THECRYSTAL STRUCTURE O F STRONTIUM BROMIDE
3259
ONOHYDRATE
This is indicative of a very low energy of activation for the triplet decay, of the order of a few hundred calories per mole or less. Preliminary measurenients of the triplet decay of erythrosin in gelatin and anthracene in polystyrene at room temperature and -25' bear this out. The rates at the lower temperatures are only slightly less than those a t room temperature and correspond to an apparent energy of activation of 310 + 180 cal./mole for erythrosin and 150 =t90 cal./niole for anthracene.
Conclusions The results indicate that flash photolysis in solid films is a simple and effeciiive means of studying the properties of transient species free of translational molecular Motion and the resulting self-quenching. Despite triplet concentrations of 6 X M and >2 X 114 with the halogenated fluoresceins and 2-naphthol in
gelatin, and > 5 X Ad with anthracene in polystyrene, no self-quenching wa6 observed. This restricted motion also minimizes the effects of impurities in the solute and matrix itself, and obviates the need for extensive purification of either. The lack of triplet self-quenching does not necessarily preclude oxygen quenching when the sample is in air. Anthracene in polystyrene is a good example of this. However, the diffusion of oxygen is restricted enough so that by simply passing nitrogen over the sample, the effect of oxygen can be greatly lessened or eliminated, and, by comparing the rates in air and nitrogen, it can be determined whether or not any significant oxygen quenching remains.
Acknowledgment. The author wishes to thank Dr.
W. West for his encouragement and for much helpful advice and criticism.
The Crystal Structure of Strontium Bromide Monohydrate
by Maurice Dyke and Ronald L. Sass Department of Chemistry, W i l l i a m March Rice University, Houston, Texas
(Received Julu 8, 1964)
The structure of strontium bromide monohydrate has been determined by X-ray single crystal diffraction techniques. The strontium ion was found to have an environment similar to the environment of the barium ion in the anhydrous barium halides.
Introduction I n 1939 Kamermans,' on the basis of a single crystal X-ray diffraction investigation, reported the crystal structure of a substance which he identified as strontium bromide. The space group of the structure is D2hI6Pnma with a = 11.42 8.,b = 4.3 8.,and c = 9.20 8. If Kamermans' notation is transformed into the international standard forim. Recently, Sass, Brackett, and Brackett2 have shown that a sample of hydrated strontium bromide kept under vacuum at room temperature for several hours will yield an X-ray powder diffraction pattern showing a single phase with an orthorhombic unit cell identical with the one reported by Kamermans
for strontium bromide. They have also found that when a weighed sample of this material is heated under vacuum at 200" there is a weight loss corresponding to 1 mole of water per mole of compound on the basis of an original sample composition of SrBrz.H20. An X-ray powder diffraction pattern of the new substance showed a single phase with a tetragonal unit cell. Sass, et al., have identified this material as strontium bromide and have determined the crystal structure by X-ray powder diffraction. We have now completed a single crystal (1) M. A. Kamermans, 2 Krist., 101, 406 (1939). (2) R. Sass, T. Brackett, and E. Brackett, J . Phys. Chem., 67,2862 (1963).
Volume 68, hiumber 11
hjovember, 1064
MAURICE DYKEAND RONALD L. SASS
3260
X-ray diffraction study of strontium bromide monohydrate.
Experimental An anhydrous sample of strontium bromide was obtained by healing hydrated strontium bromide crystals obtained from Matheson Coleman and Bell at 200' under vacuum for 12 hr. A weighed sample of anhydrous strontiuin bromide and a inole equivalent of mater were each placed into separate beakers. The uncovered beakers were immediately placed in a sealed jar and allowed to equilibrate. The beaker containing the water became empty within 24 hr. The material from the other beaker mas dissolved in absolute ethanol to form a saturated solution of SrBrs.HzO. Anhydrous ethyl acetate was lowly added from a dropping funnel to the saturated solution maintained at 4ijo to prevent the formation of the strontium bromide ethyl alcoholate complex.' Crystallization of the SrBrz.H20 was finished after the ethyl acetate had been added for 12 hr. After crystal formation the supernatant liquid was quickly decanted off and the crystals were immediately covered with paraffin oil and heated at 50" until all traces of solvent had evaporated. If an unprotected crystal is exposed directly to the air it mill turn cloudy from further hydration. A crystal 0.19 mm. in diameter was moiinted in a thin-walled glass capillary of 0.20-nim. diameter. The remaining space in the capillary was filled with paraffin oil. One end of the capillary had to be left unsealed to prevent it from exploding upon prolonged exposure in the X-ray beam. These explosions were probably due to expansion of the paraffin oil in the capillary and were not caused by any change in crystal structure since no chinge in the diffraction pattern of the crystal could be detected upon extensive exposure in the X-ray beam. Rotation and Weissenberg photographs sho\v the unit cell to be orthorhombic with a = 11.38 8.,b = 4.28 8. (rotation axis), and c = 9.19 8. The following systematic absences are observed: Okl absent if k 1 = 2% 1, and hkO absent if h = 2n 1. The preceding data indicate that the space group is Dzh16--Pnmaor CiV9-Pn2a. Our initial assumption that the former space group is the correct one for crystalline SrBwHsO is verified by the final results obtained in the structure refinement. The experimental density reported by Icamermans is 3.8 while the calculated density is 3.93 assuming four molecules of SrBrz.HzO per unit cell. This allows the molecules to be in the fourfold special positions 5 , x ; 2 , 3 1 4 , Z; l / z - x, 3 / 4 , '/z x; and x, - z. Weissenberg photographs of the k = 0 and k = 1 layers were used to determine the inte nsities of 222 independent reflections by visual corn-
+
+
The Journal of Physical Chemistry
+
+
+
parison with standard intensity strips. The intensities were corrected for absorption by the method of Bradley3 using a linear absorption coefficient of 389 cm.-1. In making the absorption correction, the slender wedgeshaped crystal was assumed to have cylindrical symmetry in order to simplify the calculations. Corrections were also made for the Lorentz, polarization, and Tunnel1 effects. The data from the 0-layer were least-squared using as trial parameters for the strontium and bromine atonis the values reported by Kamermans and given in Table I. A two-dimensional electron density projection was constructed using the observed (hOE) data with signs assigned from the least-squares analysis. The electron density map showed three peaks which might be due to the oxygen of the water molecule. However, in two of these positions there was not sufficient space for the packing of an oxygen atom into the crystal lattice and thus the position of the oxygen atom was assigned to the coordinates of the third peak. A final least-squares refinement was done on each layer using the parameters obtained from the electron density projection giving an R of l8Y0 for the 0-layer and an R of 19% for the first layer. Table I1 contains the observed and calculated structure factors for strontium bromide monohydrate.
Table I : SrBrz.HzOAtomic Parameters Atom
8r
Br( 1) Br(2)
0
Source
X
Y
2
Kamermans This paper Kamermans This paper Kamermans This paper This paper
0.311 0.3094 0.103 0,1019 0.614 0.6150 0,325
1/4
0.392 0.3845 0,119 0.1143 0.842 0.8456 0.879
'/4
"4 '/4
'/4 '/4
A two-dimensional (h01) electron density difference synthesis was attempted in order to obtain stronger evidence for the position of the water oxygen atom. The difference projection contained numerous extraneous features and was not of particular use in locating the oxygen atom. The poor resolution of the mater molecule in the difference synthesis and the inability to obtain lower R values in the least-squares refinements were probably due to the inexactness of our absorption corrections.
Results and Discussion Table I contains the final parameters obtained from the least-square refinements. The nearest-neighbor (3) A. J. Bradley, Proc. Phys. Soc. (London), 47, 879 (1935).
3261
THECRYSTAL STRUCTXJRE OF STRONTIUM BROMIDE MONOHYDRATE
Table I1 : Structure Factors for Strontium Bromide Monohydrate h
2
2 4 6 8 10 12 14
0 0 0 0 0 0 0
1
1
2 3 4 5 6 7 10 11 12 13 14 2 3 4 7 8 9 10 11 12 13 1 2 4 5 6 7 8 9 10 11 13 14 0 1 2 3 4 5 6 10 11 12 1 2 3 4 5
1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5
Fcalod
h
2
14,49 49.14 ' .40 3,30 36,35 - 6.63 19,73 12.05 20,73 15.65 19.35 -12.64 l!j,46 -17.39 19.91 8.52 1I ,34 2.92 3.81 -14.20 19.56 4.00 4.58 12.oi 14.77 5.19 4.56 3.94 -4.39 -10.13 10.42 5.02 -2.85 -57.76 49,40 5.87 !j .58 49.83 53,75 -5.94 6.73 -11.18 13,46 0.33 2.03 -10.39 l!j,00 2.33 2.76 -4.38 4.91 3.89 4.25 -3.64 3.10 -23,78 26.62 -15.86 18.25 16,92 18.66 12.74 12.77 5.88 :7,55 6.40 7,63 -2.87 2.82 8,81 -8.85 -0,87 5,89 -8.51 7.24 -68,Ol 57,33 12,22 16.74 11.02 15,69 4.20 3.56 29,63 30.68 -6,85 7.93 3.27 3,22 -23.12 23,29 5.77 4,97 4.36 3.81 -21.43 241:,93 -15.59 17 56 19.22 22.17 6.48 6.58 3.58 3 87
h
1
2
0 0 0 0 0 0 0
Foslod
6 7 9 10 11 12 13 1 2 3 4 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 0 1 2 4 5 8 10 1 2 3 5 6 7 8 9
5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7
7 7 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9
o io 1 2 3 4 5 6 7 1 2 4 5
10 10 10 10 10 10 10 11 11 11 11
4.31 4.63 8.74 7.78 7.81 -8.61 -5.52 5.53 -10.76 11.72 -5,21 4.81 9.42 8.68 -3.94 3.92 4.66 5.94: 26.79 27,13# -8.52 7,451 -3.57 3.81 -27.41 21.30 11.02 9.80 7.06 5.43' -1.54 1.49 3.82' 5.89 -4.31 5.66 4.56 -4.63 11.59 10.80 1.97 2.46 190.13 17.10 9.62 7.40 -20,27 15.97 -6,20 3.81 -7.74 6.91 -5,14 4.63 7.16 7.09 3.87 3.33 25.39 20.20 -10.40 10.65 -6,52 4.85 -8.46 7.60 6.23 6.07 -5,52 3.15 11.45 11.70 17.13 13,62 6.08 4.81 -15.43 12.34: -6,18 5.38 -2.49 2.10 -4.04 3.20 1.14: -1.70 9.28 10.14 2.39 3,02, 6.11 3.71 -3.57 3.10 -7.55 5.868 3.85 2.97 -3.31 2.39 2.21 2.12 9.34 7.58 1.35 1.19 -8.46 7.58 -11.44 10.62 -2.19 1.21
lFob6dl
h
2
21.73 54.06 62.01 21.89 30.08 7.92 4.16 19.66 19.56 11.90 15.69 9.17 10.10 3.13 19.82 24.01 3.15 11.28 6.78 5.99 5.83 1.46 49.02 14.07 44.78 4.05 16.14 2.22 7.18 26.12 2.07 23.08 2.35 19.34 2.44 54.59 25.28 12.08 8.59 11.47 10.23 20.19 11.02 3.11 3.37 22.21 38.29 11.18 33.65 5.67 17.44 6.78 18.23 6.04 4.53 1.95
0 1 2 3 4 6
5 5 5 5 5 5
7
5
8 9 11 12 1 2 3 4 5 7 9 10 11 12 1 2 3 4 5 6 7 10 11 2 3 4 5 6 7 8 9 10 0 3 4 7 8 9 1 2 3 4 5 7 0 1 2 3 4
5 5 5 5 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 10 10 10 10 10 10 11
hll
h01
h01
-14.81 -46,75 -6.11 1.59 29.67 -6.76 -15.27
Foaled
-'4
6 8 10 12 14 0 1 2 3 4 5 6
1 1 1 1
1 1 1
7
1
8 9 10
1 1
11 12 13 14 1 2 3
1
4 5 6 7 9 10 11 12 13 14 0 1 2 4 5 8 10 11 13 1 2 4 5 6 7
8 9 10 11 12 13
1 1 1 1 2 2 2 2 2 2 2 2 2 2
2
a 2 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4
-28.76 -51.70 50.04 21.52 -21.60 -5.32 -5.83 -12.06 15.85 10.11 -14.91 -8.15 -7.67 -2.93 14.47 17.37 -4.14 -9.89 6.11 -4.52 -5.38 1.89 -54.49 8.54 50.84 -2.99 13.06 -2.46 7.89 -18.99 2.18 -18.70 2.43 21.00 -2.92 -33.80 -18.93 8.90 7.70 9.68 10.22 -17.25 -10.10 3.52 3.85 16.29 38.25 -10.82 -36.39 6.16 -16.23 6.02 16.10 -4.77 3.27 -2.06
11
11 11 11
Fcalcd
hll -3.01 -3.33 -5.97 24.97 11.31 4.11 -24.29 -14.03 5.62 1.52 4.89 26.18 -13.20 -27,OO 6.54 -2.93 -7.07 9.34 -3 I74 13.63 -4.66 9.93 -5,39 3.88 -15.40 -5,40 -4.35 -2.89 17.86 6.84 -1.79 -1.82 -19.04 9.89 15.42 -6.83 7.19 -5.36 -6.54 3.15 -21.35 -5.21 21.59 5.36 -4.65 -7.90 7.41 9.73 -6.82 -3.06 5,12 -23,67 -1.95 2.50 -1 53 12 29
Volume 68, Number I 1
4.98 4.37 5.88 28.09 14.26 3.01 20.88 13.91 4.29 2.70 5.51 27.93 15.55 26.90 7.98 4.05 4.74 9.30 3.05 12.64 4.37 10.25 4.69 3.87 15.08 4.43 3.50 2.45 16.69 5.51 3.76 2.19 15.37 9.06 12.38 5.19 5.57 5.41 9.49 3.02 17.73 4.00 16.48 3.64 3.60 5 33 6.36 6.81 6.09 5.06 3.35 16.43 1.06 1.70 1.07 9.06
iVooember,1964
3262
TERESA 5. REE, TAIKYUE REE, AND HENRYEYRING
environment of the strontium ion in strontium bromide monohydrate is analogous to the environment of the barium ion in BaC12,BaBrz, and BaL4 except that two of the nearest halide ions around a barium ion are replaced by water molecules around the strontium ion. Each strontium atom is surrounded by three nearestneighbor bromine atoms in the same crystallographic mirror plane and by two bromine atoms and one water molecule on each of the equivalent mirror planes above and below. The distance from a strontium atom to a nearest-neighbor bromine atom ranges from 3.13 to 3.38 A. while each nearest-neighbor oxygen atom is a t a distance of 2.63 A. Thus, in strontium bromide monohydrate and in the barium halides each metal cation has nine nearest neighbors. Since in strontium bromide each strontium atom has only eight nearest neighbors,2 the strontium ion is probably not large enough to allow the stable coordination of nine bromide ions as nearest neighbors. However, as oxygen is snialler than bromine, a strontium ion is large enough to allow the stable coordination of seven bromide ions and two water mole-
cules. It thus seems likely that the greater stability of SrBrz.H20over SrBrz is due primarily to the increase in coordination number of the strontium ion by the water molecule to allow the same type of stabilization as found in the barium halide crystal lattices, Each bromine atom of type 1 has for nearest neighbors three oxygen atoms a t distances of 3.35 8. (2) and 3.34 H., four strontium atoms with distances ranging from 3.25 to 3.43 and seven bromine atoms with distances varying from 3.79 to 4.23 8. Each bromine atom of type 2 has for nearest neighbors one oxygen atom a t a distance of 3.31 i., three strontium atoms at distances of 3.13 8. (2) and 3.32 and seven bromine atoms with distances ranging from 3.89 to 4.36
K.,
K.,
Acknowledgments. This work was supported by grants from the Sational Aeronautics and Space Administration and The Robert A. Welch Foundation of Texas. (4) R. Sass, T. Brackett, and E. Brackett, J . P h y s . Chem., 67, 2132 [ 1963).
Significant Structure Theory of Transport Phenomena
by Teresa S. Ree, Taikyue Ree, and Henry Eyring Department of Chemistry, University of Utah, Salt Lake City, Utah
(Received J u l y 9, 1964)
By applying the significant structure theory of liquids to transport phenomena, the equation for viscosity is derived for rigid-sphere systems. When the Enskog theory of viscosity is compared to the present theory, close agreement between the two theories is found. The diffusion coefficient is also derived in terms of viscosity and V,, the solid molar volunie a t the melting point. For simple liquids, viscosities and diffusion coefficients are calculated from the theory without using any adjustable parameters. The agreement between theory and experiment is satisfactory.
I. Introduction There are three major theoretical approaches to the study of transport phenomena of liquids and dense gases. One of these theoretical approaches was intraduced by Enskog.' Although the Enskog theory is The Journal of Physical Chemistry
derived for rigid-sphere systems, it has been applied to real dense gases in el el lent agreernent with experi(1) (a) S. Chapman and T. G. Cowling, "The Mathematical Theory of Non-Uniform Gases," Cambridge University Press, Cambridge, 1939, Chapter 16; (b) ibid., Chapter io.
