I. Preparation and Description of Some Derivatives of Molybdenum Dichloride. II. Structure Determination of Complex Molecules or Ions by X-Ray Diffraction by Solutions Citation Vaughan, Philip Alfred (1949) I. Preparation and Description of Some Derivatives of Molybdenum Dichloride. II. Structure Determination of Complex Molecules or Ions by X-Ray Diffraction by Solutions. Dissertation (Ph.D.), California Institute of Technology. https://resolver.caltech.edu/CaltechTHESIS:08182025-175127143 Abstract See thesis PDF for abstract. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Chemistry and Physics) Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemistry Minor Option: Physics Thesis Availability: Public (worldwide access) Research Advisor(s): Pauling, Linus Thesis Committee: Unknown, Unknown Defense Date: 1 January 1949 Record Number: CaltechTHESIS:08182025-175127143 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:08182025-175127143 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 17631 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 18 Aug 2025 20:50 Last Modified: 18 Aug 2025 20:51 Thesis Files PDF - Final Version See Usage Policy. 24MB Repository Staff Only: item control page

I PREPARATION 1 JD DEOORI P'l'I ON OF SOME 'DERIVATIVii:S OF MOLYBD.ENUM DICHLORr'DE· II STRUCTURE DE TEm<' INATI ON OF CQ.{PLEX !/ OLEOULES OR I ONS BY X•RAY DIFFRAO TION BY SOLUTIONS Ph.111p A.l-tved Vaughan , In Partial .f,ulfillment of the Requirements For the Degree of Doctor ot Philosophy Cal i fornia I nstitut e of Teon.nology Pasadena, Oal1f"orn1a 1949 I wish t o expre1;1s my g.rat ~tude to P-rot'essor Linus Pauline; for su.gge st. ng t he problem.a preeented '1-n -t hia Thesis and to~ co1;1t1nuf,Jd ;ntereat 1n the progress of theitt solution,, I a.1a.o .f' .. ~ ' ~ kt; , , thanlt Pro essoi;- J,, M., Sturdivant f ,O'r h i s. ,:aluable ass 1~,tanoe 1n all pha.s.e s of this work• His expeJti,e noe 1n: the design of X..ray equipment mad«i possible the oa.pid and successful co:nstl'uotion or a e.u i table appartatue f ·o r p roducing diffraction photographs ot aolut1on~, ~ • I l:(1e3h , te than~ Pt-ofessor V'~rner '· Sohomakex- ror helpful. d1souss1o:ns ~oncefut.ng the pr:epara t1on and. 1nterpr:et.at1on or the- vlsul 1nte-nsi ty eur~ EHf, and Fro• 1 f'essor Herbex-t s., Harned to,:, s1v1ns the Ohemiatr, D$pa:tt_ment •·, a quant1t.y of the Ohlo~ooo1urnb1um eoJfpQund, the struct-ure or whi Qh 1e cl1souesed in t h.i s Thee1s. La.etly, I a.m gJ'atctul to my W1fe tor her eno-ollf:'-agera~nt .1 n. my W()tkt and her help 1it prepuins th1 a ma.n:uacr1pt . ABSTRAO'.l' I• Frepa.,:at;.o n a.nd Dt!§Cfiption of Some De.r1vatlvea ot Fol,:bdenum D1ohlo,;:1de ·, The comp ounds H2[ Moef 1 8)0ltt8l\aOf _(NH4\![Motflla) Ol2 •a3 o, and Jal ~~~la) Ola•HaO ·:na.ve 'been 'p i;epa.red' and .a n~lyzed.. ' sro:® The space '· / and. 'unit ee.l l dimens i ons of tlle first iw'o eompounds have .,. ~ .... : ,J been. determln.ed f~om x~ray d1ffI"aet1on photogl'al)~a; the axial ,· ' " ' . ' • rati~s were also obta.:tned' by goriiometJ;?ld measurements~ The or-ys.t allogra.phte d.a.ta a.re ' ' (NM' }2 [M o_ef 1a1 _Ol5•HaO ' 4 ' ' · O·a ji ... 0 2/¢, Posa1ble Spa.oe Groupe ·c",.. /1 • ) i.,,C _ ·(_probable __ ..S - :•· al 19,j:,' .t 17•}<? 2 a.2 14.• ,, .t 9,.la f a, ' 9,1.6 • ~ - Unit Cell Volume '· i , ! . l _l.~-~-. 9e.1° .a,to :R3 • 2910 ,tJ .Densi ty or Oompotmd :,.09:, gm/co M~leoules per Unit Oell. ' 4 ' II, 1a.6:, l 4 Sl,ryp tyrg . otermina.tton or Com.pl.ex " pleoulea or Ions b:1 ~7'.RaY 1Uf' . ' • -· f :ra.etion bY: Solut1· . .e ns ' ~ . • . Th~ t1rs t part of t his seot1on is devoted to a b~ief theoretical di souas1on of the applicati on of the visual est1ma.. tien method to the, det.erm1nat1on of the structure of a _complex compound by X-ray di ff ra.etion by its solut i on. A deeor1ption of t he experimental technique used to obtain sui table photographs is then pres ented. It i s shov-m that t he method g ive s satisfactory result s for t he Pt01 --- and PtBr 6-- ions, the struotures of whish 0 are well known. The structure s of the (Cb~l 12 }, (Ta.5Br12>, and (Taf1 ) groups We re det er mined by ;'-ray d1ffraot1on by , ethanol 12 s olut i ons of Obe(J 114 •7H o, Taefr- 14 •7H 2 o, and 'Iatf 1 14 •7H2 o. It 2 is shown that the d1f:fraotion data ar-e oonsis t en~ with t he assumption or a (MGX1a) group i n whioh the metal a tomo are at the corners of a regular octahedron and the halogen atoms on the perpendicula r bineotors of the edges of this octahedron. The shortest interatomio d1a t ancea 1n the (M(SX.12 ) g roup a re Oompound M - M, X :M - x, t X - x., 2 Cbtf 114 •7Ha0 2"85 2.41 3.,37 Ta nr •7H 0 2 2.92 2-.62 :,.64 Tae,C l14 •7Ha0 2.88 2.44 3.41 6 I 14 These r e sult s are: 1n reasonable a.gt-eement with Pauling's theory of 1ntermetallio dio t a noea in m-e taleh TABLE OF OON TENTS Page Preparation and Descr1pt1on of Some Derivatives or Mol.ybd.enum Dtchl.or1d.e ., • • • , •. • • • • • • , • Prepara.t.1on ot Molfbdenw.n D1chlor1de and Some or 1 t.a Der.1.vat.ives. • ,, • • • • , • • , • • • • a The Ory,st&llograpby or (M4) 2\ Motfll.e)Ol,5•H10 4 , • The orysta.llography ot H2 \Mof 1 1018 •8H2 o • • • 8 I II. l 7 - struoture.Determ1na.t1on or Complex Molecules or ,Ions by X-Ray Diffraction by Solut1ona. • • • , . : 12 A, Theoretical D1aouss1on. • • • • • • • • • • • • 1,. 13 Description or Apparatus • • • • • . • • • • • • ao 2. B. o. ' Trial Experiments with Compounds of Known struoture • . . . • • . . . . . . . 18 • • • • 28 28 Tantalum. • • • • • • • • • • • • • • • • • • • 36 36 l ,. a. D, 13 , Oompar1aon of Oa.loula.ted a.nd Observed Intensity Functions. • • • • • • • • • . , • The Radial Distribution iethod • • • • • • Bromopla t1n1o Acid• • •· • • • • Chloroplat1nic Acid • • • • •• • • . •· . . . . 33 Lower Halide Complexes of Oolumb1um a.nd L. 2. :,. 4-. 5. References • • Preparation and Chemistry. ,. • • •· .• • • • The Structure of the (Cb~1 12 ) Group • • • The Structure of the ('l'a6Br12 ) Group • • • The Structure of th.e ( Tao01 12 ) Group • • • D1seuss1on a.nd Summar,. • •• • • • • • • • • • • • • • • • 39 50 58 61 I SO FREFAR.ATI ON AN DEOORIFTION · OF D RIV TIVES OF MOLYBDENID , DiOHLQRIDE -2- A,.; lreparation 0:f Molybdenum Diohlorid.e and Some of its Derivatives In most of the lite.rature on the subject t he formulae for divalent molybdenum eompound s are represented e.s der1vat1vea of ( Mo x4 ) x (molybdenum diha.l1de), since it has been shown that 2 3 only one third of the halogen atoms can r eadily be rep laoed by other atoms or g roup s. Recently, Cyrill Brosset ha.a de monstrated that the grouping {Mo<fl8 ) is present in two deriva tives of molybdenum di chloride (1, 2), , Therefore , since thi~ g rouping • is probably present in all diva.lent molybdenum compounds, formulae of all such comp lex compounds will be written as derivatives of (Mo 6x8 ) x4 in this report, Lindner and cowork ers (3,.4,5) have investigated t h e preparation of diva lent molybdenum compounds. Of the various methods that have b een u sed for the preparation of molybden.ur.n dichloride • they reoommen d ch lorina t i on of molybdenum metal with phosgen~ at temperatures of 600 to 620° C • This is the method. that has been used throughout t his investiga tion. About 2-4 grams of metal was put :tnto porcelain boats which were placed in a silioa. combustion tube heated by an electric furnace. passed through the tube until t i1.e Nitrogen was correot tempe rature wa.s r eached , and then phosg ene was passed through at a r a te roughly determined by a smal l bubbler. At the completion of t he r eaction the phosgene was shut off, the tube flushed out with nitrogen, and the appara tus allowed to cool. The diqhloride was usually extracted from the mate rial remaining i n the boats with 30-50 ml of an anhydrous a lcohol-ether mixtut'e (5-50 p e rcent a.10.ohol) or - 3- ·with concentra ted hydrochlori c a.old .. The extra.ct was t h en eva porated a.nd t he product washed with dilute n1tr1c aoid and water'· to give a. partially hydrolyzed product of variable compositi on whi oh was soluble in hydroohlorio acid . 'I'he yields we.r e a.brays ama.11, usually being 3 to 7 peroent of the theoretical, L.indner, Haller, and Helwig (lr) recommend using tempera.tu.res of 600-620°0; however, I obs erved no significant dif:fere.n ee in y1ela. between 550 and 650°0, For the best results I found that the phosgene should be passed through at the r ate of about 50 to 100 ml per minute for t en to fifteen minutes .,· side products a.re higher chlorides . The prinoipal The penta.ohloride, being volatile, eolleots at the cool end of the tube; the triohlor1de , a dark red powder, is usually present in t he boa.ta a.long with. diohloride and unreacted molybdenum~ It is, however , pr a ct1oa.lly insoluble in water, acids , and organic solvents -. The following three hydrated derivatives of molybdenum dichloride have been prepared and analyzed:* (1) Compound obtai ned by oooliru..3 a hot solution of ' dichloride i n concentra ted hyd rochloric acid. (2) Compound crystallized from a dichloride sol ution in approximately 8 percent a..q ueoua amrnonium chloride aoidif'1ed with hydroohlorio acid. (3) Compotmd ob t e,ined by cool ing a hot sol ution of * I analyzed f or chlorine by the gr a vimetric silver · chloricte method . 'l'he molybd enum was titra ted with stand.a.rd potass ium per manganate solut ion afte r r eduction to Me+++ in a Jones reductor (6). In all cases , c omplete destruct i on of t he complex was assur ed by oxidati on with ni t rio a cid or .. hydrogen peroxide. -4- di chlo r ide in app roximate ly 8 p e rcent potassium chloride sol u t i on aoid ified with hydrochlori c a.ei.d The following ana lytica l data were ob tained: ~ 0 HOl oomp ound .• • • • • • • • . • • • • • 47.14 Calculated for H2 t MoeJ18 l 01 •8H2o • • 47 .25 %Cl 41.09 40.75 6 44.3 43.5 44.1 Several inve s ti ga tors ha.ve g iven t he above formula for the compotmd with hydrochloric acid , a.nd there ie little doub t that 1t is t he correct one. 'I'he monohyd r a te seems to flt the ana- lytiea.1 da t a for the p o t ass i um ohlori<l.e compo\ll1.d •. . 'Iher e is a. disorepancy i n the case of the a mmonium chloride compound; however; 1 t will be s h own t hat the monohydre.ted compound g i ves a better unit oell i nte r pr e t a tion, t he rot-mula. (NH4 ) l MoeJls 2 uncertainty. For th i s r ea s on I shal l use 1Ol6•H2 o, although t he re i s s till Othe r inve s tiga tor s report t h e formati on of d i f- fer ent hyd r a t e s; for examp l e , Lindn e r, Haller , and Helwi g 1ve t h ~ formulae K2 t 1 2 (Mo~la) Ol6•3Ha0 for· compounds formed under condl t i one aomewha t d .i fferent f'rom 0 M o e J l a C l 6 • 6 H a 0 and (4) ( . NH 4 ) those g iven above . Or-ystallop;r a phy of (NH, 2 2 Q. This compound crys talli zes fro m a c idic a.mmon1um chloride ' l h e ) l M o ~ 1 C l 6 • H 1 solutions in fairl y long , f l a t yellow crysta l s whi ch a.re stable -5- at room tempera tur e for at lea.st several months . A Laue photo- graph t aken. with the X-ray beam parallel to t he needle axis showed t e pr esence o_ a mirr or plane parallel to thi s a.xis . This i ndi oa.tes a Lc'lUe symmetry of Oah • Os1ng l oKo(. ra.d1at1on with a z irconium filter , a ro t a tion pho t ograph was mad.ea.bout the ne ed l e axis l'\ ;• _From t his an a gnomoni c p roJeotlon made f rom t hE;, Laue pho tograph it was · possible to ca lculate the unit cell paramet0rs and deduae t he spaoe l attice. The oell pa.rame• ters are a 2 ( two-fold axis ) ~ 1- 5 ,06 0A a 9.1, i ' (need.l e axis) The snomonic projection was indexed in a satisfa ctory manner wl t h r eflections oc curring only from planes wi th h + 1{ even. This indica t e s a side cente red l at tioe. The .r adi i of limi ting circles we r e oa loula.ted with tlJ,e$e pa r amet rs, and it was observed tha t no s pots of t he · corresponding order on the gnomonic p roj ect i on fell out side of these circles~ Laue photographs were t ate n along ea.oh of the pr i ncipal axes , a nd by measur ing the a.:ngle be tween zone s 011. t he Laue appa.ra.tus , angl e ·~ was found to be 115,:,0 • A pa rtial gnomon1o projeot:lon was made from a Laue photog raph taken with t he beam parallel to t he two- fo l d a x1s a. 2 • Angl e measurements on this project ion give a v a l ue of 115.1o for t he a ngle r• 'ro obtaln better va lues for t he unit cell edges , rotation pho to gr a 9h0 were ta.ken about a. 1 and a , and l ayer line 2 - 6- measurement s were ma.de . The f:lnal unit cell para mete r s a re given below: al :::: 19 . 33 i e.2 = 14. 93 i a. ;::; 91116 i 3 ~ ::: 115.2° Volume o f uni t oell:: 2390 • The ang l e ~ 13 given above is t he average of t he angl es d etermined by the t h ree methods whi eh have been d esoriibed . Tb,e density of t he aubstanoe was found by flota tion 1n a mixture of b romoform and methylene iodide to be 3.093 ~cc at approximat e ly 23°0. From t h is and t h e unit cell volume , the following data wer e e a leula.ted: Compound. Moleeules _.12er unit oell Although t he anhydrous compound would g ive a slightly better va lue t han t he monohydra.ted c ompound fo r t he m .:unber of molecules per un i t cell, t he dif f erence 1s n ot si(Snificant ; and it h as been ob oervo1 that some wate r is g iven of f when t h e c ompound. 1a h eat ed . .31nce the l atte r fo:rrmla al no seGms t o fit t h e analyti- c a l data be tte r, it is t h.e more probab le one . Gon iome tri c meanure ments ha ve b e en made o f e. cry stal mounted ·w ith t he ne edle axio v e rtical . F i e;ure 1 shows the e.ppec.ranee of the crys t a. . 1 ·w ith t h e looati on of the cr-ysta llog raph i e axes . The following measurements were made a nd t he fa.o es indexed: - 7- (100 ): ( 110) ::: 130°47' = 49°13' 48°24' {l!O): (fiO} = 82°17• (!!o) :<100) = 49°19 (110): (100 ) (100) : ( 1,r o) :::: 1 = 85°15 1 azi muth from 1 (ill) face (100); 58° 25 a ltitude If a value of 115.2° for t he angl e ~ 1.s a s sumed ; t he axial ratio s a.re a.1 : a 2 : a. :::. 1,301 : l : 0 . 613 . .lhi s compares 3 with 1.294 : 1 : 0,61.3 c a.loulated fr-o m t h e rotation photogr:-a.phs . 1 : We1s s enbe rg photog r e,ph was made of the equatorial net perpendi cular to a 2 , using 0~ radiation. 1nis and the La.ue photoc;r a phs were u sed t o deter mine t he space gro up . 'l'he fol- lowing obs ervn.t :Lons we r e made : (1) No hk ~ refl e c tions with h + l:c odd occurred in any Laue or Weis eenber g photograph , This indica tes 0--c entering ., (2 ) No hOl ref l eoti ons appeared on a Laue photogr aph t a k en \·Tith the beam pa r a l lel to a. • 3 Also , there were n o hOJ r efl e ction s with ,.{ odd app ee.r:l,n g on the Wei s nenbe r g photogr aph . This indica te s a g lide plane pa r a llel to (010 ) with a e l i de of 6 The space groups ... Co and C2h - a 2/ c are po ssib l e wit h t he o! - above e xtinct ions . Obs e rva t ion s of E:tohed figures indicated t he ab s ence of' a center of symmetry; t he r e f or e t he space group is p roba bly c ! ... Cc. C~ 'I'he Cryst£lllog:ra phy of Haf•io(501a) Cle •-8H2 0 Thi s compound a s gr o'Wll from concentra ted hydrochloric acid solution f or ms lone; , a l most square pr isms whi ch effloresce - 8- slowly . It was neces sar y t o coat crystal spec imens with paraffin Laue pho t osre.phs w1 th . wax in or der t o insure t heir eta.bill ty . t he X-ra.y beam parallel and perpen i oufa. r t a t he needle a.xi s show t he Laue symmetry to be o2h, the needl e a.~is being t h~ two- f ol d axis . ' Zirconi um fi l tered MoK~ r adiation was used to make a ro a:.ion photogr a ph about t he two- fo l axi s, ... r om whi ch 2 = 9 ,12 l . The other unit cell par ame t er s were t hen determined from a i t 1.'laa dete r mined by layer· l ine me asur ements that a. gnomon.l c projec tion made f r om a. Laue phot ograph whi ch wa s t a.ken with t he . -ray beam para l lel to a 2 • 'l:he unit eel l par a.me t er s deter mined in t his ma nner were a. l = 11.30 i (bl ::: 0 .0584 R""l) 0 - 0 . 1097 a2 = a3 = 18 . 63 i (b 3 = 0 •.0542 R•l) 9 . 12 A {b2 2-1) f = 98 ,1° a. Vol ume of unit ae ll = 2910 Q} The rad:ti of limiting c ircles were ea lcula. t ed with these pa r amete r s , a.nd i t wa.s oboerved tha t no epots of the corres ponding order on the gnomonic proje e tion fe'l l outside of t he s e c i rcles . 'I'he r e- fl eo t :\ ons hl~ with h ev€·n were ab sent in t he gnomoni c projecti on, 1nd1cating a 0-eenter ed l a t t ice. y measuring t he l aye r lines on a rota t ion photogr aph t e.lcen about a 1 , t hi s p~.r ame t e r wa.e ete r mined t o be 17 .33 i , cheo!-cing closel y wi t h t he above result . The density of th's compotmd has not yet been dete ined , hence t he n u.--nber of molecule s per un1·t c ell 1s not known w1 t h c er-tainty - Hcwevc.r , because of t he si , ila r i ty of t h is oompol.llld wi th (NH 4 ) 2 t vro~181c1 6 •H2 o ( spac e group o! - Co, unit cell volu_rne or 2400 R3 ), t he most probable n urnber is 4. F_5ur€ 1 gives a sketch of a ct·yata l of H2 (",1oe,Cla) 01 6,• 8¾0 • Tho r esults of goniome tric measur ements are (100): ( oof) == 98° 5' (oor): (roo > == 81°53' (I'00): (001) :::: 98° 7' : 81°55 ' ~ ~~l ~ <1 oo , : 46°21' a z . . muth from face (100 ); 56°5 • a ltitude = 46°28 1 azimuth from f ace (100); 56°6 1 a lti tude <Ii1) Angle~= 98 .l 0 from these measurement s , wh i ch agrees with the va lue de te r mi ned f r o , t he gnomoni c pr oject i on . measurements t he axial ratios are a.1 : a. 2 : a. 3 .!:1 rom t h ese = 2 . 06 : l : 1.892, wh:toh compar e quite well with t he r a t i oa e..1 : a. 2 : a. 3 == 2 , 04: l : 1.900 , ~ete r mined f rom , -ray photographs . In order to dete r m:l ne t he spac e g roup of th:le c ompound , a Weissenber g photogr aph wa s made of t he equatoz, _al net perpendicula r t o a. 2 , u si n g Cu.KC\ radiat i on wi th a ni ol{el filt er . The f ollow ng observations wor e made: (1) No hO reflec ti on wi th h odd appea red. because of 0-center i ng; hk Th_s is r efl ect lono do not a ppear wi t h h •., 1: od d • (2 ) No hO with odd appeared .. 1'hi s i nd iQa tes a gl ide pl ane pa r allel to 010 with a glide . qf. i a. • 3 4 6 1'he space g roups 0 8 - Oo and o2 h - a 2/e a r e possible . Rec ently I Cyrill 13roa set h&s vm r k ed , out t he compl et e J str uc tur e s of (r•'Io ~l8 ] (0H)4 •14H2 o ~d - [Fo~l8 (01 4 •2H2 o) • 6H2 o (2). 'l'lie g rouping LH0~1 8 J was found in whi c h t he c hl ori ne a toms a re - 1 0- a. t t he corners of a cube with t h e rnolyb.- enun a toms at t_e cente rs of t he fa c es (po nsibly sl ~.ghtly ou t of the p l ane s of the f aces ) • . Since t h :ls bas ic groupin g is 1mdoubt edly p r esent ln ti on was disconti nued , (i10) a, mo> f, I I I I I I I I I I I I I I Fi .::.ure ' ' ' ' ', II S'l'RUC r URE DET.LPIIINA'l'ION OP OOHP LEX MOU:CULES OR I ONS BY X-RAY DIFii"RAC TION BY :JOLU'i'IONS 1 - 13- '.i:.h eorctica.l :0;1.scusoion Compar ison of Cal culated a r1d Observed I ntens ity •unc ti on s 1. The 1ntensi ty of monoch roma.ti c ., X-ray s scattered coherently by any ma c ro s copi ca lly isotropic sy s t e m of atoms c an be repre- sented as a functi on of t he s oa tterine; angl e , s,n Sr dr sr whore e 1 :. Jo m,.c.◄ R 2 and , 1 + co.s ~q> l s : 4-rT sin-! A The pr i mary beam is assumed t o be unpolarlze • 'TI1e Sl.lI!lfil.a tiona are over every a tom i n the oy otem . anc ea ch term. the refore , r e l ates to an a tom pair (i , j} whos e sca tter :..ng a mplitude s ar•e r 1 a nd f j •* 'm e function p1 j {r) i s t he p robo,bil ity t hat the atoma 1 and j have:: the sepo,rat1on r; it is no r malize :l by the conditi on 'Ih ts equation appli e s t o all cases , l iqui d s , ar.,o rphous s ol ids • e,nd finely d ivid ed cry stalline sol i d s c onsi s t.inc; of any number of ohem1ea l apec1es . I n man y cases t he 1ntc5r a ls in Elqua.ti on 1 can be evalua.ted a n d the equation reduced t o t he form 1~11. c ollecti on of t e r ns l s ~z!ade in all rea _ syctcr.:1s , in which eaoh term occurs a l a r ge number of times . where r 1 j i s t he avero.c;e sepai:'ati on of atoms i and J; and Tij depends on t ho f unction unity when 1 f 1 / r) . 1he fc.otor Tl j i s equal to = j or ·when tho separa t ion of 1 a n . j 1s a cons t ant . In the c a s e of ge.ocs a t l ow pre ssure the t er ms due to intermolecula r d i nt s.noes bec ome n e gli 0 1bly rm1all• Equation 1 then as ::m mes a relatively simp le form i nvolvincs only i n t r amoleoul a.r di otc.nceo . Thi s enable s one , in mo s t o:l.mple c ases J to find these 'lis tanceo a..nd hence t o determin e the molec ular structure from a. knowledg e of I (f ) . In practice , howeve r , i t i s usually muc h eas i e r to u3e e l e c tron diffr c1.c tion techniques to deter mine t he s tructure of cao a olec ules . The nitua.t_on for a l :t uid _c □ore coDplex . In genoral it is not pos ciblt:i to negl e c t interrJol e c-ulm" te r ms , end the sca ttering d epend □ 0!1 functi o n □ repres;en t in.: ; t ho oepar a.t ion e,ncl r elative orient ation probabi l i ties for a pair of molcculos as well a s on t he i nternal pa r ane t c rs of a sing l e molecul e , However, ? 1renne (7) lw.o po inted out tb.8.t :i.n na.ny c ases t_ ~c s eattering a t fa:1.r l y l a.r c;e angl es io .pproxi ma ted v e ry clo sel y as a funot1.on of :1.ntr8,r::iol ocu l e.r t e rms only • Th.e s oe.tter:i.ne; func tion of l iquid c c. r bon tetrachlor ide io ~D exe.mpl e (B, 9) • T'n.i s io true bec2.usc t _. e Ti j ( s ) func tions aosoci ntecl ,.,ii th the lonse r intermol e cula r to rr:: □ this f a c t decrea s e qu i t e rap_dl y n.s s- incre c,oe s . However ., c of lit t l e Y"•,l ue for : -.:ol e cul2,r otruct.11.J'."e J.-e terminat1on, - 15- ::dnc e ..:o st l l --;1.ui <.ls a r c vol a-t ile nd the e l e c t ro __ d if .2 r c,ction teclu1iciuo0 :·,i.::1.y r eadily bo a )p l :lG • 'l'h crcfor e t he : ..iff r a ct lon p 9'. ttc rn of a li quid i o gene r ally uce:i to investi gate such struc tUJ.""a.l. properti es -.::.o fr e e rote.tio:n 0.1. i:ol e c ulos mid other quest ions o:i. zho rt l:"anc;c ord.er:2.ng i n the 1 :.qui:.l s ta t c . In gonc t..e.l tho p roblom. bcoonec oven r;:ore co2pl ex in the oc,se of a s olut.:..on , sinc e the expressi on f or t ho sc a t t0r.-ed l n ten c::.. ty Hl11 then inv olve t c r :-::::; due to all three type □ of intcr·n olecuhu• i n ter a eti ono as well a.o to i ntrc.mo leculn. r distanc en in bot,1. the so l vent and solute . Ho,..rev c t' , i f t~'le a toms c ornno oln5 t :.c oolute have a muc h hiGher a~~omlc number t han t h o s e o f t he s olv ent o.nd lw.vc, a relat i v e ly histi. conccntro.t:..on , a ll ter::ns exc ept t '.l.o se c1 ue t o t he intc ratol!:ic cl i ctnn c c 3 i n t h e s olute n ol ecules 1;,ri l l b e re l atively n::iall . If smaller t c r ws a r c neglec t ed , the s c a t terinG func t ion will be l:._-e that of a gas , ha.vlns t he fo r□ I 3 whe r e N. i e t he number of diffrac tinc; molcculco c.nd. t he summa.- t i on c 3.. ·o no ·r ove r• eve ry c,ton _n o.. oln cl c ~o l cculc of solute . In this Thesi0 tho simplified Lqua.ti on 3 h e, ::; been a ppl ied in ord er to inv c ntlgc,te t he otruc t u r es of a fei,.r c omplex ions and mol ec ules l n s oluti on . In order to a pp l y t he abov e the ory , a n ethod has been used whi ch wa r. dcvel op ed __n these Labora tor '.!.cs for :iete r rJ lning the st!'u cturc s of complex noleculeo by electron ~l:~fraotion . The -1 6- fir nt 8tori , of cour so , :'l. 3 t o obtu::.n s t -'- abl.o ::,ho to3 r a phs , whi oh , ran dono by a technique to b o clc sc r :'L bcil :ln t:ic nc: t sectio11 of tlLs Thes :i. s . From thc2e photocra.phn a curve in dr,~wn by visual ob s e rva tion emd m0aour 01:1ents whi c h rep re ncnts t :.2.e v e. riatl on of b a c .: ;:enlne; a ct•o ns t he f., l o , but which leayeo ou t the bael:g.round ecru:ionl y c a lle tho vj_sual curve . 'lni :J v:t mml curve i s to be oompat•ec1 wi t h vhe 1:1e<luc ed i ntenn1 ty function -., 4 r,;J where 1<: is a pr-oport:Lo:ne,li ty constant and fifj = { l l) "2.. ~ f 1 fj, (1 f j}_, n bcinz; thA nu : 1Jcr> o f a tomo 1.n n n 1 j t he molecule. f1f,1 If i s very nea rly h-1:dep end ent o f s .for fifj each term, t,h :i. s equation may be app1"oxin:ated b y the s:tmp ler expres s ion; 1 T, (5) : LL A,j ~ i. whe:n:•e A1 j k f1-" • • .J: • i□ SIM nis 5 J i n c...epende nt of s an""'i is an app rop ri a.te a v e rag e of ovc:,r t he r egion of observe. t ion . rij f1_f j We mu s t now cons:1.der t he forr: o f t ho :f 1..m.cti on T j . 1 For a.11 of t he molecules inves tiga ted in t his 'lnoois , it wil l be assumed tha t t he functio_ns f 1 j ( r-) in Equati on 1 oo..n be app roximated. by exp onentia l s of t he form - 17- In orde r to evaluate t he integral o:t" Equati on 1, re r1a lr e the approxima t i on tJ.'l..a t whi ch w:ll l b e very nearly 1s l arge if .1:..._)) {r - lfa and Equation 5 becomes 6 The s tructure det0rmina.t l on. con c i :.1ts of ..1. ind:lng values of the molecula r para111eters whi ch, when us ed to ca loula te a theo r etioa.1 I ~{s) from Equn,tj_on 6• will g ive the best agreement with the observed I ~( s) ,. !he p unched c a rd te chnique deve loped in these Laboratories (11 ) was used t o ca lculate these theoretl,e al ourveo . I n order t'o a pplythis technique we must use the intensity equa.t:on in the unintegrated ~orm , dr 7 ·*Sinc e t h is function is c 1.a racteristic of te:operature vi brations , the conn tant a 1 1 is ca,lled the t empe r a ture factor of the d i '.3 tance ?' 1 ; • This n~menole.ture w:..11 be used even if tem-perature vibratfons a re not c onoidered to be r espons · ble for the decline of a mpli tudo with 1ncrea;:; i ng c.115le . James (1 0 ) has di s oUD s ed ·vhe effe.a ts of temperature vib l''Uti ons on X- r a:y sca ttering funet1ons. -1 - ' he ~ ntc ;_:_~r t . l~ ln th o exprcnsion c an b e clo se l y approximated by nurn8 ; the e xpre s si on is then 8 Jr i c a n np9 ropr1 a te inte rval ,of \r .. r 1 j I a nd N is whe re cho sen so t hat t he a mp l itude i s w~0 lig ibly s .1 all ~ or d 1fferenees g r-o ter t l'1un 11 J r • which a 1 j i s z e ro . '.1.ne oc c onc_ ..;u;n is t o...: ·.n ovE. r te rm s f or r n l s is the f orm whi c h was u sed for t '1e c a lcula t 1on of o.11 theoretical curve s . 2. The Ha.dia l Di strib ut ion l:Ie thod . lthough in princ ipl e t h e fore go ing dis cus sion provides a method of d e te r n ining t h e moot p robable s e t of parame ters by trial e.nd e rror, u e would lik e to be e.ble to d e ter mine the app r oximate sizes o:f these pa r ame t c r fo by a 1:1ore d irect method . To do thl s • it is convenient to a pply t he r a d i a l d istribution method whi c h has been wid ely used in elec tron di? f r a..ctlon inves t15ations . The r adia l d istribution function (or integ ral), D{r), us od throaj1.out thie inves t i gation 1 □ d cefined by the equati on 9 where I~ ( s) i s t he obse rved i nten sity funct i on . I f a' , which is of t en c a lled t he a r t i f ic · a l t e, p eratu r c fa ctor , is chosen - 1 9- I so that e-a 6 2 1s smal l for s = smax' t hen thi s i nte r a l wi ll be given to a. satisf a ctory degree of approximation by 10 If we put into t h i s integ re.1 t he expression for I ' ( a) given by C Equat i on 6 and carry out t he intes r a ti on , t he r esult is 11 All of the t €r ms in the second. summa t i on :).r e sma l l for positive value s of r and can b € neg l e c ted . It in se en tha t D(r ) is then a sun of Gaussian ourves whose maxioa. occur at r i J' whose areas a re proportional to t he a.mpli t udes - are g i ven by w½ ij' = 41',...i_n2_·-. -x---.-(a_'_ +_ a_i_j_). an _ whose ha. lf wid t hs 'l'he r a dial distribution funct ion can. be expected t o give valuable i nforn ati on c oncer~lng the va lue s of important int er a omio distanc e s and their t emperature factors . Moreove r, t he above arguments a re in'1ependent of our negl ec t of s ol vent sca t tering and intermolecular interactions . '1'herefore , observations of D(r) may tell us if suoh negleot is permi s sible. In pract i c e D(r) 1o evaluated by approx1me. ti:p.g the integr al in Equation 9 by the sum N )2,. Do (.r) :: L ~.s e - Ci .i oS ~ =O I l (" [ '( .1 £5) $11'1 r 1 [ j 12 - • i. O :::: 0 t1 · max • 1.... Aft e r f _nclinb aprn"'oximc. t c v a J.c s f or t h e observed int ens:'.Lt} c urve , n. r ef 1.11e ":ont :l. o c n,r r_c,.. out by □ eans 1 of a. s u i t able tr _al a n c ert' Or' r.'!.othod • It is to be :no te t ia.t s _n c e t ho uni t • of the .::ir1p li tudo s Ai j _n :..qua t 1on 6 °'~" e quite a 1...bi trary , t h e oboe r1.red pcal:n .:.n I ~ ( s ) e.na 1n D0 ( r) hB,ve 011.ly rela t i vc s '.'c.5TI-:i. f i can c e . B. Description of Aopa .ra tu:a_ One of t h e d i ff i culties encountered i n a t tc□p ti ng to apply the t r}.e or y d ese ~ibed 1n the last sec t i on is that of obtaining sui table ph o tog r-a phs fro m whi ch an I ~ ( s) curve oan be dra.,m . A satl sfnctory photoe;r aph mu ot ahow en01J.gh ·-.m ·ima (or appa.1"'ent t1axima ) to .l 1 r:e a reaoona.bl y unique str uctuce selection p os s ible . It i c ''l no d es i r abl e t h.at t he spac · ng of t hese n a x.ima be s mall enough to _ r ovi e 5 00d c ontri..1.s t . In o rder to mee t these con- di t l ons 1t in neces sar y to u se e. comparative1~ nhort wave length if t he f:i. l :;1 dh;·::.a.nce is o. t h 0 o r:ler of 5 cm. Tunt3s t on K°"' • r ad1a ti on w::i.n use·.:i :in a ll of t he worl-: d e ncri bee" _n t h i s Thesis . Sinc e a J:"'ola t ... ve l y h j_5·1 vol t a.c;o i s r e qui red to excite t he t U11.Gsten ::C oe. llne o , the continuouo c.pcctrurn ~o quite strong . Th i::; u 1:-e s i t e.b solute l y n eoesn~ry to uco some s ort of cry s tal monoch ror:ia tor ln order to obtaln a r easonabl y pure spectrum . 1 hot- a t... t h ode, tungsten-target tube 111ade by t h e Lee X- ray Tube Company w .. 0 t .. ie r ad i a t ion s ource . I n r_os t c c.oc s, the ex- c i tin G vol '.:.c.so W"' O 100 .dJ.ov ol tn neal-: , o. current of e.pprox1ma tely 15 milliamp ere s bein 3 used . The Ct.U'.'l.... ent wa. o h 1?.lf- wa ve rectified -21- -,_r ,: ._.,, v• 'n~,. - ,,., - " - -~- o·r - .+.•ub c·r-. • In ~r v ::, •. •,l sr,cs sv l.. ilovo_tn p eo..1': . v - - 0"' ~ '~0 -..l. • 1"' ·'-o r e· ',=-ul~- ·ns d l." .p t,. .. ,._ ucc -~ H:J . ... ~l,.L ..i. l' - .?nc t c:'. r c;c. t c ool l n:::; 1:rn t c r 1 po.G DGd t,._r ough approx i - n e.·~e l y lOL f eet oi' rubbe r tub inc in 0 1: ,... t.Jl" to r educ e current las :: t.o ~- roo.son: -.bl o a:::ioun.t . TI10 rL2,:..1 v ol tn.ce w.s m.ipp ted by a J orclco · indu ctri a l ~- ray trans_or me r . The c c.::1c r a c on sisted oi." a oteel p l at0 on whi ch we re mounted the mono chror.-iator , t he IJ i nho le sys e::1 , t wo l oa • shielr s , and a rer:iovablc "':!.lm h old 0r- - r::iountca. ao tha t t _'l e '~- r a ys could be re ..: lectEid into e. rot.m:1 pinhole . alena crystal The mono ch roi:ia t or 1-1as a I t c oul- r ·om a (100) faee be rota ted about e. n a.xis passing thr ou3h t he r eflec t:ln 13 ourfo.ce to obtf'.IJ.n t he d esired wave l ength. The p in..11.ole we.o app rox i rn, tely o . 8 DD in d iamete r nd 3 . 2 em long . . The diffr:~,c t :i.ng s ol u t i on , con tained i n n thin-wa .l ed g l • s s c a pi l l ary tube , was wo.xed t o t he "'a ce of t he lnhole. The flat fil::.1 hold er con s isted of two shee t s of blac .c: oellulo id secured to an aluminum frarae . Th e f :U :i a nd intensifying screens were p l a c ed in a b l B.c:_,: paper envelope b e twe en the s e she et s , whioh we _~ e t he n screu "', fi r mly toe;e ther . The fil :-:i holr er t a s att aehed t o a • r .:..1e whi c :1. couLi be mo..;ed p,2,r o. l lel t o t 1s i:)lr.hole on three 5 roove ~ tr c .•:S . A l ead sh i eld was pl a c ed oonpl e t e ly a round. the monoc h romator wi th only .Et smal l ho le d ir ec t ly in ba a '.:: of t he ge.le n a. cry stal . Th'l s 't're.r:=1 to pr>evc nt any d ir ec t or s c 2. ttered r adiati on fro m r eac h:!.n g t he f l l n by any path other t han the p in..11.01 0 . I t wen a lso p o ssible t o adjus t t :.ln s creen to preve nt d ire c t r :1:ii[.I.. t ion from po.c s lnc t h r ou;.::J:1. t!,.e pinhole . Ao an e.d- dit l onal precaution, a flat sheet of l ead with a hole in it us.c pl <1.c o,:i clo s e t o the c a p ~_llary tub e , betwe en t h e noluti on Th.c cE::;tanc e fror:1 the p inhole f c.0 0 to t h e, ... r ont s urface of the f __ l ;;"! hol:le:n." wan □ e asur fid ei;-;1:;::il c t r:l p o d ca5e . within !_O. 05 r:.::-1 by n eano of a. 'I'ho remain::_ne, d :1 .cto.nce to t h e fil t1 ras juGt the rnJ.t1 c -:: the t h::_c:. :ne □ ccr., o f t' c fr ont plas ti c sheet, the front int ens:1_ fyiP..g s cr e en , o.n J_ .'.'.l. s ,I.c ot of wn s ~10 as .tr cd with a n 1c ro"::etcr c :::.1ipot· . 1 J.ac'.: p&.pe r • 'This 'I'h_c cue of these d:.s- t,an c o n , the c :1o t anc€: fr mJ t h e f 2.c c of t h e p inhole t o the fil m, was t huo a c cur ately det s r:cined and was .rnpt constant by mel!'. na of 2. spac l nc b o.r . To d0tc 1"'Lline t he s a'"'lp l o - to- flL,i dis t a nce f or each o;=:posure , it was t t.e r e for e onl y nec esso, ry to me nsure the di stanc e f r o .,, t he f a ce o f t he p inhol e t o the cen G"' l"' of the c a p ill a r y tube , whlch was don e 1•1i th e, steel s c a l e . In al l the photo5 r £1.phs made wi th t h:l. o a pparatu s , Eae t man Scre en F :1.lm WO.fl used with Pa tter son lii - Gpoed I ntensify i ng Screens• Por :. est s olu ti on pho to c raphe , thfJ exposures were of tho order oi' f ive days . 'Che appo.r n.tun ~1a.s adjusted b:y: ro t o..tinr; t h.e rmnoch.romator cryc t c.l unt :l. l t h G tu.,."'l.g sten r-:al line was r 0· l e e t rn::1 aJ _J'.' octly through t he p lnho le • ~:a x :lr.nx:i intens ity uas then obtained by n ovinz the whol e c ,9,r:1era with r e spec t to t he targe t . S:he intenoi ty and a ppee.r ance of the bGam wer e ob oc rved for di ffe rent monochromat or and c amera p osi t :ton n by r.:ieJd n c; 3 O- oec ond exrio sure s on screen film wi t:iho u t screens . -. hen t h e a :::ipa.r.?. tus wa. s :1.n correot ad- just·1ent ,. t he ::~ ca:n ,-rould p ro :luco a sp ot wh tch we,s nea r l y rour:td and had a. d a r'ti: verti c a l line t hrough 1 ts c enter . The wav e -23- l engt h wa3 measured by ta!{ ine; powd er photos r a _r., h s of a sample of gal ena , t he unit cell of whi ch (a :: 5. 92 R) had be en measured pr eviously wi t h s t a nda r d po r e r- appa r atus . ::av e lengt h measure- 1 ments we r· e maJ.e t hree times d ur'ns the pr epar c..tlon of t h e solut ion photo5 r aphs t o be des cribed . men t s a.r e e;iven i n 'l'a b le 1. Th e re s ults of t he s e measure- I n eac h c ase th,e c a lcula t ed wave 0 leng th wa:1 VF.c ry clos e to 0 . 21 0 • , t he ;-;,ve r age wa v e l engt h of t he t unss t <:an X: ol lines , an:J. t h is val ue h as been an eumed i n a ll ca lcula tions . Exam'.1.nat ion of these pow, er pho tog r aphs aln.o g ive s one an idea of t h 6 reso l u t i on obtain a ble l'! i th the a pp a.r a t u s . sohe- ma ti c diagr a .. o _,_ t he ph ot og raph da. ted 8/17/ 48 1s g iven i n F 15ur0 2 . The he ights o f - t he lines a re approximately proportional to t he intens i t i e s r c l a.t 'L v e • to other r i n gs i n t h e s am e ne ighborho 0d . F'or co:,1 pa r i r:;on , t he c a l c ula ted d iff r a c t· on pat tern of gal ena ls also given . I n this diagtam .the height s of the lines a r e propo rtional to F 2 mu l ti p l i ed by t he mu ltipl i c ity f actor and t he inte :rp l anar spacin g . Line s separated by mo r e than 0 .4- m il"! on t he fil:ri were , i n e;eneral, r esolved . In all of t he photoe;r a r)hs obtained w_ th thi s a p pat·a tus t h e pattern on t he r i ,ht s ide of t he fil ir (a s one l ook s t oward t h e K-ray tube) wa s much mo r e di s t i n c t than tha t on the l e ft. Th1e phenomenon Wcl. S so pronounc ed t he.t a ll measure me nt ~ and obs erva- t ions uer e mt,r:le on +,he r i :..)h t side , r a cU i b ein g measur ed instead of diamete r ;::; . which woul IJ.1h.1-s 1 s prob2.bly c -..u se~l by an i mpu r- e spectrum h :-.v c an •nsym 11e tri c o. l e f .i. e c t on tho photo_:ra.ph . 1 That t h.i s i s so c a.n r eadi l y be s e en by r efe rr ing t o Fi gure 3. . ! 2.10 (220) (311),(222) (400) (331) ,(420} 0.720 0.687 o.783 0.772 o.'793 0.898 0.827 0.939 1.337 1.210 1.142 0.995 ica1cu1a.ted with 2 1.61 1.70 0.2109 C.'722 0.210 0.687 0.210 - -- -1.475 0.'785 0.209 0.94 1.00 1.15 1.24 1.30 1.40 1.214 0.209 l.123 0.214 0.997 0.210 0.926 0.213 0.88'7 0.213 0.824 0.211 ... - 1.353 - 0.208 o.84 0.32 3.50 0.205 0.395 2.94 0.219 0.545 2.08 0.212 0.65 1.745 0.212 3 .55 \X - 1.67 0.2092 o.684 0.211 - 1.255 1.366 1~425 1.194 1.12 o.964 0.825 0.906 0.626 0.375 o.52"! 0.321 cm - 0 .2094 - - - 0 .210 0 .210 0 .209 0.210 0 ~2 10 0 .209 0.209 0 ~21 0 0 .210 0.210 0 .207 0.210 0.208 0 \ ,A 0.898 0. 829 0.796 0.'170 1.145 0.99'7 0~938 1.216 1.34 8 - 2.10 1."1?'3 2.95 3 .45 0 10/9/48 5.24 cm 735 m. a .h. Ra dius d * ,A - -- -- 1.474 1.442 o.783 0 ,. 210 1.565 0.'725 0.208 - 2.98 0. 203 0.210 o.53 2.08 0.210 0.63 1.754 0.211 0.743 1.494 0.208 0.825 1.349 0.208 o ,. 925 1.204 0.211 0.98 1.139 0.211 1.128 0.994 0.210 1.195 0 .940 0.210 1.25 0.899 0.210 1.345 0.844 0.206 0.3'7 0.51 cm 0 Radius d * ,A 8/17 /48 5.24 em 730 m.a.h. ,\ = o.210 !, the wave length ot WKoi. • Wave Length (average), (511),(333 ) , (600) ,(531) ,(442) (620) , ( 553 ) ., ( 622 ) (551).,(711),(640) (642) (553),(751) (642) ,(553) ,(731) (733),(820),(644) ( 660) ) ( 555) ) ( 822 ) (75'7 I ( 662 (422) 2.97 l.'757 1.484 3.43 ( 111) cm A,Ao 6/16/48 5.565 cm '720 m.a.h. d(average) Radius d * •f (200) Indices of line Exposure Date of Film Camera Dis ta nee Table 1 t' I\ .) - 25- 0 0 e p N a, en "':u< "' o e n > r 0 C: 0 r N ~ "' p c:, "' 0 :. p 1 - - - - (2201 UI - - - (311) (222) 0 i,, 0 °" :.., -------------------0:.., (331) (420) 1------------------{ f-J p 0 m1 - - - - - - - - - - - - - - - ___ Jl)----(422) i - - - - (511) (33 3) 0 co (44 0) - ""===.!(:5(600) 3 I) (442) 0 .,._________________ -{ 01- N c,, i - - - - - - - - - - - - - - - - - - - - - - - - ( 6 2 0) 3 U221 1 - - - - - - - - - - - - - - - - - - - - { ':'""i-;-;;;..;;.;,5;..;i - - - - - - - - - -- - - --------t\l 1-------------- (4 4 4/5 PJA M"l ------ ➔ i;i i - - - - - ( - 55(:,4,~)3 I) :. bi Fi g u r e 2 Ob s e rved and Calc u l a t ed Di ff r a ction Pa t tern s of Ga l ena Powde r - 26- Let x be a ray of the proper wave lengt h wh ich leaves t he targ et, i s r efl ected from the monoch romator at a Bragg angle e, and is diffra cted b y the samp l e at soQe angle ~ x • Also, let x ' be another ray whl oh lea ve s t he t arget and is r eflec ted from the monochromator at an ang le Q + A G. HowevE- r, .A G 1a amall enough so t hat x' e an still get through t he pinhole . Let ray x ' be d i ff rao ted by the sampl o at, an angle , q> x , t such that sin ½~ x, = sin ½cp x Ax' Ax /\ x' :::: ~ x + ,A • 0 '/\ ) Now , since i t s B1.•agg a ngl e i s gr eater, A x11 and henoe 'F x• = <fl x + J~ Obvious l y , t h en, t he angle between x and x' will be on the right side and A"' + 4 Q on the l eft side • If L is the perpendicular d istance f rom the samp l e to t h e line on whi oh x and x 1 cro ss on t he r ight side of t he film, and D is t h e path d istanc e f rom t h e target to t he sample , 1 t ca..l'l be s hown that L :. 0 C.0$"''1) lio.~ ¾ _ \ (approximately) t O-M ~ It is obvious t hat x' is pa r al l e l to x (since L = "° ) afte r cf - 2 a.re tan (½ tan Q), or, since Q is small , a pproxi mately if ~ = e • For diffrac tion ang l es l a r ge r than d1ff r a otion if t his , t h e b ea m oonvBrges • F'or smaller angl es , and pa rticula.i-•ly f or negativ e angles (corresponding to d i ff r a ction on t h e left side), Lis negative a nd the beam diverges . ~1th t he above equat i on i t c an be demons t r a ted that, because of t h is effect alone, the angular range of cp subtended by the two rays x and - 27- TARGET MONOCHROMATOR . x· ' DIFFRACTING SUBSTANCE D ! X -I I L I I I I I! ' I I Fi 5ure 3 Expe rimenta l Ar r angemen t a nd I l l us tra tion of t he Fo cu ss i ng Ph enomenon - 28- x' when t h ey strilce t h e f11 m is a pproz,imate l y 1. 5° for <f = 20°. 'I'he d ista.noe between principal maxima for t he compounds consid ered n this 'I'hesis 1s from 3 to 5° . 'l'he fin.i t e size of the foeal spot on the X-ray tube target also produces a...n eff0ot similal" to that dise uase1 above, 'tending t o ca.use t he diff e rent wave len~->ths t o conver ge on t he r ight a1 e and d iver ge on the l eft side . Experienee with t he a pparat us described in thl s section .nd ica.tes t hat obs ervations made on t he film beoome somewhat tmreliable at 20 to 22°, and the limit of ob servation is approximately 26° (q = 75) . The above phenomena. a.re probably the biggest factors causing decrease of r esolution , and to a l arge extent t hey deter mine how t ar out on the film useful information c an be observed . C. Trial Experimentn with Compounds of Known J truotµre 1. Bromoplatinic Aoid In ord.er to give the □ ethod outlined in the first two seo tions a satisfactory trial, a solution photograph of bromopl atinl o acid was made, t he structure of t hi s compound being well k no~m . A satura t ed aqueouo solution \ta. a used . The visual curve is given in Figure 4 and t he positions of the maxima and minima in Table 2 , The maximum labeled l is the fir s t maximum that oanbbe seen on the photograph but i s the seeond maximum on the visual ourve of '1gure 4. 'rhe first maximum on the visual curve cannot be seen on t he fil m; indeed it i s not actually present in the tmslmplified intensity function since sin §Ir does not go to zero sr ass approaches zero, However, sinee we do not incl me the - 2S- 1/s factor int.he fu.l'1.ct1on I ~( s) as giv en by l~qnation 6, this Te.ble 2 Feature max min a -ca.lo qobs ·r e l' . 1 1 2 2 3 3 4 4 5 5 6 = 0 . 01 0 <lea lo ~bs 14.2 16. 5 (1.162} 16. 8 18 . 5 (1. 102) 19. 9 21 . 0 (1. 056) 27 . 0 26.5 (0. 981) 32 . 6 32 . 5 0 . 997 39.5 39. 2 0,. 992 1+5.7 1+5 •7 1 . 002 54 . 3 54 . 6 1 . 006 61 . 6 61.4 o . 9gr 69. 3 68 . 5 (0. 988 ) 76 . 2 75. 2 ( 0 . 987) Av n r 1ge (5 f ea tures) 0. 999 expres si on d oes go to zero~ 'i.'he f ir s t maximum is inclucled .s o tha t the r adial dist r ibut i on int egr a t1on oe,n b e r:10.d e with zero as t he lower l im:i t . It was pl a ced o.t a distanc e f rom the ori g in of' a.pp roxima t ely one quart e r of t h e a v r age dis t e.noe between p r __n o ipal max i ma . 'l'he r a dial dis tribution i ntG:gr al was c a lcula t ed by means of t he punched CHU':i technique developed in these Labora tories for electron diffr ac t ion c aloule.tions (11). A transformation we.a made to the v a ri a ble q 1 whe re q == k¥ra = ~ sin f• 'l'he - 30- BROMOPLATINIC ACID VISLW. CURVE RADIAL OISTRI BUTKlN IA. 2A. 4A. 3A. 5A. THEORETICAL CURVES T.F. • 0 T.F. • 0 . 005 A• T.F. • 0.0I0A• T.F. • 0 .015119 T.F. • 0.020 A• 0 10 20 30 40 50 q F i g ur e 4 60 70 80 - 31- fol l ow :i.n6 s ummation wa s t hen mo.de u sing the I nte rna t i onal Bu sine s s !!a.chine Tabulator (see Equat i on 12): wher e a I is chosen s o that e - a'q2 = 0 .1 a t q :z <lmax :::: 80 . The cards a r e punch ed no t ha.t t he Values of t hi s funet lon a.re t abul a te(l fro m r' = 0 to r' = 14 2 r,, in s tep o of .ft ; tabula r i ntc rve.l _:l s I~ 10 • x 0 , 03 x. {£ 10 == 0 •.0525 ~ . 1hus , the pronounced \10 maxima D,re obs e rved , one at 2 . 43 R a.nd a weak er a nd broade r one z/2, S:l nce 3.,i ~1 = 1 . 403 , whi c h is v or y n e a rly t he 2 . 43 octahedr a l .mode l i s clearl y indi c a t ed , with the .Pt - Br di s t ance at 3 . 1n . e qual t o 2 . 43 A. I n ca lculat i ng the-ors t i ca l intensi ty ourven , t he amplitudes of t he Pt - .3r t er mn a r e put equal t o a con stant, k . The Br - Br a npl i t ud e s a r c t hen given t o a satioi'a.cto:t:•y degr e e of a pproximat ion by li:: r F:lr - Br~ r Pt - Br x /r p,tl) \f ritJ/ average • The ave rage v a l ue of t h e r ·&.t lo f f Brl ove r t he obs erved angular inte rva l io f Pt equa l t o 0 . 375, whi c h we.a eetimuted f r om t he a t omic sea t t er1ng fac t ors gi v cn i n t he I nte rnat ionale Tabc l len zur Beat:trnnnmB von . . .·,•· ··- · ' · · I\f:l s .t tl,llst r11}cture11 . ' • ' . . I n ot•der t hat compnr1oon s between obs erved a nd ca lculated curve s c an bo easily ma d e:<, 1 t i s conv eni ent to have t he tabular i nte rva l f or t he t heore tical curve s; A q,. equal to 1. I3ec a use of t he way in which we have de f ined q and t he way in whic h t he oa l.,d s a.re punch ed , t his will b e t he ca se if ·we eet the frequency for e a.e h t e r m, u 1 j, equal to l~/7 rij . sti tut1ng the va lue s for r 1 j ands in Equation 8 5ivee Sub• - 32• 14 The t abula tlng ma ohine ca lc ule.t e s t he va l ues of this function fo r q ::: l, 2 , 3 • • • • 144 • For e.11 the oalou l a ti ons 1n t h 1 a Thes is wh· cn involved t empera ture factors, Au was equal to 0 . 05, or A r equal t o 0 . 087 5 i . In - i gure 4 theor~tloa l curves a r> e e;~ven with the temperature factors of the Br - Br terms equal t o O, 0 . 005. 0 , 01 0, 0 . 0•·1 5· ..., .,...,..,.:i 1.1,.,1,.1.<.4 ° 0 .• 020 A2 •.. ·With no t empex-ature factor ther e is a pronounced shoul der on the outside of the fourth maximum instead of t he asym, ,e tr-y whic h is _ndi c a ted by t he ViE;ual ourve . 'rhe ~ourth minimum is also farthe r to the r i ght than obs erved, and t he sepa r a t ion of t h.e f 9urth a.n f i fth max ma ie t oo great . f These disagre ements oa.n all be r e ctif ied by a ppl ying a temperature fact.or t o t he Br - Br d i etances . 02 · 0 . 010 A ~ t emperature f e.otor of g ives good agr eement w!th the visual intensity curve wi t .h the exception of t he f .• r s t and sec ond. :::.ax." ma . . Ginc e the fi r st pea.~ on t he t heoreti ea.1 cur ve r:i i e.;h t well g ive t he appear- anoe of a doublet as ind:t oated on the v isual curve , the principal d:t eas r eements are in t he measur ement s . It w111 be r emembe red• howeve r, tha t i t ls · in t h~s par t of t he curve t hat effect s due to intermolec ula r d is t anc eo will be observe , i f they . a r e to have any effe ct at all . Horeove r; on practically a ll of t h e photogr aphs examined, there has beon a gener al tendency to - 33- Tab l e 2 :,i '.Jes a c o:npa r i son of t he si~xl::,:a, evnd. ·. :i i ni''la obs e rved on the :211·1 o..nd on the theo r e t i c ." 1 c urve •:Ti th a 1 . 01 0 l 2 t mpere.ture Table 3 T,empera turc faetor · 0 0 . 005 0 . 01 0 0 . 01 5 Avere,g e 1 . 001 0. 999 0. 999 0. 999 1 . 001 1 • 0/o o.r/c 0 . 3% 0 • 4:,! /0 q_calo/ qobs 0 . 02 0 (five fe atur e ) Avor ~ge deviati on (fi ve f ea tures) f ive mo s t a c <?ura t el :( measured feat ure s an 0. 5% a l so t h e ave rage per-cen t dev i ati on of qobs from qoa.lc for ea ch or t he models . In eac L c a ...,e t he most proba ble •• t - Br" di ;· t o.!l.ce is 2 . 43 , 2. Th l s i s in c;ood agr eement with the sum of t he octahed ral _radii, 0 whi ch is 2. 45 A. 2. Ohloroplatini o 1)r . old J . ;, ;: . Sturdi va.nt ri..aJ. obtained two d if f r a c t i on pho t o- Gr aphs df a 0at ura t e- aqueo uB s olutl on of ch l oro p lat i nic a cid be!'c r e tl;.e wo r :: desc r i b ed in t h2. :.J 'I'hesis wa s_· ecun . The appa- re.t u s uo oJ. wun nearl y i denti ca l w::.th t hat described in seetion B. 'Thcoo pho toc;r aph s ar c l abeled 3/1 0/38 , fiL: .lis t o.nce of 75 m.-:n; and. 6/ l~/38 , f i l ::.i d. is t an c e of 50 m·ll • iJs1.nc these photo'"'." ·, gr c.phc , ... he s tru:;ture or c h l orop l atlni;:; 2.c i-..i han l"; een de t e r mined . Dr • .:.,. t ur l l rant inform::.; me t h at t ;:1e rc i o some i o ub t ac to the exn.c t . iL r 1 •• c'tan c es anJ. t h;.:;, t no c .h.ec : on tho w:wc l en2_J.,.i:1 by me ans o f' a p owder photo 0 r•c.ph ls on :cocor·.1 . Len e e 1- t he para.me ter whi ch has be en cletGr mined from these f ilms might be somewhat i n e r ro r . Howeve r, t h.0 obnc r v ed ::.'l. '.i. t n, :"', r E: i n accor d wi t h the oc t",hcdr al ctr .rnturc of t l1. e c hlo r op l at:tna,::,c 1on and o.r c t h ere f ore p rc ncntod ~ s a n addi t :1.onal indlc o. t ~on of t .- e po ::1~:.:dJ • li t ::,r o f us inc; t r.ie sol 1 t i on :nethod. f o r str uctu re deter,11ination s ~ Table 4 Fee.ture max min 1 l 2 2 3 3 4 4 5 qobs q <lo_o.lc c o.le ( <loa loj /~Cle~ qobs qob s qobs 19. 1 18 . 4 ( 0 . 96:;) (0. 954) 27 . 8 26 . 6 (0. 959) (0. 950 ) :n .2 3 3 • .1+ 1 . 006 o . 9qr 39. 8 40. 5 1 . 017 1 . 0 08 1l6 . 7 1~'7 . 6 1 . 01 9 1 . 01 0 54- . 9 55 . 8 1 . 01 6 1 . 007 63. 0 63 .1 1 . 002 0 . 993 71 . 0 70 . 5 0. 993 0 . 98 4 78 . 4 77 .7 . (0, 991 ) ( 0 . 982} Aver-age ( 6 fe a tures) __ .,.. 1. 009 ave rage 1 . 000 Average ab s olute d evi at ion o. 8>t t he v:i sua l int en::c~i ty curve , r adial d i3 tr-i ", u.tion inte g ral, and t i::.cor oti ca l c urves e:"G given in F' io:;ur'e 5 • 'l'h e r ud.J.a l d i a- trlb utl cm ftm c ti :m ha n a very p :comi.n.ont pe:J..:: at 2 . 37 R and a 0 ln accord w1. th the considera bl y s□a ller one D,1., :J • ):J 1-'i"'• • .L o c to,h odr ·, 1 rno -Iel . the it. - '.J l "'7, - ...... 'The t h eoreti cal cur-vo e 1•i e r· e c a lculated wt th 0 • lntance equal to 2 . 37 ~i. • The pr oc cd.ure fo r cal- - 35- CHLOROPLATINIC ACID VISUAL CUIM: RADIAL DISTRIBUTION IA. 2A. 4A. 3A. 5A. THEORETICAL CURVES T.F.. 0 T.F. • 0 .005A1 T.F. • 0 .0I0A1 T.F. • 0.020A1 0 10 20 30 40 50 q Fi 3u r e 5 60 70 80 bromoplatina.te ion. The curves with Cl - 01 tempera ture factors of 0.005 and 0.010 i 2 are in best agreement with the visual curve. However, the difference between any of these curves is not very greo.t beoause of the relatively small eontr1but1on ot . __. the 01 - Cl terms. Ta.bl.e 4 gives the comparison between the observed and calculated q values of the maxima. and minima. Since t he observed average or 4<lalc/<lobs is 1.009, the best parameter 1s 1.009 x 2.37 = 2.39 2. This is not 1n good a.greeo ment with t he octahedral rad1 1 sum, which is 2.30 A. Pt • 01 distance 1n K Ptc1 (12) 1s 2.33 2 6 D. The i, Lower Hal,.1sJ,e Complexes, of Ooltgnb1ym e.nd 'l'an.\alym 1. Preparation and Chemistry In 1907 Cha.br1~ (13) prepared a lower ehlor1de of tantalum by the r eduction of tantalum pe.n taohlor1de w1 th sodium amalgam. He assigned to this oompound the formula Tao1 2 ~2H2 o on the baa1s of a single analysis. 'l'hi s compound was somewhat soluble in water, forming a dark green soluti on from whi ch lt oould be crystallized 1n small, hexagonal crystals. .ltour years later Ohapin (14) prepa red a compound whiah was ident1oa.l in a.ppearanoe w:t th Cha.brie•s chloride by the roduotion of tantalum penta.brom1de with sodium amalgam, that the formula. of Oareful ana.lysea indicated this compound 1a Ta 0Br14 •7H2 o. synthesis and analysis of Ohabr1,'s chloride 1nd.1oated the analogous formula. Ta&1 14 •7H2 o. Ohapin oa.rr1ed out boiling point measurements of a solut1o,n of the bromide in propyl alcohol which 1nd1cated a molecular weight co~respond1ng to Ta. 6Br 14 •7H o. 3 -37- Freezing point depre so i o.n measurements in e.queo us noluti on gave a value one-third ao gr eat . This fac t l ed Chapin to the oon- clunlon that two brom:lde 1::ms a ro p ro:luc ed in aqueous solution as well as t he compl ex ion (Tad3r ) .;,+ • Th_s hypo t hesis 1s 12 supported by t he fa.ct t hat two , o.nl only two 11 of t he bromine a.t oms co.n be r epl aced by otho:r halogen.a by eYapor a t ;ng a eolu• ti on of' t he compoun 1n dilute aqueous hydrochlori c or hyd.riodio 6 12 ).( 0H )2 .• 10H2 o 1B formed 1,i f\ slight l y aUca.l i.ne solut ion . e.o id . The oompound (T~ Br Other worlters have also investig?,t ed the e hern1.-stry of these r a t her inter e sting compoun1s. Lindner and Feit (15) prepa red . the complex chloride by reducing tantalt'IID pentachloride with lead powder at red heat in a nitrogen atmosphere . They ea.rried out analy ses which l ed t hem to bel ieve t hat the formula of t his compound is H2 Ta~1 14 •8Ha0 • nua.nt· t ative oxidat ion with pota.s~ si um permanganate wao used t o determine t he oxidation number of tantal um , which t hey concluded was +2 . t'h·s 1A in dl sagreemen t wi t h t he c onclusions of Ruff and Thomas (16 ) . These workers claim t hat the same complex is produced when a. lower ehloride of t antal um, to whlch they ascribe t he formula Tac 1 , is dis-- 3 solved in di l u t e hydr och lor i c acid an ... evaporo.ted . 'f uey also mea,s vred t be va.lenoe o:f tanta l um by observing t he volume of hydrogen liberated when a weighed quantity of t he compound was waroed in baoie a queous so l ut ion . 1h~y r eport an oxidat ion number of +3 and claim t ha t the cor rec t fo r mula is Ta(5Cl1402 •6H20 • s addi t ional evi enoe t hey cite the fact (observed also by Lindner and ,..1e lt ) that only six molecule s of water are lost on -38- mi l d h A,,_ tin. 0 • I do n ot t h:ln:_-: th:: t th ·1_c :ts v er y r:i_cn i f ic 2..nt e vid enc e in f a vo r of thei ~ f or~u la , h oweve r, sinc e this f a ct ml cht ue ll be e xpl a ina b le in t e r ::,c of the ntruc t u r c: of tJ1e In v iAF of t he ab ove dic.e.c,r e e::::ent c , - t h e va lenoe or c ompound . t h:ls c omr)l ex c omp ound r emains in d oubt. i'. otruc t ure de termine..- ti on is nt:11 quitG ponslble, howeve r, c;:lnc e ths number of he,105 en ancl te,nta l um o, t orn s p er molec ule iG ~rno1-m . H . 3 . Harned (17) p r cp a·r ecl a compound which his ana lynee ind1c ,,,ted wan Cb~1 Jt •7H o. 1· T 0 2 He a l Do showed by potcnt:tometr1o ti tration with s i lve r nitra te solut t on t hat two of t he: fourteen oh lor1nc a toms a r e ea s ~ly removed. The compound c Cb6°1 12 (oH) •SHa-O 2 1,1 p.erefore th:ls compound Br •7u o were al s o prepared . 2 12 2 seems to be analogous to t he r a,f 1 14 •7n o and Ta 6Br14 •7H 2 o 2 a.nd 0b6"1 described by Chapi n. Dr. Harned was 1tin d enough t c lend t h e I nstitute a oonsiderable Q.Uc" l.nti ty of his ohlor i cle whi ch was used f or t h e struoture determination d escribed here in. I prepaz•ed the complex lower ·chlorid e of tantal um by reduo ... t1on of t h e p0nte1,chlor1c1e by g r anula r l ead 1n a n t trog en atmoe ... phe re a t a d ull l'.'ed heat . The pen t ahu-lido ·,ms p r epa red by- paso:1.ng a s tr ea m of c h lor t n c satura t e :l with ca rbon t e tra.chloride 1 v apor. mror a.11 i ntj_r:iate mixture o:1:' tanta l um p cntoxlde and oharo.oe.1 ma intained. a t a full red h ea t i n a silic a, tube . The volatile penta.c hlo r id e wa s all oued t o c on/ tense at t h e eool end of the tuhe• It was t h en d~ still ecl into a silica !)ulb containing e, r e.nul:::i. r l ead , where the r eduot l. on wao c a.r-r1od out . 11.f ter oompletion of the reduction, the oomplex ohlor1de was leaehed -39- o ut o:f t he r.csuJ. th15 ma::ic. w.l.t h hot , :111 ute hyd rochlori c a.o id .,, re sul tln5 solut }.on ·~n vacuum• '. L'r10 prepared in a v e 1.7 slmil ·\r mann e r, c ompl ex l ow e r b r omide was TantD, l um pentabr omide waa rr1cul e by passin G a ctroa:--J o f :ni t r ogEm. s a t urc: tod w:1. th brom1ne over, a r ed ho t ·: lxtur e of' charcoa l and tan t r::i.l"LUD pentoxide. 1 The re• d uc tlon we,o e,l s o c a rt")_ed out w:1 th sranular l ead , a,nd hyd.robrom1c a c id. was u sed to extr0,ct the cleoired c ompou.n,1. At t e mpt s were mo,d.e to. synthe s ~tze the ane,l ogous coltnnbium bromide by reduction of c olumbiu.m pentr1bror:1idEH ., Both lead and ·" :, percent sodium ama.lga.m were tried as re,luolng ag ents , but 1n' neither oa se ws.s a signi:rl oant quant :i. ty of t he ctesired comp ound obtained . None of t he complex he.lid.es described above is soluble enough in we,ter to enable one to obta.1n sui t-9,ble solution photog r a phs • They ~1 1:"~, however, extrc::irnely soluble in e thanol• Therefore this solvent wa s used_ exolusi vely. .Since 'these oom- pounde a r E: pr esumably not ionized in e thanol solution, the pr1no1pal diffrac t :l ng molecules oonta.1n fourte en halogen a.nd six tan.talmr, atoms. In the follow ln5 discus sion the formulae of these complexes -will be written in tho fo r m Ta(P1 1 it71½0• ~h 'l'he s tructur e of the (Ob~l 12 ) Group , 11he four follow i ng :.' l.iff r a cti on photoe;r aphs were made of a concentrated e,lcohol i c solut t on of Cb,,...Ol 1' 4 •7H':)O: 0 c; - 40- Ja te Filr:~ .D i s t .0;,nce ('l I ,·'.:) li./ /J..:,, O I - • i: -... .. 9/ 21/4e l J/19/ 48 11/ 30/48 s. ;~ ~~s c m ti 11 II !'I )I ,, Expo nure Sa:r:p l e T,hl. c ~:ne s n o. 6 mr:: 530 m. a. . 1'1 • 1 950 m.a..h. 200 0 rn . a . h, 2120 :n . a•h• o. 8 mrn 0.7 m.m 0. 7 mm The l a.st two photographs were used in prepar:tns the visual curve since they were considerably better tha.n t he firs t two + The visual curve and radial distribution function a.re shown . in Fi gura 7• I n this investigation and in those .follow• inc;, t he units and prooedure used in calculating the r ad1a.1 distrlbution and theoreti cal curves are the same as those described in the investigation of bromoplatlnlo acid . 'l 'he radial d istribution function he.a two inc ompletel y resolved pea.Im in t he vicin:tt.y of 2.4 and 2 . 9 2, the la.tt er bei:n.3 consid erably higher t han t he former . Th ere is also a. prominent peak at 3 . 92 :( and a r a ther low one at approximat ely 5 2. In docid:lng on a trial s tructure -i t is nece Dsai."Y to ma...ite a c hoice whi ch is consist ent with the cheo istry of t hls oompound and with t ho r adlal distr>1but1on curve . I t is evldent f r om chemical cons idera tions that two of t he chlor- 1ne o,toms oannot be related b y sym,,.1 otry to the other twelve • suf35estz, i t e.0 lf lo the following: A structure wh1eh Plac e t ho six columbium a.toml at the oorn e1"s of a regula r octahedron whose edges are 2•9 long . f Then pl a.oe twelve chlorine a.t oms on the perpend.ioular biseotors of' t h e edg es so that t h e oolu:c1bium-e hlorine distances a.re a.pp rox:1..mately 2,4 ){ ( see Figure 6) • !!:. c alculation tu.'1.en shows tha t the most pr om1nent d istances wlll be - 41 - Fi 6 ure 6 Structure of the (:M 6X12 ) Gro up in Cb~ l 14 •7H 2 o, Ta 6Br • 7H 2 0 , and Ta f 1 1 4 •7H o 14 2 Do uble circle s - metal ato;. s Single circ les - halogen atoms Deocr•l pt l on Twenty - f our Cl; - .d l .t.ls t a nc e s a t 2:4J[ - Cl d i o~anc co a t 3. 95 i Twen t y-four Cb - en din t .J.n c e s a t 5.0 i ··, ·1 ,r en ...vy- f our Cb Thi s structure meets a.11 of the requirements of the mown ohemimtry of the molecule and of the radial distribution tunoti0n . No at t emp t ha s been made to account for t he two rema1ii.1ng chlor i ne a toms sinoe it i s evicl.ent th9. t their direct effect on the inten::i:lty fu.rietion will be quite sma.11 . It i s pos s ible, however , tha t t hey could ca.use enough. d istort i on of the above symmetr i cal structure to be signlf'ieant. With the assumption of oub l o sym1:iet11 y t he r o a r e only two pa r a meters to be determined , a so a le pa _rametcr arid t he ratio (r 1/ r 2 ) of t he ohortest Ob - Cb to t h e shorte st Cb - Cl distance. 'fi1e f ollowt ru.3 t heore tica l curve s w,c; r e ca lc u.liite d a:nd. a.re ahown i n F i g ure 7, Deo1gnatlon A B C D E These curve s we re a a 1cu12.ted wi th (r 1/ra) = R 1 . 137 , 1.168 1 . 187 1.207 1 . 227 f 61 ) ( f ,,,,Q .L._~ ' average a.mpl1tud.es of the va rious terms a r e t hen 5iven by 'f'he VISUAL 0 RADIAL CURVE 10 20 30 40 50 60 70 80 OISTRI BUTION IA 0 2A THEORETICAL 3A 4A SA 6A CURVES A B C D E 0 10 20 30 40 q 50 60 70 80 .'\_ x.-y occur • s Nx-y time::; '.i.n t h e o olecul. e . . ". r l , the a :1~:J l:~ tude of the s11 ort cct Cb - Cb term, ;•:a.s arb :1.tt~ar:l. ly e,1·:e:~ a VD,1 u e . 0±<·50 . ·.L'ho bczt asr ocmsnt ·11 t::1 V 1e v:. suu:i. curve between curven B il.nl G. aq wide and lAG"!:') ~~s an inter polation The r e are , h owovGr , certain . objections n. :: t ho appearanc e of t hG f :U n woul d seem to f:lfth r:i. :.1xl:nur:i , con t o,1rn:, a 1nintmum whi c h one mlght expe ct to see. These troubles seer:i t o be at lee~s t partially eo r2 roe ted. by :1.ncreas ~tnG R slif)ltly , as 1n ctirve C; but a n othe 1." dj_fficul ty then appearrj. The fourth maxlmun beoon ec more p r ominent th.n.n i t · probably should be ,. Th is maxlmum esppeal"S on t he fi l m t o be cons:tderabl J lower t .h.an t he average of t h e third. an'.:l" fifth maxima . A way of lmprovlns t hi s si tua.tion i s succ:;ested by ob oerv c.n.c t hG r-adial :listribut :'Lon functi on . Tho peAk ,11t 5 i is c on sider abl y flatter a nd lower t han it would be i:n t he ease of a syrmae tr l e r:-.J. model w:i. t hou t temperature fa ctor □ • A ca.loula.t1on s,l s o shows that t ht s hie;h frequency ter.,n has one max imum just to t he r ie,ht o f t he fourth :r1inimw11 and another. ve r y clo ne to the fourth maxi r:rum . Hence, a p plyin0 a temperature fa.c t.or to th5.s terv,1 wouL1 b oth tnereG.se t h e wi :l th of the fourth minlmum and decrease t he he1 c h t of the fourth ma.x lrrru..rn . Slnee i t is not 1 11-:ely t htt t rlJ.. wil l ha ve a fa i rly large t ernpe r a tus faetor e.nd r 3 none, it b e c omes neces sa ry to imre stigate the effect of & tempEH"'9. ture factor on both of these distnnce s . l1 number of theoretical curves were oaloulated in wh ich both of these e.:ppl:~c:d t o tl:.c 2.on s c . - Cb .::. .'. . n t :-:.nce or. to t l:..0 Cl - 01 distances. The tw o l e ,.,., t l.:np0 rta.:nt Cl · - Cl tern s •rc r e on:i t1~cd. c or::J l e tcly . paro..Do tor c u net c to c o.l c ul .:.: te e ::.c h o: tl~eso c urve s c::-.~n be fou..."ld b:r re f c rri.n::_: ·::. o .? l~:;ur e 1 0 , tn rht c h the p.:JSi t:ton of e a.c h curve locus of t he ber. t v a lues of H. Th.e 1 2.r r;E. c;_o t r ep1~e scnts the best par ame ter □ for •e a c h v a lue of the t empe t<}.tur- 0 fa ctor ratio• K".{a mj_nat :1. 0:n of t h e theore tica l curve s ln Fle;uron 8 and 9 shows tb.at t ~e t emp er·a ture fa.c toi."' on t b.e l one;E:st. Cb - Cl help s c onsLler ab l y . distanoe 02 A teraper2.turc f a c tor as SL'19.ll as 0 . 0 0 5 A would resm_lt in c ons :....de r a bl0 i mprovement . However , t oo large a t empe r-a tur c fo, c tor on r h a s a. tend enc y t o mak e tr~e fourth 3 m:tn iraun too shal low a.nd. has e.n a dv er se eff ect on the shape 'ot the bro e.d f i ft...1'-i ::iaximun ; the r.1ost t hat oan b e allowed for this t0:::1per u tur e f::1.c to r Q2 l s a b out 0 .005 .H. • 'ro:1p cr::i.ture 0 . 005 - 0 . 010 ..~l and 0 . 002 - 0 . 005 A2 for r 0.. ' factors o:t' 4 and r 3 , respec tively, r;i ve s:J,t isf '. ctory a.5re oncnt wl t h t h e v i sual cur v e and c.r0 a lso 0 c on z;isten t w:~-;:,h t hG 1rori: d one on bf'omoplo.t l n:l c a c _j_d. I t is not p oo :ilb le to a :, sigr1 any Bpco ta l phy s i cal si:Q1:. fi c 8,nCe t o the t0r:1pe r'f'. t.ure fo.~ t or s d !. scucscd ab cvo s inc e t h or e c, rc a t least three ~,ons::. 'b l o ex:1lane. t lons for· then : (l} t ~o pro s enc~ of t a.noes d.ue t o dis tortions introduced by the t wo remaining - 46- 0 10 20 30 40 50 60 70 80 F G H J K L M N 0 10 20 30 40 50 60 70 80 q Fi g ur e 5 T'he oreti c al Curv e s for the (Cb6Cl 1 2 ) Gro u p o.--_----r-I0_ _..... 20 ___ 3,_o_ _ 4.... o_ _s""To_ __,s,:..o_---'-1.,;:.o_ ___;;,,eo 0 p Q R s T u V w 0 10 20 30 40 50 60 70 q Fi 0 ure 9 Th eoretical Curvec :t'or t n.e (Cb 0Cl 12 ) Gr•oup - 48 - p•0 X a K J I 0.02 /) X " F /f ~1H iX X 0.01 A 0 1.13 1.15 1.17 1.19 1.21 1.23 R 0 p• 0.25 p 0 X ·r/;t/ / /J X 0. 02 y/ a ///I Y,/ / / "J L ,,.,, /_,-',,, N 0.01 0 1.13 ,,/, X X //1 A 1.15 1.17 R 1.19 1.21 1.23 p • 0 .50 0.02 u V w X X X 1.19 1.21 a 0.01 0 1.13 A 1.15 1.17 R 1.23 Fi c;ure 1 0 Pa r am et e r □ a p of t he 'l'heo re t ic 2..l Cu rv es Terr.~erature ~a c to r of r 4 Ra t i o of t ernper·2.t u re o.c t or of r 3 t o t hat of r 4 - !+9- c hlor i ne atoms, and (3) d ecrease of r e so l uti on due to the experi mental arrang ement .. Any one of t hese , or a c ombinat ion of them" mi ght we ll ca u se a. r Ela.l or apparent temperatur e fa ctor., Fo rtuna t e l y , the ch.o l oe of t he best v a lue of H and the scale factor va ry but li t tle wi th the temp er a ture factors a ssigned to t he longe r d is t anc e s., A compa r ison of t he observed and c alcu- lated posit i ons of the ma x ima and minima will be found in Table 5. The sca l e fa ctor has been adj u sted i n eao h c as e s o that the a verag e value of q·ca.le/q obs for t he six mo st rellabl~" measured fe a tures ls equal to 1., 000 ., I have concluded tha t the beat choice or parame t e r s is t he f ollowing: Shortest Cb - Cb 2. 85 X - Cl 2.41 X Shorte s t Cb 'l' . F . of longe st Cb .. Cl T. F . of next to t he longe s t Cb - 0 . 010 i2 0. 002 - 0,005 i2 0,005 - Cl 1'he four principal sources of error are (1) qualitative error s l n d r a wing t he obse rved inten si ty curve, (2) error s i n measuring the r a dii of the rings , (3) pos s ible errors 1n the mean wave leng t h , and (4) spectra l i mpurity of the monochroma.t1zed beam, whi ch might c a use d istortions i n the appearanc e of ' the photogra ph . The l im it of error due to the first two sources is e s tima ted f r om t he region of a ccep t a bil i ty on J:.+ i e;ure 10 and from the avera.3e deviations i n Table 5 to be a pp roxi mately +0.05 i for r 1 and r 2 • A reasonab le e s t imate of t he total 0 l i mit of error is O.Cf"( A~ - so- Table 5 qoa1c/qobs qaalo qobe max m1n a B s M B C , 14.7 16.l 16.2 · 16.2 16.3 (1.096) (1.099) l 1 17.4 19.3 2 2 3 3 4 4 5 - ... .. .... 8 1.105 (1.110) - - 23.7 24.9 24.7 24.5 24.5 (1.050)(1.0:,2) (1.035) (1.035) 29,4 29.4 29.4 29.2 29.4 1.000 1.000 0.995 1,000 33.8 33.6 33.7 33.4 33•5 0.995 0.998 0.989 0.990 37.6 37•3 37 .4 , 37 •3 37.5 0,992 0.994 0.994 0.998 · 41.9 40.9 41.1 41.8 41.7 0.977 0.981 o.9gr 0.995 57.9 59.4 58.5 58.4 58.5 1.025 1.013 1.009 1.000 6:o.• , 64.o 64.o 63.8 64.2 1.012 1.012 1.009 1.014 48.2 5 - M 6 - - - .. 69.7 69.0 69.4 69.4 69.9 (0.990) (0.994) , (0.996) (1.002) 6 74. 6 75•5 75.8 76.o 76.6 (l.012) (l. 015) (1,019) (1.027) 7 Average abs. deviation (6 features) 0.012 0.009 0.007 0.005 2.86 2.84 2.40 2.39 Parameters: • Shortest Cb Shortest Cb :5. - Ob 2.84 2.85 2.40 - Cl 2.44 12 ) Group Four d1ffra.oti on photographs of a oonoentrated soluti on ot The Structure of the ( 'l a. 0Br 1 Ta Br 14 •7H2o in ethanol were obtained: 6 Sample Thick:ness Date F1lm Distance 6/21/48 7/7/48 7/12/48 l0/12/48 5.33 cm 5.218 cm 5•218 om 5.21 om 0.7 mm 0.7 mm 0.7 mm o.8 mm Exposure 2860 m.a.h. 2020 m.a..h" 660 n:i . a .h. 1260 m.a..h. - 51- 'l'he l a.s t photograph was considerabl y s uperior t o t he o ther s • The visual curve and r adial d istr ibut i on function obtained I n t he l a t ter curve ther-e 1s a. fro m i t a re s hown 1n F igure 11. 0 0 v e r y hi gh , broad max i mum a t 2 .• 72 A and s ma l ler maxi ma at 3.64 A , 0 0 4.16 A, and. 5. 25 A. 'l'he s imi larity to the r adial dis tributi on functi on for Cb~1 14 •7H o i s i mmedi ate ly apparent. However, in 2 this oaoe all of the metal- halogen dl s t e.noe s a r e longe r beca us e of t he l a r ge r r s..diue of b romine . 'l 'he shortest 'l'a. -, Ta e.nd. , '.I'a. - Br dis t a nces a.r e so close , t oge ther t hat they are unreE?olved. The same model ls assU!!led aa for t h e (Cbe)J.12 ) ·e;rmlp , the tantal um atoms bein g at the corners o f ru;i. octahedron and the bromine atoms on the perpend1 cul s. r b d. seotors of the edge s (see Figure 6). Theoretice.J. our,.res were oa loula ted for t he . f o llowing models: Designa.t:ton A B C D E F (rf r 2 ) = R 1.066 1. 082 1.098 l.114 1.132 1.150 which a r e shown on Fi gure 11. The average va lue of the ratio of t he ocatto r ing factor of bromine to t hat of t ant a lum wa s estim.a ted to be o.40. The p rocedure u sed for calcula t ing ampli• tu.des was t he same as t hat described in t he l a st s e cti on. In c omparing t he se curves 1 t mu st b e ltept in mind t hat t he pos i t i on and shape of t he low t hi r d maximu'TI 1s v e ry d iff i c ult to determine . It i s c.e rta in t ha t this peak is very muah lower t han t h e fourth maxi mum and th-s.t , the sec ond mini.mum ie con- siderabl y de eper than t he t hird . , I nd eed, it cannot b~ aa:,.d VI SUAL CURVE 10 0 30 20 40 50 70 60 80 RADIAL DISTRIBUTION J IA 0 3A 2A THEORETICAL . I 4A 5A 6A CURVES A B C D E F 0 10 20 30 40 50 q 60 70 80 - 53 - with c er ta i nty t hat a n inimurn ls a.ctua.l l y pr"esen t betwe en the indica ted third a nd fourth maxima . The fourth naxir.1um appe ars to b e h~f:5,he r t han t he f i fth , whil e t h e fi fth , sixth, and seventh maxima a ppea.r to b e of app roxirua.tely equal height. Howeve r, some d i sagr eement wi th the l a tter obse rvat i on mu s t not be con- sid ered impo rta nt. The sixth minimum e.pp ear s to be def' ini te ly deeper t han t he fifth . It ls extremely difficu l t t o see . the ei ghth max l mum, and , since i t occur s quite fa r out on t h e fil m, one c a nnot e ven. be sur e t hat it is p res en t. Hode l C gives t he best a g r eeme n t with the vi s ual curve . r. .. odel E c annot be a ocep tea. b e oe.us e of he i(;ht of t h e third .?,nd sixth max ima and J e p th of t he t h i rd minimum. i s c on s ide r ed a cc e ptable . ~iodel D, however• Model B e ives po or agreemen t and represents t h e l imi t o f accepte.bil i ty i n t l~is di r ection . In this curve t h e fifth maxiw.um is t oo h le;h a r.d the clxth minimum too shallow c ompa r ed to the fifth . Tabl e 6 gives the obs erved a nd calcula ted (mode l 0) po s i tions of' t h e maxima. and minima . ·rhe s cale factor s have been adjus ted to give an avera~e deviation of zero for t he eight most accurately mea sured fe a tures. A s light inc r eas e in R ove r that in model C s e ems desirable a nd the best para.me ters are tak en to be 2.90 i for the Ta - Ta and 2~63 i for the Ta - Br dista nces. In spi t e of the satisfactory agre eme n t between observed and calcula t ed intens i ty curv e s, we c a nnot yet b e content with the a bove determina t ion . I n studying t h e ohlorocolumb1um a.nd the bromopl atinat e ions , the beat agreement wa.s obtained when appreci a ble t empera tur e fa ctors were a ppl ied to the longer distances. We shoul d , therefore, i nve stigate the ef f eot of suoh temperature factors on the t heore tical intensity ourve s of t h e bromotantalum ion . Theoreti ca l curv e s were calcula ted in whi oh the longe s t (r4 } and next longe st (r- ) Ta - Br di s t a.ncas were . as s igned va rious 3 temperature f ac tor s ; these c urves a.re sho1,m in Fi gure 12 . The v a r i ous pa ra.meter s of ea.oh curve ar e shown graphica lly in I"1gUJl'e 13. I n oe.loul tiru3 thes e curves , the Br - Br d is t ances we r e a s signed the same temperature fe.ctor- e a.n the Ta - Br d i sta nce n ear est t hem in leng th.· Sati s f a c tor y curves could be obtained for an y of t h e t empe r e.ture f a ctors c onside red . However , those cur v e s f or wh l. oh the t e;nperature fa otor r a.tio (p) !s -~ e.r e s lightl y better t h.an the oth e rs beca use t h e , r ela t i ve he i ghts of t he fol.lt'th and fif t h maxims, a re i n b etter agt"eemen t with the v isual curve . The hea vy full J. i ne s i n 1' 1gure 13 repr e sent the 1 loci of the optimu.,.11 va lues o f R and t he s haded a r ea. is t h e re- gion of a ccep tab i l i ty. It wi l l be noticed t hat t he most satis- fact o ry value of R i ncreases considerably R s the temperatur~ factor of r 4 increas e s . However, there is not an a pprec iable dependence on p , the t empe r a ture f a.oto r r a t i o , in t he r an ge conside red . Examinat ion of t he t heore tical curve s d oes not enabl e one to cho o se optimum v a lue s for t he tempel:'ature factors and henc e d ecide on the most s a t -isf a otory value of R.. Howeve r, p r ev :i. ous experience has shovm tha t a t emperature r a.otor of 0 . 05 - 0 .01 for t h e longest Ta. - Br distance i s most r easonable, Th e r efore I choos e a s the followi n g mos t probabl~ par a meters : r r - :y:::, - 0 10 20 30 40 50 60 70 80 G H N 0 V w X z AA cc OD 0 10 20 30 40 50 60 70 80 q Figure 12 Some Theor eti cal Curves fo r the ( Ta6Br 12 ) Group The curve betvre en curves Z and AA i s an inte rpolat i on between t he se curve s . p• 0 0.00 a 0.001 M N )1.,,,, X 0 ,X· ,,,,,,,,I ,,,,,,,,, "'~"' J X ,,,,:, :,/ 0 1.08 1.10 1.12 Ll4 1.16 R p • 0.25 0.002 a s p 0.001 u ,,,,,1 ,,,,,,,,,, T X1,;," ,,,,,,,, X .,, I 0,,,,,, . . . . X I ,,,x~,, I ,, 1 F 0 1.06 1.08 1.10 1.12 1.14 1.16 R p • 0.50 0.002 a BB X y 0.001 X cc Xt-'',,' ,,,, , DD z ;....:,,; ,, ,,~: ~,, ,,, , I ) 0 1.06 1.08 1.10 1.12 1.14 1.16 R ?igure 13 Paramet ers of the Theoreti c al Curves Cal culated for the ( Ta Br ) Gro up 6 12 a p Temperature fa c tor of r 4 Ratio of t emperature fa ctor of r3 to tha t of r4 R :a 1 ,. 115 :t 0.,0 3 Di.e ta.nee, i . Estima ted L1m1 t of Error· i 1 - Ta. 2~92 Oif.07, Shortest 'l'a. - Br 2,62 0 . 01 . Shortest Ta Table 6 4 obs max w min l 15.2 l 3 ,4 4 5 5 6 6 7 7 8 AA 15.9 ,1 6,.4. 16~0 w z AA (l . 044) (1.073) ( 1.051) ' 23,0 (0. 986) (0.,982) ' (0,978) 28,3 28.-2 28.1 0.991 0 .• 992 33.6 32.3 32.7 32.3 (0 •.960) (0.973) (0., 950) 0.988 :,5.:, 35.6 35.5 , (0 . 971) ( 0.977) ( O.<f74) -,7.9 .17•5 37il 37.7 ( 0.985) (0 . 979) (0.994)' 36.,4 3 z 'C'le 23,5 23 •.a 23.1 28.4 2 •al✓ •· q obs qoa.lc 41.5 41.5 41 . 3 41.6 0.999 0.976 1.001 47 .-, 47.4 47,5 47 .7 1.001 1.005 1.007 52.1 52.6 52,.6 52.0 1.010 1.009 0.999 56.,9 57.1 57.4 56.l 1.004 l.;008 0. 987 61.3 61,.1 61*4 60.7 0.9<.n 1.001 .0,991 6:5-1 64,9 65.2 65.4 o.9gr 1.001 1.0C17 69 .• 0 69.1 69,3 70.6 1. 002 1.004 1.003 ... (1.011) 0.003 0.007 0.009 Shortest Tt;t - Ta 2. 91 2 . 89 2.94 Shortest •r a ... Br 2.63 2. 63 2.60 72. 4 7:'~.a 75+7 7 6«/2 Average a.be . deviation. (8 features) ( 1.007) Paramet e,:-s: •' 1 A comparison of observed. and calQula ted posi t1ons of the maxima. a nd minime. are g iven i n Tab le 6. I n a ll e a s e s, the scale p a r a.me t e r h a s b e en adjusted to make the a v e r age value of q ea.1 c/ q ob e equal to 1.000 . 4. Th e Structure of the ( Ta~l 12 ) Group 'rhe f ollowi n g d 1ff' r a ot:ton photog raphs of Ta6°114 •7H o 1n 2 ethanol soluti on were ma.de: Date 4/2¼ · .48 5/8 48 5/1¾ •· 48 10/ 5 48 • F ilm Di s t a nce Sa mple 'Dhi cknes s Exposure 5.42 om 5.42 cm 5. 42 om 5.21 om 2 . 0 mm 2 . 0 mm 2.0 mm 2000 m.a.h. 462 m.a.h ,. 430 m,a . h. 990 m. a,h 8 ' o.a mm The last photograph was ao muoh s uperior to t h e other s t hat 1t was u s ed a l r:1ost excl usively for the structure . determina t i on. The vi s ual intensi t y curve and r a d i al d is tribut i on function c a lcula ted therefrom are s hown in Fi g ure 14. Th e latter c urve 1e quite c ons i stent wl t h t he str uc ture proposp,d fo r the (Cb~l 12 ) 0 and ( Ta 6Br } g roups . The lar3e max i mum at 2 .• 9 A 1s the shortest 12 Ta - Ta d istanc e and t he de c ided asymrnetr y on t he 1ns1d.e o f thi s p ea!:~ c orre s ponds t o the s h orte st Ta. - Cl d istances . nent maximum a.round 4.0 .'l'h e p romi- i and the ve ry iow one ne a r 5 i corre- spond to longer Ta - 01 and Ta - Ta terme and. oaour a t t he expected p o si t ion s .. I n order t o find the r a tio of the shortest Ta. - Ta. t o the shorte s t Ta - Cl d istanc e (rJ/r 2 ) , theoretioal curves fo r the fol l owi ng models were oa.loula.ted : Te mperature Factors Deslgnat icn A B R r4 r3 1.137 0 0 1 . 169 II " -59- 'l'empera. ture Factors Designation R r4 r:, 0 D 1.188 1 . 208 0 0 E F G H I J If 1.137 1.169 0.010 1.208 It i2 0.005 If 2a 11 1.188 If If It 1.228 1.256 II rt tt tf If These theoretioa.l eurves are a.lso shown in Figure 14. In cal• oulat1ng these curves a value of 0 . 19 was used for the average J;"atio of the -sea.tter1ng factor of chlorine to t hat of tantalum. 1'heoret1cal eurves we re no,t caloula.ted using, temperature factors other than t hose given above , s1noe these were found to be sa.tisfaotory for the (CbeP1 12 ) and ( Ta 6Br12 ) structure determinations. :Moreover, the tantalum-halogen terms are much less important in thls oe.se than 1n the others~ It will be noticed, however , tha t better a greement with the visual ourve l is obtained wrien tempera tu.re · factors are used,. L•lodel G gives the best agreement with the visual curve, and the optimum value of R ls estimated to be 1. 18 !. 0 . 04, For sma.lle.r :values of R, · as in model E, the shape of t he third ma.xlmu..rn and the position of the third m1n1mum are ln ser ious d1sagreement with what 1s observed. At la..r ger values of R, the third maximum becomes too high, the third minimum too deep, and errors in the position& of t he maxima arid minima inerea.se. A comparison betveen the observed and oaloula.ted positions or the maxima. and m1n1ma. a.re presented in Table 7 for models F and G. In ea.oh oas"'~ the soale parameter has. been adjusted so that the average value of - 60- RADIAL VISUAL CU RVE 0 10 20 30 40 50 60 70 80 DISTRIBUTION 2A IA 0 THEORETICAL 3A 4A CURVES A B C D E G H q F i gur e 14 Da t a on Tat 1 14 •7 H2 o 5A 6A Table 7 qobs <lea.le · G F G 15.4 ., 15~9 16410 (l..033) ,{i.039) 22.7 ' 23 .• e 2:;.o (1.016) (l.016) 28,4 ,, .., 331il aa .• s :,:,.2 1.000 . 1.00, 0.986 o.989 ,a.4 37.6 37.7 0.981 0-.98) 4li..4 4~5.8 44.1 (1.032) (0.99,) 51•1 52.0 51., 1.019 1.005 57,o 57.,6 57.7 1 .• 000 1.ooa 62.6 6:,,o 63.2 1.oar 1.010 58.o 68.5 69.0 1,,008 1,016 74.o 75.a 75,7 (l1Gl8) (1.oa:,) Average a.b~h deviation (r features) 0•010 0,009 ma.x min , F ' l 1 ., 2 4 5 6 1 28+4 Parameters: ShoPte·at Ta. ... Ta Shortest Ta ... 01 -2.ae % :2.4a ! /a rm"'. . th.e s11! moat re11ab1y measured fe a tur·e s 1s 1 ♦, 00·0. oalo -obs The optimum pa.ram~te~a -are t he tollow1.ng: q .. •-. D1stanc•-, · t Short,est Ta ... Ta a.aa ·snortest Ta - 01 2,44 5. ,E~t1rnated l im.1 t of error, . I. Diaouas1on and Summar, A summary of the pa.ra.~etera of the halide oomplexes or columb1um and tantalum whioh ha.Ve been 1nvest1gat.e d 1a given - t 2- below. Important dis tanc es ln a oor.;ic·;,rha t s ln j_lar e ompl ex of mo1y·x... enum d ete r mined by Cyrill Bro s irnt (1) :,,r o a l so 5i ven , Compound Shortes~ H - n, . ~hor~ e s ~ l'l - X , .l'.I. :3hot"te z~X - X, ·t (F i, M) ·t tf 1 14 •7 H2 o 2 . 85 ·2 . l~l 3.37 1 . 42 •7H2 o 2 , 88 2,44 3 . 41 1.44 Ta 6Br 14 •7H2 o 2.92 2 . 62 3 , 6.l~ 1,46 Ob Tatf 1 r-fo 14 sJ 18 ( OH ) 4, • 14R2 0 1,315 I n t he molybdenum c ompound t he 1:1e t al atomo are.--. a l so at (or neaI•) the vertices of e. r egula r octa.!1.edron; the eig."'lt h.alog0ns, howeve r, a r e loca ted at t he vertic e s of s. c :..rcu..1!1 scribad cube,. Bond s a r e o.l no formod wi t h oxygen a toms at t h o v e rt i ce s of a l a r se r ootahedron . The deviati on of t he intermeta.llic r adii of tantalum ancl columb i um in these compounds from 't h ei r .aver o.:::;e v a lue (2 . 88 i) is within tha limits of error of this de t c r mi ;:1.ati on . Henc e it c anno t bo s a id wl t : -1 c ertainty tha t a. r eo.l .. difference exists . It :is obYl o us t hat :neta.1-rneta l b onds a r c present in all of thes e c o□ p oun.ds . I t i s of int orc □ t t o investiga t e t he predi o- tion ::i wh i ch c an be me.do from ' auling ' s (15 ) equation R(l) - . (n) = 0 . 3 0 106 n Thi s equation g lve8 the d iffe rence in radius bet'we,e n bond s of boncl nu.."Jb e rs on e an.:l n . In t h io case n == v/1 2 , where v is the number o .~ e l ectron pairs f or rn inG t h e t we l v s bond c in t he Ta6 (or Cb6 or f:06) s r ouping . Th€ slngl e bond r a d. i i R(l ) a.re given in Pauling ' s paper ; they wer e calc ulated f r om th e str uc t ure s of the pnr e metals using t hio oan e equat.2.on . If the e.osumption is made t ha t t he valenc e e l e c t r ons of t lie oh lor i cle ions 1:1eJ.:e no c ontr:1.but :.. ns t o t he metalli c b ond s , th.en v = 3( 5 - w) f or c ol u .1b i i..llil and t ants.lun , whe r e w • s t . . _c oxid.:i.tlo.n numbe r. The ox idation numbe r c t hc.t corr0 svond to t he t h ree ougge sted formulae a r e +3 ~ ·+ 2 1/3, and +2. Oxi·ation Number 'I'he: p redl.otcd me tall i c radi i a re Bond Number Pr edi .oted Radius 0. 5 1 . 431~ +2 o.er i 1. 396 X 0 . 75 1. 380 5{ for t anta l u.1-:i c ompl exco ; the correspondlne; r e.d11 fo r c o l -c · bium a r e not sie;...n if .,_ c antlf diffe rent . The e xperimentally d etermined r adil a r e olos0 enough t o these va l uec. to be con oidered. quite r easonable . I the equatlon 1s used t o detc r ~ine t he bond num- bers , t he r esults a re o . 4J. f or Ta 6Br 14 •7H2 o , o . 4-7 for Ta tf 114°1H2o, and 0 . 53 for 0bff1 1 4 •7H2 o. It i s not to be i mpl:l ed that t hese r esul t s favor one of t he p roposed oxic.atlon sta t eo fo r t antal um and col umbium . The equa t ion is not consider ed zu ff'i o iently r eliable fo r such a prediot ion. Moreover, the effect of t h e hal oGen a t omo 2 ight well be fe.r from neglic;ible . molybdenu.,..., r c~dius i n the ( ioeJ18 ) + TT~ The pr ecl icted 0 group is 1 . 30 A if i t 1s ' assumed that t here "'. re 3•78 va lence e l ec t r ons per molybdenum a tom. The ohor j;eot inte r atomio d istanc es f or c hlor i ne and b ror.:ii ne in t he t antal um and oolumbium complexes ar e sonewhat s horter than twi ce t he oorreopondlng va.n der \'la.ala ' radii (1 . 80 for chlorine an::l 1 . 95 f or br omine ), This is no t at a ll unusual , - 64- howeve r, s1nce t h i s is oboe rved n a l arge nunbe r of c ases where the haloe;cns arc :l.n the ne.me mol e c ule e.nd pa rti cu larly whe r e t hey a r e boun to t he se.:;1 e a.tom. It w:!.11 be noticed t ha t subtraction of the halogen ,r adius from the c orrespon ding metal- halo5en d.is t a nc e · i ves a ve,lue for t he mete,lli c radius v ery ne e.rly e qua.1 t o one half the intermetallio clistance~ I do n ot mean to attach r.mch sie;n:tf l canoe to t hi s obs e rva t ion other t :~a.n t hat :.. t indi c 2. ten tha t , th0se bond s a r e c oval ent and of r eas onable mae;ni tud.e • ~'i ub t.ra.c tlne, t h e ionio halogen r a d ii fro m tr'!.c co rre spondin{j clistanoeo e;lves e\.bsurd ly sma l l va lue s for t he effective metall ic radii . The covalent n,a.tur e 0 .1. thes e bond s l a , of course ; to be expec ted f rom t he stabil ity of the ( Ta 6~ 1 1 2 ) group~ (1) Cyril l Bro sset , Ar kiv. f 8r Kemi, Hineralog1 och Geologi, A20 (1 9Lt;5} • (2) (3) Cyrill Bros set , ibid . A2 2 (1 946) • K. Li ndn e r, E . Haller, H. Helwig , A. Kohler, and H. Feit, Beriehte, S5B; 1458 (1922) . (4) IL Lindner, E . Haller, and H. Helw1 5 .;, Zeit • . f 1 .anorg. u . a.llgem chem. , llQ, 209 ( 1923) • ( 5) K. Lindner and H. Helwi g , ibid . (6 ) w. w, Scott, Standa rd ;.Iethods of Chemical Analysis, 4th Ed .; Van Nostrand Co . (7) 142, 180.:.8 (1925 }. P• 319,. N. H. L~ P1renne, The Diff r action of X- Raysand El eotrons by F r ee Mq_lecules , Cambridge Univers i t y Prea s , p . · 79. (8) E. E~ :Br ay a.nd N. ;3 . Gingrich , J. Chem. Pb.ys •, ll, 351-4 (1943). (9) A. Eisenstein, l?hys. Rey ., fil., 305-8 (1943 ). (lO} R . W. James, Physik . Zei t", (11) P . A . Shaffe r, v. Schomak e r, and L . Paul ing , J. Chem. Phys ••, li, 659-64 (1946) • (12) F. J. Ewin g and L. Pauling, Zeit. f .. Krist., 68 , 223-30 (1928 ). (13) 1-I • C • Cha.brie, Oomi,t , rend u (14) W. H. Che.pin, J .. A.O. $ •; jg_, 323 (1 91 0). (1 5 ) (1 6 ) ll, 737 (1932 ). 144, 804 (1907) • K. Lindner and H"' F'eit,, Zeit,, ill, 66 ( 1924) • r. anorg , u . allgern •. oh.em., o. R . Ruff and H. Thomas , Zeit , r. anorg. u. a llger,1. . chem., 148 1 l and 19 (1925)~ • • s . Harned, J- A.O. z., ~• 1078 (1913). (17) H .. (18 ) L •. Pauling 1 J . A. 0 • S ., 62, 542 {1947) • Pro positions Gubm1 tted by I'hilip · • 1/a rrhan Ph . D. Or a l Examina t ion , Ivia.y 9, 1 949, 1: 00 P . N., Cre ll in Conf e r enc e oom. Commit tee : Pr ofe sso rs Sturdiv a nt (Chairman ), Pauling , Lucas , 3chomak er , Davis; Dr e . ·Iu cs and Davidson. 1. The density of CuCrO det e r mined by ~tro upe (1), 7 . o gm/cc, a s well as his as s i ~ne n t of Z = 4, a r e probably incorrect.. . I sugg est t ha t · Z 3, corresponding t o a density of 5 . 6 gm/cc. St e rle cons i d era t 1ons and h1.e lnt E- nsity d a ta ind c a t e t ~€ fo llowl~ .p,joba b ~e.. structur0 : :;jpac.e. .. group. D - 0 6 2 2 Bas i s : Cu in 1 2 , 0, 0 ; 0, 1/2 , 2/ 3; 1/2 ,,1/2 , 1/ 3 Cr in 1/ 2 , O, 1/2; 0 , 1/ 2 , 1/ 6; 1/ 2 , 1/2 , 51' 6 · 0 in 1/2 , 0, z ; 0 , 1/2 , 2/ 3 , + : z; 1/2 , 1/ 2 , 1/3 1- z 1/2,0,z; 0,1/ 2,2/3 - z; 1/ 2,1/ 2,1/3 - z = wtth z ~ 1/4 'I'he density of th i s compo und shoul d be red~te r mined . J . D . Str oupe, tJ . A.a. s . 2. Price and Zemany (1 ) ha ve studie the equi l ibr i a. (CI-I3 )2 s 1c 12 + {CH3)4:Ji __.. 2(C H3)y)1Cl and . (cH ) SiC1 + {c H ) DiC l _., 2 (CH ) 2 s 10 1 3 an ll, 571 (1 91~9) . (1) 3 3 3 3 2 ( a) (b) have c.ete r mine d the follo wine; ther-u odynamic d a te. : dea.cti on A H0 7.ac: o ,... , 1zc a l/mol .JV;> V ""A .,...0 ~ 3850 0 , lrna 1/t1 0 1 As, e . u . (a ) (b} - 5. 4 - 4 .7 I p r op ose that t he h eat of r eac t ion is ue primar ily t o a heat o f 1nt€rao ti on o~ -1. 8 k cal/mol between a chlorine atom and a 1 methyl e;rou • h e heat 0.1. t ho reaction (cH ) s1c1 -t- 8101 --+ 2CH s 0 1 2 4 3 2 3 3 l s p ri edicted to be - 3 . 6 :rc a l / mol. Th £ hea t cont ent a t 385°c o f t he methyl chloro si lanes cnn n ov b e erived a o funot ons of t h e hea t cont ent of Si( CH ) and s 1c 1 4 • 3 4 (1) P • .J • .lemany an~l 1.:' . P . Price, J . A. C , :::; ., 7.Q , 4222 (1 948 ) . 3. Pauling (l) h.:t s sugc;e~ted a n equa t :~ on which r Gl at c ,_ b onde·:l interr:ie t s.lli c ..llot ,n c cs t o· t h e b ond OL"d er . I r10.v c t:!. ~1pl i ed t ll.i.o e qun. t .:. r.: to 1 1- quld 1 e t a l o by as::n.unin :~ t h::1t t l:ere i c; a Ga us oian di:Jt r i but ::..on of b onc" ed ne i (:' b or o . 'lli e der ived e:·pre s sion Ir= J (l) .,.. 0 . 2 6 ln( / v)+ c . 366wf e whe re D is the me a.11. bonde~ ..:Ust.: mc e , W.¼, i::i the ~lf wi t h of the bonded ne:i.ghbor dls tribution curve , ana N ic the ave rage number of 0on tled nei(;hbor s • All o f these quantl ties can be ,ob t ained by su' table r:ieasur e:nent n of the first pea!:;: of t he raJ.ial d i stribution funct ion f o r the rJetal . Us ins t he r a.: l. la.1 dlc tributlon curves cf C • Ga::ne rt ofelde r (2), the followi ng data were ob tained. : Meta l Temp . , 0 c Doa lo • R Dobs , i Tin Indium Zinc Cad.mium 11.,tr.:11.num 4 60 350 7 00 Lithium 200 (1) 3 . 40 3. 36 250 160 3 . 38 3 , 30 3 . 00 ' 3 .15 2 . 99 3. 45 L . Pa ul i n g , j . ,\ . o . s ., 2 • 9.l~ 3 . 06 2, 96 3 . 24 69. 9~2 (1 9'1-7) ~ (2 ) c . Gs.merts fe l der , J·. c-: • .e . , 2., l~50 ( 1 941 ) . 4, In order to increase t he objectlv:lty of the electron d i ff r a ct i on me thoii for t he ete r minat:1:on of t he s truc ture of. gas molec ules , l sugs est t hat f 1mtl c or:upari $ons c an be m::-,de wi th theoi,..eti oal sc a tte ring photo s raphs, whi c h c a.Ii be pr epared' by sui t able op tica l me t hods . 5 . (a) Br;ovm (1 ) ha s measur ed t he diosoc iatlon constant s · of t he addi t :i.on oom pom1.d s of boron tr ime t hy1 wi t h a;:n'.nonia a..11.d t he :c c t hy l a.mi n es with what a.ppea.r-s to be a h l ....,.h degr e e of prec i s ion . In suc h oases I s u gc;e a t t h e use of the equation 1n(/~~(1 '.L' ; 4 T rm J == l [fl. = i + b E~ - 4R + c0 + 4R lnTml T I j B (appr oximate l y) 1n der :lvinc; the thermodynami c functi ons . In th::s equa t ion Tm i s t he mean t emperature of t he measur cr:1entG and STm ::. 0 0 + 4R ln1ri_1• 3 t·o,·m ' s d ·1ta on t he ad J.i t ion c omp ound. of boron tr lme t hyl with a mmon ia. give: A ~ 0 0 0 6 S0 O 31+7 K :z _...,. ( - 6 • 58 !. 0 . 2 0 ) -i- 4R ln.1' 39, 9 oal/ mol degr ee A :Eo = 1 1 1 000 !. 7 0 oa l/mo l 0 A Ho 3470K = 13,760 c a l / rno l (b) 'l'h eore t i oa l ent r opies a nd energi es of the compounds involved in the above r eac t ion were oo.lculatod; t hey are Compound 81. 0 3800 70 2940 • ;l'hlo gives t::::. '::i0 "i"1,'{0v= li-0 . 4 e , u . fo r the d :le r,o ci ation rea ction , ' .I.\. 3 'rhG DethoJ. sucg 0s e(l by Rant1us aen (2 ) t o esti □ :-l.. t c t ·-J.e h e :c;l:lt of 1:n:i.r r loro t o :_ntc rnal ro tu.t l on a n:.: n.ppr oximat iono sln i l e.r t o t h ose S U[; __: , eote:i by Pl tz e r ( 3) t o e s t:L n,::1 t c vi bra t .:. onal entr op i es were use . H . C . Br•01:m , H . Bar tholomay , arn.l r: . .J . Tay l or , J·. t .C. D. J 66 , - 431 and 435 (1 94,1~) . F . A. Fr ench a nd H. ::i . d.a srnu no en , J .c .P. , 11}, 389 (1 94 6) . K. s . Pitzer , J . C . P . , 5., 473 (1937) . 6. '.l.'he fol l m·ring a r e;'..t.'!lont s c an be pr esent ed a.Ga.inst t h e c once pt of r•B str ain as p r esen ted by Br-m,m an.1 cowor-k:0r•e (1): (a ) 'l'he heats of d j_ssoc l a. t l_on o_ the addition prod ucts o:._ the methyl a r:1inc o a nJ. ar, c onl a u:tth bo ron tri methy l 11 c an b 8 r eadily a c c ounte 1i ::or 1:f a he o.t of i nteraction of 3- l~ k ca.1/ mol per methyl- uet hy l inte r a c ti on i s assumed . {b } Flo a s sumption of tile osoentia.l abs en c e of 11F't strain in aqueous me t hyl- aomoni um ionG i s not ne ces ~ar i ly correct . I \ ( C) B l □ ·a r guments concern111g t he r e l ative eaoe of bond a115l e distortlon b e f ore an 1 af t er :react ion with a p ro ton ar e not c onvinc l n3 . ( 1) Il . C • Brown , H. Ba.r t ho lo1:aay ; o.:id li . 66 , 435 (1 941}) . . Ta y l or ' J •.l- • 1 • G.' 7• Cb r omi . sul f :tdo_ whl c _1. c ont a.Ln'- r,bout .J.lt- !)croent s ulfur shotrn an :. . nte r est l n e; magneti c a nomaly (1). ~ t -180°0 it ls para.magnet l c ; the pare.nagne t 1c susocptlcillty incre ases with temperature u p t o about - 120° 0, at whi ch teopera turc it beco:neo . e r romagnetio . 'l'r- e f el"l"omue;netia Curie p o ·i n t 1 s about 20°0 • • Chr omium sulfi de ha s t he n i clt e l arsenid e (B- 8 ) str ucture, i n whi cl~ t h 8 rict:;:-.1 ato □ c ar e arranr;ed in paral lel, d ir ec tly ::mper posecl ; equi l ate r a l triane,u lar nets . The spac ing bet,-reen the n etn i o so,,:8wha. t sna ll e r tha.n the n ert.r est n elc;hbor diotcln.ce wl t hin a ne t . 'lhe a bove m:ie;netl c behaylo r 1:1 l r;h t occur if' t h e exchange integral between n ea r est neighbo rs (~ is negati ve, and. that between n eares t ~e i ,.J1bors i-'r.thi n. a. n e v {J 2 ) is p os i tive, 1.nd \ 3 J 2 I ') \ J 1\ • ~• (l} II. Ha ral<l.se n , Zeit ~no r ;,; . a.llgem . c hem ., 231~, 3:i7 {1937). 8. 1 J.thml[;h tho struc t Ul" e of Al f; sugge sted by 2 (cH ~ } One Pitzer and Gutowsky (1 ) i s t he oat logioa sugGested thus fa r, t 11e exp r_r'.lent al eviden c e i s cer t ainly not unequivoca l s inc e (a. t he v-a por ern:i i ty r:1ee,sure::1ent s of Laubene;ay e r and Gi lliam (2 ) de not e x clude t ho p o ooibility of hi Ghor polymer □ , and (b ) this structure 50.'ve on l y "fa.ir" a s r e c;;,e nt wj_ th the e l e c t r on d iffr a cti on da t a of :Jut ton a.rid :3!cinne r ( 3 ) w·hile another : _1mer structui:"'c was listed as c;ivin5 r' goo II a3r eement , (1) ,·: . ..., . 1,• • i tzor and I. 0 . ·utowscy , J • . f"I . S ,, 63 , (1 946) • \'! . La ubon5ayer ,;;,. ~1._ ,; • " . Gilliam , • . o . s . , . §l, ~ •• A. :Jklnr:.er and L.,. , • Su tton, rh.ture , 156, 601 (1945) . 2'.2 0 l~ 477 (1 941 ). • 9 . (a ) 'l'he exp l anat i on cus c eoted by Da.teman (1) .fo r t he shortening. of . t h e s l~l c b ond in t h e 3 po s i tion · n ·1, 5 1.ene syntcn s suc h as · 1c obs e rved l n 5 era.nylamine hy(l:r ooh l o r ide (2 ) d oes not appear plausibl e . Other similar diene s and di- ynes should b e investigat ed in or -lor t o p rov0 or d l sprove the generality o f t h~s anomaly . (b) \-velo ' s el cctrostat lc expl a nati on (3) f or t he l a r ge poc l tivc :foiE.l) c cnstn.nt obocr·v cd f o r polynuclear compl exes suc h as Cr (CH?.0 00 ) ( oH ) Cl• 8H o is proba bly incorrec t . 'I'his 2 2 6 e ffec t 3r:1 i c.,6t b e ca used by t h e c l os e juxta. 2)os l ti on of cations in the c oDpl ex . ( l) A. L. (2 ) (3 ) (} . A .• L. i •