J Sol-Gel Sci Technol (2015) 73:506–510 DOI 10.1007/s10971-014-3613-0
BRIEF COMMUNICATION
Effect of P2O5 on optical parameters of (252x) CaO–xP2O5– B2O3–SiO2–ZnO sol–gel glasses: a theoretical assessment Gurbinder Kaur • G. Pickrell • N. Sriranganathan
Received: 15 November 2014 / Accepted: 30 December 2014 / Published online: 21 January 2015 Ó Springer Science+Business Media New York 2015
Graphical Abstract Indirect /direct band gap and Urbach energy (in eV)
Abstract The present investigation is an attempt to address the effect of P2O5 on the optical properties, cross link density (nc) as well as theoretical parameters like Poisson’s ratio and bulk modulus for (25-x)%CaOx%P2O5–60%SiO2–5%B2O3–10%ZnO (x = 5, 10, 15, 20) novel sol–gel glasses. The optical basicity, oxide polarisability, direct/indirect band gaps and theoretical elastic constants have been calculated for all the glasses. In addition to this, the cross-link density, average force stretching constant and number of network bonds per unit volume (nb) have been calculated. The values of optical basicity and polarisabilty have allowed the same trend for all these glasses. The cross-link density decreases when the P2O5 content increases from 5 to 20 %.
Eg(Ind)
4
Eg(Dir)
Eu
3.5 3 2.5 2 1.5 1 0.5 0 CP5
CP10
CP15
CP20
Glass samples
Indirect/Direct band gap and Urbach energy for all the samples.
Keywords Optical band gap Urbach energy Optical basicity Force constant Cross-link density Poisson ratio 1 Introduction
G. Kaur (&) G. Pickrell Department of Material Science and Engineering, Virginia Polytechnic Institute and State University, Holden Hall, Blacksburg, VA 24060, USA e-mail:
[email protected] N. Sriranganathan Department of Biomedical Sciences and Pathobiology, Virginia Polytechnic Institute and State University, Blacksburg, VA 24060, USA
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Lots of research has been carried out on borosilicate glasses due to their wide applications as electrodes, sealants, planar optical wave-guides, optical lenses and glass fibers [1–4]. As compared to the borosilicate glasses, the phosphate glasses remain amorphous even after accommodating higher concentrations of transition ions [5]. In addition to this, the phosphate glasses also possess high electrical conductivity and thermal expansion coefficient [6, 7]. Amorphous phosphate has ultraphosphate structure, which gets converted to metaphosphate structure with the
J Sol-Gel Sci Technol (2015) 73:506–510
507
introduction of network modifiers [5]. P2O5, SiO2 and B2O3 act as basic glass formers whereas oxides like ZnO, BaO, CaO, SrO, Na2O and K2O etc. act as glass modifiers [8, 9]. These modifiers may induce certain defects in the glass structure, which influence the physical as well as chemical properties of the glasses [10]. The polynary borosilicate, aluminosilicate and borophosphate glasses posses superior structural properties because the polynary glasses have more cations participating in polyhedra and mixed units, which leads to the desired combination of properties [3]. For synthesizing multicomponent glasses of high purity and homogenous particle size, sol–gel technique is commonly implied [11, 12]. The current studies focuses on the sol–gel phosphoborosilicate glasses rather than phosphate or borosilicate glass systems. The present investigation is an attempt to address the effect of P2O5 on the optical properties, cross link density (nc) as well as theoretical parameters like Poisson’s ratio and bulk modulus for (25-x)%CaO– x%P2O5–60%SiO2–5%B2O3–10%ZnO (x = 5, 10, 15, 20) novel sol–gel glasses. This novel composition contains two modifiers i.e. ZnO and CaO and three network formers. The results have been discussed in light of optical basicity, oxide polarisability, direct/indirect band gaps and theoretical elastic constants. The information on the glass structure can be anticipated from the cross-link density, average force stretching constant and number of network bonds per unit volume (nb).
2 Experimental procedure The glass composition (25-x)%CaO–x%P2O5–60%SiO2– 5%B2O3–10%ZnO (x = 5, 10, 15, 20) was synthesized using the sol–gel technique. The glass compositions along with their sample labels are given in Table 1. The details of glass preparation are given elsewhere [13]. The glass CP5 was prepared by hydrolysis and polycondensation of 20.722 mL of tetraethyl orthosilicate (TEOS), 2.64 mL of triethyl phosphate (TEP), 7.33 g of calcium nitrate tetrahydrate, 4.62 g of zinc nitrate hexahydrate and 0.48 g of boric acid. The TEOS and TEP hydrolysis was catalyzed using 1 M HNO3 and the molar ratio was kept to be HNO3 ? deionized water: TEOS ? TEP = 8:1. The Table 1 The compositions of sol–gel glasses along with sample label (mol%) Sample
CaO
P2O5
B2O3
SiO2
ZnO
CP5
20
5
5
60
10
CP10
15
10
5
60
10
CP15
10
15
5
60
10
CP20
5
20
5
60
10
reactants were added consecutively after every 0.5 h of continuous stirring. The sol was kept in the sealed polyethylene containers at the room temperature and was allowed to gel. The gel was aged at 70 °C for 3 days and then heated at 120 °C for 12 h to eliminate residual nitrate. While heating the gel, a small hole was inserted in the lid for the escape of the gases. The dried gel was then ballmilled for 3 h to obtain homogenous particles and then stabilized at 600 °C for 12 h. The density of glass composites was calculated using the Archimedes principle and is listed in Table 2. The optical transmission spectra of the prepared samples were recorded at room temperature using a double beam, UV–Vis spectrophotometer (Model: Perkin Elmer Lambda 45) in the wavelength range of 200–700 nm. Methanol was taken as the reference solution. The spectrum of each sample was normalized to the spectrum of the blank methanol.
3 Results and discussion 3.1 Theoretical optical parameters The values of molar volume (Vm), optical basicity (Km) and oxide polarisabilty (ao) are listed in Table 2 and are calculated using following relations: Vm ¼ M=q X Km ¼ Oi =Ocm h i ao ¼ ð1:567 Km þ 0:362Þ2 þ 2:868 = 3:133
ð1Þ ð2Þ ð3Þ
where M is molecular weight and q is density of glass, O is the total number of oxygen atoms present, cm is the basicity moderating parameter and Oi is number of atoms in individual oxides. The concept of optical basicity was introduced by Duffy and Grant [14]. The optical basicity depends upon the bridging and non-bridging oxygens (NBO) present in the glass. In other words, the network modifiers and formers influence optical basicity. The glass covalency is inversely proportional to the optical basicity [15]. This can be explained as follows. A glass with high optical basicity represents higher tendency of oxygen to donate negative charges whereas small optical basicity represents the covalent linkage between oxygen and cation and hence decreased tendency of oxygen to donate the negative charges. It can be seen from Table 2 that the molar volume of glasses increases with the increase in P2O5 content. Optical basicity follows decreasing trend with the increase in P2O5 content i.e. basicity varies as CP20 \ CP15 \ CP10 \ CP5. This indicates that the electron donating capacity is
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Table 2 Density, molar volume, optical basicity and oxide polarizability for all glass samples Glass sample
Density (q) ± 0.01 (g/cc)
Molar volume (Vm) ± 0.01 (cc)
Optical basicity (Km) ± 0.01
Oxide polarizability (ao) ± 0.01
CP5
2.92
21.98
0.514
1.35
CP10
2.87
23.52
0.481
1.31
CP15
2.81
24.98
0.453
1.28
CP20
2.76
26.41
0.431
1.26
where 2b is the number of bonds, Q is the heat of formation (in kJ/mol), xo and xm are the electronegativity values of oxygen ion and metal ions, respectively. The variation of xo with respect to xm is shown in Fig. 1. The oxide electronegativity is highest for B2O3 and minimum for CaO hence indicating high covalency for the B2O3 and maximum ionicity for CaO. The oxide electronegativity follows the trend: B2O3 [ SiO2 [ P2O5 [ ZnO [ CaO whereas the ion electronegativity follows P2O5 [ B2O3 [ SiO2 [ ZnO [ CaO.
3.2 Band gap studies UV–Vis spectroscopy is an excellent tool to determine the band gap energies and hence the behavior of materials. The band gap calculations have been made by Mott and Davis [18] in more general form: ððhm Eopt Þn Þ ahm ¼ const ð5Þ hm
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4 3.5
Oxide and molar electronegavity
highest for CP5 glass composition. The oxide polarisability shares direct intrinsic relationship with the optical basicity, which is evident from the decreasing values of oxide polarisabilty from 1.35 to 1.26 with the increasing P2O5 content. The density also decreases with increasing P2O5 content (Table 2). According to Lorentz and Lorenz, the refractive index varies directly with density and polarisability [16]. Hence, the refractive index shall also decrease with increasing P2O5 content. The optical basicity of a single oxide is highly dependent on the electronegativity difference between the ions. According to Jorgensen scale, the electronegativity considers the energy involved during the transfer of an electron from an atom/ion to another one [17]. Oxygen and cation orbitals give rise to valence and conduction bands respectively. Furthermore, the electron transfer from valence to conduction bands may occur via absorption of photons and hence this electronegativity difference is regarded as the band gap. Higher electronegativity refers to high basicity and hence high band gap, which means difficulty in raising an electron from valence to conduction band. According to Duffy and Grant [14]: p xo xm ¼ ½ðQ þ 1:13Þ= 2b ð4Þ
3 2.5 2 1.5 1 Xo
0.5
Xm
0 CaO
B2O3
SiO2
ZnO
P2O5
Oxides
Fig. 1 Oxide and molar polarizability of all the glass samples
where hm is the photon energy, n is an index, a is the absorption coefficient and Eopt is the optical band gap. To obtain direct band gap n = and for indirect band gap n = 2. The degree of amorphouscity can be obtained by Urbach energy, which is calculated using following relation [19]: a ðmÞ ¼ ao exp ðhm=Eu Þ
ð6Þ
where ao is the constant and Eu is Urbach energy. The variation of direct/indirect band gap and Urbach energy is shown in Fig. 2. It is clear that the direct band-gap possesses higher values than the indirect band gap for all the glasses. In addition to this, the values of direct band-gap, indirect band gap and Urbach energy increase with increasing P2O5 content or decreasing CaO content. The values of direct band gap varies from 3.28 to 3.56 eV and the indirect band gap lies between 2.51 and 2.98 eV. This means that when P2O5 content increases or CaO content decreases, then the NBO formation is less and the ionicity of oxygen atom also decreases [20, 21]. The decreased iconicity lowers the top of valence band, hence resulting in increased band gap. The highest energy of 0.63 eV for CP5 glass indicates highest structural randomness for this glass
Indirect /direct band gap and Urbach energy (in eV)
J Sol-Gel Sci Technol (2015) 73:506–510
Eg(Ind)
4
Eg(Dir)
509
chosen. The average cross-link density can be calculated using following formula [22]: nc ¼ Ri xi ðnÞi ðNÞi = Ri xi ðNÞi ð7Þ
Eu
3.5 3
where xi is the mole fraction, N is the total number of cations per glass formula unit and n is the number of cross links per cation which is given by total number of bridging bonds minus 2. The theoretical Poisson ratio (rth) is calculated using relation:
2.5 2 1.5 1
rth ¼ 0:28ðnc Þ0:25
ð8Þ
0.5 0 CP5
CP10
CP15
CP20
Glass samples
Fig. 2 Indirect/direct band gap and Urbach energy for all the samples
network, which can be attributed to highest NBO for this glass. According to Mott and Davis [18], the Urbach energy is a function of defects due to amorphous structure and degree of disorder. Urbach energy corresponds to the optical transitions between the extended states of conduction band and localized tails of valence band. Urbach energy is lowest for the CP20 glass, which signifies its more polymerized network as compared to CP5, CP10 and CP15 glass this high polymerization is again attributed to
The Poisson ratio and cross-link density of glasses is listed in Table 3. The cross-link density decreases when the P2O5 content increases from 5 to 20 %. Poisson ratio and crosslink density varies inversely w.r.t. each other. CP5 has the highest nc which corresponds to its lowest rth. The number of network bonds per unit volume (nb) of the glass can be calculated using following relation [23]: nb ¼ ðNA q=MÞ Ri ðnf xÞi
ð9Þ
where NA is Avogadro’s number, nf is the coordination number and x is the mole fraction. From Table 3, it can be seen that the nb decreases from 1.30 9 1029 to 1.01 x 1029 m-3 with the increase in the P2O5 content. The average stretching force constant of glass is calculated from the following relation [24]:
F ¼ ½ð0:2 xÞ n1 Fi ðCa OÞ þ x n2 Fi ðP OÞ þ 0:05 n3 Fi ðB OÞ þ 0:6 n4 Fi ðSi OÞ þ 0:1 n5 Fi ðZn OÞ ½ð0:2 xÞ n1 þ x n2 þ 0:05 n3 þ 0:6 n4 þ 0:1 n5
ð10Þ
the lower NBO content for CP20 glass. Hence, the results are in well agreement with each other.
where n1, n2, n3, n4 and n5 are the coordination number of calcium, phosphorus, boron, silicon and zinc respectively. Fi is the stretching force constant of oxide i and can be given by:
3.3 Structural properties and force constants
Fi ¼ 17=r3
For multicomponent oxide glasses, the cross-linking and glass structure highly depends upon the initial composition
where r is the anion-cation bond length. Fi is 2.437, 1.525, ˚ for Ca–O, P–O, B–O, Si–O and 1.343, 1.605 and 1.946 A
ð11Þ
Table 3 Average stretching force constant (F), number of network bonds/volume, cross-link density, theoretical Poisson ratio and theoretical bulk modulus for all glass samples Glass sample
Average stretching force constant F in (N/m)
No. of network bonds/volume (nb 9 1029 atoms/m3) ± 0.01
Cross link density (nc) ± 0.01
Theoretical Poisson ratio (rth) ± 0.001
Theoretical bulk modulus (kbc) ± 0.01 (GPa)
CP5
309
1.30
2.64
0.219
72.34
CP10
337
1.16
2.43
0.224
64.55
CP15 CP20
360 389
1.05 1.01
2.25 2.08
0.229 0.233
58.41 56.21
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Zn–O respectively. According to the bond-compression model, the bulk modulus kbc for multi-component glasses can be given by [22]: kbc ¼ Ri nb r2 F =9 ð12Þ
Acknowledgment Authors are thankful to CIES, Washington D.C. for the financial assistance.
where F is the first order stretching force constant. The force constant increases with increasing P2O5 content whereas the bulk modulus follows reverse trend i.e. for CP20 sample, F is maximum of 389 N/m and kbc is minimum.
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4 Conclusions The effect of P2O5 on the optical properties, cross link density (nc) as well as theoretical parameters like Poisson’s ratio and bulk modulus for (25-x)%CaO–x%P2O5– 60%SiO2–5%B2O3–10%ZnO (x = 5, 10, 15, 20) novel sol–gel glasses have been investigated. Optical basicity and polarisability follows decreasing trend with the increase in P2O5 content i.e. CP20 \ CP15 \ CP10 \ CP5. This indicates that the electron donating capacity is highest for CP5 glass composition. The values of direct band gap varies from 3.28 to 3.56 eV and the indirect band gap lies between 2.51 and 2.98 eV. The highest energy of 0.63 eV for CP5 glass indicates highest structural randomness for this glass network, which can be attributed to highest NBO for this glass. The cross-link density decreases when the P2O5 content increases from 5 to 20 %. CP5 has the highest nc which corresponds to its lowest rth. The force constant increases with increasing P2O5 content whereas the bulk modulus follows reverse trend.
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References
