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.