1236 L. F. DAHL,T. CHIANG, P. W. SEABAUGH, AND E. M. LARSEN
(V) compound. Additional work designed to establish the composition of the tungsten(V) derivative was unsuccessful because of the difficulty of separation from the associated oxidation products. It is interesting to note, however, that the reduction was slowed in carbon tetrachloride and provided some evidence for one of the intermediates in the reduction of the hexachloride. The available evidence thus indicates that the reaction of WC16 with pyridine proceeds stepwise: W(V1) + W(V) + W(IV), or that W(V)
Inorganic Chemistry
is formed after initial reduction to W(1V) by the reaction W(IV) W(V1) = 2W(V). Evidence from the corresponding reactions of the niobium(V) halidesI0 indicated that pyridine behaved as a two-electron reducing agent, hence the latter path seems more likely.19
+
(19) NOTE ADDED I N PROOF.-Although the X-iray powder pattern data""2 for t h e halides 31x1( A 1 = Nb, T a , W ; X = C1, Br) have been indexed on the basis of a n orthorhombic unit cell, more recent evidence Irom single crystal work indicates t h e true unit cell is monoclinic. According t o a recent note [H. G. Schnering and H. Wohrle, Angere'. C h e m . , '76, 684 (1963) I, it was found from single crystal data t h a t SbCla is monoclinic with a = 12.32, b = 6.82, c = 8.21 and i3 = 134'.
a,,
CONTKIBLTIOS FROM
THE
DEPAWMENT 017 CIIEMIST~IY, 53706
~ N I V E R S I T I ' O F \t71SCONSIN, M A D I S O S , !&rISCONSIN
Structural Studies of Zirconium Trihalides and Hafnium Triiodidel BY
LAWRENCE F. DAHL,2 TAO-I CHIAXG, PYRTLE 1%'.
SEABAUGH,
AND
EDWIN M. LARSEN
Received April 8, 1964 Structural studies of ZrCls, ZrBr3, ZrIB,and HfIa have been carried out from X-ray powder diffydction patterns.* T h c isomorphous comp2unds contain two formula units in a hexagonal unit cell and have the following dimensions in A . (all with e.s.d. fO.O1 A , ) and densities in g./cc. a t 2.5': ZrCla, a = 6.36, c = 6.14, deap~l= 2.95, doaicd = 3.05; ZrBr3, a = 6.75, c = 6.315, d,,,tl = 4.32, dcaiod = 4.42;ZrIa, a = 7.25, c = 6.64,dexPtl = 5.13, doalcd = 5.20; HfI3, a = 7.225, c = 6.59, dexpti = 6.17, &&led = 6.25. Systematic absences of 1 odd for hOZ reflections indicate as probable space groups, D3~t>P63/mcm, C36,,-P63cm, and D23h-P6c2. From space group assignment ( D36h-P63/mcm), intensity calculations, and stereochemical considerations (with the assumption of no order-disorder phenomenon) a structure based on a distorted hexagonal close-packing of the halogen atoms can be proposed which consists of infinite chains along the c axis formed by MX6 octahedra joined a t opposite faces with the metal atoms regularly spaced midway between the halogen atoms; the resulting metal-metal distance is equal to one-half the c lattice constant. Evidence is presented to show that previous powder work (made on relatively impure samples) by Holze3 including another space group assignment ( D33h-PB2m)and a formulated structure of linear chains of (ZrzX6)nunits is not substantiated by our powder data. d qualitative MO theory of bonding is proposed from which direct metal-metal interactions can be postulated for a chain configuration.
Introduction Preliminary X-ray powder diffraction studies of zirconium and hafnium trihalides were carried out first by Leddy4 and later more thoroughly by Holze3on the zirconium trihalides alone. Holze3 concluded that the zirconium trihalides are isostructural with Ti133s5 and the p-form (designated by Holze3 as the &form) of TiBr3 and TiC13.3z6 On the basis of indexed powder lines obtained from samples highly contaminated with metal, Holze3 assigned a space group (D33h-P62m) and carried out a limited structural analysis which indicated that these solid zirconium trihalides consist of linear chains of (ZrsX6). units (X = C1, Br, I) in a hexagonal close-packed lattice of halogen atoms.' The present investigation was virtually completed before Holze's Ph.D. thesis3 was made available to us. This paper presents evidence that Holze's space group (1) This article is based in part on a dissertation by Tao-I Chiang in Partial fulfillment of the requirements for t h e degree of Doctor of Philosophy a t t h e University of Wisconsin. (2) Fellom of t h e Alfred P. Sloan Foundation. (3) E. H o k e , Ph.D. Thesis, Westfilische Wilhelms Universitat, Muenster, Germany, 1957. ( 4 ) J. J. Leddy, Ph.D. Thesis, The University of Wisconsin, 1955. ( 5 ) R. F. Rolsten and H. S. Sisler, J . Am. Chent. Soc., 79, 5891 (1957). (6) G. Natta, P. Corradini, I. W. Bassi, and L. Porri, Atli A c c a d . S a d . Lincei, Rend., Classe Sci. Fis., J l a 2 . Irat., 24, 121 ( 1 9 5 8 ) . (7) Cf.R. F. Rolsten, "Iodide Metals and Metal Iodides," John Wiley and Sons, Inc., lUew York, K. Y . , 1961, p. 46.
assignment and proposed structure for the zirconium trihalides are not substantiated by our powder patterns of these compounds. X-Ray powder diffraction data for HfI3 which show this compound to be isomorphous with the zirconium trihalides are presented for the first time, and experimental densities and lattice constants arc reported for the four compounds. Several synthetic investigations of these compounds recently have been published which also are pertinent to this work. The preparation of pure, anhydrous zirconium trihalides by reduction of the corresponding zirconium tetrahalides with hydrogen under a glow discharge was described by Newnham and Wattsj8 but no characterization of the resulting products by X-ray analysis was given. The synthesis of Z r L by the reduction of Zr14 with A1 was carried out by Watt and Baker,g who state that their X-ray powder data attributable to only ZrIB are in good agreement with the unpublished data (presented here) obtained by Larsen and Chiang.lo The preparation of pure ZrBr3 from the reduction of ZrBrl with Zr metal was ( 8 ) I. E. Newnham and J. A. Watts, J . A m . Chevz. Soc., 82, 2113 (1960). (9) G. \V, W a t t and W. A. Baker, Jr., J . Iizovg. Nucl. Chem., 22, 4P (1961). (10) E. M. Larscn and T. Chiang, communication t o G. W. Watt, 1958
Vol. 3, No. 9,Sefitember, 1964
STRUCTURAL STUDIES OF ZIRCONIUMTRIHALIDES 1237
reported by Schafer and Skoludek,l1 who represented their X-ray powder data in nonnumerical, line-diagram form without indexing the reflections and consequently without obtaining lattice parameters. The present study provides information which bears upon the preparation and purification procedures for these and related compounds.
these compounds are listed in Table I1 along with the values reported by previous workers for these and related compounds. The calculated densities for two MX, formula units per unit cell give good agreement with those measured experimentally (Table 11). Systematic absences of the h01 reflection for 1 odd indicate PB3/mcm (D36h), P63cm (C36”),or P8c2 (D23h) as the probable space groups.l6 Any of these three probable space groups requires the two metals and six halogen atoms per unit cell to be in special positions. Stereochemical considerations restrict the possible combinations of symmetry. Table I11 shows the special positions and resulting point symmetry available to the metal and halogen atoms for each of the three probable space groups. All three possible space groups demand that the metal and halogen layers of atoms each be regularly spaced along the c lattice direction. Consequently, i t seems reasonable to assume that these alternating metal and halogen layers are equidistant from each other, corresponding to the z parameters of the metal and halogen atoms being restricted to z = 0 and z = 1/4, respectively. By this choice the noncentrosymmetric space group PB3cm becomes equivalent to the centrosymmetric one, D36h-P63/mcm, in which the metal atoms occupy the set 2b with point symmetry 3m and the halogen atoms are in set 6g with mm point symmetry. I n order for the special positions of the other noncentrosymmetric space group, D23h-P&2, to coincide with those of the centrosymmetric space group, the halogen y coordinate must be fixed a t y = 0. Although D23hP c 2 cannot be ruled out as a possibility, a structure consistent with the space group requirements of D36hP63/m~m is supported by the intensity data. For this centrosymmetric space group the two metal atoms are fixed in the special set 2b, while the placement of the six halogens in the one set 6g introduces an alterable x coordinate (Table 111). The structure then is based only on one variable positional parameter and for an isotropic vibrational model on two independently variable thermal parameters (;.e., one for each metal and the other for each halogen). Estimated values for these individual isotropic temperature factors of 1.9 and 1.5 A.z were used for the halogen and metal atoms, respectively. For a regular hexagonal close-packed structure of halogen atoms, the halogen x parameter ideally would be 1/3. However, the c/a ratios suggest some distortion of the halogen lattice, and the actual intensity calculations carried out for several values of x (e.g., x = 0.333, 0.325, 0.319, and 0.340) definitely indicated a better fit between the observed and calculated intensities, I,, for a value of x < 1/3. For ZrC13and ZrBr3 the best agreement was obtained with an x value of 0.319, while for Zr13 and Hf13 the best fit was found with an x parameter of 0.325. For all intensity calculations the form factors utilized for chlorine are those of Viervoll and
Experimental Preparation of Zirconium and Hafnium Triha1ides.-The general method for the preparation and analysis of the trihalides has been reported previously.12 The original zirconium with a hafnium impurity of 125 p.p.m. was obtained from the Atomic Energy Commission. Hafnium metal was obtained from A. D. MacKay, Inc.; correction was made for a zirconium impurity of about 1%. The composition of the samples used for X-ray powder work and the comparison of the purity of our samples with those prepared by Holze are given in Table I. The relatively high purity of our samples of ZrBra, Zr13, and Hf18 was substantiated by the X-ray powder work. No diffraction lines characteristic of metallic zirconium were noted in our powder patterns, whereas the zirconium impurity in Holze’s zirconium trihalide samples was ’ sufficiently great that his resulting powder data were corrected by subtracting the known metallic zirconium powder lines from the experimental data. Only in listing our zirconium trichloride powder data did we follow the same procedure. Approximately 50 lines were obtained from each of our powder patterns of ZrBrs, Zr13, and Hf13, while 28 lines were recorded for ZrCla. (In contrast only 22 lines were given by Holzea for each of the three zirconium trihalides.) Efforts to prepare samples of hafnium trichloride and tribromide of high purity were unrewarding; the resulting samples were highly contaminated with metal, and their powder patterns were not of the same quality as those reported here. Densities.-Densities were determined pycnometrically with carbQn tetrachloride or kerosene a t 25.0’. The results are reliable to f 0 . 0 5 g./cc. Corrections were applied for the density of the metal powder present. X-Ray Powder Photographs .-The powder samples were loaded with the aid of a special holderla into Lindemann glass capillaries of 0.3-mm. diameter and then sealed with beeswax. All operations were performed inside a nitrogen atmosphere drybox. A 114.6mm. diameter powder camera was used, and photographs of the diffraction patterns were taken with Ni-filtered Cu Kcu radiation. Lattice constants with estimated standard deviations of 1 0 . 0 1 A. were obtained by the utilization of the Bradley- Jay extrapolation method.14 Corrections were made for film shrinkage.
TABLE I MOLERATIO
COMPARISON CENTFREEMETALIMPURITY
O F P O W D E R SAMPLES AND
Sample
AV. X / M mole ratio
ZrCl3 ZrBra 2r1~ HfIa
3.01 2.95 2.93 3.19
OF PER
free metal----
7 %
This work
38.8 3.0 3.4 6.4
~ 0 1 d
46.2 28.2
19.0
Results All of the observed X-ray diffraction lines from each of the four compounds were indexed with the aid of a hexagonal Bunn chart.I5 The lattice constants for (11) H. L. Schafer and H. Skoludek, Z . unovg. allgem. Chem., 316, 15 (1962). (12) E. M. Larsen and J. J. Leddy, J . Am. Chem. Soc., 18, 5983 (1956). (13) E.M. Larsen and J. J. Leddy, Reg. Sci. Instr., 29, 736 (1958). (14) Cf.H. P. Klugand L. E. Alexander, “X-Ray Diffraction Procedures,” John Wiley and Sons, New York, N. Y., 1954,p. 462. (15) E. V. Azaroff and M. J. Buerger, “The Powder Method in X-Ray Crystallography,” McGraw-Hill Book C o . , Inc., New York, N. Y., 1958, p. 73.
(16) International Tables for X-Ray Crystallography,” Vol. I, The Kynoch Press, Birmingham, England, 1952.
Inorganic Chemistry
1238 L. F. DAHL,T . CHIANG,P. W. SEABAUGH, A N D E.M. LARSEN TABLE I1 X-RAYDATAFOR ZrXj, HfI3, P-TiClr, P-TiBrl, Proposed space group
Compound
TiIs"
Dwlod a,
ZrC13
a
AND
D36h-P63/mCm D33b-P&m ZrBq D36h-P6~/mcm D33h-P&m ZrIs D36h-P6a/"I D33h-PB2m HfI3 D36h-P63/mcrn P-TiCl, D36h-P63/mcm P-TiBr3 D 33h-Pc2m Ti13 D 33h-P62m D33h-P62m Holze's cell constants originally cited in
A.
c, A.
6.36 6.41 6.75 6.76 7.25 7.33 7.225 6.27 6.69 7 . 13 7.17 kx. units3 have
c/a
6.14 0.965 6.25 0.9TS 6.315 0.936 6.36 0.941 6.64 0.916 6.73 0.918 6.59 0,912 5.82 0.928 0.916 6.13 6.49 0,910 6.47 0.902 been converted tu 8.
( 2 = 2)
Dexptl
Source
3.05 2.96 4.42 4.38 5.20 5.01 6.25 2.50 4.04 5.00 4.94
2.95
Present work Holze3 Present work Holze3 Present work Holze3 Present work Natta, et aZ.6 Holzes Ho!ze3 Ro!stcn5
... 4.52 ...
5.13
... 6.17 ... ...
... . . I
TABLE I11 P O S S I B L E SPACE
-Atoms
Set
PPdmcIn (DJah)-Point symEquiv. metry positions
6X
6g
mm
x,O,I/4;
GROUPP O S I T I O N S 7
O,x,'/d,
2M
2b
Hf
TRIHALIDES
Set
Equiv. positions
Set
Point symmetiy
6c
m
x,O,z; o,x,z, 2,2,z
6k
m
+
2a
3111
0grim,l7 while the atomic form factors used for the metal and other halogen atoms are those of Thomas and Umeda.I* The diffraction lines, proposed Miller indices, and relative intensities are listed in Table I V for the four compounds.
Discussion The basic structure for each of these compounds consists of infinite chains along the c axis formed by MXG octahedra joined a t opposite faces. The structure is based on a hexagonal close-packing of halogen atoms with the metal atoms occupying one-third of the available octahedral holes (Fig. 1). All of the octahedral holes along the corners of the unit cell parallel to the c axis are filled; the chains of octahedral holes parallel to c but with centers a t 2 / 3 and 2 / d , l / d are unoccupied. The distance between each metal and its six surrounding halogen atoms calculated from the data for our model is 2.54 8. for ZrC13, 2.67 8. for ZrBrd, 2.88 A. for Zr13, and 2.87 8. for HfI3 (each with e.s.d. f0.03 A.). A distortion in the hexagonal close-packing of the halogen atoms occurs such that the occupied octahedral holes are smaller than the unoccupied ones. This distortion can be explained readily from the bonding forces between each of the metal atoms and the octahedron of halogens surrounding i t which no doubt draw the halogen atoms closer to one another (;.e., x < l/3) than t o the other halogens which do not share between them a metal atom. Our space group symmetry requires the metal atoms to be regularly spaced along the c direction midway between the halogen atoms a t a distance corresponding to one-half of the "c" cell constant. This gives from our lattice constant measurements metal(17) H. Viervoll and 0. ogrim, Acta C r y s t , 2 , 227 (1949). (18) L. H. Thomas and K. Umeda, J . Chem. Phys., 26, 293 (1957).
2,0,'/2 2 ; O,R,'/* x,x,'/2 z o,o,z; 0,0,'/2 z
+ +
-
P k 2 (D%h)-----
7 -
Point symmetry
x,x,3/4
0,0,0; 0,0,'/2
ASD
P6acm (C%----
I -
2,ZF,'/4 %o,3/4; 0,Rt3/4;
3m
Zr
A N D P O I N T S Y M M E T R Y FOR
Equiv. positions
x , y , l / ~ , 9,n - y,'/4,
y -
+ z;
y
x,%'/4
- x,y,3/4;
n,x 2a
32
9,z,3in;
Y,3/4
O,O,O; 0,0,'/2
metal distances of 3.07 A.for ZrC13, 3.16 A.for ZrBrd, 3.32 K. for Zr13, and 3.30 A. for Hf13 (each with e.s d. zt0.005 A.). A detailed comparison of our structural analysis with that of Holze not only is informative but also is pertinent to other work on these and related compounds. Hoke3 selected from his X-ray powder data for the zirconium trihalides, /3-TiBr3, and Ti13 (all classified by him as isostructural), a different space group P62m (D33h)which, unlike our assignment, does not possess any symmetry restrictions corresponding to the systematic absence of h01 reflections for 1 odd. For P62m Holze3 placed the two metal atoms in one set of 2-fold special positions (2e) of point symmetry 3m, and the six halogen atoms in two sets of 3-fold special positions (3f and 3g) of point symmetry mni. The sets and coordinates of these equivalent positions16 are
o,o,?.
2e
o,o,s;
3f
x1,0,0; 0,21,0; Xl,il,O
3g xz,O,l/z; O,xz,'/2; Rz,%,'/z
The significant difference between the above equivalent positions and those for any of the three space groups considered by us (Table 111) is that for P62m the z coordinates of the metal positions (set 2e) can be varied such that the metal atoms are not required to be regularly spaced along the c direction. From limited parameter calculations carried out only for the titanium trihalides in which the sets 3f and 3g were assumed to be interrelated by the condition x2 = 1 - xl, Hoke3 obtained bromine and titanium atomic coordinates (XI = 0.318 and z = 0.290) for P-TiBra and an iodine coordinate (xl = 0.314) for Ti13 (a titanium coordinate was not estimated for Ti13). He
Vol. 3, No. 9,Sefitember, 1964 concluded that similar distortions from the so-called ideal structure (for his space group these parameters are x1 = l / 3 ; xz = 1 - x1 = 2/3; z = 0.250)19occur for the zirconium trihalides. Holze’s assignment3J of this space group for the zirconium trihalides and his subsequently formulated structure with the zirconium atoms drawn together along the c direction toward one another in pairs to give linear chains of (Zr2X6)nunits are based entirely on the presence of one observed reflection (an indexed 001 line designated by Holze3as a “metal line” attributable to the zirconium atom in ZrX3) in his powder data. This 001 line is the only observed line in Holze’s data which does not fit the systematic absences of 1 odd for h01 data required by the P6,/mcm (D36h) space group. Significantly, this line does not appear in any of our powder patterns nor in the data (indexed by us) of Watt and Bakerg for Zr13, but it does appear in the powder data (indexed by us) reported by Schafer and Skoludekll for ZrBr3. To compare the two models further, intensities based on Holze’s model (and space group) were calculated for ZrX3 (X = C1, Br, I) and Hf13 with metal z parameters of 0.27 and 0.29. The halogen x values utilized for Holze’s model were identical with ours. The strongest pure “metal line” for the above metal parameters is the 001 reflection, but even for the most favorable ratio of metal to halogen scattering power ( i e . , ZrC13),the calculated intensity of the 001 line does not account for the relatively large experimental intensities of the 001 line observed by Holze3 for ZrX3 (X = C1, Br, I) and by Schafer and Skoludek” for ZrBr3. Other reflections were found to give a more sensitive change in intensities due to small changes in parameter, but unfortunately the lack of resolution due to the accidental overlap of certain lines with similar Bragg angles does not allow a clear distinction to be made between the two models. The basic assumption underlying our proposed model has been the absence of any order-disorder phenomenon. The method of preparation of the crystalline sample may result in a nonstoichiometric structure (;.e., an “excess” structure with additional atoms occupying holes in the normal structure or a “deficient” structure with vacancies in the normal lattice positions) or may affect the degree of ordering of the atoms in the lattice (;.e., lead to the formation of layer stacking faults). Variations of intensities due to such effects may account for the presence or absence of indexable lines (e.g., the 001 reflection) for these compounds. These and the nonindexable lines (e.g., the lowestangle line (of largest d-spacing) observed by Watt and Bakerg for Zr13 and by Schafer and Skoludekl’ for ZrBr3 cannot be indexed as a P-form reflection) may result from impurities or from the presence of a superlattice indicative of a larger unit cell with more complex grouping.
-
(19) An origin shift of z 1/4 is required t o transform Holze’s parameters for t h e undistorted hexagonal close-packed arrangement into equivalent, idealized parameters for PGa/mcm.
STRUCTURAL STUDIES OF ZIRCONIUM TRIHALIDES 1239
a
/-
Fig. 1.-A packing drawing of the hexagonal structure for ZrXz ( X = C1, Br, I ) and HfIs viewed in ( a ) along the c axis and in (b) along the [ 1101 direction. The metal atoms are represented by the smaller line-shaded circles.
The similarity of cell dimensions, axial ratios, and diffraction symmetry (Table 11) for the zirconium and P-form titanium trihalides certainly suggests that the atomic arrangements including distortions are similar for all these compounds. The space group D36h-P63/mcm obtained by Natta, et aLJ6from the characteristic extinctions for P-TiC13 is identical with that chosen by us for ZrX3 (X = C1, Br, I) and Hf&, and furthermore the model reported by Natta and coworkers from intensity calculations for P-TiC13 is essentially identical ( i e . , their fractional coordinate x for C1 is 0.315) with ours. The temporary designation by Rolsten and Sislers of D33h-P82m(instead of D 3 6 h P63/mcm) for Ti18 is based on the presence of a weakly observed 003 reflection in their powder pattern for which the 001 line was absent. I n contrast to the powder data for P-TiC13 (for which the X-ray scattering power ratio of titanium with halogen is the most favorable), Holze3lists for P-TiBr3 and Ti13 three h01 reflections (001, 003, and 005) with 1 odd. Although the above results do not indicate that Holze’s model for P-TiBr3 and Ti13 can be discarded, on the basis of our powder data we feel that there is justification for the proposal of our symmetrical model for the zirconium trihalides and HfI3. The apparent discrepancies in the powder work need to be investigated further. Of interest is that the magnetic susceptibilities observed for the zirconium and titanium trihalides20,21 certainly suggest some type of cooperative metalmetal interaction involving the one unpaired electron per metal atom. We wish to point out that simple (20) J. Lewis, D. J. Machin, I. E. Newnham, and R. S. Nyholm, J. Ckem. SOC.2036 (1962). (21) W. Klemm, E. Holze, and W. Basualdo, “Inorganic Chemistry Papers, 16th International Congress of Pure and Applied Chemistry, Paris, 1957,” Butterworth Scientific Publications, London, 1958, p. 43.
w.SEABAUGH, AND E. M. LARSEN
Inorganic Chemistry
1240 L.F. DAHL,T.CHIANG, P.
TABLE IV X-hY
DIPFRACTIOS
DATA( P O W D E R METHOD) FOR ZrClj, ZrBrj, 21'13,
AND
HfIj"
-. %ad.
::m
Qc. 1
f.
bkf
10
'0,0333 0.0. lW
w
5.129
8
0.1314 0.14Ce
0.1318 0.1XQ
w+
%.O 1.3 0.2 11.0 4.0
m-
0.2053
9.0
0.-
a
0.2310 0.2w
0.2P5
m-
0.25'9
0.2972 0.391
0.2559 0.2%) 0.%7
mno
0. lzc
8 '
a-
m
0.3377
0.42r7 0.45% 0.yM
0.93
0.m1 0.4025 0.4217 0.4W7 0.4279 0.435 0.4T6 0.4693 0.913 0.9% 0.5267 0.5% 1
0.5565
no
no m no W
no W W
0.6w 0.6573 0.@3 0.7Xa
0.7W 0.&23
0.6m C .63B 0.6520 0.6551 0.6914 0.7178 0.7210 0.7316 0.7@3 0.7976 0.8199 3.8233
0.8%
0.8898
0.9315
0.8644 0 . m 0.8940 0.919 0.918
W
0.01
W
0.6
0.9W
wid
0 . W 0.9514
DO
0.02
DO W
0.4 0.00
no
0.m
DO
0.03 0.2 0.5
0.9292
0.1.cpo5 1.1.@71 1 . W 1.094
::
1.~916 1.1160 1; 1267 1. 1.1w 1.1851 1.1860 1.2181 1.@+'47 1.24T7
m-7
W
M 110
W
DO W
M
no W W
DO DO DO M
no w W
M W
DO W
110 W
DO 110 W
Do
vw
4t6 612
a+
V
m a a a M a-
0.m
m a-
IC
h U
w.5
406
0.7 6.4 64.0
3.7 7.4
0.5'93
m
0.4020
w+
3.0
W
0.1 0.3 1.B
0.4531 0.4633 0.4&1
2.9 0.403 3.4w 0.4301, 3.4513
w I
0.46%
5.7
Y
0 . m
Y
1.3 0.55
::z ;:z W
0.5203 0.593
3 . m 0.-
0.6411 0.6559 0.mo 0.7143
0.7814 0.792
0.8403
0.8203 0.8529
0 . W
W
m
:0 . 6% 09 ::32 0.6B3 E:0.7145 @
0.5
110
0.16
m-
2.9
W
no m
0.2 0.1 1.1 0.01
4.4
V+
2.1
m-
?: ? 1.9
m DO
0.05
::?E 0.7814
no
0.03
0.7897 0.8148 0.8193 0.8314 0.6316 0.8%
w m
no n-
w
1.3 .1
0.7 0.4 0.W 0.14
0.26 0.2
no
0.20
0.9559
M
0.19
0 . m 3.m 1.0369 1.0071
V-
0.9
V-
1.2
w
0.85
0.60
1;01jj
no
0.03
0.00 0.02 0.40 0.50
1.0153 1.0197 1.~446
DO
m-
0.02 0.37 0.14 1.2
P-
0167
no
0.02
.m .593
1.0076
O.Y 0.00 0.10
0.00 0.02 0.01 0.07 0.00 0.20 0.70 0.20 0.50 0.40
0.4
1.W 1.913
0.2
DO M DO DO
513
Eoll
m-
1.16%
M
no
1.1915 1.21% 1.2410
mw
1;2410 1.2412
wtd M
DO
1.292 w
0.00
0.3 0.3
M
no
1.4 1.0 0.2 0.02
1.4476
7
1.29
1.0
0.05
M
93
no no
7m\
V
1.5353 1.6213
II-
..+
103
vu V
0.161 0.1175 0.1676 0.17%
wid m wid
0.03
0.43 0.W 0.14 2.m
0.07
0.99
2.3
0.05 0.W 0.22 1.40 2.3
55.4
11.2
x.9 19.0
4.40
w
5.7
1
65.13 5.6
m-
1.03
&] 3x
0.1-
0.3195 0.3%
.
0.3959
m-
8.9
0.2283
S-
53.2
0.2634
V
0.2w
m
7.'(9 3.60
0.36
no m-
20.9
0.3193 0.Wl O . m
l.x
m
26.oc.
no
3.7c 6.31
m'
7.55
W
w
0.31 2.0
13.6 1.6
0.4m
v:d
0.469 3.4820 0.431
w:d yw vyu
0.77
0.514 0.5353
m
13.53
V
0.72 c . 12
m
17.K 2.93 16.00
l.x 1.20 0.e 3.w
3.22
1.B
0.551 0.5733 0.W5
W+
c.ap
Y+
0.6239
m m no
no
0.6357
m-
no
no vw
0 ; 53 0.19
yw
O.&
no
0.03 0.5
1.4
no no
0.3
w:d
10.x
C.&
6.F c.44
5.w
0.12 1.61 3.03 0.53 1.a
0.a
9.2 0.22
O.W 2.33 0.20 0.a
0.05 0.05
no no
2.1 5.48
no
3.m
no no
0.47 u.25 0.3
w+
3.x
1.8 ~.~
1.5 0.g5 0.40 0.10 0.20
no
0 . m
0.99
no W
0.m
1.1.516 1 . e
m
0.4-
W
0.9w
0.40 0.20 0.3 0.00 0.10
W
210
0.03
0.94 1.40 0.10
1.W
0.78
0.8691 0.8900
no
w
0.m
DO yw DO M DO
m
1.492
C %53
0.03 0.37
0.wo
0.9028
M
515 5321 622
IC
0.6
0.67 V'
1.9
0.07 2.5 3.2
V+
W
0.26
0.7146 0.7311
0.0.9193 0.9317
0.05 0.F
0.05
M
M
1.0 20.8 6.1 11.3 0.04
w+
r,
'obad.
1.4331
3. 'p 3.0 W.6 4.3 7.3
0.%53
0.4313
0.3 1 . m
vrn
0.263
0.8
M DO
0.1W 0.1127 0.1169
I
110
1.7 1.1 0.3 1.6 0.1 0.1
0.01 0.00 0.3 0.4 0.4
::s
1.1%3
V
.-
0.m
0.3147
0.6
0.6
no
:
Om-3
: zi%
0.2 0.03 0.9 2.7 1.7 0;Ce 1.3 0.05 2.0 0.2
w
no w
r,
3 j ? 0.1013 0.1143 0.1180
?: 6' 1.6
w
w
Qc.1c.
12.0 4.0 5.0 0.1
1.3 0.7 0.4 0.4 0.4 0.02 1.0 0.2
no
0.6255
100
'&ad.
0.22 0.17 1.3
3 . m 0.919
0.03 2.55 0.46
0.05 V
3.a
0.19
VoZ. 3, No. 9, Sefitember, 1964
STRUCTURAL STUDIES OF ZIRCONIUM
TRIHALIDES 1241
TABLE IV (Continued) =I,
nix,
( coatinuad) b l C .
::;g CLlJ 3.0.9B 0 . m 1.a2
xo no
:0%0
W
0: 18
M
W
0.19 0.60
v* m-
M
0.12
W
vrd
I '
1.0123 1.-
1.W6 1.69
1.678
1.072 1.a803 1.091
1.0996
no
.a-
no Y
1.149
m
no
0.24 0.24 0.14
V+
4.3
1.m
1.2952 1.315
1.m
::% 1.mo
no
no V
no W
vrd
no
w w V W W
m yw
0.07 0.12
I
2.08 0.37
W
0.00 0.05
vrd I
4.6 0.13
V+
0.10 1.20
I
1.69
Il-
0.05
V-
m
no
::s
W
1.99
1.4 100 1.4220 1.4463
wid
% :;1 .$4 9
W
no W
vM
wid
W
1.20 0.19 3.50 0.26 0.17
m-
w
0.0266 0.03%
"0% 0.W
W V
31.8
107.6 21.6 25.0
23
0.00
9.44
2:; 0.31 6.67 23.3 4.% 7.x
0.00
3.24 2.47 2.6 0.22 10.3 0.00 0.12
5.69 16.7 7.47 22.5'
17.9
0.59
6.19 0.00
0.14
Do
y. 9930 1 : s
Do
1.0lse
' I
1.0116
::gE
Do W
m I
i.W
1.W
::% LE33 1.1121 1. U13
1.1355
:::E 1.1611 1.1% 1.2035 1.m
1.2376 1.2491 1.2516 1.2516
W V
M W
1.m
1.3p 1.31 2 1.3182
1.97
W W
W
no
1.14 1.65
wid
3.33 .
Do
3.12 0.00
W
0.00
::% 1.5186 1.-
0.9
W
0.14 0.12
wid
3.22
6.97 0.05
2.62
3.a W
0. 50
0.32
1.m
3% 1.4
;:z
0.44
W
0.07
0.19
1.22
0.00
2.B
W
1.49 1.46
no uno rd
no
0.a
0.02
0.01
m
1.4333
;:3 4.25
M
1.12
2.14 7.m
W
1.3512
2.66
O*.$ i:d 0. 02
I-
9.07
W
0.67 4.99
3.50
M
w
no no
:2.213
0.12
1.34%
::a
0. a? 0.00
110
1.34%
1.19
0.19 1.39 1.96
W
::z ;:s
:0.29%
0.13 0.55 0.06
m
m
1.231
no
16k.6. 0.46 13.4
m
0.5952
m I
0.03 0.22 0.48
Do
0.03
W
O 9f 4.
E:0.91% % 0.-
W
1.1
2.17
QUlC.
1.B
35.9
0.12
W
I
w.7 20.1
4.9
AfI,
100 110
nfx, (eostind) IC
10.4 0.31
I
0.00 W
1.3421
1.4W 1.5057 1.935 1.967
W
*id
0.48 4.7 0.12
1.1429
1.2406 1. 2433 1.2519 1.2661 1.2763
II
O*? 3.
1.87 0.02
no v:d
W
5.3
no
1.2223
v+
0.05
1.1209
no
.'.-
1.84
no no
1.1018 1.1937 1.2179
v
1.8 5.0 0.05
1.1138
1.1461
(ooatinmd)
.+
IC
3.s 0.19 0.02
w w-
6.70 0.17 3.17
.2.20 Do W
W
no no
0.W 0.05
?:2
4.5 0.6
0.02
0.24 W
2.33
Legend : Qobsd = (4sin2 0,b,d)/X2; &,lod = ( 4 sin2 Ooaled)/h2; no = not observed; s', s, s-, m', m, m-, w', w, w-, vw, and vvw = order of relative (visually estimated) intensities in descending order; vw:d means a very weak diffuse line. The powder pattern for ZrCls has been corrected for known metallic Zr lines.
molecular orbital theory can be utilized to explain qualitatively a direct metal-metal interaction for a system of regularly spaced metal atoms in a linear polymeric configuration. For our proposed zirconium trihalide model the local crystallographic point group symmetry about each zirconium is gm (Dad). The nine relevant zirconium orbitals available for bonding transform under this point group to give the sum 2A1, A2, 2E, f E, where AI, is the symmetry representation of the s and d,z orbitals, Azu that of pz, E, that of the (dzz-,z, dz,) and (d,,, due)pairs, and E, that of the (pz, p,) pair. Six of these zirconium orbitals of representation AI, A2, E, E, are combined under this trigonal ligand field with the appropriate symmetry orbitals of the six coordinated halogens t o give the usual six u-bonds. The essential feature of this description is that after u-bonding, there are left three orbitals on each zirconium available for
+
+
+
+
+
possible metal-metal interaction involving the remaining electron per metal atom. These consist of a utype metal orbital of AI, symmetry which points along the chain axis and two other degenerate orbitals of E, symmetry. These orbitals as well as higher energy zirconium AO's can interact with the corresponding orbitals (of identical symmetry) of the neighboring metaIs in the chain to give molecular orbitals. For an infinite linear array of equidistant zirconium atoms the energy levels become bands. Since these bands presumably overlap and since "configuration interaction' ' involving higher energy states also may contribute to the ground state, the assignment of electrons to these bands cannot be made unambiguously, but in any case the band(s) are only partially filled. This MO description of bonding thereby provides a qualitative picture by which the zirconium atoms conforming
1242 J. MENASHI,S. FUKUSHIXA, C. FOXX, AND W. REYNOLDS
to our proposed model can interact directly with one another.2 2 The presumed antiferromagnetic behavior20,21 then may arise by direct metal-metal interaction and/or by super-exchange via the bridging halogen atoms. (22) This bonding description also is applicable t o H o l d s (ZrzXs),, model397 of alternating short and long interatomic distances. The local point group symmetry about each zirconium is decreased t o CsV for which the s, pa, and d,* orbitals transform as AI, and the three pairs (pz, py), (d,2...1/2, d z y ) , and (dZE,dyJ as E. Similarly, after o-bonding the three orbitals remain on each zirconium with the symmetry AI E. The nonequivalent bond distances will result in the energy levels splitting into gaps of bonding and antibonding states; if the dimeric ( Z r ~ x s units )~ are sufficiently separated from one another, the interaction of the zirconium atoms can be considered as distinct pairs. Since for a given (ZrzXe) unit the axially symmetric AI atomic orbitals presumably interact with each other more strongly than the degenerate orbitals making u p the E representation, the two coupling electrons can be assigned t o the totally symmetric bonding MO with the resulting formation of a direct metal-metal bond. This electron coupling in pairs is similar to t h a t found for a-NbIa and TaIa which are diamagnetic.23 The structure of solid a-A-bIa and the isomorphous TaIa consists of infinite chains formed by MI6 octahedra sharing two opposite edges; the metal atoms are shifted from the centers of the iodine octahedra toward one another in pairs t o give a resulting metal-metal distance of 3.31 a.25 (23) L. F. Dah1 and D. L. Wampler, Acta G y s t . , 15, 903 (1962).
+
Inorganic Chemistry
Of significance would be a measurement of electrical conductivity of pure single crystals (attempts to prepare suitable crystals for X-ray diffraction as yet have been unsuccessful) to determine the metallic nature of these compounds. Also, a low-temperature neutron diffraction study is needed to elucidate the atomic magnetic moment orientation of these presumed antiferromagnetic substances.
Acknowledgment.-E. AI. L. and T. C. wish to acknowledge the financial support of the National Science Foundation, Esso Corporation, and the Research Committee of the Graduate School. L. F. D. and P. W. S. wish to acknowledge the financial support of the Atomic Energy Commission. We also acknowledge the use of the IBhS 70-1computer a t MURA and the CDC 1604 computer of the Numerical Analysis Laboratory a t the University of Wisconsin.
CONTRIBUTIOS FROM THE SCHOOL OF CHEMISTRY OF MINSESOTA, MINNEAPOLIS 14, MINNESOTA UNIVERSITY
The Role of the Monofluoroiron(II1) Ion in the Iron(I1)-Iron(II1)-Fluoride Ion Isotope Exchange Reaction BY JAMEEL MENASHI, SHOUZOW FGKUSHIMA,' CHARLES FOXX,
AND
W h R I i E N L. REYIXOLDS
Received March 6, 1964
+
The iron(I1) iron(II1) exchange rate was measured in NaF-SaClOa-HC104 media a t constant pH and ionic strength. The iron( 11) concentration was increased so as to make the isotope exchange rate comparable to the rate of formation of the inner coordination shell complex FeF+2. The observed isotope exchange rate was dependent on the rate of formation of F e F + Zin the manner expected if the activated complex [FenFC4]"was formed from Fef2(aq) and FeF+2(aq).
A considerable number of anionic catalysts for the iron(I1) iron(II1) isotope exchange reaction have been reported2 In each of these cases it has been postulated that isotope exchange occurs between Fe+2and FeXn+3-nP, the latter species being a complex between F e f 3 and the anion X-q which is formed reversibly and rapidly compared to the rate of isotope exchange. As a result of the postulate the rate of the isotope exchange reaction is written as
+
where ko, ki,j kl, kz are the rate constants for isotope (1) On leave from Osaka University, Osaka, Japan. (2) (a) J. Silverman and R. W. Dodson, J . P h y s . Chem., 56, 846 (1952); (b) J. Hudis and A . C. Wahl, J . Am. Chem. Soc., 75, 4153 (1953); (c) G. S. Laurence, Trans. Favaday Soc., 53, 1326 (1957); (d) D. Bunn, F. S.Dainton, and S. Duckworth, i b i d . , 55, 1267 (1959); ibid., 57, 1131 (1961); (e) R. A. Horne, J . Phys. Chem., 64, 1512 (1960); ( f ) h-.Sutin, J. K. Rowley, and R. W. Dodson, ibid., 6 6 , 1 2 4 8 (1961); (9) W. L. Reynolds and S.Fukushima, Inoug. Chem., 2, 176 (1963); (h) K. Bachman and K. H. Lieser, Z . p h y s i k . Chem. (Frankfurt), 36, 236 (1963).
exchange between Fe+z and Fe+3, Fe(OH)+2, FeX+3-q, FeX2+3-2*, respectively, Kh is the acid dissociation constant of aquo ferric ion, and K1 and K z are the stepwise formation constants of the Fe(II1)X-4 complexes. The products MI,kaKlK2, . . . in (1) are obtained from the variation of observed rate constants with change of X-* concentration. From these products values of k l , kz, . . . are calculated using independently determined values of K1, K z , . . . for the inner coordination sphere complexes of Fe(II1). The theories concerning mechanisms of electron transfer use these rate constants without it being known whether or not the rate constant values are valid. If, for example, the exchange path involving one Fe+2,one Fe+3, and one X-9 in the activated complex was a reaction between FeX+2-'J and F e f 3 or between Fe+2 and an outer-sphere complex, Fe(H20)gX f3-*, of Fe(H20)6 +3 and X-q, then the values of K1 and kl would be very different. Hence, it is very important to obtain evidence of a rate-determining isotope exchange reaction between Fe+2 and FeXn+3-np. In the work reported here we have obtained excellent evidence that the
