scieee Open visual document viewer

The Conformation and Crystal Structure of meso-2,10-Dimethyl- 3,1 l-dimethoxycarbonyl- 1,6,9,13-tetraoxadispiro[4.2.4.2]tetradeca-2,10-diene

Conde Amiano, Alejandro; Moreno, E.; Márquez Delgado, Rafael

Abstract

The crystal and molecular structure of the title compound, C16H20Os, has been determined by singlecrystal X-ray diffraction. The compound crystallizes in the monoclinic space group P2t/c with two molecules in a cell of dimensions a = 9.199 (1), b = 12.423 (1), c = 8.047 (1) A, and fl = 114.87 (1) °. The structure was solved by direct methods (MULTAN). Full-matrix least-squares refinement gave a final agreement index of R = 0.054 for 1166 observed reflections. The sixmembered ring adopts the chair conformation around a symmetry centre. The conformation of the fivemembered rings is nearer to a twist than to an envelope, the approximate twofold axis passing through the C(4) atom. The endocyclic C-O bonds are asymmetric and the C=C distance is longer than expected for a double bond. Crystal packing is due to van der Waals interactions only.

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