Journalof Non-CrystallineSolids 196(1996)204-209
Electronic states of binary tellurite glasses Yoshiyuki Kowada a9* , KatsuyoshiMorimoto a,Hirohiko Adachi b, Masahiro Tatsumisago‘, Tsutomu Minami ’ ’ Hyogo
University of Teacher Education, 942-l Shimokume, Yashiro-cho, Kate-gun, Hyogo 673-14, Japun b Department of Metallurgy, Faculty of Engineering, Kyoto University, Kyoto 606-01, Japan ’ Department ofApplied Materials Science, Osaka Prefecture University, Sakui, Osaka 593, Japan
Abstract Electronic states of binary tellurite glasses have been calculated by the DV-XCY cluster method. The calculation was achieved for several model clusters with various polymerization degrees and with various second component ions, such as glass-forming ions, intermediate ions, and modifier ions. The bonding nature of each bond in the clusters of binary tellurite glassesis discussed and compared with the silicate glasses.In the TeO, trigonal bipyramid (tbp) unit, bond order between the Te ion and the equatorial oxygen ion (O,,) wasmuch larger than that between the Te ion and the axial oxygen ion (0,). In the cluster for the binary tellurite glasses,the bond order of the clusters with the modifier ions was almost zero. The bond order with the glass-forming ions had values larger than those with the modifier ions. In the case of the intermediate ions, the bond order ranged from -0.3 to 0.1. This change of the bond order of M-OTemOmM with second component ions had a similar tendency to that in the binary silicate glasses.
1. Introduction The glass structure of tellurite glasses is attractive because tellurite glasses have several properties such as wide infrared transmittance, high thermal expansions, and high refractive indices [l-3]. These properties may be associated with the structure of tellurite glasses. It was reported [4-71 that the structure of tellurite glasses was constructed by several asymmetric structural units such as TeO, trigonal bipyramid (tbp) and TeO, trigonal pyramid (tp). These structural units have a lone pair of electrons which may effect to the electrical and optical properties of the tellurite glasses. These are properties of the
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glass structure and differ from the glass network in ordinary silicate glasseswhich may be constructed by tetrahedral units which exhibit no lone pair of electrons. Such characteristicsof the glass structureshould result in an electronic stateof the glass network. Although there are several methods to study electronic state of the tellurite glasses, recent theoretical calculation methods [&lo] have becomevery useful. In particular, the DV-Xor dluster method [ 111,which is one of molecular orbital (MO) calculations,has been applied to study electronic states of many inorganic materials [12-141. The electronic state of small cluster for the TeO, crystal was already reported . In the present work, we calculate the electronic state of several model clusters,which have degrees of different polymerization of the TeO, tbp units. Furthermore, we used simple model clustersfor the
0022-3093/96/$15.00 0 1996ElsevierScienceB.V. All rights reserved SSDI 0022-3093(95)00587-O
et al./ Journal
binary tellurite glasses and discuss the effect of the addition of the second component ions on the electronic states of the tellurite glass network. We also compare the results of the binary tellurite glasses with those of the binary silicate glasses as a typical glass-forming system.
Solids 196 (1996)
Te Cluster (a) Te0,4-
In the present work, we used the DV-Xo! cluster method to calculate electronic states of binary tellurite glasses. This method is one of a linear combination of atomic orbitals (LCAO)-MO calculations, and it has several advantages to other MO methods. One of these is the application of the Slater exchange potential . This potential is written as
Cluster (c) Te,0,,8Cluster (d) Te,O,t-
i I -$(d
where Q is the electron density and (Y is a parameter. It has been reported that a value, CY= 0.7, is useful to calculate the electronic states of inorganic materials [ 1 1- 14,171. We fixed cr to be 0.7 throughout the present work. Another characteristic is the evaluation of the elements of Hamiltonian, Hi,, and overlap matrices, Sij. The evaluation is achieved as weighted sums of integrated values at the sample points instead of the conventional Rayleigh-Rits method,
Cluster (e) TeO,MO,“-
Fig. 1. Structure of the model clusters used in the present work.
where rk is one of the total N sample points in the three-dimensional real space and O(T& is the integration weight or reciprocal of the sample point density at rk. We used the Mulliken population analysis and obtained the overlap population between two atoms, in order to discuss the bonding nature of each bond in the tellurite clusters. The overlap population is a measure of the strength of covalent bonding and is sometimes referred to as the bond order. Model clusters used in the present work are shown in Fig. 1. Clusters (a)-(d) were used to analyze the
effect of the polymerization degree of TeO, tbp units on the electronic state of the tellurite glass network. Cluster (a) contains one TeO, tbp unit, which includes two types of oxygens called ‘equatorial oxygens’ (O,,) and ‘axial oxygens’ (O,,). These oxygen ions are non-bridging (NBO) in the cluster (a). The distances of Te-O,, and Te-O,, are 1.903 and 2.082 A, respectively. The bonding angles of O,,-Te-O,, and O,-Te-0, are 102 and 169”, respectively. These values are taken from the values in the a-TeO, crystal . The cluster (b) has two TeO, tbp units, which are connected through one bridging oxygen (BO). Since the bridging oxygen in the tellurite crystals is usually constructed by both one Te-O,, bond and one Te-0, bond (Te-,gOax-Te), such a
bonding manner between two TeO, tbp units is adopted in cluster (b). Similarly, we constructed the cluster (c) by three TeO, tbp units and the cluster (d) by four TeO, tbp units. The cluster (d) has a ring structure instead of a long chain structure. We define the polymerization degree of the model clusters as the number of TeO, tbp units which constitute the cluster. Thus, polymerization degrees of clusters (a)-(d) are 1, 2, 3 and 4, respectively. We also used clusters (e> and (f) to analyze the effect of the addition of the second component ions on the electronic state of the tellurite glass network. There are several kinds of model clusters for the binary tellurite glasses, since the coordination number of the oxygen ions to the second component ions may have several varieties, such as four coordinated, six coordinated etc., and the second component ions can connect to equatorial or axial oxygens. We adopted one of the simplest models for the binary tellurite glasses. The cluster (e) has one TeO, tbp unit with an MO, unit which is connected by an O,, as a tetrahedral MO, unit. In the present work, we 10
-----_ ----__ ------
show this connecting oxygen ion as OTeqOmM. Modifier ions, such as alkali , 2.70 (Ba*‘), 1.46 (B3’>, 1.52 (P”), 1.74 (Ge4’>, 1.74 (A13’>, 1.77 (Ti4’>, 1.77 (W6’>, and 1.95 A(Zn*‘>. These values are evaluated from the ionic radii reported by Shannon et al. 1191. The cluster (f) is the model for the binary silicate glasses in order to compare the electronic state of this cluster to the corresponding tellurite cluster (e). In this model cluster, SiO, is a regular tetrahedral unit, and the distance of Si-0 is 1.62 A.
3. Results Fig. 2 shows the valence part of the energy level structures of the clusters (a)-(d). In the figure, the
-B---B ----------_ -m---w ---me---------__ -m-m--
Solids 196 (1996)
q EBaaiiiza -m---w ----mm --w--m -
I I, 1 1 TO 6P
-40 (a) TeOd4-
Fig, 2. Valence energy level diagrams for clusters (a)-(d). The energy scale for each cluster is shifted so that the highest molecular orbital composed of the 0 2p atomic orbitals is of zero energy.
occupied orbitals are shown as the solid lines and the unoccupied orbitals as the dotted lines. In cluster (a), the band gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) is 5.4 eV. The occupied levels are mainly constructed by the orbitals of Te 4d, Te 5s, 0 2s and 0 2p, and unoccupied orbitals are chiefly made by the Te 5p orbitals. As mentioned above, the TeO, tbp unit in the tellurite glasses has a lone pair of electrons, which are in non-bonding orbitals mainly attributed to Te 5s. The position of these Te 5s orbitals located in the energy level structure of the tellurite glass network is interesting because these lone pair electrons may cause several characteristic properties of tellurite glasses. In the level structure of the cluster (a), the Te 5s orbitals are located between 0 2s and 0 2p orbitals. Such an energy level structure is characteristic of the tellurite glasses. In the cluster (b), the outline of the energy level structure is similar to that in the cluster (a), i.e., occupied energy levels are contributed by Te 4d, Te 5s 0 2s and 0 2p orbitals and unoccupied orbitals by the Te 5p orbital. The energy gap between HOMO and LUMO is 3.0 eV, which is smaller than that in the cluster (a). Since this cluster has a bridging oxygen, the energy levels contributed by the BO ion appear in the lower energy part of the 0 2s and 0 2p band. In the cluster (c), the level structure is similar to that in the clusters 1.0 0.8 20.6 a IO.4 a
Fig. 3. Relationship between the bond orders of Te-NBO,, (O), Te-NBO,(a), Te-BO,,(O), and Te-BO,, (0) bonds in clusters (a)-(d) and the degree of polymerization of the clusters.
Solids 196 (1996)
(a) and (b). The energy gap between HOMO and LUMO is 1.5 eV, which is smaller than other clusters, and the bands of 0 2s 0 2p and Te 4d are extended in energy compared to other clusters. It may be caused by the congested structure of the cluster (c), since the cluster with polymerization degree = 3 corresponds to chain structure in the actual glasses. In contrast, the energy gap between HOMO and LUMO in the cluster (d) is 2.7 eV, which is larger than that in the cluster (c). The gap, however, is smaller than that in the cluster (b). Although the energy level structure is similar to one another in the clusters (a)-(d), the energy gap between HOMO and LUMO changes with the polymerization degree of the clusters.
4. Discussion Fig. 3 shows the bond orders between two given atoms in the clusters (a)-(d). In this figure, the values for four different kinds of Te-0 bonds, i.e., Te-NBO, , Te-NBO,, , Te-BO,, , and Te-BO,,, are represented. NBO,, NBO,,, BO,,, and BO,, mean NBO with axial position, NBO with equatorial position, BO with axial, and BO with equatorial, respectively. In the cluster (a), which has NBO only, the bond order of Te-NBO,, is much larger than that of Te-NBO, . This result is different from that in silicate glasses, since there is only one kind of Si-0 bond in silicate glasses. In cluster (b), which has a bridging oxygen, the bond order of Te-NBO, is larger than that of the Te-NBO, as in the cluster (a). Furthermore, Te-BO,, has larger bond order than that of the Te-BO,. We conclude that the Te-O,, bond is more covalent than the Te-O,, bond, irrespective of bridging or non-bridging oxygen ions. This tendency is similar in clusters (c) and (d). Although the bond order of Te-NBO,, , Te-BO,, and Te-BO, has an increasing tendency with an increase in the polymerization degree of the clusters, the bond order of Te-NBO, is reversely decreased. Such tendency of the bond order with the polymerization degree of clusters is different from that in silicate glasses. In silicate glasses, one of the most common oxide glasses, the bond order of Si-NBO and Si-BO was increased with polymerization de-
-0.5 0 Fig. 4. Bond orders of M-O,-o-M (e), (B) in the cluster(f).
I 8 I I I 0.5 1 1.5 Ionic radii 1A
Solids 196 (1996) 204-209
for the modifier ions (6 ), the glass-forming ions (O),
gree of the clusters . The bond order of Te-O,, is still much larger than that of Te-0, in the cluster Cd), which is mostly polymerized in the present work. It suggests that the TeO, tbp unit in the tellurite glass network has two more covalent Te-O,, bonds and two less covalent Te-0, bonds. In order to discuss the effect of the addition of second component ions to the tellurite glass network, the bond order between the M ion and OTemOmM is shown in Fig. 4(A). In this figure, the ordinate shows the bond order of M-OTe-O-M, and abscissa shows the ionic radii of the M ions. The bond orders of M-O remO-,, are almost zero for the M of modifier ions. This result indicates that the M-OTemOmM bond with modifier ions is mostly ionic. In contrast to this, the bond order of the clusters with glass-forming ions ranges from 0.3 to 0.75. These values are larger than those with the modifier ions. In the clusters with intermediate ions, the bond order ranges from -0.3 to 0.1. In the cluster (e>, the four oxygen ions coordinate to the M ion, although the W6+ and Ti4+ ions tend to have six coordinated oxygens. The negative value of the bond order of the clusters with W6+ and Ti4+ ions may be caused by the four coordination of oxygens to these intermediate ions. For comparison to the bond order in the tellurite glasses, the bond order obtained from the cluster (f) is shown in Fig. 4(B). In these silicate clusters, the bond order of the clusters with the modifier ions is almost zero. The bond orders with the glass-forming
, I I 1 1.5 Ionic radii / A
and the intermediate ions (A); (A) in the cluster
ions have larger values than those with the modifier ions. In the case of the intermediate ions, the bond order ranges from - 0.2 to 0.1. Such a tendency of the bond order of M-Orc-O-M is similar to that in the tellurite glass clusters. The tellurium oxide is usually called the ‘conditional’ glass-forming oxide. This term means that tellurium oxide cannot become an amorphous state, although binary tellurite glasses can be easily obtained. The result obtained in the present work suggests that the bonding nature between the oxygen ion and the second component ion in the tellurite glasses is similar to that in the silicate glasses, although the bonding nature of the tellurite glass network differs from that of the silicate glass network. 5. Conclusion In the present work, the electronic states of the binary tellurite glasses have been calculated by the DV-XCY cluster method. The following results have been obtained. (1) In the TeO, tbp unit, the bond order of Te-O,, is larger than that of Te-O,, in both Te-BO and Te-NBO bonds. This result differs from the SiO, unit in the silicate glasses. (2) In the clusters of binary tellurite glasses, the change of the bond order of M-O,-,-, with second component ions has similar tendency with that in the binary silicate glasses.
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