Phase transitions in the oxyfluoride (NH<Subscript>4</Subscript>)<Subscript>3</Subscript>NbOF<Subscript>6</Subscript>

(NH₄)₃NbOF₆ single crystals were grown, polarization-optical studies were performed, and birefringence was measured over the temperature range 90–500 K. A sequence of first-order structural phase transitions was found at temperatures T _1↓ = 259.7 K and T _2↓ = 257.7 K with temperature hysteresis δT ₁ = 0.9 K and δT ₂ = 1.9 K. The transitions are accompanied by twinning and the following change in the crystal symmetry: cubic ? tetragonal ? monoclinic. Optical second harmonic generation is found to occur at room temperature, which indicates that the cubic phase is not centrosymmetric. It is assumed that the phase transitions are ferroelastic and ferroelectric in nature.     

C<Subscript>60</Subscript> heat capacity anomaly at the orientational phase transition

An orientational phase transition in C60 crystals was studied by differential scanning calorimetry with the highest resolution provided by this method. The temperature dependence of the specific heat ΔC _p (T) was found to have a double peak in the range 250–270 K. An analysis of the temperature dependences of heat capacity in the region of the peaks revealed that the lower temperature peak follows a power law of the type ΔC _p = A/(T?T₀)^1/2 characteristic of order-disorder second-order phase transitions, while the high-temperature peak can be identified with a diffuse Λ-shaped first-order phase transition.     

X-ray study of [N(CH<Subscript>3</Subscript>)<Subscript>4</Subscript>]<Subscript>2</Subscript>ZnCl<Subscript>4</Subscript> at low temperatures

The unit cell parameters a, b, and c of [N(CH₃)₄]₂ZnCl₄ have been measured by x-ray diffraction in the temperature range 80–293 K. Temperature dependences of the thermal expansion coefficients α_a, α_b, and α_c along the principal crystallographic axes and of the unit cell thermal expansion coefficient α_V were determined. It is shown that the a=f(T), b=f(T), and c=f(T) curves exhibit anomalies in the form of jumps at phase transition temperatures T₁=161 K and T₂=181 K and that the phase transition occurring at T₃=276 K manifests itself in the a=f(T) and b=f(T) curves as a break. A slight anisotropy in the coefficient of thermal expansion of the crystal was revealed. The phase transitions occurring at T₁=161 K and T₂=181 K in [N(CH₃)₄]₂ZnCl₄ were established to be first-order.     

Nature of low-temperature phase transitions in CaMn<Subscript>7</Subscript>O<Subscript>12</Subscript>

New data on the specific heat, thermal expansion, and magnetization of the CaMn₇O₁₂ phase require a revision of the current concepts of the sequence of phase transitions in this compound. It is found that a spin-glass phase transition occurs in CaMn₇O₁₂ at T _M = 49 K, whereas the transition at T _S = 89 K exhibits the features of a first-order phase transition and thereby is apparently of structural origin. In the range T _M < T< T _S , the CaMn₇O₁₂ compound exhibits negative thermal expansion, which is also indicative of structural changes.     

Optical studies of phase transitions in the (NH<Subscript>4</Subscript>)<Subscript>3</Subscript>Ti(O<Subscript>2</Subscript>)F<Subscript>5</Subscript> crystal

Polarization-optical study of twinning and measurements of the Raman spectra and birefringence in oxyfluoride (NH₄)₃Ti(O₂)F₅ were carried out over the temperature range 90–350 K. Phase transitions were detected at temperatures T ₀₁ = 266 K (second-order transition) and T ₀₂ = 225 K (first order). It is assumed that the crystal symmetry is changed as follows: Fm3m ? I4/mmm ? I4/m. Anomalies of the spectral parameters are established in the frequency range of internal vibrations of ammonium ions and Ti(O₂)F₅ complexes. An analysis of the results shows that the transition at T ₀₁ is likely due to small shifts of the tetrahedral groups from their position on the triad axis and that the transition at T ₀₂ is due to fluorine-oxygen ordering of Ti(O₂)F₅ complexes.     

Thermophysical study of structural phase transitions in Na<Subscript>0.95</Subscript>Li<Subscript>0.05</Subscript>NbO<Subscript>3</Subscript> solid solution

Temperature dependences of specific heat C_p(T) and coefficient of thermal expansion ;(T) for Na_0.95Li_0.05NbO₃ sodium-lithium niobate ceramic samples are investigated in the temperature range of 100–800 K. The C_p(T) and α(T) anomalies at T₃ = 310 ± 3 K, T₂ = 630 ± 8 K, and T₁ = 710 ± 10 K are observed, which correspond to the sequence of phase transitions N ? Q ? S(R) ? T2(S). The effect of heat treatment of the samples on the sequence of structural distortions was established. It is demonstrated that annealing of the samples at 603 K leads to splitting of the anomaly corresponding to the phase transition Q → R/S in two anomalies. After sample heating to 800 K, the only anomaly is observed in both the C_p(T) and ;(T) dependence. Possible mechanisms of the observed phenomena are discussed.     

Elastic properties of La<Subscript>0.82</Subscript>Ca<Subscript>0.18</Subscript>MnO<Subscript>3</Subscript> single crystal

The temperature dependences of the velocity of longitudinal sound waves and the internal friction in a La_0.82Ca_0.18MnO₃ single crystal with the Curie temperature T _C = 181 K have been studied. As temperature decreases, the single crystal is shown to undergo the transition from the pseudocubic O* to the Jahn–Teller O’ phase at T ~ 254 K and the reverse transition from O’ to O* phase at T ~ 84 K. The velocity of sound and the internal friction in the O’ phase are found to be significantly smaller than those in the O* phase.     

Optical and x-ray diffraction studies of the symmetry of distorted phases of the (NH<Subscript>4</Subscript>)<Subscript>3</Subscript>ZrF<Subscript>7</Subscript> crystal

(NH₄)₃ZrF₇ single crystals were grown, and polarization-optical and x-ray diffraction studies were performed on powders and crystalline plates of various cuts over a wide temperature range. Phase transitions are revealed at temperatures T _1↑ = 280 K, T _2↑ = 279.6 K, T _3↑ = 260–265 K, and T _4↑ = 238 K on heating and at T _1↓ = 280 K, T _2↓ = 269–270 K, T _3↓ = 246 K, and T _4↓ = 235 K on cooling. The sequence of changes in symmetry is established to be as follows: O _h ⁵ (Z = 4) ? D _2h ²⁵ (Z = 2) ? C _2h ³ (Z = 2) ? C _i ¹ (Z = 108) ? monoclinic²(Z = 216).     

A Phenomenological Model of Structural Phase Transitions in RbDy(Wo<Subscript>4</Subscript>)<Subscript>2</Subscript>

A phenomenological model of structural phase transitions in double rubidium–dysprosium tungstate is proposed. The model is constructed by equivariant catastrophe theory methods. The temperature dependence of the heat capacity near the phase transitions at temperatures T₁ = 9 K and T₂ = 4.9 K was calculated. Comparison with the experimental data shows a satisfactory qualitative agreement. In terms of the proposed model, the low-temperature phase transition can be interpreted as isomorphic.     

Phase transition in a KPb<Subscript>2</Subscript>Br<Subscript>5</Subscript> crystal

Crystals of the KPb₂Br₅compound are investigated using polarized light microscopy and calorimetry. The birefringence and the angle of rotation of the optical indicatrix are measured in the temperature range 270–620 K. It is found that the KPb₂Br₅ crystal undergoes a first-order ferroelastic phase transition at temperatures T_0↑ = 519.5 K and T_0↓ = 518.5 K with a change in the enthalpy ΔH = 1300 ± 200 J/mol. This transition is accompanied by both twinning and the symmetry change mmm ? P2₁/c. It is revealed that the angle of rotation of the optical indicatrix exhibits an unusual behavior under variations in the temperature due to a strong temperature dependence of the birefringence.     

Causes of the Metamagnetism in a Disordered EuMn<Subscript>0.5</Subscript>Co<Subscript>0.5</Subscript>O<Subscript>3</Subscript> Perovskite

The magnetic properties of the EuMn_0.5Co_0.5O₃ perovskite synthesized under various conditions are studied in fields up to 140 kOe. The sample synthesized at T = 1500°C is shown to exhibit a metamagnetic phase transition, which is irreversible below T = 40 K, and the sample synthesized at T = 1200°C demonstrates the field dependence of magnetization that is typical of a ferromagnet. Both samples have T_C = 123 K and approximately the same magnetization in high magnetic fields. The metamagnetism is assumed to be related to a transition from a noncollinear ferromagnetic phase to a collinear phase, and the presence of clusters with ordered Co²⁺ and Mn⁴⁺ ions leads to ferromagnetism. The noncollinear phase is formed due to the competition between positive Co²⁺–Mn⁴⁺ and negative Mn⁴⁺–Mn⁴⁺ and Co²⁺–Co²⁺ interactions, which make almost the same contributions, and to the existence of a high magnetic anisotropy.     

The influence of phase transitions in the Rb<Subscript>2</Subscript>CdI<Subscript>4</Subscript> ferroelastic on the exciton absorption spectrum

The parameters of the long-wavelength exciton band for Rb₂CdI₄ films are investigated in the temperature range 90–410 K. It is found that the Rb₂CdI₄ films undergo a sequence of phase transitions at temperatures T_c1=380 K (paraphase → incommensurate phase), T_c2=290 K (incommensurate phase → ferroelastic phase I), and T_c3 = 210 K (ferroelastic phase I → ferroelastic phase II). The parameters of the exciton band (such as the spectral position and the half-width) measured during heating and cooling of the Rb₂CdI₄ film differ significantly. This is especially true for the incommensurate phase. Upon heating of the incommensurate phase, the domain boundaries become frozen, whereas the cooling of this phase is accompanied by the generation of solitons and their pinning, which, in turn, results in a first-order phase transition at the temperature T_c2. It is revealed that the oscillator strength of the exciton band anomalously increases in the range of existence of commensurate phase I (T_c3<-T<-T_c2) due to ordering of the Rb₂CdI₄ crystal lattice.     

Heat capacity,structure, and <Emphasis Type="Italic">p-T</Emphasis> phase diagram of elpasolite (NH<Subscript>4</Subscript>)<Subscript>2</Subscript>KMoO<Subscript>3</Subscript>F<Subscript>3</Subscript>

Thermophysical and structural studies of an (NH₄)₂KMoO₃F₃ crystal show that this crystal belongs to the family of elpasolites (space group \(Fm\bar 3m\)) and undergoes an order-disorder phase transition at T ₀ = 241.5 K. Under hydrostatic pressure, this phase transition splits into two consecutive transitions at the tricritical point with parameters T _tr = 232.5 K and p _tr=0.21 GPa. It was found that anomalous hysteresis and relaxation phenomena accompany the transitions from the cubic to both distorted phases. The results are analyzed taking into account the data on the phase transition in the related elpasolite (NH₄)₂KWO₃F₃.     

Linear and nonlinear optical spectroscopy of gadolinium iron borate GdFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript>

The optical spectra and the second-harmonic generation (SHG) are studied in a noncentrosymmetric GdFe₃(BO₃)₄ magnet. In the region of weak absorption (α～20–400 cm^?1) below ～3 eV, three absorption bands are distinguished, which can be unambiguously assigned to forbidden electronic transitions from the ground ⁶A₁ state of the Fe³⁺ ion to its excited states ⁴T₁(～1.4 eV), ⁴T₂(～2 eV), and ⁴A₁, ⁴E(～2.8 eV). Intense absorption begins in the region above 3 eV (α～2–4×10⁵ cm^?1), where two bands at ～4.0 and 4.8 eV are observed, which are caused by allowed electric dipole charge-transfer transitions. The spectral features of SHG in the 1.2–3.0-eV region are explained by a change in the SHG efficiency caused by a change in the phase mismatch. It is shown that in the weak absorption region, phase matching can be achieved for SHG.     

Influence of the ground state of the Pr<Superscript>3+</Superscript> ion on magnetic and magnetoelectric properties of the PrFe<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> multiferroic

The magnetic, magnetoelectric, and magnetoelastic properties of a PrFe₃(BO₃)₄ single crystal and the phase transitions induced in this crystal by the magnetic field are studied both experimentally and theoretically. Unlike the previously investigated ferroborates, this material is characterized by a singlet ground state of the rare-earth ion. It is found that, below T _N = 32 K, the magnetic structure of the crystal in the absence of the magnetic field is uniaxial (l ∥ c), while, in a strong magnetic field H ∥ c (H _cr ～ 43 kOe at T = 4.2 K), a Fe³⁺ spin reorientation to the basal plane takes place. The reorientation is accompanied by anomalies in magnetization, magnetostriction, and electric polarization. The threshold field values determined in the temperature interval 2–32 K are used to plot an H-T phase diagram. The contribution of the Pr³⁺ ion ground state to the parameters under study is revealed, and the influence of the praseodymium ion on the magnetic and magnetoelectric properties of praseodymium ferroborate is analyzed.     

Structural Phase Transition of Perovskite-Type N(CH<Subscript>3</Subscript>)<Subscript>4</Subscript>CdBr<Subscript>3</Subscript> Studied by MAS NMR and Static NMR

The structural geometry change in the perovskite-type N(CH₃)₄CdBr₃ single crystal near the phase transition temperature of T _C = 390 K was investigated using magic angle spinning nuclear magnetic resonance techniques. For ¹H and ¹³C nuclei, the temperature dependences of their chemical shift, spectral intensity, and spin–lattice relaxation time (T _1ρ) in the rotating frame were obtained and analyzed. While the chemical shift and T _1ρ of ¹H showed change near T _C, those of ¹³C did not. In addition, the ¹¹³Cd spin–lattice relaxation time T ₁ in the laboratory frame near T _C show no evidence of anomalous change near the phase transition temperature, which coincides with the measured changes in the ¹H T _1ρ. The driving force for this phase transition was connected to the ¹H in the CH₃ groups.     

The influence of chromium impurity centers on the critical properties of a weakly polar ferroelectric Li<Subscript>2</Subscript>Ge<Subscript>7</Subscript>O<Subscript>15</Subscript>

The Cr³⁺ EPR spectra of Li₂Ge₇O₁₅ (LGO) crystals are analyzed in the temperature range of the ferroelectric phase transition. The temperature dependence of the local order parameter is determined from the measured splittings of the EPR lines in the polar phase. The experimental critical exponent of the order parameter β=0.31 in the range from the phase transition temperature T _C to (T _C -T) ～ 40 K corresponds to the critical exponent of the three-dimensional Ising model. Analysis of the available data demonstrates that, away from the phase transition temperature T _C , the macroscopic and local properties of LGO crystals are characterized by a crossover from the fluctuation behavior to the classical behavior described in terms of the mean-field theory. The temperature dependence of the local order parameter for LGO: Cr crystals does not exhibit a crossover from the Ising behavior (β=0.31) to the classical behavior (β=0.5). This is explained by the defect nature of Cr³⁺ impurity centers, which weaken the spatial correlations in the LGO host crystal. The specific features of the critical properties of LGO: Cr³⁺ crystals are discussed within a microscopic model of structural phase transitions.     

Specific features in thermal expansion of <Emphasis Type="Italic">R</Emphasis>Fe<Subscript>11</Subscript>Ti single crystals

Thermal expansion and its anomalies in the vicinity of spin-reorientation phase transitions in single crystals of RFe₁₁Ti (R=Y, Tb, Dy, Ho, and Er) compounds are investigated by the tensometric technique in the temperature range 77–400 K. The temperature dependences of the thermal expansion coefficient α(T) are obtained. It is found that the YFe₁₁Ti and HoFe₁₁Ti uniaxial magnetic materials exhibit pronounced anomalies in the α coefficient at T=200 and 290 K. For the TbFe₁₁Ti single crystal, the α coefficient is close to zero in the vicinity of the spin-reorientation phase transition (at T=325 K). For the DyFe₁₁Ti single crystal, which is characterized by two spin-reorientation phase transitions (at T=120 and 250 K), no features in the α(T) dependence are revealed in the region of the low-temperature spin-reorientation phase transition. In the ErFe₁₁Ti single crystal, the specific feature of thermal expansion is observed at T ～ 220 K.     

Crystallographic characteristics and phase transitions in the [N(C<Subscript>2</Subscript>H<Subscript>5</Subscript>)<Subscript>4</Subscript>]<Subscript>2</Subscript>CdBr<Subscript>4</Subscript> crystal in the low-temperature range

The results of x-ray structural studies of the [N(C₂H₅)₄]₂CdBr₄ crystal at low temperatures are presented. The unit cell parameters and the thermal expansion coefficients along the main crystallographic directions are measured at temperatures in the range from 90 to 320 K. The integrated intensities of the diffraction reflections are investigated as a function of the temperature. It is shown that the curves a = f(T), c = f(T), I ₅₀₀ = f(T), and I ₀₀₆ = f(T) at temperatures T ₁ ≈ 174 K and T ₂ ≈ 226 K exhibit anomalies in the form of abrupt changes in the lattice parameters and the diffraction reflection intensities. This indicates that the [N(C₂H₅)₄]₂CdBr₄ crystal undergo phase transitions at these temperatures. Moreover, there is an anomaly in the form of a small maximum at the temperature T ₃ = 293 K.     

Structural transformations of K<Subscript>3</Subscript>H(SO<Subscript>4</Subscript>)<Subscript>2</Subscript> crystals with variations in temperature

Single crystals of the K₃H(SO₄)₂ compound are investigated using X-ray diffraction on Xcalibur S and Bruker diffractometers. The structure of the low-temperature monoclinic phase is refined (space group C2/c, z = 4, a = 14.698(1) Å, b = 5.683(1) Å, c = 9.783(1) Å, β = 103.01(1)°, T = 293 K, Bruker diffractometer), the structural phase transition is revealed, and the structure of the high-temperature trigonal phase is determined (space group R \(\bar 3\) m, z = 3, a = 5.73(1) Å,c = 21.51(1) Å,T = 458 K, Xcalibur diffractometer).