ESS 109C Isotope Geochemistry Notes
April 11, 2007
Ionic Radius and Paulings Rules
1. Ionic radius (Klein & Hurlbut handout, Spinel structure model, anion packing)
a. Common elements (ask!) O, Fe, Mg, Si, Al, Ca, Na, Mn, Ti, P why?
b. The gross structure and behavior of many rock-forming minerals can be understood by looking at the relative sizes of different elements in their common oxidation states. Most common minerals can be approximately described as closely-packed oxygen anions with smaller cations wedged tightly into the holes between them. Large cations fit into larger cavities, and tend to have more nearest-neighbor oxygen anions (high coordination #). Smaller cations, and cations with high charges, tend to fit into smaller cavities (low coordination #), and form stronger bonds.
c. The size of an ion (ionic radius) depends on several factors:
a. (also d) Cations are smaller than neutral atoms, anions are larger. Illustrate with questions about ionization of an atom (high-energy electrons tend to be far way from nucleus). For a given element, size decreases with increasing charge.
b. Ionic radius increases down a chemical group. (adding additional shells of electrons in high-energy outer orbitals) note exceptions for REEs, many d-block transition elements
c. For ions with the same electronic structure within a period (i.e., Na+, Mg2+, Al3+, Si4+), size decreases with increasing charge (increasing attractive charge of nucleus)
d. The radius of the ions in a mineral structure controls the basic structure
a. Anions are larger than cations, so most of the volume of typical minerals is anions (compare O2- and Mg2+ volumes in MgO). Typically anions are nearly close packed in minerals, maximizing the number and strength of bonds.
b. Cations are needed to preserve charge neutrality. They are much smaller, so tend to fit in small spaces between adjacent O2- atoms (O2- most abundant anion!). Size of space occupied depends on ionic radius. (NOTE: In these notes I used Pauling radii, rather than Shannon crystal radii).
i. Cations want to be snug, fit into space just a little smaller than they are.
ii. The more adjacent O2-, the larger the hole --> large cations have high coordination numbers
1. R+/R- < 0.225, trigonal, work example (C-O)
2. 0.225 < R+/R- < 0.414, tetrahedral
3. 0.414 < R+/R- < 0.732, octahedral
4. 0.732 < R+/R- cubic or other large cavity
iii. Example: Mg-O (0.72/1.40 0.514 octahedral OK; 0.57/1.38 0.413 tetrahedral barely OK too, less common) -- Periclase
iv. Example: Si-O (0.26/1.34 0.194, a bit too small unusually stable due to partially covalent bonding) Silicates! most common minerals on Earth!
v. Example: Sr2+-O (1.18/1.40 0.843, too big Sr usually in cubic or larger site) rare element so it usually substitutes for more common elements (i.e., Ca).
c. Truly close-packed anions have octahedral and tetrahedral cavities > the most common high temperature- and pressure-tolerant minerals consist of high-charge elements that fit easily in these cavities. i.e., Mg2+, Al3+, Si4+, and Ca2+.
Help identify most stable (and thus most important) mineral structures. Super-important in early 20th century when mineral structures were determined without computers!
i. Anions form nearest-neighbor coordination polyhedron around cations, cation to anion distance is sum of ionic radii, for appropriate coordination number.
ii. Electrostatic valency principle: sum of bond valencies in the coordination polyhedron = cation charge i.e., MgO or NaCl
iii. Minerals with polyhedra that share edges tend to be less stable, especially with fairly small, highly charged cations.
iv. Polyhedra around highly charged cations (i.e., SiO4 tetrahedra) avoid each other, may share corners, rarely edges. Silicates with isolated SiO4 groups are often more thermally stable (higher melting T) than silicates with joined SiO4 groups.
v. Mineral structures tend to be simple, with only one or a few different cation sites but each may be accommodate many different cations, i.e., olivine. Elements that form cations with similar charge, radius, and the same preferred coordination number typically substitute for each other in the same cation sites, particularly at high temperatures (entropy). For +2 cation sites, cations within 1 charge unit (i.e., +1 and especially +2, and +3 cations) and 15% radius (i.e., 0.62-0.82 for Mg2+ in an octahedral site) are usually able to substitute relatively easily. So Fe2+, Ni2+, and to some extent Li+, Mn2+ , Cr3+ and Al3+ often substitute for Mg2+ in silicates.
3. Basic classification of silicate minerals:
a. Isolated SiO4 tetrahedra (often the most thermally stable): olivine (Mg2SiO4), less common but important are garnet (Fe3Al2Si3O12) and zircon (ZrSiO4).
b. Chains of corner-sharing SiO4 tetrahedra (next most thermally stable): pyroxene (CaMgSi2O6, Mg2Si2O6).
c. Double chains of corner-sharing SiO4 tetrahedra: amphiboles (Ca2Mg5Si8O22(OH)2).
d. Sheets of corner-sharing SiO4-tetrahedra: micas (KAl2(AlSi3O10(OH)2)), clays
e. 3-D framework of corner-sharing SiO4-tetrahedra: quartz (SiO2), feldspars (KAlSi3O8 NaAlSi3O8 CaAl2Si3O8). Feldspars with more +1 cations, more Si (rather than Al) sharing corners -> easier to melt! Ca-rich feldspar hardest to melt.
4. Olivine structure most common mineral in Earths upper mantle -- peridotite, somewhat less common in the highest-temperature igneous rocks i.e., basalt and gabbro because its so hard to melt! Usually absent in lower-temperature igneous rocks like granite, rhyolite.
a. Contains O, Mg, Si, usually Fe2+ -- most common elements!
b. O2- nearly close-packed stable at high T and P!
c. Mg2+ fits neatly into octahedral cavities, Si4+ fits in tetrahedral cavities.
d. SiO4 tetrahedra are isolated from each other most stable!
e. Basic charge balance: SiO4, (+4)x1 + (-2)x4 = -4 net charge. Must be balanced by two +2 cations. Thus, Mg2SiO4.