@article{zhao2005thermal,
  author =        {Zhao, Yusheng and Zhang, Jianzhong and
                   Pantea, Cristian and Qian, Jiang and Daemen, Luke L and
                   Rigg, Paulo A and Hixson, Robert S and
                   Gray III, George T and Yang, Yunpeng and Wang, Liping and
                   others},
  journal =       {Phys. Rev. B},
  number =        {18},
  pages =         {184119},
  publisher =     {APS},
  title =         {Thermal equations of state of the $\alpha$, $\beta$,
                   and $\omega$ phases of zirconium},
  volume =        {71},
  year =          {2005},
}

@article{Paramonov:JAP:2022,
  author =        {Paramonov,M. A. and Minakov,D. V. and Fokin,V. B. and
                   Knyazev,D. V. and Demyanov,G. S. and Levashov,P. R.},
  journal =       {J. Appl. Phys.},
  number =        {6},
  pages =         {065102},
  title =         {Ab initio inspection of thermophysical experiments
                   for zirconium near melting},
  volume =        {132},
  year =          {2022},
  doiurl =        {10.1063/5.0088504},
  url =           {https://doi.org/10.1063/5.0088504},
}

@book{young1991phase,
  author =        {Young, David A},
  publisher =     {University of California Press, Berkeley, CA},
  title =         {Phase Diagrams of the Elements},
  year =          {1991},
}

@article{sikka1982omega,
  author =        {Sikka, S K and Vohra, Y K and Chidambaram, R},
  journal =       {Prog. Mater. Sci.},
  number =        {3-4},
  pages =         {245--310},
  publisher =     {Elsevier},
  title =         {Omega phase in materials},
  volume =        {27},
  year =          {1982},
}

@article{ravindran1998density,
  author =        {Ravindran, P and Fast, Lars and Korzhavyi, P A\_ and
                   Johansson, B and Wills, J and Eriksson, Os},
  journal =       {J. Appl. Phys.},
  number =        {9},
  pages =         {4891--4904},
  publisher =     {American Institute of Physics},
  title =         {Density functional theory for calculation of elastic
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                   TiSi 2},
  volume =        {84},
  year =          {1998},
}

@article{bridgman2013resistance,
  author =        {Bridgman, Percy Williams},
  journal =       {Proc. Am. Acad. Arts Sci.},
  number =        {4},
  pages =         {165--251},
  title =         {The resistance of 72 elements, alloys and compounds
                   to 100,000 kg/cm$^2$},
  volume =        {81},
  year =          {1952},
}

@article{jamieson1963crystal,
  author =        {Jamieson, John C},
  journal =       {Science},
  number =        {3562},
  pages =         {72--73},
  publisher =     {American Association for the Advancement of Science},
  title =         {Crystal structures of titanium, zirconium, and
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  volume =        {140},
  year =          {1963},
}

@article{Xia:PRL:1990,
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                   Vohra, Yogesh K.},
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  month =         {Jan},
  number =        {2},
  pages =         {204--207},
  publisher =     {American Physical Society},
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  volume =        {64},
  year =          {1990},
  doiurl =        {10.1103/PhysRevLett.64.204},
  url =           {https://link.aps.org/doi/10.1103/PhysRevLett.64.204},
}

@article{greeff2005phase,
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  journal =       {Modell. Simul. Mater. Sci. Eng.},
  number =        {7},
  pages =         {1015},
  publisher =     {IOP Publishing},
  title =         {Phase changes and the equation of state of Zr},
  volume =        {13},
  year =          {2005},
}

@article{olinger1973zirconium,
  author =        {Olinger, B and Jamieson, J C},
  journal =       {High Temp. -- High Pressures},
  number =        {2},
  pages =         {123--131},
  title =         {Zirconium},
  volume =        {5},
  year =          {1973},
}

@article{Kresse:CMS:1996,
  author =        {Kresse, G. and Furthm{\"u}ller, J.},
  journal =       {Comput. Mater. Sci.},
  number =        {1},
  pages =         {15--50},
  title =         {Efficiency of ab-initio total energy calculations for
                   metals and semiconductors using a plane-wave basis
                   set},
  volume =        {6},
  year =          {1996},
  abstract =      {We present a detailed description and comparison of
                   algorithms for performing ab-initio
                   quantum-mechanical calculations using
                   pseudopotentials and a plane-wave basis set. We will
                   discuss: (a) partial occupancies within the framework
                   of the linear tetrahedron method and the finite
                   temperature density-functional theory, (b) iterative
                   methods for the diagonalization of the Kohn-Sham
                   Hamiltonian and a discussion of an efficient
                   iterative method based on the ideas of Pulay's
                   residual minimization, which is close to an order
                   Natoms2 scaling even for relatively large systems,
                   (c) efficient Broyden-like and Pulay-like mixing
                   methods for the charge density including a new
                   special `preconditioning' optimized for a plane-wave
                   basis set, (d) conjugate gradient methods for
                   minimizing the electronic free energy with respect to
                   all degrees of freedom simultaneously. We have
                   implemented these algorithms within a powerful
                   package called \{VAMP\} (Vienna ab-initio
                   molecular-dynamics package). The program and the
                   techniques have been used successfully for a large
                   number of different systems (liquid and amorphous
                   semiconductors, liquid simple and transition metals,
                   metallic and semi-conducting surfaces, phonons in
                   simple metals, transition metals and semiconductors)
                   and turned out to be very reliable.},
  doiurl =        {10.1016/0927-0256(96)00008-0},
  issn =          {0927-0256},
  url =           {http://www.sciencedirect.com/science/article/pii/
                  0927025696000080},
}

@article{hafner2008ab,
  author =        {Hafner, J{\"u}rgen},
  journal =       {J. Comput. Chem.},
  number =        {13},
  pages =         {2044--2078},
  publisher =     {Wiley Online Library},
  title =         {Ab-initio simulations of materials using VASP:
                   Density-functional theory and beyond},
  volume =        {29},
  year =          {2008},
}

@article{Perdew:PRL:1996,
  author =        {J. P. Perdew and K. Burke and M. Ernzerhof},
  journal =       {Phys. Rev. Lett.},
  pages =         {3865},
  title =         {Generalized Gradient Approximation Made Simple},
  volume =        {77},
  year =          {1996},
}

@article{Perdew:PRL:1997,
  author =        {J. P. Perdew and K. Burke and M. Ernzerhof},
  journal =       {Phys. Rev. Lett.},
  pages =         {1396},
  title =         {Erratum: Generalized Gradient Approximation Made
                   Simple},
  volume =        {78},
  year =          {1997},
}

@article{Blochl:PR:1994,
  author =        {Bl\"ochl, P. E.},
  journal =       {Phys. Rev. B},
  month =         {Dec},
  number =        {24},
  pages =         {17953--17979},
  publisher =     {American Physical Society},
  title =         {Projector augmented-wave method},
  volume =        {50},
  year =          {1994},
  doiurl =        {10.1103/PhysRevB.50.17953},
  url =           {http://link.aps.org/doi/10.1103/PhysRevB.50.17953},
}

@article{Kresse:PRB:1999,
  author =        {Kresse, G. and Joubert, D.},
  journal =       {Phys. Rev. B},
  pages =         {1758},
  title =         {From ultrasoft pseudopotentials to the projector
                   augmented-wave method},
  volume =        {59},
  year =          {1999},
  annote =        {PAW},
}

@book{CRC:2005,
  editor =        {David R. Lide},
  publisher =     {CRC Press, Boca Raton, FL},
  title =         {CRC Handbook of Chemistry and Physics, Internet
                   Version 2005},
  year =          {2005},
}

@article{Armiento:PRB:2005,
  author =        {Armiento, R. and Mattsson, A. E.},
  journal =       {Phys. Rev. B},
  month =         {Aug},
  number =        {8},
  pages =         {085108},
  publisher =     {American Physical Society},
  title =         {Functional designed to include surface effects in
                   self-consistent density functional theory},
  volume =        {72},
  year =          {2005},
  doiurl =        {10.1103/PhysRevB.72.085108},
  url =           {https://link.aps.org/doi/10.1103/PhysRevB.72.085108},
}

@article{Ceperley:PRL:1980,
  author =        {Ceperley, D. M. and Alder, B. J.},
  journal =       {Phys. Rev. Lett.},
  month =         {Aug},
  number =        {7},
  pages =         {566--569},
  publisher =     {American Physical Society},
  title =         {Ground State of the Electron Gas by a Stochastic
                   Method},
  volume =        {45},
  year =          {1980},
  doiurl =        {10.1103/PhysRevLett.45.566},
  url =           {https://link.aps.org/doi/10.1103/PhysRevLett.45.566},
}

@article{le2002symmetry,
  author =        {Le Page, Yvon and Saxe, Paul},
  journal =       {Phys. Rev. B},
  number =        {10},
  pages =         {104104},
  publisher =     {APS},
  title =         {Symmetry-general least-squares extraction of elastic
                   data for strained materials from ab initio
                   calculations of stress},
  volume =        {65},
  year =          {2002},
}

@article{Liu:PRB:2007,
  author =        {Liu, Wei and Li, Baosheng and Wang, Liping and
                   Zhang, Jianzhong and Zhao, Yusheng},
  journal =       {Phys. Rev. B},
  month =         {Oct},
  number =        {14},
  pages =         {144107},
  publisher =     {American Physical Society},
  title =         {Elasticity of $\ensuremath{\omega}$-phase zirconium},
  volume =        {76},
  year =          {2007},
  doiurl =        {10.1103/PhysRevB.76.144107},
  url =           {https://link.aps.org/doi/10.1103/PhysRevB.76.144107},
}

@article{Ming:JAP:1981,
  author =        {Ming,Li‐chung and Manghnani,Murli H. and
                   Katahara,Keith W.},
  journal =       {J. Appl. Phys.},
  number =        {3},
  pages =         {1332-1335},
  title =         {Investigation of a→w transformation in the Zr‐Hf
                   system to 42 GPa},
  volume =        {52},
  year =          {1981},
  doiurl =        {10.1063/1.329760},
  url =           {https://doi.org/10.1063/1.329760},
}

@article{Liu:JAP:2008,
  author =        {Liu,Wei and Li,Baosheng and Wang,Liping and
                   Zhang,Jianzhong and Zhao,Yusheng},
  journal =       {J. Appl. Phys.},
  number =        {7},
  pages =         {076102},
  title =         {Simultaneous ultrasonic and synchrotron x-ray studies
                   on pressure induced α-ω phase transition in
                   zirconium},
  volume =        {104},
  year =          {2008},
  doiurl =        {10.1063/1.2987001},
  url =           {https://aip.scitation.org/doi/abs/10.1063/1.2987001},
}

@book{brandes2013smithells,
  author =        {Brandes, Eric A and Brook, GB},
  edition =       {7th},
  publisher =     {Butterworth-Heinemann Linacre House, Jordan Hill,
                   Oxford},
  title =         {Smithells Metals Reference Book},
  year =          {1992},
}

@article{hao2008phase,
  author =        {Hao, Yan-Jun and Zhang, Lin and Chen, Xiang-Rong and
                   Li, Ying-Hua and He, Hong-Liang},
  journal =       {J. Phys.: Condens. Matter},
  number =        {23},
  pages =         {235230},
  publisher =     {IOP Publishing},
  title =         {Phase transition and elastic constants of zirconium
                   from first-principles calculations},
  volume =        {20},
  year =          {2008},
}

@article{Mouhat:PRB:2014,
  author =        {Mouhat, F\'elix and
                     Coudert, Fran\ifmmode \mbox{\c{c}}\else
  \c{c}\fi{}ois-Xavier},
  journal =       {Phys. Rev. B},
  month =         {Dec},
  number =        {22},
  pages =         {224104},
  publisher =     {American Physical Society},
  title =         {Necessary and sufficient elastic stability conditions
                   in various crystal systems},
  volume =        {90},
  year =          {2014},
  doiurl =        {10.1103/PhysRevB.90.224104},
  url =           {https://link.aps.org/doi/10.1103/PhysRevB.90.224104},
}

@article{Hill:PPSS:1952,
  author =        {Hill, Richard},
  journal =       {Proc. Phys. Soc., London, Sect. A},
  number =        {5},
  pages =         {349},
  publisher =     {IOP Publishing},
  title =         {The elastic behaviour of a crystalline aggregate},
  volume =        {65},
  year =          {1952},
}

@article{Fisher:JAP:1970,
  author =        {Fisher,E. S. and Manghnani,M. H. and
                   Sokolowski,T. J.},
  journal =       {J. Appl. Phys.},
  number =        {7},
  pages =         {2991-2998},
  title =         {Hydrostatic Pressure Derivatives of the
                   Single‐Crystal Elastic Moduli of Zirconium},
  volume =        {41},
  year =          {1970},
  doiurl =        {10.1063/1.1659351},
  url =           {https://doi.org/10.1063/1.1659351},
}