Negative thermal expansion (NTE)—the phenomenon where some materials shrink rather than expand when heated—is both intriguing and useful but remains poorly understood. Current understanding hinges on the role of specific vibrational modes, but in fact thermal expansion is a weighted sum of contributions from every possible mode. Here we overcome this difficulty by deriving a real-space model of atomic motion in the prototypical NTE material scandium trifluoride, $\mathrm{Sc}{\mathrm{F}}_3$, from total neutron scattering data. We show that NTE in this material depends not only on rigid unit modes—the vibrations in which the scandium coordination octahedra remain undistorted—but also on modes that distort these octahedra. Furthermore, in contrast with previous predictions, we show that the quasiharmonic approximation coupled with renormalization through anharmonic interactions describes this behavior well. Our results point the way towards a new understanding of how NTE is manifested in real materials.

中文翻译：

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通过中子总散射测量定量了解三氟化scan中负热膨胀

负热膨胀（NTE）是一种有趣的且有用的现象，它是某些材料在加热时会收缩而不是膨胀的现象，但仍然知之甚少。当前的理解取决于特定振动模式的作用，但实际上，热膨胀是每种可能模式贡献的加权总和。在这里，我们通过推导原型NTE材料三氟化scan中原子运动的真实空间模型来克服这一难题，$\mathrm{SC}{\mathrm{F}}_3$，来自总中子散射数据。我们表明，这种材料中的NTE不仅取决于刚性单位模态（—协调八面体保持不变形的振动），还取决于使这些八面体变形的模态。此外，与以前的预测相反，我们表明准谐波近似与通过非谐波相互作用的重新规范化很好地描述了这种行为。我们的结果指出了重新认识NTE如何在实际材料中体现的方法。