Dec., 1955
‘YHERMAL
DIFFUSION IX LIQ~JID METALS
1229
THERMAL DIFFUSION I N LIQUID METALS BY F. R. WINTERAND H. G. DRICKAMER Department of Chemistry and Chemical Engineering, University of Illinois, Urbana, Illinois Received JuEa, 32,1855
J. Phys. Chem. 1955.59:1229-1230. Downloaded from pubs.acs.org by NANYANG TECHNOLOGICAL UNIV on 08/26/15. For personal use only.
Thermal diffusion measurements have been made on a series of liquid metal mixtures. The results are totally consistent with a previously presented theory. The separations depend on the “activation energy density” AU * / V of the components. I t is also shown that the quantity X(ap/dX) in the denominator is important for quantitative prediction of the separation. Results also are presented and discussed for three ternary mixtures.
I n recent papers2 we have discussed theories of thermal diffusion in liquids and their application to data on binary organic mixtures. The two theories presented differed in their interpretation of the “net heat of transport,” a quantity which appears in the theory of thermodynamics of irreversible processes. The thermal diffusion separation in a binary mixture can be discussed in terms of the thermal diffusion ratio a defined (for the steady state) by where XI = mole fraction component 1 T = temperature
The subscripts H and C refer to the hot and cold walls, or chambers, of a single stage system. Our previous papers give for a the relationship
where Vi
Mi pi
= partial molar vol. of component i = =
mol. wt. of component i chemical potential of component i
containing 50 mole % of each component. The gallium, cadmium, zinc, tin, lead and bismuth were A. D. Mackay’s purest. The mercury was redistilled stock. The cell consisted of a ceramic tube 1/2-inch long, ‘/,-inch i.d. and J/,-inch 0.d. The bottom was sealed with a thin copper disk fastened on with sauereisen. A thermocouple was silver-soldered to the disk. The cell was filled with the molten alloy to be studied and a second couple was inserted at the top. The alloy was then solidified and the top sealed with sauereisen. The temperature gradient was imposed by means of a tubular core electric heater. By varying the current and the position in the core, almost any mean temperature and AT could be attained. The samples were run at a AT of 50” and a t the mean temperatures shown in Table 11. By successive runs it was shown that 12 hours was usually ample for the steady state to be established. All runs reported were at least 24 hours. At the end of the run the cell waB quickly lowered into ice-water to ensure inatantaneous solidification. The metal slug was removed and cut into five pieces which were weighed and analyzed by standard titrimetric methods.‘ All systems except the leadbismuth contained tin, for which we analyzed. I n the leadbismuth system the latter component was measured.
The results are shown in Table 11. Each point is the average of at least three runs, and the average deviation is less than 5% from the mean. The activation energies mere obtained from viscosity data5 using Eyring’s3 equation
The quantity AOi* is an energy quantity associated with motion of component i out of a given = -hN Oe F+ (3) v xp-ART region. Previously*a we presented an interpretation of this quantity in terms of a fraction of the latent heat. I n reference 2b we discussed it in terms of the partial molar activation energy of com- where viscosity ponent i in the mixture. The latter concept seems ? v == molar volume more reasonable and gives better agreement with the h = Planck’s constant theory for organic mixtures, but the difference is not No = Avogadro’s number clear, since, as Eyring3has shown, the ratio of latent R = gas constant A F * = activation free energy heat to activation energy is substantially constant AH* = activation enthalpy (3 to 4)/1 for most organic liquids. AU* = activation energy The liquid metals supply a very good test of these theories since the simple relationship discussed Where available, the measured values of X l ( b p / b X ) were used. Otherwise the ideal solution value RT above does not apply, as can be seen in Table I. was assumed. It was necessary to use the molar TABLE I volumes and activation energies of the pure comAHvap. AHvap. ponents as partial molar quantities were not availmtal T,OC. AH* Metal T,o c . AH* able. Tin 295 58.5 Mercury 295 23.3 For mixtures where activity data were available Cadmium 295 17.7 Gallium 295 69.9 the predicted value checks experiment quite well. Lead 295 16.0 Bismuth 295 36.0 There is a slight discrepancy for the case of tinZinc 375 9.6 bismuth, but there were only three viscosity points Thermal diffusion measurements have been available and these indicated that AH* varied sigmade for a series of binary liquid metal mixtures nificantly with temperature, but the exact value was hard to determine. (1) This work \vas supported in part by the A.E.C. (2) (a) E. L. Doughtery, Jr., and H. G. Drickamer, J . Chem. Phys., 23, 205 (1955); (b) THISJ O U R N A L69, , 443 (1955). (3) S. Glasstolie, I
