8740
J. Phys. Chem. B 2007, 111, 8740-8745
The Coordination Number of Silicon in Silicon-Oxygen Compounds: The Special Case of 6-Fold Coordination in Thaumasite J. A. Duffy* and D. E. Macphee* Department of Chemistry, UniVersity of Aberdeen, Meston Walk, Aberdeen, AB24 3UE, United Kingdom ReceiVed: February 16, 2007; In Final Form: May 18, 2007
In most silicon-oxygen compounds, the silicon atom is 4-fold coordinated. Exceptionally, silicon is found in 6-fold coordination, as in the mineral thaumasite, which also may be formed in the degradation, and sometimes subsequent weakening, of certain concretes. The connection between coordination number and chemical bonding in oxidic compounds generally is explored using the optical basicity concept to estimate the extent of negative charge provided by oxide(-II) donor atoms in the coordination sphere. A correlation is established between this charge and the heat of formation of silicate (per oxide(-II) atom), which indicates that reduction in charge decreases thermodynamic stability. Calculations for thaumasite show that 4-fold coordination would provide a very small charge, but that 6-fold provides a charge comparable with that for stable 4-fold coordinated silicates such as K2Si2O5.
Introduction The normal chemistry of silicon-oxygen compounds is dominated by the 4-fold coordination of the silicon(IV) atom. Under extreme conditions of temperature and pressure, as exist in the earth’s mantle, silicon is octahedrally coordinated, but away from these harsh conditions there are few examples where the coordination of silicon is 6-fold. Perhaps the best known is the mineral thaumasite, (Ca3Si(OH)6SO4CO3·12H2O); its structure (Figure 1), with a description of the 6-fold coordination, is in ref 1. As well as occurring naturally, thaumasite can also be formed during the degradation of normal Portland cement-based concretes. Usually, the products of cement hydration contain silicon in 4-fold coordination, and it is not understood why in the case of thaumasite the coordination is 6-fold. There is a need to address this question and to understand the thermodynamic stability of thaumasite. Indeed, this need is vital because the formation of thaumasite in concrete leads to degradation of the siliceous cementitious binder, in extreme cases resulting in catastrophic failure of concrete structures.2,3 The coordination number of silicon raises several wider questions regarding the idea of coordination in chemistry. Under normal conditions, lattice energy considerations usually indicate that coordination number depends on the relative size of atoms or ions, and for many purposes, it is convenient to use a hard sphere model where the atoms or ions have fixed (although arbitrarily assigned) radii. In general, cations are smaller than anions, and coordination number is viewed as resulting from the type of packing that the relative ionic radii allow: the larger the cation, the greater is the tendency for higher coordination numbers. As well as comparative size there are other factors affecting coordination number, but these have received much less consideration. These factors are in need of development if they are to help in accounting for coordination number. For example, in a situation where relative ionic size and stoichiometry allow more than one coordination number, what is the nature of the chemistry that determines the choice? If a cation * Corresponding authors. E-mail:
[email protected]; d.e.macphee@ abdn.ac.uk.
Figure 1. Thaumasite structure showing (a) framework silicon atoms (viewed along the cystallographic ab plane) in six-fold coordination and (b) and the structure as viewed down the crystallographic c-axis. Note that the framework units (a) are oriented in a pseudo-hexagonal arrangement, with interunit anions balancing framework positive charges.
can adopt either, e.g., 4-fold or 6-fold coordination when combining with a particular anion, what is the difference in the type of chemical bonding within the coordination sphere? Again, in compounds more complex than simple AnBm binary compounds, what are the effects of next-nearest neighbors? These problems are examined here in the context of oxidic chemistry generally and with special reference to silicates. In the following discussion it is sometimes convenient to forego the distinction between the words “atom” and “ion”. In many instances, neither term is wholly appropriate, as is obviously the case for aluminum(III) and oxide(-II) in Al2O3, for example. Stabilization of Ions Most elements in the Periodic Table tend to form cations, and only a few form anions under normal chemical conditions.
10.1021/jp071343n CCC: $37.00 © 2007 American Chemical Society Published on Web 07/04/2007
Silicon-Oxygen Compounds
Figure 2. Schematic diagram representing stabilisation of Fe2+ and Fe3+ through provision of appropriate environment of negative charge.
Monovalent anions are more stable than the atoms from which they are derived, but divalent ones such as O2- are unstable. The addition of the second electron to the singly charged Orequires energy to overcome repulsion of like charges. The O2ion becomes stable only when much of the dinegative charge is dissipated through some degree of covalent interaction with other atoms or ions, as in Al2O3 for example. All monovalent cations are less stable than the parent atom, corresponding to the sum of the ionization energies required for producing the ion. Cations are stabilized through the presence of an environment of negative charge, provided by surrounding donor anions or, in aqueous solution, the negative end of (polar) water molecules. For many dipositive ions, e.g., Mn2+, Fe2+, Co2+, and some tripositive ions, e.g., Cr3+, sufficient negative charge is provided by six water molecules thereby producing the (sometimes approximately) octahedral chromophore, FeO6 for example. It is useful to visualize the provision of a suitably negative environment as a gradual process as indicated schematically in Figure 2.4 The minimum in the curve for Fe2+, maximum stabilization, is approximately for a donor environment of six water molecules. If the medium is made more basic than this, the Fe2+ ion becomes destabilised and is more readily oxidized to Fe3+. Six water molecules provide insufficient negative charge for the tripositive Fe3+ ion, and it is necessary for proton loss to occur so that the environment is composed of, say, five water molecules and one OH- ion. This is the reason for the acidic reaction of iron(III) salts when added to water:
[Fe(H2O)6]3+(aq.) ) [Fe(H2O)5(OH)]2+(aq.) + H+(aq.) (1) The situation for both ions is summarized in Figure 2. It is of interest to note that the Cr3+ ion, having lower attraction for negative charge (its ionization energies are less than for Fe3+), requires a less negative environment than Fe3+. This means that a less basic environment suffices to stabilize the Cr3+ ion, and this results in the less acidic behavior of the aqua [Cr(H2O)6]3+ ion. However, the hexaaqua environment would appear to provide too much negative charge for the dipositive Cr2+ ion, and it is readily oxidized to the +3 state. Charges Borne by Ions The idea that ions carry charges that are numerically less than their oxidation number is accepted by many chemists. It was Pauling in 1948 who stated in his “electroneutrality principle”
J. Phys. Chem. B, Vol. 111, No. 30, 2007 8741
Figure 3. Plot of charge on Fe3+ ion, Z*(Fe), vs optical basicity of the vitreous environment, showing the sudden increase in Z*(Fe) when the coordination number changes from six (in borate and phosphate glasses) to four (in silicate glasses).
that cations undergoing chemical combination experience a reduction in charge in accordance with electronegativity differences which results in the residing charge being no greater than +1/2.5 Providing there are no steric restrictions, a cation will coordinate with the appropriate number of atoms or ions that serve to provide this effective charge. An example, often quoted, is of the Co2+ ion being satisfied by the degree of electron donation in [CoCl4]2-, but that replacing the chloride ligands by weaker donating water molecules demands not four but six, with the formation of [Co(H2O)6]2+. More recent work reveals that although the Pauling electroneutrality principle is a useful guide, the situation is more complicated. This is illustrated by the behavior of the Fe3+ ion dissolved in different glass systems.6 In silicate glasses it is coordinated by four oxide(-II) atoms yielding the chromophore FeO4 in which the oxide(-II) atoms are also attached to silicon(IV) atoms. Borate and phosphate glasses are usually less basic than silicate owing to the greater polarizing power of boron(III) and phosphorus(V) over silicon(IV) , and as a result, the oxide(-II) atoms in these glasses have less electron donor power when they coordinate with Fe3+. Accordingly, the coordination number of iron(III) in these glasses is six, with the oxide(-II) atoms of the FeO6 chromophore being chemically bonded to the boron(III) or phosphorus(V) atoms. (There is also an increasing tendency for the formation of iron(II) in accordance with the principles of Figure 2. For present purposes, however, this can be ignored.) In terms of the Pauling electroneutrality principle, it might be assumed that the positive charge borne by the iron(III) would be approximately the same in silicate glasses as in borate or phosphate glasses. However, when the charges are calculated (this is done through an analysis of the Fe3+, 3d5 d-d spectra), it is found not to be the case.6 Indeed the charge on iron(III), Z*(Fe), indicates that electroneutrality has occurred to only a small extent, the iron(III) changing from +3 to between +2.2 and +2.5 rather than to +1/2. More striking than this, however, is the plot of Z*(Fe) against glass basicity (expressed as optical basicity, to be discussed later), when it can be seen (Figure 3) that at the coordination number change from six to four, there is a sudden rise in Z*(Fe). Moreover, this increase is from +2.21 to + 2.47, corresponding to a change in neutralization of the Fe3+ ion from 0.79 electron-worth of charge to 0.53. In other words the change in neutralization is in the ratio of 0.79/0.53, which is virtually the same as the coordination number change of 6/4. Furthermore, when the amount of charge per oxide(-II) donated to iron(III) is plotted against optical basicity
8742 J. Phys. Chem. B, Vol. 111, No. 30, 2007
Duffy and Macphee TABLE 1: Basicity Moderating Parameters, γ, of Some Cations and Optical Basicities of Oxides
Figure 4. Plot of electronic charge per oxide(-II) atom donated to Fe3+ vs optical basicity of the vitreous medium, indicating lack of discontinuity when the coordination number of Fe3+ changes from six (filled circles) to four (open circles).
for the three glasses, the increase is a smooth one with no discontinuity at the coordination number change of the iron(III) (Figure 4). Optical Basicity It is apparent that the idea of an ‘environment of negative charge’ is important, and in order to develop present arguments it is necessary to show how the concept can be quantified. In effect, the partial neutralization of a cation is an acid-base interaction in the Lewis sense. Convenient media for effecting gradual changes in Lewis basicity can be provided by many glass systems, and it was a study of ultraviolet spectroscopic trends of certain “probe” ions (see below) in various oxidic glasses that resulted in the quantifying of Lewis basicity in terms of the concept of optical basicity. Since its inception in 1971,7 the optical basicity concept has undergone significant development and application. It has largely replaced the Lux-Flood p(oxide) scale for measuring so-called “oxide ion activities”, and is used extensively for slags in extraction metallurgy.8-12 Also, in glass science, it has been applied to problems related to ultraviolet/visible transparency, refractive index, and redox chemistry (e.g., of Fe2+/Fe3+ or Cr3+/ Cr6+) in glass melts.4,13-19 Furthermore, there are applications for oxide catalysts.20-25 The original optical basicity scale was set up using the ultraviolet absorption band maxima of ions such as Tl+ and Pb2+.7 The red shifts of these bands corresponded directly with the degree of Lewis acid-base interaction that these ions experienced when present in glassy or other oxidic media. Crystalline calcium oxide was chosen, for convenience, as the reference oxidic medium and was defined as having an optical basicity, Λ, of unity. On this basis, the frequency maximum, ν (for the 1S0f3P1 band) in cm-1, in an oxidic medium gave the optical basicity value:
Λ)
60 700 - ν 31 000
(2a)
γ
oxide
Λ
1.23 0.905 0.76 1.00 1.65 2.48 2.10 1.64 2.46 2.50
Li2O Na2O K2O CaO
0.81 1.105 1.32 1.00
b Al2O3 SiO2 a GeO2 b GeO2 H2O
0.40 0.48 0.61 0.40 0.40
a In 4-fold coordination. b In 6-fold. Values are derived from refractivity data.27,31
1s binding energies.28 Results obtained from all of these methods indicate that optical basicity can be calculated, quite simply, from chemical composition, as follows. For an oxidic system (a series of compounds or glasses) composed of the oxides AOa/2, BOb/2, ..., the optical basicity depends on (i) the fraction, X, of oxide(-II) provided by each oxide and (ii) the polarizing effect of each cation Aa+, Bb+, ..., expressed as the “basicity moderating parameter”, γ. Experimentally obtained optical basicity data (see above) have shown that Λ can, in general, be calculated from
Λ)
X(AOa/2) X(BOb/2) + +... γA γB
55 300 - ν 18 300
(2b)
for the Tl+. It was found that the resulting optical basicity values were the same for a given medium, irrespective of the probe ion used. More recent methods of measuring optical basicity employ farinfrared spectroscopy,26 refractivity measurements,27 and oxygen
(3)
Since for a single oxide AOa/2, X(AOa/2) is unity, it follows from eq 3 that Λ(AOa/2) is 1/γA. Hence, eq 3 can be expressed as
Λ ) X(AOa/2).Λ(AOa/2) + X(BOb/2).Λ(BOb/2) +
(4)
Calculation of optical basicity from composition is exemplified by the soda-lime-silica glass of composition 15CaO.10Na2O.75SiO2, where X(CaO) ) (15/175), X(Na2O)) (10/175) and X(SiO2) ) (150/175); the γ value for sodium, calcium, and silicon are, respectively, 0.905, 1.00, and 2.10 (see Table 1), and thus Λ for the glass is 15/(175 × 1.00) + 10/(175 × 0.905) + 150/(175 × 2.10), i.e. 0.557. The optical basicity scale also extends to fluoride systems, but with different γ values.29 It should be noted that the Λ value obtained by the above method represents an average value of the basicity. In many media, crystalline and vitreous, there exists the possibility of oxide(-II) atoms having basicities that differ significantly from each other depending on factors such as near neighbor environment.26,27,30 Refractivity Data and Basicity The refractive index, n, and density, d, of an (isotropic) material are related to the molar refractivity, Rm, by
Rm )
for the Pb2+ probe ion, and
Λ)
cation Li+ Na+ K+ Ca2+ Al3+ a Al3+ b Si4+ Ge4+ a Ge4+ b H+
( )
M n2 - 1 d n2 + 2
(5)
where M is the molar mass in grams. (Strictly, the refractive index is for infinite wavelength, but for present purposes it can be taken at the sodium D line.) Since d is in g/mL, Rm is conveniently expressed in mL, but on a molecular scale, Rm is divided by 4πN/3 (N is the Avogadro number) and is replaced by the electronic polarizability, Rmol, so that we have the familiar Lorentz-Lorenz expression:
Silicon-Oxygen Compounds
Rmol )
J. Phys. Chem. B, Vol. 111, No. 30, 2007 8743
( )
3M n2 - 1 4πNd n2 + 2
(6)
Electronic polarizability represents the degree of distortion experienced by the electron charge clouds of the atoms or ions of a molecule when subjected to an electric field. The passage of light through a material results in an oscillating electric field, and this induces corresponding distortions in the charge clouds, thereby reducing the velocity of the light beam. The effect is greater for materials where the charge cloud distortions are large, that is, where there is a large value of Rmol. The refractive index of many oxidic materials, crystalline and vitreous silicates, for instance, can be shown to be mainly owing to the polarizability, Roxide(-II), of the oxide(-II) atoms or ions. Furthermore, whereas the polarizabilities of most ions are more or less fixed, Roxide(-II) varies considerably. The reason for this variation is that the raw O2- ion bears a dinegative charge, and is very sensitive to the polarizing effects of neighboring cations (Na+, Ca2+, Si4+, etc.). Examination of refractivity data for several hundred silicate glasses has shown that the oxide(-II) polarizability (in Å3) is related to optical basicity by the expression27
Roxide(-II) ) 1.018 + 0.567 + 0.783Λ2
(7)
which also passes through the points for CaO and SiO2. For glasses with Λ
