1. Minimum Grain Size in Nanostructured Materials Produced by Cryomilling NSF Grant MET DMR-0304629 Farghalli A. Mohamed and Yuwei Xun University of California, Irvine Introduction: Nanocrystalline materials (nc-materials) are polycrystals that are characterized by a grain size in the range of 1-100 nm. The unique microstructures of nc-materials suggest that these materials have the potential of exhibiting exceptional mechanical properties. As a consequence, they have been attracting wide attention in materials research. Primary among the processing techniques that are available for synthesizing nc-materials is ball milling (simplicity, cost, and bulk production). Purpose: It has been shown that continuous milling leads to a minimum grain size, d min, which is a characteristic of each metal. The purpose of this study is to examine the possibility of the presence of correlations between the minimum average grain size, d min, and materials parameters including melting temperature, T m, and hardness, H. Such correlations, if present, should provide insight into the mechanism responsible for the production of nc-materials by milling. Fig.1: The data on the minimum grain size, d min, are plotted as normalized minimum grain size d min /b versus melting temperature, T m, where b is the Burgers vector. Data on nc-metals, regardless of their crystal structure, define a single curve. Data Analysis Fig. 1 Fig. 2 Significance: The research is notable because the results show for the first time that when the data on D min for FCC, BCC and HCP metals are plotted as a function of T m, Q or H, they coalesce into one curve. Fig. 3 Fig. 2: The data are plotted as dmin/b versus the activation energy of self-diffusion in the metal, Q. The correlation between dmin/b and Q is consistent with that of Fig.1. Fig. 3: The data on the minimum grain size, d min, are plotted as d min /b versus the normalized hardness, H/G, where G is the shear modulus and H is Vickers hardness of the metal. As indicated by the figure, the decrease in d min /b with increasing H/G, parallels in trend the decrease in d min /b with increasing T m.

2. Minimum Grain Size in Nanostructured Materials Produced by Cryomilling NSF Grant MET DMR-0304629 Farghalli A. Mohamed University of California, Irvine Primary among the processing techniques that are available for synthesizing nc-materials (grain size < 100 nm) is ball milling. It has been shown that continuous milling leads to a minimum grain size, d min, which is a characteristic of each metal. The purpose of this study is to develop a model that predicts the dependence of d min, on materials parameters. The concept used in developing the model is the presence of a balance between the hardening rate introduced by dislocation generation and the recovery rate arising from dislocation annihilation and recombination. The rate of grain size decrease (  d  t) - : Assumed to be related to the deformation energy provided by milling. This energy is a measure of plastic deformation via dislocation multiplication and motion. The rate of grain size increases, (  d  t) + : Assumed to be proportional to the rate of recovery resulting from dislocations annihilation and recombination to form sub boundaries or low angle boundaries (Fig. 1). Minimum grain size, d min :d min is obtained when (  d  t) + = (  d  t) . Rate Eq.: d min /b = A(e -  Q/4RT )(D po Gb 2 / 0 kT) 0.25 (  /Gb) 0.5 (G/H) 1.25 where A is a dimensionless constant, b is Burgers vector, G is the shear modulus,  Q is the activation energy for the recovery process,  is the stacking fault energy, H is Vickers hardness, T is the absolute temperature, D po is the frequency term for pipe diffusion, R is the gas constant, k is Boltzmann's constant, 0 is a constant. Correlation Between Model Predictions and Expt. Observations Dislocation Model Fig. 1: As milling continues, groups of dislocations approach sub boundaries where they pile- up and enter the walls. Fig. 2: Expt. data for FCC and BCC metals are plotted as d min /b versus the normalized hardness, H/G. As indicated by the figure, the data can be fitted to a straight line with a slope of about 1.3 (predicted 1.25). Fig. 3: Expt. values of d min are plotted as normalized minimum grain size dmin/b versus the activation energy for recovery, QR. The data fall very close to a straight line. According to the analysis in the model, QR scales with melting temperature, Tm, and self diffusion activation energy, Q. The research is significant since a model that provides correlation between d min and materials parameters such as hardness and stacking fault energy has been developed for the first time. Fig. 1 Fig. 2 Fig. 3