Notes Outline:  Mineralogy, EEES 2210   Fall 2004        

 

A.         GENERAL INFORMATION ABOUT MINERALS

 

1.  Mineral--- Definition: 4 criteria    (see p. 3-5)

a.        Naturally occurring

b.       Inorganic

c.        Definite chemical composition (within defined limits)

d.       Crystalline

 

2. Definitions:  atoms, ions, cations, anions

a.        Solid state

b.       Amorphous state

c.         Crystalline State  (euhedral , subhedral, anhedral crystals)

     i.) Regular arrangement of atoms/ions (Unit Cell) & Periodicity

    ii.) Difference between molecules and crystals (systematic repetition---periodicity)

d.    Solid solution (example: olivine)   “chemical composition within defined limits” (page 90-91)

f.    “Uniqueness”—each mineral “species” (quartz, calcite, etc.) has a unique set of physical and chemical properties because of its unique combination of:

i.)        its crystal structure

ii.)       its chemical composition

g.                             Physical properties:  color, hardness, specific gravity, etc. (Chap 2, pp. 17-37---will be discussed in

              more detail later –for time being just be familiar with the names of the various physical properties)

 

3.   Nomenclature

a.    Mineral may be named after (see p. 15)

                i: a geographic location (place)

ii. some physical or chemical  property

iii. after a person (living or dead)

 iv. other

 b.  IMA approved minerals and mineral names

 

4.     Mineral (Chemical) Formulae

a.   A typical mineral contains 1-4 or 5 “major” elements and a few “minor” or trace elements

b.  Chemical formula (anions on right, cations from left to right with increasing valence; (OH) right of anion (O); H2O “dotted” to far right)

 

5.    Distribution: 

  a. ~4000 known mineral “species”

  b. ~300 important minerals----abundant or economically important

c. ~25 Rock-Forming Minerals (RFM)-----those minerals that are sufficiently abundant as to   be a common, major constituent of rocks

  NOTE:  most (but NOT all) rocks consistent of 1 to 4 or 5 major (RFM) and a few minor “accessory” minerals

e.   ~25 Accessory Minerals----common, but not major constituent of rocks---typically account for between ½ to 2 or 3 % of the total rock

 

6.   Crustal Abundance of Elements/ Significance for Minerals

a. Internal structure of the Earth:  Crust, Mantle, Moho (see p. 39)

b. Element distribution (see p. 40) : O  Si  Al  Fe  Ca  Na  K  Mg                   

c. Why “only” 4000 or so minerals?

h.    Dispersed elements (p 41) Consider:  Pb (13 ppm),  Rb (90 ppm), K (25,900 ppm)

ii.   Bonding considerations (to be considered later)

d.    Why “only” 35 RFM?

                                                                                                   i.      Top 8 elements (from “b”) make up 98.6% of weight of earth’s crust                

                                                                                                  ii.      No RRM should contain any elements outside this top 8 

iii.   NOTE:  Exceptions are calcite & dolomite: Why?

               

B.      CHEMISTY CONSIDERATIONS  (REVIEW)  

 

1.  The atom---an electron cloud about the nucleus---actually mostly space  (p 42)

a)                                                                   neutron:  mass = 1.009 amu; relative charge = 0

b)                                                                   proton:  mass = 1.007 amu; relative charge = +1

c)                                                                   electron:  mass = 0.0005 amu; relative charge = -1

 

2.   Definitions:  (page 42)

a) Atomic number = # of protons in an element (also =  # of electrons in neutral atom----but atoms can lose or gain electrons to become ions)

b)  Element = all atoms of the same atomic number constitute an element

c)  Isotope = all elements with the same number of both protons and neutrons in the nucleus

d)    Atomic Weight of an element= weight of one mole of the element* with all isotopes represented proportionally to their frequency in nature.  *Note:  Avogadro’s Number = 6.023 x 1023  “ number of formula unit of atoms or ions per mole”

 

3.   Electrons:  revolve about the nucleus in orbitals, two electrons per orbital; orbitals are grouped into shells  (page 47-49)

 

a) Quantum numbers that designate the orbitals

  i) Principal QN, n, where n may assume values:  1, 2, 3, ….

      This number also corresponds to the shell designations (K, L, M, etc)

   ii) Azimuthal QN, l, where l assumes all values: 0, 1, …,(n-1) 

        This number also corresponds to the type of orbital (S, P, D, F, etc)

  iii) Magnetic QN, m, where m assume all values for any l from

                      -L, (-L+ 1), …,0, …, (L-1), L                

b) n, l, m specify a unique orbital that may  contain up to two electrons .   The two electrons are distinguished by the spin QN, either +  ½ or – 1/2 .

 

4.  Electronic Configuration: filling the orbitals  (page 50-52)

 

a) Note the sign convention for orbital energy designations---the closer the electron is to the nucleus, the lower the energy (negative value); an electron at an infinite distance from the nucleus would be 0.  It is actually the amount of energy that an electron can give up by virtue of what it gains from interacting with the positively charged nucleus.

b)  Aufbau Principal:  electron occupies lowest energy orbital available

c)  Sequence :  (K shell) 1s; (L shell) 2s, 2p; (M shell) 3s, 3p, 3d

d)  See figure 3.14, p 50:  Note that  the 4s orbital initially lies below the 3d in energy and therefore fills before 3d; but as the 3d orbitals fill, they fall below the 4s energetically favored, but in the case of d (or f) orbitals, an exactly ½ filled orbital is also somewhat stabilized (i.e., reduces the energy) and is hence favored.

 

5.     Ions-----atoms that have gained additional electrons thus assuming a negative charge  (anions) or donated them and becoming positive (cations)  (pp 53-55)

 

a)    Ionization Potential (IP), 1st, 2nd, etc.  –energy required to remove an electron from an atom

b)    Electron Affinity (EA), 1st, 2nd, etc – energy required to force an electron onto an atom

c)    Electronegativity (EN)----measure of ability of an atom in a structure to compete for electrons  Mulliken (using IP and EA), Pauling (bond dissociation energies), Allred-Rochow (revised Pauling’s)

d.) Periodic variation of IP, EA, EN  (see fig 3.15, page 54)

IP increases from left to right across the Periodic Table in energy                                         

i.      In general, completely filled or completely empty orbitals are               

ii.  EN increase from left to right across the Periodic

e).  What atoms become cations and/or anions based on IP and EA

 

6.     Bonding  (pages 56-64)

 

“Driving Force” for bonding:  it is energetically favorable for atom to have an outer most electronic shell (the valence shell) that is either completely filled or completely void of electrons.   This requires atoms to interact with one another by either sharing or transferring electrons among themselves  (i.e., “bond”)  (page 56)

Types of bonding:

                    a) Ionic bonding  (difference in Electronegativity---relatively large)

 i) Transfer of electrons---i.e. have a donor (cation) and receptor atom (anion).  Note:  requires an exact match for donors and receptors, and hence atoms (that become ions) combine in definite proportions to form chemical compounds (which includes minerals)            (page 56-57)        

ii.) example:  NaCl----note donor and receptor must remain close

                            iii.) physical representation of  “ionic bond”:  cation and anion must be tangent  (spheres that touch)

b) Covalent bonding (difference in Electronegativity----relatively small)

i.) Sharing of electrons between two atoms----Cl2  example.

ii.) Considered as “overlap of orbitals of like sign from different atoms

                          iii.) Sigma & Pi bonding:  single & double bonds

c)  Metallic bonding (difference in Electronegativity relatively small; and EN values of both atoms also small)

i.)    valence electrons are held very loosely and can migrate throughout the structure  (page 61)

ii.)       properties of metallically bonded minerals:  absorbs light (opaque), conducts electricity, low hardness, high

e)    Hydrogen bond:  in (OH) or H2O, once the hydrogen atom donates an electron to become H+,  there are no other electrons available to shield the proton, so there is a polarity that allows the hydrogen to form a weak hydrogen bond with another anion.   The (OH)-  itself is about the same size as O2-  and like it was an oxygen but with a minus 1 charge, rather that a minus 2.  On the other hand any water molecules incorporated into a structure are highly dependent on hydrogen bonding in order to attached to the structure.

f)     Van der Waals attractions:  very weak electrostatic  interactions

Ionic and Covalent Bonds                                                                                  

g)    The greater the difference in EN, the greater the ionic character of the bond (Note:  this is a model and not necessarily physical reality)  (see page 60-61 but use chart at top of the periodic table handed out in class to estimate ionic character)

h)    At ambient temperatures, covalent bonds are usually very, very strong whereas ionic bonds are just very strong.  Metallic bonding is somewhat weaker than either covalent or ionic bonding, but is much stronger than the very weak hydrogen bonds or van der Waals forces.   Covalent bonds are “directional” because they require orbitals to overlap along specific directions where ionic bonds do not. Hence, although covalent bonds tend to be stronger at RT, they tend to have lower melting points than many ionic compounds.  Conversely, ionic compounds tend to have higher solubilities than covalent compounds.

 

7.  Geochemical Classification of the Elements  ---(not covered in this textbook)

In 1922, based primarily on element partitioning in meteorites, the geochemist, V.M. Goldschmidt divided elements into 4 groups according to their geochemical affinities.  Some elements belong to more than one group.

a)    Lithophile Elements (ionic bonding predominates)

i.)       Group IA, IIA and select transition metal cations:  Li, Na, K, Be, Mg, Ca, Sr,  Ba, REE, Fe, Mn, etc.

ii.)      Anions:  O, F, Cl,, etc.

iii.)    Oxyanions:  XO3 (where X = C, B, N, etc.) or TO4  (Where T = Si, Al, P, S, Cr, Mo, As, W, etc.)

b)    Chalcophile Elements (covalent bonding predominates)                                                   

i.)    most of the transition elements (Cu, Ag, Zn, Fe, Hg, As, Sb, etc.)

ii.)   Sulfur (and other elements that can behave like S----As, Sb, Te, etc.)

c)    Siderophile Elements (tend to bond with themselves as native elements---metallic bonding and covalent bonding)

i.)    Au, Ag, Co, KI, Ir, Pt, Pd, C, As, etc.

d)    Atmophile Elements (covalent molecules or inert (noble) gases)

i.) molecules of O, N, C, S,

iii.) inert gases---He, Ne, Ar, Kr, Xe, Rn

 

C.  CRYSTAL CHEMISTRY (I)

 

1.     Size of Atoms and Ions (Atomic & Ionic Radii)  (page 64-69)

 

a.) Overview of Radii (atomic, covalent, ionic)

1 angstrom (A) = 0.1 nanometer (nm) = 10-8 cm

b.)  Atomic radius (=metallic radius for metals) > covalent radius;

Covalent radius>> cation radius); covalent radius < anion radius

c)    Ionic radius-----nucleus (+) ----electron (-) interactions affect size

d.)  Interaction between anion/cation (Morse potential)  (page 66)

e.)    Ionic Radii (VM Goldschmidt, 1926; L Pauling, 1927; LH Ahrens, 1952)

f.)     Shannon & Prewitt, 1969; Shannon 1976

 

2.     Packing of Spheres  (see CD ----Module I)   (Fig 3.37 and text, page 74)

a.)   Closest packed monolayers

i) Hexagonal closest packing: HCP     ABABABABAB…

ii.) Cubic closest packing: CCP (=fcc; face-centered-cubic)  ABCABC….

 b.) Octahedral and Tetrahedral voids in closest packed models--Sphere: O void: T void = 1:1:2

 c.) HCP-- O & T share 25% like faces; CCP O & T do not share like faces

3.     Radius Ratios       (page 70-71)                                                                        

a)  Coordination Number (CN) placing large spheres around (and tangent to) small spheres

b)    Geometric consideration:   “no rattle limit”

c) Calculating a radius ratio  (use geometry & trig)

d). Anion polyhedra surrounding a cation CN = 2, 3, 4, 6, 8, 12  (p. 73)

e)    Application of radius ratios to mineral structures: CN of common cations w/r to oxygen

 

4.  Pauling’s Rules for Stable Ionic Structures      (page 75-79) Also see CD----Module I)

a) Rule One—geometric: A coordination polyhedron of anions is formed about each cation, the cation-anion distance being determined by the sum of the ionic radii and the CN of the cation being determined by the radius ratio.

b) Rule Two –The Electrostatic Valence Rule--- the most stable ionic crystal structures are those in which the sum of strengths of bonds reaching each anion is equal to its negative charge (a little variation from ideal is OK)

i.)    [NOTE:  “bond strength” = sum of (cation charge)/(CN of cation) for the anion]

ii.) Underbonded/Overbonded:  Zachariasen Compensation          

    c.) Rule Three--Cation-Cation Repulsion---in a stable of ionic structures, the sharing of edges and particularly faces decreases the stability of structures.

     [NOTE:  corner, edge and face  = polyhedral elements that can be shared]

d.) Rule Four---In an ionic crystal structure containing different cations, those of high valence and low CN tend not to share polyhedral elements 

e.)      Rule Five---The number of essentially different kinds of constituents in a crystal structure tends to be small (“parsimony” rule)

 

5.   Simple structures based on closest packing of anion spheres with cations partially filling the octahedral (O) and tetrahedral (T) voids.       (Page 85-89)   examined in lab #2

 

6.   Solid Solution       (page 90-94)

a.)      Interstitial solid solution  (carbon steel, beryl, zeolites)

b.)     Omission solid solution  (pyrrhotite, Fe(1-x) S )

c.)      Substitutional solid solution----most common type, often just call “solid solution”

i.) size:  < 15% (extensive ss); 15-30% (limited ss); > 30% no ss 

ii) temperature:   higher temperatures favor extended solid solution

iii) examples----simple substitution (Mg/Fe in olivine); coupled substitution (Si/Na for Al/Ca in plagioclase; coupled substitutions in amphiboles)

 

          7.    Non-stoichiometry   (non-Daltonide compounds

                    a) Definition:   formula (site) occupancies are not simple integers

                    b) examples:  pyrrhotite, A-site in amphiboles, lunar plagioclases

 

          8.   Recalculating Chemical Analyses  (Pages 94-98)

a.)      weight % element to mole % element  (atomic proportions)  and vice versa  table 3.14, page 94

b.)     weight % oxide to mole % oxide and determining formulae for gypsum and olivine table 3.16 , p. 96

 

9.   Graphing chemical compositions (mole %, wt %)

a)       define:  System, Component  page 98

b)       graphing 2-component (binary) systems  page  98-99

c)       graphing 3-component (ternary) systems page 100-103

 

 

                                                                CRYSTALLOGRAPHY

 

D.  ROTATIONAL SYMMETRY READ:  p. 174 –193 text; CD ROM:  Crystallography External Form >>Symmetry Operations  (use continue and   Check out all 2-D and 3-D options)

 

1.  Introduction to Symmetry

a. What is symmetry--Intuition w/r to: square, rectangle, trapezoid, quadrilateral

b. Idea of  “indistinguishably”

c. Symmetry is inherent in nature---how do we describe what is already there Symmetry operations

i.)      What is an operation? An element?  Consider multiplication, addition, etc. as an analogy.

ii.)    What is a symmetry operation---“mapping point “P” into indistinguishable point P-prime

2.      Types of Symmetry Operations and symbols

a.     Center of Symmetry (Inversion) “i”

b.    Mirror Plane of Symmetry (Reflection)  “m”

c.     Proper Rotation Axes--- n = 1,2,3,4,6

d.    Improper Rotation Axes—Rotoinversion---“bar” n

3.     Combinations of Symmetry operations:  The 32 Crystallographic Groups

a.        Crystallographic: (n & “bar n” = only 1,2,3,4,6)

Point:  all symmetry operations must past thru a common point

Group:  mathematical groups (therefore finite)

 b.     Only certain combinations are permissible (32 possible combinations)

 Example:  try combining a 6 & a 4-fold axis

                         c.    27 AXIAL POINT GROUPS: Permissible Combinations: n, bar n, n/m, nmm, n22, n/m

e.        5 CUBIC POINT GROUPS                 

4.        The Crystal Systems                                                                                                        

a.  Symmetry definition of the 7 (6) Crystal Systems

Triclinic—no axial symmetry

Monoclinic—1 and only 1 direction of 2 and/or “bar” 2-fold symmetry

Orthorhombic—3 and only 3 directions of 2 and/or “bar” 2-fold  symmetry

Tetragonal—1and only 1 direction of 4 or “bar” 4-fold symmetry

Hexagonal—1 and only 1 direction of 6-fold symmetry

Trigonal—1 and only 1 direction of 3 or “bar” 3-fold symmetry

Cubic—4 directions of 3 or “bar” 3-fold symmetry

NOTE:  3/m = “bar” 6;  m = “bar 2;   i = center = “bar” 1

b.   Crystallographic Axes for the 7 Crystal Systems   (see pages 194-197, text)

                      Constraints:  a=b=c; alpha=beta=gamma=90   etc. for each system     

 

E. TRANSLATIONAL SYMMETRY 

READ:  Chapter 5, p. 213-239 (Note: text covers much more detail than notes in places)

                  1.   Introduction to Translational Symmetry

a.       Definition of a set of lattice points

a.           Arrays of lattice points:  1-D (line); 2-D (plane); 3-D (space)

b.          2-D lattices:  Choice of lattice vectors:  (2-D case)—maximum symmetry, shortest length

c.           The 2-D lattices and “systems”---See p. 218 text (ignore “diamond net” and use the names: clinonet, orthonet, hexanet, tetranet---not those in text)

i.)                   Systems:  Oblique, Rectangular, Square, Plane Hexagonal, Square

ii.)                  Plane Lattices:  oblique net, rectangular net, centered rectangular net, hexanet, square net

iii.)              Lattice Parameters:  a, b, gamma (2-D);

 a, b, c, alpha, beta, gamma (3-D)

2.  Types of space lattices (3-D):  primitive (P), face-centered (F), body-centered (I), and end-   centered (A, B, or C)

3.  The 14 BRAVAIS LATTICES & lattice parameters (See p. 232 text;  for Monoclinic use C, not I, for Hexagonal ignore C)

 

F. COMBINATIONS of Translational & Rotational Symmetry  (Read pages 213-238)

1.     Overview for 2-D & 3-D: Rotational Symmetry (point groups) +  Translational Symmetry (lattice types)  = 17 Plane Groups (2-D) or 230 Space Groups (3-D)

                                      2.       Hybrid Operations: glide planes (2-D, 3-D) & screw axes (3-D only)

                                      3.     Total Symmetry Groups: 

a.        2-D:  The 17 PLANE GROUPS

b.       3-D:  The 230 SPACE GROUPS

NOTE:   LAB:  Plane Groups:  rotational, translational symmetry & plane groups

 SEE:  TEXT PAGE 227:  The 17 Plane groups

 

END OF MATERIAL FOR TEST I