Full text
652 CRYSTAL AND MOLECULAR STRUCTURE OF TYRAMINE HYDROCHLORIDE
Table 5. Hyd ogen-bond leng hs (A) and angles (0)
Posi ion o
D--H-.-A accep o a om D...A H...A /_D--H...A /_H-D...A
N-H(N)... CI(1) x,y,z 3.17 2.30 151-0 21.0
N--H'(N).-. C1(2) x,y,z 3.17 2.29 161.2 13-5
N-H"(N)-..C1(2) x, 1 -y, ½+ z 3.22 2-58 133-3 35-0
O--N(O). • • CI(1) ½-x, ½+y,z 3.04 2.09 172.0 5.5
Con o ma ion
Fig. 3 is an OR TEP plo o he molecule. The
con o ma ion o he e hylamine side chain and i s
ela ion o he benzene ing in y amine hyd ochlo ide
a e desc ibed by o sion angles I and 2 in ol ing
a oms C(4)-C(3)-C(7)-C(8) and C(3)--C(7)-
C(8)-N espec i ely, he alues o I and 2 being 69
and 178 ° espec i ely. These alues ag ee well wi h
hose o mos o he o he sympa homime ic amines
in es iga ed. The phene hylamine side chain in he
molecule is maximally ex ended ( ans con o ma ion)
and he dis ance o he N a om om he cen e o he
ing has been ound o be 5.14 A, as in some o he
sympa homime ic amines, e.g. 5.14 A in dopamine
(Be gin & Ca ls 6m, 1968), 5-2 A in hyd oxy-
ephed ine (Da agup a & Saha, 1977) and 5.2 A in
phenyleph ine (Bhadu i & Saha, 1975). In mos o he
sympa homime ic amines so a s udied as well as in
some s uc u ally dissimila sympa homime ic amines
(Pos & Kenna d, 1974; Giesecke, 1973), his dis ance
o he N a om om he cen e o he benzene ing has
been ound o be a ound 5 A. This dis ance appea s o
be a signi ican equi emen o a compound o ha e
sympa homime ic p ope ies.
Re e ences
BERGIN,
R. &
CARLSTROM,
D. (1968). Ac a C ys . B24,
1506-1510.
BHADURI, D. & SAHA, N. N. (1975). P i a e communi-
ca ion.
BUSING, W. R., MARTIN, K. O. & LEVY, H. A. (1962).
ORFLS. Repo ORNL-TM-305. Oak Ridge Na ional
Labo a o y, Tennessee.
CARLSTROM,
D., BERGIN, R. & FALKENBERG, G. (1973). Q.
Re . Biophys. 6(3), 257-310.
DATTAGUPTA, J. K. & SAHA, N. N.
(1977). P i a e
communica ion.
GIESECKE, J. (1973). Ac a C ys . B29, 1785-1791.
HAHN, T. (1957). Z. K is allog . 109, 438.
LONG, R. E. (1965). Doc o al hesis, Uni . o Cali o nia, Los
Angeles.
PAULING, L. (1960). The Na u e o he Chemical Bond, 3 d
ed. I haca: Co nell Uni . P ess.
PODDER, A. ~ SAHA, N. N.
(1973). Annual Repo 1973,
Saha Ins i u e o Nuclea Physics, Vol. 85, Abs ac No.
2B, p. 9.
PODDER, A.,
SAHA,
N. N.,
DATTAGUPTA, J.
K. &
SAENGER,
W. (1975). Ac a C ys . A31, S5a
POST, M. L. & KENNARD, O. (1974). Na u e (London), 252,
493.
TAMURA, K., WAKAHARA, A., FUJIWARA, T. & TOMITA, K.
(1974). Bull. Chem. Soc. Jpn, 47(11), 2682-2685.
Ac a C ys . (1979). B35, 652-656
The Con o ma ion and C ys al S uc u e o
meso-2,10-Dime hyl-
3,1 l-dime hoxyca bonyl- 1,6,9,13- e aoxadispi o[4.2.4.2] e adeca-2,10-diene
BY A. CONDE, E. MORENO AND R. M~,RQUEZ
Depa men o de Op ica y Secci6n de F sica del Cen o Coo dinado del CSIC, Facul ad de Ciencias,
Uni e sidad de Se illa, Spain
(Recei ed 11 Augus 1978; accep ed 14 No embe 1978)
Abs ac
The c ys al and molecula s uc u e o he i le
compound, C16H20Os, has been de e mined by single-
c ys al X- ay di ac ion. The compound c ys allizes in
he monoclinic space g oup P2 /c wi h wo molecules
0567-7408/79/030652-05501.00
in a cell o dimensions a = 9.199 (1), b = 12.423 (1),
c = 8.047 (1) A, and l = 114.87 (1) °. The s uc u e
was sol ed by di ec me hods (MULTAN). Full-ma ix
leas -squa es e inemen ga e a inal ag eemen index o
R = 0.054 o 1166 obse ed e lec ions. The six-
membe ed ing adop s he chai con o ma ion a ound a
© 1979 In e na ional Union o C ys allog aphy
A. CONDE, E. MORENO AND R. MARQUEZ 653
symme y cen e. The con o ma ion o he i e-
membe ed ings is nea e o a wis han o an en elope,
he app oxima e wo old axis passing h ough he C(4)
a om. The endocyclic C-O bonds a e asymme ic and
he C=C dis ance is longe han expec ed o a double
bond. C ys al packing is due o an de Waals in e -
ac ions only.
In oduc ion
The 'Knoe enagel eac ion' o ca bonyl compounds
wi h ac i e me hylene g oups is a e y use ul ins u-
men o o ganic syn hesis o ca bon-ca bon bond
o ma ion, and, along wi h he Doebne modi ica ion, i
has been applied in many cases. The applica ion o he
Knoe enagel eac ion o he ca bohyd a e ield o e s
new ou es o he syn hesis o u ane compounds
s a ing om monosaccha ides. Howe e , in some
cases i shows some peculia i ies and he s uc u e o
he esul ing p oduc s is di e en om ha expec ed
om he usual eac ion.
R I,~ H
H CH3
H -Q
H CH3
(I) R ~ = COR'
R 2 = CH 3 o Ph
By eac ion o O-isop opylidene-D-glyce aldehyde
wi h l-dike ones o p-ke oes e s, unsa u a ed com-
pounds ha ing he s uc u e o a spi oke al (I) a e
ob ained as a esul o in amolecula cycliza ion. I s
s uc u e has been deduced om spec oscopic da a,
deg ada ion eac ions and unc ional-g oup in e con-
e sion. A new ype o cycliza ion yielding dispi oke als
is easily pe o med by ea ing (I) wi h acid in an
ap o ic sol en .
RI H
",,,,,IT._~H H H HH
R z
(II)
1 H
(III)
In spi e o hei op ical inac i i y, wo isome ic o ms
(II) and (III) a e possible owing o he exis ence o wo
chi al cen es. Mass spec oscopy da a (L6pez-
Apa icio, L6pez-He e a & Sanchez-Balles e os, 1978)
sugges he cen osymme ic ans con igu a ion (III)
bu his esul is subjec o pe sonal in e p e a ion
acco ding o a hypo he ical agmen a ion p ocess.
As men ioned abo e, he Knoe enagel eac ion in
he o ganic chemis y ield equi es a mo e de ailed
s udy and a be e knowledge o he s uc u es o he
compounds p oduced. Fo his eason an X- ay s udy
o he i le compound was unde aken a he sugges ion
o P o esso F. J. L6pez-Apa icio o he O ganic
Chemis y Depa men , Uni e si y o G anada, and is
now epo ed.
Expe imen al
The compound was in he o m o colou less p isma ic
c ys als. P elimina y uni -cell dimensions and space-
g oup in o ma ion we e ob ained om oscilla ion and
Weissenbe g pho og aphs aken wi h Cu Ka adia ion.
Wi h wo molecules in he uni cell, i was necessa y o
place he molecule cen e on a symme y cen e.
Accu a e cell dimensions (Table 1) we e ob ained by
leas -squa es e inemen o he 0 alues o 50 e lexions
measu ed on a Philips PW 1100 au oma ed ou -ci cle
di ac ome e . In ensi y da a we e also collec ed on
his ins umen using g aphi e-monoch oma ed Cu Ka
adia ion and he 09--20 s ep scanning mode. In ensi y
da a we e collec ed o e he ange 2 ° < 0 < 65 ° o gi e
a o al o 1386 independen e lexions o which 1166
we e classi ied as obse ed by he c i e ion I > 20(/).
S uc u e de e mina ion
The s uc u e was sol ed by a weigh ed mul isolu ion
angen e inemen (MULTAN, Main, Lessinge ,
Wool son, Ge main & Decle cq, 1977). 172 e lexions
wi h IEI > 1.40 (app oxima ely ou een e lexions o
non-hyd ogen a oms in he asymme ic uni ) we e used
and a choice o phasing was possible based on FOM's;
he highes combined igu e o me i de i ed using uni
weigh s o he componen s was 2.0. An E map
compu ed wi h his phase se had dis inguishable peaks
o all non-hyd ogen a oms.
Table 1. C ys al da a
Fo mula C
16H2008
Space g oup
P21/c
A(C2~h, No. 14)
a 9.199 (1)
b 12.423 (1)
c 8.047 (1)
l 114.87 (1) °
V 834.32 A 3
Z 2
Dea I 1"35 Mg m -3
Dex p 1.37 (2) Mg m -3
F(000) 680
654 THE CONFORMATION AND CRYSTAL STRUCTURE OF C16H200 8
Re inemen p oceeded by he ull-ma ix leas -
squa es me hod, using only he obse ed e lexions and
ini ially wi h all non-hyd ogen a oms ea ed iso-
opically, o gi e an R alue o 0.11. A di e ence
Fou ie syn hesis showed elec on densi y maxima in
he icini y o he H-a om calcula ed posi ions. Fu he
e inemen wi h non-hyd ogen a oms ea ed aniso-
opically, and hyd ogen a oms iso opically ( he H
posi ions and hei iso opic empe a u e ac o s we e
also included in he e inemen ) p oduced con e gence
wi h R = 0.054. The weigh ing scheme w =
1/a2(F),
whe e o2(F) is de i ed om a2(I), was employed.
A omic sca e ing ac o s we e aken om
In e -
na ional Tables o X- ay C ys allog aphy
(1974) and
compu ing p og ams o he XRAY sys em (1970)
we e used. The inal posi ional pa ame e s o non-
hyd ogen a oms a e in Table 2. Posi ional and he mal
pa ame e s o hyd ogen a oms a e in Table 3.*
Desc ip ion o he s uc u e
a oms om he leas -squa es planes h ough some
a omic g oups a e gi en in Table 4. To sional angles
de ining he con igu a ion and con o ma ion a e lis ed
in Table 5.
The six-membe ed ing adop s he chai con o -
ma ion. I is pucke ed in such a manne ha he ou
a oms O(2), O(2'), C(5) and C(5') lie on a plane bu
he a oms C(4) and C(4') a e subs an ially displaced
om his plane on ei he side, as obse ed om leas -
squa es plane I (Table 4). The alues o o sional angles
h ough he ing bonds do no show signi ican
de ia ions om hei a e age alue o 53.7 °. The endo-
cyclic C-C bond leng h o 1.508 (4) A, ag ees wi h he
a e age alue epo ed o analogous ings and he wo
C-O bonds a e equal wi hin expe imen al e o (20).
The in e nal ing angles ag ee wi h he s anda d alue
o 111.5 ° (Duni z, 1968) bu he C-O-C angle is
signi ican ly la ge .
The pucke ing o he i e-membe ed ings is in e -
media e be ween a wis and an en elope con o ma ion.
In e ms o he pseudo o a ional desc ip ion p oposed
The bond leng hs and angles in ol ing non-hyd ogen
a oms a e illus a ed in Fig. 1. Displacemen s o he
* Lis s o s uc u e ac o s and aniso opic he mal pa ame e s
ha e been deposi ed wi h he B i ish Lib a y Lending Di ision as
Supplemen a y Publica ion No. SUP 34021 (12 pp.). Copies may
be ob ained h ough The Execu i e Sec e a y, In e na ional Union
o C ys allog aphy, 5 Abbey Squa e, Ches e CH 1 2HU, England.
Table 2.
A omic coo dina es
(x 104)
o non-hyd ogen
a oms
x y z
O(1) 8391 (3) 9272 (2) -2666 (3)
O(2) 9129 (3) 9230 (2) 472 (3)
0(3) 3556 (3) 8105 (2) --4882 (4)
0(4) 3377 (3) 9332 (2) -2934 (3)
C(I) 6914 (4) 8813 (3) -3605 (5)
C(2) 5831 (4) 9144 (3) -3013 (5)
C(3) 6578 (4) 9958 (3) -1508 (5)
C(4) 8345 (4) 9866 (3) -1125 (5)
C(5) 10794 (4) 9077 (3) 943 (5)
C(6) 6844 (6) 8054 (4) -5047 (6)
C(7) 4173 (4) 8787 (3) -3738 (5)
C(8) 1739 (6) 9017 (5) -3462 (9)
Table 3.
Coo dina es
H(31)
H(32)
H(51)
H(52)
H(61)
H(62)
H(63)
H(81)
H(82)
H(83)
(X 103)
and he mal pa ame e s
(x 102)
o he hyd ogen a oms
x y z U (A 2)
621 (5) 1068 (3) -183 (5) 2 (1)
644 (4) 976 (3) -41 (5) 1 (I)
1096 (4) 859 (3) -3 (5) 1 (1)
1121 (5) 860 (3) 205 (6) 3 (1)
722 (6) 837 (4) -596 (6) 6 (1)
565 (6) 775 (4) -580 (7) 5 (1)
769 (6) 747 (4) --454 (6) 4 (1)
128 (6) 949 (4) --304 (7) 5 (1)
177 (7) 814 (4) --278 (7) 6 (1)
128 (6) 884 (5) -440 (9) 6 (2)
Table 4.
Leas -squa es planes h ough some a omic
g oups
(a) Equa ions o he planes in di ec space
I -1.410x + 5.809y + 6.874z-- 4.400
A oms de ining he plane: O(2), O(2'), C(5), C(5').
II 0.193x + 9.351y- 4.875z-= 10.132
A oms de ining he plane: O(1), C(1), C(2).
III 0.173x + 8.556y- 5.355z = 9.604
A oms de ining he plane: O(3), O(4), C(7), C(8).
(b) De ia ions o a oms (A x 10 a)
I
II
0(2) o o(1)
0(2') 0 C(1)
c(5) o c(2)
C(5') 0 C(3)
C(4) -618 C(4)
C(4') 618 C(7)
C(3) -579 C(6)
O(1) -2029
Ill
0 0(3) 6
o 0(4) 1o
0 C(7) -12
42 C(8) -5
- 196 C(2)
-66
-12 C(3) -162
-7 C(l) -13
c(6,)
~/ 0(3')
O(") j/"~'~e
'>~/
,o,o
c(8) 0(4) ~).:~ "b<z~-~,:,-ac,.J (:(5)
0(3) C(l)
"
c (6)
Fig. 1, Bond leng hs (Z~) and angles (o) o non-hyd ogen a oms.
(E.s,d,'s a e 0.004 Z~ o bond leng hs and 0.3 ° o angles.)
A. CONDE, E. MORENO AND R. M./~RQUEZ
Table 5. Selec ed o sional angles in he molecule (o)
(E.s.d.'s a e 0.5°.)
(a) Six-membe ed ing
C(4)-O(2)-C(5)-C(4') 54.4
O(2)-C (5)-C (4')-O(2') -52.9
C (5)-C (4')-O(2')-C(5') 53.8
(b) Fi e-membe ed ing
O( I)-C( I)-C (2)-C (3) 1.7
C(1)-C(2)-C(3)-C(4) -10.1
C (2)-C (3)-C (4)-0 ( 1 ) 14.3
C(3)-C(4)-O(1)-C(1) -14.2
C(4)-O(I)-C(1)-C(2) 8.1
(c) Junc ion o he ings
0(1)-C(4)-0(2)-C(5) 64.8
O(1)-C (4)-C (5')-O(2') -65.0
C (3)-C (4)-O(2)-C (5) 179. I
C (3)-C (4)-C (5')-O (2') 176.3
(d) Ca boxyl g oup
C(3)-C(2)-C(7)-O(3) -176.5
C(3)-C(2)-C(7)-O(4) 3.2
C ( l)-C (2)-C (7)-0 (3) 4.8
C(1)-C(2)-C(7)-O(4) -175.5
by Al ona, Geise & Rome s (1968), he 'phase angle' is
A = 48.3 ° and he 'ampli ude o pucke ing' ~0 m =
15.2 °. In his desc ip ion we selec A = 0 ° co e-
sponding o a wo old o a ion axis passing h ough
O(1) and he mid-poin o C(2)-C(3). The leas -
squa es plane h ough O(1), C(1) and C(2) a oms (II)
and he de ia ions o ing a oms om his plane a e
indica ed in Table 4. The endocyclic C(1)-O(1) o
1.370 (3)/~, and C(4)-O(1) o 1.459 (4) A a e asym-
me ic. The asymme y o he endocyclic C-O bonds is
obse ed in some py anose de i a i es (Sunda a-
lingam, 1968) bu in 1,2 unsa u a ed aldopy anose i is
s ill mo e p onounced due o he in luence o he C-C
double bond. The C(1)-C(2) bond o 1.388 (5) ,/k is
longe han expec ed o a double bond which sugges s
esonance o ms in ol ing he ing a oms. The junc ion
o he i e- and six-membe ed ings can be cha ac-
e ized by he o sional angles a ound C(4), wi h he
C(4)-C(3) and C(4)-O(1) bonds in quasi-equa o ial
and axial posi ions, espec i ely. As in 1,4,9,12- e a-
oxadispi o[4.2.4.2] e adecane (Chadwick, Duni z &
Schweize , 1977), he con o ma ion o he ing is nea e
o a wis han an en elope, bu he app oxima e
wo old axis passes now h ough he C(4) a om.
The ca boxyl g oup is plana as expec ed (maximum
a omic de ia ion om he leas -squa es plane III o
Table 4 is 30). The mean plane is quasi-coplana wi h
he i e-membe ed ing [ he maximum o sional angle
a ound C(7)-C(2) is 8°]. Bond leng hs and angles
ag ee wi h he s anda d alues o his g oup excep
ha he C(7)-C(2) bond is now sho ened by he
in luence o he C-C double bond. Bond dis ances and
655
~.--
Fig. 2. A iew o he s uc u e down he c axis.
angles in ol ing H a oms show a easonable ag ee-
men . A e age alues a e 0.99 (5) A o C-H bonds
and 112 (3) o H-C-C, 109 (3) o H--C-O and
107 (3) ° o H--O--C angles; he g ea es de ia ions
om hese a e age alues a e smalle han 40 o he
bond leng hs and 3a o he bond angles. The maximum
dispe sion in H-C bond dis ances co esponds o he
C(8)(me hyl)-H and his could indica e a he mal
mo ion e ec .
The molecula packing in he c ys al is illus a ed in
Fig. 2. The in e molecula dis ances do no gi e any
e idence o hyd ogen bonds. As can be seen om Fig.
2, he molecules pack in laye s app oxima ely pa allel
o (010). Molecules a e held oge he by an de Waals
in e ac ions only and he e a e no in e molecula
con ac s ha a e signi ican ly sho e han he sum o
he co esponding an de Waals adii.
All calcula ions we e ca ied ou on a DCT 2000
e minal o he Cen o de Calculo o his Uni e si y,
connec ed o a Uni ac 1108 compu e .
The au ho s a e g a e ul o P o esso J. L6pez-
Apa icio o sugges ing he s udy and supplying he
c ys als and P o esso A. L6pez-Cas o o eading he
manusc ip and o help ul discussions. They also hank
he s a o Ins i u o 'Rocasolano' CSIC (Mad id),
especially D F. Cano, o collec ing he di ac ome e
da a.
The p esen wo k is a pa o a wide esea ch
p ojec suppo ed by he Go e nmen h ough he
'Comisi6n Aseso a de In es igaci6n Cien i ica y
T6cnica'.
Re e ences
ALTONA, C., GEISE, H. J. & ROMERS, C.
(1968).
Te ahed on, 24, 13-32.
CHADWICK, D. J., DUNITZ, J. D. &
SCHWEIZER~
W. B.
(1977). Ac a C ys . B33, 1643-1645.
656 q~HE. CONFORMATION AND CRYSTAL STRUCTURE OF C16H200 8
DUNITZ, J. D. (1968).
Pe spec i es in S uc u al Chemis y,
Vol. 2, edi ed by J. D. DUNITZ & J. A. IBERS, p. 10. New
Yo k: John Wiley.
In e na ional Tables o X- ay C ys allog aphy
(1974). Vol.
IV, pp. 72-98. Bi mingham: Kynoch P ess.
LOPEZ-APARIClO,
F.
J., L,OPEZ-HERRERA,
F.
J. • SANCHEZ-
BALLESTEROS, S. (1978).
Ca bohyd . Res.
In he p ess.
MAIN, P., LESSINGER, L., WOOLFSON, M. M., GERMAIN, G.
(~ DECLERCQ, J. P. (1977).
MULTAN
77. Uni s. o Yo k
and Lou ain-la-Neu e.
SUNDARALINGAM, M. (1968).
Biopolyme s,
6, 189-213.
XRAY sys em (1970). Edi ed by J. M.
STEWART,
F. A.
KUNDELL (~, J. C. BALDWIN.
Compu e Science Cen e ,
Uni . o Ma yland.
Ae a C ys .
(1979). B35, 656-659
~-D-Glucose: Fu he Re inemen Based on Neu on-Di ac ion Da a*
BY GEORGE M. BROWN AND HENRI A. LEVY
Chemis y Di ision, Oak Ridge Na ional Labo a o y, Oak Ridge, Tennessee
37830,
USA
(Recei ed
29
Augus
1978;
accep ed
24
Oc obe
1978)
Abs ac
P ecise ansla ions we e de e mined o a-D-glucose,
C6H1206, (o ho hombic, P212~2 0 as ollows: a =
10.3662 (9), b = 14.8506 (16), c = 4.9753 (3) A a
294-296 K based on 3,(Cu
Kal)
= 1.54051 A. The
s uc u e has been u he e ined using neu on-
di ac ion da a p e iously ob ained [B own & Le y
(1965).
Science,
147, 1038-1039] and he ull-ma ix
leas -squa es me hod, wi h aniso opic ex inc ion co -
ec ions. The i o he obse a ions is much imp o ed
[R(F) = 0.048; s anda d de ia ion o i = 1.053], and
he pa ame e e o s a e sligh ly smalle . Pa ame e
changes a e sligh and o no chemical signi icance. The
segmen ed-body model has been used o calcula e
co ec ions o he bond leng hs and alence angles o
he e ec s o he mal mo ion. Bond leng hs, alence
angles, o sion angles, and de ails o hyd ogen bonding
a e abula ed.
we had a emp ed o minimize he e ec s o ex inc ion
by he somewha unsa is ac o y me hod o gi ing ze o
weigh s o he 37 obse a ions o
I Fo 2
co esponding
o he highes obse ed in ensi ies. Because o he
biochemical impo ance o a-D-glucose, we ha e now
comple ed he e inemen using ou o iginal da a and
applying aniso opic ex inc ion co ec ions (Coppens &
Hamil on, 1970). Shi s om he old pa ame e s
(B own & Le y, 1965) a e small (see below), bu he e
is s iking imp o emen in he i o he obse a ions,
and he e a e sligh dec eases in he s anda d e o s o
he pa ame e s. We ha e used he segmen ed-body
model (Johnson, 1970) o analyze he new he mal
pa ame e s and he eby p o ide co ec ions o he bond
leng hs and alence angles o he e ec s o he mal
mo ion. The bond leng h and angle da a a e also
ende ed mo e p ecise, and p esumably mo e eliable,
by use o he new, mo e p ecisely de e mined cell
pa ame e s which we also epo he e.
In oduc ion
Thi een yea s ago (B own & Le y, 1965) we epo ed
a omic coo dina es and selec ed de i a i e s uc u al
pa ame e s o a-D-glucose om a ai ly p ecise e ine-
men , based on neu on-di ac ion da a, o he s uc-
u e o McDonald & Bee e s (1952). The da a used in
he 1965 wo k appea o be o high quali y by p esen
s anda ds; bu he e a e conside able ex inc ion e ec s,
and he leas -squa es e inemen p ocedu e did no
include adjus men o ex inc ion pa ame e s. Ins ead,
* Resea ch sponso ed by he Di ision o Ma e ial Sciences, US
Depa men o Ene gy, unde con ac W-7405-eng-26 wi h he
Union Ca bide Co po a ion.
Da a and e inemen
The e ised cell pa ame e s (see
Abs ac )
we e de e -
mined, wi h he assis ance o R. D. Ellison, by he leas -
squa es me hod om he B agg angles o ! 1 high-angle
e lec ions (138 < 20 < 165 °) om a small c ys al on
an X- ay di ac ome e . In e e y signi ican de ail he
p ocedu es in eco ding neu on-di ac ion da a and in
p elimina y da a educ ion we e as in ou wo k on
suc ose (B own & Le y, 1972). A o al o 2168
in ensi y measu emen s we e made o he 1656
independen e lec ions wi h indices all posi i e o ze o
o he limi 0.760 A -1 in (sin 0)/2 (3, = 1.078 A, 0ma x --
55.0°). Fo he abso p ion co ec ions (Busing & Le y,
1957) he coe icien was ~ = 0.28 mm-1; he minimum