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Thermoelastic properties and phase diagram for rare-earth ytterbium

  • Regular Article - Computational Methods
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Abstract

We report results for finite temperature (T) cubic second-order elastic constant (SOEC), elastic moduli, Poisson ratio, Zener elastic anisotropy, and sound velocities for fcc and bcc ytterbium up to melting temperature. We assume that the thermoelasticity is predominantly controlled by equilibrium volume at a given temperature. Our previous first principles scheme for assessing various thermophysical quantities for fcc ytterbium, after including the phonon anharmonicity and the electronic contribution [J. Appl. Phys. 129, 035107 (2021)], has been extended to determine the free energy of bcc-Yb and thereby the high-T structural phase transition (SPT). Computed results for various elastic and anisotropic parameters for both the phases and at the onset of the fcc–bcc phase transformation allowed us to discuss the role of elasticity to understand the physical mechanism operative at the SPT. It is found that the spinodal and shear elastic conditions are obeyed across the SPT, but the Born criterion needs to be modified to incorporate the pressure term to encompass the SPT. For the bcc structure, relatively large lattice anharmonicity and significant thermal stress result in a softer EoS. This, in connection to the modified Born criterion (MBC), explains the elastically stable bcc state. We confirm that the zero-pressure SPT temperature due to MBC (1077 K) agrees with the thermodynamic value (1037 K). The transition temperature is in excellent agreement with experimental data from zero pressure up to 4 GPa of pressure, after which the fcc phase is elastically unstable. Thus, the high-T SPT in Yb is mechanical in origin, similar to the first-order solid–liquid-phase transition.

Graphical abstract

We report results for finite temperature (T) cubic second-order elastic constant (SOEC), elastic moduli, Poisson ratio, Zener elastic anisotropy, and sound velocities for fcc and bcc ytterbium up to melting temperature. Computed results for various elastic and anisotropic parameters for both the phases and at the onset of the fcc–bcc phase transformation allowed us to discuss the role of elasticity to understand the physical mechanism operative at the structural phase transition (SPT). It is found that the spinodal and shear elastic conditions are obeyed across the SPT, but the Born criterion needs to be modified to incorporate the pressure term to encompass the SPT. From the present study, we conclude that the bcc phase is more anisotropic. The SPT in Yb is elastic, similar to the first-order solid–liquid-phase transition. It is thus proposed that the thermal stress produced in the bcc phase, together with the opposite nature of anisotropy, favors the energetically lower bcc phase and explains the mechanical stability. The computed phonon frequencies support this assertion at high-T (≡ expanded volume), which are all positive.

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Data availability

The data supporting this study's findings are available from the corresponding author upon reasonable request.

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Acknowledgements

The authors DDS and BYT acknowledge the Department of Physics, Sardar Patel University, Vallabh Vidyanagar, Gujarat, India, for providing the necessary computing facility.

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Authors and Affiliations

  1. Department of Physics, Sardar Patel University, Vallabh Vidyanagar, 388120, Gujarat, India

    D. D. Satikunvar & B. Y. Thakore

  2. Department of Physics, Maharaja Krishnakumarsinhji Bhavnagar University, Bhavnagar, 364001, Gujarat, India

    N. K. Bhatt

Authors
  1. D. D. Satikunvar
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  2. N. K. Bhatt
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  3. B. Y. Thakore
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Contributions

DDS developed formalism, performed the computations, and draft original manuscript. NKB devised the project, the main conceptual ideas, review, and editing. BYT contributed to the interpretation of results, supervision, and writing—review and editing.

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Correspondence to D. D. Satikunvar.

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Satikunvar, D.D., Bhatt, N.K. & Thakore, B.Y. Thermoelastic properties and phase diagram for rare-earth ytterbium. Eur. Phys. J. B 95, 146 (2022). https://doi.org/10.1140/epjb/s10051-022-00414-w

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