T-BOLS Formulation Dual Competition

The measured size and temperature dependence of the yield strength and compressibility of a nanosolid can be obtained by substituting the size and bond nature-dependent rii(K), d(K), and T iK, m) for the atomic j/u, and T i. The solution is  

In Born s criterion, the additional term cp(K, m, T) includes contributions from bond nature, bond length, and the separation of [T m, K)— T] to the yield strength of a solid in the T-independent HPR treatment. The term [T m, K)— 7] in the Born s criterion is replaced by the net energy dilference in the full-energy approximation. Numerically, these approximations are substantially the same because the addition of rj2 leads to only an insignificant olfset of the relative 

By comparing the currently derived form of Eq. (28.2) with the traditional HPR of Eq. (28.1), one can readily find that the ratio of the size-dependent specific heat per bond follows the traditional T-independent HPR, j/j(A )/j7i(oo) = a K)/a oo) = 1 + Incorporating the activation energy, EpS.K) TJiK) 

The activation energy for dislocation motion is proportional to the size and bond nature dependence of the atomic cohesive energy, or the temperature difference between melting and operation, 

The pre-factor / is an adjustable parameter, which should cover both intrinsic and extrinsic contributions. The Ad K) is the contraction of the mean bond length, and Ac K,m) the perturbation to the mean cohesive energy of a nanograin. 

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