DISSOLUTION OF SOLIDOXIDES IN OXIDEMELTS
for a Senior Foreign Scientist Fellowship award to R. H. S., during the tenure of which this work was done.
2131
The Office of Saline Water also is thanked for a grant which assisted the experimental work.
Dissolution of Solid Oxides in Oxide Melts. The Rate of Dissolution of Solid Silica in Na,O-SiO, and K,O-SiO, Melts
by Klaus Schwerdtfeger Edgar C. Bain Laboratory for Fundamatal Research, United States Steel Corporation Research Center, Monroeville, Pennsylvania (Received October 36,1966)
The rate of dissolution of solid silica in static sodium and potassium silicate melts was studied in the temperature ranges 1000-1400 and 1000-1200", respectively, and in sodium silicate melt, stirred by a rotating silica disk, at 1400". Concentration profiles obtained in the static melts were measured for selected slag composition and temperature. It is concluded from the experimental data that the dissolution process is controlled by mass transfer in the liquid. Interdiflusivities as calculated from the dissolution rates under static and stirred conditions and as determined from the concentration profiles are consistent with each other.
Introduction The rates of dissolution of solid oxides in oxide melts are of considerable interest for numerous metallurgical and ceramic processes. I n the present work, the rate of dissolution of solid silica in static sodium or potassium silicate melts was studied in the temperature ranges 1000-1400 and 1000-1200", respectively, and in sodium silicate melts, stirred by a rotating silica disk, a t 1400". Previous work on the dissolution of solid silica in liquid sodium metasilicate, as done by Shurygin, Barmin, and Esin' by using the rotating-disk method, revealed that the dissolution process was controlled by mass transport in the liquid. The authors, however, state that their data are only exact to the order of magnitude because of the experimental difficulties encountered in determining the corrosion rate accurately. Experimental Section Methods. Three different experimental methods were
employed for the dissolution of silica into static melts. (a) I n the first method, silica was dissolved from silica plugs placed at the bottom of cylindrically shaped platinum crucibles. With this plug position, convection by density differences is assumed to be avoided since, according to data in the l i t e r a t ~ r e ,the ~ , ~density is lowest in the silica-poorer slag a t the top of the crucible. As an additional precaution to prevent convection currents, the crucible was suspended in a vertical tube furnace at the lower part of the hot zone so that the temperature at the top of the melt was about 3" higher than that at the bottom. After the experiment, the sample was rapidly cooled to room temperature. The platinum crucible was then sliced and the change in thickness of the plug was measured using a cathetometer. In order to have a reference point at the bottom of the plug for the length ~~
~
(1) P. M. Shurygin, L. N. Barmin, and 0.A. Esin, Izv. V ~ s s h i k h . Uchebn. Zavedenii Chernaya Met., 5 , 5 (1962). (2) J. O'M. Bockris, J. W. Tomlinson, and J. L. White, Trans. Faraday SOC.,5 2 , 299 (1956). (3) G . Heidtkamp and K. Endell, Glastech. Ber., 14, 89 (1936).
Volume YO, Number 7 July 1966
KLAUS SCHWERDTFECER
2132
Iem
I------I
-PI
CRUCIBLE
SILICATE
'-SILICA --
-,>-P!
PLUG BEAD
Figure 1. Specimen BS used in this work; L,is the length of the silica plug at the start of the experiment; b is the length of the silica plug at the end of the experiment; (corrosion Y = LI - L,).
measurements, a platinum bead was embedded a t the bottom of the silica plug. A sliced platinum crucible with plug and slag is shown in Figure 1. Since the plugs usually were more attacked a t the side of the crucible, measurements were always taken a t the center of the plug. (b) I n the second method, silica was dissolved from cylindrical silica rods of 8 to 12-mm diameter and 20 to 25-mm length which were placed in the center of a silicate melt contained in a platinum crucible. The upper part of the rod wm protected by a platinum foil to prevent the stronger corrosion a t the slag-air interface. A t low silica contents in the slag and at high temperatures this technique could be used only for limited dissolution times; a t longer r e action times the corrosion of the rod became uneven over the length of the rod. (c) I n the third technique, silica was dissolved from the walls of silica crucibles of -10-mm internal diameter. This technique was also .used to determine the liquidus curve of SiOz in the NsnO-Si02 system by equilibrating the melt with the crucible (equilibration time 2-12 weeks) and by analyzing the slag subsequently. In some experiments done with technique a, the slag was drilled out of the crucible in layers and analyzed chemically for the determination of the concentration profile. Silica concentration near the silica-melt interface was determined using an electron microprobe
analyzer. The necessary electrical conductiveness of the specimen was obtained with a 100-A thick coating of copper. It was found that the concentration in the silicate a t the interface was 86 f 4 wt % SiOt at 140O0, which is the equilibrium value (see next section, Figure 2). I n order to check the data of Shurygin, et al.,' some measurements were made with sodium silicate melts using the rotating-disk technique. The experiments were carried out in a n apparatus which was similar in construction to that described elsewhere.' The faces of silica rods, 1.3 cm in diameter, were used as disks. The sides of the rods were protected by a platinum foil. After the experiment, the adherent slag was easily dissolved in hot water, and the corrosion was determined by measuring the change in length of the rod with a cathetometer. Temperature Control, Materials, and Analysis. The temperatures of all the furnaces used were controlled automatically in the usual manner. Temperatures were measured with a Pt-PtrlO% Rh thermocouple. The reported temperatures are accurate within 1 5 " . Starting materials for the slags were reagent grade sodium metasilicate, potassium hydroxide, silicic acid, and North Carolina quartz sand. The sodium silicates were prepared by first dehydrating the commercial sodium metasilicate which was then mixed with the desired amount of North Carolina quartz sand and fused. The potassium silicates were prepared by dissolving silicic acid in an aqueous potassium hydroxide solution and by evaporating the obtained solution to dryness. About half of the slag samples used were premelted under vacuum, although no difference in the results was found when such a treatment was not applied. I n order to make slag and solid silica better distinguishable for the measurement of the corrosion thickness, the slags were colored blue with an addition of 4 . 1 % coo. The silica plugs and rods or crucibles were made from translucent quartz glass rod or tubing, respectively. During the experiment, the quartz glass crystallized to cristobalite (as identified by an X-ray test) in a layer adjacent to the slag. The samples were analyzed for SiO, by the conventional dehydration method in the concentration range 50 to 65% Si02 with an accuracy of *l%. A t higher SiO, contents, NsnO or KzO contents were analyzed by a modified technique, because of a decreased accuracy of the SiOl dehydration method. The procedure was first to evaporate all the silica with an HF-HzS04 mix(4) R. G. Olason. V. Koump. and T. F. Perzak. Tlonr. Met. Soc. A I M E , in press.
DISSOLUTION OF SOLIDOXIDESIN OXIDEMELTS
2133
1400
e
!a 3EW w 8-
twcln) Figure 3. The dissolution of solid silica in static NazO-Si02 melts a t 1000°.
1100~
-0,40
wo.
" I
N020-SlO2, 1200'C
.
ca ( w t % Si&) ROD 50 PLUG 50 0 ROD 60 A ROD 70 A CRUCIBLE 70 0
-0.30
?o
to c-NatO
00
*I SIO,
eo
~
Hx)
s14
Figure 2. The liquidus curve of silica in the system "0-SiOp.
c.
E -0"
0
ture and then to convert the residue, by evaporating excess H2S04and HzO, to Na2S04or K2S04,which was determined gravimetrically. This method yielded a reproducibility of *0.2% or better. Its reliability was checked with standard samples made up from Na2C03,KzC03, :tnd North Carolina quartz sand.
Results and Discussion Dissolution of Silica in a Static Semiinfinite Medium of Sodium or Potassium Silica Melt. Sodium Silicate Melts. Figure 2 shows the results of the equilibrium measurements to determine the liquidus curve of SiOz together with tho same curve as obtained by Kraceka5 Good agreement exists between both curves within 1% or better. The results of the dissolution experiments are given in Figures 3, 4,and 5 where the change in the length ( Y ) of silica plug, the radius of silica rod, or the wall thickness of the silica crucible is plotted against the square root of reaction time for 1000, 1200, and 1400", respectively. Within the limits of experimental error, the plots of distance Y vs. t'/' may be taken to be linear, suggesting a diff usion-controlled rate of silica dissolution. Figure 6 shows the silica concentration profile in a selected slag at 1200" as a function of the
0
100
200
"tc
300
400
'I2 1
Figure 4. The dissolution of solid silica in static NasO-Si02 melts a t 1200'.
parameter y/tl", where y is the distance in the melt from the original position of the interface. The curve depicting the profile is drawn such that the shaded areas on either side of the initial interface are equal. Interdiffusivities (D)may be calculated from the dissolution rate using expression 1 (Equation 1 is strictly valid only for diffusion into a semiinfinite medium with a plane source. However, if in the case of cylindrical sources (cylindrical rods, hollow cylinder) Y is small ( 5 ) F. C . Kracek, J.Phys. Chem., 34, 1583 (1930); J . Am. Chem. SOC., 61,2863 (1939).
Volume 70, Number 7 July 1966
KLAUS SCHWERDTFEGER
2134
ROD PLUG 0 ROD
0
-0.30
0
50 50 60
1 -0.20 * 0 -0.10
0
0
$00
t'f2(a 112 )
Figure 5. The dissolution of solid silica in static NazO-SiOZ melb at 1400".
where z = Y/2fit1 ci is the concentration of silica a t the interface (= equilibrium concentration), c, is the concentration of silica in the bulk melt, and c. is the concentration of silica in solid silica. This equation may be derived for the present conditions from the general equations as given by Danckwertss for diffusion into a semiinfinite medium involving a moving phase boundary. Density dserences2v3in the melt and between melt and solid silica are small and may be neglected. All concentrations may be taken in wt %. Equation 1 applies for the case of concentration-independent interdiff usivity. Hence, if the interdiffusivity varies with concentration, D as obtained with (1) is an average interdsusivity for the concentration range c, to ci. An approximate interdiff usivity-concentration relationship may be obtained by relating D values obtained for various c, to the corresponding average compositions c' = (c, ci)/2. Table I contains the obtained D values. As would be expected, D increases with decreasing silica content and increasing temperature. The accuracy of the reported log D values is in the order of h0.2 as was estimated from the uncertainties of the Y/l/t values and from an assumed error of f1%in the concentrations.
+
Table I: The Dissolution of Silica in Static Na20-SiOz Melts Temp,
c,
Ci
--we
% sio+--
1000
77.2
60.0 70.0
1200
79.5
1400
86.7
oc
c'
Y/di,
Log D, D in cmz
cm 8ec -'/2
8ec -1
68.6 73.6
-1.4 X lo-' -0.6 X lo-'
-7.25 -7.40
50.0 60.0 70.0
64.7 69.7 74.7
-6.4 X -3.5 X -1.3 X
lo-' lo-'
-6.30 -6.59 -7.00
50.0 60.0 70.0
68.3 73.3 78.3
- 8 . 1 X lo-' -5.2 X -2.6 X lo-'
-6.39 -6.64 -7.00
ci is the silica concentration in the melt a t the interface (= equilibriumvalue). c, is the silica concentration in the bulk
melt. c' = (ci
+ cm)/2.
y / ~ r (cm mc+*) Figure 6. Concentration profile in static sodium silicate melt (c, = 50y0 SiOl, 1200").
compared to the radius, eq 1 is also a good approximat,ion for these cases.) The Journal of Physical Chemistru
Interdiff usivities may be obtained from the concentration profile in the range 52-56% SiOz for 1200" (Figure 6) using the equation (6)
P. V. Danokwerts, Trans. Faraday Soc.,
46, 701 (1950).
DISSOLUTION OF SOLID OXIDESIN OXIDEMELTS
2135
in which
Y
A=7i An average value of log D = -5.4 * 0.2 is obtained which is satisfactorily consistent with the data obtained with eq 1 (see Table I) if these values are related to the average concentration c'. Potassium Silicate Melts. Figures 7 and 8 show the corrosion Y as a function of t"' for various KzO-Si02 melts. Calculated interdiff usivities are reported in Table 11. The liquidus concentrations were used as given by Kracek, et al.? The determination of the Si02 liquidus curve in the KzO-SiOz system by equilibrating melts in a silica crucible, in the same way as for the Na20-Si02 system, is not possible within a reasonable period of time because of the much smaller interdiffusivity values near the liquidus concentrations.
-5 *.
-0.04
-0.03 -0.02
- 0.01 0
500
i000
I500
2000
t"2(tbC I")
Figure 7. The dissolution of solid silica in static K2O-Si01 melb at 1000".
-0.15
Table II: The Dissolution of Silica in Static K20-SiOz Melts
Temp, OC
Ci
y
CCW
w
1000
77.0
1200
81.0 57.0 69.0 65.4 73.2 73.3 77.1
a
Y/dZ
C'
t% ' SiOP-
65.4 71.2 73.3 75.1
cm sec -'/a
Log D , D in cm, sec -1
-4.5 X -1.0 X lo-'
-7.97 -8.44
-12.5 X lo-' -7.5 X lo-' -3.7 x 10"
-7.65 -7.84 -7.99
-0.10
5
* %O!
See footnote in Table I.
Dissolution of Silica in Sodium Silicate Melt from a Rotating Silica Disk. Figure 9 shows the corrosion Y as a function of t (angular velocity w = 131 radians/sec) for the sodium silicate melt containing 51% SiOz at 1400". Figure 10 shows dY/dt as a function of wl". Included in this diagram is a corresponding curve for 1250" as obtained by Shurygin, et a1.l As shown by Levich,* the thickness of the diffusion boundary layer a t a rotating disk is given by 6 = 1.6l(;)(t)
a Figure 8. The dissolution of solid silica in static K2OSiO2 melk at 1200".
motion of the interface between solid and liquid is obtained as shown by Lommel and Chalmerss from the expression (eq 4) (7) F. C. Kracek, N. L. 41,1188 (1937).
(3)
when Y is the kinematic viscosity of the melt. Taking the moving phase boundary into account, the rate of
Do
Bowen, and G. W. Morey, J. Phys. Chem.,
(8) V. G. Levich, "Physicochemical Hydrodynamics," PrenticeHall, Inc., Englewood Cliffs, N. J., 1962, pp 60-72. (9) J. M. Lommel and B. Chalmers, Trana. Met. Soe. AIME, 215, 499 (1959); see also D. B. Spalding, "Convective Maas Transfer," McGraw-Hill Book Co. Inc., New York, N. Y., 1963, pp 184-186.
Volume 70,Number 7 July 1066
KLAUSSCHWERDTFEGER
2136
dY D dt = - - l6n [ l +
- c,
-1-
ci cs
ci
(4)
Inserting (3) into (4)
Equation 5 is valid only for constant viscosity and interdiffusivity; however, eq 5 may be used for the present case to obtain an approximate value of D for an average melt composition. Average values of kine-
SELRWFFUSlVlTlES OF THE CATIONS (NolK)1
-5
L -u am
OR
t (see
1
001
(O-AXY d)
w
Figure 9. The dissolution of solid silica in liquid NazO-SiOz ( c , = 51 wt % SiOz, 1400') a t a rotating disk, as determined in this work.
Figure 11. Interdiffusivities and self-diffusivities in Na&SiO* and K&SiOz melts at 1200". The curve for the interdiffusities is approximate (compare text).
Figure 10. The rate of silica dissolution in NanO-SiOz melts at a rotating disk, aa determined in this work and as reported by Shurygin, et al.1
matic viscosities were taken from the work of Heidtkamp and EndelL3 The value of D thus obtained from the present data is given in Table 111. For the same average composition this value of D is somewhat smaller than that obtained by dissolution into a static melt (Table I). Considering, however, the experimental errors in both techniques and the approximations involved in using eq 1 and 5 for a system displaying the strong concentration dependence of diff usivity and viscosity, agreement may be regarded as satisfactory. Some source of error in the rotating disk method may also be due to the finite size of the disk diameter in comparison with the relatively large thickness of the hydrodynamic boundary layer established in the present system. Comparison of Diflusiuities in Sodium Silicate and Potassium Silicate Melts. Figure 11 shows interdiffusivities in NazO-Si02 and KzO-Si02 melts, obtained from the dissolution rates of silica in the static melts, as a function of the average molar cation concentration in the melt a t 1200". It is seen that interdiffusivities in both systems can be represented essentially by one
The Journal of Phyaieal Chemistry
DISSOLUTION OF SOLID OXIDESIN OXIDEMELTS
2137
Table 111: The Dissolution of Silica in N%0-SiO2 Melt, Stirred by a Rotating Disk
Temp, O C
ci
-wt
em
c'
96 SiOP-
om sec-'/~
cm-'/I
oms
rad -I/;
600'/6'
~70C-l
(a) This work 1400 1360 1250 1170
86.7 51.0 68.8
-1.17 X lo-'
(b) From the work of Shurygin, Barmin, 84.5 49.2 66.9 -7.7 X 80.8 49.2 65.0 -4.8 X lo-' 79.0 49.2 64.1 -2.1 X
'
0.43
-6.71
and Esinc 0.43 -5.42 0.43 -5.60 0.40 -6.03
+
Y' = (vi vm)/2 = 4 2 . See footnote in Table I. Shurygin, Barmin, and Esinl use a somewhat different equation than eq 5 with a wrong driving force to interpret their data. Log D values were therefore recalculated.
transport mechanism in electrical conduction is the same as that in diffusion. The oxide interdiffusivities are smaller at 1200" by two to three orders of magnitude than the above self-diffusivities. I n the dissolution experiments, the transport of cations is accompanied by the movement of anions such that the electroneutrality is maintained. Since the anions have a much lower mobility than the cations,la the oxide interdiffusivities are expected to be smaller than the cation self-diffusivities. A quantitative analysis of the present data with respect to self-dsusivities is not possible at present, because the self-difhsivities of 0 and Si are not known in these slags.
Acknowledgment. The author wishes to thank E. T. Turkdogan for fruitful discussion, R. G. Olsson for the use of the rotating apparatus, and C. W. Haworth for the microprobe analysis. ~~~~~~~~~~
curve. Included in Figure 11 is a curve for the self, of the cations Na or K at 1200". diffusivities D * N ~D*K These values were measured either directly with tracer methodslo or were calculated by the author from electrical conductivity data11J2on the assumption that the
~
~
~
~
(10) V. I. Malkin and B. M. Mogutnov, Dokl. Akad. Nauk SSSR, 141, 1127 (1961); trans1 in PTOC. Acad. Sei. USSR, 141, 941 (1961). (11) C. L. Babcock, J . Am. Ceram. SOC.,17, 329 (1934). (12) J. O'M. Bockris, J. A. Kitchener, S. Ignatowice, and J. W. Tomlinson, Trane. Faraday Soc., 48, 75 (1952). (13) J. O'M. Bockris, J. A. Kitchener, and A. E. Davies, ibid., 48,536 (1952).
Volume 70, Number 7 Jdy 1966
