Article pubs.acs.org/IC
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 Jin-Woong Lee, Satendra Pal Singh, Minseuk Kim, Sung Un Hong, Woon Bae Park,* and Kee-Sun Sohn* Faculty of Nanotechnology and Advanced Materials Engineering, Sejong University, Seoul 143-747, South Korea S Supporting Information *
ABSTRACT: 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. which represent a so-called “experimental evaluation of objective function”. Genetic algorithm is an example of representative metaheuristics that has been of great interest in various materials science research areas.11−14 In particular, the nondominated sorting genetic algorithm (NSGA) has been used by the authors for its versatility in simultaneously treating two or more numbers of objective (fitness) functions. A governing key concept of NSGA is the Pareto optimality theory leading to nondominated sorting based on natural selection.15 More recently, an elitism-reinforced nondominated sorting genetic algorithm, the so-called NSGA-II, has been generally used mostly for faster convergence.16 The use of NSGA-II for phosphor discovery associated with pseudo-high-throughput synthesis and characterization has given rise to several remarkable discoveries, such as Ba(Si,Al)5(O,N)8:Eu2+,1 Ca 1.5 Ba0.5Si5 N6 O3:Eu2+,2 La 4‑xCa xSi12O 3+xN18‑x:Eu 2+,3 and Ca15Si20O10N30:Eu2+.4 In addition, NSGA-II has been success-
1. INTRODUCTION In the recent years a metaheuristics computation-oriented approach has been found to be very helpful for the discovery of several novel phosphors for use in light emitting diodes (LEDs).1−4 Metaheuristics (heuristics optimization) represents experience- and insight-driven optimization strategies that differ from gradient-based traditional optimization strategies.5,6 On the basis of the claim that most engineering and scientific issues are optimization problems, either the discovery or improvement of materials could also be an optimization problem for multio-bjective functions and multi-decision variables. Although metaheuristics approaches have been utilized to sort out many engineering and scientific issues thus far, even in materials science fields,7−10 most cases involve nothing but a parameter evaluation for a certain model-based regression. A notable distinction of our approach from that of conventional metaheuristics computations is that our metaheuristics tasks involve no mathematical models and the objective function values are evaluated by actual experiments. The actual synthesis and characterization of many phosphor samples provide objective function values for the metaheuristics computations, © 2017 American Chemical Society
Received: May 25, 2017 Published: August 4, 2017 9814
DOI: 10.1021/acs.inorgchem.7b01341 Inorg. Chem. 2017, 56, 9814−9824
Article
Inorganic Chemistry
photoluminescence system that included a picosecond Nd:yttrium aluminum garnet (YAG) laser with a pulse repetition frequency of 10 Hz and a charge-coupled device sensor with a time resolution of 10 ns. An excitation wavelength of 355 nm was produced by tripling the 1064 nm frequency of the Nd:YAG laser. We used a 400 nm cutoff filter when TRPL was measured to eliminate any undesired influence from the laser pulse. XRD patterns were recorded using a Rigaku Miniflex 600 with Cu Kα radiation in a 2θ range of 10 to 90° at a step size of 0.01°. Rietveld refinement was carried out using Fullprof software.24
fully utilized for discovery of other functional materials for use in dye sensitized solar cells (DSSC),17,18 metal binders,14 and Li-ion battery cathodes.19 Phosphors mentioned above were useful in phosphor converted white light emitting diodes (pc-WLEDs) for general lightings. However, WLEDs for backlights in liquid crystal displays (LCDs) differs from WLEDs for general lightings, where it needs to pass through RGB color filters to attain high color saturation of three primary colors to realize a brilliant image with high color saturation. Recently, there is huge demand for a narrow band red or green emitting phosphors to attain a high color gamut for brilliant display.20,21 The present investigation was focused on screening the Eu2+-doped Ca−Sr− Ba−Li−Mg−Al−Si−Ge−N compositional search space for a narrow-band green emitting phosphor. It was practically impossible to track down such a huge search space utilizing one-by-one tracking, which is also referred to as enumeration. We had an infinite number of compositions to synthesize and characterize. In fact, we have one of the most advanced highthroughput experimentation systems for powder-based synthesis,1 but even this system could never accomplish the complete screening of this eight-dimensional composition search space. The introduction of an optimization strategy that could reduce the experimental burden NSGA-II should be a very high priority. The goal of the present investigation was to develop a green phosphor, the emission peak wavelength of which should be located at around 530 nm. Therefore, the emission intensity (peak area) and the peak wavelength deviation from 530 nm were adopted as two fitness (objective) functions. The emission intensity was maximized and the peak deviation was minimized during the NSGA-II iteration. Although the deviation from an ideal green point on the color chromaticity diagram was used as an objective function in a previous report,22,23 the peak wavelength deviation adopted here would be a simpler parameter in representing the emission color. With no human intervention, the NSGA-II process finally pinpointed a green, single-phase, well-crystallized phosphor compound. Following the NSGA-II process, we also implemented various optical and structural examinations along with a theoretical approach to density functional theory (DFT) calculation and energy transfer (ET) analysis in order to identify the BaLi2Al2Si2N6:Eu2+ phosphor.
3. EXPERIMENTAL RESULTS AND DISCUSSION 3.1. Brief Introduction of NSGA-II. Genetic algorithm (GA), one of the most well-known stochastic global search methods, was inspired by Darwin’s principle of survival of the fittest, which is known as natural selection in the field of biological evolution.5,15,16 The decision variable was treated as a chromosome and the objective function as fitness. GA operates based on hyperparameters constituting encoding (and decoding), inheritance (insertion or elitism), mutation, selection, and crossover. GA allows individuals to survive when they are better suited to an artificially manipulated environment and individuals that are even less suited to the environment are eradicated. GA usually begins with an ancestor population consisting of randomly generated individuals. The decision variables (the phosphor composition in our case) are encoded into either binary codes or decimal vectors and constitute a chromosome (a string of binary codes or decimals). The fitness (the emission intensity and the peak deviation) of each individual in the population is evaluated experimentally through the exact measurement of emission intensity and peak wavelength of actually synthesized phosphor samples, and thereafter multiple individuals (phosphor samples) are stochastically selected from the current population based on their fitness (e.g., roulette-wheel or tournament selection). The philosophy behind either roulette-wheel or tournament forms of selection is that phosphor samples exhibiting higher fitness are more frequently selected, but those with lower fitness are not thoroughly eradicated. The selected individuals are then modified by crossover and mutation to create a new population. There are various crossover and mutation methods, but their main concept is related to that of a neighbor search. The new population created by the crossover and mutation is then used for generating the next generation, and this process is iterated until a certain predetermined convergence criterion is met. Elitism is accomplished such that one or a few brilliant individuals in the former generation are generally copied and appear in the next generation without the use of GA operations in order to retain their excellence. However, elitism is accomplished in a different way with NSGA-II, when two or more populations are merged prior to the selection procedure. More details concerning the NSGA-II are provided below. GA has been used to solve problems with multiple objective (fitness) functions.15 The goal of multiobjective optimization is not to obtain a specific solution, but to find a set of nondominated solutions (ideally with a good spread) with the assistance of a genetic algorithm. A key for multiobjective optimization is Pareto optimality, which the present investigation used to determine the relative dominance of multiple fitness functions such as emission intensity and peak deviation. We adopted a nondominated sorting genetic algorithm (NSGA), which enabled us to simultaneously optimize two different fitness (objective) functions while they were trading off of one another. Multiobjective optimization problems consist of multidimensional decision variable vectors and multidimensional fitness vectors. Consider a scenario where there are n decision variables and two fitness functions (the emission intensity f1(x) and the peak deviation from 530 nm f 2(x)). The n decision variables can be encoded into either n-dimensional decimal vectors or m-dimensional binary codes.
2. EXPERIMENTAL PROCEDURES Commercially available starting nitrides in a solid-powder state, Ca3N2 (Sigma-Aldrich, 95%), Sr3N2 (Kojundo, 99%), Ba3N2 (Cerac Specialty Inorganics, 99.7%), α-Si3N4 (Ube, unreported), AlN (Sigma-Aldrich, 98%), Li3N (Sigma-Aldrich, 99.5%), Ge (unreported), and Eu2O3 (Kojundo, 99.9%), were dispensed and dry-mixed in a highthroughput manner using a robotic platform for high-throughput dispensing (Swave, ChemSpeed Tech Co. Ltd.) under dry conditions. A so-called combi-chem container, a specially designed sample container made of Al2O3, which involved 22 sample sites, was devised for the high-throughput firing of a large number of samples. The mixed raw materials in the combi-chem container were fired at 1000 °C for 4 h under a N2 flow of 500 mL. The fired samples were subjected to X-ray diffraction (XRD), X-ray absorption near edge structure (XANES) spectroscopy, and continuous-wave photoluminescence (CWPL). The XANES spectrum was measured at the Eu L3 edge via synchrotron radiation X-ray sources in the Pohang Accelerator Laboratory (PAL). CWPL was measured using an in-house spectroscope equipped with a xenon lamp at an excitation wavelength of 360 nm with a 380 nm cutoff filter. The time-resolved emission spectra were also measured using an in-house 9815
DOI: 10.1021/acs.inorgchem.7b01341 Inorg. Chem. 2017, 56, 9814−9824
Article
Inorganic Chemistry f : Rn → R2 or f : Rm → R2 (R: real number space, B: 0 or 1, m > > n) Maximize f1 (x) = y1 , minimize f2 (x) = y2 Objective (fitness) function vector: y = (y1 , y2 )T = (f1 (x), f2 (x)) (1) Decision variable: phosphor composition Decimal vectors or binary code strings: x = (x1, x2, x3, ..., xn)T or NSGA is based on a systematic classification of individuals, which is referred to as Pareto sorting. Before the selection process is performed (tournament selection was used in the present investigation), the population is ranked according to the Pareto dominance, and all nondominated individuals are classified into the first rank with a dummy fitness value. The individuals classified as nondominated share a dummy fitness value, and are then removed from the population, whereupon a second layer of nondominated individuals is then considered. This process continues with the remaining population until all individuals are classified. Since individuals in the first Pareto front have the maximum fitness value, they always receive more chances for selection than the rest of the population. This allows us to search for nondominated solutions, to drive the first Pareto front toward a desirable direction (higher emission intensity and closer to green color), and ultimately to reach a convergence. Pareto optimality is the main issue for NSGA, which determines the relative dominance of y* and y (the thick letter denotes a vector). Each Pareto front represents a set of individuals (fitness function vectors) that are not strictly dominated by other individuals in the fitness function space. One fitness function vector, y*, strictly dominates (or “is preferred to”) other fitness function vectors, y, if each fitness of y* is not dominated by (⊇) the corresponding fitness of y and at least one fitness of y* strictly dominates (⊃) the corresponding fitness of y. This definition can be depicted as follows:
y* ⊇ y if ∀ i yi* ⊇ yi Λ ∃i yi * ⊃ yi
Figure 1. Data library visualization for all 10 generations; each generation consists of an actual photo taken at 360 nm excitations on the top, the pie graphs representing phase fractions calculated from the XRD patterns of each sample site are located in the middle, and the emission spectra for each sample site is on the bottom. of raw materials that did not participate in the reaction and remained as residues. The pie graph construction principle was well described in our previous reports.25 The blank site designates failure samples, which were tarnished, evaporated, or melted (glassified). Each of the constituent compounds was assigned to its corresponding unique color. Details of the constituent compounds along with their structural information are well described in Table 1. As the NSGA-II iteration continued toward later generations, the number of luminescent samples increased and the luminescent phase fraction was conspicuously improved. It should be noted that this sort of artificial evolution took place in a systematic manner with no human intervention. The 10th generation finally exhibited a remarkably improved feature both in terms of the luminescence and the phosphor phase fraction. Almost all sample sites in the 10th generation showed a green luminescence, as shown in the actual photo at the top of Figure 1. The emission spectra drawn in the bottom of Figure 1 also exhibits a growing intensity as the NSGA-II was driven to later generations. As for the phase fraction, most samples in the 10th generation constituted nearly a single phase, which turned out to be BaLi2Al2Si2N6:Eu2+ and included a negligible amount of impurities. Some impurity phases were identified as raw materials such as binary nitrides that exhibit no luminescence, while the other luminescent impurity turned out to be BaSiN2:Eu2+. If the NSGA-II proceeds beyond the 10th generation, a pure single phase should definitely be achieved. However, such a further experiment would be a waste of resources since a simple knowledge-based consideration would easily guide a researcher to a single-phase BaLi2Al2Si2N6:Eu2+, once it was confirmed that the NSGA-II iteration had converged on BaLi2Al2Si2N6:Eu2+. Namely, if we optimized the synthesis processing procedures including composition fine-tuning and more sophisticated controls of synthesis conditions such as firing temperature, gas flow, crucibles, etc., we should definitely get to a single-phase BaLi2Al2Si2N6:Eu2+. However, we precluded any types of human intervention in the present investigation and placed greater emphasis on the fact that the NSGA-II computation alone would converge on an almost single-phase BaLi2Al2Si2N6:Eu2+. Even though the metaheuristics computational approach adopted in the present study ended up with a unique phosphor BaLi2Al2Si2N6:Eu2+with a promising green color emission, this phosphor composition could not be claimed to be a novel because it was very recently discovered by Strobel et al.21 In this regard, the NSGA-II process did not lead to a discovery of novel phosphors, while almost every NSGA-II trial had ended up with the successful discovery of a sufficient number of novel phosphors in our previous reports.1−4 In particular, an unknown phase appeared from the fifth to seventh generations and is marked with a dark brown color in the pie graph representation. This could have been a novel compound that could
(2)
The newly defined domination symbols, i.e., curved inequality symbols such as ⊇ and ⊃, should be differentiated from the conventional symbols. In the present case, y* dominates y if { f1(x*) ≥ f1(x) and f 2(x*) ≤ f 2(x)} and { f1(x*) > f1(x) or f 2(x*) < f 2(x)}. The algorithm is similar to a simple GA, except for the classification of nondominated fronts and the sharing operation. Fitness sharing, so-called niche sharing or niching, helps to distribute the population evenly over the Pareto front. In addition to niche sharing, either crowding-distance calculation or hypervolume calculation can also be used for dummy fitness sharing. An elitism-involved NSGA, which is referred to as NSGA-II,16 was more recently developed to considerably reduce the complexity. In fact, we employed NSGA-II in the present study because it is known to lead to faster convergence. The NSGA-II process incorporates elitism in a unique manner, such that two subsequent generations are combined to find nondominated solutions, which contrast with elitism operations for use in conventional GAs, wherein only a few elitist elements were simply selected out of the preceding generation. 3.2. Results from the NSGA-II-Assisted Combinatorial Screening. We screened the Ca−Sr−Ba−Li−Mg−Al−Si−Ge−N compositional search space using NSGA-II. Generations from first to 10th, each of which contain 22 phosphor samples with different compositions, are systematically shown in Figure 1. These represent actual photos of each generation taken at 360 nm excitations on the top, pie graphs representing phase fractions for each sample site appear in the middle, and the emission spectra for each sample site is located on the bottom. Most samples in the randomly chosen first generation exhibited no luminescence. Many dark blank sites can be seen in the actual photo of the first generation exhibits. According to the phase identification, each sample site represented as a pie graph in the first generation showed no single-phase phosphor compound but was full 9816
DOI: 10.1021/acs.inorgchem.7b01341 Inorg. Chem. 2017, 56, 9814−9824
Article
Inorganic Chemistry
CaMg3SiN4, CaLiAl3N4, SrMg3SiN4, and BaMg3SiN4 phosphors, frequently appeared, and AeSiN2:Eu2+ (Ae= Ca, Sr, and Ba) also recurred in every generation. However, use of the NSGA-II pushed most of the samples toward the green light-emitting BaLi2Al2Si2N6:Eu2+ phosphor in later generations because one of the objective functions of the samples was a deviation from the green color. The NSGA-II rooted out all other color-emitting phosphors via the principle of natural selection. Figure 2 shows the average mol. fraction of each constituent component as a function of generation evolution. It is obvious that the
Table 1. Constituent Compounds Appearing in NSGA-II Iterations and Their Representative Colors Used for the Pie Graphs in Figure 1a
Figure 2. Average mol. fraction of the constituent element at each generation. mol. fractions of Ca, Sr, Mg, and Ge gradually diminished and eventually faded out in later generations. Only Ba, Al, Si, and Li survived to reach later generations. This finding is analogous to the NSGA-II convergence with the BaLi2Al2Si2N6:Eu2+ phosphor. We also examined the luminescent property of all phosphors appearing during the NSGA-II iteration in terms of luminescent intensity and peak wavelength. Figure 3 shows a plot of the luminescent intensity versus the peak wavelength, wherein a clear categorization can be observed between the UCr4C4-type phosphors and the green light-emitting BaLi2Al2Si2N6:Eu2+ phosphor. We also confirmed that most of the
a
In addition, the indices and the 2θ ranges used for the pie graph calculation are listed for each compound.
have led to a discovery of novel phosphor. However, we ruled out a further examination of this phase since it gave no luminescence. This unknown phase was eradicated by the natural selection principle during the NSGA-II iteration because the objective functions that we adopted did not include any structural parameters but only the luminescent traits such as intensity and color. Thus, the NSGA-II process did not give rise to a novel phosphor but converged on the well-known BaLi2Al2Si2N6:Eu2+ phosphor. The NSGA-II enabled the synthesis of a single phase of the BaLi2Al2Si2N6:Eu2+ phosphor without human intervention that must rely on knowledge and experience. Although the pinpointed phosphor BaLi2Al2Si2N6:Eu2+ was not a novel discovery, we rediscovered this phosphor by examining the details of theoretical aspects such as DFTbased phase stability, and, more importantly, novel-energy transfer analysis. In addition, NSGA-II results confirmed that, based on the synthesis conditions we adopted, BaLi2Al2Si2N6:Eu2+ was the only promising green light-emitting phosphor in the Eu2+-doped Ca−Sr− Ba−Li−Mg−Al−Si−Ge−N compositional search space. By altering the synthesis conditions, other novel green phosphors could appear in this compositional space, but the chances are scarce that these could be discovered using conventional synthesis conditions. Extreme synthesis conditions (e.g., higher firing temperatures and higher gas pressures) are recommended for the discovery of a novel green phosphor in the Eu2+-doped Ca−Sr−Ba−Li−Mg-Al−Si−Ge−N compositional search space. While the NSGA-II iteration was in progress, various well-known phosphors other than BaLi2Al2Si2N6:Eu2+ also appeared. For instance, UCr4C4-type phosphors,26−30 including the well-known Eu2+-doped SrLiAl 3 N 4 (SLA), CaMg 2 Al 2 N 4 , SrMg 2 Al 2 N 4 , BaMg 2 Al 2 N 4 ,
Figure 3. PL intensity vs peak wavelength for all entries that appeared during the NSGA-II iteration. Two representative clusters were obviously separated, one for UCr4C4-type phosphors and the other for the green light-emitting BaLi2Al2Si2N6:Eu2+ phosphors. The UCr4C4type phosphors were identified based on a generous categorization criterion that allowed many different symmetries to be categorized as this type when the structure exhibited cuboids (or cuboid-like eightcoordinated polyhedrons) interconnected by tetrahedron edge sharing. 9817
DOI: 10.1021/acs.inorgchem.7b01341 Inorg. Chem. 2017, 56, 9814−9824
Article
Inorganic Chemistry UCr4C4-type phosphors appeared in early generations, and the artificial evolution manipulated by the NSGA-II resulted in BaLi2Al2Si2N6:Eu2+ phosphors in later generations. 3.3. DFT Calculations. We calculated formation energy, band gap, and lattice parameters (theoretical density) for all compounds that appeared in the NSGA-II iteration based on DFT. The generalized gradient approximation (GGA) parametrized by Perdew, Burke, and Ernzerhof (PBE)37 in the Vienna ab initio simulation package (VASP5.3)38−41 was employed as an exchange correlation potential. The projector augmented wave (PAW) potentials42,43 along with a cutoff energy of 500 eV and a k-mesh space of
