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.
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,
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.
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.
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).
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.
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.
The rules of bonding and coordination in ionic crystals were deduced
and formalized by Linus Pauling in his five famous rules.
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
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.
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.
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).
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.
Mineral Structures and Properties Data Base
3.2.3. Covalent Bonds
3.2.4. Van der Waals Bonds
3.2.5. Hydrogen Bonds
3.2.6. Review of Bond Types
3.3. Physical Properties and Structure
3.4. The Rules of Bonding and Coordination in Ionic Crystals
3.4.1. Pauling's First Rule
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
3.4.3. Pauling's Third Rule
3.5. Packing of Spheres
Further Reading