High-throughput screening of the static friction and ideal cleavage strength of solid interfaces

We present a comprehensive ab initio, high-throughput study of the frictional and cleavage strengths of interfaces of elemental crystals with different orientations. It is based on the detailed analysis of the adhesion energy as a function of lateral, γ(x, y), and perpendicular displacements, γ(z), with respect to the considered interface plane. We use the large amount of computed data to derive fundamental insight into the relation of the ideal strength of an interface plane with its adhesion. Moreover, the ratio between the frictional and cleavage strengths is provided as good indicator for the material failure mode – dislocation propagation versus crack nucleation. All raw and curated data are made available to be used as input parameters for continuum mechanic models, benchmarks, or further analysis.

shows the most important results we computed for all considered interfaces. In table S2 the different values for the SFF/A are listed in detail. Together with the SFF/A along the MEP we present the values along two high symmetry directions which are orthogonal to each other. For some interfaces the differences are considerable, and the ratio between the two numbers may be viewed as a measure for the frictional anisotropy of the sliding system.
In table S3 we compare our data for the cleavage strength σ C for some example materials (the same as used in the table in the main paper) to previously calculated data for the ultimate tensile strengthσ ut of these materials. We note that the cleavage strength is fitting well for the more brittle materials at surfaces that are cleavage planes (e.g. W(110) and Si(111)) as expected. For more ductile materials or other lattice planes the materials will rather fail through slip along a lattice plane which is at an angle to the investigated interface, or through the creation and slip of dislocations. In this cases the computed cleavage strength is considerable higher than the ultimate tensile strength.
We remind the reader that a larger amount of information, including computational parameters and raw data, is available as a nested python dictionary alongside a number of python scripts that demonstrate how one can use this data for further analysis.

Details about the rigid separation model and the UBER fits
The rigid separation model might seem like a crude approximation to a material failing under tensile strain. However, it is specifically designed to model brittle fracture, for which it performs well 4 .
Including relaxations of atomic layers perpendicular to the interface plane is possible, but one has to take several finite size effects into account to achieve a physically consistent solution 5, 6 : When elastic effects are considered, the surfaces should separate when the strain energy exceeds the cleavage energy. However, the strain energy per unit area decreases with the system size, as does the critical stress wich is linearly dependent on it for small enough strains. Thus, if the crystal is large enough, both strain energy and critical stress go to zero, and the crystal is not stable with respect to uniaxial strain. To overcome this unphysical result, one has to further consider that the energy barrier for the separation, which can be calculated by transition state theory, increases with the square root of the number of layers in the system 6 . To summarize, the correct treatment of relaxations while separating interfaces under tensile strain is complex, and one needs to investigate system size dependent energies rather than stresses. On the other hand, the simple rigid body separation model we employ is not size dependent, provides reliable upper limits for the ideal tensile strengths of materials 6 and was shown to be well justified by comparison to a simulation of a crack tip under mode 1 loading 7 .
In Fig. S3 we plot the UBER fits for each lattice type. (For bcc and fcc lattices only the curves with the lowest cleavage strength σ C are plotted to avoid cluttering of the plots.) The color coding corresponds to the cleavage energy E C , with dark blue lines showing the lowest values and dark red the highest. Table S1. We report the lattice parameter a (Å), the adhesion energy (J/m 2 ), the static friction force per unit area (SFF/A) along the MEP (GPa), and the cleavage strength (GPa) for all the analysed materials and interfaces.