Ordering in second stage alkali-metal-graphite intercalation compounds

686

Applications of Surface Science 22/23 (1985) 686~'395 North-Holland, Amsterdam

O R D E R I N G IN S E C O N D STAGE A L K A L I - M E T A L - G R A P H I T E INTERCALATION COMPOUNDS G.R.S. NAYLOR Physics Department, James ()~ok University of North Oueensland, Townsville. Queensland 4811, Australia

Received 27 August 1984; accepted for publication 12 November 1984

The two-dimensional ordering in second stage alkali-metal-graphite intercalation compounds is investigated. It is shown that all hexagonal incommensurate metal lattices form commensurate superlattices. Using this, the observed orientational ordering is modelled by the simple condition that the experimental structure is a superlattice with a local minimum (varying the incommensurate lattice dimension) of the average distance of the metal atom from its nearest graphite hexagon centre. This approach is used in a detailed study of the diffraction pattern of the low temperature phase of second stage rubidium graphite.

1. Introduction G r a p h i t e i n t e r c a l a t i o n c o m p o u n d s are f o r m e d by the insertion of a t o m i c o r m o l e c u l a r layers of a guest m a t e r i a l b e t w e e n the layers of the host g r a p h i t e . T h e i n t e r e s t in t h e s e c o m p o u n d s is p r i m a r i l y t w o f o l d : (a) the possibility of the synthesis of new a n d c o m m e r c i a l l y i n t e r e s t i n g m a t e r i a l s , a n d (b) a t h e o r e t i c a l i n t e r e s t in t w o - d i m e n s i o n a l physics. In p r e p a r i n g g r a p h i t e i n t e r c a l a t i o n c o m p o u n d s it is p o s s i b l e to vary the n u m b e r of host g r a p h i t e layers b e t w e e n successive layers of guest m a t e r i a l . This p h e n o m e n o n is called staging a n d is shown s c h e m a t i c a l l y on fig. I. A stage " n " c o m p o u n d has n g r a p h i t e layers b e t w e e n each i n t e r c a l a n t layer. T h e d i s t a n c e b e t w e e n a d j a c e n t g r a p h i t e layers is a p p r o x i m a t e l y the s a m e as in p r i s t i n e g r a p h i t e a n d the d i s t a n c e b e t w e e n the g r a p h i t e layers f o r m i n g the g r a p h i t e - i n t e r c a l a t e - g r a p h i t e s a n d w i c h is a p p r o x i m a t e l y c o n s t a n t for the v a r i o u s s t a g e c o m p o u n d s , T h u s staging varies the d i s t a n c e b e t w e e n neighb o u r i n g i n t e r c a l a t e layers a n d so can be used as a c o n t r o l l e d t r a n s i t i o n from t w o - d i m e n s i o n a l b e h a v i o u r of the i n t e r c a l a n t l a y e r to t h r e e - d i m e n s i o n a l behaviour. T h e s t r u c t u r e s of a l k a l i - m e t a l - g r a p h i t e i n t e r c a l a t e s have b e e n r e v i e w e d r e c e n t l y by Solin [1]. T h e stage o n e c o m p o u n d s form a simple o r d e r e d t h r e e - d i m e n s i o n a l s t r u c t u r e that is well c h a r a c t e r i z e d . By c o m p a r i s o n the 0378-5963/85/$03.30 © E l s e v i e r Science P u b l i s h e r s B.V. ( N o r t h - H o l l a n d Physics P u b l i s h i n g D i v i s i o n )

G.R.S. Naylor / Alkali-metal-graphite intercalation compounds

687

O0 O0 O0 O0

QO

OO OQ

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5rage 3

Fig. 1. The effect of staging in graphite intercalation compounds. The circles represent layers of intercalated material between the graphite sheets denoted by solid lines.

second stage compounds form structures that are not fully understood. At room temperature the metal atoms seem to form a two-dimensional liquid. As the t e m p e r a t u r e is reduced there are two m a j o r structural phase transitions. At the first transition (165 K for Rb) the metal atoms order in two dimensions to yield a two-dimensional incommensurate lattice which is rotated relative to the graphite. The lower transition (105 K for Rb) signals the onset of three-dimensional ordering, The dependence of the rotation angle associated with the orientational ordering on the incommensurate metal lattice wave vector is shown in fig. 2 [2-4]. A second important feature of the low temperature in-plane diffraction pattern from the metal atoms is the presence of satellite reflections at reciprocal lattice points G-+ M, where G and M" are the graphite and metal reciprocal lattice vectors. In particular the intense first ring of satellites is suggestive of a strong interaction of the graphite potential on the incommensurate metal lattice. A full analysis of this pattern has not been attempted but two different approaches have been used to explain the high intensity of the first order satellites: (a) a sinusoidal static distortion wave applied to the incommensurate metal lattice [5,6], and (b) a model consisting of small domains of locally c o m m e n s u r a t e V ' 7 x X/7 domains with narrow domain walls of high density [2,4]. In the present paper, I will consider a simple explanation of the orienrational ordering of the alkali-metal lattice in terms of a c o m m e n s u r a t e superlattice of metal atoms. This leads to a useful parameterization of the distorted metal structure. As an example I will use this approach to model the entire in-plane diffraction pattern of second stage rubidium-graphite.

G.R.S. Naylor / Alkali-metal-graphite intercalation compounds

688

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2. Determination of possible superlattices F o r a m e t a l lattice graphite structure, some c o i n c i d e with a g r a p h i t e G e o m e t r i c a l l y this leads ing the r e l a t i v e size of o r i e n t a t i o n , 0:

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Fig. 4. A plot of the predicted x/~3× x¢/43superlattice structure for the second stage rubidium graphite compound. Using these equations all the superlattices with their corresponding relative orientation, 0, up to a size of 100 metal atoms, were determined over the observed experimental range of incommensurate metal lattice sizes. Also for each superlattice the average distance, dMo, of each metal atom from its nearest underlying graphite hexagon centre was calculated. The results are summarized in fig. 3. One might imagine that dMG is a measure of the energy of a particular superlattice, i.e., a large value of dMG would correspond to a less favourable structure. Choosing the superlattice with a local minimum value of dMG does agree well with the experimental data for the orientational ordering as shown in fig. 2. Due to the sharpness of the minima in dMG and the seemingly random variation of 0 with d M this method predicts very specific structures for the incommensurate metal lattice. These predictions were tested by X-ray diffraction studies of second stage rubidium-graphite where a relatively small superlattice with only seven metal atoms is predicted. This is shown in fig. 4.

3. Experimental details All the experiments were performed on second stage rubidium-graphite prepared under vacuum (5 × 10 6 Torr) from 0.5 mm thick Papyex (a commercially available partially ordered graphite with approximate mosaic

G.R.S. Naylor / Alkali-metal-graphite intercalation compounds

691

spread of c axis of 15°) using a two-oven method (Tab = 215°C, T G = 340°C). After preparation, samples were transferred via a nitrogen glove bag to a beryllium can, which was placed in a variable temperature liquid helium cryostat. The sample temperature was accurate to 1 K. Transmission X-ray diffraction experiments used Cu K a radiation, A = 1.5418,~, from a Philips sealed X-ray tube and a two circle diffractometer [7]. 0-20 scans were p e r f o r m e d to study the cylindrically smeared (hkO) plane with the sample orientated with the [001] direction in the plane of diffraction. All patterns were recorded in the range 5 ° ~< 20 ~< 80 ° in steps of 0.05 ° with a 20 s counting time at each position.

4. Diffraction results of rubidium-graphite Fig. 5 shows the diffraction pattern of the cylindrically averaged (hkO) plane of second stage rubidium-graphite at a temperature of 5 K. The wealth of satellite peaks is apparent and 31 diffraction maxima are distinguishable. These peaks can all be indexed as incommensurate metal lattice reflections, with satellite reflections as shown in table 1, and refinement of the peak positions leads to dM/d~ = 2.479_+0.001 and 0 = 11.48_+ 0.02 °. This is in very good agreement with the superlattice prediction of 2.478 and 11.51 ° . This is verified by the alternative indexing of the pattern on the predicted superlattice also shown in table 1. In the superlattice shown in fig. 4 the positions of the six non-centred metal atoms relative to the nearest underlying graphite hexagon are equivalent. Also there is another and equally probable orientation of the superlattice corresponding to the negative value of 0 = - 11.51 °. In both possible orientations the metal atoms are in equivalent positions. Thus in an

II1_z ~-

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Fig. 5. The in-plane diffraction pattern of a partially ordered sample of second stage rubidium graphite at 5 K.

G.R.S. Naylor / Alkali-metal-graphite intercalation compounds

692

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G.R.S. Naylor / Alkali-metal-graphite intercalation compounds

693

Table 2 Bragg angles, observed and calculated intensities from the ~/4-3 x ~ / ~ Rb sublattice in C24Rb at 5 K; R factor = 21% Angle (deg) 10.89000 12.58000 16.67000 18.92000 21.88000 22.79000 25.32000 27.63000 29.08000 31.80000 33.08000 33.70000 35.52000 38.38000 38.93000 40.01000 42.11000 46.54000 48.87000 50.67000 51.55000 51.99000 53.29000 55.82000 56.65000 57.06000 58.28000 59.09000 60.28000 63.02000 63.79000 65.31000 66.44000 67.56000 69.41000 69.78000 70.51000 70.87000 72.68000 74.12000 75.19000 76.26000 78.37000

I (obs) 25.30000 29.20000 10000.00000 18.20000 2.80000 18.100000 172.00000 11.50000 69.20000 33.60000 113.10000 17.50000 7.20000 3.90000 4.90000 27.30000 17.20000 47.20000 7.20000 90.60000 0.00000 0.00000 5.20000 19.60000 1.90000 6.70000 8.10000 5.00000 23.80000 6.50000 24.10000 2.20000 0.00000 0.00000 0.00000 14.60000 0.00000 3.60000 2.70000 3.00000 10.40000 0.00000 8.80000

I (calc) 57.70733 46.79482 991.96439 54.62111 4.90567 25.08340 129.32596 17.53266 89.25966 51.20413 133.69212 47.55141 12.12652 3.59959 3.75704 27.41937 74.21552 39.52230 7.91117 48.65673 2.57783 0.45489 3.55929 15.19876 0.42115 2.41837 8.27894 8.88018 20.18398 6.15833 12.71266 3.24727 0.36326 0.44898 3.30266 11.04171 1.35233 1.36306 1.40936 3.57103 7.69410 0.27922 8.63794

694

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It is interesting to note that the rubidium ions at the start of the refinement are nearly along the centre to carbon atom directions but m o v e inwards and to o n e side so as to lie along the perpendicular bisector of the graphite c a r b o n - c a r b o n bonds.

5. Discussion T h e t w o - d i m e n s i o n a l superlattice appears to give a reasonable fit to the diffraction intensities in the low t e m p e r a t u r e phase. It should be n o t e d that no account has b e e n m a d e of the t h r e e - d i m e n s i o n a l stacking of the metal layers, p r e s u m a b l y occurring at 5 K. This stacking s e q u e n c e is as yet u n k n o w n but apparently quite c o m p l i c a t e d [8]. This is possibly the limiting factor on the o b t a i n a b l e R factor for the fitting of the intensities.

G.R.S. Naylor / Alkali-metal-graphite intercalation compounds

695

The simple geometrical explanation of the orientational ordering is not of course able to predict, a priori, the incommensurate metal lattice dimension. It is however able to clearly distinguish "neighbouring" structures with similar lattice dimensions and can possibly be used to estimate the steepness of the energy minimum that the metal lattice experiences. For example, in the case of the second stage potassium compound there is a double minimum in fig. 3 with seemingly more favourable structure (i.e., with smaller dMG) that is not observed experimentally. Thus any detailed energy calculation must be able to explain the non-shrinkage of the metal lattice by approximately 0.02 ~, to this state. It is interesting to compare the empirical distortion of the metal atom determined from the least squares fitting with the two earlier models used to describe the first order satellites. The empirical distortions in the two hexagonal lattice directions are shown in fig. 6 as a function of displacement from the hexagon centre. Clearly a sinusoidal distortion is not a good fit to the results, which suggest that a sawtooth-type distortion would be a better approximation. It is possible to show that any two-dimensional periodic distortion will give satellite reflections at the same positions as a sinusoidal distortion [9]. This is easy to see in the case of the rubidium superlattice since a periodic distortion will leave the size of the superlattice unaltered and so cannot affect the positions of the peaks. In the extreme case where the metal atom distortion forces the atom onto the centre of the hexagon, it is apparent that this produces locally c o m m e n s u r a t e ~/7 × ~/7 domains and the superlattice represents the lattice formed by the centre of each domain. Thus it appears that the two previous models of the satellite reflections are essentially related, each being a specific example of a periodic static distortion wave of an incommensurate two-dimensional lattice.

References [1] [2] [3] [4] [5] [6]

S.A. Solin, Advan. Chem. Phys. 49 (1982) 445. M. Suzuki and H. Suematsu, J. Phys. Soc. Japan 52 (1983) 2761. M. Mori, S.C. Moss, Y.M. Jan and H. Zabel, Phys. Rev. B25 (1982) 1287. R. Clarke, J.N. Gray, H. Homma and M.J. Winokur, Phys. Rev. Letters 47 (1981) 1407. J.B. Hastings, Springer Tract in Solid State Science 38 (1981) 206. M. Suzuki, H. Ikeda, H. Suematsu, Y. Endoh, H. Shiba and M.T. Butchings, J. Phys. Japan 49 (1980) 671; Physica B105 (1981) 280. [7] C. Mowforth, DPhil Thesis, Oxford University (1983). [8] Y. Yamada, I. Naiki, T. Wantanabe and T. Kiichi, Physica 105B (1981) 277. [9] G.R.S. Naylor and J.W. White, in preparation.