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

第一部分：非技术总结随着温度的升高，金属铁会略微膨胀，变得不那么僵硬。热膨胀和热软化的这些特性与钢(主要是铁)相似，对于机械、基础设施或任何尺寸的设备的工程都很重要。或许令人惊讶的是，2019年还不知道如何计算铁的热膨胀(或其热软化)。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，原子的振动更剧烈，原子振动的小细节在铁的膨胀和软化方面产生了很大的不同。然而，铁面临的一大挑战是，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，而对这些影响的正确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，获得其振动频率的全部光谱。测量将在-258摄氏度到800摄氏度的温度下进行，同时在从1个大气压到90,000个大气压的压力下进行。同时准确地获得高温和高压是技术上的挑战。它将与钻石砧座压力室一起进行。阿贡国家实验室的先进光子源将用同步辐射测量压力室中非常小的样品(尺寸小于0.1毫米)的振动光谱。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，可以用类似的方法来研究其他材料，如因瓦尔。关于原子振动的一些概念，以及它们如何影响材料的热力学，适用于视频内容。一些公开的视频指导已经可用。它将被组织起来，并增加新的内容，使其对教学有用。一名高中实习生将在暑期接受指导，PI还将帮助支持编程女孩向帕萨迪纳中学代表不足的学生教授计算机编程。第2部分：技术总结这个关于体心立方(α)铁的实验项目将通过测量样品中P(压力)、T(温度)和V(体积)的不同组合下的振动熵来获得支持状态方程V(T，P)的热力学参数。为了获得压力，需要使用钻石顶压室，并且必须加热或冷却压力室中的样品。主要的工作将是57Fe的非弹性核共振X射线散射(NRIXS)，样品在压力和温度的同时进行。NRIXS可以确定声子的态密度，从而确定振动熵。同时测量原子核的前向散射会显示磁化强度的变化，而衍射会给出比体积。热力学关系式可以给出体积弹性系数的热膨胀系数β和温度依赖关系dB/dt，但现在可以分别识别振动、磁性和电子的单独贡献，并将其与量热法已知的总熵进行有用的比较。β和分贝/dt对于铁来说都很有趣，因为它们应该被原子振动和磁性之间的相互作用所改变。通过一次合作，提出了从头算理论的支持。PI现在使用翻转的课堂教学法教授他的课程，内容是材料中的相变。作为这项工作的一部分，他将策划和开发视频内容，以传达材料中关于熵、自由能和相变的基本概念，以便在YouTube等公共视频平台上分发。一名高中实习生将在暑期接受指导。PI还将支持编程女孩在帕萨迪纳中学向未被充分代表的学生教授计算机编程。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。

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.