STRAIN AND INTERDIFFUSION IN SEMICONDUCTOR HETEROSTRUCTURES

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Factors determining the magnitude of grain-size strengthening in polycrystalline metals

Grain-size strengthening of polycrystalline metals, the Hall-Petch effect, has been described for the past sixty years as a dependence of the strength of polycrystalline metals on the inverse square-root of grain size, d. The value of the coefficient of the dependence has been the subject of discussion throughout. Here, we find what known factors in the experiments may determine its value, by meta-analysis using maximum-likelihood methods of the literature values of the coefficient in sixty-one datasets. No dependence of the coefficient is found on plastic strain, and a strong dependence is found on the average grain size of each study. Combining these and other factors accounts for the reported values of about 80% of the sixty-one coefficients. The grain-size dependence of the Hall-Petch coefficient is an artefact arising from fitting the data to an incorrect expression. An alternative grain-size effect described by a lnd/d function is consistent with the theory of dislocations dynamics and generation. The corresponding analysis of the coefficients of fits based on this theory shows that none of the factors investigated are statistically significant, confirming the correctness of this approach

Easy computation of the Bayes Factor to fully quantify Occam's razor

20 pages plus 5 pages of Supplementary MaterialThe Bayes factor is the gold-standard figure of merit for comparing fits of models to data, for hypothesis selection and parameter estimation. However it is little used because it is computationally very intensive. Here it is shown how Bayes factors can be calculated accurately and easily, so that any least-squares or maximum-likelihood fits may be routinely followed by the calculation of Bayes factors to guide the best choice of model and hence the best estimations of parameters. Approximations to the Bayes factor, such as the Bayesian Information Criterion (BIC), are increasingly used. Occam's razor expresses a primary intuition, that parameters should not be multiplied unnecessarily, and that is quantified by the BIC. The Bayes factor quantifies two further intuitions. Models with physically-meaningful parameters are preferable to models with physically-meaningless parameters. Models that could fail to fit the data, yet which do fit, are preferable to models which span the data space and are therefore guaranteed to fit the data. The outcomes of using Bayes factors are often very different from traditional statistics tests and from the BIC. Three examples are given. In two of these examples, the easy calculation of the Bayes factor is exact. The third example illustrates the rare conditions under which it has some error and shows how to diagnose and correct the error

Material length scale of strain gradient plasticity: A physical interpretation

These data are related to our paper "Dabiao Liu*, and D. J. Dunstan. Material Length Scale of Strain Gradient Plasticity: A Physical Interpretation. International Journal of Plasticity, 98 (2017), 156-47." In this work,the length scales in strain gradient plasticity theories in which the plastic work density can be expressed as a function of the gradient-enhanced plastic strain are here derived from known physical quantities via critical thickness theory. A connection between the length scale and the fundamental physical quantities is elucidated. The combination of the strain and strain-gradient terms within the deformation theory of strain gradient plasticity is addressed. It is shown that, compared with the harmonic sum of the strain and strain-gradient terms in Fleck-Hutchinson theory, the linear combination gives a more reasonable value of length scale, several micrometers, which is close to that in the gradient theory of Aifantis. In contrast, the value of length scale in Nix-Gao theory is much larger, in the millimeter range. The length scales determined by critical thickness theory are in good agreement with those obtained by fitting to experimental data of wire torsion

Peculiar torsion dynamical response of spider dragline silk

This work was supported by the NSFC (No. 11472114), the Natural Science Foundation of Hubei Province (No. 2015CFB394), and the Young Elite Scientist Sponsorship Program by CAST (No. 2016QNRC001). D.L. and D.J.D. thank the support from the EU's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 704292