![]() Total energy convergence of sc Pt crystal structure with increasing cutoff energyįigure 2 shows total energy convergence as increasing the cutoff energy from 300 to 700 eV with the selected lattice parameter and the fixed 14 kpoints (3 x 3 x 3 k mesh). The DFT calculation here is done with 14 kpoints (3 x 3 x 3 k mesh) and 300 eV cutoff energy, which are randomly selected.įigure 2. When a = 2.685 Å, the system have energetically the most stable state and thus we use this lattice parameter for this optimization. Then, the lattice parameter is selected by fitting the total energy with the corresponding lattice parameter (Points) to the BM equation (Line) as shown in Figure 1. Selection of the lattice parameter of sc Pt crystal structure for optimizing the cutoff energy (Points – the total energy with the corresponding lattice parameter, Line – the BM equation)įor optimization of cutoff energy, we choose simple cubic Pt crystal. ![]() The cohesive energy is calculated by subtracting the pseudo atomic energy from the total energy and dividing it by the number of atoms in a unit cell.įigure 1. For hcp Pt crystal structure, we vary the ratio of a and c to calculate the cohesive energy and fit the data to BM equation. The optimization of lattice parameter for sc and fcc Pt crystal structure is done, by fitting the cohesive energy obtained from varying the lattice parameters (a) to the Birch–Murnaghan (BM) equation of state and finding the lowest cohesive energy value. The optimal lattice parameter (a0) makes the crystal structure of Pt the most stable, meaning that the Pt crystal has the lowest cohesive energy. All kpoints used for this project is the irreducible kpoints. The optimal value of kpoints is obtained when the total energy difference with regard to the result of highest kpoints is not more than 0.02 eV. For hcp Pt crystal structure, we use M x M x N (M and N are different) of kpoints mesh because the hcp crystal structure has two different lattice constants (a and c). For sc and fcc Pt crystal structures, we use M x M x M of kpoints mesh since sc and fcc crystal structures have the same lattice constant for all three dimensions. We also optimize kpoints for the plane wave set to ensure the convergence of the energy. And then, we determine the optimal cutoff energy when the difference of energy compared to the value obtained from the highest cutoff energy is less than 0.01 eV. Varying the cutoff energy from 300 to 700 eV, we compute the total energy of each Pt crystal structure. The optimal value of cutoff energy for the plane wave set is determined to converge the total energy before the lattice parameter optimization. we also employ On-the-fly generated (OTFG) ultrasoft pseudopotential for Pt to describe the interactions of ionic core and valance electrons, which is set to have a core radius of 2.403 Bohr (~1.27 Å) and use 32 valance electrons with 4f14 5s2 5p6 5d9 6s1 as the electronic configuration. With CASTEP, we use the generalized gradient approximation (GGA) – Perdew Burke Ernzerhof (PBE) as an exchange-correlation functional. For these three crystal structures, we have found the optimal lattice parameter that makes the crystal structure have minimum energy and determined the most favorable crystal structure of Pt comparing cohesive energy.įor the DFT energy calculation, we use material studio with CASTEP calculation package, which is based on a plane wave basis set. The metal crystal can usually have a form of simple cubic (sc), face centered cubic (fcc) and hexagonal close-packed (hcp) crystal structures. DFT is a powerful tool to calculate energy of crystal structures of metals. Simply click the "Reload" button and all will be well with the world.The main goal of this project is to predict the energetically preferred crystal structure and corresponding lattice parameter of Platinum (Pt) using Density functional theory (DFT). You do not have to restart your web browser or your computer after you enable JavaScript. Open your browser preferences, and enable JavaScript. You need to turn JavaScript on in order to control this web page. Video Tutorials Learn about CrystalMaker in these detailed audio-visual tutorials
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