Residual entropy of ordinary ice from multicanonical simulations

We introduce two simple models with nearest-neighbor interactions on three-dimensional hexagonal lattices. Each model allows one to calculate the residual entropy of ice I (ordinary ice) by means of multicanonical simulations. This gives the correction to the residual entropy derived by Pauling [J. Am. Chem. Soc. 57, 2680 (1935)]. Our estimate is found to be within less than 0.1% of an analytical approximation by Nagle [J. Math. Phys. 7, 1484 (1966)], which is an improvement of Pauling’s result. We pose it as a challenge to experimentalists to improve on the accuracy of a 1936 measurement by Giauque and Stout [J. Am. Chem. Soc. 58, 1144 (1936)] by about one order of magnitude, which would allow one to identify corrections to Pauling’s value unambiguously. It is straightforward to transfer our methods to other crystal systems.

Figure 1

(Color online) Lattice structure of one layer of ice I. The up (u) sites are at $z=1∕\sqrt{24}$ and the down (d) sites at $z=-1∕\sqrt{24}$. For each site, three of its four pointers to nearest-neighbor sites are shown.

Figure 2

Fit for $W_1$.