JORDAN D. KELLNER
3254
The Viscosity of Molten Bismuth-Bismuth Triiodide Solutions1
by Jordan D. Kellner Atomics International, Canoga Park, California 93140 (Received March 20,1967)
The viscosity of the Bi-BiI3 system was measured over the entire composition range. The values for the pure salt ranged from 1.59 cp at 500" to 1.86 cp a t the melting point of 408", with an apparent activation energy of 1.69 kcal/mole. Both t,he viscosity and the activation energy increase with added metal until a maximum is reached a t about 55 mole % bismuth. At this composition the viscosity a t 500" is 2.07 cp with an activation energy of 6.41 kcal/mole. The apparent Arrhenius behavior of these mixtures is explained by the fact that the liquids are free-volume limited and that the free volume is proportional to temperature. The maxima in the isotherms are then interpreted as a loss of free volume caused by the interstitial dissolution of bismuth in the salt.
Introduction While the viscosity of many binary fused-salt systems has been measured, only one paper has been published on the viscosity of metal-salt systems.2 Aten measured the viscosity of Bi-BiC4 solutions up to a concentration of 40 mole % Bi from 260 to 340". I n the present work, the viscosity of the Bi-BiIa system having a consolute temperature of 458" is measured across the entire composition range from pure salt to pure metal.
Experimental Section Since it was necessary to keep the system closed owing to the high vapor pressure of the salt (about 340 mm a t 500"): it was decided that a capillary technique for the determination of the viscosities of these solutions would be the most suitable. The cell design of Greenwood and Wade3 was used in which a well around the lower end of the capillary maintained a constant lower liquid level. Thus, the average driving force was independent of the volume of liquid in the cell. This design has an advantage in that the system is completely enclosed with no cold spots to which the salt may distill. Repetitive runs were simple, involving just an inversion of the cell. I n addition, there is no contamination from a manipulating gas. Two modifications of this design are incorporated into the cell shown in Figure 1. The well, D, was raised to reduce the effective head and thus lengthen the time of the flow of liquid through the capillary. Reasonable times for the flow were obtained in this manner without the use of narrow capillaries that clogged easily. Because the The Journal of Physical Chemistry
Bi-BiI3 solutions form an opaque film on the wall, a second modification, the addition of three tungsten probes sealed through the cell a t A, was used for remote sensing of the liquid level. One of the three probes terminates a t the beginning of the reservoir, C, and the other two a t the end of this reservoir. The two longer probes were insulated with a glass covering so as not to be shorted to the third probe by adhering solution. The time of flow was measured by an electronic clock (Hamner 803) that WBS turned on and off by positive pulses supplied by 1.5-v dry cells and UTC R74 transformers in the circuit shown in Figure 2. When the double-pole-single-throw switch, S, in Figure 2 is closed and the liquid level is covering all three probes (region a), about 15 ma flows through each circuit. When the liquid drops past probe 2 (region b), the current through this probe is suddenly reduced to zero. This produces a large (about $20 v) positive-going pulse from the secondary of the transformer TI that starts the clock. When the liquid level drops below probes 1 and 2 in Figure 2 (region c), the current, again dropping quickly to zero, produces another positivegoing pulse a t the secondary of transformer TS.This pulse is used to stop the clock. The clock may be read in hundredths of seconds and was calibrated to be accurate to within 1 part in lo6. The cell was calibrated at room temperature with 5y0 (1) This work was supported by the Research Division of the United States Atomic Energy Commission. (2) A. H. W. Aten, 2. Physik. Chem., 66, 641 (1909). (3) N. N. Greenwood and K. Wade, J. Sci. Instr., 34, 288 (1957).
VISCOSITYOF MOLTENBISMUTH-BISMUTH TRIIODIDE SOLUTIONS
3255
Figure 2. Remote level sensing circuit for determining time of flow: 1,2, 3, tungsten probes; TI, Tz,transformers; S, switch.
taken while increasing and decreasing temperature, in order to detect any change in viscosity caused by thermal deterioration of the solution. No such change was ever noted; the time of flow for runs with a given temperature agreed to within 0.2%.
Results
Figure 1. Pyrex viscosity cell: A, tungsten seals; B, tungsten probes; C, reservoir; D, well.
glycerine-water solution, double-distilled water, and acetone. Suitable corrections were applied to the calibration for the difference in temperature of unknown and standard liquid. The BiI3 used was obtained commercially and distilled twice in vucuo. The bismuth metal was filtered through glass wool in vucuo to remove oxide impurities. The powders were weighed in air and introduced into the cell via a long-fill tube. The cell was then evacutorr. ated and sealed at a pressure of The cell was held in an Inconel 2.5-in. i.d. tube which was placed in a Marshall furnace mounted in a rocking frame. The Inconel tube was effective in limiting the temperature gradient along the cell to less than 1". After the single-phase temperature was reached, the furnace was rocked for 10 min to assure the dissolution of the metal. The furnace was then inverted to charge the cell and the time of flow of the solution was noted. This process was repeated about 10 times a t each of at least four different temperatures and about 20-30 times while the temperature was being changed. Data were
The viscosities of pure Bi13 and of 15, 30, 45, 50, 55, 60, and 70 mole % bismuth solutions in BiI3 were determined a t temperatures ranging from 350 to 500". The values for the pure salt ranged from 1.59 cp a t 500" to 1.86 cp a t the melting point of 408". Table I and Figure 3 show the variation of viscosity with temperature and composition. Some of the measurements were obtained while the liquid had probably separated into two phases, and those results are shown by dotted lines in Figure 3. While the data in the two-phase region may be of interest, they will not be discussed, since they are not amenable to interpretation. Therefore, only data on single-phase liquids are listed in Table I. The viscosity values were determined from the kinematic viscosity results and density data. Densities up to 40 mole yo are known.4 The densities of more concentrated solution were obtained by interpolation using a 70 mole % ' point of Topol and Ransom6 and the value for pure bismuth.6 An attempt was made to determine the viscosity of pure bismuth. However, the extremely low value for the kinematic viscosity of molten bismuth resulted in very short flow times and scatter in the data due to turbulent flow. Therefore, viscosity values for pure bismuth were tapkenfrom the literature.' F. J. Keneshea, Jr., and D. Cubicciotti, J . Phys. Chem., 6 3 , 1472 (1959). (5) L.E.Topol and L. D. Ransom, J . Chem. Phgs., 3 8 , 1683 (1963). (6) E. Gebhardt and K. Kostlin, Z . M e t a l k , 48, 601 (1957). (4)
Volume 71, Number 10
September 1967
JORDAN D. KELLNER
3256
ity a t 500" is 2.07 cp compared with 1.59 cp for the pure salt at this temperature and 1.19 cp for the pure metal. The apparent activation energy for viscous flow for each composition was determined from the plots of In q against 1/T in Figures 4 and 5 and is shown in Table 11. I n general, these Eactare fairly constant with temperature except for the more concentrated solutions at lower temperatures, where the two-phase liquid region of the phase diagram is approached. As was noted for the viscosity, the Esot also goes through a maximum at a composition of about 50 mole % Bi, varying from 1.69 kcal/mole for the pure salt to 7.71 kcal/mole at 50 mole % Bi.
1 I I / I / I I I I / I 0.1 0.2 03 0.4 0.5 08
Table 11: The Constants a and b for Eq 1 for Each Composition and Apparent Energy of Activation
0.7 0.8 0.9 1.0
X Bi
-
Figure 3. Viscosity isotherms us. mole fraction of bismuth; the dotted portions denote two liquid phases.
Table I : Viscosities,
q
Temp, "C
7
Temp, "C
(in cp), of Bi-BiIa Solutions
7
Temp, "C
Temp, 7
O C
7
-0%
Bi-
-15%
Bi-
-30%
Bi-
- 4 5 % Bi-
433 438 446 449 463 482 488 491
1.76 1.77 1.74 1.73 1.69 1.64 1.63 1.62
389 395 401 406 412 418 424 433 455 472 493
2.21 2.17 2.14 2.11 2.07 2.04 2.01 1.97 1.88 1.83 1.76
445 448 450 454 460 486
2.16 2.14 2.13 2.11 2.09 1.98
350 368 400 419 426 431 435 459 461 482 494 499
5.99 4.99 3.50 3.07 2.95 2.86 2.77 2.46 2.42 2.20 2.09 2.05
-50%
Bi-
-55%
Bi-
-60%
Bi-
-70%
Bi-
366 370 375 381 385 395 400 418 443 476 494
5.71 5.57 5.39 5.13 4.97 4.60 4.40 3.74 3.02 2.41 2.16
415 426 432 440 450 456 464 496 500
3.71 3.33 3.12 2.94 2.76 2.68 2.52 2.11 2.07
438 441 445 450 455 470 491 499
2.93 2.86 2.77 2.69 2.61 2.42 2.16 2.08
448 452 455 458 472 476 481 485 495 498
2.21 2.19 2.17 2.16 2.11 2.10 2.09 2.08 2.06 2.05
The isotherms of viscosity against molar composition shown in Figure 3 exhibit rather pronounced maxima a t about 5-5-60 mole % metal. At 55% the viscosThe Journal of Physical Chemistry
b
[(V. b)/ V,] x 100 at 500'
0.1538 0.1664 0.1629 0.1711 0.1678 0.1635 0.1538 0.1402
28 23 19 6 5.6 4.1 3.9 10
Eact, ZBi
kcal/mole
0 0.15 0.30 0.45 0.50 0.55 0.60 0.70
1.69 2.19 2.25 5.46 7.71 6.41 5.86 1.59
10'a
1.132 0.7832 0.6760 0.2125 0.1737 0.1440 0,1377 0.2859
Discussion According to the hole theories of viscous flow in liquids of Frenkels and Eyring and associatesg viscous flow can be thought of as consisting of two simultaneous events. (1) The flow unit must attain sufficient energy to break away from its neighbors and ( 2 ) a hole of sufficient size must form adjacent to the flow unit. This hole is formed from the free volume ordinarily present in the liquid. The free volume may be defined as the volume of a unit weight of liquid less the volume of the liquid in a rigid, closest packed structure. Thus maxima in viscosity isotherms may be interpreted in two ways. (1) A large flow unit or a change in binding occurs in the mixture (complex formation) or ( 2 ) there is a loss of free volume in the mixture. When two events are involved, there is no theoretical reason to expect Arrhenius behavior as the tem(7) F. Sauetwald and K. Topler, Z . Anorg. Allgem. Chem., 157, 117 (1926). (8) J. Frenkel, "Kinetic Theory of Liquids," Clarenden Press, Oxford, 1946. (9) S. N. Glasstone, K. Laidler, and H. Eyring, "The Theory of Rate Processes," RIcGraw-Hill Book Co., Inc., New Pork, N. Y . , 1941.
VISCOSITY OF MOLTEN BISMUTH-BISMUTH TRIIODIDE SOLUTIONS
tOC
475
500
425
450
e -
375
400
I
3257
the viscosity of these solutions, since it is well established that the solutions contain no complexes a t the composition of the maxima." That is, in salt-rich melts bismuth dissolves in its trihalides by the formation of the monomer subhalide BiI12,13 2Bi
1 / T x lo3
Figure 4. Negative natural logarithm of the viscosity (-In ~ ( p ) us. ) 1/T for Z B ~= 0-0.50.
1%
500
,
475
450
425
400
3
I
I
4
t
ri
4.1 4.0 3.9 3.8
: I
$
3.7 3.6 3.5
3.4 3.3
3.0 29 2,8L--L-U I I 1.30 1.32 1.34 1.36 1.38 1.40
'
' '
1
1
1.45
1.50
I 1.55
UT x 103
Figure 5 . Negative natural logarithm of the viscosity us. 1/T for Z B ~= 0.55-1.0.
perature is changed a t constant pressure unless one of the above effects largely outweighs the other. As pointed out by Macedo and Litovitz,lo in liquids whose thermal expansion is very small, the free volume is virtually temperature independent, and the apparent activation energy a t constant pressure will be constant with temperature. Also, in liquids whose free volumes are proportional to the temperature, the liquid will again show Arrhenius behavior a t constant pressure.10 Since all of the compositions of Bi in BiIa show good Arrhenius behavior, one or the other condition applies. Evidently the free volume is the determining factor in
+ Bi13 +3BiI
which does not polymerize, in contrast to the chloride and bromide in which the subhalide does undergo polymeri~ation.'~Therefore the mixture at low metal compositions (below 50 mole %) consists only of Bi+, Bi+3, and I-. Evidence for the absence of complexes in the iodide system a t concentrations of 35 mole % Bi and greater can be found in thermal diffusion studies." These data show that a t these concentrations the cations are exchanging electrons so rapidly that they are indistinguishable as far as mass transport is concerned. Any one cation is rapidly changing its valence from 1 to 3 and back again even though there is a definite bulk concentration of each cation at any given moment. Such a system may be denoted by BiI, where x is between 1 and 3. Any autocomplexing or other complex formation would be detected by observing a separation of the solutions under the influence of a temperature gradient. Above a composition of 35 mole % Bi, no such thermal diffusion occurs. Therefore, no complexing of the solution takes place, and the positive deviations from additivity observed in the viscosity isotherms are not likely to be due t o complex formation. It seems likely then that the apparent Arrhenius behavior of each composition is due to the free-volume effects outweighing any energy considerations since the melts are completely ionic. Also, the partial molar volumes of bismuth are actually negative at low metal concentrations and approach the value for pure bismuth only a t large metal concentrations. This was thought* to be caused by the interstitial dissolution of bismuth metal or ions. I n the light of subsequent k n o ~ l e d g e we ~ ~ ~can ' ~ say that the bismuth species that eventually takes up interstitial positions in the quasi-lattice melt structure is the Bi+ cation. Thus as bismuth is added, more and more free space is taken up and the viscosity increases because the space available for the movement of salt is reduced. This view is further supported by the fact that the data can be given in terms of the Batchinski equation (10) P. B. hiacedo and T . A . Litovitz, J . Chem. Phys., 42, 245 (1965). (11) J. D.Kellner, J. Phys. Chem., 7 0 , 2341 (1966). (12) S. J. Yosim, L. D. Ransom, R. A. Sallach, and L. E. Topol, i b i d . , 66, 28 (1962). (13) L. E. Topol and L. D. Ransom, J . Chem. %Us., 38, 1663 (1963).
Volume 7 1 , hTumber10 September 1967
JORDASD. KELLNER
3258
+
V , = ad b (1) where a and b are constants, V , is the specific volume of the solution, and 4 is the fluidity. Table I1 shows the values of a and b from a least-squares analysis. The data follow this linear expression to within 1%. As can be seen from eq 1, b is the specific volume when 4 is zero or, in other words, when the liquid is completely rigid. Thus V , - b can be thought of as the free volume, or at least as a measure of it. The values of ( V , - b)/V, expressed as per cent are shown in Table I1 for each composition a t 500”. These values, which should be a t least qualitatively similar to the free volume. go through a minimum a t the same composition that the viscosity goes through a maximum. This type of behavior is consistent with the idea that the species formed from the added bismuth takes up interstitial positions. If the quasi-lattice salt structure is something approaching a closest packed arrangement of iodide ions, then in the pure salt one out of every three octahedral interstices would be occupied by a Bi3+ cation. At “ 8 mole fraction, in a cubic closest packed arrangement, all of the octahedral spaces would be occupied by cations and one mould expect the maximum in viscosity to occur a t about this concentration. However,
The Journal of P h y a k d Chemistry
because of the increased coulombic forces, the anion structure would be expected to shrink somewhat when more cations are introduced, thereby taking up some free volume. This effect was thought4to be the reason for the negative values of the partial molar volume of bismuth a t low concentrations of metal. The fact that the peak actually occurs a t about 55% is possibly due to this contraction. Although there is some evidence” that bismuth atoms begin to appear a t a concentration of 50 mole % metal, this species becomes predominant above 67 mole % bismuth, where the average cation charge is less than 1. At these concentrations, the melt properties approach those of the pure metal. The average flow unit size is decreasing as the large anions become more scarce, and the viscosity decreases until the value for the pure metal is reached. The apparent activation energy a t constant pressure in Table I is then largely the energy of formation of holes of flow unit size, since the viscosity of the system, as was pointed out above, is probably free-volume limited. The pure salt, having the largest free volume, has the smallest activation energy and, as the solution becomes more ‘(condensed” with added bismuth cations, the energy of hole formation, and therefore the activation energy, increases.
