Thermal expansion and spontaneous strain of KMnF3 near the 186 K-structural phase transition

Abstract

By means of high-angle double-crystal X-ray diffractometry (HADOX), the thermal expansivity of KMnF₃ has been determined. The linear thermal expansion coefficient along each crystallographic axis exhibits a divergent anomaly at the structural phase transition at 186 K. The critical exponents of these coefficients are determined: in the cubic phase α = 0.21 ± 3, and in the tetragonal phase α′ = 0.19 ± 3 for the a axis and α″ = 0.35 ± 3 for the c axis.

In addition, the critical exponent of the spontaneous strain, c/a ? 1, is determined to be 0.4248 ± 8, which is smaller than that of the order parameter 2β = 0.5714 ± 12. These values are reasonable if the transition occurs in the vicinity of a tricritical point.     

X-ray study of the thermal expansion anisotropy in the quarternary semiconductor CuGaSn□Se4

Accurate lattice parameters a and c of the tetragonal chalcopyrite quaternary semiconductor CuGaSn□Se₄ have been determined as a function of temperature by the X-ray powder diffraction method in the temperature range 300 K to about 900 K. The data have been used to evaluate the axial expansion coefficients α_a and α_c at various temperatures. The thermal expansion studies revealed the anisotropy between the axial expansion coefficients having a larger coefficient of expansion along the a-axis than that along the c-axis (α_a > α_c). The mean values α_a and α_c, in the temperature range 300–900 K, are found to be 14.02 × 10^-6K^-1 and 5.02 × 10^-6K^-1 respectively, and the axial ratio, c/a, changes with a coefficient of -8.96 × 10^-6K^-1. This result indicates an increase in the tetragonal distortion, δ = 2 - c/a with temperature. An attempt is made to explain the increase in tetragonal distortion with temperature and the anisotropic thermal expansion of CuGaSn□Se₄ in terms of the thermal expansion of the A>−;Se (where A is Cu and Ga randomly distributed) and B>−;Se (where B is Sn and vacancy randomly distributed) bonds. The results are also discussed in terms of the principal Grüneisen parameters of chalcopyrite structure compounds.     

X-ray study of the anomalous thermal hystereses of the modulation wavevectors in Cs2HgCl4

A rich sequence of structural modulations in Cs₂HgCl₄ as a function of temperature was studied by means of X-ray diffraction. Accurate satellite-position measurements on the cooling and heating paths of the crystal revealed abnormal thermal hystereses for incommensurate phases and coexistences of neighboring commensurate phases. A well-defined X-ray picture of the a-axis modulated phases in the range of 221–184 K were observed on the heating path, while the c-axis modulated phases existing below 184 K were definitely detected on the cooling path. The proper conditions for a precise phase diagram of Cs₂HgCl₄ can be correlated with relatively defect-free transformations of a-axis modulations at heating and of c-axis modulations at cooling. The peculiarity of Cs₂HgCl₄ to switch modulation direction among the a- and c-axes at 184 K allows us deliberately accumulate and thus control a majority of mobile defects on the mutually perpendicular (100) or (001) planes by possessing crystal within temperature domain of a- or c-axes modulations, respectively.     

Structural and physical properties of SrMn2As2

SrMn₂As₂ single crystals were grown by the Sn flux method. Structural features of these crystals were characterized by means of X-ray diffraction (XRD), scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The XRD results show that the single crystal has a rhombohedral structure and grows along the c-axis direction. The microstructure and layered structural features of this material have been examined by SEM and high-resolution TEM observations. The measurements of in-plane resistivity as a function of temperature demonstrate that SrMn₂As₂ undergoes a phase transition of semiconductor-insulator at a low temperature; the active energies are estimated to be Δ=0.64 and 0.29 eV for two distinct regions. Magnetic measurements show a clear antiferromagnetic (AFM) transition at about T_N=125 K. Therefore, the SrMn₂As₂ material is an AFM insulator at low temperatures and could be a potential parent compound for superconductors.     

X-ray diffraction investigations of the crystallographic parameters and thermal expansion of β-BaB2O4 crystals

The lattice parameters a and c of β-BaB₂O₄ crystals have been measured in the temperature range 80–300 K by the x-ray diffraction method. The thermal expansion coefficients α are calculated from the measured values of the parameters. A substantial anisotropy of the thermal expansion is found. It is shown that the thermal expansion coefficient α _c along the c axis is an order of magnitude greater than the thermal expansion coefficient α _a in a plane perpendicular to this axis. It is established that α _a becomes negative in the temperature range 80–190 K. Fiz. Tverd. Tela (St. Petersburg) 39, 1038–1040 (June 1997)     

The anomalous thermal expansion of VO2 crystal with the rutile structure

The large coefficient of thermal expansion parallel to the c-axis in the rutile phase of VO₂ is explained using the phonon-softening model of the metal-insulator transition.     

Thermal expansion behaviour and phase stability of AFe<Subscript>2</Subscript>As<Subscript>2</Subscript> (A = Ca,Sr and Eu) using powder diffraction technique

The thermal expansibilities and phase stabilities of AFe ₂As ₂ (A = Ca, Sr and Eu) have been investigated by powder diffraction techniques in the temperature range 5–600 K. We found the anisotropic thermal expansivities with temperature for all the compounds. The lattice parameter in the tetragonal phase ( A_T) of CaFe ₂As ₂ contracts with increasing temperature, whereas C_T expands. The rate of contraction in A_T is lower than the rate of expansion in C_T. Other compounds show normal thermal expansion behaviour along both a- and c-axes. In-plane expansion (i.e., along the a-axis) is found to be the smallest for EuFe ₂As ₂ and the highest for BaFe ₂As ₂. However, the rate of change of thermal expansivities along out-of-plane (i.e., along the c-axis) is higher as we go from Ba, Sr, Eu and Ca, respectively. Above 600 K, we notice the appearance /disappearance of certain reflections which suggest that tetragonal phase is not stable above this temperature for these compounds.     

Thermal conductivity of USb2 and UBi2 single crystals

The thermal conductivity (κ) of single crystals of tetragonal uniaxial antiferromagnets USb₂ (T _N = 202 K) and UBi₂ (T _N = 180.8 K) has been measured along the a-axis (κ_a ) over the temperature range from 0.5 to 300 K and along the c-axis (κ_c ) from 0.5 to 70 K. The as-grown samples have residual resistivity ratio (RRR) values of about 500–600 and 100–150 for UBi₂ and USb₂, respectively. The anisotropy of the thermal conductivity (κ_a (T)/κ_c (T) ～ 5) and the low-T Lorenz ratios are discussed in relation to Fermi surface topology for both compounds.     

Flux line lattice symmetries in the borocarbide superconductor LuNi2B2C

We compare the results of small angle neutron scattering on the flux line lattice (FLL) obtained in the borocarbide superconductor LuNi₂B₂C with the applied field along the c- and a-axes. For H‖c the temperature dependence of the FLL structural phase transition from square to hexagonal symmetry was investigated. Above 10 K the transition onset field. H ₂(T), rises sharply, bending away from H _c2(T) in contradiction to theoretical predictions of the two merging. For H‖a a first order FLL reorientation transition is observed at H _tr=3–3.5 kOe. Below H _tr the FLL nearest neighbor direction is parallel to the b-axis, and above H _tr to the c-axis. This transition cannot be explained using nonlocal corrections to the London model.     

Structural,elastic, electronic and thermal properties of M2SbP (M = Ti,Zr and Hf)

The structural, elastic, electronic and thermal properties of M₂SbP (M = Ti, Zr and Hf) were studied by means of a pseudo-potential plane-wave method based on the density functional theory within both the local density approximation and the generalised gradient approximation. The optimised zero-pressure geometrical parameters, i.e. the two unit cell lengths (a, c) and the internal coordinate (z), were in good agreement with available experimental and theoretical data. The effect of high pressure, up to 20 GPa, on the lattice constants shows that the contractions along the a-axis were higher than along c-axis. The anisotropic independent elastic constants were calculated using the static finite strain technique. Numerical estimations of the bulk modulus, shear modulus, Young's modulus, Poisson's ratio, average sound velocity and Debye temperature for ideal polycrystalline M₂SbP aggregates were performed in the framework of the Voigt–Reuss–Hill approximation. The calculated band structures show that all studied materials are electrical conductors. Analysis of the atomic site projected densities showed that the bonding is of covalent–ionic nature with the presence of metallic character. The density of states at the Fermi level is dictated by the transition metal d–d bands; the Sb element has little effect. Thermal effects on some macroscopic properties of M₂SbP were predicted using the quasi-harmonic Debye model, in which the lattice vibrations are taken into account. The variations of the volume expansion coefficient, heat capacity and Debye temperature with pressure and temperature in the ranges 0–50 GPa and 0–2000 K were obtained successfully.     

Structural and physical–chemical properties of the CuGa5Se8, CuGa3Se5 and CuIn3Se5 compounds

Large-block (8×4×3 mm³) CuGa₅Se₈ crystals were obtained by the horizontal Bridgman method. Homogeneous CuGa₃Se₅ and CuIn₃Se₅ single crystals 12 mm in diameter and up to 40 mm in length were grown by directed crystallization of the melt. All three compounds were found to have the chalcopyrite-related structure. The melting points of these compounds were defined by means of the differential thermal analysis. The lattice parameters a and c as well as the axial thermal expansion coefficients α_a and α_c were determined as a function of temperature in the range from 90 to 650 K by the X-ray diffraction method. It is revealed that for all three compounds the coefficients of expansion along the a-axis are larger than those along the c-axis over the entire temperature range studied.     

Magnetic phases in UNi<Subscript>2</Subscript>Si<Subscript>2</Subscript>

The tetragonal compound UNi₂Si₂ exhibits in zero magnetic field three different antiferromagnetic phases belowT _N =124 K. They are formed by ferromagnetic basal planes, which are antiferromagnetically coupled along thec-axis with the propagation vectorq=(0, 0, q _z ). Two additional order-order magnetic phase transitions are observed below T _N , namely atT ₁=108 K and T ₂=40 K in zero magnetic field. All three phases exhibit strong uniaxial anisotropy confining the U moments to a direction parallel to the c-axis. UNi₂Si₂ single crystals were studied in detail by measuring bulk thermodynamic properties, such as thermal expansion, resistivity, susceptibility, and specific heat. A microscopic study using neutron diffraction was performed in magnetic fields up to 14.5 T parallel to the c-axis, and a complex magnetic phase diagram has been determined. Here, we present the analysis of specific-heat data measured in magnetic fields up to 14 T compared with the results of the neutron-diffraction study and with other thermodynamic properties of UNi₂Si₂.     

High pressure X-ray diffraction study on icosahedral boron arsenide (B12As2)

The high pressure properties of icosahedral boron arsenide (B₁₂As₂) were studied by in situ X-ray diffraction measurements at pressures up to 25.5 GPa at room temperature. B₁₂As₂ retains its rhombohedral structure; no phase transition was observed in the pressure range. The bulk modulus was determined to be 216 GPa with the pressure derivative 2.2. Anisotropy was observed in the compressibility of B₁₂As₂—c-axis was 16.2% more compressible than a-axis. The boron icosahedron plays a dominant role in the compressibility of boron-rich compounds.     

Temperature dependences of thermal expansion and exchange magnetostriction of holmium and dysprosium single crystals

Information on the character of the temperature relationships of linear expansion coefficients (α_a, α_c) and exchange magnetostrictions (λ_a, λ_a) of single crystal Ho and Dy, based on temperature dependence of thec- anda-axis lattice constants, were accurately determined by X-ray diffraction from 4,2 to 300 K. In the helical phases we observed a large anisotropy of expansion coefficients (α_a>0, α_c<0) and their variations at 24,5, 45 and 96 in Ho and 156 K in Dy. These anomalies were caused by the commensurate transitions. The Curie transition in Ho is found to be of the 1-st order.     

Investigations of a quasi two-dimensional Heisenberg antiferromagnetic system. Nondeuterated and deuterated alkyl-ammonium-tetrachloromanganate

By neutron diffraction and susceptibility measurements the crystallographic and magnetic structures of (CH₃NH₃)₂MnCl₄ and (CD₃ND₃)₂MnCl₄ have been investigated. These compounds belong to a system of quasi two-dimensional Heisenberg antiferromagnets. At 96K a structural first order phase transition from the tetragonal high-temperature structure to an orthorhombic low-temperature structure was found. A magnetic phase transition from a two-dimensional antiferromagnetic preorder to a three-dimensional magnetic order occurs at 44.5K. The three-dimensional magnetic structure is characterized by antiferromagnetic (MnCl₄)^2- — layers perpendicular to the c-axis, with a ferromagnetic coupling between interacting next nearest (MnCl₄)^2- layers. The magnetic moments of the Mn-ions lie in the antiferromagnetic planes.     

Variations of lattice constants and thermal expansion coefficients of indium at high pressure and high temperature

ABSTRACT

The effects of pressure and temperature on the lattice constants and thermal expansion coefficients of Indium were studied up to 18.6?GPa and 506?K based on in situ X-ray diffraction method with an externally heated diamond anvil cell. The results show that the measured axial ratio (c/a) decreases with increasing temperature and its temperature dependence decreases with increasing pressure. The thermal expansion coefficient of the a-axis decreases with increasing pressure up to 7?GPa and remains almost constant above 7?GPa, whereas that of the c-axis increases monotonously with pressure and changes from negative to positive at around 7?GPa. The observed behavior suggests that temperature reduces the tetragonal distortion on the lattice, and its effect is dominant below 7?GPa; in contrast, pressure enhances lattice distortion, and tends to have a stronger effect above 7?GPa.     

正交和四方YBa2Cu3O7-x的热膨胀系数

用电容法测量了正交和四方YBa₂Cu₃O_7-x的热膨胀系数与温度的关系。结果表明,正交样品在205K附近,四方样品在92—130K之间热膨胀系数有异常。估计前者可能与晶格的不稳定性有关,说明具有较强的电-声子相互作用,后者可能与结构转变有关,因此破坏了高温超导电性。同时也发现正交样品在92K热膨胀系数有微小跳跃。由此估计了压力效应 关键词：     

Low-temperature structural phase transition in a monoclinic KDy(WO4)2 crystal

The low-temperature thermal and magnetic-resonance properties of a monoclinic KDy(WO₄)₂ single crystal are investigated. It is established that a structural phase transition takes place at T _c=6.38 K. The field dependence of the critical temperature is determined for a magnetic field oriented along the crystallographic a and c axes. The initial part of the H-T phase diagram is plotted for H∥a. The prominent features of the structural phase transition are typical of a second-order Jahn-Teller transition, which is not accompanied by any change in the symmetry of the crystal lattice in the low-temperature phase. The behavior of C(T) in a magnetic field shows that the transition goes to an antiferrodistortion phase. An anomalous increase in the relaxation time (by almost an order of magnitude) following a thermal pulse is observed at T>T _c(H), owing to the structural instability of the lattice. A theoretical model is proposed for the structural phase transition in a magnetic field, and the magnetic-field dependence of T _c is investigated for various directions of the field. Fiz. Tverd. Tela (St. Petersburg) 40, 750–758 (April 1998)     

Magnetic properties of NdCo2Ge2, ErCo2Ge2 and PrFe2Ge2 compounds

Magnetometric and neutron diffraction studies of polycrystalline NdCo₂GE₂, ErCo₂Ge₂ and PrFe₂Ge₂ compounds were carried out in the temperature range between 4.2 and 300 K. All samples are antiferromagnetic with Néel temperature 26.5, ～ 4.2 and 13 K, respectively. The RECo₂Ge₂ compounds have collinear antiferromagnetic order of +?+? type. For PrFe₂Ge₂ a sinusoidal magnetic structure is observed. Magnetic moment is localized on RE atoms only and is equal to that of RE³⁺ free ion value. In ErCo₂Ge₂ the magnetic moment of Er atoms is perpendicular to the c-axis, whereas for remaining compounds it is parallel to the c-axis.     

High-pressure neutron diffraction study of BaFe<Subscript>2</Subscript>As<Subscript>2</Subscript>

The crystal structure of BaFe₂As₂ was studied by high-pressure neutron powder diffraction in the pressure range from ambient to 6.5 GPa as well as in the temperature range from 12 K to 293 K at 4.4 GPa and no pressure or temperature induced phase changes were observed. The compression mechanism of BaFe₂As₂ was found to be anisotropic as the a- and c-axes are reduced by 2.49 and 3.66%, respectively at 6.5 GPa. Within the FeAs layers the Fe-As and Fe-Fe bonds decrease by 2.49 and 3.66%, respectively. The Ba-As distance decreases by 3.70% while the As-As inter-atomic distance along the c-axis exhibits a complex pressure dependence. The bulk modulus B ₀ and its pressure derivative B ₀' were determined to be B ₀ = 59(2) GPa and B ₀' = 6.1(7) at ambient temperature.