[Paper Review] Effect of spin-orbit coupling on the elastic, mechanical, and thermodynamic properties of Bi-Sb binaries

Sobhit Singh, Irais Valencia-Jaime+2 more|arXiv (Cornell University)|Dec 1, 2017

High-pressure geophysics and materials81 references107 citations

TL;DR

This study uses first-principles density functional theory (DFT) calculations to investigate the effects of spin-orbit coupling (SOC) on the elastic, mechanical, and thermodynamic properties of Bi-Sb binaries across various compositions (x = 0.125 to 0.9). The key finding is that SOC induces elastic softening and enhances auxetic behavior in three monoclinic phases, while elastic moduli and Debye temperature decrease monotonically with increasing Bi concentration.

ABSTRACT

Using first principles calculations, we systematically study the elastic stiffness constants, mechanical properties, elastic wave velocities, Debye temperature, melting temperature, and specific heat of several thermodynamically stable crystal structures of Bi$_{x}$Sb$_{1-x}$ ($0 < x < 1$) binaries, which are of great interest due to their numerous inherent rich properties, such as thermoelectricity, thermomagnetic cooling, strong spin-orbit coupling (SOC) effects, and topological features in the electronic bandstructure. We analyze the bulk modulus ($B$), Young's modulus ($E$), shear modulus ($G$), $B/G$ ratio, and Poisson's ratio ($ u$) as a function of the Bi concentration in Bi$_{x}$Sb$_{1-x}$. The effect of SOC on above mentioned properties is further investigated. In general, we observe that the SOC effects cause elastic softening in most of the studied structures. Three monoclinic structures of Bi-Sb binaries are found to exhibit significantly large auxeticity. The Debye temperature and the magnitude of the elastic wave velocities monotonically decrease with increasing Bi-concentration. We also discuss the specific heat capacity versus temperature data for all studied binaries. Our theoretical results are in excellent agreement with the existing experimental and theoretical data. The comprehensive understanding of the material properties such as hardness, mechanical strength, melting temperature, propagation of the elastic waves, auxeticity, and heat capacity is vital for practical applications of the studied binaries.

Motivation & Objective

• To systematically investigate the impact of spin-orbit coupling (SOC) on the elastic and mechanical properties of Bi-Sb binaries.
• To determine how elastic moduli, Debye temperature, and specific heat vary with Bi concentration (x) in stable crystal structures.
• To identify structural features such as auxeticity and mechanical stability across the Bi-Sb solid solution series.
• To validate theoretical predictions against existing experimental and theoretical data.

Proposed method

• First-principles DFT calculations using the projector augmented wave (PAW) method within the VASP code.
• Use of the PBE exchange-correlation functional and 650 eV plane-wave cutoff for electronic convergence.
• Full structural optimization with Hellmann-Feynman forces below 10−4 eV/Å and energy convergence criterion of 10−8 eV.
• Calculation of elastic stiffness constants (Cij), bulk modulus (B), shear modulus (G), Young’s modulus (E), Poisson’s ratio (ν), and Debye temperature (ΘD).
• Inclusion of spin-orbit coupling (SOC) in all calculations to assess its influence on mechanical and thermodynamic responses.
• Comparison of theoretical results with available experimental data for validation.

Experimental results

Research questions

• RQ1 How does spin-orbit coupling affect the elastic stiffness constants and mechanical properties of Bi-Sb binaries?
• RQ2 What is the variation trend of elastic moduli (B, G, E) and Poisson’s ratio (ν) with increasing Bi concentration (x)?
• RQ3 Which Bi-Sb crystal structures exhibit auxetic behavior, and how does SOC influence this property?
• RQ4 How does the Debye temperature and specific heat capacity vary with Bi concentration, and how does SOC affect these thermodynamic quantities?
• RQ5 To what extent do theoretical predictions of elastic and thermodynamic properties align with experimental measurements?

Key findings

• Spin-orbit coupling induces elastic softening in most studied Bi-Sb binary structures, reducing their elastic stiffness constants.
• Three monoclinic phases—Bi1Sb7, Bi7Sb1, and Bi9Sb1—exhibit negative Poisson’s ratio, indicating significant auxetic behavior in multiple spatial directions.
• Bulk modulus (B), shear modulus (G), and Young’s modulus (E) all decrease monotonically with increasing Bi concentration (x), indicating reduced mechanical strength in Bi-rich compositions.
• Debye temperature (ΘD) and maximum specific heat capacity increase with decreasing Bi concentration, reflecting enhanced vibrational entropy in Sb-rich systems.
• Elastic wave velocities decrease with increasing Bi content, consistent with reduced stiffness and increased softening due to SOC.
• Theoretical predictions for elastic moduli, Debye temperature, and specific heat show excellent agreement with available experimental and theoretical data.