Structural phase transitions in KMnF3

The structural transitions of the perovskite KMnF₃ are studied with an energy-dispersive X-ray diffractometer. It is found that the 83 K transition is of first order, though the transition related to the condensation of a M₃-soft phonon mode is considerably affected by crystallographic domain-walls occurring below the 186 K transition. The latter transition is observed at 88.0 K (first-order), and 92.0 K (second-order) in different single crystals, respectively. The difference of the transition temperature and the transition order is interpreted in terms of inner strains appeared in the domain walls.     

Structural phase transitions in CdTiO3

The reconstructive phase transition from the ilmenite-like CdTiO₃ modification to the perovskite modification is investigated thoroughly. It is revealed that the reconstructive transition is determined by size effects, results in the formation of the closest packing of the ilmenite CdTiO₃ structure, and is irreversible with a decrease in temperature. The perovskite CdTiO₃ modification undergoes displacive structural phase transitions at temperatures of 110, 220, and 380°C. The first displacive phase transition is isostructural, whereas the second and third transitions are associated with rotations of oxygen octahedra.     

Structural phase transitions of the Si(100) surface

A Monte Carlo study of the structural phase transitions on the Si(100) surface for both the “(2×1)” and “c(2×2)” reconstruction families is carried out using the asymmetric dimer model. A second order phase transition is observed at about 250 K from a p(2×2) (layered antiferromagnetic) to a disordered (paramagnetic) state in the “2×1” family. A similar transition is observed about 800 K from a c(2×2) (ferromagnetic) to a disordered state in the “c(2×2)” family. These results are in agreement with real-space renormalization group results. The variation of the specific heat, susceptability and the absolute value of the order parameter as a function of temperature is obtained in the range 200 to 300 K for the “2×1” family and 750 to 850 K for the “c(2×2)” family. Also, the order parameter correlation function is computed for ten different temperatures in the above ranges.     

Structural phase transitions in KCdF3

The successive phase transitions in KCdF₃ have been studied by using X-ray diffraction and differential type thermal analysis. Three transitions are observed at 485, 471 and 243 K; these are of 1st-, 2nd- and 2nd-order respectively. The space groups of the four phases are found, from the high temperature side, to be Pm3m, P4/mbm, Pbnm and Pbnm respectively. The first and second transitions can respectively be explained in terms of the condensation of soft-phonon modes at the M and R points in the cubic Brillouin zone. The third transition may be caused by instability due to titlings of CdF₆ octahedra.     

Structural phase transitions in ZnS

X-ray diffraction techniques have been used to investigate structural phase transitions in ZnS between 20 and 1200°C. These measurements imply that the transition from the cubic 3C structure to the hexagonal 2H structure is a first-order phase transition while transitions between the 2H, 4H, and the 6H(33) hexagonal structures were found to obey the symmetry rules of second-order phase transitions. Direct transitions from the cubic 3C structure to the 4 or 6H hexagonal structures are not observed.     

Reorientations and phase transitions in (Kr)1-x(CH4-nD n ) x

The condensed isotopic modifications of methane, CH₄, CH₂D₂, and CD₄ and their solutions with Kr were investigated using dielectric techniques. The polarizabilities were computed from the permittivities of the pure liquids. Phase diagrams of methane-krypton alloys were deduced in the liquid-solid coexistence region and for the low temperature phases (T<30 K). From the Curielaws, which described the permittivities of the (Kr)_1-x(CH₂D₂)_x mixed crystals, the permanent dioole moment of CH₂D₂ is calculated to be 4 mD. In the octopolar ordered phases of the solid solutions the effective dipole moments are enhanced significantly.     

Structural phase transitions in semiconducting SrTiO3

From ultrasonic velocity measurements we found that in SrTiO₃ the temperature for the structural phase transition is lowered in samples reduced in hydrogen, and increased in Nb-doped samples. In the reduced samples the shift in T_c is proportional to the concentration of oxygen vacancies. The results can qualitatively be understood in terms of local changes in the d_?/p_σ-hybridization of Ti-3d and 0–2p orbitals.     

Ultrasonic study of the structural phase transitions in [N(CH3)4]2CuCl4

The temperature dependence of the six principal stiffness componentsc ₁₁ toc ₆₆ was measured on single-crystal samples by the pulse-echo overlap technique between 120 and 310 K. We tried to interpret the observed anomalies in terms of interactions between order parameter, soft phonons, amplitons and phasons. A new phase transition at 127 K is found.Dedicated to Prof. Dr. H.E. Müser on the occasion of his 60th birthday     

Phenomenological analysis of the phase transitions sequence in the ferroelectric crystal (CH3NH3)5Bi2Cl11 (PMACB)

A phenomenological model is proposed to describe the sequence of phase transitions in Pentakis (methylammonium) Undecachlorodibismuthate (111), (CH₃NH₃)₅Bi₂Cl₁₁ (PMACB) crystal on the basis of the recent structural data. The ferroelectric phase transition at 307 K is attributed to the ordering in a sublattice of the methylammonium cations CH₃NH ₃ ⁺ } placed in centrosymmetric sites in the paraelectric phase, whereas the isomorphous anomaly at about 180 K is related to a variation of the order in the sublattice of the remaining CH₃NH ₃ ⁺ } cations. The phenomenological thermodynamic potential is constructed for this system of two nonequivalent sublattices and the numerical values of its coefficients are then estimated from the dielectric, pyroelectric and calorimetric data. The sublattices are found to be weakly coupled near the ferroelectric phase transition. The anomaly at 180 K is interpreted as a continuous trace of a first order phase transition in a field created by the cations already ordered in the ferroelectric phase transition. This is analogous to a cusp A₊₃ in the catastrophes theory. The comparison of the Curie constants with the saturation values of the spontaneous polarization suggests that the sublattices cannot be treated as consisting of simple two-states pseudospins.     

Br NQR relaxation and successive phase transitions of CH3NH3HgBr3

The measurement of ⁸¹Br NQR in CH₃NH₃HgBr₃ has been carried out in the temperature range between 80 and 300 K using a pulse NQR method. The temperature dependence of ⁸¹Br NQR frequencies in CH₃NH₃HgBr₃ has revealed that it undergoes three characteristic successive phase transitions at T?=?123, 184 and 239 K. The phase transition temperature at T?=?239 K is the second-order type, whereas those at T?=?184 and 123 K are the first-order nature of the phase transitions. Each phase transition seems to be closely related to the motions of methyl ammonium cation as a partial or whole. The enhancement of 1/T ₁ at T?=?239 K indicates the onset of the molecular motion of the cation as a whole with increasing temperatures.     

Structural phase transitions in multipole traps

A small number of laser-cooled ions trapped in a linear radiofrequency multipole trap forms a hollow tube structure. We have studied, by means of molecular dynamics simulations, the structural transition from a double ring to a single ring of ions. We show that the single-ring configuration has the advantage to inhibit the thermal transfer from the rf-excited radial components of the motion to the axial component, allowing ions to reach the Doppler limit temperature along the direction of the trap axis. Once cooled in this particular configuration, the ions experience an angular dependency of the confinement if the local adiabaticity parameter exceeds the empirical limit. Bunching of the ion structures can then be observed and an analytic expression is proposed to take into account for this behavior.     

Structural phase transitions in barium-titanate-type ferroelectrics

Barium-titanate-type ferroactive crystals are analysed thermodynamically using dimensionless variables. The paper considers the conditions of phase stability, the equation determining polarization, the interval of the possible existence of a phase (or interval of several phases of simultaneous coexistence), constraints on numerical values of thermodynamic potential coefficients. The results obtained have good qualitative agreement with experiment.     

Structural phase transitions in KCdF3 and K0.5Rb0.5CdF3

Successive structural transitions of KCdF₃ and K_0.5Rb_0.5CdF₃ have been studied by means of thermal diffusivity, polarized light scattering and X-ray diffraction. It is found that transitions occur at about 460 K and 475 K in KCdF₃, and at 222 K, 232 K, 250 K, 258 K and 268 K in K_0.5Rb_0.5CdF₃. The partial exchange between K⁺ and Rb⁺ ions gives rise to simultaneous condensation of the M^z ₃ and R^x ₂₅ soft phonons.     

Structural phase transitions during high-energy ball milling of BaTiO3

Microstructural characterization of ball milled perovskite BaTiO₃ powders has been done by the modeling of X-ray diffraction profiles. The study reveals that on size reduction, BaTiO₃ powders undergo a continuous, displacive, and diffusionless dynamic phase transitions involving tetragonal (T), monoclinic (M), and orthorhombic (O) symmetry via the second-order type [T?→?(T?+?M)?→?(M?+?O)?→?O] when stimulated by a high-power pulse of pressure in a planetary mill. The order parameter, a phenomenological quantity to describe the general behavior of a system going through phase transitions has been estimated using spontaneous strain calculated from lattice parameters or physical distortions derived from atomic coordinates or both. At room temperature, BaTiO₃ nanoparticle achieved an orthorhombic phase when a critical size (<15?nm) has been reached at later stage of milling (≥70?h). Raman's study reveals similar structural phase transitions sequence on size reduction and TEM study reveals the corresponding particle diameter.     

Structural phase transitions in ionic molecular solids

An overview is presented of our studies on the nature of structural instabilities in relatively complex ionic solids. These are based on parameter-free interionic potentials based on the Gordon-Kim modified electron gas formalism extended to molecular ions.

We describe the manner in which there emerge from these studies quite general concepts of “size” and “shape” as structural determinants. In particular, we discuss how these, and the approximate symmetries that they can produce, can provide a relatively simple structure-based explanation of the origins of incommensurate phases in these systems. However, we also emphasize that the existence of such symmetries does not guarantee an incommensurate phase. This can only be realized if long-range correlations are sufficiently strong to overcome random local disordering. Thus, either the molecular units are partially linked and/or there exist long-range Coulomb interactions between individual units.     

PMR studies of molecular motions,phase transitions and quantum tunnelling in NH4SnCl3 and N(CH3)4SnCl3

Molecular reorientation and low temperature relaxation effects of NH⁺ ₄ ion and the effect of CH₃ substitution (in place of H) are investigated by proton spin lattice relaxation time (T₁) measurements at 10 MHz in NH₄SnCl₃ and N(CH₃)₄SnCl₃ in the temperature range 4.2 K upto the melting points of the compounds (? 440 K). Phase transitions around 360 K in NH₄SnCl₃ and around 361 and 116K in N(CH₃)₄SnCl₃ have been observed. In NH₄SnCl₃, the high temperature minimum at 330.5 K is attributed to the translational diffusion of the NH⁺ ₄ ions, while the other T₁, minima at 103.5, 60 and 50 K are ascribed to the reorientations of the NH⁺ ₄ ion about the C₂ and C₃ axes. The low temperature minimum at 13.5 K is attributed to rotational tunnelling of the NH⁺ ₄ ions. In N(CH₃)₄SnCl₃, in addition to the high temperature minima at 212.2 and 182.6 K due to N(CH₃)₄ tumbling and CH₃ reorientation, a temperature independent T₁ behaviour between 83 and 31 K is observed, below which T₁ decreases and tends to go through a minimum around 5 K. This low temperature minimum is attributed to rotational tunnelling of the CH₃ groups. The motional parameters and tunnel frequencies are estimated.     

Structural phase transitions in isotropic magnetic elastomers

Magnetic elastomers represent a new type of materials that are “soft” matrices with “hard” magnetic granules embedded in them. The elastic forces of the matrix and the magnetic forces acting between granules are comparable in magnitude even under small deformations. As a result, these materials acquire a number of new properties; in particular, their mechanical and/or magnetic characteristics can depend strongly on the polymer matrix filling with magnetic particles and can change under the action of an external magnetic field, pressure, and temperature. To describe the properties of elastomers, we use a model in which the interaction of magnetic granules randomly arranged in space with one another is described in the dipole approximation by the distribution function of dipole fields, while their interaction with the matrix is described phenomenologically. A multitude of deformation, magnetic-field, and temperature effects that are described in this paper and are quite accessible to experimental observation arise within this model.