Rattling Vibrations and Phonon Density of States in Low Thermal Conductivity Defect Pyrochlores

We have used chemical substitution of non-framework (A) cations to reduce the thermal conductivity of defect pyrochlores, to produce materials for use as thermal insulation in thermal batteries. The weakly bound A cations, located within a cavity formed by metal-centered octahedra, act as Einstein oscillators, undergoing localized vibrations, termed rattling modes. These scatter heat-carrying phonons and reduce thermal conductivity. That of mixed-phases K1-xCsxTaWO6 is determined by the balance between two effects. The lighter, more weakly-bound K+ is expected to show increased rattling vibrations within the cavity, decreasing the thermal conductivity of potassium-rich phases but the increased mass-fluctuation scattering of phonons, resulting from substitution of K+ by Cs+, also reduces the thermal conductivity. The balance of these two effects results in a minimum thermal conductivity at x = 0.25. Calculations of the radial distribution function of the two ions indicate greater delocalization of K+, consistent with increased rattling. Fitting the temperature dependence of atomic displacement parameters from X-ray diffraction data leads to estimates of 144 K and 84 K for the Einstein temperatures of K+ and Cs+ respectively. We wish to measure the rattling modes of K+ and Cs+ by inelastic neutron scattering and investigate the impact of changes in the K/Cs ratio on the rattling modes and phonon density of states of the two end-member and three mixed phases in this series.我们通过对非骨架（A位）阳离子进行化学取代，以降低缺陷烧绿石的热导率，制备可用于热电池隔热的材料。位于金属中心八面体形成的空腔内的弱结合A位阳离子，可作为爱因斯坦振子（Einstein oscillators），发生局域振动，该振动被称为晃动模式（rattling modes）。此类振动会散射载热声子，从而降低热导率。 混合相K₁₋ₓCsₓTaWO₆的热导率由两种效应的平衡所决定。质量更轻、结合强度更低的K⁺在空腔内的晃动振动会更强，这会降低富钾相的热导率；而通过Cs⁺取代K⁺所引发的质量涨落声子散射，同样会降低热导率。这两种效应的平衡使得当x=0.25时，体系的热导率达到最小值。 对两种离子的径向分布函数（radial distribution function）的计算结果表明，K⁺具有更强的离域特性，这与增强的晃动振动相符。 通过拟合X射线衍射数据得到的原子位移参数的温度依赖性，我们估算出K⁺和Cs⁺的爱因斯坦温度分别为144 K和84 K。 我们计划通过非弹性中子散射（inelastic neutron scattering）测量K⁺和Cs⁺的晃动模式，并探究K/Cs比例变化对该系列中两种端元相以及三种混合相的晃动模式和声子态密度（phonon density of states）的影响。