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line from which the relative values of the various parameters can be evaluated. Details of the experiments have been reported elsewhere.2a Care has been taken to ensure that no excitation of argon gas occurs through acceleration of the electron in the field and corrections have been applied to the measured current increment in order to remove the effect of the change in electron drift velocity as the organic molecule is introduced into the system. Gas mixtures were all prepared and analyzed by mass spectrometry and further diluted to the required concentrations. The results for a number of gases are shown in Figure 1 and their relative rate constants as measured through the slopes and intercepts of the lines are tabulated in Table I. The over-all accuracy of the tabulated values is not considered to be better than 30%, owing to the accumulated errors including that involved in the extrapolation of the best drawn line through the data for intercept measurements. The relative values are regarded, however, to be more accurate.
Table I: Relative Rate Constants for Energy Transfer from Excited Argon Atoms to Various Organic Molecules
Acetylene Methylacetylene Ethylene Propane n-Butane Neopentane Acetone Benzene
1.25 1.56 2.00 2.06 2.27 1.69 2.10 1.0
1.00 1.09 0.45 0.36 0.61 0.55 0.48 0.42
1.00 0.87 0.28 0.22 0.33 0.41 0.29 0.53
From the results in Table I, it is evident that the quenching of the excited species, although roughly similar for most of the gases, is not reflected in the ionization of the molecules. These results appear ~ have evaluated different from thoseof Hurst, et U Z . , ~ who these rate constant ratios through computer calculations of their data which covered up to 100% of the organic gas, but by no means at the extremely low concentrations at which present measurements were made. The only other data available in the literature are those due t o Jesse4for acetylene and ethylene which if treated in this manner give the rate constant ratios (kl kg)/kd of 1.5 X lo3 and 2.6 X loa, respectively. These values are similar to our 1.25 X loa and 2.0 X lo3 and contrast with 8.5 X lo3 and 18.3 X lo3 as deduced from the results of Hurst, et a1.2b
+
Enthalpy of Solid Solution for a Metastable Silver-Copper Alloy1*
by Ronald K. Lindelb W . M . Keck Laboratory of Engineering Materials, California Institute of Technology, Pasadena, California (Received July 8, 1966)
Prior experimental work on the enthalpy of solid solution of Ag-Cu alloys has been confined to the narrow limits of compositions which exist as equilibrium solid solutions at elevated temperatures. A liquidquenching technique described in another paper3 has made possible the acquisition of data at a composition considerably beyond the limits of solid solubility which exist in the equilibrium phase diagram.4 By this technique suitable foils of single-phase metastable 75.0 atomic % Ag-Cu solid solutions were prepared (from Ag of purity 299.99% and Cu of purity >99.999%) and checked for single-phase composition (using X-ray diffraction). Half of the foils were retained in the metastable condition, while half were heated at 205" in an argon atmosphere for about 200 hr. and were checked by X-ray diffraction to ensure transformation to the stable state (50.2 atomic % solute in solution4). Foils were then cleaned (to remove oxides, etc.) by swabbing with a 28.46 wt. % HN03 solution, rinsed with distilled water, then swabbed with acetone, and allowed to dry in air. The calorimeter consisted of a small, well-insulated double-walled dewar flask provided with a tightfitting cover containing a small inlet door for introducing the specimen. For each experiment, a solution of 28.46 wt. % "03 was added to the calorimeter, which was maintained at 23.0 f 0.5" but which was held constant to within 0.01" during any given experiment. The foils were weighed into sample lots of 0.300 g. each and introduced into the acid solution after the temperature of the system had stabilized. The low rate of heat loss from the system made it possible to wait for all stirring to occur by natural convection currents. The rise in temperature when
(l! (a) This work was sponsored by the U. S. Atomic Energy Commission; (b) Poulter Laboratories, Stanford Research Institute, Menlo Park, Calif. (2) (a) N. Swindells and C. Sykes, Proc. Roy. Sac. (London), A168, 237 (1938); (b) R. A. Oriani and W. K. Murphy, J. Phys. Chem., 62, 199 (1958). (3) R. K. Linde, Trans. A I M E , in press. (4) M. Hansen, "Constitution of Binary Alloys," 2nd Ed., McGrawHill Book Co., Inc., New York, N. Y., 1958, pp. 18-20.
Volume 69, Number 12 December 1966
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NOTES
the foils were dissolved in the acid was detected by two glass bead thermistors and recorded by means of a Wheatstone bridge circuit. (See Figure 1 for typical temperature records.) The use of 25.16 ml. of acid solution in the case of transformed €oils resulted in a temperature rise of 0.71 f 0.02’. I n the case of metast,able foils, 31.01 ml. was required to maintain the same temperature rise. It was thus possible to calculate the enthalpy difference from a knowledge of the heat capacity of the acid solution and without a precise knowledge of heat losses or of the energy equivalent of the entire calorimeter although this procedure precluded a meaningful measurement of the total energy release for a given type of foil.
24.50
-
0 Lc 2
0 I-
3 0 ul
D
u LL
0 W
a
3
I-
a W
n
I w
I-
TIME (MIN.1
Figure 1. Two typical temperature records for dissolution of foils in acid solution.
As an indication of accuracy and a check that no significant error would be introduced by any uncompensated effects associated with changes in contact area encountered for the acid solution, several pairs of experiments were performed using specirnen weights and amounts of acid solution substantially different from the values quoted above. Thus, for example, in one pair of experiments the quantities were adjusted SO that the weight of each type of foil was doubled, while the contact area between the acid solution and the dewar walls was increased by 6001,; the computed value of the enthalpy difference was unchanged, howThe Journal of Physical Chemistrv
ever. Experiments were repeated several times to ensure reproducibility. When the metastable foils were dissolved, additional energy corresponding to the enthalpy of solid solution was released. Within the error limits stated below, the contribution from atoms in grain boundaries and other high-energy configurations could be considered the same for both types of foils (deduced primarily on the basis of microscopy and X-ray diffraction studies). All experimental conditions were kept identical. Thus, the enthalpy of solid solution should be closely equal to the enthalpy difference between the metastabIe and stable foils and can be calculated from the corresponding difference in amount of acid solution required to maintain the same temperature rise for both cases. Results show an enthalpy of solid solution equal to 1150 f 200 cal./g.-atom. By way of comparison, Scheil’s analysis5predicts B value of about 1110 cal./g.atom, while Hardy’s “sub-regular” model6 results in a value of 964 cal./g.-atom if any temperature dependence is neglected. Heumann’ has computed the “distortional energy” (contribution to the enthalpy of solid solution due to difference in sizes of Ag and Cu atoms) for the composition in question to be about 1230 cal./g.-atom and has concluded that this represents, by far, the major factor in the enthalpy of solid solution. On the other hand, Oriani and MurphyZbstudied an 89 atomic % Ag-Cu alloy and concluded that the energetics for introducing solute species are independent of rigidity of the phase, despite the size difference between Ag and Cu atoms. A careful comparison between the most reliable experimental studies reported to date2v8 and the present investigation indicates that, in agreement with Scheil’s prediction,h the contribution of the phase rigidity may be of relatively minor importance for low solute concentrations but may be of considerable importance for high enough concentrations of Cu in Ag. On the other hand, even for high solute concentrations, the phase rigidity may not represent the only major factor in the enthalpy of solid solution. The rapid-quench technique in its present state is not suitable for an extension of this work to include other new compositions. (5) E. Scheil, Z. Elecktrochem., 49, 242 (1943).
(6) H. K. Hardy, Acta Met., 1, 202 (1953). (7) T. Heumann, 2. Metallk., 42, 182 (1951). (8) 0. Kubaschewski and J. A. Catterall, “Thermodynamic Data of Alloys,” Pergamon Press Ino., New York, N. Y., p. 60.
