Mineralogy - Ch 13 + Goldschmidt's Rules

Used condensed version of study guide; ch 13 & 2

Why can a single ion have a range of effective radii?

ionic radius depends on CN and bondstrength

higher coordination number =

higher charge = smaller radius

When is ionic radi smaller?

across a period (more protons taking up space)

When is anionic radi larger?

down a group (more shells)

Order coordination polygons (smallest to largest)

tetra(4), octa(6) cubic(8), dodeca(12)

Predict CN from radi ratio: 0.15

CN 2 - linear

Predict CN from radi ratio:0.15 - 0.225

CN 3 - triangular

Predict CN from radi ratio: 0.225 - 0.414

CN 4 - tetrahedral

Predict CN from radi ratio: 0.414 - 0.732

CN 6 - octahedral

Predict CN from radi ratio: 0.732 - 1.0

CN 8 - 12 cubic/dodecahedral

CN of Al³⁺

4 or 6

CN of Si⁴⁺

4

CN of Fe²⁺/Mg²⁺

6

CN of K⁺

8-12

CN of Na⁺

6-8

Why is K⁺ the only common ion with CN = 12

its large enough that 12 O^2- anions can surround it without repulsion

Why octahedral for CN = 6?

six anions surround the cation at the corners of an octahedron

Effects of Pressure on substitution

favors smaller ions

Effects of Temperature on substitution

allows greater tolerance in ionic substitution

Effects of composition on substitution

depends on element availbility

Goldsmidt’s rules

ionic radii must be within 15%, same charge preferred or balance, ions with higher EN sub less easily, similar coordination environments favor sub

Why can magnesium sub for iron and vice versa in olivine?

similar radius and charge

what about (Al³⁺ + Si⁴⁺) ↔ (Fe²⁺ + Mg²⁺)

coupled sub in feldspars

define simple substitution

one for one (Mg²⁺ ↔ Fe²⁺ in olivine)

Define coupled substitution

multiple ions sub to maintain charge (Ca²⁺ + Al³⁺ ↔ Na⁺ + Si⁴⁺ in plagioclase)

define omission substitution

cation vacancy balances charge (Fe²⁺ ↔ 2Li⁺ + □).

define interstitial substitution

small ion enters empty site (H⁺ or Li⁺ in amphiboles)