Electronic Material Properties - und Geowissenschaften ...

In this study, we have therefore determined the Pt-Rh phase diagram by calculating
the grand canonical potential. We applied the thermodynamic integration method
using lattice-based Monte Carlo simulations in the semi-grand canonical ensemble,
where the total number of atoms is fixed, while the difference between the number of
A and B type atoms is allowed to fluctuate for a fixed chemical potential. A
numerically efficient lattice based Hamiltonian was developed by fitting an improved
version of DePristo’s bond-order simulation (BOS) mixing model [4] to a set of input
data obtained from DFT calculations. The calculated the phase diagram of Pt-Rh is
shown in Fig. 1. The phase boundaries are obtained by looking for discontinuities in
the order parameter when integrating down over temperature at constant chemical
potential, and for discontinuities in concentration when integrating over the chemical
Fig. 2: The first eight Warren-Cowley short range order parameters in the vicinity of the
order-disorder transition for Pt-50 at.% Rh. The ordered structure below the transition
temperature is “40”.
potential at constant temperature.
The order-disorder transition of both ordered phases were furthermore analyzed by
calculating the Warren-Cowley short range order parameters (see Fig. 2).
The jump in the order parameters occurs at 239 K if we start with an ordered
configuration and is slightly higher if a random distribution is cooled from high
temperatures. The order-disorder transition was also examined for the stable D022
structure at a concentration of 75 % rhodium. In that case we find a transition
temperature of 210K. Just as for the case of the “40” structure the phase transition is
of first order.
[1] E. Raub, J. Less-Common Met 1, 3 (1959)
[2] Z. Lu, B. Klein and A. Zunger, J. Phase Equilib. 16, 36 (1995)
[3] C. Steiner et al., Phys. Rev. B 71, 104204 (2005)
[4] L.Zhu and A. DePristo, J. Chem. Phys. 102, 5342 (1995)
[5] A. Kohan, P. Tepesch, G. Ceder and C. Wolverton, Comp. Mat. Sci. 9, 389 (1998)
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