Lattice parameter12/29/2023 Using modern software such as Olex2, one can solve a crystal structure from crystallographic output files. Crystallographic information can be collected via x-ray diffraction, providing information on the locations of electron density within a crystal structure. Calcium fluoride is a classic example of a crystal with a fluorite structure. These relationships can help predict the behavior of crystalline materials, as well as introduce the ability to tune their properties. It is important to understand the crystal structure of materials to form structure-property relationships. Lattice constants for fluorite and antifluorite materials at 300 K MaterialĬrystallography is a powerful tool to investigate the structures of crystalline materials. Choosing other functionals and performing more calculations may give a more accurate result.The antifluorite structure of magnesium silicide Mg 2Si. The difference between our calculated result and experimental results may be due to the fact that we don’t know the “true exchange-correlation functional”. The small error in lattice constant value indicates the accuracy of our DFT calculation. The calculated result is relatively closer to the experimentally observed data at room temperature, with an error of less than 0.1%. Compare to the measured lattice parameter at 4.2 K, our result is a little larger with an error of 0.17%. The result of our calculation is shown in Figure 4. The lattice parameter c is determined by the lattice constant ratio (c/a) 1.592 and the value of the lattice parameter a. The ultrasoft pseudopotential was generated with 12 valence electrons (4s2 4p6 4d2 5s2). It encompasses the superposition of wave fronts scattered by lattice planes, leading to a strict relation between. The core radius for ultrasoft pseudopotential for Zr is 2.1 Bohr (~1.11 Å). In physics and chemistry, Bragg's law, Wulff Bragg's condition or LaueBragg interference, a special case of Laue diffraction, gives the angles for coherent scattering of waves from a large crystal lattice. K-point set of 14*14*11 and cutoff energy of 475eV are used to calculate energy corresponding to different lattice parameters ranging from a=2.6Å to a=3.7Å. The step energy difference was under 0.01eV when k points reached 144 (14*14*11) and under 0.001eV when cut-off energy reached 475 eV.įigure 3 Energy and energy difference versus cutoff energy. The step energy difference (energy calculated in the current step subtract energy calculated in the last step) of two convergence tests was also calculated and has been shown in Figure 2 and Figure 3. 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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