The Origin of Thermal Expansion, and the Temperature Dependence of the Bulk Modulus, of Iron and Iron Alloys

随着温度的升高，金属铁会稍微膨胀，变得不那么坚硬。这些热膨胀和热软化的特性在钢（主要是铁）中是相似的，并且对于机械、基础设施或任何尺寸的设备的工程都很重要。也许令人惊讶的是，2019年还不知道如何计算铁的热膨胀（或其热软化）。这个故事的一些部分，以及它们之间的一些关系，原则上是已知的。例如，随着温度的升高，原子的振动会更剧烈，而原子振动的小细节会对铁的膨胀和软化产生很大的影响。然而，铁的一大挑战是它的磁性也会随着温度的变化而变化。铁原子的振动受到磁性变化的影响，对这些影响的适当计算直到今天才出现。这个项目将通过实验来完成这个故事。它将测量铁原子的振动，获得它们振动频率的全谱。测量将在-258℃到+800℃的温度下进行，同时在1个大气压到9万个大气压的压力下进行。同时精确地获得高温和高压是一项技术挑战。它将采用金刚石砧压力单元。压力电池中非常小的样品（小于0.1毫米）的振动光谱将在阿贡国家实验室的先进光子源上用同步辐射测量。PI希望了解磁性随温度和压力的变化如何改变铁的热膨胀。如果时间允许，可以用类似的方法研究其他材料，如英瓦尔材料。一些关于原子振动的概念，以及它们如何影响材料的热力学，都适合作为视频内容。一些公开的视频教学已经可以获得。它将被组织起来，并添加新的内容，使其对教学有用。一名高中实习生将在夏季接受指导，PI还将帮助支持“编程女孩”组织向帕萨迪纳中学中代表性不足的学生教授计算机编程。这个关于bcc （alpha）铁的实验项目将通过测量样品中P（压力）、T（温度）和V（体积）不同组合下的振动熵来获得状态方程V（T，P）的热力学量。为了获得压力，需要金刚石砧槽，压力槽中的样品必须加热或冷却。主要工作将是57Fe的非弹性核共振x射线散射（NRIXS），样品在同一压力和温度下。NRIXS可以确定状态的声子密度，从而确定振动熵。同时测量核正向散射将显示磁性的变化，而衍射将给出具体体积。热力学关系可以给出热膨胀，beta和体积模量的温度依赖性dB/dT，但现在振动，磁性和电子的单独贡献可以单独确定，并且可以与从量热法中已知的总熵进行有用的比较。对铁来说，β和dB/dT都很有趣，因为它们会被原子振动和磁性之间的相互作用改变。通过合作提出了从头算理论的支持。PI现在使用翻转课堂教学法教授他的材料相变课程。作为这项工作的一部分，他将策划和开发视频内容，以在诸如YouTube等公共视频平台上发布的材料中传达熵、自由能和相变的基本概念。一名高中实习生将在夏季接受指导。PI还将支持“编程女孩”组织向帕萨迪纳中学中代表性不足的学生教授计算机编程。该奖项反映了美国国家科学基金会的法定使命，并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，被认为值得支持。

PART 1: NON-TECHNICAL SUMMARYWith increasing temperature, metallic iron expands a little bit, and it becomes less stiff. These properties of thermal expansion and thermal softening are similar in steels (which are mostly iron), and are important for the engineering of machines, infrastructure, or devices of any size. Perhaps surprisingly, in 2019 it is not known how to calculate the thermal expansion of iron (or its thermal softening). Some of the parts of the story, and some relations between them, are known in principle. For example, atoms vibrate more vigorously with increasing temperature, and small details about atom vibrations make a big difference in how iron expands and softens. A big challenge for iron, however, is that its magnetism also changes with temperature. The vibrations of iron atoms are affected by the change in magnetism, and proper calculations of these effects are only emerging today. This project will complete this story by experiments. It will measure the vibrations of iron atoms, obtaining the full spectrum of their vibrational frequencies. Measurements will be performed at temperatures from -258 C to +800 C, simultaneously at pressures varying from 1 atmosphere to 90,000 atmospheres. Obtaining high temperatures and high pressures simultaneously and precisely is the technical challenge. It will be undertaken with diamond anvil pressure cells. The vibrational spectra of very small samples (less than 0.1 mm in size) in the pressure cells will be measured with synchrotron radiation at the Advanced Photon Source at the Argonne National Laboratory. The PI expects to learn how the change in magnetism with temperature and pressure alters the thermal expansion of iron. Other materials such as Invar may be studied in a similar way if time permits. Some of the concepts about atom vibrations, and how they influence the thermodynamics of materials, are appropriate for video content. Some public video instruction is already available. It will be organized, and new content added, to make it useful for teaching. A high school intern will be mentored during the summer, and the PI will also help support Girls Who Code to teach computer programming to underrepresented students in Pasadena middle schools. PART 2: TECHNICAL SUMMARYThis experimental project on bcc (alpha) iron will obtain thermodynamic quantities underlying the equation of state V(T,P) by measuring the entropy of vibrations at different combinations of P (pressure), T (temperature), and V (volume) in the sample. Diamond anvil cells are required to obtain the pressures, and the sample in the pressure cell must be heated or cooled. The main effort will be inelastic nuclear resonant x-ray scattering (NRIXS) of 57Fe, with samples at simultaneous pressure and temperature. NRIXS can determine the phonon density of states and hence the vibrational entropy. Simultaneous measurements of nuclear forward scattering will show changes in the magnetism, and diffraction will give the specific volume. Thermodynamic relationships can give the thermal expansion, beta, and the temperature dependence of the bulk modulus, dB/dT, but now the individual contributions from vibrations, magnetism and electrons can be identified separately, and usefully compared to the total entropy known from calorimetry. Both beta and dB/dT are interesting for iron because they should be altered by interactions between atom vibrations and magnetism. Support from ab initio theory is proposed through a collaboration. The PI now teaches his course on phase transitions in materials using a flipped classroom pedagogy. As part of this work, he will curate and develop video content to convey essential concepts in entropy, free energy and phase transformations in materials for distribution on public video platforms such as YouTube. A high school intern will be mentored during the summer. The PI will also support Girls Who Code to teach computer programming to underrepresented students in Pasadena middle schools.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.