Crystallooraphlc 6

Ellipsoids of thermal vibration

Crystallooraphlc 6 Crystallooraphlc 6

Figure 1. Cyanuric Triazide Distances and Angles from Knaggs (8).

zine ring was reported to be 1 - 2 per cent. The average C-N dis- tance in the ring was 1. 34

•

5 A. It is, the re fore, apparent that the individual C-N distances deviate from the average by little more than the estimated error. Nevertheless, an explanation for this bond al- ternation was proposed which involved fixation of the ^Tr bonds by the unsymmetrical position of the azide chains (8). The present work was undertaken with the objective of accurately measuring the C-N distances in order to learn if this bond alternation is significant.

-53-

EXPERIMENTAL Low Temperature Equipment

Because of the low temperatures which were attained in this study, the usual method of crystal mounting (in which the crystal is glued to a glass fiber which in turn is glued to a brass pin) was abandoned. (".['he different coefficients of exp ans ion for glass and brass cause s}rfficient strain at these temperature$ to rupture the

glass-to-bras~ joint.) Instead, the crystal was glued to a glass pin, one end of which had been pulled down to. a very small diameter from a piece of 1 /8¹¹ glass rod in the very narrow flame of a natural gas - oxygen torch. The other end of the pin, which was 1 /8¹¹ in diameter, was clamped directly into the goniometer head. To protect the crys- tal from buffeting in the stream of cold nitrogen, a glass capillary 1. 5 mm. in diameter with O. 01 mm. walls was then glued in place around the crystal (see figure 2). Duco cement diluted with an equal volume of amyl acetate was found to be very satisfactory for this low temperature work.

Z

^crystal

sealed end of ~=-

1. 5 mm. capillary ---'><~~§5:J::::J)

Figure 2. Crystal Mount.

1/8¹¹ glass pin

The - l 10°C temperature at which the intensity data for this study were collected was attained by a blower apparatus which was designed and built by J. Rollet (12). This apparatus is very similar

to the one !le scribed by Abrahams, Collins, Lipscomb, and Reed ( 1 ).

A stream of very cold nitrogen was directed at the crystal by a Dewar-type blower tube which, for a Weissenberg camera, is in- serted through the open end of the layer-line screen. The other end of the blower tube is bell-shaped and situated directly above a heat- ing coil. The bell-shaped end of the tube and heating coil were .sub- merged in a reservoir of liquid nitrogen, and the stream of cold nitrogen was provided by boiling the nitrogen into the blower tube (see figure 3 ).

(To

Potentiometer

~ layer- Line Sceen~

7 Volts A.C.

~~----"---

1 T:!Crystol

'-Blower Tube

0

Heating Coil

Liquid Nitrooen

Copper- C onstantan Thermocouple

Figure 3. Schematic Drawing of the Cooling Apparatus.

-55-

The temperature was measured by a copper-constantan thermocouple which is situated at the nozzle of the blower, directly in front of the crystal. The thermocouple potential at which these measurements were made was -.4. 7 mv. (reference junction at room temperature), which corresponds to a temperature of - ll0°C (12).

Unit Cell Parameters

Cyanuric triazide is hexagonal, space group P 6

3 /m with two molecules per unit cell. The crystals which were used in this

'

study were taken from the original sample of crystals used by Hughes (5). T}l.ey were elongated along the £. axis in hexagonal

·:

prisms. The crystalline faces were covered with a white powder;

however, the d~ffraction patterns were quite normal. The colorless crystals quickly turned brown when exposed to X-rays, but a zero- layer Weis senberg picture of the ;:_, axis crystal made at the conclu-

sion of this work gave no evidence of disorder and showed the same relative intensities as were observed on the first zero-layer picture.

Excellent cleavage perpendicular to the ;:_, axis was observed and used to obtain approximately equidimensional crys_talline fragments from the needles. Two crystal fragments approximately one milli- meter in every direction were used for the measurement of intensi- ties. One fragment was mounted along the c axis; the other, along the Re, axis.

The unit cell dimensions at - l 10°C were calculated from measurements which we re made on a zero-layer .Weissenberg picture of the crystal which was rotated about the a axis. Mo K radiation

a

was used, and the following · wavelengths were assumed.

MoK =

a.l.

o.

10926

A.

0

MoK = ^0.71354A

a.2

"

MoK = ^0.7107A

a.

The film was calibrated to eliminate errors due to film shrinkage by marking it with a known distance before developing. Ten high-angle reflecti.ons were used as input to the CR YRM ¹¹Unit Cell Least Squares Program" (r,e,f~rence 3, chapter 10) which was written by Mr. George Reeke. Th~·{unction which was minimized was

N

" ( . 2

L; w sin 8 b

n=l n o s.

. 28. ) 2 ( 4 )²

- sin - -

calc. A 2 n

where N is the total number of observations and w is the weight n

f or t h e n th b o servatlon. .

Fn ⁼

The weighting function was E/ sin2 9

n

where E is an external weight. In this calculation, E was I. 0 ex- cept for a couple of doubtful observations for which E was 0. 5 . Corrections for eccentricity and absorption were included in the cal- culation. The following unit cell dimensions wer~ obtained.

"

a - 8. 7 5 + O. 03 A

0

c

=

5. 85

+

O.- 02 A

The estimated uncertainties are an order of magnitude larger than the sigmas which were .obtained from the l.east squares calculation.

They were estimated by assuming an uncertainty of 0. 3 mm. in' the camera radius.

- 57- Intensity Data

The intensity data were collected photographically at - 11

o

⁰

c

by the multiple-film,equi-inclillation Weissenberg method. Layers zero through seven about the ~ axis and layers zero through four about the a axis were photographed with Mo K radiation. For lay-

~

a

ers zero through four about the c axis and the zero layer about the

~

~ axis, two packs of four films were used. Each of the other layers was photographed with a single pack of four films. Within each film pack, the four films were separated by three sheets of 0.001 inch nickel foil which provided a film to film attenuation factor of about 0. 3 for Mo K radiation. Intensities were estimated visually by com-

a

paring the diffraction maxima on the films with a calibrated intensity scale which had been prepared by timed exposures.

The data reduction and all subsequent calculations were per- formed on an IBM 7094 computer by the CR YRM crystallographic. computing system (3). As each reflection was entered into the data reduction, a standard deviation for the intensity, a(I) , was com- puted according to the following function.

a { I ) = -1 B+0.1331+ O.ll

2

x

1+0.25e-S0(0.· ⁵-sin 9)

l '

^{2 ] [ ' 2 2]}

we· (70. O;..I) for I < 70. 0 ,

a{I) = a very large number for I>- 70. 0 B = O. 6667 for the data from axis c , B = O. 3333 for the data from axis a .

The I is the raw intensity, and w is an external weight which was e

1. 0 for most reflections. Values of 0. 2 or 0. 5 were entered for a

few questionable reflections. The cr(I)' s were carried through the rest of the data reduction and scaling by propagation-of-error meth- ods.

Factors for film to film s.caling were calculated in the usual way from intensities which were measurable on more than one film.

Since the successive films (A, B, C, and D) in each film pack had nickel foil between them, a certain amount of fluorescence was pos- sible. There were, consequently, three different film environments within each film pack (A, B and C, and D). Therefore, the three film factors were not expected to be equal. For this reason, an over-all general film factor was not used for film fo film scaling.

Instead, the following procedure was used. The film factors which had been calculated during the first pass of the "Initial Data Proces- sing Program" were sorted into three groups. The film factors re- lating film A to film B were put in group l; film B to film C, group 2; and .film C to film D, ·group 3. It was observed that the group 1 film factors for the ~ axis pictures were significantly smaller than the corresponding film factors for the c axis pictures. (This is,

. ^~

perhaps, due to the reduced background on the A films for the ~ axis pictures which resulted from the narrower wid~h of the layer line slit which was used for these exposures. ) Consequently, group 1 was divided into two groups; group la for the ~ axis pictures and group

le for the ~ axis pictures. After accounting for the angle of inci- dence between the X-rays and the film, the ' ~ilm factors within each group were averaged. The four average fl.lm factors which resulted

-59-

are: Fla:::': 2. 6765, F ^le

=

3. 0232, F

2

=

3. 4632, and F

3

=

3. 4085 . The average film factors were then corrected for non-normal inci- dence of X-rays and applied in the film to film scaling.

The raw intensities were then corrected for the Lorentz and Polarization factors and reduced to a common scale by a comparison of .reflections which were observed on photographs about both axes. Absorption correc~ions were neglected because of the small linear coefficient of absorption for cyanuric triazide in Mo K radiation

a

(µ = 1. 47 cm. -1 ). A data tape suitable for subsequent calculations with the CRYRM system was then prepared by Dr. Duchamp's ¹¹Data

Tape Preparation Program" (reference 3, chapter 5). This data tape listed for each reflection the indices, the observed F, the atomic scattering factors for carbon (valence) and nitrogen (7), and a weight

-v:;;;;

which is equal to the reciprocal of cr(I).

l

REFINEMENT

The asymmetric unit consists nf four nitrogen atoms and one carbon (one third of a molecule) which are all in the six-fold special positions (h) of Wyckoff (5). These positions are:

x, y, 1I4 ; y,x-y,1/4; y-x,x, 1/4

x,y,3/4; y, y-x, 3

I

4; . x-y, x, 3/4.

There are, consequently, only ten spatial parameters to be deter- mined. The layered structure which results from atoms in these special positions produces a diffraction pattern which, except for the attenuation associated with increasing diffraction angle, depends upon t only insofar as it is even or odd (5, 8). Nevertheless, three-

dimensional data were collected in order to increase the accuracy of · the spatial parameters and to calculate the c axis temperature fac- tors.

Knaggs' (8) spatial coordinates were used as input to a three- dimensi6nal least squares refinement (6) which was performed by the CR YRM "Hexagonal Least Squares Program" (reference 3, chap- ter 6) which was written by the author. (See Appendix for details of this program. ) The atomic sca~tering factors for nitrogen and car- bon (valence) were taken from the "International Tables for X-ray Crystallography" (7). Initially, the individual isotropic temperature

. 0 2

factors were arbitrarily set at l. 2 A . The function which was min- imized is

where w is the weight; k , the scaling factor by which F must obs.

-61-

be multiplied to be on an absolute scale. Those reflections which were not observed above the background (hereafter called ''less- thans") were included in the least squares refinement only if F al

c c.

exceeded the minimum observable F b . Of the 2, 316 recorded

0 s.

reflections, i, 360 were "less-thans",of which only 74 were included in the final least squares cycles. All seven 0 0 t reflections (t

=

an .even integer) were given weights of zero because of extinction.

(All atoms scatter in phase for the 0 0 t reflections.) Seven other reflections were given zero weights because of extinction errors.

Another forty reflections were given zero weights because of poor agreement between values measured on both axes or other indica- tions of unreliability. Consequently, only 976 of the 2, 316 reflec- tions were used in the final least squares cycle. The progress of the refinement is summarized in Table I.

The initial R-value,

R = r: j

lkFobs.1 - IFcalc.11 I:lkFobs.1

for the copper sphere was • 35. The first six cycles (the B series) were performed two cycles at a time with a full matrix utilizing data for which sin 2

9

h

² < 0. 42 (the copper sphere).

TABLE I

Initial R-value for the Copper Sphere = . 35

>:c . 2 >!<

L. S. Cycle

-vw:

^(Sl~ A.

⁸⁾

max ^{R Remarks} Bl 1 /F b . 0.42 . 12 Full matrix, iso-

0 s

tropic.

TABLE I (continued)

*

^{2 ':<}

L. S. Cycle

-vw; ^{(si~ e)}

^{R Remarks}

A. -max

!/Fobs.

>,<>l<

B2 0.42 . 28 Four negative tem-

'~'~':c perature factors.

B3 l/cr(I) . 16 Four negative tem-

perature factors.

B4 . 18

B5 l/(Fobs. )2 . 094 One negative tem-

. oszt

perature factor .

B6

Data Were Re-scaled

Cl l/cr(I) . 082

CZ . 11

tt

C3 1. 0 . 11

C4 . 12

t t t

C5 Complete . 085 . Anisotropic

Mo Sphere

!

C6 . 083

C7 . 082

cs

^{. 081}

C9 . 081

ClO . 081

>:<

Values listed under these headings remain constant from cycle to cycle unless noted otherwise.

;!~'le

This R is large because new temperature factors were used in place of the negative ones from B2.

:>:C>'c>:C

' It was found that these cr(l)'s were in error.

t This R was improved by re-scaling the data before the structure factor calculation.

tt

This R is large because data out to sin2 8/t... 2

=

1. 0 were used for the structure factor calculation.

-63-

TABLE I (continued)

ttt This R is large because the complete Mo sphere was used for the structure factor calculation.

Isotropic temperature factors were used .. The weighting scheme was 1 /F b for the first two cycles. Four of the isotropic

0 s. .

temperature factors were negative after these two cycles. The as- sumption was made that the weighting scheme was responsible for the negative temperature factors. The temperature factors were reset

~ 2

at 1. 2 A , and the weighting scheme was changed to 1 /a(I) for cycles B3 and B4. Again, four temperature factors were negative following cycle B3, but cycle B4 made them all positive. The temperature fac-

o 2

tors were reset to values in the neighborhood of 1. 2 A , and the weighting scheme was changed to 1 /(F b )2

for cycles B5 and B6.

0 s.

In the meantime, a close examination of the data revealed serious errors in the assignment of weights by the "Initial Data Pro- cessing Program" and in the inter-axial scaling. These errors were corrected by re-scaling the data, and the final ten cycles (the C

series) of least squares were performed. The data were expanded to sin2

e IA

²

=

^I. 0 for cycle C3 and to the molybdenum limiting sphere for cycle C5. The isotropic temperature factors were replaced at cycle C5 with anisotropic temperature. factors as described in the fol- lowing expression.

Since all of the atoms are situated on a crystallographic mirror plane, one axis of each thermal ellipsoid must be perpendicular to

this plane. Therefore, [3

13 and [3

23 for each atom must be identically zero.

Convergence was attained with cycle C8, but two additional cycles were performed after various doubtful reflections had been given zero weights. All shifts in the final cycle of least squares were less than a tenth of the corresponding standard deviations. The final R-value was . 081 .

Since the only evidence for the crystallographic mirror plane was the indirect evidence for a layered structure, four anisotropic cycles of least squares were performed in space group P 6

3 . Con- vergence was reached with an R-value of 0. 080 . The bond distances and angles which resulted did not differ significantly from those for the structure in P 6

3/m. The terminal azide nitrogen, N(5), (see figure 5 for the numbering of the atoms) showed the greatest devi- ation from the plane of the triazine ring. This deviation, 0. 089 A

.

along the c axis, however, was less than the root mean square vi- brational amplitude in this direction. Consequently, the presence of the crystallographic mirror plane was considered as established.

As an independent check on the correctness of the structure, a Fourier synthesis and a difference Fourier synthesis were calculated for the section, z

=

^{1 /4. The} Fourier section is presented in figure

0 3

4. The contours are at intervals of 5 electrons/ A . The positions of the atoms as determined by least squares are indicated in the Fourier for one asymmetric unit by x' s . . An electron density of 40 electrons/

0 3

A is indicated at the centers of the atoms within the ring and the first nitrogens, N(3 ), of the 'azide groups. The middle and terminal nitro-

b - --

e e .

~,/ ^{- ... :r}

~. - ^~

9 0 -

• -

Figure 4. Fourier Synthesis of Cyauric Triazide. Section at z

=

1/4. Contours are at Intervals of 5 electrons/A3

.

gens of the azide groups possess an electron density of 35 electrons/

A 03 at their centers. The larger temperature factors for these mid- dle and terminal azide nitrogens spread the atoms over a larger vol- ume and decrease the electron densities at their centers. The sharp- ness of the peaks in the Fourier results from two factors: 1) Knaggs observed very sharp peaks in the room temperature Fpurier, which were attributed to the absence of hydrogens in the structure (8); 2) the low temp~ fature at which the present study was conducted sub- stantially red.uced thermal vibration. , . The.noise level in the differ- ence Fourier y.ras about 1 electron/A3

with maximurri positive and

D 3

negative peaks, 1. 75 and - 1. 33 electrons/A , respectively. The noise appeared to be concentrated in the plane of the molecule, and was substantially lower throughout the rest of the unit cell. When compared with the peak heights at the atomic centers, the noise level is insignificant.

The final spatial and temperature parameters (for the struc- ture in space group P 6

3 /m) are presented in Table II. The struc- ture factors which were calculated from the parameters in Table II

TABLE II

Final S;eatial and Tem;eerature Coordinates (All z coordinates are 1/4.)

Atom x y

J311

f322 1333 /312

>:<

N(l) • 2120(2) . 487 8(2) . 0025(1) . 0027(1) . 0061(2) . 0025(2) C(2) . 3864(2) . 5533(2) . 0026(2) . 0024{l) . 0045{2) . 0027{2) N(3) . 4543(2) . 4385(2) . 0035(1) . 0029(2) . 0075(3) • 0042(3)

Atom N(4) N(5)

-67-

TABLE II (continued)

x y

. 3329(2) . 2772(2) . 2412(2) . 1308(2)

J311 /322 . 0039(2) . 003 2(2) . 0060(2) . 0032(2)

f333 . 0076(3) .0154(4)

f312 . 0045(3) . 0052(3)

>:<

The figures in the parentheses are the standard deviations multi- plied by 104 .

are compared with the observed structure factors in Table III. Each data group in Table III is preceded by the value for h , the letter k , and the value for ,f, which define the indices for the particular data group. The columns of Table III are k , F b X 10 , F al X 10, in

0 s. c c.

that order. A minus sign in the second column indicates a "less- than", and the numerical value which follows the negative sign is the minimum observable F . An asterisk following a value in the second column means that the reflection in question has been given a weight of zero in the least squares refinement.

\ ' . _{IU -Ul} I l l

....

IU IH .. , •1"1 _,.

IU ur

•• -11•

• 41 , .

' -u •

10 _, . . . . l l 41 _,,,

l l -u _,

I ) - l l _, ' " -2' -11

:: ^:;:

-::

I f -z• -n

:: ^{:;: -~~}

IO H Jt

'

..

0 ,, . , I ZJJ · l 4 l

z -10 -n J I . , UI

...

'-11 -··

• ) I _,,,

1 ·IO

• l t •ll

• - l l lO 10 ' ' -H

II UO 11'

II 1l 14

l ) _ , , _ ,

'" ., _.,

:: _{n -n l l} =~= _-lf =~~ -1• _{_,}

,, -u -u

' . ' U1 •IJJ 10 _,_, ll• I l l

...

.,.. _{•u -100} '

• ,, -u

! -!i -u

. ^... ..

u ro -•1

I I 'ti '1 1l •,H · J I ) .. , ...

:; !: :!

u -11 -n n -ir n II ·14 l'H

.

IH ll

IH •IU 104 ID'J

-••• -n

• ·U I

' ' 4 '°

.

' -u ^'' -u ^...

: ;; :;!

10 -H · l l l l -u -u u .. , ... , u " _,.

'" -n -1

n -u n

II · H · l l

11 ·14 II

I I · I I ·11

' ' .

0 ' ' _,.

I 111 •114

l HI JOI

' l•J •lot

· P I

' ., "

• 110 l l J

1 ' ' , ,

...

^,,

• •O II

to J• -n II - l l 10

l l -n I

tJ " ' 41

•• -u _,

" -u lZ I I •lJ I I f

.

t

..

-u tu

^..

-·

l , ' " -It

...

., -u

...

_{' -n}

... ...

lO ·l l II -n

~!

:H

• ., -11

.. . .

^, _:~ ^..

^'.

_~!

1~: ~!~

JI · H

-l" ,. u '

'JI ·'JO

: ^{-~~ ~:}

U · H · • I I ·19 I t l l " -'1 1> ... _" _,. _-n " "

-

_-•

·

II •IO · l

.

-11 ^'

.

' "

~::

..

~;: ^_,, -u -·

-n ,.

11 - · ·

" -u

•H II

H ti

10 _,, _,.

n ^-~; .::

11 ' " . , ..

14 _ , . -t•

u - l l ,

. _{_.,}

^{)1 '}

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^{J )} )

...

,.

"

n '"

... _,.,

• u ...

' "0 , .

I •n t•

. ^_,.

:! ^-!;

:~ ::;

.

"

"

"' . .-u

..

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..

_,., u

-·

JI ^, U" IOI

U -IO

• " _,l

' "' - .. o

I -n II

• _,. -u

10 · U I"

I t - l l 0 l l · U U' . , IJ "

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I - l l 0 :l , _, , " ' -4S 11

• u ,.

' t ) . ,

• ' _,, ' ' -n -u

.

^{" _,,}

• -u -u

10 -u J

n _II ^=~: _-11 ^-!!

t u l •

• 40 ....

t 0 " '

'_,.

-·

:

^{-~: ~~}

' -n -u

• -u zz

' '" ,.

• JJ n

• -u -Z4

10 -n '

l l -n I•

IJ II 0

o n -1' I UI ., .

I •U •lO

' _,.

....

" ,. _,,.

' _ , . -u

• _,. u

' -u u

.

_• ^__-u ^{,. _,,} _t

10 -u -10

14 l 0 _, ... 14

,, "

_,,

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!~ -::

" _,,

_,. u -u -u

, .. )4

-u l u l 0

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-n ,, _,. "

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....

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- ·

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_,, -u -l• I'

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-z• -u

l , _, , _, , - · · IJ

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_,. _,

z 19 4

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4 II 16

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o -n -10 I - l l -JJ

z -u "

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....

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^_.,

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:::

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_{: 1::} ^"

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