Space correlations in succinonitrile observed by X-ray scattering

Solid State Communications,

Vol. 14, pp. 77—81, 1974.

Pergainon Press.

Printed in Great Britain

SPACE CORRELATIONS IN SUCCINONITRILE OBSERVED BY X.RAY SCATFERING M. Descamps Laboratoire de Thysique du Solide (Dynamique des Cristaux), Umversité de Lille I B.P. 36 59650, Villeneuve D’Ascq, France —

—

(Received 16 July 1973; in revisedform 5 October 1973 by P.G. de Gennes)

The succinomtrile offers a plastic phase (m3m) for the usual surrounding temperature; its molecule is not globular and the quite structured areas ofX-ray scattering appearing on LaUe photographs can be interpreted in a quantitative way whenever the effect of space correlations of steric origin is taken into account.

IN THE course of the study of plastic crystals by X-ray process, only a small number of reflections can be detected, each of their intensities are falling off with increasing Bragg angle and the diffuse background is sizable. This scattering, in some way, might be compared both to that of a liquid and the thermal scattering of a common molecular crystal, but

~Bi A

—

/ / 12

/1

—

~A

2,,’

correlations induce modulations in reciprocal lattice. The choice of the succinonitrile enabled us to study the correlations effect of steric origin and therefore of a short range.

A

~

/

A2’ I ------

The structure of succinonitrileNEC—CH2 CH2 CE Nin plastic phase has been lately published:’ the crystal is body centred cubic. The parameter is 6.34 A and the space group (m3m). There is an equilibrium between Trans and Gauche isomers of succinomtrile: —

--

/

\

i

/ -—

__.~ A1

~

-

—

FIG. 1. An example of configurationsfor two first neighbour molecules A (Gauche) and B (Trans). The different positions of nitrogen atoms in the cubic cell are indicated.

Trans isomer of C2h symmetry in the proportion of 20% Gauche isomers G1 and G2 of C2 symmetry (G1 and (32 can be derived from Trans isomer by a ±2ir/3 rota~onof one of the CE Nbonds regarding the other around the middle bond C C) in the proportion of 40% for each. Ori its lattice site the equilibrium positions of the molecule are as follows: middle bond C C ofaxis the of molecule may direct itselfThe along the four three-fold the cubic ccli. Around the three-fold axis bearing its middle-bond, —

the molecule may occupy three equilibrium positions derived from one another by a 2,r/3 rotation around this am

—

Each isomer can take twelve equilibrium positions which determine a mean molecular configuration

—

compatible with the symmetry of the crystalrefine. (Fig. I). 2’8 positioning The structure The rotational shifting In the of the molecule has been set off. ment1 has been performed on assuming that there are two modes of vibration: an isotropic vibration of the

—

77

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SPACE CORRELATIONS IN SUCCINONITRILE

Vol. 14, No. I

centre ofmass (u), an anisotropic libration (0) of the

means of a diffractometer using C~K0,radiation.

CH2 C E N group around the three-fold axis, the results are i? 1/2 = 0.29 A, ~ 1/2 = 0.6 rd.

Figure 3 points out its variations along the three fold axis after corrections for Compton scattering and air scattering.

—

______________________________________

For a plastic crystal the effect of large vibrations, orientational disorder and correlations that may be encountered, have to be taken into account while formulating the scattered Intensity To such an end it is assumed that the frequency of the shifting is lower compared to the frequency of the vibrations, which is usual with plastic crystals. The average intensity must be reckoned In two times, on the vibrations for a given orientation and on the differentorientations as well

mf

FIG.2. Laüe photograph; Three-fold axis perpendicular. Radiation: CulCa, distance film-crystal =3 cm.

Then

I(S)

=

4(5) m,p ~ ~fj

_______________________

ei2~~S(l~m ~ e12 S(r~_rf)ei2~r5(h1r-ui)

The diffuse areas which are observed on LaUe photographs (Fig. 2) show a set of concentric ‘structured halo rings’ which observes the symmetry of the Laile group. Such halo rings are therefore different from those of liquids. Besides they don’t seem to be of a merely thermal origin and they don’t reveal so anisotropic a pattern as the one related to correlation in chains. Aquantitative interpretation is needed in such a case. The mean global scattering power (F~),ratio of the intensity scattered by an electron of the crystal to the intensity scattered by a free electron in the same conditions has been measured on single crystals by

~r

+ ~,m is the instant position of the / atom in the m molecule. N = number of molecules in the crystal, n = number of electrons in one molecule. Rm +

Being assumed there is but one kind of molecule and that vibrations of different molec les are independent, a usual process4 enablesus to write (1) as being the sum of the three following terms: (a) the intensity diffracted by the mean crystal, reduced by the D.W. factor Je(S)

{ ~~

~ Pgm 7

S I—.’

5 4

3

,

/

/ I

1

(1)

= fl’N’Ie•Pgm

S along [111~’

.xp.rlm.ntal

~ FIG.3. X-ray scattering along the three-fold axis.

_____

ei2~Otm .Rp))

IFr(S)12

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SPACE CORRELATIONS IN SUCCINONITRILE

79

((3) the scattering term of a disordered crystal without correlations, taking account of the thermal agitation: D(S) = NIe(S)(Fi~(S)HFT(S)I2}

In the case of an ordered crystal, the formulation of the D.F.T. of Amoros6 is found again. (‘y) The effect of the correlations, the D.W. factor being taken into account of C(S)

=

NIB(S) ~

N~ C

f I FT(fZm)P’(~2m)

p*O ~1mnp

[P’(~p)p2(~ZpIClm,r)] ~

P’(~Z)is the probability of the ~2orientation. P2 (~pf~2m , r) is the conditional probability of the 12~,orientation with £Zm from the outset

C C

001

C

N

(r=Rp—Rm)-[P’(~2p)—p2(czpZm,r)1~3’0asIrN°° I

The computing ofD(S) in the case of the succinonitrile has been performed using the results that were got while structure refinement: the D.W. factors and the equilibrium positions.

c-—’

‘-s

/

C ThenFT(S) = e~ 2~f,ei2w5e_2~~3UhJl~2 The sum Is to be based on the mean molecule, thef 2u2. U/” = 0Ai~.The 1 are ponderate. B =the 2irthree-fold axis are pointed variation of D(S) along out on the Fig. 3. This term features the importance of the scattered radiance and the great angles scattering, but the first peak does not coincide with the innermost experimental ring ( ~ 0.3 A-’). The approximations used for the D.W. factors evaluation are not the cause of the discordance for use other factors does not bring about a sliding of the first peak. Within the reciprocal range corresponding to the innermost ring the intermolecular correlations have their most important effect. The computing of C(S) for succinonitrile is based on the next structure analysis: whatever the equilibrium position of the molecule on its site may be, nitrogen atoms of

C

o

C N

FiQ .4. An example of steric hindrance between two

Trans molecules in succession. the middle of the side. Along the [0011 direction, for example there cannot be two Trans molecules such as those shown on Fig. 4, In succession. Though there is no long range order for the orientations, steric hindrance imposes some spatial correlations at short range. To compute the corresponding scattering term all the conditional probabilities must be estimated.

CH 2—C N groups fill the middle of one of the sides of the cubic cell issuing from the origin of the group. For two second neighbours molecules, there is cornplete steric hindrance between configurations thSt would bring, for both of them, a nitrogen atom to

The evolution of one of them is given as an example along dour-fold axis (Fig. 5). The complete contribution to scattering is repre~tedon Fig. 3 for S along a three-fold axis; it has been computed within the limits of the fourth neighbours and along the basic crystallographic directions of the reference cubic cell.

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SPACE CORRELATIONS INSUCCINON1TRILE

Steric hindrance correlations [C(S)] imply the annthiI~ticnof the first peak ofD(S) and the sliding outwards of the innermost calculated ring. The effect of correlations is null beyond 0.5 A-1. The accordance is good along the three fold axis and less satisfactory along the other directions (Fig. 6) but the basic Influence is the same. We expect to Improve this result by completing the calculating and by Introducing dipolar interactions.

P2(OP/0mnt) 0.04

P~Q~ 0.03

s~

Sc

,~?

~_----~‘~

0.02

/

0.01

Vol. 14, No. 1

I

0

FIG .5. An example of evolution for p2 (12p/12m.r) along a fourfold axis (c). (110)

~gm

7 6

/1

/

/

•

5

/

4 3,

:

\ I

~:

I ~I

\ I

~:

(220)

S

/~%~‘\

/

I ,j

/

____

H I’

~•

. —

along

[1101

experimental D(S) o (~+ C(S)

/~~/~ ~--~

0

I

I

0,1

0,2

0,3

0,4

0,5

0,6

5,

0,7

0,8

0,9

FIG.6. X-ray scattering along the two-fold axis. REFERENCES FONTAINE H. and BEE M.,Bull. Soc. Fr. Mineral. O~stallogr.95,441—450(1972). 2. LONGUEVILLE W., FONTAINE H. and CHAPOTON A., J. C7iem. Phys. 68,436(1971). 3. 4. 5.

BOYER L. and COLL,Thys. Rev. Le#. 26,1435(1971). FOURNET G., These, Université de Paris, (1950). AMOROS J., Molecular &ystals Monographs in Qystallogniphy, Wiley, New York. -

Vol. 14, No. I

SPACE CORRELATIONS IN SUCCINONITRILE Le succinonitrlle présente une phase plastique (m3m) a tempórature amblante. Sa mo1~cu1en’est pas globulaire et les zones de diffusion X três stnscturées qul apparaissent sur les diagrammes de La~1es’interprètent quantitativement quand on tient compte de l’effet des correlations spatiales d’origine stCrique.

81