Date of Award


Degree Name

Master of Science


Computational Science


Jorge A. Munoz


This study aims to assess the mechanical stability of body-centered cubic (BCC) structure, focusing on pure iron as a representative case. The primary approach involves utilizing phonon dispersion curves analysis to gain insights into the vibrational properties and overall stability of the crystal lattice through a multi-faceted computational approach. The goal of the study is to find the regions (pockets) in Born-von Kármán (BvK) parameter space where the crystal is stable for certain temperature and pressure.

This involves setting up the crystal parameters, creating a body-centered cubic (BCC) crystal with specific lattice parameters (2.86 for iron) establishing force constants, and employing Phonopy for phonon dispersion analysis. We developed a genetic algorithm to investigate the mechanical stability of body-centered cubic (BCC) iron in reduced BvK parameter space. For each genetic solution, we calculate the phonon dispersion relations by computing the dynamical matrix at various grid points across the Brillouin Zone. We then evaluate the stability of each solution by measuring deviations from predefined mechanical stability conditions.

Introduction of the RMSE metric provides a quantitative assessment of the accuracy of the computational model. The imaginary frequencies identified during the phonon dispersion analysis highlight potential areas of instability in the BvK space, and application of a genetic algorithm serves as an innovative approach to optimize the model and enhance its accuracy.

The comprehensive nature of this analysis positions it as a foundational study for further exploration into the mechanical stability of metallic crystals, with potential applications in materials science and engineering.




Received from ProQuest

File Size

45 p.

File Format


Rights Holder

Amir Husen