- Email: [email protected]
Redox relaxation in a sodium borosilicate glass doped with copper and arsenic, antimony, or tin
Journal of Non-Crystalline Solids 356 (2010) 2528–2533
Contents lists available at ScienceDirect
Journal of Non-Crystalline Solids j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j n o n c r y s o l
Redox relaxation in a sodium borosilicate glass doped with copper and arsenic, antimony, or tin E. Meechoowas, M. Müller, C. Rüssel ⁎ Otto-Schott-Institut, Universität Jena, D-07743 Jena, Germany
a r t i c l e
i n f o
Article history: Received 15 October 2009 Received in revised form 3 February 2010 Available online 3 June 2010 Keywords: Redox reactions; Redox relaxation; Polyvalent ions
a b s t r a c t Glasses with the nominal chemical composition 25Na2O·15B2O3·60SiO2 (mol%) doped with copper and arsenic, antimony, or tin as redox agents were studied by optical absorption spectroscopy in the temperature range from 25 to 620 °C. In general, the redox agents decrease the Cu2+-concentration in the glasses. Increasing the temperature to 620 °C resulted in a shift of the Cu2+ absorption band from 12,600 to 11,800 cm− 1. In glasses solely doped with copper or with copper and tin, the absorptivity decreased by about 5% in that temperature range. In principle, glasses doped with both copper and arsenic or antimony showed the same behaviour up to a temperature of 420 °C. For these glasses, heating to higher temperatures resulted in a minimum at around 540 to 500 °C and a subsequent strong re-increase in absorptivity. During cooling from 620 °C a steep decrease in absorptivity down to a temperature of 520 °C and after passing through a minimum a slight re-increase was observed. The Cu2+ concentration, and hence the absorptivity, after cooling depends on cooling rate (10 to 0.5 K min− 1). © 2010 Elsevier B.V. All rights reserved.
1. Introduction Glass components are considered as polyvalent if they occur in glass melts in different oxidation states. In the case of copper, the occurring species are Cu+ and Cu2+ and in the case of the redox agents arsenic As3+ and As5+, antimony Sb3+ and Sb5+, and tin Sn2+ and Sn4+, respectively. In the studied system, the absorptivities in the visible and NIR range are widely proportional to the Cu2+-concentration. The absorption bands of all the other species are in the UV range and superimposed with the base glass absorption bands. At high temperatures, these polyvalent elements are in equilibrium with the physically dissolved oxygen in the melt [1–4].
A
ðn−zÞ+
+
KA′ ðT Þ z z 2− n+ O2 ⇌ A + O 4 2
ð1Þ
This equilibrium can be described by the equilibrium constant K′A (T), defined as follows:
KA′ ðT Þ =
n+ aA ðn−zÞ+ aA
z= 2
aO2−
z= 4
aO
2
with ai = activity of the respective species. ⁎ Corresponding author. Tel.: +49 3641 9 48501; fax: +49 3641 9 48502. E-mail address: [email protected] (C. Rüssel). 0022-3093/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2010.03.034
ð2Þ
For small total concentrations of A (smaller than 1 mol%), the redox ratio [An+]/[A(n − z)+] does not change with the concentrations. Therefore, the activity coefficients can be considered to be unity (if referenced to infinitely diluted solutions) and the activities be replaced by the respective concentrations. h
An+
i
1 KA ðT Þ = ðn−zÞ+ z = 4 A aO
ð3Þ
2
Then, the equilibrium constant KA(T) depends on the glass composition. As known from literature, KA(T) increases with decreasing temperature for all polyvalent elements studied up to now in glass melts. Thus, if a melt is cooled down, the equilibrium is shifted towards the oxidized species [3–7]. However, the concentration of physically dissolved oxygen in the melt is very small, and hence cooling the melt does not lead to a noticeable increase in the concentration of the oxidized species, if only one redox pair is present. In highly viscous silicate melts, oxygen diffusion is usually a very slow process and does only occur in a noticeable extend, if the cooling rates supplied are very small. Hence in a good approximation, it is justified to assume that in (boro-)silicate melts containing one polyvalent element in a concentration greater than 0.1 mol%, the redox ratio [An+]/[A(n − z)+] remains constant [7] during cooling. However, the redox ratios cannot longer be considered as constant during cooling, if more than one polyvalent element is present. Then, redox reactions between these two polyvalent species might occur during cooling. Redox reactions during changing the temperature
E. Meechoowas et al. / Journal of Non-Crystalline Solids 356 (2010) 2528–2533
have already been reported in the case of soda–lime–silica melts doped with both As2O3 and Fe2O3 using high temperature EPR-spectroscopy [4], and in the systems As3+/As5+/Fe2+/Fe3+ [8], Fe2+/Fe3+/Cu+/Cu2+ [10] and Mn2+/Mn3+/Cr3+/Cr6+ [11,12] by means of high temperature UV–vis–NIR spectroscopy. By analogy, the Sb3+/Sb5+/Cu+/Cu2+- and As3+/As5+/Cu+/Cu2+-systems in a soda–lime–silica melt has been investigated [9,17]. In these studies, it was observed, that the equilibrium shifts with temperature, and below a certain temperature is frozen in. The kinetics of the redox reactions up to now have only been described in the case of a soda–lime–silicate melt doped with manganese and copper [12]. Here also rate constants have been determined. This paper provides a study on the kinetics of a redox reaction between Cu+/Cu2+ and As3+/As5+, Sb3+/Sb5+, or Sn2+/Sn4+ and using high temperature vis–NIR-spectroscopy in a borosilicate glass. The glass composition used is just a model system for some low refractive index borosilicate glasses. 2. Theory
þ
Cu +
As
1 1 2− 2+ O ⇌ Cu + O 4 2 2
ð4Þ
2+
+
1 4+ 2− O ⇌ Sn +O 2 2
ð5aÞ
3+
+
1 5+ 2− O ⇌ As +O 2 2
ð5bÞ
3+
+
1 5+ 2− O ⇌ Sb +O 2 2
ð5cÞ
Sn
Sb
The attributed equilibrium constants Ki(T) (see Eq. (3)) of these reactions depend on temperature. 0
0
0
−RT ln Ki = ΔGi = ΔHi −TΔSi 0
ð6Þ
kþ = KCu = Sb ðT Þ k−
ð9Þ
h h i i 2 2 dx x h þ i x h 2+ i 5+ 3+ Cu Cu = Sb + + x kþ − Sb − −x k− 0 0 0 0 dt 2 2
ð10Þ
with [X]0 equal to the initial concentration values at t = 0. The rate constants k+ and k− depend on temperature according to Arrhenius equation. E kþ = k exp − þ RT ΔS0Cu = Sb R
ð11Þ ! exp −
0 Eþ + ΔHCu = Sb RT
! ð12Þ
with k equal to pre-exponential factor and E+ activation energy of the forward reaction. For small deviations from an equilibrium, ΔC0, the concentration changes according to t ΔC = ΔC0 exp − τ
ð13Þ
with τ equal to the relaxation time which depends on the rate constant and for a reaction order greater than 1 on the concentrations. With Eq. (7), it follows: h i 1 h 2+ i h 3+ i2 3+ Cu + Sb τ = kþ 2 Sb 2 h i 1 h þ i h 5+ i2 5+ Cu + Sb + k− 2 Sb 2
f
ð14Þ
g
−1
Corresponding equations arise for the other redox reactions.
0
with ΔG equal to standard free enthalpy, ΔH equal to standard enthalpy and ΔS0 equal to standard entropy of the assigned redox reactions in the given glass matrix in a state of infinite dilution. If copper and antimony, as an example of the already mentioned redox agents, are simultaneously present in the melt, the following redox reaction with the equilibrium constant KSb/Cu(T) may take place: þ
The kinetics of the reaction according to Eq. (7) are given by the respective rate constants k+ (forward) and k− (backward). The quotient of k+ and k− is equal to the equilibrium constant.
k− = k exp
In melts doped solely with copper, arsenic, antimony, and tin, respectively, the following redox equilibria are formed:
2529
2Cu + Sb
5+
⇌2Cu
2+
+ Sb
3+
ð7Þ
The equilibrium constant KSb/Cu(T) and its temperature dependence can then be calculated from Eq. (6) inserting the values for copper and the respective redox agent (see Refs. [4,6,8]).
! KSb ðT Þ −ΔG0Sb + 2ΔG0Cu = exp RT ðKCu ðT ÞÞ2 ! ! 0 0 0 −ΔHSb + 2ΔHCu ΔSSb −2ΔS0Cu exp = exp RT R
KSb = Cu ðT Þ =
ð8Þ
The equilibrium constant KSb/Cu(T) depends on temperature, if 0 0 ΔHSb ≠ ΔHCu . In that case, also the respective redox ratios [Cu+]/[Cu2+] and [Sb3+]/[Sb5+] depend on temperature.
3. Experimental procedure Glasses with the nominal base composition 25Na2O·15B2O3·60SiO2 (mol%) doped with 1.2 mol% CuO or with 1.2 mol% CuO and 1.2 mol% of the redox agents As2O3, Sb2O3, or SnO were melted from raw materials Na2CO3, B(OH)3, SiO2, CuO, As2O3, Sb2O3 and Sn(COO)2 (all reagent grade from MERCK) in an open to air platinum crucible at a maximum temperature of 1160 °C. The glasses were cast in a graphite mould and then annealed from 570 °C to room temperature. The glass transformation temperature Tg is 554 °C (by thermal expansion measurements). High temperature vis–NIR spectra of these glasses were recorded in the temperature range from 25 to 620 °C in a specially constructed spectrometer. The Cu2+ absorption bands are situated at around 12,000 cm− 1, at the border between visible and NIR range. Thus, it is necessary to exclude experimentally the radiation emitted by the heating chamber of a microscope heating stage (TS 1500, LINCAM, Waterfield, Great Britain) where the sample is placed during the measurements. A halogen lamp was used as light source. The light was reflected by a planar mirror, passed through a chopper (chopper frequency: 113 s− 1) and subsequently the sample. The transmitted light was reflected by 90° using an off-axis parabolic mirror and focused to the entrance slit of a monochromator (TRIAX 320, JobinYvon, Edison, N. Y. USA). The signals collected by an Si-detector were given to a lock-in amplifier (SR830, Stanford Research Systems, Stanford, CA, USA) adjusted to the chopper frequency. A more detailed
2530
E. Meechoowas et al. / Journal of Non-Crystalline Solids 356 (2010) 2528–2533
description of the spectrometer is given in Refs. [8,9]. The samples had a diameter of 6 mm and a thickness of 2 mm. The surfaces were ground and polished to optical quality.
4. Results Fig. 1 shows the vis–NIR spectra recorded at room temperature of the samples doped solely with 1.2 mol% CuO and with both 1.2 mol% CuO and 1.2 mol% As2O3, Sb2O3, or SnO. The Cu2+ concentration in the samples is influenced by the redox agents added. Obviously, SnO has the smallest effect; the Cu2+ concentration is decreased by 33% with respect to the sample without any added redox agent, whereas additional doping with Sb2O3 and As2O3 decreased the Cu2+ concentration by 80% or even more. The shape of the spectrum and the position of the maximum is the same for all four samples. Fig. 2 shows a set of vis–NIR spectra of a sample with 1.2 mol% CuO recorded at temperatures in the range from 25 to 600 °C. All spectra have very similar shape and possess only one maximum attributed to the absorption of Cu2+. With increasing temperature, the position of the maximum of the Cu2+ absorption band is shifted from 12,700 cm− 1 (at 25 °C) to larger wavelengths until at 600 °C a value of 11,800 cm− 1 is reached. The absorptivity at room temperature is 8.8 cm− 1 and then decreases slightly (approximately 5%) in the temperature range studied. A similar behavior is found for the sample doped with CuO and SnO. The absorptivities at maximum position of the Cu2+ absorption band measured at different temperatures during heating and subsequent cooling for samples doped solely with CuO or samples doped with CuO and SnO are shown in Fig. 3. For each of these two samples, the absorptivities at any temperature during heating and cooling are the same within the accuracy of measurement. Above a certain temperature, the samples doped with CuO and As2O3 or Sb2O3 show a different behavior in comparison to the samples mentioned above. Because these two samples are very similar to each other, only the results for the sample doped with 1.2 mol% CuO and 1.2 mol% Sb2O3 are given in detail. In Fig. 4, the absorption spectra of a glass doped with 1.2 mol% CuO and 1.2 mol% Sb2O5 are shown while heating the sample using a rate of 0.5 K min− 1. In the range from 25 to 500 °C, a decrease in the absorptivity was observed, while further increasing temperatures led to a notable re-increase in absorptivity. In Fig. 5, the temperature dependence of the absorptivity at the maximum position of the Cu2+ absorption band is shown for this
sample for different heating rates in the range from 0.5 to 10 K min− 1. Up to 420 °C, the effect of the temperature on the absorptivity is small and does not depend on heating rate. At temperatures above 420 °C, the curves exhibit a minimum in the range from 540 to 570 °C and increases drastically for larger temperatures. The heating rate strongly affects the absorptivity, especially the minimum. The smaller the heating rates, the smaller is the absorptivity at the minimum, i.e. the more pronounced is the minimum. Furthermore, this minimum is shifted to lower temperatures at smaller heating rates. At temperatures more that 30 K larger than that attributed to the minimum, the absorptivity of all samples is approximately equal again, and hence does not depend on the heating rate. The difference of the absorptivity in the respective minima between heating rates of 10 and 0.5 K min− 1 was approximately 0.1 cm− 1. In Fig. 6, vis–NIR absorption spectra of a sample with 1.2 mol% CuO and 1.2 mol% Sb2O3 are shown for different temperatures in the range from 25 to 600 °C. The spectra were recorded during cooling the sample from 620 °C using a rate of 0.5 K min− 1. The absorptivity at 600 °C was much smaller than in the glass only doped with CuO. Furthermore, a steep decrease in absorptivity was observed in the
Fig. 1. Absorption spectra at room temperature of glasses doped with 1.2 mol% CuO (curve A), with 1.2 mol% CuO and 1.2 mol% As2O3 (curve B), with 1.2 mol% CuO and 1.2 mol% Sb2O3 (curve C), and with 1.2 mol% CuO with 1.2 mol% SnO (curve D).
Fig. 3. Absorptivity at maximum position of the Cu2+ absorption band as a function of temperature during heating and subsequent cooling for the sample doped with 1.2 mol% CuO and for the sample doped with 1.2 mol% CuO and 1.2 mol% SnO.
Fig. 2. Absorption spectra of a glass doped with 1.2 mol% CuO at temperatures of 25, 300, 500, 540 and 600 °C.
E. Meechoowas et al. / Journal of Non-Crystalline Solids 356 (2010) 2528–2533
2531
Fig. 4. Absorption spectra of a glass doped with 1.2 mol% CuO and 1.2 mol% Sb2O3 at temperatures of 25, 300, 500, 550 and 600 °C during heating using a rate of 0.5 K min− 1.
Fig. 6. Absorption spectra of a glass doped with 1.2 mol% CuO and 1.2 mol% Sb2O3 at temperatures of 25, 400, 500, 580 and 600 °C during cooling using a rate of 0.5 K min− 1.
temperature range from 600 to 500 °C. During further cooling, a slight decrease in the absorptivity was observed. If larger cooling rates were used, the decrease in absorptivity in the temperature range from 600 to 500 °C was not as large as shown in Fig. 6. The temperature dependence of the absorptivity at the maximum position of the Cu2+ absorption band is shown in Fig. 7 for the glass doped with 1.2 mol% CuO and 1.2 mol% Sb2O3 using cooling rates of 0.5, 1, 5, and 10 Kmin− 1. The cooling rate has a strong effect on the Cu2+ absorptivity: while at temperatures above 570 °C the absorptivities were the same, at lower temperatures larger absorptivities are observed, if larger cooling rates were used. Also the resulting absorptivities at room temperature are larger, if higher cooling rates were supplied. The respective absorptivities are 1.42 (cooling rate 0.5 K min− 1), 1.48 (1 K min− 1), 1.52 (5 K min− 1), and 1.54 cm− 1 (10 K min− 1) for the sample doped with copper and antimony. Fictive freezing temperatures for the redox reaction are given in Table 1. The change of Cu2+ concentration as a function of time for three temperatures in this range is given in Figs. 8 (glass with 1.2 mol% CuO and 1.2 mol% As2O3) and 9 (glass with 1.2 mol% CuO and 1.2 mol% Sb2O3). The respective relaxation times were used to calculate the rate constants k+ for these reactions, an Arrhenius plot of the k+ is given in Fig. 10.
5. Discussion All spectra recorded exhibit a well pronounced absorption peak of Cu2+ which according to the literature [15] is attributed to the 2 E → 2 T2 transition. The dependency of absorption upon wavenumber can fully be described by a fit to a curve of Gaussian shape. The wavenumbers attributed to the peak maximum are slightly shifted to smaller values with increasing temperature as already reported in Refs. [8,13]. In principle, the dependencies of the absorptivity on temperature for T smaller than 450 °C is similar for all glasses studied and during heating and cooling. Since in the glass solely doped with copper the Cu2+-concentration can be considered as constant, the slight decrease in absorptivity is due to the temperature dependence of the molar absorptivity. A similar behaviour has already been reported for the Cu2+ molar absorptivity in soda–lime–silicate glasses [9,10,13]. In the glasses studied, the absorptivities of that solely doped with copper are approximately 50% larger than those in the glass doped with both copper and tin and more than five times larger than those in the glasses doped with both copper and arsenic or antimony. In order to calculate the Cu2+-concentration from Lambert–Beer's law, the molar absorptivity must be known. Unfortunately, the molar absorptivity has
Fig. 5. Absorptivity at maximum position of the Cu2+ band of glass doped with 1.2 mol% CuO and 1.2 mol% Sb2O3 as a function of temperature using different heating rates.
Fig. 7. Absorptivity at maximum position of the Cu2+ band of glass doped with 1.2 mol% CuO and 1.2 mol% Sb2O3 as a function of temperature using different cooling rates.
2532
E. Meechoowas et al. / Journal of Non-Crystalline Solids 356 (2010) 2528–2533
Table 1 Fictive freezing temperatures Tf for the redox reaction in sodium borosilicate glasses doped with 1.2 mol% CuO and 1.2 mol% As2O3 or Sb2O3 as a function of cooling rate. Cooling rate (K min− 1)
0.5 1 5 10
Tf (°C) Cu/As
Cu/Sb
536 542 546 554
539 549 556 560
not yet been determined for the studied glass composition, but according to the literature does not depend much on the base glass composition. Assuming a molar absorptivity of 25 L mol− 1 cm− 1 [16], the Cu2+ concentration is 0.95 mol%. This means 80% of the total copper occurs as Cu2+ in the sample containing solely copper. This value is much larger than those given in the literature for example for soda– lime–silica glasses. It should be noted, however, that the borosilicate glass studied was melted at 1160 °C while the silicate glasses usually were prepared using maximum temperatures in the range from 1450 to 1550 °C. The higher the temperature, the more the equilibrium between Cu+ and Cu2+ is shifted towards the reduced state Cu+ (see Eq. (4)). The glass additionally doped with tin shows the same behaviour at a lower Cu2+ concentration level. It is already known that tin is not such a strongly reducing agent in soda–lime–silica glasses in comparison to arsenic and antimony [16]. On the contrary, the results presented here demonstrate that a redox reaction, according to Eq. (7), 2Cu+ + Sn4+ ⇌ 2Cu2+ + Sn2+ will not occur in a noticeable extend in this sample during heating and cooling. The reaction enthalpy for this reaction was calculated to be only 6 kJmol− 1 in a soda-silica glass [8,14]. It is reasonable to assume that the reaction enthalpy in this sodium borosilicate glass is in the same order of magnitude. Therefore, no evidence for redox relaxation was found for this glass. This is in contrast to Ref. [18], where Sn2+ is described as an effective reducing agent towards Cu+. The decreased Cu2+ concentration in the sample investigated here is the result of the reducing ability of the (tin) oxalate during its thermal decomposition when the glass batch is heated up. As shown in Figs. 5 and 7, the absorptions both during heating and cooling increase strongly at temperatures higher than 550 °C in glasses doped with both copper and antimony or arsenic. This effect is not observed in the glass solely doped with copper or with copper and tin. It proves that in presence of antimony and/or arsenic, a redox
Fig. 8. Absorptivity at maximum position of the Cu2+-absorption band of a glass doped with 1.2 mol% CuO and 1.2 mol% As2O3 as a function of time. The samples were held at 510, 520, and 530 °C.
Fig. 9. Absorptivity at maximum position of the Cu2+-absorption band of a glass doped with 1.2 mol% CuO and 1.2 mol% Sb2O3 as a function of time. The samples were held at 520, 530, and 540 °C.
reaction according to Eq. (7) takes place. As shown in Eq. (8), such a redox reaction should always take place if 2ΔH0Cu ≠ ΔH0Sb. At temperatures lower than 420 °C, the absorptivities did not change much with temperature and the redox reaction can be considered as frozen. In the range between these two temperatures, Cu2+ absorptivities and, hence, the Cu2+ concentrations, depend on heating and cooling rates and, at a constant temperature, on time. A redox relaxation behaviour was first proved experimentally in a soda–lime–silica glass doped with chromium and manganese [9]. From the relaxation times, rate constants of the redox reaction were calculated. The estimated activation energy calculated from these rate constants (535 ± 30 kJmol− 1) was (within the limits of error) in agreement with the activation energy for viscous flow (560 kJmol− 1) in this temperature range. It was concluded that in this case the rate determining step of the redox reaction is the re-arrangement of the coordination spheres around the polyvalent species since, during electron transfer, in the case of chromium the coordination spheres change: Cr3+ occurs in coordination number 6, whereas Cr6+ prefers the coordination number 4. The activation energy for the redox reaction 2Cu+ + As5+ ⇌2Cu2+ + As3+ obtained in a soda–lime–silica glass is only 210 kJmol− 1 [17]. The coordination numbers for arsenic and copper remain the same (As3+/5+: tetrahedral coordination, Cu2+: with respect to c-axis, stretched octahedral coordination [15], Cu+: with respect to c-axis, compressed octahedral coordination [19]) during the redox reaction. Thus, a change in the coordination spheres does not to occur. A redox reaction involves
Fig. 10. Arrhenius plot of the rate constants k+ for the samples doped with 1.2 mol% CuO and 1.2 mol% As2O3 or Sb2O3.
E. Meechoowas et al. / Journal of Non-Crystalline Solids 356 (2010) 2528–2533
two consecutive steps, (i) the diffusion of the species and (ii) the electron transfer. If during cooling, a reaction between As3+ and Cu2+ occurs, the diffusion of Cu2+ should be decisive. Unfortunately, experimentally determined copper diffusion coefficients are not available in literature for these temperatures. However, the calculated activation energy for the redox reaction was in the same order of magnitude as the activation energy of diffusion estimated for Ca2+ as another divalent ion [20]. Then, it can be assumed, that the diffusion of Cu2+ is the rate determining step of the redox reaction. The time dependences of the Cu2+ concentrations at three temperatures in the range between the frozen-in (below 420 °C) and the equilibrium state (above 550 °C) of the redox reactions are given in Fig. 8 for a glass doped with both 1.2 mol% CuO and 1.2 mol% As2O3 and in Fig. 10 for the glass doped both with 1.2 mol% CuO and 1.2 mol% Sb2O3. Eq. (13) was used to calculate the respective relaxation times: 3261 s (510 °C), 2158 s (520 °C) and 1156 s (530 °C) for the glass with arsenic and 7059 s (520 °C), 5128 s (530 °C) and 2620 s (540 °C) for the glass with antimony. Using Eq. (14), rate constants k+ were calculated from these relaxation times: 1.02 · 10− 3, 1.54 · 10− 3 and 2.87 · 10− 3 s− 1 mol%− 3 for the glass with arsenic, and 1.36 · 10− 3, 1.87 · 10− 3 and 3.36 · 10− 3 s− 1 mol%− 3 respectively, for the glass with antimony. An Arrhenius plot of the rate constants k+ is shown in Fig. 10. The attributed activation energies are very similar to each other: 270 kJmol− 1 (Cu/As) and 265 kJmol− 1 (Cu/Sb). These activation energies are slightly larger (by 20%) than that determined for the soda–lime–silica glass but drastically smaller than the activation energy for viscous flow in this sodium borosilicate glass which was calculated to be about 850 kJmol− 1. Thus, it is concluded that the diffusion of Cu2+ is the rate determining step for the redox reactions between copper and arsenic or antimony also in this sodium borosilicate glass. As expected, the results obtained for the sodium borosilicate glass correspond to the results obtained during the investigations of the soda–lime–silica glasses and the already discussed conclusions were confirmed. Cooling experiments with different cooling rates (10 to 0.5 K min− 1) from 620 °C to room temperature result in some new aspects, as shown in Fig. 7: the Cu2+ concentrations at room temperature in the investigated samples depend on cooling rates. The higher the cooling rate, the higher is the Cu2+ concentration at room temperature. In principle, such a course of the cooling curves was already predicted for the soda–lime–silica glass doped with copper and different concentrations of arsenic [17] at cooling rate of 10 K min− 1. Also, fictive redox freezing temperatures were calculated. It was found that with increasing arsenic concentration the fictive redox freezing temperatures are decreased. The fictive freezing temperatures for the two sodium borosilicate glasses under investigation are given in Table 1. With increasing cooling rates, the fictive freezing temperature increases by about 20 K from 536 °C (0.5 K min− 1) to 554 °C (10 K min− 1) for the glass doped with copper and arsenic and from 539 °C to 560 °C for the glass with antimony. The fictive freezing temperature for the soda–lime–silica glasses doped with copper and arsenic and for a cooling rate of 10 K min− 1 are 20 to 50 K higher.
2533
6. Conclusions Sodium borosilicate glasses (25Na2O·15B2O3·60SiO2 (mol%)) doped with copper and one of the redox agents arsenic, antimony, and tin, were studied by high temperature vis–NIR spectroscopy. Glasses doped with both copper and a redox agent showed smaller absorptivities at room temperature than those only doped with copper. During heating the Cu2+ absorptivity is slightly decreased in the glasses only doped with copper and with both copper and tin in the entire studied temperature range. During subsequent cooling these changes are completely reversible. Glasses doped with both copper and arsenic or antimony at low temperatures show the same behavior. But at temperatures above 420 °C, the Cu2+ absorptivity goes through a minimum, and is strongly increased again at temperatures higher than 550 °C. This minimum was more pronounced and shifted to lower temperatures if smaller cooling rates were supplied. This behavior is due to a redox reaction 2Cu2+ + M3+ ⇌ 2Cu+ + M5+ (M: As; Sb). At temperatures lower than 420 °C, this reaction is kinetically frozen in, and at temperatures higher than 550 °C in equilibrium. Between 420 and 550 °C, the kinetics play an important part. Rate constants of the redox reactions were calculated from experimentally determined relaxation times. The calculated rate constants showed Arrhenius behavior. The activation energy was 270 kJmol− 1 (Cu/As) and 265 kJmol− 1 (Cu/Sb), respectively. Thus, the rate determining step should be the diffusion of Cu2+ and not the structural rearrangement. The Cu2+ concentration at room temperature is influenced by the cooling rate from temperatures above 550 °C. The higher the cooling rate, the larger is the Cu2+ concentration in the glass.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
A. Paul, J. Non-Cryst. Solids 71 (1985) 269–278. H.D. Schreiber, A.L. Hockman, J. Am. Ceram. Soc. 70 (1987) 591–594. E. Freude, C. Rüssel, Glastech. Ber. 60 (1987) 202–204. C. Rüssel, Glastech. Ber. 66 (1993) 68–75. C. Rüssel, R. Kohl, H.A. Schaeffer, Glastech. Ber. 61 (1988) 209–213. C. Rüssel, Glastech. Ber. 62 (1989) 199–203. G. Gravanis, C. Rüssel, Glastech. Ber. 62 (1989) 345–350. L. Kido, M. Müller, C. Rüssel, Phys. Chem. Glasses 45 (2004) 21–26. L. Kido, M. Müller, C. Rüssel, Chem. Mater. 17 (2005) 3929–3934. L. Kido, M. Müller, C. Rüssel, J. Non-Cryst. Solids 352 (2006) 4062–4068. C. Rüssel, E. Freude, Phys. Chem. Glasses 30 (1989) 62–68. H. Schirmer, M. Müller, C. Rüssel, Glass Sci. Technol. 76 (2003) 49–55. L. Kido, M. Müller, C. Rüssel, Glass Sci. Technol. 77C (2004) 397–401. O. Claußen, C. Rüssel, A. Matthai, Fundamentals of Glass Sci Technol, Glafö, Växjö, 1997, pp. 57–64. A. Paul, Chemistry of Glass, Chapman and Hall, London, 1990, p. 315. Z.D. Xiang, M. Cable, Phys. Chem. Glasses 38 (1997) 167–172. E. Meechoowas, M. Müller, C. Rüssel, J. Am. Ceram. Soc. 94 (2010) 1032–1038. H. Schreiber, B.T. Bryan, M.C. Dixon, C.W. Schreiber, Ceram. Trans. 109 (2000) 357–365. B.U. Koehler, M. Jansen, Z. Kristallogr. 165 (1983) 313–314. G.H. Frischat, Glastech. Ber. 52 (1979) 143–144.
Contents lists available at ScienceDirect
Journal of Non-Crystalline Solids j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j n o n c r y s o l
Redox relaxation in a sodium borosilicate glass doped with copper and arsenic, antimony, or tin E. Meechoowas, M. Müller, C. Rüssel ⁎ Otto-Schott-Institut, Universität Jena, D-07743 Jena, Germany
a r t i c l e
i n f o
Article history: Received 15 October 2009 Received in revised form 3 February 2010 Available online 3 June 2010 Keywords: Redox reactions; Redox relaxation; Polyvalent ions
a b s t r a c t Glasses with the nominal chemical composition 25Na2O·15B2O3·60SiO2 (mol%) doped with copper and arsenic, antimony, or tin as redox agents were studied by optical absorption spectroscopy in the temperature range from 25 to 620 °C. In general, the redox agents decrease the Cu2+-concentration in the glasses. Increasing the temperature to 620 °C resulted in a shift of the Cu2+ absorption band from 12,600 to 11,800 cm− 1. In glasses solely doped with copper or with copper and tin, the absorptivity decreased by about 5% in that temperature range. In principle, glasses doped with both copper and arsenic or antimony showed the same behaviour up to a temperature of 420 °C. For these glasses, heating to higher temperatures resulted in a minimum at around 540 to 500 °C and a subsequent strong re-increase in absorptivity. During cooling from 620 °C a steep decrease in absorptivity down to a temperature of 520 °C and after passing through a minimum a slight re-increase was observed. The Cu2+ concentration, and hence the absorptivity, after cooling depends on cooling rate (10 to 0.5 K min− 1). © 2010 Elsevier B.V. All rights reserved.
1. Introduction Glass components are considered as polyvalent if they occur in glass melts in different oxidation states. In the case of copper, the occurring species are Cu+ and Cu2+ and in the case of the redox agents arsenic As3+ and As5+, antimony Sb3+ and Sb5+, and tin Sn2+ and Sn4+, respectively. In the studied system, the absorptivities in the visible and NIR range are widely proportional to the Cu2+-concentration. The absorption bands of all the other species are in the UV range and superimposed with the base glass absorption bands. At high temperatures, these polyvalent elements are in equilibrium with the physically dissolved oxygen in the melt [1–4].
A
ðn−zÞ+
+
KA′ ðT Þ z z 2− n+ O2 ⇌ A + O 4 2
ð1Þ
This equilibrium can be described by the equilibrium constant K′A (T), defined as follows:
KA′ ðT Þ =
n+ aA ðn−zÞ+ aA
z= 2
aO2−
z= 4
aO
2
with ai = activity of the respective species. ⁎ Corresponding author. Tel.: +49 3641 9 48501; fax: +49 3641 9 48502. E-mail address: [email protected] (C. Rüssel). 0022-3093/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2010.03.034
ð2Þ
For small total concentrations of A (smaller than 1 mol%), the redox ratio [An+]/[A(n − z)+] does not change with the concentrations. Therefore, the activity coefficients can be considered to be unity (if referenced to infinitely diluted solutions) and the activities be replaced by the respective concentrations. h
An+
i
1 KA ðT Þ = ðn−zÞ+ z = 4 A aO
ð3Þ
2
Then, the equilibrium constant KA(T) depends on the glass composition. As known from literature, KA(T) increases with decreasing temperature for all polyvalent elements studied up to now in glass melts. Thus, if a melt is cooled down, the equilibrium is shifted towards the oxidized species [3–7]. However, the concentration of physically dissolved oxygen in the melt is very small, and hence cooling the melt does not lead to a noticeable increase in the concentration of the oxidized species, if only one redox pair is present. In highly viscous silicate melts, oxygen diffusion is usually a very slow process and does only occur in a noticeable extend, if the cooling rates supplied are very small. Hence in a good approximation, it is justified to assume that in (boro-)silicate melts containing one polyvalent element in a concentration greater than 0.1 mol%, the redox ratio [An+]/[A(n − z)+] remains constant [7] during cooling. However, the redox ratios cannot longer be considered as constant during cooling, if more than one polyvalent element is present. Then, redox reactions between these two polyvalent species might occur during cooling. Redox reactions during changing the temperature
E. Meechoowas et al. / Journal of Non-Crystalline Solids 356 (2010) 2528–2533
have already been reported in the case of soda–lime–silica melts doped with both As2O3 and Fe2O3 using high temperature EPR-spectroscopy [4], and in the systems As3+/As5+/Fe2+/Fe3+ [8], Fe2+/Fe3+/Cu+/Cu2+ [10] and Mn2+/Mn3+/Cr3+/Cr6+ [11,12] by means of high temperature UV–vis–NIR spectroscopy. By analogy, the Sb3+/Sb5+/Cu+/Cu2+- and As3+/As5+/Cu+/Cu2+-systems in a soda–lime–silica melt has been investigated [9,17]. In these studies, it was observed, that the equilibrium shifts with temperature, and below a certain temperature is frozen in. The kinetics of the redox reactions up to now have only been described in the case of a soda–lime–silicate melt doped with manganese and copper [12]. Here also rate constants have been determined. This paper provides a study on the kinetics of a redox reaction between Cu+/Cu2+ and As3+/As5+, Sb3+/Sb5+, or Sn2+/Sn4+ and using high temperature vis–NIR-spectroscopy in a borosilicate glass. The glass composition used is just a model system for some low refractive index borosilicate glasses. 2. Theory
þ
Cu +
As
1 1 2− 2+ O ⇌ Cu + O 4 2 2
ð4Þ
2+
+
1 4+ 2− O ⇌ Sn +O 2 2
ð5aÞ
3+
+
1 5+ 2− O ⇌ As +O 2 2
ð5bÞ
3+
+
1 5+ 2− O ⇌ Sb +O 2 2
ð5cÞ
Sn
Sb
The attributed equilibrium constants Ki(T) (see Eq. (3)) of these reactions depend on temperature. 0
0
0
−RT ln Ki = ΔGi = ΔHi −TΔSi 0
ð6Þ
kþ = KCu = Sb ðT Þ k−
ð9Þ
h h i i 2 2 dx x h þ i x h 2+ i 5+ 3+ Cu Cu = Sb + + x kþ − Sb − −x k− 0 0 0 0 dt 2 2
ð10Þ
with [X]0 equal to the initial concentration values at t = 0. The rate constants k+ and k− depend on temperature according to Arrhenius equation. E kþ = k exp − þ RT ΔS0Cu = Sb R
ð11Þ ! exp −
0 Eþ + ΔHCu = Sb RT
! ð12Þ
with k equal to pre-exponential factor and E+ activation energy of the forward reaction. For small deviations from an equilibrium, ΔC0, the concentration changes according to t ΔC = ΔC0 exp − τ
ð13Þ
with τ equal to the relaxation time which depends on the rate constant and for a reaction order greater than 1 on the concentrations. With Eq. (7), it follows: h i 1 h 2+ i h 3+ i2 3+ Cu + Sb τ = kþ 2 Sb 2 h i 1 h þ i h 5+ i2 5+ Cu + Sb + k− 2 Sb 2
f
ð14Þ
g
−1
Corresponding equations arise for the other redox reactions.
0
with ΔG equal to standard free enthalpy, ΔH equal to standard enthalpy and ΔS0 equal to standard entropy of the assigned redox reactions in the given glass matrix in a state of infinite dilution. If copper and antimony, as an example of the already mentioned redox agents, are simultaneously present in the melt, the following redox reaction with the equilibrium constant KSb/Cu(T) may take place: þ
The kinetics of the reaction according to Eq. (7) are given by the respective rate constants k+ (forward) and k− (backward). The quotient of k+ and k− is equal to the equilibrium constant.
k− = k exp
In melts doped solely with copper, arsenic, antimony, and tin, respectively, the following redox equilibria are formed:
2529
2Cu + Sb
5+
⇌2Cu
2+
+ Sb
3+
ð7Þ
The equilibrium constant KSb/Cu(T) and its temperature dependence can then be calculated from Eq. (6) inserting the values for copper and the respective redox agent (see Refs. [4,6,8]).
! KSb ðT Þ −ΔG0Sb + 2ΔG0Cu = exp RT ðKCu ðT ÞÞ2 ! ! 0 0 0 −ΔHSb + 2ΔHCu ΔSSb −2ΔS0Cu exp = exp RT R
KSb = Cu ðT Þ =
ð8Þ
The equilibrium constant KSb/Cu(T) depends on temperature, if 0 0 ΔHSb ≠ ΔHCu . In that case, also the respective redox ratios [Cu+]/[Cu2+] and [Sb3+]/[Sb5+] depend on temperature.
3. Experimental procedure Glasses with the nominal base composition 25Na2O·15B2O3·60SiO2 (mol%) doped with 1.2 mol% CuO or with 1.2 mol% CuO and 1.2 mol% of the redox agents As2O3, Sb2O3, or SnO were melted from raw materials Na2CO3, B(OH)3, SiO2, CuO, As2O3, Sb2O3 and Sn(COO)2 (all reagent grade from MERCK) in an open to air platinum crucible at a maximum temperature of 1160 °C. The glasses were cast in a graphite mould and then annealed from 570 °C to room temperature. The glass transformation temperature Tg is 554 °C (by thermal expansion measurements). High temperature vis–NIR spectra of these glasses were recorded in the temperature range from 25 to 620 °C in a specially constructed spectrometer. The Cu2+ absorption bands are situated at around 12,000 cm− 1, at the border between visible and NIR range. Thus, it is necessary to exclude experimentally the radiation emitted by the heating chamber of a microscope heating stage (TS 1500, LINCAM, Waterfield, Great Britain) where the sample is placed during the measurements. A halogen lamp was used as light source. The light was reflected by a planar mirror, passed through a chopper (chopper frequency: 113 s− 1) and subsequently the sample. The transmitted light was reflected by 90° using an off-axis parabolic mirror and focused to the entrance slit of a monochromator (TRIAX 320, JobinYvon, Edison, N. Y. USA). The signals collected by an Si-detector were given to a lock-in amplifier (SR830, Stanford Research Systems, Stanford, CA, USA) adjusted to the chopper frequency. A more detailed
2530
E. Meechoowas et al. / Journal of Non-Crystalline Solids 356 (2010) 2528–2533
description of the spectrometer is given in Refs. [8,9]. The samples had a diameter of 6 mm and a thickness of 2 mm. The surfaces were ground and polished to optical quality.
4. Results Fig. 1 shows the vis–NIR spectra recorded at room temperature of the samples doped solely with 1.2 mol% CuO and with both 1.2 mol% CuO and 1.2 mol% As2O3, Sb2O3, or SnO. The Cu2+ concentration in the samples is influenced by the redox agents added. Obviously, SnO has the smallest effect; the Cu2+ concentration is decreased by 33% with respect to the sample without any added redox agent, whereas additional doping with Sb2O3 and As2O3 decreased the Cu2+ concentration by 80% or even more. The shape of the spectrum and the position of the maximum is the same for all four samples. Fig. 2 shows a set of vis–NIR spectra of a sample with 1.2 mol% CuO recorded at temperatures in the range from 25 to 600 °C. All spectra have very similar shape and possess only one maximum attributed to the absorption of Cu2+. With increasing temperature, the position of the maximum of the Cu2+ absorption band is shifted from 12,700 cm− 1 (at 25 °C) to larger wavelengths until at 600 °C a value of 11,800 cm− 1 is reached. The absorptivity at room temperature is 8.8 cm− 1 and then decreases slightly (approximately 5%) in the temperature range studied. A similar behavior is found for the sample doped with CuO and SnO. The absorptivities at maximum position of the Cu2+ absorption band measured at different temperatures during heating and subsequent cooling for samples doped solely with CuO or samples doped with CuO and SnO are shown in Fig. 3. For each of these two samples, the absorptivities at any temperature during heating and cooling are the same within the accuracy of measurement. Above a certain temperature, the samples doped with CuO and As2O3 or Sb2O3 show a different behavior in comparison to the samples mentioned above. Because these two samples are very similar to each other, only the results for the sample doped with 1.2 mol% CuO and 1.2 mol% Sb2O3 are given in detail. In Fig. 4, the absorption spectra of a glass doped with 1.2 mol% CuO and 1.2 mol% Sb2O5 are shown while heating the sample using a rate of 0.5 K min− 1. In the range from 25 to 500 °C, a decrease in the absorptivity was observed, while further increasing temperatures led to a notable re-increase in absorptivity. In Fig. 5, the temperature dependence of the absorptivity at the maximum position of the Cu2+ absorption band is shown for this
sample for different heating rates in the range from 0.5 to 10 K min− 1. Up to 420 °C, the effect of the temperature on the absorptivity is small and does not depend on heating rate. At temperatures above 420 °C, the curves exhibit a minimum in the range from 540 to 570 °C and increases drastically for larger temperatures. The heating rate strongly affects the absorptivity, especially the minimum. The smaller the heating rates, the smaller is the absorptivity at the minimum, i.e. the more pronounced is the minimum. Furthermore, this minimum is shifted to lower temperatures at smaller heating rates. At temperatures more that 30 K larger than that attributed to the minimum, the absorptivity of all samples is approximately equal again, and hence does not depend on the heating rate. The difference of the absorptivity in the respective minima between heating rates of 10 and 0.5 K min− 1 was approximately 0.1 cm− 1. In Fig. 6, vis–NIR absorption spectra of a sample with 1.2 mol% CuO and 1.2 mol% Sb2O3 are shown for different temperatures in the range from 25 to 600 °C. The spectra were recorded during cooling the sample from 620 °C using a rate of 0.5 K min− 1. The absorptivity at 600 °C was much smaller than in the glass only doped with CuO. Furthermore, a steep decrease in absorptivity was observed in the
Fig. 1. Absorption spectra at room temperature of glasses doped with 1.2 mol% CuO (curve A), with 1.2 mol% CuO and 1.2 mol% As2O3 (curve B), with 1.2 mol% CuO and 1.2 mol% Sb2O3 (curve C), and with 1.2 mol% CuO with 1.2 mol% SnO (curve D).
Fig. 3. Absorptivity at maximum position of the Cu2+ absorption band as a function of temperature during heating and subsequent cooling for the sample doped with 1.2 mol% CuO and for the sample doped with 1.2 mol% CuO and 1.2 mol% SnO.
Fig. 2. Absorption spectra of a glass doped with 1.2 mol% CuO at temperatures of 25, 300, 500, 540 and 600 °C.
E. Meechoowas et al. / Journal of Non-Crystalline Solids 356 (2010) 2528–2533
2531
Fig. 4. Absorption spectra of a glass doped with 1.2 mol% CuO and 1.2 mol% Sb2O3 at temperatures of 25, 300, 500, 550 and 600 °C during heating using a rate of 0.5 K min− 1.
Fig. 6. Absorption spectra of a glass doped with 1.2 mol% CuO and 1.2 mol% Sb2O3 at temperatures of 25, 400, 500, 580 and 600 °C during cooling using a rate of 0.5 K min− 1.
temperature range from 600 to 500 °C. During further cooling, a slight decrease in the absorptivity was observed. If larger cooling rates were used, the decrease in absorptivity in the temperature range from 600 to 500 °C was not as large as shown in Fig. 6. The temperature dependence of the absorptivity at the maximum position of the Cu2+ absorption band is shown in Fig. 7 for the glass doped with 1.2 mol% CuO and 1.2 mol% Sb2O3 using cooling rates of 0.5, 1, 5, and 10 Kmin− 1. The cooling rate has a strong effect on the Cu2+ absorptivity: while at temperatures above 570 °C the absorptivities were the same, at lower temperatures larger absorptivities are observed, if larger cooling rates were used. Also the resulting absorptivities at room temperature are larger, if higher cooling rates were supplied. The respective absorptivities are 1.42 (cooling rate 0.5 K min− 1), 1.48 (1 K min− 1), 1.52 (5 K min− 1), and 1.54 cm− 1 (10 K min− 1) for the sample doped with copper and antimony. Fictive freezing temperatures for the redox reaction are given in Table 1. The change of Cu2+ concentration as a function of time for three temperatures in this range is given in Figs. 8 (glass with 1.2 mol% CuO and 1.2 mol% As2O3) and 9 (glass with 1.2 mol% CuO and 1.2 mol% Sb2O3). The respective relaxation times were used to calculate the rate constants k+ for these reactions, an Arrhenius plot of the k+ is given in Fig. 10.
5. Discussion All spectra recorded exhibit a well pronounced absorption peak of Cu2+ which according to the literature [15] is attributed to the 2 E → 2 T2 transition. The dependency of absorption upon wavenumber can fully be described by a fit to a curve of Gaussian shape. The wavenumbers attributed to the peak maximum are slightly shifted to smaller values with increasing temperature as already reported in Refs. [8,13]. In principle, the dependencies of the absorptivity on temperature for T smaller than 450 °C is similar for all glasses studied and during heating and cooling. Since in the glass solely doped with copper the Cu2+-concentration can be considered as constant, the slight decrease in absorptivity is due to the temperature dependence of the molar absorptivity. A similar behaviour has already been reported for the Cu2+ molar absorptivity in soda–lime–silicate glasses [9,10,13]. In the glasses studied, the absorptivities of that solely doped with copper are approximately 50% larger than those in the glass doped with both copper and tin and more than five times larger than those in the glasses doped with both copper and arsenic or antimony. In order to calculate the Cu2+-concentration from Lambert–Beer's law, the molar absorptivity must be known. Unfortunately, the molar absorptivity has
Fig. 5. Absorptivity at maximum position of the Cu2+ band of glass doped with 1.2 mol% CuO and 1.2 mol% Sb2O3 as a function of temperature using different heating rates.
Fig. 7. Absorptivity at maximum position of the Cu2+ band of glass doped with 1.2 mol% CuO and 1.2 mol% Sb2O3 as a function of temperature using different cooling rates.
2532
E. Meechoowas et al. / Journal of Non-Crystalline Solids 356 (2010) 2528–2533
Table 1 Fictive freezing temperatures Tf for the redox reaction in sodium borosilicate glasses doped with 1.2 mol% CuO and 1.2 mol% As2O3 or Sb2O3 as a function of cooling rate. Cooling rate (K min− 1)
0.5 1 5 10
Tf (°C) Cu/As
Cu/Sb
536 542 546 554
539 549 556 560
not yet been determined for the studied glass composition, but according to the literature does not depend much on the base glass composition. Assuming a molar absorptivity of 25 L mol− 1 cm− 1 [16], the Cu2+ concentration is 0.95 mol%. This means 80% of the total copper occurs as Cu2+ in the sample containing solely copper. This value is much larger than those given in the literature for example for soda– lime–silica glasses. It should be noted, however, that the borosilicate glass studied was melted at 1160 °C while the silicate glasses usually were prepared using maximum temperatures in the range from 1450 to 1550 °C. The higher the temperature, the more the equilibrium between Cu+ and Cu2+ is shifted towards the reduced state Cu+ (see Eq. (4)). The glass additionally doped with tin shows the same behaviour at a lower Cu2+ concentration level. It is already known that tin is not such a strongly reducing agent in soda–lime–silica glasses in comparison to arsenic and antimony [16]. On the contrary, the results presented here demonstrate that a redox reaction, according to Eq. (7), 2Cu+ + Sn4+ ⇌ 2Cu2+ + Sn2+ will not occur in a noticeable extend in this sample during heating and cooling. The reaction enthalpy for this reaction was calculated to be only 6 kJmol− 1 in a soda-silica glass [8,14]. It is reasonable to assume that the reaction enthalpy in this sodium borosilicate glass is in the same order of magnitude. Therefore, no evidence for redox relaxation was found for this glass. This is in contrast to Ref. [18], where Sn2+ is described as an effective reducing agent towards Cu+. The decreased Cu2+ concentration in the sample investigated here is the result of the reducing ability of the (tin) oxalate during its thermal decomposition when the glass batch is heated up. As shown in Figs. 5 and 7, the absorptions both during heating and cooling increase strongly at temperatures higher than 550 °C in glasses doped with both copper and antimony or arsenic. This effect is not observed in the glass solely doped with copper or with copper and tin. It proves that in presence of antimony and/or arsenic, a redox
Fig. 8. Absorptivity at maximum position of the Cu2+-absorption band of a glass doped with 1.2 mol% CuO and 1.2 mol% As2O3 as a function of time. The samples were held at 510, 520, and 530 °C.
Fig. 9. Absorptivity at maximum position of the Cu2+-absorption band of a glass doped with 1.2 mol% CuO and 1.2 mol% Sb2O3 as a function of time. The samples were held at 520, 530, and 540 °C.
reaction according to Eq. (7) takes place. As shown in Eq. (8), such a redox reaction should always take place if 2ΔH0Cu ≠ ΔH0Sb. At temperatures lower than 420 °C, the absorptivities did not change much with temperature and the redox reaction can be considered as frozen. In the range between these two temperatures, Cu2+ absorptivities and, hence, the Cu2+ concentrations, depend on heating and cooling rates and, at a constant temperature, on time. A redox relaxation behaviour was first proved experimentally in a soda–lime–silica glass doped with chromium and manganese [9]. From the relaxation times, rate constants of the redox reaction were calculated. The estimated activation energy calculated from these rate constants (535 ± 30 kJmol− 1) was (within the limits of error) in agreement with the activation energy for viscous flow (560 kJmol− 1) in this temperature range. It was concluded that in this case the rate determining step of the redox reaction is the re-arrangement of the coordination spheres around the polyvalent species since, during electron transfer, in the case of chromium the coordination spheres change: Cr3+ occurs in coordination number 6, whereas Cr6+ prefers the coordination number 4. The activation energy for the redox reaction 2Cu+ + As5+ ⇌2Cu2+ + As3+ obtained in a soda–lime–silica glass is only 210 kJmol− 1 [17]. The coordination numbers for arsenic and copper remain the same (As3+/5+: tetrahedral coordination, Cu2+: with respect to c-axis, stretched octahedral coordination [15], Cu+: with respect to c-axis, compressed octahedral coordination [19]) during the redox reaction. Thus, a change in the coordination spheres does not to occur. A redox reaction involves
Fig. 10. Arrhenius plot of the rate constants k+ for the samples doped with 1.2 mol% CuO and 1.2 mol% As2O3 or Sb2O3.
E. Meechoowas et al. / Journal of Non-Crystalline Solids 356 (2010) 2528–2533
two consecutive steps, (i) the diffusion of the species and (ii) the electron transfer. If during cooling, a reaction between As3+ and Cu2+ occurs, the diffusion of Cu2+ should be decisive. Unfortunately, experimentally determined copper diffusion coefficients are not available in literature for these temperatures. However, the calculated activation energy for the redox reaction was in the same order of magnitude as the activation energy of diffusion estimated for Ca2+ as another divalent ion [20]. Then, it can be assumed, that the diffusion of Cu2+ is the rate determining step of the redox reaction. The time dependences of the Cu2+ concentrations at three temperatures in the range between the frozen-in (below 420 °C) and the equilibrium state (above 550 °C) of the redox reactions are given in Fig. 8 for a glass doped with both 1.2 mol% CuO and 1.2 mol% As2O3 and in Fig. 10 for the glass doped both with 1.2 mol% CuO and 1.2 mol% Sb2O3. Eq. (13) was used to calculate the respective relaxation times: 3261 s (510 °C), 2158 s (520 °C) and 1156 s (530 °C) for the glass with arsenic and 7059 s (520 °C), 5128 s (530 °C) and 2620 s (540 °C) for the glass with antimony. Using Eq. (14), rate constants k+ were calculated from these relaxation times: 1.02 · 10− 3, 1.54 · 10− 3 and 2.87 · 10− 3 s− 1 mol%− 3 for the glass with arsenic, and 1.36 · 10− 3, 1.87 · 10− 3 and 3.36 · 10− 3 s− 1 mol%− 3 respectively, for the glass with antimony. An Arrhenius plot of the rate constants k+ is shown in Fig. 10. The attributed activation energies are very similar to each other: 270 kJmol− 1 (Cu/As) and 265 kJmol− 1 (Cu/Sb). These activation energies are slightly larger (by 20%) than that determined for the soda–lime–silica glass but drastically smaller than the activation energy for viscous flow in this sodium borosilicate glass which was calculated to be about 850 kJmol− 1. Thus, it is concluded that the diffusion of Cu2+ is the rate determining step for the redox reactions between copper and arsenic or antimony also in this sodium borosilicate glass. As expected, the results obtained for the sodium borosilicate glass correspond to the results obtained during the investigations of the soda–lime–silica glasses and the already discussed conclusions were confirmed. Cooling experiments with different cooling rates (10 to 0.5 K min− 1) from 620 °C to room temperature result in some new aspects, as shown in Fig. 7: the Cu2+ concentrations at room temperature in the investigated samples depend on cooling rates. The higher the cooling rate, the higher is the Cu2+ concentration at room temperature. In principle, such a course of the cooling curves was already predicted for the soda–lime–silica glass doped with copper and different concentrations of arsenic [17] at cooling rate of 10 K min− 1. Also, fictive redox freezing temperatures were calculated. It was found that with increasing arsenic concentration the fictive redox freezing temperatures are decreased. The fictive freezing temperatures for the two sodium borosilicate glasses under investigation are given in Table 1. With increasing cooling rates, the fictive freezing temperature increases by about 20 K from 536 °C (0.5 K min− 1) to 554 °C (10 K min− 1) for the glass doped with copper and arsenic and from 539 °C to 560 °C for the glass with antimony. The fictive freezing temperature for the soda–lime–silica glasses doped with copper and arsenic and for a cooling rate of 10 K min− 1 are 20 to 50 K higher.
2533
6. Conclusions Sodium borosilicate glasses (25Na2O·15B2O3·60SiO2 (mol%)) doped with copper and one of the redox agents arsenic, antimony, and tin, were studied by high temperature vis–NIR spectroscopy. Glasses doped with both copper and a redox agent showed smaller absorptivities at room temperature than those only doped with copper. During heating the Cu2+ absorptivity is slightly decreased in the glasses only doped with copper and with both copper and tin in the entire studied temperature range. During subsequent cooling these changes are completely reversible. Glasses doped with both copper and arsenic or antimony at low temperatures show the same behavior. But at temperatures above 420 °C, the Cu2+ absorptivity goes through a minimum, and is strongly increased again at temperatures higher than 550 °C. This minimum was more pronounced and shifted to lower temperatures if smaller cooling rates were supplied. This behavior is due to a redox reaction 2Cu2+ + M3+ ⇌ 2Cu+ + M5+ (M: As; Sb). At temperatures lower than 420 °C, this reaction is kinetically frozen in, and at temperatures higher than 550 °C in equilibrium. Between 420 and 550 °C, the kinetics play an important part. Rate constants of the redox reactions were calculated from experimentally determined relaxation times. The calculated rate constants showed Arrhenius behavior. The activation energy was 270 kJmol− 1 (Cu/As) and 265 kJmol− 1 (Cu/Sb), respectively. Thus, the rate determining step should be the diffusion of Cu2+ and not the structural rearrangement. The Cu2+ concentration at room temperature is influenced by the cooling rate from temperatures above 550 °C. The higher the cooling rate, the larger is the Cu2+ concentration in the glass.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
A. Paul, J. Non-Cryst. Solids 71 (1985) 269–278. H.D. Schreiber, A.L. Hockman, J. Am. Ceram. Soc. 70 (1987) 591–594. E. Freude, C. Rüssel, Glastech. Ber. 60 (1987) 202–204. C. Rüssel, Glastech. Ber. 66 (1993) 68–75. C. Rüssel, R. Kohl, H.A. Schaeffer, Glastech. Ber. 61 (1988) 209–213. C. Rüssel, Glastech. Ber. 62 (1989) 199–203. G. Gravanis, C. Rüssel, Glastech. Ber. 62 (1989) 345–350. L. Kido, M. Müller, C. Rüssel, Phys. Chem. Glasses 45 (2004) 21–26. L. Kido, M. Müller, C. Rüssel, Chem. Mater. 17 (2005) 3929–3934. L. Kido, M. Müller, C. Rüssel, J. Non-Cryst. Solids 352 (2006) 4062–4068. C. Rüssel, E. Freude, Phys. Chem. Glasses 30 (1989) 62–68. H. Schirmer, M. Müller, C. Rüssel, Glass Sci. Technol. 76 (2003) 49–55. L. Kido, M. Müller, C. Rüssel, Glass Sci. Technol. 77C (2004) 397–401. O. Claußen, C. Rüssel, A. Matthai, Fundamentals of Glass Sci Technol, Glafö, Växjö, 1997, pp. 57–64. A. Paul, Chemistry of Glass, Chapman and Hall, London, 1990, p. 315. Z.D. Xiang, M. Cable, Phys. Chem. Glasses 38 (1997) 167–172. E. Meechoowas, M. Müller, C. Rüssel, J. Am. Ceram. Soc. 94 (2010) 1032–1038. H. Schreiber, B.T. Bryan, M.C. Dixon, C.W. Schreiber, Ceram. Trans. 109 (2000) 357–365. B.U. Koehler, M. Jansen, Z. Kristallogr. 165 (1983) 313–314. G.H. Frischat, Glastech. Ber. 52 (1979) 143–144.