First-principles Investigation of Phonon, Elastic, and Thermodynamic Properties of Co₂MnSi, FeCo₂Si, and CrCo₂Si Heusler Compounds
D. B. Patel *
Department of Physics, Center of Education Indian Institute of Teacher Education, Gandhinagar, Gujarat, India.
B. B. Patel
Backman Coulter, 11800SW 147th Ave, Miami, FL 33196, USA.
N. H. Vasoya
Center of Toy Science, Children’s Research University, Gandhinagar Gujarat India.
J. H. Markana
Department of Nanoscience and Advanced Materials Saurashtra University, Rajkot, India.
*Author to whom correspondence should be addressed.
Abstract
Co-based full-Heusler compounds provide a useful platform for examining how transition-metal substitution modifies lattice dynamics and mechanical response. In this work, a comparative analysis is presented for Co₂MnSi, Co₂FeSi, and Co₂CrSi using the crystallographic, phonon, elastic-tensor, and harmonic-thermodynamic datasets supplied for the three compounds. The structural files describe four-atom cells with nearly identical metrics (a = 3.94914 Å, b = 3.94914 Å, c = 3.94914 Å; α ≈ β ≈ γ = 60°), corresponding to an equivalent cubic parameter of approximately 5.585 Å. Each phonon dataset contains 12 branches sampled at 1,010 reciprocal-space points. No negative entries occur along the supplied phonon paths, with maximum phonon energies of 43.3971, 42.3177, and 43.8669 meV for Co₂MnSi, Co₂FeSi, and Co₂CrSi, respectively. In contrast, analysis of the complete displayed 6 × 6 stiffness matrices gives six positive eigenvalues for Co₂MnSi and Co₂CrSi, whereas Co₂FeSi has two negative eigenvalues (−4.330 and −3.571 GPa), indicating loss of positive definiteness with respect to homogeneous strain. The smallest positive stiffness eigenvalues are 25.85 GPa for Co₂MnSi and 3.44 GPa for Co₂CrSi, demonstrating markedly different soft-strain responses. The reported harmonic thermodynamic functions show increasing entropy and heat capacity and decreasing vibrational Helmholtz free energy with temperature. A systematic normalisation discrepancy is identified in the exported phonon density of states: direct integration gives approximately 49–50 modes, whereas a four-atom primitive cell must contain 12 modes. Division by 4.13567, the approximate THz-to-meV conversion factor, recovers 11.93–12.08 modes, strongly suggesting a frequency-axis/DOS-amplitude conversion inconsistency. The study therefore provides a rigorous comparative assessment of the supplied computational outputs while distinguishing path-specific dynamical behaviour from complete stability and identifying the additional calculations required for a fully reproducible first-principles study.
Keywords: Full-Heusler alloy, MnCo₂Si, FeCo₂Si, CrCo₂Si, phonon dispersion, elastic constants, mechanical stability, vibrational density of states, harmonic thermodynamics