The Inductive Effect in Nitridosilicates and Oxysilicates and Its Effects

Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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The Inductive Effect in Nitridosilicates and Oxysilicates and Its Effects on 5d Energy Levels of Ce3+ 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 S Supporting Information *

ABSTRACT: The inductive effect exists widely in inorganic compounds and accounts well for many physicochemical properties. However, until now this effect has not been characterized quantitatively. In this work, we collected and analyzed the structural data of more than 100 nitridosilicates and oxysilicates, whose structures typically consist of [SiN4] or [SiO4] tetrahedra. We introduce a new parameter, the inductive effect factor μΔχ, related to the difference of electronegativity between constituent metal elements and silicon. Then, a linear relationship is established between average length of Si−N/Si− O bonds and the inductive factor with the help of statistical method, that is, l ̅ = 1.7313 + 0.0166 μΔχ (Å) with adjusted (adj) R2 = 0.800 for Si−N and l ̅ = 1.6221 + 0.0035 μΔχ(Å) with adj R2 = 0.240 for Si−O. Furthermore, our research shows that the distinct positive correlation does exist between the inductive factor and the centroid shift of 5d levels of Ce3+. This work will help us understanding the inductive effect deeply and quantitatively.

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INTRODUCTION Chemical bonds are central to chemistry and materials science. A chemical bond forms between two atoms if the resulting arrangement of the two nuclei and their electrons have a lower energy than the total energy of the separate atoms. The properties of materials are determined by their structures, that is, the reasonable arrangements of their atoms, ions, and molecules in space with the help of chemical bonds. For a ternary compound TxMyXz, where X is anion and T and M are cations, if T is less electronegative than M, it will tend to become an electron donor, which will exert electron pressure on the M−X bond.1 Then, the anion X prefers to get the electron density from T instead of M, causing the changes of M−X bond. This is called “the inductive effect”, which was first introduced into inorganic solids by Noll2 to explain the tiny changes in Si−O bond in some silicates. In 1992, Etourneau and Portier1 reported that there are several correlations between the inductive effect of T counteraction and physicochemical properties of many inorganic compounds, such as electrical conductivity, magnetical and optical properties, as well as Fe3+/Fe2+ redox potential position. Although the inductive effect exists widely in solid-state chemistry and accounts well for many physical properties, until now this effect has not been characterized quantitatively from the viewpoints of chemical bond and structural chemistry. The chemical bonds of inorganic solids mainly include three extreme typesmetallic, ionic, and covalent. The chemical bonds of many inorganic nonmetal solids are intermediate between the simple ionic and covalent extremes, and they can be characterized by the ionicity/covalency degree. In 1941, the Dutch chemist Anton Eduard van Arkel proposed an attractive © XXXX American Chemical Society

triangular diagram to represent the progressive transition between the three limiting-cases of ionic, covalent, and metallic bonding,3 which is merely an intuitive estimate. In 1993, by dividing covalent materials into two types, covalent network and van der Waals molecular, Michael Laing expanded the twodimensional van Arkel-Ketelaar triangle of bonding into a tetrahedron.4 On the basis of Allen’s semiquantitative model,5 William B. Jenson raised a quantitative van Arkel diagram3 by introducing two key parametersthe ionicity parameter I and the covalency parameter Cwhich were closely related to the electronegativity of component elements. However, all the above triangles are only applicable to binary compounds. There is no doubt that the electronegativity, described by Linus Pauling as “The power of an atom in a molecule to attract electrons to itself”,4 must be one of the critical factors in the study of inductive effect. Electronegativity is recognized as a basic elemental property by Mark R. Leach, because it integrates the physical and chemical atomic parameters into a single dimensionless number, which is often used to predict the covalency or ionicity of chemical bond.4 There are dozens of methods for empirically quantifying electronegativity, including the original thermochemical technique, numerical averaging of the ionization potential and electron affinity, effective nuclear charge and covalent radius, averaged successive ionization energies of an element’s valence electrons, etc. Those materials cause several electronegativity scales such as Pauling, Mulliken, Sanderson, Allerd-Rochow, Lang & Smith, etc. The various Received: December 26, 2017

A

DOI: 10.1021/acs.inorgchem.7b03253 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Table 1. Symmetry Multiplicity mi, the Weighted Average Si−N Bond Length l ̅, the Weighted Average Valence of Si V̅ i, the Inductive Factor μΔχ in Ternary Nitridosilicate Compounds MxSiyNz ICSD

mi

α-Si3N4 β-Si3N4 γ-Si3N4 Ca2Si5N8

90 146 8263 97 566 79 070

6,6 6 8,16 4,4, 4,4, 4

HP-Ca2Si5N8

419 318

8,8, 8,8, 8

Sr2Si5N8 Ba2Si5N8 MgSiN2 α-CaSiN2 BaSiN2 SrSiN2 BaSi7N10

401 500 401 501 90 730 170 267 170 265 170 266 405 772

SrSi7N10

154 166

BaSi6N8 SrSi6N8 La3Si6N11 La7Si6N15 LaSi3N5 La5Si3N9 LiSi2N3 Li2SiN2 Li53.33Si10.67N32 (Li5SiN3) Li54.88Si9.12N30.98 (Li21Si3N11) Li8SiN4 NaSi2N3 Eu2SiN3 BeSiN2 ZnSiN2 MnSiN2 CeSi3N5 Ce3Si6N11 Ce5Si3N9 Ce7Si6N15(tricl.) Ce7Si6N15(trig.) Ca4SiN4 α-Ca5Si2N6 β-Ca5Si2N6 Ca16Si17N34 Ba5Si2N6 Eu2Si5N8 Pr3Si6N11 Pr5Si3N9 Pr7Si6N15 Sm3Si6N11

81 570 59 257 402 178 260 288 420 201 80 183

compound

li̅ /Å 1.7397,1.7305 1.7323 1.7825,1.8875 1.736,1.751, 1.727,1.749, 1.7303

l ̅/Å

V̅ i

V̅

μΔχ

ref

PS

1.7351 1.7323 1.8525 1.7387

3.8873 3.9187 3.7098 3.8594

0.000 0.000 0.000 0.360

17 18 19 20

×

3.8710

0.360

21

×

3.8892 3.7896 3.7211 3.7526 3.7475 3.7755 3.9393

0.380 0.404 0.590 0.900 0.950 1.010 0.144

22 22 23 24 24 24 25

3.9463

0.136

26

3.6293 3.6751 3.8696

0.168 0.158 0.400

×

417 444 391 265 248 709 N/A 130 022 419 064 34 118 420 126 25 582

1.7448, 1.7487, 1.7283, 0.7500, 1.7203 4,2, 2,2 1.744,1.7123, 1.7401,1.7431 4,2, 2,2 1.7585,1.7174, 1.7579,1.752 4 1.7511 8,8 1.7417,1.7538 8 1.7492 4 1.7473 2,2, 2,2, 1.73,1.7387, 1.7329,1.7459, 2,2, 2 1.7235,1.7263, 1.7229 2,2, 2,2, 1.7362,1.7308, 1.7437,1.7216, 2,2, 2 1.7394,1.7184, 1.7243 4,8 1.8999,1.7347 4,8 1.8905,1.7285 8,4 1.743,1.7252 superstructure 4,4, 4 1.7304,1.7465, 1.735 8,8, 8 1.7173,1.7424, 1.7531 8 1.7478 8,8, 8,8 1.7554,1.7451, 1.7505,1.755 16 1.9107

1.7898 1.7825 1.7371

3.8398,3.9347 3.9187 3.4149,3.8573 3.8742,3.7316, 3.9819,3.7560, 3.9532 3.8115, 3.7617, 3.9671, 3.7670, 4.0476 3.8163,4.1349, 3.8681,3.8103 3.7256,4.0687, 3.6864,3.7417 3.7211 3.8135,3.6916 3.7475 3.7755 3.9733,3.8637, 3.9470,3.7851, 4.0100,3.9747, 4.0214 3.9060,3.9532, 3.8104,4.0304, 3.8627,4.0629, 3.9985 3.0216,3.9331 3.0849,3.9702 3.8054,3.9979

1.7373 1.7376 1.7478 1.7515 1.9107

3.9583,3.7767, 3.9095 4.3370,4.2466, 3.8904 3.7647 3.6900,3.7788, 3.7288,3.6844 2.4183

3.8815 4.1580 3.7647 3.7205 2.4183

0.267 1.333 0.460 1.840 4.598

11 12 27 28 29 30 31 32 33

191 135

8,8, 8

1.9698

1.6705,3.4037, 1.7082

2.2608

5.536

34

×

N/A 72 466 420 679 25 704 656 276 172 193 402 910 401 679 419 063 420 199 420 200 250 872 414 462 250 873 248 945

unresolved fully structure 8 1.7419 8 1.7431 4 1.7574 4 1.7157 4 1.7412 4,4, 4 1.7255,1.7415, 1.73 8,4 1.7422, 1.7378 8,8, 8 1.7555, 1.7026, 1.7284 superstructure disordered crystal 4 1.7912 8 1.7701 4,4 1.7746,1.7782 4,16, 1.7561,1.7236, 1.7765,1.6985, 16,16, 16 1.7647 4,4 1.7868,1.7915 2,2, 2,4 1.7445,1.7331, 1.7164,1.7441 8,4 1.7411,1.7227 8,8, 8 1.7474, 1.7062, 1.7278 superstructure 8,4 1.73,1.7227

1.7419 1.7431 1.7574 1.7157 1.7412 1.7323 1.7407 1.7288

4.0186 3.8021 3.6563 4.0969 3.8220 4.0115,3.8282, 3.9596 3.8098,3.8674 3.6740,4.2400, 3.9570

4.0186 3.8021 3.6563 4.0969 3.8220 3.9331 3.8290 3.9570

0.485 1.400 0.330 0.250 0.350 0.260 0.390 1.300

34 35 36 37 38 39 40 41 30 28 28 42 43 42 44

× ×

1.7384 1.7367 1.7489 1.7511 1.7478 1.7492 1.7473 1.7315 1.7306

2.0528,1.7755, 2.0811

1.7912 1.7701 1.7764 1.7417

3.3433 3.5577 3.4979 3.8439

3.600 2.250 2.250 0.847

1.7892 1.7364 1.7350 1.7271

3.3433 3.5577 3.5166,3.4791 3.6686,4.0067, 3.4716,4.3019, 3.6391 3.3902,3.3519 3.8097,4.0821, 3.9243,3.8097 3.8253,4.0271 3.7601,4.1981, 3.9575

3.3711 3.8871 3.8926 3.9719

2.525 0.280 0.385 1.283

1.7276

3.9397,4.0287

3.9694

0.365

45 46 47 48 28 29

×

× × × ×

× ×

× ×

×

× ×

the nephelauxetic effect, which is often attributed to the covalency between the 5d electron and the p-orbitals of the anions. In the work of Xiao et al.,9 the inductive effect of neighboring cations in tuning luminescence properties of the solid solution phosphors is stated. They mentioned that the Eu− O bonds covalency reduction, on the one hand, leads to a smaller centroid shift of the 5d levels; on the other hand, it also enlarges the Stokes shift of 5d emission. Later, Kate et al.10 qualitatively related the bandgap and structural properties to the

electronegativity scales are equivalent, but the revised Pauling’s scale is the most complete, which ranges from Cs, χ = 0.7 to F, χ = 4.0. On the basis of the revised Pauling’s electronegativity accomplished by Allerd,6 Dorenbos7 related the centroid shift of Ce3+, εc, which is defined as the difference between the average energy of the five 5d levels in gaseous Ce3+ and Ce3+ doped in solids, to the host electronegativity. He pointed out that8 the centroid shift of 5d levels of Ce3+ is commonly associated with B


Article

Inorganic Chemistry

Table 2. Symmetry Multiplicity mi, the Weighted Average Si−N Bond Length l ̅, the Weighted Average Valence of Si V̅ i, the Inductive Factor μΔχ in Quaternary Nitridosilicate Compounds M1×1M2×2SiyNz compound

li̅ /Å

mi

ICSD

l ̅/Å

V̅ i

V̅

μΔχ

ref

3.7149 3.5786

0.423 0.310

49 50

3.7434 3.6966

0.408 0.438

51 52 53

BaYSi4N7 SrAlSi4N7

98 276 163 667

SrYSi4N7 SrYbSi4N7 SrScSi4N7 (Sr0.95Eu0.05) ScSi4N7 EuYSi4N7 EuYbSi4N7 CaYSi4N7 (Ca0.8Y1.2) (Si4N6.8C0.2) BaYbSi4N7 Ca5Al2Si2N8 CaMg3SiN4 SrMg3SiN4 EuMg3SiN4 BaMg3SiN4 CaAl0.54Si1.38N3 (CaAlSiN3) CaLaSiN3 Ca3Sm3Si9N17 Ca3Yb3Si9N17 Li5La5Si4N12 Li5Ce5Si4N12 Li2CaSi2N4 Li2SrSi2N4 Li4Sr3Si2N6 Li4Ca3Si2N6 Li2Sr4Si2N6 LiCa3Si2N5 Ba3Ca2Si2N6 Ba4MgSi2N6 Si(NCS)4 La17Al4Si9N33 Ba2Nd7Si11N23

150 459 405 625 189 117

solitary occupancy 2,6 1.7348,1.7737 1.7640 4,4, 4,4, 1.7522,1.758, 1.7866,1.7536, 1.7666 4,4, 4,4 1.7519,1.7865, 1.7656,1.7786 2,6 1.7413,1.7684 1.7616 2,6 1.7369,1.7731 1.7641 approximate structure

150 460 59 258 152 975

2,6 1.7785,1.7078 2,6 1.7367,1.7731 approximate structure

1.7255 1.7640

3.4704,4.3216 3.9372,3.6113

4.1088 3.6928

0.345 0.375

51 46 54

405 194 414 469 427 074 427 076 427 075 428 510 161 796

2,6 8 16 16 16 2,2 8

1.7502,1.7818 1.7854 1.769 1.8014 1.7683 2.0216,2.0382 1.8053

1.7739 1.7854 1.7690 1.8014 1.7683 2.0299 1.8053

3.8046,3.5417 3.4170 3.5422 3.2459 3.5501 1.7957,1.7711 3.2208

3.6074 3.4170 3.5422 3.2459 3.5501 1.7834 3.2208

0.453 2.975 1.490 2.720 2.470 2.780 0.766

52 55 56 56 56 57 58

1.7484,1.7542, 1.7286 1.7422 1.7011,1.757, 1.7268 1.7374 1.7527 1.7527 1.7329 1.7329 1.7346 1.7346 1.7377 1.7377 1.7918 1.7918 1.771 1.7710 1.7571 1.7571 1.7647,1.7652 1.7650 1.7796 1.7796 1.7767 1.7767 1.6786 1.6786 1.777,1.749, 1.7487 1.7520 1.7096,1.7041, 1.7144,1.6964 1.7082 1.712 1.7531,1.7783 1.7657 1.7411 1.7411 1.7496 1.7496 mixed occupancy 1.7783 1.7783 1.744,1.8988 1.7956 1.7436,1.728 1.7384 1.7409,1.7275 1.7364 1.7011,1.757, 1.7268 1.7374 1.7129,1.7148, 1.7812,1.793 1.7430 1.7428,1.7621, 1.7019,1.7639, 1.7414 1.7365 1.7498,1.7115, 1.7542,1.7575 1.7454 1.7757 1.7757

3.7488,3.7517, 3.9693 4.2565,3.7324, 3.9910 3.7045 3.9102 3.8909 3.8576 3.3713 3.5707 3.6569 3.5942,3.5935 3.4656 3.4887 4.5227 3.4662,3.7991, 3.7546 4.1646,4.2246, 4.1143,4.3096, 4.1572 3.7142,3.4711 3.8308 3.7431

3.8481 3.9056 3.7045 3.9102 3.8909 3.8576 3.3713 3.5707 3.6569 3.5939 3.4656 3.4887 4.5227 3.7423 4.1829

0.543 0.567 2.15 2.125 1.37 1.395 3.265 3.19 2.82 1.81 2.416 2.61 −1.33 1.64 0.667

59 60 60 61 61 62 62 63 64 65 66 67 67 68 69 70

3.5927 3.8308 3.7431

3.3 0.39 1.01

43 71 72

3.4818 3.7989,3.0361 3.8084,3.9841 3.8309,3.9790 4.2565,3.7324, 3.9910 4.3719,4.2606, 3.5784,4.3364 3.9169,3.6901, 4.3505,3.6631, 3.9065 3.7598,4.1366, 3.7068,3.6852 3.7833

3.4818 3.5446 3.8670 3.8803 3.9056 4.1838 3.9054

2.423 0.399 0.399 0.393 0.567 0.378 0.357

67 73 73 73 60 74 75

3.7990 3.7833

0.388 0.948

76 77

N/A 421 644 421 645 421 528 421 527 421 548 421 549 421 259 420 675 422 596 420 676 187 336 187 335 281 520 416 358 407 202

Ca7NbSi2N9 ZnGe0.5Si0.5N2 Pr9Se6Si3N9

414 461 656 278 414 020

1,4, 4 1,4, 4 8 8 24 24 4 8 8 8,8 8 16 16 4,16, 16 8,8, 16,8, 4 2,2 4 18

Ba1.6Sr3.4Si2N6 Ce0.2La2.8Si6N11 Ce0.27La2.73Si6N11 Ce2.1La0.9Si6N11 Ca3Yb3Si9N11 Sr1.95Eu0.05Si5N8 Ca1.91Eu0.09Si5N8

187 337 237 441 237 442 237 443 421 645 252 030 169 028

8 8,4 8,4 8,4 1,4, 4 4,2, 2,2 4,4, 4,4, 4

Ba1.74Eu0.26Si5N8 Sr0.99Eu0.01SiN2

194 143 239 872

2,2, 4,2 4

3.9472,3.6375 3.7105,3.6516, 3.3969,3.6961, 3.7318,3.3901, 3.5935,3.4579 4.0144,3.6531 3.9358,3.6169

PS

×

× ×

×

×

influences of metal atoms on Si−N bonds or Si−O bonds of these tetrahedra by introducing a special parameter, the inductive factor related to the electronegativity difference between metal elements and silicon. We established linear relationship between length of Si−N bonds or Si−O bonds and the inductive factor using a statistical method. Finally, we presented a relation between the centroid shift of 5d levels of Ce3+ and the inductive

condensation degree in nitridosilicates but without considering electronegativity. Following these ideas, in this work, we want to characterize quantitatively the tiny structure changes from the viewpoint of structural chemistry. We collected the structural data of more than 100 nitridosilicates and oxosilicates. The structures typically consist of [SiN4] or [SiO4] tetrahedra. We analyzed the C


Article

Inorganic Chemistry

Table 3. Symmetry Multiplicity mi, the Weighted Average Si−N Bond Length l ̅, the Weighted Average Valence of Si V̅ i, the Inductive Factor μΔχ in Ternary Oxysilicate Compounds MxSiyOz compound

ICSD

α-SiO2 β-Y2Si2O7 Lu2Si2O7 Lu2SiO5 Lu2SiO5 Mg2SiO4 Gd2SiO5 Y2SiO5 Yb2SiO5 BaSiO3 Ba2SiO4 BaSi2O5 Ba3SiO5 CaSiO3 β-Ca2SiO4 Sr3SiO5 β-Sr2SiO4 SrSiO3 β-Eu2SiO4 Li2SiO3 ThSiO4 Ca3Si2O7 Li4SiO4

16 331 281 312 412 249 279 584 89 624 9688 27 728 291 358 4446 6245 291 355 100 314 1449 30 884 963 28 534 36 041 26 1228 1510 853 1615 2282 8222

MgSiO3 ZrSiO4 Pr2Si2O7 Pb3Si2O7 Er2Si2O7 Nd2Si2O7 Sm2Si2O7 Sc2Si2O7 Sc2Si2O7 Zn2SiO4 La2Si2O7 Yb2Si2O7 HfSiO4 β-Na2Si2O5 Ag2SiO3 Cd2SiO4 Ce2Si2O7 Ho2Si2O7 Bi4(SiO4)3 Tm2SiO5 CuSiO3 Na2Si3O7 Tb2Si2O7 Dy2Si2O7

9328 71 942 14 252 15 371 16 049 16 051 16 167 16 214 75 925 20 093 20 775 28 097 31 177 34 688 36 589 50 527 74 776 74 777 86 277 89 623 89 669 95 690 98 724 98 725

mi 3 4 4 8 4 4 4 8 8 4 4 8,8, 8 4 4,4, 4 4 4 4 8,4 4 4 4 4,4 2,2, 2,2, 2,2, 2 8,8 18 4,4 36 4 4,4 4,4, 4,4 4 4 18 4,4, 4,4 4 4 4,4 4 8 4,4 4,4 12 4 2 4,4, 4 2,2, 2,2 2,2, 2,2

li̅ /Å 1.6156 1.634 1.6244 1.6242 1.6442 1.6303 1.6318 1.6259 1.4774 1.6232 1.6378 1.6187,1.6164, 1.6164 1.6394 1.6199,1.6269, 1.6346 1.6314 1.6389 1.6376 1.5898,1.5994 1.6089 1.6359 1.6346 1.6194,1.621 1.6235,1.6349, 1.6457,1.6382, 1.6281,1.6393 1.6312 1.6288,1.6404 1.6269 1.6133,1.6181 1.6366 1.6207 1.6207,1.6315 1.6263,1.6345, 1.6235,1.6165 1.6236 1.6234 1.6231 1.6333,1.6301, 1.6382,1.6422 1.6222 1.6202 1.6223,1.6262 1.633 1.6347 1.6321,1.6186 1.6328,1.682 1.6261 1.6282 1.6106 1.6147,1.6288, 1.6322 1.6198,1.6404, 1.6289,1.6333 1.6165,1.645, 1.6245,1.6371

l ̅/Å 1.6156 1.6340 1.6244 1.6242 1.6442 1.6303 1.6318 1.6259 1.4774 1.6232 1.6378 1.6172 1.6394 1.6271 1.6314 1.6389 1.6376 1.5930 1.6089 1.6359 1.6346 1.6202 1.6344 1.6346 1.6269 1.6157 1.6366 1.6207 1.6261 1.6252 1.6236 1.6234 1.6231 1.6360 1.6222 1.6202 1.6243 1.6330 1.6347 1.6254 1.6574 1.6261 1.6282 1.6106 1.6252 1.6306 1.6308

factor μΔχ in (qua)ternary nitridosilcates or oxosilicates. This work will help us understand the inductive effect deeply and quantitatively and get insight into the structural modulation due to the inductive effect.

■

V̅ i 4.0933 3.9132 3.9951 3.9991 3.8047 3.9378 3.9257 3.9826 6.3260 4.0255 3.8541 4.0713,4.0953, 4.0982 3.841081 4.0546,3.9751, 3.8968 3.9256 3.8421 3.8580 4.5069,4.6611 4.1565 3.9044 3.8828 4.0577,4.0477 4.0185,3.8994, 3.7786,3.8531, 3.9582,3.8523 3.9223 3.9574,3.8470 3.9682 4.1263,4.0646 3.87221 4.0372 4.0407,3.9284 3.9811,3.9018, 4.0104,4.0971 4.0060 4.0084 4.0094 3.9082,3.9388, 3.8578,3.8165 4.0212 4.0435 4.0307,3.9842 3.9098 3.8860 3.9244,4.0473 4.2111,3.5603 3.9784 3.9678 4.1610 4.1052,3.9691, 3.9335 4.0484,3.8554, 3.9585,3.9128 4.0953,3.7946, 4.0039,3.8682

V̅

μΔχ

ref

4.0933 3.9132 3.9951 3.9991 3.8047 3.9378 3.9257 3.9826 6.3260 4.0255 3.8541 4.0883 3.8411 3.9755 3.9256 3.8421 3.8580 4.5583 4.1565 3.9044 3.8828 4.0527 3.8975

0 1.22 1.27 2.54 2.54 2.62 2.40 2.44 2.20 1.01 1.78 0.445 2.67 1 2 2.85 1.90 0.95 2.4 1.96 1.30 1.5 3.92

78 79 80 81 82 83 84 85 86 87 85 88 89 90 91 92 93 94 95 96 97 98 99

3.9022 3.9682 4.0955 3.8722 4.0372 3.9846 3.9976 4.0060 4.0084 4.0094 3.8803 4.0212 4.0435 4.0075 3.9098 3.8860 3.9859 3.8857 3.9784 3.9678 4.1610 4.0026 3.9438 3.9405

1.31 1.33 1.13 3.495 1.24 1.14 1.17 1.36 1.36 3.30 1.10 1.10 1.30 0.93 3.86 3.38 1.12 1.23 2.693 2.5 1.9 0.62 1.10 1.22

100 101 102 103 104 104 105 106 107 108 109 110 111 112 113 114 115 115 116 82 117 118 119 119

PS

×

×

×

We introduce a new dimensionless parameterthe inductive factor μΔχwhich could be obtained by eq 1: x μΔχ = ·[χ (Si) − χ (M)] y (1) where Δχ is the difference of electronegativity between silicon and metallic element, and μ is defined as the ratio of metal element to silicon in chemical formula MxSiyNz. Herein the electronegativity defined in revised Pauling scale is selected because of its concern of transition-metal contraction and lanthanide contraction,6 besides the relatively higher complete-

ALGORITHM AND DATA

In this section, the concepts and algorithms appearing in this work are introduced. We mainly focus on ternary nitridosilicate compounds with chemical formula MxSiyNz, in which M, Si, and N represent metal, silicon, and nitrogen elements, respectively. D


Inorganic Chemistry

■

THE CHANGE OF CHEMICAL BOND The weighted average length of all Si−N bonds l ̅ of the nitridosilicate compounds from Table 1 is plotted in Figure 1

ness of elemental electronegativity values in reference to other scales. It is assumed that silicon is only tetrahedrally coordinated to four nitrogen atoms in most compounds. The cases when [Si2N6] complex is formed, such as BaSi6N811 and SrSi6N8,12 are excluded from our statistics. Then, we calculate the weighted average bond length of all Si−N bonds by eq 2; that is, we take the weighted mean value of the average Si−N bond radii li̅ in all kinds of crystallographic sites of silicon as the weighted average bond length l ̅: n

n

l̅ =

∑i = 1 mi li̅ n

∑i = 1 mi

=

4

∑i = 1 ∑ j = 1 milij n

4∑i = 1 mi

(2)

where n is the number of crystallographic sites of silicon, mi is the symmetry multiplicity of the ith silicon site, and lij is the length of the jth Si−N bond of the ith Si site. According to bond valence theory,13 the sum of the valences of all the bonds formed by an atom is equal to the valence of the atom. Subsequently, we calculate the weighted average valence V̅ of silicon valences Vi in all crystal sites by the empirical eq 3:14 n

n

V̅ =

∑i = 1 miVi n ∑i = 1 mi

=

4

r0 − rij

( 0.37 )

∑i = 1 ∑ j = 1 mi exp n ∑i = 1 mi

Figure 1. Correlation between the weighted average Si−N bond length l ̅ and the inductive factor μΔχ in ternary nitridosilicate compounds MxSiyNz.

against the inductive factor μΔχ, and the dependence can be well-approximated by linear function. By the least-squares method, the relationship is obtained as

(3)

where rij is the same meaning of lij, and r0 is a constant depending on the bond type. For Si−N bond it is equal to 1.724(3) Å.15 When it comes to quaternary nitridosilicate compounds M1×1M2×2SiyNzin which M1 and M2 represent the first and second metal elements, respectively, the metal electronegativity is treated as the weighted average of both M1 and M2, as defined in eq 4. The ratio μ is calculated by eq 5. The weighted average bond length and valence are also calculated in the same way as for ternary nitride compounds just described above. χ (M) =

μ=

x1χ (M1) + x 2χ (M 2) x1 + x 2

x1 + x 2 y

Article

l ̅ = 1.7313 + 0.0166μΔχ (Å)

(6)

2

The adjusted (adj) R for eq 6, which is usually smaller but more accurate than the unadjusted one and excludes the influence of the number of data, is 0.800, indicating that this model has strong ability to interpret, and the inductive factor is able to explain 80.0% change of weighted average Si−N bond length l ̅. As shown in Table S1a in the Supporting Information, the slope and the intercept are significantly different from zero, which pass the hypothesis test of the parameters successfully at the 0.95 confidence level. Meanwhile, the correlativity is also significant at the 0.95 level. It is noteworthy that all the confidence levels in the following text are 0.95 if not mentioned. Extending the method of constructing the Student’s tdistribution in statistics to predict dependent variable, here we plot the 95% confidence band and prediction band in Figure 1. Figure 2 shows the relationship between l ̅ and V̅ calculated using eq 3, which gives a significant linear dependence

(4)

(5)

Furthermore, all the algorithms designed for nitridosilicate compounds analysis were also applied to silicates MxSiyOz, owing to the similarity between [SiO4] and [SiN4] tetrahedron.The only difference lies in r0, which is 1.624(1) Å15 for Si−O bond. Herein, only the ternary oxysilicates MxSiyOz are given, and the quaternary ones M1×1M2×2SiyOz are missed for its unimaginable amount but the minor change of l ̅. Here, all the statistical data are listed in Table 1 for MxSiyNz, Table 2 for M1×1M2×2SiyNz, and Table 3 for MxSiyOz. In these tables, the data of bond length, that is, lij, is extracted using VESTA16 through the import of the corresponding crystal structure data. The data of symmetry multiplicity mi is taken from the compounds’ crystal information files. The column of “ICSD” means the collection codes in the inorganic crystal structure database, and the right column of “ref” means the cited paper of the corresponding crystal information file. The symbol of“×”in the “PS” column means that it is not included in statistics for some reasons mentioned later.

Figure 2. Correlation between the weighted average valence of Si V̅ and the weighted average Si−N bond length l ̅ in ternary nitridosilicate compounds MxSiyNz. E


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Inorganic Chemistry

into Si3N4. The Si−N tetrahedron will be distorted but still preserve the bonding topology that Si is coordinated with four nitrogen atoms; otherwise, it is called “no enough valence of Si” such as BaSi6N8 and SrSi6N8, which are not included in our statistics to avoid ambiguity. Re7Si6N15 (Re = La, Ce, Pr)28 with superstructure, Li5SiN333 and Li21Si3N1134 with sharing Li and Si crystallographic site, Li8SiN434 with unresolved structure, and compounds synthesized only at high pressure or stabilized only at high temperature are also excluded in statistics. As shown in Figure 4, all nitridosilicates are simplified as a universal model with only one [SiN4] tetrahedron adjoined with

(7)

V̅ = 21.0769 − 9.9025 l ̅

with adj R2 = 0.995, as shown in Table S2b in the Supporting Information. This linearity is expected by the first-order Taylor expansion of exponential function; that is, ex ≈ 1 + x, when x approaches zero. Coincidentally, rij is very close to r0 in eq 3 for almost all the nitride compounds compiled in Table 1, which fulfills the Taylor expansion requirement. Therefore, if mi is ignored temporarily, eq 3 can be rewritten as V̅ =

n 4 r −r ⎞ ⎛ 1 ∑ ∑ ⎜⎝1 + 0 ij ⎟⎠ n i=1 j=1 0.37 n

4

⎛ r ⎞ 1 ∑ ∑ rij =4 1+ 0 ⎟− ⎝ ⎠ 0.37 0.37n i = 1 j = 1 ⎜

⎛ r ⎞ 4 l ̅ = 22.6378 − 10.8108 l ̅ = 4⎜1 + 0 ⎟ − ⎝ ⎠ 0.37 0.37

(8)

The result almost duplicates eq 7. This relationship could be applied to exclude the exceptional data such as La5Si3N9 and NaSi2N3 located far from the line. It is worthwhile to mention that four data points, BeSiN2, ZnSiN2, Pr5Si3N9, and Ce5Si3N9, which are far from the 95% prediction band in Figure 2 and seem like abnormal data for the reason that even if included they are nearby or beyond the prediction band and enlarge the prediction band sharply, are deleted in fit process of eq 6. ZnSiN2 is synthesized at 6.0 GPa,38 which may cause the contraction of crystal structure. As for the real reason about the abnormity for the other three compounds, it is not clear yet and may be related to their crystal structure details. To keep data process consistent and the accuracy and predicted capacity of the models, all the six data points mentioned above are excluded in the following fit of eq 9. As Figure 3 demonstrates, a significant linear correlation V̅ = 3.9315 − 0.1688μΔχ

Figure 4. Schematic diagram of the inductive effect of M. The thickness of arrow represents the degree of ability of donating electron.

x/4yM atom distributed uniformly at four nitrogens. What we are concerned about now is the extremely average effect. If M is less electronegative than Si, it will tend to become an electron donor, which will exert electron pressure on the Si−N bond.1 To construct stable full-shell structure more easily, the N atom prefers to get the electron from M instead of Si, causing the extension of the average Si−N bond length and the reduction of the average valence of Si. In this sense, the stoichiometric ratio between Si and M could be regarded to represent the pressureexerting ability. But the relative position of M atom and the tetrahedron is not accounted. More complicated quaternary nitridosilicate compounds, M1×1M2×2SiyNz, are categorized into two types depending on whether M1 and M2 occupy the same crystallographic site or not. They are illustrated in Figures 5−7 according to eqs 4 and 5. Four compounds are excluded from the statistics. Three of them, BaMg3SiN4, CaAlSiN3, and ZnGe0.5Si0.5N2, are excluded due to the sharing of crystallographic site between metal and Si, which has a profound influence on the coordination surrounding of Si.

(9)

Figure 3. Correlation between the weighted average valence of Si V̅ and the inductive factor μΔχ in ternary nitridosilcate compounds MxSiyNz.

with adj R2 = 0.847 is fitted for MxSiyNz of the reference data set. The slope and intercept pass the hypothesis test of the parameters successfully. The model is of significance, the inductive factor μΔχ explains 84.7% change of the weighted average valence of Si at the center of the tetrahedron. The formation of ternary compound MxSiyNz could be regarded as introducing the third component M, the metal ion,

Figure 5. Weighted average Si−N bond length l ̅ vs the inductive factor μΔχ in quaternary nitridosilcate compounds M1×1M2×2SiyNz. F


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Inorganic Chemistry

so we get an important result that the inductive factor μΔχ possesses approximately additive property. The relative dispersion of data proves that there must exist interatomic mutual effect between M1 and M2; that is, the composite atom M cannot represent totally constituent elements of M1 and M2. For the sake of comparison to nitridosilicate compounds, the ternary silicate compounds are analyzed, and the analogous results with eqs 6, 7, and 9 appear, that is: l ̅ = 1.6221 + 0.0035μΔχ

(11)

2

with adj R = 0.240 V̅ = 21.2206 − 10.5996 l ̅

(12)

2

with adj R = 0.992, and Figure 6. Weighted average valence of Si V̅ vs the weighted average Si− N bond length l ̅ in quaternary nitridosilcate compounds M1×1M2×2SiyNz.

V̅ = 4.0254 − 0.0376μΔχ

(13)

2

with adj R = 0.240. The similar results of processes of hypothesis testing with nitridosilicates are listed in Tables S4−S6 in the Supporting Information. The similar correlations are plotted in Figures 8−10. The range of changes of l ̅ and V̅ in silicates (1.61−

Figure 7. Weighted average valence of Si V̅ vs the inductive factor μΔχ in quaternary nitridosilcate compounds M1×1M2×2SiyNz. Figure 8. Correlation between the weighted average Si−O bond length l ̅ and the inductive factor μΔχ in ternary silicate compounds MxSiyOz

The fourth one, Si(NCS)4, is excluded because of the nonmetal composition, although it may match well with the predicted model. For the mixed occupancy compounds, one metal element enters crystal as microdopant. Obviously, most data points fall into or nearby the 95% prediction bands (a part is lost) of Figure 3, though the data seem more dispersive than ternary compounds. Apart from the doubt on data accuracy, for example, in Ce0.2La2.8Si6N11,73 the Si atom is almost located on the plane determined by three nitrogen atoms in the tetrahedron, causing the sharp increase of the weighted average length of Si−N bonds and the abrupt decrease of the weighted average valence of Si, which is obviously different from Ce0.27La2.73Si6N11 and Ce2.1La0.9Si6N11; the predictive ability of μΔχ to the weighted average bond length and bond valence is verified again. Furthermore, the weighted average method of eqs 4 and 5 can be rearranged as μ[χ (Si) − χ (M)] =

1.64 Å) is much smaller than those in nitridosilicates (1.73−1.80 Å), which should be attributed to the difference of electronegativity between N and O (χ(N) = 3.04, χ(O) = 3.44). The bigger the electronegativity of coordinated anion is, the stronger bond the Si tetrahedron will have. So, the Si−O bond is relatively

x1 + x 2 ⎡ ⎢χ (Si) y ⎢⎣

−

x1χ (M1) + x 2χ (M 2) ⎤ x ⎥ = 1 [χ (Si) − χ (M1)] ⎥⎦ x1 + x 2 y

+

x2 [χ (Si) − χ (M 2)] = y

2

∑ μi Δχi i=1

Figure 9. Correlation between the weighted average valence of Si V̅ and the weighted average Si−N bond length l ̅ in ternary silicate compounds MxSiyOz.

(10) G


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Inorganic Chemistry

Table 4. Centroid Shift of 5d Levels of Ce3+ in Nitridosilicates compound CaAl0.54Si1.38N3 (CaAlSiN3) Ca2Si5N8 Ba2Si5N8 Sr2Si5N8 CaMg3SiN4 La3Si6N11 SrAlSi4N7 SrSiN2 BaSiN2 LaSi3N5 BaYSi4N7 SrYSi4N7 BaSi7N10

Figure 10. Correlation between the weighted average valence of Si V̅ and the inductive factor μΔχ in ternary silicate compounds MxSiyOz.

stronger than the Si−N bond, and it has higher ability to resist the induction from outside.

THE CENTROID SHIFT OF 5D LEVELS OF CE3+ Dorenbos7 defined the average electronegativity χav of the cations in the compound as ∑i niziχi ∑i nizi

(14)

where ni is the number of cations of type i with charge +zi and electronegativity χi in the compound formula. Then, the spectroscopic polarizability αsp can be obtained by αsp = α0(X) +

b(X) χav 2

centroid shift of 5d levels of Ce3+, εc/eV

ref

0.766

2.83

121

0.360 0.404 0.380 1.490 0.400 0.310 1.010 0.950 0.267 0.423 0.408 0.144

2.76 2.51 2.52 3.10 3.10 3.02 2.89 2.76 2.28 2.33 2.38 2.26

122 122 122 123 124 125 126 126 127 128 51 129

Table 5. Centroid Shift of 5d Levels of Ce3+ in Oxosilicates120

■

χav =

μΔχ

(15)

compound

μΔχ

centroid shift of 5d levels of Ce3+, εc/eV

BaSiO3 SrSiO3 Lu2Si2O7 Sr2Si2O7 Ba3Mg(SiO4)2:(Ce1) Ba2SiO4 Sr2SiO4 Li2SrSiO4 Li2CaSiO4 LiYSiO4 LiLuSiO4 X2-Lu2SiO5:(Ce1)

1.01 0.95 1.27 1.36 1.81 1.78 1.90 2.79 2.74 2.52 2.64 2.54

1.96 1.91 1.30 1.50 1.40 1.99 1.45 1.44 1.44 1.45 1.57

where α0(X) is the limiting spectroscopic polarizability of anion X in the case of very large χav, that is, strong binding of the anion valence electrons to cations, and b(X) is interpreted as the susceptibility of anion X to change its polarizability due to bonding with coordination cations. In this model, the centroid shift εc is exactly proportional to αsp; that is, it should be attributed to the host electronegativity by means of the following equation: N

εc = 1.79 × 1013αsp∑ i=1

1 (R i − 0.6ΔR )6

(16) 3+

where Ri is the individual bond length from Ce to ligand i in the unrelaxed lattice, and ΔR is the difference between the ionic radius of cation replaced by Ce3+ and the ionic radius of Ce3+. The summation is over all N coordinating anion ligands. According to our model, we compile the value of centroid shift εc of Ce3+ in nitridosilicates and oxysilicates in Table 4 and Table 5. In the second column of Table 4, the centroid shift is averaged over the five band maxima of the excitation spectra corresponding to the transitions from the 2F5/2 ground state to the five splitted 5d levels. The data of Table 5 are taken directly from Dorenbos’ analytical results.120 If the metal element M, M1, or M2 is substituted partially by Ce3+, it is discovered that the centroid shift of 5d levels of Ce3+, as plotted in Figure 11 and Figure 12, shows obviously positive correlation with the inductive factor. Because of the uncertain estimation degree, it is hard to determine the linearity. The result agrees with Dorenbos’ analysis.7 However, our model is mainly dependent on host property, whereas Dorenbos’ model also accounts for the

Figure 11. Centroid shift of 5d levels of Ce3+, εc, vs the inductive factor μΔχ in (qua)ternary nitridosilcates

local bond length between coordinated anion ligand and Ce3+, which is more complex. With the increase of inductive factor, the N/O atom tends to get electron shared by M instead of Si, causing the lengthening of the Si−N/O bonds and the shortening of the M−N bonds. It means that the framework of [SiN4] or [SiO4] tetrahedra takes more space and leaves less to M for accommodation. So, when Ce enters the crystal, the binding between Ce and its nitric ligands becomes stronger, and the covalency increases, which generates the greater change of centroid of 5d levels of Ce3+. The difference between the data distribution level of the tilt of nitridosilicates and oxysilicates reveals that the centroid shift of H


Article

Inorganic Chemistry

Quanlin Liu: 0000-0003-3533-7140 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

This work is supported by the National Natural Science Foundation of China (Nos. 51472028 and 51602019) and Fundamental Research Funds for the Central Universities (FRFTP-17-005A2).

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Figure 12. Centroid shift of 5d levels of Ce , εc, vs the inductive factor μΔχ in (qua)ternary oxysilcates 3+

nitridosilicates is affected more easily by internal metal elements than oxysilicates except for some special compounds such as BaSiO3, SrSiO3, and Sr2SiO4, which is in correspondence with the analysis above on the variation of bond length and atomic valences.

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CONCLUSIONS The purpose of this paper is to quantify the inductive effect of metal element from the viewpoint of structural chemistry by introducing the pivotal parameterthe inductive factor μΔχ and to verify the dependence of established model by applying statistical method. The analysis of more than 100 nitridosilicates and oxysilicates conveys that significant linear relation does exist between the inductive factor and the weighted average bond length and the weighted average valence of Si; that is, l ̅ = 1.7313 + 0.0166 μΔχ (Å) and V̅ = 3.9315 − 0.1688 μΔχ for [SiN4] tetrahedra, l ̅ = 1.6221 + 0.0035 μΔχ and V̅ = 4.0254 − 0.0376 μΔχ (Å) for [SiO4] tetrahedra. All the 95% confidence bands and predicted bands are plotted. Furthermore, it seems that the inductive effect is much stronger in nitridosilicates than that in oxysilicates and that the inductive factor has approximately additive property. As for physicochemical property, the centroid shift of 5d levels of Ce3+ in (qua)ternary nitridosilcate compounds is taken as an example, which shows significant positive correlation to the inductive factor. This work is intended to enlighten us on the inductive effect, help us to understand it deeply and quantitatively, and get insight into its non-negligible role in the structural modulation.

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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.7b03253. The analytical statistical results of the linear fits of eq (6), (7), (9), (11), (12), and (13) are output in the software of SPSS and listed in Tables S1−S6 (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Zhiguo Xia: 0000-0002-9670-3223 I


Article

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