Otmar M.
ten Kate
*^{a},
Zhijun
Zhang
^{b} and
H. T. (Bert)
Hintzen
^{c}
^{a}Product and Process Engineering, Chemical Engineering, Applied Sciences, Delft University of Technology, Van der Maasweg 9, 2629 HZ, Delft, The Netherlands. E-mail: o.m.tenkate@tudelft.nl
^{b}School of Materials Science and Technology, Shanghai University, Shanghai, 200444, China
^{c}Luminescent Materials Group, Radiation Science and Technology, Applied Sciences, Delft University of Technology, Mekelweg 15, 2629 JB, Delft, The Netherlands
First published on 17th October 2017
Relations between the bandgap and structural properties and composition of the M–Si–N nitridosilicates (M = alkali, alkaline earth or rare earth metal) have been obtained, using experimental data collected from literature; and qualitative models are presented to explain the observed trends. Compounds with a higher degree of condensation, i.e. a higher Si/N ratio, generally have longer M–N bonds and shorter Si–N bonds. The observations can be explained based on the effective charge of N, dependent on its coordination with Si (NSi_{x}). With increasing Si/N ratio the coordination number of N by Si increases, making the effective charge of the nitrogen atom less negative, resulting in a longer and less covalent M–N bond. This also shifts the N 2p levels down in energy, lowering the top of the valence band (mainly composed of N orbitals); while decreasing the Si–N distance shifts the bottom of the conduction band (mainly composed of Si and M orbitals) upward. Some nitridosilicates show deviations to the general trends, such as γ-Si_{3}N_{4} and several Li-containing compounds. These deviations have been discussed and possible explanations have been given based on peculiarities in their structural characteristics.
The nitridosilicates are compounds with the overall composition of M_{x}Si_{y}N_{z} where M is an alkali (1+), alkaline earth (2+) or rare-earth (3+) metal ion or combination thereof. The structures generally consist of a framework of interconnected SiN_{4} tetrahedra with the metal ions located in the cavities of the framework. This makes the nitridosilicates comparable to the oxosilicates, which consist of interconnected SiO_{4} tetrahedra. However, in the oxosilicates the O atoms are usually one-fold or twofold coordinated by Si, with only a few compounds showing threefold coordination, as occurs in high-pressure phase stishovite (SiO_{2}).^{20} In the nitridosilicates on the other hand, in addition to terminal (NSi_{1}) and bridging (NSi_{2}) nitrogen, the threefold coordination of N by Si (NSi_{3}) is much more common, and N can even be fourfold coordinated by Si (NSi_{4}). This allows for a much wider range of structures ranging from highly condensed Si_{3}N_{4} with low M/Si ratio and high degree of condensation (Si/N ratio is 0.75), to Ca_{4}SiN_{4} with a very low degree of condensation (Si/N ratio is 0.25) as a consequence of a high M/Si ratio. Such structural features strongly determine the chemical stability of the materials, showing a lower stability for compounds with a lower degree of cross-linking between SiN_{4} tetrahedra.^{21} Nitridosilicates such as Ca_{4}SiN_{4}^{22,23} and Eu_{2}SiN_{3}^{24} with a low degree of cross-linking are highly sensitive to water, while BaSi_{7}N_{10}^{25} with a high degree of cross-linking is very stable against oxidation and not corroded by water.
In addition to stability variations among the nitridosilicate structures, there is also a large variation in their optical properties depending on the chemical composition (i.e. M/Si ratio). The bandgap of the M_{x}Si_{y}N_{z} compounds can vary greatly from as small as 2.7 eV in Li_{8}SiN_{4}^{26} to as large as 6.9 eV in LiSi_{2}N_{3}.^{27,28} This has its influence on the performance as a luminescent material when the nitridosilicate host lattice is doped with lanthanide ions. For example, the position of the lowest 5d level of Eu^{2+} with respect to the bottom of the conduction band strongly influences the efficiency and thermal stability of the Eu^{2+} 5d–4f emission. When positioned inside or close to the conduction band, auto-ionization or thermal ionization of the 5d electron to the conduction band may occur and the 5d–4f emission will be quenched.^{29} Other examples are the position of the valence band with respect to the lanthanide 4f ground states that determines the energy of charge transfer transitions,^{30} and the position of the 4f ground state of the divalent ion with respect to the valence and conduction band that determines the valence stability of a divalent ion.^{31} These examples demonstrate the importance for the development of luminescent materials to know how the positions of the valence and conduction band of the phosphor host lattice are influenced by its composition and can be tuned.
This work presents the relations between the composition, structural properties and bandgap of the nitridosilicates and presents qualitative models that can explain the observed trends. For this we collect and analyse experimental data presented in literature on all M_{x}Si_{y}N_{z} nitridosilicates where M is an alkali (1+), alkaline earth (2+) or rare earth (3+) metal or combination thereof. In the first part of the manuscript we discuss the structural characteristics of the nitridosilicates, such as bond lengths and coordination numbers, and relate it to the chemical compositions of the materials. A qualitative model is then developed to explain the influence that the Si/N ratio has on the bond lengths and coordination numbers. In the final part of the manuscript the relation between the bandgap and the structure and composition of the nitridosilicates is discussed. A second model is then developed to explain the influence of the Si/N ratio on the positions of the valence and conduction band.
Compound | Space group | ICSD | Si–N network (CS = corner sharing, ES = edge sharing, 3D = 3-dimensional) | N by Si coordination N^{[x]} | Average M–N distance (Å) | Shortest Si–N distance^{a} (Å) | Ref. |
---|---|---|---|---|---|---|---|
a If there are multiple Si sites with different Si–N distances in a structure, the average is taken of the shortest Si–N distance of each site. b Li_{21}Si_{3}N_{11} and Li_{5}SiN_{3} both crystallize in an anti-fluorite (Li,Si)_{2}N structure with N 8-fold coordinated by Si and Li. c Ca_{16}Si_{17}N_{34} is also known as cubic-CaSiN_{2}. d Structures may also be considered a 3D network of corner-sharing and edge-sharing SiN_{4} and LiN_{4} and/or MgN_{4} tetrahedra. e Compound contains mixed Sr/Ba, Ca/Sm, Ca/Yb or Ca/Y sites. f Distances based on a structure doped with 5% Eu. g CaYSi_{4}N_{7} is actually Ca_{0.8}Y_{1.2}Si_{4}N_{6.8}C_{0.2}. | |||||||
α-Si_{3}N_{4} | (159) | 79797 | 3D CS SiN_{4} network | N^{[3]} | — | 1.673 | 34 |
β-Si_{3}N_{4} | (173) | 8263 | 3D CS SiN_{4} network | N^{[3]} | — | 1.704 | 35 |
γ-Si_{3}N_{4} | (227) | 97566 | 3D ES/CS SiN_{4}/SiN_{6} network | N^{[4]} | — | 1.853 | 36 |
Li_{21}Si_{3}N_{11} | (79) | 191135 | ^{ } | ^{ } | 2.111 | 1.656 | 37 |
Li_{5}SiN_{3} | (206) | 25582 | ^{ } | ^{ } | 2.084 | 1.910 | 38 |
Li_{2}SiN_{2} | (61) | 420126 | 3D CS SiN_{4} network | N^{[2]} | 2.160 | 1.728 | 39 |
LiSi_{2}N_{3} | (36) | 98524 | 3D CS SiN_{4} network | 1N^{[2]}:2N^{[3]} | 2.263 | 1.681 | 40 |
MgSiN_{2} | (33) | 90731 | 3D CS SiN_{4} network | N^{[2]} | 2.249 | 1.732 | 41 |
Mg_{2}Si_{5}N_{8} | (9) | 3D CS SiN_{4} network | 1N^{[2]}:1N^{[3]} | 2.305 | 1.660 | 42 | |
Ca_{4}SiN_{4} | (14) | 250872 | Isolated SiN_{4} tetrahedrons | N^{[1]} | 2.522 | 1.767 | 23 |
α-Ca_{5}Si_{2}N_{6} | (15) | 414462 | Isolated pairs of ES SiN_{4} | 2N^{[1]}:1N^{[2]} | 2.575 | 1.713 | 43 |
β-Ca_{5}Si_{2}N_{6} | (12) | 250873 | Isolated pairs of ES SiN_{4} | 2N^{[1]}:1N^{[2]} | 2.578 | 1.735 | 23 |
α-CaSiN_{2} | (61) | 170267 | 3D CS SiN_{4} network | N^{[2]} | 2.583 | 1.729 | 44 |
Ca_{16}Si_{17}N_{34}^{c} | (216) | 248945 | 3D CS SiN_{4} network | 2N^{[1]}:14N^{[2]}:1N^{[4]} | 2.536 | 1.645 | 45 |
Ca_{2}Si_{5}N_{8} | (9) | 79070 | 3D CS SiN_{4} network | 1N^{[2]}:1N^{[3]} | 2.646 | 1.671 | 46 |
β-Ca_{2}Si_{5}N_{8} | (4) | 3D CS SiN_{4} network | 1N^{[2]}:1N^{[3]} | 2.730 | 1.618 | 42 | |
HP-Ca_{2}Si_{5}N_{8} | (61) | 419318 | 3D CS SiN_{4} network | 1N^{[2]}:1N^{[3]} | 2.577 | 1.664 | 47 |
SrSiN_{2} | (14) | 170270 | 3D CS/ES SiN_{4} network | N^{[2]} | 2.859 | 1.711 | 44 |
Sr_{2}Si_{5}N_{8} | (31) | 401500 | 3D CS SiN_{4} network | 1N^{[2]}:1N^{[3]} | 2.949 | 1.675 | 48 |
SrSi_{7}N_{10} | (7) | 154166 | 3D CS and ES SiN_{4} network | 1N^{[2]}:4N^{[3]} | 3.069 | 1.683 | 49 |
SrSi_{6}N_{8} | (44) | 319265 | 3D CS SiN_{4} network (Si–Si bonds) | 1N^{[2]}:3N^{[3]} | 3.028 | 1.691 | 50 |
Ba_{5}Si_{2}N_{6} | (19) | 81570 | Isolated pairs of ES SiN_{4} | 2N^{[1]}:1N^{[2]} | 2.862 | 1.747 | 51 |
BaSiN_{2} | (64) | 170268 | 3D CS/ES SiN_{4} network | N^{[2]} | 2.991 | 1.719 | 44 |
Ba_{2}Si_{5}N_{8} | (31) | 401501 | 3D CS SiN_{4} network | 1N^{[2]}:1N^{[3]} | 2.999 | 1.686 | 48 |
BaSi_{7}N_{10} | (7) | 405772 | 3D CS and ES SiN_{4} network | 1N^{[2]}:4N^{[3]} | 3.269 | 1.683 | 25 |
BaSi_{6}N_{8} | (44) | 417444 | 3D CS SiN_{4} network (Si–Si bonds) | 1N^{[2]}:3N^{[3]} | 3.062 | 1.667 | 52 |
Eu_{2}Si_{5}N_{8} | (31) | 59257 | 3D CS SiN_{4} network | 1N^{[2]}:1N^{[3]} | 2.894 | 1.681 | 53 |
La_{5}Si_{3}N_{9} | (64) | 419064 | Branched chains of CS SiN_{4} | 2N^{[1]}:1N^{[2]} | 2.711 | 1.564 | 54 |
La_{3}Si_{6}N_{11} | (100) | 248709 | 3D CS SiN_{4} network | 9N^{[2]}:2N^{[3]} | 2.676 | 1.711 | 55 |
LaSi_{3}N_{5} | (19) | 130022 | 3D CS SiN_{4} network | 3N^{[2]}:2N^{[3]} | 2.802 | 1.690 | 56 |
Ce_{5}Si_{3}N_{9} | (64) | 419063 | Branched chains of CS SiN_{4} | 2N^{[1]}:1N^{[2]} | 2.685 | 1.725 | 54 |
Ce_{7}Si_{6}N_{15} (tricl.) | (2) | 420199 | 3D CS SiN_{4} network | 2N^{[1]}:5N^{[2]} | 2.772 | 1.705 | 57 |
Ce_{7}Si_{6}N_{15} (trig.) | (148) | 420200 | 3D CS SiN_{4} network | 2N^{[1]}:5N^{[2]} | 2.770 | 1.625 | 57 |
Ce_{3}Si_{6}N_{11} | (100) | 237444 | 3D CS SiN_{4} network | 9N^{[2]}:2N^{[3]} | 2.661 | 1.725 | 58 |
CeSi_{3}N_{5} | (19) | 402910 | 3D CS SiN_{4} network | 3N^{[2]}:2N^{[3]} | 2.783 | 1.686 | 56 |
Pr_{5}Si_{3}N_{9} | (64) | 260288 | Branched chains of CS SiN_{4} | 2N^{[1]}:1N^{[2]} | 2.672 | 1.719 | 59 |
Pr_{7}Si_{6}N_{15} | (2) | 420201 | 3D CS SiN_{4} network | 2N^{[1]}:5N^{[2]} | 2.762 | 1.693 | 57 |
Pr_{3}Si_{6}N_{11} | (100) | 402178 | 3D CS SiN_{4} network | 9N^{[2]}:2N^{[3]} | 2.646 | 1.703 | 60 |
Sm_{3}Si_{6}N_{11} | (100) | 80183 | 3D CS SiN_{4} network | 9N^{[2]}:2N^{[3]} | 2.618 | 1.697 | 56 |
Li_{4}Ca_{3}Si_{2}N_{6} | (12) | 420675 | Isolated pairs of ES SiN_{4}^{d} | 2N^{[1]}:1N^{[2]} | 2.596 (Ca) | 1.711 | 61 |
Li_{4}Sr_{3}Si_{2}N_{6} | (12) | 421259 | Isolated pairs of ES SiN_{4}^{d} | 2N^{[1]}:1N^{[2]} | 2.735 (Sr) | 1.735 | 61 |
Li_{4}Ca_{2}MgSi_{2}N_{6} | (12) | 427077 | Isolated pairs of ES SiN_{4}^{d} | 2N^{[1]}:1N^{[2]} | 2.482 (Ca) | 1.743 | 62 |
Li_{2}Ca_{2}Mg_{2}Si_{2}N_{6} | (12) | 427078 | Isolated pairs of ES SiN_{4}^{d} | 2N^{[1]}:1N^{[2]} | 2.588 (Ca) | 1.720 | 62 |
Li_{2}Ca_{3}MgSi_{2}N_{6} | (12) | Isolated pairs of ES SiN_{4}^{d} | 2N^{[1]}:1N^{[2]} | 2.554 (Ca) | 1.720 | 63 | |
Li_{2}Sr_{4}[Si_{2}N_{5}]N | (119) | 422596 | Layered CS SiN_{4} network | 1N^{[0]}:2N^{[1]}:3N^{[2]} | 2.694 (Sr) | 1.751 | 64 |
LiCa_{3}Si_{2}N_{5} | (15) | 420676 | Double chain of ES/CS SiN_{4} | 2N^{[1]}:1N^{[2]} | 2.540 (Ca) | 1.726 | 65 |
Li_{2}CaSi_{2}N_{4} | (205) | 421548 | 3D CS SiN_{4} network | N^{[2]} | 2.528 (Ca) | 1.714 | 66 |
Li_{2}SrSi_{2}N_{4} | (205) | 421549 | 3D CS SiN_{4} network | N^{[2]} | 2.699 (Sr) | 1.738 | 66 |
Li_{5}La_{5}Si_{4}N_{12} | (117) | 421528 | Non-br. chains CS SiN_{4} | 2N^{[1]}:1N^{[2]} | 2.609 (La) | 1.740 | 67 |
Li_{5}Ce_{5}Si_{4}N_{12} | (117) | 421527 | Non-br. chains CS SiN_{4} | 2N^{[1]}:1N^{[2]} | 2.605 (Ce) | 1.709 | 67 |
CaMg_{3}SiN_{4} | (88) | 427074 | Isolated SiN_{4} tetrahedrons^{d} | N^{[1]} | 2.638 (Ca) | 1.763 | 68 |
SrMg_{3}SiN_{4} | (88) | 427076 | Isolated SiN_{4} tetrahedrons^{d} | N^{[1]} | 2.802 (Sr) | 1.791 | 68 |
EuMg_{3}SiN_{4} | (88) | 427075 | Isolated SiN_{4} tetrahedrons^{d} | N^{[1]} | 2.680 (Eu) | 1.757 | 68 |
BaMg_{3}SiN_{4} | (2) | 428510 | 3D CS (Si,Mg)N_{4} network | — | 2.953 (Ba) | 1.892 | 69 |
Ba_{4}MgSi_{2}N_{6} | (70−2) | 187335 | Isolated pairs of ES SiN_{4} | 2N^{[1]}:1N^{[2]} | 2.953 (Ba) | 1.739 | 70 |
Ba_{3}Ca_{2}Si_{2}N_{6} | (15) | 187336 | Isolated pairs of ES SiN_{4} | 2N^{[1]}:1N^{[2]} | 2.910 (Ba) | 1.730 | 70 |
Ba_{1.6}Sr_{3.4}Si_{2}N_{6} | (15) | 187337 | Isolated pairs of ES SiN_{4} | 2N^{[1]}:1N^{[2]} | ^{ } | 1.718 | 70 |
CaLaSiN_{3} | (64) | Non-branched chains CS SiN_{4} | 2N^{[1]}:1N^{[2]} | 71 | |||
Eu_{2}SiN_{3} | (64) | 420679 | Non-branched chains CS SiN_{4} | 2N^{[1]}:1N^{[2]} | 2.764 (Eu^{2+}) | 1.731 | 24 |
Ba_{2}Nd_{7}Si_{11}N_{23} | (65) | 407202 | 3D CS SiN_{4} zeolite network | 2N^{[1]}:21N^{[2]} | 3.164 (Ba) | 1.685 | 72 |
Ca_{3}Sm_{3}Si_{9}N_{17} | (215) | 421644 | 3D CS SiN_{4} network | 16N^{[2]}:1N^{[4]} | ^{ } | 1.696 | 73 |
Ca_{3}Yb_{3}Si_{9}N_{17} | (215) | 421645 | 3D CS SiN_{4} network | 16N^{[2]}:1N^{[4]} | ^{ } | 1.687 | 73 |
Ba_{1.5}Eu_{1.5}YbSi_{6}N_{11} | (198) | 407300 | 3D CS SiN_{4} network | 9N^{[2]}:2N^{[3]} | 3.012 (Ba) | 1.701 | 74 |
SrScSi_{4}N_{7} | (186) | 189117 | 3D CS SiN_{4} network | 6N^{[2]}:1N^{[4]} | 2.957 (Sr)^{f} | 1.688^{f} | 75 |
CaYSi_{4}N_{7}^{g} | (186) | 152975 | 3D CS SiN_{4} network | 6N^{[2]}:1N^{[4]} | ^{ } | 1.709 | 32 |
SrYSi_{4}N_{7} | (186) | 150459 | 3D CS SiN_{4} network | 6N^{[2]}:1N^{[4]} | 3.012 (Sr) | 1.699 | 76 |
BaYSi_{4}N_{7} | (186) | 98276 | 3D CS SiN_{4} network | 6N^{[2]}:1N^{[4]} | 3.014 (Ba) | 1.701 | 77 |
EuYSi_{4}N_{7} | (186) | 150460 | 3D CS SiN_{4} network | 6N^{[2]}:1N^{[4]} | 3.019 (Eu) | 1.668 | 76 |
SrYbSi_{4}N_{7} | (186) | 405625 | 3D CS SiN_{4} network | 6N^{[2]}:1N^{[4]} | 2.996 (Sr) | 1.708 | 78 |
EuYbSi_{4}N_{7} | (186) | 59258 | 3D CS SiN_{4} network | 6N^{[2]}:1N^{[4]} | 2.993 (Eu) | 1.713 | 53 |
BaYbSi_{4}N_{7} | (186) | 405194 | 3D CS SiN_{4} network | 6N^{[2]}:1N^{[4]} | 3.017 (Ba) | 1.717 | 78 |
In all the previously mentioned cases, the Si and N atoms are present in SiN_{4} tetrahedra. As a consequence, there is a direct relation between the degree of condensation κ (here defined as the Si/N ratio) and the average coordination number x of nitrogen by silicon (NSi_{x}), with x = 4 × κ, as is shown in Fig. 2. There are a just few nitridosilicates in which not all Si and N atoms are present in SiN_{4} tetrahedra and the relation x = 4 × κ is not followed: γ-Si_{3}N_{4} and (AE)Si_{6}N_{8} (AE = Sr, Ba), which are indicated with blue squares in Fig. 2. In γ-Si_{3}N_{4} with cubic spinel structure^{83} all N atoms are fourfold coordinated by Si and SiN_{6} octahedra exist in addition to SiN_{4} tetrahedra. In (AE)Si_{6}N_{8} (AE = Sr, Ba)^{50,52} N_{3}Si–SiN_{3} entities are present in which two Si atoms are directly bonded to each other.
The M cations are the positive counterions of the negative nitridosilicate framework and are located in the cavities of the network. They are usually coordinated by six or more N atoms. However, if the metal ion is relatively small, as is the case for Mg^{2+} and Li^{+}, they can also form TN_{4} (T = Mg, Li) tetrahedrons similar to the SiN_{4} tetrahedrons. It may then be more appropriate to consider them part of the framework instead of as counterions. This is for example the case in Li_{5}SiN_{3} with antifluorite structure where Si and Li are located on mixed sites forming (Si,Li)N_{4} tetrahedrons.^{37,38} In several other Li and Mg containing nitridosilicates the situation is however less obvious. Li_{4}Ca_{3}Si_{2}N_{6} consists of SiN_{4} and LiN_{4} tetrahedra with octahedrally coordinated Ca^{2+} ions in between, so Si and Li can be considered part of the 3D framework and the compound could be written as Ca_{3}[Li_{4}Si_{2}N_{6}].^{61,62} However, for the same structure one of the Ca^{2+} ions can be replaced by two Li^{+} ions, while at the same time 4 Li^{+} ions are replaced by 2 Mg^{2+} ions resulting in Li_{2}Ca_{2}[Mg_{2}Si_{2}N_{6}] in which tetrahedrally coordinated Mg is now part of the framework and Li^{+} is now a counterion forming [Li_{2}]N_{6} octahedra.^{62} Starting form Ca_{3}[Li_{4}Si_{2}N_{6}] the Mg can also be positioned on a Ca site, while the remaining Ca^{2+} ions switch positions with the Li^{+} ions on the [Li_{2}]N_{6} positions, forming Ca_{2}Mg[Li_{4}Si_{2}N_{6}] in which now Li is part of the framework in a tetrahedral coordination and Mg^{2+} is a counterion in a fourfold planar rectangular coordination.^{62}
However, because Li^{+} and Mg^{2+} have a larger ionic radius, a lower electronegativity, and a lower oxidation number than Si^{4+}, the influence of Li^{+} and Mg^{2+} on parameters like bond lengths and bandgap will be different. Consequently, it is not appropriate to simply add up the Si, Li and Mg atoms and use the (Si + Mg + Li)/N ratio as the principal parameter. Therefore, the Si/N ratio is used as the principal parameter in this manuscript, even when Mg and/or Li may be considered part of the cross-linking framework. As a result, a compound like Ba[Mg_{3}SiN_{4}] that is reported^{69} to have a degree of condensation of 1 based on its (Mg + Si)/N ratio, is listed as a compound with a Si/N ratio of 0.25 in this work.
As expected, a larger M–N distance with increasing Si/N ratio is indeed the trend that can be qualitatively observed from the experimental data collected from literature (Table 1), and shown in Fig. 4. For the Ca, Sr, Ba and La sites the average distance to nitrogen tends to increase with increasing Si/N ratio in correspondence with a more positive effective charge for N. It should be noted here that, even though a linear fit through the data is presented, this does not imply that the relation between Si/N ratio and M–N distance should be linear. The purpose of the linear fit is to show that there seems to be a general trend showing an increase of M–N distance with increasing Si/N ratio, but several secondary effects might be present that cause an increased scattering of the data. Nevertheless, the deviation from the general trend is in most compounds less than 0.05 Å. The strongest increase of M–N distance with increasing Si/N ratio is observed for M = Sr, while the increase is weakest for M = Ca. The reason for the surprising order Sr–N > Ba–N > Ca–N (while in terms of size and atomic number Ba > Sr > Ca) is unclear and further studies would be necessary to clarify its cause. It might be a consequence of scattering of the data due to secondary effects as some data points have a relatively strong influence on the steepness of the slope.
Fig. 4 Average M–N distance (M = Ca, Sr, Ba or La) in the nitridosilicates versus the Si/N ratio. The green dashed line represents a trend line obtained by a linear fit through the data points. |
For the Ca sites, the increase of the Ca–N distance with increasing Si/N ratio is rather limited with only about 0.1 Å difference between Ca_{4}SiN_{4} and Ca_{2}Si_{5}N_{8}. This makes the increase smaller than the scattering of the data. For example, among the compounds with a Si/N ratio of 1/3, Li_{4}Ca_{3}Si_{2}N_{6} has an almost 0.2 Å larger average Ca–N bond length than Li_{4}Ca_{2}MgSi_{2}N_{6}. As was discussed above Li_{4}Ca_{2}MgSi_{2}N_{6} is homeotypic to Li_{4}Ca_{3}Si_{2}N_{6} but Ca^{2+} ions have been partly replaced by Mg^{2+} ions and the remaining Ca^{2+} ions have switched places with the Li^{+} ions, which can explain the relatively short Ca–N bond length in Li_{4}Ca_{2}MgSi_{2}N_{6}. For the Sr sites the absolute scattering of the data is similar as for the Ca sites. However, among the Sr sites there is a large increase of the Sr–N distance with increasing degree of condensation, making the scattering relatively small. For the Ba sites the observed dependence on Si/N ratio is also strong, but the deviation from the general trend is quite large for BaSi_{7}N_{10} and Ba_{2}Nd_{7}Si_{11}N_{23}, having relatively large Ba–N distances. This may be due to the large coordination numbers for Ba in these compounds. In BaSi_{7}N_{10} the coordination number is 13,^{25} while in Ba_{2}Nd_{7}Si_{11}N_{23}, which has an unusual zeolite-analogous structure,^{72} the coordination number of some of the Ba atoms goes up to even 16.
Some scattering in the data of Fig. 4 may also be due to the fact that the Si/N ratio, which basically is a measure for the average N coordination number (see Fig. 2), may not exactly represent the actual N by Si coordination number of the N atoms surrounding the metal ion. In BaYSi_{4}N_{7} for example, the N atoms have an average coordination number of 2.29 because the ratio of twofold/fourfold coordinated N atoms is 6/1. However, the N atoms surrounding Ba have an average coordination number of 2 as the fourfold coordinated N atoms are far away from and not coordinated to Ba. In addition, the scattering of the data in Fig. 4 may be enhanced due to the presence of different types of metal ions M within one compound.
While the M–N bond lengths increase with increasing degree of condensation, the Si–N bond lengths tend to decrease with increasing degree of condensation, as has previously been observed by Schnick et al.^{12,84} This can also be observed from the data shown in Fig. 5a: the average Si–N distance is relatively large in for example Ca_{4}SiN_{4} (1.791 Å) with very low degree of condensation, while relatively small in SrSi_{7}N_{10} (1.731 Å) with a very high degree of condensation.
If the shortest Si–N distance is plotted versus the Si/N ratio (Fig. 5b) instead of the average Si–N distance (Fig. 5a), a similar trend is observed. The correlation of the data is then somewhat stronger, considering that the Pearson correlation coefficient changes from −0.53 for the fit of the average Si–N distance versus Si/N ratio to −0.67 for fit of the shortest Si–N distance versus Si/N ratio. Note that the slope of the trend line in Fig. 5b (shortest Si–N distance) is also steeper than in Fig. 5a (average Si–N distance).
A few compounds do not follow the general trend in Fig. 5a and b and have either a relatively large or relatively small shortest Si–N bond. Among them is γ-Si_{3}N_{4} with a relatively large Si–N distance of 1.853 Å. Note that this is the only compound listed in which SiN_{6} octahedra are present in addition to SiN_{4} tetrahedra. Two Li compounds also deviate with Li_{5}SiN_{3} having a much larger Si–N distance and Li_{21}Si_{3}N_{11} having a relatively small distance. Both compounds crystallize in distorted antifluorite structures and both are very Li rich, with the Li and Si atoms present in TN_{4} (T = Li, Si) tetrahedra. So, based on their crystal structures both Li_{5}SiN_{3} and Li_{21}Si_{3}N_{11} are not really nitridosilicates composed of cross-linked tetrahedra such as the other compounds. It has been reported^{37} that in Li_{21}Si_{3}N_{11} the Si is mainly present on the smallest TN_{4} site (because Si^{4+} is smaller than Li^{+}), resulting in a small Si–N bond length. In Li_{5}SiN_{3} on the other hand, Si occupies a mixed Si/Li site making the Si–N distance actually a significantly larger (Si,Li)–N distance. Something similar also happens in BaMg_{3}SiN_{4} with mixed Mg/Si sites and thus a large shortest (Mg,Si)–N distance (1.892 Å) since Mg^{2+} is larger than Si^{4+}. The average (Mg,Si)–N distance in BaMg_{3}SiN_{4} is also very large (2.030 Å) and falls outside the plotted range of Fig. 5a. In the other (AE)Mg_{3}SiN_{4} compounds (AE = Ca, Sr, Eu) the Mg and Si sites are not mixed and the Si–N bond lengths are as expected for compounds with low Si/N ratio and in the same range as in Ca_{4}SiN_{4}. The very small shortest Si–N distance of 1.564 Å reported^{54} for La_{5}Si_{3}N_{9} seems to be not reliable, because for Ce_{5}Si_{3}N_{9} and Pr_{5}Si_{3}N_{9}, that both crystallize in the same crystal structure as La_{5}Si_{3}N_{9}, the reported^{54,59} shortest Si–N distances are much larger (1.725 Å for Ce_{5}Si_{3}N_{9} and 1.719 Å for Pr_{5}Si_{3}N_{9}) and fall in line with the trend observed in Fig. 5b. Hence that the La^{3+} ion is similar in size as the Ce^{3+} and Pr^{3+} ions. Note that the average Si–N distance in La_{5}Si_{3}N_{9} is not an exception, but in range with the other compounds.
Compound | E _{VC} (eV) | Ref. |
---|---|---|
a Ca_{16}Si_{17}N_{34} is also known as cubic-CaSiN_{2}. b CaYSi_{4}N_{7} is actually Ca_{0.8}Y_{1.2}Si_{4}N_{6.8}C_{0.2}. | ||
α-Si_{3}N_{4} | 5.9 | DR^{87} |
γ-Si_{3}N_{4} | 5.1 | X-rays,^{88} PLE^{89} |
Li_{8}SiN_{4} | 2.7 | ABS^{26} |
Li_{5}SiN_{3} | 2.8 | ABS^{90} |
LiSi_{2}N_{3} | 6.9 | DR,^{28} PLE^{27} |
Li_{2}SiN_{2} | >6.9 | DR^{91} |
MgSiN_{2} | 5.5 | DR,^{92,93} X-rays^{94} |
α-CaSiN_{2} | 5.0 | DR,^{95,96} PLE^{95} |
Ca_{16}Si_{17}N_{34}^{a} | 4.7 | ABS,^{97} DR^{97,98} |
Ca_{2}Si_{5}N_{8} | 5.2 | DR,^{99} PLE^{99,100} |
SrSiN_{2} | 5.0 | ABS,^{93} DR,^{93,101} PLE^{93,101} |
Sr_{2}Si_{5}N_{8} | 5.1 | DR,^{99,102} PLE^{99,100} |
SrSi_{6}N_{8} | 3.7 | DR,^{103} PLE^{104} |
BaSiN_{2} | 4.9 | ABS,^{93} DR,^{93} PLE^{93} |
Ba_{2}Si_{5}N_{8} | 5.1 | ABS,^{105} DR,^{99} PLE^{99,100} |
BaSi_{7}N_{10} | 5.8 | DR,^{106} PLE^{107} |
LaSi_{3}N_{5} | 5.0 | ABS,^{108} DR,^{109} PLE^{109,110} |
CaMg_{3}SiN_{4} | 4.1 | PLE^{68} |
SrMg_{3}SiN_{4} | 4.1 | DR^{68} |
BaMg_{3}SiN_{4} | 4.1 | DR^{69} |
Li_{2}Ca_{2}Mg_{2}Si_{2}N_{6} | 4.8 | DR^{111} |
Li_{4}Ca_{3}Si_{2}N_{6} | 4.1 | ABS,^{112} DR,^{112} PLE^{112} |
CaLaSiN_{3} | 3.1 | DR^{113} |
CaYSi_{4}N_{7}^{b} | 5.2 | DR^{114} |
SrYSi_{4}N_{7} | 5.2 | DR,^{76,77,114} PLE^{76} |
BaYSi_{4}N_{7} | 5.2 | DR^{77,114,115} |
Among the nitridosilicates listed in Table 2, Li_{2}SiN_{2} has the largest bandgap (>6.9 eV) and Li_{8}SiN_{4} has the smallest bandgap (2.7 eV). In general the bandgap increases with increasing Si/N ratio, as shown in Fig. 6. This is in accordance with what was previously predicted by Fang et al.^{116} using first principle calculations for the barium nitridosilicates: the bandgap increases with increasing degree of cross-linking between SiN_{4} tetrahedra in the order Ba_{5}Si_{2}N_{6} < Ba_{2}Si_{5}N_{8} < BaSi_{7}N_{10} < β-Si_{3}N_{4}. In the previous section it was explained that with increasing degree of condensation (Si/N ratio) the N atom will get a less negative effective charge. This less negative effective charge will result in a downward shift in energy of the N 2p levels, and because the top of the valence band consists mainly of N 2p levels, this will make the bandgap larger. This is also in line with the calculation by Fang et al.,^{116} showing a downward shift of the N 2p levels when going from singly coordinated N atoms towards N atoms coordinated by 4 Si atoms.
The increase of the bandgap with increasing degree of condensation is not only caused by a shift of the top of the valence band to lower energy, but should also be partly due to a shift of the bottom of the conduction band to higher energy (with respect to the vacuum level). As was discussed above, the Si–N bond length decreases with increasing Si/N ratio (Fig. 5). The shorter, and therefore stronger bond will give a larger splitting between the bonding orbitals at the top of the valence band (mainly N orbitals) and antibonding orbitals at the bottom of the conduction band (Si orbitals). This will result in a shift of the bottom of the conduction band to higher energy, next to a shift of the top of the valence band to lower energy. Based on analysis of the thermal quenching behaviour of the Eu^{2+} and Ce^{3+} 5d–4f emission in doped nitridosilicates it can be argued that the bottom of the conduction band should indeed shift upwards in energy with increasing degree of condensation, as will be explained in more detail in our next paper. So the increasing bandgap of the nitridosilicates with increasing degree of condensation (increasing Si/N ratio) is the consequence of the combined effect of the downward shift of the valence band and the upward shift of the conduction band as illustrated in Fig. 7. It should be noted here that this model does not take into account that the bottom of the conduction band may not only consist of Si orbitals but may also consist of M orbitals. For example, calculations on the electronic structure of LaSi_{3}N_{5} and La_{3}Si_{6}N_{11} show that the bottom of the conduction band of these compounds contains La 4f and 5d states.^{117} Nevertheless, the calculations still show that La_{3}Si_{6}N_{11}, which has a lower Si/N ratio, has a smaller bandgap than LaSi_{3}N_{5} and a conduction band minimum at lower energy. The smaller bandgap may seem contradictory to the shorter La–N distance in La_{3}Si_{6}N_{11}, but could be explained by the larger crystal field splitting and centroid shift of the 5d levels in La_{3}Si_{6}N_{11} as compared to LaSi_{3}N_{5}, lowering the bottom of the conduction band.
Fig. 7 Schematic diagram, showing the influence of the degree of condensation (Si/N ratio) on the positions of the valence and conduction bands and the size of the bandgap E_{g}. |
The bandgaps of SrSi_{6}N_{8} (about 3.7 eV) and γ-Si_{3}N_{4} (about 5.1 eV) are small considering their high Si/N ratios and deviate from the trend established for the other nitridosilicates. As already mentioned, in γ-Si_{3}N_{4} not all Si atoms are tetrahedrally coordinated by N. The presence of SiN_{6} octahedra causes a lowering of the Si 3s states at the bottom of the conduction band.^{116} The smaller bandgap is also in line with the larger Si–N bond length in γ-Si_{3}N_{4} as compared to those bonds in α-Si_{3}N_{4} and β-Si_{3}N_{4} (Fig. 5). In SrSi_{6}N_{8} as another exception not all Si atoms are tetrahedrally coordinated by N, as part of the Si atoms form Si–Si bonds. The Si–Si bonds create an empty σ* anti-bonding state forming the bottom of the conduction band, resulting in the smaller bandgap.^{118} Therefore it is likely that BaSi_{6}N_{8}, in which also Si–Si bonds are present, has a relatively small bandgap as well, but to our knowledge its bandgap has not yet been experimentally determined.
For Li_{2}SiN_{2} the exact value of the bandgap is unknown, but it should be larger than 6.9 eV since it has a high reflectivity down to 200 nm radiation.^{91} The bandgap is thus very large considering that the Si/N ratio is only 0.5 and in the same range with that of LiSi_{2}N_{3}, which also has a relatively large bandgap. Such large bandgaps can be attributed to the presence of Li. As Li^{+} ions are relatively small, the Li–N bond is short compared to the M–N bond in other nitridosilicates. Instead of considering the coordination number of N based on the number of Si atoms around it, also the coordinating Li atoms should therefore be taken into account. This increases the N(Si,Li)_{x} coordination number to about 4 in LiSi_{2}N_{3} and even to 6 in Li_{2}SiN_{2}, meaning that the effective charge around N becomes more positive, the top of the valence band shifts downwards and the bandgap becomes large. Note that the same reasoning does not apply for Li_{5}SiN_{3} which has a very small bandgap. The Si atoms are here located on the large Li sites, making the (Si,Li)–N bonds much longer (see Fig. 5) and weaker than in LiSi_{2}N_{3} and Li_{2}SiN_{2}, making it more ionic with a more negative effective charge for N. Something similar may also apply for Li_{8}SiN_{4} as it also has a small bandgap, but the crystal structure of Li_{8}SiN_{4} has not fully been resolved in order to clarify this.
The obtained insights on the relations between bandgap, structure and composition can be used when developing new materials with certain structural or optical properties. For example for the development of novel luminescent materials, for which the positions of the valence and conduction band are of direct influence on the photoluminescence properties.
Although we have focused ourselves in this manuscript on the nitridosilicates, the observed trends are expected to be more general and hold also for other series of compounds whose structure consists of a framework of cross-linked tetrahedra with larger counterions located in the cavities, such as the oxosilicates, oxoaluminates, nitridoaluminates and phosphates. Indeed, a decrease of the Si–O bond length with increasing Si/O ratio has been previously observed for the oxosilicates.^{119–121} One can therefore expect that there might also be an increase of the bandgap and increase of the M–O bond length with increasing Si/O ratio. The smaller variation in Si/O ratio among the oxosilicates versus the variation in Si/N ratio among the nitridosilicates may have hampered the establishment of such a relationship so far.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c7tc04259k |
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