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

热流无处不在。物质如何有效地传递热量是至关重要的。了解热传输对许多工程和科学工作至关重要，例如设计微型电子设备或模拟大型行星体的冷却速率。测量热传输特性的最精确的方法（激光闪光分析）已经表明，不同类型的固体的值取决于热量流动的长度。静态属性（例如，密度）不以这种方式表现，因此之前没有进行针对长度的测试。这一发现导致了新的公式描述热动力学行为（传导率，扩散率和热容）作为压力的函数。这些公式描述了稳态条件。这与19世纪发展起来的经典热力学方程形成了鲜明的对比，这些方程描述了诸如恒温等理想化。这些发现对地球物理学至关重要，因为地球内部深处的物质处于极端压力之下。在这里，研究人员将进一步测试他们先前针对有限数量的固体和有限温度范围验证的配方。 他们现在量化了更广泛的固体和其他物质状态以及更大温度范围内的热性质。他们使用一种新的激光闪光装置来测量液体（特别是水）;新装置可以测量热容并获得低温。他们重新分析了文献中有关气体的数据。目标是测量的极端准确性，特别是初始斜率和接近环境条件的温度。 测试了新旧配方的热性能。这个项目可能会引发我们量化热流方式的范式转变。它的结果提高了我们对微观机制的理解，对纯物理科学和应用物理科学具有潜在的广泛影响。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）和热导率（k）取决于测量的长度尺度（L）的发现对纯物理科学和应用物理科学产生了影响。线性依赖于L的小长度尺度同意傅立叶的热方程的量纲分析。它表明，金刚石对顶砧室实验的结果是有问题的，首先是因为这些是对1大气压的数据L 100倍大的基准。 可靠的数据低于2 GPa的压力存在于毫米大小的样品从磨损的方法。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。数学分析允许k取决于L（即，体积）也将其对数压力响应与状态方程性质相关，D.根据20种固体的可靠数据证实了新的k与P关系式。因此，该团队的初步测试表明，但不能证明，新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。等温不是，因为热辐射无处不在。因此，来自经典热力学的与时间无关的公式不能正确地描述地球中热量流动的与时间相关的条件。为了测试cP与P的新公式，可以使用现有的数据库。由于稳态的普遍适用的公式是目标，不同的物质状态和债券类型正在测试。研究人员还收集了关于液体和冰的数据（例如，水，金属在298 K附近熔化）。他们使用了一种新的激光闪光装置-LFA 467仪器及其商用低压电池，压力可达10 MPa -覆盖约100至500°C，可同时测量D和cP。 通过用石墨涂覆电池内部来去除寄生辐射传递。当无法获得密度与T的关系时，使用跨越此T范围的温度计来约束k。使用机器学习来参数化cP，D和k与P，L，T，将区分新的或以前的公式是否正确，或者将导致新的和准确的公式，允许外推到地球内部的高压。因此，拟议的工作提供了基本的物理学是必不可少的地球物理学。已证实的cP和k（或D）的P导数适用于地球和其他大型天体内部的任何过程。工作成果导致提高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。 由于新的热力学恒等式已经有100年没有被开发出来了，其他物理科学，如化学反应的研究，可能会受到影响。这个奖项反映了NSF的法定使命，并被认为是值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估的支持。

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.