Inverse Burch-Murnaghan equation using spline interpolation.
In pytheos and also other apps, such as dioptas and burnman, to get volume at a given pressure, root search is used.
However, for extremely incompressible or compressible materials, root search can fail.
In the notebook below, we set up calibration function based on spline interpolation. the function takes the following form:
V = f(P)
Therefore, it becomes very easy to calculate volume from presssure.
Ref: https://en.wikipedia.org/wiki/Spline_(mathematics)
S.-H. Shim (2022) Inverse Birch-Murnaghan equation with spline interpolation. Zenodo. http://doi.org/10.5281/zenodo.6349563