references.bib

@article{Klement1963,title = {Transformations in Mercury at High Pressures},author = {Klement, W. and Jayaraman, A. and Kennedy, G. C.},journal = {Phys. Rev.},volume = {131},issue = {1},pages = {1--6},numpages = {0},year = {1963},month = {Jul},publisher = {American Physical Society},doi = {10.1103/PhysRev.131.1},url = {https://link.aps.org/doi/10.1103/PhysRev.131.1}},
@article{Bridgman1911,
 ISSN = {01999818},
 URL = {http://www.jstor.org/stable/20022750},
 author = {Bridgman, P. W.},
 journal = {Proceedings of the American Academy of Arts and Sciences},
 number = {12},
 pages = {347--438},
 publisher = {American Academy of Arts & Sciences},
 title = {Mercury, Liquid and Solid, under Pressure},
 urldate = {2025-07-01},
 volume = {47},
 year = {1911}
},
@article{Bridgman1935,
  title = {Polymorphism, Principally of the Elements, up to 50,000 kg/${\mathrm{cm}}^{2}$},
  author = {Bridgman, P. W.},
  journal = {Phys. Rev.},
  volume = {48},
  issue = {11},
  pages = {893--906},
  numpages = {0},
  year = {1935},
  month = {Dec},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRev.48.893},
  url = {https://link.aps.org/doi/10.1103/PhysRev.48.893}
},
@article{Zhokhovskii1955,
  author    = {Zhokhovskii, M. K.},
  title     = {Unknown title},
  journal   = {Izmeritel'naya Tekhnika},
  year      = {1955},
  note      = {In Russian}
},
@article{Zhokhovskii1957,
  author    = {Zhokhovskii, M. K. and Razumikhin, V. N.},
  title     = {Unknown},
  journal   = {Izmeritel'naya Tekhnika},
  year      = {1957},
  number    = {4},
  pages     = {43},
  note      = {In Russian}
},
@article{Swenson1958,
  title = {Phase Transition in Solid Mercury},
  author = {Swenson, C. A.},
  journal = {Phys. Rev.},
  volume = {111},
  issue = {1},
  pages = {82--91},
  numpages = {0},
  year = {1958},
  month = {Jul},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRev.111.82},
  url = {https://link.aps.org/doi/10.1103/PhysRev.111.82}
},

@article{Dorogokupets2007, 
year = {2007}, 
rating = {0}, 
title = {Equations of state of MgO, Au, Pt, NaCl-B1, and NaCl-B2: Internally consistent high-temperature pressure scales}, 
author = {Dorogokupets, P. I. and Dewaele, A.}, 
journal = {High Pressure Research}, 
issn = {0895-7959}, 
doi = {10.1080/08957950701659700},
url = {https://www.tandfonline.com/doi/abs/10.1080/08957950701659700}, 
abstract = {{Semiempirical equations of state (EoS) of Au, Pt, MgO, NaCl-B1, and NaCl-B2 based on expanded Mie–Grüneisen–Debye approach, which are consistent both with the Mie–Grüneisen–Bose–Einstein approach and the thermochemical, X-ray, ultrasonic and shock-wave data in a wide pressure-temperature range, have been constructed. It is shown that to determine the volume dependence of the Grüneisen parameter, not only shock-wave and static compression data, but also experimental information on heat capacity, bulk moduli, volume, and thermal expansion coefficient at zero pressure need to be taken into account. Intrinsic anharmonicity is of great importance at construction of EoS at high temperatures and x=V/V 0>1. Cross-comparison of the current equations of state with independent measurements shows that these EoS may be used as the internally consistent and independent pressure scales in a wide range of temperatures and pressures.}}, 
pages = {431--446}, 
number = {4}, 
volume = {27}, 
language = {English}, 
keywords = {}, 
local-url = {file://localhost/Users/glotl/.CMVolumes/Oliver%20Lord%202/Library/Papers%20Library/Dorogokupets/2007/Dorogokupets_High%20Pressure%20Research_2007.pdf}
},


@article{Drewitt2020, 
year = {2020}, 
title = {Structural Ordering in Liquid Gallium under Extreme Conditions}, 
author = {Drewitt, J. W. E. and Turci, F. and Heinen, B. J. and Macleod, S. G. and Qin, F. and Kleppe, A. K. and Lord, O. T.}, 
journal = {Physical Review Letters}, 
issn = {0031-9007}, 
doi = {10.1103/physrevlett.124.145501}, 
pmid = {32338984}, 
abstract = {{The atomic-scale structure, melting curve, and equation of state of liquid gallium has been measured to high pressure (p) and high temperature (T) up to 26 GPa and 900 K by in situ synchrotron x-ray diffraction. Ab initio molecular dynamics simulations up to 33.4 GPa and 1000 K are in excellent agreement with the experimental measurements, providing detailed insight at the level of pair distribution functions. The results reveal an absence of dimeric bonding in the liquid state and a continuous increase in average coordination number n¯GaGa from 10.4(2) at 0.1 GPa approaching ∼12 by 25 GPa. Topological cluster analysis of the simulation trajectories finds increasing fractions of fivefold symmetric and crystalline motifs at high p-T. Although the liquid progressively resembles a hard-sphere structure towards the melting curve, the deviation from this simple description remains large (≥40\%) across all p-T space, with specific motifs of different geometries strongly correlating with low local two-body excess entropy at high p-T.}}, 
pages = {145501}, 
number = {14}, 
volume = {124}, 
keywords = {},
url = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.124.145501}
},


@article{Kechin2001, 
year = {2001}, 
rating = {0}, 
title = {Melting curve equations at high pressure}, 
author = {Kechin, V.}, 
journal = {Physical Review B}, 
doi = {10.1103/physrevb.65.052102}, 
pages = {052102}, 
number = {5}, 
volume = {65}, 
language = {English}, 
keywords = {}

},


@article{Simon1929, 
year = {1929}, 
rating = {0}, 
title = {Bemerkungen zur Schmelzdruckkurve}, 
author = {Simon, F and Glatzel, G}, 
journal = {Zeitschrift f�r anorganische und allgemeine Chemie}, 
doi = {10.1002/zaac.19291780123}, 
pages = {309 -- 316}, 
number = {1}, 
volume = {178}, 
language = {German}, 
keywords = {}, 
month = {01}
}

@article{Cottaar2014, 
year = {2014}, 
rating = {0}, 
title = {{BurnMan: A lower mantle mineral physics toolkit}}, 
author = {Cottaar, Sanne and Heister, Timo and Rose, Ian and Unterborn, Cayman}, 
journal = {Geochemistry, Geophysics, Geosystems}, 
issn = {1525-2027}, 
doi = {10.1002/2013gc005122}, 
abstract = {{We present BurnMan, an open-source mineral physics toolbox to determine elastic properties for specified compositions in the lower mantle by solving an Equation of State (EoS). The toolbox, written in Python, can be used to evaluate seismic velocities of new mineral physics data or geodynamic models, and as the forward model in inversions for mantle composition. The user can define the composition from a list of minerals provided for the lower mantle or easily include their own. BurnMan provides choices in methodology, both for the EoS and for the multiphase averaging scheme. The results can be visually or quantitatively compared to observed seismic models. Example user scripts show how to go through these steps. This paper includes several examples realized with BurnMan: First, we benchmark the computations to check for correctness. Second, we exemplify two pitfalls in EoS modeling: using a different EoS than the one used to derive the mineral physical parameters or using an incorrect averaging scheme. Both pitfalls have led to incorrect conclusions on lower mantle composition and temperature in the literature. We further illustrate that fitting elastic velocities separately or jointly leads to different Mg/Si ratios for the lower mantle. However, we find that, within mineral physical uncertainties, a pyrolitic composition can match PREM very well. Finally, we find that uncertainties on specific input parameters result in a considerable amount of variation in both magnitude and gradient of the seismic velocities.}}, 
pages = {1164--1179}, 
number = {4}, 
volume = {15}, 
language = {English}, 
keywords = {},
url = {https://agupubs.onlinelibrary.wiley.com/doi/10.1002/2013GC005122}
}


@article{Zwolak2007,
year = {2007}, 
title = {{Algorithm 869: ODRPACK95: A weighted orthogonal distance regression code with bound constraints}}, 
author = {Zwolak, Jason W. and Boggs, Paul T. and Watson, Layne T.}, 
journal = {ACM Transactions on Mathematical Software (TOMS)}, 
issn = {0098-3500}, 
doi = {10.1145/1268776.1268782}, 
abstract = {{ODRPACK (TOMS Algorithm 676) has provided a complete package for weighted orthogonal distance regression for many years. The code is complete with user selectable reporting facilities, numerical and analytic derivatives, derivative checking, and many more features. The foundation for the algorithm is a stable and efficient trust region Levenberg-Marquardt minimizer that exploits the structure of the orthogonal distance regression problem. ODRPACK95 was created to extend the functionality and usability of ODRPACK. ODRPACK95 adds bound constraints, uses the newer Fortran 95 language, and simplifies the interface to the user called subroutine.}}, 
pages = {27}, 
number = {4}, 
volume = {33}, 
keywords = {},
url = {https://dl.acm.org/doi/10.1145/1268776.1268782}
}