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Chapter 11 Mixed-Valence MX Chain Compounds and Related Systems
Chapter 11
Mixed-Valence MX Chain Compounds and Related Systems
The MX chain compounds that we shall discuss in the present chapter are closely related to the systems we have discussed in the previous chapter. Nevertheless, we shall devote a special section to these materials for one reason: the materials became the centre of interest at the end of the 1980s and the beginning of the 1990s as a class of materials that had many properties similar to those of the conjugated polymers (synthetic metals) that we shall discuss further later in this presentation (Chapter 12). Thus, the MX chain compounds form, for our purpose, a bridge between inorganic crystalline materials and organic polymeric materials. And therefore they are discussed in a separate chapter.
11.1.
The MX chain compounds
The MX chain compounds are crystalline materials consisting of linear chains with alternating M and X atoms. M is a metal like Ni, Pt, or Pd, whereas X is a halogen like Cl, Br, or I. Most often, the metal atoms have further (groups of) atoms attached to them, leading to a coordination larger than two. One example of such a system is shown in Figure 11.1 for which M equals Pt and X equals Br [1]. It is seen that each Pt atom is surrounded not only by the two Br nearest neighbours along the chain but also by two further Br atoms and two NH3 groups, giving a total coordination for the Pt atoms of six. Another example, ½NiðchxnÞ2 BrBr2 with ðchxnÞ ¼ 1R; 2R – cyclohexanediamine, is shown in Figure 11.2 [2]. In this case, M equals Ni and X equals Br, whereas additional Br atoms are placed between the chains, ultimately leading to a situation where the chains are charged and surrounded by counterions. A similar situation is encountered for ½PtðenÞ2 ½PtðenÞ2 X2 ðClO4 Þ4 with (en) being ethylenediamine. Here the chains are also charged. AuX2 (dibenzylfide) with X being Cl or Br also belongs to these materials [3,4]. If the X atoms are placed symmetrically between the neighbouring M atoms (cf. Figure 11.3), one arrives at a structure like M3þ X M3þ X M3þ X M3þ X ,
(11.1)
whereas when the X atoms are shifted alternatively in one or the other direction along the chain, another structure is obtained, Mð3qÞþ X Mð3þqÞþ X Mð3qÞþ X Mð3þqÞþ X . (11.2) 191
192
Chapter 11. Mixed-Valence MX Chain Compounds and Related Systems
Figure 11.1. Structure of a single chain of ½PtðNH3 Þ2 Br2 ½PtðNH3 Þ2 Br4 : Reproduced with permission of the American Physical Society from [1].
The different materials differ in the size of the displacement of the halogen atoms and, consequently, in the value of q: For M ¼ Ni; the displacement and q are small, whereas they are larger for M ¼ Pt and Pd. For later purpose we notice that the two structures Mð3qÞþ X Mð3þqÞþ X Mð3qÞþ X Mð3þqÞþ X , X Mð3þqÞþ X Mð3qÞþ X Mð3þqÞþ X Mð3qÞþ ð11:3Þ are energetically degenerate. Therefore, as we shall see, domain walls (solitons) on individual chains between the two structures may exist. In two papers, Gammel et al. [5,6] presented a thorough theoretical study of the ground-state and excitation properties of these materials. We shall here briefly outline their approach and results. The starting point was to assume that each atom, M or X, along the chain contributes with only one orbital to the bands closest to the Fermi energy. We shall briefly discuss this assumption below. Assuming that the chain is lying along the
193
11.1. The MX chain compounds
N1
Br2
Br1
(a) Br1 C10
C1 C2 N2
C9
N1 Ni
C3
N2
C4
N3 CS
C8
C7 C6 Br2 (b)
Figure 11.2. (a) The structure of ½NiðchxnÞ2 BrBr2 : (b) The building block of the MX chain compound. Reproduced with permission of the American Physical Society from [2].
Figure 11.3. Structure of the backbone of an M–X chain (upper part) without or (lower part) with an alternation along the backbone. Black and white circles represent M and X atoms, respectively.
194
Chapter 11. Mixed-Valence MX Chain Compounds and Related Systems
z axis, this orbital is the valence d z2 orbital for the M atom and the valence pz orbital for the halogen atom. Having two orbitals per MX unit, the resulting model is correspondingly a two-band model. Moreover, they allowed the atoms to be displaced along the z axis away from the position where all M–X interatomic distances have the same length. The displacement for the lth atom is denoted yl with l being even (odd) for the metal (halogen) atoms. Thus, for the two structures of equation (11.3) we have y2n ¼ 0 y2nþ1 ¼ ð1Þn u0
ð11:4Þ
where u0 is a constant, and where the two structures of equation (11.3) have the same value of ju0 j but the opposite sign of u0 : Gammel et al. [5,6] noticed that a critical parameter was the difference in the onsite energies for the metal and the halogen orbitals, 2e0 ; compared with the average hopping integral between the neighbouring metal and halogen orbitals, t0 ; and depending on the value of e0 =2t0 the ground state has different structures. Thereby the difference between the Ni-based and the Pt- or Pd-based chain compounds could be rationalized. Gammel et al. [5,6] also included many-body terms like those of the Hubbard model that we have discussed in Section 3.6 as well as additional terms that should assure that the proper ground-state structure was obtained. These details are, however, not relevant to the present discussion. Through proper choice of the values of the parameters, Gammel et al. [5,6] could identify different types of ground states. For some of those the lowest total energy was found for a system containing a charge-density wave as that of equation (11.2), whereas for others the metal atoms but not the halogen atoms would be displaced. Still others were characterized by a spin-density wave, i.e., whereas the former two solutions can be considered Peierls transitions, the latter is a spin-Peierls transition. Finally, yet other parameter values led to other structures with an even lower symmetry. Whereas the first solutions correspond to physical realizations for specific MX chain compounds, this is not really the case for the latter. More interesting is to study the response of the system to extra charge or to excitation. This was also studied by Gammel et al. [5,6]. The fact that the two structures of equation (11.3) are energetically degenerate leads to the possibility of the formation of solitons or polarons. A soliton can in this case be considered a domain wall between two segments of the (approximately) infinite chain across which the structure changes from one of the two forms of equation (11.3) to the other form. The domain wall may be more or less wide. On the other hand, a polaron is a spatially confined region where the structure is perturbed, e.g., from that of the one form of equation (11.3) towards the other form and back again. Thus, the existence of polarons does not require the existence of two energetically degenerate structures, whereas that of solitons does. Often all these structural defects lead to extra states in the gaps. Studying those, Gammel et al. [5,6] found the results of Figures 11.4, 11.5, and 11.6. Figure 11.4 shows that the occurrence of solitons or polarons indeed leads to extra gap states that ultimately can be used experimentally in identifying these
11.1. The MX chain compounds
195
Figure 11.4. The energy levels for different MX chains with M being Pt and X being (a) Cl, (b) Br, or (c) I. U marks the neutral, undistorted chain, P polarons, B bipolarons, and K solitons. Moreover, the upper indices indicate whether the chain is neutral (0), having one extra electron ðÞ; or having one less electron (+). The energy zero is placed at the top of the occupied bands for the neutral, undistorted chain. Reproduced with permission of the American Physical Society from [5].
196
Chapter 11. Mixed-Valence MX Chain Compounds and Related Systems
Figure 11.5. Excess charge (solid curves) and spin (dashed curves) density distribution of some of the structural distortions of Figure 11.4 for MX chains with M being Pt and X being Cl, except for (c) where X equals I. Reproduced with permission of the American Physical Society from [5].
structural distortions. This has been done, e.g., by Sakai et al. [7] and by Okamoto et al. [8] on a charged PtCl compound, thereby obtaining support for their existence. In Figure 11.5 we show the calculated extra charge and spin density due to some of the defects of Figure 11.4. It is seen that the extra charge and spin is localized to the region of the lattice distortion. Parameters that quantify the charge-density and spin-density waves are shown in Figure 11.6. For the neutral, undistorted chain,
11.1. The MX chain compounds
197
Figure 11.6. Parameters quantifying the occurrence of charge-density (solid curves) or spin-density waves (dashed and dot-dashed curves; here the dashed curves are for the X atoms, the dot-dashed curves for the M atoms) as functions of site index for the same systems as in Figure 11.5. The parameters are the order parameters that are constant for the regular, periodic structure, but non-constant for structures containing local distortions. The width of the distortions can be extracted from the figures. Reproduced with permission of the American Physical Society from [5].
there is a vanishing spin-density wave, whereas a charge-density wave is uniform throughout the whole chain. Introducing the local distortions as in Figure 11.5 leads to either local variations [Figure 11.6(a) and (b)] or shifts [Figure 11.6(c)] in the charge-and/or spin-density wave, as one would expect. We finally address the question as to whether the model used by Gammel et al. [5,6] is realistic. Alouani et al. [1] have performed parameter-free density-functional
198
Chapter 11. Mixed-Valence MX Chain Compounds and Related Systems
Figure 11.7. The band structures for the system of Figure 11.1. The dots mark results from densityfunctional calculations, whereas the full curves are results from a tight-binding fit. Finally, the Fermi energy is set equal to 0. Reproduced with permission of the American Physical Society from [1].
Figure 11.8. Variation in the total energy for the system of Figure 11.1 as a function of a parameter that describes the position of the Br atoms relative to the positions in the middle between the neighbouring Pt atoms both without (dashed curve) and with (full curve) the inclusion of the NH3 groups. Reproduced with permission of the American Physical Society from [1].
calculations on ½PtðNH3 Þ2 Br2 ½PtðNH3 Þ2 Br4 : For this system they found that indeed the band structures closest to the Fermi level resemble those of the model, i.e., the bands are formed essentially by Pt d z2 and Br pz functions; cf. Figure 11.7. A surprising result was that the inclusion of the (closed-shell) NH3 (ammonia) molecules was important. Ignoring them, extra orbitals centred on the Pt atoms showed up around the Fermi level and, more importantly, the proper charge-density wave could not be obtained, cf. Figure 11.8.
11.2. The MMX chain compounds
11.2.
199
The MMX chain compounds
As an extension of the systems of the previous section, Kimura et al. [9] synthesized a chain compound, ðNH3 Þ4 ½Pt2 XðpopÞ4 with (pop) being P2 O5 H2 2 and X being Cl, Br, or I. The resulting structure is shown in Figure 11.9. The fact that here two metal atoms are placed between the halogen atoms give rise to more variations in the possible valence pattern of the metal atoms, like Pt2þ Pt2þ X Pt3þ Pt3þ X Pt2þ Pt3þ X Pt2þ Pt3þ X Pt2:5þ Pt2:5þ X Pt2:5þ Pt2:5þ X
ð11:5Þ
Using NMR spectroscopy, Kimura et al. [9] could identify signals related to the occurrence of Pt3þ and Pt2þ ; thus ruling out the third pattern above. A further
Figure 11.9. Structure of the MMX chain compound (NH3 Þ4 ½Pt2 XðpopÞ4 ] with (pop) being P2 O5 H2 2 and X being Cl. The positions of the Cl atoms are disordered. Reproduced from [9].
200
Chapter 11. Mixed-Valence MX Chain Compounds and Related Systems
analysis gave that the first pattern is the one that is observed in accordance with x-ray diffraction studies [10]. Nevertheless, the richness in the possible valence patterns is most likely matched by a similar richness in the possible excitations. However, to the best of our knowledge this has not been studied in further detail.
11.3.
Magnus’ green salt
As the last example of a crystalline compound with a dominating quasi-one-dimensionality we shall, once more, discuss a material based on Pt atoms, this time the so-called Magnus’ green salt, PtðNH3 Þ4 PtCl4 : Its structure, cf. Figure 11.10, consists of chains with alternating PtðNH3 Þ4 and PtCl4 units. The Pt atoms form the backbone of the linear chain, and as for the other systems of this section one may formally ascribe the Pt atoms a valence that alternate along the chain. Magnus’ green salt has been known for almost 200 years (see, e.g., Ref. [11]) and over the years a number of related compounds have been produced upon substituting Pt with Pd and/or some of the sidegroups through other ones. Also mixed compounds like PtðNH3 Þ4 PdCl4 and PdðNH3 Þ4 PtCl4 have been produced [12]. Lately the interest in these materials has grown, partly due to the prospects of varying the (semiconducting) properties of those materials in a controlled way, and partly due to their solubility properties [13–15].
NH3 H3N
Pt
H3N Cl
Pt
Cl H3N
Pt
H3N Cl
Pt
Cl H3N
Pt
H3N Cl Cl
NH3 Cl
2-
Cl NH3
2+
NH3 Cl
2-
Cl NH3
2+
NH3 Cl
Pt
2+
2-
Cl
Figure 11.10. Structure of Magnus’ green salt, PtðNH3 Þ4 PtCl4 : Reproduced with permission of the Royal Society of Chemistry from [13].
11.4. Conclusions
11.4.
201
Conclusions
Pt and the other elements of its group in the periodic table (i.e., Pd and Ni) have been the central elements in this section. The materials were crystalline and highly anisotropic so that the quasi-one-dimensionality could be clearly identified in their properties. The interesting properties were related to being able to modulate the charge or spin distribution along the backbone of the chains, i.e., of the metal atoms. This option was made possible by including further atoms or groups of atoms in the structure. A structural modulation like the small displacements of the halogen atoms in the MX and the MMX chain compounds could be used in obtaining a strong modulation in the electronic properties, i.e., the electrons respond strongly on the relatively small perturbations of the structure. This means, on the other hand, that manipulating the modulation may lead to strong responses. These responses are, e.g., the occurrence of solitons or polarons. Here, we add that the generation of a soliton requires a much larger structural perturbation than that of a polaron: in the former case, half-part of an essentially infinite chain has to be perturbed, whereas in the latter case the perturbation is confined to a finite region. Independent of whether solitons or polarons are generated, extra electronic orbitals localized to the region of the structural distortion and with energies in the gap between occupied and unoccupied orbitals are generated. When the distortion is not very localized, it can move up and down the chain with only small energy costs, ultimately being able to carry extra charge or spin from electrons occupying the defect-induced gap states. Accordingly, these materials can conduct. This type of charge-transport processes is not unique to the present type of materials. Actually, it is closely related to the Grotthus mechanism [16] which since the first part of the 19th century has been used in explaining the high electrical conductivity in hydrogen-bonded systems with H2 O being the most prominent example (it may be added here that the conductivity requires the addition of charge carriers, e.g., ions). For this presentation it is more important to notice that exactly the same mechanism have been used in explaining the conduction properties of the conjugated polymers (also called synthetic metals) that we shall treat in detail in the next chapter. The interest in the MX chain compounds during the late 1980s and early 1990s evolved actually from the research activity in the conjugated polymers and many of the concepts from the latter were modified and adapted to the MX chain compounds. The MX chain compounds (and later the MMX chain compounds) have provided an interesting additional class of materials which, compared with the conjugated polymers, had the advantages of being crystalline and ordered. Moreover, they offer additional possibilities of fine tuning the materials properties. As we have discussed, through variation of the metals, the halogens, and side groups a variety of properties can be obtained. Finally, it is interesting to notice that the last example of the present section, i.e., Magnus’ green salt, has become of interest as another material with materials properties like those of the conjugated polymers.
202
Chapter 11. Mixed-Valence MX Chain Compounds and Related Systems
References [1] M.E. Alouani, R.C. Albers, J.M. Wills, and M. Springborg, Phys. Rev. Lett. 69, 3104 (1992). [2] H. Okamoto, Y. Shimada, Y. Oka, A. Chainani, T. Takahashi, H. Kitagawa, T. Mitani, K. Toriumi, K. Inoue, T. Manabe, and M. Yamashita, Phys. Rev. B 54, 8438 (1996). [3] H. Tanino, K. Syassen, and K. Takahashi, Phys. Rev. B 39, 3125 (1989). [4] H. Tanino, M. Holtz, M. Hanfland, K. Syassen, and K. Takahashi, Phys. Rev. B 39, 9992 (1989). [5] J.T. Gammel, A. Saxena, I. Batistic´, A.R. Bishop, and S.R. Phillpot, Phys. Rev. B 45, 6408 (1992). [6] S.M. Weber-Milbrodt, J.T. Gammel, A.R. Bishop, and E.Y. Loh, Jr., Phys. Rev. B 45, 6435 (1992). [7] M. Sakai, N. Kuroda, and Y. Nishina, Phys. Rev. B 40, 3066 (1989). [8] H. Okamoto, T. Mitani, K. Toriumi, and M. Yamashita, Phys. Rev. Lett. 69, 2248 (1992). [9] N. Kimura, H. Ohki, R. Ikeda, and M. Yamashita, Chem. Phys. Lett. 220, 40 (1994). [10] S. Jin, T. Ito, K. Toriumi, and M. Yamashita, Acta Crystallogr. C 45, 1415 (1989). [11] M. Atoji, J.W. Richardson, and R.E. Rundle, J. Am. Chem. Soc. 79, 3017 (1957). [12] M.E. Cradwick, D. Hall, and R.K. Phillips, Acta Crystallogr. B 27, 480 (1971). [13] J. Bremi, W. Caseri, and P. Smith, J. Mat. Chem. 11, 2593 (2001). [14] M. Fontana, H. Chanzy, W.R. Caseri, P. Smith, A.P.H.J. Schenning, E.W. Meijer, and F. Gro¨hn, Chem. Mat. 14, 1730 (2002). [15] W.R. Caseri, H.D. Chanzy, K. Feldman, M. Fontana, P. Smith, T.A. Tervoort, J.G.P. Goossens, E.W. Meijer, A.P.H.J. Schenning, I.P. Dolbnya, M.G. Debije, M.P. de Haas, J.M. Warman, A.M. van de Craats, R.H. Friend, H. Sirringhaus, and N. Stutzmann, Adv. Mat. 15, 125 (2003). [16] C.J.T. Grotthus, Ann. Chim. Phys. 58, 54 (1806).
Mixed-Valence MX Chain Compounds and Related Systems
The MX chain compounds that we shall discuss in the present chapter are closely related to the systems we have discussed in the previous chapter. Nevertheless, we shall devote a special section to these materials for one reason: the materials became the centre of interest at the end of the 1980s and the beginning of the 1990s as a class of materials that had many properties similar to those of the conjugated polymers (synthetic metals) that we shall discuss further later in this presentation (Chapter 12). Thus, the MX chain compounds form, for our purpose, a bridge between inorganic crystalline materials and organic polymeric materials. And therefore they are discussed in a separate chapter.
11.1.
The MX chain compounds
The MX chain compounds are crystalline materials consisting of linear chains with alternating M and X atoms. M is a metal like Ni, Pt, or Pd, whereas X is a halogen like Cl, Br, or I. Most often, the metal atoms have further (groups of) atoms attached to them, leading to a coordination larger than two. One example of such a system is shown in Figure 11.1 for which M equals Pt and X equals Br [1]. It is seen that each Pt atom is surrounded not only by the two Br nearest neighbours along the chain but also by two further Br atoms and two NH3 groups, giving a total coordination for the Pt atoms of six. Another example, ½NiðchxnÞ2 BrBr2 with ðchxnÞ ¼ 1R; 2R – cyclohexanediamine, is shown in Figure 11.2 [2]. In this case, M equals Ni and X equals Br, whereas additional Br atoms are placed between the chains, ultimately leading to a situation where the chains are charged and surrounded by counterions. A similar situation is encountered for ½PtðenÞ2 ½PtðenÞ2 X2 ðClO4 Þ4 with (en) being ethylenediamine. Here the chains are also charged. AuX2 (dibenzylfide) with X being Cl or Br also belongs to these materials [3,4]. If the X atoms are placed symmetrically between the neighbouring M atoms (cf. Figure 11.3), one arrives at a structure like M3þ X M3þ X M3þ X M3þ X ,
(11.1)
whereas when the X atoms are shifted alternatively in one or the other direction along the chain, another structure is obtained, Mð3qÞþ X Mð3þqÞþ X Mð3qÞþ X Mð3þqÞþ X . (11.2) 191
192
Chapter 11. Mixed-Valence MX Chain Compounds and Related Systems
Figure 11.1. Structure of a single chain of ½PtðNH3 Þ2 Br2 ½PtðNH3 Þ2 Br4 : Reproduced with permission of the American Physical Society from [1].
The different materials differ in the size of the displacement of the halogen atoms and, consequently, in the value of q: For M ¼ Ni; the displacement and q are small, whereas they are larger for M ¼ Pt and Pd. For later purpose we notice that the two structures Mð3qÞþ X Mð3þqÞþ X Mð3qÞþ X Mð3þqÞþ X , X Mð3þqÞþ X Mð3qÞþ X Mð3þqÞþ X Mð3qÞþ ð11:3Þ are energetically degenerate. Therefore, as we shall see, domain walls (solitons) on individual chains between the two structures may exist. In two papers, Gammel et al. [5,6] presented a thorough theoretical study of the ground-state and excitation properties of these materials. We shall here briefly outline their approach and results. The starting point was to assume that each atom, M or X, along the chain contributes with only one orbital to the bands closest to the Fermi energy. We shall briefly discuss this assumption below. Assuming that the chain is lying along the
193
11.1. The MX chain compounds
N1
Br2
Br1
(a) Br1 C10
C1 C2 N2
C9
N1 Ni
C3
N2
C4
N3 CS
C8
C7 C6 Br2 (b)
Figure 11.2. (a) The structure of ½NiðchxnÞ2 BrBr2 : (b) The building block of the MX chain compound. Reproduced with permission of the American Physical Society from [2].
Figure 11.3. Structure of the backbone of an M–X chain (upper part) without or (lower part) with an alternation along the backbone. Black and white circles represent M and X atoms, respectively.
194
Chapter 11. Mixed-Valence MX Chain Compounds and Related Systems
z axis, this orbital is the valence d z2 orbital for the M atom and the valence pz orbital for the halogen atom. Having two orbitals per MX unit, the resulting model is correspondingly a two-band model. Moreover, they allowed the atoms to be displaced along the z axis away from the position where all M–X interatomic distances have the same length. The displacement for the lth atom is denoted yl with l being even (odd) for the metal (halogen) atoms. Thus, for the two structures of equation (11.3) we have y2n ¼ 0 y2nþ1 ¼ ð1Þn u0
ð11:4Þ
where u0 is a constant, and where the two structures of equation (11.3) have the same value of ju0 j but the opposite sign of u0 : Gammel et al. [5,6] noticed that a critical parameter was the difference in the onsite energies for the metal and the halogen orbitals, 2e0 ; compared with the average hopping integral between the neighbouring metal and halogen orbitals, t0 ; and depending on the value of e0 =2t0 the ground state has different structures. Thereby the difference between the Ni-based and the Pt- or Pd-based chain compounds could be rationalized. Gammel et al. [5,6] also included many-body terms like those of the Hubbard model that we have discussed in Section 3.6 as well as additional terms that should assure that the proper ground-state structure was obtained. These details are, however, not relevant to the present discussion. Through proper choice of the values of the parameters, Gammel et al. [5,6] could identify different types of ground states. For some of those the lowest total energy was found for a system containing a charge-density wave as that of equation (11.2), whereas for others the metal atoms but not the halogen atoms would be displaced. Still others were characterized by a spin-density wave, i.e., whereas the former two solutions can be considered Peierls transitions, the latter is a spin-Peierls transition. Finally, yet other parameter values led to other structures with an even lower symmetry. Whereas the first solutions correspond to physical realizations for specific MX chain compounds, this is not really the case for the latter. More interesting is to study the response of the system to extra charge or to excitation. This was also studied by Gammel et al. [5,6]. The fact that the two structures of equation (11.3) are energetically degenerate leads to the possibility of the formation of solitons or polarons. A soliton can in this case be considered a domain wall between two segments of the (approximately) infinite chain across which the structure changes from one of the two forms of equation (11.3) to the other form. The domain wall may be more or less wide. On the other hand, a polaron is a spatially confined region where the structure is perturbed, e.g., from that of the one form of equation (11.3) towards the other form and back again. Thus, the existence of polarons does not require the existence of two energetically degenerate structures, whereas that of solitons does. Often all these structural defects lead to extra states in the gaps. Studying those, Gammel et al. [5,6] found the results of Figures 11.4, 11.5, and 11.6. Figure 11.4 shows that the occurrence of solitons or polarons indeed leads to extra gap states that ultimately can be used experimentally in identifying these
11.1. The MX chain compounds
195
Figure 11.4. The energy levels for different MX chains with M being Pt and X being (a) Cl, (b) Br, or (c) I. U marks the neutral, undistorted chain, P polarons, B bipolarons, and K solitons. Moreover, the upper indices indicate whether the chain is neutral (0), having one extra electron ðÞ; or having one less electron (+). The energy zero is placed at the top of the occupied bands for the neutral, undistorted chain. Reproduced with permission of the American Physical Society from [5].
196
Chapter 11. Mixed-Valence MX Chain Compounds and Related Systems
Figure 11.5. Excess charge (solid curves) and spin (dashed curves) density distribution of some of the structural distortions of Figure 11.4 for MX chains with M being Pt and X being Cl, except for (c) where X equals I. Reproduced with permission of the American Physical Society from [5].
structural distortions. This has been done, e.g., by Sakai et al. [7] and by Okamoto et al. [8] on a charged PtCl compound, thereby obtaining support for their existence. In Figure 11.5 we show the calculated extra charge and spin density due to some of the defects of Figure 11.4. It is seen that the extra charge and spin is localized to the region of the lattice distortion. Parameters that quantify the charge-density and spin-density waves are shown in Figure 11.6. For the neutral, undistorted chain,
11.1. The MX chain compounds
197
Figure 11.6. Parameters quantifying the occurrence of charge-density (solid curves) or spin-density waves (dashed and dot-dashed curves; here the dashed curves are for the X atoms, the dot-dashed curves for the M atoms) as functions of site index for the same systems as in Figure 11.5. The parameters are the order parameters that are constant for the regular, periodic structure, but non-constant for structures containing local distortions. The width of the distortions can be extracted from the figures. Reproduced with permission of the American Physical Society from [5].
there is a vanishing spin-density wave, whereas a charge-density wave is uniform throughout the whole chain. Introducing the local distortions as in Figure 11.5 leads to either local variations [Figure 11.6(a) and (b)] or shifts [Figure 11.6(c)] in the charge-and/or spin-density wave, as one would expect. We finally address the question as to whether the model used by Gammel et al. [5,6] is realistic. Alouani et al. [1] have performed parameter-free density-functional
198
Chapter 11. Mixed-Valence MX Chain Compounds and Related Systems
Figure 11.7. The band structures for the system of Figure 11.1. The dots mark results from densityfunctional calculations, whereas the full curves are results from a tight-binding fit. Finally, the Fermi energy is set equal to 0. Reproduced with permission of the American Physical Society from [1].
Figure 11.8. Variation in the total energy for the system of Figure 11.1 as a function of a parameter that describes the position of the Br atoms relative to the positions in the middle between the neighbouring Pt atoms both without (dashed curve) and with (full curve) the inclusion of the NH3 groups. Reproduced with permission of the American Physical Society from [1].
calculations on ½PtðNH3 Þ2 Br2 ½PtðNH3 Þ2 Br4 : For this system they found that indeed the band structures closest to the Fermi level resemble those of the model, i.e., the bands are formed essentially by Pt d z2 and Br pz functions; cf. Figure 11.7. A surprising result was that the inclusion of the (closed-shell) NH3 (ammonia) molecules was important. Ignoring them, extra orbitals centred on the Pt atoms showed up around the Fermi level and, more importantly, the proper charge-density wave could not be obtained, cf. Figure 11.8.
11.2. The MMX chain compounds
11.2.
199
The MMX chain compounds
As an extension of the systems of the previous section, Kimura et al. [9] synthesized a chain compound, ðNH3 Þ4 ½Pt2 XðpopÞ4 with (pop) being P2 O5 H2 2 and X being Cl, Br, or I. The resulting structure is shown in Figure 11.9. The fact that here two metal atoms are placed between the halogen atoms give rise to more variations in the possible valence pattern of the metal atoms, like Pt2þ Pt2þ X Pt3þ Pt3þ X Pt2þ Pt3þ X Pt2þ Pt3þ X Pt2:5þ Pt2:5þ X Pt2:5þ Pt2:5þ X
ð11:5Þ
Using NMR spectroscopy, Kimura et al. [9] could identify signals related to the occurrence of Pt3þ and Pt2þ ; thus ruling out the third pattern above. A further
Figure 11.9. Structure of the MMX chain compound (NH3 Þ4 ½Pt2 XðpopÞ4 ] with (pop) being P2 O5 H2 2 and X being Cl. The positions of the Cl atoms are disordered. Reproduced from [9].
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Chapter 11. Mixed-Valence MX Chain Compounds and Related Systems
analysis gave that the first pattern is the one that is observed in accordance with x-ray diffraction studies [10]. Nevertheless, the richness in the possible valence patterns is most likely matched by a similar richness in the possible excitations. However, to the best of our knowledge this has not been studied in further detail.
11.3.
Magnus’ green salt
As the last example of a crystalline compound with a dominating quasi-one-dimensionality we shall, once more, discuss a material based on Pt atoms, this time the so-called Magnus’ green salt, PtðNH3 Þ4 PtCl4 : Its structure, cf. Figure 11.10, consists of chains with alternating PtðNH3 Þ4 and PtCl4 units. The Pt atoms form the backbone of the linear chain, and as for the other systems of this section one may formally ascribe the Pt atoms a valence that alternate along the chain. Magnus’ green salt has been known for almost 200 years (see, e.g., Ref. [11]) and over the years a number of related compounds have been produced upon substituting Pt with Pd and/or some of the sidegroups through other ones. Also mixed compounds like PtðNH3 Þ4 PdCl4 and PdðNH3 Þ4 PtCl4 have been produced [12]. Lately the interest in these materials has grown, partly due to the prospects of varying the (semiconducting) properties of those materials in a controlled way, and partly due to their solubility properties [13–15].
NH3 H3N
Pt
H3N Cl
Pt
Cl H3N
Pt
H3N Cl
Pt
Cl H3N
Pt
H3N Cl Cl
NH3 Cl
2-
Cl NH3
2+
NH3 Cl
2-
Cl NH3
2+
NH3 Cl
Pt
2+
2-
Cl
Figure 11.10. Structure of Magnus’ green salt, PtðNH3 Þ4 PtCl4 : Reproduced with permission of the Royal Society of Chemistry from [13].
11.4. Conclusions
11.4.
201
Conclusions
Pt and the other elements of its group in the periodic table (i.e., Pd and Ni) have been the central elements in this section. The materials were crystalline and highly anisotropic so that the quasi-one-dimensionality could be clearly identified in their properties. The interesting properties were related to being able to modulate the charge or spin distribution along the backbone of the chains, i.e., of the metal atoms. This option was made possible by including further atoms or groups of atoms in the structure. A structural modulation like the small displacements of the halogen atoms in the MX and the MMX chain compounds could be used in obtaining a strong modulation in the electronic properties, i.e., the electrons respond strongly on the relatively small perturbations of the structure. This means, on the other hand, that manipulating the modulation may lead to strong responses. These responses are, e.g., the occurrence of solitons or polarons. Here, we add that the generation of a soliton requires a much larger structural perturbation than that of a polaron: in the former case, half-part of an essentially infinite chain has to be perturbed, whereas in the latter case the perturbation is confined to a finite region. Independent of whether solitons or polarons are generated, extra electronic orbitals localized to the region of the structural distortion and with energies in the gap between occupied and unoccupied orbitals are generated. When the distortion is not very localized, it can move up and down the chain with only small energy costs, ultimately being able to carry extra charge or spin from electrons occupying the defect-induced gap states. Accordingly, these materials can conduct. This type of charge-transport processes is not unique to the present type of materials. Actually, it is closely related to the Grotthus mechanism [16] which since the first part of the 19th century has been used in explaining the high electrical conductivity in hydrogen-bonded systems with H2 O being the most prominent example (it may be added here that the conductivity requires the addition of charge carriers, e.g., ions). For this presentation it is more important to notice that exactly the same mechanism have been used in explaining the conduction properties of the conjugated polymers (also called synthetic metals) that we shall treat in detail in the next chapter. The interest in the MX chain compounds during the late 1980s and early 1990s evolved actually from the research activity in the conjugated polymers and many of the concepts from the latter were modified and adapted to the MX chain compounds. The MX chain compounds (and later the MMX chain compounds) have provided an interesting additional class of materials which, compared with the conjugated polymers, had the advantages of being crystalline and ordered. Moreover, they offer additional possibilities of fine tuning the materials properties. As we have discussed, through variation of the metals, the halogens, and side groups a variety of properties can be obtained. Finally, it is interesting to notice that the last example of the present section, i.e., Magnus’ green salt, has become of interest as another material with materials properties like those of the conjugated polymers.
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