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Third Order Elastic Constants and Debye Temperature of MgB2 Under Different Pressure: First-Principles Methods

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Abstract

The second-order elastic constants (SOECs) and third-order elastic constants (TOECs) of superconducting MgB2 are investigated by first principles methods combined with homogeneous deformation theory. The Anderson-Grüneisen parameter is obtained from the SOECs and TOECs. The obtained value is 2.13, that is in consistent with the experimental result. The effective elastic constants and Debye temperature are also predicted from SOECs and TOECs, which increase with the increasing of pressure.

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Acknowledgments

This work is supported by the Natural Science Foundation of China (11104361), State Key Laboratory of Coal Mine Disaster Dynamics and Control in Chongqing University (2011DA105287FW201210), and the Fundamental Research Funds for the Central Universities(CDJZR14328801)

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Authors and Affiliations

  1. State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing, 400044, China

    Ke Wang & Xiaozhi Wu

  2. College of Physics and Institute for Structure and Function, Chongqing University, Chongqing, 401331, China

    Ke Wang, Xiaozhi Wu & Rui Wang

  3. College of Materials Science and Engineering, Chongqing University, Chongqing, 400044, China

    Xiaozhi Wu & Qunyi Wei

  4. College of Aerospace Engineering, Chongqing University, Chongqing, 400044, China

    Weiguo Li

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  1. Ke Wang
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  2. Xiaozhi Wu
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  3. Weiguo Li
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  4. Rui Wang
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Corresponding author

Correspondence to Xiaozhi Wu.

Appendix

Appendix

$$ \eta_{ij}= \left( \begin{array}{ccc} \xi & 0 & 0\\ 0 & 0 & 0\\ 0 &0 & 0\\ \end{array} \right), $$
(20)
$$ \eta_{ij}= \left( \begin{array}{ccc} \xi & 0 & 0\\ 0 & \xi & 0\\ 0 &0 & 0\\ \end{array} \right), $$
(21)
$$ \eta_{ij}= \left( \begin{array}{ccc} \xi & 0 & 0\\ 0 &\xi & 0\\ 0 &0 &\xi\\ \end{array} \right), $$
(22)
$$ \eta_{ij}= \left( \begin{array}{ccc} 0 & 0 & 0\\ 0 &\xi & 0\\ 0 &0 &0\\ \end{array} \right), $$
(23)
$$ \eta_{ij}= \left( \begin{array}{ccc} 0 & 0 & 0\\ 0 &0 & 0\\ 0 &0 &\xi\\ \end{array} \right), $$
(24)
$$ \eta_{ij}= \left( \begin{array}{ccc} 0 & 0 & 0\\ 0 &\xi & 0\\ 0 &0 &\xi\\ \end{array} \right), $$
(25)
$$ \eta_{ij}= \left( \begin{array}{ccc} 0 & 0 & \xi\\ 0 &\xi & 0\\ \xi &0 &0\\ \end{array} \right), $$
(26)
$$ \eta_{ij}= \left( \begin{array}{ccc} 0 & 0 & \xi\\ 0 &0 & 0\\ \xi &0 &\xi\\ \end{array} \right), $$
(27)
$$ \eta_{ij}= \left( \begin{array}{ccc} \xi & 0 & 0\\ 0 &0 & \xi\\ 0 &\xi &\xi\\ \end{array} \right), $$
(28)
$$ \eta_{ij}= \left( \begin{array}{ccc} \xi & 0 & \xi\\ 0 &\xi & 0\\ \xi &0 &0\\ \end{array} \right), $$
(29)

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Wang, K., Wu, X., Li, W. et al. Third Order Elastic Constants and Debye Temperature of MgB2 Under Different Pressure: First-Principles Methods. J Supercond Nov Magn 28, 1483–1489 (2015). https://doi.org/10.1007/s10948-014-2927-z

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