Diffusion of Cations in Sodium Potassium and Sodium Barium Silicate ...

ISSN 10876596, Glass Physics and Chemistry, 2013, Vol. 39, No. 2, pp. 130–135. © Pleiades Publishing, Ltd., 2013. Original Russian Text © S.I. Sviridov, 2013, published in Fizika i Khimiya Stekla.

Diffusion of Cations in SodiumPotassium and SodiumBarium Silicate Melts S. I. Sviridov Grebenshchikov Institute of Silicate Chemistry, Russian Academy of Sciences, St. Petersburg, 199155 Russia email: sviridov@isc.nw.ru Received November 1, 2011

Abstract—Diffusion coefficients of sodium and potassium ions in molten glasses with the composition (25 ⎯ x)Na2O · xK2O · 75SiO2 have been determined by the sectioning method with measurement of the residual activity 22Na and 42K isotopes. Diffusion of sodium and 133Ba ions has been studied in melts of the (30 ⎯ x)Na2O · xBaO · 5Ga2O3 · 65SiO2 system. It has been found that the concentration dependences of dif fusion characteristics in melts containing alkali and alkalineearth cations principally differ from the regular ities diffusion in dialkali melts. Keywords: silicate melts, diffusion of alkali and alkalineearth ions, effect of the composition and tempera ture DOI: 10.1134/S1087659613020156

INTRODUCTION

EXPERIMENTAL

It is not possible to solve problems connected with the intensification of the processes of ionexchange hardening [1] and coloration of glass [2] during the creations of the optical media with the regular distri bution of the refraction index—selffocusing fibers, planar waveguides, switches, microlenses, diffraction grids, and other elements of integral optics [3]—with out understanding the regularities of diffusion in oxide glasses and melts. Diffusion processes are important for the technology of metallurgy production [4] during the formation of the glassceramic coatings for the protection of metals from the action of the aggressive media [5]. Among other problems that require the study of diffusion in oxide glasses, one should mention the problem of the utilization of the radioactive waste by their vitrification [6]. Problems of geochemistry and geochronology stimulated the study of diffusion of different elements in volcanic glasses, basalt, and other natural oxide minerals [7].

The study was performed on the samples of glasses of the (25 – x)Na2O · xK2O · 75SiO2 (x = 0, 5, 10, 15, 20, 25 mol %) and (30 – x)Na2O · xBaO · 5Ga2O3 · 65SiO2 (x = 0, 7.5, 15, 22.5, 30 mol %) systems. Glasses were synthesized from chemically pure reagents in a platinum crucible. The results of the chemical analysis indicate that the deviations of the compositions of glasses from the calculated ones do not exceed 1 mol %.

The overwhelming majority of the published exper imental data on diffusion in oxide glasses and melts contains the results of the determination of the diffu sion coefficients of alkali cations, in particular sodium ions. Information about the diffusion mobility of diva lent cations is rather scarce [8]. The task of this work was to systematically study the effect of temperature and composition on the diffu sion characteristics of cations in two glassforming sil icate systems during the equimolecular substitution of the sodium oxide for potassium and barium oxides.

The diffusion coefficients of the sodium, potas sium, and barium ions were determined by the sec tioning method with the measurement of the residual activity of 22Na, 42K, and 133Ba isotopes. The water alcohol solution of the radioactive indicator was put on the polished surface of the cylindrical samples with the diameter of 10 mm and dried and the samples were placed in graphite forms with the active side down. The isothermal exposure in the temperature interval of 800–1100°C was performed in a pressurized cell in the inert atmosphere. To obtain the rather high penetra tion depth (≥100 μm), the diffusion annealing time depending on the temperature, the composition of glasses, and the chemical nature of the cation was var ied from 1 h to 2 months. To obtain a diffusion profile, thin layers were successively polished from the surface, and the residual activity of the sample was measured after the deletion of each layer.

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DIFFUSION OF CATIONS IN SODIUMPOTASSIUM

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5Ga2O3 · 65SiO2 glass after the diffusion annealing at 805°C for 1 h. The diffusion coefficients D* were cal culated according to the equation

1.0 0.8 0.6

⎡ ⎛ ⎞⎤ (1) I ( x, t ) = I 0 ⎢1 − erf ⎜ x ⎟⎥ , ⎜ ⎟⎥ ∗ ⎢⎣ ⎝ 2 D t ⎠⎦ where I is the residual activity of the sample, I0 is the initial activity, t is time, x is the penetration depth, and

I/I0

1

0.4

z 2 erf ( z ) = 2 exp (− y ) d y is the Gaussian error inte π 0 gral. Figure 2 shows the dependences of logarithms of the diffusion coefficients of sodium and barium ions in melts of glasses of the (30 – x)Na2O ⋅ xBaO ⋅ 5Ga2O3 ⋅ 65SiO2 system on the reciprocal temperature. These dependences in the studied temperature interval are satisfactorily described by the Arrhenius equation

∫

2 0.2 0 0

0.5

1.0

1.5

2.0 2.5 x, mm

3.0

3.5

4.0

Fig. 1. Diffusion profiles of (1) sodium and (2) barium ions in 30Na2O ⋅ 5Ga2O3 ⋅ 65SiO2 glass after annealing at 805°C for 1 h.

( )

(2) D = D0 exp Δ H , RT where D0 is the preexponential factor, ΔH is the activa tion enthalpy, R is the gas constant, and T is the abso lute temperature. Similar dependences are also

RESULTS AND DISCUSSION Figure 1 shows the profiles of the residual activity of 22Na and 133Ba in the sample of the 30Na2O · (a)

(b)

–4 –6 1

–5

–7 2

1

–6 log(DBa, cm2/s)

2

log(DNa, cm /s)

–8 3 –7 4 –8

2

–9

3

–10

4

–11

–9 5

5 –12

–10 0.0007

0.0008 0.0009 –1 1/T, K

0.0010

0.0007

0.0008 0.0009 –1 1/T, K

0.0010

Fig. 2. Temperature dependence of the diffusion coefficients of (a) Na+ and (b) Ba2+ ions in the (30 – x)Na2O ⋅ xBaO ⋅ 5Ga2O3 ⋅ 65SiO2 system, where x (mol %) = (1) 0, (2) 7.5, (3) 15, (4) 22.5, (5) 30. GLASS PHYSICS AND CHEMISTRY

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Table 1. Experimental diffusion coefficients of sodium and barium ions and Arrhenius parameters in melts with the com position (30 – x)Na2O ⋅ xBaO ⋅ 5Ga2O3 ⋅ 65SiO2 Diffusion 22Na CBaO, mol % 0 7.5 15 22.5 30

Diffusion 133Ba

log(D0, cm2/s) ΔH, kcal/mol –log(D900°C, cm2/s) log(D0, cm2/s) ΔH, kcal/mol –log(D900°C, cm2/s) –2.24 ± 0.36 –1.44 ± 0.22 0.30 ± 0.63 0.92 ± 0.28 1.17 ± 0.67

14.3 ± 2.0 20.6 ± 1.2 33.3 ± 3.6 39.8 ± 1.5 51.0 ± 3.6

4.91 5.27 5.90 6.50 8.33

0.78 ± 0.40 0.74 ± 0.33 1.90 ± 0.80 2.42 ± 0.56 5.00 ± 0.98

39.9 ± 2.2 41.7 ± 1.8 51.6 ± 4.6 57.9 ± 3.0 80.5 ± 5.3

6.65 7.03 7.71 8.37 10.00

Table 2. Diffusion coefficients of sodium and potassium ions and Arrhenius parameters in melts with the composition (25 – x)Na2O ⋅ xK2O ⋅ 75SiO2 CK2O, mol % 0 5 10 15 20 25

Diffusion 22Na –log(D0, cm2/s)

ΔH, kcal/mol

2.54 ± 0.15 2.66 ± 0.22 2.55 ± 0.19 2.12 ± 0.14 1.72 ± 0.27 1.37 ± 0.26

12.2 ± 0.8 12.7 ± 1.2 14.0 ± 1.0 16.7 ± 0.7 19.1 ± 1.4 21.3 ± 1.4

Diffusion 42K

–log(D900°C, cm2/s) –log(D0, cm2/s) ΔH, kcal/mol –log(D900°C, cm2/s) 4.81 5.03 5.16 5.23 5.28 5.34

observed for diffusion of Na+ and K+ ions in melts of the (25 – x)Na2O ⋅ xK2O ⋅ 75SiO2 system. Parameters of the temperature dependence of the diffusion coeffi cients and the diffusion mobility values of cations at 900°C are given in Tables 1 and 2. Figure 3 shows the dependences of logarithms of the diffusion coefficients and activation enthalpy of diffusion of Na+ and K+ ions in sodiumpotassium sil icate melts. With the equimolecular replacement of Na2O by K2O, the diffusion mobility of sodium ions decreases monotonically, and the mobility of potas sium ions increases. The diffusion coefficients of both ions have the same value in the composition region with nearly the concentration of alkali oxides. The concentration dependences of the activation enthalpy of diffusion have the opposite character. The quanti ties ΔH Na and Δ H K have the minimum values in monoalkali sodium and potassium melts and increase with the introduction of the second alkali oxide. This character of the concentration dependence of the dif fusion parameters is typical for all dialkali oxide glasses and melts [9–11]. Information about the combined study of the diffu sion mobility of the alkali and alkalineearth cations in glasses with the equimolecular substitution of one oxide for another is absent in the literature. Figure 4a shows the concentration dependences * and log DBa * for the temperature of 900°C. The log DNa character of the dependences does not change at other

1.26 ± 0.31 1.58 ± 0.26 1.75 ± 0.22 2.01 ± 0.16 2.33 ± 0.21 2.49 ± 0.18

22.1 ± 1.7 20.1 ± 2.0 18.9 ± 1.3 17.1 ± 1.5 14.8 ± 1.1 12.9 ± 0.9

5.38 5.32 5.27 5.20 5.09 4.89

temperatures. The diffusion coefficient of sodium ions in the 15Na2O ⋅ 15BaO ⋅ 5Ga2O3 ⋅ 65SiO2 glass may be ∗ value in the glass with the com compared with the DNa position Na2O ⋅ BaO ⋅ 4SiO2 [12]. At 1000°C, the * value in these glasses is –5.42 and –5.61, and log DNa the activation enthalpy of diffusion is 33.3 and 34.8 kcal/mol, respectively. It is seen in the figure that the diffusion coefficients of sodium ions decrease monotonically with replacing Na2O by BaO. The decrease in the diffusion mobility of Na+ is probably connected, first, with the total decrease in the number of mobile carriers and increase in the distance between the equilibrium positions of alkali cations. Secondly, it is known that, in a wide temperature interval, the diffusion coefficients of Na+ in glasses containing alkalineearth oxides, are much less than those in binary sodium silicate glasses con taining the same amount of alkali oxide [9, 13]. It has been found that the diffusion coefficient of the alkali ion depends on the ionic radius of the introduced diva lent cation, namely, it decreases with the increase in the latter. An analogous effect was observed in the study of the conductivity in the R2O–RO–SiO2 sys tem [14]. The blocking effect of the doubly charged cations on the exchange of alkali cations in the “glass– molten salt” system was found in [15]. It is possible to suppose that the decrease in the diffusion mobility of sodium ions is mainly due to the mutual effect of the cations.

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DIFFUSION OF CATIONS IN SODIUMPOTASSIUM (a)

133 (b)

25

–4.8

1

–5.0

ΔH, kcal/mol

log(D, cm2/s)

20 2

15

2 1

–5.2

10 –5.4 0

5

10 15 CK O, mol %

20

25

5

0

2

10 15 CK O, mol %

20

25

2

Fig. 3. Dependence of the diffusion coefficients at (a) 900°C and (b) the activation enthalpy of diffusion of (1) Na+ and (2) K+ ions on the composition in (25 – x)Na2O ⋅ xK2O ⋅ 75SiO2 melts.

(b)

(a) 80

–5 1

–6

ΔH, kcal/mol

log(D, cm2/s)

60

–7 2

2

40

–8

1

20

–9

–10

0 0

5

10 15 20 CBaO, mol %

25

0

30

5

10

15 20 CBaO, mol %

25

30

Fig. 4. Dependence of diffusion coefficients at 900°C (a) and the activation enthalpy of diffusion (b) Na+ (1) and Ba2+ (2) ions on the composition in (30 – x)Na2O ⋅ xBaO ⋅ 5Ga2O3 ⋅ 65SiO2 melts. GLASS PHYSICS AND CHEMISTRY

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SVIRIDOV

where α is the geometrical factor that takes into account the number of the equivalent directions of the hopping of atoms, δ is the distance of a single displace ment, ν is the frequency of the thermal vibrations, f is the correlation factor, ΔS and ΔH are the entropy and activation enthalpy of diffusion, respectively, R is the gas constant, and T is the absolute temperature. It is possible to suppose that, under the isothermal condi tions, the geometrical factor α, frequency of the ther mal vibrations ν, distance of a single displacement δ, and correlation factor f do not change strongly during diffusion of different cations. It is possible to estimate the value of the entropy term ΔS during diffusion of different cations by ana lyzing the deviation of the value of the experimental value of the preexponential factor D0e in Eq. (2) from the theoretical value D0T of 1 × 10–3 cm2/s according to [17],

40

ΔS, cal/degree mole

35 30 25 20 15

1 (Na) 2 (K) 3 (Na) 4 (Ba)

10 5 0

10

20

30 40 50 ΔH, kcal/mol

60

70

80

Fig. 5. Dependence of activation entropy of diffusion on the activation enthalpy of diffusion for (1) Na+ and (2) K+ ions in (25 – x)Na2O ⋅ xK2O ⋅ 75SiO2 melts and (3) Na+ and (4) Ba2+ in (30 – x)Na2O ⋅ xBaO ·5Ga2O3 ⋅ 65SiO2 melts.

ΔS = R (ln D0e − ln D0T ) .

It is not possible to compare the concentration dependence of the diffusion coefficients of Ba2+ ions shown in Fig. 4a with any other results since informa tion about the diffusion coefficient of barium is absent in the literature. At the same time, this dependence is not quite usual. As shown above, with replacing one oxide by another in dialkali glasses and melts, the mobility of the substituted cation decreases gradually (Fig. 3a). The diffusion coefficients of Ba2+ have the minimum value in the purely barium glass and increase with increasing concentration of sodium oxide, and, in the whole concentration interval, the mobility of Ba2+ is much less than the mobility of Na+. The comparison of the diffusion coefficients in the 30BaO ⋅ 5Ga2O3 ⋅ 65SiO2 glass shows that the selfdif * is less than the heterodiffusion fusion coefficient DBa * . This relation between the self and coefficient DNa heterodiffusion coefficients is characteristic for met als, semiconductors and ion crystals [16] and was yet not observed for oxide glasses. Figure 4b shows the calculated values of the activa tion enthalpy of diffusion for Na+ and Ba2+ ions depending on the content of barium oxide in the glass. Both values increase monotonically with increasing BaO content in the glass, and, in the whole interval of compositions, the activation enthalpy of diffusion for Ba2+ is larger than that for Na+. The theoretical expression for the temperature dependence of the diffusion coefficient D has the form [16]

( )

D = αδ 2 ν f exp Δ S exp − Δ H , R RT

(3)

(4)

This approach makes it possible to consider the activation entropy of diffusion as the quantity that characterizes the features of the theoretical model of the diffusion processes that were not taken into account before the experiment. In solid glasses, the D0e values for diffusion of intrinsic cations are close to the theoretical value and it is conventionally considered that the migration processes occur entropyless. Nevertheless, the analysis of the log D0e values (Tables 1, 2) shows that, for all studied silicate melts and all cations, log D0e > log D0T . Consequently, accord ing to Eq. (4), the change of the activation entropy of diffusion ΔS is positive and varies from 2 to 8 cal/degree mole for dialkali melts. In melts of glasses that contain alkali and alkalineearth cations, ΔS changes in the interval from 3 to 37 cal/degree mole. Figure 5 shows the dependence of the activation entropy of diffusion on the value of the activation enthalpy of diffusion for different cations in the stud ied glassforming melts. This dependence may be sat isfactorily approximated by a general equation of a direct line. This regularity is apparently a consequence of the socalled compensation law [18] that connects the preexponential factor and the activation enthalpy of diffusion

log D0 = a + bΔ H .

(5)

The parameters of the linear dependence give the Tx and Dx coordinates of a hypothetical crossing point of the temperature dependences of the diffusion coef ficients of different ions (logDx = a, 1/Tx = 2.3Rb). The physical meaning of the compensation law is that the activation entropy increases linearly with increas ing activation enthalpy of diffusion.

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DIFFUSION OF CATIONS IN SODIUMPOTASSIUM

CONCLUSIONS The equimolecular substitution of sodium oxide for K2O in dialkali silicate melts leads to the monotonic decrease in the diffusion coefficients of Na+ and increase in the diffusion coefficients of K+. The oppo site character has been observed for the concentration dependence of the activation enthalpy of diffusion. The concentration dependences of the diffusion parameters in melts that contain alkali and alkaline earth cations principally differ from the regularities of diffusion in dialkali glassforming melts. The replace ment of Na2O by BaO leads to the sharp decrease in the diffusion mobility of Na+ and Ba2+ ions and increase in the activation enthalpy. The mobility of barium ions is less than the mobility of sodium ions in the whole concentration interval. The selfdiffusion

* in the 30BaO ⋅ 5Ga2O3 ⋅ 65SiO2 melt is coefficient DBa *. less than the heterodiffusion coefficient DNa It has been established that the compensation law holds in the studied melts. As a consequence, the acti vation entropy increases linearly with increasing acti vation enthalpy of diffusion. REFERENCES 1. Sobolev, E.V., Tikhomirova, N.E., Chernyakova, T.G., Shcheglova, O.V., and Zhabrev, V.A., Ion Exchange Method in Glass Production, Steklo Keram., 1989, no. 6, pp. 26–29. 2. Peters, E. and Frischat, G.H., Farbionenaustausch an Gläsern unter Wirkung eines Elektrischen Feldes, Glastech. Ber., 1977, vol. 50, no. 4, pp. 63–67. 3. Nikonorov, N.V. and Petrovskii, G.T., IonExchanged Glasses in Integrated Optics: The Current State of Research and Prospects (A Review), Glass Phys. Chem., 1999, vol. 25, no. 1, pp. 16–55. 4. Ukyo, Y. and Goto, K.S., The Interdiffusivity Matrix of Fe2O3–CaO–SiO2 Melt at 1693 to 1773 K, Metall. Trans. B, 1981, vol. 12, no. 3, pp. 449–454. 5. Sviridov, S.I. and Isakov, A.I., Kinetics of the Interac tion in a Layer of Vitreous Coating, in Zharostoikie neorganicheskie pokrytiya. Trudy XIII Vsesoyuznogo soveshchaniya (Proceedings of the XIII AllUnion Workshop “HeatResistant Inorganic Coatings”), Leningrad: Nauka, 1990, pp. 18–22.

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6. Ivanov, I.A., Sedov, V.M., Gulin, A.N., Stefanovskii, S.V., and Shatkov, V.M., Diffusion of Radionuclides in the Glasses Simulating Vitrified Radioactive Wastes, Fiz. Khim. Stekla, 1991, vol. 17, no. 2, pp. 351–354. 7. Hofmann, A.W. and Magaritz, M., Diffusion of Ca, Sr, Ba, and Co in Basalt Melt: Implications for Geochem istry of the Mantle, J. Geophys. Res., 1977, vol. 82, no. 10, pp. 5432–5440. 8. Zhabrev, V.A. and Sviridov, S.I., Ion Diffusion in Oxide Glasses and Melts: I. Bibliography, Glass Phys. Chem., 2003, vol. 29, no. 2, pp. 140–159. 9. Evstrop’ev, K.K., Diffuzionnye protsessy v stekle (Diffu sion Processes in a Glass), Leningrad: Stroiizdat, 1970. 10. Zhabrev, V.A., Diffuzionnye protsessy v steklakh i stek loobrazuyushchikh rasplavakh (Diffusion Processes in Glasses and GlassForming Melts), St. Petersburg: Institute of Silicate Chemistry of the Russian Academy of Sciences, 1998. 11. Frischat, G.H., Ionic Diffusion in Oxide Glasses, Aeder mannsdorf (Switzerland): Trans. Tech. Publ., 1975. 12. Malkin, V.I. and Mogutnov, B.M., SelfDiffusion of Alkali Ions in Silicate Melts, Dokl. Akad. Nauk, 1961, vol. 141, no. 5, pp. 1127–1130. 13. Terai, R. and Kitaoka, T., The Effects of Various Diva lent Ions on the Migration of Sodium Ions in the Sili cate Glasses, J. Ceram. Assoc. Jpn., 1968, vol. 76, no. 11, pp. 393–399. 14. Mazurin, O.V. and Brailovskaya, R.V., Electrical Con ductivity of Glasses in the Na2O–RO–SiO2 System Sov. Phys. Solid State, 1960, vol. 2, no. 7, pp. 1341– 1345. 15. Kolitsch, A., Richter, E., and Hinz, W., Zum Einfluß Geringer Kationisher Verunreinigung auf Alkaliselbst diffusion Zwischen Salzschmelze und Glas, Silikattech nik, 1981, no. 10, pp. 311–312. 16. Mehrer, H., Diffusion in Solids: Fundamentals, Meth ods, Materials, and DiffusionControlled Processes, Ber lin: SpringerVerlag, 2007. Translated under the title Diffuziya v tverdykh telakh, Dolgoprudnyi (Moscow oblast, Russia): Intellekt, 2011. 17. Frenkel, Ya.I., Kineticheskaya teoriya zhidkostei, Len ingrad: Academy of Sciences of the Soviet Union, 1945. Translated under the title Kinetic Theory of Liquids, Oxford: Oxford University Press, 1946. 18. Rüetschi, P., The Relation between Frequency Factor and Activation Energy (Compensation Law), Z. Phys. Chem., Neue Folge, 1958, vol. 14, nos. 5/6, pp. 277– 291. Translated by L. Mosina

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