EAGER: Testing New Formulae for Pressure Derivatives of Specific Heat, Thermal Conductivity, and Thermal Diffusivity

热流无处不在。物质传输热量的效率是至关重要的。了解热传输对于许多工程和科学努力至关重要，例如设计微型电子设备或对大型行星的冷却速度进行建模。测量热传输特性的最准确方法(激光闪光分析)表明，不同类型固体的数值取决于热量流动的长度。静态属性(例如，密度)不会以这种方式运行，因此没有更早地进行针对长度的测试。这一发现导致了描述作为压力函数的热动态行为(传导性、扩散性和热容)的新公式。这些公式描述了稳态条件。这与19世纪开发的描述恒定温度等理想化的经典热力学方程形成了鲜明对比。这些发现对地球物理学至关重要，因为地球深处的物质处于极端压力下。在这里，研究人员将进一步测试他们之前在有限数量的固体和有限的温度范围内验证的配方。他们现在量化了更大范围的固体和其他物质状态以及更大温度范围内的热性质。他们使用了一种新的液体(特别是水)激光闪光装置；这种新装置可以测量热容并达到较低的温度。他们重新分析了文献中可用气体的数据。目标是在测量中达到极高的精度，尤其是环境条件附近的初始斜率和温度。测试了旧配方和新配方的热性能。这个项目可能会在我们量化热流的方式上引发一场范式转变。它的结果提高了我们对导致它的微观机制的理解。它们可能会对纯粹的和应用的物理科学产生广泛的影响。该项目还支持一名残疾女科学家，并为华盛顿大学的本科生提供培训。绝缘体、半导体、金属、合金和玻璃的热扩散率(D)和导热系数(K)取决于测量的长度尺度(L)这一发现对理论物理科学和应用物理科学都有影响。对L的小尺度线性依赖符合傅立叶热方程的量纲分析。它表明，钻石砧座细胞实验的结果是有问题的，最重要的是，这些结果是以L的100倍大的1个ATM数据为基准的。在毫米大小的样品上，存在低于2 Gpa压力的可靠数据，这些样品来自磨损严重的方法。对25种不同键型固体的分析结果表明，比热(Cp)的对数压力导数等于线性压缩系数的-1倍。考虑到k依赖于L(即体积)的数学分析也将其对数压力响应与状态方程的性质相关联，对于D也是如此。新的k-P公式根据20个固体的可靠数据得到了证实。因此，该团队的初步测试表明，新的公式是描述稳态条件的热力学恒等式，这是一个常见的限制。等温并非如此，因为热排放无处不在。因此，经典热力学中与时间无关的公式不能恰当地描述地球上热量流动的依赖时间的条件。要检验CP与P的新公式，可以使用已有的数据库。由于目标是一个普遍适用的稳态公式，因此正在测试物质的不同状态和键类型。研究人员还收集了关于液体和冰的数据(例如，在298K附近融化的水和金属)。他们使用一种新的激光闪光仪-LFA467仪器及其商用低压池-覆盖~100至500°C，可同时测量D和Cp。通过在电池内部涂覆石墨来消除虚假的辐射传递。当密度与温度之比不可用时，使用横跨此T范围的膨胀计来约束k。使用机器学习来对CP、D和k与P、L、T进行参数化，要么将区分新的或以前的公式是否正确，要么将产生新的准确的公式，从而允许外推到地球内部的高压。因此，拟议的工作提供了对地球物理至关重要的基础物理学。已证实，CP和K(或D)的P衍生物与地球和其他大型天体内的任何过程有关。这些工作成果提高了地球物理和岩石学模型的准确性，并有可能提高我们对行星内部的理解。由于近100年来没有发展出新的热力学特性，其他物理科学，如化学反应的研究，可能会受到影响。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Heat flow is ubiquitous. How efficiently matter transports heat is of fundamental importance. Understanding heat transport is critical to numerous engineering and scientific endeavors, such as designing tiny electronic devices or modeling the cooling rate of large planetary bodies. The most accurate method for measuring heat transport properties (laser-flash analysis) has shown that values from diverse types of solids depend on the length over which heat is flowing. Static properties (e.g., density) do not behave in this manner, so tests against length were not made earlier. This finding led to new formulae describing thermal dynamic behavior (conductivity, diffusivity, and heat capacity) as functions of pressure. The formulae describe steady-state conditions. This contrasts with equations of classical thermodynamics developed in the 1800s to describe idealizations such as constant temperature. These findings are critical for Geophysics because matter in Earth’s deep interior is under extreme pressures. Here, the researchers will further test the formulation which they previously validated for a limited number of solids and over a limited range of temperature. They now quantify heat properties in a wider range of solids, and other states of matter, and over a greater temperature range. They use a new laser flash apparatus for liquids (water in particular); the new apparatus allows measuring heat capacity and attains low temperature. They re-analyze data on gases available in the literature. The goal is extreme accuracy in the measurement, notably that of initial slope and temperatures near ambient conditions. Both the old and the new formulation for thermal properties are tested. This project may initiate a paradigm shift in the way we quantify heat flow. Its outcomes improve our understanding of the microscopic mechanism responsible for it. They have potentially wide repercussions for pure and applied physical sciences. The project also supports a female scientist with disability and provides training to undergraduate students at University of Washington. Discovery that thermal diffusivity (D) and thermal conductivity (k) of insulators, semi-conductors, metals, alloys, and glasses depends on the length-scale (L) of measurements has repercussions for pure and applied physical sciences. Linear dependence on L for small length-scales agrees with dimensional analysis of Fourier’s heat equation. It shows that results from diamond anvil cell experiments are problematic, foremost because these are benchmarked against 1 atm data for L 100 times larger. Reliable data below 2 GPa pressure exist on mm-sized samples from well-worn methods. Analyzing these results for 25 solids of diverse bond type show that the logarithmic pressure derivative of specific heat (cP) equals -1 times the linear compressibility. Mathematical analysis allowing for k depending on L (i.e., volume) also related its logarithmic pressure response to equation-of-state properties, and likewise for D. The new k vs. P formula was confirmed against reliable data for 20 solids. Therefore, the team’s preliminary tests suggest, but do not prove, that the new formulae are thermodynamic identities describing steady-state conditions, which is a commonly encountered restriction. Isothermal is not, because thermal emissions are ubiquitous. Thus, the time-independent formulations from classical thermodynamics do not describe properly the time-depended conditions in the Earth where heat is flowing. To test the new formula for cP vs. P, databases already in existence can be used. Since a generally applicable formula for steady state is the goal, diverse states of matter and bond type are being tested. The researchers also collect data on liquids and ices (e.g., water, metals melting near 298 K). They use a new laser flash apparatus – the LFA467 instrument and its commercial low-pressure cell to 10 MPa - covering ~100 to 500°C, that simultaneously measures D and cP. Spurious radiative transfer is removed via coating the interior of the cell with graphite. A dilatometer spanning this T range is used when density vs T is not available, to constrain k. Using machine learning to parameterize cP, D, and k vs. P, L, T, will either distinguishing whether the new or previous formulae are correct, or will lead to new and accurate formulae, permitting extrapolation to high pressure inside Earth. Thus, the proposed work provides basic physics that is essential to Geophysics. Confirmed P derivatives of cP and k (or D) pertain to any process inside Earth and other large bodies. The work outcomes lead to improving accuracy of geophysical and petrologic models and has potential to improve our understanding of planetary interiors. Since new thermodynamic identities have not been developed for ~100 years, other physical sciences, such as study of chemical reactions, may be impacted.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.