H E Stanley Oxford: University Press 1971 pp xx + 308 price ?5 In the past fifteen years or so there has been a lot of experimental and theoretical work on the nature of critical phenomena in the neighbourhood of second order phase transitions. It has not been easy to get a good overall view of this work without digging through the rather complex original literature, although there are some good review articles covering particular aspects of the work.

https://iopscience.iop.org/article/10.1088/0031-9112/23/4/018/pdf

Introduction to Phase Transitions and Critical Phenomena

Interest in the mechanical properties of water ice under the conditions in which it exists in the outer solar system has motivated the development and use of a new high-pressure, low-temperature triaxial deformation apparatus. Constant displacement rate tests on 70 samples of pure polycrystalline water ice have been performed at temperatures 77≤T≤258 K, confining pressures 0.1≤P≤350 MPa, and strain rates 3.5×10−6≤ e˙≤3.5×10−4 s−1. In most cases, the ice polymorph tested was ice Ih. Both brittle and ductile behavior have been observed. Brittle behavior of ice, promoted by lower pressure, lower temperature, and higher strain rate, is analogous to that in rocks, with the important exception that brittle fracture strength becomes independent of confining pressure above 50 MPa pressure and the fracture angle is approximately 45° to the loading direction (i.e., the coefficient of internal friction is approximately zero). Ductile flow, the predominant behavior in our tests at T≥195 K, follows a law of form e˙ = Aσn exp (−H*/RT) (σ is stress; R is the gas constant; A, n, H* are material constants). Three sets of material constants are required to fit the data, with changes in sets (or mechanisms) occurring near 243 K and 195 K. The value of n remains near 4 throughout the measured ductile field, but H* drops from 91 to 61 to 31 kJ/mole as temperature decreases. The maximum brittle strength measured was 171 MPa; the maximum ductile strength measured was 91 MPa. At confining pressures near the phase transition pressure of ice Ih → ice II, the ductile strength is observed to drop dramatically. Some overlap with previous work occurs at higher temperatures and lower pressures. Agreement with present work is generally good, both quantitatively in the values of n and H*, and qualitatively in the mechanism of deformation. Although the ductile strengths measured here are somewhat higher than expected on the basis of extrapolations of previous work, the low value of H* at T<195 K indicates that the ice Ih layer on icy bodies in the solar system is much weaker than has generally been predicted.

Experimental deformation of polycrystalline H2O ice at high pressure and low temperature - Preliminary results. [implications for Ganymede and Callisto]

Order-disorder phenomena

Physico-chemical constants of pure organic compounds

The first (so-called) lambda transition in solids was found in the specific heat measurements for NH4Cl at 242 K by F. Simon in 1922 [Simon (1922). Ann. Phys. 68, 241–280]. Analogous phenomena found in many other solids gave rise to doubts (expressed most clearly by A. R. Ubbelohde some 50 years ago) about the applicability of classical thermodynamics to some phase transitions [Ubbelohde (1956). Brit. J. Appl. Phys. 7, 313–321]. However, Y. Mnyukh's studies of enantiotropic phase transitions in eight organic crystals showed that all proceed by a nucleation-and-growth mechanism [summarized in Mnyukh (2001), Fundamentals of Solid State Phase Transitions, Ferromagnetism and Ferroelectricity. 1st Books]. Nucleation is localized at defects in the parent phase; growth can be epitaxic and oriented if parent and daughter phases have closely similar structures, or random (not oriented) if there are substantial structural differences. This conclusion is supported by a critical review of Mnyukh's eight examples and other results published in the interim. It seems that Ubbelohde's invocation of `hybrid crystals' and `smeared transitions' can mostly be accounted for by lack of equilibrium in the phase-transition studies cited by him. However, the intermediate phase in 4,4′-dichlorobenzophenone appears to have structural resemblances to Ubbelohde's' `hybrid crystal'.

/pdf/on-the-mechanism-of-some-first-order-enantiotropic-solid-23twlc86j5.pdf

On the mechanism of some first-order enantiotropic solid-state phase transitions: from Simon through Ubbelohde to Mnyukh

This work presents our investigations of mezomorphic properties of two polymorphic liquid crystals, namely, 4-nonyloxy-4-butoxyphenyl benzoate and N-(-4-heptyloxybenzylidene-4-butylaniline) in a wide temperature range, particularly, in the phase transition regions. By means of an original experimental method, the heterophase regions and also the phase transition temperatures have been determined for these materials with high accuracy. These phase transition intervals have been analyzed using a mean field model.

Study of Phase Transitions in Polymorphic Liquid Crystals

In this study we have developed a mean field model to obtain the phase diagrams for NH4Cl and NH4Br. The phase diagrams obtained from our macroscopic theory are in good agreement with those obtained experimentally.

A phase diagram for ammonium halides

In this study we have developed a model which is mainly for a spin system (Ising model) superimposed on a system of lattice vibrations (Einstein and/or Debye model). Under this model we have derived the thermodynamic functions and predicted their critical behaviour near Tc. Our predictions are that C v and β −1 have a temperature dependence described by a power law formula with critical exponent a, whereas C p and α remain constant but show anomalous behaviour near Tc. This then implies that the γ Gruneisen parameter remains constant throughout the phase transitions. Regarding some previous model studies, our predictions seem to indicate that the model under consideration exhibits a phase transition of weakly first-order or nearly second-order.

Weakly first-order or nearly second-order phase transitions

The mechanism responsible for the λ-phase transitions in ammonium halides is investigated within the framework of an extended theory of the disorder-induced Raman scattering. The Raman spectra of ammonium halides have been predicted for both the disordered β phase (NH4Cl and NH4Br) and the ordered γ phase (NH4Br). It is postulated that those terms which dominate the dynamic distortions of the lattices and thereby cause the bulk of the disorder-allowed Raman scattering, will also dominate the quasi-static distortion which is the λ-phase transition in these crystals. From this we find that the four-spin correlation function for the M-point boundary phonons in the disordered phase (β), and the two-spin correlation function for the zone centre phonons in the ordered phases (δ and δ) dominate the mechanism of the λ-phase transitions in ammonium halides. Predictions obtained for the Raman scattering agree in most cases with our Raman observations on NH4Cl and NH4Br.

Disorder-induced Raman scattering in ammonium halides

The Raman frequency of a soft-optic mode associated with the order parameter is calculated as a function of temperature from the mean field theory for barium titanate (TC =222 K). Using the Raman frequencies calculated, the damping constant is evaluated and it is compared with the observed one for this soft-optic mode. Using the temperature dependence of the damping constant which is calculated from the pseudospin-phonon coupled model and from the energy fluctuation model, activation energies are also deduced for the soft-optic mode of barium titanate. For the temperatures to 330 K, the activation energy U varies from 0.03 to 0.01 eV, which can be compared with the value of kBTC ≅ 0.02 eV. Above 330 K, it decreases as predicted from both models. It is shown here that the calculated Raman frequency and the damping constant of the soft-optic mode describe adequately the observed behaviour of barium titanate. The activation energies deduced are also reasonable.

Hamit Yurtseven

Papers

Study of Phase Transitions in Polymorphic Liquid Crystals

A phase diagram for ammonium halides

Weakly first-order or nearly second-order phase transitions

Disorder-induced Raman scattering in ammonium halides

Temperature Dependence of the Raman Frequency, Damping Constant and the Activation Energy of a Soft-Optic Mode in Ferroelectric Barium Titanate