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Lattice parameter1/3/2024 The result of energy to cut-off energy and k-points relation was shown in Figure 2 and Figure 3. K-points are tested from 1 to 198 and values of cutoff energy vary from 100 eV to 600 eV. The lattice constant of a= 2.6 Å and c=4.1392 Å (smallest value) is used for the convergence test since the smaller lattice constant usually requires a larger k-point number and this can ensure all the calculations performed in this work converge. Convergence tests were performed on both cutoff energy and k-points. Our calculation used plane-wave bases with on the fly generated ultrasoft (OTFG-ultrasoft) pseudopotentials in CASTEP. The blue atoms are zirconium atoms and the red line indicates the unit cell of α-zirconium. The built α-zirconium is shown in Figure 1.įigure 1 α-zirconium in hcp structure. The lattice constant ratio (c/a) is set to 1.592 and the γ angle was set to be 120 degrees. The space group of α-zirconium is P6 3/mmc (194). The unit cell of Zr single crystal was built according to data from Materials Project. Our calculated result is then compared to the experimentally observed one to verify the accuracy of density functional theory in calculating lattice parameters for single crystals. The lattice parameter corresponding to the lowest energy is the predicted lattice parameter. We first fix a/c ratio and calculate energy corresponding to different lattice constants. In this work, we used DFT calculation to predict the lattice constant for α-zirconium. ĭensity functional theory (DFT) calculation with generalized gradient approximation (GGA) is regarded to be a powerful tool for determining properties of bulk single crystals. The room temperature lattice parameter reported by Easton and Betterton is a= 3.2327 Å and c= 5.1471 Å. The experimentally observed lattice constant for hcp structure α-zirconium by Goldak et al. The high-temperature β phase zirconium is a bcc structure while the room temperature α phase zirconium is in hcp structure. Zirconium single crystal is experimentally observed to have two different crystal structures.
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