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Determination of the 19F shielding tensors in α-SnF2
M. Le Floch-Durand, U. Haeberlen, C. Müller
To cite this version:
M. Le Floch-Durand, U. Haeberlen, C. Müller. Determination of the 19F shielding tensors inα-SnF2.
Journal de Physique, 1982, 43 (1), pp.107-112. �10.1051/jphys:01982004301010700�. �jpa-00209366�
Determination of the 19F shielding tensors in 03B1-SnF2
M. Le Floch-Durand, U. Haeberlen (*) and C. Müller (*)
Université de Rennes, Laboratoire de Chimie Minérale D (**), avenue du Général-Leclerc, 35042 Rennes Cedex, France.
(*) Max-Planck Institut für Medizinische Forschung, Abteilung für Molekulare Physik,
Jahnstrasse 29, 6900 Heidelberg, Germany.
(Rep le 19 mai 1981, accepté le 4 septembre 1981)
Résumé. 2014 Une expérience de RMN du fluor 19 en haute résolution solide par séquence d’impulsions multiples
a été réalisée sur SnF203B1. Quatre monocristaux respectivement orientés suivant leurs axes cristallographiques b, c*, a
et 111 ont été utilisés pour déterminer les huit tenseurs de déplacement chimique correspondant aux huit fluors
magnetiquement différents. L’attribution des tenseurs aux différents fluors est faite en considerant le caractère fortement axial des tenseurs et de la symétrie dans le cristal, ainsi que l’anisotropie importante de ces tenseurs,
associée au caractère covalent des liaisons. Les spectres large bande obtenus avec les mêmes cristaux sont en
accord avec l’interprétation faite en haute résolution.
Abstract. 2014 A NMR 19F multiple pulse solid state high resolution experiment has been performed on 03B1-SnF2.
Four single crystals have been used with rotation axes, parallel to b, c*, a and 111 crystallographic directions respectively and eight shielding tensors have been determined. The assignment of these tensors to the eight magne- tically inequivalent fluorines is made by considering the strongly axial properties of both the fluorine sites and the
shielding tensors, and the large shielding anisotropy associated with the covalent character of the boudings. Wide
line spectra are in agreement with the high resolution experiments.
Classification Physics Abstracts 76.60C
1. Introduction. - Tin fluoride exhibits three diffe- rent structural phases [ 1-6] : the low temperature, monoclinic, stable a-phase, the high temperature tetragonal y-phase and the fl-phase which is a meta-
stable low temperature modification of the y-phase.
Several studies of SnF2 have been undertaken such as
photoelectron spectroscopy [7], neutron and wide line
NMR [8], thermal expansion [9] and Mossbauer spectroscopy [10] but much is still to be learned in the
understanding of these three phases and of the two
corresponding phase transitions. Our contribution
to this task. in the present paper consists of 19F high
resolution (H.R.) solid state NMR measurements made at room temperature on the stable a-phase.
For a solid the Hamiltonian of a system of spins I
in an external magnetic field Bo is : :
where 1iHz = hE(o’ 0 Izi is the Zeeman Hamiltonian due to the external magnetic field Bo and hhin, des-
cribes different interactions among the spins, the most important being, in our case, hHD and hhcs. hHD originates in the direct coupling of spins I with each
(**) Laboratoire Associ6 au C.N.R.S. no 254.
other through their magnetic dipole moments and hhcs is the magnetic shielding interaction we want to
study; this last interaction is due to the coupling of
nuclear spins with orbital motions of electrons. By
the use of the interaction representation [ 11 ] induced by the operator
and restriction to non oscillating terms, we are left with the secular or truncated Hamiltonians :
where
and
When we perform a multiple pulse H.R. solid state NMR experiment, we impose by a periodic and cyclic pulse sequence, a periodic time dependence on the spin operators and Hint,sec becomes Hi.,,re,(t) [12, 13].
Ho,sec(t) which transforms in spin space like a tensor of rank two averages to zero. over one cycle, but
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01982004301010700
108
Hcs,sec(t) which in spin space behaves like a tensor of rank one is not averaged out. Therefore, when we apply such a selective time averaging pulse sequence
[14] to cx-SnF2 the F-F dipolar interactions are removed and the various chemical shift interactions appear alone.
Although the chemical shift range of fluorine usually spreads over a few hundreds of ppm, we were expecting (and we obtained) partly unresolved spectra because of two major reasons : (a) the number of lines is rather
large. 8 lines are expected for a general orientation as we will see at the beginning of next paragraph; (b) a
residual linewidth exists due to dipolar coupling
between tin and fluorine spins, for the multiple pulse experiment we used removes only the homonuclear F-F dipolar coupling.
A major part of a study like this consists of the
assignment of the measured chemical shift tensors to the corresponding nuclear sites. The assignments we
propose are based on a comparison of the characte- ristics of the chemical shift tensors (orientation of principal axes system; shift anisotropy) with the
local (near) symmetries of the various fluorine sites in a-SnF2. They are well corroborated by wide line experiments and calculations of wide line spectra.
2. Experimental. - All the single crystals we used
were grown by slow evaporation of a saturated solution of SnF2 in HF acidified water. Their size was several millimeters in every space direction. The indexing of
the principal faces was first determined by X-Ray diffraction; their good optical quality allowed. to orientate them very precisely with an optical gonio-
meter, then each crystal was glued on a glass rod and
sealed in a standard 5 mm NMR sample tube.
High resolution solid state 19F spectra were recorded
at 90 MHz. The pulse sequence used to remove the F-F dipolar interaction is the compensating MREV cycle which consists of 16 pulses, the four basic pulses
of which are the well known WAHUHA [12] sequence.
This 16 pulses sequence offers the advantages of the
MREV sequence [15,16] in comparison to the WAHU-
HA sequence (larger oscillatifig signal amplitude and
better base line) and owing to its compensating pro-
perties is less sensitive than the MREV sequence to
misadjustments and drifts of flip angles and radio- frequency phases. All pulses were ninety degrees pulses of duration 2-, 0.75 ps and the shortest interval between two pulses was 3 J.1s. All the experiments were
made at room temperature.
3. Results and discussion. - 3.1 DETERMINATION
OF THE SHIELDING TENSORS. - a-SnF2 crystallizes
in the monoclinic system, the space group is C2/c and
there are four crystallographically inequivalent fluo-
rine atoms. The unit cell contains four tetramers
Sn4Fg (see Fig. 1) and thus, 4 x 8 = 32 different
fluorine atoms. The tetramers lie roughly in the (a, c) plane; if these 32 fluorines were not related by symme- try elements of the space group, we would in general
Fig. 1. - Structure of a-SnF2.1: Sn ; 0 : F. Upper part of the figure:
(a, c) projection of the unit cell. The y coordinate of the average plane
of each tetramer is given. Bottom part of the figure : projection of a
tetramer Sn4F8 in the (b, c) plane.
observe 32 lines and correspondingly 32 shift tensors;
but a fluorine atom of a given tetramer is related to a
fluorine of another tetramer by an inversion centre and
to another fluorine of this last tetramer by a translation in the (b, c) glide plane, which reduces the number of magnetically inequivalent fluorine atoms to
32 x 1/2 x 1/2 = 8. Spectra with eight individual
components are then expected for non special orien-
tations of the crystal in the magnetic field Bo. Further-
more, a two-fold axis parallel to the b axis of the crystal
goes through the centre of each tetramer and relates
one half of a tetramer to the other half of the same
tetramer, but for magnetic resonance experiments a n-
fold axis is equivalent to a mirror plane if the applied magnetic field Bo lies in the plane perpendicular to the
n-fold axis and in that case the number of expected
lines has to be divided by two.
Therefore, in our case, when Bo is rotated about the b axis which is a crystallographic two-fold symmetry axis, we expect at most four lines and when Bo is
rotated around any other direction of the crystal, eight
lines at most are expected. We now clearly see that we
have eight shielding tensors to determine for the eight
fluorine atoms of the tetramer and that four of these tensors are related to the four others by the mono-
clinic axis of the crystal.
For the determination of a tensor of rank two, three rotation patterns around three crystallographic axes,
non lying in the same plane, are needed; we first used
three single crystals and rotated them successively in
the applied static magnetic field Bo around three
mutually orthogonal crystallographic directions : b, c*
and a, the rotation axis being perpendicular to Bo in
every case. All the spectra were single shot Fourier transform spectra. The bottom parts of figures 2 and 3
Fig. 2. - Spectra obtained with the a axis perpendicular to Bo
and O(BO, b) = 43° 5 : (a) wide line dipolar spectrum; (b) corres- ponding « high resolution » spectruni. The units of the two hori- zontal scales are ppm relative to C6F6 to allow direct comparison
between the two spectra.
Fig. 3. - Spectra obtained with the b axis perpendicular to Bo and O(BO, a) = 11 °. (a) dipolar spectrum; (b) high resolution spectrum.
show two examples of the kind of experimental spectra
we obtained. We never observed eight lines for spectra where c* or a axis was the rotation axis, but after careful examination, and decomposition of our spectra,
we could determine all eight traces in the rotation patterns; they are shown on figures 4 and 5 with the
experimental values superposed on the fitted curves.
For the crystal which was rotated about the b axis,
we could resolve all the expected four lines; the corres- ponding rotation pattern is shown in figure 6. All the shifts are given in ppm relative to C6F6. From the
three diagrams, the « crossing points » (rotation angles in two rotation patterns for which Bo has iden-
tical orientation in the crystal axis system) can easily be
obtained but leave us with an ambiguity with respect
to the question : which of the traces in each pattern
Fig. 4. - Angular dependence of the fluorine chemical shifts of
a-SnF2 for a single crystal rotated about the c* axis.
Fig. 5. - Angular dependence of the fluorine chemical shifts of
a-SnF2 for a single crystal rotated about the a axis.
110
Fig. 6. - Angular dependence of the fluorine chemical shifts of
a-SnF2 for a single crystal rotated about the b axis. Units of shifts
are parts per million relative to liquid C6F6. The dots are the experimental values and the solid lines are the values obtained by fitting.> : F1, A : F2, 0 : F 3’ P : F4.
corresponds to which trace in the other patterns ? At
the crossing points each line always corresponds to at
least two fluorines and mathematically sixteen shield-
ing tensors are still possible at this level. To remove
this degeneration and come down to the eight physi- cally true tensors, we had to rotate a fourth crystal
around a new crystallographic direction; we chose the 111 axis and obtained a rotation pattern that allowed
us to determine crossing points with the c* and a
rotation patterns at rotation angles where no degene-
ration was present. Finally, by computer fitting the
data from fggrr’s 4 to 6 to second rank tensors, we obtained eight chemical shift tensors corresponding
to the eight magnetically different fluorine atoms.
These eight shift tensors come, as they must, in four sets of two tensors with the two tensors in each set related by the two-fold axis of the crystal. In table I,
we report the characteristics of the four independent 19F shielding tensors in a-SnF2 anticipating already
the assignment which we discuss in the following paragraph. To obtain the four other tensors, the components x, y, z of the direction cosines have to be
changed in to - x, y, - z or the polar angles 0 and ~ of the principal directions become x - 0 and x - (p.
3.2 ASSIGNMENT OF THE SHIELDING TENSORS TO THE CORRESPONDING FLUORINE ATOMS. - If we look at the anisotropy factor :
where (133 is the most shielded eigenvalue and 03C311 1
the least shielded one, we quickly see that the shielding
Table I. - The four independent 19F chemical shift tensors and their assignment. The eigenvalues 03C3ii of the tensors
and the average chemical shifts (1 Av are given in ppm relative to C6F6. The direction cosines are expressed in the a, b, c* crystal frame with a 1 b 1 c*.
tensors in table I can be grouped into two sets of two
tensors; one set has a large anisotropy (21b ppm, 165 ppm), while the two tensors of the other set have
a much smaller anisotropy : A a 100 ppm.
By looking at the structure of a-SnF2, we can also
define two sets of fluorine atoms, the terminal F and F3 fluorines and the bridging fluorines in the ring F2
and F4 ; then we make the following first assumption :
either F1 and F3 are the fluorines with the most aniso-
tropic shielding tensors or F2 and F4 have the most anisotropic chemical shifts.
An other important parameter for a tensor of rank
two is the asymmetry factor q defined as :
with
All four tensors in table I have a small asymmetry factor : 0.201 t¡ 0.354. Thus, in first approxi- mation, we consider them as axially symmetric. Their unique principal direction corresponds to that of the most shielded eigenvalue. These important directions
are particularly well defined for the group of very
anisotropic tensors which can be seen by looking at the
rotation patterns in figures 4 and 5.
On the other hand, the local symmetry at the sites of all the fluorines is roughly axial; F1 and F3 just bond
to one Sn. For F2, the angle between the Sn2-F2 and Snl-F2 directions is nearly 1800 (exactly 171 °); this
defines a pronounced unique direction for F2. The angle between the F4-Sn 1 and F4-Sn2 direction is 1320. We may say that a symmetry plane exists for fluorine F4.
With these arguments in mind, we make the second
assumption, namely : the tensors are orientated at least approximately with their unique axis parallel to
local symmetry directions. In fact, we note that the
difference between the Sn-F2 and Sn-F3 directions
is only a few degrees and these two directions are not very far from the most shielded direction of two tensors. In the same way, the Sn-F and Sn-F4 direc-
tions are close to each other and in the vicinity of the unique axes of the two other tensors (within about 10°).
This second assumption on principal directions is made by analogy with results on CF3 group in silver trifluoroacetate [17] where the most shielded directions
are a few degrees away from the C-F bond directions.
Only one ambiguity is remaining at this stage; the assignment may be the one of table I : Fl, F2, F3 and F4 or it may be F4, F3, F2 and F1.
It seems reasonable to say that the chemical shift tensor of fluorine F2 is the sum of two contributions :
one comes from the Snl-F2 bond and the other one
from the Sn2-F2 bond whereas only one Sn-F bond
occurs for F1 and F3. Thus, if we apply the additivity
rule for anisotropies, we expect
The tensor associated with F2 will then be the one with
the largest anisotropy and the smallest asymmetry factor (’1 = 0.2) which is consistent with the very stretched bonds’ around F2. This argument removes the remaining ambiguity. It follows that the last tensor of table I with 039403C3 = 165 ppm and a = 0.24 corres-
ponds to fluorine F4 whose bonds are more bent than
those of F2 ; furthermore we have calculated the direction cosines of the normal to the plane (Sn 1-F4, Sn2-F4) and from this calculation we find that the
unique axis (most shielded direction) of this last tensor
is in the plane defined above. Finally, the first and the third tensors of table I belong to the terminal fluorines
F1 and F3 respectively.
One salient feature of these results is the fact that two fluorine atoms - the bridging F2 and F4 atoms
in the ring - have very anisotropic shielding tensors
and the lines from these nuclei appear much more
shifted than the others for certain orientations. Thus,
we may hope to see them « isolated » in dipolar experiments if the linewidths are not too large.
4. Verification of the assignments by comparison
with dipolar results. Calculations and experiments. -
We have made rigid lattice second moment calcula-
tions for the single crystals rotated about the b, c*
and a axes by taking into account only F-F dipolar
interactions. A few favourable cases with regard to seeing lines from individual sites have appeared especially for rotation about the a axis when the angle
between c* axis and Bo is 0 = 430 5 or
For these two positions of the crystal in the magnetic field, a very narrow dipolar line from F2 is expected.
Accidentally, but fortunately in the high resolution
rotation pattern of the figure 5, the line attributed to
F2 is also the most shielded one at this position in the steady magnetic field. The dipolar spectra will then allow us to verify if our assignment is right.
Dipolar spectra have been recorded at 270 MHz to increase the frequency separations of the lines due to
chemical shifts. The four crystals have been rotated around b, c*, a and 111 axes. The figure 2 shows the dipolar spectrum and the corresponding H.R. spectrum for rotation about a and 0 = 430 5; on the right side
of the wide line spectrum, a very narrow and very shifted line appears confirming the assignment to F2.
From the calculation second moment and by making
the assumption of a gaussian line shape [18], the full
linewidth at half height of this line is 6 = 2.6 G if
only F-F dipolar interactions are considered. The
experimental linewidth A V1/2 is 2i 11 kHz which is
equivalent to 2.7 G and in excellent agreement with the theoretical value.
In the spectra shown in figures 2 and 3, small shifts between the maxima of the wide line and the high reso-
lution spectra are observed. This is most probably due
to the fact that the wide line spectra are not pure first order spectra (F-F dipolar couplings are not negligibly
