THE CRYSTAL STRUCTURE OF ANHYDROUS LITHIUM PERCHLORATE

DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

By

Richard Edwin Gluyas, B.S.» M.S. The Ohio State University 1952

* •» * • • » • a> • i j • • • • • * i i ’ «« »- t• > i> *

Approved by:

Adviser I

TABUS OF CONTENTS Page

I. Introduction ...... 1 II. Experimental Work and Preliminary Deductions ...... 4 III. Determination of the Structure ...... 16 IV. Discussion of the Structure ...... 57 V. Summary ...... 66 VI. Bibliography...... 67 VII. Appendix ...... 69 VIII. Acknowledgment ...... 82 IX. Autobiography ...... 83

S09405 1

THE CRYSTAL STRUCTURE OF ANHYDROUS LITHIUM PERCHLORATE

I. INTRODUCTION.

The crystalline structures of many anhydrous ionic solids of the stoichiometric type ABX4 have been determine ed, 1 * 2 However, except for the rather unusual compound 3 1 LiEH4 , the quartz pseudomorph A1P04 , and the cristobalite pseudomorph BP041 a structure has not been established for a case in which 11 A" is a small cation such as in LiC104 , MgS04, BeS04> etc. Since the structure of LiBH4 is essentially different from the structures of the other known ABX4 crystals such as BaS04 , CaS04 , etc., it was considered worth while to examine a typical member of this class having an especially small cation. For this reason LiC104 was selected for detailed study. In the case of small cations like Li+ , Be++, Mg++, and Al+++ the oxygen coordination number ranges from four to six whereas for large cations like Ca++, Ba++, and K+ the oxygen coordination number ranges 4 from six to twelve . This suggests that the structure of

LiC104 is probably quite different from the structure of a compound like CaS04 . Undoubtedly the reason that the structures of no anhydrous crystals of this class such as LiC104 have been examined is that these substances are highly deliquescent. In this respect LiC104 closely resembles Mg(C104 )8 which is sold commercially as a very effective drying agent. This deliquescence is an interesting property in itself and must certainly be oonnected with the smallness of the cation size. The hydrated phase with its hydrated cations is essentially a different substance chemically than the an­ hydrous phase. The structure of the hydrate LiC104 *3Hg0 5 has been reported in the literature , This structure is closely related to those of a large group of isomorphous hexahydrates R(MX4 )2 *6HgQ where R is Mg, Mn, Re, Co, Ni, or Zn and the complex ion is BF4” or C104“ . A monohydrate of LiCl04 is reported to exist but its structure has not been determined. Crystals of the type compound ABX4 generally have mirror planes and oommonly possess a center of symmetry which makes them good subjects for the X-ray diffraction method of structure determination. There were reasons for ohoosing LiC104 rather than another compound like LiAlH4 , LiMh04 , BeS04 , LiI04 , etc. First, the prospect for obtain­ ing single orystals suitable for X-ray examination seemed quite favorable in the case of LiC104 . This is due to the faot that the melting point of LiC104 is below the tempera­ ture at which it decomposes so crystals may be grown from the melted salt. Secondly, in the interest of obtaining aoourate bond length measurements and of locating the light atom A compounds containing very heavy atoms B or X were 3 not considered. Furthermore, since the hydrogen atom is so small and therefore such a poor scatterer of X-rays, materials like LiAlH4 were ruled out. E. P. Meibohm has prepared X-ray diffraction photographs of anhydrous powdered LiC104 incidental to his work on LiBH4 . He did not show whether or not LiBH4 and

LiC104 have the same structure— a complete analysis for

LiC104 would allow one to make a direct comparison of the structures. There is general agreement that the configuration of the perchlorate complex is tetrahedral but there is some variation in reported bond lengths. Probably among the best values are those published for LiC104 *3H20 and

Mg{C104 )g#6H20 by C. D. West5. For the 01-0 bond lengths he gives 1.52 A to 1.56 A in the case of the lithium salt O Q and 1.46 A to 1.50 A in the case of the magnesium salt. Another more precise determination of the Cl-0 tetrahedral bond length is an aim of the present investigation. 4

II. EXPERIMENTAL WORK AND PRELIMINARY DEDUCTIONS.

The lithium perchlorate used in this study was prepared by adding a slight excess of Mallinckrodt reagent grade perchloric acid to Mallinckrodt lithium carbonate which had been purified by recrystallization 6 . A batch of crystals of hydrated lithium perchlorate contaminated with perchloric acid was then obtained. The perchloric acid was removed by passing a stream of air saturated with water vapor over the crystals at about 200°G. Finally the water was driven off by heating for several hours at about 7 300°C. in a partial vacuum . The purity of the product was checked by a spectro­ scopic examination, by cooling curves, and by a qualitative test. The spectrum revealed no important impurity. Sodium was present but in amount le-ss than ten parts per million. The cooling curve was followed by means of a chromel-alumel thermocouple standardized against Bureau of Standards tin. Over the two phase range corresponding to the melting point the temperature was constant to 0.2°C. indicating sufficient purity for structure investigation. The melting point of

LiC104 was found to be 247.7°C. which disagrees with that of 256°C. given by A. Potilitzen8. However, he points out that traces of water may have been present in his prepara­ tion and that the melting point reported is probably low. 5

No chloride was detected by testing an acidified solution with AgN03 , showing that little or no decomposition of

LiC104 to 0S and LiCl had taken place during the purifi-

7 cation process . Since anhydrous lithium perchlorate takes up water very readily all samples were handled in an atmos­

phere of N2 dried over anhydrous magnesium perchlorate

(Dehydrite) and P205. Lithium perchlorate crystallizes in a solvated form from all solvents tried in which it is appreciably soluble. Such solvents as water, ethyl alcohol, and.pyridine which have relatively high dielectric constants were the ones tried. The method selected to obtain single crystals was to cool a melt. A disadvantage (not serious) of this method is that it does not give crystals with face development. Some salt in a cone-shaped Pyrex container was melted in a furnace and slowly lowered from a zone maintained at a temperature slightly above the melting point into a zone maintained at a temperature slightly below the melting point. The clear solid obtained was broken up and selected frag­ ments placed in small thin-walled Pyrex tubes which were then sealed. The Pyrex tubes were designed so that the crystal fragments could be shaken into different orienta­ tions. Of the several fragments examined by X-rays all proved to be single crystals. One sample was aligned and oriented by making use 6

of X-ray diffraction symmetry. A set of 15° oscillation

photographs9 with 3° overlap were taken (about what was later designated as the /OOl/ axis) using a cylindrical camera of radius 57.3 mm. and Cu K

C0 - n X ______sin (tan“*i £ ) r n - number of the layer line o X - 1.5418 A the doublet weighted mean wave length of Cu K<* 10 y - distance of layer line n from the zero layer r - the effective radius of the camera

o The 0o distance was found to be 8.659 ± 0.01 A . Assuming an orthorhombic unit cell and determining the smallest common divisors of the zero layer ^ values as read from a Bernal chart the dimensions aQ and bQ were estimated

(Note: aQ = -X-) . Using these estimated dimensions it was found possible to completely index the oscillation photo­ graphs. Then using indexed spots (h k 0) on the zero layer line of a full rotation photograph more precise measurements were made and aQ and bc redetermined using the expression:

d * i_____ = X hZ + k2 2 sin© Q'O^ t>o^

d - interplanar spacing © - Bragg angle

The dimensions aQ and bQ were found by measuring © for two i different(h k o)reflections and solving two simultaneous equations. This was done for ten sets of two planes each + O and the best values found to be: a0 = 4.836 - 0.01 A and . o b0 = 6.926 1 0.01 A. The orthorhombic unit cell of these dimensions was then confirmed from the Weissenberg photo­ graphs. The number of molecules (m) per unit cell was determined using:

^ _ N ^ aohq Oo

^ L iClO*

N - Avogadro’s number (6.0235 x 1023)

^ - density of LiC104 (2.4284 9/cc at

2 5 ° / 4 . ) 7 o a0h0c0 ” unit cell dimensions in A

^ L i d O * - 106.397

The calculated number of molecules is 3.978; since m must be integral,the actual number must be four. As stated above the normal beam oscillation photo­ graphs were completely indexed using an orthorhombic unit cell with the dimensions found. The recorded planes 1 correspond to those accessible by rotating the crystal about the /po]/ axis. The classes of reflections found on examination of a listing of(h k l) data are: (h k l) in all classes indicating a primitive cell P;(h o l) in all classes; (h k O^only for h + k = 2n indicating a net glide plane n perpendicular to cQ ; (o k l) only for 1 = 2n 9 indicating a c- glide plane perpendicular to aQ . These laws also hold for more extensive data taken from Weissenberg equi-inclination photographs. Therefore the space group is P cgn or Pfirnn. Now one cannot distinguish between these by consideration of symmetry of photographs in this case since |Fhkli “ I^SklI (Friedel’s Law).

A choice must be made on the basis of an analysis of in­ tensity data or on the basis of other experimental data. An analysis of the statistical distribution of intensities; as recently point out by Howells, Phillips, and Rogers'^; may indicate the presence or absence of a center of symmetry. A more obvious approach is to select one of the possible space groups and to account for the observed in­ tensities by a proper choice of atomic parameters. If this cannot be done for a centro-symmetrical space group it is necessary to try one lacking a center of symmetry. Evidence for piezo-electric or pyro-electric properties would indicate the lack of a symmetry center. The trial method was used with success in this work. The space group Pcmw was selected to start with because the center of symmetry 10 makes for less involved computations and because of some precedent for the existence of the mirror plane (for example, LiBH4 and many other RMX4 compounds have mirror planes (see Wyckoff)1). All photographs were taken using a pack of three thicknesses of Eastman Kodak Type K X-ray film. The film to film factor (ratio of blackening on film (i + 1 ) of the pack to blackening on film i) for Gu K<* radiation was determined using a Geiger counter X-ray spectrometer and a packet containing one, two, and three layers of film. The factor was found to be close to 1/3 (actual measured values were 0.313, 0.345, 0.329). This means that the blackening of a spot on the second film is 1/3 of the blackening of its counterpart on the first film. The blackenings of the reflections on a full rotation photo­ graph were then determined by first assigning an arbitrary magnitude to one reflection and then assigning relative magnitudes to the rest of the reflections by inter­ comparison between the three films. On all photographs, Weissenberg as well as normal beam, an area factor was estimated for each spot using a spectrum magnifying lens with a scale graduated in tenths of a millimeter. A raw integrated intensity value (I) was then arrived at by taking the product of the area and blackening measurements for each reflection. 11

For a normal beam single crystal rotation photo­

graph^2 the intensity of each spot is proportional to:

/ 1 + cos8 2 0 \ I cos 0 r p I------j -7= = = = _ I :e a sin 2 0 / \V(cos2 4> - sins Q )

F - structure amplitude p - multiplicity factor 6 - temperature correction factor A - absorption correction

1 + C0S2 2 0 \ / cos $ combined sin 2 0 / \V( coss - sins 0 ),

Lorentz and polarization factor 0 - Bragg angle - angle between the reflecting plane and the axis of rotation.

Values of [ 2 — ) are listed versus sin 0 by M. J. \ 1 + COS2 20/ 1 Buerger *35 . Values of

Vooa8^ - slnaQ . z\j~^r a - oos 0 (<5 8 + 5")

V 4 - 5s - ? 8 were calculated from ^ and data obtained using a Bernal 12 chart. Values for F2 B A were then calculated for all (h k l) • The normal beam data have been used to begin cal­ culations of structure with B A assumed equal, to unity. Also no attempt was made to reduce these relative data to data on an absolute scale. The approximate dimensions of the crystal fragment used' for the rotating crystal photo­ graphs were 0.2 mm. x 0.5 mm. x 0.3 mm. The Weissenberg equi-inclination photographs were taken using Mo K * radiation (weighted mean doublet wave length X = 0.7107 A) and three films interleaved with shim brass to give a wide coverage of intensity data. The blackenings were estimated using a prepared scale. The film to film absorption factor was estimated by use of direct measurements of blackening on the three films. Next the raw intensities (I) were corrected by applying Lorentz and polarization factors. Values for were determined from a nomograph published by W. L. Bond**-4 relating ^ , ^u (the angle of inclination), and % (the angle between the direct beam and diffracted ray). A sin 0 scale was included on this nomograph by D. T. Tuomi 15 so that a sin© reading could be taken for each h kZ (P = l..+ ...goa2 2 ? ; cos 2 0 = 1 - sin2 2 0 - cos2 p cos - sin2 p .). Readings of j- were obtained from a nomograph relating i , jll, and prepared by D. T. Tuomi. 13

For the equi-inolination method ^ = cos8 jol sintf .

An absorption factor was not applied. To do this would involve a great amount of labor because of the complicated shape of the fragment. Such a factor would be small since the size of the crystal used was only about 0.45 mm. x 0,50 mm, x 0,3-mm. and Mo Kot radiation is not highly absorbed by LiC104. The linear absorption -l 12 factor ji for Mo Kot in LiCl04 is 13.8 cm . The maximum range of dimensions for the crystal fragment used is from -JU A XmoTr 0.3 mm. to 0.5 mm. The largest possible value of e is approximately 1.35. Since separate photographs were taken of each layer line in the case of the Weissenberg method it was felt necessary to determine a factor for the intensities on each layer line photograph to place all observed intensities on the same scale. Such a correction would be direct if one used an actinometer to measure total radiation per exposure and developed all photographs simultaneously. Although the exposure times, X-ray intensity, and development were held close to the same conditions, quantitative precautions were not taken. Correction was made possible by the fact that layer line photographs were taken for two different axes of rotation TOlJ and /0107) • A semi-empirical method used to make the correction is discussed in Appendix A. 14

The resulting intensities (

X F2 expl. In H = In i - £!_ sin2 0 K X s

F2 expl. - corresponds to the estimated quantities (\JL= I)

F2 expl, - is the sum of observed F2 expl. for N all N reflections in a selected range of sin 0 (e.g. 0 - 0 .1 )

£ fi“ - 4 fLi + 4 fCl2 + 16 foS

f - atomic scattering factor estimated

from sin0 ^ versus f curves plotted for oxygen by using data for fluorine appearing in Internationale Tabellen, for chlorine by using data for sili­ con, and for lithium by using data directly available for Li+ .

K - a factor to bring F2 expl. to an absolute scale. 15

B - an isotropic temperature factor. - X - wave length of Mo radiation.

By applying Harker's equation and fitting the constants by the method of least squares it has been found that K = 72.1 and that exp. ~ exP* (5.951 sin20 ). In orde r 2 to adjust the IP##! values to an absolute basis they were all multiplied by 72.1 yielding a set of Fobs2 quantities. The temperature correction term was then applied by multiplying 2 e x a k .951 sin2^) the FQt>s quantities by to give values ^ designated as F0^s. 2 . These , after extracting the £ r ® square roots, gave a set of structure factors to which structure factors calculated from a model assuming no thermal vibration could be compared. 16

III. DETERMINATION OF STRUCTURE (see Appendix E ) .

With the assumption of a mirror plane, in the absence of evidence to the contrary, the space group sym­ metry of the crystal is P___.omn This symmetry is described 17 by eight asymmetric or general point positions (see Figure 1):

(a) 1 ) x, y, z 5) + x, 1 + y, i - z

2 ) | - x, y, | +■ z 6 ) x, | + y, 5

3) x, 1 - y, z 7) 1' + x, y, i - z

4) i - X, i - y, i + z 8 ) x, y, z

There are four molecules per unit cell which means that the chlorine and lithium atoms are constrained to occupy special positions. The three sets of special positions are:

(b) (m) (o) I (d) 1

1 ) !> z 1 ) 2 > °» 0 1 ) o, o, 0 1 1 x I 1 + z 1 1 ) o, 0 2 ) £ ~ 4* r + z 2 ) 2 ’ 2 * 0 2 2 *

3) 1. + x — — — z 1 1 1 2 4 2 3) 0 , 0 , 'S 3) 2*’ o, 2 1 1 4) 4 > ^ 4) 0 ~ 4) 1 1 U » 2 1 2 2 * 2 * S’ 17

The perchlorate group is tetrahedral and therefore it has mirror planes and two and three-fold axes of symmetry hut it does not have a center of symmetry. It follows that the chlorine and two oxygens of the perchlorate group must lie in the mirror plane and set (b) of special positions must be used to designate their coordinates. The oxygens related by the mirror plane lie in the general point positions (a). The four lithiums may lie in positions specified by any one of the sets (b), (c) or (d). Location of one molecule will fix the structure. All together there are three coordinates for each of six atoms. Three coordinates are already determined by symmetry; therefore, it is necessary to specify fifteen coordinates.

I. 7 For the oxygens - *i; 4 > zi For chlorine xci; x*> ZC1 1 J; z2 For lithium “ xL i » yLi; zLi x3 ; y3 > z3 x4 ; y4 ; z4

The number of unknown parameters is reduced to twelve by the fact that (x3 = x4 ) ; (z3 = z4 ) ; and (y4 * 1 - y3 ). The parameter y^j. can only be or 0. F IG U R E I Co Oo

U n it cell viewed in - bo direction

Unit cell viewed in - o0 d ire ctio n — net glide phne o center of symmetry — c—glide plane §s cre w axis m irror plane Q point position 19

The structure factor (F) contains the effect of the distribution of scattering matter in the unit cell on the intensity of a diffracted ray. Now ingeneral:

I,2hkl - A8 + B*

A = -2- f . cos 2 tt (hx + ky + 1 z) J j B f. sin 2 tt (hx + ky + Iz) J J

In these expressions f . signifies the diffracting power of atom . and x, y, z are the coordinates of the atoms in J fractions of the unit cell edges. For a crystal with a center of symmetry at the origin B equals zero since sin & r — sin (- 0 ): therefore; F = A = ^ f • cos 2 TT (hx + ky + J J lz) * And using the extinction laws for the space group 3Pcmn it follows that (see Appendix B ) :

Fhkl 8 X f j (cos 2rr ( lz + 1—

cos 2 tt (ky - cos 21t (hx - k ., + 1

Magnitudes of F together with phase angles would allow a direct determination of the atomic parameters (for example, TO by use of electron density sections . prepared from 20

^V = F 'hk. j cos 27T (hx + ky +■ lz) .

However, only quantities proportional to | ^ j are directly available and the phase angles 0 or TT (in this case corresponding to a plus or minus sign on the Fhk.j ) are not known. Vector maps and trial and error methods have been used to arrive at rough estimates for the atomic parameters which in turn can be used to calculate phase angles. Using the values proportional to lFhkl I determined from the normal beam photographs a Patterson section 1R

(see Fig. 2) has been calculated from:

This section gives peaks corresponding to vectors between atoms displaced from one another by j? along y. The origin of the section is taken at a screw axis. Peaks should be n 1 found at (2x, 2z) and {4r> -5- - 2z). Since 01 is the largest atom in the cell Cl-Cl vectors may be expected to contribute to the most prominent peaks observed on the vector map. From a peak at w = 0.433 and u = 0.100 tentative parameters {z q ^ = 0.217 and x cl = 0.050) were obtained for 21 one of the chlorine atoms. Furthermore the peak at z * 0.117 and x = — suggests that zcl ® 0.192 in close agree­ ment with the value of z = 0.217.

The Patterson section P,,„MUOW (see Fig. o 2). # » which gives maxima for atoms with the same y parameters, is expressed as: o° C<> / C0 \

VPuow = jiE JE f z^|f' cos 2 TT (hu + lw)

and has a peak at w = i and u = 0.400 corresponding to the parameter xqi = 0.050. Maxima are to he expected on this section at (1 - 2x, and (0 , 0 ).

Assuming the Cl parameters to be approximately cor­ rect trial orientations of the perchlorate group about an axis through the chlorine and parallel to the y axis were tested by trial and error to find suitable x and z para­ meters for the oxygen atoms. At first for the sake of 19 visualization and speed Bragg-Lipson charts for some of the (hoi) data and a scale model of the x-z projection of the perchlorate ion were used to calculate approximate structure factors. In order to use the Bragg-Lipson method and to simplify numerical calculation of structure factors during the trial and error process the observed quantities F IG U R E 2.

U

P u L - ^ W

u

P uoiv

Potters on Sections 23 proportional to | Fh^T | were modified to | | values where {^hic] 1 ^-s ‘fche structure factor for point atoms. This was done by use of an average electronic scattering factor (f) for all of the atoms. This f w$s calculated as a function of ( — ) utilizing Hartree atomic scat- A tering factor data (fj) listed in Internationale Tabellen 12 zur Bestimmung von Kristallstukturen. The values for chlorine were approximated by use of the factors given for silicon, for oxygen by use of the values for fluorine, and for lithium by use of data for Li+ which were directly available. For a particular value of (sin 0/ \ ) :

5 - Aj - *ci/aol - fLi+/Ztl+ + 4 f°/Zo N N

W I _ lFhkll hkl I — =--

where Zq-^ = 14, = 2, zQ » 9, and N *» 6 (the number of ZO atoms per molecule of LiC104 ). Now expression 3} reduces to:

Fhkl * j cos 2Tr hxj cos 2TTkyj cos 2irJz.j for (h + 1 = J 2n; k = 2n) Fhki ss~8 sin 2TThXj cos 2 TTkyj sin 2TrJzj for (h +1 =

^ 2n + 1 ; k = 2n) 24

-sTfjcos 27ThXj sin 2Trky.j sin 2 t t 1zj for (h + 1 Fhkl j « 2n,; k = 2n

+ 1 )

Fhkl = ~ ^ T f j sin 2TrilXj sin 2 rrkyj oos 2 Trlzj

i for (h + 1 » 2n + 1 ; k = 2n + 1 )

Or for point atoms:

—- ■^hkl = 8/ z .i 003 2 7rhXj cos 277"ky^ cos 2 7TlZj 3 for (h + 1 = 2n; k = 2n)

etc.

Since the unit cell contains only four molecules the co­ efficient 8 must be replaced by 4. For (h 0 1) planes:

■^hkl “ zj 003 ZTT"hXj cos 2 rTlZj (h + 1 = 2n) 3

Fhkl = “ 4^ z j. sin 2TThXj sin 2 7T1z j (h + 1 » 2n+ 1) j

For a particular hOl it is possible to construct a Bragg- A Lipson diagram showing loci for = O and areas where an atom will give a positive or negative contribution to A Fhk-i . Such diagrams have been constructed for (hOl) with 25 relatively large observed | Fj^jJ (e.g. 400, 201, 601, 103) and for (h O l ) with relatively small (e.g. 101, 200, 203, 403, 102, 303, 402, 202). Use of these charts and a scale model of the perchlorate ion (assuming Cl-0 bond lengths of C. D. West (1.48 A) and normal tetra­ hedral bond angles (/^109o) ) indicates that some orienta­ tions of the perchlorate ions are more reasonable than others. Of course, the more extensive zone data one has, the greater are the restrictions that can be imposed on the parameters using this method. However, in this case the method has been used to suggest reasonable orienta­ tions to be tested by comparison of numerically calculated hicl to observed | Fhkl | . Good agreement between calculated and observed FhkX tabulations was obtained for the (h 0 1 ) reflections by means of the orientation represented by parameter set (1 ) (Table 1). Calculation of F ^ ^ was done including chlorine and oxygen parameters but omitting the lithium parameters

(which were unknown at this point in the analysis). (a s A a matter of record an insignificant improvement in R was achieved by shifting all of the atoms by 0.02 in 5C to give ✓V * /\ parameters set (2) ). The R for the calculated Fhkj data

nc During the course of a structure determination it is important to know how well a proposed model of the structure fits the facts and also whether or not changes in a proposed model constitute an improvement. This amounts to comparing calculated values of structure factors with observed values. In this discussion the comparison has been made by means of a reliability factor2^ defined as: r = M^obsl f^calcil

Z. K b s l In the ea^ly stages of the structure determination compari­ sons of quantities instead of /f ^ i / quantities have been made because of greater ease of calculating jFhicij values. at this point was found to be 0.23 where:

X l ^ o b s l

At this stage a Fourier projection (cr"xo __) z was prepared but the resolution of the atoms was not good. However, a change in atomic parameters was made on the basis of the projection to obtain set number (3) of parameters. For the one hundred and eleven observed values of | obtained from the A normal beam photographs the overall R was 0.30. Equi-inclination Weissenberg data was obtained before continuing with the analysis. These data were then used throughout the remainder of the analysis because of the 27

greater coverage of reciprocal space they afford. There are 588 (h k 1 ) as compared to the 111 (h kl ) available from the normal bean photographs. Furthermore there are 61 (h 0 I ) instead of only 13 (h 01 ) (the Fourier pro­ jection mentioned above undoubtedly did not resolve vwell because important terms were omitted). Using set (3) of A. parameters Fce estimates were calculated for the 61 (h 0 I )

A subscript o on F (e. g. FQ) indicates an observed quantity. The subscript c indicates a calculated value. The subscript e means that the effect of thermal vibration has been removed from observed values of F or has jjot been included in calculated values of F. For example, Fce indicates a calculated structure factor assuming fixed point atoms and Foe refers to structure factors calculated from observed structure factors (Fo) removing approximately the effect of thermal vibration and reducing to point atom values. Unless pointed out otherwise all observed structure factors include the contribution from lithium atoms whereas the calculated structure factors do not.

planes. Comparison of these calculated Fcefs to observed 1 ^ 1 ^ ' •B’oelt s gave R = 0.52. Use of the algebraic signs of the

Fee data on the |f q| data (this refers to the original ob- served structure factors before any temperature factor was applied) made possible the preparation of a Fourier project ion ( CT"xoz) from the expression: 2 8 oo

> F q o L 003 2TrI*z\ + 4^ A ? H O L 003 27THx cos 27TLz H + L = 2n

3L ^ FH O L sin 2 ~7T_ sin 2TTZ.Z i l . H + L = n or in more condensed form:

OO o d

Z CTxoz * A 1 j^Fooo +^ ? b,hol COS 2 T7* H x COS 277“X>Z - 0° &o ./T" sin 2 TT Hx sin 27T"Lz 3 -

This projection gave the set of parameters (4) (Table 1). The maxima defining the x and parameters were located by use of a table prepared by A. D. Booth 21 . His table pro­ vides a consistent criterion for locating the maximum of an electron density peak. In preparing his table Booth assumes that near the maximum the electron density ^ is a function of the form ^ = ax2 bx where x is a coordinate expressed as a fraction of the unit cell edge. Also assuming the in­ formation is in the form:

y&o x 0 1 2

0 f e* 2 9

and that O it follows that a= (pg -2p-L)/2 and b = - ( 2 - 4 ^ 1)/2. The value of x which makes a maximum is xm = (r " 4)/2r - 4) where r * P 2/ . Booth*s ^ 1 table gives xm to four decimal places at intervals of r = 0.001. The necessary summations to prepare the projection were made with the aid of Patterson-Tunell card strips 2 2 a . Recalculation of FC0 estimates for the (h 0 1 ) planes using parameter set (4) yielded R = 0.34. Another Fourier pro- A jection (O'xoz) led to parameter set (5) for which R = 0.32. Comparison of calculated Fce to observed l^oel instead of ^ I ^ I calculated values of FC0 to observed | Foe I showed R = 0.25 where R is defined by:

Z|KJ - Kell R = ---- !------;------L ^ lFoe|

Repeating the process of preparing a Fourier projection (CTxoz), locating a new set of parameters (6), and calcu­ lating a new set of Fce for all (h 0 1 ) it was found that R = 0.22, Finally two Fourier projections (CTxoz) were calculated using original F0 data in one case and Fc data (calculated including an isotropic temperature factor cor­ rection to introduce an estimate of the effect of thermal vibration in modifying Fce) in the other case. On the basis of these projections set (7) of para­ meters was determined using a method for locating the 30

parameters from the difference in peak positions on the F0 and Fc projection described by A. D. Booth23. The Fo projection is shown in Fig. 3. At the same time a Fourier projection (CT^xoz) was ma

established. Sets (o) and (d) correspond to two possible sets of positions lying on symmetry centers. Now the peak at x = o and z = 0.500 of the projection mentioned above suggests special positions (b) or (c). The (b) positions appear to be unlikely from packing considerations. , © o Assuming van der Waals radii of 1.4 A for oxygen and 0.6 A for Li+ 4 and assuming parameter set (7) room would not be allowed for the Li+ on the planes of symmetry at y = |

°r y = | in the neighborhood of x = o and z = 0.500. Packing considerations also make the (d) positions seem unlikely. Further support for the choice of positions (c) is presented later in this discussion. Since 0, 02, and Cl (See Fig. 4) lie in a mirror plane (y = i) and since refinement of their parameters was carried as far as possible by use of xoz electron density projections it was considered worth while to prepare a three dimensional electron density section at y » | , To this end a complete set of Fce were calculated with the aid of International Business Machines (see Appendix C). Magnitudes and signs of all Fce were calculated with and without lithium ions included (see parameter set (7) ). In the case where the lithium ions were included they were placed on special point positions (c). Comparison of Foe bo l^oel listings for all of the 588 planes observed gave R (with Li+ ) = 0.267. For the planes to which Li+ makes a FIGURE 3

azoz. (Fo c o e ffic ie n ts ) Fo Observed si ructure factors all atoms contribute

v

o*oz ((F o -Ft)coefficients) Fc Calculated structure factors lithium not included (F o - F c ) Observed s t r u c t u r e factors with chlorine and oxygen contributions removed approximately 33 contribution (h + 1 ■» Zn; k = 2n) . R (with Li+ ) = 0.238 and R (without Li+) = 0*245. Calculation of R for these planes as a function of sin© gave the following set of v alues: sin 0 R (with Li+ ) R (without Li+) N(no. of H O 0.0 - • 0.078 0.115 3 0.1 - 0.2 0.128 0.258 9 0.2 - 0.3 0.148 0.180 19 0.3 - 0.4 0.194 0.201 40 1 0 • 0.5 0.320 0.284 41 0.5 - 0.6 0.294 0.281 41 0.6 - 0.7 0.361 0.372 16

For low values of sin© (e. g. 0. to 0.4) for which the structure factors are least sensitive to thermal vibration the agreement appears to be somewhat better with the lithium ions included. _ 1 8 The Fourier section ( ^ x A z) was prepared from the expression (see Appendix D for expanded form): oo oO j z P(X t Z) =* F000 + 008 STTHx cos 2TTLz ' . ■ » i (H + L = 2n; K = 2n)

OO oO -IX 3?HICL sin 2TTHx sin 2t t ;l z (K + L = n; K = 2n) 34

o o o o j - COS 2_rrH:x: sin STTLz (H + L = 2n; K = n)

oo00 o* . - ^ 1 %^HKL s^-n 2rrE[x cos SrrLz 1 i (H + L = n; K » n)

®HKL ;®'11 the above expression were evaluated by sorting and combining selected individual FQ with proper regard to signs and multiplicity factors. International Business Machines were used to do this sorting and combining. The section was evaluated in the neighborhood of the atoms to OO be located by means of Patterson-Tunell strips . Revised x and z parameters for 0X , 02, and Cl were obtained from the section* These new values may be found in Table 1 under set (8). The x and z parameters of atoms 03 and 04 as given In set (7) (Table 1) were the result of the Fourier pro­ jection (cr'xoz) refinements discussed above. The y para­ meters (see parameters (7) } for the 03 and 04 (which lie out of the mirror plane) were located by minimizing R for (oko) ref lections. The x and z parameters for 03 and 04 were then carried over to set (8) but a (CTxyo) Fourier pro­ jection was evaluated to obtain the y parameters (unfor­ tunately somewhat in error because of a mistake in preparing the projection). Three sets of Fce were then 35 calculated on the basis of parameter set (8). In one case the calculation was made without including the lithium ions; in the other two cases the lithiums were included but were assigned different parameters. In one of the latter two cases the lithiums were placed in set (b) of special positions with the x and z parameters chosen so that the lithiums occupy spaces left in the cell after packing the oxygen and chlorine atoms. In the other of the latter two cases the alternative positions (c) were assigned to the lithiums (as in set (7) of parameters). The reliability factor R calculated as a function of sin gave: sin 0 R (without R (with R (with Li+ N Li+ ) Li+ on at centers mirror of symmetry) planes)

0 - 0.1 0.092 0.172 0.058 6 0.1 - 0.2 0.290 0.347 0.262 24 0.2 - 0.3 0.177 0.195 0.176 44 0.3 - 0.4 0.241 0.256 0.255 111 0*4 - 0.5 0.302 0.312 0.311 147 0.5 - 0.6 0.304 0.308 0.312 161

0.6 t 0.7 0.345 0.351 0.344 76 36

The values for R in the sin 0 range 0 to 0.4 seem to be slightly better for the case in which the lithiums are placed at symmetry centers. However, the results are not conclusive. R (with Li+ at centers of symmetry) for the sin© range of 0 to 0.4 equals 0.219. Examination of R for (oko) data at this point shows that:

R (without Li+ ) = 0.204 R (with Li+ on mirror plane) = 0.236 R (with Li+ at centers of symmetry) = 0.16

These results add some support to the idea that the lithium ions occupy special positions (c). Using the equation:

K FQ = Fcft exp. (-B sinsQ ) X 2 sin2© X 2 the Fce data calculated with the lithium ions at the sym­ metry centers (c) were fitted by the method of least squares to original F0 data. After this fitting the F0 data compared to the Fc values gave an R = 0.25 over all of the observed (h k J ). For all data up to sin© = 0.4 the reliability factor R was equal to 0.196. This process amounts to applying an isotropic temperature factor to all 37

FC0 terms which were structure factors calculated without introducing any correction for thermal vibration. Appli­ cation of the temperature factor decreases the F__v © terms for the higher order (h kl ) and results in a smaller R. Further improvement of the atomic parameters (of 03 and 04 in particular) was sought by preparing the Fourier electron density projection (crbyZ). For 03 the parameters found were:

From CT0yS 0.080 0.127 From crXy0 0.186 0.079

From C7”xoz 0.175 0.132

On the basis of these projections the parameters of 03 were designated as x = 0.178, y * 0.079, and . z = 0.130. The parameters of 04 follow from these by reflection in the mirror plane. It is to be noted that on the basis of the projections the x parameter appears to be the most uncer­ tain. To obtain more reliable 03 and 04 parameters it would be necessary to prepare three-dimensional Fourier sections. To prepare such sections would involve a con­ siderable amount of labor to make small refinements in the parameters. The final set of parameters (9) are the same as those of set (8) except for those of 03 and 04. From 38

the final set of parameters a complete set of F q ^ s were calculated on International Business Machines. This was done for two cases. In one case the lithium ions were included at set (c) of special positions and in the other case the lithium ions were omitted and the structure factors calculated accounting for the chlorine and oxygen atoms only. The agreement factor R (with Li+ ) for sih0 up to 0.4 is 0.184 showing some improvement in the parameters. Computing R as a function of sin0 for those planes to which Li+ can contribute gives: sin 0 R for Fce (without Li+) R for Fce (with Li+)

0 - 0.1 0.10 0.0833 0.1 - 0.2 0.300 0.199 0.2 - 0.3 0.152 0.108 0.3 - 0.4 0.203 0.198 0.4 - 0.5 0.304 0.316 0.5 - 0.6 0.282 0.307 0.6 - 0.7 0.423 0.413

Again it appears that R is improved when Li+ is included at the symmetry centers. Furthermore this is supported by 39

Fce»s calculated for (oko) planes using parameter set (9). The results are:

oko ■®oe Fce (without Fce (with Li F C0 (with Li+ Li+ ) in mirror at centers) planes)

0 2 0 63 71 79 63 0 4 0 59 57 63 63 0 6 0 66 77 81 73 0 S 0 23 27 31 31 0 10 0 24 27 29 25 0 12 0 28 38 39 39

R 0.144 0.224 0.118

To place the calculated structure factors in final form for comparison to original observed structure of factors an isotropic temperature factor and a scale factor were again applied to the calculated structure factory. A listing of h k J , sinO , F0 and Fc for the final structure is given in table 2. The overall value of R (with lithium) is 0,235. For structure factor values corresponding to sin 8 up to 0.4 the value of R (with lithium) is 0.180. A complete listing of the parameters of all atoms 4 0 in a unit cell is given in Appendix E together with an outline of the procedure used to determine and refine the structure of lithium perchlorate. 41

Table 1.

1 2 3 4 5 6 7 8 9 Oi .050 .070 .071 .063 .048 .050 .054 .047 .047 °s .760 .780 .744 .742 .742 .744 .753 .747 .747 °s .197 .217 .176 .175 .178 .178 .175 .175 .178 04 .197 .217 .176 .175 .178 .178 .175 .175 .178 Cl .050 .070 .042 .027 .036 .043 .040 .041 .041 Li .000 .000 .000 Li2 .550

Oi .250 .250 .250 os .250 .250 .250 o3 .079 .086 .079

04 .421 .414 .421 Cl .250 .250 .250 Li .500 .500 .500 Lig .250

Oi .564 .369 .357 . 344 .350 .351 .351 .351 .136 .158 .147 .143 .134 .133 .129 .129 0 3 .136 .134 .134 .132 .133 .132 .132 .130

O4 .136 .134 .134 .132 .133 .132 .132 .130 Cl .192 .199 .186 .182 .182 .180 .182 .182 Li .500 .500 .500 •H 01 .373 A A A R R R .52 .34 .32 R R R R R .25 .22 .23 .20 .18 42

Table 2

Listing of Observed and Calculated Structure Factors

tL lc 1 Indices of plane sin © 0 is the Bragg angle Fo Observed value of structure factor

Fc Calculated value of structure factor including all atoms and an isotropic temperature factor correction. 43 Tobt* 2 (a) h k 1 sin & F 0 F 0

0 0 2 • 070 47.3 - 36.5 0 0 4 .165 69.0 - 78.8 0 0 6 .245 44.8 45.5 1 0 1 .070 15.8 10.8 1 0 3 .136 44.8 - 35.1 1 0 5 .222 14.0 11.0 1 0 7 .293 7.4 - 9.6 1 0 9 .372 7.0 - 6.6 1 0 11 .458 15.3 8.6 1 0 13 .542 9.4 - 10.7 2 0 0 .144 13.0 4.9 2 0 2 .166 18.8 - 15.4 2 0 4 .223 19.0 25.4 2 0 6 .286 21.1 24.4 2 0 8 .360 24.0 - 26.6 2 0 10 .444 4.6 5.4 2 0 12 .516 9.4 13.4 2 0 14 .596 6.8 - 4.8 3 0 1 .228 15.9 - 21.8 3 0 5 .301 21.6 21.2 3 0 7 .364 13.0 - 21.6 3 0 9 .432 9.1 - 11.2 3 0 11 .506 12.0 14.0 3 0 13 .581 3.2 - 3.4 4 0 0 .298 21.0 25.1 4 0 2 .302 6.3 - 4.9 4 0 4 .337 4.1 - 5.3 4 0 6 .384 11.8 12.1 4 0 8 .448 10.0 .7 5 0 1 .372 5.9 6.1 5 0 3 .388 9.0 - 13.8 6 0 4 .437 2.2 - 1.6 7 0 1 .494 2.3 .5 0 2 0 .085 69.7 - 62.1 0 2 2 .124 45.8 39.3 0 2 4 .198 21.4 22.9 0 2 6 .265 28.6 - 25.6 0 2 8 .345 20.7 19.1 0 2 12 .500 4.8 - 3.7 0 2 14 .582 9.4 4.4 1 2 1 .130 5.2 .6 1 2 3 .177 7.7 - 1.3 1 2 5 .242 31.8 - 31.6 1 2 7 .313 10.4 12.4 1 2 • 9 .390 7.1 5.5 1 2 11 .470 18.2 - 17.3 44 Table: Z (b) h k 1 sin 0 F0 Fc

1 2 13 .550 4.1 6.0 2 2 0 .184 35.6 - 31.6 2 2 2 .200 29.1 27.4 2 2 4 .244 8.3 13.1 2 2 6 .305 21.8 - 18.6 2 2 8 .372 18.4 19.8 2 2 12 .530 3.3 - 3.6 2 2 14 .607 4.1 3.4 3 2 1 .248 12.5 - 18.1 3 2 3 .270 15.1 15.8 3 2 5 .318 12.3 - 10.2 3 2 9 .442 2.0 .9 3 2 11 .513 6.7 - 5.0 3 2 13 .590 4.9 4.9 4 2 0 .315 20.3 - 23.2 4 2 2 .322 8.3 12.3 4 2 4 .351 9.8 17.0 4 2 6 .395 8.4 - 7.4 5 2 1 .390 2.1 .4 5 2 5 .428 3.2 - 8.3 6 2 0 .454 6.9 12.6 6 2 4 .478 5.4 - 8.3. 6 2 12 .663 5.3 - 3.6 0 4 0 .200 59.3 57.2 0 4 2 .224 23.8 - 18.1 0 4 4 .268 8.8 - 11.3 0 4 6 .322 27.9 28.3 0 4 8 .392 14.7 - 8.8 0 4 12 .536 3.8 4.4 1 4 3 .256 18.2 - 13.4 1 4 5 .305 18.8 16.6 1 4 7 .364 9.9 - 14.8 1 4 9 .432 8.6 - 8.3 1 4 11 .506 13.6 11.4 1 4 13 .582 6.9 - 7.0 2 4 0 .255 34.7 31.7 2 4 2 .267 14.0 - 12.6 2 4 6 .358 19.0 20.7 2 4 8 .417 12.7 - 10.6 2 4 10 .482 2.2 1.9 2 4 12 .558 5.7 5.7 2 4 14 .628 2.9 - 1.8 3 4 1 .308 4.6 4.7 3 4 3 .326 16.0 - 18.0 3 4 5 .367 7.5 4.1 45 'Tabic 2 (c) h k 1 sin 6 F0 f c

3 4 7 .413 2.9 3.2 3 4 9 .454 4.8 _ 3.4 3 4 11 .548 7.2 2.9 3 4 13 .617 4.5 — 5.6 4 4 0 .366 18.6 23.6 4 4 2 .370 4.4 — 4.3 4 4 4 .396 5.2 — 8.4 4 4 6 .436 7.8 10.1 5 4 1 .429 2.3 — 3.6 6 4 Q .487 2.6 — 6.9 6 4 4 .510 2.7 8.9 0 6 0 .305 56.6 — 58.5 0 6 2 .318 19.6 22.0 0 6 4 .352 25.4 36.0 0 6 6 .396 17.2 — 18.9 0 6 8 .456 4.4 - 3.4 1 6 1 .318 9.8 — 12.2 1 6 3 .343 16.1 12.4 1 6 5 .380 11.8 — 12.8 1 6 7 .428 2.3 1.0 1 6 9 .488 4.0 ,7 1 6 11 .554 9.0 — 7.3 1 6 13 .621 6.1 5.7 2 6 0 .344 6.9 • 1.7 2 6 2 .354 11.9 14.4 2 6 6 .425 10.4 — 9.3 2 6 8 .476 15.4 19.1 2 6 12 .603 4.8 — 7.6 3 6 5 .433 13.4 - 16.0 3 6 7 .476 6.9 9.8 3 6 9 .530 6.5 4.6 3 6 11 .594 8.4 - 11.0 4 6 0 .432 8.2 - 9.7 4 6 2 .434 5.0 7.1 4 6 4 .458 3.4 6.8 4 6 6 .491 5.0 - 4.4 6 6 1 .482 4.4 - 6.9 5 6 3 .500 4.8 5.4 0 8 0 .408 15.8 20.8 0 6 2 .419 7.2 - 8.4 0 8 6 .480 9.5 13.4 0 8 8 .529 8.8 6.4 1 8 1 .42$. 6.6 mm 2.4 46 Table Z (sD h k 1 sin 0 *o *0

1 8 3 .437 7.9 - 6.4 1 8 5 .468 10.4 9.2 1 8 7 .508 5.2 - 8.5 1 8 3 .547 4.2 - 4.8 1 8 11 .618 6.8 7.3 1 8 13 .683 5.1 - 4.2 2 8 0 . 438 15.4 16.6 2 8 2 .447 6.4 - 6.4 2 8 6 .504 8.9 10.7 2 8 8 .548 6.4 - 4.6 3 8 1 .468 3.2 4.4 3 8 3 .482 8.3 - 10.6 3 8 5 .510 3.3 .9 3 8 9 .601 3.1 .5 4 8 0 .510 8.7 12.7 4 8 2 .508 2.7 - 2.5 4 8 4 .532 2.5 - 5.5 4 8 6 .558 3.0 5.6 0 10 0 .511 12.3 - 13.7 0 10 2 .523 5.1 7.8 0 10 6 .573 10.4 - 7.0 0 10 8 .603 4.1 3.6 0 10 10 .681 3.5 1.2 1 10 3 .533 4.5 • 2.1 1 10 5 .568 5.5 - 7.0 1 10 11 .692 5.2 - 5.5 2 10 0 .538 5.5 - 6.0 2 10 2 .544 3.5 6.1 2 10 6 .592 4.0 - 5.0 3 10 3 .573 4.5 2.8 3 10 5 .600 2.7 - 3.3 3 10 7 .622 3.3 .2 4 10 0 .592 4.6 - 6.6 0 12 0 .617 10.1 16.3 0 12 6 .663 3.2 6.8 1 0 2 .100 22.2 - 22.4 1 0 4 .175 7.2 7.5 1 0 8 .335 1.8 - 1.2 2 0 1 .151 49.1 - 52.5 2 0 3 .192 10.9 - 17.7 2 0 5 .259 25.7 30.7 2 0 7 .317 6.5 - 3.4 3 0 2 .235 14.3 - 12.2 47 T a b le Z fe) h 1 sin 0 F 0

3 0 4 .273 13,7 12.4 3 0 6 .331 6.5 — 6.8 3 0 10 .470 7.5 4.4 3 0 12 .543 8.1 — 6.9 4 0 1 .299 14.5 — 10 ^0 4 0 3 .319 8.2 14.5 4 0 5 .362 4.7 2.7 4 0 7 .410 18.7 — 20.4 4 0 9 .470 9.9 11.9 4 0 13 .612 6.6 — 7.5 5 0 4 .397 11.7 8.1 5 0 6 .441 16.4 — 21.8 5 0 10 . 550 ' 11.5 14.0 5 0 12 .616 7.3 — 9.2 6 0 1 .470 16.7 — 17.0 6 0 5 .485 10.0 13.2 6 Q 7 .528 11.1 — 7.0 7 0 2 .521 12.2 — 14.5 7 0 4 .538 9.4 6.8 8 0 1 .598 7.3 — 7.8 1 2 2 .146 37.0 — 45.6 1 2 6 .274 23.0 28.5 1 2 10 .432 10.1 — 13.6 1 2 12 .512 6.2 5.8 2 2 1 .186 11.1 11.5 2 2 3 .218 11.5 — 9.4 2 2 5 .273 5.4 — 5.2 2 2 7 .336 14.2 14.7 2 2 9 .412 7.0 — 6.9 3 2 2 .258 20.3 19.9 3 2 4 .294 14.1 - 12.6 3 2 6 .348 3.9 1.1 3 2 10 .509 4.3 — 1.0 3 2 12 .552 6.4 5.8 4 2 1 .318 28.5 30.4 4 2 5 .370 17.5 - 20.7 4 2 7 • 424 11.1 9.9 4 2 9 .482 4.4 .8 5 2 2 .392 7.4 2.9 5 2 4 .417 10.6 - 9.8 5 2 6 .454 10.5 10.8 5 2 10 .559 7.1 - 7.1 5 2 12 .624 7.3 7.0 6 2 1 .460 10.7 13.1 6 2 3 .467 3.2 - 2.6 48 Table 2 (f) h k 1 sin 0 Fo F c

6 2 5 .498 6.4 8.0 6 2 7 .536 13.4 9.2 6 2 9 .584 6.4 — 3.0 7 2 2 .534 6.0 2.2 7 2 4 . 550 10.0 — 5.0 7 2 6 .579 4.9 5.2 7 2 10 .669 5.9 — 3.8 8 2 1 .600 4.7 4.7 1 4 2 .235 18.0 23.6 1 4 4 .272 3.5 2.0 1 4 6 .330 13.7 — 19.7 1 4 10 .468 7.4 10.6 1 4 12 .543 3.5 — 4.7 1 4 14 .637 4.0 — 3.1 2 4 1 .260 11.7 — 11.7 2 4 3 .285 5.9 5.5 2 4 3 .329 5.8 6.0 2 4 7 .385 13.2 — 11.1 2 4 9 .451 5.4 4.8 2 4 13 .613 3.3 — 2.8 3 4 2 .316 14.9 — 15.2 3 4 4 .347 12.5 10.4 3 4 6 .390 1.68 — 1.5 3 4 10 .528 4.7 1.0 3 4 12 .582 5.9 — 5.0 4 4 1 .365 22.2 — 23.2 4 4 5 .414 11.7 15.5 4 4 7 .463 9.6 — 8.9 5 4 2 .432 5.2 — 1.5 5 4 4 .458 10.0 8.0 5 4 6 .490 7.8 — 10.0 5 4 10 .591 7.1 6.6 5 4 12 .650 6.6 — 6.4 6 4 1 .493 10.3 — 11.5 6 4 3 .499 2.4 1.9 6 4 5 .525 3.4 7.4 6 4 7 .568 9.3 — 7.6 6 4 9 .616 5.0 2.2 7 4 2 .565 4.9 — 2.7 7 4 4 . 581 7.6 4.3 8 4 1 .628 4.2 — 4.4 8 4 3 .635 6.0 - 1.4 1 6 2 . 331 5.4 8.3 1 6 4 .361 2.7 — 4.2 1 6 8 .459 4.2 .7 49 Table 2(g) h k 1 s i n © *0 S’c

1 6 12 .579 3.1 1.2 2 6 1 . 346 17.5 21.8 2 6 5 .400 9.9 _ 15.8 2 6 7 .447 2.7 2.3 2 6 13 .653 4.2 — 2.5 3 6 2 .391 7.1 7.2 3 6 4 .414 7.7 — 7.5 3 6 6 .453 4.4 4.0 3 6 10 .560 3.0 _ 2.5 3 6 12 .623 5.8 4.8 4 6 1 .431 8.9 6.3 4 6 3 .447 5.6 — 8.0 4 6 5 .472 3.3 — 1.7 4 6 7 .514 12.3 12.7 4 6 9 .564 5.8 — 7.5 4 6 13 .682 3.0 5.5 5 6 4 .510 8.3 — 5.1 5 6 6 .540 10.5 14.2 5 6 10 .632 6.2 — 9.8 5 6 12 .686 5.0 6.7 6 6 1 .544 10.8 11.9 6 6 5 .578 4.8 — 8.7 6 6 7 .609 4.7 4.6 7 6 2 .610 7.7 9.7 7 6 4 • 626 5.2 — 4.3 7 6 6 .653 4.0 — 3.3 8 6 1 .652 4.1 6.1 1 8 2 .429 3.9 11.3 1 8 6 .487 7.3 — 11.9 1 8 10 .581 3.2 8.0 2 8 1 . 440 3.6 - 4.0 2 8 3 .455 3.4 4.0 2 8 7 .524 4.2 - 6.7 3 8 2 .477 4.8 - 8.0 3 8 4 .496 6.0 5.3 3 8 6 .528 3.7 - .1 3 8 8 .574 3.1 .2 4 8 1 .509 12.6 — 13.7 4 8 5 .547 6.4 10.1 4 8 7 .583 5.9 - 3.8 5 8 2 .560 4.2 • 1.3 5 8 4 .554 6.0 4.8 5 8 6 .604 3.3 - 5.0 5 8 12 .731 3.3 — 4.1 6 8 1 .609 5.1 - 6.1 50 'Table Z (h) h sin © F0 Fc

6 8 5 .636 3.4 4.0 7 8 4 .679 5.2 2.4 1 10 6 .579 3.0 5.8 2 10 5 .580 3.0 _ 2.4 3 10 2 .567 4. 3 4.6 3 10 4 .583 3.0 — 3.2 4 10 1 .596 5.1 7.4 4 10 5 .625 3.5 5.5 4 10 7 .653 3.5 3.7 5 10 6 .680 3.6 4.7 0 1 2 .094 70.6 60.1 0 1 4 .174 32.2 25.7 0 1 10 .415 9.7 1.9 0 1 12 .498 16.3 — 9.8 O 1 14 .572 7.9 9.2 1 1 1 .092 74.4 — 67.7 1 1 5 .224 34.2 34.4 1 1 7 .301 24.8 — 21.8 1 1 9 .382 8.0 3.9 1 1 13 .549 6.6 — 2.6 2 1 2 .171 15.7 26.8 2 1 4 .225 18.0 14.8 2 1 6 .294 28.6 — 33.0 2 1 10 .442 16.3 18.2 2 1 12 .518 12.3 — 11.9 3 1 1 .234 15.3 — 16.2 3 1 3 .254 10.2 9.9 3 1 5 .305 7.4 7.7 3 1 7 .364 16.5 - 17.3 3 1 9 .436 10.0 8.3 3 1 13 .585 3*2 — 4*9 4 1 2 .309 10.3 — 12.5 4 1 4 .348 8.7 8.3 4 1 12 .533 5.6 - 3.3 5 1 1 .376 7.0 — 8*2 5 1 3 .421 1.9 - 1.4 5 1 5 .417 4*4 5.7 5 1 7 .482 3.2 - 1.4 5 1 9 .584 5*6 - .7 0 3 2 .167 6*4 - 15.4 0 3 4 .225 22.5 17.4 0 3 6 .289 28.4 30.0 0 3 10 .438 16.7 - 16.8 51 Table ZO) 12 k 1 sin 0 *c

1 3 1 .170 41.4 31.9 1 3 3 .212 11.8 _ 12.3 1 3 5 .270 16 • 5 — 15.7 1 3 7 .336 28.0 25.2 1 3 9 .406 10.3 _ 10.5 1 3 13 .562 6.6 6.3 2 5 2 , .230 13.3 10.1 2 3 4 .270 19.7 — 16.4 2 3 6 .327 11.2 12.3 2 3 10 .465 9.8 — 8.0 2 3 12 .538 10.9 8.4 2 3 14 .608 4.2 — 3.1 3 3 1 .274 34.2 39.2 3 3 3 .292 5.0 11.2 3 3 5 .340 19.8 — 26.7 3 3 7 *393 9.0 5.0 3 3 9 .443 1.3 5.4 4 3 2 .342 11.8 16.8 4 3 4 .368 7.5 — 8.4 4 3 6 .411 4.6 - 3.4 4 3 12 .597 2.7 2.4 5 3 1 .410 2.2 — 3.1 5 3 3 .406 1.8 — 7.5 5 3 7 .505 3.1 6.3 6 3 2 .478 7.1 — 11.9 6 3 6 .527 3.8 10.2 0 5 2 .265 31. 0 — 34.7 0 5 4 .306 20.7 18.6 0 5 6 .356 3.3 2.5 0 5 10 .484 6.2 — .2 0 5 12 .556 10.6 — 7.1 1 5 1 .266 36.8 — 36.3 1 5 5 .339 19.5 21.9 1 5 7 .394 16*4 - 14.6 1 5 9 .457 7.1 2.2 2 5 4 .339 12.6 11.0 2 5 6 .386 17.3 — 23.1 2 5 10 .507 10.7 14.2 2. 5 12 .576 9.7 — 9.2 3 5 1 .344 8.6 - 9.7 3 5 3 .358 7.1 7.7 3 5 5 .396 3.5 4.0 3 5 7 . 444 11.8 — 12.8 3 5 9 .502 7.4 7.0 52 Tabic 2. (j ) ft b. k 1 sin 0 o

5 5 13 .642 3.4 4.4 4 5 2 .400 5.7 — 8.0 4 5 4 .422 6.2 6.1 4 5 12 .621 2.8 2.8 5 5 1 .451 5.7 — 6.6 5 5 5 .490 3.9 4.9 0 7 2 .370 13.3 18.1 0 7 4 .400 12.9 — 12.5 0 7 6 .436 3.6 1.5 O 7 10 .548 4.7 — 1.2 0 7 12 .612 8.2 6.0 1 7 1 .367 21.0 22.5 1 7 5 .422 9.8 — 13.8 1 7 7 .468 11.4 11.1 1 7 9 .522 4.0 — 2.1 2 7 2 .392 2.7 4.4 2 7 4 .422 10.7 — 8.2 2 7 6 .463 10.2 14.7 2 7 10 .568 9.9 — 9.6 2 7 12 .631 4.4 7.0 3 7 1 .426 8.2 9.2 3 7 3 .445 3.9 — 3.4 3 7 5 .471 4.0 — 4.9 3 7 7 .512 9.1 8.2 3 7 9 .562 3.0 — 3.6 4 7 2 .473 4.5 6.4 4 7 4 .494 5.0 — 4.3 0 9 4 .498 7.9 6.3 0 9 6 .528 10.8 - 10.2 0 9 8 .573 2.6 2.1 0 9 10 .622 8.2 7.0 0 9 12 .678 5.1 — 6.4 1 9 1 .468 10.0 — 10.3 1 9 5 .512 5.1 5.6 1 9 7 .552 9.3 — 9.2 1 9 9 .601 4.1 3.9 2 9 2 .493 4.9 — 3.8 2 9 4 .512 7.1 5.9 2 9 10 .657 2.9 3.0 3 9 1 .516 10.3 — 13.3 3 9 5 .555 5.6 10.2 3 9 7 .588 4.0 — 1.5 4 9 2 .549 2.9 — 6.6 0 11 2 .573 9.1 9.5 O 11 4 .597 5.7 - 4.7 53 Table 2 (Ac) h k 1 sin 0 So Sc

0 11 8 .600 3.5 .5 0 11 10 .681 3.5 1.4 1 11 1 .573 7.4 9.4 1 11 7 .638 4.0 4.2 z 11 4 .611 3.1 2.7 2 11 6 .638 2.8 8.1 1 1 0 .092 17.7 15.0 1 1 2 .119 9.8 8.9 1 1 6 .260 8.1 — 8.5 1 1 8 .340 4.4 5.1 1 1 10 .420 1.7 .3 2 1 1 .157 8.9 — 11.6 2 1 3 .196 14.7 16.1 2 1 5 .259 7.9 -- 5.0 2 1 11 .480 5.5 -- 3.5 2 1 13 .563 4.5 4.8 3 1 0 .223 41.6 -- 44.1 3 1 2 . 241 17.3 16.2 5 1 4 .278 13.0 18.8 3 1 6 .336 15.9 — 17.8 3 1 8 .395 6.8 3.4 4 1 1 .302 2.3 4.8 4 1 3 .324 8.3 1.7 4 1 5 .360 14.7 — 17.7 4 1 7 .414 3.2 12.3 4 1 9 .471 3.4 5.9 4 1 11 .544 11.3 — 11.7 4 1 13 .617 5.8 4.2 5 1 0 .376 14.3 — 11.7 5 1 2 .381 12.9 11.8 5 1 6 .444 14.0 - 12.8 5 1 8 .497 14.7 13.9 5 1 12 .620 3.9 — 6.6 6 1 1 .451 3.9 - 3.7 6 1 3 .462 10.3 8.2 6 1 5 .491 10.1 — 7.1 6 1 7 .549 4.1 2.9 6 1 11 .634 5.0 — 5.1 7 1 0 . 518 17.4 — 19.4 7 1 2 .528 6.0 6.6 7 1 4 .551 5.8 10.1 7 1 6 .577 8.6 8.2 8 1 3 .602 5.5 3.4 54 7 able Z(L) h k 1 sin © So Fc

1 3 0 .170 35.7 43.1 1 3 2 .188 4.0 - — 3.9 1 3 4 .236 27.3 35.5 1 3 6 .296 3.0 2.2 1 3 8 .370 17.0 — 23.6 1 3 10 .447 3.2 4.0 1 3 12 .524 6.9 11.2 2 3 1 .218 13.8 — 15.6 2 3 3 .244 3.8 10.9 2 3 5 .298 19.0 19.0 2 3 7 .357 11.8 — 15.8 2 3 9 .428 5.7 — 6.7 2 3 11 .502 9.3 11.9 2 3 13 .572 4.0 — 1.9 3 3 0 .270 41.4 43.9 3 3 2 .283 14.1 — 14.3 3 3 4 .315 14.7 — 21.9 3 3 6 .365 16.9 16.6 3 3 8 .422 4.7 * 4 4 3 1 .340 11.3 13.1 4 3 3 .356 20.4 — 19.4 4 3 5 .390 5.8 4.2 4 3 11 .563 6.0 2.1 4 3 13 .634 5.7 6.6 5 3 0 .401 20.5 22.6 5 3 2 .409 10.0 — 11.1 5 3 4 .428 2.9 — 7.8 5 3 6 .466 12.2 13.1 5 3 8 .516 8.9 — 5.5 5 3 10 • 568 3.4 — 1.0 6 3 3 .484 7.6 — 3.0 6 3 5 .512 10.5 9.2 6 3 7 .544 5.7 — 6.6 6 3 9 .590 4.1 — 3.2 6 3 11 .647 10.4 7.5 7 3 0 .539 10.6 6.9 7 3 2 .544 5.0 — 5.4 7 3 6 .598 5.7 5.9 7 3 8 .628 5.6 — 6.2 8 3 3 .617 3.3 — .3 1 5 0 .272 9.4 — 11.0 1 5 2 .281 4.8 5.2 1 5 4 .303 2.6 4.2 1 5 6 .362 4.6 - 6.0 2 5 1 .300 7.1 — 9.3 55 T a b le Z (m) h k 1 sin S *0

2 5 3 .322 10.3 12.1 2 5 5 .361 5.3 — 3.0 2 5 11 .546 3.8 — 1.7 3 5 0 .340 22.1 — 26.5 3 5 2 .350 10.3 10.7 3 5 4 .375 7.9 11.5 3 5 6 .419 10.3 — 12.2 3 5 8 .471 6.3 2.5 4 5 3 .412 6.0 .5 4 5 5 .442 11.5 — 13.2 4 5 7 .485 6.0 10.1 4 5 11 .599 9.2 — 9 .8 5 5 0 .451 9.8 — 7.5 5 5 2 .459 9.4 8.2 5 5 6 .510 9.6 — 9.1 5 5 8 .560 11.4 10.8 6 5 3 .528 6.8 6.0 6 5 5 .552 7.9 4.8 7 5 0 .580 11.7 _ 15.4 7 5 2 .584 4.5 5.0 8 5 3 .653 5.1 2.8 9 5 0 .709 4.2 — .1 1 7 0 .369 5.1 — 3.4 2 7 3 .409 5.2 — 6.2 2 7 5 .440 3.5 3.6 2 7 11 .600 2.8 2.3 3 7 0 .427 13.7 18.5 3 7 2 .433 6.1 - 7.4 3 7 4 .452 3.4 — 8.8 3 7 6 .490 8.8 9.0 3 7 8 .537 4.2 — 1.1 4 7 3 .484 6.7 — 1.9 4 7 5 .510 7.0 8.2 4 7 7 .547 3.2 — 6.2 4 7 11 .651 5.4 6.6 5 7 0 .518 10.4 6.5 5 7 2 .523 6.5 — 6.1 5 7 4 .552 4.3 1.1 5 7 6 .572 7.7 6.8 5 7 8 .612 6.2 - 7.6 6 7 3 .586 5.6 — 3.8 6 7 5 .608 5.6 4.0 7 7 0 .633 7.4 11.0 2 9 5 .526 5.2 - 6.8 56 T a b le 2 (tn) k 1 sin © F 0 Fc

9 9 .478 3.8 5.2 9 0 .517 11.4 - 14.7 9 2 .522 4.6 5.0 9 4 .538 2.9 8.2 9 6 .569 4.6 - 6.4 9 1 .566 4.3 -4.6 9 3 *568 7.7 7.0 9 0 .599 7.1 - 8.9 9 6 .643 4.8 - 5.7 9 5 .671 5.2 - 4.3 11 0 .606 5.7 7.8 11 3 .636 3.2 1.3 57

IV. DISCUSSION OF THE STRUCTURE

A complete list of the parameters of all atoms in a unit cell of crystalline LiC104 as determined in this work is given in the Appendix. An illustration of the arrangement of the atoms in a unit cell is given in Figure 4. A collection- of bond lengths is listed in Table 5. Attention is called to the chlorine to oxygen bond distances. Of these the most reliable are those designated as Qi-Cl and 02-Cl because the parameters of Oii 02, and Cl are based on a Fourier section utilising all O available intensity data. These bond lengths are 1.46 A O and 1.50 A, respectively; these values may be in error by O about 0.03 A so that the difference is not necessarily significant. Therefore the Cl-0 bond is assigned the length 1.48 - 0.03 A. The uncertainty (± 0.06 A) in the O distance (1.43 A) measured for 03-Cl and 04-Cl is greater than that for either Oi-Cl or 02-Cl due to the fact that the parameters for 03 and 04 are computed from two compo­ nents each of which is measured from Fourier projections utilizing zone data only. For Mg(C104)2•6H20, C. D. West O o determined Cl-0 bond lengths of 1.46 A and 1.50 A in good agreement with the results obtained here. L. Pauling 24 has recently discussed bond distances in complexes such as the perchlorate ion. He points out that the sum of the J o

O F IG U R E A -

Qo

Unit cell viewed in —bo d^ection

o o o o CO o CO o o cs o o A CD o O o o o o ...... ------o — - o 'Co­

if cell viewed in —aQ direction

O O x y g e n O C h lo rin e o L it h iu m 59

Table 3 Inter-atomic Distances on the Basis of Parameter Set Number Nine

A. Intra-molecular Distances

- 02 2.41 A °2 — °3 2.40 Oi - Cl 1.46 A °£ - o4 2.40 o Oi - Li 2.17 A °3 — 04 2.37 - “ °3 2.34 1 °3 Cl 1.43 O Oi - 04 2.34 A o4 — Cl 1.43 Og - Cl 1.50 1 °3 - Li 2.00 o

Og - Li 2.38 A o4 — Li 2.00 £>0 {>0 0 }t> i>0 [>0 ft>0 *t=*0

B. Some Inter-molecular Oxygen to Oxygen Distances

4.56 A 3-i:L A 2.62 A 5.21 A 2.90 A 5.73 X 3.00 I 60

single bond radii of Cl and 0 is 1.73 A and that this can O he shortened to 1.68 A by applying a correction due to Schomaker and Stevenson^^ for partial ionic character of the bond. For resonance involving one sigma bond and two pi bonds giving rise to multiple bond character in the Cl-0 bond Pauling makes use of an empirical equation relating interatomic distances and bond number to arrive O at a bond length of 1.48 A, Since with care it is possible O to measure bond lengths to at least 0.01 A it would be of interest to refine the parameters of LiC104 by use of three dimensional sections to provide a better experi­ mental value for the Cl-0 distance. It is concluded that the configuration of the perchlorate group is tetrahedral, as expected. Within the reliability of the parameters determined for the oxygens the perchlorate group has the configuration of a regular (undistorted) tetrahedron. The experimental value for the Oi-Cl-C^ bond angle is 109°3/ i 5°. The location of the lithium ions at the symmetry centers designated by set (c) of special positions results in the lithium-oxygen distances listed in table 4. O Assuming a van der Waal’s radius for oxygen of 1.40 A and an ionic radius for lithium of 0.60 A° (see Pauling 4- ) a + O Li -0 distance would be expected to be 2.00 A. The actual o o o measured distances are 2.17 A, 2.38 A, and 2.00 A. The 61

lack of a single, short, directed lithium-oxygen distance rules out a covalent bond £or lithium, arid it may be con­ cluded that the lithium is ionic. Each lithium ion is ® O surrounded by two oxygens at 2.17 A, two oxygens at 2.00 A and two oxygens at 2.38 A giving a somewhat distorted octahedral arrangement of oxygens about each lithium ion (see Figure 5). The perchlorate tetrahedra are knitted together at corners by lithium ions to form a three- dimensional network. Comparison of the structure of anhydrous lithium perchlorate as determined here and the structure of lithium borohydride as determined by E. P. Meibohm reveals that both crystals have the symmetry of the space group Pcmn. However, the similarity ceases there and the atomic para­ meters differ— especially those of the lithium ions. In lithium perchlorate the lithium ions lie at symmetry centers (midway between mirror planes) whereas in lithium boro­ hydride they lie in the mirror planes. It must be con­ cluded that the crystals of LiBH4 and LiC104 are not isomorphous. The literature contains no case of an ABX4 compound which is isomorphous with LiC104 . The structures of certain crystals of the type ABX4 in which A has a small radius are known. One of these, BPQ4 , has a tetragonal unit cell containing two molecules. The space group is Ij. The coordination number for both 62

FIGURE 5

3.00 A

2 .90 A

/*-\ 2J7A 2.38A / / ■2.90 A 3.00A \r-2.00A\

Arrangement of Oxygens Around a Lithium Ion 65 boron and phosphorus is four suggesting covalent bonding, a type of structure different from the ionic structure found for LiC104. Lithium perchlorate is also unlike an­ hydrite (CaS04) in structure. Anhydrite has tetrahedral sulphate anions and an orthorhombic unit cell having, how­ ever, the symmetry of space group Bbmn* addition, the coordination number of the calcium ions is found to be eight. Both potassium perchlorate (the low temperature modification) and barium sulphate are of a class of crystals which have the symmetry of the same space group as LiC104. These crystals are usually assigned to Pnrnfl which becomes f n m n by an axial transformation. There is some disagreement about the parameters for these crystals. The most reliable structural investigation to date (that for low KC1G4 ) assigns an orthorhombic unit cell containing four molecules with the potassium ions lying in the mirror planes. The structure is not isomorphous with that of LiC104. The oxygen coordination of the potassium ions is not clear cut. The structures of LiBH4 and low KC104 are rather similar. For low KC104 (space group Pnma) tiie atomic parameters are:

x y z 01 0.075 0.250 0.689 0 0.175 0.250 0.550 0 0.922 0.250 0.606 0 0.085 0.042 0.819 K+ 0.192 0.250 0.167 64

For LiBH4 (apace group PCmn) ^lie parameters are:

x y z B 0,070 0.250 0.661 H 0.203 0.250 0.520 H 0.886 0.250 0.589 H 0.096 0.000 0.768 Li+ 0.086 0.250 0.304

Due to the interchange of the glide planes (Pnma — »- ^cmn) the resulting packing of the other three molecules in the unit cell is different in the two cases. This, perhaps, fortuitous correspondence of parameters is intriguing if not amazing. The sulphate ion and the perchlorate ion are very o 2 4 close to the same size. The 0-0 distances are 1.50 A o and 1.48 A respectively. The ionic crystal radius of Mg++ is 0.65 A 4 compared to 0.60 A for Li+. The oxygen coordination number for Mg++ is six. In view of these facts it would not be surprising to find that MgS04 is isomorphous with LiC104 . Unfortunately, a structure for MgS04 has not been reported in the literature. In the case of the trihydrate of lithium perchlorate the lithium ions are surrounded octahedrally by six water molecules. The lithium ions and water molecules are arranged in columns in the sequence -3HS0-Li-3H20-Li-. The perchlorate ions are packed between these columns and held in position by hydrogen bonds. In the anhydrous salt 65 i the perchlorate groups are packed between columns of lithium ions and held in position directly by the lithium ions. The lithium ions are surrounded octahedrally by oxygens in both structures. The crystals have quite different symmetry, however. Lithium perchlorate trihydrate has a hexagonal unit cell with the symmetry C.mc . 0 66

SUMMARY

Single crystal fragments of anhydrous lithium perchlorate have been prepared and Weissenberg and normal- beam X-ray photographs have been taken. It has been shown that anhydrous lithium perchlor­ ate crystals have a four molecule unit cell of symmetry

Pp.mn with the dimensions &0 = 4.836 1, bQ = 6.926 A, and • cQ = 8.659 A. A set of parameters for the lithium, oxygen, and chlorine atoms have been determined which account quite well for the observed intensities. The perchlorate group is found to have the expected tetrahedral symmetry. The Cl-0 bond length has been specified as 1.48 - 0.03 A. The lithiums have been demonstrated to be ionic and to be surrounded approximately octahedrally by six oxygens. The structure of lithium perchlorate is not iso­ morphous with any of the known structures for ABX4 type compounds. 67

VI. BIBLIOGRAPHY.

1. Wyckoff, R. W. G., "Crystal Structures". New York: Interscience Publishers, Inc., (1951) Vol. II. 2. "Struktur-Bericht", A Photo-Lithoprint Reproduction. Ann Arbor: Edwards Brothers, Inc., (1943). 3. Meibohm, E. P., Ph. D. Dissertation, The Ohio State University,(1947). 4. Pauling, L., "The Nature of the Chemical Bond". Ithaca, New York: Cornell University Press. 1940. 5. West, C. D., Z. Krist., 91, 480 (1935). West, C. D., Z. Krist, 88, 198 (1934). 6. Booth, H. S., "Inorganic Syntheses". New York: McGraw- Hill Book Company, Inc. (1939) Vol. I, 1. 7. Richards, T. W. and Willard, H.H., J. Am. Chem. Soc., 3 2 . 4 (1910). 8. Potilitzin, A., Chemisches Central-Blatt, 1_, 72 (1890). 9. Buerger, M. J., "X-Ray Crystallography". New York: John Wiley and Sons, Inc., (1942). 10. Wood, E. A., Phys. Rev., 72, 436 (1947). 11. Howells, E. R., Phillips, D. C., and Rogers, D., Acta Crystallographies, 2, (1949). 12. "Internationale Tabellen zur Bestimmung von Kristall- strukturen", Berlin: Gebruder Borntraeger, (1935)

Vol. II. 68

15. Buerger, M. J., "Numerical Structure Factor Tables". Baltimore: Waverly Press, Inc., (1941). 14. Bond, W. L . , J. App. Phys., 1£, 82 (1948). 15. Tuomi, D. T., Ph. D. Dissertation, The Ohio State University, (1952). 16. Harker, D. , Am. Mineral., 53, 749 (1948). 17. "Internationale Tabellen zur Bestimmung von Kristall- strukturen" , Berlin: Gebruder Borntraeger, (1935) Vol. I. 18. James, R. W., "The Optical Principles of the Diffraction of X-Rays", London: G-. Bell and Sons, Ltd. (1948). 19. Bragg, W. L. and Lipson, Z. Kristallogr. £5, 323 (1936). 20. Lonsdale, K. , "Structure Factor Tables". London: G. Bell and Sons Ltd. (1936). 21. Booth, A. D., "Fourier Technique in X-Ray Organic Structure Analysis". Cambridge: The University Press (1948). 22. Patterson, A. L. and Tunnel, G. , Am. Mineral., 27, 655 (1942). 23. Booth, A. D . , Proc. Roy. Soc., A, 188, 77 (1946). 24. Pauling, L. , J. Phys. Chem. , 56_, 361 (1952). 25. Schomaker, V. and Stevenson, D. P., J. Am. Chem. Soc., 63, 37, (1941). 69

VII. APPENDIX.

A. Layer Line Photograph Scale Factors.

In the Weissenberg method of photographing the reciprocal lattice a separate photograph is taken for each of several, layers of reciprocal lattice points. The ex­ posure time, X-ray intensity, and development conditions may be somewhat different for the different layers unless careful precautions are taken. Since quantitative pre­ cautions were not taken in this work the intensities of reflections measured on one layer photograph will not neces sarily be on the same scale as those measured on another layer photograph. In view of this fact a semi-empirical statistical method has been worked out to refer all measured intensity data to the same scale. This method depends on the fact that equi-inclination photographs of reciprocal lattice layers were taken for two different axes of rotation (the /Toi/ axis and the /Old/ axis). The thirteen photographs taken for the /Toi/axis of rotation were designated as the j set and the nine photographs taken for the i/0107’axis were called the i set. Examination of any member of set i and any member of set j showed that the pair of photographs selected have recorded some dif­ fraction spots corresponding to the same reciprocal lattice points. Eor these common spots the measured intensities 70

(d ) were summed for each of the pair of films selected. This was done for all combinations of pairs and then the definition was made that:

Z T t h - H±J ----- Z t lj

is the sum of all of the intensities of spots appearing on a selected member of set i which also appear on a selected member of set j.

Zdj is the sum of spot intensities on the j film.

The intensities ( ) correspond to the raw intensi­ ties (I) corrected for Lorentz and polariza­ tion factors ( - I where the I values were obtained by multiplying measured area and blackening factors.)

Next an array of Rj_j (9 x 13) was formed in which all Rj_j were assumed to be equally reliable. The following matrix lists all of the R^j terms inter-relating all of the photographs. Rij Matrix Tablet 4 sSet j

• a b c d e f g h i J k 1 m it i \

1 1.11 1.00 1.25 1.11 1.23 0.92 0.66 0.67 0.65 0.70 1.22 0.70 1.18

2 0.82 0.98 0.94 0.91 1.00 0.74 0.66 0.77 1.00 0.700.90 0.94 0.65

3 0.95 0.86 0.96 0.87 1.02 0.80 0.54 0.460.5 0.78 0.72 0.99 0.76

4 0.97 1.04 0.92 0.94 1.37 0.82 0.65 0.66 0.63 0.75 0.68 0.91 0.73

5 0.92 1.01 1.08 1.00 1.43 0.77 0.82 0.69 0.67 0.80 0.93 0.70 0.70

6 0.99 0.77 0.86 1.04 1.03 0.66 0.62 0.65 0.64 0.80 0.90 1.11 0.86

7 1.18 0.93 1.04 1.03 1.30 0.79 0.81 0,60 0.63 0.680.63 0.84 0.83

8 0.73 0.77 0.88 1.31 1.03 0.56 0.55 0.95 0.48 0.68 0.73 0.65 0.83

9 1.31 0.48 0.77 0.78 1.06 0.71 0.59 0.44 0.51 0.56 0.49 0.85 0.82 verage 1.00 0.87 0.97 1.00 1.16 0.75 0.65 0.66 0.64 0.72 0.80 0.86 0.82 Tiie average of each column was obtained (each column corresponding to a film of set j compared to each of the films of set i. These values were then used to set all j films to the same intensity scale. This resulted in a new set of Rij terms (called Rij' ) since each Rij term in a column is divided by .the average of the column of Rij values. Using the resulting array of Rij quantities the average value for each row was computed, the reciprocals calculated, and a normalizing factor applied so that the

/ / * // average value of all Rij (Rij ) would be equal to unity. // / The Rij values result from multiplying each row of Rij terms by the reciprocal of the average of the Rij quantities in the row. The correction factors are:

For set i For set j 1. .876 a. .998 2. .990 b. .871 3. 1.059 c . .968 4: • .983 d. .998 5. .950 e . 1.161 6. .997 f . .748 7. .965 g. .654 8. 1.074 h. .658 9. 1.178 i. .644 j. .718 k. .801 1. .857 m. .818

All of the tx measurements on a particular layer photograph were multiplied by the factor listed above for that photo­ graph to place all measured hd values on the same relative 73

scale*

B. The Structure Factor

12 The structure factor for the amplitude of the wave scattered by the unit cell in a direction defined by (h k 1) is:

I

or:

II

In these expressions fj is the structure factor for an atom at the point x, y, z (atomic coordinates in fractions of unit cell edges) and the summations are taken over all atoms in the unit cell. When the crystal has a center of sym­ metry (e.g. one belonging to space group Fnmr[) chosen as origin of coordinates, the sin terms vanish leaving:

Fhkl = Z cos 2rr (hx + ky + Iz) III

For a given crystal depends on (h k 1) only since fj depends on — , which is determined by (h k 1), A ’ Now for the space group Pcmn symmetry is 74- described by the eight general point positions:

1 1 ) x, y, z 5 ) 2 + x > J + y, 2 ) § - *, y. 1 ♦ * 6) X, y, z

3 ) x, 1 - y, s 7 ) 1 + X 2 * 1 - 1 1 1 _ _ 4) § - x, jg - y, 2 + 2 8) x,y, z

Then substitution of the about eight sets of coordinates into expression III and noting that cos(-0 ) = cos( + 0 ) yields the expression:

^hkl = Z Je c o s 2tT f hx + ky + lz^ +

2 cos 2rr|h(i - x) + ky + 1 (z + +

IV 2 cos 2TT fhx + k - y )+ lz^ +

2 cos 2TT I h (§ - x) + k (i - y) + 1. (z +

Use of the trigonometric identity:

cos o( + cos ^ = 2 cos |j- ( °< + ^ ) cos (<* - £ ) makes it possible to reduce IV to: is

Jhk-1 " 8 0 0 8 S7r [l* + ~ 4 T * ■ -■ J

oos 2TT [ky - ^ ] cos 2 7T [tix - h * 76 Computation of Structure Factors on International BusinessM a c h in e s

hkt ‘}(h+l)l sine j Foe. *,y, Z parameters £1 Fo) fa ] fo i fu s for OjCljOndLi

1 * . . l Manually punched on smsLrrhx; j cos Zirhx/ jetc I 3 M cards ~5~8& cards Obtained from tables for

for T8& hkl - Master deck Ibble all hjk,! and x, t y, ,z, \ Sorted into Four sets Table rrtamja fhj punched On (hr I) and k Oh 1.3 . M. card5 I E i / £ I I I 3CTT57T E7t = n h+kznI k» an k s ^h K= n c u • I Cx >*■-X .—-N ^ fl t: b fc

I T y- 4* 3tSZS de ta i I card s T i L« 0 3 — *■ hkl H i Li — Three Product F t v sefec ted of t and * ° * — ► hk < ici a — * Values rf trig, fane's trij- tunc *s O fo o — » obtained Sf 5 punc hed for each c ohS t?« eaah — * hkl to o — •* detail card !§-?w L ^ detail 'a r J (OS.6 *4- W£ — + hkl fo o |—►■

^ hkl fo o — ^

Products 5 urn meci L istinjs frach product m ultiplied algebraically prepared punched on Masher h*j four to for six heb Figs defat I cards* deck For each hkl 77

D. Expanded form of Fourier Section ( P v i „) \

( °° °° K/g i, z) - Fooo + s {2!%o0: COS SIT Hx -fZgmm (-1)

oooO / / »00 cc00 K /

+ c o s 2 t t L z j + 4 | ^ Z - ^HTrn cos 2TTHx (-1)I / !

H = 2n; K = 2n

OO , . r r (k - 1 ) / - Z.Z-FEKO sin 2TT Hx (-1) '2 + / f H = n; K - n

OO OO jr ZZ*O KL 003 3Tr:L2 I " 1) K = 2n: L » 2n

O O CO

ZZ^OKLt I sin STr Lz ‘-1* 2 K = n; L = 2n

00 00

FH ox, 003 2Tr Hx 003 27T^Z - 1 1 H + L = 2n

00 ad ^ y~ ^uoi, s^n srr ^ s^n 2Tr ■Lz / 1 H + L - n

( • ? ? K / + 8)/ ^1_FHKL 003 S7F ^ COS 27T Lz (“!) 2 ~ (K = 2n; H + L * 2n) 78

O O OO 3^n 2tt Hx sin 2ttLz (-1) K » 2n; H + L » n

f f

(K - 1} /_ ^ / fHKL ?in 2TrHx cos 2rrLz (-1) /2

(K = n, H + L - n) 79

E. Outline Plan of Structure Determination and Refinement.

1. Assignment of space group. 2. Specification of fifteen parameters to be determined to fix the structure. 3. Location of possible x and z coordinates for one chlorine by means of Patterson sections. 4. Location of reasonable x and a parameters for four oxygens by trial and error methods (comparison of calculated and observed F ’s). 5. Refinement of x and a parameters for the oxygens and chlorine by successive calculation of phase angles and preparation of Fourier projections ( CTxoz)• 6* The y parameters of two oxygens lying out of the mirror plane were first estimated by adjusting the y parameters to minimize the reliability factor R for (oko) reflections and refined by use of CT~Xy0 and O~0yZ Fourier project­ ions . 7. Further refinement of the x and z parameters for the two oxygens and the chlorine lying in the mirror plane was made by preparation of a Fourier section 8. A Fourier projection

, as coefficients to obtain a suggestion as to the lithium x and z parameters. 9. A reasonable y parameter for the lithium was determined 60

from packing considerations and verified by comparison of calculated to observed structure factors. 10. Finally structure factors were calculated on I.B.M. machines using the parameters found and were then compared with the observed structure factors. 81

Listing of parameters (set (9) )

0 .747, .250, .129 b o. os 1 i, 0 .753, .250, .629 2 * •g’* .247, .750, .571 0, 0, 1 2 .253, .750, .871 1 °> b 2

.041, .250, .182 °3 .178, .079 , .130 .459, .250, .682 .322, .079 , .630 .541, .750, .318 .678, .579, .370 .959, .750, .818 • 822, .579, .870

.047, .250, .351 o4 .178, .421, .130 .453, .250, .851 .322, .421, .630 .547, .750, .149 .678, .921, .570 .953, .750, .649 .822, .921, .870 82

ACKNOWLEDGMENT

To Professor P. M. Harris I am grateful for His patient counsel and constant interest during the course of this research. His friendly enthusiasm, wealth of ideas, and provision of excellent laboratory facilities have been great sources of encouragement to me. I wish to thank Mr. D. T. Tuomi for the use of some of his nomographs and Professor E. N. Lassettre for the opportunity of working on an Ohio State University Research Foundation project supervised by him. My appreciation is also due to Miss Joan Housholder for carrying out the International Business Machine calcula­ tions. Her cheerful cooperation saved me a great deal of labor.