x-ray analysis of the dibenzyl series. iii. the structure of stilbene, tolane, and azobenzene

X-Ray Analysis of the Dibenzyl Series. III. The Structure of Stilbene, Tolane, and AzobenzeneAuthor(s): J. Monteath Robertson, Mata Prasad and Ida WoodwardSource: Proceedings of the Royal Society of London. Series A, Mathematical and PhysicalSciences, Vol. 154, No. 881 (Mar. 2, 1936), pp. 187-195Published by: The Royal SocietyStable URL: http://www.jstor.org/stable/96478 .

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X-Ray Analysis of the Dibenzyl Series 187

The authors express their thanks to Professor Donnan for his interest in this work and to Dr. Teller for his very valuable assistance in the theoretical interpretation.

SUMMARY

The extinction coefficients of hydrogen iodide have been measured. The approximate course of the upper potential energy curve has been calculated from the eigenfunction of the ground state and the observed extinction. The results favour the dissociation into normal atoms and indicate the difficulties of extrapolation of absorption thresholds in the determination of heats of dissociation.

X-Ray Analysis of the Dibenzyl Series IIJ-The Structure of Stilbene, Tolane, and Azobenzene

By J. MONTEATH ROBERTSON, MATA PRASAD, and IDA WOODWARD

(Communicated by Sir William Bragg, O.M., F.R.S.-Received October 14, 1935)

The first two parts of this work* described a detailed quantitative analysis of the structure of dibenzyl, which crystallizes in the monoclinic system, space group C5h (P21/a), with two centro-symmetrical molecules in the unit cell. From preliminary data already publishedt it is known that stilbene, azobenzene, and tolane, also monoclinic, are in many ways similar to dibenzyl, but differ from it in the fact that their c axes are doubled in length, the unit cells containing four instead of two chemical molecules. The comparison is best seen from the figures given in Table I.

TABLE I Molecules

a b c per unit cell

A A A ? Dibenzyl ...... 12-77 6-12 7T70 116-0 2 Stilbene ...... 12 35 5-70 15-92 114.0 4 Tolane ........ 12>80 5 -68 15-74 114-9 4 Azobenzene .. 1265 6-06 15-60 114-4 4

* 4 Proc. Roy. Soc.,' A, vol. 146, p. 473 (1934); vol. 150, p. 348 (1935). t Prasad, 'Phil. Mag.,' vol. 10, p. 306 (1930); vol. 16, p. 639 (1933).



188- J. M. Robertson, M. Prasad, and I. Woodward

The structural change encountered when we pass from dibenzyl to the other three compounds is not merely a simple doubling of the c axis with some small displacement of what were formerly (in dibenzyl) an identically oriented set of molecules. This is shown by rotation photographs taken about the c axis of stilbene, where the new reflexions of odd 1 index, forming the intermediate layer lines, are not weak but have an average intensity quite comparable to the other reflexions. Further, it has previously been shown (Prasad, loc. cit.) that stilbene, tolane, and azobenzene possess a pseudo-orthorhombic structure, with the (201) as an approximate plane of symmetry. Thus the (202) and the (200) reflexions are of nearly equal intensity and spacing, and so are the (203) and (201), (204) and (202), (403), and (401), etc. With stilbene, which has been examined in greater detail than the other two compounds, it is found that this approximate symmetry breaks down to some extent in the higher orders. For example, the (207), (208), and (209) reflexions are definitely present, although weak, but only a very faint trace of their symmetrical reflexions, the (209), (2010), and (2011) can be seen. Perhaps the most notable exception occurs in the (601) reflexions, where the (601) is entirely absent, but the (607) has medium intensity. These observations, for stilbene, also serve to define which of the two almost identical crystal directions we have chosen as the c axis. If the c axis were taken in the (202) plane instead of the (200), then its length would be 15 7 instead of 15 9 A, and the angle , would be 112? instead of 1140.

STRUCTURE DETERMINATION

General Arrangement of the Molecules

Any proposed str-ucture for these crystals must explain the observed X-ray intensities and in particular the approximate halving of the (201) and the more nearly exact halving of the (001) series of reflexions. It must also be able to account for the other physical properties of the crystals. The magnetic properties of azobenzene and stilbene crystals have been studied by Krishnan, Guha, and Banerjee,* but unfortunately their conclusions regarding the molecular structure are quite at variance with the results reached in this investigation. We believe, however, that this is due not to erroneous measurement of the magnetic susceptibilities but rather to a mistake regarding the implications of the space group and the symmetry properties. They conclude, from a study of the magnetic data and the axial ratios a: b, that the two component rings of the azobenzene molecule cannot have either their lengths parallel

* ' Phil. Trans.,' A, vol. 231, p. 235 (1933).




to each other or their planes parallel to each other, and that hence the molecule has no element of symmetry. A quantitative estimate is given of the amount of twist and " folding up " of the azobenzene molecule in the crystal. In stilbene also it is concluded that the molecule has no element of symmetry.

In the space group C', (P21/a) four is the minimum number'of asymmetric units necessary to complete the symmetry. Thus if there were only two chemical molecules in the unit cell, as in dibenzyl, we should rightly conclude that the molecules themselves must contain an element of symmetry; that is, the molecules must be so situated in the crystal that the operation of some of the symmetry elements gives rise, not to another differently oriented molecule, but merely to another part of the same molecule.

But when four ch;emical molecules are present in the unit cell, the converse of this proposition does not necessarily hold. It does not follow that the four molecules are asymmetric. In fact, three distinct possibilities may be distinguished.

1. The molecules may be asymmetric. This will probably apply to the majority.

2. The molecules may possess a certain element or elements of symmetry in the free state which do not happen to coincide with any of the crystal elements of symmetry. No use is then made of the potential molecular symmetry in building up the crystal. For example, in naphtha- lene, anthracene, and several benzene derivatives, the molecules might have a plane and several axes of symmetry (compare, for example, the analysis of hexa-aminobenzene by Knaggs*) in addition to the observed centre of symmetry. But only the centre contributes to the crystal symmetry. Moreover, in other compounds, like pyrene and 1: 2: 5: 6-dibenz- anthracene, the molecules do not appear to contribute even a centre of symmetry to the crystal, but there is 'no reason to suppose that the molecules themselves may not possess such a centre.

3. The four molecules may each possess a centre of symmetry which does coincide with a crystal centre. There are actually eight centres of symmetry contained within the primitive translations of the space group C2, (P21/a), and it is not necessary that only two of these should be occupied by centro-symmetrical molecules. Two is certainly the usual number, because two is sufficient to complete the symmetry. A larger number will probably in general tend to produce a space group of higher symmetry; but the possibility of a larger number in this space group should not be excluded from consideration.

* 'Proc. Roy. Soc.,' A, vol. 131, p. 612 (1931).



190 J. M. Robertson, M. Prasad, and I. Woodward

It is to this last type that we believe the structures of stilbene, tolane, and azobenzene conform. The four molecules in the unit cell each possess an exact centre of symmetry which coincides with one of the crystal centres. Only in this manner can structures be formulated which will explain all the X-ray data, and it will be shown that these structures are not inconsistent with the other physical properties of the crystals.

Measurements of Stilbene

The X-ray work was carried out by completely immersing small crystals in a beam of copper radiation (? = 1 54 A) and recording the reflections by moving film cameras. Rotation photographs about the a, b, and c axes giving the {Okl}, {hOl}, and {hkO} zones of refilexions were measured on the integrating photometer.* For the absolute values of the intensities, two small stilbene crystals were weighed and comparisons with a known standard were made on the two crystal moving film spectro- meter.t The correction factor to allow for the absorption of the beam in the small crystals was calculated from the known absorption coefficients and the dimensions of the specimens. Some results are given below in Table II.

TABLE II

Correction Absolute values of F Stilbene Weight factor for (corrected)

absorption 002 004

mg Crystal a.......... 0052 1140 17-4 44-8 Crystal b.......... 0-216 1X294 20X2 47X4

These two axial reflexions are quoted because they afford a correlation between the {Okl} and the {hOl} zones of reflexions. Crystal a, however, is rather small for accurate measurement, and more weight was attached to the results from b. The absolute values of 24 other reflexions were determined from crystal b, and this list was then employed to correlate more detailed surveys. Some of the results are given in Table IV.

THE STRUCTURE OF STILBENE

It is quite evident that the stilbene structure still displays some of the features of the dibenzyl structure. The axial lengths a and b and the

* Robinson, 'J. Sci. Instr.,' vol. 10, p. 233 (1933).

t 'Phil. Mag.,' vol. 18, p. 729 (1934).




angle P are closely similar. In dibenzyl the strongest reflexions were given by the (202) and the (011) planes. The corresponding planes in stilbene, allowing for the doubling of the c axis, are the (204) and the (012), and it is found that these are still amongst the strongest reflexions. But if the reflexion is expressed, not in absolute units, but as a fraction of the maximum value which would apply if all the atoms were in phase, then it is found that these stilbene reflexions are only approximately one-half of the corresponding dibenzyl reflexions, as shown in Table III.

TABLE III

Dibenzyl Stilbene

(202) (01 1) (204) (012)

F .............. 70 59 68 55 F/Fmax. 062 0*47 0*30 0.23

This result is readily explained if we suppose that two of the stilbene molecules (a and b) have nearly the same shape and orientation as the dibenzyl molecules, but that the other two stilbene molecules (c and d) have quite a different orientation, and contribute little or nothing to these strong refilexions. As a next step, the stilbene molecules c and d must be placed in' positions which will explain the pseudo-orthorhombic symmetry, and the approximate halvings of the (201) and the -(001). The method of doing this will be clear from a study of fig. 1, which repre- sents a projection of the proposed structure on the (010) plane.

All four molecules, a, b, c, d, are placed on centres of symmetry at (000), (I1-0), (001), and (41D1. Molecules c and d might as an alternative be placed at (0121) and (10j), an arrangement which would give the same projection on the (010); but this position can be eliminated by a consideration of the intensities of the reflexions, particularly from the {hkO} zone.

In molecule a the benzene rings have been given the same orientations as was found for dibenzyl, viz.:-

XL = 46.70 XM = 120.60

PL - 77*3 4m 34.30

C)L ~46 * 10 W1M = 76.00

The arrangement of the central -CH= CH- group must almost certainly be different, but discussion of this is deferred. Molecule b, corresponding to the second or reflected dibenzyl molecule, can be derived from a by



192 J. M. Robertson, M. Prasad, and I. Woodward

a reflexion in the plane of the paper and a translation of (la, lb). The molecules c and d can to a first approximation be derived from a and b by rotations of 1800 about the a axis, and translations of Xc. This movement, of course, is not a real symmetry operation of the crystal, but is -required to account for the pseudo-symmetry and the observed intensities. It cannot be exactly right, because the (001) series is not exactly halved, a small (007) being measurable.

With the molecules arranged as in fig. 1, the benzene rings having the dibenzyl orientation and being placed with their planes at right angles to the plane of the connecting -CH-CH- zig-zag, the structure factors

C~~~

012 345A

Scale ---

a b

FIG. 1-Projection on (010).

for some of the more prominent reflexions have been calculated, and they are compared with the measured values in Table IV.

The general agreement is sufficiently good to show that the structure is essentially correct as regards the general. disposition of the molecules. It should be noted that the dibenzyl orientation has been employed, and no attempt made to refine the structure in these preliminary calculations. It is natural therefore that the agreements are found to break down for the weaker and higher order reflexions; because we should not expect the dibenzyl orientation figures to apply exactly to stilbene, and further, we know from the imperfect halving of the (001) etc., that a small difference




TABLE IV-STILBENE

sin 0 F F hkl (x = 1-54) measured calculated

200 0-137 32 -32 020 0-270 9 +29 001 0-053 <2 0 002 0-106 20 +27 003 0-159 <2 0 004 0-212 48 -34 005 0-265 <5 0 006 0-318 11 +18 007 0-371 5 0 008 0-423 17 -19 011 0-145 17 0 012 0-172 55 +79 013 0-208 25 0 014 0-251 36 -30 204 0-294 <3 -2 203 0-248 45 -40 202 0-205 75 +91 201 0-165 45 -63 201 0-125 7 -3 202 0-135 31 -41 203 0-162 42 +63 204 0-200 68 +93 205 0-244 45 +41 206 0-290 7 +1 207 0-339 5 +5 208 0-389 11 +31 405 0-451 <3 +11 404 0-408 38 +34 403 0-368 36 +26 402 0-330 30 +24 401 0-298 6 +10 110 0-151 36 +31 210 0-192 22 -43 310 0-246 <7 -23 410 0-304 25 -24 120 0-279 <7 -8 220 0-303 13 -11

in structure or orientation must be introduced between the two sets of molecules ab and cd.

A large amount of further calculation has been carried out for stilbene, and the latest results seem to indicate that the molecules themselves are flatter than the dibenzyl molecules, that is, the planes of the benzene

VOL. CLIV.-A. 0



194 X-Ray Analysis of the Dibenzyl Series

rings lie nearer to the plane of the central -CHz-CH- zig-zag. In dibenzyl the planes of the rings were nearly at right angles to the -CH2-CH2- plane.

But a discussion of the refined structure must be deferred until a Fourier analysis of the stilbene results is completed.

We must now consider whether the proposed structure is compatible with the other physical properties of the crystal. From magnetic measurements on azobenzene, together with assumptions concerning the values of the magnetic susceptibilities of the individual molecule, Krishnan, Guha, and Banerjee (loc. cit.) deduced that the " long axes (1: 4- direction) of the two component benzene rings in the molecule were inclined at about +480 and -48? to the a axis. Now if we imagine the upper ring of molecule a, fig. 1, connected with the lower ring of c or d, we obtain a distorted molecule which may be compared with Krishnan's. The angles which the long axes of the rings make with the a crystal axis are about +470 and -47?, corresponding to our orientation figure XL.

Similarly, Krishnan deduced that the planes of the two rings are inclined at +390 and -39? to the (001). This figure, measuring the " twist " of the molecule, may be compared with the inclinations of the rings of our molecules to the plane containing the long axis (1: 4-direction) and the b crystal axis, an inclination which corresponds to X 'in Krishnan's notation. From our orientation figures this angle can be calculated, and is found to be 320. It will be seen, therefore, that our structure is just as compatible with the magnetic data as the one proposed by Krishnan, though it may lead to slightly different values of the molecular magnetic susceptibilities. His structure, however, would not explain the X-ray data, because the insertion of the connecting -CH - CH- group between the upper ring of molecule a and the lower ring of c or d would consider- ably destroy the intensity agreements calculated in Table IV.

In conclusion, we wish to thank Sir William Bragg, O.M., F.R.S., and the Managers of the Royal Institution for the facilities afforded at the Davy Faraday Laboratory where this work was carried out.

SUMMARY

Stilbene, tolane, and azobenzene form a series of closely similar monoclinic crystals, space group CQ- (P21/a) with four molecules in the unit cells. A quantitative X-ray investigation of stilbene, with absolute measurements of intensities, shows that the four molecules have centres of symmetry which coincide with four of the crystal centres. Two of the



Scattering of Positrons by Electrons 195

molecules have orientations similar to the dibenzyl orientation,; and the other two can approximately be derived from them by a rotation of 1800 about the a axis, and a translation of Ic. The resulting structure explains the pseudo-orthorhombic properties, the approximate halvings, and the principal X-ray intensities. It is contrary to a structure previously deduced from magnetic measurements by Krishnan, Guha, and Banerjee, who predicted a twisted. and distorted molecule; but it is shown that the new structure is equally capable of explaining the magnetic data. Detailed measurements have not yet been made on tolane and azobenzene, but the preliminary data are sufficient to show that they are both closely similar to the stilbene structure.

The Scattering of Positrons by Electrons with Exchange on Dirac's Theory of the Positron

By H. J. BHABHA, Ph.D., Gonville and Caius College

(Communicated by R. H. Fowler, F.R.S.-Received October 20, 1935)

It has been shown by Mottt that exchange effects play a considerable part in the collision and consequent scattering of one electron by another. Mott's original calculation was non-relativistic, and there the exchange effect vanishes when the two electrons have their spins pointing in opposite directions. M0llerl later developed relativistically invariant expressions for the collision of two charged particles with spin, and it may be seen directly from M0ller's general formula for the collision cross-section that, in the collision of two identical particles, the effect of exchange does not in general vanish even when the two colliding particles initially have their spins pointing in opposite directions. It tends however to zero in this case as the relative velocity of the particles becomes small compared to c, the velocity of light, in agreement with the calculation of Mott.

The effect of exchange in the general relativistic case will still be considerable if one of the two electrons be initially (and therefore finally) in a state of negative energy. (If one of the electrons be initially in a negative energy state, then it follows from the conservation of energy

t ' Proc. Roy. Soc.,' A, vol. 126, p. 259 (1930). i 'Ann. Physik,' vol. 14, p. 531 (1932).

o 2



x-ray analysis of the dibenzyl series. iii. the structure of stilbene, tolane, and azobenzene

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