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 ${\mathrm{Bi}}_{x}{\mathrm{Sb}}_{1\ensuremath{-}x}$ ($0lxl1$) 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 band structure. We analyze the bulk modulus ($B$), Young's modulus ($E$), shear modulus ($G$), $B/G$ ratio, and Poisson's ratio ($\ensuremath{\nu}$) as a function of the Bi concentration in ${\mathrm{Bi}}_{x}{\mathrm{Sb}}_{1\ensuremath{-}x}$. The effect of SOC on the 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 auxetic behavior due to the hingelike geometric structure of bonds. The Debye temperature and the magnitude of the elastic wave velocities monotonically increase with increasing Sb concentration. However, anomalies were observed at very low Sb 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.

Elastic, mechanical, and thermodynamic properties of Bi-Sb binaries: Effect of spin-orbit coupling

Linear coefficients of thermal expansion have been measured from 2 to 30 K, 55 to 90 K, and at 283 K for single crystals of As, Sb and Bi inclined at various orientations to the symmetry axis. The principal coefficients alpha /sub /// and alpha perpendicular to and volume coefficient beta are reported, together with the Gruneisen parameters gamma , gamma /sub /// and gamma perpendicular to . The anisotropy of expansion is most marked for As and least for Bi: alpha is negative for As below about 150 K, for Sb below 20 K, but always positive for Bi. beta and hence gamma is positive for each: the limiting value is gamma 0=4.4+or-0.3 for As, 1.00+or-0.03 (Sb) and 1.9+or-0.1 (Bi). gamma (T) has a minimum at 8 to 10 K, a broad maximum between 20 and 40 K, and at room temperature approaches 1.5 for As and 1.0 for Sb and Bi.

https://iopscience.iop.org/article/10.1088/0022-3719/5/19/006/pdf

Thermal expansion of trigonal elements at low temperatures: As, Sb and Bi

The thermal expansion of axial metals is surveyed with particular reference to recent very low temperature data for zinc, cadmium, magnesium, β-tin, indium, bismuth and antimony. For a given solid, the independent thermal expansion coefficients α⊥ and α‖ are conveniently compared at low temperatures by plotting α⊥/T 3 and α‖/T 3 against T. The plots show clearly how contraction in one principal symmetry direction ensues from rapid expansion in the other direction. The Gruneisen functions γ⊥ and γ‖ are discussed for each solid using data from lattice-dynamical models and neutron-diffraction measurements. They show how features of the individual thermal expansions arise from a combination of vibrational, elastic and electronic effects. For these solids and for zirconium, titanium, yttrium and thallium the larger of γ⊥ and γ‖ at high temperatures is that referring to strains in the direction of the stronger forces (judged from the axial ratio). At lower temperatures the inequality reverses, except f...

The Thermal Expansion of Axial Metals

Ultrafast x-ray diffraction at the LCLS x-ray free electron laser has been used to resolve the structural behavior of antimony under shock compression to 59 GPa. Antimony is seen to transform to the incommensurate, host-guest phase Sb-II at $\ensuremath{\sim}11\text{ }\text{ }\mathrm{GPa}$, which forms on nanosecond timescales with ordered guest-atom chains. The high-pressure bcc phase Sb-III is observed above $\ensuremath{\sim}15\text{ }\text{ }\mathrm{GPa}$, some 8 GPa lower than in static compression studies, and mixed Sb-III/liquid diffraction are obtained between 38 and 59 GPa. An additional phase which does not exist under static compression, $\mathrm{Sb}\text{\ensuremath{-}}{\mathrm{I}}^{\ensuremath{'}}$, is also observed between 8 and 12 GPa, beyond the normal stability field of Sb-I, and resembles Sb-I with a resolved Peierls distortion. The incommensurate Sb-II high-pressure phase can be recovered metastably on release to ambient pressure, where it is stable for more than 10 ns.

/pdf/identification-of-phase-transitions-and-metastability-in-1u69vi1clr.pdf

Identification of Phase Transitions and Metastability in Dynamically Compressed Antimony Using Ultrafast X-Ray Diffraction.

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 ($\nu$) 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.

The elastic, mechanical and thermodynamic properties of Bi-Sb binaries: Effect of spin-orbit coupling

Results of measurements of the linear thermal expansion of single-crystal rods of pure antimony and bismuth over the temperature range 200 °K to 8 °K, and 200 °K to 45 °K respectively, made using an optical lever dilatometer, are discussed. The principal linear expansion coefficients αperpendicular and αparallel in the directions perpendicular and parallel to the trigonal axis are tabulated and shown graphically as functions of temperature. For both materials αperpensicular is considerably less than αparallel, with antimony showing the greater anisotropy. αperpendicular for antimony is negative below 20 °K, passing through a minimum at 148 °K. Calculated values of the Gruneisen parameters, γperpendicular and γparallel, corresponding to αperpendicular and αparallel are tabulated together with estimates of the high-temperature limiting values of γperpendicular and γparallel.

https://iopscience.iop.org/article/10.1088/0022-3719/2/1/317/pdf

G V Bunton

Papers

The thermal expansion of antimony and bismuth at low temperatures