Phase transitions in molecular crystals of dicarboxylic acids

A comparative analysis of phase transitions in molecular crystals of saturated dicarboxylic acids with {COOH(CH₂) _n COOH} chains of different lengths has been performed by differential scanning calorimetry, which revealed a number of new effects related with specific features of the phase transitions. A quantitative analysis of temperature dependence of the heat capacity has been carried out in the context of the theory of smeared (Λ-shaped) first-order phase transitions.     

Phase transitions in molecular crystals of n-alkanes: Tri-, tetra-, and pentacosane

Phase transitions in normal alkanes, such as tricosane (C₂₃H₄₈), tetracosane (C₂₄H₅₀), and pentacosane (C₂₅H₅₂), were studied by differential scanning calorimetry. The elimination of some procedural errors provided the possibility to obtain true values for the thermodynamic parameters of phase transitions and ascertain their nature. The comparative analysis of heat capacity jumps was performed on the basis of the theory of diffuse first-order phase transitions.

     

Phase transitions in ferroelectric liquid crystals

Molecular chirality plays an important role in the science of liquid crystals, leading to cholesteric liquid crystal, blue phases, ferroelectric and antiferroelectric smectic phases and twist grain boundary phases. In all of these mesogens, chirality is an intrinsic property built into the chemical structure of mesogenic molecules. The study of ferroelectric liquid crystals has seen substantial experimental strides. In theoretical aspects, there has been relatively little basic work on this fascinating class of material. This review will try to present a comprehensive overview of the current status of the phase transitions in ferroelectric smectic liquid crystals. The article begins with a brief introduction about the symmetry and structure of ferroelectric mesophases. An attempt is made to identify a range of problems and related questions associated with the study of phase transitions. In the remaining parts of the article the important experimental and theoretical developments are summarized. Finally, some of the future directions have been identified.     

Phase transitions in AgTaO3 single crystals

AgTaO₃ single crystals have been obtained by the molten salt method; two different solvents, AgCl and V₂O₅, were used. X-ray investigations have been carried out in the temperature region from 300 K to 800 K. At room temperature AgTaO₃ possesses a pseudocubic perovskite-type unit cell with rhombohedral distortion. Two structural phase transitions, to tetragonal at 650 K and to cubic symmetry at 770 K, have been observed. In the tetragonal phase a jump of the lattice constants has been observed at approximately 680 K. DTA and domain structure investigations confirm the presence of these phase transitions.     

Phase transitions in melt-grown PbI2 crystals

Employing the method of zone- refining single crystals of PbI₂ of different purities were grown. Using X-ray diffraction technique their structure was found to be of the type 12R and in some cases 12R+4H. The crystals were re-examined after prolonged storage of several months at room temperature. Neither the crystals of very high purity nor of relatively less purity transformed. But thecrystals having intermediate purities did transform from 12R to 2H. This observation establishes a clear link between impurities and phase transitions. The results have been explained on the basis of nucleation and growth mechanism of stacking faults. Also it has been concluded that the presence of impurities is a must for the formation of polytypes.     

Phase transitions in the adsorbed molecular chains

Rotational excitations of molecular adsorbed layers are studied theoretically. Nonlinear dynamical equations are obtained with accounting of quadrupolar interactions between molecules and freezing of translational degrees of freedom. The equilibrium positions of the molecules are found to be experimentally observed structures with alternating rotational ordering of planar rotors along the direction to the nearest neighbor (for linear or square structures) under low temperature. Dynamical analysis gives an integral of motion (energy) of the chain that in the long-wave limit leads consequently to the existence of four phases. The first one corresponds to oscillations near equilibrium ordered states. The second phase corresponds to low-energy rotational excitations along ‘valleys’ (easy directions in the effective potential) that do not destroy strong correlations between molecules while structural data can show rotational disorder (melting). The third phase corresponds to an energy that is enough to travel between ‘valleys’; only some ‘islands’ in the angle space are forbidden. Complete destruction of correlation when the energy is over the peaks of the effective potential corresponds to the fourth phase. Therefore rotational melting is a complex phenomenon that has several stages. Presented at the 2nd International Conference “Physics of Liquid Matter: Modern Problems” (September 2003, Kyiv, Ukraine).     

Phase transitions in crystals of protein amino acids

The temperature dependence of the piezoelectric response of many protein amino acids and their compounds exhibits a sharp increase in the piezoelectric response signals at a certain temperature. It has been shown using the example of the known ferroelectrics without a piezoelectric effect in the paraphase (triglycine sulfate, glycine phosphite, trisarcosine calcium chloride) that such an increase in the piezoelectric response is associated with the structural phase transition to the low-symmetry piezoelectric phase with a large number of piezoelectric coefficients. The specific features of the phase transitions with the symmetry change D ₂-C ₂ have been discussed.     

Phase transitions in CuBiP2Se6 crystals

Investigation results of dielectric (20?Hz–1?MHz) properties of layered CuBiP₂Se₆ crystals are presented. The temperature dependence of the static dielectric permittivity reveals the first-order “displacive” antiferroelectric phase transition at T _c?=?136?K. In the paraelectric phase, at low frequencies, dielectric spectra are highly influenced by the high ionic conductivity with the activation energy of 2473?K (0.21?eV). In the antiferroelectric phase the electrical conductivity and its activation energy (531.1?K (0.045?eV)) are considerably smaller. At low temperatures, the temperature behaviour of the distribution of relaxation times reveals complex freezing phenomena. A part of long relaxation time distribution is strongly affected by external direct current (DC) electric field and it is obviously caused by antiferroelectric domain dynamics.     

Phase transitions in liquid crystals under negative pressures

We report the first measurements of orientational order parameters and phase transition temperatures in nematic and smectic A liquid crystals under negative pressures generated by an isochoric cooling of small droplets embedded in a glass former. Comparison of isobaric and isochoric measurements allows us to estimate the coefficients coupling the order parameter and density of an extended Landau--de Gennes model of the nematic phase.     

Phase transitions in crystals with competitive Jahn-Teller subsystems

A statistical thermodynamic model of phase transformations caused by the cooperative Jahn-Teller effect in spinels containing two types of Jahn-Teller cations has been proposed. It has been shown that the specific features of the phase diagrams of compounds similar to Cu_{1 ? x} Ni _x Cr₂O₄, such as the presence of one orthorhombic and two anti-isostructural tetragonal phases, are associated with the competition between orderings of the subsystems of tetrahedra distorted due to the Jahn-Teller effect. The degree and character of the ordering of each subsystem of the solid solution have been determined. The main factors responsible for the thermodynamic properties and phase diagrams, in particular, the conditions for splitting of an isolated critical point into two triple points, have been investigated.     

Phase transitions in 1,3,4-oxadiazole crystals under high pressure

Crystalline 2,5-di(4-nitrophenyl)-1,3,4-oxadiazole (DNO) has been investigated at pressures up to 5 GPa using Raman and optical spectroscopy as well as energy dispersive X-ray techniques. At ambient pressure DNO shows an orthorhombic unit cell (a=0.5448 nm, b=1.2758 nm, c=1.9720 nm, density 1.513 g cm⁻³) with an appropriate space group Pbcn. From Raman spectroscopic investigations three phase transitions have been detected at 0.88, 1.28, and 2.2 GPa, respectively. These transitions have also been confirmed by absorption spectroscopy and X-ray measurements. Molecular modeling simulations have considerably contributed to the interpretation of the X-ray diffractograms. In general, the nearly flat structure of the oxadiazole molecule is preserved during the transitions. All subsequent structures are characterized by a stack-like arrangement of the DNO molecules. Only the mutual position of these molecular stacks changes due to the transformations so that this process may be described as a topotactical reaction. Phases II and III show a monoclinic symmetry with space group P2₁/c with cell parameters a=1.990 nm, b=0.500 nm, c=1.240 nm, β=91.7°, density 1.681 g cm⁻³ (phase II, determined at 1.1 GPa) and a=1.890 nm, b=0.510 nm, c=1.242 nm, β=89.0°, density 1.733 g cm⁻³ (phase III, determined at 2.0 GPa), respectively. The high-pressure phase IV stable at least up to 5 GPa shows again an orthorhombic structure with space group Pccn with corresponding cell parameters at 2.9 GPa: a=0.465 nm, b=1.920 nm, c=1.230 nm and density 1.857 g cm⁻³. For the first phase a blue pressure shift of the onset of absorption by about 0.032 eV GPa⁻¹ has been observed that may be explained by pressure influences on the electronic conjugation of the molecule. In the intermediate and high-pressure phases II–IV the onset of absorption shifts to increased wavelengths due to larger intermolecular interactions and enhanced excitation delocalization with decreasing intermolecular spacing.     

Specific features of phase transitions in molecular crystals of diols

A comparative analysis of the phase transitions in molecular crystals of diols with different chain lengths [1,15-pentadecanediol (CH₂)₁₄(OH)₂ and 1,16-hexadecanediol (CH₂)₁₅(OH)₂] has been performed using differential scanning calorimetry. A quantitative analysis of the temperature dependence of the heat capacity within the theory of diffuse (Λ-shaped) first-order phase transitions and the use of the temperature hysteresis have revealed a number of new effects associated with the specific features of the phase transitions in molecular crystals of diols.     

Phase transitions in a cluster molecular field approximation

Cluster molecular field approximations represent a substantial progress over the simple Weiss theory where only one spin is considered in the molecular field resulting from all the other spins. In this work we discuss a systematic way of improving the molecular field approximation by inserting spin clusters of variable sizes into a homogeneously magnetised background. The density of states of these spin clusters is then computed exactly. We show that the true non-classical critical exponents can be extracted from spin clusters treated in such a manner. For this purpose a molecular field finite size scaling theory is discussed and effective critical exponents are analysed. Reliable values of critical quantities of various Ising and Potts models are extracted from very small system sizes. Received 30 September 2002 / Received in final form 25 November 2002 Published online 27 January 2003 RID="a" ID="a"e-mail: pleim@theorie1.physik.uni-erlangen.de     

Polymorphic transitions in molecular crystals—III.: Transitions exhibiting unusual behavior

Some polymorphic transitions in molecular crystals, among the few classified earlier as displacive or martensitic on the basis of the existence of a definite orientation relationship between the lattices of the phases and the “instantaneous” transformation rate, have been experimentally investigated. The investigation showed no evidence of a high rate of transition. All occurred through nucleation at the lattice imperfections and continuous growth of the new phase at a rate depending on ΔT = T_tr ? T_a, where T_tr is the actual transition temperature and T_o is the temperature of the thermodynamic equilibrium of the phases. The interface can be observed; its motion can be controlled, be done so slow as it is desirable, or be stopped. The “instantaneous transformations” reported in the literature are caused by temperature delays of nucleation in the absence of appropriate lattice defects. In reality these are polymorphic transitions which appear to be instantaneous only when observed through an optical microscope; actually they occur at the rate corresponding to ordinary temperature dependence. It was established that lamination or cleavage of the crystals in a definite direction is a common feature of the substances exhibiting “atypical” behavior. (Typical behavior has been described in [1,2]). The observed characteristics of the polymorphic transitions (uniform direction of the interfaces, definite orientation relationship of the lattices, small temperature hysteresis of the transition, etc.) can be readily explained in terms of epitaxial growth of the new phase on the cleavage planes of the original phase. At the same time the role of the proximity of crystal structural parameters is elucidated. Simple model calculations showed that a coherent interface may occur when the structural differences in the junction plane of the two phases are small, while in the other cases the contact interface described in [2] is energetically advantageous. However, a cooperative rearrangement at the coherent interface is rejected. There is not any evidence that polymorphic transitions in molecular crystals may occur by means of a “shift”, a “displacement”, a “deformation”, an “overturn”, etc. It is concluded that they always occur as a result of growth. The molecular mechanism of the growth in solids has been described in [2].     

Phase transitions in silicon single crystals resulting from directional plastic deformation

The formation of polytypic modifications is observed in dislocation-free silicon single crystals under directional plastic deformation. It is shown that the deformation-stimulated phase appears on the surface of the sample in the form of small grains ranging from several hundred to several thousand angstroms in size. A twin structure in the individual grains is observed. Fiz. Tverd. Tela (St. Petersburg) 40, 746–749 (April 1998)     

Phase transitions in RbxK1−x LiSO4 mixed crystals

Structural phase transitions in Rb_xK_1−x LiSO₄ mixed crystals (with x varying from 0 to 1) have been studied from the melting point to liquid-nitrogen temperature. Calorimetric (DTA and DSM) data, birefringence and optical polarization measurements were used to construct the full phase (T-x) diagram. It has been established that crystals of most compositions (x⩽0.95) grow in the hexagonal-trigonal KLiSO₄ structure. Replacement of K by the larger Rb atom results in a considerable increase of the region of existence of the P31c phase and expulsion of the high-temperature hexagonal phase. Fiz. Tverd. Tela (St. Petersburg) 40, 1341–1344 (July 1998)