J . Phys. Chem. 1986, 90, 235-238
235
SPECTROSCOPY AND STRUCTURE Interlayer Spacing of 3d Transition-Metal Intercalates of IT-Cd1,-Type Tis, Masasi Inoue* and Hiroshi Negishi Department of Materials Science, Faculty of Science, Hiroshima University, Hiroshima 730, Japan (Received: January 4, 1985)
The lattice spacings a and c of M,TiS2 (M = V, Cr, Mn, Fe, Co, and Ni) grown by a chemical vapor transport technique have been measured over the whole metal concentration range 0 I x I 1. The concentration dependence of the interlayer spacing c is reasonably explained by a semiempirical model based on the concept of “resonance” in chemical bonding, in which ionic radii, interatomic distances, force constants, bond covalency of the guest and constituent atoms, as well as the formation of a superstructure at x = ‘/4-‘/2, are taken into consideration.
Introduction For many years the physics and chemistry of intercalation compounds of transition-metal dichalcogenides TX2 (T = groups IV, V, and VI (groups 4-6);14 X = S, Se, Te) with layered structures have been extensively studied. In these compounds various guest species, such as alkali metals’ and 3d transition metal^,^,^ enter into van der Waals gaps of TX2 layers. The intercalation of these guest species is usually accompanied by a change in the lattice spacings a and c, and at some guest concentrations the formation of a superstructure is found. In particular, the interlayer spacing c is varied appreciably with the guest concentration x, as found in Li,TiS; and M,ZrS, ( M = Fe, Co, Ni).S However, much less has been reported on a systematic study of 3d transition-metal intercalates of 1T-Cd12-typeTis,, M,TiS2 ( M = V, Cr, Mn, Fe, Co, and Ni). Some 3d transition metals are known to occupy the octahedral holes in the Tis2layers, and gradual filling of the available holes lead to the rhombohedral defect NiAs type s t r u c t ~ r e . ~ ~ ~ In this work we have carried out exhaustive studies on M,TiS2 (0 Ix I 1) as an attempt to understand the changes in the interlayer spacings c with 3d metals and their concentration based on the concept of “resonance” in chemical bonding introduced by Pauling.6 Our semiempirical model takes into account the ionic radii, interatomic distances, force constants, bond covalency, as well as the formation of a superstructure. To our knowledge, these parameters have been used only to classify the structures (trigonal prismatic or octahedral) of TX2’ and alkali-metal intercalates A,TX2 (A = alkali metals).* Experimental Procedure and Results The 3d transition-metal intercalates M,TiS2 (M = V, Cr, Mn, Fe, Co, and Ni) were grown by a chemical vapor transport technique in a single-zone furnace with a small temperature gradient? rather than the commonly employed two-zone furnace. The starting elements all in powder form and 5-15 mg/cm3 of (1) Whittingham, M. S. Prog. Solid State Chem. 1978,12, 41. (2) Lee, P. A. “Optical and Electrical Properties”; Reidel: Dordrecht, 1976. Vandenberg-Voorhoeve, J. M., Ibid. p 423. (3) Levy, F. “Intercalated Layered Materials”; Reidel: Dordrecht, 1979. Subba Rao, G . V.;Shafer, M. W. Ibid. p 99. (4) Whittingham, M. S.J . Electrochem. SOC.1976, 123, 315. (5) Trichet, L.; Rouxel, J.; Pouchard, M. M. J . Solid State Chem. 1975, 14, 283. (6) Pauling, L. “The Nature of the Chemical Bond”; Cornel1 University Press: Ithaca, 1960; 3rd ed. ( 7 ) Madhukar, A. Solid State Commun. 1975,16, 383. (8) Whittingham, M. S.;Jacobson, A. J. ‘Intercalation Chemistry”; Academic Press: New York, 1982. Hibma, T. Ibid. Chapter 9. (9) Inoue, M.; Negishi, H. J . Phys. SOC.Jpn. 1984,53, 943.
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TABLE I: Interlayer Spacing c ( l ) , Interatomic Distance d2(l),Ionic Radii ri(M2’) of Divalent Metal Ion M2+,and Ionic Bond Distance d,’(M2+) Defined by Eq 3a V Cr Mn Fe Co Ni 41) d2(1) ri(M2+)c
d,l(M2+)
5.89 2.49 0.93 2.63
5.93 2.50 0.96 2.66
6.06b 2.54 0.96 2.66
5.81 2.46 0.91 2.61
5.62 2.41 0.79d 2.49
5.74 2.44 0.84 2.54
“All in units of A. Other parameters used: a = 3.41, c = 5.70, and r1(S2-)= 1.70. bExtrapolated value from Figure 1. ‘Reference 12. dValue at a low-spin state.
iodine as carrier gas were charged in an evacuated quartz ampule (10-20 mm in diameter and 100-150 mm long); the purity was 99.5% for V, 99.9% for Ti, and 99.99% for other elements. The ampule was heated for 3 days-1 week at 800-900 “C in a single-zone furnace with a temperature difference AT = 20-30 “C at both ends of the ampule. The sizes of the grown intercalates were different among the 3d metals. Typically, V and Cr intercalates were small crystallites (roughtly 1 X 1 mm2 for x < and less than 0.2 X 0.2 mm2 for x > I/,), while those of Mn, Fe, Co, and Ni were grown in the form of thin flakes or platelets for x > up to 8 X 8 mm2 for x < it was usually difficult to grow platelets as large as 5 X 5 mm2. In particular, Mn beyond which a intercalation was available only up to x = metal sulfide like MnS was produced because the chemical affinity between Mn and S is strong. All the grown intercalates were ground by a mortar and pestle into fine powders for X-ray diffraction analysis. The observed diffraction patterns showed the trigonal 1T-Cd12-type structure over the whole composition range 0 d x d 1, though monoclinic reflections have been reported to appear at higher x, showing the defect NiAs-type structure.1° Furthermore, we have confirmed that the electron diffraction patterns from the Mn, Fe, Co, and Ni intercalated crystals show a superstructure at the characteristic and as found by many worker^.^.^ We concentrations x = attempted to analyze the metal concentration x in the grown M,TiS, by an isotachophoresis method (Shimazu Ind. Corp., Ip-2A type) but the separation of each ion in aqueous solutions made it difficult to determine the values of x accurately. We have used the nominal concentration x throughout the present work. Figure 1 shows the observed lattice spacings a and c plotted against the metal concentration for different guest atoms. The intralayer spacing a remains almost unchanged while the interlayer (10) Plovnick, R. H.; Perloff, D. S.; Vlasse, M.; Wald, A. J. Phys. Chem. Solids 1968,29, 1935.
0 1 9 8 6 American Chemical Society
236 The Journal of Physical Chemistry, Vol. 90, No. 2, 1986
Inoue and Negishi
,-/,
6.1
e Ti
os @M 0 vacancy a) Ti52
b) M T I S ~
C) M,TIS~
Figure 3. ( 1 120) sections of (a) Tis, (x = 0), (b) MTiS, ( x = l ) , and (c) M,TiS2 (0 < x < 1). A square in (a) is a vacant site in the van der Waals gap with octahedral symmetry, into which the guest atom M intercalates (see text for other notations).
ions in TX2 layers are reported to be divalent or t r i ~ a l e n t ,Figure ~?~ 2 indicates that the valence state of the M atom is divalent with mostly a high-spin state; only the Co ion is considered to be at a low-spin state (dt)6(dr)’, in agreement with our ESR data.13
3.5
3.3
Discussion
t
i
11111111111 0.2
0
0.4
0.6
0.8
1.0
X
Figure 1. Observed lattice spacings a and c plotted against the nominal metal concentration x for M,TiS2 (M = V, Cr, Mn, Fe, Co, and Ni). The solid curves are the calculated interlayer spacing c(x) for M,TiS2 obtained by using eq 1, 2, and 6 , with the best fit values of Table 11.
6.1
I
I
1
I
I
1 1.00
6.0 5.9
h
0
4
5.8
V
5.7
, ,
5.6
5.5
0
11.:;
Cr Mn Fe Co Ni Figure 2. Variation of the interlayer spacing c as a function of the atomic number of M for MTiS2. The ionic radii ri(M2+)for each divalent ion Mz+with the coordination number 6 are also shown; open circles denote a high spin state and solid circles a low spin state.’, V
spacing c varies appreciably with the 3d metals and their concentraction. Similar variations have been found for M,ZrS2 (M = Fe, Co, Ni),5 in which the M atom occupies the tetrahedral holes of ZrS, layers. Figure 2 depicts the value c at x = 1 as a function of the atomic number of M; for Mn the extrapolated value at x = 1 from Figure 1 is used. As found in M1/,NbS2,” where the M atom is at octahedral sites,,such a plot is in good agreement with a similar plot of ionic radii r‘(M2+)of the divalent metal ions Mz+ where the values of r‘(M2+) are denoted by solid circles for a low-spin state and by open circles for a high-spin state, with the coordination number 6 (see Table I).], Though the 3d metal (11) Rouxel, L.; Le Blanc,
2019.
A.; Royer,
A. Bull. Sot. Chim. Fr. 1971, 6,
(12) Shannon, R. D.; Prewitt, C. T. Acta Crystallogr.,Sect. B 1969, 25, 925.
In what follows, we shall give a semiempirical explanation for the variation of the interlayer spacing c with intercalation of 3d transition metals into Tis2layers on the basis of the concept of “resonance” in chemical bonding. The change in the intralayer spacing a is negligibly small which hereafter we take as a constant. As shown in Figure 1, the value of c is not a monotonic function of x, but in some cases it attains a minumum or maximum at x = 1/4-1/2, where the formation of a superstructure or atomic ordering is f ~ u n d . In ~ , the ~ following we shall first neglect such an atomic ordering and later take it into consideration. A . Resonance Model. Figure 3 shows schematically the (1 120) planes of (a) IT-Cd12-type Tis2 (x = 0), (b) a completely intercalated state of MTiS2 (x = l), and (c) a partially intercalated state of M,TiS2 (0 C x C 1) which we regard as a “resonant state” between the Tis2 and MTiSz states at a ratio of (1 - x):x. In the Tis2the octahedral position between the van der Waals gap is vacant, denoted by a square, while in MTiS, the guest atom M occupies this position. Furthermore, we assume the interlayer spacing c to be the sum of two sublayer spacings as shown in Figure 3. Thus the interlayer spacing of Tis,, denoted here by c(O), is given by the sum of c1 and c2(0),where c1 is the spacing of a S-Ti-S sublayer and c2(0)that of a S-vacancy-S sublayer (van der Waals gap). Similarly the interlayer spacing of MTiS2, denoted by c( l), is given by the sum of c1 and c2(l), where c2(1) is the spacing of a S-M-S sublayer. Also we take into account the interatomic distances or bond lengths, dl between the S and Ti atoms and d,(O) between the vacancy and S atom for Tis,; similarly dl and d2(1) for MTiS, are shown. Hereafter we assume that cl, d l , and the intralayer spacing a are all constant. Then for a partially intercalated compound M,TiS2, the interlayer spacing c(x) can be expressed by c(x) =
c1
+ c2(x)
(1)
where from a simple geometrical relation cI and c2(x) are given as CI = 2(dI2 - U2/3)*/2 Cz(X) = 2(d2(x)2- u2/3)1’2 (2) respectively. Here d2(x) is the bond length between the S atom and M atom or vacancy. In this model we assume that only d2(x) is dependent on x and the M,TiS2 state is the resonant state between the Tis2 and MTiS, at the ratio (1 - x):x, as mentioned above. Now the lattice constants of Tis, are found to be a = 3.41 A and c = 5.70 A, and the positions of the S atoms are (0, 0,O) and (,/+J, 2 / 3 u ,1/2c). Thus dl and d2(0)for x = 0 are calculated to be dl = d2(0) = 2.43 8, from eq 1 and 2. Similarly the interatomic distances d2(l) for x = 1 are evaluated from the observed interlayer spacings c( 1 ) by using eq 1 and 2. These values are given (13) Inoue, M.; Negishi, H. J . Phys. SOC.Jpn. 1985, 54, 381. (14) This group notation is in accord with recent actions by IUPAC and ACS nomenclature committees. A and B notation is being eliminated because of wide confusion. Group I becomes groups 1 and 11, group I1 becomes groups 2 and 12, group I11 becomes groups 3 and 13, etc.
Interlayer Spacing of M,TiS2
The Journal of Physical Chemistry, Vol. 90, No. 2, 1986 237 1
Mn0
2.551
'' h
i
1
1
1
'
1
0
Y
2.50
(v
p=1
91
h
X
Y
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2.45
0 "
1 u 2.50 2.55 2.60 2.65 2.70 :0
I
2.35 2.45
di(M2*)
(A)
Figure 4. The interatomic distance d2(l) between the M and S atoms for a completely intercalated compound MTiS2plotted against the ionic bond distance d;(M2+) = r'(Mz+) + r'(Sz-).
in Table I, where the ionic radii r'(M2+) of each divalent cation M2+ with a coordination number 6 at a high-spin state (Co2+: low-spin state)12 and the ionic bond distances d;(M2+) for M2+ ion defined as di(M2+) = r'(M2+)
+ r'(S2-)
(3) are also shown. Here rl(S2-) is the ionic radius of a S2-ion (= 1.70 A). As shown in Figure 4, it is apparent that there is a strong correlation between the interatomic distance d2(1) and ionic bond distance di(M2') compared with the lattice constant c vs. ionic radii r'(M2+) relation shown in Figure 2. However, d2(l) is not exactly equal to di(M2+),but d2(l) < di(M2+)always, indicating that the M-S bond is not completely ionic but partially covalent. Then the interatomic distance d2(x) for M,TiS2 (0 < x < 1) can be estimated. By analogy with the potential function for resonant bonding between a single bond and double bond for carbon-carbon bonds such as in benzene? we express the potential function for the M-S bond as the sum of two parabolic functions, representing the vacancy-S bond and the M-S bond potential functions, with coefficients (1 - x ) and x, respectively: V(d2W) = XCl - x)k2(O)[d2(x) - d2(0)I2 + )/2Xk2(1)[dZ(X) - d2(1)I2 (4)
where the metal concentration x is used instead of the bond number n employed by Pauling. k2(0)and k2(1) are the force constants for the vacancy-S and M-S bonds, respectively. The equilibrium value of d2(x) can be found by setting the derivative of eq 4 with respect to d 2 ( x ) equal to zero. Thus we have 1 (a@- 1)x d2(0) (5) d 2 ( x ) = 1 ( a - 1)x
+ +
where a = k2(l)/k2(0) is the ratio of the force constants and /3 = d2(1)/d2(0)that of the bond lengths for the M-S and vacancy-S bonds. The equilibrium interatomic distance d2(x) is therefore a hyperbolic function of x and it can be specified by the two ratios a and fi. The schematic forms of d 2 ( x ) are plotted in Figure 5 for various cases. We see that d2(x) is an increasing function for 0 > 1, decreasing for p < 1, or constant for 0 = 1. Furthermore, the ratio a specifies the form of the curve, whether it is convex, concave, or linear. In M,TiS2 the force constant k2(1) for the M-S bond is considered to be larger than k2(0)for the vacancy-S bond ( a > l ) , and the variation of d 2 ( x ) is expected to be that of curves 1 or 7 in Figure 5 . Similar curves for the interlayer spacing c(x) are readily obtained from eq 1,2, and 5 . However, these calculated curves do not simulate the observed results (except for Mn intercalates) shown in Figure 1 having a maximum or minimum at x = lI4-Il2. B. Modification of the Resonance Model. The foregoing simplified model has shown that d 2 ( x ) is a monotonically in-
0
0.2 0.4
0.6 0.8 1.0 X
Figure 5. Schematic drawing of d 2 ( x ) as a function of x for different values of a and a. TABLE II: Best Fit Values a = k2(l)/k2(0)and y in Eq 6 Used in the Calculation of Figure 1 V Cr Mn Fe Co Ni a 10 10 4 10 10 1 0.08 0.0 0.035 0.01 0.03 y, k, 0.08
creasing or decreasing function of x , independent of the distribution of guest atoms. In actual case, a superstructure is formed at particular concentrations (x = 1/4-1/2), where the interlayer spacing c attains a maximum or a mininum. In order to take account of such an atomic ordering in the calculation of d 2 ( x ) , we have attempted to add an extra entropic term to eq 5 : 1 (ab- l ) x d2(0) + y[x In x + (1 - x ) In (1 - x)] d 2 ( x ) = 1 ( a - 1)x
+ +
where y is an adjustable parameter denoting the degree of lattice conttaction caused by a bond covalency due to the atomic ordering. Using eq 1, 2, and 6, we have calculated the values c ( x ) as a function of x for each guest atom, and the results are shown in Figure 1. The best fit values of a and y used are listed in Table 11; the parameter = d2(1)/d2(0) is evaluated from Table I. The calculated and observed curves are in qualitative agreement; the fitting is good for V, Mn, Co, and Ni, while it is poor for Fe and Cr. Furthermore, in the range < x < 1 the calculated values are a little smaller than the observed values; in this range atomic ordering may be neglected. From the present model calculation the following features are noted. The ratio of the force constants a = k2(l)/k2(0) is of the order of 10 (except for Ni atom), which means that upon intercalation with the 3d transition metals a much stronger bonding between the sublayers than the original van der Waals bonding is induced, making their character more three-dimensional; in other words, the intercalation compounds M,TiS2 lose their two-dimentional character and they are no longer layer compounds, as described by Vandenberg-Voorhoeve.2 In addition, except for Mn intercalates (y = 0), we note that the values of y for V and Cr intercalates, whose M-S bond ionicity is high,6 are large compared with those of Fe, Co, and Ni intercalates whose M-S bond ionicity is low, which in turn suggests that the atomic ordering is more effective for the M-S bonds of higher ionicity than for those of lower ionicity (or more covalent M-S bond), leading to a lattice contraction. Summary Based on the concept of "resonancen in chemical bonding introduced by Pauling, we have attempted to explain semiempirically the variation of interlayer spacing c with intercalation of 3d transition metals into 1T-Cd12-type Tis2 layers, by taking into account the ionic radii, bond lengths, force constants, and bond ionicity. We have shown that overall agreement between the model calculation and experiments is excellent. However, the bonding nature is actually not so simple but complicated. Our proposed model must further be refined by considering the changes in the
J . Phys. Chem. 1986, 90, 238-243
238
intralayer spacing a and the interatomic distance d l between the Ti and S atoms, which we have assumed constant, or the interactions between next-nearest atomic bonds. These studies will be reported later.
Acknowledgment. The authors thank Dr. A. Kumao (Kyoto University of Industrial Arts and Textile Fibers) for carrying out
the electron diffraction observations on our samples at his laboratory and for valuable suggestions. Professor Y. Komura is gratefully acknowledged for the use of X-ray diffraction apparatus and helpful discussions. We also thank Y. Muneta, Y. Nakahara, and N. Nakaso for their help in obtaining the experimental data. Part of this work was supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture.
Structure of Rhodium( III)Nitrate Aqueous Solutions. An Investigation by X-ray Diffraction and Raman Spectroscopy R. Caminiti,*t D. Atzei,t P. Cucca,t A. Anedda,’ and G . Bongiovannil Istituto di Chimica Generale, Inorganica ed Analitica, and Dipartimento di Scienze Fisiche, Uniuersitd di Cagliari, 09100 Cagliari, Italy (Received: March 20, 1985)
X-ray scattering and Raman spectra of Rh(N03), aqueous solutions have been measured. The spectral features of the solutions studied suggest the presence of NO3- groups bonded to a rhodium(II1) ion. Though neither the Raman nor X-ray data alone are sufficient in themselves to be univocally interpreted, taken together, the two independent sets of data support only one model in which the following dimeric species is present.
N
0 ’
Introduction In a previous work’ we studied the coordination of Rh(II1) in aqueous solutions of Rh(C10J3. The diffractometric technique has also proved to be suitable in investigating the structural parameters of the rhodium(II1) ion in dilute aqueous solution. In this study we demonstrated the existence of well-defined Rh(H20)63+ions in perchlorate aqueous solution acidified by an excess of perchloric acid. Besides the monomeric complex, the possibility of the formation of dimeric products with increasing pH values has been s ~ g g e s t e d . ~An , ~ electrophoresis study reveals the existence of two kinds of Rh(II1) in 1 N HNO3.’ The author assumes that, at equilibrium, the rhodium species under these acid conditions are Rh(H20)63+and [Rh(H20)5N03]2+.In addition to diffractometric studies, Raman spectroscopy has proved to be a powerful tool to investigate anion-solvent and cation-anion interactions in solutions containing NO< The polarization effects arising from the different environments of NO,- ions are easily detectable93l0in the Raman spectra and can be summarized as follows: (a) the vl mode of vibration which usually occurs at 1050 cm-l or lower shows a slight asymmetry in the low-frequency side. (b) The v 2 infrared-active mode becomes Raman active at about 830 cm-I. (c) The v 3 mode is characterized by two bands, whose separation increases in energy when cation-NO,- ion contacts are present. The polarization of the lower frequency band denotes unidentate cation-NO,- ion binding while the bidentate configuration is revealed by the higher frequency band polarization. (d) The deformation mode v4 is found at a frequency higher that 718 cm-I. Therefore, all the lines of the NO3- ion are doubled in a Raman spectrum when anion-solvent and cation-anion interactions are present. It has to be noted that some of the theoretically predicted lines can be hidden in the experimental spectra because of line width, line overlapping ( v , mode),
’Istituto di Chimica Generale, Inorganica ed Analitica ‘Dipartimento di Scienze Fisiche.
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\ 0
TABLE I: Analytical Data of the Studied Solutions“ soh [Rh3+] [NO
