Crystal Structure of Tripotassium Cuprocyanide Citation Axelrod, Joseph (1938) Crystal Structure of Tripotassium Cuprocyanide. Master's thesis, California Institute of Technology. doi:10.7907/y1s0-5g15. https://resolver.caltech.edu/CaltechTHESIS:11182024-180405592 Abstract No abstract. Item Type: Thesis (Master's thesis) Subject Keywords: (Chemistry) Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemistry Thesis Availability: Public (worldwide access) Research Advisor(s): Unknown, Unknown Thesis Committee: Unknown, Unknown Defense Date: 1 January 1938 Record Number: CaltechTHESIS:11182024-180405592 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:11182024-180405592 DOI: 10.7907/y1s0-5g15 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16862 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 20 Nov 2024 19:08 Last Modified: 20 Nov 2024 19:08 Thesis Files PDF - Final Version See Usage Policy. 9MB Repository Staff Only: item control page

CRYSTAL STRUCTURE UF TRlPOTASSIUl\il CU£ROCYANIDE Thesis by J OSE:PH AXELROD In Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE California 1nsti tute of 'l'echnology ~asadena, California 1938 because there were inconsistencies in work of Cox, Wardlaw, and Webster done on t he crystal s t ructure of tripotassium cuprocyanide 1 , it was thought that a new and more extensive investigation of the structnre would,. be useful and interesting. 1t was proposed to attempt a complete structure determination, but, at /this time, only the space group and one of four parameters have been determined. Cox, Wardlaw, and vwebeter say of pota ssium cnprocyanide, it 11 forms large rhombohedral crystals w!!ich, in view of their strong pyroelectric properties and the absence of verti.cal planes of symmetry (as shown by Laue p~otographsJ, must be assigne f to the tr'apezohedral class I n 3 J." They found two molecules per unit cell, and because of the trigonal axis and low birefringence of the crystals, they assume the cuprous tetracyanide complex to be tetrahedral. 'l'hey report that the crystals form with lllO} faces predominant and occasional small {100) faces. dimension is a = 8 .ooi and or..=77° 32'. 'l'O quote, "the cell The mumber of molecules in the unit cell is 2, whence d( calc. j.:::2.06g./cc. ( obs. 2.07) .'' 'l he 1 report has two errors, one of whic h ma;, be real, and the other of which is probably a misprint. ln the first case, .Laue photo- graphs cannot dis tinguis h between point groups v3 d, v3 , and u3 v . An X-ray experiment adds a center of symmetry as a result of t he centrosymmetric character of X-ray diffraction, and t t e three mentioned point groups, by addition of a symmetry center, all become D3 d. Actually t he point group will b e s ~own to be u 3v . .l!,urthermore, .Laue symmetry n3d, wr.ich tt.ey reported, shows vertical planes of symmetry -- not their absence. The misprint occurs in the report on t he cell dimensions. 2. A crystal with two molecules per unit in the cell given would have a d.ensi ty of l .96g./cc. and it is probable that the ce they found was about 74°. ln 1924, the phase diagram of the system K.CN-CuCN-H20 was investigated at 26sC. by Bassett and Corbet. 2 They found that • only two complex salts could be recrystallized, K3Cu(CN) 4 and K Cu(C~) 4 •M20• The hydrated salt was reported to form larg~ 3 colorless rhombohedra and the anhydrous salt to have "a more prismatic tendency". They said the hydrated crystals were meta- stable in contact with solution at 25°c. 1 crystallized tri- potassium cuprocyanide at 20°c. and at 40°c., and largeJ rhombohedral crystals formed at both temperatures. These crystals were, however, found to be anlcydrous and there was no indication of the formation of hydrated salt. Crystals of K3 Cu(CN)4 were made according to t he directions of Bassett and Corbet. A hot> a11ueous solution of .KCH was added slowly to a hot solution of copper sulfate,and paracyanogen formed was filtered out. 80~- +- 2Cu-t+ ➔ xC2N2 ~ 2Cu( Cl\l) 3 + C2 N 1' 2 ( CI-4) 2x The resultant brown solution was slightly acidified with dilute sulfuric acid. A white, curdy precipitate of cuprous cyanide was formed and filtered out on a jjuchner funnel. 'l'!:. e J)J'ecipitate was washed and then dried in a desiccator over calcium chl.o ride. When saturated potassium cyanide solution was added to the dry precipitate, there was a vigorous evolution ·Of gas and t t e temperature of the solution rose to about so 0 c. filtere d and allowed to evaporate. This solution was To prevent excess formation 3. of the paracyanogen, it might be better to add a mud of the CuCN to the solution of KON in making the cuprocyanide and to use cold, dilute solutions in precipitation of the cuprous cyanide. rlecrystallization of the salt is necessary to get crystals well suited for analytical work, but, for crystallographic purposes, excessive purification is not desirable. ihe pure salt does not easily form perfect crystals, but tends to climb the sides af the dish and form porous masses of salt, and to form very large crystal aggregates on the bottom of the dish . Small crystals forming on the bottom were almost invariablj sh.own to be split on Xray examination,though they were superficially perfect. The crystal faces, though practically perfect in the solution, quickly deteriorated in the air as a result of the hygroscopic nature of the crystals. For i:; onioaetric measurements, it was necessary to put a drop of oil on each crystal,and even then the faces gradually roughened. Over a period of several days, the crystals would form small growths on t ~e surface in spite of treatment with oil. The interior of t he crystal underwent no apparent decomposition. Single crystals formed as large cololless rhombohedra with the form l110} predominant. Occasionally., faces of the form tlOO} occurred,and very rarely a llll} face was seen. The angles between {110} faces were found. to be 77° 8' and 102° 52' in the } best set of measurements and, from th.is, the angle ce between edges GONIOMETlRIC MEASUREMENTS ON K3Cu(CN)4 F\C>TI\TING T~E cf\YSTP..L f,,.Oour [_!'ii] Mean Difference 303° 2' 303 0 5' 20° 10' 20° 12' 123° 123° 2000 O' ~· 4' 200° 11' 303° 6' 20° 14 I 1230 6' 200° 12' 303° 4' 20° 12' 123° 3' 200° 11' 77° 8' 102° 51' 77° 8I 102° 53 : 4. formed by the intersection of {110) faces was calculated to be 102° 52' . The rhom·b ohedral angle, o<.., was then found by further calculation to be 74° 14'. Several such large crystals, all about 0.1cc. in volume were colledted and dried in a desiccator over calcium chloride for use i n a density determination. The crystals were waighed in a p y .cnometer calibrated with water at room temperature; the pycnometer was then filled with machine oil and weighed; and finally the density of ail was determined in the same p~.cnometer. The weights used were not calibrated,and the temperature was not carefully controlled. The oil was of high viscosity, and minute air bubbles may t ave been trapped in the pile of crystals in excess of.the amount in the oil itself. The crystals also very likely con~ained some included moisture. to be 1. g'.} :t..10 g./ml at 1a 0 c. The density was found Cox found 2 .07, which is within · the limit of error of my determination and is also different in the direction indicated by my two chief sources of error, entrapped air and entrapped water. The crystals were found to scratch rock salt and to be scratched by galena. The hardness was fixed at between 2.1 and 2.5 by a series of,experiments and esti r'~ ated at 2.4. Galena is listed a s having hardness 2.5. 3 The crystals scratch and are scratched by galena,though the galena seems slightly harder. Blue vitriol and the crystals have the same hardness and blue vitriol is scratche ~ definitely by galena. Therefore, if galena has hardness 2.5, the crystals have a hardness of about 2.4. Cox reported t hat the crystals were pyroelectric,and they are very strongly so. A crystal suspended on a tr~read and 5. dippe d into a dewar of liquid air moves rapidly to the side and sticks there. The pyroelectricity is several times as strong as that of quartz. the cr:,y . da.i On removing~i:t rrom liquid air, streamers of ice radiating from all corners of the crys t al, inclutling the corners with the three-fold axis, were observed and so the ends of the axis must have acquired a charge. The three-fold axis is, therefore, polar. Cox, Wardlaw, and Webster described large,rhombohedral crystals of K3 Cu(CN) 4 • Bassett and 6orbet spoke of large, rhombohe- dral crystals of K3Cu(CN) 4 °H20. I got the large, rhombo hedral crystal~ but, to be sure of their composition, had to analyze them. Recrystallized K3Cu(CN) 4 was separated from the mother liquor and allowed to dry for several days. The large crystals were separated from the small, and the floating from those on the bottom, In all, there were six samples. What was probably the best sample was set aside in case of mishap, and analyses were made on the other five. Each samnle was washec1 once with a small quantit~r of distilled water and blotted dry with filter paper. They were dried uvernight in a desiccator and for one half hour at 125°0. five beakers. Three-quarter gram samples were weighed into Each was dissolved in about 20ml . of water, 15 ml. of 0.546.N H2So4 were added, and the solution allowed to stand. overnight. Next day, the white precipitate was filtered out on sintered glass crucibles and washed four to six times with a total of about 25 ml. of water each. The precipitate was dried at 13o 0 c for t wo and one half hours and weighed. (Another half hour of drying did not change t he waight appreciably.) The filtrate was titrated with half normal sodium hydroxide t1s ing 6. methyl orange as indicator, and the alkali content of the crystals thus determined. Assuming KCN, CuCN, and H2 o to be the only possible constituents, the analys ts averaged 69.89~ KCN and 30.42'jo CuCN. (Calculated for K Cu(CN) 4 , 68.6910 and 31.45o/o, fo.r 3 K3 Cu(CN) 4 •H 2 o, 6¼.4~~ and Z9.59~) 1n one analysis, (results discarded) after tr~e back titration and several hours' standing, a greenish precipitate ( Cul OH) 2 ·() was observed. Since acid dis- solves CuCN also, it is probable that CuCN precipitation was not complete in any sample. The analysis was probably g ood to 2~ in the case of CuCN and to l1o in the case of the alltali de te rmination. An impurity such as KOH formed by loss of MCN on drying, o.r of KCN from the mother liquor would cause variations from the calcnla ted percentages such as are observed.. nESUL'rS Uli1 ANA.LtSES Sample vleight ml. l~am-r ml.H~So4 UB d .Meq .f:t =- Wt. KCN 7oKCN meq KCN #1 .7232 0.736 14.18 7.740 .5040 69 .69 #2 .7354 0.525 14,39 7.855 .5116 69 .59 #3 .7088 0.88 14.035 7.664 .4992 70.40 Sample Wt. CuCH 1ocuc1~ =Ji:l .2187 30.41 #=2 .2238 30.43 #3 .2158 30.43 7. &ay de termination of a crystal structure de ·p ends on the fact that a crystal acts as a three dimensional grating, diffracting, .electromagnetic JE-radiation. ·rne intensity of diffraction in various directions depends in a definite manner on the nature of the spacings in the grating, or on its lattice structure, and on the nature of the points in the grating, or the arrangement of matter about the points of the lattice. Because tr.ere are but a definite number, fou.rteen, of possible lattices, it is possible to determine directly in a straightforward manner on wtich of these lattices the crystal is based. All possible comb inations of all the conceivable symmetry elements result in only two hundred anci thirty such combinations, which are called space groups, and, in a straightforward manner, it is possible to distinguish almost all of these space groups from each other. Exceptions are enantio- morphic space groups, which cannot yet be diatinguished, and two special pair of iaomorphous space groups which have the same symmetry elements in di f ferent translational ra.J."~angement~ To find the arrangement of matter around a lattice point is not so strai 6 htforward and not always as simple. When the arrangement is fairly complicate d, the problem is analogous to that of solving n equations with m unknowns. Them unknowns rep- resent the arrangement of the matter, and then equations, the observations of direction and intenaity of diffracted beams of X-t"ays. What makes the problem hard is that the equations are not simple, but are sums of sines and cosines of combinations of t he unknowns. However, specific problems may be simplified by using knowledge gained from stereochemistry, complex formation, and studies of similar structures. 8. A crystal grating may be regarded as a system of points sending out electromagnetic radiation from each point as that point is excited by incident radiation. ln the case of a line of such points with incident radiation normal to the line, the spherical wave fronts sent out by the line will reinforce and interfere so that a cylindrical wave front and several conical wave fronts will be f orme d just as an ordinary line grating g ives first, second, and third order reflections of any wave length. The equally spaced line of radiating points, then, sends out rays in a series of cones and in a plane normal to the line (a degenerate cone corresponding to t he cylindrical wave front). If the incident ray is not norma l, the cylindrical wave front will not, in general, exist. so: Analytically, the phenomenon may be descrived lf radiation strikes a line of diffracting points such that the cosine of t he angle between the radiation and the line is ~ o , there will be reinforcement in all directions suc h that, if~ i s the cos i ne of the angle between any direction and the line of points, where his an inte g er and a is the distance between points in the line. When a series of suc h lines , parallel and equally space d so that they for m a two dimensional grating, is under the influence of radiation, cones of radiation are sent out f rom all the lines in all directions in the grating and these radiations reinforce and interf ere wit~ each ot her as did the radiations forming the spherical wave fronts. Reinforcement occurs where the cones of radiation inter- sect and interference is practicalljcOmplete else where if the grating is larg e, so that the only detectable diffracted radiation is 9. in a series of sin6le rays insteau of conical sheets. Analytically, there are two equations to be satisfied, for any two nonparallel lines of points. 1Jiffraction from a three dimensional grating, made up of regularly space d similar layers of points, will occur when rays from all the · layers, planes, coincide and reinforce each ot her. 01· 1f t ~is does not occur, interference will blot out the already weak radiation and there will be no diffraction observable. 1n t his case there are three equations to be satisfied, h'~.:: a( cC. - c(o ) t k }..= b( ~ - ~ .. ), 9, )..= c('(- ~ .. J, and and they will not, . ii:L•.: general, be simultaneously satisfied unless something other than ex, ~ , and l is made variable. 'i1hese are the Laue equations, named for their discoverer, M. v. Laue. ~ir William H. ~ragg has expressed the sama facts by the equation, n 11.=2dsin$ This equation emphasizes the fact that every beam of diffracted radiation raay be superficially regarded as a specular reflection from some plane of p oints in the crystal lattice. in that dase, e is half the angle betwee n t he incident and diffracted beams, and dis the smallest distance between parallel reflecting lattice planes. ordinarily, then, it is necessary to introduce some va-:- - tiable in an experiment involvini diffraction of X-raye by a three dlmensional grating, and this may be done by using white X-radiation made up of a wide band of frequencies, or by rotating the lattice in a beam of monochromatic radiation. are used in crystal structure investigations. Hott methods 10. ln the first method, originally use d by M. v . .Laue, it is best to use a tube with a heavy metal target at high voltage to get the most efficient production of conttnuous X.rac1iation. 1n this laboratory, the source of continuous radiation is a permanently evacuated glass Coolid.ge tube vii t r: a tungsten target which is operated at about 66,000 volts. I1 he minimum wave length is about 1 The radiation used is confine d to a narnow beam by use of 0.24A. two pinholes lined up with the source, and this beam is directed onto the crystal which is in front of a photographic film. The crystal is mounted with wax on a goniometer head with provision for precisely adjusting the position of the crystal by rotation or translation about or along three fjlutually perpendicular axes. The film is flat and perpendicular to the beam of ~'frays • .l!'o.c the other type of p!iotograph made wi tb monochr·omatic radiation and a moving crystal, this laboratory uses aJ1paratns wit[! molybdenum, iron, and copper targets and arrangements for oscillating a crystal about a given position or rotating it through 360°. i'l:e Xrays are produced in a tube of t r: e ionization type. 1 g lass tube is evacuated to a pressure of about .02 mm. of mercury anc1 an al t~minum ca t ~1 ode inside the tube is ca.arged to about 40,000 volts. Air is ionize d by t he high voltat e and positive particles strike t }1e aluminum cat t: oa.e and knock out electrons which shoot away from the ca th ode and strike the walls of tr!e tube or tb.e ta.rge t. 1i'he aluminum at the end of the ca th ode is shaped so that the ,1eotrons shooting away from it are focussed e i t~1er to a short line or a point I dependi!1£ on the shape of the aluminum) on the copper, molybdenum. or iron target. These hig h energy eleotrons,in entering the atomic fields of the target,are quickly deceler~ted in one or more steps and emit Xrays with A 11. frequencies depending on the energy lost by t he electron !hn a single step. Some electrons knock out electrons from the inner shells of the atom, and, when ot her electrons in outer shells drop into the hol e s so formed, X-rays of frequency corresponding to the difference in ener§ y level of the two shells are emitted. The X-rays emitted as a result of simple deceleration have frequ encies covering a wide range and are called general radiation. X- rays emitted by electrons droppine from one shell to another have fixed frequencies which depend on the atom and the orgits involved, and are callec:t characteristic radiation. The voltage of 40,000 is such that the intensity of the characteristic~~ radiation of the target is about a maxi r,!um with respect to the continuous radiation. Usually the background of continuous ra- diatiofs effectively removed by a filter, 40--4 of nickel in the case of co·p per radiation and 100,)-( of zirconium in the case of molybdenum radiation. The filter strongly ab s orb s most of t he radi- ation of higher energy than the cha1·acte ris t ic frequency and a ,t -., the same time lets through about one t i, ird of the characteristic radiation. The net effect of the filter is to cut down the inten- sity of the fogging continuous radiation more t t an the intensity of the useful monochromatic rad.ia tion. The filtered X-rays are confined to a narrow beam by means of a series of pinholes or slits and the crystal placed in t he ir path on a g oniometer head wr.icl"! is in turn placed on a rots.table mo u11t. 'i'he slit system is part of a stationary cylind1·ical ca.me ra whic r: snr ..rounds the cr;ystal. An arran t.. e ment of mo tor and cams allows t he mount to escillate t t. ro ug h angles of 5°, 10°, and 30° and a gear arrangement provides for complete rotation. 12 . r here i s also an appa ra tu s whic h is si ··1i l a r to t Lose describe El. except that it uses a perma nentl y evacuated hot ca t hode tube wit h a mol~;· bdenum tar6 et, and has arrangements a llowing oscilla tion of t he crystal t hront_ h angles of 1t0 , 6°, 12°, and 24 °. 'l'he Xray beam has about one 1Bnth t he intensity of that fro m t ~~e ionization tubes so that in this investigation it was use d without a filter. The permanently evacuated tube, however, has two i ffiportant ad vantages over the ionization tubes. lt requires practically no attentio n and but one simple adjustment,and it is more constant in its be havior since there is no aluminum cathode to wear out. '11.he first .&ray photog rap~1 taken wa s a reflection from a natural rhombo t:.edral face (110) using CuKoe. r a diation and oscilla ting throug h an angle of 30°. Measurements on this photogra ph we.rs used, with t he goniometrically determined angle oC, to check Cox ' s results and to make sure that it was t t e same cry stal he used. MEASU REivlENTS AUD CA.LCVUT l UL~S U.N .l!' l ltST llH OTOGRAPH Spot Radius of camera = 5.00cm. Dist. from 91 rad.) sine cent. image Sin{ f>-t6½ I ) l 1 .266 .1266 .12620 .12812 2 2.573 .2573 .25446 .25628,::: 2 ( .12814) 3 3 .924 .3924 . 38241 sin6i =- -1281 .38415 ~ 3 1- .12805) mean i The .rlragg e,uation, nfl.. =- 2dsine A : ?\ r, .1_51ne = l.53'U. L(.ll.ill..) solved for d/n g ives ::: t;, oo"l'l :: • b.o, ~ UsinG a previous va lue of o(. f r om less pr ecise mea su r ements of 73° 55 1 and the wquation, J ~ ~ ~ l.. = ( n ~ 1- ln: ~ h ~ b~ +- 2 ( h ,h + h ,'n 3 1- h J1 J b-z. c o s ? 2. Oscillation Photograph Reflecting CulC«:_ from (llO)rh 1 ...,'7. . where)\, h,_,h-<-,and~ 3 a.re tbe indices of the reflecting plane. b = ~IY\oC. o... VI+ l.£o~'lo(, - 3 U)!, .,_ C.o ~.,_o(, - (OS<:£. ~,n.,_ oC.. o<.. and so that n=I a.= (<...ci0'14) (1.41<!\i..) V1+ ."l..1104-2. (.rno4)'2. Using cl=- 74 0 14 1 we would g e t a larger valL~e of a.. 'f he next <;u.r-..{. photograph used was a 11 complete rotation photograph" using a small crystal bathed in the kray beam and rotating the crsstal at a constant speed about its vertical three - fold axis. Distances between the horizontal lines of spots, called layer lines. on the film were measured. distance, the 11.denti ty distance 01· ~ro m the smallest la ttlice dimension in t t e d irec- tion of the three-fold axis was calcnl2. tea by means of the .Pa>la.n;yi equation, hilt.= ai sin«:. wherein h is the number of a layer line countint · from the equator as ~ero, oc. is the angle formed by the ti layer line, crystal. and equa to1·, and a is the dde.l\tJ; distance parallel to the axis about whic r.:. the crystal is rotated. .tram measurements of equatorial reflections (reflections normal to t r. e axis of rotation}, the smallest identity distance normal to th.e three fold axis was calculated. it was assu med that tr.ere were no absences in t '. !8 aqua tor be cause all t}:.e re flee tions could be indexed on t .t.at basis, and. because suer.. indexing led to a value of ~ in a 6 ree ment with the goniometric value. The two distances defined a hexa6onal unit describint; tbe lattice and from them the rhombohedral axis and angle were calculated . a = 7.942.A. andoG=74° 20' . .My measurements gave .Measurements by Dr. ;:;turdivant of th.is laboratory gave 7.9771 and 73° 59'. 14. MEASUREMEN'l'S 0~ 360° :BHOTOGRJU..,H VHTH CA1,CU.LA 1r10NS Layer lines tanoc. 6 .82 1-1 .0925 _l 09211 2-2 .184 .1810 6 7.49 8.09 3 8.61 2 9.09 9.55 l 0 10.00 -1 10.475 -2 10.93 -3 11.42 -4 11.945 -5 12 .54 -6 13.21 5 4 sinoC.. 7'-h 1. 538 7 ~ 3-3 .281 .2705 4-4 .3855 .3597 5-5 .505 .45075 6-6 .639 .5384 sin~ Mean -y---- :::: .09011 7 Equatorial measurements Dist. f1·om cent.image e sine sine VS/3 ( hk.1.) hex • US/3 16.25 90 19' a61?7 l 28.2 16° 32.8 1s 45.8 26° 50.3 .161 77 ( 110 J 9 I .27824 1.732 .1606 ( 300) 48' .32216 2 .16108 ( 220) 6' .42415 2 .646 .1604 ( 410) 28° 51 1 .48244 3 .16081 ( 330) 68.7 330 38' .55386 3.464 .1698 ( 60 0 ) 61.5 35° 14' .57693 3.606 .1600 ( 520) 69 .6 39o 49' .64040 4 .1601 0 ( 440) 77 .1 440 10' 1 69681 4. 259 .1599 ( 710) 82 .o 47° 1 •• .73155 4.583 .1596 ( 630) 92. 5 53o 0' ~ 79864 5 .15973 ( 550) 9 '1. 9 100.7 100.7 56° 55' .82993 5.196 .1597 (900) 57° 42' .84522 5.292 .1598 ( 820) 109 .4 62° 41' .88848 5.568 .1596 ( 740) - .1603 0 Mean I\_ Al = 51V"I (. ~381 7 0'745R A3 = sinc,(_=~090117 = 1 • e/\J51.3 = . lloD 'oh = q, S9 S- t\ Com;le t-e /(o fu.- f 1on :P/Jof°)'ryh 4.J,t/, C<-u/1o<_ 15 . .!!'Dom these values of the he xae:: onal axe s, t he 1·h ombo hedra l dimensions were calculated. After the determinatiDn of a possible unit, the next step was its confirmation anc_ a determination of the space g roup. 'i1his is best done by means of ~aue pLotographs whic l::: use a s mall wave .length X-ray anc_ consequently show a larg e numb er of reflections. ~aue p~otog raphs were ta ken with the beam of ~-rays parallel to the three-fold axis. 'l'he photograph had symmetry D showinv a three-fold axis and three n. lanes of symmetry. 0 3d mo.re ptotographs were taken with the three-fol d axia at 4° and s 0 to the beam of X-rays and , the three photo6 rapt!S were indexe·d on the basis of a unit cell of the dimensions _fo~nd previously. l!'aom the sine of the angle of reflection and. the indices, the wave length of the radiation refleoti~g from each plane was calculated and, since no reflection out of severa l hundred see med to come from a wave length below t he lower limit of wave lengt h in the beam, one can be fairly certain that the unit ct:.osen is not too small. Because several of the wave lene;ths calculate d to be quite close to the minir'.mm wave length, the unit was assumed not to be too large. Calcnlation .on the basis of the unit chosen and the density determination s howed there were only tvw molecules per unit cell. lf the unit c hosen were too la1;g e, it might be a body centere c1 unit containing two simple uni ts with «:.>100°. ln that case, all reflections wit t the sum of the indices odd · would be absent. large. 'i' b.ey are not. 'l' he unit, then, is not too 16 . .Laue symmetry .o 3 d permits point groups u 3 d' u ,;_·' and .v 3 3 since each of these groups combined wi t r: a center of symmetry gives il 3 d, and, because .x.ray experi ments are centrosymmetric, they cannot distinguish between these point groups . c,. Jm D1 ditrigonal pyramidal 32 trigonal trapezoedri sch D,. - 2 3m .tlowever, )m ditrigonal skalenoedrisch Stereographic Projections of the ~6int troups the crystals are pyroelectric and mt1st, therefore, have a polar axis. u3 d ha s none, so the crystals had to be c3 v or D3 . lt was further observed in the pyroelectric experiment that the ends of three fold axis became <G:harged and that tbat axis was, therefore, polar. the j6int group, then, can only be~u3 v. ~ourteen feflections from different planes of th~ g eneral form {hhiJ with~ odd were not observed when they were in position to reflect. r hese were t"ll .11), tlI9J, 1117), t115J, 1227), 1 l 225), t 223), 1335 ) , t 443), t 445}, 1447), t 557/, I 665}, .No first order teflectione of this form were obser·ved. and l 771). 6 c 3 v is the only space group which re quires these absences so it would seem that that is t he space group. c~v is also the only u 3v space g roup that requires two molecules per unit cell. When KC1~ and CuCN are mixed· to form the potassium cuprocyanide, heat is evolved and the resulting salt is colorless. Addition of ammonia does not produce a blue color and addition of ferricyanide does not give a red precipitate. Addition of ferricyanide and acid does, however,~ give a red precipitate. lt would seem 17. from this evidence that the copper is strongly bound. tiowever, there wa s always a smell of cyanide fro m the crystallizing solutions which may mean that the tetracyano complex is not ext.remeJj· stable . .1:ou.r cyanides a.re p.resuuab l y bound to one copper and, since there is a threefold axis in a unit cell with only two copper molecules, the cyanides must be arranged in some form with a trigonal axis. It is assumed on the basis of work of Cox, Ward1/aw, and Webster and of valence bond conslderations t~at the arrangement is tetrahedral. Since the chosen space group has a glide plane parallel to the three fold axis, the two o,ne c.ic,.."'i,J.e tetracyani.de tetrahedra are arranged wit:~~parallel to and coincident with the trigonal axis and pointing in t .r..e same ditection. and the other three ate, e+120°, and 9~240° to a plane containing the trigonal axis and a rhombohedral axis in one case and -e, -(0+120°), -(9+£40°) in the other case. The Cu-C and C:N bond distances can be estimated fairly accurately from known atomic radii and bond lengths determine d. in previous work. 4 The Cu+ tetrahedral covalent radius was ta.ken as 1.351 and 4 the C single bona. radius taken as .771. so that the Cu-C distance 5 becomes 2.121. The C=N triple distance of 1.151 was used. No si mple method was found for fixing t l:e position of the potassil1.ms in ans way. There are, t:ien, four variables or parameters which m~st be determined to fix the struc t ure completely. Tr.ey are -te for the cyanide tetrahedra and three for the K. These three riiay be listed as ek( angle between the plane of the rhombohedral axis and the radius from the three-fold axis to t ~1e K-r), r_lc( the length of the radius), an d _zk( the distance parallel to the three-t- fol d axis between a copper a tom and a K ). SYMMETRY ELEMENTS, EQUIVALENT POSITIONS, AND ABSENCES OF c:v i+ 1+ G) 0, 06+ t+O i+ 0 !+O i+0 I ¼+ j+ 01+ !+ ¼+ i+0!0~+ t+ G) t-Q +- 0 0r+ G) ¼• 0 G)t+ j+0 O!+ t+G)Q+ -------- C1 ,, 6 -R3c. Rhom boedr. Beschrei bung . • Hexa.gonale Beschreibung: Pn nktlagen: (000; H½; Hi)+ Punktlagen: 6: (a) 00z; 0, 0, ½+z. 2: (a) xxx; ½+x, ½+x, ½+x. 18: (b) xyz; fl, x-y, z ; y-x, x, z; 6: (b) xyz ; zxy, y zx; y,i:,½+z; x,x-y, ½+z; ½+ Y, ! + x, ½+z; ½+z, ½+ Y,½ + x; y-x, y, ½+z. ½+x, ½+z, ½+y. Gitterkomplexe: Punktsymmetrie: ·1 ' D l-R~m (~). in (a). 3 0 3 -3 in (a). 0 3 ,, 6 -R3c (b) 'in (b). C -1 in (b). 1 - - - - ·-- · - -- --------- A uslosc h ung e 11 : Hhoruboe<lrisdll' •l~sc hreilmng : Allgemein : (hkl) in allen Orduungen vorhanden; (hhl) nur mit l =2n vorha nde n. Spczie ll : F(ir die spezielle Punktlage (a) bestche n die weiteren Aus l(i,:,d111ngen: (hkl) nnr mit h -\ k t-· l = 2n vorha11cle11. Hexagona le Beschreibnng : Allgernein: (hkil) nur mit h-k + t ~~ 3n vorlmndt>11 ; (h,h,lh , l) nnr mit 1~ 3n vorhanden, (hli0l) nur mit 2h -+ l -- 3n ull(l l = 2n vorhanden. Rpeziell : Fi.ir die spczielle P unktl,Lge (a) ge1ten die weiteren Ausloschungen: (hkil) nur mit h -- k , / _ 311 111ul l = 2n vorhan<len. 18. If we consider the hexagonal unit of KzCu(CN} 4 containing six mol ,: icules, it is evident that, if the cyanide tetraherl.ra are assumed to be regular, the positions of all the atoms except K+ are fixed in the z direction or direction of the - tHree-fold axis. Reflections from planes normal to the three-fold axis are dependent only on the location of atoms along the three-fold axis and not on their di~tribution in a plane normal th that axis. Con- sideration o:f the structu·re factor of C~v, hexagonal unit, shows this analytically and suggests a way of fixing the zk parameter independently of the other parameters. The general form of the structure factor is 1 6 .H ex"'go"'"' l • ,' n J,·c:e.s . ---- • ooo 1 333' 2. i 2 - - - .L. x,x-:1,r+3; !:J-x..,j , 2+f>· 1 333 + Ix:.;3j ~,.x-:1,3;~-x,x,3;~.x,~+.3; I I I I I • A = l{ I+ l ,., l If h-;• t ){ cos ,r{(h-k){x -:1)H 13+}] c os1f[,'(x•:,) + ½] + ! + cosir[(k-«:)(x-~)+ll3~f] cos1f[h(x+~)+ + c~3ri[(,·-h)(x-!1)+1.l3+ ' B = 1..( I+ 2 eos Z1f"h-;+ L )[ _j,·.._ rrf(h-k)(x-j )+ 2l3+ iJ-t- i] c sn[k(x+::1) ~ 1J1 iJ + .s,~Tl"[(k-,)(x-!;1)+2l3 + 0 cos 1r[,"(x+-::1) + ½] + i] coslf[h( x.~'j)-t-½ 1 +s,;..1r[(i-h)(x-j)+:z_!yt ;] c.osn[k(x -1-~ )+ h-k-t- L = 3"' 1]} A= " { c<>~7f [U,-k)(x-j)+2l3] cos 7rC:(x+::i)+ u.nr[(k-i)(x-j)..-i13J J, " Co~l(h(,c+'j) +e,osri[c;-k)(x-:,)+ 2i3) cos7fk(.iu-::, )} l =' i'"' B "' (, { 0.:.., I\ [ ,< u, -k )( :J) X - +Al 3 ) C --5.Tt i" ( >< -t ::, ) + s I " ' II [ ( k - i )( .)( - ~ ) + 2 l 3] ,._ cos 1fh{;-,-j) + s,.:._Ti[(;-h)(,v~}+.zL3J c o~ iTk{x+~)} 13 = 0 h =- k ~ "'J l ==: 0 ( c tc . c le. .) For planes of t~e type (00.l),this reduces to A= 18 c os21tlz and B == 18 si~lz F2 , which is proportional to the corrected intensity, == (~A) 2 + (iA) 2 z is the z parameter of each atom in the cell. The z are fixed for every a.tom but the K+- so i t is possible to plot the structure I, 1 9. factor, F2 , against all possible values of zk ■ The z parameters were calculate d. for Cu, C, and Non the basis of the assumed bond angles and distances and their contribution to the structure factor wor.lced out. Contributions to the structure factor of the potassium for ea~h of several. zk were worked out and tabulated. These values were added to the rest of the structure factors and the results plotted against the zk parameter. Scattering factors for Cu , C, and N were abtained 7 from a paper of Pauling and Sherman and for K+ from the Interna- tional Crystal Structure Tables 8 Photographs were then taken of reflections from planes of the form (00.i.)hex·using a large, ground (00.1) face. Because only planes of the form (00.6n) had structure factors not zero, only three such planes could be photographed wit::i.. CuKoe radiation. Intensity measurements were made but were not used in the final evaluation of the potassium z parameter. Use of MoK~ radiation made it possible to get reflections from eight planes up to (00.48), but only five were photographed because the feflections from (00.24) and (00.30) were already extremely weak and because five reflections were enough to determine the parameter wit~ fair accuracy. The inte.nei ty astima ting scale or wedge was made by photographing a slit i mage on a strip of film with varying time of •• exposure. The slit was cut to the approximate s hape of the re- flections as observe d on the film a nd p.maced far enough from the film durin6 t he exposures to give t r: . e righ t a_egree of fuzziness. Intensities were estimate d by superimposing the film and wed6 e and compa r ing the spots by transmitte d light . All the spo ts in the final measurements were made at the s a me time under the 20. same conditions except as to t he amount of fo g on t he fil :n and they all were of about the same intensity. Since the wedge and film, in the comparison, had the same fog for background, the chance for error on that account is small. Estimates of inten- sity were reproducible to within ten percent and the error in estimation of relative intensity was probably not greaterthan ten percent. The exposures were probably measured to witl:': in three perc ~nt, but variations in the voltage may have increased ttis error to fifteen percent, probably to less ti1an ten percent. Two types of film were use, but the relative sensitivity had been 8 measured and i s probably i ,Ood to .one percent . The Lorentz and polarization factors were obtaine d. by interpolation from t 2'l e . crystal structure tables 9 ~ INTENSITY COMPARISON ON FINAL MoKcoc. ( 00.1..) PHOTOS Plane re fle cti!lt; Intensity Lorentz Temp. &Polar.Fact. Factor 2 F;<Const. ( 00. 6) 2.24 7 .973 .961 2.93 ( ()() .12) .790 3.746 .866 2.437 (00.18) .423 2.295 .680 2.710 ( 00. 24) .0758 1.486 .506 1.007 ( 00 .30) .0181 1.096 .461 0.4115 In the crystal structure tables, there is a list of crystals and their c r itical temperatures. A critical temper- ature wa s chosen to corresponi to the hardness of the crystal and and the t'emperature factor calculated with the help of the tables 10 . 0 The critical temperature chosen was 2so z . and, from •it, B, in the fo1·mula for the temperature factor, [ e _ 2 was calculate d to be 0.5951 • • G('';_e)'r-- CALCULATION 01!1 CONTRIBU'l' HDN TO STRU CTU RE ~1ACTORS uF (00.i)h OF ATOMS OT HER TNAN POTASSlUM (00.6)hex Atom lz cos.21Tlz f Cu o.o l -.0879 .0314 .6613 -.7203 24.89 4.04 12.12 5. 33 15.:.,99 C 30 N 3N .736 .755 .135 .622 fcos2'fl'lz sin2-rrlz fsin2'T'(lz ·24 .89 0 3.524 -11.515 16.9246 .7501 - . 6937 0 - 4.024 -12.114 4.000 -11.09 .0377 18,.19 . 2 .11 6.33 2 ·. 77 8.31 . 1s:.19 - 2 : o78 - 5.818 - 0.347 0.313 10.260 0 .1750 - .0628 .9921 .9993 0 0.3692 - 6.3976 2.748 8.304 11.0236 l .2608 -.0941 -.32Sl .6660 12.27 1.64 4.92 1.84 5.52 12.27 .4277 .463 .6020 3.677 15.3097 0 .9654 .9956 .5621 - . 7459 0 1.583 4.918 1.035 -4.118 3.418 l 8.04 1.51 4.53 1.56 4.68 0 0 - . 9961 - .3551 .3807 -.9995 -23.221 (00.12)hex Cu C 30 N 3N o.o .472 .510 .270 .244 l -.9846 -.9980 -.1253 ( 00 .18 )hex Cu C 3C .N 3.N o.o .208 .265 .405 .866 - - (00.24ihex Cu C 30 1~ 3.N.N o.o .944 .020 .540 .488 .9387 . 9921 -.9686 - .9972 ' 8.04 1.417 5 4.493 - l .511 - 4.666 - .5201 .1253 .5678 - .3446 - .2487 .0753 - .3880 .3524 .0121 7.7736 ( 00.30) hex Cu C 3C .N 3N o.o .680 .776 . 675 .110 l -.4258 .1564 - .4540 .7705 7 .59 7.59 - .5746 4.05 .5834 1.35 1.45 4.35 .654 - 3.353 10.2978 0 -.9048 -.9877 -.8911 .6374 0 - 1.2215 - 4.000 - 1.292 2. 772 3. 7415 - STRUCTURE FACTOliS U]1 ( 00.~ )h PLANES FOR VARIOUS ZK VALUES (00.6)hex .t2 964.4 804.0 489.7 203.8 62 .6 10.5 12.1 62.8 229.5 526.3 833.0 539.4 996.0 1323 • 1379. 1126. 716.6 356.5 152 .6 85.2 109.2 245.l 1504. 1800. 1803. 1583. 1179. 727.0 368 .6 215.4 314.7 635.5 1078. 0 - 9.30 - 6.70 3.60 9.76 4.71 5.75 9 .60 - 2.43 7.54 400.2 176.3 9.8 1.4 93.1 354.5 330.1 71.1 0.6 16.2 121.3 413.1 314.l 55.l 1.6 39 .8 281.4 425.7 181.0 12.2 521.5 589.4 0 542.0 164 .9 65.5 363.9 460.0 91.6 497.8 11. 7 17.4 46.6 103.3 2.8 4.2 62 .a 553.7 192.3 112.0 457.2 462 .8 223.6 118.5 11.6 0.7 41.4 184.3 200.7 42.4 30.8 3.1 49.6 17.7 o.o 223.6 160.9 42.4 3.8 91.0 202.0 212.6 fkoos2'i7J.z f k:sin2rrlz tE f 1 coe211'lzt) 1.0 14.13 11.43 6.20 -2.65 - 9.68 -13.68 -13.44 - 9.00 - 1.77 6.02 11.~3 0 - 8.30 -13.14 -13.88 -10.30 - 3.52 4.36 10.89 14.02 12.79 7.56 190 . 81 .72 .63 .54 .46 .36 .27 .18 .09 2 tE f 1 sin2'l11zt) 2 lzk (00.12)hex 2.0 ~80 .62 .44 .26 .08 .90 • 72 . 54 .36 .18 9.78 3.02 - 7.13 - 9.10 - 0.61 8.57 7.92 1.83 - 9.47 - 6.23 - - 323 -49 56.5 94.7 394.3 611.5 496.8 181.6 28.4 (00.18)hex 3.0 :. 10 .43 .16 .89 .62 .oa 7.98 - 2.47 - 7.22 4.23 6.16 - 6. 74 7.00 7 .59 - 3.40 6.74 - 6.08 5.46 -. 3.84 95.8 650.6 ( 00 .24 )hex .~5o .0375 1.35 5.81 0 6.50 5.53 - 1. 79 - 7.05 - 4.22 .046 6.39 - 3.46 .0075 .015 .0225 .030 - 7.18 3.11 4.58 6.96 11.9 21. 2 Final F values corrected for the temperature effect were 2 compared wit~ the plot of F againsi zi and one spot found where a qualitative _fit could be made . Various values of B were now assumed and new ratios of F 2 calculated in an attempt to get a perfect fit. The beet fit, with a variation from the plot of only ±6~, was obtained for B =l.45, corresponding to a critical temperature of about 130°K. Since, however, the total error in intensity ratios may have amounted to over 60~, this calculati on cannot be regarded as significant except in that it s hows tha t the temperature factor is not of very g re a t importance in fi l:ing parameters. The zk paramete r turne d out to be 1042-.046 --t-n/6. 2 F RATIOS FOR VARIOUS TEMPERATURE FACTORS B=O B =- • 59 5 B = l •0 B = 1.4 B = l. 5 b =2.0 2.81 2.93 3. 00 3.07 3.09 3.20 2.11 2.44 2.70 2 .97 3.04 3.46 1.84 2.71 ;-j.17 3.94 4.17 5.46 0.51 1.01 1.34 1.98 2.18 3.52 0.17 o.41 o.74 1.35 1.57 3.32 The critical temperature for B =2 .o is about 90°z . Probably the g•eatest source of error in the determination of the intensities was caused by the deteriorating surface of t he crystal. From the time of grinding the crystal face to the time of taking the final photogra phs, crystal g rowths formed on the g round face and were ~iped off three or four times. It would probably be advisable before starting the determination of the other three parameters to regrind the crystal face or grind a new face Structure Factors of K3 Cu(CN) 4 for Various ZK+ 22. and take new photographs for more accurate intensity measurements and a more accurate parameter determination. Summary Crystals of potassium cuprocyanide were prepared and analyzed. The analysis showed them to be K3 Cu(CN) 4 . The hardness was found to be 2.4; the density was found to be 1.99±.1. The crystals were found, by a pyroelectric experiment, to have a polar threefold axis. The crystal habit and unit cell reported by Cox, Wardlaw, and- Webster were confirmed and the space group found, by examination of Laue photographs, to be C~v· It was assumed that t~e tetracyanide complex fDrmed a regular tetrahedron, and, by intensity measurements made on five (00.l)hex reflections, the hexagonal z parameter of the potas- sium ion was found to .042- .046-t- n/6. REFERENCES 1. Cox, Wardlaw, and Webster, 2. ~assett and Corbet, 3. Uhemical Rubber Co. Handbook, 4. Internationale Tabellen zur "estimmung von Kristallstrukturen, J. c. s. J.C. S. 125 1936 p. 775 P• 1667 (1924} 17th Ed. p. 964 P• 6i6 J. A. c. 3. 5. Pauling and "rockway, 6. Lonsdale, 7. £auling and Sherman, 8. uamertefelder and Gingrich, 9. lnt . Tab. s. Best. v. !Crist., 10. Ibid., P• 674 59 p. 1223 81 p. l (1937) Structure Factor Tables z. Krist. ~ev. Sci. instr. p. 667 \ 1932) P P• 154 (1938)