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The effect of intercalation on the lattice constants of graphite
THEEFFECTOFINTERCALATIONONTHELATTICE CONSTANTSOFGRAPHITE T. KRAPCHW,?R. OGILVIE~and M. S. DRESSELHAUS$ Center for Materials Science and Engineering,MassachusettsInstitute of Technology, Cambridge, MA 02139, U.S.A. (~ec~~~edIO Deeember 1981)
Abstract-A study of Q&O)X-ray reflections has been carried out on well-staged donor and acceptor intercalation compounds based on HOPG, and including stages 24 potassium donor compounds and stages 1 and 2 acceptor compounds with AK& and Fe&. The measured expansion of the in-plane carbon-carbon distance d,, for the donors is consistent with previous data on potassium. The present study, however, focuses on measurement of the contraction of dcx. in acceptor compounds; this lattice contraction is consistent with previous predictions based on the upshift of the in-plane Raman active mode frequencies. The in-plane structure and lattice constant for the intercalant in a stage 2 graphite-FeCll compound have been studied, and the results show no symmetry changes of the intercalate lattice, but an expansion of its in-plane lattice constant by a much larger magnitude than the contraction of the graphite in-plane lattice!. 1. INTRODUCTION
Small but measurable changes occur in the in-plane carbon-carbon distance do in graphite upon intercalcation f 1,2j. A quantitative mea5urem~nt of these changes gives important information about the nature of the bonding, electronic structure and lattice mode structure in these materials. Since these changes in lattice constant are very small, the modification to the electronic and lattice mode structure is correspondingly small and can be considered in perturbation theory. The interpretation of Raman spectra suggests an inplane contraction of d,_, in acceptors [3,4), in contrast with the in-plane expansion observed by structural studies of the donor compounds[l, 21. The present X-ray data confirm the interpretation of the Raman upshift for acceptors and downshift for donors as a function of intercalate concentrationI5]. The results of this X-ray study further show that the in-plane contraction for the acceptors is much smaller than is the donor expansion for samples of comparable stage, in agreement with previous work[6-81. In the present work the recent empirical model [7] and theoretical calculations [9, IO] relating the magnitude of the change in lattice constant to the charge transfer between the graphite and the intercalate layer are applied to the interpretation of measurements of the change in the in-plane d,_, distance denoted by Ad,_,. To obtain the necessary precision, we used the Gordon-Giessen X-ray technique [ 1l] which employs an energy dispersive diffractometer operating at a fixed diffraction angle. With this technique we can measure the in-plane lattice constant of graphite intercalation compounds with a precision of f 0.0002 A at room temperature. This technique also enables us to work with samples prepared from an HOPG host and encapsulated in glass, so that the intercalation compounds can be studied in their as-grown state.
2. EXPERIMENTAL The samples studied in this work were prepared using the two-zone vapor transport method[3]. The donor compounds were grown by keeping the intercalant temperature, T;, constant and varying the graphite temperature, T,, to obtain different stages. For the acceptor intercalants, TB was held constant and Ti was varied. The metal chloride intercalants (AIC13and FeClJ were first produced in situ by direct reaction of the heated metal wire with Cl, gas. Before sealing off the glass ampoule and inserting it in the two-zone furnace, the ampoule was back filled with Cl, gas to encourage staging. All the samples used in this study were single stage compounds. The stage index, fidelity and homogeneity of the specimens were determined by (~~) diffractograms using 8-28 scans taken in the reflection mode. In addition, all of the samples (except for the graphite-FeCl,) were encapsulated in glass to prevent intercalate desorption. Since we were looking for very small changes in the in-plane lattice parameter, we made use of the GordonGiessen technique [ I I] because this technique enables us to measure large samples in situ with great precision and resolution. With this technique a polychromatic X-ray source and a high resolution solid-state Si(Li) drifted X-ray detector are used. A chromium target X-ray tube was used in this study. because it lacks characteristic lines in the range of the diffracted energies[ll]. Each set of interplanar spacings dhrt will then diffract the proper wavelength from the continuous spectrum through the fixed 28 diffraction angle. With the GordonGiessen technique, it is the energy of the diffracted beam Es that is measured and related to the X-ray wavelength by EB = he/A. From Bragg’s law for the first order diffracted beam h = 2dhk, sin 0, a relation between EB and dhkr is obtained dhkl =6199&E, sin 8)
tlkpartment of MaterialsScience and Engineering. *Department of Electrical Engineering and Computer Science.
where Es is in eV and dhkr is in A. 331
(I)
332
T.
KRAPCHEVet al.
The experiments were performed on a G.E. diffractometer using an Ortec Si(Li) drifted solid state detector, attached to a Tracer Northern multi-channel analyzer. The samples were positioned on a single crystal goniometer head, allowing one rotational and two translational degrees of freedom. A schematic representation of the experimental configuration is shown in Fig. 1. To determine the in-plane lattice constant, we need only measure (MO) reflections, and, therefore, the symmetrical transmission geometry shown in the diagram was used. This geometery requires very thin samples (-0.2 mm) and the proper choice of collimators. To improve the precision of the measurement, the samples were aligned both mechanically and with the help of the X-ray beam. To eliminate angular errors associated with the positioning of the center of the specimen with respect to the axis of rotation of the goniometer, two sets of data points were taken for every peak position, each set of data corresponding to a rotation of the specimen by 180”. The experimental value reported here for each peak position is the average of the above two readings. Also long counting times were necessary to reduce statistical fluctuations. The determination of the peak position of each X-ray reflection was related to the channel number N at maximum intensity. This peak position was calculated, as shown in Fig. 2, by fitting the data points (open circles) to a Gaussian function (solid circles) using a least squares procedure. In this way N was determined to 20.2 of a channel number, which corresponds to ~0.0002 A for the interplanar spacing dllo of the (110)
940
960
Chnnw
980
l3cc
number I
19.2
18.8
Energy
I
20.0
19.6 CkeV)
Fig. 2. Least squares fit to a Gaussian function for the intensity of the (1IO)-graphiteline, where the X-ray energy E in keV is related to the channel number N by E(keV)= 0.02N. reflection. Once the d-spacing and the line index are determined, the lattice parameter can be calculated directly from the relation
1
I y?+hW+If at [ dhkr - 3
(2)
c2’
and de-c is related to the in-plane lattice constant a0 by d,_, = ao1d3.
(3)
Since the actual measurements focus on the determination of Adcz, the change in the nearest neighbor
Si(Li) Detector
I
KQ
A
4okev
-a a c-
2
2 C
Ll Kg
1 Analyzer
1
0.31
2.291
2.085 Wovelength(8 )
IhkO)
Fig. 1. A schematic representation of the experimental set-up for the Gordon-Giessen technique showing the X-ray beam path, the three degrees of freedom of the sample holder, an expanded view of the transmission geometry and the data flow chart.
The effectof intercalationon the lattice constants of graphite carbon-carbon distance due to intercalation, the samples for a given intercalant were fabricated from the same piece of highly oriented pyrolytic graphite (HOPG) and in each case &- for the particular HOPG host material was also measured. Thus the present determination of AdO depends on measurement of the intercalant-induced change in EB for the (110) reflection. The experimental set-up permitted measurement of lattice spacing with a resolution of kO.01 A, and a precision for d, 1o,the particular lattice spacing of interest, of +0.0002 A. For indexing the intercalant superlattice and determining the lattice constant of the intercalant layer, we used the Debye-Scherrer technique rather than the Gordon-Giessen in order to obtain more diffraction lines. For analysis of the intercalate superlattice, not only the (MO) lines. but also the (001) and (Ml) lines were used. Furthermore, the precision of the measurement in the energy range where the superlattice lines occur is not as high with the Gordon-Giessen technique as it is in the energy range of the graphite (110) reflection. 750
333
The X-ray patterns for pristine FeCI, and for the intercalate superlattice were obtained using a Cr target with the Debye-Scherrer camera and a Gondolfi attachment, the latter giving us an additional degree of freedom by tilting the sample. The stage 2 graphiteFe& sample that was examined with the Debye-Scherrer technique was cut from a larger sample which was used for measurement of Adc-c by the energy dispersive Gordon-Giessen method. 3.RESULTSANDDISCUSSION
Typical energy diffractograms of (MO) reflections taken in the transmission mode are shown on Fig. 3, where results for both donor and acceptor compounds are compared with those for HOPG. The most prominent peak in the diffractograms for the intercalation compounds is that associated with the graphite (1 IO) in-plane reflections and labeled G,,,,,, in the figure. The peaks labeled CrK, and CrK, are due to the characteristic lines of the target material of the X-ray tube. These Al&
K
Stage 2
Stage 1
Gl1l0l
600
h
0
-4
5.412
Fe&(m) 1
315c
CrK8
75-
FeCl3
5946
800
Stage 1
150-
K
Stage 3
600
I
19.497
Fe03 Stage
CrKa ACrKg
300 0 5412’
,“I kc&Jk&
Guoo,
& ‘5946
2400
Quo)
19.472
HOPG k3co
G(IIO)
1200
QIOOI
1 /, HOPG
1200 t 600 300 0
C&X,, ,C~KB 5412
!-IL 11.235
‘5946
Energy (keV) (a)
2
19.460
~L-lL~,L 11.226
Energy
( keV i
19.460
(b)
Fig. 3. X-ray energy diffractograms taken with the Gordon-Giessen technique: (a) for graphite-K compounds and HOPG; (b) for graphite-AK&and FeQ compounds.The energy range is selected to show the intercalant-induced shift of the graphite (110) diffraction peak, denoted by Go,,,. The CrK, and CrK, lines are used to calculate the energy scale. Various diffraction lines of interest are indicated on the diffractograms.
334
T. KRAPCHEV
characteristic lines were used to calibrate the energy scale of the diffractogram. The intercalant-induced shifts m energy for the Go,,, line for the intercalation compounds are obtained by comparison to the energy for the pristine graphite line. These shifts are used to determine A&. Because of their low intensities and corresponding lower resolution, the (100) reflections labeled Go,, were not used directly in the determination of the inplane lattice constant aO, but were rather used as a consistency check. From the intensity vs energy spectra in Fig. 3, it is seen that the intensity of the G,,,,, reflection varies both with stage and intercalant. The stage dependent intensity of the Go,,,, line is proportional to the fraction of carbon scattering centers that are in the sample (obtained from the chemical formula), and the relative cross section of the carbon scattering centers as compared with the intercalant scattering centers. For example in Fig. 3, Golo, has the lowest relative intensity in the case of the FeCl, samples, since FeCl, has the largest mass absorption coefficient, and is therefore the strongest X-ray absorber. The results obtained for Ad,_, in this study are summarized and compared with previously reported data in Table 1. These results show an expansion of the nearest neighbor in-plane carbon-carbon distance for donor compounds (A& is positive) and a contraction for acceptor compounds (A& is negative), in agreement with previous structural studies [l, 2, 7, 81 and with predictions based on Raman scattering studies[3]. The measured expansion of A&-c for the potassium compounds (measured to an accuracy of ~0.0002~) is in
et al.
good agreement with values previously published by Nixon and Parry, and measured using the Debye-Scherrer technique[l]. A comparison of the results for donor and acceptor compounds shows that Adc-c is significantly larger for donor compounds of the same stage. A small magnitude for Adc_c was previously reported for a stage 2 graphite-NiCl* acceptor compound by Flandrois et al. [7] based on measurements on a single crystal intercalated flake and using a two-circle semiautomatic Stoe diffractometer. To show the stage dependence of the in-plane lattice expansion/contraction the change of the in-plane carboncarbon distance Ad,, is plotted in Fig. 4(a) vs reciprocal stage l/n for both donor and acceptor compounds. The dependence of Adc-c on l/n is approximately linear, as shown by a least squares fit of the data to a straight line, yielding a coefficient of determination (COD) of 1.00 for the potassium donor compounds, and 0.96 for the FeC& acceptor compounds. A somewhat better linear relation is obtained (see FigAb) by plotting Ad,_c vs l/Q where l/t is the intercalate in-plane density, determined directly from integrated intensity measurements of (001) diffractometer scans [ 12,131 for each of the samples used in the present study. (See Table 2 for the l/r values thus obtained). In the case of Fig. 4(b), the COD value for a straight line fit to the Adc_c vs l/n6 plots is 1.00 for the donor-K samples, and 0.98 for the acceptor-FeCl, samples. A better fit to a linear dependence is expected for the Ad,, vs l/n6 plots since the intercalate concentration is related more directly to l/Q than to l/n. Flandrois et al. [7] found empirically that the measured
Table I. Ad,, for various graphiteintercalationcompounds(“) Intercalant
Adc-C
stage
(A)
K
1
40.0109~DJ
K
2
+0.00478(b) +0.0050(c)
K
DOllOlYS
+o.oom(b)
3
+0.0028(C) K
+0.00191(b)
4
+O.QO18(c)
AX13
1
-0.0022(c)
F&13
1
-0.0027(C)
F&13
2
-0.0009(C~e)
NlCl2
2
-0.0009(d)
Acceptors
(a)
Ad c-c
is
the
relative
to
expansion;
difference that
in
a negative
(b)
Results
from
cc)
Results
of
(d)
Results
from
(e)
*b’ IS
value
Ref.
this
is
between the
d C-C
HOPG host.
sign
indicates
in
work.
the
7. average
for
two
intercalation
contraction.
1.
Ref.
the
A positive
samples.
sign
compound
indicates
in-plane
The effect of intercalation on the lattice constants of graphite
33.5
Ados values for the acceptor compounds (Table l), and using the corresponding measured in-plane densities (Table 2), estimates of the charge transfer per carbon atom were obtained and the values are listed in Table 2. Using the measured values for 5 (also listed in Table 2), the charge transfer per intercalate unit fX was determined according to the relation fX = (n[)fc and the results are also listed in Table 2 Recently Pietronero and Strgssler [9,10] presented a model calculation relating the magnitude of Adc_t to & the charge transferred per carbon atom: Adc_c = 0.1575, + 0.146~~~~”+ 0.236fcz.
0 005
nd
0 004 0 003 “d-iI 0.002
/
,/’
: 7 000;
. 0 12
0.16 lh[ I” C”fX
-0.002 -0 003 t
@I Fig. 4. Plot of the change of the in-plane carbon-carbon distance ihdp ,-l for the potassium donor and the FeCll and AICI, combounds as: (a) a function of reciprocal stage (I/n). The results of ihe present work are indicated by open symbols and the closed circles are from Ref. 111.The lines are a least squares fit of the data to a straight Ii&~(b) A function of (ltn~) where l/E is in-plane inter&ate density and is related to the chemical formula C&f. The closed symbols are for those densities determined from (001) integrated intensity measurements while the open symbols are for “accepted” stoichiometries (see Table 2). The lines are a least squares fit of the data to a straight line.
Ad,_, values for the donor compounds and for his stage 2 acceptor NiCI, compound followed a linear relation between Ad,_, and fc, the fractional charge transferred from (or to) each carbon atom. For the case of the donor compounds, it was assumed that the alkali metal intercalant was fully ionized, while for the acceptors, the charge transfer was deduced from the measured stoichiometry x in CM, where M denotes the intercalant. The negative sign of Adc_c in their plot corresponds to an electron transfer from graphite to the intercalant in the acceptors, while the positive sign for donors indicates an electron transfer from the intercalant to the graphite n-bands. Of particular interest is the observation[7] that in the donor limit x = 1, the correct bond length of 1.52A is obtained for the single C-C bond, while for the acceptor limit x = - 1 the correct bond length of 1.32A is obtained for the double bond. Applying the same empirical relation to our measured
(4)
Using eqn (4), values were also obtained for fc using our measured Adc_, values, and the results are presented in Table 2. Also given in Table 2 are values for the charge transfer per intercalate unit fX obtained using the measured [ values. These results suggest that fX may be stage dependent, but such a conclusion awaits confirmation using other measurement techniques. Using either the Flandrois[7] or the Pietronero[ IO] model, the larger magnitude of the Ad,_, expansion for donors compared with the Ad,, contraction for acceptors of comparable stage is attributed in part to a smaller charge transfer fX for acceptors than for donors. In addition, the model of Pietronero and StrasslerllO] contains terms going as lfc(3’2and fc2 due to electronphonon coupling, which contribute to an increase in Ad,_, independent of the sign of the charge transfer. In the case of the acceptor compounds studied in the present work, these terms are, however, small relative to the linear term. In the diffractograms for the graphite-Fe& samples, we observed additiona reflections (Fig. 3b) not found in the scan for HOPG, and we therefore attributed these reflections to the intercalant FeCl, superlattice. To study these additional reflections, a stage 2 graphite-FeCb sample was examined in more detail using a DebyeScherrer camera with a Gondolfi attachment to give all possible (Ml) reflections. The film was read1141 and indexed in terms of two independent lattices (i.e. both for graphite and FeCl,) using the same c-direction lattice parameter. These results which are summarized in Table 3, show that at room temperature the in-plane intercalant is arranged in an ordered state, with a hexagonal in-plane Cl-Fe-Cl sandwich structure that is the same as that for pristine FeCh (space group C$ or R3). In the intercalation compound each sandwich is separated from neigh~ring sandwiches by graphite layers which tend to destroy the interlayer ordering between the sandwiches, though preferred orientational interplanar correlation may be retained. Our measurements have, however, focussed on the change in the ordering within the intercalate sandwich, and not on the interlayer correlation between intercalate sandwiches. Using 20 diffraction lines above 80” and Cohen’s least squares method[l5], the lattice parameters of the two lattices were determined yielding in-plane lattice constants of uc= 2.4590’- 0.0@04A for the graphite and f&j=
336
T. KRAPCHEVet al. Table 2. Measured in-plane intercalate densities I/( and estimates for charge transfer from Ad,, 1ntercalant
model
FeC13
1
F&13
0.154CCJ
-0.036
o.m(d)
-0.036
0*13(e)
-0.012
A(e)
o.ls(df
-0.012
0.121(c)
-0.cl29 -0.029
0.114(c)
0.057
0.083(d)
0.042
0.100(c)
0.033
-0.23
-0.14
-0.24
-0.14
-0.17
-0.09
-0.16
-0.09
-0.24
-0.13
-0.25
-0.13
B
1.00
to.47
1.00
+0.64
1.00
+0.46
1.00
Hi.56
1.00
+o.45
1.00
+0.50
a.0155
4
0.083(d)
0.028
0.093(c)
0.023 +0.0105 0.021
0.083(d)
ca)
Charge
transfer
per
carbon
(b)
Charge
transfer
per
intercalate
(c)
Calculated
from measurements
(d)
Calculated
from an assumed stoichiometry
atom. unit of
fX -
(00~)
(nt)fc.
line
intensities. of
5 = 12,
8.4
and 6.6
for
K,
and FeC.13 respectively.
(e)
In Model A, fc
is
calculated
from the model
of
Flandrois
(f)
In Model
is
calculated
from the model
of
Pietronero
(Ref.
model
+0.0265
3
K
A
-0.016
2
K
model
-0.0065
1
K
B(f)
-
-0.021
0.119(d)
AlC13
model
2
AlC13
fK(b)
fcfa)
115
stage
measurements
B, fc
et
al.
(Ref.
7).
and Strkler
IO).
6.0951tO.003 8, for the Fe&
layers, together with a c-axis repeat distance of Z, = 12.766i:O.O02i(. This value is in excellent agreement with the 1, value obtained for the same sample from (001) scans taken to characterize the sample stage I, = 12.76t 0.05 A. Excellent agreement is also obtained with 1, values reported by other workers[3]. Compared with the in-plane lattice parameters of the pristine compounds (a0 = 2.4605 A for graphite and 6.062 8, for FeCI,), which were obtained by the same technique, the graphite shows a small contraction of 0,0015& while the FeCI, shows a very much larger expansion of 0.033 A. The graphite contraction is the same as that measured by the energy dispersive Gordon-Giessen method (see Table 1). Since the graphite and intercalant lattices are incommensurate, it is possible for the graphite to expand while the intercalant contracts. In fact, the expansion of the graphite and the contraction of the intercalant correspond to making the two lattices more nearly commensurate. The larger expansion of the intercalant results from the weaker in-plane bonding of the intercalant relative to that of the graphite. Numerically the results for the nearest neighbor
intercalant distances graphite-FeC& are: &-Fe = 4.063 ? 0.003 8, dc,_c, = 3.519+ 0 003 A, and dFexI = 1.361f 0.003 A. The corresponding results in the pristine FeCl, host are: dFc-pe= 4.041+ 0.003 A, a&c, = 3.499 ? 0.003 A and dFGci= 1.338+ 0.003 A. Fourier synthesis of the (OOl)integrated intensities[l3], yields a value of 1.37A for the Fe-Cl layer separation, which is consistent with the ~bye-Scherrer results quoted above. These results on the intercalate superlattice confirm the concept that the graphite and the intercalant layers are closely related to the corresponding layers in their parent materials.
4.
CONCLUSIONS
The X-ray measurements presented in this work support the view that intercalation does not change the basic symmetry of the host and the intercalant for incommensurate graphite intercalation compounds. Small changes are, however, found in the lattice dimensions. All of the changes are based on: (i) electronic interactions between the graphite bounding layers and the
337
The effect of intercalation on the lattice constants of graphite Table 3. Interplanar spacings (&.) measured on a stage 2 graphite-FeCI, sample from a Debye-Scherrer film using Cr radiation
(a)
Intensity(c)
(hka)(a)
dhkP
001
12.54
002
6.32
medium
100(F)
5.24
vv
003
4.23
strong
004
3.179
strong
210(F)
1.983
vv
weak
300(F)
1.756
vv
weak
008
1.5914
+
0.0007(d)
medium
310(F)
1.4388
t
o.oolo(d)
vv
009
.4154
t
o.oooz(d)
medium
110(G)
.zz95
t
o.ooo,(d)
weak
320(F)
.2148
?
0.0003(d)
strong
0011
.1578
+
o.oooz(d)
vv
The the
notation intercalate
(b)
The
reported
(c)
Very
very
(d)
The the
(F)
standard lattice
and F&13
dhkp weak
is
weak
refer
respectively
sandwich
values
are
denoted
deviation parameters
(G)
(a)(b)
by is
by
layers
the
average
vv
weak.
Cohen’s
intercalant and (ii) strains acting to make both types of layers more nearly commensurate. Comparing the results for donor and acceptor compounds of comparable stage, we find that the dimensional change for the donor compounds (expansion) is much larger than that for acceptor compounds (contraction). These results support Raman and IR measurements, which exhibit larger property changes for the donor intercalation compounds than for the acceptor compounds of comparable stage. Correlating the X-ray measurements with the reciprocal stage index l/n indicates a linear dependence for both donor and acceptor compounds, with the largest dimensional change occurring for the most concentrated compound, (n = 1). Also, the calculated charge transfer is consistent with other experimental measurements. Acknowledgements-We
wish to thank Dr. G. Dresselhaus for helpful discussions and Dr. A. W. Moore of Union Carbide for his generous contribution of HOPG material. We gratefully acknowledge support for this work from AFOSR Contract No. F49620-31C-0006. REFERENCES 1. D. E.
and
an
reported
Nixon and G. S. Parry, J. Phys, C2, 1732 (1969).
to from of
only
for
least
in-plane the
four
the square
weak
(broad)
weak
(broad)
reflections
graphite independent
lines
weak
used
from
layers. readings.
for
determining
method.
2. D. Guerard, C. Zeller and A. Herold, CR. Acad. Sci., Ser. C283, 437 (1976).
3. C. Underhill, S. Y. Leung, G. Dresselhaus and M. S. Dresselhaus, Solid State Commun. 29,769 (1979). 4. G. M. Gualberto, C. Underhill, S. Y. Leung and G. Dresselhaus, Phys. Rev. B21, 862 (1980). 5. M. S. Dresselhaus and G. Dresselhaus, Adv. Phys. 30, 139 (1981).
6. M. Shayegan, B.S. Thesis, MIT. (unpublished) (1979). 7. S. Flandrois, J. M. Masson, J. C. Rouillon, J. Gaultier and C. Hauw, Synthetic Metals 3, I (1981). 8. R. S. Markiewicz, J. S. Kasper and L. V. Interrante, Synthetic Metals 2, 363 (1980).
9. L. Pietronero and S. Strlssler, J. Phys. Sot. Japan 49 Suppl. A, 895 (1980). 10. L. Pietronero and S. Strlssler, Phys. Rev. Lett. 47, 593 (1981).
11. R. E. Ogilvie, Proc. VIII INT. Conf. on X-Ray Optics and Microanal., Boston, Vol. 62A (1979). 12. S. Y. Leung, C. Underhill, G. Dresselhaus, T. Krapchev, R. Ogilvie and M. S. Dresselhaus, Solid State Commun. 32. 635 (1979). 13. S. Y. Leung, M. S. Dresselhaus, C. Underhill, T. Krapchev, G. Dresselhaus and B. J. Wuensch, Phys. Rev. B24, 3505 (1981).
14. The film was read by two independent readers and the reported value is the average of the two readings. 15. B. D. Cullity, Elements of X-Ray LIiffraction, 2nd Edn, p. 366. Addison-Wesley, Reading, Massachusetts (1978).
Abstract-A study of Q&O)X-ray reflections has been carried out on well-staged donor and acceptor intercalation compounds based on HOPG, and including stages 24 potassium donor compounds and stages 1 and 2 acceptor compounds with AK& and Fe&. The measured expansion of the in-plane carbon-carbon distance d,, for the donors is consistent with previous data on potassium. The present study, however, focuses on measurement of the contraction of dcx. in acceptor compounds; this lattice contraction is consistent with previous predictions based on the upshift of the in-plane Raman active mode frequencies. The in-plane structure and lattice constant for the intercalant in a stage 2 graphite-FeCll compound have been studied, and the results show no symmetry changes of the intercalate lattice, but an expansion of its in-plane lattice constant by a much larger magnitude than the contraction of the graphite in-plane lattice!. 1. INTRODUCTION
Small but measurable changes occur in the in-plane carbon-carbon distance do in graphite upon intercalcation f 1,2j. A quantitative mea5urem~nt of these changes gives important information about the nature of the bonding, electronic structure and lattice mode structure in these materials. Since these changes in lattice constant are very small, the modification to the electronic and lattice mode structure is correspondingly small and can be considered in perturbation theory. The interpretation of Raman spectra suggests an inplane contraction of d,_, in acceptors [3,4), in contrast with the in-plane expansion observed by structural studies of the donor compounds[l, 21. The present X-ray data confirm the interpretation of the Raman upshift for acceptors and downshift for donors as a function of intercalate concentrationI5]. The results of this X-ray study further show that the in-plane contraction for the acceptors is much smaller than is the donor expansion for samples of comparable stage, in agreement with previous work[6-81. In the present work the recent empirical model [7] and theoretical calculations [9, IO] relating the magnitude of the change in lattice constant to the charge transfer between the graphite and the intercalate layer are applied to the interpretation of measurements of the change in the in-plane d,_, distance denoted by Ad,_,. To obtain the necessary precision, we used the Gordon-Giessen X-ray technique [ 1l] which employs an energy dispersive diffractometer operating at a fixed diffraction angle. With this technique we can measure the in-plane lattice constant of graphite intercalation compounds with a precision of f 0.0002 A at room temperature. This technique also enables us to work with samples prepared from an HOPG host and encapsulated in glass, so that the intercalation compounds can be studied in their as-grown state.
2. EXPERIMENTAL The samples studied in this work were prepared using the two-zone vapor transport method[3]. The donor compounds were grown by keeping the intercalant temperature, T;, constant and varying the graphite temperature, T,, to obtain different stages. For the acceptor intercalants, TB was held constant and Ti was varied. The metal chloride intercalants (AIC13and FeClJ were first produced in situ by direct reaction of the heated metal wire with Cl, gas. Before sealing off the glass ampoule and inserting it in the two-zone furnace, the ampoule was back filled with Cl, gas to encourage staging. All the samples used in this study were single stage compounds. The stage index, fidelity and homogeneity of the specimens were determined by (~~) diffractograms using 8-28 scans taken in the reflection mode. In addition, all of the samples (except for the graphite-FeCl,) were encapsulated in glass to prevent intercalate desorption. Since we were looking for very small changes in the in-plane lattice parameter, we made use of the GordonGiessen technique [ I I] because this technique enables us to measure large samples in situ with great precision and resolution. With this technique a polychromatic X-ray source and a high resolution solid-state Si(Li) drifted X-ray detector are used. A chromium target X-ray tube was used in this study. because it lacks characteristic lines in the range of the diffracted energies[ll]. Each set of interplanar spacings dhrt will then diffract the proper wavelength from the continuous spectrum through the fixed 28 diffraction angle. With the GordonGiessen technique, it is the energy of the diffracted beam Es that is measured and related to the X-ray wavelength by EB = he/A. From Bragg’s law for the first order diffracted beam h = 2dhk, sin 0, a relation between EB and dhkr is obtained dhkl =6199&E, sin 8)
tlkpartment of MaterialsScience and Engineering. *Department of Electrical Engineering and Computer Science.
where Es is in eV and dhkr is in A. 331
(I)
332
T.
KRAPCHEVet al.
The experiments were performed on a G.E. diffractometer using an Ortec Si(Li) drifted solid state detector, attached to a Tracer Northern multi-channel analyzer. The samples were positioned on a single crystal goniometer head, allowing one rotational and two translational degrees of freedom. A schematic representation of the experimental configuration is shown in Fig. 1. To determine the in-plane lattice constant, we need only measure (MO) reflections, and, therefore, the symmetrical transmission geometry shown in the diagram was used. This geometery requires very thin samples (-0.2 mm) and the proper choice of collimators. To improve the precision of the measurement, the samples were aligned both mechanically and with the help of the X-ray beam. To eliminate angular errors associated with the positioning of the center of the specimen with respect to the axis of rotation of the goniometer, two sets of data points were taken for every peak position, each set of data corresponding to a rotation of the specimen by 180”. The experimental value reported here for each peak position is the average of the above two readings. Also long counting times were necessary to reduce statistical fluctuations. The determination of the peak position of each X-ray reflection was related to the channel number N at maximum intensity. This peak position was calculated, as shown in Fig. 2, by fitting the data points (open circles) to a Gaussian function (solid circles) using a least squares procedure. In this way N was determined to 20.2 of a channel number, which corresponds to ~0.0002 A for the interplanar spacing dllo of the (110)
940
960
Chnnw
980
l3cc
number I
19.2
18.8
Energy
I
20.0
19.6 CkeV)
Fig. 2. Least squares fit to a Gaussian function for the intensity of the (1IO)-graphiteline, where the X-ray energy E in keV is related to the channel number N by E(keV)= 0.02N. reflection. Once the d-spacing and the line index are determined, the lattice parameter can be calculated directly from the relation
1
I y?+hW+If at [ dhkr - 3
(2)
c2’
and de-c is related to the in-plane lattice constant a0 by d,_, = ao1d3.
(3)
Since the actual measurements focus on the determination of Adcz, the change in the nearest neighbor
Si(Li) Detector
I
KQ
A
4okev
-a a c-
2
2 C
Ll Kg
1 Analyzer
1
0.31
2.291
2.085 Wovelength(8 )
IhkO)
Fig. 1. A schematic representation of the experimental set-up for the Gordon-Giessen technique showing the X-ray beam path, the three degrees of freedom of the sample holder, an expanded view of the transmission geometry and the data flow chart.
The effectof intercalationon the lattice constants of graphite carbon-carbon distance due to intercalation, the samples for a given intercalant were fabricated from the same piece of highly oriented pyrolytic graphite (HOPG) and in each case &- for the particular HOPG host material was also measured. Thus the present determination of AdO depends on measurement of the intercalant-induced change in EB for the (110) reflection. The experimental set-up permitted measurement of lattice spacing with a resolution of kO.01 A, and a precision for d, 1o,the particular lattice spacing of interest, of +0.0002 A. For indexing the intercalant superlattice and determining the lattice constant of the intercalant layer, we used the Debye-Scherrer technique rather than the Gordon-Giessen in order to obtain more diffraction lines. For analysis of the intercalate superlattice, not only the (MO) lines. but also the (001) and (Ml) lines were used. Furthermore, the precision of the measurement in the energy range where the superlattice lines occur is not as high with the Gordon-Giessen technique as it is in the energy range of the graphite (110) reflection. 750
333
The X-ray patterns for pristine FeCI, and for the intercalate superlattice were obtained using a Cr target with the Debye-Scherrer camera and a Gondolfi attachment, the latter giving us an additional degree of freedom by tilting the sample. The stage 2 graphiteFe& sample that was examined with the Debye-Scherrer technique was cut from a larger sample which was used for measurement of Adc-c by the energy dispersive Gordon-Giessen method. 3.RESULTSANDDISCUSSION
Typical energy diffractograms of (MO) reflections taken in the transmission mode are shown on Fig. 3, where results for both donor and acceptor compounds are compared with those for HOPG. The most prominent peak in the diffractograms for the intercalation compounds is that associated with the graphite (1 IO) in-plane reflections and labeled G,,,,,, in the figure. The peaks labeled CrK, and CrK, are due to the characteristic lines of the target material of the X-ray tube. These Al&
K
Stage 2
Stage 1
Gl1l0l
600
h
0
-4
5.412
Fe&(m) 1
315c
CrK8
75-
FeCl3
5946
800
Stage 1
150-
K
Stage 3
600
I
19.497
Fe03 Stage
CrKa ACrKg
300 0 5412’
,“I kc&Jk&
Guoo,
& ‘5946
2400
Quo)
19.472
HOPG k3co
G(IIO)
1200
QIOOI
1 /, HOPG
1200 t 600 300 0
C&X,, ,C~KB 5412
!-IL 11.235
‘5946
Energy (keV) (a)
2
19.460
~L-lL~,L 11.226
Energy
( keV i
19.460
(b)
Fig. 3. X-ray energy diffractograms taken with the Gordon-Giessen technique: (a) for graphite-K compounds and HOPG; (b) for graphite-AK&and FeQ compounds.The energy range is selected to show the intercalant-induced shift of the graphite (110) diffraction peak, denoted by Go,,,. The CrK, and CrK, lines are used to calculate the energy scale. Various diffraction lines of interest are indicated on the diffractograms.
334
T. KRAPCHEV
characteristic lines were used to calibrate the energy scale of the diffractogram. The intercalant-induced shifts m energy for the Go,,, line for the intercalation compounds are obtained by comparison to the energy for the pristine graphite line. These shifts are used to determine A&. Because of their low intensities and corresponding lower resolution, the (100) reflections labeled Go,, were not used directly in the determination of the inplane lattice constant aO, but were rather used as a consistency check. From the intensity vs energy spectra in Fig. 3, it is seen that the intensity of the G,,,,, reflection varies both with stage and intercalant. The stage dependent intensity of the Go,,,, line is proportional to the fraction of carbon scattering centers that are in the sample (obtained from the chemical formula), and the relative cross section of the carbon scattering centers as compared with the intercalant scattering centers. For example in Fig. 3, Golo, has the lowest relative intensity in the case of the FeCl, samples, since FeCl, has the largest mass absorption coefficient, and is therefore the strongest X-ray absorber. The results obtained for Ad,_, in this study are summarized and compared with previously reported data in Table 1. These results show an expansion of the nearest neighbor in-plane carbon-carbon distance for donor compounds (A& is positive) and a contraction for acceptor compounds (A& is negative), in agreement with previous structural studies [l, 2, 7, 81 and with predictions based on Raman scattering studies[3]. The measured expansion of A&-c for the potassium compounds (measured to an accuracy of ~0.0002~) is in
et al.
good agreement with values previously published by Nixon and Parry, and measured using the Debye-Scherrer technique[l]. A comparison of the results for donor and acceptor compounds shows that Adc-c is significantly larger for donor compounds of the same stage. A small magnitude for Adc_c was previously reported for a stage 2 graphite-NiCl* acceptor compound by Flandrois et al. [7] based on measurements on a single crystal intercalated flake and using a two-circle semiautomatic Stoe diffractometer. To show the stage dependence of the in-plane lattice expansion/contraction the change of the in-plane carboncarbon distance Ad,, is plotted in Fig. 4(a) vs reciprocal stage l/n for both donor and acceptor compounds. The dependence of Adc-c on l/n is approximately linear, as shown by a least squares fit of the data to a straight line, yielding a coefficient of determination (COD) of 1.00 for the potassium donor compounds, and 0.96 for the FeC& acceptor compounds. A somewhat better linear relation is obtained (see FigAb) by plotting Ad,_c vs l/Q where l/t is the intercalate in-plane density, determined directly from integrated intensity measurements of (001) diffractometer scans [ 12,131 for each of the samples used in the present study. (See Table 2 for the l/r values thus obtained). In the case of Fig. 4(b), the COD value for a straight line fit to the Adc_c vs l/n6 plots is 1.00 for the donor-K samples, and 0.98 for the acceptor-FeCl, samples. A better fit to a linear dependence is expected for the Ad,, vs l/n6 plots since the intercalate concentration is related more directly to l/Q than to l/n. Flandrois et al. [7] found empirically that the measured
Table I. Ad,, for various graphiteintercalationcompounds(“) Intercalant
Adc-C
stage
(A)
K
1
40.0109~DJ
K
2
+0.00478(b) +0.0050(c)
K
DOllOlYS
+o.oom(b)
3
+0.0028(C) K
+0.00191(b)
4
+O.QO18(c)
AX13
1
-0.0022(c)
F&13
1
-0.0027(C)
F&13
2
-0.0009(C~e)
NlCl2
2
-0.0009(d)
Acceptors
(a)
Ad c-c
is
the
relative
to
expansion;
difference that
in
a negative
(b)
Results
from
cc)
Results
of
(d)
Results
from
(e)
*b’ IS
value
Ref.
this
is
between the
d C-C
HOPG host.
sign
indicates
in
work.
the
7. average
for
two
intercalation
contraction.
1.
Ref.
the
A positive
samples.
sign
compound
indicates
in-plane
The effect of intercalation on the lattice constants of graphite
33.5
Ados values for the acceptor compounds (Table l), and using the corresponding measured in-plane densities (Table 2), estimates of the charge transfer per carbon atom were obtained and the values are listed in Table 2. Using the measured values for 5 (also listed in Table 2), the charge transfer per intercalate unit fX was determined according to the relation fX = (n[)fc and the results are also listed in Table 2 Recently Pietronero and Strgssler [9,10] presented a model calculation relating the magnitude of Adc_t to & the charge transferred per carbon atom: Adc_c = 0.1575, + 0.146~~~~”+ 0.236fcz.
0 005
nd
0 004 0 003 “d-iI 0.002
/
,/’
: 7 000;
. 0 12
0.16 lh[ I” C”fX
-0.002 -0 003 t
@I Fig. 4. Plot of the change of the in-plane carbon-carbon distance ihdp ,-l for the potassium donor and the FeCll and AICI, combounds as: (a) a function of reciprocal stage (I/n). The results of ihe present work are indicated by open symbols and the closed circles are from Ref. 111.The lines are a least squares fit of the data to a straight Ii&~(b) A function of (ltn~) where l/E is in-plane inter&ate density and is related to the chemical formula C&f. The closed symbols are for those densities determined from (001) integrated intensity measurements while the open symbols are for “accepted” stoichiometries (see Table 2). The lines are a least squares fit of the data to a straight line.
Ad,_, values for the donor compounds and for his stage 2 acceptor NiCI, compound followed a linear relation between Ad,_, and fc, the fractional charge transferred from (or to) each carbon atom. For the case of the donor compounds, it was assumed that the alkali metal intercalant was fully ionized, while for the acceptors, the charge transfer was deduced from the measured stoichiometry x in CM, where M denotes the intercalant. The negative sign of Adc_c in their plot corresponds to an electron transfer from graphite to the intercalant in the acceptors, while the positive sign for donors indicates an electron transfer from the intercalant to the graphite n-bands. Of particular interest is the observation[7] that in the donor limit x = 1, the correct bond length of 1.52A is obtained for the single C-C bond, while for the acceptor limit x = - 1 the correct bond length of 1.32A is obtained for the double bond. Applying the same empirical relation to our measured
(4)
Using eqn (4), values were also obtained for fc using our measured Adc_, values, and the results are presented in Table 2. Also given in Table 2 are values for the charge transfer per intercalate unit fX obtained using the measured [ values. These results suggest that fX may be stage dependent, but such a conclusion awaits confirmation using other measurement techniques. Using either the Flandrois[7] or the Pietronero[ IO] model, the larger magnitude of the Ad,_, expansion for donors compared with the Ad,, contraction for acceptors of comparable stage is attributed in part to a smaller charge transfer fX for acceptors than for donors. In addition, the model of Pietronero and StrasslerllO] contains terms going as lfc(3’2and fc2 due to electronphonon coupling, which contribute to an increase in Ad,_, independent of the sign of the charge transfer. In the case of the acceptor compounds studied in the present work, these terms are, however, small relative to the linear term. In the diffractograms for the graphite-Fe& samples, we observed additiona reflections (Fig. 3b) not found in the scan for HOPG, and we therefore attributed these reflections to the intercalant FeCl, superlattice. To study these additional reflections, a stage 2 graphite-FeCb sample was examined in more detail using a DebyeScherrer camera with a Gondolfi attachment to give all possible (Ml) reflections. The film was read1141 and indexed in terms of two independent lattices (i.e. both for graphite and FeCl,) using the same c-direction lattice parameter. These results which are summarized in Table 3, show that at room temperature the in-plane intercalant is arranged in an ordered state, with a hexagonal in-plane Cl-Fe-Cl sandwich structure that is the same as that for pristine FeCh (space group C$ or R3). In the intercalation compound each sandwich is separated from neigh~ring sandwiches by graphite layers which tend to destroy the interlayer ordering between the sandwiches, though preferred orientational interplanar correlation may be retained. Our measurements have, however, focussed on the change in the ordering within the intercalate sandwich, and not on the interlayer correlation between intercalate sandwiches. Using 20 diffraction lines above 80” and Cohen’s least squares method[l5], the lattice parameters of the two lattices were determined yielding in-plane lattice constants of uc= 2.4590’- 0.0@04A for the graphite and f&j=
336
T. KRAPCHEVet al. Table 2. Measured in-plane intercalate densities I/( and estimates for charge transfer from Ad,, 1ntercalant
model
FeC13
1
F&13
0.154CCJ
-0.036
o.m(d)
-0.036
0*13(e)
-0.012
A(e)
o.ls(df
-0.012
0.121(c)
-0.cl29 -0.029
0.114(c)
0.057
0.083(d)
0.042
0.100(c)
0.033
-0.23
-0.14
-0.24
-0.14
-0.17
-0.09
-0.16
-0.09
-0.24
-0.13
-0.25
-0.13
B
1.00
to.47
1.00
+0.64
1.00
+0.46
1.00
Hi.56
1.00
+o.45
1.00
+0.50
a.0155
4
0.083(d)
0.028
0.093(c)
0.023 +0.0105 0.021
0.083(d)
ca)
Charge
transfer
per
carbon
(b)
Charge
transfer
per
intercalate
(c)
Calculated
from measurements
(d)
Calculated
from an assumed stoichiometry
atom. unit of
fX -
(00~)
(nt)fc.
line
intensities. of
5 = 12,
8.4
and 6.6
for
K,
and FeC.13 respectively.
(e)
In Model A, fc
is
calculated
from the model
of
Flandrois
(f)
In Model
is
calculated
from the model
of
Pietronero
(Ref.
model
+0.0265
3
K
A
-0.016
2
K
model
-0.0065
1
K
B(f)
-
-0.021
0.119(d)
AlC13
model
2
AlC13
fK(b)
fcfa)
115
stage
measurements
B, fc
et
al.
(Ref.
7).
and Strkler
IO).
6.0951tO.003 8, for the Fe&
layers, together with a c-axis repeat distance of Z, = 12.766i:O.O02i(. This value is in excellent agreement with the 1, value obtained for the same sample from (001) scans taken to characterize the sample stage I, = 12.76t 0.05 A. Excellent agreement is also obtained with 1, values reported by other workers[3]. Compared with the in-plane lattice parameters of the pristine compounds (a0 = 2.4605 A for graphite and 6.062 8, for FeCI,), which were obtained by the same technique, the graphite shows a small contraction of 0,0015& while the FeCI, shows a very much larger expansion of 0.033 A. The graphite contraction is the same as that measured by the energy dispersive Gordon-Giessen method (see Table 1). Since the graphite and intercalant lattices are incommensurate, it is possible for the graphite to expand while the intercalant contracts. In fact, the expansion of the graphite and the contraction of the intercalant correspond to making the two lattices more nearly commensurate. The larger expansion of the intercalant results from the weaker in-plane bonding of the intercalant relative to that of the graphite. Numerically the results for the nearest neighbor
intercalant distances graphite-FeC& are: &-Fe = 4.063 ? 0.003 8, dc,_c, = 3.519+ 0 003 A, and dFexI = 1.361f 0.003 A. The corresponding results in the pristine FeCl, host are: dFc-pe= 4.041+ 0.003 A, a&c, = 3.499 ? 0.003 A and dFGci= 1.338+ 0.003 A. Fourier synthesis of the (OOl)integrated intensities[l3], yields a value of 1.37A for the Fe-Cl layer separation, which is consistent with the ~bye-Scherrer results quoted above. These results on the intercalate superlattice confirm the concept that the graphite and the intercalant layers are closely related to the corresponding layers in their parent materials.
4.
CONCLUSIONS
The X-ray measurements presented in this work support the view that intercalation does not change the basic symmetry of the host and the intercalant for incommensurate graphite intercalation compounds. Small changes are, however, found in the lattice dimensions. All of the changes are based on: (i) electronic interactions between the graphite bounding layers and the
337
The effect of intercalation on the lattice constants of graphite Table 3. Interplanar spacings (&.) measured on a stage 2 graphite-FeCI, sample from a Debye-Scherrer film using Cr radiation
(a)
Intensity(c)
(hka)(a)
dhkP
001
12.54
002
6.32
medium
100(F)
5.24
vv
003
4.23
strong
004
3.179
strong
210(F)
1.983
vv
weak
300(F)
1.756
vv
weak
008
1.5914
+
0.0007(d)
medium
310(F)
1.4388
t
o.oolo(d)
vv
009
.4154
t
o.oooz(d)
medium
110(G)
.zz95
t
o.ooo,(d)
weak
320(F)
.2148
?
0.0003(d)
strong
0011
.1578
+
o.oooz(d)
vv
The the
notation intercalate
(b)
The
reported
(c)
Very
very
(d)
The the
(F)
standard lattice
and F&13
dhkp weak
is
weak
refer
respectively
sandwich
values
are
denoted
deviation parameters
(G)
(a)(b)
by is
by
layers
the
average
vv
weak.
Cohen’s
intercalant and (ii) strains acting to make both types of layers more nearly commensurate. Comparing the results for donor and acceptor compounds of comparable stage, we find that the dimensional change for the donor compounds (expansion) is much larger than that for acceptor compounds (contraction). These results support Raman and IR measurements, which exhibit larger property changes for the donor intercalation compounds than for the acceptor compounds of comparable stage. Correlating the X-ray measurements with the reciprocal stage index l/n indicates a linear dependence for both donor and acceptor compounds, with the largest dimensional change occurring for the most concentrated compound, (n = 1). Also, the calculated charge transfer is consistent with other experimental measurements. Acknowledgements-We
wish to thank Dr. G. Dresselhaus for helpful discussions and Dr. A. W. Moore of Union Carbide for his generous contribution of HOPG material. We gratefully acknowledge support for this work from AFOSR Contract No. F49620-31C-0006. REFERENCES 1. D. E.
and
an
reported
Nixon and G. S. Parry, J. Phys, C2, 1732 (1969).
to from of
only
for
least
in-plane the
four
the square
weak
(broad)
weak
(broad)
reflections
graphite independent
lines
weak
used
from
layers. readings.
for
determining
method.
2. D. Guerard, C. Zeller and A. Herold, CR. Acad. Sci., Ser. C283, 437 (1976).
3. C. Underhill, S. Y. Leung, G. Dresselhaus and M. S. Dresselhaus, Solid State Commun. 29,769 (1979). 4. G. M. Gualberto, C. Underhill, S. Y. Leung and G. Dresselhaus, Phys. Rev. B21, 862 (1980). 5. M. S. Dresselhaus and G. Dresselhaus, Adv. Phys. 30, 139 (1981).
6. M. Shayegan, B.S. Thesis, MIT. (unpublished) (1979). 7. S. Flandrois, J. M. Masson, J. C. Rouillon, J. Gaultier and C. Hauw, Synthetic Metals 3, I (1981). 8. R. S. Markiewicz, J. S. Kasper and L. V. Interrante, Synthetic Metals 2, 363 (1980).
9. L. Pietronero and S. Strlssler, J. Phys. Sot. Japan 49 Suppl. A, 895 (1980). 10. L. Pietronero and S. Strlssler, Phys. Rev. Lett. 47, 593 (1981).
11. R. E. Ogilvie, Proc. VIII INT. Conf. on X-Ray Optics and Microanal., Boston, Vol. 62A (1979). 12. S. Y. Leung, C. Underhill, G. Dresselhaus, T. Krapchev, R. Ogilvie and M. S. Dresselhaus, Solid State Commun. 32. 635 (1979). 13. S. Y. Leung, M. S. Dresselhaus, C. Underhill, T. Krapchev, G. Dresselhaus and B. J. Wuensch, Phys. Rev. B24, 3505 (1981).
14. The film was read by two independent readers and the reported value is the average of the two readings. 15. B. D. Cullity, Elements of X-Ray LIiffraction, 2nd Edn, p. 366. Addison-Wesley, Reading, Massachusetts (1978).