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Mineral structures!
Mineral structures!
ü Metallic bonding!ü Packing of spheres!
ü Covalent bonding!ü Strong and directional – prevents close packing!
ü Molecular bonding!ü Shape and charge distribution of the individual
molecule!ü Ionic bonding!
ü Paulingʼs rules!
Pauling’s Rules - summary!1. Around every cation, a coordination polyhedron of anions
(mostly O2-) forms, in which the cation-anion distance is determined by the radius sums and the coordination number is determined by the radius ratio"
2. An ionic structure will be stable to the extent that the sum of the strengths of the electrostatic bonds that reach an ion equal the charge on that ion"
3. Shared edges, and particularly faces of two anion polyhedra in a crystal structure decreases its stability"
4. In a crystal structure containing several cations, those of high valence and small coordination number tend not to share polyhedral elements"
5. The number of different kinds of constituents in a crystal tends to be small"
Coordination numbers in minerals!
ü What are the main CN?!
Rc/Ra limits!
ü See Nesse’s book for how to calculate the Rc/Ra limits!
Common CN with O2-!
Radii as a function of CN!
ü Ionic radius increases with increasing # of electrons
ü Ionic radius also increases with increasing coordination number ü electron cloud is drawn
out by the presence of more surrounding ions
Silicate Mineral Structures!The basic building block of silicate structures is the silica tetrahedron [SiO4]4-. Silicate minerals
are classified on the basis of the linkages of these tetrahedra.!
“Ball and stick” model of tetrahedron “Polyhedral” model of tetrahedron
Si has a coordination number of 4
Octahedron!
ü CN?!
Variability in Nature!
ü Same molecule with different CN (changes in pressure and temperature)!ü Polymorphs !
ü Different molecule leading to the same ionic ratios, same CN, and same structure!ü Isostructural minerals!
Stishovite
Coesite
!- quartz"- quartz
Liquid
TridymiteCristobalite
600 1000 1400 1800 2200 2600
2
4
6
8
10
Pre
ssur
e (G
Pa)
Temperature oC
Polymorphism!
Different structural forms for compounds of the same composition ⇒ different minerals!
ü SiO2!
After Swamy and Saxena (1994) J. Geophys. Res., 99, 11,787-11,794.
Isostructural minerals!
ü Different molecule with nearly identical structure!
NaCl PbS
See http://rruff.geo.arizona.edu/AMS/amcsd.php for detail information about minerals
http://www.webelements.com/ , http://en.wikipedia.org/wiki/Ionic_radius for ionic radii
3D structures of minerals!
http://virtual-museum.soils.wisc.edu/displays.html
Check Halite, Beryl, Alpha - Quartz, Olivine, Diamond - Graphite
How do elements distribute themselves in minerals?!
ü Chemical complexities in minerals!ü Elemental substitutions!ü Major and trace elements!
Abundance in Bulk Silicate Earth!
ü White’s book (chap 7)!
The Big Six: O, Si, Al, Mg, Fe, and Ca
99.1% of BSE
Major and trace elements!
ü White’s book chap 7!
Some major and trace elements have similar valences and/or sizes as major elements!
42 Si4+
15 C4+
Chemical complexities of minerals and major vs. trace elements!
ü Solid solutions !ü E.g., Fe-Mg substitution!
ü Major elements: > ~0.5-1 wt% !ü Form basic molecules!
ü Trace elements: low concentrations elements (in ppm)!ü Fit where they can!!
How can we quantify the distribution of trace elements into minerals/rocks?!
ü Same as major elements!ü At equilibrium, elements will distribute themselves
between co-existing phases so that the chemical potential of that element is the same in every phase of the system (White, Chap.7, p.272).!
ü Low concentration!ü Activity coefficients are constants and can be
determined (Obey Henry’s law)!
K =aisolid
ailiquid =
! i Xisolid
! i Xiliquid
Partition Coefficients!
!!!
ü Many D values tabulated…!
http://www.earthref.org/databases/index.html?main.htm
Trace elements: Compatible vs. incompatible!
Incompatible elements (D<1): Elements that are too large and/or too highly charged to fit easily into common rock-forming minerals that crystallize from melts. These elements become concentrated in melts.
Large-ion lithophile elements (LIL’s): Incompatible owing to large size, e.g., Rb+, Cs+, Sr2+, Ba2+, (K+).
High-field strength elements (HFSE’s): Incompatible owing to high charge, e.g., Zr4+, Hf 4+, Ta4+, Nb5+, Th4+, U4+, Mo6+, W6+, etc.
Compatible elements (D>1): Elements that fit easily into rock-forming minerals, and may in fact be preferred, e.g., Cr, V, Ni, Co, Ti, etc.
Goldschmidt’s Rules!
ü Victor Moritz Goldschmidt (1888-1947): Father of modern Geochemistry and of Crystal Chemistry!
Goldschmidt’s Rule 1!
ü Ions of one element can extensively replace those of another if they have the same charge and their radii differ by less than about 15%!• e.g., Fe2+ replacing Mg2+ in many silicate
structures, or Cl- replacing F-.!
Goldschmidt’s Rule 2!
ü Ions whose charges differ by one unit substitute readily for another provide electrical neutrality of the crystal is maintained. This requires coupled substitution. !ü Ca2+ can replace Na+ in feldspars as long as
Al3+ replaces Si4+ at the same time to maintain local charge balance. For charge difference greater than one, substitution is quite limited.!
Goldschmidt’s Rule 3!
ü When two different ions can occupy a position in a crystal lattice, the ion with the higher ionic potential forms a stronger bond with surrounding anions (ionic potential = charge/radius). Therefore, these elements are concentrated in “early” formed minerals. !
ü Mg-rich olivines form at a higher temperature than more Fe-rich olivines.!
Goldschmidt’s Rule 4!
ü Even if size and charge are the same, substitution may be limited if two ions have different electronegativities and thus form bonds of different ionic character.!• Na+ and Cu+ have similar ratios and same charge but very
different electronegativities; they rarely substitute to one another!
Goldschmidt’s classification!
Goldschmidt’s classification!
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