Average Volume Thermal Expansion Coefficient Research Articles

Synthesis, characterization and thermal expansion of the zinc-containing phosphates with the mineral-like framework structures

The new phosphates ZnxMg0.5+xE2−x(PO4)3 (E = Ti, Zr) were synthesized by the sol–gel method followed by heat treatment. Obtained samples were characterized with X-ray, IR, DTA and microprobe electron analyses. The ZnxMg0.5+xTi2−x(PO4)3 solid solution (0 ≤ x ≤ 0.5, kosnarite-type, sp. gr. R$$\bar{3}$$) is stable up to 1323 K. The ZnxMg0.5+xZr2−x(PO4)3 solid solution (0 ≤ x ≤ 0.5, Sc2(WO4)3-type, sp. gr. P21/n) is thermally unstable above 1273 K. The thermal expansion of ZnxMg0.5+xE2−x(PO4)3 solid solutions was studied in the temperature range 298–1073 K. The magnitudes of average volume thermal expansion coefficients vary from 1 × 10−5 to 5 × 10−6 K−1. The composition regulation of these medium- and high-expanding materials allows you to change the characteristics of thermal expansion in the required direction.

Investigations of thermophysico-chemical properties of Ba2TiSi2O8(s) and Sr2TiSi2O8(s)

The titanosilicates: Ba2TiSi2O8(s)(BTS) and Sr2TiSi2O8(s)(STS) were synthesized by citrate nitrate gel combustion and complex polymerisation method, respectively and characterized using X-ray diffraction (XRD) technique. The heat capacity, thermal diffusivity, average thermal expansion coefficient, the standard molar Gibbs energy of formation of BTS and STS were measured with a heat flux-type differential scanning calorimeter, laser flash technique, high temperature XRD and solid oxide Gavanic cell, respectively. The heat capacities of BTS and STS were found to be comparable upto 600 K and afterwards, the increase is higher in BTS. Thermal conductivity of BTS was found to be higher than that of STS. The average volume thermal expansion coefficient of BTS was found to be lower than that of STS. The enthalpy of formation of BTS and STS were derived from their respective Gibbs energy data and their thermodynamic functions were calculated.

Thermophysical properties of Ba1−xSrxMoO3(s)

Ba1−xSrxMoO3(s) (x=0, 0.2, 0.4, 0.5, 0.8, 1) solid-solutions were synthesized by reduction of corresponding Ba1−xSrxMoO4(s) and were characterized using X-ray diffraction (XRD). Thermal expansion behavior of Ba1−xSrxMoO3(s) (x=0, 0.4, 0.8 and 1) were investigated in the temperature range 298–873K by high temperature X-ray diffraction (HTXRD). The average volume thermal expansion coefficient of Ba1−xSrxMoO3(s) (x=0, 0.4, 0.8 and 1) was found to be 2.83×10−5, 2.20×10−5, 2.02×10−5 and 2.27×10−5K−1, respectively. Heat capacity of Ba1−xSrxMoO3(s) (x=0, 0.4, 0.8, 1) was measured with a heat flux-type differential scanning calorimeter (DSC) in the temperature range 290–870K. The specific heat of Ba1−xSrxMoO3(s) was found to increase with increase in concentration of strontium. The thermodynamic functions such as enthalpy increment, entropy and Gibbs energy functions of Ba1−xSrxMoO3(s) were also calculated.

Thermo physico-chemical investigations on A–Te–O (A=Cr, Fe, Ni) system

Abstract The compounds, Cr2TeO6 (s), Fe2TeO6 (s) and Ni3TeO6 (s) were synthesized by solid-state route and characterized using X-ray diffraction technique. Thermal expansion of Fe2TeO6 (s) and Ni3TeO6 (s) were studied by high temperature X-ray diffraction technique in the temperature range 298–973 K and 298–923 K, respectively. The average volume thermal expansion coefficient of Fe2TeO6 (s) and Ni3TeO6 (s) were determined to be 2.46 × 10−5 and 3.02 × 10−5 K−1, respectively. Heat capacity of Cr2TeO6 (s), Fe2TeO6 (s) and Ni3TeO6 (s) was measured, in the temperature range of 300–870 K, employing temperature modulated differential scanning calorimeter. The Gibbs energy of formation of Fe2TeO6 (s) and Ni3TeO6 (s) were measured using transpiration method. An empirical function was derived to compute enthalpy of formation of AnTeO6 (s) (where A = various elements of periodic table, n = 2, 3 or 6). Self consistent thermodynamic functions of Cr2TeO6 (s), Fe2TeO6 (s) and Ni3TeO6 (s) were calculated. The chemical potential diagrams of A–Te–O (A = Cr, Fe, Te) system were also constructed.

Preparation and structure of BiCrTeO6: A new compound in Bi–Cr–Te–O system. Thermal expansion studies of Cr2TeO6, Bi2TeO6 and BiCrTeO6

A new compound BiCrTeO6 in Bi–Cr–Te–O system was prepared by solid state reaction of Bi2O3, Cr2O3 and H6TeO6 in oxygen and characterized by X-ray diffraction (XRD) method. It could be indexed on a trigonal lattice, with the space group P-31c, unit cell parameters a=5.16268(7)Å and c=9.91861(17)Å. The crystal structure of BiCrTeO6 was determined by Rietveld refinement method using the powder XRD data. Structure shows that there is one distinct site for bismuth (Bi) atom, one chromium rich (Cr/Te=68/32), and one tellurium rich (Te/Cr=68/32) sites, and one distinct site for oxygen (O) atom in the unit cell. All cations in this structure show an octahedral coordination with oxygen atoms at the corners. The thermogravimetric analysis (TGA) of the compound in air shows that it is stable up to 1103K and decomposes thereafter. The thermal expansion behavior of Cr2TeO6, Bi2TeO6 and BiCrTeO6 was studied using High Temperature X-ray diffraction (HTXRD) method from room temperature to 973, 873 and 923K respectively under vacuum of 10−8 atmospheres. All the compounds showed positive thermal expansion with the average volume thermal expansion coefficients of 14.38×10−6/K, 22.0×10−6/K and 16.0×10−6/K respectively.

Combustion synthesis and thermal expansion of RE6UO12 (RE = Dy and Tb)

Citrate–nitrate combustion method was adopted for the synthesis of RE6UO12 (RE = Dy and Tb). These compounds were characterized by X-ray diffraction. Thermal expansion coefficient of these compounds were measured in the temperature range of 298–1,273 K by high temperature X-ray powder diffractometry (HT-XRD) and compared with other rare earth compounds reported in the literature. There was no observed phase transition in Dy6UO12, but Tb6UO12 showed a second-order phase transition at 670 K which was confirmed using differential scanning calorimeter. The average volume thermal expansion coefficient of Dy6UO12 in the temperature range of 298–1,273 K is (29.82 ± 4.02) × 10−6 and that of Tb6UO12 in the temperature range of 298–673 K is (13.76 ± 2.64) × 10−6 K−1.

Characterization and thermo physical property investigations on Ba1−xSrxMoO4 (x = 0, 0.18, 0.38, 0.60, 0.81, 1) solid-solutions

Ba1−xSrxMoO4 (x=0, 0.18, 0.38, 0.60, 0.81, 1) solid-solutions were synthesized by complex polymerization method. The solid solutions were characterized using X-ray diffraction (XRD) and the Raman spectroscopy. Heat capacity measurements on Ba1−xSrxMoO4(s) were performed with heat flux-type differential scanning calorimeter in the temperature range of 140–870K. The measured heat capacity values were used to calculate different thermodynamic functions such as enthalpy increment, entropy and Gibbs energy functions. Thermal expansion behavior of Ba1−xSrxMoO4(s) (x=0, 0.6 and 1) were investigated in the temperature range 298–1273K by high temperature X-ray diffraction (HTXRD). The specific heat and average volume thermal expansion coefficient of Ba1−xSrxMoO4(s) was found to increase with increase in concentration of strontium. The average volume thermal expansion coefficient of Ba1−xSrxMoO4(s) (x=0, 0.6 and 1) was found to be 25.59×10−6, 33.86×10−6 and 34.37×10−6K−1 respectively.

Negative Thermal Expansion of Tm<sub>2</sub>Fe<sub>15</sub>SiCr Compound

The thermal expansion and the Curie temperature of Tm2Fe15SiCr compound have been investigated by means of x-ray diffraction and magnetization measurements. The result shows that the Tm2Fe15SiCr compound has a hexagonal Th2Ni17-type structure. One Cr and one Si atoms substituting for two Fe atoms can increase the Curie temperature obviously. In magnetic state, an anisotropic anomalous thermal expansion was observed. Along the c-axis, the average linear thermal expansion coefficient αc=-2.04×10-5/K in the temperature range 303-460K. Along the a-axis, the average linear thermal expansion coefficient αa=-8.09×10-5/K in 370-410K. In the temperature range 370-450K, the average volume thermal expansion coefficient αv =-2.08×10-5/K. The mechanism of the thermal expansion anomaly of Tm2Fe15SiCr compound was discussed in this paper.

Negative Thermal Expansion of Gd<sub>2</sub>Fe<sub>16.5</sub>Cr<sub>0.5</sub> Compound with Th<sub>2</sub>Ni<sub>17</sub>-Type Structure

The thermal expansion and the Curie temperature of Gd2Fe16.5Cr0.5 compound have been investigated by means of x-ray diffraction and magnetization measurements. The result shows that the Gd2Fe16.5Cr0.5 compound annealed at 1243°C has a hexagonal Th2Ni17-type structure. Cr atom substituting for Fe atom can increase the Curie temperature obviously. In magnetic state, an anisotropic anomolous thermal expansion was observed. Along the c-axis, the average linear thermal expansion coefficient αc=-2.79×10-6/K in the temperature range 294-472K, and αc =-3.09×10-5/K in 472-592K. Along the a-axis, the average linear thermal expansion coefficient αa =9.22×10-6/K in 294-552K, and αa =-1.41×10-5/K in 552-592K. In the temperature range 472-592K, the average volume thermal expansion coefficient αv =-2.14×10-5/K. The mechanism of the thermal expansion anomaly of Gd2Fe16.5Cr0.5 compound was discussed in this paper.

Lattice thermal expansion of zircon-type LuPO4 and LuVO4: A comparative study

We report the lattice thermal expansion of zircon-(xenotime-)type LuPO 4 and LuVO 4 in the temperature range of 25-1000 °C from high-temperature powder XRD studies. The details of the high-temperature crystal chemistry of both phases have been determined from Rietveld analysis of the powder XRD data. Both the compounds show appreciably higher thermal expansion than analogous zircon-type silicates. Despite isomorphism, the axial thermal expansion of LuVO 4 shows significant anisotropy compared to LuPO 4 . In the studied temperature range, the average axial thermal expansion coefficients of LuPO 4 are α a = 6.0 × 10 -6 and α c = 7.2 × 10 -6 (°C -1 ) and those of LuVO 4 are α a = 3.6 × 10 -6 and α c = 11.8 × 10 -6 (°C -1 ). However, the average volume thermal expansion coefficients are almost identical. The differences in the thermal expansion behavior of the two structures originate from differences in the expansion and distortion of the LuO 8 polyhedra. The LuO 8 polyhedron in LuVO 4 shows about 30% higher thermal expansion than that in LuPO 4 . The overall thermal expansion behaviors of these two structures are predominantly related to the distortion in the LuO 8 unit, inter-cation distances and spatial arrangement of the Lu-O bonds in the structure.

Specific volumes of the Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 alloy in the liquid, glass, and crystalline states

The specific volumes of the Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 alloy as a function of temperature, T, are determined by employing an image digitizing technique and numerical calculation methods applied to the electrostatically levitated spherical alloy. The linear fitting of the volumes of the alloy in the liquid, Vl, glass, Vg, and crystalline Vc, states in the temperature ranges shown in parentheses are Vl(T)=0.1583+8.877×10−6T(cm3/g) (700–1300 K);Vg(T)=0.1603+5.528×10−6T (400–550 K);Vc(T)=0.1583+6.211×10−6T(400–850 K). The average volume thermal expansion coefficients within the temperature ranges are determined to be 5.32, 3.39, and 3.83×10−5 (1/K) for the liquid, glass, and crystalline states, respectively.

In situ high P‐T X ray diffraction studies on three polymorphs (α, β, γ) of Mg2SiO4

Unit cell volumes of the beta (β) and spinel (γ) phases (Mg2SiO4) have been measured under simultaneous high pressure and high temperature using synchrotron X ray radiation, in a cubic anvil apparatus. With volume‐temperature data at constant pressure, we determine the average volume thermal expansion coefficients of the β phase from 724 to 872 K at 7.6 GPa to be 2.28(±0.45)×10−5/K and of the γ phase from 759 to 962 K at 9.8 GPa to be 1.71(±0.14)×10−5/K. Thermodynamic relations are used to constrain the temperature derivative of the isothermal bulk modulus (KT) from the high‐pressure thermal expansion data: (∂KT/∂T)P is found to be −2.7(±0.5)×10−2 GPa/K for the β phase and −2.8(±0.3)×10−2 GPs/K for the γ phase. Unit cell volumes of the olivine (α) phase, back‐transformed from the β and γ phases at high temperatures, have been measured under pressure at temperatures above the Debye temperature; using thermal pressure equations, we find (∂KT/∂T)P for the α phase to be −2.1(±0.2)×10−2 GPa/K. These new data on the temperature derivatives of the bulk modulus for the three phases are consistent with an upper mantle containing 60 to 65% olivine and the absence of a velocity signature for the β to γ phase transition near 520 km depth.

MgSiO3 ilmenite: Heat capacity, thermal expansivity, and enthalpy of transformation

A new determination, using high temperature drop-solution calorimetry, of the enthalpy of transformation of MgSiO3 pyroxene to ilmenite gives ΔH298 = 59.03 ±4.26 kJ/mol. The heat capacity of the ilmenite and orthopyroxene phases has been measured by differential scanning calorimetry at 170–700 K; Cp of MgSiO3 ilmenite is 4–10 percent less than that of MgSiO3 pyroxene throughout the range studied. The heat capacity differences are consistent with lattice vibrational models proposed by McMillan and Ross (1987) and suggest an entropy change of -18 ± 3 J-K-1 ·mol-1, approximately independent of temperature, for the pyroxene-ilmenite transition. The unit cell parameters of MgSiO3 ilmenite were measured at 298–876 K and yield an average volume thermal expansion coefficient of 2.44 × 10-5 K-1. The thermochemical data are used to calculate phase relations involving pyroxene, β-Mg2SiO4 plus stishovite, Mg2SiO4 spinel plus stishovite, and ilmenite in good agreement with the results of high pressure studies.