br Introduction Materials on the

Introduction Materials on the basis of the copper–niobium system with dimensions of structural elements in the nanoscale such as nanolaminates and nanowires [1] represent the prototype of materials for advanced practical applications, due to the combination of high strength characteristics, good electrical conductivity, possible use as superconductors and radiation resistance [2–4]. The radiation resistance of nanolaminates grows with a decrease in the thickness of the component layers [3], which indicates a significant influence of interfacial boundaries on the processes of annihilation of radiation defects. The role of diffusion conductivity of the interphase boundary for annihilation of defects in the copper–niobium system was confirmed by a study of low-temperature diffusion under irradiation [5]. However, the details of this process are yet to be understood completely. In this paper, we study the Cu/Nb system by atomistic simulations to establish the mechanism of interfacial diffusion.
Research technique To perform a molecular-dynamic modeling of diffusion, a sample of Cu/Nb nanolaminate containing an interfacial boundary was used. The prismatic sample contained 36,000 atoms and measured 8.9×9.8×6.0nm. The copper and niobium layers were 3.0nm thick. The layers of the Cu–Nb sample had Kurdyumov–Sachs mutual orientation observed experimentally [6]. An example of such a structure is shown in Fig. 1, where the face-centered cubic (FCC) Cu plane (111) is bordered by the body-centered cubic (BCC) Nb plane (110), and the Cu direction [110] is parallel to the Nb one [111]. Periodic boundary conditions are used. A procedure for constructing samples and interatomic potentials was successfully used in [7–9]. The well-approved copper potentials constructed by Mishin et al. [10] were used in the molecular dynamic modeling by the embedded-atom method (EAM). The EAM potentials for niobium and the pairwise copper–niobium potentials have been constructed on the 6-O-α-Maltosyl-β-cyclodextrin of the experimental data and results of ab initio calculations and presented in our papers [7–9]. A molecular dynamic experiment was carried out with the use of a Verlet algorithm in velocity form [11] and the molecular dynamic simulation step was 2fs (femtoseconds). The sample with the minimized interfacial boundary energy was used for modeling. Then the required temperature of the modeling experiment was set: from the beginning, within 2000 molecular dynamic steps, using the technique of velocity scaling, and then within 3000 steps using a Nose–Hoover algorithm [12]. Temperatures were set in the range from 700 to 1200K in increments of 50K. After setting the required temperature, the sample was kept within 5000 steps without affecting the system. At this time, temperature was controlled in the modeling process. The temperature fluctuation near the constant values with an amplitude not exceeding 0.08% indicated the establishment of the thermodynamic equilibrium in the system under the specified conditions of the modeling. Further, the diffusion experiment was carried out according to our developed procedure for a molecular dynamics computer experiment which was described in Ref. [14]. 20 starting positions of atoms for the states were separated by 5000 molecular dynamics steps. Then, within 1.5 million molecular dynamic steps, the sum of squares for diffusion displacements of atoms for each of the initial moments was calculated. 300 points of the time dependence for the sum of squares of atom displacements on the modeling time were recorded. For each of these points, there was an averaging of 20 starts to reduce the impact of random fluctuations. As diffusion displacements of atoms, we took into account the displacement that was more than 1.5 the average distance between the nearest atoms in ideal copper lattice and 1.0 of the average distance between nearest atoms in the case of niobium. We showed the adequacy of such an approach for the diffusion characteristics of interfacial boundaries in Ref. [15]. We took the time interval of modeling the diffusion experiment as equal to 3ns.