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Experimental Study on the Thermodynamic Interactions of Phonons and Magnetism in Fe Systems


Hägeli Lohaus, Stefan P. (2023) Experimental Study on the Thermodynamic Interactions of Phonons and Magnetism in Fe Systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/5sb5-fm96.


The macroscopic thermophysical behavior of materials is governed by their atomic level excitations and how they store heat. Most of the thermal energy excites oscillations of the atoms, quantized as phonons, but in magnetic materials a considerable amount of heat is also absorbed by fluctuations of the electronic spins. This thesis explores the thermodynamics of phonons and magnetic spins in Fe-systems: we investigate the coupling between these excitations in Fe, Fe-Ni, and Fe-C, quantify their size dependency in nanocrystalline in Ni₃Fe, and assess their individual roles in the anomalous thermal expansion of Fe-Ni Invar.

Most materials expand when heated due to enhanced atomic oscillations. However, in 1895 C.E. Guillaume combined Fe and Ni to discover a material with near-zero thermal expansion, called Invar. This discovery was awarded the 1920 Physics Nobel Prize and sparked thousands of scientific investigations. Since the anomalous Invar effect is associated with magnetism, nearly all studies have focused on the electronic and spin structure of Fe-Ni. But phonons are needed to complete the picture, and to date, the anomalous Invar behavior is not fully understood. Here, we explore a method for measuring thermal expansion that is capable of isolating contributions from phonons and spins. Since the thermal energy of materials is related to entropy, the thermal expansion can be indirectly determined through individual entropic contributions by using a Maxwell relation. The phonon and magnetic entropies were measured by combining two nuclear resonant x-ray scattering techniques, with samples under pressure in diamond-anvil cells. We show that the Invar behavior stems from a competition between phonons and spins, that oppose each other for near-zero thermal expansion. A spin-phonon coupling improves the precision of this cancellation, extending the range of Invar behavior.

Such a coupling of phonons and spin was also observed in pure Fe and Fe₃C cementite, as their phonon energies correlate to the change in magnetization. This motivated us to develop a magnetic quasi-harmonic model for Fe and Fe₃C, which accounts well for the deviation of phonon energies from pure volumetric effects of the conventional quasi-harmonic approximation.

The thermodynamics of materials is also affected by the size of their crystallites. We determined the size effects on the heat absorption by phonons, electrons, and spins in nanocrystalline Ni₃Fe. All excitations become enhanced in the nanomaterial. In particular, the redistribution of spectral weights amplifies the phonon entropy. This helps stabilize the nanostructure against the enthalpy from its extra grain boundaries. However, the nanostructure is meta-stable, and the grains will grow into their bulk counterpart when diffusion is enabled at elevated temperatures.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Thermodynamics, Materials Science
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Materials Science
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Fultz, Brent T.
Thesis Committee:
  • Faber, Katherine T. (chair)
  • Johnson, William Lewis
  • Alp, Esen E.
  • Scott, Valerie
  • Fultz, Brent T.
Defense Date:5 May 2023
Funding AgencyGrant Number
National Science Foundation1904714
Department of Energy (DOE)DE-FG02-03ER46055
Projects:Thermodynamic origin of the Invar effect, Magnetic quasi-harmonic model for Fe and Fe3C, Thermodynamic stability and heat absorption of nanocrystalline Ni3Fe
Record Number:CaltechTHESIS:06012023-173549089
Persistent URL:
Related URLs:
URLURL TypeDescription related to Chapter 3 "Thermodynamic stability and heat absorption of nanocrystalline Ni3Fe" related to Chapter 4 "Magnetic quasi-harmonic model for Fe and Fe3C"
Hägeli Lohaus, Stefan P.0000-0002-4430-3834
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:15259
Deposited By: Stefan Haegeli Lohaus
Deposited On:02 Jun 2023 23:35
Last Modified:20 Jun 2023 22:43

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