Bruce AD, Jackson AN, Ackland GJ, Wilding NB
Department of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3JZ, Scotland, United Kingdom.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Jan;61(1):906-19. doi: 10.1103/physreve.61.906.
We present a Monte Carlo method for the direct evaluation of the difference between the free energies of two crystal structures. The method is built on a lattice-switch transformation that maps a configuration of one structure onto a candidate configuration of the other by "switching" one set of lattice vectors for the other, while keeping the displacements with respect to the lattice sites constant. The sampling of the displacement configurations is biased, multicanonically, to favor paths leading to gateway arrangements for which the Monte Carlo switch to the candidate configuration will be accepted. The configurations of both structures can then be efficiently sampled in a single process, and the difference between their free energies evaluated from their measured probabilities. We explore and exploit the method in the context of extensive studies of systems of hard spheres. We show that the efficiency of the method is controlled by the extent to which the switch conserves correlated microstructure. We also show how, microscopically, the procedure works: the system finds gateway arrangements which fulfill the sampling bias intelligently. We establish, with high precision, the differences between the free energies of the two close packed structures (fcc and hcp) in both the constant density and the constant pressure ensembles.
我们提出了一种蒙特卡罗方法，用于直接评估两种晶体结构自由能之间的差异。该方法基于晶格切换变换，通过将一组晶格向量“切换”为另一组晶格向量，同时保持相对于晶格位点的位移不变，将一种结构的构型映射到另一种结构的候选构型上。位移构型的采样采用多正则偏差，以有利于通向网关排列的路径，对于这些路径，蒙特卡罗切换到候选构型将被接受。然后，可以在单个过程中高效地采样两种结构的构型，并根据测量的概率评估它们自由能之间的差异。我们在对硬球系统的广泛研究背景下探索并应用了该方法。我们表明，该方法的效率由切换保留相关微观结构的程度控制。我们还展示了该过程在微观层面上的工作方式：系统会智能地找到满足采样偏差的网关排列。我们高精度地确定了在恒密度和恒压系综中两种密堆积结构（面心立方和六方密堆积）自由能之间的差异。
