Showing papers on "Debye model published in 2012"

Quantum effect on thermally activated glide of dislocations.

Abstract: Crystal plasticity involves the motion of dislocations under stress. So far, atomistic simulations of this process have predicted Peierls stresses, the stress needed to overcome the crystal resistance in the absence of thermal fluctuations, of more than twice the experimental values, a discrepancy best-known in body-centred cubic crystals. Here we show that a large contribution arises from the crystal zero-point vibrations, which ease dislocation motion below typically half the Debye temperature. Using Wigner's quantum transition state theory in atomistic models of crystals, we found a large decrease of the kink-pair formation enthalpy due to the quantization of the crystal vibrational modes. Consequently, the flow stress predicted by Orowan's law is strongly reduced when compared with its classical approximation and in much closer agreement with experiments. This work advocates that quantum mechanics should be accounted for in simulations of materials and not only at very low temperatures or in light-atom systems.

Electronic structural, elastic properties and thermodynamics of Mg17Al12, Mg2Si and Al2Y phases from first-principles calculations

Abstract: Electronic structures, elastic properties and thermal stabilities of Mg17Al12, Mg2Si and Al2Y have been determined from first-principle calculations. The calculated heats of formation and cohesive energies show that Al2Y has the strongest alloying ability and structural stability. The brittle behavior and structural stability mechanism is also explained through the electronic structures of these intermetallic compounds. The elastic constants are calculated, the bulk moduli, shear moduli, Young's moduli and Poisson ratio value are derived, the brittleness and plasticity of these phases are discussed. Gibbs free energy, Debye temperature and heat capacity are calculated and discussed.

Seeing Is Believing: Weak Phonon Scattering from Nanostructures in Alkali Metal-Doped Lead Telluride

Abstract: Alkali metal doped p-type PbTe is a canonical thermoelectric material studied extensively for heat-to-power generation at high temperature. Most reports have indirectly indicated alkali metals to be conventional with PbTe forming homogeneous solid solutions. Using transmission electron microscopy (TEM), we show the presence of platelet-like nanostructures in these systems containing Na and/or K. By combining further TEM and semiclassical theoretical calculations based on a modified Debye model of the lattice thermal conductivity, we explain the lack of efficacy of these nanostructures for strong phonon scattering. These findings are important in the understanding of alkali metals as carriers in p-type lead chalcogenides. These results also underscore that not all nanostructures favorably scatter phonons in a matrix; an insight that may help in further improvements of the power factor and the overall figure of merit.

Lattice dynamics, thermodynamics, and bonding strength of lithium-ion battery materials LiMPO4 (M = Mn, Fe, Co, and Ni): a comparative first-principles study

Abstract: Gaps in our knowledge of phonon and thermodynamics still remain despite significant research efforts on cathode materials LiMPO4 (M = Mn, Fe, Co, and Ni) for rechargeable Li-ion batteries. Here, we employ a mixed-space approach of first-principles phonon calculations to probe the lattice dynamics including LO–TO splitting (longitudinal and transverse optical phonon splitting), quantitative bonding strength between atoms, and finite-temperature thermodynamic properties of LiMPO4. In order to take into account the strong on-site Coulomb interaction (U) presented in transition metals, the GGA + U calculations are used for LiMPO4. It is found that the oxygen–phosphorus (O–P) bond with the minimal bond length is extremely strong, which is roughly five times larger than the second strongest O–O bond. The atom P-containing bonds are apparently stronger than the corresponding atom O-containing bonds, indicating the stability of LiMPO4 is mainly due to atom P. It is observed that the equilibrium volume of LiMPO4 decreases from Mn, Fe, Co, to Ni, and the bulk modulus, zero-point vibrational energy, and Debye temperature increase. Phonon results indicate that the largest vibrational contribution to Gibbs energy is for LiMnPO4, followed by LiFePO4, LiCoPO4, and then LiNiPO4, due to the decreasing trend of phonon densities of state at the low frequency region of LiMPO4. Computed phonon and thermodynamic properties of LiMPO4 are in close accord with available experiments, and provide knowledge to be validated experimentally.

A study of energy band gap versus temperature for Cu2ZnSnS4 thin films

Abstract: The temperature dependent band gap energy of Cu2ZnSnS4 thin film was studied in the temperature range of 77–410 K. Various relevant parameters, which explain the temperature variation of the fundamental band gap, have been calculated using empirical and semi-empirical models. Amongst the models evaluated, the Varshni and Passler models show the best agreement with experimental data in the middle temperature range. However, the Bose–Einstein model fits reasonably well over the entire temperature range evaluated. The calculated fitting parameters are in good agreement with the estimated value of the Debye temperature calculated using the Madelung–Einstein approximation and the Hailing method.

Efficient energy transfer in light-harvesting systems: Quantum-classical comparison, flux network, and robustness analysis

Abstract: Following the calculation of optimal energy transfer in thermal environment in our first paper [J. L. Wu, F. Liu, Y. Shen, J. S. Cao, and R. J. Silbey, New J. Phys. 12, 105012 (2010)], full quantum dynamics and leading-order "classical" hopping kinetics are compared in the seven-site Fenna-Matthews-Olson (FMO) protein complex. The difference between these two dynamic descriptions is due to higher-order quantum corrections. Two thermal bath models, classical white noise (the Haken-Strobl-Reineker (HSR) model) and quantum Debye model, are considered. In the seven-site FMO model, we observe that higher-order corrections lead to negligible changes in the trapping time or in energy transfer efficiency around the optimal and physiological conditions (2% in the HSR model and 0.1% in the quantum Debye model for the initial site at BChl 1). However, using the concept of integrated flux, we can identify significant differences in branching probabilities of the energy transfer network between hopping kinetics and quantum dynamics (26% in the HSR model and 32% in the quantum Debye model for the initial site at BChl 1). This observation indicates that the quantum coherence can significantly change the distribution of energy transfer pathways in the flux network with the efficiency nearly the same. The quantum-classical comparison of the average trapping time with the removal of the bottleneck site, BChl 4, demonstrates the robustness of the efficient energy transfer by the mechanism of multi-site quantum coherence. To reconcile with the latest eight-site FMO model which is also investigated in the third paper [J. Moix, J. L. Wu, P. F. Huo, D. F. Coker, and J. S. Cao, J. Phys. Chem. Lett. 2, 3045 (2011)], the quantum-classical comparison with the flux network analysis is summarized in Appendix C. The eight-site FMO model yields similar trapping time and network structure as the seven-site FMO model but leads to a more disperse distribution of energy transfer pathways.

Raman spectroscopic determination of the length, strength, compressibility, Debye temperature, elasticity, and force constant of the C-C bond in graphene

Abstract: From the perspective of bond relaxation and bond vibration, we have formulated the Raman phonon relaxation of graphene, under the stimuli of the number-of-layers, the uni-axial strain, the pressure, and the temperature, in terms of the response of the length and strength of the representative bond of the entire specimen to the applied stimuli. Theoretical unification of the measurements clarifies that: (i) the opposite trends of the Raman shifts, which are due to the number-of-layers reduction, of the G-peak shift and arises from the vibration of a pair of atoms, while the D- and the 2D-peak shifts involve the z-neighbor of a specific atom; (ii) the tensile strain-induced phonon softening and phonon-band splitting arise from the asymmetric response of the C3v bond geometry to the C2v uni-axial bond elongation; (iii) the thermal softening of the phonons originates from bond expansion and weakening; and (iv) the pressure stiffening of the phonons results from bond compression and work hardening. Reproduction of the measurements has led to quantitative information about the referential frequencies from which the Raman frequencies shift as well as the length, energy, force constant, Debye temperature, compressibility and elastic modulus of the C‐C bond in graphene, which is of instrumental importance in the understanding of the unusual behavior of graphene.

Lattice constants from semilocal density functionals with zero-point phonon correction

Abstract: In a standard Kohn-Sham density functional calculation, the total energy of a crystal at zero temperature is evaluated for a perfect static lattice of nuclei and minimized with respect to the lattice constant. Sometimes a zero-point vibrational energy, whose anharmonicity expands the minimizing or equilibrium lattice constant, is included in the calculation or (as here) is used to correct the experimental reference value for the lattice constant to that for a static lattice. A simple model for this correction, based on the Debye and Dugdale-MacDonald approximations, requires as input only readily available parameters of the equation of state, plus the experimental Debye temperature. However, particularly because of the rough Dugdale-MacDonald estimation of Gr\"uneisen parameters for diatomic solids, this simple model is found to overestimate the correction by about a factor of two for some solids in diamond and zinc-blende structures. Using the quasiharmonic phonon frequencies calculated from density functional perturbation theory gives a more accurate zero-point anharmonic expansion (ZPAE) correction. However, the error statistics for the lattice constants of various semilocal density functionals for the exchange--correlation energy are little changed by improving the ZPAE correction. The Perdew-Burke-Ernzerhof generalized gradient approximation (GGA) for solids and the revised Tao-Perdew-Staroverov-Scuseria (revTPSS) meta-GGA, the latter of which is implemented self-consistently here in the band-structure program BAND and applied to a test set of 58 solids, remain the most accurate of the functionals tested, with MAREs below 0.7$%$ for the lattice constants. The most positive and most negative revTPSS relative errors tend to occur for solids for which full nonlocality (missing from revTPSS) may be important.

First-principles study of the structural, elastic, electronic, optical, and vibrational properties of intermetallic Pd 2 Ga

Abstract: The structural, elastic, electronic, optical, and vibrational properties of the orthorhombic Pd2Ga compound are investigated using the norm-conserving pseudopotentials within the local density approximation in the frame of density functional theory. The calculated lattice parameters have been compared with the experimental values and found to be in good agreement with these results. The second-order elastic constants and the other relevant quantities, such as the Young's modulus, shear modulus, Poisson's ratio, anisotropy factor, sound velocity, and Debye temperature, have been calculated. It is shown that this compound is mechanically stable after analysing the calculated elastic constants. Furthermore, the real and imaginary parts of the dielectric function and the optical constants, such as the optical dielectric constant and the effective number of electrons per unit cell, are calculated and presented. The phonon dispersion curves are derived using the direct method. The present results demonstrate that this compound is dynamically stable.

Modeling of Thermoelectric Properties of MagnesiumSilicide (Mg2Si)

Abstract: Thermoelectric (TE) materials based on alloys of magnesium (Mg) and silicon (Si) possess favorable properties such as high electrical conductivity and low thermal conductivity. Additionally, their abundance in nature and lack of toxicity make them even more attractive. To better understand the electronic transport and thermal characteristics of bulk magnesium silicide (Mg2Si), we solve the multiband Boltzmann transport equation within the relaxation-time approximation to calculate the TE properties of n-type and p-type Mg2Si. The dominant scattering mechanisms due to acoustic phonons and ionized impurities were accounted for in the calculations. The Debye model was used to calculate the lattice thermal conductivity. A unique set of semiempirical material parameters was obtained for both n-type and p-type materials through simulation testing. The model was optimized to fit different sets of experimental data from recently reported literature. The model shows consistent agreement with experimental characteristics for both n-type and p-type Mg2Si versus temperature and doping concentration. A systematic study of the effect of dopant concentration on the electrical and thermal conductivity of Mg2Si was also performed. The model predicts a maximum dimensionless figure of merit of about 0.8 when the doping concentration is increased to approximately 1020 cm–3 for both n-type and p-type devices.

Electron- and phonon-mediated ultrafast magnetization dynamics of Gd(0001)

Abstract: Here we report on the ultrafast magnetization dynamics of Gd(0001), which we investigated as a function of equilibrium temperature by employing the femtosecond time-resolved magneto-optical Kerr effect (MOKE) and modeling by the Landau-Lifshitz-Bloch equation in combination with the two-temperature model. Based on the observed temperature-dependent transient MOKE signals, we separate the magnetization dynamics into two regimes at delays of (i) a few picoseconds and (ii) several 100 femtoseconds. In the picosecond regime, the demagnetization time determined from the experiment increases with temperature from 0.8 ps at 50 K to 1.5 ps at 280 K. A successful description of this observation was achieved by considering the dynamics of the $4f$ spin system coupled to $5d$ conduction electrons within two coupling mechanisms: (a) through electronic scattering and (b) spin-flip scattering mediated by phonons. We conclude that at temperatures below the Debye temperature, a hot electron-mediated process describes the experimentally found demagnetization times of $\ensuremath{\approx}$$0.8$ ps well. At higher temperatures phonon-mediated processes have to be included to explain the 2 times longer demagnetization time. In the second regime at time delays of few 100 fs we find an increase in the MOKE rotation and ellipticity at 50 K at delays before demagnetization sets in. Above 50 K the transient changes in rotation and ellipticity are of opposite sign. We explain this behavior by competing magnetic and nonmagnetic contributions in the transient MOKE signals at these delays directly after optical excitation when excited phonons do not yet facilitate angular momentum transfer to the lattice.

Transport properties of HfO 2 − x based resistive-switching memories

Abstract: Transport measurements of both the dc and the low-frequency ac are performed on Pt/HfO2−x/TiN resistiveswitching memory cells at various temperatures. The conductance of the pristine cells has a power law ω S T N relationship with temperature and frequency. To account for the much larger conductance of both the high resistance states (HRSs) and the low resistance states (LRSs), an additional conductance term associated with oxygen vacancy filaments is added, which is independent of the cross-sectional area of the memory cell. This additional component of conductance in a HRS is frequency independent but temperature dependent, showing the small polaron originated transport, with an activation energy of 50 (2.1) meV at temperatures above (below) half of the Debye temperature, which agrees with the analysis of the electric field dependence data. The frequencyand temperature-dependent conduction of HRSs indicate the existence of polarization centers which facilitate the transport and make HfO2−x highly polarizable. However, the additional conductance term associated with filaments in LRS, of an order of ∼10 5 Sm −1 , exhibits a weak metallic behavior in temperature-dependent measurements. Properties of aligned oxygen vacancy chains on the (¯ surface are calculated byfirst-principles simulation. Through analysis of the partial density of states and spatial distribution of the wave function of impurity states generated by oxygen vacancies, this weak metallic behavior is attributed to the delocalization of the impurity band associated with aligned oxygen vacancies.

Mechanical relaxation in a Zr-based bulk metallic glass: Analysis based on physical models

Abstract: The mechanical relaxation behavior in a Zr55Cu30Ni5Al10 bulk metallic glass is investigated by dynamic mechanical analysis in both temperature and frequency domains. Master curves can be obtained for the storage modulus G′ and for the loss modulus G′′, confirming the validity of the time-temperature superposition principle. Different models are discussed to describe the main (α) relaxation, e.g., Debye model, Havriliak-Negami (HN) model, Kohlrausch-Williams-Watt (KWW) model, and quasi-point defects (QPDs) model. The main relaxation in bulk metallic glass cannot be described using a single relaxation time. The HN model, the KWW model, and the QPD theory can be used to fit the data of mechanical spectroscopy experiments. However, unlike the HN model and the KWW model, some physical parameters are introduced in QPD model, i.e., atomic mobility and correlation factor, giving, therefore, a new physical approach to understand the mechanical relaxation in bulk metallic glasses.

Raman spectroscopy determination of the Debye temperature and atomic cohesive energy of CdS, CdSe, Bi2Se3, and Sb2Te3 nanostructures

Abstract: We have formulated the size and temperature dependence of the phonon relaxation dynamics for CdS, CdSe, Bi2Se3, and Sb2Te3 nanostructures based on the framework of bond order–length–strength correlation, core-shell configuration, and local bond averaging approach. The Raman shifts are correlated directly to the identities (nature, order, length, and energy) of the representative bond of the specimen without needing involvement of the Gruneisen mode parameters or considering the processes of phonon decay or multi-phonon resonant scattering. Quantitative information of the Debye temperature, the atomic cohesive energy, the reference frequencies from which the Raman shifts proceed, and the effective coordination numbers of the randomly sized particles, as well as the length and energy of the representative bond, has been obtained. It is clarified that the size-induced phonon softening arises intrinsically from the cohesive weakening of the undercoordinated atoms in the skin up to three atomic layers and the ...

Elastic, electronic and thermodynamic properties of fluoro-perovskite KZnF3 via first-principles calculations

Abstract: The elastic, electronic and thermodynamic properties of fluoro-perovskite KZnF3 have been calculated using the full-potential linearized augmented plane wave (FP-LAPW) method. The exchange-correlation potential is treated with the generalized gradient approximation of Perdew-Burke-Ernzerhof (GGA-PBE). Also, we have used the Engel and Vosko GGA formalism (GGA-EV) to improve the electronic band structure calculations. The calculated structural properties are in good agreement with available experimental and theoretical data. The elastic constants C ij are calculated using the total energy variation with strain technique. The shear modulus, Young’s modulus, Poisson’s ratio and the Lame coefficients for polycrystalline KZnF3 aggregates are estimated in the framework of the Voigt-Reuss-Hill approximations. The ductility behavior of this compound is interpreted via the calculated elastic constants C ij . Electronic and bonding properties are discussed from the calculations of band structure, density of states and electron charge density. The thermodynamic properties are predicted through the quasi-harmonic Debye model, in which the lattice vibrations are taken into account. The variation of bulk modulus, lattice constant, heat capacities and the Debye temperature with pressure and temperature are successfully obtained.

Simultaneous sound velocity and density measurements of NaCl at high temperatures and pressures: Application as a primary pressure standard

Abstract: The elastic compressional (P) and shear (S) wave velocities in NaCl were measured up to 12 GPa at 300 K, and up to 8 GPa at 473 and 673 K, by combining ultrasonic interferometry, in situ synchrotron X-ray diffraction, and X-ray radiographic techniques in a large-volume Kawai-type multi-anvil apparatus. The simultaneously measured sound velocity and density data at 300 K and high pressures up to 12 GPa were corrected to transform the adiabatic values to isothermal values and then used to estimate the 300 K equation of state (EOS) by a least-squares fit to the fourth-order Birch-Murnaghan finite strain equation, without pressure data. For a fixed isothermal bulk modulus K T0 of 23.7 GPa at 0 GPa and 300 K, we obtained the first and the second pressure derivatives of K T0, K ′T0 = 5.14 ± 0.05 and K ″T0 = −0.392 ± 0.021 GPa−1, respectively. A high-temperature and high-pressure EOS of NaCl was then developed using the Mie-Gruneisen relation and the Debye thermal model. To accomplish this, the simultaneously measured sound velocities and densities up to 8 GPa at both 473 and 673 K, as well as previously reported volume thermal expansion data of NaCl at 0 GPa were included in the fit. This resulted in a q parameter of 0.96, while holding the Gruneisen parameter and the Debye temperature, both at 0 GPa and 300 K, fixed at 1.56 and 279 K, respectively. Our EOS model accurately modeled not only the present measured K T data at pressures up to 12 GPa and temperatures between 300 and 673 K, but also the previously reported volume thermal expansion and the temperature dependence of K T, both at 0 GPa. The new temperature-pressure-volume EOS for NaCl, presented here, provides a pressure-independent primary pressure standard at high temperatures and high pressures.

Relaxation of the normal electrical resistivity induced by high-pressure in strongly underdoped YBa2Cu3O7–δ single crystals

Abstract: We investigate the relaxation of the normal electrical resistivity, induced by high-pressure in YBa 2 Cu 3 O 6.45 single crystals. It is determined that the pressure affects to the phase composition of the sample. Under pressure phases with different (but similar) critical temperatures form. It is determined that the application-removal pressure process is completely reversible. Above T c the temperature dependence of the resistivity in the layers' plane at different hydrostatic pressures can be approximated with high accuracy with the scattering of electrons by phonons model. With increasing pressure, the residual resistance is reduced and the contribution of intraband s–s scattering increases. Additionally, the role of the interband s–d scattering and the Debye temperature is enhanced.

First-principle calculations to investigate the elastic and thermodynamic properties of RBRh 3 (R =Sc, y and La) perovskite compounds

Abstract: We have performed first-principle calculations using the full-potential linear augmented plane wave (FP-LAPW) method within density functional theory (DFT) to investigate the structural, elastic and thermodynamic properties of the cubic perovskite RBRh3 (R = Sc, Y and La) compounds. The exchange-correlation potential is treated within the generalized gradient approximation of Perdew–Burke–Ernzerhof (GGA-PBE). Single-crystal elastic constants are calculated using the total energy variation versus strain technique, then the shear modulus, Young's modulus, Poisson's ratio and anisotropic factor are derived for polycrystalline RBRh3 using the Voigt–Reuss–Hill approximations. Analysis of the calculated elastic constants and B/G ratios shows that these compounds are mechanically stable and ductile in nature. Using the quasi-harmonic Debye model, the effect of pressure P and temperature T on the lattice parameter a 0, bulk modulus B 0, thermal expansion coefficient α, Debye temperature and the heat capacity C v ...

Image Reconstruction in Microwave Tomography Using a Dielectric Debye Model

Abstract: In this paper, quantitative dielectric image reconstruction based on broadband microwave measurements is investigated. A time-domain-based algorithm is derived where Debye model parameters are reconstructed in order to take into account the strong dispersive behavior found in biological tissue. The algorithm is tested with experimental and numerical data in order to verify the algorithm and to investigate improvements in the reconstructed image resulting from the improved description of the dielectric properties of the tissue when using broadband data. The comparison is made in relation to the more commonly used conductivity model. For the evaluation, two examples were considered, the first was a lossy saline solution and the second was less lossy tap water. Both liquids are strongly dispersive and used as a background medium in the imaging examples. The results show that the Debye model algorithm is of most importance in the tap water for a bandwidth of more than 1.5 GHz. Also the saline solution exhibits a dispersive behavior but since the losses restrict the useful bandwidth, the Debye model is of less significance even if somewhat larger and stronger artifacts can be seen in the conductivity model reconstructions.

Thermal expansions of Ln2Zr2O7 (Ln = La, Nd, Sm, and Gd) pyrochlore

Abstract: The thermal expansions of the rare earth zirconate (Ln2Zr2O7, Ln = La, Nd, Sm, and Gd) pyrochlore were studied by the Debye and quasi harmonic approximation combined with the first principles calculations. The difference between CV and CP was obtained. The temperature dependence of thermal expansions is mainly caused by the restoration of thermal energy due to phonon excitations at relatively a low temperature. When the temperature is much higher than Debye temperature, i.e., above 600 K for Ln2Zr2O7 compounds, the volumetric coefficient is increased linearly by increasing the temperature. The calculations are in good agreement with the experiments.

Properties of single crystalline AZn2Sb2 (A = Ca,Eu,Yb)

Abstract: Single crystals of CaZn2Sb2, EuZn2Sb2, and YbZn2Sb2 were grown from melts of nominal composition AZn5Sb5 (A = Ca,Eu,Yb) with the excess melt being removed at 1073 K. The electrical transport properties are consistent with those previously reported for polycrystalline samples. This confirms that the p-type carrier concentrations ranging from 2 × 1019 cm−3 to ∼1 × 1020 cm−3 are intrinsic to these materials. Also consistent with transport in polycrystalline materials, the carrier mobility is found to be lowest in CaZn2Sb2, suggesting the trends in mobility and thermoelectric efficiency within these compounds are inherent to the material systems and not due to inhomogeneity or impurities in polycrystalline samples. These results suggest CaZn2Sb2 has the strongest coupling between the doping/defects and the electronic framework. Magnetization measurements reveal an antiferromagnetic transition near 13 K in EuZn2Sb2, and the observed magnetic anisotropy indicates the spins align parallel and anti-parallel to c in the trigonal lattice. Powder neutron diffraction on polycrystalline samples of CaZn2Sb2 and YbZn2Sb2 reveals smooth lattice expansion to 1000 K, with c expanding faster than a. The Debye temperatures calculated from specific heat capacity data and the isotropic displacement parameters are found to correlate with the carrier mobility, with the CaZn2Sb2 displaying the largest Debye temperature and smallest mobility.

P-V-T equation of state for ε-iron up to 80 GPa and 1900 K using the Kawai-type high pressure apparatus equipped with sintered diamond anvils

Abstract: [1] In order to determine the P-V-T equation of state of e-iron, in situ X-ray observations were carried out at pressures up to 80 GPa and temperatures up to 1900 K using the Kawai-type high pressure apparatus equipped with sintered diamond anvils which was interfaced with synchrotron radiation The present results indicate the unit cell volume at ambient conditionsV0 = 2215(5) A3, the isothermal bulk modulus KT0 = 202(7) GPa and its pressure derivative K′T0 = 45(2), the Debye temperature θ0 = 1173(62) K, Gruneisen parameter at ambient pressure γ0 = 32(2), and its logarithmic volume dependence q = 08(3) Furthermore, thermal expansion coefficient at ambient pressure was determined to be α0(K−1) = 37(2) × 10−5 + 72(6) × 10−8(T-300) and Anderson-Gruneisen parameterδT = 62(3) Using these parameters, we have estimated the density of e-iron at the inner core conditions to be ∼3% denser than the value inferred from seismological observation This result indicates that certain amount of light elements should be contained in the inner core as well as in the outer core but in definitely smaller amount

Application of the CALPHAD method to predict the thermal conductivity in dielectric and semiconductor crystals

Abstract: A novel method, based on the Debye model of the density of the lattice vibration energy [1] , [2] , is used to predict the thermal conductivity of insulator materials from room temperature up to the melting point. The model links the density of the lattice vibration energy and the mean free path of the phonons to the high temperature limit of the Debye temperature, θ D ¯ ( ∞ ) , and to the Gruneisen parameter, γ(∞). The phonon contribution to the thermal conductivity can be predicted from the knowledge of θ D ¯ ( ∞ ) and γ(∞). The contribution of the present work is a new CALPHAD (CALculation of PHAse Diagrams) Method, based on physical models, where the heat capacity, the thermal expansion and the adiabatic bulk modulus are optimized simultaneously in order to calculate θ D ¯ ( ∞ ) and γ(∞). In addition, a simple method to predict θ D ¯ ( ∞ ) and γ(∞), and thus the thermal conductivity without any experimental data, is also presented. Results are given for the thermal conductivities of some typical insulator materials such as salts (halides), oxides and semiconductors. It is found that the agreement between the calculations and the available experimental data is excellent.