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t9F and 45Sc nuclear spin relaxation for the hexafluoroscandate, hexafluorotitanate, and hexafluorogermanate ions in aqueous solution
JOURNAL
OF MAGNETIC
RESONANCE
25, 197-203
(1977)
lgFand 45ScNuclear Spin Relaxation for the Hexafluoroscandate,Hexafluorotitanate, and HexafluorogermanateIons in AqueousSolution V. P. TARASOVAND Yu. A. BUSLAEV Institute of General and Inorganic Chemistry, Academy of Sciences, Moscow V-71, USSR
ReceivedApril 12,1976; revisionreceivedJuly 12,1976 19F NMR spectra of aqueous solutions containing the 48TiFsz--49TiF62-and 74GeF62--73GeF62ions and ?Sc NMR spectraof an aqueoussolution containing %cFs3- ion are reported for a range of temperatures. Computer fitting of the observedlineshapesshows that both quadrupole-inducedtransitions between the spin states of a high-spin nucleus and chemical exchange of the fluorine atoms contribute to thelineshapes.The quadrupolecouplingconstantswereestimatedto be 4.5 MHz for 49TiFsZ-,5.8 MHz for 73GeFsZ-,and 9.5 MHz for Y~cF~~--ions. INTRODUCTION Nuclear spin relaxation and chemical exchange processes produce qualitatively similar effects on the intensity distribution in NMR multiplets which arise from scalar spin-spin coupling. The quantitative difference between the effects of relaxation and exchange arises from the fact that relaxation processes obey selection rules on the change in the magnetic quantum number m while chemical exchange is completely nonselective as far as changes in m are concerned. The expected multiplet structure will be seen only if the high-spin nucleus is in a highly symmetric environment. Examples of this case are lgF spectra of hexafluoroions having 0, symmetry. A previous study of the 19F spectrum of aqueous (NH,),TiF, and (NH,),GeF, has been reported by Deen and Evans (I), who found coupling constants for 73Ge-1gF (98 t- 0.5 Hz) and 4gTi-19F (33.0 F 0.2 Hz) in GeFG2- and TiFs2- anions, respectively. The 45S~-1gF coupling constant for ScFc3- was found to be 172 Hz by use of lgF NMR (2) and 180 & 10 Hz by 45Sc NMR (3). Pfadenhauer and McCain (2) observed 19F NMR of (NH,),ScF, in aqueous solution at -1.8 to 36” and studied the influence of the quadrupole and exchange effects on 19F lineshape. In the present note we report lgF resonance measurements for a range of temperatures on aqueous solutions of (NH,),TiFG and (NH,),GeF, for 4gTi- and 73Geenriched samples and also 4sSc resonance measurements on aqueous solutions of (NH4),ScFB, along with a calculation of lineshapes of both lgF and 45Sc, due to quadrupole and exchange effects. These hexafluoroanions were chosen for our study for the following reasons. They possess (i) high-spin nuclei, (ii) relatively large coupling constants, and (iii) fluorine atoms which undergo chemical exchange in aqueous solutions (4). Copyright 0 1977 by Academic Press, Inc. 197
All rights of reproduction Printed in Great Britain
in any form
reserved.
198
TARASGV
AND
BUSLAEV
EXPERIMENTAL
lgF NMR spectra were recorded on a Varian A56/60A and Varian XL-loo-15 spectrometers operating at 56.4 and 94.1 MHz using the Varian variable temperature controller. NMR signals of 45Sc were observed at 15 MHz with a Varian WL-112 spectrometer equipped with a variable-temperature probe and variable-temperature control unit. The 45Scresonances wererecorded as the derivative of the dispersion mode. The modulation frequency was 35 Hz and the modulation amplitude was set to be small compared to the observed linewidths. Sample tubes of 9.5 mm o.d. were used. (NH&ScF6 was prepared following the method of Ivanov-Emin et ccl.(5) and (NH,), TiF, and (NH4)ZGeF6 were prepared by standard procedures using the isotopically enriched TiO, and metallic Ge (4). The solutions of (NH4)2TiF6 and (NH4)2GeF, were prepared as saturated ones, and the aqueous solution of ammonium hexaffuoroscandate was made by dissolving (NH&ScF, with the large excess of NH4F. (See Table 1.) TABLE
1
Characteristicsof the isotope-enrichedstarting materials TiOz Ge (met)
Isotope percent Isotope Percent
46Ti 1.7 7oGe 1.10
47Ti 1.9 72Ge 2.28
48Ti 22.6 73Ge 91.4
4gTi 71.5 74Ge 4.66
50Ti 2.3 76Ge 0.56
Properties of the magnetic isotopes” Nucleus
Abundance
45sc
100 1.9 71.5 91.5
47Ti 49Ti 73Ge
(%)
Spin
Q x 10z4 (cm”)
3 3 2 3
-0.22 -0.20
a Even-mass nuclei have zero spin. RESULTS
AND
DISCUSSION
The lineshape of the NMR spectrum of a group of magnetically equivalent S = 3 nuclei, which are spin coupled to a nucleus I > 1 has been discussed previously (6-S). A method of calculating lineshape which is particularly suited to the systems studied in this paper is that based on the work of Kubo (7) and Sack (a), which has been described by Aksnes et al. (6). This method gives the intensity of the NMR absorption of the S spins by the equation X(o) cc Re (WA-‘l}, where Y(o) is the spectral intensity at angular frequency o, Re{ } denotes “the real part of,” W is a row vector whose components are proportional to the relative populations of the spin states of the I nucleus (all unity except m = 0), and 1 is a unit column vector. The elements of W are (1,1,1,1,2.96,1,1,1,1) for the system 48TiF,2--4gTiF,2-,
RELAXATION
OF HEXAFLUORO
IONS
199
and (1,1,1,1,1,0.96,1,1,1,1,1) for the system 74GeFs2--73GeF,2-. The quantity A-’ is the inverse of the matrix A, whose elements are given by expression
o0 is the frequency of the center of the multiplet; a,,, is the delta function; C(Z,m,n) is a coefficien’ depending on Z,m, and rz; and p is a mean-squared value of the quadrupole coupling constant of the Z spins. f is the scalar spin-spin coupling constant between the Zand S spins in hertz, equal to 33 Hz for 4gTiF62-, 100 Hz for 73GeF62- and 180 Hz for 45S~F,3-. Using the definition of Aksnes et at. (6),
a E 7, p/27@,
p f z-‘/p 2719,
where 7-l is the probability per unit time that a fluorine spin detects a change in the spin state of nucleus Z due to chemical exchange. r’, is the correlation time, p is a factor depending on a number and relative populations of the spin states of the Z nucleus. CI and /3 parameters may be used to reproduce the observed lineshape. An Algol program for calculating lineshape was written for a BECM-4 computer. For a given experimental spectrum the values of u and p were varied until a minimum value of the mean-squared deviation was obtained.
. . : . . .‘.. .. -* . ..... ..... -./
.:’ .
:
,:: . ..
... ‘.: . .* ’...*.....
..........
-4’
.., : . ..
-. -. ........’
:‘.. ..
: ... .....
. ~ 5..%..,
30 Ha
FIG. 1. Theoretical and observed lineshape of the 19F NMR at 3.5” for aqueous solution, containing 48TiF62--49TiF6Z- ions.
200
TARASOV
AND
BUSLAEV
The observed lgF spectra of aqueous (NHJ,TiF, and (NH,),GeF, together with computer-simulated spectra are shown in Figs. 1 and 2. The nine-line spectrum consists of an octet due to coupling of 4gTi (I = 3 with lgF and a central line due to 48TiF6Z-. The eleven-line spectrum consists of a decet due to coupling of 73Ge (I= 3 with lgF and a central line arising from 74GeF, ‘- . Tables 2 and 3 give the values of the relaxation
. .
. . -._.’
‘. .
.
-. .
: : “J
FIG. 2. Theoretical and 74GeF62--73GeE62ions.
‘j
. :.
; .-,.
-
. .
.
. .
.
-*
-*
.*
.
1.
.-
_.
: ‘s,..’
*: L./
.,
. ...“’
~
:.
. .
.
b .,
..
. ..,d.
.
. .
. .
,. .,
I
.
: ‘L.
.: .. ..“,..
:
. . ,_,.
*
. . ., \...
observed lineshape of the “F NMR at 30” for aqueous solution, containing
RELAXATION
OF
HEXAFLUORO
IONS
201
(a) and exchange (p) parameters for aqueous solutions of (NH,),TiF6 and (NH,),GeF6 at various temperatures obtained by computer fitting of the 19F NMR lineshapes. TABLE
2
THE a AND b PARAMETERS OF THE 19F NMR SHAPES FOR 48TiF,2--49TiF62-
T”C
a
10 35 63 70 83 93
B x lo3 (k20
(2720%) 4.49 3.08 3.13 3.31 3.64 4.08
THE a AND b PARAMETERS
3 OF THE 19F NMR
SHAPES FOR 74GeF62--73GeF62-
-20 0 20 30 63 68 73 83 93 103 108
a
0% 4.8 3.6 2.2 1.1 1.6 2.0 2.0 2.0 2.2 3.0 3.6
%)
3.9 3.7 11.6 10.7 35.5 39.8
TABLE
T”C
LINE-
%)
LINE-
ions
D x lo3 (k20
74)
4.4 3.9 1.6 1.3 1.3 1.8 2.0 3.4 6.7 7.7 8.3
The spectra well illustrate the different effects that the two processes of relaxation and ,exchange have on lineshape. Spectra from lower temperatures, at which the quadrupole relaxation of the 4gTi or 73Ge nuclei is the dominant effect, all have characteristically tall peaks at the extremes of the multiplet, while at higher temperatures intensity builds toward the center of the multiplet. It is worth noting that a(T), which is proportional to the quadrupole relaxation rate, shows unusual temperature dependence for the 4gTi and 73Ge relaxation rates. A plot of cIagainst T"C passes through a minimum at 35” for 49TiF,2- and 30” for 73GeF,2- ions. In a stable complex unperturbed by chemical processes, p should be approximately constant and CIshould decrease with 2, when the temperature increases, just as we observe in the low-temperature range. Evidently at higher temperatures the effective p increases with temperature. To explain this fact, Aksnes et al. have proposed the existence of a fluorine exchange process between the species with lower than octahedral symmetry and a much larger d;“. To understand the effect of this situation on the apparent quadrupole relaxation rate as observed via a study of the lineshape of the 19F NMR spectrum, it is worthy studying
202
TARASOV
AND
BUSLAEV
the dependence of the resonance of the high-spin nucleus upon temperature. For this aim we observed the 45Sc spectra of ammonium hexafluoroscandate, (NH4)$cFg, in aqueous solution at various temperatures. 45Schas 100 o/0abundance, I = 5. The lineshape for the high-spin nucleus 45Schas been calculated using the second derivative of 9 (w) with respect to o. In this case, with the notation already adopted, W = (1,6,10, l&10,6,1) and the elements of the A matrix (7 by 7) are defined by
The values of m are -3,-2,-1,0,1,2,3. The 45Scspectra of aqueous solution containing ScFe3- ions at various temperatures are shown in Fig. 3. Values of CIand /? which give the best fit are listed in Table 4.
plDJ-!Z
.
FIG . 3 . ?Gc NMR spectra of aqueous solution, containing ScF, 3- ions observed at 40” (a), 30” (b), and 11’ (c). Curve (d) represents the best Iit to the 11’ spectrum.
RELAXATION
OF
HEXAFLUORO
TABLE THE
a
AND
4
B PARAMETERS
LINESHAPE
FOR
OF THE
B(k30%)
4.5 5.0 4.8
0.075 0.120 0.150
11
‘?3c
ScFe3-
a(k30%)
30 40
203
IONS
The a as determined from the fitting of the 45Sc spectra shows a temperature independence within the experimental error. Evidently the knowledge of both CI and z, would allow calculation of the nuclear quadrupole coupling constant. For a solution of a given compound, the temperature-dependent spectral changes will be due almost entirely to changes in r, (9). The calculations of z, were based on the Stokes hydrodynamic equation, which treats the tumbling ion as a sphere rotating in a homogeneous medium of macroscopic viscosity y, z, = 4na3r]/3kT, where a is the ionic radius, equal to 3.27 A for TiFe2- (lo), 3.01 A for GeF,‘- (IO), and 3.53 w for ScFb3-.l The calculated 7,‘s were combined with amin(T) values obtained in the computer simulation, to yield estimates of e’qQ/h. We estimate the nuclear quadrupole coupling constants in 4gTiF, ‘- , 73GeF62-, and 45S~F63- to be 4.5, 5.8, and 9.5 MHz. It is important to note that other relaxation mechanisms such as dipole-dipole and spin-rotational coupling may also contribute to the experimentally measured values of /?. From the results for /? in Tables 2 and 3 it is apparent that 19F-19F and 19F-metal dipole-dipole interactions contributed at low temperatures. Increasing influence of spin-rotational relaxation would be expected at higher temperatures, but the values of the spin-rotational tensor component which are necessary to account for all of /3 would have to be excessively large (~0.5 MHz). Thus we interpret these results as showing that chemical exchange is probably the dominant relaxation mechanism. ACKNOWLEDGMENTS
We are indebted to Dr. S. Petrosyans for sample preparation and for running the 19F NMR spectra and we thank D. Maksimov and M. Hofman for help in computer programming. REFERENCES Sot. A, 698 (1967). J. Phys. Chem. 74,329l (1970). V. P. TARASOV AND V. I. CHAGIN, RUSS.J. Inorg. Chem. 19,
1. P. A. DEAN AND D. F. EVANS, J. Chem. 2. E. H. PFADENHAUER AND D. C. MCCAIN,
3. Yu.
A. BUSLAEV,
S. P.
PETROSYANS,
1790(1974). 4. Yu. A. BUSLAEV, S. P. PETROSYANS, AND V. 5. B. N. IVANOV-EMIN, T. N. SUSANINA, AND
P. TARASOV, Russ. J. Struct. Chem. lo,41 1 (1969). L. A. OGORODNIKOVA, Russ. J. Inorg. Chem. 11, 274
(1966). 6. D. W. AKSNES, S. M. HATCHISON, 7. R. KUBO, Nuooo Cimento, Suppl.
8. R. 9.
A.
E. A.
AND J. K. PACKER,
Mol. Phys. 14,301
(1968).
6,1063 (1957).
SACK, Mol. Phvs., 1, 163 (1958). LUCKEN, “Nuclear Quadrupole
Coupling Constants,”
Chap. 8, Academic Press, London,
1969. 10.
J. B. LEANE
AND R. E. RICHARDS,
Spectrochim. Acta 10,154
(1957).
1 The value 3.53 A was taken as the sum of the Sc3+ (0.81 A) and the fluorine ionic diameter (2.72 A)
OF MAGNETIC
RESONANCE
25, 197-203
(1977)
lgFand 45ScNuclear Spin Relaxation for the Hexafluoroscandate,Hexafluorotitanate, and HexafluorogermanateIons in AqueousSolution V. P. TARASOVAND Yu. A. BUSLAEV Institute of General and Inorganic Chemistry, Academy of Sciences, Moscow V-71, USSR
ReceivedApril 12,1976; revisionreceivedJuly 12,1976 19F NMR spectra of aqueous solutions containing the 48TiFsz--49TiF62-and 74GeF62--73GeF62ions and ?Sc NMR spectraof an aqueoussolution containing %cFs3- ion are reported for a range of temperatures. Computer fitting of the observedlineshapesshows that both quadrupole-inducedtransitions between the spin states of a high-spin nucleus and chemical exchange of the fluorine atoms contribute to thelineshapes.The quadrupolecouplingconstantswereestimatedto be 4.5 MHz for 49TiFsZ-,5.8 MHz for 73GeFsZ-,and 9.5 MHz for Y~cF~~--ions. INTRODUCTION Nuclear spin relaxation and chemical exchange processes produce qualitatively similar effects on the intensity distribution in NMR multiplets which arise from scalar spin-spin coupling. The quantitative difference between the effects of relaxation and exchange arises from the fact that relaxation processes obey selection rules on the change in the magnetic quantum number m while chemical exchange is completely nonselective as far as changes in m are concerned. The expected multiplet structure will be seen only if the high-spin nucleus is in a highly symmetric environment. Examples of this case are lgF spectra of hexafluoroions having 0, symmetry. A previous study of the 19F spectrum of aqueous (NH,),TiF, and (NH,),GeF, has been reported by Deen and Evans (I), who found coupling constants for 73Ge-1gF (98 t- 0.5 Hz) and 4gTi-19F (33.0 F 0.2 Hz) in GeFG2- and TiFs2- anions, respectively. The 45S~-1gF coupling constant for ScFc3- was found to be 172 Hz by use of lgF NMR (2) and 180 & 10 Hz by 45Sc NMR (3). Pfadenhauer and McCain (2) observed 19F NMR of (NH,),ScF, in aqueous solution at -1.8 to 36” and studied the influence of the quadrupole and exchange effects on 19F lineshape. In the present note we report lgF resonance measurements for a range of temperatures on aqueous solutions of (NH,),TiFG and (NH,),GeF, for 4gTi- and 73Geenriched samples and also 4sSc resonance measurements on aqueous solutions of (NH4),ScFB, along with a calculation of lineshapes of both lgF and 45Sc, due to quadrupole and exchange effects. These hexafluoroanions were chosen for our study for the following reasons. They possess (i) high-spin nuclei, (ii) relatively large coupling constants, and (iii) fluorine atoms which undergo chemical exchange in aqueous solutions (4). Copyright 0 1977 by Academic Press, Inc. 197
All rights of reproduction Printed in Great Britain
in any form
reserved.
198
TARASGV
AND
BUSLAEV
EXPERIMENTAL
lgF NMR spectra were recorded on a Varian A56/60A and Varian XL-loo-15 spectrometers operating at 56.4 and 94.1 MHz using the Varian variable temperature controller. NMR signals of 45Sc were observed at 15 MHz with a Varian WL-112 spectrometer equipped with a variable-temperature probe and variable-temperature control unit. The 45Scresonances wererecorded as the derivative of the dispersion mode. The modulation frequency was 35 Hz and the modulation amplitude was set to be small compared to the observed linewidths. Sample tubes of 9.5 mm o.d. were used. (NH&ScF6 was prepared following the method of Ivanov-Emin et ccl.(5) and (NH,), TiF, and (NH4)ZGeF6 were prepared by standard procedures using the isotopically enriched TiO, and metallic Ge (4). The solutions of (NH4)2TiF6 and (NH4)2GeF, were prepared as saturated ones, and the aqueous solution of ammonium hexaffuoroscandate was made by dissolving (NH&ScF, with the large excess of NH4F. (See Table 1.) TABLE
1
Characteristicsof the isotope-enrichedstarting materials TiOz Ge (met)
Isotope percent Isotope Percent
46Ti 1.7 7oGe 1.10
47Ti 1.9 72Ge 2.28
48Ti 22.6 73Ge 91.4
4gTi 71.5 74Ge 4.66
50Ti 2.3 76Ge 0.56
Properties of the magnetic isotopes” Nucleus
Abundance
45sc
100 1.9 71.5 91.5
47Ti 49Ti 73Ge
(%)
Spin
Q x 10z4 (cm”)
3 3 2 3
-0.22 -0.20
a Even-mass nuclei have zero spin. RESULTS
AND
DISCUSSION
The lineshape of the NMR spectrum of a group of magnetically equivalent S = 3 nuclei, which are spin coupled to a nucleus I > 1 has been discussed previously (6-S). A method of calculating lineshape which is particularly suited to the systems studied in this paper is that based on the work of Kubo (7) and Sack (a), which has been described by Aksnes et al. (6). This method gives the intensity of the NMR absorption of the S spins by the equation X(o) cc Re (WA-‘l}, where Y(o) is the spectral intensity at angular frequency o, Re{ } denotes “the real part of,” W is a row vector whose components are proportional to the relative populations of the spin states of the I nucleus (all unity except m = 0), and 1 is a unit column vector. The elements of W are (1,1,1,1,2.96,1,1,1,1) for the system 48TiF,2--4gTiF,2-,
RELAXATION
OF HEXAFLUORO
IONS
199
and (1,1,1,1,1,0.96,1,1,1,1,1) for the system 74GeFs2--73GeF,2-. The quantity A-’ is the inverse of the matrix A, whose elements are given by expression
o0 is the frequency of the center of the multiplet; a,,, is the delta function; C(Z,m,n) is a coefficien’ depending on Z,m, and rz; and p is a mean-squared value of the quadrupole coupling constant of the Z spins. f is the scalar spin-spin coupling constant between the Zand S spins in hertz, equal to 33 Hz for 4gTiF62-, 100 Hz for 73GeF62- and 180 Hz for 45S~F,3-. Using the definition of Aksnes et at. (6),
a E 7, p/27@,
p f z-‘/p 2719,
where 7-l is the probability per unit time that a fluorine spin detects a change in the spin state of nucleus Z due to chemical exchange. r’, is the correlation time, p is a factor depending on a number and relative populations of the spin states of the Z nucleus. CI and /3 parameters may be used to reproduce the observed lineshape. An Algol program for calculating lineshape was written for a BECM-4 computer. For a given experimental spectrum the values of u and p were varied until a minimum value of the mean-squared deviation was obtained.
. . : . . .‘.. .. -* . ..... ..... -./
.:’ .
:
,:: . ..
... ‘.: . .* ’...*.....
..........
-4’
.., : . ..
-. -. ........’
:‘.. ..
: ... .....
. ~ 5..%..,
30 Ha
FIG. 1. Theoretical and observed lineshape of the 19F NMR at 3.5” for aqueous solution, containing 48TiF62--49TiF6Z- ions.
200
TARASOV
AND
BUSLAEV
The observed lgF spectra of aqueous (NHJ,TiF, and (NH,),GeF, together with computer-simulated spectra are shown in Figs. 1 and 2. The nine-line spectrum consists of an octet due to coupling of 4gTi (I = 3 with lgF and a central line due to 48TiF6Z-. The eleven-line spectrum consists of a decet due to coupling of 73Ge (I= 3 with lgF and a central line arising from 74GeF, ‘- . Tables 2 and 3 give the values of the relaxation
. .
. . -._.’
‘. .
.
-. .
: : “J
FIG. 2. Theoretical and 74GeF62--73GeE62ions.
‘j
. :.
; .-,.
-
. .
.
. .
.
-*
-*
.*
.
1.
.-
_.
: ‘s,..’
*: L./
.,
. ...“’
~
:.
. .
.
b .,
..
. ..,d.
.
. .
. .
,. .,
I
.
: ‘L.
.: .. ..“,..
:
. . ,_,.
*
. . ., \...
observed lineshape of the “F NMR at 30” for aqueous solution, containing
RELAXATION
OF
HEXAFLUORO
IONS
201
(a) and exchange (p) parameters for aqueous solutions of (NH,),TiF6 and (NH,),GeF6 at various temperatures obtained by computer fitting of the 19F NMR lineshapes. TABLE
2
THE a AND b PARAMETERS OF THE 19F NMR SHAPES FOR 48TiF,2--49TiF62-
T”C
a
10 35 63 70 83 93
B x lo3 (k20
(2720%) 4.49 3.08 3.13 3.31 3.64 4.08
THE a AND b PARAMETERS
3 OF THE 19F NMR
SHAPES FOR 74GeF62--73GeF62-
-20 0 20 30 63 68 73 83 93 103 108
a
0% 4.8 3.6 2.2 1.1 1.6 2.0 2.0 2.0 2.2 3.0 3.6
%)
3.9 3.7 11.6 10.7 35.5 39.8
TABLE
T”C
LINE-
%)
LINE-
ions
D x lo3 (k20
74)
4.4 3.9 1.6 1.3 1.3 1.8 2.0 3.4 6.7 7.7 8.3
The spectra well illustrate the different effects that the two processes of relaxation and ,exchange have on lineshape. Spectra from lower temperatures, at which the quadrupole relaxation of the 4gTi or 73Ge nuclei is the dominant effect, all have characteristically tall peaks at the extremes of the multiplet, while at higher temperatures intensity builds toward the center of the multiplet. It is worth noting that a(T), which is proportional to the quadrupole relaxation rate, shows unusual temperature dependence for the 4gTi and 73Ge relaxation rates. A plot of cIagainst T"C passes through a minimum at 35” for 49TiF,2- and 30” for 73GeF,2- ions. In a stable complex unperturbed by chemical processes, p should be approximately constant and CIshould decrease with 2, when the temperature increases, just as we observe in the low-temperature range. Evidently at higher temperatures the effective p increases with temperature. To explain this fact, Aksnes et al. have proposed the existence of a fluorine exchange process between the species with lower than octahedral symmetry and a much larger d;“. To understand the effect of this situation on the apparent quadrupole relaxation rate as observed via a study of the lineshape of the 19F NMR spectrum, it is worthy studying
202
TARASOV
AND
BUSLAEV
the dependence of the resonance of the high-spin nucleus upon temperature. For this aim we observed the 45Sc spectra of ammonium hexafluoroscandate, (NH4)$cFg, in aqueous solution at various temperatures. 45Schas 100 o/0abundance, I = 5. The lineshape for the high-spin nucleus 45Schas been calculated using the second derivative of 9 (w) with respect to o. In this case, with the notation already adopted, W = (1,6,10, l&10,6,1) and the elements of the A matrix (7 by 7) are defined by
The values of m are -3,-2,-1,0,1,2,3. The 45Scspectra of aqueous solution containing ScFe3- ions at various temperatures are shown in Fig. 3. Values of CIand /? which give the best fit are listed in Table 4.
plDJ-!Z
.
FIG . 3 . ?Gc NMR spectra of aqueous solution, containing ScF, 3- ions observed at 40” (a), 30” (b), and 11’ (c). Curve (d) represents the best Iit to the 11’ spectrum.
RELAXATION
OF
HEXAFLUORO
TABLE THE
a
AND
4
B PARAMETERS
LINESHAPE
FOR
OF THE
B(k30%)
4.5 5.0 4.8
0.075 0.120 0.150
11
‘?3c
ScFe3-
a(k30%)
30 40
203
IONS
The a as determined from the fitting of the 45Sc spectra shows a temperature independence within the experimental error. Evidently the knowledge of both CI and z, would allow calculation of the nuclear quadrupole coupling constant. For a solution of a given compound, the temperature-dependent spectral changes will be due almost entirely to changes in r, (9). The calculations of z, were based on the Stokes hydrodynamic equation, which treats the tumbling ion as a sphere rotating in a homogeneous medium of macroscopic viscosity y, z, = 4na3r]/3kT, where a is the ionic radius, equal to 3.27 A for TiFe2- (lo), 3.01 A for GeF,‘- (IO), and 3.53 w for ScFb3-.l The calculated 7,‘s were combined with amin(T) values obtained in the computer simulation, to yield estimates of e’qQ/h. We estimate the nuclear quadrupole coupling constants in 4gTiF, ‘- , 73GeF62-, and 45S~F63- to be 4.5, 5.8, and 9.5 MHz. It is important to note that other relaxation mechanisms such as dipole-dipole and spin-rotational coupling may also contribute to the experimentally measured values of /?. From the results for /? in Tables 2 and 3 it is apparent that 19F-19F and 19F-metal dipole-dipole interactions contributed at low temperatures. Increasing influence of spin-rotational relaxation would be expected at higher temperatures, but the values of the spin-rotational tensor component which are necessary to account for all of /3 would have to be excessively large (~0.5 MHz). Thus we interpret these results as showing that chemical exchange is probably the dominant relaxation mechanism. ACKNOWLEDGMENTS
We are indebted to Dr. S. Petrosyans for sample preparation and for running the 19F NMR spectra and we thank D. Maksimov and M. Hofman for help in computer programming. REFERENCES Sot. A, 698 (1967). J. Phys. Chem. 74,329l (1970). V. P. TARASOV AND V. I. CHAGIN, RUSS.J. Inorg. Chem. 19,
1. P. A. DEAN AND D. F. EVANS, J. Chem. 2. E. H. PFADENHAUER AND D. C. MCCAIN,
3. Yu.
A. BUSLAEV,
S. P.
PETROSYANS,
1790(1974). 4. Yu. A. BUSLAEV, S. P. PETROSYANS, AND V. 5. B. N. IVANOV-EMIN, T. N. SUSANINA, AND
P. TARASOV, Russ. J. Struct. Chem. lo,41 1 (1969). L. A. OGORODNIKOVA, Russ. J. Inorg. Chem. 11, 274
(1966). 6. D. W. AKSNES, S. M. HATCHISON, 7. R. KUBO, Nuooo Cimento, Suppl.
8. R. 9.
A.
E. A.
AND J. K. PACKER,
Mol. Phys. 14,301
(1968).
6,1063 (1957).
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1 The value 3.53 A was taken as the sum of the Sc3+ (0.81 A) and the fluorine ionic diameter (2.72 A)