Thermodynamics from ab initio computations

Links are established between the standard states and variables of thermodynamics and those of ab initio methods. This is a potentially powerful connection, not only improving the link between thermodynamics and atomic-level computations, but also increasing the predictability of ab initio techniques. The free energies connecting ab initio and thermodynamic standard states are called connection energies. Standard state connection energies for solids are written in terms of specific heats and entropies of the solids. Gaseous state connection energies can be written in terms of either gaseous properties or in terms of properties of the solids that are in thermodynamic equilibrium with the gases. Having two different references for these energies improves the robustness of the method. Equating these two gaseous connection energy expressions yields a simple relationship that must be obeyed by solid formation entropies. Finally, an ab initio structural phase diagram of ultrathin ${\text{Al}}_x{\mathrm{O}}_y$ films on Al-doped Cu(111) is obtained.

Figure 1

Comparison of the oxygen-ambient connection energy ${\Delta }_{O_2}^0\left(T,p_{O_2}^0=1\text{atm}\right)$ from the present model [Eq. (14)] with that from the direct gas approach (JANAF tables, Refs. 8, 35).

Figure 2

Phase diagram (as a function of the Al activity and ambient oxygen partial pressure) for ultrathin ${\text{Al}}_x{\mathrm{O}}_y\left(0001\right)$ films on Al-doped $\text{Cu}\left(111\right)$. A temperature of $1200\mathrm{K}$ is assumed and logarithms are to the base 10.