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. 2015 Jul 10;6:7748. doi: 10.1038/ncomms8748

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(a) Schematic illustrations of a big pillar and a small one, with D the pillar diameter and d the grain size. (b) A three-dimensional (3D) graph shows the relation of normalized resolved shear strength (τ/G) versus (D versus d) for the HEA pillars in this study, single-crystalline (sc) HEA11, bcc W20,21, fcc Au18, Ni19 pillars and nanocrystalline (nc) Cu22, Ni23, Ni–W24, Pt44 and Rh45 pillars, with τ resolved shear strength and G the corresponding shear modulus. The Schmid factors of 0.417 and 0.5 are used for the bcc HEA pillar and the nc pillars in the available literature data, respectively. The sample sizes of sc pillars can be regarded as their grain sizes as well. (c) A 3D illustration of size and temperature dependence of the strengths for the HEA pillars ((τ/G) versus (D/b) versus (T_t/T_c)), as described in equation (1). (d) A comparison between the calculated strengths using equation (1) and the experimental values for the HEA pillars. The inset compares pillar strengths, average grain sizes and resistivity of Normal and IBAD HEA films.