The Phonon Thermodynamics of Iron and Cementite

Citation

Mauger, Lisa Mary (2015) The Phonon Thermodynamics of Iron and Cementite. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z9TQ5ZH3. https://resolver.caltech.edu/CaltechTHESIS:06092015-103051110

Abstract

The vibrational properties of materials are essential to understanding material stability and thermodynamics. In this thesis I outline vibrational thermodynamic models and the experimental tools that provide evidence on phonon behavior. The introductory section discusses the history of metallurgy and thermodynamic theory, with an emphasis on the role of iron and cementite, two important components of steels. The thermodynamic framework for understanding vibrational material behavior is provided alongside the growing body of experimental and computational tools that provide physical insight on vibrational properties. The high temperature vibrational behavior of iron and cementite are explored within this context in the final chapters.

Body-centered-cubic iron exhibits decreasing phonon energies at elevated temperatures. The observed energy change in not uniform across phonon modes in iron, and specific phonon modes show significant decreases in energy that are not explained by simple vibrational models. This anomalously energy decrease is linked to the second-nearest-neighbor interactions in the bcc structure, through examination of fitted interatomic force constants. The large changes in phonon energy result in a significant increase in the vibrational entropy, called the nonharmonic vibrational entropy, which emulates the temperature behavior of the magnetic entropy across the Curie temperature. The nonharmonic vibrational entropy is attributed to interactions between the vibrations and state of magnetic disorder in the material, which persists above the magnetic transitions and extends the stability region of the bcc phase.

Orthorombic cementite, Fe₃C, exhibits anisotropic magneto-volume behavior in the ferromagnetic phase including regions very low thermal expansion. The phonon modes of cementite show anomalous temperature dependence, with low energy phonon modes increasing their energy at elevated temperatures in the ferromagnetic phase. This behavior is reversed after the magnetic transition and these same phonon modes lower their energies with temperature, consistent with observed thermal expansion. This atypical phonon behavior lowers the vibrational entropy of cementite up to the Curie temperature. The experimentally observed increase in low energy acoustic phonons affects the elastic behavior of Fe₃C, increasing the isotropy of elastic response. First principles calculations link the observed phonon energy increases to specific vibrational modes that are polarized along the b-axis, which aligns with the closest Fe-Fe bonding direction. The nonharmonic behavior of the vibrational modes are discussed in the context of other observations of anomalous anisotropic magneto-volume behavior in Fe₃C.

Thesis Files