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Sep 10, 2018 - correlation occurs, which is shown by parallelogram in Figure. 4a,iii;b,iii. ... to Vegard,s law.44 In addition to the previous analysi...
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Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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Charge Transfer, Local Structure, and the Inductive Effect in RareEarth-Doped Inorganic Solids Yuwei Kong, Zhen Song, Shuxin Wang, Zhiguo Xia, and Quanlin Liu* The Beijing Municipal Key Laboratory of New Energy Materials and Technologies, School of Materials Sciences and Engineering, University of Science and Technology Beijing, Beijing 100083, China

Inorg. Chem. Downloaded from pubs.acs.org by UNIV OF SOUTH DAKOTA on 09/10/18. For personal use only.

S Supporting Information *

ABSTRACT: The charge transfer (CT) process is widely present in inorganic compounds. However, the explanation of this process accounting the inductive effect was not reported. In this work, through the analysis of local structure about the second nearest cations (SNCs) in some compounds doped with trivalent lanthanide, we verify successfully the important role of the inductive effect in the CT process. By introducing electronegativity factor ∑iχi(Ai)/N − x(M), and ionic radius factor ∑iri(Ai)/N, the semiquantitative model is proposed. Strong positive correlation between the electronegativity factor and CT energy and strong negative correlation between the ionic radius factor and CT energy are given. At last, the interrelationship among these two inductive factors, the CT process, the change of local coordination structure, and the chemical composition is revealed. This work will facilitate our understanding of the CT process and the delicate role of the local structure and the inductive effect.

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INTRODUCTION Rare-earth (RE)-doped inorganic solids are attractive owing to their unique luminescence features and thereby their wide applications, such as optical communications, laser, solid state lighting, display, sensing, and imaging, etc.1−4 The electricdipole-allowed transition of the rare earth ions is of two different types, i.e., charge transfer (CT) transition (4fn ↔ 4fn+1L−1, where L = ligand) and 4fn ↔ 4fn−1 5d transition.5 For rare earth ions, CT transitions like to get an electron from their ligands and to be reduced; for example, the tetravalent ions (Ce4+, Pr4+) and trivalent ions (Sm3+, Eu3+, Yb3+) have a tendency to become trivalent and divalent ions, respectively, and show a CT absorption band, while 4f−5d transitions seem to be oxidized, e.g., the trivalent ions (Ce3+, Pr3+) and divalent ions (Eu2+, Sm2+, Yb2+) have a tendency to become tetravalent and trivalent ions, respectively, and exhibit a 4f−5d absorption band.5 Generally, the CT process and corresponding optical properties are mainly controlled by crystal/local structure and electronic structure.6,7 Therefore, on one hand, we can tune CT process and optical properties by adjusting the compositions and structure;8−10 on the other hand, we can get insight into their local structure and electronic structure by using optical spectrum technique with RE ions as probes.11 The substances of the world always exist and stabilize in certain forms at lower energy. In most occasions, the atoms making up the materials are inclined to interact with each other instead of being isolated to reach the minimum energy that they can. When one atom loses an electron and another atom gains that electron, the electron transfer process occurs, which is beneficial to lowering the energy of the system. The covalent © XXXX American Chemical Society

bond, as a result of a special electron transfer process to share valence electrons by two or more atoms in order to decrease energy, is widely present in solid compounds. The electrons are always unequally shared by the atoms, especially for different types of atoms, and spend more time close to one atom than the other.12 The electronegativity difference of the bonding atom should be responsible for the formation of the polar or nonpolar covalent bond. In addition to the electronegativity difference, another factor determining the relative position of the shared electron pair is the local structure of the surrounding environment from the perspective of the inductive effect. More specifically, for an A−M−X ternary compound, exotic cation A will exert electron pressure13 on the bond between cation M and anion X and change some parameters of the M−X bond, such as bond length, bond valence,14 etc. When stimulated by external force, the electron, which should have been shared, may be totally transferred from anion to cation. This phenomenon of electron transfer can be well-characterized by spectroscopy techniques, and it is well-known as CT energy whose position indicates the degree of difficulty of electron transfer. Here, the photon with specific energy is taken as the external force. In many compounds doped with trace rare earth elements, the trivalent rare earth ion as central atom will get an electron from its ligand anions and become divalent, with a broad band in the excitation spectrum called the charge transfer band (CTB). Received: July 29, 2018

A

DOI: 10.1021/acs.inorgchem.8b02141 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry This provides a useful tool to investigate the local structure and the CT process. The CT process is very important in applications, such as the CT luminescence of Yb3+ in Yb3+-containing compounds,15−17 and the CT state sensitized luminescence in red phosphor Y2O3:Eu3+.15,18 Meanwhile, many theoretical research studies have been made about the CT energy. Jö rgensen first proposed an empirical formula ECT = 3.72(χopt(X) − χopt(M)) eV,19 which hints that the CT energy is closely related to the optical electronegativity of anion X, χopt(X), and that of central cation M, χopt(M). Later on, Dorenbos raised a set of constant differences among the CT energies for different trivalent lanthanides in the same host by analyzing plenty of compounds.20 Combining this systematic variation with other additional compound dependent parameters,21 he proposed the host referred binding energy (HRBE) scheme which is widely used in analyzing and predicting the energy level structure and luminescent properties of the rareearth-doped materials. Subsequently, using a dielectric chemical bond method, Li et al.22−24 employed an exponential relation ECT = A + Be−khe to convey the relationship between ECT and environmental factor he in Eu3+, Sm3+, and Yb3+ singledoped compounds, which are in good agreement with experimental results. Although much work has been done, researchers are still lacking details regarding the relationship between the CT process and the local structure. Recently, we have investigated the inductive effect of the metal ions to the crystal structure and 5d energy levels of Ce3+ in nitridosilicates and oxysilicates.14 The inductive effect exists widely in inorganic compounds and accounts well for many physical properties, such as electrical conductivity, optical and magnetic properties, as well as Fe3+/Fe2+ redox potential position.13 It reflects well the relationships among chemical composition (electronegativity), local structure (next-neighbor-atom effect), and the CT process. Therefore, the CT process should be inductively affected by surrounding environment causing the change of CT energy ECT. Considering that the change of local crystal structure must be responsible for electron redistribution, herein we want to explore trivalent lanthanide CT energy from the viewpoint of the inductive effect. In this paper, by looking into the local structure, the second nearest cations (SNCs) of the central atom in a series of lanthanide-doped compounds and solid-solutions, we propose the inductive mechanism for analyzing the CT process by introducing two factors, the electronegativity factor and the ionic radius factor. The former is strongly positively correlated to the CT energy while the latter is negatively correlated, which is verified by some examples of changing only one, two, three, and more types of crystallographic sites of SNCs. Finally, the trial is given to reveal the relationship among these two factors, the CT energy, the average bond length, and the chemical composition. This work will help us to understand deeply the relationhips among chemical composition, local structure, the inductive effect, and optical properties of rareearth-doped inorganic solids.

Figure 1. Schematic of the local structure of the central cation and the inductive effect of the competitive relationship during the electron transfer process. The top right illustration without atom labels is the same as the left one and is intended to show the local structure more clearly.

nearest cations or SNCs. This term refers to all of the surrounding cations around the coordinated polyhedron, which are considered to be bonding to the coordinated anion in the ball-and-stick model. The electron from the anion is transferred between anions and cations including the central cation (white arrow in Figure 1) and the SNCs (black arrow in Figure 1). Therefore, these two kinds of electron-transferring routines form a competitive balance, which has a significant effect on the CT energy ECT(M) for the central atom. On the other hand, electronegativity χ, as a key parameter to measure the power of an atom in a molecule to attract electrons to itself,25 must play an important role in the competitive relationship. For the SNCs, the bigger the electronegativity is, the more power the atom possesses to attract the electrons from the anion, causing the electron to shift far away from the central atom and causing the CT energy ECT(M) to increase. At the same time, ionic radius r, almost a basic parameter for ions in a certain coordinated environment, is also employed in the analysis of crystal structural variation, which is closely related to the variation in performance. Here, the larger the size of the SNCs is, the farther the distance from the anion is, that causes the electron to move from the anion to the closer central cation instead of the farther SNCs, and the CT energy ECT(M) decreases. So a generalized relation

ji zy E CT = E CTjjjj∑ χi (Ai ), ∑ ri(Ai ), N , ...zzzz j i z (1) i k { is proposed, where χi(Ai) and ri(Ai) are the electronegativity and ionic radius of the ith SNCs Ai, and N is the number of anions coordinated to central cation. This means that ECT is a function of the integrated effect of electronegativity values ∑i χi (Ai ) and ionic radius ∑i ri(Ai ), and it is also a function of ligand anion number N and other unknown factors. To make it more definite, after leaving these unknown factors out and making some adjustments, this general relation is revised as ij ∑ χ (Ai ) ∑ ri(Ai ) yz zz E CT = E CTjjj i i − χ (M ), i z j N N z{ k

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ALGORITHM AND INDUCTIVE MECHANISM Just as the local structure illustrated in Figure 1, the original fundamental unit is a classical polyhedron composed of a central cation M and several ligand anions X (or the first nearest anions), surrounded by adjacent cations which are labeled Ai. Also, we call these adjacent cations the second

(2)

where ∑i χi (Ai )/N − χ (M ) means the power of the SNCs to compete with the central cation and get the electron from each ligand anion, and ∑i ri(Ai )/N is used to measure indirectly the B

DOI: 10.1021/acs.inorgchem.8b02141 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Table 1. CT Energy ECT, Electronegativity, and Ionic Radius Factor Values of SNCs in Several Simple Compounds and Solid-Solutions

distance between the SNCs and the ligand anions. Both of these factors should be closely related to the CT energy ECT(M). The CT energy should be positively correlated to the former factor and negatively correlated to the latter one as will be proven in the following analysis. The denominator part, 1/ N, is introduced for two reasons. One is to consider the average effect of all SNCs on the ligands. The other is to reduce the effect of the ambiguous number of SNCs owing to the different ligand anionic number for some compounds in different literature sources.26 If one Ai site is occupied by different types of atoms in the structure, the weighted average method is adopted to get the values of electronegativity and ionic radius. Especially for a solid-solution, for example, if atom Ai and atom Bi occupy the same crystallographic site in a unit cell, then χi is handled as linear combination of χi(Ai) and χi(Bi), i.e. χi = (1 − x)χi (Ai ) + xχi (Bi )

compd

∑iri(Ai)N/Å

Ln2O3:Eu (Ln = Gd, Y, Lu), CN = 6 4.71 1.200 1.876 4.88 1.240 1.800 4.92 1.340 1.722 LnPO4:Eu3+, CN = 9 (Ln = La, Gd) or 8 (Ln = Y, LaPO4 4.84 1.237 2.514 GdPO4 5.10 1.303 2.441 YPO4 5.66 1.053 1.913 LuPO4 5.74 1.078 1.894 ScPO4 6.05 1.123 1.847 La0.95−xGdxPO4:0.05Eu3+, CN = 9 x=0 4.84 1.200 0.902 x = 0.2 4.96 1.213 0.888 x = 0.95 5.17 1.263 0.833 LuxY1−xPO4:Eu3+, CN = 8 x=0 5.49 1.053 0.6370 x = 0.1 5.52 1.055 0.6349 x = 0.3 5.54 1.060 0.6307 x = 0.5 5.55 1.065 0.6265 x = 0.7 5.57 1.070 0.6223 x = 0.9 5.62 1.075 0.6181 x=1 5.66 1.078 0.6160 Ca1.98−xSrxNa0.01Al2SiO7:0.01Eu3+, CN = 8 x=0 4.97 1.510 1.155 x = 0.5 4.94 1.502 1.177 x = 1.0 4.92 1.494 1.199 x = 1.5 4.88 1.486 1.221 x = 1.98 4.79 1.479 1.243 Sr1.98Na0.01Al2Si1−xGexO7:0.01Eu3+, CN = 8 x=0 4.79 1.479 1.243 x = 0.25 4.67 1.486 1.251 x = 0.5 4.66 1.4925 1.259 x = 0.75 4.65 1.499 1.267 x=1 4.63 1.506 1.275 Ba2−xSrxSiO4:Eu3+, CN(Ba2) = 9 x=0 4.45 1.550 1.550 1.473 x = 0.5 4.49 1.575 1.571 1.407 x = 1.0 4.55 1.600 1.593 1.340 x = 1.5 4.91 1.625 1.621 1.273 x = 1.9 4.99 1.645 1.644 1.22 Gd2O3 Y2O3 Lu2O3

(3)

(4)

It is easy to notice that the SNCs are always the ions with just one, two, or several types of crystallographic sites. So, if these SNCs are classified by their crystallographic sites, the abstract model in eq 2 can be revised as ∑j mjrj zy ji ∑j mjχj zz E CT = E CTjjjj − χ (M ), z j N N zz k {

∑iχi(Ai)N − χ(M)

ref

3+

where x is the atomic percent of atom Bi. The similar relation is applied to ionic radii r, i.e. ri = (1 − x)ri(Ai ) + xri(Bi )

ECT/eV

(5)

where χj and rj refer to the electronegativity and ionic radius of the jth type of crystallographic site of SNCs, and mj is the corresponding site number. So mj/N can be described as the weight coefficient of the jth type of crystallographic site. The clue to the following analysis is verified from changing only one to two, three, and more crystallographic site types of SNCs according to eq 5.

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DATA In this section, the CT energy ECT data collected from different literature studies and the two calculated factor values are listed. Here, what we are most interested in are the atomic electronegativities and ionic radii of SNCs around the ligand anions. All the electronegativity data are taken from Allerd’s revised results,27 and all the ionic radii are taken from Shannon’s results.28,29 Table 1 lists some relevant results for simple compounds, including Ln2O3:Eu3+ (Ln = Gd, Y, Lu), LnPO4:Eu3+ (Ln = La, Gd, Y, Lu, Sc), and several solid-solutions. For Ca 1 . 9 8 − x Sr x Na 0 . 0 1 Al 2 SiO 7 :0.01Eu 3 + and Sr 1 . 9 8 Na 0 . 0 1 Al2Si1−xGexO7:0.01Eu3+, the fourth column in Table 1 is split into two columns: the left one contains the values of ionic radius factors, and the right one includes the average M−O bond lengths taken from the same original literature source as that for the CT energy. The third and fourth columns are split into two columns for Ba2−xSrxSiO4:Eu3+: the left one contains the corresponding results of nonpreferred occupation, and the right one contains the preferred occupation results. Table 2 lists the results of Ln3(Al1−xGax)5O12:Ce3+ (Ln = Gd, Y, Lu). There is only one changed site type of SNCs in Table 1 except for two for Ba2−xSrxSiO4:Eu3+ and three changed site types in Table 2, which will all be analyzed to approve the existence of

30 30 30 Lu, Sc) 31 31 31 31 31 32 32 32 33 33 33 33 33 33 33 2.562 2.578 2.596 2.610 2.629

34 34 34 34 34

2.629 2.637 2.644 2.652 2.659

35 35 35 35 35

1.473 1.417 1.358 1.285 1.222

36 36 36 36 36

the inductive effect in the CT process. More details about these tables and relevant analysis will be presented together in the following section.

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INDUCTIVE EFFECT OF ONE TYPE OF CRYSTALLOGRAPHIC SITE OF SNCS Here, the specific local structure of the coordinated polyhedral environment including the SNCs is shown in Figure 2, and all the data of CT energy ECT in Table 1 are plotted against the corresponding two factors’ values of ∑i χi (Ai )/N − χ (M ) and ∑i ri(Ai )/N in Figure 3. At first, let us discuss the change in CT energy caused by only one changed crystallographic site. In simple oxides Ln2O3:Eu3+ (Ln = Y, Lu, Gd), as shown in Figure 2a,b, there are two lanthanide sites (Ln1 and Ln2) for the Eu atom to occupy, which are all octahedrally coordinated.38 For the coordinated polyhedron of the Ln1 site, there are 12 Ln1 around it, and for the Ln2 site there are 4 C

DOI: 10.1021/acs.inorgchem.8b02141 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry Table 2. CT Energy ECT, the Simplified Two Factor Values of Electronegativity, and Ionic Radius of SNCs in Ln3(Al1−xGax)5O12:Ce3+ (Ln = Gd, Y, Lu) (CN = 8)37 Gd ECT/eV x=0 x=1 x=2 x=3 x=4 x=5 χ(Ln) r(Ln)

3.83 3.76 3.7 3.61 3.54 3.45 1.2 1.053

Y

4χ(Ln) + 10χ(AG)

4r(Ln) + 10r(AG)

20.9 21.3 21.7 22.1 22.5 22.9

8.692 8.852 9.022 9.182 9.352 9.512

ECT/eV 3.89 3.67 3.72 3.65 3.59 3.52 1.22 1.019

Lu

4χ(Ln) + 10χ(AG)

4r(Ln) + 10r(AG)

20.98 21.38 21.78 22.18 22.58 22.98

8.556 8.716 8.886 9.046 9.216 9.376

ECT/eV 4.11 4.07 3.96 3.87 3.67 3.45 1.27 0.977

4χ(Ln) + 10χ(AG)

4r(Ln) + 10r(AG)

χ(AG)

r(AG)

21.18 21.58 21.98 22.38 22.78 23.18

8.388 8.548 8.718 8.878 9.048 9.208

1.61 1.65 1.69 1.73 1.77 1.81

0.448 0.464 0.481 0.497 0.514 0.530

Figure 2. Local structure including the SNCs of the central cation in some compounds: (a) Ln1 site; (b) Ln2 site in Ln2O3:Eu3+ (Ln = Y, Lu, Gd); (c) Ln = La, Gd; (d) Ln = Lu, Y, Sc in LnPO4:Eu3+; (e) Ca/ Sr site in (Ca, Sr)2Al2(Si,Ge)O7:Eu3+; (f) Ba2 site in Ba2−xSrxSiO4:Eu3+; and (g) Ln site in Ln3(Al1−xGax)5O12:Ce3+ (Ln = Gd, Y, Lu).

Ln1 and 8 Ln2. However, they are the same Ln atoms, and the coordination numbers are identical. So, they have the same electronegativity and ionic radius values. It makes no difference in calculating these two factors, and they can be treated as one site’s SNCs varied. We can easily come to the conclusion that the bigger the electronegativity factor ∑i χi (Ai )/N − χ (M ) is or the smaller the radius factor ∑i ri(Ai )/N is, the higher the CT energy ECT(Eu3+) is, as shown in Figure 3a. The same results occur in the La0.95−xGdxPO4:0.05Eu3+ and LuxY1−xPO4:Eu3+ solid-solutions, whose coordination details are shown in Figure 2c,d with the inductive relationship in Figure 3c,d. As for LnPO4:Eu3+, there is only one type of Ln site. For Ln = La, Gd, it is 9-fold coordinated, surrounded by 6 Ln and 7 P; for Ln = Y, Lu, Sc, it is 8-fold coordinated, surrounded by 4 Ln and 6 P. So, when the results of these two different structures are plotted together as shown in Figure 3b, strange things happen: the radius factor ∑i ri(Ai )/N shows a normal negative relationship with ECT; however, there is a significant change for the electronegativity factor ∑i χi (Ai )/N − χ (M ). For the same N value, i.e., for the identical local structure, the normal positive relationship between the electronegativity factor and the CT energy is retained, as shown in each ellipse in Figure 3b,ii. However, for the different local structures with different N values, the CT energy is not comparable. So, the local structure plays an important role in the CT process, as do the electronegativity and the ionic radius.

Figure 3. CT energy, ECT, vs two inductive factor values in some compounds compiled in Table 1: (a) Ln2O3:Eu3+ (Ln = Y, Lu, Gd), (b) LnPO4:Eu3+ (Ln = La, Gd, Lu, Y, Sc), (c) La0.95−xGdxPO4:0.05Eu3+, (d) LuxY1−xPO4:Eu3+, (e) Ca1.98−xSrxNa0.01Al2SiO7:0.01Eu3+, (f) Sr1.98Na0.01Al2Si1−xGexO7:0.01Eu3+, and (g) Ba2−xSrxSiO4:Eu3+.

In (Ca, Sr)2Al2(Si,Ge)O7:Eu3+ (Figure 2e), Al1 and Si occupy the same site, and there is only one site for Eu to occupy, which is surrounded by 5 Ca, 4 Al1/Si, and 6 Al2. For the Ca−Sr solution series, similar negative and positive relationships are displayed in Figure 3e. However, for the Si−Ge series, negative relationship ECT(Eu3+) − ∑i ri(Ai )/N and negative relationship ECT(Eu3+) − ∑i χi (Ai )/N − χ (M ) appear. This is caused by the higher ionic radius for Ge4+, but higher electronegativity of Ge than Si, i.e., r(Ge4+, CN = 4) = 0.39 Å > r(Si4+, CN = 4) = 0.26 Å28,29 but χ(Ge) = 2.01 > χ D

DOI: 10.1021/acs.inorgchem.8b02141 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry (Si) = 1.90.27 The same phenomenon is found in the Al−Ga solution series with r(Ga3+, CN = 4) = 0.47Å > r(Al3+, CN = 4) = 0.39 Å28,29 and χ(Ga) = 1.81 > χ(Al) = 1.61,27 which causes similar results in the following analysis of Ln3(Al1−xGax)5O12:Ce3+(Ln = Gd, Y, Lu) in Figure 4.

without losing its accuracy. In a similar or identical structure, coordination number N does not change. Respectively, with regard to the same central cation, only the numerator part in eq 5 can be taken into account; i.e., the relation can be simplified as ij j E CT = E CTjjj∑ mjχj , jj k j

yz

∑ mjrj , ...zzzzz j

z {

(6)

According to this model, the inductive effect of three site types of SNCs on CT energy will be discussed next. Here, Ln3(Al1−xGax)5O12:Ce3+ (Ln = Gd, Y, Lu) is taken as the verified example. It is noteworthy that we do not consider the situation of preferred occupation and just think that the Ga atom entering later has the same probability to occupy different original Al atom sites. One reason for this consideration is the inconsistent results about preferred occupation degrees from different literature sources; the other is that it has only a negligible impact on the calculated weighted values, which have been compared in the analysis of Ba2−xSrxSiO4:Eu3+. In fact, in the garnet series compounds, the Ga atom has priority to occupy the tetrahedral site, but there is another choice of octahedral site for Ga to occupy.39−43 In the following analysis, an equal probability to occupy octahedral and tetrahedral sites is accepted for the Ga atom. The SNCs of Ln3(Al1−xGax)5O12:Ce3+ (Ln = Gd, Y, Lu), including 4 Ln, 4 octahedral Al1/Ga1, and 6 tetrahedral Al2/ Ga2 sites, are depicted in Figure 2g. Without regard to the preferential occupation of Ga to tetrahedral Al2 sites, the calculated two simplified factors values of isoprobability occupation to Al1 and Al2 sites combined with CT energy are compiled in Table 2. Owing to the assumption of isoprobability occupation, these two sites of octahedral Al1/ Ga1 and tetrahedral Al2/Ga2 change together and can be treated as a composite site, AG, with electronegativity

Figure 4. CT energy, ECT, vs the two simplified factor values in Ln3(Al1−xGax)5O12:Ce3+ (Ln = Gd, Y, Lu).

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χ (AG) = (1 − x)χ (Al) + xχ (Ga)

INDUCTIVE EFFECT OF TWO, THREE, AND MORE TYPES OF SNC CRYSTALLOGRAPHIC SITES If the local structure of the central cation is more complicated, two or more SNC sites may change simultaneously. In this section, this situation will be discussed. In Ba2−xSrxSiO4:Eu3+, there are two Ba sites for Sr to enter: Ba1 (CN = 10) and Ba2 (CN = 9).36 This gives the results for the CT energy for Eu3+ occupied at the Ba2 site whose SNCs are 6 Ba2, 9 Ba1, and 6 Si, as shown in Figure 2f. There are two SNC sites changing together when Sr enters. According to the preferred occupation of Sr in Ba 1 and Ba2 sites reported in ref 36, the preferred and nonpreferred results of ∑i ri(Ai )/N and ∑i χi (Ai )/N − χ (M ) values are simultaneously compiled in Table 1 (for more calculation details, see the Supporting Information). The similar results for the positive ECT(Eu3+) − ∑i χi (Ai )/N − χ (M ) relationship and negative ECT(Eu3+) − ∑i ri(Ai )/N relationship are shown in Figure 3g. The two very close lines, as shown in Figure 3g, are caused by the similarities of Sr and Ba atoms in terms of electronegativity and ionic radius, and this shows that the two factors for the inductive effect on the CT process caused by preferred occupation can be ignored. For the more complicated local structure, the model in eq 5 can be further simplified for the convenience of analysis

(7)

and ionic radius r(AG) = 0.4 × [(1 − x)r(Al1) + xr(Ga1)] + 0.6 × [(1 − x)r(Al2) + xr(Ga2)]

(8)

in which 0.4 and 0.6 are the weighted coefficients based on the number of SNCs. So, the SNCs become 4 Ln and 10 AG. The inductive effect of each site on CT energy is studied and shown in Figure 4. By univariate analysis of variance (ANOVA) in SPSS software, the significance levels of χ(Ln), χ(AG), r(Ln), and r(AG) (Table S2) are very close to zero, which shows that both Ln and AG definitely have a significant effect on the CT process. As we expect, almost all the relationships between the CT energy and each factor of each site are negatively (for χ(AG), r(Ln), r(AG)) or positively (for χ(Ln)) correlated, as described in Figure 3. When the effect of these three sites (one for Ln, two for AG) are superimposed, nearly a linear negative correlation occurs, which is shown by parallelogram in Figure 4a,iii;b,iii. As for more types of crystallographic sites, it is difficult to find enough efficient reports owing to the sharp increase of experiment workload with the increase of variables. It is believed that the positive or negative correlation will remain but may start to weaken. Although the numerous data points here, also including the data in Figure 3, are not fitted, this will E

DOI: 10.1021/acs.inorgchem.8b02141 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry not affect the overall trend of the curve and does not have any impact on the qualitative and semiquantitate analysis. The above analysis is aimed at investigating the inductive effect on the CT process by changing only one, two, three, and more types of crystallographic sites of the SNCs. All of the results without exception verify the objective existence of the inductive effect during the CT process caused by the SNCs. Generally, a higher electronegativity factor exerts a negative effect to prevent the CT process causing higher CT energy whereas the higher radius factor exerts the absolutely opposite effect on this process. Sometimes, the negative relationship between the electronegativity factor and the CT energy will occur when smaller radius ions have greater electronegativity, such as in the Al−Ga and Si−Ge solution series.

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INTERRELATIONSHIP AMONG CT PROCESS, THE INDUCTIVE EFFECT, AND LOCAL STRUCTURE So, what will happen if the CT process occurs under the inducting local structure (the SNCs)? One may come up with many aspects. Here, what we will talk about now is the change of local crystal structure of the M−X polyhedron through the discussion of bond length. The covalent bond originates from sharing the electrons of two atoms. However, the CT process must have an influence on the sharing electrons, and so, something might be changed for the covalent bonds. Here, the average bond length of M−O in (Ca, Sr)2Al2(Si, Ge)O7:Eu3+ is also given in Table 1. In order to analyze deeply the relationship among five the variables, E C T , ∑i χi (Ai )/N − χ (M ), ∑i ri(Ai )/N , average M−O bond length, and the change of chemical composition x are plotted in Figure 5a. The two inductive factors are completed in a linear relation with the change in chemical composition x. Meanwhile, the average M−O bond length is well-fitted linearly to x, which is caused by the near linear change of cell parameters according to Vegard’s law.44 In addition to the previous analysis, the complex relationships of the inductive effect to the CT process, as described in Figure 5b, start to emerge. On one hand, the change of chemical composition causes the change of local structure outside the M−X coordinated polyhedron. On the other hand, owing to the inductive effect from the SNCs (outer structure of M−X polyhedron), the bond length of M− X polyhedron changes. More specifically, the SNCs change the covalency degree of the bond between central cation M and ligand anions X through adjusting their own ability to donate electron to ligands. In other words, this really changes the CT process, which, in turn, changes the M−O bond length in Figure 5a. All of these complex and interrelated interactions can be derived from a careful comparative analysis of Figure 5a,b. This figure shows the interrelationship among the CT process, the inductive effect, the local structure, and the chemical composition. The variation of chemical composition and local structure can change the CT process by the inductive effect.

Figure 5. (a) Scatter matrix graphic of the interrelationship among CT energy, two inductive factors, average M−O bond length, and chemical composition x in (Ca, Sr)2Al2(Si, Ge)O7:Eu3+. The upper triangle is for Sr1.98Na0.01Al2Si1−xGexO7:0.01Eu3+, and the lower triangle is for Ca1.98−xSrxNa0.01Al2SiO7:0.01Eu3+. (b) The detailed interrelationship among the charge transfer process, the inductive effect, local structure, and chemical composition.

CT energy and a strong negative correlation between the ionic radius factor and the CT energy are given. The interrelationship among these two inductive factors, CT process, optical properties, local coordination change, and chemical composition is revealed in oxide compounds. This work is intended to deeply understand the CT process and enlighten us regarding the delicate role of the inductive effect on the modulation of local structure and physicochemical properties.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b02141. Detailed calculation methods of the electronegativity factor and the ionic radius factor and analytical statistical results of univariate ANOVA output in SPSS (PDF)

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CONCLUSIONS The purpose of this paper is to explore the delicate role of the local structure and the inductive effect during the CT process. With the collection of CT energy of a trivalent lanthanide in some solid compounds and the study of the local structure about SNCs, we introduce two inductive factors, the electronegativity factor and the ionic radius factor. A strong positive correlation between the electronegativity factor and

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Zhiguo Xia: 0000-0002-9670-3223 Quanlin Liu: 0000-0003-3533-7140 Notes

The authors declare no competing financial interest. F

DOI: 10.1021/acs.inorgchem.8b02141 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (No. 51472028 and 51602019) and Fundamental Research Funds for the Central Universities (FRF-TP-17-005A2).

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DOI: 10.1021/acs.inorgchem.8b02141 Inorg. Chem. XXXX, XXX, XXX−XXX