Fig. 1: Schematic description of the entire workflow using fcc Ni as an example. | npj Computational Materials

Fig. 1: Schematic description of the entire workflow using fcc Ni as an example.

From: High-accuracy thermodynamic properties to the melting point from ab initio calculations aided by machine-learning potentials

Fig. 1

The upper box illustrates different stages of direct upsampling: a TILD at different temperatures from effective QH to MTP (whose force RMSEs are shown in (b, c)), and d, e the upsampling to high-DFT. The center box is the crux of the workflow. f is a representation of the free-energy surface, with the (V, T) mesh on which free-energy calculations are performed represented by blue dots, volumes at Tmelt chosen for MTP training set represented by green dots, volumes for the low-temperature effective QH fitting represented by green crosses, the 0 K E–V curve in purple and different derivatives represented by black arrows. g is the free energy as a function of volume at the melting point calculated while including different excitations. The lower box shows the numerically computed (h) isobaric heat capacity Cp, i linear thermal expansion coefficient α and j adiabatic bulk modulus BS along with a comparison to experimentally calculated values41,51,52. (Veq = Veq(T) denotes the equilibrium volume at T and a given pressure, V0K = Veq(0 K) and Vmelt = Veq(Tmelt), where Tmelt is the experimental melting temperature at ambient pressure; S is the entropy).

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