Thermal Conductivity Of Single Crystals Research Articles

Thermal conductivity of single crystals zirconia stabilized by scandium, yttrium, gadolinium, and ytterbium oxides

The phase composition and heat conductivity of (ZrO2)0.9(R2O3)0.1 solid solution single crystals have been studied, where R = (Gd, Yb, Sc, Y), (ZrO2)0.9(Sc2O3)0.09(Gd2O3)0.01 and (ZrO2)0.9(Sc2O3)0.09(Yb2O3)0.01. Single crystals have been grown by directional melt crystallization in a cold skull. The phase composition of the crystals has been studied using X-ray diffraction and Raman spectroscopy. The heat conductivity of the crystals has been studied using the absolute steady-state technique of longitudinal heat flow in the 50—300 K range. We show that at a total stabilizing oxide concentration of 10 mol.% the phase composition of the crystals depends on the ionic radius of the stabilizing cation. The (ZrO2)0.9(Sc2O3)0.1 crystals have the lowest heat conductivity in the 50—300 K range while the (ZrO2)0.9(Gd2O3)0.1 solid solutions have the lowest heat conductivity at 300 K.Analysis of the experimental data suggests that the heat conductivity of the crystals depends mainly on the phase composition and ionic radius of the stabilizing cation. Phonon scattering caused by the difference in the weight of the co-doping oxide cation has a smaller effect on the heat conductivity.

Thermal conductivity of single crystals zirconia stabilized by scandium, yttrium, gadolinium, and ytterbium oxides

The phase composition and heat conductivity of (ZrO2)0.9(R2O3)0.1 solid solution single crystals have been studied, where R = (Gd, Yb, Sc, Y), (ZrO2)0.9(Sc2O3)0.09(Gd2O3)0.01 and (ZrO2)0.9(Sc2O3)0.09(Yb2O3)0.01. Single crystals have been grown by directional melt crystallization in a cold skull. The phase composition of the crystals has been studied using X-ray diffraction and Raman spectroscopy. The heat conductivity of the crystals has been studied using the absolute steady-state technique of longitudinal heat flow in the 50–300 K range. We show that at a total stabilizing oxide concentration of 10 mol.% the phase composition of the crystals depends on the ionic radius of the stabilizing cation. The (ZrO2)0.9(Sc2O3)0.1 crystals have the lowest heat conductivity in the 50–300 K range while the (ZrO2)0.9(Gd2O3)0.1 solid solutions have the lowest heat conductivity at 300 K. Analysis of the experimental data suggests that the heat conductivity of the crystals depends mainly on the phase composition and ionic radius of the stabilizing cation. Phonon scattering caused by the difference in the weight of the co-doping oxide cation has a smaller effect on the heat conductivity.

(Invited) Novel Technique to Measure Thermal Diffusivity of Soft Crystal in Micro Scale

To control thermal properties in nano- and micro scale is one of the important topics with regards to the phonon engineering. Recently, the mechanical molecular crystals have been developed, which have the potential applications of actuators and soft robots. Most of the crystal motions are induced by photoisomerization or mechanical stress.Thermal phase transition and the photothermal effect are considered as the underlying mechanism for the motions, such as bending, twisting, jumping, and rotating, etc., of the mechanical molecular crystals, called soft crystals. However, due to the lack of the measured data of heat transport properties such as thermal diffusivity or thermal conductivity of single crystals in micro volume size, the quantitative analysis of thermal phenomena in the molecular crystals has not yet been quantitatively analyzed. For example, the photo-thermally induced temperature rise produces the localized temperature distribution near the surface, and thermal diffusivity should be utilized to calculate the temperature distribution in the specimen.To overcome such situation, we propose a micro scale temperature wave analysis (micro-TWA) method to measure the thermal diffusivity of soft crystals in micro scale. (Figure 1) This method enables to measure the axial orientation in single crystals. Furthermore, coupled with the photo-thermal stimulation, the kinetic measurement of thermal diffusivity under the stress induced and photo induced field has been realized. Demonstration of the super elastic phase transition of soft crystal, 3,5- difluorobenzoic acid (3,5−F2bza) and terephthalamide(TPA) will be presented. This is a proposal of the new measurement method, because the experimental determination of the thermal diffusivity in micro scale of organic single crystals, under operating the deformation control, is still a challenge. The experimental validity is discussed with the theoretical analysis using the reference sample. Figure 1

THERMOELECTRIC FIGURE OF MERIT IN (AGSB)1-ХPBХSE2 SINGLE CRYSTALS

This article is devoted to studies the dependence of the thermal conductivity coefficient and thermoelectric figure of merit in (AgSb)1-xPbxSe2 single crystals on their composition. We found that the lattice component provides the main contribution to the thermal conductivity of solid solutions (AgSb)1-xPbxSe2 at x=0-0,4. The electronic thermal conductivity in single crystals with values of x at 0,92-1, becomes close to the lattice component. An increase in the Pb fraction of (AgSb)1-xPbxSe2 in the range from x=0 to x=0,4 leads to a decrease in the thermal conductivity (AgSb)1-xPbxSe2 from 0.56 W / K · m to 0.27 W / K · m, and an increase in x from 0,92 to 1 leads to an increase in the thermal conductivity in the range from 0,45 W / K · m to 1,11 W / K · m. The thermoelectric figure of merit was the highest in all compositions: (AgSb)1-xPbxSe2 at x = 0, 0,1, 0,2 0,92, 1 (ZT≈0,014-0,46). Having a high value of the thermoelectric figure of merit, single crystals of such composition are promising materials for thermoelectric energy generation. The smooth change of thermoelectric properties (AgSb)1-xPbxSe2 with a formation in the content of Pb atoms can find practical use in semiconductor instrumentation, where AgSbSe2 and PbSe materials are used.

Effect of Heat Treatment on the Thermal Conductivity of Single Crystals of ZrO2-Based Solid Solutions Stabilized with Scandium and Yttrium Oxides

The effect of heat treatment at 1000°C for 400 h on the thermal conductivity of zirconium dioxide crystals stabilized with scandium oxide (ZrO2)1 – x(Sc2O3)x (x = 0.08–0.10) and simultaneously with scandium and yttrium oxides (ZrO2)1 – x – y(Sc2O3)x(Y2O3)y (x = 0.003–0.20, y = 0.02–0.025) has been studied. In the crystals of zirconium dioxide stabilized with scandium oxide, the most noticeable changes in the thermal conductivity are observed in the 9ScSZ crystals, in which the phase composition is changed and a marked content of the rhombohedral phase appears. These changes are less noticeable in the 8ScSZ crystals and they are mainly due to the ordering of oxygen vacancies and the changes in the microstructures of the samples, and there are no changes in the 10ScSZ crystals. The 10ScSZ crystals have the minimum electrical conductivity before and also after annealing, which is determined by the highest content of scandium oxide in the solid solution. Insignificant changes in the thermal conductivity are observed in crystals of partially stabilized zirconium dioxide co-alloyed with scandium and yttrium oxides. The cubic 8Sc2YSZ and 10Sc2YSZ crystals demonstrate only slight changes in the thermal conductivity, the character of the temperature dependence of the thermal conductivity, and the phase compositions. The alloying of the zirconia–based solid solutions with yttrium oxide simultaneously with scandium oxide enables one to increase the stability of their phase compositions and structurally dependent thermal and electrical physical characteristics.

Ангармонизм колебаний решетки и тепловые свойства твердых растворов Сd-=SUB=-1-x-=/SUB=-Sr-=SUB=-x-=/SUB=-F-=SUB=-2-=/SUB=-

The temperature changes in the crystal lattice parameters a (T) of cadmium and strontium difluorides, as well as their mutual solid solutions Сd1-xSrxF2 (x = 0.23, 0.50), were studied experimentally at temperatures of 5-300 K. The temperature dependences of the unit cell volume of the fluorides studied were analyzed in the Debye-Einstein model . An increased effect of the anharmonism of lattice vibrations of solutions due to the disorder of the crystal structure on their thermal properties is established. The model parameters and characteristics of the anharmonic contribution are determined. Based on the data obtained, the concentration dependence of the thermal conductivity of Сd1-xSrxF2 solid solutions at T = 300 K was calculated in the Calaway model, compared with published experimental data. The possibility of assessing the thermal conductivity of single crystals of solid solutions of the studied system on the basis of data on the thermal properties of solution components obtained on powder samples is shown.

Peak intrinsic thermal conductivity in non-metallic solids and new interpretation of experimental data for argon

The inelastic nature of 3-phonon processes is investigated within the framework of perturbation theory and linearized Boltzmann transport equation (BTE). By considering the energy conservation rule governing this type of interaction in a statistical average sense, the impact of different forms of the regularized energy-conserving Dirac delta function on 3-phonon scattering rates was evaluated. Strikingly, adopting Lorentz distribution, in accordance with the shape of eigenenergy broadening of phonon normal modes due to the leading term of crystal anharmonicity, was found to play a critical role in activating umklapp processes at low temperature, leading to intrinsic lattice thermal conductivity peak at finite temperature for perfect crystal. This characteristic behavior, unique to the Lorentzian, lays foundation for developing adjustable-parameter-free computational models for reliable prediction of the finite lattice conductivity at low temperature, even in the absence of extrinsic scattering processes (e.g., by crystal imperfections and boundary). An iterative solution scheme for BTE was used to compute the intrinsic thermal conductivity of solid argon over the entire temperature range (2–80 K). For the first time, the experimentally observed T2 behavior in the low temperature, T, limit and the peak temperature (∼8 K) were successfully recovered, in addition to the classical high temperature T−1 behavior above 20 K by the sole use of 3-phonon processes. The good agreement with experiment indicates that phonon–phonon interactions dominate over the entire temperature range in argon, contrary to previous hypotheses that the subpeak regime is dominated by phonon-defect scattering. Anisotropy in thermal conductivity of single crystal at low temperature due to phonon focusing was observed. In addition, argon conductivity is underestimated by an order of magnitude in single mode relaxation time approximation, where the collective nature of phonon mode relaxation is ignored.

Thermal conductivity of single crystals of Ba1–x R x F2 + x (R = La, Ce, Nd, or Gd) solid solutions

The thermal conductivity of single crystals of Ba1–х R х F2 + х (R = La, Ce, Nd, or Gd) solid solutions has been experimentally investigated in the temperature range of 50–300 K. With an increase in the content of rare-earth elements, the thermal-conductivity behavior in these series changes from that characteristic of defect single crystals to the behavior typical of glasslike materials. The thermal-conductivity concentration dependences are almost identical, which can be explained by the same type of defect clusters arising upon heterovalent ion substitution.

Thermal Conductivity in the Frustrated Two-Leg Spin- Ladder System BiCu2PO6

We have measured temperature and magnetic-field dependences of the thermal conductivity of single crystals of the frustrated two-leg spin-ladder system BiCu2PO6 in magnetic fields up to 14 T. It has been found that the temperature dependence of the thermal conductivity along every principal crystallographic axis shows two peaks in zero field but that the magnitude of the thermal conductivity along the b-axis parallel to spin ladders, κb, is significantly larger than those of the thermal conductivity along the a-axis, κa, and along the c- axis, κc, at high temperatures above 7 K. These results suggest that the thermal conductivity due to spins probably exists only in κb. Furthermore, it has been found that both magnetic-field dependences of κa and κb at 3 K show kinks at ~ 7 T and ~ 10 T, where the spin state may change.

Relative importance of grain boundaries and size effects in thermal conductivity of nanocrystalline materials.

A theoretical model for describing effective thermal conductivity (ETC) of nanocrystalline materials has been proposed, so that the ETC can be easily obtained from its grain size, single crystal thermal conductivity, single crystal phonon mean free path (PMFP), and the Kaptiza thermal resistance. In addition, the relative importance between grain boundaries (GBs) and size effects on the ETC of nanocrystalline diamond at 300 K has been studied. It has been demonstrated that with increasing grain size, both GBs and size effects become weaker, while size effects become stronger on thermal conductivity than GBs effects.

Thermal conductivity of single crystals of the Ca1 − x Y x F2 + x solid solution

The thermal conductivity of single crystals of the solid solution of yttrium fluoride in calcium fluoride Ca1 − xYxF2 + x with the fluorite structure (x ≤ 0.20) and the Ca0.27Y0.73F2.73 phase with the tisonite structure has been studied by the absolute steady-state longitudinal heat flow method in the temperature range 50–300 K. It has been established that the thermal conductivity drops sharply with increasing yttrium trifluoride concentration, especially in the low-temperature region.

Calculation of the lattice thermal conductivity in granular crystals

This paper provides a general model for the lattice thermal conductivity in granular crystals. The key development presented in this model is that the contribution of surface phonons to the thermal conductivity and the interplay between phonon anharmonic scattering and phonon scattering by boundaries are considered explicitly. Exact Boltzmann equation including spatial dependence of phonon distribution function is solved to yield expressions for the rates at which phonons scatter by the grain boundaries in the presence of intrinsic phonon scattering mechanisms. The intrinsic phonon scattering rates are calculated from Fermi's golden rule, and the vibration parameters of the model are derived as functions of temperature and crystallographic directions by using a lattice dynamics approach. The accuracy of the model is demonstrated with reference to experimental measurements regarding the effects of surface orientation and isotope composition on the thermal conductivity in single crystals, and the effect of grains size and shape on the thermal conductivity tensor in granular crystals.

Mechanical deformation modes and anisotropy of IVB transition metal nitrides

This paper studies the deformation modes and anisotropy of the IVB transition metal nitrides TiN, ZrN, and HfN using the plane-wave density functional theory. The values of elastic modulus and hardness of the TiN, ZrN, and HfN are calculated and analyzed in detail. This result suggests typical elastic anisotropy, which increases in the order of TiN→ZrN→HfN. This phenomenon results in inevitable lattice distortion and microcracks. The minimum value of thermal conductivity of the polycrystalline system decreases in the order of TiN→ZrN→HfN. The thermal conductivity of single crystals in each crystal orientation presents a nearly anisotropic thermodynamic property.

Thermal conductivity of single crystals of M1−x M x ′F2 (M = Ca, Sr; M′ = Mn, Co) isovalent solid solutions

The thermal conductivity of single crystals of the Ca0.99Co0.01F2, Ca0.97Co0.03F2, Sr0.99Mn0.01F2, Sr0.989Mn0.01Co0.001F2, and Sr0.995Co0.005F2 solid solutions has been measured in the temperature range 50–300 K. The results demonstrate that doping of CaF2 and SrF2 crystals with small amounts of isovalent transition metal impurities is accompanied by a significant reduction in thermal conductivity.

Thermal conductivity of single crystals of Ca1 − x Er x F2 + x and Ca1 − x Tm x F2 + x solid solutions

The thermal conductivity of single crystals of Ca1 − xErxF2 + x (x = 0.01, 0.05, 0.07, and 0.10) and Ca1 − xTmxF2 + x (x = 0.02, 0.04, and 0.06) solid solutions is studied in the temperature ranges 50–300 and 298–673 K. With increasing content of rare-earth elements, the behavior of thermal conductivity in these solid solutions changes from the characteristic of defect single crystals to glasslike. The concentration dependences of thermal conductivity for the two systems differ insignificantly.

Heat capacity and thermal conductivity of Fe x Mn1 − x S single crystals

This paper reports on the results of investigations of the thermal properties and thermal conductivity of single crystals of homogeneous solid solutions FexMn1 − xS with a cubic NaCl structure, which have been prepared by the cation substitution for divalent manganese ions in manganese monosulfide. It has been revealed that the heat capacity and thermal conductivity exhibit anomalies in the range of the magnetic transition. The cation substitution is accompanied by an increase in the phase transition temperature.

Transition from crystal-like to glass-like behavior of thermal conductivity in the Sr0.16Ba0.54La0.30F2.30 solid solution

Using a steady-state axial flow technique, we have measured the thermal conductivity of single crystals of congruently melting SrF2-BaF2-LaF3 solid solutions from 50 to 300 K: Ba0.66Sr0.34F2 (minimum in the melting curves), Ba0.70La0.30F2.30 (maximum in the melting curves), and Sr0.16Ba0.54La0.30F2.30 (saddle point on the melting surfaces). The thermal conductivity of the isovalently doped fluorite solid solution is typical of crystals containing point defects. Heterovalent substitution leads to glass-like behavior of thermal conductivity.

Thermal conductivity of single crystals with a fluorite structure: Cadmium fluoride

The thermal conductivity of Ca, Sr, Ba, and Cd difluoride single crystals and the CdF2 samples doped by 3 mol % NdF3, 15 mol % HoF3, and 10 mol % ErF3 has been studied using the method of steady longitudinal heat flow in the temperature range 50–300 K. The thermal conductivity of the matrices of these compounds decreases in the order CaF2-SrF2-BaF2-CdF2. The temperature dependences of the phonon mean free path for these crystals have been calculated from experimental data and exhibit different behaviors. It has been assumed that the intense phonon scattering observed in the undoped CdF2 sample is caused by the specific features of the processes of phonon-phonon scattering. The formation of heterovalent solid solutions of cadmium difluoride and rare-earth trifluorides is accompanied by a drastic decrease in the thermal conductivity and a change in its character from that typical of dielectric single crystals to that typical of glassy materials.

Thermal conductivity of single crystals of Sr1 − x Yb x F2 + x solid solution

Thermal conductivity of single crystals of Sr1 − x Yb x F2 + x solid solution

Thermal conductivity of single crystals of Ba1 − x Yb x F2 + x solid solution

Thermal conductivity of single crystals of Ba1 − x Yb x F2 + x solid solution