Cu has been used extensively to replace Al as interconnects in ULSI and MEMS devices. However, because of the difference in the thermal expansion coefficients between the Cu film and the Si substrate, large biaxial stresses will be generated in the Cu film. Thus, the Cu film becomes unstable and even changes its morphologies which affects the device manufacturing yield and ultimate reliability. The structural stability and theoretical strength of Cu crystal under equal biaxial loading have been investigated by combining the MAEAM with Milstein-modified Born stability criteria. The results indicate that, under sufficient tension, there exists a stress-free BCC phase which is unstable and slips spontaneously to a stress-free metastable BCT phase by consuming internal energy. The stable region ranges from −15.131 GPa to 2.803 GPa in the theoretical strength or from −5.801% to 4.972% in the strain respectively.

Combining molecular dynamics (MD) simulation with modified analytic embeddedatom method (MAEAM), the formation, migration and activation energies of the point defects for six-kind migration mechanisms in B₂-type TaW alloy have been investigated. The results showed that the anti-site defects TaW and W$_{\text{Ta}}$ were easier to form than Ta and W vacancies owing to their lower formation energies. Comparing the migration and activation energies needed for six-kind migration mechanisms of a Ta (or W) vacancy, we found that one nearest-neighbour jump (1NNJ) was the most favourable because of its lowest migration and activation energies, but it would lead to a disorder in the alloy. One next-nearest-neighbour jump (1NNNJ) and one third-nearest-neighbour jump (1TNNJ) could maintain the ordered property of the alloy but required higher migration and activation energies. So the 1NNNJ and 1TNNJ should be replaced by straight [100] six nearestneighbor cyclic jumps (S[100]6NNCJ) (especially) or bent [100] six nearest-neighbour cyclic jumps (B[100]6NNCJ) and [110] six nearest-neighbor cyclic jumps ([110]6NNCJ), respectively.

Many real-world networks such as the protein–protein interaction networks and metabolic networks often display nontrivial correlations between degrees of vertices connected by edges. Here, we analyse the statistical methods used usually to describe the degree correlation in the networks, and analytically give linear relation in the degree correlation. It provides a simple and interesting perspective on the analysis of the degree correlation in networks, which is usefully complementary to the existing methods for degree correlation in networks. Especially, the slope in the linear relation corresponds exactly to the degree correlation coefficient in networks, meaning that it can not only characterize the level of degree correlation in networks, but also reflects the speed that the average nearest neighbours’ degree varies with the vertex degree. Finally, we applied our results to several real-world networks, validating the conclusions of the linear analysis of degree correlation. We hope that the work in this paper can be helpful for further understanding the degree correlation in complex networks.

This paper analyses the unsteady stagnation-point flow of Oldroyd-B-power-law nanofluid, which has the characteristics of viscoelasticity and shear thinning simultaneously. Modified Cattaneo–Christov heat flux modelis used to describe thermal relaxation and thermal retardation in the heat transfer process. Meanwhile, different from the viscous dissipation of Newtonian fluid, based on the constitutive relation of Oldroyd-B–power-law fluid, the effect of relaxation–retardation viscous dissipation is studied. Additionally, 2 g/l xanthan gum solution is considered as the base fluid and copper oxide (CuO), aluminium oxide (Al$_2$O$_3$) and silver (Ag) with 5% volume fraction areused as nanoparticles. Their thermal conductivities are calculated by experiments. Utilising similar transformations, partial differential equations are cast into ordinary differential equations.And non-linear analyses are done by takingadvantage of the double-parameter transformation expansion method with the base function (DPTEM-BF) method. The outcome illustrates that the velocity holds an opposite trend for Deborah numbers for relaxation and retardationtimes. Furthermore, among the three nanofluids, Ag–xanthan gum nanofluid has the strongest ability to increase heat transfer, which can provide a theoretical basis for industrial processing.