Theoretical study of the phonon–phonon scattering mechanism and the thermal conductive coefficients for energetic material

Abstract

The elastic constants and force constants of an energetic material named as 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) are calculated by first-principles method under the GGA+vdW functional. Based on them, a physical picture to describe the phonon–phonon scattering mechanism is obtained, and a method to evaluate the thermal conductive tensor is developed. The resulting thermal conductivities are in agreement with the available experiments. We find that 20 vibrational modes play important roles in determining the heat exchange process of TATB. The vibrational direction, symmetry, displacement field and the detailed information of the key vibrational modes are obtained.     

高压下金属Ba的结构稳定性以及热动力学的第一原理研究

采用第一原理方法计算了高压下金属Ba的三个高压相 Ba-I, Ba-Ⅱ和Ba-V的稳定性及热动力学性质.结果表明, Ba的三个高压相在0 K时在其压力范围内都是动力学和力学稳定的;但随压力增加, Ba-I 和Ba-Ⅱ 的声子谱频率出现异常"软化",而Ba-V则出现"硬化".虽然 Ba-Ⅱ 和 Ba-V 同为六方密堆(hcp)结构,计算表明它们在高压下表现出了不同的弹性各向异性.计算同时发现 Ba-Ⅱ 在更高的压力下仍满足力学稳定条件,但声子谱有虚频存在, 表明动力学失稳是Ba-Ⅱ在压力下向Ba-I!V相转变的原因. 计算和比较了同为六方密堆(hcp)结构的Ba-Ⅱ和Ba-V在高压下的声速、 德拜温度、体模量、剪切模量等力学和热学性质, 展现了金属Ba在压力下的稳定机制和热动力学性质.     

高温高压下铁热导率的第一性原理研究

铁在高压高温下的热导率是研究地球动力学和热演化的关键参数.在以往的研究中,铁的热导率主要归结于电子热导率,我们发现铁在高压下晶格振动对热导率的贡献不可忽略.本文利用晶格动力学和玻尔兹曼输运理论计算了铁的声子色散、Hugoniot状态方程和热导率.预测了铁在核幔边界附近温度约为3500K,在地球内核边界条件约为6500K.考虑晶格振动的热导率在地球核幔边界附近为112W/m K,在内核边界条件约为200W/mK.     

Dynamical stability and phase transition of ZrC under pressure

A comprehensive first principles study of structural, elastic, electronic, and phonon properties of zirconium carbide (ZrC) is reported within the density functional theory scheme. The aim is to primarily focus on the vibrational properties of this transition metal carbide to understand the mechanism of phase transition. The ground state properties such as lattice constant, elastic constants, bulk modulus, shear modulus, electronic band structure, and phonon dispersion curves (PDC) of ZrC in rock-salt (RS) and high-pressure CsCl structures are determined. The pressure-dependent PDCs are also reported in NaCl phase. The phonon modes become softer and finally attain imaginary frequency with the increase of pressure. The lattice degree of freedom is used to explain the phase transition. Static calculations predict the RS to CsCl phase transition to occur at 308?GPa at 0?K. Dynamical calculations lower this pressure by about 40?GPa. The phonon density of states, electron–phonon interaction coefficient, and Eliashberg's function are also presented. The calculated electron–phonon coupling constant λ and superconducting transition temperature agree reasonably well with the available experimental data.     

Ab initio study on the high superconducting transition temperature in calcium under high pressure

For calcium in the phases IV and V, we estimated the superconducting transition temperature T _c by the use of the Allen–Dynes formula. Setting the effective screened Coulomb repulsion constant μ* at 0.1 in the formula, we obtained T _c =23.42 K at 100 GPa for Ca-IV and T _c =15.87 K at 120 GPa for Ca-V. In order to clarify the origin of such high values of T _c , first, we investigated the band character of electrons and found that the high T _c is not necessarily related to the so called s–d transfer. Then we analyzed the electron–phonon coupling at each phonon mode in Ca-V where the highest T _c in elements has been experimentally observed. As a result, we discovered that an optical mode at the Γ point has the strongest electron–phonon coupling. Such phonon mode can exist only in the complex crystal structure of Ca-V, and the result shows that the high T _c seems to be closely linked with the complex crystal structures like Ca-IV and Ca-V.     

多约束纳米结构的声子热导率模型研究

纳米技术的快速发展使得对微纳尺度导热机理的深入研究变得至关重要. 理论和实验都表明, 在纳米尺度下声子热导率将表现出尺寸效应. 基于声子玻尔兹曼方程和修正声子平均自由程的方法得到了多约束纳米结构的声子热导率模型, 可以描述多个几何约束共同作用下热导率的尺寸效应. 不同几何约束对声子输运的限制作用可以分开计算, 总体影响则通过马西森定则进行耦合. 对于热流方向的约束, 采用扩散近似的方法求解声子玻尔兹曼方程; 对于侧面边界约束, 采用修正平均自由程的方法计算边界散射对热导率的影响. 得到的模型能够预测纳米薄膜(法向和面向)及有限长度方形纳米线的热导率随相应特征尺寸的变化. 与蒙特卡罗模拟及硅纳米结构热导率实验值的对比验证了模型的正确性.     

固体氩的晶格热导率的非简谐晶格动力学计算

用一种非简谐晶格动力学方法, 使用相互作用势作为惟一的输入参数, 准确地计算了固体氩的各个声子的频率和弛豫时间. 并将这些结果进一步和玻尔兹曼输运方程相结合, 预测了固体氩从10 K 到80 K 区间的热导率, 并得到了与实验值非常符合的结果. 分析了运用非简谐晶格动力学方法进行数值计算过程中的各个相关的计算参数, 包括布里渊区中倒格子矢量的选取, δ 函数的展宽的选择等对热导率和声子弛豫时间预测结果的影响. 通过对各个声子模式对热导率贡献的分析, 发现随着温度升高, 高频声子对于热导率的贡献率也逐渐变大, 结果和理论预测完全一致. 关键词： 热导率 固体氩 非简谐晶格动力学 声子     

蓝宝石Al_2O_3晶体的高压热传导系数研究

对蓝宝石Al2O3晶体在高压下的热传导系数这一在的理论和实验仍处于探索中的问题,本文从较严格的固体理论出发,考虑到晶格声子的最小平均自由程、Debye温度、Gruneisen参数以及冲击温度在冲击压缩状态下的变化,进而对在高压实验中最常用的窗口材料蓝宝石Al2O3晶体的导热系数进行了理论分析,计算结果较好解释了实验结果.     

Anomalous reduced sound velocity of multiferroic TbMn2O5

The anomalous reduced sound velocity of multiferroic TbMn₂O₅ (TMO) has been studied using Green's function technique. To achieve this aim, the anharmonic phonon-phonon interaction and the spin-phonon interaction were used. It was shown that the reduced velocity of sound of TMO exhibits a kink at the ferroelectric phase transition temperature T_C. This can be explained as an effect of vanishing ferroelectric ordering above T_C. It was found that the reduced sound velocity increases with increasing V⁽³⁾ (the third-order atomic force constants of the anharmonic phonons) in the interval T?<?T_C, whereas the reduced sound velocity remains unchanged in the interval T_C?<?T?<?T_N. It was also found that the reduced sound velocity increases with the increase of V⁽⁴⁾ (the fourth-order atomic force constants of the anharmonic phonons) in the interval T?<?T_N. In addition, the ferroelectric phase transition temperature T_C decreases when V⁽⁴⁾ increases in the interval T?<?T_N. Those theoretical results are in agreement with the experimental data.     

The first-principle study on the equation of state of HMX under high pressure

The equation of states (EOS) of high energy explosive HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) has been studied by using the first principle method. Our results include the lattice constants, elastic constants, and the dependence of total energy and pressure on volume for βand δ-HMX. The calculated elastic constants and the pressure-volume relationship of β-HMX are also compared with the experimental values. The theoretical tensile experiments are implemented on the β-HMX. The atomic-scale ana...     

Role of thermal vibrations in magnetic phase transitions

This article addresses the contradiction that exists in studies on magnetic phase transitions between theoretical models that ignore the role of thermal vibrations and analysis of neutron diffraction data that always incorporates them. Ignoring thermal vibrations in both theoretical models and analysis of diffraction data leads to the latter giving different magnetic-order parameters for different reciprocal lattice lines. This leads to a unique consequence, the assumption to neglect a physical phenomenon turns a single-valued experimental observable into a multiple-valued one where all values are equally valid. This assumption is clearly unacceptable and must be rejected. Diffraction data constrain all theoretical models to incorporate thermal vibrations and represent the exchange interaction as temperature dependent, J_ij (T), instead of the current practice, J_ij (0).     

Tuning the thermal conductivity of strontium titanate through annealing treatments

Strontium titanate(SrTiO_3) is a promising n-type material for thermoelectric applications. However, its relatively high thermal conductivity limits its performance in efficiently converting heat into electrical power through thermoelectric effect.This work shows that the thermal conductivity of SrTiO_3 can be effectively reduced by annealing treatments, through an integrated study of laser flash measurement, scanning electron microscopy, Fourier transform infrared spectroscopy, x-ray absorption fine structure, and first-principles calculations. A phonon scattering model is proposed to explain the reduction of thermal conductivity after annealing. This work suggests a promising means to characterize and optimize the material for thermoelectric applications.     

Investigating the thermal conductivity of materials by analyzing the temperature distribution in diamond anvils cell under high pressure

Investigating the thermal transport properties of materials is of great importance in the field of earth science and for the development of materials under extremely high temperatures and pressures. However, it is an enormous challenge to characterize the thermal and physical properties of materials using the diamond anvil cell (DAC) platform. In the present study, a steady-state method is used with a DAC and a combination of thermocouple temperature measurement and numerical analysis is performed to calculate the thermal conductivity of the material. To this end, temperature distributions in the DAC under high pressure are analyzed. We propose a three-dimensional radiative-conductive coupled heat transfer model to simulate the temperature field in the main components of the DAC and calculate in situ thermal conductivity under high-temperature and high-pressure conditions. The proposed model is based on the finite volume method. The obtained results show that heat radiation has a great impact on the temperature field of the DAC, so that ignoring the radiation effect leads to large errors in calculating the heat transport properties of materials. Furthermore, the feasibility of studying the thermal conductivity of different materials is discussed through a numerical model combined with locally measured temperature in the DAC. This article is expected to become a reference for accurate measurement of in situ thermal conductivity in DACs at high-temperature and high-pressure conditions.     

Effect of phonon scattering mechanisms on the lattice thermal conductivity of skutterudite-related compound

We have prepared the skutterudite-related compounds FeCo_3Sb_{12} and La_{0.75}Fe_3CoSb_{12} with different average grain sizes (about 0.8 and 3.9μm) by hot pressing. Samples were characterized by XRD, EPMA and SEM. The lattice thermal conductivity was investigated in the temperature range from room temperature to 200℃. Based on the Debye model, we analyse the change in lattice thermal conductivity due to various phonon scattering mechanisms by examining the relationship between the weighted phonon relaxation time τ(ω/ω_D)^2 and the reduced phonon frequency ω/ω_D. The effect of grain boundary scattering to phonon is negligible within the range of grain sizes considered in this study. The large reduction in lattice thermal conductivity of FeCo_3Sb_{12} compound contributes to the electron－phonon scattering. As for La_{0.75}Fe_3CoSb_{12} compound, the atoms of La filled into the large voids in the structure of the skutterudite produce more significant electron－phonon scattering as well as more substitute of Fe at Co site at the same time. Moreover, the point-defect scattering appears due to the difference between the atoms of La and the void. In addition, the scattering by the rattling of the rare-earth atoms in the void is another major contribution to the reduced lattice thermal conductivity. Introducing the coupling of the electron－phonon scattering with the point-defect scattering and the scattering by the rattling of the rare-earth atom is an effective method to reduce the lattice thermal conductivity of the skutterudite-related compounds by substitution of Fe for Co and the atoms of La filled in the large voids in the skutterudite structure.     

Effect of normal processes on thermal conductivity of germanium,silicon and diamond

The effect of normal scattering processes is considered to redistribute the phonon momentum in (a) the same phonon branch — KK-S model and (b) between different phonon branches — KK-H model. Simplified thermal conductivity relations are used to estimate the thermal conductivity of germanium, silicon and diamond with natural isotopes and highly enriched isotopes. It is observed that the consideration of the normal scattering processes involving different phonon branches gives better results for the temperature dependence of the thermal conductivity of germanium, silicon and diamond with natural and highly enriched isotopes. Also, the estimation of the lattice thermal conductivity of germanium and silicon for these models with the consideration of quadratic form of frequency dependences of phonon wave vector leads to the conclusion that the splitting of longitudinal and transverse phonon modes, as suggested by Holland, is not an essential requirement to explain the entire temperature dependence of lattice thermal conductivity whereas KK-H model gives a better estimation of the thermal conductivity without the splitting of the acoustic phonon modes due to the dispersive nature of the phonon dispersion curves.      

Thermodynamics properties and thermal conductivity of Mg2Pb at high pressure

The thermodynamics properties and thermal conductivity of Mg2Pb at high pressures have been calculated by first-principles.The enthalpy of formation and heat capacity obtained at 0 GPa are in good agreement with the experiments and other theoretical results.The thermal conductivity and coefficient of thermal expansion of Mg2 Pb at high pressure were evaluated.The thermal conductivity presents a second-order polynomial with pressure.The calculated thermal conductivity of Mg2Pb indicates that it is suitable to be used as thermal conductor at 0 K.     

A method to calculate Boltzmann entropy

A method is proposed to calculate the Boltzmann non equilibrium entropy as a Taylor series expansion in terms of the successive moments of the velocity distribution function. As a first application, the entropy of the BKW solution of the Boltzmann equation is calculated for both even and odd dimensions. The properties of the entropy of the Tjon Wu modeld=2) are studied and a quantitative condition is derived, showing that the McKean conjecture is incorrect. As a second application of the method, the entropy of one of the solutions of the very hard particle model for the Boltzmann equation is also derived.     

A transfer matrix program to calculate the conductivity of random resistor networks

We describe technical details on a new method of calculating the conductivity of random resistor networks which uses transfer matrix ideas. We give a program which calculates the conductivity of three-dimensional bars, and we provide a few comments on the advantages of this method and its performances.     

Behavior of thermocouples under high pressure in a multi-anvil apparatus

We have conducted experiments to study the behavior of W5%Re–W26%Re (type C) and Pt10%Rh–Pt (type S) thermocouples under high pressure in a multi-anvil apparatus. The electromotive force (emf) between four different or three identical thermocouple wires was measured up to 15?GPa and 2100?°C. Mechanical and chemical stability of the thermocouples was examined during and after the experiments. Due to the effect of pressure on the emf/temperature relation, the temperature reading of the type C minus that of the type S thermocouple rises to +5?°C then falls to ?15?°C between room temperature and 1500?°C at 5?GPa, and to +25?°C and then ?35?°C between room temperature and 1800?°C at 15?GPa. In addition, we observed variations in the emf/temperature relation caused by uncertainties in the position and geometry of hot junctions in a steep temperature gradient, and by variable distribution of pressure gradient and non-hydrostatic stress on the thermocouple wires. These errors are estimated at 1.6% for the type S thermocouple up to 1700?°C, and 0.8% for the type C thermocouple up to 2100?°C. Self-diffusion and chemical contamination of the thermocouples by high-purity insulating ceramics appear negligible for the type S thermocouple at 1700?°C for one hour, and for the type C thermocouple at 2100?°C for half an hour. In contrast, large-scale displacement of the hot junction due to dislocation of the type C thermocouple wires and plastic deformation of the type S thermocouple wires may lead to large errors in temperature measurement (±200?°C).