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Anisotropy of the chemical shift tensor in solid fluorine
Volume 8, number 5
ANISOTROPY
CHEMICAL PHY&2S LETTERS
tiF
:CHE
CHEMICAL&IF-T D. E. O’REILLY,
Ar,zonne NationaL Laboratoy,
.
1 March 1971
TENSOR
IN SOLID
FLUORINE
*
E. M. PETERSON IZlinois 60439. U.S.4
Argonne.
2. M. EL SAFFAR DePauZ University, Cl:icago, IZZinois, US4
I
and C. E. SCHEIE
Concordia CoZZege, Moorhead, Minnesota 56560. USA Received
30 Norember
1970
The anisotropy of the chemical shift tensor in solid fluorine has been measured by several independent methods to he (1050*50} x 10-6. This value is slightl,v smaller than the estimated paramagcetic part of the chemical
shift from the spin-rotation
constant in the gaseous
Flliorine is one of ihe few elements that have not b&n studied by NMR in the condensed
.pha&s. In this note we report the anisotropy of the chemica1 shift tensor Aa = IT‘,,- a,for F2 whidh was determined in conjunction with a complete study [l] of the relaxation times and selfdiffusion coefficients in liquid and solid (ol and ,!I phases) F2. Five independent methods were used to evaluate do. These are: (1) determination of the first moment (Ml) of the lineshape, (2) determination of the second moment (M2) of -. the lineshape, ‘-(3) measurement of the separation A between the unshifted “center of the spectrum” and the hilmp in the derivative of the absorption at high field, (4) fitthe lineshape by cdmputer to the theor&c* powder pattern with gaussian broadening and, (5) measurement of the shift (6) between the resonance line in the &quid and the center of the- spectruti of‘the _solid It may readily be shown that
* Based~on w&k performed under the &&es U.S.‘@omic Energy Commission. .-. ,
state.
3 rtiA =HTC R
AuH
and 6 = (Ao/3)Ef,
(4)
where it has been assumed that the chemical shift tensor has axial symmetry (u,, = ad,, Us = udL + Up; Od, VP = diamagnetic and paramagnetic part of the chemical shift tensor respectively) and B is the bFOadening parameter of the gaussian single crystal lineshape S(H-Ho): s(H-Ho)
=
l3(2&
@=P - rcR-~o)2/2@2].
(5)
The results of the measurements, which were performed near 29’K (BOOKfor the liquid). and from 4 to 40 MHz are summarized in figs. 1 - 5 and tabie 1. In fig. 1, ‘Ml is plotted versus resona+ze2frequency vo; in fig. 2, M2’is plotted veerBUSvo; in fig. 3, A is plotted versus vo: in fig. 4, 8 typical computer_ fit to the lineshape is shown and in fig. 5, AC+ versus vd is given as. deter: mined from the.best iilk to the lineshapes. - Methods l-- 4 yield consistent resulti: the -ave&ge value‘of Au-is (1050350) 5 19-9.: From the bbs&tied spi&roJation c@st&t !n ihe g as ,.’ phase [2] bne calcul_tit&S ip = :ll?O X 10’ us.: r All p&b of &e&da;, shift ‘&cusstid &I this pa@r .are c&x&xted relative to-tie Fluo;lne nu+us as the bf .(he.. . ’._ : uri&ia of_++@ates. : ._ ,-. ,.. ._’ _, . .-. . _ _. ,. _---. .-. ’ - ,._- -, _:I ,a, ;.‘ . : “-’ .. I.-..,.-. ., ..,. . ..-: ,. ‘-’ ,.. ,..,;,_;, .,_ ,_.._:.. ,, : :, _ .,
1 March 1972
CHEMICAL PHYSICS LETTERS
Volume 8, number 5
24-
I
4
II 8
12
I
I
f
I
I
,6
20
24
28
32
RESOHANCE
FREQUENCY,
I1 36
40
q,. HHz
Fig. 1. First moment (Ml) of ISF resonance lineshaps versus resonance frequency @I,).
Fig. 3.
Separation
between
field hump
MFSUS
center of spectrum and high frequency.
res5nance
Fig. 2. Second moment (hf2} versus equare of resonance frequency.
Fig. 5. Anisotropic shift (4crH) from computer fit of lineshspe versus resonance frequency uo.
.
:.
’ Fig. 4. Derivative of.Ig F resonance. wii$ v5 = 40.3~MEIz. &shed awve is computer fit with param&ers given in text . md tab!e l., Frequency markers are from proton gaussmeter. .‘ .’ ._ . -’. .. * _-..‘. ._“’ 471 . . ; ”-.. . 1
VoIume8, number5 : -
CHEkfICAL PIIY&S Table 1
-: Anisotropyaf the &err&a! shift tensor f&o) by varioue - methods
Ahoxlo6
. Method‘
MI vemus &b ’ M2 wrsui
v#
A versus Y,,
1110 t 100 1090 f
50
990 4 60
tineshape fit
ICI0 ;: 40
6, Yo’ 40.4 M&l
1230 f 200
&&f&?
1050 f
a1
so
a) Value derived from 6 not included, eee text.
.
ing the well known relationship [33 between the spin-rotation and chemicaI shift tensors. If this result is valid for the fluorine moiecule in the solid State, the A’Jd = od,, - mddl= (-70&50)x Lo-6 and the anisotropic diamagnetic part _of the chemical shift tensor is negligible as is often assumed. In the gas phase [4], the average diamagnetic art of the chemical shift tezX%X??d= 513 x 10- 8. The liquid state value of ho is within experimental error of the average of methods (1) - (4), but 6 has an uncertainty in the experimental error due to d~~cu~~ in the location of thb precise center of the solid state spectrum.
LEZTTEiS
’
1 March lS?l
This &as done bv determinim? the mi&oint between the ‘extremes of the de&&e spectrum. The p-phase of Fz (helow ‘45.4°1Q-is a rel&tivety dense structure 153but it seems very un-. Ukel~ that up could be greatly changed by the perturbation of the eolid state structure. The value of.yA/!3 from.methods (a), (3) and (4) is 9.5 i 0.3 G correspondin&to a value of R = 1.416 O.Olk The gasphase value [6] of R = l-418& 13was calculated from the crystal struc. twe of the Q!-phase to be 2..4 G; best computer fits to the lineshape seemed to be obtained with B = 2.6 CL In view of the nature of the gaussian approximation this discrepancy is to be expected. REFERENCES {l] D. E. ORellly, E. M. Peterson, D.L.Hogenboomand C.E. Scheie, J. Chem. Phys., to be published. [2JI. Oaier, L. M. Crap% J. W.CederbergandN.F. Runsey, Phye.Rev. Letters 13 (1964) 482.
[3] N. F.Ramsey, Molecular beams (Clarendon Press, oxford, 1956) pp. 162, 208. ‘[4J D.K.Hindermar?n and L.L.Wiiliams, J. Chem. Phys. 50 (19!$) 2839. f5J L. Meyer, .C.9. Barrett and S. C. Greter, J. Chem. Phys. 49 (1968) 1902. (SJ D,Andrychuk, Cs.n.J.Phys. 29 (1951) 151.
ANISOTROPY
CHEMICAL PHY&2S LETTERS
tiF
:CHE
CHEMICAL&IF-T D. E. O’REILLY,
Ar,zonne NationaL Laboratoy,
.
1 March 1971
TENSOR
IN SOLID
FLUORINE
*
E. M. PETERSON IZlinois 60439. U.S.4
Argonne.
2. M. EL SAFFAR DePauZ University, Cl:icago, IZZinois, US4
I
and C. E. SCHEIE
Concordia CoZZege, Moorhead, Minnesota 56560. USA Received
30 Norember
1970
The anisotropy of the chemical shift tensor in solid fluorine has been measured by several independent methods to he (1050*50} x 10-6. This value is slightl,v smaller than the estimated paramagcetic part of the chemical
shift from the spin-rotation
constant in the gaseous
Flliorine is one of ihe few elements that have not b&n studied by NMR in the condensed
.pha&s. In this note we report the anisotropy of the chemica1 shift tensor Aa = IT‘,,- a,for F2 whidh was determined in conjunction with a complete study [l] of the relaxation times and selfdiffusion coefficients in liquid and solid (ol and ,!I phases) F2. Five independent methods were used to evaluate do. These are: (1) determination of the first moment (Ml) of the lineshape, (2) determination of the second moment (M2) of -. the lineshape, ‘-(3) measurement of the separation A between the unshifted “center of the spectrum” and the hilmp in the derivative of the absorption at high field, (4) fitthe lineshape by cdmputer to the theor&c* powder pattern with gaussian broadening and, (5) measurement of the shift (6) between the resonance line in the &quid and the center of the- spectruti of‘the _solid It may readily be shown that
* Based~on w&k performed under the &&es U.S.‘@omic Energy Commission. .-. ,
state.
3 rtiA =HTC R
AuH
and 6 = (Ao/3)Ef,
(4)
where it has been assumed that the chemical shift tensor has axial symmetry (u,, = ad,, Us = udL + Up; Od, VP = diamagnetic and paramagnetic part of the chemical shift tensor respectively) and B is the bFOadening parameter of the gaussian single crystal lineshape S(H-Ho): s(H-Ho)
=
l3(2&
@=P - rcR-~o)2/2@2].
(5)
The results of the measurements, which were performed near 29’K (BOOKfor the liquid). and from 4 to 40 MHz are summarized in figs. 1 - 5 and tabie 1. In fig. 1, ‘Ml is plotted versus resona+ze2frequency vo; in fig. 2, M2’is plotted veerBUSvo; in fig. 3, A is plotted versus vo: in fig. 4, 8 typical computer_ fit to the lineshape is shown and in fig. 5, AC+ versus vd is given as. deter: mined from the.best iilk to the lineshapes. - Methods l-- 4 yield consistent resulti: the -ave&ge value‘of Au-is (1050350) 5 19-9.: From the bbs&tied spi&roJation c@st&t !n ihe g as ,.’ phase [2] bne calcul_tit&S ip = :ll?O X 10’ us.: r All p&b of &e&da;, shift ‘&cusstid &I this pa@r .are c&x&xted relative to-tie Fluo;lne nu+us as the bf .(he.. . ’._ : uri&ia of_++@ates. : ._ ,-. ,.. ._’ _, . .-. . _ _. ,. _---. .-. ’ - ,._- -, _:I ,a, ;.‘ . : “-’ .. I.-..,.-. ., ..,. . ..-: ,. ‘-’ ,.. ,..,;,_;, .,_ ,_.._:.. ,, : :, _ .,
1 March 1972
CHEMICAL PHYSICS LETTERS
Volume 8, number 5
24-
I
4
II 8
12
I
I
f
I
I
,6
20
24
28
32
RESOHANCE
FREQUENCY,
I1 36
40
q,. HHz
Fig. 1. First moment (Ml) of ISF resonance lineshaps versus resonance frequency @I,).
Fig. 3.
Separation
between
field hump
MFSUS
center of spectrum and high frequency.
res5nance
Fig. 2. Second moment (hf2} versus equare of resonance frequency.
Fig. 5. Anisotropic shift (4crH) from computer fit of lineshspe versus resonance frequency uo.
.
:.
’ Fig. 4. Derivative of.Ig F resonance. wii$ v5 = 40.3~MEIz. &shed awve is computer fit with param&ers given in text . md tab!e l., Frequency markers are from proton gaussmeter. .‘ .’ ._ . -’. .. * _-..‘. ._“’ 471 . . ; ”-.. . 1
VoIume8, number5 : -
CHEkfICAL PIIY&S Table 1
-: Anisotropyaf the &err&a! shift tensor f&o) by varioue - methods
Ahoxlo6
. Method‘
MI vemus &b ’ M2 wrsui
v#
A versus Y,,
1110 t 100 1090 f
50
990 4 60
tineshape fit
ICI0 ;: 40
6, Yo’ 40.4 M&l
1230 f 200
&&f&?
1050 f
a1
so
a) Value derived from 6 not included, eee text.
.
ing the well known relationship [33 between the spin-rotation and chemicaI shift tensors. If this result is valid for the fluorine moiecule in the solid State, the A’Jd = od,, - mddl= (-70&50)x Lo-6 and the anisotropic diamagnetic part _of the chemical shift tensor is negligible as is often assumed. In the gas phase [4], the average diamagnetic art of the chemical shift tezX%X??d= 513 x 10- 8. The liquid state value of ho is within experimental error of the average of methods (1) - (4), but 6 has an uncertainty in the experimental error due to d~~cu~~ in the location of thb precise center of the solid state spectrum.
LEZTTEiS
’
1 March lS?l
This &as done bv determinim? the mi&oint between the ‘extremes of the de&&e spectrum. The p-phase of Fz (helow ‘45.4°1Q-is a rel&tivety dense structure 153but it seems very un-. Ukel~ that up could be greatly changed by the perturbation of the eolid state structure. The value of.yA/!3 from.methods (a), (3) and (4) is 9.5 i 0.3 G correspondin&to a value of R = 1.416 O.Olk The gasphase value [6] of R = l-418& 13was calculated from the crystal struc. twe of the Q!-phase to be 2..4 G; best computer fits to the lineshape seemed to be obtained with B = 2.6 CL In view of the nature of the gaussian approximation this discrepancy is to be expected. REFERENCES {l] D. E. ORellly, E. M. Peterson, D.L.Hogenboomand C.E. Scheie, J. Chem. Phys., to be published. [2JI. Oaier, L. M. Crap% J. W.CederbergandN.F. Runsey, Phye.Rev. Letters 13 (1964) 482.
[3] N. F.Ramsey, Molecular beams (Clarendon Press, oxford, 1956) pp. 162, 208. ‘[4J D.K.Hindermar?n and L.L.Wiiliams, J. Chem. Phys. 50 (19!$) 2839. f5J L. Meyer, .C.9. Barrett and S. C. Greter, J. Chem. Phys. 49 (1968) 1902. (SJ D,Andrychuk, Cs.n.J.Phys. 29 (1951) 151.