Chapter 3. Mineral Crystal Chemistry

3.1 Elemental Abundances

The distribution of solar element abundances is a consequence of element building in stars. Our solar system condensed from a gas which was produced from an exploding star (nova). The distribution (abundance) of the various elements is a function of the fusion cross section and the neutron capture cross section of the various parents and the neutron flux and other conditions in the parent star. Elements up to Fe (iron, Z=26) formed by direct fusion of lighter elements. The rest have formed by neutron capture and beta-decay.

Elements of even atomic number and isotopes of even atomic weight are the most stable and hence have the greatest abundances. Alpha-particle stability is a prime example.

The crustal abundances result from the convoluting of solar abundances by the chemical reactions in earth's accretionary processes. The accretionary processes are essentially chemical processes as opposed to nuclear reactions of the stars. H, He and the other noble gases plus C, N, S and the gases CH3, H2S, N2, and NH3 remained in the gaseous state by the time earth condensed and are hence called atmophile elements. They are strongly depleted in the earth relative to their abundances in solar system as a whole. As a result of the post-accretion differentiation of the earth, Fe, Ni, Co and related elements have been concentrated in the metal phase (i.e. the earth's core) and are called siderophile elements. They are strongly depleted in the earth's crust relative to their solar abundances, but are believed to be present in the earth as a whole in approximately their solar abundances. Those elements which predominantly bond with oxygen and are concentrated in the mantle and the crust are called lithophile elements. These lithophile elements have closed (filled) outer electron shell ionic configurations. These elements are enriched in the Earth's crust relative to their solar abundances. Elements which prefer to bond with sulfur are called chalcophile elements. These elements are believed to have separated with the siderophiles into the core and are depleted in the earth's crust, but to a lesser degree than the siderophiles. This geochemical classification of elements roughly follows the type of chemical bonds an element forms and is fundamental to geochemistry and mineralogy. This classification is as follows:

Four Classifications 1. Atmophile (A) - noble gases and covalently bonded gaseous molecules. The atoms and molecules are bonded by weak Van der Waals forces and so these elements remain gaseous at room temperature.

2. Siderophile (S) - The metals near iron in the periodic table (i.e. the transition metals) that exhibit metallic bonding.

3. Chalcophile (C) - The elements that bond to S, Se, Te, Sb, and As. These bonds are predomi nantly covalent in character.

4. Lithophile (L) - Those elements which form ionic bonds generally have filled outer electron shells. They typically bond to oxygen in silicates and oxides.

Fig 3.1. The geochemical periodic table of the elements showing the geochemical classification of the elements. Those elements indicated with an X are naturally radioactive witha sufficiently short half-life that they do not have an independent geochemistry. That is, they may exist in nature but at very low abundances and short half life that they do not form their own minerals.

The relative solar and crustal abundances are given in Table 3.1 for the naturally occurring elements

Table 3.1. Element Abundances Given in log10 of Numbers of Atoms Per 106 Si Atoms.

Element	Solar	Crustal	Class	Element	Solar	Crustal	Class

1. H 10.7 5.2 A 44.Ru 0.2 -2.0 S 2. He 9.6 0.0 A 45.Rh -.5 -2.3 S 3. Li 1.2 2.5 L 46.Pd 0.1 -2.0 S 4. Be -.1 1.5 L 47.Ag -.5 -.7 C 5. B .8 2.0 L 48.Cd 0.1 -.7 C 6. C 7.2 3.2 A 49.In -1.0 -1.1 C 7. N 6.7 2.2 A 50.Sn 0.23 0.23 C,L 8. O 7.4 6.5 L 51.Sb -.7 -.8 C 9. F 3.4 3.5 L 52.Te 0.49 -2.1 C 10.Ne 6.6 0.0 A 53.I -.4 -.4 L 11.Na 4.5 5.1 L 54.Xe 0.5 0.0 A 12.Mg 6.0 4.9 L 55.Cs -.7 .4 L 13.Al 4.9 5.5 L 56.Ba 0.7 3.5 L 14.Si 6.00 6.00 L 57.La -.3 1.3 L 15.P 3.9 3.5 L 58.Ce 0.1 1.6 L 16.S 5.9 2.9 C 59.Pr -.7 -.2 L 17.Cl 3.3 2.6 L 60.Nd -.1 .3 L 18.Ar 5.5 0.0 A 62.Sm -.6 .6 L 19.K 3.3 4.8 L 63.Eu -1.0 -.1 L 20.Ca 4.9 5.0 L 64.Gd -.4 .5 L 21.Sc 1.5 1.7 L 65.Tb -1.2 -.2 L 22.Ti 3.4 4.0 L 66.Dy -.4 .3 L 23.V 2.8 2.4 L 67.Ho -1.0 -.1 L 24.Cr 4.1 2.3 L 68.Er -.6 .2 L 25.Mn 3.8 3.2 L 69.Tm -1.4 -.5 L 26.Fe 5.4 5.0 L,C,S 70.Yb -.7 .3 L 27.Co 3.3 1.6 S 71.Lu -1.4 -.5 L 28.Ni 4.7 2.1 S 72.Hf -.5 .2 L 29.Cu 2.6 1.9 C 73.Ta -1.7 .1 L 30.Zn 2.8 2.0 C 74.W -.8 -.1 L 31.Ga 1.5 1.3 C 75.Re -1.2 -3.2 S 32.Ge 1.9 0.3 C 76.Os -.1 -2.6 S 33.As 0.6 0.4 C 77.Ir 0.0 -3.3 S 34.Se 1.4 -1.1 C 78.Pt 0.15 -2.3 S 35.Br 0.7 0.5 L 79.Au -.7 -2.7 S 36.Kr 1.4 0.0 A 80.Hg -.2 -1.4 C 37.Rb 0.6 2.0 L 81.Tl -.9 -.6 C 38.Sr 1.4 2.6 L 82.Pb 1.1 .8 C 39.Y 0.7 1.6 L 83.Bi -.7 -1.0 C 40.Zr 1.4 2.3 L 90.Th -1.4 .5 L 41.Nb -.05 1.3 L 92.U -2.0 -.1 L 42.Mo 0.2 0.2 C

Fig. 3.1. This is a plot of the logarithm of relative (solar) abundance versus atomic number. It shows that the even-numbered elements are more abundant than odd-numbered elements and that there is a peak in abundance at about Fe and abundance falls off at higher atomic numbers. This curve indicates the efficiency of nucleo-synthesis and results from the nuclear processes in the precurser star to our solar system.

3.2. Chemical Bonding

3.2.1. Ionic Bonding

Ionic bonding is dominant in the non-opaque minerals and involves a complete transfer of electron(s) from cation to anion. This allows the atoms to be treated as if they were point charges. Such charges (ions) attract each other until they approach so closely that the electron orbitals repel each other. The energy of electrostatic attraction may be expressed as U = A q1 q2/r or for a charge of 1e on each ion the above equation becomes

U = A e2/r When ions begin to touch the electrons begin to repel each other.

The repulsive energy that arises is of the form:

U = B exp(-r/a)

where a = the constant related to the ionic radius sum ro such that a = 0.1 ro. The sum of the energies from attractive and repulsive forces can be expressed as

U = A e2/r + B exp(-r/a)

and can be plotted as a function of distance.

For NaCl a minimum in the sum occurs at about 2.8 Å separation which is equivalent to the sum of the ionic radii of Na and Cl. At room temperature we have ionic crystals of NaCl. The same would be true of MgO which is isostructural with NaCl but in which two electrons transfer instead of one. This gives four times the net attractive force. MgO has correspondingly more strongly bonded ions and this quality is reflected in its physical properties.


NaCl MgO Melting Point 801ºC 2800ºC Hardness 2.5 6.5

Fig. 3.3. This diagram indicates the steps in the Born-Haber cycle for the formation of an ionic compound such as NaCl (halite).

Born-Haber Cycle. One can evaluate the utility of this view of bonding by examining the magnitudes of the various terms in the ionic bonding cycle and comparing them with the experimentally determined values of enthapy of formation. The sum of the enthalpies of the various processes in formation of an ionic compound should equal the enthapy of formation of the compound from its constituents at their ground state. The enthalpy of formation, D Hf298, a standard state is measurable by combining the elements in a calorimeter. The total electrostatic energy, U, of combining point charges into NaCl structure array is called the Madelung energy and is readily calculated. The heat of vaporization, DHv, of Na metal to Na gas is measurable as is the enthalpy of dissociation, DH d, of Cl2 gas to the monatomic gas . The enthalpy of ionization, DeltaHIP, of Na gas to Na+ gas and the electron affinity, DeltaHEA, of Cl- gas are also known. Because the sums of the enthalpies of going through the vaporization, ionization, and condensation steps (known as the Born-Haber cycle) must equal the enthalpy of the measurable direct formation step, we can compare these quantities to estimate the total repulsive energy term which is typically about 10% of the total energy of the crystal. If the repulsive term gives us the wrong sign or is some very large proportion of the total energy of the crystal, we know that the ionic model is not a good model for the bonding of the crystal, and there are other (probably covalent) terms in the total bonding energy of teh crystal.

Electronegativity is the tendency of a neutral atom to accept electrons into its outer shell (i.e to form anions). The Mulliken electronegativity is just the average of the electron affinity (i.e. the energy released when one electron is added) and the ionization potential (i.e. the energy required to remove one electron). Review the chart of electronegativities by Bloss in Crystallography and Crystal Chemistry. The elements on the left side of the periodic table have low electronegativities and those on the right have high electronegativities. The difference in the electronegativities of two atoms gives an idea of the bond character. If two atoms of very different electronegativity bond, the bond is dominantly ionic in character (e.g. NaCl, MgO). If the two atoms have low electronegativities, nei ther atom has a tendency to accept electrons and the bond is metallic.

3.2.2. Metallic Bonds

If two atoms of similar low electronegativities bond, there is an "excess" of electrons which do not localize but form an electron "gas" in the substance. This electron "gas" of delocalized electrons is the reason for the high conductivity of these materials. The delocalization of bonding electrons also gives rise to bonding forces at greater distances imparting these compounds with greater tensile strength and hence ductility and sectility (maleability). It also causes these compounds to be opaque to optical frequencies of electromagnetic radiation. Two examples of elements that form this type of bonding are Au and Fe. Other siderophile elements include Co, Ni, Ru, Rh, Pd, Os Ir, and Pt. These elements are strongly depleted in the Earth's crust relative to their solar abundances, and the Earth's supply of these elements is believed to be in the core.

3.2.3. Covalent Bonds

If two atoms of high electronegativity bond, there is a deficiency of electrons, and the electrons are "shared" in the highly localized bonding orbitals. This type of bond is called a covalent bond and is highly directional in character, but only gives rise to nearest neighbor attractions. Covalently bonded crystal structures are not as easily predicted on the basis of the rules for stacking of spheres as are metallic and simple ionic compounds.

The geochemical classification of elements that form covalent bonds is the chalcophiles which include the elements most commonly found in sulfide minerals. These elements include Cu, Zn, Ga, Ge, As, Se, Ag, Cd, In, Sn, Sb, Te, Hg, Tl, Pb, and Bi, and are depleted in the Earth's crust relative to their solar abundances. These elements are typically found in sulfide minerals in hydrothermal deposits.

K 1s shell spherical

L 2s shell spherical

L 2p shell octahedral

Hybrid sp orbitals

sp2

sp linear (180º) example: cuprite

sp2 Trigonal (120º) example: graphite

4sp3 Tetrahedral (corners at 109.28º) example: diamond, sphalerite

sp3d2 octahedral (90º) example: Fe in pyrite

Carbon (ground state)

Carbon (graphite)

Carbon (diamond)

Illustration of electron configurations in diamond and graphite.

3.2.4. Van der Waals Bonds

When part of a structure is ionically or covalently bonded, there usually is some residual charge or polarization of the charge distribution. These negatively and positively polarized charge distributions attract each other a to form weak bonding effects called Van der Waals or residual bonds. The geochemical classification of elements that form Van der Waals bond is the atmophiles which in clude the noble gases He, Ne, Ar, Kr, and Xe plus H, C (forms methane CH3), and N (forms ammonia NH4).

3.2.5. Hydrogen Bonds

If hydrogen bonds to a highly electronegative element such as F or O, its single electron will be confined to an orbital of the F or O leaving the proton exposed. The proton may then attract other negative charges forming a hydrogen bond. This is common in hydroxyl-containing minerals such as amphiboles and micas.

3.2.6. Review of Bond Types

  • 1. Ionic
  • 2. Covalent
  • 3. Metallic
  • 4. Van der Waals
  • 5. Hydrogen

    3.3. Physical Properties and Structure

    There can be more than one type of bonding in a crystal. This can lead to strongly anisotropic physical properties such as in graphite. Such substances are said to be anisodesmic. Minerals whose bonds are all of equal strength are said to be isodesmic (e.g. Halite, diamond).

    Many substances have anisotropic physical properties. These properties are related to the atomic structures of these substances (minerals). The physical properties also obey the symmetries of the structure. In this course, we will be relating all the physical properties of minerals to the structure. An understanding of the characteristic physical properties requires an understanding of the structure. We will, therefore, be spending a great deal of time discussing the structural chemistry of minerals.

    All physical properties are related to structure and may be isotropic or anisotropic. Halite is a good example of an isotropic structure with equal hardness in all directions.

    3.4. The Rules of Bonding and Coordination in Ionic Crystals

    The rules of bonding and coordination in ionic crystals were deduced and formalized by Linus Pauling in his five famous rules.

    3.4.1. Pauling's First Rule

    Around every cation, a coordination polyhedron of anions forms, in which the cation-anion distance is determined by the radius sums and the coordination number is determined by the radius ratio.

    In this view anions are large and cations are small. To a first approximation they behave in ionic structures as hard spheres such that cations just touch anions. Thus, what the second part of the first rule is based on is constant inter-atomic distance.

    Si-O 1.62 + .03Å Mg-O 2.08 + .09Å

    The third part of the first rule says that the CN is determined by the radius ratio. A couple of exam ples of how this can be determined geometrically follows: Table 3.2 Radius ratios for various coordination polyhedra


    CN Polyhedron Example Radius Ratio Range
    3 Triangle C in Calcite 0.155-0.22 4 Tetrahedron Si in Quartz 0.22-0.41 5 Trigonal Bipyramida Al in Andalusite - 6 Octahedron Mg in Forsterite 0.41-0.645 8 Square Antiprism Ca in Garnet 0.645-0.730 8 Cube Ca in Fluorite 0.73-1.00 12 Dodecahedron Native gold 1.00

    3.4.2. Pauling's Second Rule: The Electrostatic Valence Rule

    An ionic structure will be stable to the extent that the sum of the strengths of the electrostatic bonds that reach an anion equals the charge on that anion.

    Work this out for the NaCl structure:

    Each Na is surrounded by 6 Cl- ions, 1/6 of each Cl is in turn coordinated by 6 Na+ ions. Hence, each are balanced.

    3.4.3. Pauling's Third Rule

    The sharing of edges, and particularly faces by two anion polyhedra decreases the stability of a crystal.

    This is related to the second rule. Two Si tetrahedra never share faces because this would completely saturate the oxygens of the shared face leaving no more bond strength available for the rest of the structure.

    3.4.4. Pauling's Fourth Rule - an extension of the third rule

    In a crystal which contains different cations, those with high charge and low coordination numbers tend not to share elements of their coordination polyhedra.

    3.4.5. Pauling's Fifth Rule: The Rule of Parsimony

    The number of essentially different kinds of constituents in a crystal tends to be small.

    This rule states that structures tend to be simple and contain only two or three types of cation sites. There is no single mineral which can encompass all the different elements in, say, a granite or a ba salt. Hence, most rocks are poly-mineralic.

    3.5. Packing of Spheres

    Although there is considerable reason to doubt hard sphere models for anions, consideration of how hard spheres pack to fill space can yield much insight into how atoms arrange themselves into crystals.

    Let us begin with the simple cubic packing (primitive cubic) because it is the easiest to visualize. No known minerals crystallize with the simple cubic structure because the packing is inefficient. However, some anions are packed in this way in ionic structures. There is a more efficient way to stack a simple cubic array. This is the body centered cubic (bcc) structure. Native Fe in meteorites has this structure and is known as the mineral kamacite (a=2.80 Å).

    But there are two more efficient ways to pack spheres: Hexagonal closest packing and Cubic Closest Packing. Hexagonal closest packed layers may be stacked in two different ways. If we put one layer over the B interstices, then when we put the third layer on it can be in the B or the C positions. If we put the third layer in the B position we have a stacked se quence ABABAB..., and we preserve 6-fold symmetry. This is called Hexagonal Close Packing (HCP). It is rare for elements to crystallize in this form in nature. However, the mineral Iridosmine (Os-Ir-Fe) and many synthetic alloys have this structure. It is most important as a way to stack anions in ionic crystals.

    If the third layer is place over the C interstices, then the repeat is ABCABCABC... and you have Cubic Close Packing (CCP). Only a three-fold is preserved, but four-fold and two-fold symmetry axes are generated. This type of packing has more symmetry than HCP and is represented by many structures of metallic elements (e.g. Cu, Ag, Pb, Pt, Pd, Ir). It also forms the basis for stacking oxygens in numerous minerals and complex oxides. We can use the NaCl model to point out octahedral and tetrahedral voids and the relationship of NaCl to face-centered cubic (FCC).


    Further Reading

    Bloss, F. Donald (1971) Crystallography and Crystal Chemistry . Holt Rinehart, Winston, New York.

    Henderson, Paul (1982) Inorganic Geochemistry. Pergamon, New York.

    Huheey, James E. (1983) Inorganic Chemistry, Third Edition. Harper and Row, New York.

    Pauling, Linus (1960) The Nature of the Chemical Bond, Third Edition. Cornell Univ. Press, Itha ca, NY.

    Smyth, J.R. and D.L. Bish (1988) Crystal Structures and Cation Sites of the Rock Forming Minerals. Allen and Unwin, London.


    GEOL 3010 Syllabus

    Chapter 2 Mineralogy Notes

    Chapter 4 Mineralogy Notes

    Mineral Structures and Properties Data Base

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