Aug., 1946
REDETERMINATION OF THE LATTICECONSTANT OF LEAD
1493
centrations in all cases differ considerably from dissolve appreciably in solutions of paraffinthose found by surface tension measurements on chain colloidal electrolytes with concentrations aqueous solutions of the sulfonates.'" This akove the critical values; solution evidently change is considerably greater with the saturated occurs in the hydrocarbon interior of the micelle. than with the unsaturated solutions. With the The data presented above indicate that the benlatter the shift is probably caused by a partial zene not only dissolves in the micelles but actually saturation a t the interface during the time that aids in their formation. elapsed between the formation of the drop :and Sonie portion of the difference between the interthe exposure of' the photographic film. facial tension values for equilibrium and nonThe critical concentrations of the sulfonate equilibrium conditions might possibly be due to solutions as shown by the equilibrium interfacial solution of some sodium alkane sulfonate in the tension together with the values found by surface benzcne,I4 although this would seem unlikely betension meiisurements on the sulfonate solutio~is'~ cause of the low solubility of the sodium salt in are recorded in Table 111, the percentage change b e n ~ e n e . ~Further work is being done in an in concentration being included. There is a attempt to answer this question. marked relationship between this percentage and Summary the carbon chain length of the sulfonate. The 1. The equilibrium surface tensions of solufindings of Powney and Addison* are similar to tions of dodecane sulfonic acid and of magnesium the hon-equilikaium values. octane sulfonate have been determined a t 40'. TABLE I11 The data, considered with others, indicate the CHAXGE OF C R ~ T C CCONCENTRATION AL UPON SATURATING iiiarked role the gegen ion plays in micelle forma!LQUEOUS SO1,UrIOh.S O F LOSG-CHAIN SODIUM SULFONATES tion. 2 . Both equilibrium and non-equilibrium interIVITH BEXZENE Length of Critical concentration Change, facial tensions have been measured for solutions chain Surf. ten. Interfac. ten. 7G of sodium decane, dodecane and tetradecane sul10 0.0370 0.0317 14 fonate against benzene. The data show that the 12 ,0100 .0073 27 critical concentration for micelle formation with 14 ,0027 .0017 37 benzene-saturated solutions is lower than that The primary factor causing the shift in the for aqueous solutions of the corresponding sulfoncritical concentration when the solution is ates not containing benzene; the decrease is a saturated with benzene is not clearly understood. function of the carbon chain length. Benzene Most likely it is clue mainly to the well-known appears to aid in micelle formation. solvent action of the mi~e1les.l~Many organic SEATTLE, WASHINGTON KECE:VED'% APRIL 9, 1946 substances, which are normally insoluhle in water, ence." Interscience Publishers, New York, N. Y . , 1912, p. XI; (13) S m i t h , J . P h y s . C h u m . 36, 1401, Trans. F a r a d a y Soc., 33, 3 2 3 , 815 (1937); THISJ U U K N A L , 68, :%loi l 9 B G ) ; 60, 223 I n d . Ewz, C h r ~, 34, 913 (1942); "Recent
1672 (1932); Lawrence, McBain a n d co-workers,
(1938); 63, 670 (1941); Advances in Colloid Sci-
Hartley, "Aqueous Solutions of Paraffin-Chain S a l t s , ' ' IIerniann e t Cie, Paris, 1936. (14) Davis a n d Bartell, J . Phys. Chem., 47, 40 (1943). (15) Original manuscript received October 8, 1043.
[CONTRIBVTIOU mox
THE SCHOOL OF CIIBXISTRY OF THE INSTITCTE OF TECHNOLOGY OF THE UXIVFREITY OF ~ I I N N E S O T A A N D THE DEPARTMENT O F RESEARCH I N CHEMICAL PHYSICS O F &TELLON INSTITUTE O F INDCS'IRIAL RESEARCH]
A. Redetermination of the Lattice Constant of Lead BY HAROLD P. KLUG The lattice constants of the elements are of such fundamental importance in both theoretical and applied chemistry that i t is desirable to know them with the highest precision possible. One of the problems of precise lattice constant determination is the acquisition of a sample of sufficient purity to warrant such a study. Recent1;y a sample of lead of very exceptional purity became available, so i t seemed desirable to make a redetermination of the lattice constant.' The results of the investigation are reported in this communication. (1) T h e a u t h o r wishes t o express his appreciation to H. R . IIarner, chief chemist, Eagle-Picher Lead Company, Joplin. Mo., for generously providing this sample.
Spectrographic analysis indicated the sample to have a purity of 99.999-y0 lead. The only metallic impurity lines observed were a very weak bismuth line and a very weak copper line. The best sample of lead to have a diffraction study up to the present is apparently that used for a deterniination of its thermal expansion by Stokes and V X x n , 2 which they report to have a purity of 99.99iyG, the impurities observed being silver, copper, antimony and bismuth. The details of the X-ray technique used in the precision lattice constant determination have been described earlier.3 CuK radiation was used (2) Stokes and Wilson, P W L .P h y s . Sor. I,ondun, 6 S j 668 (1941). ( 3 ) Klug and Alexander, 'THIS J O U R X A L , 62, 1492 (l!J40).
HAROLD P. KLUG
1494
VOl. 6s
TABLEI DIFFRACTION AND LATTICE CONSTANT DATAFOR LEADAT 25 Film no. -.+ Indices
(531)ai (531)n? (60O)ai (G0O)az (62c)ai (G20)m Lattice constant, ao, in kX units
* 0.1 ‘
M395
Specimen A M397 M398
M399
Sin
Sin 0
Sin 0
Sin 0
0.92092 ,92336 .93400 .93642 ,98405 .98658
0.92086 .92339 .93398 .93639 .98422 .98660
0.92105 .92335 .93397 ,93647 .98418 .98657
0,92110 .92351 ,93395 .93652 ,98422 .98656
0.92087 .92331 .93389 .93630 ,98416 ,98656
0.92093 .92330 .93396 .93641 .98421 .98654
4.94095
4.94036
4.94064
4.94087
4.94060
4.94054
c
e
in this study. The specimen consisted of fine filings sealed inside a thin-walled ethyl cellulose tube of 0.6 mm. internal diameter. A summary of the results from six separate determinations using two different specimens is given in Table I. These findings show an average value of a0 = 4.94066 =t 0.00006 kX units a t 25”, in which the error indicated is the probable error of the mean. This value must be corrected for refraction4 by the addition of the calculated correction 0.00014. Accordingly, the final value for a0 is 4.9408 * 0.0001 kX units. The density of lead a t 25’ calculated from this new value for the lattice constant is 11.341. The experimentally determined value i s reported by the “I. C. T.” as 11.348 a t 16.34’ and 11.337 a t 19.94’. I n Table I1 the present value for the lattice constant of lead is compared with earlier data. Still earlier values are in the literature, but they cannot be considered to be precision values in any sense of the word. Where the observer did not determine his value precisely a t 25’, i t has been calculated a t 25’, using Stokes and Wilson’s2 value of the coefficient of expansion, for inclusion in Table 11. I n addition to the present value, only that of Owen and Yates has been corrected for refraction. The present value is slightly larger than previous values, being in line with its higher purity than other samples. Lead atoms are larger than other atoms commonly found as impurities. The (4) O a e n and Yates, Phrl. M a g , [VII] 15, 472 (1933); Wilson, PYOCCmnbrrdpe Phil Soc , 36, 485 (1940).
---Specimen
M411 Sin
e
B-----. M412 Sin 0
TABLEI1 COMPARISON WITH EARLIER LATTICE CONSTANT DATAFOR LEAD a. a t 25’
Observer
in k X units
Sample purity report&
4.9408 99.999f % 4.9406 99.9 4.9405 99.9 4.9404 99.997 4.9400 ? (Hilger H.S.) 4.9385 99.9 (room temp.) Obinata and Schmidt’ 4.938 99.99 a Ref. 4. b Owen and Iball, Phil. Mug. [VII] 13, 1020 Lu and Chang, Proc. Phys. Soc. (1932). Ref. 2. (London), 53, 517 (1941). e Jette and Gebert, J . Chem. Phys., 1, 753 (1933). f Obinata and Schmidt, Metallwirtschuft, 12, 101 (1933).
Klug (this study) Owen and Yates” Owen and Iballb Stokes and Wilson’ Lu and Changd Jette and Gebert‘
atomic radii5 for lead and the impurities reported by Stokes and Wilson are as follows: Pb, 1.746; Ag, 1.441; Cu, 1.275; Sb, 1.439; Bi, 1.55 kX units. Such impurities in substitutional solid solution would decrease the lattice constant from its value for pure lead. Accordingly successively purer samples should yield increasingly larger values of ao.
Summary The best value for the lattice constant of lead * 0.1’ is 4.9408 * 0.0001 kX units.
at 25
PITTSBURGH 13, PA.
RECEIVED MARCH 20,1946
(5) Stillwell, “Crystal Chemistry,” McGraw-Hill Book Co., New York, N. Y . , 1938, p. 417.
