- Email: [email protected]
Correlation among electronegativity, cation polarizability, optical basicity and single bond strength of simple oxides
Journal of Solid State Chemistry 196 (2012) 574–578
Contents lists available at SciVerse ScienceDirect
Journal of Solid State Chemistry journal homepage: www.elsevier.com/locate/jssc
Correlation among electronegativity, cation polarizability, optical basicity and single bond strength of simple oxides Vesselin Dimitrov a, Takayuki Komatsu b,n a b
Department of Silicate Technology, University of Chemical Technology and Metallurgy, 8, Kl. Ohridski Blvd., Sofia 1756, Bulgaria Department of Materials Science and Technology, Nagaoka University of Technology, 1603-1 Kamitomioka-cho, Nagaoka 940-2188, Japan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 June 2012 Received in revised form 13 July 2012 Accepted 15 July 2012 Available online 22 July 2012
A suitable relationship between free-cation polarizability and electronegativity of elements in different valence states and with the most common coordination numbers has been searched on the basis of the similarity in physical nature of both quantities. In general, the cation polarizability increases with decreasing element electronegativity. A systematic periodic change in the polarizability against the electronegativity has been observed in the isoelectronic series. It has been found that generally the optical basicity increases and the single bond strength of simple oxides decreases with decreasing the electronegativity. The observed trends have been discussed on the basis of electron donation ability of the oxide ions and type of chemical bonding in simple oxides. & 2012 Elsevier Inc. All rights reserved.
Keywords: Polarizability Electronegativity Optical basicity Simple oxide Single bond strength
1. Introduction Electronic polarizability of ions demonstrates the easy deformation of their electronic clouds by applying an electromagnetic field. It is an important parameter because it is closely related to many properties of the solids such as refraction, conductivity, ferroelectricity, electro-optical effect, optical nonlinearity along with optical basicity [1–3]. Electronic polarizability a of an atom or ion could be given through a one-dimensional Hooke’s-law potential energy by
a ¼ e2
X ni ki
ð1Þ
where e is the elementary charge and ni is the number of electrons with binding force constant ki [4]. According to this model, Hooke’s-law potential energy is assumed to be equal to the ionization energy IE as twice the value of effective ionic radii, 2reff. By this manner electron binding force constant ki can be given by k¼
IE 2r 2ef f
ð2Þ
or electronic ion polarizability is X ni a ¼ 2e2 r2ef f IE
As can be seen the loosely bound valence electrons with low ionization energy, i.e., small force constant will contribute more to the electronic polarizability of an atom or ion than the tightly bound inner-shell electrons. Recently, Dimitrov and Komatsu [5] have found suitable relationship between free-ion polarizability and element outermost binding energy on the basis of the similarity in physical nature between electron binding energy and ionization energy. It has been suggested that outermost corelevel binding energy can be used for relative measure of the cation polarizability. In general, cation polarizability increases with decreasing element binding energy. Simultaneously, a systematic periodic change in the polarizability against the binding energy has been observed in the isoelectronic series [5]. On the other hand, the element electronegativity demonstrates the ability of an atom or ion to attract electrons from the atoms or ions bonded to it. Also recently, Li and Xue [6] have published electronegativities of 82 elements in different valence states and with the most common coordination numbers calculated on the basis of an effective ionic potential defined by the ionization energy and ionic radii. The following equation for the electronegativity wi has been proposed:
n
Corresponding author. Fax: þ81 258 47 9300. E-mail addresses: [email protected] (V. Dimitrov), [email protected].(T. Komatsu) 0022-4596/$ - see front matter & 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jssc.2012.07.030
ð3Þ
wi ¼ 0:105nn
Im R1
1=2 1 þ0:863 ri
ð4Þ
V. Dimitrov, T. Komatsu / Journal of Solid State Chemistry 196 (2012) 574–578
where nn is the effective principal quantum number, RN is the Rydberg constant, Im is the ionization energy and ri is the ionic radii. Li and Xue [6] have discussed that the Lewis acid strength can be quantitatively measured as a function of their electronegativity scale. The Lewis acid strength Sa has been introduced by Brown [7] to predict which Lewis acids will bond to which Lewis bases. It is defined for a given cation by Sa ¼
V Nt
ð5Þ
where V is the oxidation state of the cation and Nt is the average of the coordination numbers to oxygen observed in a large sample of compounds [8]. Brown and Skowron [8] have established that for main group elements in their highest oxidation state a scale of Lewis acid strength derived from observed structures correlates with a scale of electronegativity derived from electron energies in the free atom. Eqs. (3) and (4) show that the physical origin of electronic ion polarizability and electronegativity obtained by Li and Xue is very similar, since both of them are related to the ionization energy and ionic radii. Therefore, it is of interest to check the correlation between these quantities. That is why in this paper we have examined the relationship between electronegativity and electronic polarizability of different ions. The relationship with optical basicity as well as single bond strength of numerous simple oxides is also discussed.
2. Results and discussion 2.1. Dependence of cation polarizability on electronegativity A couple of sets of free-ion polarizabilities have been proposed by Pauling [9], Born and Heisenberg [10], Fajans and Joos [11], Mayer and Mayer [12] and Kordes [13], The most comprehensive sets among them are those proposed by Pauling [9] and Kordes [13]. Pauling’s values have been obtained on a theoretical treatment of the quadratic Stark effect by means of the following equation: R ¼ 0:047n4 ð15n2 þ21Þ
X
1 ðZSR Þ4
ð6Þ
R is the ionic refraction, n is the principal quantum number, Z is the electron number and SR is the mole refraction screening constant. On the other hand, Kordes [13] has calculated the free-ion polarizabilities on the basis of ionic radii by the equation " 1=3 #2=3 R ¼ kr u ¼ kr z Z 2=ðnB 1Þ ð7Þ 0:603 where ru is the univalent crystal radii, rz is the actual crystal radii, nB is the Born repulsion exponent and k is the constant. The cation polarizabilities of ions under consideration in this paper obtained by Pauling and by Kordes are presented in Table 1 (columns 3 and 4). As can be seen a good correspondence exists between two independently obtained sets. In the present study we used polarizability data reported by Kordes (Table 1, column 3) which we have been used in our previous papers [5,14–17]. Recently, condensed phase ionic polarizabilities from plane wave density functional theory calculation were reported by Heaton et. al. [18] which are in good agreement with the polarizabilities used by Dimitrov and Sakka [14] for a free ion [13]. In column 6 of Table 1 the values of element electronegativity according to Li and Xue [6] are listed, taking into account the valence state of cation and its most common coordination number in the oxides. On the basis of
575
Table 1 Ion, outermost electron orbital, cation polarizability (ai), coordination number (CN) and electronegativity (wi). Ion
1 B3 þ Be2 þ Li þ P5 þ Si4 þ Al3 þ Mg2 þ Na þ Cr6 þ V5 þ Ti4 þ Sc3 þ Ca2 þ Kþ Se6 þ As5 þ Ge4 þ Ga3 þ Zn2 þ Mo6 þ Nb5 þ Zr4 þ Y3 þ Sr2 þ Rb þ Te6 þ Sb5 þ Sn4 þ In3 þ Cd2 þ Ce4 þ La3 þ Ba2 þ W6 þ Ta5 þ Hf4 þ
Outermost orbital
ai (A˚ 3; Kordes)
ai (A˚ 3;
2 1s2 1s2 1s2 2p6 2p6 2p6 2p6 2p6 3p6 3p6 3p6 3p6 3p6 3p6 3d10 3d10 3d10 3d10 3d10 4p6 4p6 4p6 4p6 4p6 4p6 4d10 4d10 4d10 4d10 4d10 5p6 5p6 5p6 4f14 4f14 4f14
3 0.002 0.007 0.024 0.021 0.033 0.054 0.094 0.175 0.085 0.122 0.184 0.287 0.469 0.821 0.073 0.100 0.137 0.195 0.283 0.169 0.242 0.357 0.544 0.861 1.437 0.242 0.333 0.479 0.662 1.054 0.702 1.052 1.595 0.147 0.185 0.368
4 0.003 0.008 0.029 0.021 0.033 0.054 0.094 0.181 0.087 0.123 0.187 0.290 0.472 0.841 0.075 0.103 0.143 0.198 0.286 0.190 0.262 0.377 0.560 0.865 1.417 0.262 0.361 0.500 0.730 1.087 0.738 1.048 1.563
CN wi (Li and Xue)
Pauling) 5 3 4 4 4 4 6 6 6 6 6 6 6 8 9 4 4 4 4 4 6 6 8 8 8 10 6 6 6 6 6 6 7 8 6 6 6
6 3.189 1.453 1.043 3.003 2.245 1.513 1.234 1.024 2.475 2.030 2.278 1.415 1.132 0.987 2.977 2.499 2.116 1.755 1.426 2.101 1.862 1.518 1.291 1.123 0.987 2.180 1.971 1.706 1.480 1.276 1.608 1.301 1.115 2.175 1.925 1.706
the data presented in Table 1, it is possible to investigate the change in the polarizability of the cations with electronegativity through classification based on their outermost electron configuration. In this connection the data of cation polarizability are plotted as a function of element electronegativity in Fig. 1. As can be observed there is systematic periodic change in the cation polarizability and related element electronegativity. Cation polarizability increases and electronegativity decreases in all series. Therefore, from electronegativity point of view the increase in the cation polarizability in each series means decreased ability of an ion to attract electrons from the atoms bonded to it. The observed good correlation between cation polarizability and element electronegativity in isoelectronic series could be explained taking into consideration their common physical ground. As can be seen in Eqs. (3) and (4) both quantities are related to the ionization energy and ionic radii. Similar trend as that shown in Fig. 1 has been found studying the relationship between cation polarizability and element binding energy based on the similarity in physical nature between electron binding energy and ionization energy [5]. 2.2. Dependence of optical basicity of simple oxides on element electronegativity The estimation of the electronic polarizability of ions is subject to the so-called polarizability approach in the materials science, which is well known especially in the field of glass science [19]. The polarizability approach has been systematically developed in our recent papers concerning the origin of electronic polarizability
576
V. Dimitrov, T. Komatsu / Journal of Solid State Chemistry 196 (2012) 574–578
a combination of cation oxidation state and coordination number leads to Pi log pB ¼ 1:9ðCNÞ0:02 0:023 ð10Þ CN
1.8
Cation polarizability (Å3)
1.6 1.4 1.2
where CN is the cation coordination number and Pi is ionization potential corresponding to its oxidation state [24]. For many purposes as was mentioned by Duffy [21], the pB scale serves in a fashion similar to the optical basicity scale and, for certain glass compositions where electronegativity is a common link, the two scales parallel each other. Asokamany and Manjula [25] introduced the concept of average electronegativity and defined an average electronegativity parameter w1av in the following manner:
1.0 0.8 0.6 0.4 0.2 0 0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
wlav ¼
N X wn
i i
i¼1
Electronegativity Fig. 1. Cation polarizability as a function of electronegativity: J, for (1s2 orbital) B3 þ -Be2 þ -Li þ ; ’, for (2p6 orbital) P5 þ -Si4 þ -Al3 þ -Mg2 þ -Na þ ; K, for (3p6 orbital) Cr6 þ -V5 þ -Ti4 þ -Sc3 þ -Ca2 þ -K þ ; &, for (3d10 orbital) Se6 þ As5 þ -Ge4 þ -Ga3 þ -Zn2 þ ; m, for (4p6 orbital) Mo6 þ -Nb5 þ -Zr4 þ -Y3 þ Sr2 þ -Rb þ ; W, for (4d10 orbital) Te6 þ -Sb5 þ -Sn4 þ -In3 þ -Cd2 þ ; ~, for (5p6 orbital) Ce4 þ -La3 þ -Ba2 þ ; , for (4f14 orbital) W6 þ -Ta5 þ -Hf4 þ .
N
where wi is the Pauling electronegativity, ni is the number of atoms of the ith element and N is the number of elements present in the compound. On this basis Reddy et al. [26] have derived the following empirical relationship for the optical basicity of simple oxides:
L ¼ 1:590:2279wlav and optical basicity in simple oxides [14,15] and oxide glasses [16,17]. The most familiar and widely used relationship in this approach is the Lorentz–Lorenz equation. Dimitrov and Sakka [14] calculated by means of this equation the electronic oxide ion polarizability (aO2-) of large number of single component oxides on the basis of linear refractive index (no) and energy gap (Eg). On this ground the refractive index based L(no) and energy gap based L(Eg) optical basicity of the oxides has been also estimated. The simple oxides have been classified in three groups: a, semicovalent (predominantly acidic); b, ionic (basic) and c, very ionic (very basic) oxides [15]. Simultaneously, the relationship between optical basicity of simple oxides and electronegativity has been searched by several authors. Duffy and Ingram [20,21] have suggested that a good correlation exists between basicity L and Pauling-type electronegativity w:
L¼
0:75
ð8Þ
w0:25
The optical basicity of main group elements holds well with the electronegativity rule but for other elements Eq. (8) must be used with caution, especially with transition metal and heavy metal oxides. Optical basicity values for K2O, Na2O, BaO, Li2O, CaO, MgO, Al2O3, ZnO, SiO2, B2O3, H2O, P2O5, CO2, SO3, N2O5 and Cl2O7 have been determined [20,21]. Lebouteiller and Courtine [22] have tried to apply the electronegativity approach using a modifying Pauling-type electronegativity, taking into consideration the valence and the coordination of the ions. They have used an ionic–covalent parameter (ICP), which represents the influence of ionic–covalent bonding in an oxide or oxysalt on the acid strength of cations ICP ¼ log P1:38w þ2:07
ð9Þ (z/r2i
where P is the polarizing power of the cation with formal charge z and Shannon ionic radius ri) and w is the modifying electronegativity of the cation. The use of electronegativity for determination of optical basicity has been made in the pB scale proposed by Balta [23]. Later modification concerning replacement of electronegativity by
ð11Þ
ð12Þ
where wlav is the average electronegativity of the simple oxide. Reddy et al. [26] have calculated L for many oxides and in general there is agreement with previously obtained data by Duffy [21] and Dimitrov and Sakka [14]. In the present paper we tried to correlate optical basicity of simple oxides with element electronegativity estimated by Li and Xue [6]. The data of optical basicity are taken from Ref. [15], where the average values between refractive index based L(no) and energy gap based L(Eg) optical basicity are given. The data are listed in Table 2, column 3. The optical basicity of P2O5, Al2O3, Na2O, K2O and Rb2O are according to Duffy [27]. The optical basicity of B2O3, SiO2 and GeO2 are picked up from Ref. [28]. The data of optical basicity of simple oxides are plotted as a function of element electronegativity in Fig. 2. As can be seen there is a general trend of increase in optical basicity with decreasing electronegativity but with a scatter of the data point. Irrespective of that good agreement could be found with the recently proposed polarizability classification of simple oxides [15]. Semicovalent predominantly acidic oxides are found in the E0.4–0.8 basicity range and E2–3.5 electronegativity range. For instance, the highest values equal to 3.189, 3.003 and 2.245 possess the acidic oxides such as B2O3 (0.46), P2O5 (0.48) and SiO2 (0.53). The very ionic and very basic oxides such as Na2O, K2O, Rb2O, SrO, BaO and CdO with basicity above 1 are located in a narrow range of low electronegativity values at about 1–1.2. The ionic (basic) oxides with basicity close to that of CaO are found in the E1–2.2 electronegativity range. The results presented in Fig. 2 show that generally high values of electronegativity correspond to low values of optical basicity and vice versa. In fact, the optical basicity L represents the polarizability state of an average oxide ion in the oxides and its ability to donate electron density to surrounding metal ions. High values of electronegativity of these ions mean that they have increased ability to attract electrons from the oxide ions bonded to them. As a result the oxide ions in acidic oxides are considerably tightened and their donation ability is week. As a result the optical basicity is low. In contrast, low values of electronegativity of metal ions show that they possess decreased ability to attract electrons from the oxide ions. That is why the oxide ions in basic and very basic oxides are more free and their electron donation is high.
V. Dimitrov, T. Komatsu / Journal of Solid State Chemistry 196 (2012) 574–578
Table 2 Oxide, ion, optical basicity (L), coordination number (CN), single bond strength (BM–O) and electronegativity (wi). Oxide
Ion
L
CN
BM–O (kJ/mol)
wi (Li and Xue)
1 B2O3 BeO Li2O P2O5 SiO2 Al2O3 MgO Na2O CrO3 V 2 O5 TiO2 Sc2O3 CaO K2O SeO3 As2O3 GeO2 Ga2O3 ZnO MoO3 Nb2O5 ZrO2 Y2O3 SrO Rb2O TeO3 Sb2O5 SnO2 In2O3 CdO CeO2 La2O3 BaO WO3 Ta2O5
2 B3 þ Be2 þ Li þ P5 þ Si4 þ Al3 þ Mg2 þ Na þ Cr6 þ V5 þ Ti4 þ Sc3 þ Ca2 þ Kþ Se6 þ As5 þ Ge4 þ Ga3 þ Zn2 þ Mo6 þ Nb5 þ Zr4 þ Y3 þ Sr2 þ Rb þ Te6 þ Sb5 þ Sn4 þ In3 þ Cd2 þ Ce4 þ La3 þ Ba2 þ W6 þ Ta5 þ
3 0.46 0.87 0.48 0.53 0.61 0.68 1.10 1.055 0.935 0.87 0.975 1.31 0.80 0.755 1.08 1.07 1.035 0.825 0.99 1.14 1.43 0.85 1.07 1.115 1.01 1.07 1.22 1.045 0.925
4 3 4 4 4 4 6 6 6 6 6 6 6 8 9 4 4 4 4 4 6 6 8 8 8 10 6 6 6 6 6 6 7 8 6 6
5 498 262 150 464 443 251 155 84 309 312 305 251 133 54 365 365 343 279 151 386 255 209 134 50 284 236 192 180 84 243 138 318
6 3.189 1.453 1.043 3.003 2.245 1.513 1.234 1.024 2.475 2.030 2.278 1.415 1.132 0.987 2.977 2.499 2.116 1.755 1.426 2.101 1.862 1.518 1.291 1.123 0.987 2.180 1.971 1.706 1.480 1.276 1.608 1.301 1.115 2.175 1.925
1.6 Rb
1.4
K Ba Sr Na
1.0
Cd Zn
Ca
Y Sc
W Ti
Ta Zr
Ge
600
Ga
Mg
0.6
V
Sn
Li
0.8
Mo
Nb
In
La
three groups, namely, glass-formers, intermediates and modifiers. According to Sun [29], single bond strength BM–O of glass-formers is found in the 119–81 kcal/mol range, that of intermediates in the 73–60 kcal/mol range and that for modifiers in the 60– 10 kcal/mol range, respectively. In the pointed sequence dissociation energy and single bond strength decrease. In other words, high value of single bond strength increases glass forming tendency. Recently, good correlation has been established among basicity and single bond strength for many oxides [30]. In general, the optical basicity increases with decreasing the single bond strength of the oxides. On this basis, comparatively good agreement has been found between the polarizability classification of simple oxides [15] and that proposed by Sun [29]. Also recently, Dimitrov and Komatsu [31–35] have established that good correlation exists between optical basicity and average single bond strength even in La2O3–P2O5, Na2O–SiO2, Na2O–B2O3, PbO– SiO2, Na2O–GeO2, R2O–TeO2 (R¼Li, Na and K), MnOm–V2O5 (M¼ P, Ge, Sr and Pb), Sb2O3–B2O3, Bi2O3–B2O3, Na2O–TiO2–SiO2, BaO– TiO2–SiO2, BaO–TiO2–B2O3, ZnO–Bi2O3–B2O3 and R2O–B2O3–SiO2 (R ¼Li, Na and K) glasses. In all glass systems the optical basicity increases with decreasing average single bond strength. Therefore, since the relationship between electronegativity and optical basicity of simple oxides was already discussed in the present paper it is of interest to check also the correlation between electronegativity and single bond strength of the oxides. Data on the single bond strength BM–O of the oxides under consideration in the present paper are taken from the original paper of Sun [29] and those of GeO2 and V2O5 are from Ref. [30]. The data on the single bond strength of BeO, CrO3, SeO3, As2O5, MoO3, WO3, TeO3 and Sb2O5 were calculated by us dividing the dissociation energy Ed of the oxides reported by Sun and Huggins [36] by the coordination number CN of the cation shown in Table 2, column 4. All data of single bond strength of the oxides are collected in Table 2, column 5. Note that in Table 2 Sun’s data are multiplied by 4.184 and the single bond strength is given in kJ/mol. The data of BM–O are plotted as a function of electronegativity wi in Fig. 3. As can be seen a remarkable correlation exists between these independently obtained quantities as well as with the proposed classification of simple oxides [15]. Three groups of oxides can be observed in Fig. 3. Semicovalent predominantly acidic oxides possess large single bond strength (300–500 kJ/mol) and high values of electronegativity (E2–3.5). It should be noted that these oxides are classical glass-formers. The very ionic and very basic oxides such as alkali and alkaline-earth oxides with smallest
Al Si
0.4
P
B
0.2 0
0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Electronegativity Fig. 2. Optical basicity of simple oxides as a function of element electronegativity.
2.3. Dependence of single bond strength on element electronegativity Many years ago Sun [29] has reported comprehensive data on single bond strength BM–O in kcal per Avogadro bond for various simple oxides based on their dissociation energy Ed. That is the energy required to dissociate the oxide into its constituent gaseous atoms. On this basis the oxides have been divided into
Single bond strength (kJ/mol)
Optical basicity
1.2
577
500 B Si Mo V Ge
400
P
V
300 Sc Y Li
Ca
100
Na K Rb
Al In
Ba
Ti
Ga
La
200
W
Zr
Sn
Zn
Sr Cd
0 0
0.5
1.0
1.5 2.0 Electronegativity
2.5
3.0
3.5
Fig. 3. Single bond strength of simple oxides as a function of element electronegativity.
578
V. Dimitrov, T. Komatsu / Journal of Solid State Chemistry 196 (2012) 574–578
single bond strength (30–130 kJ/mol) have low values of electronegativity at about 1–1.2. These oxides are modifiers in the field of glass science and technology. The ionic and basic oxides such as V2O5, TiO2, Sc2O3, ZnO, ZrO2, and In2O3 are located in the intermediate position. The results presented in Fig. 3 show that generally high values of electronegativity correspond to high values of single bond strength and vice versa. At the same time it is obvious that the observed trend in Fig. 3 is closely related to the type of chemical bonding in corresponding oxide. High electronegativity values of for example B3 þ (3.189), P5 þ (3.003), Si4 þ (2.245) show that the metal ions possess increased ability to attract electrons from the oxide ions. From polarizability point of view B3 þ , P5 þ and Si4 þ cations possess an extremely low polarizability (0.002, 0.021 and 0.033 A˚ 3, see Table 1) and most of them have a large positive charge. Their polarizability power is very large and they affect strongly the electron charge density of the surrounding oxide ions. As a result strong covalent B–O, P–O, Si–O chemical bonds are formed and large overlap between O2p and valence metal orbitals exists in the structure of B2O3, P2O5 and SiO2. This corresponds to the highest single bond strength of 498, 464 and 443 kJ/mol, respectively. Small electronegativity of for example Na þ (1.024), K þ (0.987), Rb þ (0.987), Cd2 þ (1.276), Ba2 þ (1.115), etc. indicates that the metal ions have decreased ability to attract electrons from the oxide ions. These cations possess high polarizability (0.175, 0.821, 1.437, 1.054, 1.595 A˚ 3, respectively) and small positive charge. Their polarizing power is too small and they affect weakly the electron charge density of the surrounding oxide ions. Very ionic chemical bonds are formed in the structure of Na2O, K2O, Rb2O, CdO, BaO, etc., due to the small overlap between O2p and valence metal orbitals. In this respect the single bond strength of Na–O (84 kJ/mol), K–O (54 kJ/ mol), Rb–O (50 kJ/mol), Cd–O (84 kJ/mol), Ba–O (138 kJ/mol) chemical bonds is small which supports their ionic character.
3. Conclusion It is established on the basis of the similarity in physical nature between free-cation polarizability and electronegativity of elements in different valence states and with the most common coordination numbers that good correlation exists between these quantities. A systematic periodic increase in cation polarizability is observed in isoelectronic series with decreasing electronegativity. It is found that in the case of simple oxides the increase in optical basicity and decrease in single bond strength is accompanied with decrease in electronegativity. It is concluded that the
observed trends are closely related to the electron donation ability of the oxide ions and type of chemical bonding in simple oxides.
References [1] A.R. West, Solid State Chemistry and Its Applications, John Wiley & Sons, New York, 1984. [2] H. Rawson, Properties and Applications of Glass, Elsevier, Amsterdam, 1980. [3] J.A. Duffy, Phys. Chem. Glasses 30 (1989) 1. [4] M. Karplus, R. Porter, Atoms and Molecules, W.A. Benjamin Inc., Menlo Park, CA, 1970 255. [5] V. Dimitrov, T. Komatsu, J. Ceram. Soc. Jpn. 107 (1999) 879. [6] K. Li, D. Xue, J. Phys. Chem. A 110 (2006) 11332. [7] I.D. Brown, Acta Crystallogr. B 44 (1988) 545. [8] I.D. Brown, A Skowron, J. Am. Chem. Soc. 112 (1990) 3401. [9] L. Pauling, Proc. R. Soc. Lond. A 114 (1927) 181. [10] M. Born, W. Heisenberg, Z. Phys. 23 (1924) 388. [11] K. Fajans, G. Joos, Z. Phys. 23 (1924) 1. [12] J.E. Mayer, M.G. Mayer, Phys. Rev. 43 (1933) 605. [13] E. Kordes, Z. Phys. Chem. B 44 (1939) 249. [14] V. Dimitrov, S. Sakka, J. Appl. Phys. 79 (1996) 1736. [15] V. Dimitrov, T. Komatsu, J. Solid State Chem. 163 (2002) 100. [16] V. Dimitrov, T. Komatsu, J. Solid State Chem. 178 (2005) 831. [17] V. Dimitrov, T. Komatsu, J. Univ. Chem. Technol. Metall. 45 (2010) 219. [18] R.J. Heaton, P.A. Madden, S.J. Clark, S. Jahn, J. Chem. Phys. 125 (2006) 144104. [19] W.A. Weyl, E.G. Marboe, The Constitution of Glasses, Wiley-Interscience, New York, 1962. [20] J.A. Duffy, M.D. Ingram, in: D. Uhlman, N. Kreidl (Eds.), Optical Properties of Glass, American Ceramic Society, Westervill, 1991. [21] J.A. Duffy, Electrochemistry of Glasses and Glass Melts, in: H. Bach, F. Baucke, D. Krause (Eds.), Including Glass Electrodes, Springer, 2000. [22] A. Lebouteiller, P. Courtine, J. Solid State Chem. 137 (1998) 94. [23] P. Balta, in: Proceedings of the XV International Congress on Glass, Leningrad, 1989, vol. 1b, p. 211. [24] P. Balta, Proceedings of the Fifth Conference European Society of Glass Science and Technology, Prague, 1999, vol. B4, p. 3. [25] R. Asokamany, R. Manjula, Phys. Rev. B 39 (1989) 4217. [26] R.R. Reddy, Y. Nazeer Ahammed, P. Abdul Azeem, K. Rama Gopal, T.V.R. Rao, J. Non-Cryst. Solids 286 (2001) 169. [27] J.A. Duffy, Phys. Chem. Glasses 46 (2005) 500. [28] V. Dimitrov, T. Komatsu, Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B 49 (2008) 97. [29] K.H. Sun, J. Am. Ceram. Soc. 30 (1947) 277. [30] V. Dimitrov, T. Komatsu, Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B 49 (2008) 33. [31] V. Dimitrov, T. Komatsu, Phys. Chem. Glasses 46 (2005) 521. [32] V. Dimitrov, T. Komatsu, Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B 47 (2006) 638. [33] V. Dimitrov, T. Komatsu, Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B 52 (2011) 225. [34] V. Dimitrov, T. Komatsu, J. Non-Cryst. Solids 356 (2010) 258. [35] V. Dimitrov, T. Komatsu, Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B, in press. [36] K.H. Sun, M.L. Huggins, J. Phys, Colloid Chem. 51 (1947) 438.
Contents lists available at SciVerse ScienceDirect
Journal of Solid State Chemistry journal homepage: www.elsevier.com/locate/jssc
Correlation among electronegativity, cation polarizability, optical basicity and single bond strength of simple oxides Vesselin Dimitrov a, Takayuki Komatsu b,n a b
Department of Silicate Technology, University of Chemical Technology and Metallurgy, 8, Kl. Ohridski Blvd., Sofia 1756, Bulgaria Department of Materials Science and Technology, Nagaoka University of Technology, 1603-1 Kamitomioka-cho, Nagaoka 940-2188, Japan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 June 2012 Received in revised form 13 July 2012 Accepted 15 July 2012 Available online 22 July 2012
A suitable relationship between free-cation polarizability and electronegativity of elements in different valence states and with the most common coordination numbers has been searched on the basis of the similarity in physical nature of both quantities. In general, the cation polarizability increases with decreasing element electronegativity. A systematic periodic change in the polarizability against the electronegativity has been observed in the isoelectronic series. It has been found that generally the optical basicity increases and the single bond strength of simple oxides decreases with decreasing the electronegativity. The observed trends have been discussed on the basis of electron donation ability of the oxide ions and type of chemical bonding in simple oxides. & 2012 Elsevier Inc. All rights reserved.
Keywords: Polarizability Electronegativity Optical basicity Simple oxide Single bond strength
1. Introduction Electronic polarizability of ions demonstrates the easy deformation of their electronic clouds by applying an electromagnetic field. It is an important parameter because it is closely related to many properties of the solids such as refraction, conductivity, ferroelectricity, electro-optical effect, optical nonlinearity along with optical basicity [1–3]. Electronic polarizability a of an atom or ion could be given through a one-dimensional Hooke’s-law potential energy by
a ¼ e2
X ni ki
ð1Þ
where e is the elementary charge and ni is the number of electrons with binding force constant ki [4]. According to this model, Hooke’s-law potential energy is assumed to be equal to the ionization energy IE as twice the value of effective ionic radii, 2reff. By this manner electron binding force constant ki can be given by k¼
IE 2r 2ef f
ð2Þ
or electronic ion polarizability is X ni a ¼ 2e2 r2ef f IE
As can be seen the loosely bound valence electrons with low ionization energy, i.e., small force constant will contribute more to the electronic polarizability of an atom or ion than the tightly bound inner-shell electrons. Recently, Dimitrov and Komatsu [5] have found suitable relationship between free-ion polarizability and element outermost binding energy on the basis of the similarity in physical nature between electron binding energy and ionization energy. It has been suggested that outermost corelevel binding energy can be used for relative measure of the cation polarizability. In general, cation polarizability increases with decreasing element binding energy. Simultaneously, a systematic periodic change in the polarizability against the binding energy has been observed in the isoelectronic series [5]. On the other hand, the element electronegativity demonstrates the ability of an atom or ion to attract electrons from the atoms or ions bonded to it. Also recently, Li and Xue [6] have published electronegativities of 82 elements in different valence states and with the most common coordination numbers calculated on the basis of an effective ionic potential defined by the ionization energy and ionic radii. The following equation for the electronegativity wi has been proposed:
n
Corresponding author. Fax: þ81 258 47 9300. E-mail addresses: [email protected] (V. Dimitrov), [email protected].(T. Komatsu) 0022-4596/$ - see front matter & 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jssc.2012.07.030
ð3Þ
wi ¼ 0:105nn
Im R1
1=2 1 þ0:863 ri
ð4Þ
V. Dimitrov, T. Komatsu / Journal of Solid State Chemistry 196 (2012) 574–578
where nn is the effective principal quantum number, RN is the Rydberg constant, Im is the ionization energy and ri is the ionic radii. Li and Xue [6] have discussed that the Lewis acid strength can be quantitatively measured as a function of their electronegativity scale. The Lewis acid strength Sa has been introduced by Brown [7] to predict which Lewis acids will bond to which Lewis bases. It is defined for a given cation by Sa ¼
V Nt
ð5Þ
where V is the oxidation state of the cation and Nt is the average of the coordination numbers to oxygen observed in a large sample of compounds [8]. Brown and Skowron [8] have established that for main group elements in their highest oxidation state a scale of Lewis acid strength derived from observed structures correlates with a scale of electronegativity derived from electron energies in the free atom. Eqs. (3) and (4) show that the physical origin of electronic ion polarizability and electronegativity obtained by Li and Xue is very similar, since both of them are related to the ionization energy and ionic radii. Therefore, it is of interest to check the correlation between these quantities. That is why in this paper we have examined the relationship between electronegativity and electronic polarizability of different ions. The relationship with optical basicity as well as single bond strength of numerous simple oxides is also discussed.
2. Results and discussion 2.1. Dependence of cation polarizability on electronegativity A couple of sets of free-ion polarizabilities have been proposed by Pauling [9], Born and Heisenberg [10], Fajans and Joos [11], Mayer and Mayer [12] and Kordes [13], The most comprehensive sets among them are those proposed by Pauling [9] and Kordes [13]. Pauling’s values have been obtained on a theoretical treatment of the quadratic Stark effect by means of the following equation: R ¼ 0:047n4 ð15n2 þ21Þ
X
1 ðZSR Þ4
ð6Þ
R is the ionic refraction, n is the principal quantum number, Z is the electron number and SR is the mole refraction screening constant. On the other hand, Kordes [13] has calculated the free-ion polarizabilities on the basis of ionic radii by the equation " 1=3 #2=3 R ¼ kr u ¼ kr z Z 2=ðnB 1Þ ð7Þ 0:603 where ru is the univalent crystal radii, rz is the actual crystal radii, nB is the Born repulsion exponent and k is the constant. The cation polarizabilities of ions under consideration in this paper obtained by Pauling and by Kordes are presented in Table 1 (columns 3 and 4). As can be seen a good correspondence exists between two independently obtained sets. In the present study we used polarizability data reported by Kordes (Table 1, column 3) which we have been used in our previous papers [5,14–17]. Recently, condensed phase ionic polarizabilities from plane wave density functional theory calculation were reported by Heaton et. al. [18] which are in good agreement with the polarizabilities used by Dimitrov and Sakka [14] for a free ion [13]. In column 6 of Table 1 the values of element electronegativity according to Li and Xue [6] are listed, taking into account the valence state of cation and its most common coordination number in the oxides. On the basis of
575
Table 1 Ion, outermost electron orbital, cation polarizability (ai), coordination number (CN) and electronegativity (wi). Ion
1 B3 þ Be2 þ Li þ P5 þ Si4 þ Al3 þ Mg2 þ Na þ Cr6 þ V5 þ Ti4 þ Sc3 þ Ca2 þ Kþ Se6 þ As5 þ Ge4 þ Ga3 þ Zn2 þ Mo6 þ Nb5 þ Zr4 þ Y3 þ Sr2 þ Rb þ Te6 þ Sb5 þ Sn4 þ In3 þ Cd2 þ Ce4 þ La3 þ Ba2 þ W6 þ Ta5 þ Hf4 þ
Outermost orbital
ai (A˚ 3; Kordes)
ai (A˚ 3;
2 1s2 1s2 1s2 2p6 2p6 2p6 2p6 2p6 3p6 3p6 3p6 3p6 3p6 3p6 3d10 3d10 3d10 3d10 3d10 4p6 4p6 4p6 4p6 4p6 4p6 4d10 4d10 4d10 4d10 4d10 5p6 5p6 5p6 4f14 4f14 4f14
3 0.002 0.007 0.024 0.021 0.033 0.054 0.094 0.175 0.085 0.122 0.184 0.287 0.469 0.821 0.073 0.100 0.137 0.195 0.283 0.169 0.242 0.357 0.544 0.861 1.437 0.242 0.333 0.479 0.662 1.054 0.702 1.052 1.595 0.147 0.185 0.368
4 0.003 0.008 0.029 0.021 0.033 0.054 0.094 0.181 0.087 0.123 0.187 0.290 0.472 0.841 0.075 0.103 0.143 0.198 0.286 0.190 0.262 0.377 0.560 0.865 1.417 0.262 0.361 0.500 0.730 1.087 0.738 1.048 1.563
CN wi (Li and Xue)
Pauling) 5 3 4 4 4 4 6 6 6 6 6 6 6 8 9 4 4 4 4 4 6 6 8 8 8 10 6 6 6 6 6 6 7 8 6 6 6
6 3.189 1.453 1.043 3.003 2.245 1.513 1.234 1.024 2.475 2.030 2.278 1.415 1.132 0.987 2.977 2.499 2.116 1.755 1.426 2.101 1.862 1.518 1.291 1.123 0.987 2.180 1.971 1.706 1.480 1.276 1.608 1.301 1.115 2.175 1.925 1.706
the data presented in Table 1, it is possible to investigate the change in the polarizability of the cations with electronegativity through classification based on their outermost electron configuration. In this connection the data of cation polarizability are plotted as a function of element electronegativity in Fig. 1. As can be observed there is systematic periodic change in the cation polarizability and related element electronegativity. Cation polarizability increases and electronegativity decreases in all series. Therefore, from electronegativity point of view the increase in the cation polarizability in each series means decreased ability of an ion to attract electrons from the atoms bonded to it. The observed good correlation between cation polarizability and element electronegativity in isoelectronic series could be explained taking into consideration their common physical ground. As can be seen in Eqs. (3) and (4) both quantities are related to the ionization energy and ionic radii. Similar trend as that shown in Fig. 1 has been found studying the relationship between cation polarizability and element binding energy based on the similarity in physical nature between electron binding energy and ionization energy [5]. 2.2. Dependence of optical basicity of simple oxides on element electronegativity The estimation of the electronic polarizability of ions is subject to the so-called polarizability approach in the materials science, which is well known especially in the field of glass science [19]. The polarizability approach has been systematically developed in our recent papers concerning the origin of electronic polarizability
576
V. Dimitrov, T. Komatsu / Journal of Solid State Chemistry 196 (2012) 574–578
a combination of cation oxidation state and coordination number leads to Pi log pB ¼ 1:9ðCNÞ0:02 0:023 ð10Þ CN
1.8
Cation polarizability (Å3)
1.6 1.4 1.2
where CN is the cation coordination number and Pi is ionization potential corresponding to its oxidation state [24]. For many purposes as was mentioned by Duffy [21], the pB scale serves in a fashion similar to the optical basicity scale and, for certain glass compositions where electronegativity is a common link, the two scales parallel each other. Asokamany and Manjula [25] introduced the concept of average electronegativity and defined an average electronegativity parameter w1av in the following manner:
1.0 0.8 0.6 0.4 0.2 0 0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
wlav ¼
N X wn
i i
i¼1
Electronegativity Fig. 1. Cation polarizability as a function of electronegativity: J, for (1s2 orbital) B3 þ -Be2 þ -Li þ ; ’, for (2p6 orbital) P5 þ -Si4 þ -Al3 þ -Mg2 þ -Na þ ; K, for (3p6 orbital) Cr6 þ -V5 þ -Ti4 þ -Sc3 þ -Ca2 þ -K þ ; &, for (3d10 orbital) Se6 þ As5 þ -Ge4 þ -Ga3 þ -Zn2 þ ; m, for (4p6 orbital) Mo6 þ -Nb5 þ -Zr4 þ -Y3 þ Sr2 þ -Rb þ ; W, for (4d10 orbital) Te6 þ -Sb5 þ -Sn4 þ -In3 þ -Cd2 þ ; ~, for (5p6 orbital) Ce4 þ -La3 þ -Ba2 þ ; , for (4f14 orbital) W6 þ -Ta5 þ -Hf4 þ .
N
where wi is the Pauling electronegativity, ni is the number of atoms of the ith element and N is the number of elements present in the compound. On this basis Reddy et al. [26] have derived the following empirical relationship for the optical basicity of simple oxides:
L ¼ 1:590:2279wlav and optical basicity in simple oxides [14,15] and oxide glasses [16,17]. The most familiar and widely used relationship in this approach is the Lorentz–Lorenz equation. Dimitrov and Sakka [14] calculated by means of this equation the electronic oxide ion polarizability (aO2-) of large number of single component oxides on the basis of linear refractive index (no) and energy gap (Eg). On this ground the refractive index based L(no) and energy gap based L(Eg) optical basicity of the oxides has been also estimated. The simple oxides have been classified in three groups: a, semicovalent (predominantly acidic); b, ionic (basic) and c, very ionic (very basic) oxides [15]. Simultaneously, the relationship between optical basicity of simple oxides and electronegativity has been searched by several authors. Duffy and Ingram [20,21] have suggested that a good correlation exists between basicity L and Pauling-type electronegativity w:
L¼
0:75
ð8Þ
w0:25
The optical basicity of main group elements holds well with the electronegativity rule but for other elements Eq. (8) must be used with caution, especially with transition metal and heavy metal oxides. Optical basicity values for K2O, Na2O, BaO, Li2O, CaO, MgO, Al2O3, ZnO, SiO2, B2O3, H2O, P2O5, CO2, SO3, N2O5 and Cl2O7 have been determined [20,21]. Lebouteiller and Courtine [22] have tried to apply the electronegativity approach using a modifying Pauling-type electronegativity, taking into consideration the valence and the coordination of the ions. They have used an ionic–covalent parameter (ICP), which represents the influence of ionic–covalent bonding in an oxide or oxysalt on the acid strength of cations ICP ¼ log P1:38w þ2:07
ð9Þ (z/r2i
where P is the polarizing power of the cation with formal charge z and Shannon ionic radius ri) and w is the modifying electronegativity of the cation. The use of electronegativity for determination of optical basicity has been made in the pB scale proposed by Balta [23]. Later modification concerning replacement of electronegativity by
ð11Þ
ð12Þ
where wlav is the average electronegativity of the simple oxide. Reddy et al. [26] have calculated L for many oxides and in general there is agreement with previously obtained data by Duffy [21] and Dimitrov and Sakka [14]. In the present paper we tried to correlate optical basicity of simple oxides with element electronegativity estimated by Li and Xue [6]. The data of optical basicity are taken from Ref. [15], where the average values between refractive index based L(no) and energy gap based L(Eg) optical basicity are given. The data are listed in Table 2, column 3. The optical basicity of P2O5, Al2O3, Na2O, K2O and Rb2O are according to Duffy [27]. The optical basicity of B2O3, SiO2 and GeO2 are picked up from Ref. [28]. The data of optical basicity of simple oxides are plotted as a function of element electronegativity in Fig. 2. As can be seen there is a general trend of increase in optical basicity with decreasing electronegativity but with a scatter of the data point. Irrespective of that good agreement could be found with the recently proposed polarizability classification of simple oxides [15]. Semicovalent predominantly acidic oxides are found in the E0.4–0.8 basicity range and E2–3.5 electronegativity range. For instance, the highest values equal to 3.189, 3.003 and 2.245 possess the acidic oxides such as B2O3 (0.46), P2O5 (0.48) and SiO2 (0.53). The very ionic and very basic oxides such as Na2O, K2O, Rb2O, SrO, BaO and CdO with basicity above 1 are located in a narrow range of low electronegativity values at about 1–1.2. The ionic (basic) oxides with basicity close to that of CaO are found in the E1–2.2 electronegativity range. The results presented in Fig. 2 show that generally high values of electronegativity correspond to low values of optical basicity and vice versa. In fact, the optical basicity L represents the polarizability state of an average oxide ion in the oxides and its ability to donate electron density to surrounding metal ions. High values of electronegativity of these ions mean that they have increased ability to attract electrons from the oxide ions bonded to them. As a result the oxide ions in acidic oxides are considerably tightened and their donation ability is week. As a result the optical basicity is low. In contrast, low values of electronegativity of metal ions show that they possess decreased ability to attract electrons from the oxide ions. That is why the oxide ions in basic and very basic oxides are more free and their electron donation is high.
V. Dimitrov, T. Komatsu / Journal of Solid State Chemistry 196 (2012) 574–578
Table 2 Oxide, ion, optical basicity (L), coordination number (CN), single bond strength (BM–O) and electronegativity (wi). Oxide
Ion
L
CN
BM–O (kJ/mol)
wi (Li and Xue)
1 B2O3 BeO Li2O P2O5 SiO2 Al2O3 MgO Na2O CrO3 V 2 O5 TiO2 Sc2O3 CaO K2O SeO3 As2O3 GeO2 Ga2O3 ZnO MoO3 Nb2O5 ZrO2 Y2O3 SrO Rb2O TeO3 Sb2O5 SnO2 In2O3 CdO CeO2 La2O3 BaO WO3 Ta2O5
2 B3 þ Be2 þ Li þ P5 þ Si4 þ Al3 þ Mg2 þ Na þ Cr6 þ V5 þ Ti4 þ Sc3 þ Ca2 þ Kþ Se6 þ As5 þ Ge4 þ Ga3 þ Zn2 þ Mo6 þ Nb5 þ Zr4 þ Y3 þ Sr2 þ Rb þ Te6 þ Sb5 þ Sn4 þ In3 þ Cd2 þ Ce4 þ La3 þ Ba2 þ W6 þ Ta5 þ
3 0.46 0.87 0.48 0.53 0.61 0.68 1.10 1.055 0.935 0.87 0.975 1.31 0.80 0.755 1.08 1.07 1.035 0.825 0.99 1.14 1.43 0.85 1.07 1.115 1.01 1.07 1.22 1.045 0.925
4 3 4 4 4 4 6 6 6 6 6 6 6 8 9 4 4 4 4 4 6 6 8 8 8 10 6 6 6 6 6 6 7 8 6 6
5 498 262 150 464 443 251 155 84 309 312 305 251 133 54 365 365 343 279 151 386 255 209 134 50 284 236 192 180 84 243 138 318
6 3.189 1.453 1.043 3.003 2.245 1.513 1.234 1.024 2.475 2.030 2.278 1.415 1.132 0.987 2.977 2.499 2.116 1.755 1.426 2.101 1.862 1.518 1.291 1.123 0.987 2.180 1.971 1.706 1.480 1.276 1.608 1.301 1.115 2.175 1.925
1.6 Rb
1.4
K Ba Sr Na
1.0
Cd Zn
Ca
Y Sc
W Ti
Ta Zr
Ge
600
Ga
Mg
0.6
V
Sn
Li
0.8
Mo
Nb
In
La
three groups, namely, glass-formers, intermediates and modifiers. According to Sun [29], single bond strength BM–O of glass-formers is found in the 119–81 kcal/mol range, that of intermediates in the 73–60 kcal/mol range and that for modifiers in the 60– 10 kcal/mol range, respectively. In the pointed sequence dissociation energy and single bond strength decrease. In other words, high value of single bond strength increases glass forming tendency. Recently, good correlation has been established among basicity and single bond strength for many oxides [30]. In general, the optical basicity increases with decreasing the single bond strength of the oxides. On this basis, comparatively good agreement has been found between the polarizability classification of simple oxides [15] and that proposed by Sun [29]. Also recently, Dimitrov and Komatsu [31–35] have established that good correlation exists between optical basicity and average single bond strength even in La2O3–P2O5, Na2O–SiO2, Na2O–B2O3, PbO– SiO2, Na2O–GeO2, R2O–TeO2 (R¼Li, Na and K), MnOm–V2O5 (M¼ P, Ge, Sr and Pb), Sb2O3–B2O3, Bi2O3–B2O3, Na2O–TiO2–SiO2, BaO– TiO2–SiO2, BaO–TiO2–B2O3, ZnO–Bi2O3–B2O3 and R2O–B2O3–SiO2 (R ¼Li, Na and K) glasses. In all glass systems the optical basicity increases with decreasing average single bond strength. Therefore, since the relationship between electronegativity and optical basicity of simple oxides was already discussed in the present paper it is of interest to check also the correlation between electronegativity and single bond strength of the oxides. Data on the single bond strength BM–O of the oxides under consideration in the present paper are taken from the original paper of Sun [29] and those of GeO2 and V2O5 are from Ref. [30]. The data on the single bond strength of BeO, CrO3, SeO3, As2O5, MoO3, WO3, TeO3 and Sb2O5 were calculated by us dividing the dissociation energy Ed of the oxides reported by Sun and Huggins [36] by the coordination number CN of the cation shown in Table 2, column 4. All data of single bond strength of the oxides are collected in Table 2, column 5. Note that in Table 2 Sun’s data are multiplied by 4.184 and the single bond strength is given in kJ/mol. The data of BM–O are plotted as a function of electronegativity wi in Fig. 3. As can be seen a remarkable correlation exists between these independently obtained quantities as well as with the proposed classification of simple oxides [15]. Three groups of oxides can be observed in Fig. 3. Semicovalent predominantly acidic oxides possess large single bond strength (300–500 kJ/mol) and high values of electronegativity (E2–3.5). It should be noted that these oxides are classical glass-formers. The very ionic and very basic oxides such as alkali and alkaline-earth oxides with smallest
Al Si
0.4
P
B
0.2 0
0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Electronegativity Fig. 2. Optical basicity of simple oxides as a function of element electronegativity.
2.3. Dependence of single bond strength on element electronegativity Many years ago Sun [29] has reported comprehensive data on single bond strength BM–O in kcal per Avogadro bond for various simple oxides based on their dissociation energy Ed. That is the energy required to dissociate the oxide into its constituent gaseous atoms. On this basis the oxides have been divided into
Single bond strength (kJ/mol)
Optical basicity
1.2
577
500 B Si Mo V Ge
400
P
V
300 Sc Y Li
Ca
100
Na K Rb
Al In
Ba
Ti
Ga
La
200
W
Zr
Sn
Zn
Sr Cd
0 0
0.5
1.0
1.5 2.0 Electronegativity
2.5
3.0
3.5
Fig. 3. Single bond strength of simple oxides as a function of element electronegativity.
578
V. Dimitrov, T. Komatsu / Journal of Solid State Chemistry 196 (2012) 574–578
single bond strength (30–130 kJ/mol) have low values of electronegativity at about 1–1.2. These oxides are modifiers in the field of glass science and technology. The ionic and basic oxides such as V2O5, TiO2, Sc2O3, ZnO, ZrO2, and In2O3 are located in the intermediate position. The results presented in Fig. 3 show that generally high values of electronegativity correspond to high values of single bond strength and vice versa. At the same time it is obvious that the observed trend in Fig. 3 is closely related to the type of chemical bonding in corresponding oxide. High electronegativity values of for example B3 þ (3.189), P5 þ (3.003), Si4 þ (2.245) show that the metal ions possess increased ability to attract electrons from the oxide ions. From polarizability point of view B3 þ , P5 þ and Si4 þ cations possess an extremely low polarizability (0.002, 0.021 and 0.033 A˚ 3, see Table 1) and most of them have a large positive charge. Their polarizability power is very large and they affect strongly the electron charge density of the surrounding oxide ions. As a result strong covalent B–O, P–O, Si–O chemical bonds are formed and large overlap between O2p and valence metal orbitals exists in the structure of B2O3, P2O5 and SiO2. This corresponds to the highest single bond strength of 498, 464 and 443 kJ/mol, respectively. Small electronegativity of for example Na þ (1.024), K þ (0.987), Rb þ (0.987), Cd2 þ (1.276), Ba2 þ (1.115), etc. indicates that the metal ions have decreased ability to attract electrons from the oxide ions. These cations possess high polarizability (0.175, 0.821, 1.437, 1.054, 1.595 A˚ 3, respectively) and small positive charge. Their polarizing power is too small and they affect weakly the electron charge density of the surrounding oxide ions. Very ionic chemical bonds are formed in the structure of Na2O, K2O, Rb2O, CdO, BaO, etc., due to the small overlap between O2p and valence metal orbitals. In this respect the single bond strength of Na–O (84 kJ/mol), K–O (54 kJ/ mol), Rb–O (50 kJ/mol), Cd–O (84 kJ/mol), Ba–O (138 kJ/mol) chemical bonds is small which supports their ionic character.
3. Conclusion It is established on the basis of the similarity in physical nature between free-cation polarizability and electronegativity of elements in different valence states and with the most common coordination numbers that good correlation exists between these quantities. A systematic periodic increase in cation polarizability is observed in isoelectronic series with decreasing electronegativity. It is found that in the case of simple oxides the increase in optical basicity and decrease in single bond strength is accompanied with decrease in electronegativity. It is concluded that the
observed trends are closely related to the electron donation ability of the oxide ions and type of chemical bonding in simple oxides.
References [1] A.R. West, Solid State Chemistry and Its Applications, John Wiley & Sons, New York, 1984. [2] H. Rawson, Properties and Applications of Glass, Elsevier, Amsterdam, 1980. [3] J.A. Duffy, Phys. Chem. Glasses 30 (1989) 1. [4] M. Karplus, R. Porter, Atoms and Molecules, W.A. Benjamin Inc., Menlo Park, CA, 1970 255. [5] V. Dimitrov, T. Komatsu, J. Ceram. Soc. Jpn. 107 (1999) 879. [6] K. Li, D. Xue, J. Phys. Chem. A 110 (2006) 11332. [7] I.D. Brown, Acta Crystallogr. B 44 (1988) 545. [8] I.D. Brown, A Skowron, J. Am. Chem. Soc. 112 (1990) 3401. [9] L. Pauling, Proc. R. Soc. Lond. A 114 (1927) 181. [10] M. Born, W. Heisenberg, Z. Phys. 23 (1924) 388. [11] K. Fajans, G. Joos, Z. Phys. 23 (1924) 1. [12] J.E. Mayer, M.G. Mayer, Phys. Rev. 43 (1933) 605. [13] E. Kordes, Z. Phys. Chem. B 44 (1939) 249. [14] V. Dimitrov, S. Sakka, J. Appl. Phys. 79 (1996) 1736. [15] V. Dimitrov, T. Komatsu, J. Solid State Chem. 163 (2002) 100. [16] V. Dimitrov, T. Komatsu, J. Solid State Chem. 178 (2005) 831. [17] V. Dimitrov, T. Komatsu, J. Univ. Chem. Technol. Metall. 45 (2010) 219. [18] R.J. Heaton, P.A. Madden, S.J. Clark, S. Jahn, J. Chem. Phys. 125 (2006) 144104. [19] W.A. Weyl, E.G. Marboe, The Constitution of Glasses, Wiley-Interscience, New York, 1962. [20] J.A. Duffy, M.D. Ingram, in: D. Uhlman, N. Kreidl (Eds.), Optical Properties of Glass, American Ceramic Society, Westervill, 1991. [21] J.A. Duffy, Electrochemistry of Glasses and Glass Melts, in: H. Bach, F. Baucke, D. Krause (Eds.), Including Glass Electrodes, Springer, 2000. [22] A. Lebouteiller, P. Courtine, J. Solid State Chem. 137 (1998) 94. [23] P. Balta, in: Proceedings of the XV International Congress on Glass, Leningrad, 1989, vol. 1b, p. 211. [24] P. Balta, Proceedings of the Fifth Conference European Society of Glass Science and Technology, Prague, 1999, vol. B4, p. 3. [25] R. Asokamany, R. Manjula, Phys. Rev. B 39 (1989) 4217. [26] R.R. Reddy, Y. Nazeer Ahammed, P. Abdul Azeem, K. Rama Gopal, T.V.R. Rao, J. Non-Cryst. Solids 286 (2001) 169. [27] J.A. Duffy, Phys. Chem. Glasses 46 (2005) 500. [28] V. Dimitrov, T. Komatsu, Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B 49 (2008) 97. [29] K.H. Sun, J. Am. Ceram. Soc. 30 (1947) 277. [30] V. Dimitrov, T. Komatsu, Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B 49 (2008) 33. [31] V. Dimitrov, T. Komatsu, Phys. Chem. Glasses 46 (2005) 521. [32] V. Dimitrov, T. Komatsu, Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B 47 (2006) 638. [33] V. Dimitrov, T. Komatsu, Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B 52 (2011) 225. [34] V. Dimitrov, T. Komatsu, J. Non-Cryst. Solids 356 (2010) 258. [35] V. Dimitrov, T. Komatsu, Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B, in press. [36] K.H. Sun, M.L. Huggins, J. Phys, Colloid Chem. 51 (1947) 438.