979, 43, 1407. The Plastically Crystalline State, ed. J. N. Sherwood (Wiley, London, 1979). C. A. Wulff and E. F. Westrum Jr, J . Phys.Chem., 1963,67,2376. W. A. Roth, in Landolt-Bornstein Physikalisch-Chemische Tabellen EG IIIC, 2695 (Springer, Berlin, 1936). J. G. Aston, G. J. Szasz and H. L. Fink, J. Amer. Chern. Soc., 1943,65, 1135. W. G. Merritt, G . D. Cole and W. W. Walker, Mol. Cryst. Liq. Cryst., 1971,15, 105 and W. W. Walker, Appl. Phys., 1978, 16, 433 and references therein. W. W. Walker and D. C. Kline, J . Chem. Phys., 1974, 60,4990. ’ J. R. Green and C. Scheie, J . Phys. Chem. Solids, 1967, 28, 383. lo W. W. Walker, W. G. Merritt and G. D. Cole, Phys. Letters, 1972,40A, 157. l1 S. Y . Chuang and S. J. Tao, in Phase Transitions, ed. L. E. Cross (Pergamon, London, 1973), l2 A. M. Cooper, G. Deblonde and B. G. Hogg, Phys. Letters, 1969,29A, 275. l3 W. W. Walker, W. G. Merritt and G. D. Cole, J . Chetn. Phys., 1972, 56, 3729. l4 V. G. Kulkarni and N. K. Dave, Phys. Stat. Sol., 1975, B67, K79. l5 J. M. Bruce, D. Lightbody, B. McArdle and J. N. Sherwood, to be published. l6 S. J. G. Lund, Riser, unpublished. l7 P. Kirkegaard and M. Eldrup, Comp. Phys. Comm., 1974, 7, 401. l8 W. Brandt, S. Berko and W. W. Walker, Phys. Rev., 1960, 120, 1289. l9 J. G. Powles, A. Begum and M. 0. Norris, Mol. Phys., 1969, 17, 489. 2o G. N. Zhizhin, E. L. Terpugov, M. A. Moskaleva, N. I. Bagdanskis, E. I. Balabanov, and A. I. *l D. E. O’Reilly, E. M. Petersen and D. L. Hogenboom, J. Chem. Phys., 1972,57,3969. 22 N. T. Corke, N. C. Lockhart, R. S. Narang and J. N. Sherwood, Mol. Cryst. Liq. Cryst., 1978, 23 N. Boden, S. Hanlon, M. Mortimer and S. Ross, unpublished results referred to by N. Boden in 24 A. Eucken and H. Veith, Z. phys. Chem., 1936, 34, 275. 25 0. E. Mogensen, J. Chem. Phys., 1974, 60, 998. p. 363. Vasil’ev, Sov. Phys. Solid State, 1973, 14, 3028. 44, 45. The Plastically Crystalline State, ed. J. N. Sherwood (Wiley, London, 1979), p. 171.

ISSN:0301-7249    

DOI:10.1039/DC9806900175

出版商:RSC    

年代:1980

数据来源: RSC

摘要:

Diamagnetism and Phase Transformations in Molecular Crystals BY J ~ Z E F W. ROHLEDER Institute of Organic and Physical Chemistry, Technical University of Wroclaw, Wroclaw, Poland Received 28th November, 1979 The applicability of the Oriented Gas Model to describing the length and orientation of the principal axes of the susceptibility tensor in molecular crystals is discussed. The influence of tempera- ture on diamagnetic anisotropy is interpreted as being a result of small but continuous changes in the orientation of molecular tensors. The elucidation of this effect is given by means of a " rigid box" model. The presentation of effects associated with a phase transformation is followed by the discussion of some damping effects occurring in high-temperature phases. Unlike valence and ionic crystals, molecular crystals are composed of structural units which are bound together with very weak forces in comparison with the inter- actions between individual atoms in a given molecule.Because of this, molecules very frequently display features like those of molecules in the gaseous state and collective behaviour of the lattice appears only in rather rare circumstances (lattice vibrations, dynamical splitting of infrared frequencies, local electric field, etc.). In cases where the interaction effects can be neglected, the measurement of a macroscopic crystal property can lead to the knowledge of properties of the free molecule. Among known physical properties only two seem to meet these conditions: diamagnetic susceptibility and intensity of infrared absorption, at least in certain spectral regions.The mean molar susceptibility of diamagnetic solids, (x), is of the order of - 100 x c.g.s. M units. * Therefore, molecular field effects can safely be neglected and we can assume that the field in the crystal is practically equal to the external field strength, H.' This leads us to the Oriented Gas Model of diamagnetic susceptibility, presented in the next section. In following sections certain properties of real crystals are discussed in connection with anharmonic effects due to thermal motion . DIAMAGNETIC SUSCEPTIBILITY OF AN IDEAL CRYSTAL PHASE Measurements of diamagnetic anisotropy of crystals were introduced first by Krishnan2 and a molecular interpretation of the macroscopic tensor x was given by Lonsdale and Kri~hnan.~ Denoting by K the molecular tensor, given most frequently in LMN symmetry axes of the molecule, and by dr) the orientation matrix of LMN axes of the rth molecule with respect to the orthogonalized frame of the unit cell, abcx, we can summarize the relationship between macroscopic and microscopic susceptibilities by means of the expression184 DIAMAGNETISM OF CRYSTALS where cT means c transposed.structural data, and for the other 2 - 1 molecules Matrix c(') for the " first " molecule is to be taken from Arc(') AT. (2) c t r ) = A, are matrices corresponding to the symmetry elements inherent in the symmetry factor group of the unit cell. Expression (1) may be called the Oriented Gas Model Approximation and in analogy with what is known from the infrared spectroscopy of crystal^,^ it is a special case of the additivity rule of physical properties.It may be expected that the model will hold only for well-ordered crystalline phases. However, if molecular properties are known, some structural information can be obtained from crystal susceptibilities for disordered structures also. An example of such investigations may be found in ref. (5). Usually eqn (1) is used to calculate the molecular tensor K from measured crystal properties, and many examples of this application have been reviewed by La~heen.~.' In principle, this problem can be solved uniquely only for triclinic crystals for which the number of experimentally available pieces of information exactly corresponds to the number of components of the tensor K (length of three principal axes and three orientation angles).In crystals with higher symmetry certain assumptions must be made about the orientation of the K axes which are difficult to verify. Recently, much progress has been made with the problem in two papers of Van den Bossche and Sobry?v9 Assuming that the additivity law holds for molecular susceptibility the authors have shown how to derive the particular tensors for the carbon skeleton and the substituents separately. Using the known incre- ments we are able to obtain the orientation of the principal axes of K in an independent manner.9* lo The particular shape of x(abcx) depends on the symmetry of the unit cell: the higher the symmetry, the more of the off-diagonal components are equal to zero.' For instance, assuming that the two-fold symmetry axis in a monoclinic crystal is parallel to the crystallographic axis b, we have cj4Kj 0 cj123Kj) x(abc") = 0 cjZK, (3) i cjlcj3Kj 0 cj$K, where summation over j is inferred.The graphical picture of eqn (3) is, in all cases yet found, a triaxial ellipsoid with all axes negative. Let us assume now that we are given a triaxial ellipsoid in a monoclinic crystal with the axes fulfilling the inequality 1x11 > 1x31 > 1x21. (4) The orientation of the x1 axes is assumed here, as usual, in such a manner that x3]lb, and x1 and x2 both lie in the (010) plane. The angle of orientation of x1 with respect to the crystallographic axis a, w, is meant to be positive if measured in positive mono- clinic angle, p.With these assumptions we can always find a direction OP, fig. 1, such that the susceptibility along OP will be equal to x3. The section through OP and x3 is isotropic, i.e., the crystal will show no anisotropy when hung in a magnetic field along its normal, OQ. Therefore, OQ is one of two magnetic axes of the crystal, and the axial angle, 2V, is given by the expression Making use of eqn (3) we can see that the anisotropy of molecules and their distribu- tion are factors determining the direction of macroscopic magnetic axes. Experi-J . W. ROHLEDER 185 FIG. 1.-Circular section of an ellipsoid of magnetic susceptibility: susceptibility along OP is equal to x3. OQ is the direction of magnetic axis. mental evidence of an isotropic section has been given in ref.(10) for the example of 1,5-dinitronaphthalene. Therefore, in analogy with the classification known in optics, we can divide dia- and para-magnetic crystals into biaxial, uniaxial and iso- tropic classes. DIAMAGNETISM OF A REAL CRYSTAL PHASE It is well known that the atoms execute thermal vibrations with an amplitude increasing as the temperature is raised. In the harmonic approximation the atomic vibrations can be presented in a compact form by means of tensors T, L and S, describing translational, librational and composed motion, respectively, of the mole- cule as a whole."-13 By a " real " crystalline phase we understand a periodic struc- ture composed of molecules which execute thermal oscillatory motions. Other defects, such as stacking faults, dislocations or dissolved admixtures, will be ignored.However, the vibrations cannot be harmonic, as is indicated by the anisotropy of thermal expansion, leading to a homogeneous deformation of the lattice. As a con- sequence, the actual position of the molecule will change slightly when the temperature is raised. The overall effect may be resolved into two components: a small trans- latory shift of the centre of mass and a small change of orientation of molecula, 1' axes with respect to the frame of the unit cell. Of primary importance here is the angular position of the molecule. The translatory shift leading to a small density change can be neglected because of the low accuracy of magnetic measurements. However, it can have a significant role in the much more accurate measurements of the tempera- ture function of optical birefringence.l4-I6186 DIAMAGNETISM OF CRYSTALS Direct information about the angular shift of a molecule can be derived from structural data known for a given structure at least at two different temperatures.Let us take as an example the well known structure of anthracene which was investigated very accurately by Mason at TI = 290 and T2 = 95 K." The orientation matrices, c(290) and 4 9 9 , differ significantly from each other. Calculating the Eulerian angles x, 9, 0, for these two temperatures we obtain the following values of mean temperature coefficients (in seconds of arc per degree K) : !!Z = -11.5, A 9 - = -3.6, A0 - = +20.5 "K-l, AT AT AT or 61(L) = - 10.2, d,(M) = - 18.2, &(N) = - 13.0 "K-l.The figures given in the second row are smali rotations round LMN symmetry axes of the molecule. Of course, the temperature function of Eulerian angles will not be, in general, linear. This is clearly seen on an example of anthraquinone crystal shown in fig. 2. The structure of this crystal has been solved at five temperatures" indicated by arrows on the abscissae. 100 150 200 250 TIK FIG. 2.-Temperature function of Eulerian angles of the molecular LMN symmetry axes in anthra- quinone crystal. 0, x ; Points correspond to the values calculated from crystal structure data.'* 0, 8 and a, P.1 . W . ROHLEDER 187 I 1 I I 100 150 200 250 300 TIK FIG. 3.-Temperature function of crystal susceptibilities in anthraquinone. Arrows indicate tem- perature points at which the structure was analysed." (a) -xl, (b) -xz and (c) -x3.We may now ask to what extent is the macroscopic susceptibility influenced by these small structural changes? The answer is illustrated in fig. 3 where the principal susceptibilities are shown for anthraquinone, calculated using eqn (1) and the tem- perature functions of Eulerian angles from fig. 2. Susceptibilities x2 and x3 change in a manner similar to the Eulerian angles but x1 is temperature independent. Un- fortunately no experimental data are available for anthraquinone so that direct corn- parison is not possible. Instead we may quote some results known for benzene. The crystal anisotropies (orthorhombic) have been measured by Hoarau et al.19 in a wide temperature range. Two curves taken from this paper and shown in fig.4 (solid lines) are similar in shape to those from fig. 3. A comment concerning the broken lines in fig. 4 will be made later in this section. Note that the mean crystal susceptibility, (x), is independent of temperature within the limits of experimental error. This has been experimentally proved for crystalline benzene by Hoarau and others in a temperature interval from 80 to 270 K.19 28 r T K from ref (19), broken lines (1') and (2') calculated according to RBM. FIG. 4.-Temperature function of crystal anisotropies in benzene. (1) (xb - xa); (2) (xb - xc) taken188 DIAMAGNETISM OF CRYSTALS The considerations of this section supported by experimental facts may be sum- marized by the following statement. The change in temperature of a crystalline phase in the region of thermodynamic stability is followed by a continuous change in the angular position of the molecule of the order of magnitude of few seconds of arc per degree Kelvin, and this is reflected in the temperature function of magnetic sus- ceptibility or of its anisotropy.It is not easy, even if possible, to give a quantitative explanation of the temperature effects at the present state of knowledge of the anharmonic behaviour of the crystal lattice. However, we can get an idea about the magnitude of angular shifts by means of an argument which will be called the " rigid box " model (RBM). Suppose that we have a crystal structure at 0 K. Each unit cell containing 2 molecules can be divided into 2 parallelopipeds of symmetry identical to that of the unit cell and with edge parameters d,, d2, d3 which are simple fractions of the cell parameters so that 2 x d,d2d3 = abc.(4) This elementary parallelopiped containing only one molecule is called a " rigid box " because we will assume that its parameters and shape are fixed and independent of 0 FIG. 5.-Two possibilities of rotation of (010) profile of a rigid box (dl, d3) within a cell {dl(l + Al), d3(l + A3)}, schematic. temperature so far as the size and shape of the molecule are temperature independent. When the temperature is raised the lattice expands and the rigid box gains more and more space. The profile of the box can then change its position by the angle (p for which there are two possibilities, shown in fig. 5 for a (010) section of a monoclinic crystal. If i, j , k denote the unit vectors along the cell edges, respectively, M is the tensor of thermal expansion and aAT=B (7) we have for the case shown in fig. 5 4 4 q2 = - (iTBi) sin (dl, d3) d,(iTBi) < d3(kTBk), (9)J .W . ROHLEDER 189 or if dl(iTBi) > d3(kTBk). (1 1) Analogous relationships will hold for another section of the unit cell. The choice between the two possibilities, eqn (8) or (lo), can be made by means of inequalities (9) and (1 l), and the selection of sign must be made by correlation with the experiment- ally observed direction of changes of diamagnetic anisotropy or optical birefringence. Numerical values of the angle 9 calculated from a, b, c, 2 and a for various crystals are summarized in table 1. The results given by RBM are very sensitive to a, as is TABLE RO ROTATION ANGLES ROUND LMN AXES OF MOLECULES (seconds of arc per Kelvin) (A) anthracene 1 -10.3 0.1 -18.10 & 0.07 -12.9 + 0.09 directly from crystal structure: 2 - 14.8 - 14.0 -1.6 RBM,a: Mason17 3 -6.1 - 3.5 0.5 RBM, a: Kozhin'' 4 -18.2 -11.8 0.9 RBM, a: Ryzhenkovzl 5 - 10.2 -3.2 2.3 RBM, a: Jakubowski22 Mason l7 (B) carbazole 1 -9.8 0 0 from birefringence : Kusto l6 2 - 7.0 0 0 RBM, a: SwiqtkiewiczZ3 (C) benzene 1 73.7 - 13.7 - 12.8 from diamagnetic anisotropy: 2 60.3 - 15.2 -37.2 RBM, a: Coxz4 Hoarau l9 seen for anthracene.In certain crystals, e.g., carbazole, only one degree of angular shift is allowed because of symmetry restrictions. It may be interesting to see how far the angular shifts deduced from RBM are able to reproduce the temperature function of diamagnetic anisotropy.This is exempli- fied for benzene by the broken lines in fig. 4. If we assume, in accordance with molecular symmetry, that KL = KM # KN, all principal susceptibilities, xn, X b and xc automatically become functions of only two Eulerian angles: 9 and 8. Using mean temperature coefficients given by the RB model we cannot reproduce the non- linear behaviour of xi(T). The position and mean slope of experimental curves in fig. 4 agree only qualitatively with predictions given by the model. DIAMAGNETISM AND PHASE TRANSITIONS So far we have dealt with the temperature behaviour of crystalline phases which are thermodynamically stable in some temperature region ; in particular their symmetry remains unaltered within this region.During a phase transformation a sharp symmetry change occurs at the transition temperature, at least in the case of the first- order transition. This is usually accompanied by far greater changes in the orienta- tion matrix, c, and, consequently, by more dramatic behaviour of magnetic suscepti-190 DIAMAGNETISM OF CRYSTALS 60 40 bility. This need not be true for crystals composed of molecules which have small or zero magnetic anisotropy. Experiments performed on pentachlorophenol crystals (monoclinic) have shownz5 that, on heating, the diamagnetic anisotropy rapidly diminishes in the vicinity of 63 "C, corresponding to the transition temperature of this compound. Similar effects observed in 1,s-dinitronaphthalene z6 (orthorhombic) are illustrated in fig.6. - - &ol 1 I I I I I 10 30 50 70 90 110 130 t/"C FIG. 6.-Temperature function of diamagnetic anisotropy in 1 ,%dinitronaphthalene crystals (ortho- rhombic) for two different types of suspension. Small and usually linear changes in the anisotropy are fallowed by a sharp drop at the transition point. For certain suspension directions, e.g., along the crystallographic axis a, even a change in sign of the anisotropy is observed. As a rule large hysteresis effects occur while cooling the sample, and the anisotropy of the low-temperature phase after a complete cycle never reaches the value measured initially. These phenomena are doubtless connected with relatively large volume changes accompanying these two phase transformations, which thus lead to a destruction of long-range order.Therefore, in spite of large effects, these and similar cases may not be very interesting from the structural point of view as they escape microscopic interpretation. More profitable experiments could be performed with crystals exhibiting a crystal-to-crystal transition, but according to our knowledge they have not yet been done. However, the difference in density between low- and high-temperature phases can also lead to new and interesting conclusions concerning some aspects of the lattice dynamics of the high-temperature phase. A crystal sample, when hung on a thinJ . W. ROHLEDER 19 1 thread in a homogeneous magnetic field, can execute torsional vibrations whose period is governed as much by the anisotropy of the crystal as by the elastic constant of the thread.If the sample oscillates in air, the motion is damped. This is partially caused by the viscous properties of air but is also due to the inner, microscopic state of the sample. Depending on the particular substance and its temperature the reasons for the appearance of an “inner viscosity” may be different. Using the oscillation method for quartz samples, which can surely be considered as a “ rigid phase ”, c 0 0 - 0 0 0 0 0 0 0 2 4 6 H/kOe FIG. 7.-Damping constant, B, of torsional vibrations of a sample of potassium ferrocyanide tri- hydrate as a function of the field strength, H. Braginski has shownz7 that it is an enormously sensitive tool for measuring the quality of the crystals. The high-temperature phase of a molecular crystal with its specific dynamics may be another example of enhanced damping.This is believed to be illustrated by fig. 7 which shows the damping constant measured in air for potas- sium ferrocyanide trihydrate, K,Fe(CN),. The crystal suspended along the b axis shows very small anisotropy and in this case a sharp dependence of H is observed. Further investigations are in progress. J. F. Nye, Physical Properties of Crystals (Clarendon Press, Oxford, 1957). K. S. Krishnan, B. C. Guha and S. Banerjee, Phil. Trans. A, 1933, 231, 235. K. Lonsdale and K. S. Krishnan, Proc. Roy. SOC. A , 1936,156, 597. J. W. Rohleder and T. Luty, Mol. Cryst. Liq. Cryst., 1968, 5, 145. G. Fulinska-W6jcik and J. W. Rohleder, Actu Phys. Polon., 1974, A45, 3.192 DIAMAGNETISM OF CRYSTALS M. A. Lasheen, Phil. Trans. A , 1964,256, 357. M. A. Lasheen, Actu Cryst. A, 1968, 24, 289. G. Van den Bossche and R. Sobry, Acta Cryst. A , 1974,30, 616. R. Sobry and G. Van den Bossche, Acta Cryst. A , 1974, 30, 721. D. W. J. Cruickshank, Actu Cryst., 1956, 9, 754. lo J. W. Rohleder and A. Mierzejewski, Materials Sci. ( Wrocluw), 1978, 4, 97. l2 G. S. Pawley, Actu Cryst., 1963, 16, 1204. l3 B. T. M. Willis and A. W. Pryor, Thermal Vibrations in Crystullogruphy (Cambridge University l4 P. J. Bounds and R. W. Munn, Mol. Cryst. Liq. Cryst., 1978,44, 301. l5 J. W. Rohleder, Krist. Technik, 1978, 13, 517. l6 W. J. Kusto and J. W. Rohleder, Mol. Cryst. Liq. Cryst., in press. l7 R. Mason, Actu Cryst., 1964, 17, 547. K. Lonsdale, H. J. Milledge and K. El Sayed, Actu Cryst., 1966, 20, 1. l9 J. Hoarau, N. Lumbroso and A. Pacault. Compt. rend., 1956, 242, 1702. 2o W. M. Kozhin and A. I. Kitaigorodski, Zhur. fiz. Khim., U.S.S.R., 1953, 27, 1676. 22 B. Jakubowski, Krist. Technik, 1979, 14, 991. 23 J. Swiqtkiewicz, unpublished results. 24 E. G. Cox, D. W. J. Cruickshank and J. A. S. Smith, Proc. Roy. SOC. A, 1958, 247, 1. 25 J. W. Rohleder, J. chim. Phys., 1970, 67, 1270. 26 A. Mierzejewski, unpublished results. 27 W. B. Braginski, N. B. Brandt and W. I. Osika, Vestnik Mosk. Univ. Ser. IZI, Phys. Astron., Press, Cambridge, 1975). A. J. Ryzhenkov, W. M. Kozhin and P. M. Myasnikova, Kristulfogrufiyu, 1967, 13, 1028. 1970, 11, 91.

ISSN:0301-7249    

DOI:10.1039/DC9806900183

出版商:RSC    

年代:1980

数据来源: RSC

摘要:

GENERAL DISCUSSION Prof. A. J. Leadbetter (University of Exeter) said : It is a great pleasure to see high- pressure techniques now being applied to the study of phase transitions in molecular solids. However, most of the techniques described are concerned essentially with static molecular properties, and dynamic properties provide a more sensitive probe of the intermolecular potential. What are the prospects for making such measurements as a function of pressure? Dr. A. Wurflinger (University of Bochum) said : The high-pressure equipment described in the paper allows dielectric measurements only below 10 MHz. There are only a few substances (e.g., cyclopentanol) which reveal dielectric relaxation phenomena at such low frequencies. Cyclopentanol has already been studied dielectrically both at atmospheric' and elevated2 pressures.A reinvestigation of the high-pressure behaviour of this substance is under way. In order to extend the measurements to substantially higher frequencies a different technique has to be used that requires a new high-pressure d e ~ i g n . ~ J. R. Green, S. J. Dalich and W. T. Griffith, Mol. Cryst. Liq. Cryst., 1972, 17, 251. D. N. Glidden, Thesis (University of New Mexico, 1972). R. I'ottel and E. Asselborn, Ber. Bunsenges. Phys. Chem., 1979, 83, 29. Dr. B. Ewen (University of Mainz) said: Dr. Wurflinger has shown us measure- ments on cyclohexanone which exhibit very clearly the existence of different phase transitions. Is anything known about the molecular origin ? Dr. A. Wurflinger (University of Bochum) said : The solid I-solid I11 transition at atmospheric pressure has been discussed for example by Corfield and Davies.' It is generally assumed that the quasispherical cyclohexanone molecule rotates with little restriction in the high-temperature solid phase.As far as the high-pressure transition 1-11 is concerned no structural information is available. It should be mentioned that the dielectric decrease at the 1-11 transition is of the same order as the dielectric dispersion observed by Corfield and Davies at 50 MHz in the solid I state. They suggested the absorption to arise from a correlation of the neighbouring molecules. Furthermore, the possibility of the axial-equatorial ring inversion has been discussed, but according to their results this conformational change should not be detectable dielectrically.It might be interesting to compare the phase behaviour of cyclohexanone with cyclohexane which also exhibits an additional high-pressure phase transition.2 The structure of the high-pressure solid phase I11 is not yet known, and the question may arise whether this phase has something to do with the chair-boat inversion of cyclo- hexane. The large energy difference3 between the chair and boat form does seem to rule out the possibility of the boat form to exist at low temperatures. However, Ludemann et aL4 found a negative activation volume for the ring inversion, using high-pressure n.m.r. spectroscopy. Possibly the intermediate twist-boat form (see figure below that has been taken from Squillacote)3 has a smaller volume than the chair form, therefore the ring inversion could be favoured with increasing pressure.194 GENERAL DISCUSSION If this were true, the solid phase I11 could be characterized by a steady conformational change between the two equivalent chair forms, whereas in the low-temperature phase I1 the ring inversion might be frozen in, thus reducing the possible orientations of the cyclohexane molecule to 1/2.This would correspond to an entropy change of Rln2 which indeed is observed for this t r a n s i t i ~ n . ~ . ~ . ~ J p - y HC HC r A 5 . 3 ; AH = 10.8 AXo= 5.5 C C FIG. 1 .-Energy diagram (units are kcal mol- l) for ring inversion in the cyclohexane chair (C), show- ing the twist-boat (TB) and the half-chair (HC) i.e., the transition state for the C to TB interconver- sion). Pseudorotation in the TB and HC is not shown.In the case of cyclohexanone the entropy change of the solid I-solid I1 transition is much less5s7 and it is open to question whether this transition is associated with the axial-equatorial interchange or not. G. Cornfield and M. Davies, Trans. Furuduy SOC., 1964, 60, 10. A. Wurflinger, Ber. Bunsenges. Phys. Chem., 1975, 79 1195. M. Squillacote, R. S. Sheridan, 0. L. Chapman and F. A. L. Anet, J. Amer. Chem. SOC., 1975, 97, 3244. H. D. Ludemann, R. Rauchschwalbe and E. Lang, Angew. Chem., 1977, 89, 340. K. D. Wisotzki, Diplom. Thesis (University of Bochum, 1980). H. Arntz and G. M. Schneider, Furuduy Disc. Chem. Soc., 1980, 69, 139. A. Wiirflinger and J. Kreutzenbeck, J . Phys. Chem. Solids, 1978, 39, 193.Dr. J. A. Venables (Sussex Uniuersity) said: It seems particularly difficult to grow large single crystals of the low-temperature forms of molecular solids, because of the volume change and defect production associated with phase transitions. These defects do not anneal out at all rapidly when the transitions take place far below the melting point. Even when single-crystal-like patterns are produced, troubles can arise from defects such as twins giving spurious reflections. Thus it seems that powder patterns in conjunction with packing calculations could be very helpful, as Dr. Pawley suggests, An alternative approach which we have taken is to examine the necessarily small crystals produced, by high-energy electron diffraction in a transmission electron microscope.The crystals are produced by vapour deposition in a small enclosed cell, separated from the microscope vacuum by thin electron transparent windows: crystals in the 1-10 prn size range can give good single-crystal patterns after moderate anneal- ing, and twinning and other defects can be identified in the corresponding electron micrographs. It may also be possible to observe the phase transitions as they occur. Previous work of this type has enabled us to show that the a-N2 structure is indeed Pa3, and twins were the almost certain cause of extra spots (in X-ray patterns) which had been interpreted as evidence for the P2, 3 structure.' Presently we are working on SF6, whose low-temperature structure is unknown, and it is possible that the low-temperature structure of CD4 could be tackled in this way.An elegant example of a similar approach is the work of Ramdas et al. on the various structures of anthracene, presented as a poster at this meeting.2 Thus single-crystal electron diffraction to determine unit-cell dimensions may be a useful tool in conjunction withGENERAL DISCUSSION 195 packing calculations, especially when X-ray or neutron single-crystal data are either not obtainable or are suspect. J. A. Venables and C. A. English, Acta Crysf., 1974, B30, 929; G. J. Tatlock, R. Mevrel and J. A. Venables, Phil. Mag., 1977, 35, 641. S. Ramdas, G. M. Parkinson, C. M. Gramaccioli, G. Filippini, M. Simonetta and M. J. Goringe, Nature. 1980, 284, 153. Dr. G. S. Pawley (Uniuersity of Edinburgh) said: It is good to know that there are other techniques which could be used in conjunction with the powder diffraction technique.Electron diffraction could well be used to suggest a unit cell for a structure, as this is the major stumbling block. With the unit cell established the technique of powder diffraction becomes much more powerful. Dr. A. Huller (KFA Jiilich) said: Can Dr. Pawley's method also be applied to orientationally disordered molecular crystals where the individual molecules possess several equilibrium orientations? Phase I1 of the ammonium halides with two different orientations of the ammonium tetrahedron and a statistical distribution over the two possibilities may serve as a simple example. Dr. G. S. Pawley (Uniuersity of Edinburgh) said: It is quite possible to tackle structures with disorder in them, if constraints can be used to reduce the number of parameters significantly.This has been done on tetraiodoethylene, where the disorder parameters could be found to a fair statistical reliability, whereas this was not possible in an unconstrained refinement. G. S. Pawley, Acfa Cryst. B, 1978, 34, 523. Dr. S. Ramdas (Uniuersity of Cambridge) said: This comment pertains to Dr. Pawley's work on structure refinement by powder diffraction. In the case of molecular crystals with usually high anisotropy, there is the problem of preferred orientations in the powder. In general we may encounter reflections mainly from the basal planes and those nearly parallel to them. There should be some way of finding the distribu- tion of accessible planes and make the corresponding corrections on the measured intensities of these reflections.Dr. G. S. Pawley (Uniuersity of Edinburgh) said: The program does not contain any means of overcoming the problems of preferred orientation, but it would not be difficult to include some extra function to modify the intensities which is dependent on the Miller indices in any systematic fashion. However, prospective users should know that there is a device at I.L.L. for obtaining powder diffraction scans from a spherical sample which is set spinning on a cushion of air. This process soon averages out over all the crystaliites in the sample, and a single crystal can even be used as the sample. Dr. A. D. Taylor (Rutherford and Appleton Laboratories, Didcot) said: On pulsed neutron sources such as SNS it is obligatory to exploit time-of-flight techniques for powder diffraction, i.e., the Bragg angle is fixed and the scan obtained from the polychromatic beam.Different detectors on the same Debye-Scherrer ring see identical patterns, in the absence of preferred orientation. The SNS powder diffrdcto- meters will have segmented annular detectors (2") with each segment giving a simul- taneous measurement of the powder pattern. This will allow preferred orientation effects to be routinely investigated.196 GENERAL DISCUSSION In designing the SNS powder diffractometers, we have been conscious of the necessity of measuring the lowest-order reflections in any pattern. A low-angle detector is included specifically for this purpose and, on the High Resolution Powder Diffractometer, the provision exists to reduce the pulse repetition frequency of the diffractometer when required. Dr.G. S. Pawley (University of Edinburgh) said: It is good to hear that the new instruments for the SNS are being designed so that we will be able to measure the lowest orders of diffraction to a sufficiently accurate level as to make unit cell deter- mination almost routine. The program described has been modified for the LINAC already, but the form of the peak shape used is not ideal. Once this is known, further modifications are very easily made. Dr. A. I. M. Rae (University of Birmingham) said: We have successfully used Dr. Pawley's powder profile refinement program including rigid-body constraints to refine X-ray data from the a-phase of malononitrile as reported in a comment on our paper.Dr. G. S. Pawley (University of Edinburgh) said : The peak shape function which is necessary for X-ray work will not be as complex as that for the pulsed neutron machines (see answer to Dr. Taylor), and it is not surprising that the Gaussian form already programmed gives a satisfactory refinement. Prof. G. Chapuis (University of Lausanne) said: I would like to remark that there is a class of phase transitions that can hardly be elucidated by powder diffraction, namely those associated with the appearance of satellites or diffuse scattering for which their orientation in reciprocal space is of great importance to derive the nature of the modulation or the disorder.I would like to ask Dr. Pawley if the program EDINP has been used for analysing structures with weak intensities arising from superlattice reflections? Dr. G. S. Pawley (University of Edinburgh) said : We have recently been able to solve a structure where the pseudocell is a cube of ca. 13 A, but which forms a large cell which is doubled in all directions.' This would not have been possible without the use of constraints. This is probably about at the limit of complexity that can be tackled at the moment, but the high-resolution machines which are now being designed for the SNS and the synchrotron X-ray source may well change this. The powder diffraction from a highly anharmonic molecular system shows very few peaks, and therefore this technique is not usable. It would appear that in some cases there is structure in the background of a powder pattern, as is evidenced by the work of Dolling and Powell on P-NZ (work in progress).To extract information from this background a simulation calculation is required, which is what we intend to do, G. A. Mackenzie, R. W. Berg and G. S. Pawley, Acta Cryst. B, 1980,36,1001. Dr. M. Schott (University of Paris) said : Most conducting polymers do not form crystals. They are actually poorly organized and show only a few diffraction lines. But even the modest information extracted from these lines would be useful. Could your program be adapted to such problems? Dr. G. S. Pawley (University of Edinburgh) said : The method can certainly be used for polymers, and already we are prepared for the refinement of isotactic polypropy- lene.In this example, one of the unit cell edges is an exact multiple of the polymerGENERAL DISCUSSION 197 chain, so that, as the unit cell edge refines to its optimum value, the whole structure of the polymer must be altered. The constraint needed to do this was rather more complicated than the usual constraints applied, but now this is done it is hoped that other systems will need only a modification of this constraint. Prof. A. J. Leadbetter (University ofExeter) said: I should like to describe briefly the results of a structural determination made by myself, J. C. Frost and R. M. Richardson using Pawley's EDINP profile refinement programme. This was for the material t-butyl cyanide discussed in our paper at this meeting, for which we have carried out a low-resolution structural study by profile refinement of the data for (4nsinO/A) <2.6 A-1 using results collected using the DIA powder diffractometer at I.L.L., Grenoble and the PANDA diffractometer at A.E.R.E..Harwell. The fully deuterated sample was supplied by Prof. G. W. Gray and Dr. J. W. Goodby, University of Hull. Refinement was successfully carried out at several temperatures in the low-tem- perature phase (T<233 K) from 5 K to just below the transition. As pointed out by Dr. Pawley it is first necessary to establish the unit cell and this is often very difficult. However, by following the changes from the high-temperature tetragonal phase we could show the cell to the monoclinic with space group P2, P2/m or P2,/m.Subsequent refinement established the space group to be P2Jm with the following parameters at 5 K a = 6.109 A, b = 6.863 A, c = 6.706 A (all & 0.007 A,) /? = 95.6" z = 2. The fit to the data is shown in fig. 2 and a projection of the structure along a is shown in fig. 3 . Tn this constrained refinement the structure of the molecule was taken to be 2.42 2.15 1.88 1.61 1.34 $ 1.07 0.81 0 . 5 4 0.27 0.00 *1 0 v) Y I I I I I I I I I I I I I 1 0.70 1.36 2.03 2.69 3 . 3 5 4 . 0 ) 4 . 6 8 5.34 2 6/10 deg FIG. 2.-Calculated (full line) and experimental (circles) diffraction profile of t-butyl cyanide (D9) at 5 K (Panda).198 GENERAL DISCUSSION that deduced in the gas phase from electron diffraction and microwave experi- ments. The structure of the tetragonal high-temperature phase has not yet been refined to the same extent but it is closely related to that of the low-temperature phase with the addition of considerable translational-rotational disorder (see our paper).E o( 0 FIG. 3.-Structure of t-butyl cyanide at 5 K viewed down the P axis. One might also remark that there is a danger of this discussion getting off track because Dr. Pawley is not advocating the use of powder in preference to single crystal methods but rather pointing out the possibilities when one is forced to use powders. Furthermore it may be that powder methods may provide a much more convenient route to the answer of specific limited questions, for example some aspect of molecular packing when the molecular structure is known. Perhaps I could cite as an example some structural work on the smectic A phase of C8HI7PhPhCN in which only two Bragg reflections are observed.By using X-ray and neutron scattering and variously deuterated samples the amount of data was significantly increased but remained very small indeed by crystallographic standards. Nevertheless it was possible to answer a limited but important question about the smectic layer structure to show that this consisted of overlapping molecular cores at the centre of the layers with alkyl tails pointing to the layer b0undaries.l A. J. Leadbetter et al., J. Physique, 1979, 40. 375. Dr. G. S. Pawley (University of Edinburgh) said : I am glad that it has been pointed out that this technique is not being advocated as an alternative to single-crystal methods.The results from the method cannot be as good as single-crystal work in a normal system, but in systems where single crystals are not available for any reason it does give us a chance to find the aspects of the structure which are to us of most importance. A question arose concerning the possibility of finding out the symmetry of a crystal structure from the diffraction pattern. It is very difficult to make deductions about the symmetry of any substance being studied, and the only way to do this is to do two refinements, one with and one without the symmetry in question, and then perform a significance test on the result. Such significance tests are very difficult to make, given the current disagreement over the correct way to treat the error analysis. This is an aspect requiring considerable effort.GENERAL DISCUSSION 199 Dr.A. Huller (KFA Julich) said: I would like to ask Dr. White two questions: (1) What would the electron mobility be in an atomic crystal, say krypton, where (2) What is the significance of the second maximum of luminescence around 37 K the building blocks do not possess rotational degrees of freedom? in CH, or 30 K in CD4? Dr. M. A. White (Oxford Uniuersity) said : The electron mobility in an irradiated rare-gas solid is several orders of magnitude greater than that in most solid alkanes. This is primarily due to the molecular shape : as the molecules become more spherical (with the rare-gas molecules at the perfectly spherical limit), the anisotropy of the molecular polarizability decreases, and an increased electron mobility results.There- fore, the rotational degrees of freedom, per se, do not greatly influence the electron mobility; however, their effect on the determination of the molecular shape is important. The polymorphism that is exhibited by many molecular solids can, of course, be associated with rotational degrees of freedom and at such solid-solid phase transitions the electron mobility would be greatly increased, resulting in thermoluminescence. However, it is not clear at this time whether this is to be associated primarily with increased rotational or translational motion, or both. In answer to Dr. Huller’s second question, I remark that the origin of the broad thermoluminescence peaks (i.e., those with widths of the order of several degrees) should be clearly distinguished from that of the sharper peaks which occur at the phase transitions.The latter are associated with recombination which is accelerated by the increased molecular motion at the solid-solid phase transitions; these peaks are found at T NN 20 K in CH4 + benzene (fig. 5 of our paper) and at T z 22 K and 27 K in CD4 + benzene (fig. 7). All the remaining (broad) thermoluminescence peaks illustrated (fig. 4-7) can be ascribed to the thermal detrapping of electrons at tem- peratures that are characteristic of the activation energies necessary for their re- combination with the parent cations. These are the so-called Randall-Wilkins peaks. The persistent peak at T NN 37 K in the CH4 + aromatic systems illustrated indicates the continued presence of electrons which are at a trap depth that can be thermally depopulated at T ,> 37 K.Similarly, the results indicate the presence of an electron trap that will depopulate at T ,> 30 K for CD4 + aromatic. Dr. M. Schott (University of Paris) (partly communicated): In connection with the question asked by Dr. Huller, I believe that the transport properties of thermalized charge carriers in methane may be unimportant in Dr. White’s experiments. Two reasons are (a) the low dielectric constant allows strong, long-range, coulombic electron-hole interactions implying very large capture cross-sections, and a Langevin recombination process, at least if the carriers’ mean free paths are not more than a few hundred A; (b) at low temperatures, recombination of carriers, both trapped, by tunnelling, may well be the dominant process outside the phase-transition tempera- tures.The isothermal luminescence of irradiated rigid organic glasses can be explained in that way. It is puzzling that the emitted light is purple, at least when it can be seen: benzene and toluene are not expected to emit visible light. Could it be that reaction products are emitting as well? It is known that toluene for instance easily forms the benzyl radical C6H5-CH2 and a hydrogen; I am not suggesting that benzyl emission is seen, since it should be green rather than purple, but other photochemical processes un- known to me are certainly possible. This remark raises the question of whether some200 GENERAL DISCUSSION of the light seen, especially at phase transitions, could be due to radical recombination, not to charge carrier recombination.The thermoluminescence curves show that not all possible recombinations occur at the lowest phase-transition temperature (or below). Why should some charges become mobile, and others stay trapped? This could be related to the different microscopic environments of different traps. A more trivial explanation could be competition between recombination and retrapping, some charges liberated outside the capture radius of any charge of the opposite sign being retrapped before meeting any of these, in traps deep enough to hold them. Dr. M. A. White (Oxford University) said : I would like to reply first to your com- ment concerning electron mobilities.Although tunnelling may be the dominant recombination mechanism in isothermal luminescence (and it is still not entirely clear that diffusion does not play a role in some systems), it is quite possible that at phase transitions, the lattice is sufficiently reorganized so that classical recombination pro- cesses may take place. In reply to your second comment, perhaps I should qualify the statement of the colour of the emission. The glow curves that were reported were observed with a photomultiplier tube that was sensitive to wavelengths in the range 3000-6000 A. The light intensities during thermoluminescence were very weak, and therefore spec- tral analysis was not carried out. The luminescence that was allowed to decay isothermally before heating the sample was, however, much more intense and, when observed by eye, it was seen to be violet in colour.This neither implies that the iso- thermal emission had a maximum in the violet range (since its maximum could have been in the U.V. region), nor that the thermoluminescence had a large violet component. It is, of course, possible that the violet emission that was observed was due to reaction products, as you suggest, or even due to small amounts of impurities. Finally, I would add that we, too, were rather surprised to see the evidence of recombination at both phase transitions in CD4 (rather than complete recombination at the lower transition). In addition to your suggested explanations, we could speculate that it is possible that this is due to intrinsic differences in the III+II and II-tI phase transitions, with some electrons mobilized only at the upper transition.Dr. M. A. White (Oxford University) (partly communicated). Some elaboration on the mechanism of energy absorption and luminescence in the methane solid might be useful. It is well known that it is difficult, if not impossible, to trap electrons in pure solid alkanes. In our experiments, we did not observe any luminescence when pure CH4 or CD4 was irradiated with 5 keV electrons. This was most likely due to the inability of these pure solids to trap electrons, with the result that the recombination process was too rapid for observation in our experiments. We also failed to see an emission when pure methane was irradiated by U.V. light, This is not the result of high electron mobility, but rather of the absence of ionic species when the pure sample is subjected to photolysis.As mentioned in our paper, a large population of triplet states is generated by u.v.-irradiation of the impure sample, so that the prob- ability of second photon absorption is significant. This results in the generation of a cation-electron population, which leads to recombination luminescence. In summary then, the aromatic impurity is necessary for the observation of recombination lumi- nescence in both photolysis and radiolysis experiments. In U.V. photolysis, it allows the production of an ion population and it creates electron traps. In radiolysis, the impurity generates electron traps but it is not necessary for the production of ionic species.GENERAL DISCUSSION 20 1 Prof.A. J. Leadbetter (University of Exeter) said : Could Prof. Rohleder tell us something more about his experimental method ? Prof. J. W. Rohleder (Technical University, Wroclaw) said: The method of mea- suring magnetic anisotropy of crystals is not new, and had been elaborated by Krishnan and co-workers by about 1935. In principle, the anisotropy is measured by means of the period of oscillation of the crystal when suspended on a thin and elastic thread in a homogeneous magnetic field. What seems to be new here is the fact that the amplitude of oscillations subsequently diminishes even in experiments carried out in a vacuum. This effect is due to the so-called " internal friction " within the solid and depends on the physical state of the sample. Prof. G. J. Hills (University of Southampton) said: In his verbal introduction to his paper, Prof. Rohleder drew attention to the observation that the damping co- efficients of the oscillations of the diamagnetic single crystals studied here were markedly dependent on the strength of the magnetic field. The reason for this is not clear although it seems not unlikely that mobile charges in the moving solid would respond to the magnetic field and thus enhance the damping. Any coupling of magnetic and electric phenomena in chemical systems is interesting and it would seem worth- while to pursue the observation reported here for its own sake. I hope Prof. Rohleder will do this. Prof. J. W. Rohleder (Technical University, Wroclaw) said: In a diamagnetic crystal we are concerned with closed electronic shells of structural units. In the most simple case of a NaCl or KCl crystal the electronic shells are more or less of spherical symmetry which presumedly cancels out the electromagnetic interactions. As a matter of fact, a very pure and nearly perfect NaCl crystal shows a low damping constant that is independent of the field strength. Experiments on these and other materials are still in progress and will be reported later.

ISSN:0301-7249    

DOI:10.1039/DC9806900193

出版商:RSC    

年代:1980

数据来源: RSC