Searching for the Optimized Luminescent Lanthanide Phosphor Using

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Searching for the Optimized Luminescent Lanthanide Phosphor Using Heuristic Algorithms Ruichan Lv,*,† Liyang Xiao,† Yanxing Wang,† Fan Yang,† Jie Tian,*,† and Jun Lin*,‡ †

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Engineering Research Center of Molecular and Neuro Imaging, Ministry of Education, School of Life Science and Technology, Xidian University, Xi’an, Shaanxi 710071, China ‡ State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China S Supporting Information *

ABSTRACT: In this research, four heuristic algorithms (HAs), including simulated annealing (SA), improved annealing with a harmony search algorithm (HSA), particle swarm optimization (PSO), and genetic algorithm (GA), were used to optimize the luminescent intensity of phosphor. Among the four HAs, the improved algorithm HSA got better phosphors than SA (without using the known coded concentration). The PSO algorithm got gradually better results with increased generation, and the GA could find the best local phosphors with shorter time. After further analysis of the 340 phosphors, we found that the final brightness has an optimized activator concentration (Tb: 0.21−0.26), and the results were further proved by another uniform host of NaGdF4:Ce,Tb nanoparticles. The HA was proper to find the optimal concentration of the activator of Tb. Furthermore, the optimal phosphor could be used as a bioimaging agent and improved QR code.

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INTRODUCTION Lanthanide-based materials with typical advantages such as stable physical/chemical properties, various excitation wavelengths and emissions, and adjustable emission color have attracted wide attention.1−6 These kinds of materials have been extensively researched and commercially applied in different fields like cinema projectors and mobile headlamps.7−11 Besides their application in industrial illumination, they have also been widely utilized in the photosensor, optogenetic, photoactive therapy, and bioimaging fields.12−24 Finding phosphors with optimal luminescent properties (intensity, lifetime, and quantum yield) is a hot but challenging topic.25−29 Research using “trial-and-error” methods or intuitive experiments based on existing experiences usually costs too much time, and improvement was not very obvious.30−32 General procedures with the artificial intelligence (AI) algorithm have been rapidly developed with the ability to adapt to the environment.33−39 However, there is very little literature on developing or improving the AI algorithm to search for the optimal luminescent lanthanide compound. The heuristic algorithm (HA), included in the AI algorithm, is the typical optimization strategy to guide researchers to find better results, and it was considered superior to any other © XXXX American Chemical Society

method based on gradient local optimization. Also, computational chemistry is a science that studies the properties of molecular clusters and chemical reactions based on the basic physical chemistry theory and a large number of numerical calculation methods, which may consume a large amount of computing power to obtain the final expected optimization. Compared with computational chemistry, HA transforms the relationship between the element ratio and luminescence intensity into a simple mathematical question. The HA does not depend on the physical chemistry theory, and this calculation process is based on intuitive experience to give a feasible result with an acceptable cost (refers to the computing time and space).40−42 It is well-known that the phosphors were codoped with host, activator, and sensitizer. HA could use the known parameters and corresponding fitness to predict the parameters in the next generation; thus, it is very suitable for use in finding new better phosphors. We developed the genetic algorithm (GA) to optimize the phosphors, and the luminescence could be improved compared to the proposed brightest phosphor.43 This gives us inspiration to further Received: March 7, 2019

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DOI: 10.1021/acs.inorgchem.9b00667 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Scheme 1. Schematic Diagram of the Improved HSA Program

rate of 10°/min in the 2θ range from 20° to 80° with graphitemonochromatized Cu Kα radiation (λ = 0.15405 nm). Photographs of the phosphors and the QR code under a UV lamp (lamp power: 24 W) were measured using a wavelength of 254 nm. The computed tomography (CT) imaging experiments were performed on a microCT scanner at a voltage of 50 kV and an electric current of 0.3 mA. HA. The first objective of the four HAs for the optimized phosphors with higher luminescence intensity is to design the encoding strategy for the research subject. The phosphors’ codes are the direct application objective of these HAs, and a good coding strategy is beneficial to finding phosphors with high luminescence intensity. The total amount of gadolinium, lanthanum, lutetium, cerium, and terbium is 1, and we encode the individual amounts of these five elements by the decimal coding method. All of the following algorithms start with the same first-generation data. The detected brightness is used as the fitness. The phosphors are denoted as generation−sample number, for example, the 20th phosphor in the first generation is named as No. 1−20. SA Algorithm. The parameters involved are as follows: (1) the state database of the particles (S), containing 20 phosphors’ codes; (2) the new state database of the particles (SN); (3) the Metropolis accept criterion P = exp[dE/(Tδn−1)]. dE is the enhanced energy value after cooling. Here, it means the enhanced fitness/brightness value between the phosphors in the next and current generations. T is the initial temperature, which is set as 2.3. δ is the cooling coefficient, which is set as 0.4. n is the number of iterations (generations). The algorithm process is carried out as follows: (1) SN is generated from S by using the state-generating function, and the state-generating function is similar to the single-point mutation operator of GA. (2) SN is normalized and used to synthesize the phosphors. Then the fitness values are detected if the fitness value of SNi (i = 1, ..., 20) is higher than that of Si (i = 1, ..., 20), and SNi is taken as the new code in the next generation. Otherwise, there is still a probability {P = exp[dE/(Tδn−1)]} to accept SNi as the Si codes. Improved SA with HSA. HSA is one new HA processed by imitating a musician composing music. The schematic diagram of the original HA is shown in Scheme S1, and the schematic diagram of the improved HSA is shown in Scheme 1. During the creating harmony process, the musician changes, repeats, or adjusts some harmonic

develop better algorithms to outperform conventional fluorescent phosphors.44,45 In this research, several HAs, including simulated annealing (SA), improved annealing with a harmony search algorithm (HSA), particle swarm optimization (PSO), and GA, were used to optimize the luminescent intensity of phosphor. Among the four HAs, the improved annealing with HSA got better phosphors than SA (without using the known coded concentration). The PSO algorithm got gradually better results with increased generation, and the GA could find the best local phosphor with shorter time. After further analysis of 340 phosphors, we found that the final brightness has an optimized activator concentration (Tb: 0.21−0.26), and the results were further proven by another host of NaGdF4:Ce,Tb. The HA was proper to find the optimal concentration of the activator of Tb. Furthermore, the optimal phosphor could be used as a bioimaging agent and improved QR code.

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EXPERIMENTAL SECTION

Reagents and Materials. All of the chemicals were purchased from the company without any further purification. The chemicals included Gd(NO3)3·6H2O (99.9%), La(NO3)3·6H2O (99.99%), Lu(NO3)3·6H2O (99.99%), Ce(NO3)3·6H2O (99.95%), Tb(NO3)3· 5H2O (99.9%), urea, and potassium fluoride (KF) (from Aladdin Industrial Corp., Shanghai, China) and tetraphenylethylene (TPE; from Shanghai Macklin Biochemical Co., Ltd., Shanghai, China). Synthesis of REOF:xCe,yTb (RE = Gd, La, and Lu). The synthesis process was carried out according to our published literature.46,47 First, 0.5 M calculated RE(NO3)3 was put into the beaker with 50 mL of deionized water added, and then 1.5 g of urea and 0.05 g of KF were added to the solution. After being stirred for 5 min, the mixture was taken into a pot in a water bath with a temperature of 90 °C for 3 h. Then, the precipitate was obtained after centrifugation (three times). Then, the powders were calcined with a temperature of 200 °C to obtain the final phosphor. Characterization. Transmission electron microscopy (TEM) images of the phosphors were obtained digitally by FEI Tecnai G2 STwin. X-ray diffraction (XRD) patterns of the phosphors were detected on a Rigaku D/max TTR-III diffractometer at a scanning B

DOI: 10.1021/acs.inorgchem.9b00667 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 1. (A) Photograph of the phosphors under 365 excitations in different generations. (B) Average brightness and (C) maximum brightness of the phosphors versus the generation using different HAs. tones on the basis of the existing harmonic melodies, to eventually get a happy melody of harmony. The involved parameters are as follows: (1) the harmony memory database (HM). The ith phosphor of the HM, HMi = (HMi1, HMi2, HMi3, HMi4, and HMi5); (2) the new creative harmony (HN), HN = (HN1, HN2, HN3, HN4, and HN5); (3) the current best harmony (HB), HB = (HB1, HB2, HB3, HB4, and HB5); (4) the harmony memory considering rate (HMCR = 0.98); (5) the pitch adjusting rate (PAR = 0.47). In the global HSA (GHS), it is not constant, but in this Article, GHS is only used to generate new phosphors’ codes; thus, the PAR is set as a fixed value. The algorithm process is carried out as follows, of which r, r1, and r2 are positive numbers of less than 1: (1) HN is equal to HMi (i = 1, 2, 3, ..., HMS). (2) If r1 is lower than HMCR, then HNi is not changed. If r1 is higher than HMCR, then HNi = r. (3) If r1 is less than HMCR and r2 is less than PAR, then HNi = HBj. (4) Through P2 and P3 being carried out, all of HNi are obtained. (5) The data of HN are normalized and used to synthesize the phosphors. Then the brightness is detected. If the fitness value of HN is higher than that of HMi, HN is taken as the new HMi codes in the next generation. Otherwise, there is still a probability {P = exp[dE/ (Tδn−1)]} of accepting HN as the new HMi codes. If HN is not accepted as the new HMi, the new HMi is the former HMi. (6) P1−P5 are used for the all codes in HM to obtain the new HM. PSO. The PSO algorithm is based on the observations of birds foraging. It is assumed that there is a group of birds in the square to chase food. They are scattered around the square at first but could gradually go ahead in the direction of the food over time and finally find the food. The simplest way of looking for food is to search the

surrounding positions of the nearest bird. The schematic diagram of PSO is shown in Scheme S2. The involved parameters are as follows: (1) the position of the ith particle (Pi), namely, the codes of the ith phosphors: Pi = (Pi1, Pi2, Pi3, Pi4, and Pi5); (2) the movement speed of the ith particle (Vi): Vi = (Vi1, Vi2, Vi3, Vi4, and Vi5); (3) the best position of the ith particle passed (PBi), PBi = (PBi1, PBi2, PBi3, PBi4, and PBi5); (4) the global best position of the particle group passed (PG), PG = (PG1, PG2, PG3, PG4, and PG5); (5) the fitness of the ith particle (Fi), namely, the brightness of the ith phosphor; (6) the fitness of the global best (FG); (7) the shifting value of ith particle (Si). The following formulas (F1, F2, F3, and F4) are used in this PSO algorithm: (1) Si = Pi − Pi′. Here, Pi is on behalf of the particles in the current position, and Pi′ represents the position of the particles before the current position. (2) Vi = wSi + c1r1(PBi − Pi) + c2r2(PG − Pi). w means the velocity inertia factor, and w = 1 − 0.2 × iteration. It decreases with increasing iteration (generation numbers). c1 = 1.6 and c2 = 2.0. r1 and r2 are both random, with the value less than 1 and higher than 0. (3) Pi = Pi + Vi. The next positions of the particles could be obtained by the sum of the current positions and the movement speed. (4) Pi = R1Pi + R2PBi + R3PG. R1 + R2 + R3 = 1. The values of R1, R2, and R3 are random, with the value less than 1 and higher than 0. The process of the GA is carried out as follows (P1−P6): (1) The Si of the particle swarm is calculated according to formula 1. For the original particle swarm, Pi′ does not exist, and it is set to a random positive number. C

DOI: 10.1021/acs.inorgchem.9b00667 Inorg. Chem. XXXX, XXX, XXX−XXX

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average brightness in the five generations shows no obvious increase: 0.68, 0.61, 0.78, 0.62, and 0.72, respectively. Also, there is almost no change of the maximum brightness in the five generations. The brightest phosphor is No. 2−4, with an intensity of 1.63. An important point in the HA optimization and the synthesis is trying to make full use of the current information available for luminescent powders. It is necessary to use the information of the existing luminescent powders’ codes to construct new luminescent powders’ codes. To improve the ability to search the higher optimized phosphor, the SA algorithm combined with the HSA is improved to another new algorithm (HSA) in order to use the code information of the existing luminescent powder, and much better optimization results will be obtained. The average brightness changes as follows: 0.68, 0.91, 0.81, 1.11, and 0.82, respectively, with the highest increased multiple as 162% (as shown in Figure S2 and Table S2). The brightest phosphor is No. 4−19 (intensity: 2.17), and the maximum brightness is also enhanced with 142%. The comparison of the two algorithms indicates that if the coding information is utilized, the optimization effect could be better. For the PSO algorithm, the parameters of the formula in the algorithm can be parameterized. As mentioned above, Vi = wSi + c1r1(PBi − Pi) + c2r2(PG − Pi). The velocity inertia factor (w) decreases with increasing iteration (generation numbers). Decreasing the inertia factor w can enhance the local searching ability, while increasing the parameter w can enhance the global searching ability to balance the local searching ability of the algorithm. If the parameters of the PSO algorithm are adjusted to enhance the local searching ability, the convergence speed of the algorithm would be slow and it will be easy to find a better solution. Therefore, if the designers focus on finding a better solution without considering the experimental time and material cost, we believe that the PSO algorithm with strong local searching ability is a good choice. As shown in Table S3 and Figure S3, when the PSO algorithm is used to guide the synthesis of the phosphors, interestingly, the average and maximum brightness gradually increase from 0.68 to 1.71 (2.50-fold) and from 1.53 to 2.01 (1.31-fold), respectively. The phosphor with the highest brightness occurs in the final fifth generation, and also in this fifth generation, the average brightness is obtained with the highest enhancement. The brightest phosphor is No. 5−1, with an intensity of 2.01. It could be imagined that if the generation increased, the intensity would be further enhanced. When the GA is used to optimize the brightness, the average brightness is changed as follows: 0.68, 0.95, 1.31, 1.45, and 1.40, respectively (Table S4 and Figure S4). Meanwhile, the maximum brightness is changed as follows: 1.53, 1.40, 2.36, 2.09, and 2.14, respectively. The local maximum brightness happens in the third generation (No 3−16, with a brightness of 2.36), which is earlier than all of the other three algorithms. It seems that the GA has the highest searching ability in the whole field. However, the highest enhanced multiple is 1.91fold, which is lower than that of the PSO algorithm, indicating that the GA has a relatively lower ability to prevent local optimization. In practical applications, the algorithm converges quickly and easily falls into the local optimal result. That means that the algorithm will find a necessary satisfied solution faster but is therefore stagnant and struggles to find a further better solution. If the designers want to find an acceptable solution within a relatively lower experimental cost, we suggest that the GA is a good choice.

(2) The Vi is calculated according to formula 2. For the original particles, PG is the positions of the particles in the original particles in the fitness. (3) The position of each particles is updated using formula 3. Yet, if the sum of Pi n and Vi n is less than zero, the new Pi n should be obtained by using formula 4. (4) The updated P1−P20 are min−max-normalized to synthesize the corresponding phosphors. (5) The fitness/brightness are detected. If Fi increases, PBi is defined as the current positions of the particles. If there is an obtained Pi with a higher fitness than FG, then update FG and PG. (6) Repeat the above processes to obtain more groups of phosphors’ codes and their corresponding brightness data. GA. The process of the GA is carried out as follows (P1−P7): (1) The 20 phosphors in the first generation are synthesized based on the published literature, and the brightness value is obtained by the Matlab R2015b program. Here, the control phosphor (21st) in every generation is GdOF:0.05Ce,0.15Tb. (2) The phosphors with higher brightness are more likely to be selected. Considering that the elitism may promote the local optimum occurring, the code of the phosphor with the highest brightness could not be selected. That means that the other 19 codes could be selected to generate new codes. (3) The selective two codes are single-point-crossed to generate two new codes in the next generation. (4) Then, the single-point mutation is operated on the two new codes in process (3). The mutation is adjusted in the range below 2fold of the corresponding coding value. (5) The coding values are min−max-normalized to make the sum of these codings 1. (6) P2−P5 are recycled to generate the 20 new codes, and these 20 new codes are used to synthesize the phosphors in the next generation.

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RESULTS AND DISCUSSION Comparison of SA, HSA, PSO, and GA. The photographs of the phosphors under 365 excitations in different generations Scheme 2. Schematic Diagram of a Comparison of the Different Algorithms of SA, HSA, PSO, and GA

using different HAs are shown in Figure 1A. Here, the first generation using the four different algorithms is the same original group with 20 samples. The maximum and average intensity are 1.53 (No. 1−4) and 0.68 in the first generation. The average brightness and maximum brightness of the phosphors versus the generation using different HAs are shown in Figure 1B, and the reason for obtaining such results will be shown as follows. During the conventional SA algorithm, the synthesis information is not utilized, and the optimization results are very dissatisfied. As shown in Figure S1 and Table S1, the D

DOI: 10.1021/acs.inorgchem.9b00667 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 2. Intensity of the phosphors versus the concentration of (A1−D1) Ce ions and (A2−D2) Tb ions using different algorithms.

Figure 3. (A and B) Intensities of 340 phosphors and (C and D) intensity divided by 8 windows versus the concentrations of the Ce and Tb ions. Variance of (E) all concentrations and (F) the Ce/Tb concentrations in different generations.

A schematic diagram of the cost and optimization result using different algorithms is shown in Scheme 2. The conclusions are as follows: (1) The traditional SA algorithm has a slow convergence rate, with poor optimization results and high cost. Although iterations are repeated many times, the effect is not obvious. After the SA algorithm is combined with the HSA, the global searching ability of the new HSA is significantly improved. HSA is a new HA, and the significance is very important. (2) If the researchers do not care about the experimental cost, PSO has adjustable parameters that can help to find a better result. (3) If the researchers need to find an acceptable solution within a relatively lower experimental time and cost, the GA is a good choice. Relationship between the Intensity and Host/ Activator/Sensitizer. Generally, there is an obvious relation-

Figure 4. (A) Down-conversion emission spectra and (B) TEM images of NaGdF4:Ce,Tb with different codoped Tb ion concentrations.

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DOI: 10.1021/acs.inorgchem.9b00667 Inorg. Chem. XXXX, XXX, XXX−XXX

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Figure 5. Applications of phosphors. (A) Typical excitation spectrum of the brightest GdOF:Ce,Tb in the first generation. (B) Down-conversion luminescence spectra of the brightest GdOF:Ce,Tb phosphors using different HAs. (C) Down-conversion luminescence spectrum of the typical aggregation-induced-emission TPE powder. (D) X-ray luminescence and (E) CT imaging of a mouse before and after subcutaneous injection with the GdOF:Ce,Tb phosphors. (F and G) New application on the QR code using the GdOF:Ce,Tb phosphor combined with TPE.

the following: When the codopant is similar to the “Ce,Tb” doping, the optimized concentration may have some affect when the host is changed (0.21−0.26 of Tb for lanthanide oxyfluoride and 0.25−0.30 of Tb for lanthanide fluoride) because of the different phases and structures between different hosts. The extent of this difference of the phases and structures determines the difference of the final optimized concentration. The points in the same generation are more dispersed if the global searching ability is higher, while the points are more aggregated if the local searching ability is higher. Meanwhile, the variance of the Euclidean distances indicates the local and global searching ability of the algorithm. Here, the Euclidean distances between the calculated points and (0.2, 0.2, 0.2, 0.2, 0.2) are calculated, and the variance of the distances is on behalf of the points’ dispersion. As shown in Figure 3E, the variance of all concentrations using the PSO algorithm decreases gradually, indicating its highest local searching ability. Also, the variance of the CE/Tb concentrations of all of the algorithms decreases, revealing that the optimization direction is correct (Figure 3F). New Applications of the GdOF:Ce,Tb Phosphor. The typical excitation spectrum of GdOF:Ce,Tb and the downconversion luminescence emission spectra of the brightest GdOF:Ce,Tb phosphors using different HAs are shown in parts A and B of Figure 5, respectively. As shown, the phosphors emit higher green emissions than the control sample. The excitation spectra of the GdOF:Ce,Tb phosphor (rare earth, RE) and TPE (a typical aggregation-inducedemission powder) indicate that they have wide excitation peaks in the UV region, with peak wavelengths of 250−300 nm (Figure 5B) and 240−400 nm (Figure 5C), respectively. That means that the RE and TPE have a shared excitation region in

ship between the brightness and activator/sensitizer. The intensity of the phosphors versus the concentration of Ce ions (sensitizer) using different HAs are shown in Figure 2A1−D1, and the intensity versus the concentration of Tb ions (activator) is shown in Figure 2A2−D2. A similar law can be directly concluded: the intensity decreases with enhanced Ce concentration, and the intensity first increases and then decreases with the enhanced Tb concentration. To better clarify the rule and give accurate optimized data for future research, the intensities of all 340 phosphors versus Ce and Tb ions are shown in Figure 3A,B. After further dividing the concentration into 8, 10, 15, and 20 windows (Figures 3C,D and S5), we could clearly conclude that the phosphors could be obtained with the highest brightness when the Ce concentration is 0.02−0.03 and the Tb concentration is 0.21−0.26. Note that there is no obvious significance between the brightness and host of REOF (RE = Gd, La, and Lu). The XRD patterns of the brightest phosphors using different HAs are shown in Figure S6, indicating a low amount of the dopant with the same lanthanide oxyfluoride host has no obvious effect on the final phase. We synthesized NaGdF4:0.02Ce,yTb (y = 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, and 0.4) nanoparticles with highly uniform structure and dispersibility to verify the rule obtained by HAs (Figure 4A). As shown in Figure 4A, the maximum intensity occurs at 0.25−0.30, which corresponds well with the predicted rule. Also, different codopants in the same fluoride have almost no influence on the final morphology (Figure 4B). These results verify two rules that we had already known: (a) The intensity of the phosphors increases first when the activator concentration is lower than that of the optimized concentration. (b) A low dopant concentration of the phosphors has almost no influence to the final morphology and phase. Furthermore, we could conclude F

DOI: 10.1021/acs.inorgchem.9b00667 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry 250−300 nm. The X-ray luminescence imaging effect (Figure 5D) and CT imaging results (Figure 5E) of a mouse before and after subcutaneous injection with the GdOF:Ce,Tb phosphors show that the phosphor may have potential applications in the in vivo radiotherapy and CT imaging fields. Also, the in vitro and in vivo X-ray luminescence imaging effect of NaGdF4:0.02Ce,0.25Tb is shown in Figure S7, which presents an obvious bright imaging effect compared with the surrounding environment. On the basis of the different chemical/physical stabilities of RE and TPE under toasting by fire, we used the combined inorganic/organic phosphor as the novel QR code to be applied in the encrypted field. A schematic diagram is shown in Figure 5F. The emission of TPE could hide information on the rare earth under UV-lamp irradiation, and one can obtain the real information after the emission of TPE is disabled. Also, the experimental results are presented in Figure 5G, and the bright emission of RE under UV-lamp irradiation (lamp wavelength: 254 nm) can be obtained only after toasting by fire for 30 s. After fire toasting, the information on TPE disappears, with only the QR code information on stable RE left. The new QR code application of the GdOF:Ce,Tb phosphor together with TPE could potentially be used in the encrypted field.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (R.L.). *E-mail: [email protected] (J.T.). *E-mail: [email protected] (J.L.). ORCID

Ruichan Lv: 0000-0002-6360-6478 Jie Tian: 0000-0003-0498-0432 Jun Lin: 0000-0001-9572-2134 Author Contributions

R.L. designed the experiments, analyzed the data, and wrote the manuscript; L.X. built the algorithm; F.Y. and Y.W. performed the experiments; J.L. and J.T. revised the manuscript. All authors read and approved the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from the Natural Science Foundation of China (Grant NSFC 81801744), the National Key R&D Program of China (Grant 2017YFA0205202), and the Fundamental Research Funds for the Central Universities (Grants XJS17011 and JBX181202) is greatly acknowledged.

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CONCLUSIONS In this research, several HAs, including SA, HSA, PSO, and GA, were used to optimize the luminescent intensity of the phosphor: (1) Besides the most used GA, other algorithms also present good guidance for the synthesis of luminescent powder. The average and maximum intensities of each generation in different algorithms were different, indicating that different HAs can be searched in different ways. Also, different optimized results were obtained, contributing to the different tendencies of each generation. (2) The traditional SA algorithm has a slow convergence rate, and the optimization effect was not obvious after several repeated iterations. After the SA algorithm was combined with the HSA, the global searching ability of HSA was significantly improved. The significance of HSA as a new HA is very important. (3) If the experimenter needs to find an acceptable solution within a relatively lower experimental time and cost, we recommend GA as a good choice. (4) PSO with the highest local searching ability has relatively more parameters that can find better fitness with increased generation. Meanwhile, we conclude that the optimized Tb concentration is about 0.25 and the optimized Ce concentration is about 0.02. Furthermore, the phosphor could be used for multiple down-conversion luminescence/X-ray luminescence/CT bioimaging experiments and for the novel QR code in the encrypted field.

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patterns, and in vitro and in vivo X-ray luminescence properties of NaGdF4:0.02Ce,0.25Tb (PDF)

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.9b00667. Schematic diagrams of the original HA and PSO programs, brightness and intensity data of the phosphors in different generations using SA, HSA, PSO, and GA optimization, respectively, intensities of all 340 phosphors divided by 8, 10, 15, and 20 windows versus the concentration of Ce and Tb ions, respectively, XRD G

DOI: 10.1021/acs.inorgchem.9b00667 Inorg. Chem. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.inorgchem.9b00667 Inorg. Chem. XXXX, XXX, XXX−XXX