Thermal expansion and a new phase transition in pyroelectric LiKSO4

Single crystal macroscopic thermal expansion coefficient measurements have been made on uniaxial lithium potassium sulphate crystal both along and normal to the six fold axis, employing Fizeau’s interferometer method. Measurements were made in the range of −120°C to 500°C. The results show that lithium potassium sulphate exhibits two major anomalies in its expansion coefficients around −95°C and 422°C respectively, the one at −95°C has been observed for the first time. The nature of dimensional changes of the crystal at the upper and lower transition points are opposite in nature. The crystal shows considerable lattice anisotropy. Megaw’s tilt concept has been invoked to explain the relative magnitudes of expansion coefficients alonga andc directions. Structural features responsible for the absence of ferroelectricity in this crystal have been pointed out.     

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)     

Thermal expansion of sodium nitrate (I)

The thermal expansion coefficients, α, of sodium nitrate have been measured along the trigonal axis of the crystal (α_∥) and in a direction perpendicular to this axis (α_⊥) by means of a Fizeau interferometer in the temperature range 77–300 K. α_∥ is large, while α_⊥ is relatively small, showing a large anisotropy. The results have been compared with earlier observations and the possible origin of large anisotropy has been suggested. Some details are given of the cryostat used for this experiment.     

Low temperature thermal expansion of praseodymium between 0.5 and 25 K

The linear thermal expansion coefficients parallel and perpendicular to the hexagonal axis of single crystal Praseodymium have been measured between 0.5 and 25 K and in external magnetic fields up to 12 kOe. α₆ ? α_⊥ is found to be of the order of 10^?4 at 20 K, decreasing with decreasing temperatures. Below 1 K we found evidence of a nuclear hyperfine contribution to the thermal expansion. A separation of the electronic term allows a determination of the electronic Grüneisenparameter.     

Lattice thermal expansion of silver indium disulphide

Lattice parameters of chalcopyrite type compound silver indium disulphide (AgInS₂) were determined as a function of temperature by the x-ray method in the temperature range 28 to 685°C. Using these data, the coefficients of thermal expansion,a _⊥ anda _‖, were evaluated by a graphical method. The temperature dependence ofa _⊥ anda _‖ is represented by a suitable equation. The anisotropic thermal expansion of AgInS₂ is explained in terms of the thermal expansion of the Ag-S and In-S bonds of the AgInS₂ lattice.     

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.     

Thermal expansion and thermal conductivity of single-crystal Cu<Subscript>x</Subscript>Ag<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>InS<Subscript>2</Subscript> solid solutions grown by the moving solvent method

Single crystals of Cu_xAg_1−x InS₂ solid solutions are grown by the moving solvent method. The compositions and structures of the single crystals are determined. The thermal expansion coefficients of these crystals are determined with a dilatometer. The thermal expansion coefficients are found to vary linearly with concentration x. The thermal conductivity of the crystals is measured by the absolute method, and the concentration dependence of the thermal conductivity is constructed. This dependence is shown to have a minimum near the equimolar composition.     

Zero-field splitting in NiSiF6−6H2O and its pressure, stress and temperature dependences: A supplementary study

The zero-field splitting in NiSiF₆?6H₂O was studied as a function, of hydrostatic pressure and uniaxial stress at temperatures above and below 220 K, at which the crystal exhibits a secondorder phase transition. The anisotropy of the thermal expansion coefficients parallel and perpendicular to the trigonal symmetry axis was measured in a wide range of temperatures. On the basis of the obtained data the spin-phonon interaction has been separated from the thermal expansion of the crystal. At high and low temperatures the two contributions have opposite signs and exhibit much higher values above 220 K than below this temperature. This is explained by the high anisotropy of the thermal expansion of the crystal characteristic of the high-temperature phase.     

Thermal expansion anisotropy of β-TlInS2 crystals in the course of phase transitions

Basing on the thermal expansion studies performed for β-TlInS₂ crystals in the course of their phase transitions, we have found that the crystals aged for one year are composed from at least two polytypes, which undergo phase transitions at different temperatures. The detailed analysis of anisotropy of the thermal expansion demonstrates that all of the diagonal components of the thermal expansion tensor associated with the eigensystem have almost the same modules but differ by their signs. This leads to appearance of an elliptical conical surface of zero thermal expansion. The orientation of this surface does not depend on the temperature in the temperature interval under study. We have also found that the thermal expansion coefficients along the crystallographic a and b axes are close to zero.     

Thermal expansion of nanocrystalline and coarse-crystalline silver sulfide Ag<Subscript>2</Subscript>S

In situ studies of the thermal expansion of polymorphic phases of coarse-crystalline and nanocrystalline silver sulfide, namely, monoclinic acanthite α-Ag₂S and cubic argentite β-Ag₂S, have been performed for the first time by high-temperature X-ray diffraction. The temperature dependences of the unit cell parameters of acanthite and argentite have been measured from temperatures in the range of 300–623 K, and the thermal expansion coefficients of acanthite and argentite have been determined. The observed difference between the thermal expansion coefficients of nano- and coarse-crystalline acanthite is shown to be due to a small size of nanocrystalline silver sulfide particles, which leads to an increase in the anharmonicity of atomic vibrations.     

Anisotropic thermal expansion of AEFe2As2 (AE = Ba,Sr, Ca) single crystals

We report anisotropic thermal expansion of the parent, AEFe₂As₂ (AE = Ba, Sr, and Ca), compounds. Above the structural/antiferromagnetic phase transition anisotropy of the thermal expansion coefficients is observed, with the coefficient along the a-axis being significantly smaller than the coefficient for the c-axis. The high temperature (200 K ≤ T ≤ 300 K) coefficients themselves have similar values for the compounds studied. The sharp anomalies associated with the structural/antiferromagnetic phase transitions are clearly seen in the thermal expansion measurements. For all three pure compounds, the ‘average’ a-value increases and the c-lattice parameter decreases on warming through the transition, with the smallest change in the lattice parameters observed for SrFe₂As₂. The data are in general agreement with the literature data from X-ray and neutron diffraction experiments.     

Investigation of phase transitions and thermal expansion of some complex tungsten-containing oxides

The phase transitions have been investigated and the thermal expansion coefficients have been determined in compounds with a structure of brannerite, defect pyrochlore, and tungsten bronze of the general formula M ^I A ^VWO_{6 − δ} (M ^I = □, H₃O, Li, Na, K, Rb, and Cs; A ^V = V, Nb, Sb, and Ta; δ = 0, 0.5) by high-temperature X-ray diffraction and differential thermal analysis. It has been shown that brannerites and tungsten bronze do not undergo phase transitions and the compounds are characterized by a significant anisotropy of the thermal expansion, whereas pyrochlores undergo phase transitions of three types, and thermal deformations in them are determined by the size of M ^I atoms.     

Spontaneous magnetostriction of Y2Fe16Al compound

The structure and magnetic properties of Y₂Fe₁₆Al compound have been investigated by means of x-ray diffraction and magnetization measurements. The Y₂Fe Fe₁₆Al compound has a hexagonal Th$_{2}$Ni$_{17}$-type structure. Negative thermal expansion was found in Y₂Fe₁₆Al compound in the temperature range from 332 to 438K by x-ray dilatometry. The coefficient of the average thermal expansion is \alpha =-3.4\times 10^-5K^-1. The spontaneous magnetostrictive deformations from 293 to 427K have been calculated based on the differences between the experimental values of the lattice parameters and the corresponding values extrapolated from the paramagnetic range. The result shows that the spontaneous volume magnetostrictive deformation \textit{$\omega $}$_{\rm S}$ decreases from 5.4$\times $10^-3to near zero with temperature increasing from 293 to 427K, the spontaneous linear magnetostrictive deformation \textit{$\lambda $}$_{\rm c}$ along the $c$ axis is much larger than the spontaneous linear magnetostrictive deformation \textit{$\lambda $}$_{\rm a}$ in basal-plane in the same temperature range except near 427K.     

Magnetoelastic contribution to the thermal expansion of the rare-earth phosphates TbPO4 and TmPO4

The thermal expansion of the rare-earth phosphates TbPO₄ and TmPO₄ having zircon structure has been investigated experimentally and theoretically. Significant magnetoelastic anomalies of the thermal expansion have been identified and the magnetoelastic contributions have been isolated allowing for corrections to the variation of the phonon contribution along the rare-earth ion series. It is shown that the magnetoelastic contribution to the thermal expansion of terbium and thulium phosphate is well described by the temperature dependence of the quadrupole moments of the rare-earth ions. The fully symmetric magnetoelastic coefficients for Tb³⁺ and Tm³⁺ are determined and a comparison is made of the magnetoelastic anomalies of the thermal expansion and the magnetoelastic coefficients of rare-earth phosphates and vanadates allowing for the differences in the crystal fields of the two isomorphic groups of zircons. Fiz. Tverd. Tela (St. Petersburg) 39, 106–111 (January 1997)     

Wärmeausdehnung von H2O- und D2O-Einkristallen

The linear thermal expansion coefficients of ice and heavy ice single crystals have been measured in both hexagonal crystallographic axes between the melting point and 18° K. The expansion coefficients of H₂O and D₂O become negative below 63° K.     

The structure of the glass phase of Rb1−x(ND4)xD2PO4

X-ray scattering techniques have been used to study the diffuse scattering from a single crystal of Rb_1–x(ND₄)_xD₂PO₄ withx=0.65. This system has a structural glass phase at low temperatures resulting from the competing ferroelectric interactions of RbD₂PO₄ and antiferroelectric interactions of (ND₄)D₂PO₄. The diffuse scattering shows a broad peak with a maximum occurring at a wavevector of about 0.3a ^*, and the intensity of these peaks is surprisingly different for wavevectorsq on opposite sides of the Bragg reflections. A model of the D bonding is developed which suggests that the diffuse scattering arises from the interaction between ferroelectric displacements alongc, ferroelectric displacements alongb, and transverse acoustic modes polarized alongb andc. The model accounts for the incommensurate wavevector and, qualitatively, for the intensity of the diffuse scattering around different Bragg reflections. The temperature dependence of the scattering is also measured.     

Fluctuations and Landau-Devonshire expansion for barium titanate

The experimentally observed temperature dependence of the quartic coefficients in the Landau-Devonshire expansion for BaTiO₃ is naturally accounted for within a proper fluctuation model. It is explained, in particular, why one of the quartic coefficients varies with temperature above T _c , while the second is constant. It is argued that the tetragonal phase in BaTiO₃ exists essentially due to thermal fluctuations, while the true Landau-Devonshire expansion with temperature-independent coefficients favors the rhombohedral ferroelectric phase.     

Thermal expansion and thermal conductivity of CuGa<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>In<Subscript>x</Subscript>Te<Subscript>2</Subscript> solid solutions

The thermal expansion coefficients and the thermal conductivity of Bridgman-grown crystals of CuGa_1−x In_xTe₂ solid solutions are investigated. It is found that the thermal expansion coefficient varies with x linearly, while the thermal conductivity is minimal when x=0.5. The Debye temperature and the rms dynamic atomic displacements are calculated from experimental data. It is shown that the Debye temperature decreases and the rms displacements in the crystal lattice sharply increase as the In content in the solid solutions grows.     

Measurement of the thermal expansion coefficients of ferroelectric crystals by a moiré interferometer

A moiré interferometer is used to measure the thermal expansion of two ferroelectric crystals, LiNbO₃ and KTiOPO₄. The crystal samples are patterned with a chromium reflective grating and used as a diffractive component in a reflective grating interferometer. The thermal expansion of all the three axes of congruent LiNbO₃ and of x and y axes of the flux-grown KTiOPO₄ were measured from room temperature to 200 °C. For this temperature range the thermal expansion coefficient has been modeled by a second-order polynomial and its coefficients have been estimated by accurate analysis of the resulting moiré fringe pattern.     

Investigation of the structure,physical properties,and phase transition in SrAlF<Subscript>5</Subscript>

Crystals of SrAlF₅ have been grown by the Bridgman method from the melt and by sintering of the components. Optical polarization studies and measurements of the thermal expansion and birefringence coefficients have been carried out over a wide temperature range. The electromechanical coefficient d ₃₃ has been measured, and the optical second harmonic, dielectric hysteresis loop, and optical quality of the crystal have been assessed. X-ray diffraction investigations have been performed to identify the revealed compounds. It has been demonstrated that the SrAlF₅ crystals obtained under the growth conditions chosen have I4₁/a symmetry and do not undergo structural phase transitions in the temperature range 100–800 K. Crystalline inclusions of the AlOF oxyfluoride have been revealed in crystals grown with an AlF₃ excess. The birefringence of the AlOF crystal is an order of magnitude higher than that of SrAlF₅, does not depend on temperature, and has no anomalies up to 800 K.