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NMR study of the low temperature structure of HfV2·4
Physica 132B (1985) 170-176 North-Holland, Amsterdam
N M R STUDY OF T H E L O W T E M P E R A T U R E S T R U C T U R E OF HfV 2 • D 4 D.T. D I N G * , A.P. S E D E E , T.O. K L A A S S E N and N.J. P O U L I S Kamerlingh Onnes Laboratorium der Rijksuniversiteit Leiden, Nieuwsteeg 18, 2311 SB Leiden, The Netherlands
Received 19 November 1984
The NMR powder spectrum of 51V in the low temperature tetragonal phase of HfV2.1)4 has been studied in fields up to 4 T. A detailed lineshape analysis proves that only one V-site is present, with strongly anisotropic nuclear spin interaction parameters. The results are in full agreement with neutron diffraction data and exclude the recently proposed existence of two inequivalent V-sites.
1. I n t r o d u c t i o n
The C-15 type intermetallic c o m p o u n d H f V 2 has a relatively high superconducting transition t e m p e r a t u r e ( T c ~ 9 K). It can easily absorb large quantities of hydrogen (or deuterium), forming stable hydrides H f V 2 - H x (0~
vq = 500kHz, 17 = 0.13 and an isotropic Knight shift Kilo = 0.68. O u r experiments had been perf o r m e d in relatively low fields, H ~< 0.9 T, which m a d e it hard to obtain reliable information concerning anisotropy in the Knight shift. These conclusions on the x = 4 c o m p o u n d were in full accordance with neutron diffraction by I r o d o v a et al. [3] on H f V 2 • D 4. Their results show that the low t e m p e r a t u r e phase belongs to the tetragonal space group I 4 J a , in which only one type of V-sites is present. Recently Belyaev et al. [5] published the results of their investigation on the cubic to tetragonai phase transition in H f V 2 • H3. 9. They determined the 51V N M R spectrum by integration of the spin echo signal while sweeping t h e magnetic field. The authors conclude from the analysis of the t e m p e r a t u r e d e p e n d e n c e of the spectrum in fields of 1.1 and 1.7 T that in the tetragonal phase at least two distinctly inequivalent V-sites are present, both characterized by axial symmetric nuclear spin interaction parameters. They argue that also the N M R s p e c t r a in fields of 0.5 and 0.9 T published by us for the x = 4 c o m p o u n d can be well described by their two sets of interaction parameters. As we p l a n - as part of o u r investigation into the electronic properties of the H f V 2 . H x s y s t e m - to carry out band structure calculations on these compounds, we have p e r f o r m e d ad-
0378-4363/85/$03.30 t~) Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
D.T. D i n g et aL / N M R study o f the structure o f H f V 2 "D4
ditional N M R experiments in higher fields to settle the question of the low temperature structure of the x = 4 compound.
171
°
2. Experimental results The experiments have been performed on powdered samples, with an average grain size of 100 Ixm. The grains were isolated with bee wax. The first derivative of the N M R spectra was recorded using a marginal oscillator, either by sweeping the field or the frequency. The calibration of the magnetic field of the superconducting solenoid was carried out by proton N M R of the bee wax isolation. The experiments were mainly performed at T = 1.2K. To possibly diminish the contribution of nuclear spin dipoledipole interaction to the 51V linewidth we used the deuteride compound H f V 2 • D 4 instead of the hydride. It was observed that the spectra of the hydride and deuteride compounds were essentially equivalent. It was carefully checked that the shape of the resonance spectrum was not influenced by any nuclear spin relaxation effects. The 51V spectrum has been recorded for a number of fields between 1.3 and 4 T. In most cases, all 0 = 90 ° powder spectrum discontinuities of the quadrupole satellites could be observed; sometimes also the 0 = 0 ° discontinuities (see fig. 2 and eq. (1)). At lower fields the spectrum of this ! = 7/2 nucleus is largely determined by first and second order effects of the electric quadrupole interaction. At higher fields, however, the influence of the second order quadrupole interaction (-~'~/~'0) has diminished strongly, while features due to anisotropy o f the Knight shift (-~'0) become more clearly visible. In fig. 1 experimental recorder traces are given for H = 1.3 T and H = 2.9 T, respectively. For clarity only the central line and the first satellites are shown. It can be seen that the structure on the central line becomes more pronounced towards high field and that a threefold splitting develops. The satellites show a, strongly field dependent, asymmetric pattern around the central line. In fig. 2 the nearly complete spectrum at H = 2.9 T
~I
"- .........
I!'
""
"---
'
II
t
I
'~'
I
I
l
12200
12400
t
t
12000
H [o~3
b
',!.,:'~ I 28600
I
I
I
28400
I 28200
I
I 28000
. I:oel
Fig. 1. Experimental first derivative of 51V NMR absorption spectrum at T = 1.2 K, showing central line and first satellites. Dashed lines are computer simulations. The arrow indicates the resonance line due to non-metallic vanadium. (a) v = 13.7 MHz. (b) ~, = 31.9 MHz.
is given; only the two (actually observed) outermost 0 = 0 ° discontinuities have been omitted for the sake of clarity. Inspection of the satellite spectrum at the various field strengths show that there are more satellite discontinuities than expected for a single site 1 = 7/2 spectrum with axially symmetric electric field gradient. For the explanation of the spectrum there are evidently two possibilities. Either there exist two or more V-sites or there is only one V-site with non-axial symmetry. We
D. T. Ding et al. / NMR study of the structure of HfVe "D4
172
F © r ,'~
~
i
X x
>-
1 c~
>- ~ r., ! t
1 I I
,
g
I I I
lI J r~
-2
Fig. 2. Overall 51V N M R ~aectrum at v = 31.9 MHz, T = 1.2K. The discontinuities are identified by a(m). (a(m) stands for the m - * m - 1 transition with the magnetic field along the -,-direction; ~t = x, y, z.) The arrow indicates the
resonance line due to non-metallicvanadium.
will first discuss the second possibility. The low temperature crystal structure as determined by Irodova et al. [3] belongs to the tetragonal space group I4Ja, in which the V atoms are situated at equivalent sites with point symmetry 1. The implication of this data for the electric field gradient (EFG) tensor is straightforward. There are no symmetry restrictions for the form of the EFG tensor, that means, there is no a priori reason to expect axial symmetry. The same holds for the magnetic interaction; also the Knight shift will not show axial symmetry. In fact for this point symmetry the Knight shift has to be described by a non-symmetric tensor K with 9 independent components. Consequently K cannot be diagonalized, and there are no relations between "principal axes" of K and those of the EFG tensor. We will describe K in the Cartesian coordinate system (x, y, z) coupled in the conventional way to the principal axes of the EFG tensor. Two remarks concerning the importance of the various components of K to the shape of the NMR spectrum can be made. Firstly, the Knight shift is small (K ~0.006) and consequently the frequency shifts in the spectrum due to K are only determined by the component of the internal field parallel to the external field. Therefore the effects of an antisymmetric part of K do not show up in the shape of the resonance spectrum, and that part will thus be left out of consideration throughout the paper. Secondly, in a powder spectrum the observable discontinuities of the satellite transitions originate from those V sites for which the external magnetic field is close to or along, respectively, the x, y and z axes of the EFG tensor (see fig. 4). So the influence of K on the shape of the satellite discontinuities is mainly determined by the diagonal components K,~, Kyy and K~. To simplify the discussion (and the computer simulations) we will take into consideration only these three unequal diagonal elements of K. To get a qualitative picture of the shape of the resonance spectrum for such a set of anisotropic interaction parameters, we have plotted in fig. 3 and fig. 4 schematically the theoretical powder patterns for the central transition and the first satellites, respectively. The influence of the
173
D. T. Ding et al. / N M R study of the structure of HfV2 "D4
quadrupole' interaction has been accounted for only in first order perturbation (high field situation). The central line exhibits a three-fold splitting. The 0 = 90 ° satellites are split up due to the finite value of the asymmetry parameter 7?. The splitting of the satellites on both sides of the central line is unequal and field dependent because of the unequality of K= and Kyy. It appears that, on the basis of this qualitative picture, all peaks in the experimental derivative spectra can be identified. To obtain accurate values for the interaction parameters, computer simulations of the powder spectra have been performed. As the quadrupolar interaction is rather large, the expressions for the resonance frequencies as given by other authors [6-9] have been extended to incorporate the effects of the quadrupolar interaction up to second order for the central line as well as for the satellites. Including also the anisotropy in the Knight shift the expressions are:
¢-90" .I 0-90" I
0 O*
,,!l\j
I
I %%
SI
L ",, ,, i
~=00 ~"..
e=90*
V=V0(l+ Kiso)
,I
~,~VO K Z - - . (Kz<0)
I
x/)
I
t
'
I- -
I
,
VoK X-
~'1 I
',1
CKx>0)
V0 Ky (Ky <0)
t Fig. 3. Schematic theoretical powder iineshape of the central transition (Am = +1/2--*-1/2) for a completely anisotropic Knight shift. Effects of second-order electric quadrupole interaction have been omitted.
(~-1/2)!
!(v3/2)
I
I
i (I,= o"
(v 3/2) e:o"
0=90" @=90" ~ 0:9°°~! ~ =
(1,= o"
9 J
--,,,,
e=90° o I ¢=90 0 ° ~
(
•
V=Vo(~+Ki~o) ! ] ,I]
e:°'(qV2)
(qV2: b
Cv3/2) e=o' f
q
VoK z
(Kz
VoKy (Ky'(O)
VoKx
(Kx>O)
VoKx
VoKy
VoKz
(Kx.,%0)(Ky'~O) ('Kz'~O)
Fig. 4. Schematic theoretical powder lineshape of the first satellites. (a) Non-axial-symmetric EFG tensor, isotropic Knight shift. (b) Non-axial-symmetric EFG tensor, completely anisotropic Knight shift.
D.T. Ding et aL / NMR study of the structure of HfV2" D4
174
Gaussian broadening of the theoretical spectrum has been assumed:
v m = Vo(1+ Ki,o) + vo[Kx sin 20 cos2 ~b + Ky sin 20 sin 2 &
f(v) oc e x p [ - ( v - /f')2120"2] .
+ Kz COS20] + ~q(~-- m)fH(O, dP)
(;){
+ ~12v0 If1H( 0, &)12124m(m - 1 ) - 4a + 9]
- ~ If~(O, &)12[12m(m - 1 ) - 4a + 6] ,
(1)
where 1
Ki~=-~ (K~ + K,y + K = ) ,
= K.-
um : frequency of the m ~ m - 1 transition m=I,I-1,...,-I+l, v o = gflHo, a = I ( I + 1), and
f~(O, ~) =
cos2 0 - ~ + ~ n sin2 0 cos(240,
(2)
If (o, 4012= 1 sin2 0[n2 + 9 c0¢ 0 IkJ
- 6n cos2 O cos(2~b) _
,/2 cos2(2&) sin20],
(3)
[fr( o, . )[Z = sin4 0[~ + - 1~ n2 cos2(2&)]
(4) 0 and 4~ are spherical coordinates, defined in the usual way with respect to the principal axes x, y, z, of the EFG tensor. In order to simulate realistic powder spectra a
The finite linewidth is due to nuclear spin dipolar interactions together with a possible spread in the strength of the quadrupolar interaction. The shape of the central line is effected only in second order by the quadrupolar interaction, whereas that of the satellites is determined by both first and second order effects. Therefore different values for the respective linewidths trc and o-s have been allowed for in the fitting procedure. The programming work is similar to that reported by Narita et al. [8], apart from an additional normalisation procedure. This procedure ensures a correct ratio of the relative intensities of the various satellite lines and the central line. The results of the best fit are shown as dotted lines in figs. 1 and 2. All peaks but one in the experimental spectra are reproduced very well. The remaining peak can be attributed to originate from non-metallic V impurities, probably oxides. The values of the parameters used are listed in table I. In a preliminary report slightly less accurate values have been given [10]. It must be stressed that the experimental spectra in the complete field region covered are reproduced correctly using these parameters. The position of the peaks in the experimental spectra reported by Belyaev [5] et al. can also be accounted for by our parameters. Because the experimental resolution of their spin echo spectra is less than that of our derivative spectra a precise comparison of the shape of their spectra with calculations cannot be performed. The similarity between their and our spectra strongly suggests, however, that the structure of the samples is identical. Concerning the conclusion by Belyaev that there exist two different V sites with axial symmetry, a few remarks can be made. First of all, their conclusion is in contradiction with the neutron diffraction work by Irodova et al. [3] from which it is concluded that only one V site exists. Moreover, the point symmetry of that site does not account for axial symmetry of the
D.T. Ding et al. / NMR study of the structure of HfVe . D4
Table I Ki~ = 0.0066 Kx = 0.0022 Ky = -0.0002 Kz = -0.0020
71 = 0.13 vq= 500 kHz o-¢= -7 kI--Iz trs = 15 kHz
nuclear spin interaction parameters. Certainly not if, as suggested by Belyaev, the low temperature phase of their sample HfV 2 • H3.9 has even a lower symmetry than I41/a. Secondly, although the position of the x(1/2,-3/2) and y(1/2,-3/2) satellites and the central line in our spectra can be accounted for approximately by the Belyaev parameters, the more precise shape and relative intensities are not reproduced by these parameters. More important, the positions of the /7=0 ° satellites in our spectra are in disagreement with the Belyaev parameters. These positions are not influenced in first order by the value of the asymmetry parameter r/ and second order effects are negligible for small values of +7 (see eqs. (1), (4)). Therefore, they yield straightforwardly the values of vq and Kz~, as given in table I. These facts unambiguously prove the validity of our fitting results and thereby the existence of only one V-site in HfV 2 • D+.
4. Discussion It is clear that to analyse properly complicated NMR powder spectra the choice of realistic nuclear spin interaction parameters, consistent with the possibly known point symmetry of the nuclear site, is of prime importance. Moreover, well-resolved experimental spectra are necessary in order to obtain as much detailed experimental information as possible. Therefore, in general, spectra of the absorption derivative using CW NMR are far more suitable than integrated spin echo spectra. For the low point symmetry encountered in this situation some simplifying assumptions concerning the interaction parameters are necessary, as a realistic fitting of 9 independent Knight shift components is virtually impossible. As can be seen, especially in
175
fig. 2, there still exist some discrepancies between theory and experiment for the detailed shape of the central line. These might quite well be due to the neglect of the symmetrical offdiagonal elements of /(. However, a more detailed fitting is hardly possible in view of the fact that in that case also the influence of a spread in the EFG and /( tensor components has to be taken into account. That such a spread, in any case for the EFG tensor, exists, is indicated by the necessity to use different values for the basic linewidth for central line and satellites (see table I) to obtain a good fit to the experiments. The very large anisotropy of the Knight shift constitutes a problem for the analysis of both R" and nuclear spin relaxation data. The relaxation rate R = (TTI) -1 will be strongly anisotropic, which will cause the recovery of the longitudinal magnetization after a saturating pulse to be nonexponential. We did actually observe this experimentally. A unique value for R cannot therefore be obtained. Because of the strong influence of dipolar contributions, the conventional analysis of the 51V Knight shift and relaxation rate in terms of density of states of s- and d-electrons at the Fermi level cannot be applied any more [11, 12]. A detailed knowledge of the relative contribution of the various conduction electrons (decomposed by angular momentum l and ml) to the density of states is needed for a realistic analysis. In addition, the off-diagonal elements, which are not or hardly detectable in Knight shift experiments, can give a large unknown contribution to the relaxation rate. It is evident that, because of the low point symmetry of the V site in the tetragonal phase of HfV2.D 4, only with great caution, information concerning the electronic properties, can be obtained from Knight shift and nuclear relaxation data.
Acknowledgments This investigation is part of the research program of the "Stichting voor +Fundamenteel Onderzoek der Materie ( F O M ) " , which is finan-
176
D.T. Ding et al. / N M R study of the structure of HfVe "D4
cially supported by the "Nederlands Organisatie voor Zuiver Wetenschappelijk Onderzoek
(ZWO)". References
[6] [7] [8] [9]
[1] P. Duffer, D.M. Gualtieri and V.U.S. Rao, Phys. Rev. Lett. 37 (1976) 1410. [2] J. Shinar, D. Davidov and R.D. Hogg, Solid State Commun. 37 (1981) 175. [3] A.V. Irodova, V.P. Glaskov, V.A. Somenkov and S.Sh. Shilstein, J. Less-Common Met. 77 (1981) 135. [4] D.T. Ding, J.I. de Lange, T.O. Klaassen, N.J. Poullis, D. Dadidov and J. Shinar, Solid State Commun. 42 (1982) 137. [5] M. Yu. Belyaev, A.V. Skripov, V.N. Kozhanov, A.P.
[10]
[11]
[12]
Stepanov and E.V. Galoshina, Solid State Commun. 48 (1983) 1049. N. Bloemhergen and T.J. Rowland, Acta Metailurgica 1 (1953) 731. M.H. Cohen and F. Reif, Solid State Phys. 5 (1957) 321. W.H. Jones, T.P. Graham and R.G. Barnes, Phys. Rev. 132 (1963) 1898. Koziro Narita, Tuniehi Umida and Hazime Kusumoto, J. Chem. Phys. 44 (1966) 2719. A.P. Sedee, D.T. Ding, T.O. Klaassen and N.J. Poulis, Proc. 17th Intern. Conf. on Low Temperature Physics, LT17, eds. U. Eckern, A. Shmid, W. Weber and H. Wiihl (North-Holland, Amsterdam, 1984) p. 125. L.A.G.M. WultIers, G.A.M. Ffijters, C.A. van Schie, T.O. Klaassen, N.J. Poulis, H.R. Khan and Ch.J. Raub, Physica 93B (1978) 180. A. Gevers, T.O. Klaassen, N.J. Poulis, H.R. Khan and Ch.J. Raub, Physica 122B (1983) 55.
N M R STUDY OF T H E L O W T E M P E R A T U R E S T R U C T U R E OF HfV 2 • D 4 D.T. D I N G * , A.P. S E D E E , T.O. K L A A S S E N and N.J. P O U L I S Kamerlingh Onnes Laboratorium der Rijksuniversiteit Leiden, Nieuwsteeg 18, 2311 SB Leiden, The Netherlands
Received 19 November 1984
The NMR powder spectrum of 51V in the low temperature tetragonal phase of HfV2.1)4 has been studied in fields up to 4 T. A detailed lineshape analysis proves that only one V-site is present, with strongly anisotropic nuclear spin interaction parameters. The results are in full agreement with neutron diffraction data and exclude the recently proposed existence of two inequivalent V-sites.
1. I n t r o d u c t i o n
The C-15 type intermetallic c o m p o u n d H f V 2 has a relatively high superconducting transition t e m p e r a t u r e ( T c ~ 9 K). It can easily absorb large quantities of hydrogen (or deuterium), forming stable hydrides H f V 2 - H x (0~
vq = 500kHz, 17 = 0.13 and an isotropic Knight shift Kilo = 0.68. O u r experiments had been perf o r m e d in relatively low fields, H ~< 0.9 T, which m a d e it hard to obtain reliable information concerning anisotropy in the Knight shift. These conclusions on the x = 4 c o m p o u n d were in full accordance with neutron diffraction by I r o d o v a et al. [3] on H f V 2 • D 4. Their results show that the low t e m p e r a t u r e phase belongs to the tetragonal space group I 4 J a , in which only one type of V-sites is present. Recently Belyaev et al. [5] published the results of their investigation on the cubic to tetragonai phase transition in H f V 2 • H3. 9. They determined the 51V N M R spectrum by integration of the spin echo signal while sweeping t h e magnetic field. The authors conclude from the analysis of the t e m p e r a t u r e d e p e n d e n c e of the spectrum in fields of 1.1 and 1.7 T that in the tetragonal phase at least two distinctly inequivalent V-sites are present, both characterized by axial symmetric nuclear spin interaction parameters. They argue that also the N M R s p e c t r a in fields of 0.5 and 0.9 T published by us for the x = 4 c o m p o u n d can be well described by their two sets of interaction parameters. As we p l a n - as part of o u r investigation into the electronic properties of the H f V 2 . H x s y s t e m - to carry out band structure calculations on these compounds, we have p e r f o r m e d ad-
0378-4363/85/$03.30 t~) Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
D.T. D i n g et aL / N M R study o f the structure o f H f V 2 "D4
ditional N M R experiments in higher fields to settle the question of the low temperature structure of the x = 4 compound.
171
°
2. Experimental results The experiments have been performed on powdered samples, with an average grain size of 100 Ixm. The grains were isolated with bee wax. The first derivative of the N M R spectra was recorded using a marginal oscillator, either by sweeping the field or the frequency. The calibration of the magnetic field of the superconducting solenoid was carried out by proton N M R of the bee wax isolation. The experiments were mainly performed at T = 1.2K. To possibly diminish the contribution of nuclear spin dipoledipole interaction to the 51V linewidth we used the deuteride compound H f V 2 • D 4 instead of the hydride. It was observed that the spectra of the hydride and deuteride compounds were essentially equivalent. It was carefully checked that the shape of the resonance spectrum was not influenced by any nuclear spin relaxation effects. The 51V spectrum has been recorded for a number of fields between 1.3 and 4 T. In most cases, all 0 = 90 ° powder spectrum discontinuities of the quadrupole satellites could be observed; sometimes also the 0 = 0 ° discontinuities (see fig. 2 and eq. (1)). At lower fields the spectrum of this ! = 7/2 nucleus is largely determined by first and second order effects of the electric quadrupole interaction. At higher fields, however, the influence of the second order quadrupole interaction (-~'~/~'0) has diminished strongly, while features due to anisotropy o f the Knight shift (-~'0) become more clearly visible. In fig. 1 experimental recorder traces are given for H = 1.3 T and H = 2.9 T, respectively. For clarity only the central line and the first satellites are shown. It can be seen that the structure on the central line becomes more pronounced towards high field and that a threefold splitting develops. The satellites show a, strongly field dependent, asymmetric pattern around the central line. In fig. 2 the nearly complete spectrum at H = 2.9 T
~I
"- .........
I!'
""
"---
'
II
t
I
'~'
I
I
l
12200
12400
t
t
12000
H [o~3
b
',!.,:'~ I 28600
I
I
I
28400
I 28200
I
I 28000
. I:oel
Fig. 1. Experimental first derivative of 51V NMR absorption spectrum at T = 1.2 K, showing central line and first satellites. Dashed lines are computer simulations. The arrow indicates the resonance line due to non-metallic vanadium. (a) v = 13.7 MHz. (b) ~, = 31.9 MHz.
is given; only the two (actually observed) outermost 0 = 0 ° discontinuities have been omitted for the sake of clarity. Inspection of the satellite spectrum at the various field strengths show that there are more satellite discontinuities than expected for a single site 1 = 7/2 spectrum with axially symmetric electric field gradient. For the explanation of the spectrum there are evidently two possibilities. Either there exist two or more V-sites or there is only one V-site with non-axial symmetry. We
D. T. Ding et al. / NMR study of the structure of HfVe "D4
172
F © r ,'~
~
i
X x
>-
1 c~
>- ~ r., ! t
1 I I
,
g
I I I
lI J r~
-2
Fig. 2. Overall 51V N M R ~aectrum at v = 31.9 MHz, T = 1.2K. The discontinuities are identified by a(m). (a(m) stands for the m - * m - 1 transition with the magnetic field along the -,-direction; ~t = x, y, z.) The arrow indicates the
resonance line due to non-metallicvanadium.
will first discuss the second possibility. The low temperature crystal structure as determined by Irodova et al. [3] belongs to the tetragonal space group I4Ja, in which the V atoms are situated at equivalent sites with point symmetry 1. The implication of this data for the electric field gradient (EFG) tensor is straightforward. There are no symmetry restrictions for the form of the EFG tensor, that means, there is no a priori reason to expect axial symmetry. The same holds for the magnetic interaction; also the Knight shift will not show axial symmetry. In fact for this point symmetry the Knight shift has to be described by a non-symmetric tensor K with 9 independent components. Consequently K cannot be diagonalized, and there are no relations between "principal axes" of K and those of the EFG tensor. We will describe K in the Cartesian coordinate system (x, y, z) coupled in the conventional way to the principal axes of the EFG tensor. Two remarks concerning the importance of the various components of K to the shape of the NMR spectrum can be made. Firstly, the Knight shift is small (K ~0.006) and consequently the frequency shifts in the spectrum due to K are only determined by the component of the internal field parallel to the external field. Therefore the effects of an antisymmetric part of K do not show up in the shape of the resonance spectrum, and that part will thus be left out of consideration throughout the paper. Secondly, in a powder spectrum the observable discontinuities of the satellite transitions originate from those V sites for which the external magnetic field is close to or along, respectively, the x, y and z axes of the EFG tensor (see fig. 4). So the influence of K on the shape of the satellite discontinuities is mainly determined by the diagonal components K,~, Kyy and K~. To simplify the discussion (and the computer simulations) we will take into consideration only these three unequal diagonal elements of K. To get a qualitative picture of the shape of the resonance spectrum for such a set of anisotropic interaction parameters, we have plotted in fig. 3 and fig. 4 schematically the theoretical powder patterns for the central transition and the first satellites, respectively. The influence of the
173
D. T. Ding et al. / N M R study of the structure of HfV2 "D4
quadrupole' interaction has been accounted for only in first order perturbation (high field situation). The central line exhibits a three-fold splitting. The 0 = 90 ° satellites are split up due to the finite value of the asymmetry parameter 7?. The splitting of the satellites on both sides of the central line is unequal and field dependent because of the unequality of K= and Kyy. It appears that, on the basis of this qualitative picture, all peaks in the experimental derivative spectra can be identified. To obtain accurate values for the interaction parameters, computer simulations of the powder spectra have been performed. As the quadrupolar interaction is rather large, the expressions for the resonance frequencies as given by other authors [6-9] have been extended to incorporate the effects of the quadrupolar interaction up to second order for the central line as well as for the satellites. Including also the anisotropy in the Knight shift the expressions are:
¢-90" .I 0-90" I
0 O*
,,!l\j
I
I %%
SI
L ",, ,, i
~=00 ~"..
e=90*
V=V0(l+ Kiso)
,I
~,~VO K Z - - . (Kz<0)
I
x/)
I
t
'
I- -
I
,
VoK X-
~'1 I
',1
CKx>0)
V0 Ky (Ky <0)
t Fig. 3. Schematic theoretical powder iineshape of the central transition (Am = +1/2--*-1/2) for a completely anisotropic Knight shift. Effects of second-order electric quadrupole interaction have been omitted.
(~-1/2)!
!(v3/2)
I
I
i (I,= o"
(v 3/2) e:o"
0=90" @=90" ~ 0:9°°~! ~ =
(1,= o"
9 J
--,,,,
e=90° o I ¢=90 0 ° ~
(
•
V=Vo(~+Ki~o) ! ] ,I]
e:°'(qV2)
(qV2: b
Cv3/2) e=o' f
q
VoK z
(Kz
VoKy (Ky'(O)
VoKx
(Kx>O)
VoKx
VoKy
VoKz
(Kx.,%0)(Ky'~O) ('Kz'~O)
Fig. 4. Schematic theoretical powder lineshape of the first satellites. (a) Non-axial-symmetric EFG tensor, isotropic Knight shift. (b) Non-axial-symmetric EFG tensor, completely anisotropic Knight shift.
D.T. Ding et aL / NMR study of the structure of HfV2" D4
174
Gaussian broadening of the theoretical spectrum has been assumed:
v m = Vo(1+ Ki,o) + vo[Kx sin 20 cos2 ~b + Ky sin 20 sin 2 &
f(v) oc e x p [ - ( v - /f')2120"2] .
+ Kz COS20] + ~q(~-- m)fH(O, dP)
(;){
+ ~12v0 If1H( 0, &)12124m(m - 1 ) - 4a + 9]
- ~ If~(O, &)12[12m(m - 1 ) - 4a + 6] ,
(1)
where 1
Ki~=-~ (K~ + K,y + K = ) ,
= K.-
um : frequency of the m ~ m - 1 transition m=I,I-1,...,-I+l, v o = gflHo, a = I ( I + 1), and
f~(O, ~) =
cos2 0 - ~ + ~ n sin2 0 cos(240,
(2)
If (o, 4012= 1 sin2 0[n2 + 9 c0¢ 0 IkJ
- 6n cos2 O cos(2~b) _
,/2 cos2(2&) sin20],
(3)
[fr( o, . )[Z = sin4 0[~ + - 1~ n2 cos2(2&)]
(4) 0 and 4~ are spherical coordinates, defined in the usual way with respect to the principal axes x, y, z, of the EFG tensor. In order to simulate realistic powder spectra a
The finite linewidth is due to nuclear spin dipolar interactions together with a possible spread in the strength of the quadrupolar interaction. The shape of the central line is effected only in second order by the quadrupolar interaction, whereas that of the satellites is determined by both first and second order effects. Therefore different values for the respective linewidths trc and o-s have been allowed for in the fitting procedure. The programming work is similar to that reported by Narita et al. [8], apart from an additional normalisation procedure. This procedure ensures a correct ratio of the relative intensities of the various satellite lines and the central line. The results of the best fit are shown as dotted lines in figs. 1 and 2. All peaks but one in the experimental spectra are reproduced very well. The remaining peak can be attributed to originate from non-metallic V impurities, probably oxides. The values of the parameters used are listed in table I. In a preliminary report slightly less accurate values have been given [10]. It must be stressed that the experimental spectra in the complete field region covered are reproduced correctly using these parameters. The position of the peaks in the experimental spectra reported by Belyaev [5] et al. can also be accounted for by our parameters. Because the experimental resolution of their spin echo spectra is less than that of our derivative spectra a precise comparison of the shape of their spectra with calculations cannot be performed. The similarity between their and our spectra strongly suggests, however, that the structure of the samples is identical. Concerning the conclusion by Belyaev that there exist two different V sites with axial symmetry, a few remarks can be made. First of all, their conclusion is in contradiction with the neutron diffraction work by Irodova et al. [3] from which it is concluded that only one V site exists. Moreover, the point symmetry of that site does not account for axial symmetry of the
D.T. Ding et al. / NMR study of the structure of HfVe . D4
Table I Ki~ = 0.0066 Kx = 0.0022 Ky = -0.0002 Kz = -0.0020
71 = 0.13 vq= 500 kHz o-¢= -7 kI--Iz trs = 15 kHz
nuclear spin interaction parameters. Certainly not if, as suggested by Belyaev, the low temperature phase of their sample HfV 2 • H3.9 has even a lower symmetry than I41/a. Secondly, although the position of the x(1/2,-3/2) and y(1/2,-3/2) satellites and the central line in our spectra can be accounted for approximately by the Belyaev parameters, the more precise shape and relative intensities are not reproduced by these parameters. More important, the positions of the /7=0 ° satellites in our spectra are in disagreement with the Belyaev parameters. These positions are not influenced in first order by the value of the asymmetry parameter r/ and second order effects are negligible for small values of +7 (see eqs. (1), (4)). Therefore, they yield straightforwardly the values of vq and Kz~, as given in table I. These facts unambiguously prove the validity of our fitting results and thereby the existence of only one V-site in HfV 2 • D+.
4. Discussion It is clear that to analyse properly complicated NMR powder spectra the choice of realistic nuclear spin interaction parameters, consistent with the possibly known point symmetry of the nuclear site, is of prime importance. Moreover, well-resolved experimental spectra are necessary in order to obtain as much detailed experimental information as possible. Therefore, in general, spectra of the absorption derivative using CW NMR are far more suitable than integrated spin echo spectra. For the low point symmetry encountered in this situation some simplifying assumptions concerning the interaction parameters are necessary, as a realistic fitting of 9 independent Knight shift components is virtually impossible. As can be seen, especially in
175
fig. 2, there still exist some discrepancies between theory and experiment for the detailed shape of the central line. These might quite well be due to the neglect of the symmetrical offdiagonal elements of /(. However, a more detailed fitting is hardly possible in view of the fact that in that case also the influence of a spread in the EFG and /( tensor components has to be taken into account. That such a spread, in any case for the EFG tensor, exists, is indicated by the necessity to use different values for the basic linewidth for central line and satellites (see table I) to obtain a good fit to the experiments. The very large anisotropy of the Knight shift constitutes a problem for the analysis of both R" and nuclear spin relaxation data. The relaxation rate R = (TTI) -1 will be strongly anisotropic, which will cause the recovery of the longitudinal magnetization after a saturating pulse to be nonexponential. We did actually observe this experimentally. A unique value for R cannot therefore be obtained. Because of the strong influence of dipolar contributions, the conventional analysis of the 51V Knight shift and relaxation rate in terms of density of states of s- and d-electrons at the Fermi level cannot be applied any more [11, 12]. A detailed knowledge of the relative contribution of the various conduction electrons (decomposed by angular momentum l and ml) to the density of states is needed for a realistic analysis. In addition, the off-diagonal elements, which are not or hardly detectable in Knight shift experiments, can give a large unknown contribution to the relaxation rate. It is evident that, because of the low point symmetry of the V site in the tetragonal phase of HfV2.D 4, only with great caution, information concerning the electronic properties, can be obtained from Knight shift and nuclear relaxation data.
Acknowledgments This investigation is part of the research program of the "Stichting voor +Fundamenteel Onderzoek der Materie ( F O M ) " , which is finan-
176
D.T. Ding et al. / N M R study of the structure of HfVe "D4
cially supported by the "Nederlands Organisatie voor Zuiver Wetenschappelijk Onderzoek
(ZWO)". References
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