Effect of Long-Range Interactions on Order

Abstract

Harrison and Paskin (HP) have calculated the ordering energy of $\beta$-CuZn using recent theoretical techniques of treating electron screening and Mott's polar model of an alloy. Good agreement is obtained between the calculated total energy of the order-disorder transformation and specific-heat measurements. A consequence of the HP calculation is that the ordering energy is long-range and oscillates in sign. Walker and Keating recently measured the neutron diffuse scattering of $\beta$-CuZn above the critical temperature $T_c$ and find their data are in agreement with order calculated by only considering a nearest-neighbor interaction. Using the Cowley statistical theory of order, we compare the order generated by a nearest-neighbor interaction and the long-range interaction of HP at a temperature $1.1T_c$. We find the average behavior of the order generated by the nearest-neighbor and long-range interaction to be similar. The major difference is the nearest-neighbor interaction generates order that asymptotically, varies smoothly with neighbor distance whereas the order resulting from the long-range interaction fluctuates markedly about the nearest-neighbor generated order. This result may explain the success of statistical theories, based on nearest-neighbor interactions, in both order-disorder of alloys as well as in some magnetic systems which are also believed to have a similar long-range oscillatory interaction.