EPSC501 Crystal Chemistry

WEEK 6

Compositional variation in zircon

How does its structure adjust?

Images from http://gsc.nrcan.gc.ca/diamonds/kirkland/kimberlite_e.php

A potential final exam question: why should Cr give different colours in garnets and diopside?

Problem set #2: Why should Fe2+ give different colours in almandine and olivine?

Zircon and zircon-like minerals & compounds

General formula ATO4

Where

- T is a high field-strength element in tetrahedral coordination

- AO8 are larger coordination polyhedra

What is a high-field strength element?

From MIT Open Courseware http://ocw.mit.edu12.479 Trace-Element Geochemistry Spring 2009

= Low Field Strength Elements

Ionic radii from Whittaker and Muntus(1970)

All HFSE are considered incompatible.However, these HFSE partition do not always partition in the same manner...

Note that the crystal radii of Shannon (1976) would give different values.

Ionic radii for use in geochemistryWhittaker, E. J. W.; Muntus, R.

Geochimica et Cosmochimica Acta, 1970, vol. 34, Issue 9, pp. 945-956

The ionic radii proposed by and as the effective values in oxides and fluorides have been analysed for their conformity with the radius ratio principles of crystal chemistry. It is shown that a set of values intermediate between the "IR" and "CR" values of and provides the best conformity in this respect, and a table of the values adopted is provided in periodic form.

These values correspond to a VI co-ordinate oxygen radius of 1.32 Å and a VI co-ordinate fluorine radius of 1.25 Å, and the radii of the cations are therefore appreciably larger than those previously accepted, although not as large as and 's "CR" values. It is suggested that the radii obtained are the most suitable for use in silicate geochemistry, and constitute a major improvement over previous values for this particular purpose. Although it is impossible to maintain the accuracy with which radius sums represent interatomic distances and at the same time to extend the range of the radii to other anions, it seems desirable to provide compatible (although only very approximate) values of radii for Cl, Br, I, S and Se anions. Use of the new cation radii with these anion radii cannot be expected to be an improvement over the use of older radii, but should be about as satisfactory. The changes of cation radii relative to one another, as compared with radii, are tabulated in order to draw attention to their possible geochemical significance, and the implications are discussed in the case of scandium.

DOI: 10.1016/0016-7037(70)90077-3

Atomic and ionic radii: a comparison with radii derived from electron density distributions

G. V. Gibbs, Osamu Tamada and M. B. Boisen Jr.

Physics and Chemistry of Minerals (1997)Volume 24, pp. 432-439

The set of radii proposed by Whittaker and Muntun(1970) is an example of the different goals of geochemists and crystallographers. The latter wish to predict the stability of crystal structures and the former are interested in the geochemical behavior of individual elements/ions in igneous melts and in minerals. And chemists (see below) have other ideas still…

Finch and Hanchar (2003) stress that some properties of zircon are related to the dominant direction of A-O and T-O bonds and the edge-sharing among AO8 and TO4

- habit

- prismatic (elongated along c axis)

- cleavage

{110} (best seen by looking at the structure down c axis)

Why does this make sense? Look at the structure using XtalDraw… The bonds are dominantly along the a and b axes rather than along the oblique [110] directions.

Because of the large charge on Zr4+ and Si4+, the Zr-O and Si-O bonds are strong and don’t much stretch nor compress.

The thermal expansion of zircon (when heated) is quite low: an average (bulk) coefficient of thermalexpansion (β) of approximately 4.5 × 10-6/°C.

- As would be expected from the structure, thethermal expansion of zircon is anisotropic

- expansion along [001] greater than- expansion along <100>… i.e. a1, a2 axes where the AO8 and TO4 polyhedra share an edge.

- On the other hand, zircon is one of the most incompressible silicate minerals known.

Are these coordination polyhedra distorted?

How can we tell?

What might be the reason?

How does this help accommodate compositional variation?

Zircon, ZrSiO4

Robinson K, Gibbs G V, Ribbe P HAmerican Mineralogist 56 (1971) 782-790 The structure of zircon: A comparison with garnet 6.607 6.607 5.982 90 90 90 *I4_1/amd0 -.25 .125atom x y z B(1,1) B(2,2) B(3,3)...Zr 0 .75 .125 .00096 .00096 .0012Si 0 .75 .625 .0014 .0014 .00270 0 .0661 .1953 .0037 .0031 .0029

Note that this is a special setting, with origin at 0 -.25 .125

The corresponding Wyckoff sites are:

Zr on Wyckoff position 4a

Si on Wyckoff position 4b

O on Wyckoff position 16h

Zr4Si4O16 or 4*ZrSiO4

Z = 4 formula units/cell

Zircon is tetragonal and crystallizes in space group I41/amd.

Both A and T cations (Zr4+ and Si4+) occupy special positions (4a, 4b) with site symmetry -4 2m.

(We saw how to check on this, last time… The positions have different Wyckoff site labels because they are surrounded by a different arrangement of oxygen atoms.)

The SiO4 group is not a perfectly symmetrical tetrahedron.

Is this common in silicate minerals?What about other minerals with TO4 or TS4 groups?

The SiO4 tetrahedra show different degrees of distortion among silicate minerals.

What are the Si-O bond lengths in zircon?

(1.62Å)

What about the O-O distances?

They aren’t identical: 2.75Å and 2.43Å… See the printed file, from the AMC Hazen & Finger (1979).

(This is why the site symmetry does not include a -3 rotoinversion axis, as the tetrahedra do in spinels.)

What else is changing? Find, in the geometry file, where you check on the O-Si-O angle.

The two O-Si-O angles in the SiO4 group of zircon are approximately 97° and 116° (geometry file for a zircon X-rayed by Hazen and Finger, 1979).

The O-O distance along the polyhedral edge shared with the ZrO8 polyhedron is 2.43 Å(opposite the smaller O-Si-O angle) and 2.75 Åalong the unshared edge (opposite the larger O-Si-O angle).

Is the same effect observed in the SiO4 group for the garnet structure? Look up a geometry file in XtalDraw.

What about other minerals? In which structures is the tetrahedron “free” to distort, or constrained by symmetry to keep the same bond lengths and angles?

Chalcopyrite CuFeS2

Fluorite CaF2

Spinels: magnetite, chromite, gahnite

Apatite Ca5 (PO4)3 (OH,F,Cl)

Diamond C

Quartz SiO2

Each O atom is bonded to:- one Si atom, 1.62 Å and - two Zr atoms

at 2.13 and 2.27 Å

Zircon versus garnet

Similarities:

MeO8 polyhedra

SiO4 polyhedra

Each O atom is bonded to:- one Si atom, 1.63 Å and - one Al atom, 1.89 Å- two Mg atoms

at 2.20 and 2.34 Å

In pyrope (garnet)

In almandine (garnet)Each O atom is bonded to:- one Si atom, 1.63 Å and - one Al atom, 1.90 Å- two Fe atoms

at 2.22 and 2.38 Å

The Si-O bond length is fairly constant among silicate minerals. But the O-Si-O angle varies.

In zircon-like compounds, A site cations range from:- low field-strength cations such as Ca2+ in chromatite CaCrO4Each oxygen is bound to...2 A-cations, 1 T-cationCa2+ -- O: ev = 0.25* ... 2 bonds provide 0.50* Cr6+ -- O: ev = 1.50* ... 1 bond provides 1.50*

(* valence units)When A=Zr4+, A—O, ev =0.50*

T=Si4+, T—O, ev =1* .... 2A—O + T—O =1*

- high field-strength cations such as Ta5+ and Nb5+ in (Ta,Nb) BO4

Ta5+ -- O, ev = 0.625* ... 2 such bonds = 1.25*B3+ -- O, ev = 0.75* .... 1 bond = 0.75*

Xenotime (REE)PO4REE+3—O, CN=8, bond = 0.375 valence unitP5+--O, CN=4, bond strength =1.25 valence unit2 REE-O bonds + 1 P—O bond = 0.75 + 1.25 = 2 v.u.

Consider the hypothetical intermediate end-member xenotime50zircon50 : (Zr.5REE.5)(Si.5P.5)O4Zr—O: 0.5 v.u.; REE—O: 0.375 v.u. Sum = 0.875 v.u.P—O: 1.25 v.u.; Si—O:1.0 v.u.

Any oxygen will bond to P+Zr+REE (total: 2.125 v.u.) or will bond to Si, Zr + REE (total: 1.875 v.u.)

The P-O bond (1.54Å) is shorter than the Si-O bond (1.62Å). The valence excess (“overbonding”) or deficit (“underbonding”) to individual oxygen ions creates strain (destabilizes) the structure.

This may be one reason for non stoichiometry in zircon…

Hanchar JM, Finch RJ, Hoskin PWO, Watson EB, Cherniak DJ, Mariano AN (2001)

Rare earth elements in synthetic zircon: Part 1. Synthesis, and rare earth and phosphorous doping.

American Mineralogist, vol. 86, pp. 667-680

Where are the interstitial sites in zircon? Go back to XtalDraw. There are “channels”along the oblique [110] directions, between the polyhedra.

Effect of repulsion between cations on the crystal structure... ATO4

Axial ratios (c/a) vary from- 0.869 (for chromatite, CaCrO4)to0.908 (for hafnon, HfSiO4)

What is happening?... Is the repulsion getting stronger along the c axis (T and A cations) or along the a axis (where AO8 are side by side).Compare the product of charges A*T (c axis) and A*A cations (a,b axis)... What goes up or down?

What do you expect for ZrGeO4? Its c/a = 0.936…

Chromatite (CaCrO4) is a rare chromate isostructuralwith zircon (Weber and Range 1996).

The CaO8 dodecahedron in chromatite is larger than the ZrO8 dodecahedron in zircon, and the CrO4tetrahedron, which is also slightly larger than the SiO4 tetrahedron in zircon, is less distortedthan in zircon (compare their O-cation-O angles).

This can be rationalized by there being less repulsion between Ca2+ and Cr6+ in chormatite compared to Zr4+ and Si4+ in zircon.

The c axis (vertical) lengthens if the A, T cations are larger (e.g. Ge4+ vs Si4+) or more highly charged (Zr4+ vsCa2+).

The a1, a2 axes (horizontal and perpendicular to page) lengthen when the A cations (in edge-sharing AO8 polyhedra) are more highly charged, as they repulse each other.

Next week (Week 7, Tuesday February 16)

We look at the relationship between mineral hardness and the individual bond strengths and bond orientations within their structure.

Gather data on your minerals’ hardness and have a list of their bonds, bond lengths, C.N. for their cations and anions. Be ready to show us where are the weakest bonds in the structure using XtalDraw.

Two articles are posted as readings in “Week6 Notes and Readings”, on www.eps.mcgill.ca/~courses/c186-501/