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VIBRATIONAL PROPERTIES OF FERROCENE
C. Hill, P. Debrunner
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, supple'ment au no 12, Tome 37, de'cembre 1976, page C6-41
VIBRATIONAL PROPERTIES OF FERROCENE
C. R. HILL and P. G. DEBRUNNER
Physics Department, University of Illinois at Urbana-Champaign, U. S. A.
R6sum6. - On a mesure les fractions Mossbauer f(T), rapports superficiels R(T) et deplacements isomkriques 6(T) dans du ferrockne (FC), Fe(CsH5)z (fer dicyclopentadienylique) sous forme poly- cristalline et en solution congelee.
Le comportement de f (T) a basse-tempkrature dans les Bchantillons polycristallins revkle unpoten- tie1 intermoleculaire anharmonique. FC subit une transition de phase A T c = 164 K, au-dessus de laquelle f diminue et R augmente. Cela suggkre une relation entre la transition de phase et l'anhar- monicitk du potentiel inter-molCculaire.
Le rapport superficiel des polycristaux de FC sY6carte beaucoup plus de l'unite que celui des solutions congelees, indiquant que la valeur de R pour les poudres est due principalement aux vibra- tions propres du rkseau. On montre B l'aide d'un modkle trks simple que l7anharmonicit6 du reseau peut rendre compte de la valeur inhabituellement grande du rapport superficiel du FC polycristal- lin. Les donnees recueillies par spectroscopie Mossbauer, ainsi que par spectroscopies infra-rouge et Raman, caractkrisent la transition de phase comme Ctant une transition de d6placement.
Abstract.
-
Recoilless fractions f (T), area ratios R(T) and isomer shifts 6(T) have been measured for ferrocene (FC), Fe(C5Hs)z (di-cyclopentadienyle iron) in polycrystalline form and frozen solution. The low-temperature behaviour off (T) for polycrystalline samples implies anharmonicity of the intermolecular potential. FC undergoes a phase transition at Te = 164 K which is associated with a decrease in f and an increase in R above Tc. This behaviour suggests a connection between the anharmonicity of the intermolecular potential and the phase transition. The fact that the area ratio of polycrystalline FC deviates from unity much more than that of a frozen solution implies that the powder value of R is mainly due to lattice modes. A simple model indeed shows that the lattice anharmonicity can account for the unusually large area ratio of polycrystalline FC. Toge- ther with IR and Raman results the Mossbauer data support a displacive mechanism for the phase transition.1. Introduction. - Recoilless fractions f (T) and second-order Doppler shifts dsO,(T) are known to depend on the dynamics of the matrix in which the Mossbauer nuclei are bound. For simple crystal struc- tures these parameters are readily interpreted, and much useful information has been obtained from measurements off (T) and ds0,(T) in metals and ionic crystals [l, 21. O n the other hand, comparatively little Mossbauer work has been done on the lattice dynamics of organic systems. The reason may be that the struc- tures of organic crystals are more complex and that a satisfactory analysis is possibly only if additional data are known. We will show below that ferrocene (FC), Fe(C5H5), (di-cyclopentadienyle iron), is a n example of a molecular crystal for which the necessary infor- mation exists t o allow a meaningful interpretation of the recoilless fraction. The molecules of F C consist of a n iron atom sandwiched between two pentadienyle rings ; FC is diamagnetic and exhibits a practically temperature independent quadrupole splitting. The arrangement of the molecules in the crystal is sketched in figures la and l b [3].
F C is interesting for a number of other reasons 13-61 :
(i) I t undergoes a phase transition (PT) at 164 K from FIG. 1.
-
Ferrocene crystal structure [3] showing the &-planea (P2~/a) phase an unknown ordered in (a) and the ac-plane in (b). 2,
y
andz^
define the coordinate phase [3,4, 51. Figure 1 illustrates the high-temperature system used to describe the anisotropic recoilless fraction.C6-42 C. R. HILL AND P. G . DEBRUNNER
phase ; the low-temperature X-ray data are limited by crystal distortion. (ii) The thermal expansion is quite anisotropic [4] and all but very small crystals disinte- grate near 110 K [6]. (iii) FC and derivatives have been used as probe solutes for Mossbauer studies of liquid crystals [7-91. (iv) FC exhibits an unusually large Goldanskii-Karyagin effect
( R E
f 1 for a Area (+)
Heat capacity measurements for FC [4] give the following thermodynamic parameters for the PT :
T, = 163.9 K, AH=0.204 kcal/mole, A S = R In 1.89. The closeness of A S to R ln 2 suggests that each molecule has 2 more configurations in the disordered phase than in the ordered phase. A rotational order- disorder model has been proposed which is analogous to a 'system of interlocking gears, the ring protons representing the gear teeth. Proton NMR results indicate a large decrease in the ring reorientation rate below the PT [lo], in support of the gear model.
Recent far-infrared results for FC, however, show that two of the symmetric skeletal modes (ring stretch 312 cm-l, ring tilt 388 cm-l) become weakly IR active in the ordered phase [ll]. There are also varia- tions of intensity across the PT of the Raman lines corresponding to these modes [6]. These facts imply changes in the unit cell other than ring orientation, and argue for a displacive mechanism for the PT. The Mdssbauer results for FC (Fig. 2) support this idea, and indicate that the PT is related to low-temperature
Tc=164 K 1 I . I 0.50 5 I I = powder
i
FIG. 2. - Logarithm of the experimental recoilless fraction
-
In fp(T) (top), isomer shifts 6(T) (middle) and area ratios Rfor ferrocene.
anharmonicity of the intermolecular interaction. Assuming the chemical shift to be temperature inde- pendent, the behaviour of the isomer shift 6(T) is
consistent with a softening of lattice modes on heating above
-
120 K.2. Experimental.
-
A difficulty always encountered in measuring recoilless fractions f (T) of an absorber is saturation due to finite and temperature-dependent effective thickness of the absorber, t = no,f
(T),
where n is the area density of resonant nuclei and o, = 2.6 x 10-l8 cm2. There are different ways to account for saturation :(i) Use the transmission integral to fit the data,
I(E) = BNR
+ BR
I:m
dE' S(E - E') e-nf"(E''.
(ii) Deconvolute the source function S(E) and take the logarithm to obtain
nfo(E).
To do this, S(E) has tobe known, and the resonant background, BR, and non-
resonant background, BNR must be determined. The use of a fast Fourier transform (FFT) program makes this method very economical [16].
Each procedure has its advantages and disadvan- tages. While (i) is exact, it is also expensive since many numerical integrations are required. FFT deconvolu- tion, on the other hand, introduces artificial broadening since it is necessary to filter out some of the high- frequency noise. The second method was used for the results reported here, and a filter function was chosen to give a least square reproduction.
To minimize the relative errors in f (T), a standard ferrocyanide absorber at room temperature was included in each run. This procedure gave a set of relative f (T) values which were calibrated absolutely against a
4
mil iron foil. The standard absorber tech- nique also reduces the need to determine BR and BNR accurately for deconvolution.The spectrometer was of the constant acceleration type, both halves of the scan being stored in a TI-960A minicomputer. The data were folded, deconvoluted and fit with Lorentzians. Sample temperature was measured and feedback stabilized to f 1 K.
VIBRATIONAL PROPERTIES OF FERROCENE C6-43
The properties of the moments 8(n) are treated in (1). For anisotropic f there is more than one set of 8(n). The gi depend on the details of the crystal structure. Application of this formalism to the f (T) data, figure 2, assuming an isotropic f yields 8(- 1) = 64 K,
0(- 2) = 80 K. However, these values do not satisfy the inequality B(n)
<
8(n+
1) which holds in any harmonic model for all n. We therefore conclude that anharmonicity is important in polycrystalline FC and use the results of Dash et al. [2], who analyzed the effect of low-temperature anharmonicity on the recoilless fraction.f (T). The experimentally observed Goldanskii-Karya-
gin effect implies a strong anisotropy off (T). Further- more, the large thermal expansion coefficient along the c axis [4] suggests the anharmonicity to be predomi- nantly in that direction. It turns out that a satisfactory model is obtained by assuming an axially symmetric fH about the molecular axis with an anharmonic com-
ponent fAH in the z-direction, figure 1. We write
The most important result from Dash et al. is the and obtain for the powder average separation off, for aflattened potential, into an anhar-
monic temperature-independent part, and a harmonic f P =
,
1J
d Q f (Q)temperature-dependent part.
f
(TI = ~ A H ~ H ( T ) ( T -* a)-
ln fp=
lnfil+
+
lnfi
+
4
hfAH.
Before this high-temperature limit can be combined The area ratio R for axial symmetry of the EFG and with eqs (1) and (2) to extractfA,, 8(- 2) and,q-
1) the anisotropic recoilless fraction described above from the powder data o f f (T), f i s r e 2, one has to Can be written in terms of the anisotropy parameters em, make certain assumptions about the anisotropy of E; 11211
[
dR(3+
3 sin2 8 cos2 yr) eap(;
eL sin2 0 cos 2 yr-
sm cos2 8)J \A /
R = /
dQ(5-
3 sin2 8 cos2 yr) expE,!,, sin2 0 cos 2
-
E, cos2 8In our model then, R depends on both fH and fAH ;
and fAH is related to both the area ratio and the zero-
temperature intercept of the high-temperature limit
In the case of FC there are two intercepts, one for
T
<
Tc and one for T>
Tc. They are listed with theassociated values of In fAH in table I, while K, is
Parameters of the anharmonic potential of FC above and below the transition temperature T,
The harmonic anisotropy
EL
at 4 and 295 K deter- mined by eq. (3) and In fAH is listed in table 11. The 8parameters (eqs (1) and (2)) for fL(T) and f;,(T) are listed in table 111.
Anisotropy parameters, eq. (3)
T range KI
-
I ~ ~ A HRo
(A)
TABLE 111-
-
-
-
> i"c 0.30(5) 0.9 0.12 Parameters of the harmonic potential of FC
< T c 0.20(5) 0.6 0.10 Direction -In fi(0) --- -d Infi
d T (K-1) 0i(-1) (K) 0i(-2) (K)
0.05
0.0070 (2) (K)-' both above and below T.. The
if
1
o.200.005 4 460 90
0.007 8 115 75
quantity
R,
in table I represents the width of the flat region of the intermolecular potential [2], and iscalculated from The harmonic anisotropy turns out to be larger than
AH
= COS'(Ky
Ro)
can be explained by the molecular modes. A simplecalculation using the IR frequencies shows that the where
molecular contribution to the anisotropy parameter
EL
K
A
is N 0.04 at 0 K and N 0.11 at 300 K. This is borneCB-44 C . R. HILL AND P. G. DEBRUNNER
ethanol-glycerol glass (open circles, bottom graph of ing [14, 151 of lattice modes in this temperature range figure 2). At low temperature the area ratio of the glass and a corresponding increase in vibrational entropy S,, is close to unity which is consistent with essentially no
molecular contribution
( 5
0.1) toEL.
Thus the large s v-
ln(&)
KT harmonic anisotropy observed in crystalline FC mustbe due to lattice modes or coupling between lattice - N
and molecular modes. u N =
lJ
mii = 1
4. Second order Doppler shift. - Interpretation of the experimentally determined isomer (centroid) shift, 6(T), suffers from the difficulty in separating the contribution due to second order Doppler shift, 6,,,, from the purely chemical contribution,
a,,.
Since the quadrupole splitting of FC hardly varies with tempe- rature, we assume thata,,
is temperature independent. In any case, SSoD for FC is dominated by the molecular modes (asym. bend at 180 cm-I and asym. stretch atFIG. 3. -Lattice part of second order Doppler shift. The molecular contribution is subtracted using an Einstein model for the IR frequencies 180 cm-1 (asymmetric bend) and 480 cm-1
(asymmetric stretch).
480 cm-I 151. A naive calculation using the IR fre- quencies and an Einstein model [13] to remove the molecular contribution suggests that the lattice contri- bution to dsoD has a flat region (Fig. 3) from
-
120 K to--
210 K. This behavior is consistent with a soften-The tentative interpretation of 6(T) is compatible with the model proposed for f ( T ) and with the displacive mechanism of the p h a s ~ transition to be discussed. 5. Discussion. - The fact that the linear part of In
f,
vs. T of polycrystalline FC extrapolates to values considerably below zero at T = 0 is interpreted to result from low-temperature anharmonicity. A simple single particle model descrives fp(T) and R(T) consis- tently both above and below the phase transition if the anharmonic potential is allowed to change at the tran- sition. Specifically, the flat part R, of the anharmonic potential [2] turns out to increase from R, = 0.1A
for T<
Tc to R, = 0.12A
for T > T,. This change suggests that the PT may be associated with a displa- cement of the molecules. The large thermal expansion of FC in the2
direction [4] implies weaker average forces in the c direction than in the ab plane. We may therefore assume that within each ab crystal plane, nearest neighbors displace out of the plane in opposite directions below Tc. The iron atoms no longer reside at symmetry points of the high-temperature lattice. This conclusion is supported by IR and Raman results [5,6, 111. The transition at 164 K can be pictured as produc- ing a domain structure which increasingly stresses a crystal upon cooling and may lead to its disintegra- tion [6]. A model for the phase transition can be made analogous to the two dimensional antiferromagnetic Ising model. More work on this system is in progress.Acknowledgement.
-
This work was supported by the National Science Foundation under Grant PCM 74- 1366.References
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