Đang chuẩn bị nút TẢI XUỐNG, xin hãy chờ
Tải xuống
Tham khảo tài liệu 'thermodynamics kinetics of dynamic systems part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Closing the Gap Between Nano- and Macroscale Atomic Interactions vs. Macroscopic Materials Behavior 139 predict a mostly linear decrease of the solution energy with increasing volumetric strain. This Fig. 5. Calculations of the strain-dependent solubility of C in an octahedral position in a-iron indicated as the blue atom in left panel show that only few empirical potentials are able to reproduce the results of corresponding DFT calculations Hristova et al. 2011 right panel . 0.8 0.6 0.4 b 0.2 0.0 tq -0.2 -0.4 -0.6 0.94 0.96 0.98 1 1.02 1.04 1.06 V V0 can be understood intuitively in terms of the additional volume of the supercell that can be accommodated by the carbon atom. Despite this comparably simple intuitive picture the majority of investigated EAM and MEAM potentials deviate noticeably from the DFT results. The overall trend a decreasing solution energy with increasing strain is present in all cases. However the error in the slope ranges from qualitatively wrong to quantitatively reasonable. This example shows the need for developing predictive atomistic models. Once they are available they can be employed in determining effective material properties as outlined in the next sections. 3. Lattice kinematics and energy Beyond the task of more or less accurate description of atomic interactions presented in the previous section the question remains how to quantify macroscopic materials data and behaviour by considering the energy of an atom. The example in Section 2.5 already indicates the strategy to predict the un- mixing behaviour. However in order to investigate further mechanical and thermodynamic materials properties a more sophisticated analysis of the atomic energy is necessary which will be done in the subsequent Sections. 3.1 Crystal deformations We start with the consideration of bulk material no surfaces and assume a perfect periodic lattice. The current positions xa xfi x . of all atoms a ft Y . are described by the reference positions Xq Xq X0Y .
