- Email: [email protected]
Structural properties of low dimensional potassium metal in intercalated graphite
lOURlAL
OF
NON-CRYSTALIJNESOL Journal
of Non-Crystalline
Solids 205-207
(1996)
803-806
Structural properties of low dimensional potassium metal in intercalated graphite Y. Arai a, Y. Shirakawa a, S. Tamaki b3* a Graduate School of Science and Technology, Niigata Univemity, b Department of Physics, Faculty of Scieme, Niigata University,
Ikarashi, Niigata-ski, Ikarashi, Niigata-siti,
Niigata-ken Niigata-ken
950-21, Jupm 950-21, Japm
Abstract X-ray diffraction experiments for stage-2 potassium-intercalated graphite C,,K and stage-l CsK have been carried out. Disordered profiles have been observed for both samples. The measured structure factor S(Q) for the disordered potassium in C,K shows a characteristic subpeak in the small angle region below the first peak, which suggests that there exists a short-range order in the potassium layers. The phases of the pair distribution function g(r) and S(Q) for the potassium layers in CsK disagree with those in C,,K. To check the influence of the carbon layers, the profiles of g(r)s of CsK and C,,K are compared with that of normal liquid potassium.
1. Introduction It is well known that graphite intercalation compounds exhibit a regular layer-stacking sequence along the C axis. Alkali-metal intercalated graphite shows interesting behaviour, such as an order-disorder transition in the structure of alkali metal layers. Parry El] showed that the stage-l C,M (M = K, Rb and Cs) of highly oriented pyrolitic graphite (HOPG) has a commensurate order along the direction of the C-axis at room temperature. They also found a disordered structure for the stage-2 compound C&K. The order-disorder transition temperatures, obtained inferred from the temperature dependenceof the resistivity measurements for C,,M (M = K, Rb and Cs), were 98, 1.59and 163 K, respectively [2]. * Corresponding 263 3961.
author.
Tel.:
0022-3093/96/$15.00 Copyright PZi s0022-3093(96)00385-7
+81-25
262 6136; fax:
0 1996 Elsevier
-t-81-25
Science
In the caseof C,,Cs, Clarke et al [3] measuredthe (I&O) X-ray reflections at 300 K to derive the structure factor of cesium atoms in the in-plane layers S(Q) and the resulting pair distribution function g(r) for the Cs layer. It is very interesting to investigate the structural properties of the potassiumlayers in C,K and C,,K and to compare these with that of liquid K, because this investigation is very much related to the behaviour of two-dimensional properties. In Fig. 1, schematic layer stackings for C, K and C,,K are shown. In this paper, we present the structure factor S(Q) and the pair distribution function g(r) of potassium layers in the stage-2 compound and in the stage-l at room temperature. Such 2-D liquid potassium structures will be discussedin comparison with that of the three-dimensional liquid structure, and we propose a model of
B.V. All rights reserved.
Y. Arai et al. /Journal
804
of Non-Crystalline
HOPG ~
-
__ __.___. _-......-_-._. --___
Carbon
----------
layer
Poiassium
Fig. 1. The stacking sequence of the stage-l intercalation compounds and HOPG.
layer and stage-2 graphite
the disorderedpotassiumlayers by using the reverse Monte Carlo simulation.
Solids 205-207
(1996)
803406
factors S(Q) of the potassiumlayer in the C,,K and C,K samplesare shown in Fig. 2. As shown in this figure, the first peak posi$on of C,K is 1.50 A-’ and that of C,K is 1.20 A-‘. These agree with the resultsof in situ X-ray measurements[8]. Thesepeak positionsindicate that the liquid-like potassiummetal layers in the graphite are different from simpleliquid potassiummetal at 70°C [9], in which the first peak position of S(Q) is 1.65 A-‘. In addition, the S(Q) tf the potassiumlayer in C,K has a subpeakat 1.00 A-‘. The profiles of S(Q) of the potassium layer in C 8K and C 24K are, more or less,very similar to the liquid structure; however, there is an influence of the sandwichingcarbon layers [lo]. Introducing the in-plane pair distribution function g(r) (= p(r)/p,,), we have Pm gw
2. Experimental and results
=
z,sph
-
(W
-
w’
&--&s(e)
= l+
- 1)
x4,( Qr)dQ,
X-ray scattering experiments have been performed for the two different types of intercalated samples.They were preparedby the two-bulb method developed by H&old [4]. Well-annealed pyrolitic graphite (PG) was sealedin evacuated Pyrex tubes with purified excesspotassium.In the caseof C,,K, the sampleswere preparedby holding the PG at 658 K and potassiummetal at 510 K for 40 h. The C,K was also prepared by holding the PG at 650 K and potassium metal at 490 K for 40 h [5]. The (IzkO) X-ray diffraction measurementswere carried out by using MoK, radiation operatedat 40 kV and 20 mA. To reduce the statistical errors, we set the maximum counts higher than 10000 counts with a fixed time mode. The sampleswere sealed off in a cylindrical sampleholder. Using the Faber-Ziman formula, the coherent scatteredintensity per atom Z,sP”(Q>is related to the total structure factor S(Q) for the potassiumlayer in C, K and C,,K by the following form: S(Q)
= --x-
(2)
where p,, is the average atomic number density, which is equal to 2.73 X lo-’ and 4.77 X low2 atoms/A2 for C,,K and C,K, respectively. The term J&Qr) is the zeroth-order Besselfunction. The in-plane pair distribution function for potassium metal in C,K and C,,K has been obtained by using the above Fourier-Bessel transformation, as shown in Fig. 3. As shown in Fig. 3, the first peak positions o,f g(r) for pptassiumin C,K and C,,K of are 4.62 A and 5.48 A, and the secondpeak positions are 8.32
I
’
’
1
’
’
’
’
I
W”)
’
where f is the form factor [6]. Sharp reflections from the graphite host were subtracted from the raw data [7] and corrections were made for polarization, absorption and Compton scattering. The net structure
Fig. 2. Structure temperature.
factors
for the potassium
layer
in and at room
Y. Arai et al. / Journal
-
t
of Non-Crystalline
Solids 205-207
803406
CsK
Nearest neighbour
20 @I
functions
805
Table 1 Nearest neighbour distances in the ordered of uotassium atoms in normal liauid. C,K
Potassium CsK C,, K
Fig. 3. Pair correlation room temperature.
(1996)
for the potassium
layer in and at
i and 10.62 A, respectively. The first peak position of the potassium layers in C,K is ~10s: to that in normal liquid potassium, which is 4.60 A [S].
3. Discussion The structure factor S(Q) for the layered potassium in C,K has an obvious subpeak below the first peak position, which may indicate the existence of some short-range orders [ll]. In the present experiment for Cz4K, the Giffraction intensity in the low & region (Q I 0.8 A-‘) is not enouOghto establish the existence of the shoulder at 0.90 A-‘. However it is certain that the structure factor in has a slight asymmetry of the first peak. Comparing S(Q) for C,K with that for C,,K, the peaks of S(Q) for C,K are slightly sharper than those for C,,K. Hence the potassium atoms in C,K have a stronger correlation than those in C,,K. The charge transfer from a potassium atom to the carbon net is, 0.6 for C,K [12] and 0.21 for C,,K [13] in the ordered state. These facts suggest that the carbon layers with lower stage number may have a stronger influence on the potassium layers [14]. The nearest neighbour distances of K-6( in C,K and Cz4 K in their ordered states are 4.92 A and 6.51 A, respectively. On the other hand, the firstOpeak posititns of g(r) for C,K and C,,K are 4.62 A and 5.48 A, respectively. The contraction of the nearest neighbour distances due to disordering is 6% and 16% for C,K and C,,K, respectively. This consider-
and disordered and C,,K
distance
phases
(A)
order
disorder
4.54 (solid) 4.92 6.51
4.60 (liquid) 4.62 + 0.01 5.48 f 0.01
able change in the nearest neighbour distance for C,,K may be caused by a disordering effect and also by a relaxation of the restriction of being bunched by carbon layers. The pair distribution function of in-plane liquid potassium in C,K and that in C,,K are out of phase, as shown in Fig. 3. This discrepancy may be caused by the difference in potassium density and also by the difference in the effective ionic size of potassium ions; this could be the result of the difference of the degree of charge transfer to the carbon layers. The positions of first peaks in g(u) for normal liquid potassium, for potassium layers in C,K, and, also in C,K are tabulated in Table 1. McGreevy et al. [15] have developed a new technique, called RMC, based on the standard Monte Carlo simulation method with Markov chain sampling, which gives three-dimensional particle configurations. Using these experimental data, RMC produces particle configurations. Therefore, RMC is useful for modelling the structures of non-crystalline materials as an experimental analysis.
Fig. 4. The results of the reverse Monte Car10 simulation for CsK. Evidence of the local configuration of triangle and hexagonal short range orders.
806
Y. Arai et al. /Journal
of NocCqvtalline
Fig. 4 shows a RMC simulation based on our data, performed with K atoms in regarded as 2-D liquid metals. The configuration of K atoms seems to be without a strong influence from the carbon layers. Clarke et al. [3] have indicated that the Cs atoms in C,,Cs are not essentially governed by the positions of carbon atoms in graphite layers at about room temperature. Replacement of Cs with K in stage-2 graphite intercalation compound may not change such a condition, in the sense that either K or Cs atoms are bunched by the carbon layers. This fact implies that the potassium atoms in C,,K are also not governed by the graphite layers.
4. Conclusion The pair distribution functions g(r) have been obtained for the potassium layers in C,K and C,,K at room temperature. Both results have large differences in peak positions, yielding out-of-phase character in the oscillating curve of g(r). The contraction of the nearest neighbours distance for K-K pairs in C,,K from the ordered to disordered states is considerably large than that in C,K. The RMC simulation for potassium layers in C,, K suggests the existence of local configuration as triangular and
Solick 205-207
(1996)
803-506
hexagonal short-range order, which may be related to an asymmetry of the first peak in S(Q).
References [l] G.S. Parry, Mater. Sci. Eng. 31 (1977) 99. [2] G.M.T. Foley and J.E. Fischer, Phys. Rev. B (1979) 6474. [3] R. Clarke, N. Caswell, S.A. Solin and P.M. Horn, Physica I399 (1980) 457. [4] A. H&old, Bull. Sot. Chim. Fr. 187 (1955) 999. [5] D.E. Nixon and G.S. Parry, Br. J. Appl. Phys. 2(l) (1968) 291. [6] LA. James and H.C. Walter, International Tables for X-ray Crystallography (Kynoch, Birmingham, 1974). [7] M. Mod, SC. Moss and Y.M. Jan, Phys. Rev. B27 (1983) 6385. [8] Y. Uno and H. Suematsu, Phys. Rev. Lett. 52 (1983) 1504. [9] Y. Waseda, The Structure of Non-Crystalline Materials (New York, 1980) p. 54. [lo] H. Zabel, Y.M. Jan and SC. Moss, Physica B99 (1980) 453. [II] S. Takeda, S. Tamaki and Y. Waseda, J. Phys. Sot. Jpn. 53 (1984) 3447. [12] T. Inoshita, K. Nakao and H. Kamimura, J. Phys. Sot. Jpn. 43 (1977) 1237. [13] K. Higuchi, H. Suematsu and S. Tanuma, J. Phys. Sot. Jpn. 48 (1980) 1532. [14] N. Kambe, G. Dresselhaus and S. Dresselhaus, Phys. Rev. B21 (1980) 3491. [15] R.L. McGreevy and L.Pusztai, Proc. R. Sot. London A430 (1990) 241.
OF
NON-CRYSTALIJNESOL Journal
of Non-Crystalline
Solids 205-207
(1996)
803-806
Structural properties of low dimensional potassium metal in intercalated graphite Y. Arai a, Y. Shirakawa a, S. Tamaki b3* a Graduate School of Science and Technology, Niigata Univemity, b Department of Physics, Faculty of Scieme, Niigata University,
Ikarashi, Niigata-ski, Ikarashi, Niigata-siti,
Niigata-ken Niigata-ken
950-21, Jupm 950-21, Japm
Abstract X-ray diffraction experiments for stage-2 potassium-intercalated graphite C,,K and stage-l CsK have been carried out. Disordered profiles have been observed for both samples. The measured structure factor S(Q) for the disordered potassium in C,K shows a characteristic subpeak in the small angle region below the first peak, which suggests that there exists a short-range order in the potassium layers. The phases of the pair distribution function g(r) and S(Q) for the potassium layers in CsK disagree with those in C,,K. To check the influence of the carbon layers, the profiles of g(r)s of CsK and C,,K are compared with that of normal liquid potassium.
1. Introduction It is well known that graphite intercalation compounds exhibit a regular layer-stacking sequence along the C axis. Alkali-metal intercalated graphite shows interesting behaviour, such as an order-disorder transition in the structure of alkali metal layers. Parry El] showed that the stage-l C,M (M = K, Rb and Cs) of highly oriented pyrolitic graphite (HOPG) has a commensurate order along the direction of the C-axis at room temperature. They also found a disordered structure for the stage-2 compound C&K. The order-disorder transition temperatures, obtained inferred from the temperature dependenceof the resistivity measurements for C,,M (M = K, Rb and Cs), were 98, 1.59and 163 K, respectively [2]. * Corresponding 263 3961.
author.
Tel.:
0022-3093/96/$15.00 Copyright PZi s0022-3093(96)00385-7
+81-25
262 6136; fax:
0 1996 Elsevier
-t-81-25
Science
In the caseof C,,Cs, Clarke et al [3] measuredthe (I&O) X-ray reflections at 300 K to derive the structure factor of cesium atoms in the in-plane layers S(Q) and the resulting pair distribution function g(r) for the Cs layer. It is very interesting to investigate the structural properties of the potassiumlayers in C,K and C,,K and to compare these with that of liquid K, because this investigation is very much related to the behaviour of two-dimensional properties. In Fig. 1, schematic layer stackings for C, K and C,,K are shown. In this paper, we present the structure factor S(Q) and the pair distribution function g(r) of potassium layers in the stage-2 compound and in the stage-l at room temperature. Such 2-D liquid potassium structures will be discussedin comparison with that of the three-dimensional liquid structure, and we propose a model of
B.V. All rights reserved.
Y. Arai et al. /Journal
804
of Non-Crystalline
HOPG ~
-
__ __.___. _-......-_-._. --___
Carbon
----------
layer
Poiassium
Fig. 1. The stacking sequence of the stage-l intercalation compounds and HOPG.
layer and stage-2 graphite
the disorderedpotassiumlayers by using the reverse Monte Carlo simulation.
Solids 205-207
(1996)
803406
factors S(Q) of the potassiumlayer in the C,,K and C,K samplesare shown in Fig. 2. As shown in this figure, the first peak posi$on of C,K is 1.50 A-’ and that of C,K is 1.20 A-‘. These agree with the resultsof in situ X-ray measurements[8]. Thesepeak positionsindicate that the liquid-like potassiummetal layers in the graphite are different from simpleliquid potassiummetal at 70°C [9], in which the first peak position of S(Q) is 1.65 A-‘. In addition, the S(Q) tf the potassiumlayer in C,K has a subpeakat 1.00 A-‘. The profiles of S(Q) of the potassium layer in C 8K and C 24K are, more or less,very similar to the liquid structure; however, there is an influence of the sandwichingcarbon layers [lo]. Introducing the in-plane pair distribution function g(r) (= p(r)/p,,), we have Pm gw
2. Experimental and results
=
z,sph
-
(W
-
w’
&--&s(e)
= l+
- 1)
x4,( Qr)dQ,
X-ray scattering experiments have been performed for the two different types of intercalated samples.They were preparedby the two-bulb method developed by H&old [4]. Well-annealed pyrolitic graphite (PG) was sealedin evacuated Pyrex tubes with purified excesspotassium.In the caseof C,,K, the sampleswere preparedby holding the PG at 658 K and potassiummetal at 510 K for 40 h. The C,K was also prepared by holding the PG at 650 K and potassium metal at 490 K for 40 h [5]. The (IzkO) X-ray diffraction measurementswere carried out by using MoK, radiation operatedat 40 kV and 20 mA. To reduce the statistical errors, we set the maximum counts higher than 10000 counts with a fixed time mode. The sampleswere sealed off in a cylindrical sampleholder. Using the Faber-Ziman formula, the coherent scatteredintensity per atom Z,sP”(Q>is related to the total structure factor S(Q) for the potassiumlayer in C, K and C,,K by the following form: S(Q)
= --x-
(2)
where p,, is the average atomic number density, which is equal to 2.73 X lo-’ and 4.77 X low2 atoms/A2 for C,,K and C,K, respectively. The term J&Qr) is the zeroth-order Besselfunction. The in-plane pair distribution function for potassium metal in C,K and C,,K has been obtained by using the above Fourier-Bessel transformation, as shown in Fig. 3. As shown in Fig. 3, the first peak positions o,f g(r) for pptassiumin C,K and C,,K of are 4.62 A and 5.48 A, and the secondpeak positions are 8.32
I
’
’
1
’
’
’
’
I
W”)
’
where f is the form factor [6]. Sharp reflections from the graphite host were subtracted from the raw data [7] and corrections were made for polarization, absorption and Compton scattering. The net structure
Fig. 2. Structure temperature.
factors
for the potassium
layer
in and at room
Y. Arai et al. / Journal
-
t
of Non-Crystalline
Solids 205-207
803406
CsK
Nearest neighbour
20 @I
functions
805
Table 1 Nearest neighbour distances in the ordered of uotassium atoms in normal liauid. C,K
Potassium CsK C,, K
Fig. 3. Pair correlation room temperature.
(1996)
for the potassium
layer in and at
i and 10.62 A, respectively. The first peak position of the potassium layers in C,K is ~10s: to that in normal liquid potassium, which is 4.60 A [S].
3. Discussion The structure factor S(Q) for the layered potassium in C,K has an obvious subpeak below the first peak position, which may indicate the existence of some short-range orders [ll]. In the present experiment for Cz4K, the Giffraction intensity in the low & region (Q I 0.8 A-‘) is not enouOghto establish the existence of the shoulder at 0.90 A-‘. However it is certain that the structure factor in has a slight asymmetry of the first peak. Comparing S(Q) for C,K with that for C,,K, the peaks of S(Q) for C,K are slightly sharper than those for C,,K. Hence the potassium atoms in C,K have a stronger correlation than those in C,,K. The charge transfer from a potassium atom to the carbon net is, 0.6 for C,K [12] and 0.21 for C,,K [13] in the ordered state. These facts suggest that the carbon layers with lower stage number may have a stronger influence on the potassium layers [14]. The nearest neighbour distances of K-6( in C,K and Cz4 K in their ordered states are 4.92 A and 6.51 A, respectively. On the other hand, the firstOpeak posititns of g(r) for C,K and C,,K are 4.62 A and 5.48 A, respectively. The contraction of the nearest neighbour distances due to disordering is 6% and 16% for C,K and C,,K, respectively. This consider-
and disordered and C,,K
distance
phases
(A)
order
disorder
4.54 (solid) 4.92 6.51
4.60 (liquid) 4.62 + 0.01 5.48 f 0.01
able change in the nearest neighbour distance for C,,K may be caused by a disordering effect and also by a relaxation of the restriction of being bunched by carbon layers. The pair distribution function of in-plane liquid potassium in C,K and that in C,,K are out of phase, as shown in Fig. 3. This discrepancy may be caused by the difference in potassium density and also by the difference in the effective ionic size of potassium ions; this could be the result of the difference of the degree of charge transfer to the carbon layers. The positions of first peaks in g(u) for normal liquid potassium, for potassium layers in C,K, and, also in C,K are tabulated in Table 1. McGreevy et al. [15] have developed a new technique, called RMC, based on the standard Monte Carlo simulation method with Markov chain sampling, which gives three-dimensional particle configurations. Using these experimental data, RMC produces particle configurations. Therefore, RMC is useful for modelling the structures of non-crystalline materials as an experimental analysis.
Fig. 4. The results of the reverse Monte Car10 simulation for CsK. Evidence of the local configuration of triangle and hexagonal short range orders.
806
Y. Arai et al. /Journal
of NocCqvtalline
Fig. 4 shows a RMC simulation based on our data, performed with K atoms in regarded as 2-D liquid metals. The configuration of K atoms seems to be without a strong influence from the carbon layers. Clarke et al. [3] have indicated that the Cs atoms in C,,Cs are not essentially governed by the positions of carbon atoms in graphite layers at about room temperature. Replacement of Cs with K in stage-2 graphite intercalation compound may not change such a condition, in the sense that either K or Cs atoms are bunched by the carbon layers. This fact implies that the potassium atoms in C,,K are also not governed by the graphite layers.
4. Conclusion The pair distribution functions g(r) have been obtained for the potassium layers in C,K and C,,K at room temperature. Both results have large differences in peak positions, yielding out-of-phase character in the oscillating curve of g(r). The contraction of the nearest neighbours distance for K-K pairs in C,,K from the ordered to disordered states is considerably large than that in C,K. The RMC simulation for potassium layers in C,, K suggests the existence of local configuration as triangular and
Solick 205-207
(1996)
803-506
hexagonal short-range order, which may be related to an asymmetry of the first peak in S(Q).
References [l] G.S. Parry, Mater. Sci. Eng. 31 (1977) 99. [2] G.M.T. Foley and J.E. Fischer, Phys. Rev. B (1979) 6474. [3] R. Clarke, N. Caswell, S.A. Solin and P.M. Horn, Physica I399 (1980) 457. [4] A. H&old, Bull. Sot. Chim. Fr. 187 (1955) 999. [5] D.E. Nixon and G.S. Parry, Br. J. Appl. Phys. 2(l) (1968) 291. [6] LA. James and H.C. Walter, International Tables for X-ray Crystallography (Kynoch, Birmingham, 1974). [7] M. Mod, SC. Moss and Y.M. Jan, Phys. Rev. B27 (1983) 6385. [8] Y. Uno and H. Suematsu, Phys. Rev. Lett. 52 (1983) 1504. [9] Y. Waseda, The Structure of Non-Crystalline Materials (New York, 1980) p. 54. [lo] H. Zabel, Y.M. Jan and SC. Moss, Physica B99 (1980) 453. [II] S. Takeda, S. Tamaki and Y. Waseda, J. Phys. Sot. Jpn. 53 (1984) 3447. [12] T. Inoshita, K. Nakao and H. Kamimura, J. Phys. Sot. Jpn. 43 (1977) 1237. [13] K. Higuchi, H. Suematsu and S. Tanuma, J. Phys. Sot. Jpn. 48 (1980) 1532. [14] N. Kambe, G. Dresselhaus and S. Dresselhaus, Phys. Rev. B21 (1980) 3491. [15] R.L. McGreevy and L.Pusztai, Proc. R. Sot. London A430 (1990) 241.