Thermal Expansion Alpha Research Articles

The thermodynamical response functions and the origin of the anomalous behavior of liquid water

The density maximum of water dominates the thermodynamics of the system under ambient conditions, is strongly P-dependent, and disappears at a crossover pressure P(cross) approximately 1.8 kbar. We study this variable across a wide area of the T-P phase diagram. We consider old and new data of both the isothermal compressibility K(T)(T, P), the pressure constant specific heat C(P)(T) and the coefficient of thermal expansion alpha(P) (T, P). We observe that K(T)(T) shows a minimum at T* approximately 315 +/- 5 K for all of the studied pressures, whereas, at the same temperature, C(P)(T) has the minimal variation as a function of P in the interval 1 bar-4 kbar. We find the behavior of alpha(P) also to be surprising: all the alpha(P)(T) curves measured at different P cross at T*. The experimental data show a "singular and universal expansivity point" at T* approximately 315 K and alpha(P)(T*) = 0.44 10(-3) K(-1). Unlike other water singularities, we find this temperature to be thermodynamically consistent in the relationship connecting the three response functions. By considering also the P-T behavior of the self-diffusion coefficient D(S) and of the NMR proton chemical shift delta we have the information that at T* the water local order points out, with decreasing T, the crossover from a normal fluid to the anomalous and complex liquid characterized by the many anomalies.

Universal signatures of the metamagnetic quantum critical endpoint: Application toCeRu2Si2

A quantum critical endpoint related to a metamagnetic transition causes distinct signatures in the thermodynamic quantities of a compound. We argue that, irrespective of the microscopic details of the considered material, the diverging differential susceptibility combined with the Ising symmetry of the endpoint give rise to a number of characteristic metamagnetic phenomena. In the presence of a magnetoelastic coupling, one finds a correspondence of susceptibility, magnetostriction and compressibility and, as a result, a pronounced crystal softening, a diverging Grueneisen parameter, a sign change of thermal expansion alpha(H), and a minimum in the specific heat coefficient gamma(H). We illustrate these signatures and their relation on the metamagnetic crossover at 8 T in the prototypical heavy-fermion system CeRu2Si2.

Analysis of thermal expansivity of solids at extreme compression

Thermodynamics of solids in the limit of innite pressure formulated by Stacey reveals that the thermal expansivity (alpha) of solids tends to zero at innite pressure. The earlier models for the volume dependence of thermal expansivity do not satisfy the innite pressure behaviour of thermal expansivity. The expressions for the volume dependence of the isothermal Anderson- Gr¤ uneisen parameter (delta T) considered in the derivation of earlier formulations for alpha (V) have been found to be inadequate. A formulation for the volume dependence of delta T is presented here which is similar to the model due to Burakovsky and Preston for the volume dependence of the Gr¤ uneisen parameter. The new formulation for alpha (V) reveals that delta T innity must be greater than zero for satisfying the thermodynamic result according to which alpha tends to zero at innite pressure. It is found that our model ts well the experimental data on thermal expansivity alpha (V) for hcp iron corresponding to a wide range of pressures (0n360 GPa).

Thermodynamic response functions of fluids: A microscopic approach based on NpT Monte Carlo

On the basis of NpT Monte Carlo simulations, a detailed analysis on the microscopic origins of some specific features of thermodynamic response functions of fluids is performed. Specifically, the residual isobaric heat capacity C(p) (res), the isobaric thermal expansivity alpha(p), and the isothermal compressibility kappa(T) for Lennard-Jones methane and optimized potential for liquid simulations (OPLS) methanol have been determined via standard techniques. For the former, data along the liquid, gas, and supercritical regions are presented, while a wide temperature range at a single supercritical pressure is covered for the latter. They have been obtained by computing the various pairwise fluctuations contributing to each property. Attention is mainly focused on isothermal and isobaric maxima found for both C(p) (res) and alpha(p), which have been rationalized at a molecular level using qualitative arguments. It is encountered that maxima emerge as a natural consequence of the destruction of fluid structure as temperature is increased or as pressure is decreased. The results for Lennard-Jones methane reveal the competition of energetic and volumetric effects, while those for OPLS methanol evidence that hydrogen-bonding is dominant as energetic effects are concerned. Further discussion on previous results and alternative approaches using equations of state as well as on closely related topics such as "maxima and critical phenomena" is included.

Dimensional Crossover of Quantum Critical Behavior inCeCoIn5

The nature of quantum criticality in CeCoIn5 is studied by low-temperature thermal expansion alpha(T). At the field-induced quantum critical point at H = 5 T a crossover scale T* approximately 0.3 K is observed, separating alpha(T)/T proportional, variant T(-1) from a weaker T(-1/2) divergence. We ascribe this change to a crossover in the dimensionality of the critical fluctuations which may be coupled to a change from unconventional to conventional quantum criticality. Disorder, whose effect on quantum criticality is studied in CeCoIn(5-x)Sn(x) (0 < or = x < or = 0.18), shifts T* towards higher temperatures.

Thermal expansion between 480 and 940 C of Cr-doped mullites derived from single-phase precursors

The lattice parameters were determined by in situ X-ray powder diffraction between room temperature (RT) and 940 ^oC for the Cr-doped mullite derived from single-phase precursors containing up to 9.60 wt% Cr_2O_3. Mullites were orthorhombic, space group Pbam. Chromium doping caused the increase in unit-cell parameters. Strongest expansion caused by Cr incorporation into mullite was noticed along the c-axis followed by a and b. In temperature region from 480 to 940 ^oC the lattice parameters a, b, and c expanded almost linearly, and the linear coefficients of thermal expansion along crystallographic axes were calculated for this region. Strongest expansion caused by the thermal treatment was noticed along the b-axis followed by c and a. The linear thermal expansion coefficients were also dependent on the chromium content in mullite. All thermal expansion coefficients, alpha(a), alpha(b) and alpha(c), exhibited minima for 6.97 wt% Cr_2O_3.

Elastic and thermodynamic properties of c-BN from first-principles calculations

The elastic constants and thermodynamic properties of c-BN are calculated using the first-principles plane wave method with the relativistic analytic pseudopotential of the Hartwigen, Goedecker and Hutter (HGH) type in the frame of local density approximation and using the quasi-harmonic Debye model, separately. Moreover, the dependences of the normalized volume V/V-0 on pressure P, as well as the bulk modulus B, the thermal expansion alpha, and the heat capacity C-V on pressure P and temperature T are also successfully obtained.

Structural and thermodynamic properties of AlB2compound

We employ a first-principles plane wave method with the relativistic analytic pseudopotential of Hartwigsen, Goedecker and Hutter (HGH) scheme in the frame of DFT to calculate the equilibrium lattice parameters and the thermodynamic properties of AlB2 compound with hcp structure. The obtained lattice parameters are in good agreement with the available experimental data and those calculated by others. Through the quasi-harmonic Debye model, obtained successfully are the dependences of the normalized lattice parameters a/a(0) and c/c(0) on pressure P, the normalized primitive cell volume V/V-0 on pressure P, the variation of the thermal expansion alpha with pressure P and temperature T, as well as the Debye temperature circle minus(D) and the heat capacity C-V on pressure P and temperature T.

Critical linear thermal expansion in the smectic-Aphase near the nematic-smectic phase transition

Recent high-resolution x-ray investigations of the smectic- A (SmA) phase near the nematic-to-SmA transition provide information about the critical behavior of the linear thermal expansion coefficient alpha// parallel to the director. Combining such data with available volume thermal expansion alpha(V) data yields the in-plane linear expansion coefficient alpha(perpendicular) . The critical behaviors of alpha// and alpha(perpendicular) are the same as those for alpha(V) and the heat capacity Cp. However, for any given liquid crystal, alpha//(crit) and alpha(perpendicular)(crit) differ in sign. Furthermore, the quantity alpha// (crit) is positive for SmAd partial bilayer smectics, while it is negative for nonpolar SmAm monomeric smectics. This feature is discussed in terms of the molecular structural aspects of these smectic phases.

Temperature Dependent X‐Ray Diffraction Study on Gd5Sn4 Compound.

AbstractFor Abstract see ChemInform Abstract in Full Text.

Universally diverging Grüneisen parameter and the magnetocaloric effect close to quantum critical points.

At a generic quantum critical point, the thermal expansion alpha is more singular than the specific heat c(p). Consequently, the "Grüneisen ratio," Gamma=alpha/c(p), diverges. When scaling applies, Gamma approximately T(-1/(nu z)) at the critical pressure p=p(c), providing a means to measure the scaling dimension of the most relevant operator that pressure couples to; in the alternative limit T-->0 and p not equal p(c), Gamma approximately 1/(p-p(c)) with a prefactor that is, up to the molar volume, a simple universal combination of critical exponents. For a magnetic-field driven transition, similar relations hold for the magnetocaloric effect (1/T) partial differential T/ partial differential H|(S). Finally, we determine the corrections to scaling in a class of metallic quantum critical points.

AXISYMMETRICAL THERMOELASTIC BEHAVIOR FOR A NONHOMOGENEOUS MEDIUM WITH A PENNY-SHAPED CRACK

Axisymmetrical thermoelastic singular stress problems for a nonhomogeneous infinite body and thick plate are considered, theoretically. It is assumed that the nonhomoge neous material properties of shear modulus of elasticity G, the coefficient of linear thermal expansion alpha, and the thermal conductivity lambda vary with the axial coordinate z according to the power product form. As an analytical model, a nonhomogeneous infinite body and thick plate with a penny-shaped crack subject to an arbitrarily distributed axisymmetrical heat supply on its crack surface are considered. The distributions of the displacement component and the stress component are analyzed using the fundamental equation system proposed in our previous paper, and the thermal stress intensity factor at a crack tip is evaluated theoretically. Numerical calculations are carried out for several cases taking into account the variety of nonhomogeneity of G, alpha, and lambda. Thereafter, the distributions of the displacements, stresses, and thermal stress intensity factor at the crack tip are shown graphically, and the influence of these nonhomogeneous material properties on the thermoelastic field and the thermal stress intensity factor is discussed.

In situ X-ray diffraction study of enstatite up to 12 GPa and 1473 K and equations of state

Crystal structures and phase transitions of enstatite (MgSiO 3 ) were studied by in situ X-ray diffraction experiments using synchrotron radiation and a multi-anvil high-pressure apparatus at pressures to 12 GPa and temperatures to 1473 K. Low clinoenstatite with space group P2 1 /c transforms to high-pressure C2/c clinoenstatite at high pressures and high temperatures, accompanied by a volume reduction of about 2.5%. The beta angle of this high-pressure C2/c phase ranges from 101.4 degrees to 101.7 degrees , shows almost no variation with pressure and temperature, and is about 8 degrees smaller than that of the high-temperature C2/c phase previously reported. This confirms the suggestion (Hugh-Jones et al. 1994) that these two clinoenstatite phases differ at high pressures and high temperatures. The pressure-volume-temperature data for P2 1 /c and high pressure C2/c clinoenstatite were fit to room-temperature third-order Birch-Murnahan equations of state (EOS) using the parameters: volume of V = 415.4 (5) Aa 3 , isothermal bulk modulus of K = 108.5 (6.4) GPa, and its pressure derivative of K' = 4.5 (1.3) for the P2 1 /c phase, and V = 405.1 (1.7) Aa 3 , K = 106.4 (17.4) GPa, and K' = 5.4 (2.7) for the C2/c phase. These values are at ambient conditions. For the C2/c phase, we determined the high-temperature EOS, expressed as P = 3/2 K T [V T /V) (super 7/3) -(V T /V) (super 5/3) ] {1-3/4 (4-K' T )[(V T /V) (super 2/3) -1]}, where K T = K +(delta K T /delta T) P (T-300), K' T = K' , V T = V [exp( T Sigma 300 alpha (T)dT)], where thermal expansivity alpha (T) is a + a 1 T. The parameters are V = 405.0 (2.6) Aa 3 , K = 106.9 (25.9) GPa, K' = 5.3 (3.9), a = 2.01 (44)X10 (super -5) K (super -1) , a 1 = 2.10 (1.1)X10 (super -8) K (super -2) , and (delta K T /delta T ) P = -0.021 (10) GPa/K. Although the K values are nearly the same with those of previous studies for both the P2 1 /c and C2/c phases, the K' values are slightly smaller.

DERIVATION OF SYSTEMS OF FUNDAMENTAL EQUATIONS FOR A THREE-DIMENSIONAL THERMOELASTIC FIELD WITH NONHOMOGENEOUS MATERIAL PROPERTIES AND ITS APPLICATION TO A SEMI-INFINITE BODY

A method of analytical development of three-dimensional thermoelastic problems for a medium with nonhomogeneous material properties is developed in this article. Assuming that the shear modulus elasticity G, the thermal conductivity lambda, and the coefficient of linear thermal expansion alpha vary with the power product form of axial coordinate variable z and introducing two kinds of displacement functions and the thermoelastic displacement function, the system of fundamental differential equations for such a three-dimensional field is established. As an illustrative example, we consider the thermoelastic problem of a semi-infinite body. The three-dimensional temperature solution in a steady state is obtained and the associated components of thermal displacement and stress are evaluated theoretically. Numerical calculations are carried out for several cases taking into account the variety of the nonhomogeneous material properties of G, lambda, and alpha, and these results are shown graphically.

Mantle values of thermal conductivity and the geotherm from phonon lifetimes

A model for thermal conductivity kappa, based on phonon lifetimes obtained from infrared reflectivity, replicates experimental data at ambient conditions. The pressure and absolute temperature dependences of transport properties are accurately obtained from the Gruneisen parameter gammaTh, bulk modulus KT, and thermal expansivity alpha: The lattice contribution kappalat equals kappa298(298/T)a exp[-(4gammaTh + 1/3) integral298Talpha(theta)dtheta] with a = 0.33 for silicates (or 0.9 for MgO), and partial differential[ln(kappalat)]/ partial differentialP = (1/3 + 4gammaTh)/KT. The smaller, pressure-independent radiative contribution kapparad equals 0.0175 - 0.0001037T + (2.245T2/10(7)) - (3.407T3/10(11)), in units of watts per meter-kelvin, if Fe2+ is present. The resulting lithospheric geotherm is steep. Consequently, the mantle geotherm is hot if the low-velocity zone is anhydrous, but cold if hydrated.

Vibrational anharmonicity of oxide and fluoride scheelites

Lattice parameter measurements of LiYF4 and LiY0.5Tb0.5F4 made between -100 degrees C and +550 degrees C show that the anisotropy of the thermal expansion ( alpha 11> alpha 33) of these scheelite structure fluorides has the opposite sense to oxide scheelites ( alpha 33> alpha 11). This, together with corresponding differences found between the anisotropy of linear compressibility and elastic stiffness constants, can be understood if the oxides, but not the fluorides, are considered to show a tendency towards layer-like behaviour. Pulse echo overlap measurements of ultrasonic wave velocities have been used to obtain the hydrostatic pressure derivatives delta CIJ/ delta P of the elastic constants of CaWO4. Since the acoustic symmetry axes do not shift appreciably with pressure, the pressure derivatives delta CIJ/ delta P, like the elastic constants CIJ themselves, can be transformed (with useful simplification) to reference bases comprised of acoustic symmetry axes (( kappa and kappa + pi /2) or ( gamma and gamma + pi /2)) and the Z axis. The acoustic mode Gruneisen gammas in the long-wavelength limit obtained for CaWO4 show that shear acoustic mode softening occurs under pressure along the gamma and gamma + pi /2 acoustic symmetry axes, in contrast to that for LiYF4 and LiY0.5Tb0.5F4 which takes place along the other type ( kappa and kappa + pi /2) of acoustic symmetry axes in the (001) plane.

Bond-correlated percolation model and the unusual behaviour of supercooled water

It is shown that the partition function of an interaction Hamiltonian for the hydrogen bonding in water molecules may be expressed as the generating function of a bond-correlated percolation model with a bond probability p depending on the hydrogen-bond strength and the temperature T. Assuming that the molecules with larger number of active bonds have a larger volume per molecule, one may show that, for temperatures near but higher than the temperature of maximum bond fluctuations, the isothermal compressibility KT and the constant pressure specific heat Cp increase, while the thermal expansivity alpha p becomes more negative, as T decreases. Other unusual behaviour of supercooled water can also be explained by this model.

An electrical method for the measurement of thermal expansion of thin films

A two-terminal capacitance method has been devised to measure the coefficient of linear thermal expansion ( alpha ) of thin films as conventional methods are unsuitable. The formula to evaluate the observed value of the thermal expansion coefficient ( alpha obs) has been obtained and the relevant correction factor has been incorporated in the final formula alpha true= alpha obs+ alpha el where alpha el and alpha true are the thermal expansion coefficients of electrode film and sample thin film respectively. The design of the dilatometric cell, the preparation of the thin-film specimen and the electrode film configuration are described. The change in capacitance with temperature of the vacuum capacitor, where the specimen film is the spacer, is used to evaluate alpha obs. This technique has been standardised using thin platelets ( approximately 100 mu m) of a single crystal of NaCl. The other considerations which are important for the precision of this measurement technique are also discussed.

Temperature dependence of tetragonal distortion and thermal expansion of copper indium selenide

Accurate lattice parameters of chalcopyrite semiconductor copper indium selenide (CuInSe2) have been determined as a function of temperature by X-ray powder diffraction method in the temperature range 28 to 566 degrees C. The data have been used to evaluate the coefficients of thermal expansion alpha perpendicular to and alpha /sub ///, perpendicular and parallel to the principal axis, at various temperatures by a graphical method. The average thermal expansion coefficients, alpha perpendicular to and alpha /sub ///, thus evaluated in the temperature range 28 to 566 degrees C are found to be 10.32*10-6 K-1 and 7.89*10-6 K-1. This result indicates an 'increase' in tetragonal distortion (2-c/a) with temperature. An attempt is made to explain the temperature dependence of the anisotropic thermal expansion and the tetragonal distortion of this compound, in terms of the thermal expansion of the I-VI and II-VI bonds.

The temperature dependence of lattice parameter, thermal expansion, Gruneisen parameter and lattice vibrational frequencies of barium nitrate

The lattice parameter aT of barium nitrate has been measured in the temperature range 260 to 767K using a high-temperature X-ray diffractometer and a 10 cm diameter symmetrically focusing back-reflection camera, aT in AA is related to the temperature T by aT=8.0790+1.1196*10-4T+5.983*10-8T2. The linear thermal expansivity alpha is calculated by differentiation of aT with respect to T and the values tabulated, together with those of the Gruneisen parameter gamma . The values of alpha and gamma are used to calculate the temperature dependence of the lattice vibrational frequencies which is shown graphically.