Metaheuristics-Assisted Combinatorial Screening of Eu2+-Doped Ca-Sr-Ba-Li-Mg-Al-Si-Ge-N Compositional Space in Search of a Narrow-Band Green Emitting Phosphor and Density Functional Theory Calculations.

A metaheuristics-based design would be of great help in relieving the enormous experimental burdens faced during the combinatorial screening of a huge, multidimensional search space, while providing the same effect as total enumeration. In order to tackle the high-throughput powder processing complications and to secure practical phosphors, metaheuristics, an elitism-reinforced nondominated sorting genetic algorithm (NSGA-II), was employed in this study. The NSGA-II iteration targeted two objective functions. The first was to search for a higher emission efficacy. The second was to search for narrow-band green color emissions. The NSGA-II iteration finally converged on BaLi2Al2Si2N6:Eu2+ phosphors in the Eu2+-doped Ca-Sr-Ba-Li-Mg-Al-Si-Ge-N compositional search space. The BaLi2Al2Si2N6:Eu2+ phosphor, which was synthesized with no human intervention via the assistance of NSGA-II, was a clear single phase and gave an acceptable luminescence. The BaLi2Al2Si2N6:Eu2+ phosphor as well as all other phosphors that appeared during the NSGA-II iterations were examined in detail by employing powder X-ray diffraction-based Rietveld refinement, X-ray absorption near edge structure, density functional theory calculation, and time-resolved photoluminescence. The thermodynamic stability and the band structure plausibility were confirmed, and more importantly a novel approach to the energy transfer analysis was also introduced for BaLi2Al2Si2N6:Eu2+ phosphors.

Density functional theory calculations for the band gap and formation energy of Pr4-xCaxSi12O3+xN18-x; a highly disordered compound with low symmetry and a large cell size.

A novel oxynitride compound, Pr4-xCaxSi12O3+xN18-x, synthesized using a solid-state route has been characterized as a monoclinic structure in the C2 space group using Rietveld refinement on synchrotron powder X-ray diffraction data. The crystal structure of this compound was disordered due to the random distribution of Ca/Pr and N/O ions at various Wyckoff sites. A pragmatic approach for an ab initio calculation based on density function theory (DFT) for this disordered compound has been implemented to calculate an acceptable value of the band gap and formation energy. In general, for the DFT calculation of a disordered compound, a sufficiently large super cell and infinite variety of ensemble configurations is adopted to simulate the random distribution of ions; however, such an approach is time consuming and cost ineffective. Even a single unit cell model gave rise to 43 008 independent configurations as an input model for the DFT calculations. Since it was nearly impossible to calculate the formation energy and the band gap energy for all 43 008 configurations, an elitist non-dominated sorting genetic algorithm (NSGA-II) was employed to find the plausible configurations. In the NSGA-II, all 43 008 configurations were mathematically treated as genomes and the calculated band gap and the formation energy as the objective (fitness) function. Generalized gradient approximation (GGA) was first employed in the preliminary screening using NSGA-II, and thereafter a hybrid functional calculation (HSE06) was executed only for the most plausible GGA-relaxed configurations with lower formation and higher band gap energies. The final band gap energy (3.62 eV) obtained after averaging over the selected configurations, resembles closely the experimental band gap value (4.11 eV).

Systematic Approach To Calculate the Band Gap Energy of a Disordered Compound with a Low Symmetry and Large Cell Size via Density Functional Theory.

An ab initio calculation based on density functional theory (DFT) was used to verify the disordered structure of a novel oxynitride phosphor host, La4-x Ca x Si12O3+x N18-x , with a large unit cell (74 atoms), low level of symmetry (C2), and large band gap (4.45 eV). Several Wyckoff sites in the La4-x Ca x Si12O3+x N18-x structure were randomly shared by La/Ca and O/N ions. This type of structure is referred to as either partially occupied or disordered. The adoption of a supercell that is sufficiently large along with an infinite variety of ensemble configurations to simulate such a random distribution in a partially occupied structure would be an option that could achieve a reliable DFT calculation, but this would increase the calculation expenses significantly. We chose 5184 independent unit cell configurations to be used as input model structures for DFT calculations, which is a reduction from a possible total of 20 736 unit cell configurations for C2 symmetry. Instead of calculating the total energy as well as the band gap energy for all 5184 configurations, we pinpointed configurations that would exhibit a band gap that approximated the actual value by employing an elitist nondominated sorting genetic algorithm (NSGA-II) wherein the 5184 configurations were represented mathematically as genomes and the calculated total and band gap energies were represented as objective (fitness) functions. This preliminary screening based on NSGA-II was completed using a generalized gradient approximation (GGA), and thereafter, we executed a hybrid functional calculation (HSE06) for only the most plausible GGA-relaxed configurations with higher band gap energies and lower total energies. Finally, we averaged the HSE06 band gap energy over these selected configurations using the Boltzmann energy distribution and achieved a realistic band gap energy that more closely approximated the experimental measurement.