Effect of randomness on the ESR hyperfine structure of Cd+

Journal of Non-Crystalline Solids 44 (1981) 149-155 North-Holland Publishing Company

EFFECT OF RANDOMNESS ON THE ESR HYPERFINE STRUCTURE OF Cd ÷ H. HOSONO, H. KAWAZOE, J. NISHII and T. KANAZAWA Department of lndustrial Chemistry, Faculty of Technology, Tokyo Metropolitan University, Fukasawa, Setagaya-ku, Tokyo 158, Japan Received 7 August 1980 Revised manuscript received 19 November 1980

The ESR spectra of the 5s 1 state of Cd+, induced with gamma-ray irradiation, were measured for polycrystalline CaO, ~-Ca(POa)2 and glassy Ca(PO3)2 matrices. It has been found out that one of the hyperffme absorptions due to the magnetic nuclei (111Cd and 113Cd) reflects very senstively the structural fluctuation around the center in terms of pronounced line broadening. Such a feature was explained reasonably well by introducing the distribution of the hyperf'me coupling constant. It was emphasized that Cd2+, the precursor of Cd+, is a very suitable probe to study the local randomness around Ca~ in solids.

1. Introduction Cd 2+ in a solid traps an electron and is converted into a paramagnetic Cd ÷with 5S 1 electronic configuration when irradiated by gamma rays. The induced Cd + gives hyperfine structures (hfs) due to 111Cd [I=21, /a = - 0 . 5 9 2 2 nuclear magneton (nm), natural abundance = 12.86%] and 1laCd (½, - 0 . 6 1 9 5 nm, 12.34%) nuclei in addition to a signal due to the non-magnetic nuclei [1,2]. In this paper we report that one of the hyperf'me (hi') absorptions o f Cd + reflects very sensitively the structural randomness around the center in terms o f pronounced line broadening through the fluctuation of the hyperfme coupling constant.

2. Experimental Divalent cadmium ion was doped in three matrices, polycrystaUine CaO, fl-Ca(PO3)2 and glassy Ca(PO3)2. Very pure CaCO3, CdCO3 and guaranteed grade H3PO4 were used as starting materials. CaO doped with Cd 2+ was prepared by heating the mixture of CaCO3 and CdCO3 (50 : 1, mol ratio) at 1100°C for 2 h under vacuum. Glass batches with the composition 48 CaO • 2 CdO • 50 P2Os (in mol.%) were melted in fused silica crucibles. The melts were poured onto a stainless steel plate and pressed with another one. Polycrystalline/3-Ca(PO3)2 was obtained 0 0 2 2 - 3 0 9 3 / 8 1 / 0 0 0 0 - 0 0 0 0 / $ 02.50 © North-Holland

150

H. Hosono et al. / The ESR hyperfine structure o f Cd +

111CD I II3cD J

~IcD [ i00

113CD_~//~ i 200

i 300

MAGNETIC FIELD ( GAUSS )

I 400

440

,

I 4500

MAGNETIC FIELD (G)

Fig. 1. Hyperffme structure of Cd ÷ in polycrystaUine CaO.

by heating the glass with the composition 48 CaO • 2 CdO • 50 P 2 0 s (in mol.%) at 700°C for 24 h. Each polycrystalline phase produced was identified by the powder X-ray diffraction method. For ESR measurements, the samples were sealed in fused silica glass tubes under degassing and subjected to the 7-irradiation from a 6°Co source with a dose of 106 R at 77 K. The ESR measurements were conducted at -100°C without an intervening warm-up using a JEOL model PE-3X X-band spectrometer with 100 kHz field modulation. The resonance fields and microwave frequency were calibrated using a proton NMR field marker and a cavity wave meter, respectively.

3. Results Figures 1 and 2 exhibit the hfs of Cd* in CaO and/3-Ca(POa):, respectively. In the case of CaO : Cd + no significant difference is noticed between the line widths of the two hf absorptions for each isotope, and the ratio between the peak heights of the two absorptions for each isotope is equal to that of the transition probability [4] for each absorption. On the other hand, for/3-Ca(POa)2 : Cd* a remarkable difference is apparent between the line widths of the two hf absorptions for each isotope (note that two sites for Cd+ can be seen in it). The peak height of the narrower absorption for 1X3Cd at site-2 * is greater than that of the broader absorption by a factor of about 150. The hf absorption of Cd ÷ in Ca(PO3)2 glass is shown in fig. 3. The splitting due to the two isotopes and the conjugate hf absorption cannot be observed experimentally.

* Only these two hf absorptions do not overlap with the other absorptions.

151

H. Hosono et al. / The ESR hyperfine structure o f Cd +

SJT~-2 SITE I~L.~II iii 113 CD

113 CD

SITE-2

SITE 1

I15

I Co 460D

I I I I 135J0 NUO0 45100 5000 MAGNETIC

I

I

I

5500

6000

6500

4700

FIELD ( GAUSS )

Fig. 2. Hyperfine structure of Cd + in polycrystaUine #-Ca(PO3)2. Two sites for Cd + (abbreviated as sites 1 and 2) are seen in the host. The detail of the absorptions around 4600 G is shown in the upper right corner.

The ESR spectra o f Cd ÷ were analyzed b y the following spin-Hamaltonian; =

.

+ at

. S

(1)

,

where g and a are the spectroscopic splitting factor a n d h f coupling constant, respectively. As the solutions o f the H a m i l t o n i a n , eq. (1), are given b y the B r e i t Rabi e q u a t i o n [3,4], the E S R parameters, g and a, are calculated from eqs. (2) and

(3); a = {hu(1 - K ) + hv[(1 - K ) 2 + 8(1 + K ) 2 ] 1/2 }/2(1 + K )

I 4300

I

]

I

4400 4500 4600 ~GNETIC FIELD( G )

(2)

I 4700

Fig. 3. HyperFme structure of Cd ÷ in Ca(PO3) 2 glass. The conjugate absorption could not be detected experimentally. Apparently this absoiption is anisotropic. However, the line shape can be interpreted by assuming isotropic g and A tensors for the individual Cd + and the symmetrical distribution function of a for the ensemble of Cd*. The curvature of the H - a/hu relation for transition A results in the lower field-tailing through the non-linear transformation as noted in fig. 4 [4].

152

H. Hosono et a L / The ESR hyperfine structure o f Cd +

R

B rl-

R i

~TRANSITION

A

...... i M(H)

d

0

I

I

1

5

i0

15

Fig. 4. The relation between resonance field H and a/hv. 2hv 1 + (a/hv)

H = --

g# 2 + (a/h v)

for the transition A;

H=

2hu (a/hu) - 1 gfl

for the transition B ,

2 - (a/hv)

(l < a/hv < 2) .

This diagram was made under the following conditions; g = 2.000, hv = 0.3070 cm -l (9.204 GHz). The distribution function of a/hu [F(a/hv)] was transformed into that of H[M(H)] according to the scheme given in the figure. Since the curvature of the H - a/hu relation for transition B is considerably smaller than those for the other transitions, the deformation of shape function is not pronounced compared with that for higher field 2°7Pb3+ hf absorption (a/hv = 5.3) if symmetricala[hu-distribution function is assumed [4].

2hv

hv + a

(3)

g = [3H A 2 h v + a '

where K indicates the ratio H A [ H B ( H A a n d H B express the resonance fields for the transitions A and B, respectively. The relations b e t w e e n H and a / h v for the transitions A and B are shown in fig. 4. The evaluated E S R parameters for each s p e c t r u m are s u m m a r i z e d in table 1.

H. Hosono et al. / The ESR hyperflne structure o f Cd +

153

Table 1 The ESR parameters and line widths of hyperfine absorptions of Cd + Matrices

Isotopes

ESR parameters g

CaO ~-Ca(PO3)2 c Site-1 Site-2

Line width b (G) a(cm - 1 )

111 113

1.996 1.996

0.3112 0.3255

111 113 111 113

_ e 1.997 2.000 2.000 1.993 f

_ e 0.4264 0.4392 0.4595 0.3906 f

Ca(PO3) 3 glass

Transition A a 4.0 4.0 17 (13) d) (12) d) 15 113

Transition B a 4.5 4.5 _ e 93 94 124 Not detected

a The relation between H and a/hv for each transition is shown in fig. 4. b The peak-to-peak width AHms I o f the absorption in a derivative spectrum. c As the atomic arrangement in #-Ca(POa)2 has never been reported, the geometrical structures about the two sites for Cd + are u n k n o w n at present. d The values of AHms 1 are not so precise owing to the overlap o f the two absorptions. e The intense signals o f the P O ~ - hole center hinder t h e conjugate h f absorption and the signal due to the non-magnetic nuclei. f T h e ESR parameters are evaluated from the signal due to the non-magnetic nuclei and one o f t h e h f absorptions using the following equations:

2C- 1 - a=hv 1-C '

g=

hv ~-~

'

where C is the ratio H A / 2 H ° (H ° is the resonance field for t h e absorption o f the non-magnetic nuclei and H A indicates the zero-crossing field in a derivative spectrum).

4. Discussion

The characteristics of the three spectra are explained by intro~lucing the fluctuation of the hf coupling constant a reflecting the local randomness around the center. By applying the spin selection rule and a condition that the resonance field H is positive to the energy eigenvalues for the Hamiltonian, eq. (1), the relation between H and a/hv is derived [4]. We illustrate the relation graphically in fig. 4. The values of a which were evaluated were located in the region 1 < a/hv < 2, where the resonance field for the transition B varies to a great extent when the value ofa/hv varies slightly. The extent of the line broadening for transition B is much greater than that for transition A for the same mangnitude of a/hv.fluctuation. Therefore, the distribution of a for Cd* in/~-Ca(PO3)2 (the skeleton of the crystal structure is composed of PO4-1ong chains [5]) originating from the distribution of the geometry for the coordination spheres causes considerable broadening of the absorption responsible for transition B. This is in sharp contrast to the fact that line broadening was not observed for CaO : Cd ÷, where the a-distribution is negligibly small. A mathematical expression for the line broadening of hf absorptions due to the

154

H. Hosono et al. / The ESR hyperfine structure o f Cd +

structural distribution is given in the following; the relation between H and a/hv is given as H A = 2hv 1 + (a/hv) g:3 2 + (a/hu) '

(4)

HB = 2hv 1 - (a/hv) (5) g13 ( a / h v ) - 2 ' where/T" indicates the resonance field for the/-transition. From eqs. (4) and (5), the standard deviation for the distribution of H is derived as given by eqs. (6) and (7) by assuming that the line width is completely dominated by the fluctuation of a; o~ - 2hv hv g13 (2hu + a) 2 0 a ,

(6)

oB4 = 2hv hv g(3 ( 2 h v - a) = Oa,

(7)

where OH A and or] mean the standard deviations for the distributions of the hf absorptions for the transitions A and B, respectively, On the assumption that the hf absorptions have the same and symmetric shape function, the following relation is valid: Z]XHmsl oc OH ,

(8)

where AHrnst expresses the peak-to-peak width of the absorption in a derivative spectrum. From eqs. (6), (7) and (8), the following relation is obtained; Z3J-IAs, ( 2hv - a ~2 AHBsi = \2h-~--~a! "

(9)

Furthermore, it can be easily explained by considering the line broadening due to the a-distribution that in the case of Cd + in Ca(PO3)2 glass the absorption for transition B was too broad to be detected. By using eq. (9), the estimated line width (,M-Imsl) for the transition B reaches about 2300 G and its peak height is reduced by a factor of 2.5 X 10 -4 compared with that of transition A; peak height for the transition B ._ R__{AHmAa~: peak height for the transition A -: 2 kAttnma] - 2.5 X 10 . 4 ,

(10)

where the coefficient ½ means that the two absorptions due to the isotopes are distinctly separated in the transition B, while they are united into a single peak for the transition A, and R expresses the ratio between the transition probabilities [4] for the two transitions (R is 0.26 in this case). Therefore, such a very weak and enormously broadened absorption cannot be detected under our experimental conditions.

H. Hosono et al. / The ESR hyperfine structure o f Cd +

155

The ESR characteristics of ns 1 centers such as Cd + [1,2], Pb 3+ [4,6] T12+ [7] Ago [8,9] and Au ° [10] can be deduced from the facts that the magnitude of the hf coupling constant a responds sensitivily to a change in the electronic state of the ligands, while the g-shift (2.002 - g ) is insensitive to it. Such features can be interpreted by recognizing that the magnetic electron of the ns 1 center occupies an anti-bonding molecular orbital [11], i.e. the magnitude of its population in the ns atomic orbital is considered to respond sensitively to the variation of the chemical environment around the center.

5. Concluding remarks As discussed above, the linewidth of one of the Cd ÷ hf absorptions responds sensitively to the randomness in the local structure around the center through the fluctuation of Fermi-contact coupling constant. As the chemical properties and ionic radius of Cd 2+ are very close to those of Ca 2÷, we hope that the ESR of Cd + will be very useful for the detection of the local disorder around Ca 2+ in solids. Since the structural randomness is greatly magnified as evidenced by the line broadening, Cd + is appropriate for the detection of small degrees of randomness, for instance in X-ray amorphous materials (for which the existence of a glass transition temperature cannot be recognized using conventional methods and sharp X-ray diffraction peaks cannot be found. This work was supported in part by The Asahi Glass Foundation for Industrial Technology.

References [1] [2] [3] [4]

H. Imagawa,Phys. Chem. Glasses 10 (1969) 187. R.S. Eachus and M.C.R. Symmons,J. Chem. Soc. (A) (1970) 3080. G. Breit and I.I. Rabi, Phys. Rev. 38 (1931) 2082. H. Hosono, J. Nishii, H. Kawazoe, T. Kanazawa and K. Ametani, J. Phys, Chem. 84 (1980) 2316. [5] D.E.C. Corbridge, The structural chemistry of phosphorus (Elsevier, Amsterdam, 1974). [6] E.J. Friebele, 11th Proc. Int. Cong. Glass, Prague 3 (1977) p. 87. [7] H. Hosono, H. Kawazoeand T. Kanazawa, J. Mat. Sci., in press. [8] R. Yokota and H. Imagawa,J. Phys. Soc. Jpn. 23 (1966) 1038. [9] F. Assabghy, S. Arafa, E. Boulos, A. Bishay and N.J. Kreidl, J. Non-Crystaliine Solids 23 (1977) 81. [10] H. Imagawa,J. Non-CrystaliineSolids 1 (1969) 262. [11] H. Watanabe, Phys. Rev. 149 (1966) 402.