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Phonon softening in the ternary graphite intercalation compound K1−xRbxC8
513
Letters to the Editor Proceedings of the Materials Research Society, 1984. P. C. Ekhmd, M. S. Dresselhaus and G. Dresselhaus, Eds., p, 177. T. C. Chieu, G. Tiimp and M. S. Dresselhaus, Proceedings of the Materials Research Society Symposium, Intercalated Graphite 20, 5 I (1983). J. A. Woollam. H. Rashid, V. Natarajan, B. Banks, D. A. Jaworske, J. R. Gaier, C.-C. Hung and A. Yavrouian, Gruphite Intercalation Compounds, Proceedings of the Materials Research Society, 1984. P. C. Eklund, M. S. Dresselhaus and G. Dresselhaus, Eds., p, 202. V. Natarajan and J. A. Woollam. in Proceedings of 3rd
International Conference on Graphite Intercalation Compounds, Pont a Mousson, France, 1983, J. SwtheticMetals 8, 291 (1983).
9. H. Oshima, V. Natarajan, J. A. Woollam, A. Yavrouian, E. J. Haugland and T. Tsuzuku, Japan. J. Appl. Phys. 23. 49 (1984).
10. J. R. Gaier, in Graphite Intercalation Compounds, Proceedings of the Materials Research Society, 1984, P. C. Ecklund, M. S. Dresselhaus and G. Dresselhaus, Eds. II. J. A. Woollam, A. Khan, G. Bu-Abbud, D. Mathine, V. Natarajan, J. Lamb, H. Rashid, B. Banks, S. Domitz and D. C. Liu, Thin Solid Films 119, 121 (1984).
000X-6223186 c 1986 Perpamon
$3 CKl+ 00 Journal\ LKI
Phonon softening in the ternary graphite intercalation compound K,-,Rb,C8 (Received 22 April
1985; in revised form
Key WordsPhonon
The phonon dispersion in alkali ternary solid solution graphite intercalation compounds (GIG’s) A, _,B,C,, 0 5 x s 1, A.B = K,Rb or Cs, has been the focus of a considerable amount of theoretical and experimental research activity during only the last year. Recently Solin et al.[ I] have reported the first Raman Studies of K,_,Rb,C, at M point phonons as they describe the sharpest Raman features. They showed that the M point interplanar optic phonona of K, ,Rb,C, show a dramatic asymmetric softening and line width enhancement at x = 0.67 and suggested that these anomalies result from electronic band structure alterations that are associated with the formation of KRb, like clusters. Neutron scattering studies of the inter layer phonons by Neumann et a[.[21 also showed that K, _,Rb& exhibits anomalous softening of the C,, elastic constant at x = 0.67 and proposed that this softening is electronically driven by composition dependent charge transfer between the mixed layers and graphite layers. They further suggested that the composition dependence of the force constants is caused by a composition dependent charge transfer between the mixed alkali layers and the graphite layers. In this letter, we have studied the phonon anomaly in the mixed layered K,. ,Rb,C, compound over the whole composition range 0 5 x 5 1 at the M [loo] point. It is inferred that the interactions between the graphite and the alkali layers play an important role in explaining the phonon anomaly in mixed layer graphite intercalation K,_,Rb,C, compound. We have used the de Launr;y[3] type angular force model approach to study initially the phonon dispersion curves of grdphite[4]. The same model has been extended to calculate the phonon dispersion of stage I Potassium-GIG, KC, (4) and Rubidium-GIC, RbC, (5). In our earlier studies of the extension from graphite to GIC-KC8 and RbC,, we have retained the force constants of graphite as such for GIG’s and the metal graphite force constants were evaluated from experimental phonon frequency information of the metals[6, 71. Therefore, in the present study of K, _,Rb,C,, the force constants of graphite are retained as such and the force constants between the alkali-graphite layer have been varied from KC, to RbC, to study the phonon softening in the mixed layered system, K,.,Rb,C,. The interlayer interaction (graphite-alkali layer) force constant p, for different values of x has been evaluated by expanding the dynamical matrix
softening,
21 October
1985)
intercalation.
in the long-wavelength limit, which gives the expression for the elasttc constant C,, as [5].
c
=
ii
P c’(2 o.3 + P,i2)
(I)
4(2 m, + m,)
where p is the density, c is the distance between adjacent graphite planes and m,, m, are the masses of carbon and intercalant. respectively. Q? represents the central force constant between adjacent graphite-graphite layers, its value being 0.3 X 104 dyni cm[4]. As the central force constant for graphite has been retained invariable, the graphite alkali layer interaction force constant PI, has been calculated from the composition dependence of the elastic constant C,, of Neumann et a1.[3]. Using then the central force constant given in Table 1, the M point frequencies have been calculated in the [ 1001 direction for the mixed layered graphite intercalation compound K, ,Rb,C, for 0 5 x 5 1. It has been observed that the mixed system exhibits a phonon anomaly for the M point at x = 0.67, e.g. the phonon frequency increases for increasing values of x and at x = 0.67 it shows a minima and for x > 0.67 it again starts increasing in accordance with the experimental facts. The experimental phonon frequencies from the Raman spectra of Solin et al.[l] and the presently calculated phonon frequencies are presented in Table 2. In both cases a minimum at x = 0.67 is observed.
Table 1. Central X 0.0
force constant (p,) between layer B, (in units
alkali-graphite
of 104D/cm)
0.542
0.3
0.745
0.45
0.789
0.67
0.539
0.92
0.875
1.0
0.974
514
Letters to the Editor
Table 2. The x dependence of the phonon K,_,Rb,C, at M point x
frequencies
for
Experimental")(cm')
Computed(cm-l)
0.0
534.33
549.5
0.3
537
561
0.45
537.33
558
0.67
534.33
549
0.92
536.33
564
1.0
539.66
564
given in Table 1 derived from the elastic constant C&. The present work indicates an anomaly in the graphite-alkali layer central force constant at x = 0.67, as is obvious from the Table I. Therefore, an inference is drawn that the phonon anomaly at M point in K,_,Rb,C, is due to the interaction between graphite and alkali layer and not because of graphite-graphite or alkalialkali layer interactions. Physics Department Indian Institute of Technology New Delhi-110016 India
Solin et al.[ l] observed that the species-dependent frequency shift must be associated with changes in the force constants which determine the mode frequency, and not with changes in the intercalant mass. Keeping this in view, we have found that it is predominantly the graphite-alkali central force constant which determines the M point frequency and explains satisfactorily the anomaly at x = 0.67. The present analysis rules out the formation of KRb,-like clusters, which if present will exhibit the local or gap mode behaviour in the experimental results. A straight forward comparison of the force constants in the present angular force model and the force constants of linear chain model of Neumann er a!.[21 is not possible. Further, the force constants of linear chain model[2] have been derived from the phonon dispersion of the mixed system in the longitudinal [OOl] direction, whereas the present work utilises the force constants of graphite[4] and the graphite-alkali force constants as
C&ETA So00 VJJAY BABCOGUFTA NEELIMA RANI H. C. GUPTA B. B. TRIPATHI
REFERENCES 1. S. A. Solin, P. Chow and H. Zabel, Phys. Rev. Len. 53, 1927 (1984). 2. D. A. Neumann, H. Zabel, J. J. Rush and N. Berk, Phys. Rev. Left. 53, 56 (1984). 3. J. de Launey, Solid State Phys. 2, 220 (1965). 4. H. C. Gupta, R. S. Narayanan, N. Rani and B. B. Tripathi, Synthetic Metals 7, 347 (1983). 5. R. S. Narayanan, Lattice dynamics of graphite, its intercalation compounds and alkali halides, thesis, unpublished (1984). 6. R. A. Cowley, A. D. B. Woods and G. Dolling, Phys. Rev. 128, 1112 (1962). 7. J. R. D. Copley and B. N. Brockhouse, Can. J. Phys. 51, 657 (1973).
ooO8-6223/86 $3.oO+.Ml 0 1986Pergamon Journals Ltd.
Carbon Vol. 24.No.4.pp.514-516. 1986 Printed in Great Britam
On the “soluhility coefficient” of activated carbons (Received 30 May 1984; in revised form 13 December Key Words-Activated
carbons,
The prediction of the adsorption of organic solutes from aqueous solutions on activated carbons is of great importance for water purification process development. Therefore, some attempts have been undertaken to estimate the interaction energy of the components involved in the adsorption system from their physical properties. In the “net adsorption energy” concept by McGuire and Suffet[l], the mutual interaction energies E,,, of organic solute, solvent and adsorbent are estimated using the so-called solubility coefficients 8, of the constituentsj,k of a binary system: E,,, = v, 8, 8,
.
(1)
In eqn (l), V, is the molar volume of the solventj. The solubility coefficient 6, is a weighted sum of contributions from an unpolar component 8: due to dispersion forces and several polar components caused by dipol moments, hydrogen bond contributions and inductive forces. In the following, only dispersive contributions are considered, because the carbon/organic interaction is assumed to be mainly due to such forces. The solubility coefficient 8, of a pure liquid j is defined as the square root of the cohesive energy, that is the square root of the specific internal heat of vaporization:
8, =
J
AHv.,m,,- RT
v,
1985)
solubility coefficient.
In this case, the interaction energy of equal molcules jj is calculated from the energy necessary to break the bonds between them and to transfer the liquid to the gaseous phase. In the theory of regular solutions, the interaction energy between different molecules j.k is calculated and used to predict the solubility of k in j according to eqn (1)[2,3]. This approach has been formally adapted to adsorption systems including the active carbons[ 11. The net adsorption energy is then obtained by combining the mutual interaction energies of carbon/water, carbon/ organic solute and organic solute/water. However, even the authors of [l] concluded that this approach is an empirical but nevertheless useful manner to qualitatively predict the adsorbability ranking order of adsorptives. The “solubility coefficient” of activated carbons in an adsorption system cannot be obtained in as clear a physical manner as that of the liquids. It can only be calculated from an interaction energy with a known 8, using eqn (1). McGuire and Suffet[ l] (MS) calculated a value of 8:. (MS) = 25 (J/cm’)“* for the dispersion component using gas phase adsorption enthalpies AH,,,# of several organics on a graphitized carbon black, measured by Avgul and Kiselev[4] by gas chromatography at lower coverage - AH,,g
= V,S;S$(MS).
(3)
(2) However, the adsorption
from the gas phase is a rather complex
Letters to the Editor Proceedings of the Materials Research Society, 1984. P. C. Ekhmd, M. S. Dresselhaus and G. Dresselhaus, Eds., p, 177. T. C. Chieu, G. Tiimp and M. S. Dresselhaus, Proceedings of the Materials Research Society Symposium, Intercalated Graphite 20, 5 I (1983). J. A. Woollam. H. Rashid, V. Natarajan, B. Banks, D. A. Jaworske, J. R. Gaier, C.-C. Hung and A. Yavrouian, Gruphite Intercalation Compounds, Proceedings of the Materials Research Society, 1984. P. C. Eklund, M. S. Dresselhaus and G. Dresselhaus, Eds., p, 202. V. Natarajan and J. A. Woollam. in Proceedings of 3rd
International Conference on Graphite Intercalation Compounds, Pont a Mousson, France, 1983, J. SwtheticMetals 8, 291 (1983).
9. H. Oshima, V. Natarajan, J. A. Woollam, A. Yavrouian, E. J. Haugland and T. Tsuzuku, Japan. J. Appl. Phys. 23. 49 (1984).
10. J. R. Gaier, in Graphite Intercalation Compounds, Proceedings of the Materials Research Society, 1984, P. C. Ecklund, M. S. Dresselhaus and G. Dresselhaus, Eds. II. J. A. Woollam, A. Khan, G. Bu-Abbud, D. Mathine, V. Natarajan, J. Lamb, H. Rashid, B. Banks, S. Domitz and D. C. Liu, Thin Solid Films 119, 121 (1984).
000X-6223186 c 1986 Perpamon
$3 CKl+ 00 Journal\ LKI
Phonon softening in the ternary graphite intercalation compound K,-,Rb,C8 (Received 22 April
1985; in revised form
Key WordsPhonon
The phonon dispersion in alkali ternary solid solution graphite intercalation compounds (GIG’s) A, _,B,C,, 0 5 x s 1, A.B = K,Rb or Cs, has been the focus of a considerable amount of theoretical and experimental research activity during only the last year. Recently Solin et al.[ I] have reported the first Raman Studies of K,_,Rb,C, at M point phonons as they describe the sharpest Raman features. They showed that the M point interplanar optic phonona of K, ,Rb,C, show a dramatic asymmetric softening and line width enhancement at x = 0.67 and suggested that these anomalies result from electronic band structure alterations that are associated with the formation of KRb, like clusters. Neutron scattering studies of the inter layer phonons by Neumann et a[.[21 also showed that K, _,Rb& exhibits anomalous softening of the C,, elastic constant at x = 0.67 and proposed that this softening is electronically driven by composition dependent charge transfer between the mixed layers and graphite layers. They further suggested that the composition dependence of the force constants is caused by a composition dependent charge transfer between the mixed alkali layers and the graphite layers. In this letter, we have studied the phonon anomaly in the mixed layered K,. ,Rb,C, compound over the whole composition range 0 5 x 5 1 at the M [loo] point. It is inferred that the interactions between the graphite and the alkali layers play an important role in explaining the phonon anomaly in mixed layer graphite intercalation K,_,Rb,C, compound. We have used the de Launr;y[3] type angular force model approach to study initially the phonon dispersion curves of grdphite[4]. The same model has been extended to calculate the phonon dispersion of stage I Potassium-GIG, KC, (4) and Rubidium-GIC, RbC, (5). In our earlier studies of the extension from graphite to GIC-KC8 and RbC,, we have retained the force constants of graphite as such for GIG’s and the metal graphite force constants were evaluated from experimental phonon frequency information of the metals[6, 71. Therefore, in the present study of K, _,Rb,C,, the force constants of graphite are retained as such and the force constants between the alkali-graphite layer have been varied from KC, to RbC, to study the phonon softening in the mixed layered system, K,.,Rb,C,. The interlayer interaction (graphite-alkali layer) force constant p, for different values of x has been evaluated by expanding the dynamical matrix
softening,
21 October
1985)
intercalation.
in the long-wavelength limit, which gives the expression for the elasttc constant C,, as [5].
c
=
ii
P c’(2 o.3 + P,i2)
(I)
4(2 m, + m,)
where p is the density, c is the distance between adjacent graphite planes and m,, m, are the masses of carbon and intercalant. respectively. Q? represents the central force constant between adjacent graphite-graphite layers, its value being 0.3 X 104 dyni cm[4]. As the central force constant for graphite has been retained invariable, the graphite alkali layer interaction force constant PI, has been calculated from the composition dependence of the elastic constant C,, of Neumann et a1.[3]. Using then the central force constant given in Table 1, the M point frequencies have been calculated in the [ 1001 direction for the mixed layered graphite intercalation compound K, ,Rb,C, for 0 5 x 5 1. It has been observed that the mixed system exhibits a phonon anomaly for the M point at x = 0.67, e.g. the phonon frequency increases for increasing values of x and at x = 0.67 it shows a minima and for x > 0.67 it again starts increasing in accordance with the experimental facts. The experimental phonon frequencies from the Raman spectra of Solin et al.[l] and the presently calculated phonon frequencies are presented in Table 2. In both cases a minimum at x = 0.67 is observed.
Table 1. Central X 0.0
force constant (p,) between layer B, (in units
alkali-graphite
of 104D/cm)
0.542
0.3
0.745
0.45
0.789
0.67
0.539
0.92
0.875
1.0
0.974
514
Letters to the Editor
Table 2. The x dependence of the phonon K,_,Rb,C, at M point x
frequencies
for
Experimental")(cm')
Computed(cm-l)
0.0
534.33
549.5
0.3
537
561
0.45
537.33
558
0.67
534.33
549
0.92
536.33
564
1.0
539.66
564
given in Table 1 derived from the elastic constant C&. The present work indicates an anomaly in the graphite-alkali layer central force constant at x = 0.67, as is obvious from the Table I. Therefore, an inference is drawn that the phonon anomaly at M point in K,_,Rb,C, is due to the interaction between graphite and alkali layer and not because of graphite-graphite or alkalialkali layer interactions. Physics Department Indian Institute of Technology New Delhi-110016 India
Solin et al.[ l] observed that the species-dependent frequency shift must be associated with changes in the force constants which determine the mode frequency, and not with changes in the intercalant mass. Keeping this in view, we have found that it is predominantly the graphite-alkali central force constant which determines the M point frequency and explains satisfactorily the anomaly at x = 0.67. The present analysis rules out the formation of KRb,-like clusters, which if present will exhibit the local or gap mode behaviour in the experimental results. A straight forward comparison of the force constants in the present angular force model and the force constants of linear chain model of Neumann er a!.[21 is not possible. Further, the force constants of linear chain model[2] have been derived from the phonon dispersion of the mixed system in the longitudinal [OOl] direction, whereas the present work utilises the force constants of graphite[4] and the graphite-alkali force constants as
C&ETA So00 VJJAY BABCOGUFTA NEELIMA RANI H. C. GUPTA B. B. TRIPATHI
REFERENCES 1. S. A. Solin, P. Chow and H. Zabel, Phys. Rev. Len. 53, 1927 (1984). 2. D. A. Neumann, H. Zabel, J. J. Rush and N. Berk, Phys. Rev. Left. 53, 56 (1984). 3. J. de Launey, Solid State Phys. 2, 220 (1965). 4. H. C. Gupta, R. S. Narayanan, N. Rani and B. B. Tripathi, Synthetic Metals 7, 347 (1983). 5. R. S. Narayanan, Lattice dynamics of graphite, its intercalation compounds and alkali halides, thesis, unpublished (1984). 6. R. A. Cowley, A. D. B. Woods and G. Dolling, Phys. Rev. 128, 1112 (1962). 7. J. R. D. Copley and B. N. Brockhouse, Can. J. Phys. 51, 657 (1973).
ooO8-6223/86 $3.oO+.Ml 0 1986Pergamon Journals Ltd.
Carbon Vol. 24.No.4.pp.514-516. 1986 Printed in Great Britam
On the “soluhility coefficient” of activated carbons (Received 30 May 1984; in revised form 13 December Key Words-Activated
carbons,
The prediction of the adsorption of organic solutes from aqueous solutions on activated carbons is of great importance for water purification process development. Therefore, some attempts have been undertaken to estimate the interaction energy of the components involved in the adsorption system from their physical properties. In the “net adsorption energy” concept by McGuire and Suffet[l], the mutual interaction energies E,,, of organic solute, solvent and adsorbent are estimated using the so-called solubility coefficients 8, of the constituentsj,k of a binary system: E,,, = v, 8, 8,
.
(1)
In eqn (l), V, is the molar volume of the solventj. The solubility coefficient 6, is a weighted sum of contributions from an unpolar component 8: due to dispersion forces and several polar components caused by dipol moments, hydrogen bond contributions and inductive forces. In the following, only dispersive contributions are considered, because the carbon/organic interaction is assumed to be mainly due to such forces. The solubility coefficient 8, of a pure liquid j is defined as the square root of the cohesive energy, that is the square root of the specific internal heat of vaporization:
8, =
J
AHv.,m,,- RT
v,
1985)
solubility coefficient.
In this case, the interaction energy of equal molcules jj is calculated from the energy necessary to break the bonds between them and to transfer the liquid to the gaseous phase. In the theory of regular solutions, the interaction energy between different molecules j.k is calculated and used to predict the solubility of k in j according to eqn (1)[2,3]. This approach has been formally adapted to adsorption systems including the active carbons[ 11. The net adsorption energy is then obtained by combining the mutual interaction energies of carbon/water, carbon/ organic solute and organic solute/water. However, even the authors of [l] concluded that this approach is an empirical but nevertheless useful manner to qualitatively predict the adsorbability ranking order of adsorptives. The “solubility coefficient” of activated carbons in an adsorption system cannot be obtained in as clear a physical manner as that of the liquids. It can only be calculated from an interaction energy with a known 8, using eqn (1). McGuire and Suffet[ l] (MS) calculated a value of 8:. (MS) = 25 (J/cm’)“* for the dispersion component using gas phase adsorption enthalpies AH,,,# of several organics on a graphitized carbon black, measured by Avgul and Kiselev[4] by gas chromatography at lower coverage - AH,,g
= V,S;S$(MS).
(3)
(2) However, the adsorption
from the gas phase is a rather complex