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Proton magnetic resonance in the paramagnetic state of GdH3
Journal of the Less-Common
PROTON MAGNETIC OF GdH3*
Metals,
130 (1987)
RESONANCE
187 - 192
187
IN THE PARAMAGNETIC
STATE
0. J. TOGAE Institute for Low Temperature Wrodtr w (Poland)
and Structure
Research,
Polish Academy
of Sciences,
(Received May 26,1986)
Summary
Proton magnetic resonance (‘H NMR) measurements of the linewidths and their shifts have been made in GdH,. The results are presented for the frequencies 5.9 < f < 35 MHz and temperatures 78 < T < 293 K. The linewidths were found to be temperature and field dependent. Even at the smallest applied field and room temperature, the contributions other than proton-proton dipolar coupling are large. The ‘H NMR line shifts are negative and their absolute values increase with lowering temperature. An effective hyperfine field H,,, = -1.4 X lo3 Oe could account for the observed behaviour.
1. Introduction
With the exception of europium and ytterbium, the rare earth (RE) binary hydrides crystallize with two types of metal matrix structure, i.e. f.c.c. and h.c.p. While the former is observed in the light RE hydrides, the h.c.p. structure is typical of the heavy RE trihydrides. The physical properties of the h.c.p. trihydrides have been studied less than the f.c.c. hydrides. It is known that they may exhibit magnetic ordering but at much lower temperatures than dihydrides with the same elements. GdH2, for example, orders antiferromagnetically below 15.5 K [ 11, whereas GdH3 is magnetically ordered only below 1.8 K [2]. The electrical conductivity of gadolinium hydrides diminishes with an increase of hydrogen content from GdH2 to GdH,.,,. The extrapolation of that dependence results in a zero conductivity at [H]/[Gd] = 2.3 [3]. In this paper we present the ‘H NMR data for the paramagnetic state of GdH3. The proton linewidths us. temperature and magnetic field together with ‘H NMR line shifts are given. *Paper presented at the International Symposium on the Properties and Applications of Metal Hydrides V, Maubuisson, France, May 25 - 30, 1986. 0022-5088/87/$3.50
@ Elsevier Sequoia/Printed in The Netherlands
188
2. Experimental details The GdHs sample was prepared by exposing 99.9% pure elemental gadolinium metal to hydrogen gas. Before hydrogenation, the metal was heated to 600 “C in a vacuum. At 580 “C gaseous hydrogen generated by heating titanium hydride was introduced into the reaction vessel. The absorption was performed at hydrogen pressure lower than 0.1 MPa. Debye X-ray diffraction patterns were used to obtain the structure and lattice parameters. The h.c.p. structure was identified with a = 3.76 A and c = 6.705 A. The continuous wave NMR measurements were performed with a Varian wide-line spectrometer. The spectra were measured at room temperature and liquid nitrogen bath temperatures, and at other temperatures a gasflow cryostat was employed.
3. Results and discussion The measured proton linewidths 6H in GdHs increase with increasing magnetic field and with decreasing temperature. The behaviour of 6H as a function of magnetic field to temperature ratio (H/T) at fixed temperature (293 K) and at fixed frequency (f= 5.979 kHz) is shown in Fig. 1. Similar field dependence of 6H for GdH, is also presented there. The gadolinium hydride NMR line should be broadened by the following factors: (i) the demagnetization fields associated with the 4f electron Curie susceptibility of the powdered sample; (ii) the dipolar interaction between the fluctuating electronic moment of the Gd3+ ion and the proton; (iii) a possible distribution of the line shifts since there are three different types of proton sites in the crystal lattice of GdH3 ; (iv) the nuclear protonproton dipolar coupling and (v) the lifetime broadening associated with the
g 30 5 g 20 i 10
0
10
20 H/T lOelK)
I
30
Fig. 1. The linewidths 6H (defined as the separation between the absorption derivative extrema) of ‘H NMR as a function of magnetic field to temperature ratio (H/T). The open circles (GdHs) and open squares (GdH2) present the data taken at room temperature (293 K), whereas the magnetic field H was varied. The filled circles are the results obtained at constant field. (In fact the resonance frequency (5979 kHz) was kept constant, but since the line shifts AH were small in comparison with H, the corrections can be neglected.)
189
finite value of the spin-lattice relaxation time T, . The latter effect is usually ignored. However, in such magnetically dense material as GdHa, it probably cannot be completely neglected. The demagnetization field broadening [ 41 is Since xv = C/T, 6Hd = 6H, - 3xvH, where xv is the volume susceptibility. 3C(H/T). A non-zero contribution of factor (ii) is expected because of the non-cubic symmetry of the proton sites in the crystal lattice (see Table 1). Both (ii) and (iii) are proportional to the gadolinium ion magnetic moment and therefore this would also lead to an H/T dependence of their broadenings. Nuclear dipolar coupling is a main source of the proton NMR line shape TABLE 1 The crystal structure and ‘H NMR moments for GdHs Space group
P% 1
Atoms
Positions
Lattice parameters [51a
a = 3.73 A x
c = 6.71 8, Y
z
Gd
(6f)
213
-
-
H H H
(12g) (4d) (2a)
0.356 -
0.028 -
0.096 0.167 -
Theoretical
moments
Second average (oe2)
Fourth average (oe4)
18.4 17.2 14.9 17.7
780 640 470 714
aAlthough the gadolinium atoms form an h.c.p. structure, the deuterium atoms are situated such that the unit cell is three times larger than the h.c.p. unit cell. This makes a equal to (3)‘12a = 6.46 A rather than the value shown in this table, whereas c remains the same as in the h.c.p. structure.
in many non-magnetic hydrides [6, 71. In GdH, it is expected to be significant in the vicinity of small values of H/T. An estimate of the dipolar contribution for a “rigid” lattice regime is possible using the van Vleck [8] method of moments and the available crystal structure data. The crystal structure information together with calculated second (M2) and fourth (M4) moments are summarized in Table 1. The structure data were taken from Mansmann and Wallace [9]. The moments have been calculated using the van Vleck formulae [ 81 and a numerical technique described elsewhere [lo]. In these calculations the lssGd and “‘Gd nuclei contributions have been neglected because of their low gyromagnetic ratios and low isotopic abundances. Having calculated second and fourth moments, we can now estimate the linewidth using the information theory approach of Powles and Carazza [ 111, as has been done in ref. 6. A linewidth of 6H = 13.2 Oe is obtained. A comparison of this value with the observed (293 K, 1412 Oe) value of 9.2 Oe, suggests that other mechanisms contribute. A lower experimental 6H
190
might indicate a proton self-diffusion line narrowing. However, in the isomorphic YHs_. , this process has been observed [7] only above room temperature. In addition, when observed under these conditions, the second moment is equal to 60 0e2 and is larger than the calculated one for the rigid lattice. The linewidth owing to spin-lattice relaxation is of the order of l/T, and if it is in the range of microseconds, the resonance spectra may be influenced to a measurable degree. In fact, very short Ti values were reported in the cases of several RE hydrides [ 12, 131. Based upon the cerium hydride system [ 121, it was demonstrated that the direct dipolar coupling between the electronic magnetic moment of RE ion and the proton could be the dominant mechanism in the spin-lattice relaxation. This contribution is [ 121
(TJ’
= ; Y2/.12Te1 F
ri-6
where cc2 is the square of the effective magnetic moment of the RE ion, y is the gyromagnetic ratio for protons, r,i is the RE ion spin-lattice relaxation time and the sum on rip6 runs over all RE lattice sites taking one hydrogen site as the origin. Assuming that eqn. (1) also holds for GdHs a value of 30 ~.tsis estimated for T, at 293 K if T,,~ is taken as being the same as in the cerium hydrides [ 121. This would change the proton linewidth in a meaningful way. This contribution presents some interesting features. (T,)-’ does not depend on the magnetic field but may exhibit l/T dependence through would such behaviour of the r,i relaxation time. Hence, this contribution explain the different slopes of 6H us. H/T graphs for GdHs, shown in Fig. 1. Therefore, experimental determination of Ti in GdH3 would be very useful in checking the expectations mentioned above. It is worthwhile adding that some of the mechanisms mentioned tend to produce a lorentzian line shape. In fact, the relation 6H = a (M2)l” with 1.2 < (Y< 1.7 has been observed and the experimental line shapes were close to the lorentzian ones. The results of the ‘H NMR line shift measurements are shown in Fig. 2. All shifts were measured to the zero-signal intercepts in the differential
-;i -1.b -\ + y -1.4VI g
-l.O-
-=m- *_/i -0.q 2
4
: ,
,
6
6
j 10
12
y(K-II
Fig. 2. The relative (AH/H) taken at f = 5979 kHz.
‘H NMR
line shifts
us. reciprocal
temperature
for GdH3,
191
spectra with respect to H,O. No structure that could be associated with the three types of proton site in the crystal lattice was observed. The effects of the demagnetization field are not included in the AH/H plot. A rough estimate of this error in AH/H indicates that it could be less than 10% or 20% [ 14, 151. A good fit with the experimental data is obtained assuming the relation AH/H(%) = a + bxM with a = -0.18 and b = -21.3. The molar susceptibility X~ = 6.6/(2’ + 3) was taken from Wallace et al. [16]. The observed AH/H dependence may be understood in terms of the hyperfine coupling between the nuclear moment I of the proton and the spin component S of the rare earth 4f total magnetic moment With this interaction, the slope b can be expressed as [ 151 b
=
(gJ - 1)&f N/-h&
(2)
where is the Land& factor and He,, is the effective hyperfine field at the protons. The remaining symbols have their usual meaning. A value of -1.4 X lo3 Oe for He,, is derived from eqn. (2) in which b is replaced by its experimental value. The negative value of He,, is quite common as observed in other lanthanide hydrides [15]. Two models for Heff have generally been employed. The first involves the indirect hyperfine interaction usually referred to as the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction [ 171. In this model a rare earth ion polarizes the conductive electrons in its vicinity and the polarization propagates outward from the ion in a damped oscillatory fashion. Neighbouring ions interact with the polarized conduction electrons and align either with or against the polarization wave. The conduction electrons are thus the coupling mechanism involved in the magnetic interactions between the paramagnetic ions. Therefore, if the conduction electrons are removed, one expects the interactions to be significantly suppressed. In consequence, a substantial lowering of the magnetic ordering temperature in semimetallic or semiconductor type of the RE hydrides occurs as compared with that in the metallic hydrides. This seems to be the case in the gadolinium hydrides. Therefore, the hyperfine field at the hydrogen nucleus in GdHs is very likely owing to a transferred hyperfine interaction (the second model). In this model, the wavefunctions describe the electrons at a given ion, and admix a small fraction of wavefunctions of neighbouring ions. This corresponds to a transfer or a sharing of electrons. Since some of the electron shells on the paramagnetic ion are strongly polarized by an external magnetic field, the transfer of the ligand electron depends on whether its spin is aligned parallel or antiparallel to the spin of the polarized 4f electrons of the paramagnetic ion. This leaves behind a polarized hole at the ligand which interacts either directly with its nucleus, or indirectly by polarizing the core electron shells. Such tranferred hyperfine interactions have been postulated for an interpretation of the observed 13C NMR shifts in uranium carbides [ 181. However, the lack of information on the electron band structure in GdH3, prevents a detailed analysis of the above estimated value of He,, . gJ
192
References 1 R. R. Arons, in K.-H. Hellwege (ed.), Landolt-BGmstein Tables, New Series, Vol. 12, Springer, Berlin, 1982, p. 397. 2 R. L. Carlin, R. D. Chirico, K. 0. Joung, G. K. Shenoy and D. G. Westlake, Phys. Lett. A, 75 (1980) 413. 3 G. G. Libowitz, Ber. Bunsenges. Phys. Chem., 76 (1972) 831. 4 L. E. Drain,Proc. Phys. Sot., 80 (1962) 1380. 5 G. E. Sturdy and R. N. R. Mulford, J. Am. Chem. Sot., 73 (1956) 1083. 6 0. J. Zogat and B. Nowak, in N. Pislewski (ed.), Proc. 10th Conf. Radio and Microwave Spectroscopy, A. Mickiewicz University Press, Poznaii, Poland,, 1985, p. 73. I B. Stalinski, 0. J. Zogak and H. Drubs, Bull. Acad. Polon. Sci. Ser. Sci. Chim., 17 (1969) 121. 8 J. H. van Vleck, Phys. Rev., 74 (1948) 1168. 9 M. Mansmann and W. E. Wallace, J. Phys. (Paris), 25 (1964) 454. 10 B. Nowak, J. Kowalewski and 0. J. Zogak, J. Magn. Reson., 54 (1983) 9. 11 J. G. Powles and B. Carazza, in C. K. Coogan, N. S. Ham, S. N. Stuart, J.R. Pilbrow and G. V. H. Wilson (eds.), Magnetic Resonance, Plenum, New York, 1973, p. 113. 12 D. Zamir, R. G. Barnes, N. Salibi, R. M. Cotts, T.-T. Phua, D. R. Torgeson and D. T. Peterson, Phys. Rev. B, 29 (1984) 61. 13 L. Shen, J. P. Kopp and D. S. Schreiber, Phys. Lett. A, 29 (1969) 438. 14 E. D. Jones, Phys. Rev., 180 (1969) 455. 15 0. J. Zogak, Phys. Status Solidi B, 117 (1983) 717. 16 W. E. Wallace, Y. Kubota and R. L. Zanowick, Advan. Chem. Ser., 39 (1963) 122. 17 M. A. Ruderman and C. Kittel, Phys. Rev., 96 (1954) 99. T. Kasuya, Progr. Theor. Phys. (Kyoto), 16 (1956) 45. K. Yoshida, Phys. Rev., 106 (1957) 893. 18 W. Burton Lewis, S. W. Rabideau, N. H. Krikorian and W. G. Witterman, Phys. Rev., 170 (1968) 455.
PROTON MAGNETIC OF GdH3*
Metals,
130 (1987)
RESONANCE
187 - 192
187
IN THE PARAMAGNETIC
STATE
0. J. TOGAE Institute for Low Temperature Wrodtr w (Poland)
and Structure
Research,
Polish Academy
of Sciences,
(Received May 26,1986)
Summary
Proton magnetic resonance (‘H NMR) measurements of the linewidths and their shifts have been made in GdH,. The results are presented for the frequencies 5.9 < f < 35 MHz and temperatures 78 < T < 293 K. The linewidths were found to be temperature and field dependent. Even at the smallest applied field and room temperature, the contributions other than proton-proton dipolar coupling are large. The ‘H NMR line shifts are negative and their absolute values increase with lowering temperature. An effective hyperfine field H,,, = -1.4 X lo3 Oe could account for the observed behaviour.
1. Introduction
With the exception of europium and ytterbium, the rare earth (RE) binary hydrides crystallize with two types of metal matrix structure, i.e. f.c.c. and h.c.p. While the former is observed in the light RE hydrides, the h.c.p. structure is typical of the heavy RE trihydrides. The physical properties of the h.c.p. trihydrides have been studied less than the f.c.c. hydrides. It is known that they may exhibit magnetic ordering but at much lower temperatures than dihydrides with the same elements. GdH2, for example, orders antiferromagnetically below 15.5 K [ 11, whereas GdH3 is magnetically ordered only below 1.8 K [2]. The electrical conductivity of gadolinium hydrides diminishes with an increase of hydrogen content from GdH2 to GdH,.,,. The extrapolation of that dependence results in a zero conductivity at [H]/[Gd] = 2.3 [3]. In this paper we present the ‘H NMR data for the paramagnetic state of GdH3. The proton linewidths us. temperature and magnetic field together with ‘H NMR line shifts are given. *Paper presented at the International Symposium on the Properties and Applications of Metal Hydrides V, Maubuisson, France, May 25 - 30, 1986. 0022-5088/87/$3.50
@ Elsevier Sequoia/Printed in The Netherlands
188
2. Experimental details The GdHs sample was prepared by exposing 99.9% pure elemental gadolinium metal to hydrogen gas. Before hydrogenation, the metal was heated to 600 “C in a vacuum. At 580 “C gaseous hydrogen generated by heating titanium hydride was introduced into the reaction vessel. The absorption was performed at hydrogen pressure lower than 0.1 MPa. Debye X-ray diffraction patterns were used to obtain the structure and lattice parameters. The h.c.p. structure was identified with a = 3.76 A and c = 6.705 A. The continuous wave NMR measurements were performed with a Varian wide-line spectrometer. The spectra were measured at room temperature and liquid nitrogen bath temperatures, and at other temperatures a gasflow cryostat was employed.
3. Results and discussion The measured proton linewidths 6H in GdHs increase with increasing magnetic field and with decreasing temperature. The behaviour of 6H as a function of magnetic field to temperature ratio (H/T) at fixed temperature (293 K) and at fixed frequency (f= 5.979 kHz) is shown in Fig. 1. Similar field dependence of 6H for GdH, is also presented there. The gadolinium hydride NMR line should be broadened by the following factors: (i) the demagnetization fields associated with the 4f electron Curie susceptibility of the powdered sample; (ii) the dipolar interaction between the fluctuating electronic moment of the Gd3+ ion and the proton; (iii) a possible distribution of the line shifts since there are three different types of proton sites in the crystal lattice of GdH3 ; (iv) the nuclear protonproton dipolar coupling and (v) the lifetime broadening associated with the
g 30 5 g 20 i 10
0
10
20 H/T lOelK)
I
30
Fig. 1. The linewidths 6H (defined as the separation between the absorption derivative extrema) of ‘H NMR as a function of magnetic field to temperature ratio (H/T). The open circles (GdHs) and open squares (GdH2) present the data taken at room temperature (293 K), whereas the magnetic field H was varied. The filled circles are the results obtained at constant field. (In fact the resonance frequency (5979 kHz) was kept constant, but since the line shifts AH were small in comparison with H, the corrections can be neglected.)
189
finite value of the spin-lattice relaxation time T, . The latter effect is usually ignored. However, in such magnetically dense material as GdHa, it probably cannot be completely neglected. The demagnetization field broadening [ 41 is Since xv = C/T, 6Hd = 6H, - 3xvH, where xv is the volume susceptibility. 3C(H/T). A non-zero contribution of factor (ii) is expected because of the non-cubic symmetry of the proton sites in the crystal lattice (see Table 1). Both (ii) and (iii) are proportional to the gadolinium ion magnetic moment and therefore this would also lead to an H/T dependence of their broadenings. Nuclear dipolar coupling is a main source of the proton NMR line shape TABLE 1 The crystal structure and ‘H NMR moments for GdHs Space group
P% 1
Atoms
Positions
Lattice parameters [51a
a = 3.73 A x
c = 6.71 8, Y
z
Gd
(6f)
213
-
-
H H H
(12g) (4d) (2a)
0.356 -
0.028 -
0.096 0.167 -
Theoretical
moments
Second average (oe2)
Fourth average (oe4)
18.4 17.2 14.9 17.7
780 640 470 714
aAlthough the gadolinium atoms form an h.c.p. structure, the deuterium atoms are situated such that the unit cell is three times larger than the h.c.p. unit cell. This makes a equal to (3)‘12a = 6.46 A rather than the value shown in this table, whereas c remains the same as in the h.c.p. structure.
in many non-magnetic hydrides [6, 71. In GdH, it is expected to be significant in the vicinity of small values of H/T. An estimate of the dipolar contribution for a “rigid” lattice regime is possible using the van Vleck [8] method of moments and the available crystal structure data. The crystal structure information together with calculated second (M2) and fourth (M4) moments are summarized in Table 1. The structure data were taken from Mansmann and Wallace [9]. The moments have been calculated using the van Vleck formulae [ 81 and a numerical technique described elsewhere [lo]. In these calculations the lssGd and “‘Gd nuclei contributions have been neglected because of their low gyromagnetic ratios and low isotopic abundances. Having calculated second and fourth moments, we can now estimate the linewidth using the information theory approach of Powles and Carazza [ 111, as has been done in ref. 6. A linewidth of 6H = 13.2 Oe is obtained. A comparison of this value with the observed (293 K, 1412 Oe) value of 9.2 Oe, suggests that other mechanisms contribute. A lower experimental 6H
190
might indicate a proton self-diffusion line narrowing. However, in the isomorphic YHs_. , this process has been observed [7] only above room temperature. In addition, when observed under these conditions, the second moment is equal to 60 0e2 and is larger than the calculated one for the rigid lattice. The linewidth owing to spin-lattice relaxation is of the order of l/T, and if it is in the range of microseconds, the resonance spectra may be influenced to a measurable degree. In fact, very short Ti values were reported in the cases of several RE hydrides [ 12, 131. Based upon the cerium hydride system [ 121, it was demonstrated that the direct dipolar coupling between the electronic magnetic moment of RE ion and the proton could be the dominant mechanism in the spin-lattice relaxation. This contribution is [ 121
(TJ’
= ; Y2/.12Te1 F
ri-6
where cc2 is the square of the effective magnetic moment of the RE ion, y is the gyromagnetic ratio for protons, r,i is the RE ion spin-lattice relaxation time and the sum on rip6 runs over all RE lattice sites taking one hydrogen site as the origin. Assuming that eqn. (1) also holds for GdHs a value of 30 ~.tsis estimated for T, at 293 K if T,,~ is taken as being the same as in the cerium hydrides [ 121. This would change the proton linewidth in a meaningful way. This contribution presents some interesting features. (T,)-’ does not depend on the magnetic field but may exhibit l/T dependence through would such behaviour of the r,i relaxation time. Hence, this contribution explain the different slopes of 6H us. H/T graphs for GdHs, shown in Fig. 1. Therefore, experimental determination of Ti in GdH3 would be very useful in checking the expectations mentioned above. It is worthwhile adding that some of the mechanisms mentioned tend to produce a lorentzian line shape. In fact, the relation 6H = a (M2)l” with 1.2 < (Y< 1.7 has been observed and the experimental line shapes were close to the lorentzian ones. The results of the ‘H NMR line shift measurements are shown in Fig. 2. All shifts were measured to the zero-signal intercepts in the differential
-;i -1.b -\ + y -1.4VI g
-l.O-
-=m- *_/i -0.q 2
4
: ,
,
6
6
j 10
12
y(K-II
Fig. 2. The relative (AH/H) taken at f = 5979 kHz.
‘H NMR
line shifts
us. reciprocal
temperature
for GdH3,
191
spectra with respect to H,O. No structure that could be associated with the three types of proton site in the crystal lattice was observed. The effects of the demagnetization field are not included in the AH/H plot. A rough estimate of this error in AH/H indicates that it could be less than 10% or 20% [ 14, 151. A good fit with the experimental data is obtained assuming the relation AH/H(%) = a + bxM with a = -0.18 and b = -21.3. The molar susceptibility X~ = 6.6/(2’ + 3) was taken from Wallace et al. [16]. The observed AH/H dependence may be understood in terms of the hyperfine coupling between the nuclear moment I of the proton and the spin component S of the rare earth 4f total magnetic moment With this interaction, the slope b can be expressed as [ 151 b
=
(gJ - 1)&f N/-h&
(2)
where is the Land& factor and He,, is the effective hyperfine field at the protons. The remaining symbols have their usual meaning. A value of -1.4 X lo3 Oe for He,, is derived from eqn. (2) in which b is replaced by its experimental value. The negative value of He,, is quite common as observed in other lanthanide hydrides [15]. Two models for Heff have generally been employed. The first involves the indirect hyperfine interaction usually referred to as the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction [ 171. In this model a rare earth ion polarizes the conductive electrons in its vicinity and the polarization propagates outward from the ion in a damped oscillatory fashion. Neighbouring ions interact with the polarized conduction electrons and align either with or against the polarization wave. The conduction electrons are thus the coupling mechanism involved in the magnetic interactions between the paramagnetic ions. Therefore, if the conduction electrons are removed, one expects the interactions to be significantly suppressed. In consequence, a substantial lowering of the magnetic ordering temperature in semimetallic or semiconductor type of the RE hydrides occurs as compared with that in the metallic hydrides. This seems to be the case in the gadolinium hydrides. Therefore, the hyperfine field at the hydrogen nucleus in GdHs is very likely owing to a transferred hyperfine interaction (the second model). In this model, the wavefunctions describe the electrons at a given ion, and admix a small fraction of wavefunctions of neighbouring ions. This corresponds to a transfer or a sharing of electrons. Since some of the electron shells on the paramagnetic ion are strongly polarized by an external magnetic field, the transfer of the ligand electron depends on whether its spin is aligned parallel or antiparallel to the spin of the polarized 4f electrons of the paramagnetic ion. This leaves behind a polarized hole at the ligand which interacts either directly with its nucleus, or indirectly by polarizing the core electron shells. Such tranferred hyperfine interactions have been postulated for an interpretation of the observed 13C NMR shifts in uranium carbides [ 181. However, the lack of information on the electron band structure in GdH3, prevents a detailed analysis of the above estimated value of He,, . gJ
192
References 1 R. R. Arons, in K.-H. Hellwege (ed.), Landolt-BGmstein Tables, New Series, Vol. 12, Springer, Berlin, 1982, p. 397. 2 R. L. Carlin, R. D. Chirico, K. 0. Joung, G. K. Shenoy and D. G. Westlake, Phys. Lett. A, 75 (1980) 413. 3 G. G. Libowitz, Ber. Bunsenges. Phys. Chem., 76 (1972) 831. 4 L. E. Drain,Proc. Phys. Sot., 80 (1962) 1380. 5 G. E. Sturdy and R. N. R. Mulford, J. Am. Chem. Sot., 73 (1956) 1083. 6 0. J. Zogat and B. Nowak, in N. Pislewski (ed.), Proc. 10th Conf. Radio and Microwave Spectroscopy, A. Mickiewicz University Press, Poznaii, Poland,, 1985, p. 73. I B. Stalinski, 0. J. Zogak and H. Drubs, Bull. Acad. Polon. Sci. Ser. Sci. Chim., 17 (1969) 121. 8 J. H. van Vleck, Phys. Rev., 74 (1948) 1168. 9 M. Mansmann and W. E. Wallace, J. Phys. (Paris), 25 (1964) 454. 10 B. Nowak, J. Kowalewski and 0. J. Zogak, J. Magn. Reson., 54 (1983) 9. 11 J. G. Powles and B. Carazza, in C. K. Coogan, N. S. Ham, S. N. Stuart, J.R. Pilbrow and G. V. H. Wilson (eds.), Magnetic Resonance, Plenum, New York, 1973, p. 113. 12 D. Zamir, R. G. Barnes, N. Salibi, R. M. Cotts, T.-T. Phua, D. R. Torgeson and D. T. Peterson, Phys. Rev. B, 29 (1984) 61. 13 L. Shen, J. P. Kopp and D. S. Schreiber, Phys. Lett. A, 29 (1969) 438. 14 E. D. Jones, Phys. Rev., 180 (1969) 455. 15 0. J. Zogak, Phys. Status Solidi B, 117 (1983) 717. 16 W. E. Wallace, Y. Kubota and R. L. Zanowick, Advan. Chem. Ser., 39 (1963) 122. 17 M. A. Ruderman and C. Kittel, Phys. Rev., 96 (1954) 99. T. Kasuya, Progr. Theor. Phys. (Kyoto), 16 (1956) 45. K. Yoshida, Phys. Rev., 106 (1957) 893. 18 W. Burton Lewis, S. W. Rabideau, N. H. Krikorian and W. G. Witterman, Phys. Rev., 170 (1968) 455.