Bonding in silicates: an assessment of bonding in orthopyroxene

&m&k&a

et Cosmochtmba

A&a, 1973, Vol. 37, pp. 249 to 257.

Perg~~ir~on Pm.

Printed in Northern Ireland

R. K. O’NIONS Department

of Geology and Mineralogy, Parks Road, Oxford, England and

D. G. Department

w.

of Mineralogy and Petrology,

fhITH*

Downing Plate,

Cambridge, England

AbstraCtThe

molecular orbital and oqtal field theories are compared and their app~~ab~t~~ to Bonding in silicates are discussed, A mok~&~ orbital bonding model is favoured for orthopyroxene since bonding in both tetrs,h&~~J and non-tetrahedral sites within the crystal structure can be described and accommodated by the theory. It is suggestid that Fe located in M, sites has more electron delocalisation (or covaIence) associated with it than Fe located in the M, site. Order-disorder phenomena in orthopyroxene are discussed in relationship to MUELLER’s (1970) two-step exchange mechanism, whereby the first step corresponds to vacancy activation and the second step to exchange of Fe between an “octahedral’ site and a vacancy. INTRODDCTXON &KU?OSED bonding models fall, broadly speaking, into three catqpries : valence bond theory (VBT), crystal field theory (CFT) and its modifications, and molecular orbital theory (MOT}. CFT has become increasingly popular in recent years, especially with those earth scientists concerned with the geochemistry of transition metals. The success of CPT in mineralogy and geochemistry has largely resulted from it usefufness in interpreting spectroscopic data (the so-called crystal field spectra). Its application to transition metal geochemistry has been justified on the assumption that transition metals form essentially ionic bonds in silicate structures. The fhird model (MOT) has been widely applied by chemists to covalent compounds, but can accommodate within its framework bond polarities up to those which are completely ionic. Recently MOT has been successfully utilised for the interpretation of those X-ray emission spectra which are the result of transitions from valence shell orbitals, from minerals normally regarded as essentially ionically bonded. The purpose of the present paper is to point out certain inadequacies in the use of @F’S to describe bonds between transition metal cations and oxygen in silicate structures, and to outline in a qualitative manner the natnre of bonding in silicates as deduced from HOT. Orthopyroxene will be used to illustrate the approach taken. THE

CRYSTAL

FIELD

AND

MOLECULAR

ORBITAL THEORIES

Before making a comparison of the CFT and MOT models, and assessing their usefulness in silicate geoohemistry, it is necessary to establish the meaning of the terms ionicity and covalency as applied to the description of chemical bonds. PHILLIPS (1970a, b) reviewed the definitions of ionicity and covalency based upon the thermochemical approach, the valence-bond-molecular orbital approach and proposed a * Permanent Canada.

address:

Department

of Geology, University 249

of Alberta, Edmonton,

Alberta,

250

R. J. O’NIONS and D. G. W. Saurn

spectroscopic definition of ionicity for certain classes of compounds. In the thermochemical approach advocated by PAULING (1960) the covalent bond energy for a compound AB is based upon the heat of formation of compounds AA and BB and is proportional to (D BB. + 0,,)/2. The ionic bonding energy, on the other hand, is proportional to A,,-- the square of the electronegativity differences between AA and BB. In contrast to the thermochemical approach, the valence-bond-molecular orbital approaches have a quantum mechanical basis for their definition (COULSON et al. 1962). The covalent bonding energy term is proportional to the overlap parameter @, and the ionic bonding energy term is proportional to cc* - ug, where a is the arithmetic mean of the ionisation energy plus electron affinity. PHILLIPS (1970a, b) pointed out inadequacies in both of these approaches and attempted to evaluate separately, on an equal footing, the ionic and covalent parts of the bond using dispersion theory. Considerable support for Phillips’ approach is derived from the much improved predictions of the structures of the AnB8-” class of crystals. It is necessary to bear in mind these different definitions of ionicity and covalency when using these terms to describe bonds in silicates. Evaluation of the ionic and covalent parts of bonds in silicates is still in a very crude state and it is considered premature to attempt to use these terms in relation to any quantitatively useful formulae. We shall therefore make use of them only in a qualitative manner in the ensuing discussion, consistent, for example, with the usage by ORGEL (1964) ; i.e. when we speak of a covalent bond we mean that it involves a high degree of electron delocalisation and the more ionic a bond is said to be the less electron delocalisation there is associated with it. Crystal field theory describes the electrostatic interactions between ligand and metal, making the simplifying assumption that ligands can be represented as point charges, and in its unadjusted form completely ignores orbital overlap. Whenever a transition metal ion is in a non-spherical field, some degeneracy is removed from the 3d atomic energy levels-the amount of orbital degeneracy decreasing with decreasing symmetry. CFT has been extensively reviewed by BALLHATJSEN(1962), and in the earth science literature, BURNS (1970a) has reviewed some of the ways in which CFT may be applied to mineralogical problems. The theory has been successfully employed to interpret absorption spectroscopic data from first series transition elements occupying sites of differing symmetries in silicate structures (see review by BURNS, 1970). The crystal field splitting parameters have been deduced from these data for cations in sites of differing symmetry, and site preference energies computed. Conceptually the molecular orbital model is equally simple, assuming that elechrons occupy polycentric orbitals, which are molecular in nature, and filled in the same way (i.e. consistent with the azcfbazl principle) as are monocentric atomic orbitals. Molecular orbitals (y) may be regarded as linear combinations of atomic orbitals (4) 7yi = X a& , where the coefficient a,.i describes the contribution of the atomic orbital 4 to the molecular orbital y. In a regular octahedron with o,, symmetry, a central cation surrounded by six similar ligands will form molecular orbitals consistent with the

Bonding in silic&tes: an assessment of bonding in orthopyroxene

261

above equation. In situations where the eoord~ation ~lyhe~o~ is more distorted, interaction between the ligands and central cation will be variable and we may expect the charge density in molecular orbitals to be strongly polarised towards those ligands having the largest values of a,,. The linear combination of atomic orbitals procedure (LCAO) assumes that when an electron in a polycentrio orbital is close to one nucleus it will be influenced in a similar manner to an electron in an atomic orbital at that point, hence the wave function can be described by LCAO if anything other than overlap with immediately adjacent atoms is ignored. Comprehensive reviews of the subject may be found, for example, in COULSON (1961), BALLRAUSEN and GRAY (1964) and MURBELLet al. (1970). In a situation where no electron delocalisation occurs {i.e. a purely ionic situation) the XlOT and CFT description of the metal 3d energy levels become essentia~y identioal (COTTON,1964). However, the predictions of CFT concerning 3d electrons of transition metal cations become progressively imperfect as the degree of electron delocalisation increases. The relative energies of bonding and antibonding molecular orbitals are controlled by the extent of 0 and n-interactions, on the MOT model, and this has important implications with respect to the true character of the so-called crystal field levels based upon CFT. As an example, let us consider the case of ferrous iron, octahedrally coordinated to oxygen, in a simple oxide or silicate mineral. The antibonding molecular orbit& (ABMO’s) resulting from Fe 3& and 0 213atomic orbital overlap are ta,7~*and ego*, these will be largely F8 3d in character, but will contain a finite amount of 0 2~ character. Conversely, ts,?~~and possibly egabmay be expected to have some Fe 3d character. CFT focuses attention entirely on relationships amongst ABMO’s and ~accurately describes their character when some degree of electron delocalisation occurs. Furthermore, differences in the energies, character and occupancy of BMO’s, which may account for the largest part of the total bond energy, are not assessed at all with CFT. Much evidence now exists for electron delocalisation in transition metal compounds (see OR~EL, 1964 and COTTONand WILKINSON,1966) including electron spin resonance studies, intensities of d-d transitions, antiferromagnetic coupling and the nephelauxetic effect. In the light of this evidence Cotton and Wilkinson have discussed the theoretical failure of the ionic model of bonding. Investigations of soft X-ray emission spectra from transmission and third row metal oxides (SMITHand O’NIONS, 1971,1972a,b: O’Nrorss and SETH, 1971a,b; DODDand GLEN,1968,1969) which are the result of transitions from valence shell orbitals, have suggested that su~cient electron delooalisation occurs to necessitate the use of MOT for the interpretation of the spectral components. These results are particularly significant since they demonstrate that even in these oxides, which are usually considered to be largely ionically bonded, sufficient electron delocalisation occurs to necessitate the use of MOT for the interpretation of the spectra. Also, URCH (1969, 1970) offered a molecular orbital interpretation of low-energy satellite lines in X-ray emission spectra, and demonstrated that the ionic model (where satellites are considered to result from crossover transitions) predicts generated intensities which are several orders of magnitude too small. The evidence cited above for electron delocalisation in transition metal compounds leaves little doubt that the MOT model is a better description of the bonding scheme in transition metal oxides than the CFT model. By inference we might to,

262

EL K.

OXIONS

fbndD. C. pi.Sxrix

a first approximation, anticipate a similar degree of orbital ~teraction for transition metals hexacoordinated by oxygen in silicate crystal structures. The marked preference shown by transition metals in silicates for distorted sites, however, makes the direct application of the data obtained from oxide minerals to silicates unreasonable. In addition to these stereochemical differences, we must expect further discrepancies from the presence of OH and F in the coordination polyhedra around the metals and differences in the environments of the coordinating ligands in the silicate structures. For example, valence electrons of a bridging oxygen may be more delocalised than those of a non-bridging oxygen, because of the more covalent character of Si-0 bonds compared with M-O bonds and, as a consequence, may have a lower orbital overlap potential with a coordinating transition metal ion. V~iabi~ty in the ionicity of bonds between transition metals and ligand oxygens in silicates, resulting from changes in the coordination polyhedron about the metal and changes in the environment of the ligand, cannot be assessed using CFT. CFT describes the relative energy changes between ABMO’s but tells us nothing about variability in the amount of ligand character in the ABMO’s and the concomitant changes in the energies and character of BMO’s. The case for the use of MOT for the description of the more covalent bonds between Si and 0 is better established (CRUICKSHANK, 1961; URCH, 1970; O’NIONS and SMITH, 1971a), hence it is now well justified to attempt an assessment of bonding in the complete silicate structure using the MOT description of bonds. BONDINGIN ORTHO~~OXE~E That crystal field theory is inadequate for unde~tan~ng intracrystalline cation dist~bution in some silicate minerals is well exemplified by Fe2+ in olivine and orthopyroxene. BURNS(1970a) calculated a site preference energy for the M, site of 0.2 kcall mole for orthopyroxene (difference between the M, and M, CFSE’s), which predicts the correct site enrichment. However, it is unlikely that such a small energy difference is responsible for the degree of ordering observed of the orthopyroxene. For olivine, BURNS(1970a) calculated site preference energies in between 0.8 and O-3kcal/ molefortheM,site-withnodetectableordering (BURNS,1970b). However,Mossbauer investigations of olivines by BUSHet al. (1970) did indicate a small amount of ordering of Fe in an Mg-rich olivine. In the o~hop~o~ene crystal structure (CHOSE, 1965) there are two six-fold coordination sites, M, and M2. Cations in M1 sites are each linked to oxygens bonded to only one silicon atom, whereas in M2 sites four of the oxygens are linked to one silicon atom and two are linked to two silicon atoms. The orthopyroxene studied by GHOSE (1965), with a composition Mg,.,, Fe,.,, S&O, has an essentially regular coordination polyhedron about M, with an average M-O distance of 2.09 H and a maximum deviation of this value of 0.07 8. The coordination polyhedron is highly distorted, four M-O distances average 2.10 A (2.119, 2.066, 2.175 and 2.037 A for O,, O,, 0, and 0, respectively) and the remaining two M-O distances of 2.405 MI,--0,) and 2.519 ,& (M%---0,), are both particularly long and involve bridging oxygens (Fig. 1). In the present discussion, the effective local symmetry for M, sites will be taken as C, (WHITE and HEESTER, 1967)and because the distortion of the M, site is so small, 0, symmet~ will be assumed. The structure of orthofe~os~ite (BOREAL,

Bonding in silicates: a.n assessment of bonding in orthopyroxena

%-Jig

253

o~~~~

5

01 Fig. 1. Projection of &heMI and MS coo&in&ion polyhedra on to (loo}. (After CHOSE,1965). 1966) is similar to that of the o~hop~oxene studied by GH~SE (1965) with a larger mean M-O distance for the Ma site than the M, site. However, whereas in the hypersthene sample studied by Ghose the smallest M-O distances in the M, and M1 coordination polyhedra are almost identical, (2.037 A and 2.036 A, respectively), in orthoferrosilite the smallest M,--0 distance is 2.013 A and the smallest Ml--O distance is 2,093 A. Similarly, in the orthopyroxene of composition Ca,,.,,Mg~,,Fe,.,,Si,O,r studied by BTJRNHAM et al. (1971), the smallest M-O distance is associated with the M, site (1.997 A compared with 2.086 A for the M, site). Absorption spectral measurements on orthopyroxenes have been obtained in polarised (BANCROFTand BURNS, 1967) and unpolarised radiation (WHITE and KEESTER, 1967). The slightly smaller value of the isomer shift (EVANS et a&, 1967) and the much smaller value of I-r,, (GHOSEand HAFNXR, 1967) associated with the Mz site of o~hofe~osilite suggest a higher degree of covalency associated with the M2 site. BURNHAMet al. (1971) in their comparative study of X-ray diffraction and resonant absorption measurements on orthopyroxene suggested that non-spherical electronic effects, most likely resulting from partially covalent bonding, contribute to the thermal vibration ellipsoid from the M, site, in general agreement with the above results. These data, taken together with X-ray emission spectroscopic data pertaining to bonding in simple oxides, and information concerning the nature and orientation of oxygens within the coordination polyhedra, enable us to deduce, in a qualitative manner, the scheme of bonding in orthopyroxene. Bonds between the Mz cation and the 0, and 0, ligands are likely to be weak because 0, and 0, are each bonded to two silicon atoms, with which they are likely to form covalent bonds, and also the large M%--0 distances make signifie~t orbital overlap improbable. Consequently, n-bonding of any kind is considered unlikely between Mz--0, and &I,--0,. If it is assumed that z is parallel with M,--0,, y will then be sub-parallel with M,---0,. Consideration of a model of the M, coordination polyhedron shows that the Fe d,, orbital then has the greatest potential to form a,l; 7r bonds--especially with 0, and to a lesser extent with 0, and 0,. d,, and d,, are less favourably oriented to form d-p r bonds and will interact to lesser degrees. Of the c&p rrbonds, d,, should be the most stabIe followed in order of decreasing stability by dcy and d,,. These deductions are in qualitative agreement with the absorption spectra assignments for the M, site (BANCROPTand BUEKS, 1967; WHITE and KEESTER, 1967), which suggests the reverse order to the above for the co~espon~ng ABMO’s. Other T-bonds are likely to

R. I(.~'NIONS and D. G. W. SMITH

254

form as a result ofm orbital overlap. The M,p, orbital is oriented to receive the maximum interaction with ligand 2~ orbitals and will form a stable BMO. The orientation of pa and p, is such that they will probably form similar, but lower stability bonds, than .pV. All of these pp bonds a,re likely to be more stable than the above d-p bonds. Of the p-p cr bonds, that involving 4~~ should be the most stable, interacting with 0, and 0,. The less favourably oriented 491~and 4~~ orbitals should interact to a smaller degree and form less stable bonds. The Sd,a+,z is likely to interact more strongly than 34% with the ligands to form G bonds-this is again compatible with the above cited spectroscopic data which suggests that the ABM0 resulting from interaction of 3d,a_,Bis less stable than that from 3d+ Some of these inferred features of bonding in the Mz coordination polyhedron are indicated in Fig. 2. IRON

SILICON

OXYGEN

-I-

Ml

Si I, iI

M2

4s 3P_ -s9ILL,,-.___ 3d

3s

3dff* 3 3dff’

tzg_%z__,~~

IP-

__h”_C__-- c-. ‘.

T

.P

3 4pnb enb tznb

ew!_._,-Al”

E

-_

b CL.-<_-, ‘.

at&__

I

1 3

2s Atomic

t,kG.

3dflb

_tz,_re,_--&

Orbitals

3d

b t2ub

LpUb 4siJb

a,rb

tp9 Motocular

Orbitals

atub

Fig. 2. Schematicsillustration of molecular orbital energy levels for Fe in the MI and M, sites of orthopyroxene. Energy levels shown are deduced from symmetry considerations and are not based on spectroscopic data for orthopyroxenes. Molecular orbital energy levels for bonding in the tetrahedrsl portions are based on SiO, (URCH, 1970).

The departure of the M, site from 0, symmetry is so small, that the MO energy level diagram in Fig. 2 has been constructed assuming full 0, symmetry. The energy levels of the BMO’s and ABMO’s are drawn assuming that the M, ligand interaction is similar to that deduced for Fe2* in simple oxide minerals (SMITH and O'NIONS, 197 1). This assumption is reasonable for the MI site, since each coordinating oxygen has a similar env~o~ment. The energy levels of the ABMO’s have been drawn fo be Gonsis~nt~ththe data of BANCROFT and BURNS (1967),assumingthat the d--p rr

Bonding in silicates:

an assessment of bonding in orthopyroxene

255

overlap between Fe located in M, and the ligands is similar in magnitude to that of the Fe 34, orbital and the ligands in the M, site. For comparative purposes the deduced bonding scheme in the Si-0 tetrahedra is shown, making the very simplifying assumption that bonding is similar to that in SiO, (URCH, 1970). Note also the participation of 0 2s orbitals for which there is good spectroscopic evidence (URCH, 1969). Because of the greater degree of covalence associated with the Fe-O bonds in the M, coordination polyhedron, and possibly the greater stability of the n-bonding orbitals, we would expect Fe 2+ to energetically favour the M, site over the M, site. In the case of orthopyroxene, these factors are thought to be more significant than merely the distribution of d-electrons between ABMO’s. Conversely, Mg shows a preference for the M, site where it forms more ionic bonds. These deductions are largely in agreement with those of RAMBERCJ(1952) concerning the preference of Fe2+ for more covalent environments compared with Mg. Of some interest at this juncture are the relative electron densities in bonding and non-bonding MO’s. In an isolated molecular unit, simple MO theory predicts the symmetries of bonding and non-bonding orbitals. However, in an infinite molecular network, such as a silicate mineral structure, orbitals which are non-bonding with respect to one unit may have a symmetry which permits interaction with a neighbouring molecular unit. Relative electron densities in bonding and non-bonding molecular orbitals predicted from simple MO theory are unlikely to be realised in practice. Indeed, the real density of electrons in non-bonding orbitals will always be less than the predicted. Related to this latter point is the simple observation that in simple compounds (MgO, FeO, etc.) insufficient valence electrons are available to fully occupy all of the predicted BMO’s. It is still not clear from spectroscopic evidence whether the correct concept is one involving sharing electrons between all of the predicted MO’s or whether MO’s are occupied in accordance with the aufbau principle . INTRACRYSTALLINE CATION DISTRIBUTIONS IN ORTHOPYROXENE EVANS, GHOSE and HAFNER (1967) demonstrated a temperature dependence of the Fe2+-Mg distribution in orthopyroxene using Mijssbauer spectroscopy, and GHOSE and HAFNER (1967) further showed a higher degree of order in metamorphic pyroxenes compared with volcanic pyroxenes. Investigations of cation distributions at different temperatures (VIRGO and HAFNER, 1969) indicated an average free energy exchange difference for Fe-Mg exchange of 3.65 kcal. Analysis of the Fe distribution data using reaction rate methods of MUELLER (1967,1969) enabled Virgo and Hafner to calculate approximate activation energies of ordering of 16.5 kcal mole-l and for disordering of 20 kcal mole-l. These energies are considerably less than the likely total Fe bond energy and clearly do not correspond to the breaking of all M-O bonds within the Fe coordination polyhedron. If the exchange mechanism is dependent upon the presence of vacancies within, and their migration through, the structure, then the above activation energies may correspond to exchange of Fe with a vacancy as follows M,O + M2F” + MIFe + M20, where zero denotes a vacancy.

256

R. K. G’NIONS and D. G. W. Sa61r~

The above reaction for disordering tells us nothing of atomic mechanisms. If the exchange process between Fe iu either M1 or MM, and a vacancy takes place by a ligand replacement-type reaction, i.e. Iigands are changed consecutively and at no time are all bonds broken, then we might expect such smaIZactivation energies. MUELLER (1970)in a discussion of the apparent cut-off in the ordering process in orthopyroxenes at approximately 48O”C, postulated an energy barrier to the disordering process which results from a two step mechanism for Fe-Mg exchange. Mueller estimated an activation energy of approximately 140 kcal mole-l associated with the Grst step. The cut-off temperature in this model then corresponds to the cross-over point between the two rate processes, the low-temperature one characterised by the bigher activation energy being operative below the cross-over point. This high activation energy associated with the low tem~rat~e process may correspond to the activation of vacancies (DIENES and I&MASK, 1965 ; MUEIJ;ER, 1970). The activation energy associated with the second step in the model would then correspond to the Fe exchange processes outlined above. Aokmowledgeme7tts-One of us (D. G. W. S.) acknowledgesGnancialsupport for this work from the National Research Councilof Canada and a NuffieldTravel Fellowshipduring the tenure of which this work w&s carried out. REFERENCES BAELE&JSENC?,J, (1962) In$ro&otiolz to l~ga~d~e~ them-y. McGraw-Hill. BALL~AUSE~C. J. and GRAY H. 3. (1964) ~0~~ orbital themy. Benjamin. B~Eonorr G. M. and Bnaxs R. G. (1967) ~~~ret~tion of the electronic spectra of iron in pyroxenes. Amer. ~~~~. 52,1278-1287. BUSH W. R., HAFNERS. S. &nd VIRGOD. (1970) Some ordering of iron a;nd magnesium St the octahedrally coordinated sites in a magnesium-rich olivine. Nature 227, 1339-1341. B~ENHAMC. W. (1966) Ferrosilite. Carnegie1st. Wash. Yearb. Bci, 285-290. B~RNHANC. W., OEASHIY., ILPIFNER S. S. and Vmao D. (1971) Cation distribution and atomic thermal vibrations in an iron-rich orthopyroxene. Amer. Mineral. 56, 850-876. BURNS R. G. (1970a) Mineralogical applications of crystal jield theory. Cambridge Univ. Press. BURNS R. G. (1970b) Crystal field spectra and evidence of cation ordering in olivine minerals. Amer. Mineral. 55, 1608-1632. COTTON F. A. (1964) Ligand field theory. J. Chem. Educ. 41,466-476. COTTONI?. A. and WILKINSONG. W. (1966) Advamed I?wrga&c Chemistry. Interscience (Wiley). COULSON C. A. (1961) VaEence.Oxford Univ. Press. COULSON C. A., R&DEI L. B, and STOCKERD. (1962) The electronic properties of tetr~~&l i~~~et~l~~ compounds. 1. Chsrge distribution. Proe. R~vy.SOG.London Ser. A, 270, 357372. CRUIO~SHAE~D. W. J. (1961) The role of 3d orbit& in = bonds between (a) silicon, phosphorus. sulphur or chlorine, and (b) oxygen or nitrogen. J. Chem. SOL 5486-5504. DIEEES G. J. and DA~SK A. C. (1966) The role of point defects in solid-state reactions. In Reactivity of solids, (editor N. M. Schwab), pp. 427-437. Elsevier. DODD C. G. and GLEN G. L. (1968) Chemical bonding studies of silicates and oxides by X-ray K-emission spectroscopy. J. Appl. Phys. 29, 5377-5384. DODD C. G. and GLEN G. L. (1969) A survey of chemical bonding in silicate minerals by X-ray emission spectroscopy. Amer. Mineral. 54, 1299-1311. EVANS B. J., GHOSE S. and HAFNER S. S. (1967) Hyperhne splitting of Fe5’ and Mg-Fe orderdisorder in orthopyroxenes (MgSiOs-FeSiOs) solid solution. J. GLeoE. 75, 306-322. GHOSE S. (1965) Mgs+-Fez-+ order in an orthopyroxene Mge.ssFer.,, S&O,. 2. kZristal+-. 122, 81-99.

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GHOSE. S. and HA~NER S. (1967) Mg2+-Fe %I-distribution in metamorphic end volcanic orthopyroxenes. 2. Kristallogr. 125, 157-162. MUELLERR. F. (1967) Model for order-disorder kinetics in certain quasi-binary crystals of continuously variable composition. J. Phys. Chem. Solids 28, 2239-2243. MUELLERR. F. (1969) Kinetics and thermodynamics of intracrystallinedistributions. Miner&. Sot. Amer. Spec. Paper 2, 83-93. MUELLERR. F. (1970) Two-step mechanism for order-disorder kinetics in silicates. Amer. Mineral. 55,1210-1218. MURRELL J. N., KEYCTLES. F. A. and TEDDERJ. M. (1970) Vulencetheory. Wiley. O’NIONS R. K. and %UTH D. G. W. (1971e) Bonding in SiO, and Fe,Os by oxgyen Ku emission spectra. Nature. Phys. Sci. 231,130-133. O’NIONSR. K. and &UTH D. G. W. (1971b) Investigations of the L,,,,,, X-ray emission spectra of Fe by electron microprobe. Part 2. The Fe Lir,iri spectra of Fe and Fe-Ti oxides. Amer. Mineral. 56, 1452-1463. ORQELL. E. (1964) An introductionto traltsitiola-metal chemistry: Eigand$eld theory. Methuen. PAULINUL. (1960) The na&re of the chemicalbond. Cornell. PHILLIPSJ. C. (1970a) Ionicity of the chemical bond in crystals. Rev. Mod. Phys. 42,317-356. PHILLIPSJ. C. (1970b) Bonds and bands in semiconductors. Science 169,1035-1042. RA~~BERU H. (1952) Chemicalbonds and distributionof cations in silicates. J. UeoZ.60,331-355. SMITHD. G. W. and O’NIONS R. K. (1971) Investigations of the L,,,,,, X-ray emissionspectra of Fe by the electron microprobe. Part 1: Some aspects of the Fe L,,,,,, spectra from metallic iron and haematite. J. Phys. D: Applied Phys. 4, 147-159. SMITH D. G. W. and O’NIONS R. K. (1972a) Investigations of bonding in some oxide minerals by oxygen Ku emission spectroscopy. Chem. Geol. 9,29-43. SMITH D. G. W. and O’NIONS R. K. (1972b) Investigations of bonding by oxygen Kcr emission spectroscopy: further evidence concerning the true character of the oxygen Ku emission band.

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for the spectra of