#### SurfaceEnergyCubicCrystalBrokenBondFit__TD_955413365818_004

Title A single sentence description. High-symmetry surface energies in cubic lattices and broken bond model v004 Calculates the surface energy of several high symmetry surfaces and produces a broken-bond model fit. In latex form, the fit equations are given by: E_{FCC} (\vec{n}) = p_1 (4 \left( |x+y| + |x-y| + |x+z| + |x-z| + |z+y| +|z-y|\right)) + p_2 (8 \left( |x| + |y| + |z|\right)) + p_3 (2 ( |x+ 2y + z| + |x+2y-z| + |x-2y + z| + |x-2y-z| + |2x+y+z| + |2x+y-z| +|2x-y+z| +|2x-y-z| +|x+y+2z| +|x+y-2z| +|x-y+2z| +|x-y-2z| ) + c E_{BCC} (\vec{n}) = p_1 (6 \left( | x+y+z| + |x+y-z| + |-x+y-z| + |x-y+z| \right)) + p_2 (8 \left( |x| + |y| + |z|\right)) + p_3 (4 \left( |x+y| + |x-y| + |x+z| + |x-z| + |z+y| +|z-y|\right)) +c. In Python, these two fits take the following form: def BrokenBondFCC(params, index): import numpy x, y, z = index x = x / numpy.sqrt(x**2.+y**2.+z**2.) y = y / numpy.sqrt(x**2.+y**2.+z**2.) z = z / numpy.sqrt(x**2.+y**2.+z**2.) return params[0]*4* (abs(x+y) + abs(x-y) + abs(x+z) + abs(x-z) + abs(z+y) + abs(z-y)) + params[1]*8*(abs(x) + abs(y) + abs(z)) + params[2]*(abs(x+2*y+z) + abs(x+2*y-z) +abs(x-2*y+z) +abs(x-2*y-z) + abs(2*x+y+z) +abs(2*x+y-z) +abs(2*x-y+z) +abs(2*x-y-z) + abs(x+y+2*z) +abs(x+y-2*z) +abs(x-y+2*z) +abs(x-y-2*z))+params[3] def BrokenBondBCC(params, x, y, z): import numpy x, y, z = index x = x / numpy.sqrt(x**2.+y**2.+z**2.) y = y / numpy.sqrt(x**2.+y**2.+z**2.) z = z / numpy.sqrt(x**2.+y**2.+z**2.) return params[0]*6*(abs(x+y+z) + abs(x-y-z) + abs(x-y+z) + abs(x+y-z)) + params[1]*8*(abs(x) + abs(y) + abs(z)) + params[2]*4* (abs(x+y) + abs(x-y) + abs(x+z) + abs(x-z) + abs(z+y) + abs(z-y)) + params[3] None Matt Bierbaum Matt Bierbaum 2019 This Test Driver is archived in OpenKIM [1-3]. [1] High-symmetry surface energies in cubic lattices and broken bond model v004. OpenKIM; 2019. doi:10.25950/6c43a4e6 [2] Tadmor EB, Elliott RS, Sethna JP, Miller RE, Becker CA. The potential of atomistic simulations and the Knowledgebase of Interatomic Models. JOM. 2011;63(7):17. doi:10.1007/s11837-011-0102-6 [3] Elliott RS, Tadmor EB. Knowledgebase of Interatomic Models (KIM) Application Programming Interface (API). OpenKIM; 2011. doi:10.25950/ff8f563a Click here to download the above citation in BibTeX format. Not available TD_955413365818_004 SurfaceEnergyCubicCrystalBrokenBondFit__TD_955413365818_004 10.25950/6c43a4e6 https://doi.org/10.25950/6c43a4e6 https://search.datacite.org/works/10.25950/6c43a4e6 Test Driver 2.0 ase SurfaceEnergyCubicCrystalBrokenBondFit__TD_955413365818_003