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Supplementary Material for manuscript βViscoelasticity of stepped interfacesβ by S. A. Skirlo and M. J. Demkowicz Derivation of shear resistance equation ππ A derivation of the expression relating steady state shear resistance π and strain rate ππ‘ given in the paper may be found in references 8 or 19. We also give a brief derivation here. Consider a two-state model describing atoms in the interface under the influence of stress. At zero stress, the activation energy for transitions between these states is πΈπ . Additionally, the energy of each well is stress-dependent and equals βππ and +ππ. Thus, under non-zero stress, the activation energy from transitions from the former state to the latter is πΈπ + ππ while the reverse transition has activation energy πΈπ β ππ. Thus, at non-zero temperature, the probability of an atom transitioning between states is proportional to π βπΈπ±ππ /πππ . To get the transition rate, we multiply this probability by an attempt frequency π. From this we, find that the net transition rate of atoms from one state to the other is given by π (π βπΈπ +ππ ππ π βπ βπΈπ βππ ππ π ) = ππ βπΈπ /πππ sinh[ππ /ππ π]. In steady state, the continuous net transition rate from one state to the other under a constant applied stress π causes a continuous accumulation of strain at a constant strain rate. We associate each transition with an average atom displacement increment βπ. The strain rate ππ ππ‘ may then be expressed as ππ ππ‘ where πΜ0 = πβπ π = πΜ0 π βπΈπ /πππ sinh[ππ /ππ π], . ππ This expression describes the average relationship between π and ππ‘ and does not account for fluctuations arising from individual transitions. 1