Property trends in simple metals: An empirical potential approach

We demonstrate that the melting points and other thermodynamic quantities of the alkali metals can be calculated based on static crystalline properties. To do this we derive analytic interatomic potentials for the alkali metals fitted precisely to cohesive and vacancy energies, elastic moduli, the lattice parameter, and crystal stability. These potentials are then used to calculate melting points by simulating the equilibration of solid and liquid samples in thermal contact at ambient pressure. With the exception of lithium, remarkably good agreement is found with experimental values. The instability of the bcc structure in Li and Na at low temperatures is also reproduced and, unusually, is not due to a soft T1N phonon mode. No forces or finite-temperature properties are included in the fit, so this demonstrates a surprisingly high level of intrinsic transferability in the simple potentials. Currently, there are few potentials available for the alkali metals, so in addition to demonstrating trends in behavior, we expect that the potentials will be of broad general use.

Figure 1

Effective pairwise potentials (Table 3) showing trends down the group.

Figure 2

Temperature evolution of coexisting crystalline and liquid K in the NPHp ensemble. Simulations had temperatures initialized above or below. After relaxation all systems equilibrated to a single coexistence temperature. The inset is a snapshot of the simulation, with the periodic boundary conditions removed in the graphics to show the two distinct phases. Similar behavior was observed for other elements

Figure 3

Volume against temperature for steady heating in $NPT$ molecular dynamics. Volumes are scaled to their low-$T$ bcc value to show trends in thermal expansion across the group, from lowest to highest, Li (red), Na (green), K (blue), Rb (black), and Cs (brown). The heating rate was 1 K per 4000 time steps, with the time step varying with the atomic mass from 0.1 fs for Li to 1 fs for Cs. Ringing-mode volume oscillations come from the Nose thermostat and Parrinello-Rahman barostat and persist for hundreds of picoseconds. Sharp rises in volume around 400 K for Cs, Rb, and K indicate melting, although hysteresis means this is not the thermodynamic melting point. The large oscillations for Li show the immediate transformation to close packing at low $T$. The two changes in slope for Na come from the (metastable) bcc-fcc transition at about 100 K and the subsequent fcc-bcc retransformation around 200 K.

Figure 4

Coexistence line for Na integrated from a single simulation at $P=0.0$ using the Clausius-Clapeyron equation. Solid line: Best estimate based on the specific enthalpy and volume differences between the solid and liquid at the zero-pressure melting point of 405 K. Dashed lines: 67% confidence intervals based on the relative errors in the initial slope.

Figure 5

Phonon spectra calculated using lattice dynamics in lithium in bcc (left, fitted) and fcc (right).

Figure 6

Phonon spectra calculated using lattice dynamics in Cs bcc (left, as fitted) and fcc (right, unstable phase).