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We present a detailed investigation on mechanical properties of Zr-X (X=Ti, Hf and Sc) alloy systems using the first-principles calculations in conjunction with special quasi-random structures (SQSs). It is found that the strength of mechanical coefficients such as elastic constants and elastic modulus depend linearly on the composition in Zr-Hf and Zr-Sc systems, whereas they depend parabolically...
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