Volumetric Thermal Expansion Coefficient Research Articles

Correlation Characteristics of the Volumetric Thermal Expansion Coefficient and Specific Heat of Corundum

The correlation between the volumetric thermal expansion coefficient (VLEC) o(T ) and specific heat C(T) of corundum α-Al2O3 is examined in detail. It is shown that there is a clear correlation o(C) not only at low temperatures (to about 50 K), where it is linear (Gruneisen’s law), but also in a wider temperature range, viz., up to the melting point of corundum. Asignificant deviation from the low-temperature linear behavior of the temperature dependence of the VTEC o(C) occurs when the specific heat reaches the Dulong–Petit classical limit 5.3R. The results of the present work can be used to verify the data from primary calorimetric and dilatometric studies of ceramic and other materials.

Correlation between the thermal expansion coefficient and heat capacity of an inert-gas single crystal: Krypton

Correlation dependence of volumetric thermal expansion coefficient o(T) on heat capacity C(T) for single-crystal krypton is studied. It is shown that the dependence o(C) is observed not only at low temperatures, where it is linear and is known as the Gruneisen law, but also in a much wider temperature range up to the melting point of krypton. When the specific heat reaches a classical limit of 3R (according to the Dulong-Petit law), the o(C) dependence considerably deviates from the low-temperature linear behavior. The concept of the differential Gruneisen parameter of krypton, γ′ ∼ (∂o/∂C), is introduced, and its temperature dependence is estimated.

Synthesis of sodium nickel phosphate and its crystallographic, spectroscopic, and temperature-controlled X-ray diffraction study

Sodium nickel phosphate NaNiPO4 has been synthesized by crystallization from salt solutions containing corresponding metals and phosphoric acid and subsequent heat treatment. NaNiPO4 with a maricite structure has been studied by a combination of methods. Its structure has been refined by the Rietweld method (space group Pnma, a = 8.7839(2) A, b = 6.7426(2), c = 5.0368(2) A, V = 298.31(2) A3, Z = 4). The structure framework is composed of edge-sharing NiO6 octahedra arranged in columns running along the b axis and linked with each other through PO4 tetrahedra. The cavities in the structure accommodate Na+ ions. No temperature-induced changes in the X-ray diffraction pattern of NaNiPO4 in the temperature range 25–700°C have been observed. The volumetric thermal expansion coefficient of the phosphate, αV = 34 × 10−6 K−1, allows one to classify it as a strongly expanding substance. Maricite structure stabilities are compared for NaEIIPO4 (EII = Mn, Fe, Co, Ni).

Density and Thermal Expansion of High Purity Nickel over the Temperature Range from 150 K to 2030 K

The paper presents the results of an investigation of the nickel density and thermal expansion over the temperature range from 145 K to 2030 K. The measurements have been carried out by using the dilatometer method and the \(\upgamma \)-ray attenuation technique (gamma method). The errors of the density and coefficients of thermal expansion measurements are estimated to be within 0.05 % to 0.25 % and 1 % to 2.5 %, respectively. The accuracy of determination of the volumetric thermal expansion coefficient of the melt by the \(\upgamma \)-ray attenuation technique is substantiated. The density change on melting (\(4.70 \pm 0.15\)) % has been directly measured. The temperature dependences and reference tables of the volumetric properties of solid and liquid nickel have been developed. A comparison of the obtained results with literature data has been made.

Thermal equation of state of majoritic knorringite and its significance for continental upper mantle

AbstractThe P‐V‐T equation of state (EoS) for majoritic knorringite Mg3.19Cr1.60Si3.19O12 at pressures to 17 GPa and temperatures to 1673 K was obtained from in situ X‐ray diffraction experiments using a Kawai‐type multi‐anvil apparatus. Fitting of the room‐temperature P–V data to a third‐order Birch‐Murnaghan EoS yielded an isothermal bulk modulus, K0,300 = 154 (4) GPa, and a pressure derivative, K′0,300 = 5.4 (1.2). When fitting a high‐temperature Birch‐Murnaghan EoS using all of the P‐V‐T data at a fixed V0 = 1549.08 Å3, we find that K0,300 = 157 (2) GPa, K′0,T = 4.5 (6), (∂K0,T/∂T)P = −0.019 (4) (GPa K−1), a = 3.00 (14) × 10−5 K−1, and b = 0.65 (24) × 10−8 K−2, where α = a + bT is the volumetric thermal expansion coefficient. Fitting the Mie‐Grüneisen‐Debye EoS with the present data with a Debye temperature fixed at θ0 = 731 K yielded a Grüneisen parameter, γ0 = 1.34 at q = 1.0 (fixed). The thermoelastic parameters of pure knorringite were estimated and were compared with the previous data on other garnet compositions. The presence of Cr2O3 in pyrope garnets in the upper mantle decreases P‐ and S‐velocities by 1.6% and the density increases by 1.7% (for 20 mol.% knorringite end member) compared to pure pyrope. The results show the importance of accounting knorringite end‐member for accurate estimation of mantle garnet acoustic velocities.

On the correlation between thermal expansion coefficient and heat capacity of argon cryocrystals

A detailed analysis of the correlation between the volumetric thermal expansion coefficient o(T) and heat capacity C(T) of a rare-gas (Ar) cryocrystal has been performed. It has been shown that there is a clear correlation dependence o(C) not only in the low-temperature range, where it is linear and known as the Gruneisen law, but also in a significantly wider temperature range (up to the melting point of argon). The dependence o(C) substantially deviates from the low-temperature linear behavior when the heat capacity reaches the classical Dulong-Petit limit of 3R.

Properties of an aqueous solution of ionic liquid [Emim][Cl] at standard atmospheric pressure

The density, viscosity, electric conductivity, volumetric thermal expansion coefficient, melting point, and refractive index of an aqueous solution of the [Emim][Cl] ionic liquid are measured over wide ranges of temperature and concentrations at standard atmospheric pressure. Analytical dependences of the investigated properties on the concentration and temperature are suggested.

Structure, phase transition, and controllable thermal expansion behaviors of Sc(2-x)Fe(x)Mo₃O₁₂.

The crystal structures, phase transition, and thermal expansion behaviors of solid solutions of Sc(2-x)Fe(x)Mo3O12 (0 ≤ x ≤ 2) have been examined using X-ray diffraction (XRD), neutron powder diffraction (NPD), and differential scanning calorimetry (DSC). At room temperature, samples crystallize in a single orthorhombic structure for the compositions of x < 0.6 and monoclinic for x ≥ 0.6, respectively. DSC results indicate that the phase transition temperature from monoclinic to orthorhombic structure is enhanced by increasing the Fe(3+) content. High-temperature XRD and NPD results show that Sc(1.3)Fe(0.7)Mo3O12 exhibits near zero thermal expansion, and the volumetric coefficients of thermal expansion derived from XRD and NPD are 0.28 × 10(-6) °C(-1) (250-800 °C) and 0.65 × 10(-6) °C(-1) (227-427 °C), respectively. NPD results of Sc2Mo3O12 (x = 0) and Sc(1.3)Fe(0.7)Mo3O12 (x = 0.7) indicate that Fe substitution for Sc induces reduction of the mean Sc(Fe)-Mo nonbond distance and the different thermal variations of Sc(Fe)-O5-Mo2 and Sc(Fe)-O3-Mo2 bond angles. The correlation between the displacements of oxygen atoms and the variation of unit cell parameters was investigated in detail for Sc2Mo3O12.

Analysis and Experimental Study of the Package Stresses in a QFN Plastic-Encapsulated Package

Plastic-encapsulated packages are known to suffer package stress issues which often cause undesired shifts in the IC electrical parameters. Two types of package stress are analyzed and their contributions to the overall package stress in a Quad-Flat No-leads (QFN) Package are experimentally studied in this paper. The volumetric package stress generated by the mold compound is analyzed using the material properties of the bulk modulus and the volumetric coefficient of thermal expansion (vCTE). The in-plane package stress generated by the die and the die-attach material is analyzed using the structural analysis method with the introduction of an improved Suhir solution to evaluate the in-plane normal stress at the active area of the IC die. These theoretical analysis results are further experimentally studied with the functional measurements on a precision CMOS bandgap voltage reference in a QFN package. Using the combination of two different die-attach methods and two different die-coating conditions, the parametric variations in the bandgap voltage can be correlated with the different types of package stress. The actual test data presented in this paper are in good agreement with the theoretical analysis results.

Ab initiobased thermal property predictions at a low cost: An error analysis

Ab initio calculations often do not straightforwardly yield the thermal properties of a material yet. It requires considerable computational efforts, for example, to predict the volumetric thermal expansion coefficient alpha(V) or the melting temperature T-m from first principles. An alternative is to use semiempirical approaches. They relate the experimental values to first-principles predictors via fits or approximative models. Before applying such methods, however, it is of paramount importance to be aware of the expected errors. We therefore quantify these errors at the density-functional theory level using the Perdew-Burke-Ernzerhof functional for several semiempirical approximations of alpha(V) and T-m, and compare them to the errors from fully ab initio methods, which are computationally more intensive. We base our conclusions on a benchmark set of 71 ground-state elemental crystals. For the thermal expansion coefficient, it appears that simple quasiharmonic theory, in combination with different approximations to the Gruneisen parameter, provides a similar overall accuracy as exhaustive first-principles phonon calculations. For the melting temperature, expensive ab initio molecular-dynamics simulations still outperform semiempirical methods.

Thermal stability and thermal expansion studies of cubic fluorite-type MgF2 up to 135 GPa

The thermal expansion of MgF2 with a fluorite structure has been investigated at high pressures using plane-wave pseudopotential scheme within the local density approximation correction in the frame of density functional theory based on the analysis of thermal stability using classical molecular dynamics simulations up to 6500K. To investigate the thermodynamic properties like as the P–V–T equation of state and volumetric thermal expansion coefficient αV of cubic fluorite-type MgF2 at extended pressure and temperature ranges, we apply the quasi-harmonic Debye model in which the phononic effects are considered. The P–V relationship and αV dependence of the pressure up to 135GPa at different temperatures, and the V–T relationship and αV dependence of the temperature up to the melting temperature 1500K at different pressures have been obtained.

Thermal properties of bulk polyimides: insights from computer modeling versus experiment

Due to the great importance for many industrial applications it is crucial from the point of view of theoretical description to reproduce thermal properties of thermoplastic polyimides as accurate as possible in order to establish "chemical structure-physical properties" relationships of new materials. In this paper we employ differential scanning calorimetry, dilatometry, and atomistic molecular dynamics (MD) simulations to explore whether the state-of-the-art computer modeling can serve as a precise tool for probing thermal properties of polyimides with highly polar groups. For this purpose the polyimide R-BAPS based on dianhydride 1,3-bis(3',4-dicarboxyphenoxy)benzene (dianhydride R) and diamine 4,4'-bis(4''-aminophenoxy)biphenyl sulphone) (diamine BAPS) was synthesized and extensively studied. Overall, our findings show that the widely used glass-transition temperature Tg evaluated from MD simulations should be employed with great caution for verification of the polyimide computational models against experimental data: in addition to the well-known impact of the cooling rate on the glass-transition temperature, correct definition of Tg requires cooling that starts from very high temperatures (no less than 800 K for considered polyimides) and accurate evaluation of the appropriate cooling rate, otherwise the errors in the measured values of Tg become undefined. In contrast to the glass-transition temperature, the volumetric coefficient of thermal expansion (CTE) does not depend on the cooling rate in the low-temperature domain (T < Tg) so that comparison of computational and experimental values of CTE provides a much safer way for proper validation of the theoretical model when electrostatic interactions are taken into account explicitly. Remarkably, this conclusion is most likely of generic nature: we show that it also holds for the commercial polyimide EXTEM, another polyimide with a similar chemical structure.

P–V–T equation of state of Na-majorite to 21 GPa and 1673 K

The P–V–T equation of state (EoS) for Na-majorite at pressures to 21GPa and temperatures to 1673K was obtained from in situ X-ray diffraction experiments using a Kawai-type multi-anvil apparatus. Analyses of the room-temperature P–V data to a third-order Birch–Murnaghan EoS yielded ambient unit cell volume, V0=1476 (1) (Å3); isothermal bulk modulus, K0,300=181 (9) GPa; and its pressure derivative, K0,300′=4.4 (1.2). When fitting a high-temperature Birch–Murnaghan EoS using entire P–V–T data at a fixed V0=1475.88Å3, K0,300=184 (4) GPa, K0,300′=3.8 (6), (∂K0,T/∂ T)P=−0.023 (5) (GPaK−1), and a=3.17 (16)×10−5K−1, b=0.16 (26)×10−8K−2, where α=a+bT is the volumetric thermal expansion coefficient. Fitting the Mie–Grüneisen–Debye EoS with the present data to Debye temperature fixed at θ0=890K yielded Grüneisen parameter, γ0=1.35 at q=1.0 (fixed). The new data on Na-majorite were compared with the previous data on majorite type garnets. The compression mechanism of majoritic garnets was described in detail. The entire dataset enabled to examine the thermoelastic properties of important mantle garnets and these data will have further applications for modeling P–T conditions in the transition zone of the Earth’s mantle using ultradeep mineral assemblages.

An Equation of State-Based Modeling Approach for Estimating the Partial Molar Volume of Penetrants and Polymers in Binary Mixtures

Partial molar volumes (PMVs) of highly soluble hydrocarbon gases and polymers in macromolecular mixtures have been estimated by using a model-based methodology that utilizes binary gas/polymer sorption data. It has been shown that the PMVs of the penetrants and polymers as well as other volumetric properties (e.g., molar volume per repeating unit and volumetric thermal expansion coefficients) can be accurately calculated over a wide range of temperatures and pressures. The advantages of the proposed methodology are that it relies on available experimental sorption data of gases in polymers and an equation of state, provides an attractive alternative to the more onerous experimental procedures of densimetery and sorptive dilation for obtaining volumetric data of polymeric mixtures, and it can be extended to multicomponent systems.

Determination of the thermal properties of AlB2-type WB2

Thermal expansion coefficient of AlB2-type WB2 was investigated using in-situ x-ray diffraction (XRD) measurements and quasi-harmonic Debye approximation combined with density functional theory (DFT) calculations. The calculated average volumetric thermal expansion coefficient 24.86×10−6K−1 agrees with the experimental value 21.52×10−6K−1 in the temperature range of 298K to 473K. Different linear thermal expansion coefficients along the a (6.04×10−6K−1) and c (9.39×10−6K−1) directions have been found experimentally. This anisotropic behavior is attributed to the different bonding characteristics along the two directions. A Lindemann-like melting rule has been found for AlB2-type MB2 (M=Ti, Zr, V, Nb, Ta, Cr, Mo and Mn), and the melting point of AlB2-type WB2 has been estimated about 2833.80±18.4K according to this rule. Furthermore, the temperature and pressure dependence of thermal expansion and heat capacity is also studied. To our knowledge, it is the first time to investigate the thermal properties of AlB2-type WB2.

Negative thermal expansion in transversely isotropic space frame trusses

The negative thermal expansion (NTE) of a type of space frame structure is investigated herein. On the basis of a space frame structure consisting of tetrahedral representative volume elements, a volumetric thermal strain and a volumetric coefficient of thermal expansion (CTE) models are developed in this paper. The NTE trusses developed herein exhibit a special case of anisotropy known as transverse isotropy. This is achieved by using two types of rod materials, each for the three apex rods and the three base rods. From these models, the conditions for attaining negative volumetric strain and negative coefficients of volumetric expansion due to change in temperature are established. Two definitions of NTE are given herein: (a) overall NTE and (b) incremental NTE. Based on these two definitions of NTE, the conditions that lead to (i) definite NTE and (ii) selective NTE are established. Plotted results reveal a trend in which the extent of negative thermal expansion is increased for lower apex‐to‐base rod length and CTE ratios, and higher base rod CTE.

Crystal structure, thermal expansion and electrical properties of GdCo0.67Ga1.33 compound

A new ternary compound GdCo0.67Ga1.33 was synthesized and its crystal structure was determined by the Rietveld refinement of X-ray powder diffraction data. This compound crystallizes in the orthorhombic, space group Imma (No. 74) with the CeCu2 structure type, and a=0.43625(2)nm, b=0.70935(3)nm, c=0.75705(4)nm, Z=4 and Dcalc=8.207g/cm3. The thermal expansion of GdCo0.67Ga1.33 was studied by high temperature powder X-ray diffraction technique in the temperature range of 301–598K. The volumetric coefficient of thermal expansion, αV, can be represented by αV(T)=4.73×10−6+8.45×10−8T. The Debye temperature of GdCo0.67Ga1.33 is calculated to be ΘD=261.6K. The electrical properties of this compound were measured between 5 and 300K. Temperature variations of electrical resistivity suggest that magnetic ordering occurs at low temperature. The residual resistivity ratio RRR of the compound is about 1.2.

Stabilizing the triclinic structure of Mn2V2O7 via isovalent cationic substitution

The thermal expansion of Mn2V2O7 in the temperature range of −190 to 1030°C is studied. The volumetric thermal expansion coefficients for triclinic (α) and monoclinic (β) modifications are 2.57 × 10−5 and 3.86 × 10−5 1/deg, respectively. It is shown that as the Ni2+ concentration in Mn2−2xNi2xV2O7 rises, the point of the α → β phase transition point moves from room temperature for Mn2V2O7 to 155 ° 5°C for Mn1.46Ni0.54V2O7 (27 mol % Ni2V2O7).

Effect of carbide powder characteristics on the PVT behavior of powder injection molding compounds

Effect of powder concentration and particle size distribution of highly filled cemented carbide compounds on their pressure–volume–temperature (PVT) characteristics and thermal properties was investigated. PVT data of compounds containing up to 50 vol.% of powder evaluated on a high-pressure mercury dilatometer reveals that the pressure influences both detected phase transitions, but it causes a different effect on the melting and crystallization of the material only for the higher transition (corresponding to binder components with melting temperatures 100 and 107 °C). The discrepancies in specific volumes at an applied pressure diminish with increasing powder content, whereas melting temperatures – derived from differential scanning calorimetry – remain unaffected. Volumetric thermal expansion coefficient and compressibility are linearly and exponentially, respectively, dependent on pressure. Further, the variance in the particle size distributions of carbide compounds resulted in shifts in both volumetric thermal expansion coefficients and compressibility values.

Thermo-optical properties of uniaxial NaT(XO4)2 laser host crystals (where T = Y, La, Gd or Bi, and X = W or Mo)

Thermo-optic coefficients dn o/dT and dn e/dT were measured in tetragonal double tungstate and double molybdate crystals NaT(XO4)2 (where T = Y, La, Gd or Bi and X = W or Mo) by a laser beam deviation method in the spectral range 0.4–1.1 μm. Thermal expansion coefficients in the directions of a and c crystallographic axes were also measured. Analytical expressions for thermo-optic dispersion formulas were derived as series in 1/λ 2. All dn/dT values for NaT(XO4)2 crystals were found to be negative. Their absolute values satisfy the relation |dn e/dT| > |dn o/dT| for crystals without Bi and |dn o/dT| > |dn e/dT| for crystals with Bi. A clear tendency for dn/dT values to decrease with the increase of the volumetric thermal expansion coefficient α vol of the crystal was observed. This is related with dominant contribution of volumetric thermal expansion effect to the temperature dependence of the refractive index. Thermal coefficients of the optical path W = dn/dT + (n − 1)α T governing thermal lensing effect were calculated for different light propagation directions and polarizations as well as crystal athermal directions.