SUCLEAR QUADRUPOLE RESONANCE OF BizoeIN BiBr3
949
Nuclear Quadrupole Resonance of Bi2O9in BiBr,’
by Elizabeth D. Swiger,2 Paul J. Green, Gary L. McKown, and Jack D. Graybeal Department of Chemistry, West Virginia University, Morgantown, West Virginia
(Received October 2 , 1964)
,4n investigation of the nuclear quadrupole coupling of the BiZognucleus in solid BiBr3 was undertaken in order to determine if the crystal structure was related to that of either BiC13 or Bi13. A 50-g. sample of anhydrous BiBra, prepared by the direct reaction of Bi and Br2,was investigated between 20 and 40 Mc./sec. using a super-regenerative spectrometer. Three of the four allowed transitions of the BiZognucleus were measured. By plotting calculated frequency ratios us. asymmetry parameters and by plotting relative frequency factors us. asymmetry parameters, the experimental values for the asymmetry parameter and the nuclear quadrupole coupling constant of the BiZo9nucleus were determined to be 0.553 and 340.5 Mc./sec., respectively. The large value of the asymmetry parameter indicates considerable cross bonding among the BiBr3 molecules in the solid.
Introduction Since the crystal structure of BiBr3 has not been determined, nuclear quadrupole resonance spectroscopy is being used to determine if the structure of solid BiBr3 is more closely related to that of BiC13,Swhich is also undetermined, or to that of Bi13,4known to crystallize with the I atoms in a hexagonal close-packed arrangement and the Bi atoms in the octahedral holes. This work presents an interpretation based only on the BiZo9nuclear quadrupole coupling constant. Further discussions of the structure can follow the determination of the Br nuclear quadrupole coupling constants.
An externally-quenched super-regenerative spectrometer, similar to one described in the literature,6 was used to observe the resonance absorption lines. A 90-cycle on-off square-wave Zeeman-modulation magnetic field and phase-sensitive detection were used for searching. Measurements were made at room temperature. The identification of the side-band or main frequency component being absorbed and the measurement of frequencies followed the method given by Graybeal and Cornwel16 except that a HewlettPackard 524C frequency counter was used.
Experimental Anhydrous BiBr3 was prepared by a modification of the method of Pattison-Muir.6 Bismuth metal, 110 g., screened to a size of 1-3 mm., was placed in a singlenecked round-bottomed flask fitted with a reflux condenser. A stoichiometric amount, 120 g., of Brz was added and the reaction mixture refluxed for 72 hr. During the refluxing a deposit of yellow crystals of BiBrs accumulated in the upper parts of the system. The unreacted Brz was removed by treating the reaction mixture with CC1, and decanting. The BiBr3 was separated froin unreacted Bi by stirring the mixture into suspension in CC1, and rapidly decanting, leaving the heavy Bi metal behind. After drying in vacuo, 110 g. of BiBr3 was obtained. Duplicate analyses gave 53.52 and 53.55% Br (theory, 53.44y0 Br). A 50-g. sample was sealed in a glass vial for studies.
Three transitions were observed with a fourth expected to fall above the operating range of the spectrometer. All of the transitions were broad, of the order of 30-40 kc./sec. The appearance of the spectrum was that of a single resonance, indicating that all Bi sites in the unit cell are equivalent. The identification of transitions and the calculation of the asymmetry parameter, 7 , for the Bi209nucleus
Results
(1) This research was supported by Research Grant G-21048 from the National Science Foundation. (2) National Science Foundation Predoctoral Fellow, 1963-1964. (3) H. G. Robinson, P h y s . Rev., 100, 1731 (1955) (4) R . W. G. Wyckoff, “Crystal Structures,” Vol. 11, Interscience Publishers, Inc., New York. N. Y., 1960, Chapter V , p. 12. ( 5 ) M. M. Pattison-LMuir, J . Chem. Soc., 2 9 , 144 (1876). (6) J. D. Graybeal and C. D. Cornwell, J . P h y s . Chem., 6 2 , 483 (1958).
Volume 69, ,Vumber 3
March 1966
E. D. SWIGER, P. J. GREEN,G. L. MCKOWN, AND J. D. GRAYBEAL
950
Figure 1 .
Determination of 7 and line assignments.
were made by using frequency ratios and relative frequency factors calculated from the energies as functions of the asymmetry parameter. For the BiZoQ nucleus, having a nuclear spin I = 9/2, the secular equation from which the energy levels, as a function of 7 , can be found is
E5 - 11(3 -- v 2 ) E 3- 44(1 - q 2 ) E 2+ 4 4 / 3 ( 3 ?')'E
+
+ 48(3 + q2)(1 - q 2 ) = 0
where E is in units of 6e2Qq/41(21- 1). By using the solutions of this equation, for values of 7 from 0 to 1 in intervals of 0.1,' one can plot the calculated frequency ratios, for the allowed Am = 1 transitions, as a function of v and, from the intercepts of these curves with the values for the observed frequency ratios, calculate the value of 7. Since a single value of 7 gives rise to a unique set of frequency ratios the measured frequency ratios should intercept the calculated curves in a vertical line corresponding to the experimental value of 7. Figure 1 shows an enlarged The Journal of Physical Chemistry
section of such a plot. The accuracy of the determination of 7 is limited by this graphical solution. While perturbation methods have also been applied for direct solution of the secular equationI6such methods are limited to small values of 4 and this is not the case for BiBr8. The nonapplicability of such methods is further demonstrated by the strong observed dependency of the calculated frequency ratios on 7. The nuclear quadrupole coupling constant, e'&, can be found by plotting the calculated relative frequency factor, ri, us. 7 and determining the experimental relative factors from the intercepts of these curves with the vertical corresponding to the experimental value of 7 . The relative frequency factor, r i J is given by vi = ri]e2Qq1/24
This procedure is shown in Figure 2 . The results of (7) M. H.Cohen, Phys. Rev., 96, 1278 (1954). (8) R.Berson, J. Chem. P h y e . . 20, 1605 (1952).
NUCLEAR QUADRUPOLE RESONANCE OF BiZo9 IN BiBr3
951
t
3*5
Figure 2. Determination of the relative frequency factors, rl.
the previously discussed methods as applied to the Bi209nucleus in BiBr3 are given in Table I.
Table I : Measured Transitions of Biaooin BiBr, (300'K.)
Obsd. frequencies, Mc./sec.
26.756 33.865 39.884 26.756
f 0.002 f 0.002 f 0.002 f 0.002
Obsd. frequency ratios
Calcd. Calcd. relative frefrequency quency ratios factors
1.89 1,262 1,178 1'263 2 . 3 8 1,486 1'179 2 . 8 2 1.487
Assignment
e1Qe/h9 Mc./sec.
340.7 341.5 1/t+6/~ 339.4 Av. 340.b f 0.8 6/2
-., 8/2
6/~+1/1
Discussion The fact that, a nuclear quadrupole resonance spectrum was observed precludes BiBr, from having a crystal structure analogous to Bi13. The observation of the resonance frequencies in the same region as those
observed for BiC133indicates that BiBr3 has a crystal structure similar to BiC13; however, crystal structure data for neither compound are available. The melting point of BiBr,, 218') is in the range expected for molecular crystals having comparable molecular weights; hence, solid BiBr3 is viewed as a molecular crystal in which the individual BiBr3 units retain their identity. Although d-electrons undoubtedly contribute to the bonding in solid BiBr3, the contribution will be predominantly in the form of cross bonding between BiBr3 units and they will contribute little compared to p-electrons to the Bi-Br bonding within a single BiBrB molecule. The contribution of d-electrons to the bonding will be to affect the value of 9 more than that of e2Qq. The observed value of the coupling constant for Biz"@in BiBr3 is not related to that in BiC13 (318.8 M ~ . / s e c . )in~ the manner expected from consideration of electronegativity values alone. The relationship between the fraction ionic character, @,and fraction s-character, 01, in an A-X bond and the quadrupole Volume 60, Number 3 March 1966
E. D. SWIGER, P. J. GREEN,G. L. IC~CKOWN, A N D J. D. GRAYBEAL
952
coupling constant, (eP&qLZ)Al where A is the positive species, is given by9 I'e2&&uaZ)A =
- 3 a ( l f 2b)(e2&q0)A
where (e2&qo)is the value for a single p-electron in the state ml = 0 in an A atom. This relation shows that a decrease in fraction ionic character, as electronegativity values indicate, in going from a Bi-C1 to a Bi-Br bond, will produce a decrease in the coupling constant, assuming no change in s-hybridization. It is also evident from this relation that the observation of a coupling constant signifies the presence of some shybridization and that an increase in this factor will increase the coupling constant. Using the conventional Pauling electronegativity differences, Ax = 0.9 f 0.1, and ( e 2 & q o ) B 1 = 1500 ;\Ic./sec.,'O the per cent s-character and subsequently the Br-Bi-Br bond angle are calculated to be 5.6 f 0.3% and 93.4 f 0.2", respectively. The bond angle in gaseous BiBrs as measured by electron diffraction" is 100 f 4", which is consistent with a per cent s-character of 14.8%. In the solid state the increased value of ( e 2 Q q ) B 1 of BiBr3 over BiC13 can then be accounted for by a larger bond angle than in solid BiC133caused by an increase in s-hybridization, as indicated in the above calculations, by an increase in cross bonding, since this effect would produce the same change in the coupling constant as increasing s-hybridization, or a combination of the two.
The Journal of Physical Chemistry
There is little structural data available for solid group VA halides but available values for gaseous SbCla ( L = 99.5 f 1.5")12and solid SbC13 ( L = 95.2 f 0.2') l 3 indicate that there is a decrease in the bond angle in going from the gas to the solid. The change for SbCIS, 4.2", is not as large as that predicted for BiBr3, 6.6', assunling the magnitude of the coupling constant is determined primarily by the amount of s-hybridization. While there is an uncertainty associated with comparing the behavior of antimony and bismuth conipounds, the values for SbC13,coupled with the existence of appreciable cross bonding, involving d-orbitals, as indicated by the large asymmetry parameter, leads to the conclusion that the increase in ( e 2 & q ) B , between BiC13 and BiBr3 is due to a Combination of an increase of s-hybridization and an increase of cross bonding compared to the BiC13 case. A study of the bromine coupling constants and asymmetry parameters could give further information regarding the extent of cross bonding. (9) W. Gordy, W. V. Smith, and R. Trambarulo, "Microwave Spectroscopy," John Wiley and Sons, Inc., New York, N. Y., p. 281. (10) H. G. Robinson, H. G. Dehmelt, and W. Gordy, Phys. Rev., 89, 1305 (1953). (11) H.H.Skinner and L. E. Sutton, Trans. Faraday Soc., 36, 681 (1940). (12) P.Kisliuk, J . Chem. Phys., 22, 680 (1954). (13) I. Lindquist and A. Niggli, J . Inorg. A\rucl. Chem., 2, 345 (1956)
