Monte Carlo (MC) methods have a long-standing history as partners of molecular dynamics (MD) to simulate the evolution of materials at the atomic scale. Among these techniques, the uniform-acceptance force-bias Monte Carlo (UFMC) method [G. Dereli, Mol. Simul. 8, 351 (1992)] has recently attracted attention [M. Timonova et al., Phys. Rev. B 81, 144107 (2010)] thanks to its apparent capacity of being able to simulate physical processes in a reduced number of iterations compared to classical MD methods. The origin of this efficiency remains, however, unclear. In this work we derive a UFMC method starting from basic thermodynamic principles, which leads to an intuitive and unambiguous formalism. The approach includes a statistically relevant time step per Monte Carlo iteration, showing a significant speed-up compared to MD simulations. This time-stamped force-bias Monte Carlo (tfMC) formalism is tested on both simple one-dimensional and three-dimensional systems. Both test-cases give excellent results in agreement with analytical solutions and literature reports. The inclusion of a time scale, the simplicity of the method, and the enhancement of the time step compared to classical MD methods make this method very appealing for studying the dynamics of many-particle systems.

The uniform-acceptance force-bias Monte Carlo ͑UFMC͒ method ͓G. Dereli, Mol. Simul. 8, 351 ͑1992͔͒ is a little-used atomistic simulation method that has strong potential as alternative or complementary technique to molecular dynamics ͑MD͒. We have applied UFMC to surface diffusion, amorphization, melting, glass transition, and crystallization, mainly of silicon. The purpose is to study the potential and the limitations of the method: to investigate its applicability, determine safe and effective values of the two UFMC parameters-a temperature and a maximum allowed atomic displacement per iteration step-that lead to reliable results for different types of simulations, assess the computational speed increase relative to MD, discover the microscopic mechanisms that make UFMC work, and show in what kind of simulations it can be useful and preferable over MD. It is found that in many simulations, UFMC can be a very efficient alternative to MD: it leads to analogous results in much fewer iteration steps. Due to the straightforward formalism of UFMC, it can be easily implemented in any MD code. Thus both methods can be combined and applied in turn, using UFMC for the acceleration of certain processes and MD for keeping precision and monitoring individual atom trajectories.

The structural and dynamic properties of the interface during the fcc-bcc transformation in pure iron have been investigated by molecular dynamics simulations. An embedded atom method potential was used for the atomic interactions. Two interfaces, close to the Bain and Kurdjumov-Sachs orientation relations, have been examined during the fcc-to-bcc transformation. In each simulation the system was left to evolve freely at the imposed temperature. In a system with fully periodic boundaries no interface motion has been observed, whereas systems with at least one free boundary do show a mobile interface. After an incubation time, there is a very fast transformation from fcc to bcc, with interface velocities reaching values in the range of 200-700 m / s, depending on the interface orientation and on temperature. The characteristics of the transformation are of a martensitic nature, without this being imposed on the system. During the incubation time a complex interface structure is formed, which appears to be essential for the martensitic transformation. From the atomic displacements during the transformation, the occurrence of slip planes can be identified.

Diffusion-induced solid-state amorphization (SSA) was studied in (fcc Ni)/(hcp Ti) multilayers at 523 K. The multilayers had a modulation length of 24.4 nm and an overall composition of Ni4OTi«.They were polycrystalline without coherency between the Ni and Ti sublayers. The phase changes, composition changes, and strain development were studied for annealing times up to 220 h, primarily using x-ray-diffraction methods. Upon annealing, an amorphous phase developed, concurrently with dissolution of Ti in crystalline Ni. The amorphous phase not only formed along the Ni/Ti interfaces, but also along the grain boundaries in the sublayers. Continued amorphization along the original grain boundaries on prolonged annealing implies that fast-diffusion paths in the amorphous phase remained active. Diffusion coefficients were determined, using methods described in a separate paper. The interdiffusion coefficient for the amorphous phase is smaller than the tracerdiffusion coefficient of Ni in hcp Ti and larger than the chemical diffusion coefficient in fcc (Ni, Ti) solid solutions. The reaction virtually stopped after 16 h, when appreciable amounts of crystalline Ni and Ti were still present, which is ascribed to ordering in the crystalline (Ni, Ti) solid solution.Both the dissolution of Ti in crystalline Ni and the amorphization are associated with the development of stress profiles in the multilayer. These are quantitatively discussed and analyzed using the x-ray-diffraction and Fizeau interferometric data.

Uniform acceptance force biased Monte Carlo (UFMC) simulations have previously been shown to be a powerful tool to simulate atomic scale processes, enabling one to follow the dynamical path during the simulation. In this contribution, we present a simple proof to demonstrate that this uniform acceptance still complies with the condition of detailed balance, on the condition that the characteristic parameter λ = 1/2 and that the maximum allowed step size is chosen to be sufficiently small. Furthermore, the relation to Metropolis Monte Carlo (MMC) is also established, and it is shown that UFMC reduces to MMC by choosing the characteristic parameter λ = 0 [Rao, M. et al. Mol. Phys.1979, 37, 1773]. Finally, a simple example compares the UFMC and MMC methods.