Mineralogy Midterm 2026

What is a mineral?

Solid, homogenous, naturally occurring, crystalline, definite but not fixed chemical composition, possibly inorganic

2D symmetry

Types: Rotation axes, mirror planes (reflections)

Rotation: A1:360, A2:180, A3:120, A4:90, A5:60 (characterized by moving certain # of degrees)

Axis of rotation: imaginary line through the center of the crystal about which the motif is rotated

3D symmetry

Types: Inversion, rotation, rotoinversion

Center of symmetry/inversion (i): A point is reflected through the center of the crystal and is equidistant from the center on the opposite side

Rotoinversion: rotation and inversion, all faces must be the same

3D symmetry types of roto

1 fold: center of symmetry

2 fold: mirror plane

3 fold: 3 fold rotation and center of symmetry

4 fold: completely independent symmetry

6 fold: 3 fold rotation and mirror plane

Point group notation/H-M notation

Unit cell

smallest unit of a structure or pattern that can be infinitely repeated to generate the entire structure

Triclinic

least symmetrical – 3 axes with different lengths, no angles at 90°, 1-fold symmetry or bar 1 rotoinversion

Monoclinic

3 axes of unequal lengths, with β not equal to 90°, and α=γ=90°, may have 2-fold rotation or mirror or both

Orthorhombic

3 axes of unequal lengths, axes are all perpendicular to each other, must have 2- fold rotations +/- Mirror planes

Tetragonal

2 axes of equal lengths (a1 and a2), vertical axis (c) shorter or longer than other two, axes are all perpendicular to each other, must have 4-fold rotation

Hexagonal

3 axes of equal lengths (a1, a2, a3), vertical axis (c) shorter or longer than other two, c is perpendicular to a1, a2, a3, and a-axes intersect at 120°, must have 3- or 6-fold rotation

Isometric

3 axes of equal lengths (a1, a2, a3) all perpendicular to each other, must have 4 3-fold axes inclined to crystallographic axes

Principal of parsimony

There are only a few possible crystallographic sites in a given mineral. If that mineral has a range of composition, different ions will swap in or out of the same crystallographic site.

• Leads to principal of solid solution

Polymorph

two (or more) minerals with the same chemical formula, but a different crystal structure

Solid solution

mineral w particular crystallographic spot but diff elements can be in that spot

Requirements:

• cations of the same size (roughly)

• cations have the same charge

Al and Ca

ex: NaAlSi3O8 (sodium plag) vs. CaAl2Si2O8

• to compensate for charge differences, Al3+ and Si4+ can swap

What minerals commonly have solid solution and why that solid solution is possible

Fe and Mg, similar size and same charges

Na and Ca but only if Al and Si also switch

Nesosilicates/orthosilicates Si:O ratio

1:4

Includes: olivine, garnet, aluminosilicates (silimanite, kyanite, andalusite), zircon

Sorosilicates/disilicates Si:O ratio

2:7

includes: tourmaline, beryl, cordierite

Inosilicates/chain silicates Si:O ratio

Single chains 1:3

Double chains: 4:11

includes: pyroxenes, pyroxenoids, amphiboles (doub chain)

phyllosilicates/sheet silicates Si:O ratio

2:5

Includes: micas, kaolinite, talc, serpentine

Tectosilicates/framework silicates

1:2

Includes: qtz, feldspars, feldspathoids

O-sheets (octahedral)

octahedral sites either occupied by divalent cations (fe2+, Mg2+) or trivalent cations (Fe3+, Al3+)

Divalent cations = trioctahedral

Pyroxene group idealized formula

XYZ₂O₆

_{X=M2 sites}

_{Y=M1 sites}

_{Z=tetrahedral sites}

Amphibole group idealized formula

W_0-1X₂Y₅Z₈O₂₂(OH)₂

W= A site, usually Na or K

X= M₄ site, Na or Ca (if 8-fold), Fe or Mg (if 6-fold)

Y=M_1,M₂,M₃ sites, octahedral, Mg, Fe, Al

Z=tetrahedral sites, Si or Al

Silicates ideal formula (i think?)

X_mY_n(Z_pO_q)W_r

X: K⁺, Na⁺, Ca²⁺

Y: Mn2⁺, Fe²⁺, Mg²⁺, Fe³⁺, Ti⁴⁺, Al³⁺

Z: Al³⁺, Si⁴⁺

Phyllosilicates TO structure formula

Si2O5

+(OH)

+Al or Mg

= TO structure

ex:

Kaolinite (Al₂Si₂O₅(OH)₄

Lizardite (Mg₃Si₂O₅(OH)₄

O (octahedral) sheets

Octahedral sites either occupied by divalent (Fe²⁺, Mg²⁺) or trivalent cations (Fe³⁺, Mg³⁺)

Net cation charge is +6

Net charge of sheets is 0

***Every sheet silicate will have a trioctahedral  version and a dioctahedral version!***

Ex. Biotite and muscovite are structurally identical, but biotite=trioctahedral (Fe,Mg), muscovite=dioctahedral (Al)

Divalent cations

Trioctahedral

If divalent cations: all 3/3 octahedral sites are filled, forming a trioctahedral sheet

Mg₃(OH)₆ = ideal formula, mineral brucite

Trivalent cations

Dioctahedral

If trivalent cations, not all (2/3) octahedral sites are filled, forming a dioctahedral sheet

Al₂(OH)₆ = ideal formula, gibbsite

T (tetrahedral) sheets

sheets of tetrehedrally coordinated cations

T₂O₅, where T = Si₄₊, Al₃₊ (occasionally Fe₃₊)

Arranged in 3-fold rings so that 3 O^2- shared w/ adjacent tetrahedra

Tetrahedral layers ~2 oxygen atoms thick

If Si⁴⁺, then (Si₂O₅)^2- à not neutrally charged, must bond w/ O layer

If Al³⁺ (or Fe³⁺), net negative charge is greater

TO layers

1:1 serpentine and kaolinite

TOT

2:1 pyrophyllite and talc

TOT + c

2:1 muscovite, biotite, brittle micas

TOT + O

2:1+1 chlorite

TO sheet silicates

Repeating TO layers

Layers are electrically neutral, so weakly bonded (vdW and H bonds)

All very soft

TOT sheet silicates

Repeating TOT layers

Layers are electrically neutral, so weakly bonded

very soft

TOT +c

Repeating TOT layers bonded together w/ interlayer cation

Al³⁺ subs for Si⁴⁺ in T layers, low-charge cations (K^+, Ca²⁺) b/w layers balance charge

In micas, Al:Si ration is 1:3 (ratio higher in brittle micas)

Muscovite (d) KAl₂AlSi₃O₁₀(OH)₂

Biotite (t) K(Fe,Mg)₃AlSi₃O₁₀(OH)₂

TOT +O sheet silicates

Repeating TOT layers bonded with additional O layer

Talc (trioctahedral TOT) plus an extra O layer

TOT layers have net (-) charge (Al for Si), O layers have a net (+) (Al for Mg)

Chlorite  Mg₆(Si,Al)₄O₁₀(OH)₈

Inosilicates

chain silicates - chains of Si tetrahedra

• pyroxene group

• pyroxenoids

• amphiboles

pyroxene group

single chains of tetrahedra extend parallel to c axis

octahedral sites are either an M1 site or an M2 site

M2- either 6-fold or 8-fold sites

• if 6 fold, orthorhombic

• if 8 fold, monoclinic

• occupied by Mg²⁺, Fe²⁺, Ca²⁺, Na⁺, or Li⁺

M1 pyroxene group

occupied by Mg²⁺, Fe²⁺, Al³⁺, or Fe

M2 pyroxene group

either 6-fold or 8-fold sites

• if 6 fold, orthorhombic

• if 8 fold, monoclinic

• occupied by Mg²⁺, Fe²⁺, Ca²⁺, Na⁺, or Li⁺

Pyroxene group ideal formula

XYZ₂O₆

X = M2 sites

Y = M1 sites

Z = tetrahedral sites

Clinopyroxenes

have a solid solution – Fe and Mg swap

Orthopyroxenes

have a solid solution – Fe and Mg swap

Amphibole group

Double chains of tetrahedra extend parallel to c axis

3 different structural sites created b/w apical oxygens - M1, M2, and M3 (Structural sites created btw layers of tetrahedra)

**much wider in amphibole

Amphibole group ideal formula

W_0-1X₂Y₅Z₈O₂₂(OH)₂

W = A site, usually Na or K

X = M₄ site, Na or Ca (if 8-fold), Fe or Mg (if 6-fold)

Y = M₁,M₂,M₃ sites, octahedral, Mg, Fe, Al

Z = tetrahedral sites, Si or Al

Cleavage in Amphiboles

2 cleavages at 56°/124°