Let I f ^(hkl) I be the calculated structure factor which can be
DIRECT (%),(°) PARAMETER RECIPROCAL (RLU)
11.458 0.1356
9.245
0.19649.241
^T 0.1976 121,7 58.13 96.1 ^T82.99
89.?
86.54 '^GT 0.1669828.
^T 0.00121 'È103
I
« 4 ;s- space group PI or pl. iFrom the oscillation photograph, zero and upper layer Neissenherg -ÿ
I
photographs, approximate cell parameters were calculated by direct £ measurement and by the angular-lag procedure as described in Chapter 2. | Results obtained by these procedures are shown below (Table 5.3)«I
:
%
.1
Flotation in a (1:1) mixture of CHgBr-CHgBr (l,2-dibromo-ethane) and GH^I (iodomethane) gave an observed density, = 2.23 Mg. m The calculated density was, = 2.48 Mg. m for Z = 1.80 (■^2,0) units of
28bCl^.l-0]^QHyCl (M=618.9). j
■
5.4 DETERMINATION OF APPROXIMATE STRUCTURE -
Intensity data were collected using nickel filtered GuKoc
radiation on a multiple film 'pack. Layers 0 to 2 about "c^'* axis were recorded.
Corrections for Lorentz and Polarization factors were applied in
computing the structure amplitudes, IFhklI , hut no corrections were made for absorption or extinctionj( /t « 339 cm“l),
All the hkl reflections (I9I in total) were used to compute a three- dimensional Patterson map in order to locate the heavy atoms. This showed the following highest vector peaks;
TABLE 3.4 "
PATTERSON GOOREŒNATSS (U,V,W) OF HIGHEST PEAKS FOR SbCl-.l-OjoHyOl.
No. Height Fractional vector coordinate U V W Interpreted Source of Vector 1 730 0.31 . 0.61 0.01 2 710 0.11 0.46 0.88 Sb^-Sbg' 3 440 0.00 0.00 0.50 4 390 0.41 0.17 0.12 Sb^'-Sbg 5 360 0,15 0.12 0.27 6 330 0.34 0.75 0.16 7 330 0.40 0.92 0.08 Sb^'-Sb^ 8 280 0.34- 0.37 0.17 9 270 0.24 0.37 0.13 10 270 0.63 0.33 0.23
where x ’=-x, y‘=-y and z'=-z. Equivalent centrosymmetrically related peaks are not listed.
Interpretation of the vector map was carried out assuming the space group PI. Considering two formula units of 2SbC 1 ^, 1-C^^gHyC1
in the unit cell, there are 4 Antimony, 14 Chlorine and 20 Carbon atoms (leaving out the H atoms).
Out of the expected total of 38 x 3? ~ 1406 vector peaks in P(U,V,W), the Sb-Sb vectors will be the greatest in height (apart from possible overlapping). Thus in the interpretation of the vector map peaks of smaller value can be ignored to leave an expected 12
Sb~vSb vectors in the unit cell. Less than this number is observed
due to overlapping.
The space group PI requires two types of antimony atoms in the cell. Vectors between non-related Sb atoms will be augmented (doubled, vector Sb^-Sbg overlaps Sb^'-Sb^') relative to those between related Sb atoms. Thus with Sb^ at (x^, y^, Zq) and Sb^'at (xg, Yg» 2^) generating Sb^' at ("x^, -y^, ~zq) and Sbu' at (-Xg, -y^, “z^) the largest peaks, P, will be peak 1 (Tab 5*4), Sb^-Sb^ at (xq~x^) etc. and Peak 2 Sb^-Sb^' at (x^tx^), etc. The coordinates of the two asymmetric Sb atoms may be evaluated as half the sum and half the
"2 1
difference of the vector coordinates for peak 1 and 2,x-, — —p ~.p ■ -1- ,
Xg-"^p^ i.e. Sb]^ at (O.3IO, O.535, 0.445) and Sb^ at (07^ , oTÔÿj, O.435) so that Sb ' is at (O.200,0.075»0*565)* A lower vector due to Sb^'-Sb^ at
(“0.62, ”0.07,
“0.89)^(0.30, 0.93» 0.11)
is then equated to peak7
and that due to Sb^'-Sb^ at (0.40 O.I5 O.I3) is peak 4.
To locate the remaining atoms an electron-density synthesis was computed using all the observed structure amplitudes with signs calculated from the Sb atoms as located. Tiis showed some peaks corresponding to the chlorine atoms Cl,^ at (O.369, 0,700, 0.355)» 01^ at (0.444, 0.629, 0.703), Gig at (0.846, O.29O, 0.387)-(0.l54 O.7IO . 0.613) and Gl^ at (O.I28 O.323 O.58I). A second 30 electron density synthesis with structure factors given by two antimony atoms and four chlorine atoms showed the fifth chlorine atom 01, at (0.954 1.048 0.694)“
(0.046 0,952 0.306). From a third 30 electron density synthesis the remaining chlorine atoms were located.
They were Gig at (0.330, 0.08?, O.368) and 01% at (0.68?, O.fjZ, 0.039). At this stage it was decided to refine the position of antimony and chlorine atoms using a Stanley Shift parameter method. After several cycles the overall R,factor was 0.175*
A difference synthesis calculated using all hkl reflections with signs calculated for two antimony and seven chlorine atoms in the asymmetric unit did not show outstanding peaks corresponding to the carbon atoms. Therefore it was thought that packing consideration might suggest the possible position of the l-G^^HyOl molecule. With
this in view it was decided to calculate the best position of the
1-C^qH^G1 rigid molecule to fit in the cell space available and then to use it in further refinements. Thus a FORTRM IV (HONEYWELL/TSS) computer program was written to perform such a calculation (see appendix .A- ).
The strategy for this consists in taking the known Gl% coordinates and rotating the rigid molecule about this point (angles 6 , cf , Ÿ" about three orthogonal axes X, Y# 2 respectively). Atoms belonging to the 4 SbGl^ molecules (4 Sb and 12 Cl) are kept in fixed positions so that distances from these atoms to the rigid molecule can be calculated after each rotation step. Brovided all these distances exceed a minimal value (the distance limit) there is space for the rigid molecule to fit into the structure. Such acceptable positions are expressed by the magnitudes of the rotation angles
0
, <j> , 'Ÿ' • A typical example of computer output is given in Table 5*5* From the acceptable rotations of the rigid molecule, triclinic fractional coordinates for each carbon atom were then calculated. Each set of coordinates were comparedwith the difference map and false unacceptable coordinates were taken to be those in markedly negative regions. In this way only two of the possible positions of the rigid molecule remained acceptable
(3 and 9 in Table 5*3)•
■ TABLE 5*5
possible ROTATIONS OP THE RIGID MOLECULE GCMIUTED