The hamiltonian for the disordered phase (Oh 1) of the ammonium halide crystals is derived on the basis of a point charge model which also takes into account the repulsion between nearest neighbour ions (NH4 + - X -). This hamiltonian is reduced to that for interacting one dimensional hindered rotors, where rotation of NH4 + ions is restricted to that around the z axis. Order-disorder phase transitions in pure ammonium halide crystals (NH4Cl, NH4Br and NH4I) and NH4Br x Cl1-x mixed crystals are discussed in terms of the dynamic susceptibilities calculated from the model hamiltonian. The present model seems to reproduce the general behaviour of the phase diagrams. It also provides a plausible explanation for the mechanisms of the phase transitions. By considering the effect of pressure in the model hamiltonian, the possibility of occurrence of new ordered phases at high pressure is discussed within the framework of the present model.

Classical and quantum mechanical models for the phase transitions in the polyphenyls are developed. Starting with the high symmetry phases of these crystals, the models are able to predict several key features of the polyphenyl transitions. First, the nature of the phase transitions, order-disorder in p-terphenyl and displacive in biphenyl, is confirmed. Second, the transition is predicted to occur at a substantially lower temperature for biphenyl than for p-terphenyl. Third, the models predict a decrease of the p-terphenyl transition temperature with pressure, in agreement with experiment. The trasition to an incommensurate phase for biphenyl is discussed, and the origin of the observed isotope effect is explored.

Brillouin scattering spectra are reported and analyzed for the layered perovskite compound (CH3NH3)2FeCl4. Particular attention has been given to successive phase transitions in this system: D174h ↔ D182h ⇄ D164h. It is found that the elastic constant c66 is the major contributor to instabilities in this system. A two-dimensional order parameter at the Brillouin zone boundary X point is introduced into the Landau free-energy to account for this sequence of transitions. An additional secondary instability (one-dimensional order parameter) at the Z point is used to generate the D182h ⇄ D164h phase transition: inclusion of the two order parameters circumvents the need for postulating a D102h phase between the D182h and D164h phases and for higher order temperature dependent terms in the free energy expansion. The D174h ↔ D182h phase transition is characterized by a strong Landau–Khalatnikov contribution to c66 and a large dynamical critical behavior.

Chemischer InformationsdienstVolume 14, Issue 38 Article ChemInform Abstract: BRILLOUIN AND RAYLEIGH SCATTERING STUDIES OF THE PHASE TRANSITION IN CHLORANIL A. YOSHIHARA, A. YOSHIHARASearch for more papers by this authorE. R. BERNSTEIN, E. R. BERNSTEINSearch for more papers by this authorJ. C. RAICH, J. C. RAICHSearch for more papers by this author A. YOSHIHARA, A. YOSHIHARASearch for more papers by this authorE. R. BERNSTEIN, E. R. BERNSTEINSearch for more papers by this authorJ. C. RAICH, J. C. RAICHSearch for more papers by this author First published: September 20, 1983 https://doi.org/10.1002/chin.198338080AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume14, Issue38September 20, 1983 RelatedInformation

A mean field approach to the dynamics of structural phase transitions in molecular crystals is presented. The approach is based on a description of the rotational and translational molecular motions, and the coupling between them, in terms of generalized susceptibilities. Two models for the orientational susceptibility are used. One is a classical description in terms of two-dimensional rotors, the other a two-dimensional anharmonic oscillator model. The specific example considered is sym-triazine. In this crystal molecules experience a very strong orienting field which restricts the molecular rotational motion to libration. The coupling between the molecular rotations and translations is shown to lead to a softening of acoustic phonons. This softening has considerable anisotropy in reciprocal space. An approximate solution for the high temperature phase is shown to be in good agreement with experiments.

The nonferroic (constant rotational symmetry) phase transition at ∼93 K in chloranil (C6Cl4O2) is investigated by Brillouin and Rayleigh light scattering. The phase transition is driven by a zone boundary soft mode at the (00 1/2) point which, through various coupling mechanisms, can affect the zone center strains. The major conclusions of these investigations are: (1) the LA-phonon mode propagating along the [010*] direction exhibits a step function anomaly at Tc with an associated transition region in the low temperature phase and a linewidth anomaly. The frequency of this LA mode in the transition region decreases below its low temperature phase value near Tc; (2) the lowest frequency QTA phonon propagating around [010*] has a negative temperature coefficient in the high temperature phase which goes to zero in the low temperature phase; (3) external stress induced relaxation processes can be observed by correlation scattering spectroscopy which are highly polarization, experimental scattering geometry, and stress direction dependent; (4) the relaxation time and intensity of scattered light behave anomalously in the vicinity of the phase transition; and (5) a similar intensity anomaly without a relaxation time anomaly is observed in the absence of external stress applied to the sample. These data are analyzed using a theory developed by Yao, Cummins, and Bruce for improper ferroelastic–ferroelectric phase transitions. The negative temperature slope of the QTA mode in the high temperature phase is thought to be associated with an incipient, unrealized phase instability driven by an optical mode at 16 cm−1 with similar temperature dependence.

New Brillouin scattering data are presented for benzil single crystals near the phase transition at 83.5 K. These data demonstrate that for the c11 governed longitudinal acoustic (LA) mode at ∼15 GHz, critical fluctuations are quite large near the phase transition and dominate the behavior of this mode within +40 K of the transition. These observations are analyzed in terms of four contributing soft modes; an optical soft mode and two transverse acoustic (TA) soft modes at the zone center and a zone boundary M-point soft mode. It is argued that the zone boundary mode is the major contributor to the width and elastic constant anomalies of the LA mode. Calculations of these properties support these conclusions. Critical exponents are evaluated for Δc11 and ΔΓa, the critical contributions to the elastic constant and width of the c11 governed LA mode, based on the experimental data.

Chemischer InformationsdienstVolume 13, Issue 15 Article ChemInform Abstract: STRUCTURAL PHASE TRANSITION OF BENZIL H. TERAUCHI, H. TERAUCHISearch for more papers by this authorT. KOJIMA, T. KOJIMASearch for more papers by this authorK. SAKAUE, K. SAKAUESearch for more papers by this authorF. TAJIRI, F. TAJIRISearch for more papers by this authorH. MAEDA, H. MAEDASearch for more papers by this author H. TERAUCHI, H. TERAUCHISearch for more papers by this authorT. KOJIMA, T. KOJIMASearch for more papers by this authorK. SAKAUE, K. SAKAUESearch for more papers by this authorF. TAJIRI, F. TAJIRISearch for more papers by this authorH. MAEDA, H. MAEDASearch for more papers by this author First published: April 13, 1982 https://doi.org/10.1002/chin.198215103AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume13, Issue15April 13, 1982 RelatedInformation

The dynamic suceptibility of a free rotor is calculated in the high temperature limit. The result is used to study a system of rotors coupled to a phonon mode of frequency ω(q) with a coupling constant g(q). It is shown that the coupled system has an instability at a temperature Tc = g2(q)/2ω2(q). The calculated spectra exhibit either soft phonon behavior or a sharp central component, depending on the ratio of the phonon energy to the average, rotational energy and the strength of the coupling.

A description of the phase transition in sym-triazine based on an Onsager equations of motion approach is presented. Using a hamiltonian which includes the full dynamics (kinetic and potential energies) of the coupled rotations and translations, Green's functions and correlation functions for librational and acoustic modes are obtained. The method employed here is similar to pseudospin-phonon theories in which spin coordinates are higher order rotational variables such as RxRy and (Rx 2) - Ry 2). Calculations for phonon groups in the small osciallator limit are presented and compared with neutron scattering data between 300 K and 205K (T c ∼ 198 K). Good agreement is obtained outside the immediate region of the phase transition (T > 205 K).

The phase transition in crystalline benzil [(C6H5CO)2] at 84 K is investigated through Brillouin scattering. The major experimental findings are two transverse acoustic phonon modes exhibiting softening near the phase transition, a longitudinal acoustic mode that is temperature sensitive, and the ratio of the Rayleigh peak intensity to the soft mode intensity behaves anomalously. These results are discussed using a theory developed for an elastic phase transition in sym-triazine (C3N3H3). It is found that bilinear-coupling terms involving strains and the order parameter can explain transverse mode behavior but not that of the longitudinal acoustic mode.

Simultaneous Brillouin-correlation light scattering results obtained under an external applied stress pulse are presented for annealed and unannealed (as grown) crystals of benzil. Critical fluctuations are characterized for the LA a-axis mode governed by the elastic constant c11 and are shown to contribute to this elastic anomaly in the high temperature phase. Both a central peak intensity anomaly and a critical relaxation time anomaly are characterized for unannealed crystals. These effects disappear in well-annealed crystals and without the external stress pulse even in as grown crystals. The critical relaxation behavior in benzil is coupled to the external stress compression wave generated by the mechanical refrigerator used to cool the sample. The latter interaction and relaxation anomaly are observed in polarized scattered light with the stress applied along the b (or a) axis as required for a c11 coupling. These observations are qualitively analyzed employing the theory of anelastic solids with higher order fluctuation terms incorporated into the free energy expansion. The relationship of this description to the Halperin–Varma theory of defect induced central peaks is outlined.

Contrary to the statement in a recent publication by A.I.M. Rae (1982), the present authors demonstrate that both the quasi-harmonic lattice approximation and orientation strain order parameter approach to the phase transition in sym-triazine give identical results. Both treatments rely on a Landau mean field expansion of the free energy in the vicinity of the phase transition. The usefulness of one theoretical treatment over the other is a function of the details of the experimental findings and just which properties are chosen to be modelled.

Rae’s1 comments on the author’s paper concerning the phase transition in sym-triazine2 are answered. (AIP)

The dynamic susceptibility of a one-dimensional rotor in crystal fields of various symmetry is calculated within the framework of classical mechanics. The contributions from oscillatory and rotary motions are treatable separately. This approach serves to clarify the structure of the spectrum. The nature and magnitude of the quantum effect are investigated and a comparison with earlier quantum mechanical calculations is made.

Chemischer InformationsdienstVolume 13, Issue 50 Physical Organic Chemistry ChemInform Abstract: CRITICAL BEHAVIOR IN ANNEALED AND UNANNEALED CRYSTALS OF BENZIL A. YOSHIHARA, A. YOSHIHARASearch for more papers by this authorE. R. BERNSTEIN, E. R. BERNSTEINSearch for more papers by this authorJ. C. RAICH, J. C. RAICHSearch for more papers by this author A. YOSHIHARA, A. YOSHIHARASearch for more papers by this authorE. R. BERNSTEIN, E. R. BERNSTEINSearch for more papers by this authorJ. C. RAICH, J. C. RAICHSearch for more papers by this author First published: December 14, 1982 https://doi.org/10.1002/chin.198250040AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume13, Issue50December 14, 1982 RelatedInformation

Dynamical behavior of the coupled system of molecular orientations and acoustic phonons is investigated in order to provide a description of the structural phase transition in s-triazine, s-triazine molecular reorientations are in the fast relaxation limit. A softening of the acoustic phonon frequencies is found as T → Tc.

A Landau mean field description of the nearly second order phase transition in sym-triazine crystals at ∼200 K is presented. A model Hamiltonian is generated which consists of the appropriate symmetry elastic constant terms, molecular rotational energy, and rotation–translation coupling terms (to second order in both strains and rotations). Due to the symmetry of the crystal in the high (R3̄c) and low (C2/c) temperature phases, third order terms in the rotational order parameter are nonvanishing; the transition is thereby a first order one (although only weakly so). This Hamiltonian is then converted to a free energy by addition of an entropy term calculated for an orientation distribution (about the z axis) based on pocket state functions. The Landau mean field model is developed by choosing a set of order parameters Ry (molecular rotation about the y axis) and strains e5 and (e1-e2). The free energy expression is used to calculate relations between order parameters by setting ∂F/∂Ry=∂F/e5=∂F/∂e7=0. Coupling terms including bilinear products of eρ’s and Ry are employed in this development. Renormalized temperature dependent elastic constants are derived. e5(T) is solved for and found to be in good agreement with observed temperature dependences. Librational frequencies are determined from (∂2H/∂RiRj)ep=Iω2iδij. It is found that in the low temperature phase Δω=‖ωy−ωx∝α e5 in lowest order. Observed power laws for frequencies, splittings and strains with respect to ε≡(T−Tc/T) are discussed in light of these new results. The role of third order terms in (Rx, Ry) is considered and found to be an important factor in apparent deviation from mean field exponents.