Using maximum likelihood estimation approach to adjust parameters of multiphase equations of state: Molybdenum as an example

Abstract

We present a promising systematic and quite automated approach for constructing multiphase equation of state (EOS). The maximum-likelihood-estimation, a well-known statistical tool, is applied to tune the EOS model parameters to better agree with a calibration database. To perform that, we use POOH, a newly developed code for constructing sophisticated EOS. The calibration database is made up of a variety of experimental measurements and theoretical data. As statistics is involved, one crucial point is to create a calibration database including error bars. The error bars are routinely defined when experimental data are involved. We discuss how we have introduced this notion for theoretical calculations. Focusing on molybdenum, the calibration database includes isobaric data, isothermal data, density functional theory-calculations of the melt curve, liquid isotherms, and the critical point. We demonstrate the capability of our methodology to adjust model parameters, creating a reliable multiphase EOS P O O H _ M o _ 21 that fits accurately our calibration database and data not previously considered such as principal and porous Hugoniot.