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

California Institute Of Technology, Pasadena CA

Investigators

Abstract

PART 1: NON-TECHNICAL SUMMARY With 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 SUMMARY This 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.