THE EFFECT OF LATTICE SUBSTITUTIONS ON THE DERIVATION OF QUANTITATIVE SITE POPULATIONS FROM THE MÖSSBAUER SPECTRA OF 2 : 1 LAYER LATTICE SILICATES

(1)

HAL Id: jpa-00216695

https://hal.archives-ouvertes.fr/jpa-00216695

Submitted on 1 Jan 1976

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

THE EFFECT OF LATTICE SUBSTITUTIONS ON

THE DERIVATION OF QUANTITATIVE SITE

POPULATIONS FROM THE MÖSSBAUER

SPECTRA OF 2 : 1 LAYER LATTICE SILICATES

B. Goodman

To cite this version:

B. Goodman. THE EFFECT OF LATTICE SUBSTITUTIONS ON THE DERIVATION OF

QUANTITATIVE SITE POPULATIONS FROM THE MÖSSBAUER SPECTRA OF 2 : 1

(2)

JOURNAL DE PHYSIQUE Colloque C6, supplkment au no 12, Tome 37, Dtcembre 1976, page C6-819

THE EFFECT OF LATTICE SUBSTITUTIONS ON THE DERIVATION OF

QUANTITATIVE SITE POPULATIONS FROM THE MOSSBAUER SPECTRA

OF

2 :

1 LAYER LATTICE SILICATES

B. A. GOODMAN

The Macaulay Institute for Soil Research, Craigiebuckler, Aberdeen, AB9 245, Scotland

Rbsumb. - La contribution du rkseau au gradient de champ klectrique dans deux silicates

a

structure rkticulaire feuilletke a 6te calculke a partir d'un modde de charges ponctuelles. En parti- culier on a determine les contributions des atomes

a

moins de 20A de distance et les effets obtenus par substitution des sites cationiques voisines

a

moins de 5 8 de distance. Les rksultats montrent

que la contribution du rkseau au gradient des champs Bectriques au site Fe2 (avec des groupes

cis OH) est plus petite que celle au site Fe1 , mais que le premier est le plus sensible aux substitutions de sites cationiques voisins.

On montre que les spectres obtenus lorsque la substitution est modkrke aux sites octakdrals, s'ajustent d'une manikre satisfaisante a deux doublets pour chaque site. On discute le dkpouillement des spectres des mineaux par comparaison

a

ces calculs et on explique l'importance du choix des modhles sur les populations des sites.

Abstract.

-

Calculations of the lattice contributions to the electric field gradients at the two types of structural site in a layer lattice silicate have been performed using a simple point charge model. In particular, contributions from atoms c 2 0 8 distant and the effects of substitutions at neighbouring cation sites < 5 8 distant have been assessed. The results indicate that the lattice contribution to the electric field gradient at the Fe2 site (with cis OH groups) is smaller than that at the Fe1 site, but that the former is the more sensitive to substitutions at neighbouring cation sites.

It is shown that spectra generated with a moderate degree of substitution at neighbouring octahedral sites can be fitted satisfactorily with two doublets for each site. The fitting of spectra from minerals is discussed with.reference to these calculations and the effect of the choice of model on the derived site populations is emphasised.

1. Introduction.

-

The basic structure of the layer lattice silicates consists of composite sheets in each of which a layer of octahedrally coordinated cations is sandwiched between two identical layers of linked (Si, Al) 0, tetrahedra. The octahedral cations have four coordination positions satisfied by 0's from the silicate tetrahedra, with the two remaining positions occupied by OH groups. The composite sheets are held together by further cations which may have up to 12 coordination. These bonds are relatively weak and 'can be readily broken to produce a cleavage plane so that the materials are in general of a platy appea- rance. In micas the interlayer sites are usually completely filled with K or Na the principal cations present, and these balance the negative charges created in the composite sheets as a result of cationic charge deficiencies. These deficiencies can arise from substitution of a trivalent ion for silicon in a tetrahedral site and/or from substitutions in the octahedral layers.

The structures can be divided into two classes, dioctahedral and trjoctahedral, depending on whether approximately

3

or all of the octahedral sites are occupied. However, limited substitutions of the type 3 X M2+ for (2 X M3'

+

1 vacancy) may occur in the

dioctahedral structures and 2 X M3+ for 3 X M2+ in

the trioctahedral minerals. These substitutions main- tain the average charge balance of 2

+

per site, but, as stated above, further substitutions which produce a surplus or deficiency of octahedral charge can occur. In the tetrahedral layers replacement of some silicon by a trivalent cation, usually aluminium, is common, and the extent pf such substitution may be conside- rable especially when there is a surplus of cation charge in the octahedral layers e. g. in muscovite the Si : AI ratio in tetrahedral sites is approximately 3 : 1, with an average charge per octahedral site of 2 + , while in biotites the Si : A1 ratio may be somewhat lower with a corresponding increase in the average charge per octahedral site. The octahedral and tetrahedral cations may be randomly distributed throughout the structures or, alternatively, ordering of the cations may occur in either or both types of coordination site [l].

It will be obvious, therefore, with substitutions occurring in both the octahedral and tetrahedral layers, that the cation sites will be only partially defined in terms of the anions attached to them since the neighbouring cations may differ throughout the structure. Thus, if these neighbouring cations have some influence on the electric field gradient at the site

(3)

in question, different Mossbauer spectra can be obtained from iron in crystallographically similar sites. As a result of this, instead of each site being characterized by one doublet in the Mossbauer spectrum, the situation will exist in which each site can be characterized only by an envelope of peaks, the distribution within this envelope being governed by the overall substitutions within the lattice.

The peaks in the Mossbauer spectra corresponding to iron in the individual sites in the layer lattice silicates are not well resolved from one another ; in fact only asymmetrically broadened peaks are usually obtained. It is possible, therefore, that the range of distribution of quadrupole splittings from one site may be comparable to or even greater that the difference between the quadrupole splittings from different sites. If this is the case then the interpretation of the Moss- bauer spectra will be extremely difficult, and probably impossible, without a detailed knowledge of the cation contents of the sample being examined.

Because of this problem some theoretical calculations have been performed on the lattice contributions to the electric field gradients at the two octahedral sites in a lattice silicate, using the structure published for ferriannite [2].

2. Computation of the lattice contributions to the electric field gradient. - The components

vj

of the electric field gradient (efg) tensor may be written :

-

where dij = 1 for i = j, = 0 for i f: j and xik is the component (i = X, y, z) of the radius vector rk from

the origin to the ion k having charge qk. Calculation of the various Vij values was performed using the atomic coordinates of ferriannite [2] and the normal charges for each atom. Because a cartesian axis system is required for the efg calculation and ferriannite is monoclinic, the first stage was to express all atoms being considered relative to mutually orthogonal axes. The Vij values were then calculated for each atom and summed. The resulting matrix was then dia- gonalized to give the principal values of the efg tensor. Values of the lattice contribution to the quadrupole splitting, ' A ' = V,,(1 +q2/3)1/2 and q = (Vxx- Vyy)/V,,

were obtained from the program using a value of

-

9.14 for y , and with Vxx V,, V,, being ordered in the usual way with

I

V,,

I

>

I

V,,

1

>,

I

V,,

I.

Several different calculations were performed using the program. Firstly the contribution to the efg at each site arising from charges on neighbouring 0 and OH only was computed. This calculation was then extended to take into account the charges on all atoms within the lattice up to 20

A

distant from the central atom. However, the main object of this work was to examine the distribution of quadrupole splittings which could arise from substitutions in tetrahedral

or octahedral sites close to the central atom. This was achieved by calculating the contributions to the efg tensor from atoms in tetrahedral or octahedral sites, respectively,

<

5

A

away from the central atom. ,This contribution was then subtracted from the total lattice contribution to give the efg tensor for all atoms except the neighbouring tetrahedral or octahedral cations. The charges on these sites were then generated by a Monte Carlo-method for various ratios of possible charge components. 4 000 trials were usually performed in order to ensure adequate randomization of charge distribution. For each trial ' A ' was calculated from the trace of the matrix of V'. A Mossbauer spectrum was then generated by assuming peaks of Lorentzian shape and full width at half height of 0.2 mm/s for each component of the efg distribution. Finally this synthetic spectrum was fitted with 1 or 2 doublets using the usual least squares fitting procedure.

3. Results and Discussion.

-

The calculated values of

'

A ' for an atom at each of the crystallographically distinct sites are shown in table I. Values obtained from a consideration of the neighbouring 0 and OH groups alone are considerably larger for each site than the corresponding values obtained by considering the whole lattice < 20

A

distant. These latter values are similar to the experimental quadrupole splittings obtained from Fe3+ in micas (e. g. [3]), indicating perhaps that appreciable contributions to the quadrupole splitting arise from atoms not directly attached to the central iron. The value of

'

A ' for the site labelled Fel, which has trans OH groups, is somewhat larger than that from the Fe2 site with cis. OH groups (l).

This is the order that has been assumed by most authors when interpreting Mossbauer spectra of layer silicates, but the difference between the values is much less than the 2 : 1 ratio predicted by a point charge model for regular octahedral coordination.

The effects on the lattice contributions to the quadrupole splitting of octahedral and tetrahedral cation substitutions have been considered separately for each site. Spectra generated as described in the pre- vious section were fitted with the usual least squares fitting programme. Since no random scatter was introduced into the calculated data, X' should be zero for a perfect fit. In fact if X'

<

100 it is unlikely that the line shape effects producing the misfit would be detect- ed in experimental Mossbauer spectra. The computed values of

'

A

',

the peak full width at half height,

I',

and X' are also listed in table I for various octahedral and tetrahedral substitutions.

On fitting the spectra to single doublets, for tetrahedral substitutions

r

and

x2

both increased for the (1) Some confusion exists in the literature because different

(4)

THE EFFECT O F LATTICE SUBSTITUTIONS ON THE DERIVATION

Computed parameters for the spectra generated from the calculated electricJield gradient distributions at the octahedral cation sites in ferriannite

Neighbouring 0 , OH only All atoms < 20 L%distant (all tetra-

hedral sites 4+)

All atoms c 20 A but with a distribution of charges at octahedral sites < 5 A distant

2+ : 3+ : vacancy = 94 : 4 : 2

All atoms c 20 A but with a distribution of charges at tetrahedral sites < 5 A distant 4 + : 3 + = 9 0 : 1 0 80 : 20 50 : 50 a : 1 doublet fits. b : 2 doublet fits. ' A '

r

yj

-

- -

1.47 0.2

-

0.85 0.2

-

Fe1 ' A '

-

- 1.21

-

1.23

-

1.24

-

Fe2 ' A '

-

1.03

-

1.02

-

1.02

-

M2 site as the tetrahedral M3+ content was increased from 10 to 50

%.

The M1 site, however, was quite insensitive to these substitutions. For substitutions at octahedral sites,

r

and particularly

x2

increased mar- kedly as the proportion of (2 X M3+ -t 1 vacancy)

was increased from 5 to 15

%

of the sites. Again the M2 site was appreciably more sensitive than the M1 site to substitutions at neighbouring lattice sites. The spectra resulting from substitutions at neighbouring octahedral sites were also fitted with two doublets, and in each case much lower values of

x2

were obtained. A typical example is illustrated in figure 1 which

compares the qualities of one and two doublet fits to one set of calculated data. It is interesting to note that the main component from the two doublet fit has similar parameters to the single doublet fit and that the addi- tional component has a significantly larger value of

'

A

'.

Thus in a practical situation the effect of octahedral substitution of the type considered here is the production of a spectrum which is best fitted with two doublets for each site, with the minor components in each case having

'

A ' values about 40-50

%

larger than the major components.

The values of ' A ' calculated here are qualitatively similar to those obtained experimentally for two doublet fits to the Fe3+ sites in weathered biotites [5].

In that work an increase in the relative contribution to l V

the spectrum of the component with the larger qua- V e l o c ~ t y mm. S " . drupole splitting was observed as the degree of oxida-

tion of the lattice increased. This was interpreted FIG. 1. - Computer fits to the Mossbauer spectrum calculated from the lattice contributions to the electric field gradient at the

(5)

C6-822 B. A. GOODMAN the present paper). The present results, however,

indicate that increasing importance of a component with a larger than usual quadrupole splitting for Fe3+ should accompany the oxidation and partial remo- val of iron from the lattice, so it may not be neces- sary to assume any great changes in relative site pre- ferences for iron during biotite weathering.

The situation for Fe2+ is rather more complicated because the quadrupole splitting consists of valence and lattice components with the former being dominant. It might be expected however that variations in the lattice contribution would produce a spread of quadrupole splittings similar to that discussed for the Fe3+ case. Figure 2 illustrates a computer fit to the spectrum of a biotite using 6 doublets based on the model discussed above. If peaks AA' and CC' corres-

pond to Fe2 sites and peaks BB' and DD' to Fe1 then

3 2 1 0 l -2 -3

I l I I I l I

V e l o a ~ t y m m . S-'.

FIG. 2.

-

A computer fit to the Mossbauer spectrum of a bio- tite using 6 doublets. Parameters were constrained such that each component of a doublet had equal areas and widths. Additio- nal constraints were : - widths AA' = BB' = CC' = DD' ;

widths EE' = FF' ; areas CC' =

+

AA' ; areas DD' =

t

BB' ;

centroid CC' = AA' ; centroid DD' = BB' ; centroid FF' = EE' flat baseline.

the computed areas indicate 45 and 12

%

of the iron, respectively in these sites. This fit then implies a preference of Fe2+ for the Fe2 site of almost 2 : 1 and this ratio would be even greater if the assignments of BB'

and CC' were reversed. However, when this same spectrum was fitted in the usual manner with 3 dou- blets (2 corresponding to Fe2+ and 1 corresponding to Fe3+) the two Fe2+ components had similar areas thereby implying a preference of Fe2+ for the Fe1 site. The problem, therefore, of interpreting Mossbauer spectra in order to obtain quantitative site populations must first of all be to obtain the correct model on which to base the computer fits.

A number of criticisms can be levelled against the

calculations described in this paper and some of the more important of these will be discussed below.

Firstly a completely ionic model has been assumed throughout the calculations. Covalency effects will reduce the net charges on all of the atoms thereby decreasing the lattice contributions to the quadrupole splitting. However, because of the low degree of symmetry at the lattice sites in question there will be a non-zero valence constribution to the quadrupole splitting and this will take the same form as the calculated contributions from the nearest neighbour atoms. Also MO calculations on iron-oxygen compounds [6] have indicated that the atomic charge of the oxygen is reduced to

--

-

1.6. The charge on cations might be expected to be reduced by a similar factor so that the results quoted in table I may represent over-estimates by

-

20

%

of the lattice contributions to the quadrupole splittings.

Secondly, only lattice substitutians which retain an average site charge of 2 +have been considered at octahedral sites. Deviations from this value are common and biotites for example often have an average site charge

>

2+ [7]. Thus in addition to the generation of vacancies within the lattice, sometimes to levels greater than those considered in these calculations, further substitutions of M3+ for M 2 + also occur. The

lattice contributions to the efg may therefore have a greater range of values than those predicated by these calculations.

Thirdly, the consideration of a random distribution of charges at neighbouring cation sites may lead to too great importance being given to combinations of cations which produce a high local charge imbalance. Also variation of charges on atoms > 5

A

from the site in question have been ignored. Consideration of these effects would be expected to modify the composition of the envelope of efg values which make up the spectrum.

Fourthly the application of these calculations to Fe2+ is not straightforward because of complica- tions involving the valence contribution to the efg. In addition to the problem of partial occupation of excit- ed state orbitals at ambient temperatures the actual atomic orbital composition of the ground state is unknown because of the low degree of symmetry, particularly at Fe2 sites. It may also vary slightly from site to site because of differences in neighbouring atoms. The calculation of efg values for ~ ein these ~ + structures is therefore very complex but it is expected that the lattice contributions will produce variations in the quadrupole splittings similar to those calculated for Fe3

+.

(6)

THE EFFECT OF LATTICE SUBSTITUTIONS ON THE DERIVATION C6-823 substitution produce a greater effect at Fe2 than at

Fe1 sites. Since the amounts of lattice substitutions vary from one sample to another it is not appro- priate to simply produce a new line shape function for fitting spectra. In fact, interpretation of the results from any computer fit to a layer lattice silicate spectrum in terms of quantitative site populations can scarcely be justified without at least a detailed knowledge of the analytical composition of the sample. The effects described here will be particularly impor-

tant in spectra obtained from intermediate phases in oxidation or reduction reactions, since in these cases a random distribution of vacancies, divalent and trivalent ions may be present.

Acknowledgement.

-

The assistance of

Dr. F. W. D. Woodhams, Department of Natural Philosophy, University of Aberdeen, in the perfor- mance of the electric field gradient calculations is gratefully acknowledged.

References

BAILEY, S. W., Amer. Mineral. 60 (1975) 175. [6] TRAUTWEIN, A., KREBER, E., GONSER, U. and HARRIS, F. E., DONNAY, G., MORIMOTO, N., TAKEDA, H. and DONNAY, J. Phys. Chem. Sol. 36 (1975) 325.

J . D. H., Acta Cryst. 17 (1964) 1369. [7] DEER, W. A., HOWIE, R. A. and ZUSSMAN, J., Rock-forming GOODMAN, B. A., Mineral. Mag. 40 (1976) 513. Minerals Sheet Silicates (Longmans, London) 1962 [4] GOODMAN, B. A., Amer. Mineral. 61 (1976) 169. Vol. 3, p. 58.