CHAPTER 2: ATOMIC ARRANGEMENTS AND MINERALOGICAL STRUCTURES Sarah Lambart
RECAP CHAP. 1 Mineral: naturally occurring (always) a structure and a composition that give it defined macroscopic properties (always) inorganic (always) Solid (most of the time) crystalline solid (most of the time) Homogeneous (most of the time)
RECAP CHAP. 1 Mineral occurrences: Igneous, Metamorphic, Sedimentary Classification (based on the dominant anion): - sulfates - oxides - native - silicates - phosphates - hydroxides - sulfides - borates - carbonates - halides Silicate classification: (based on polymerization) - orthosilicates - sorosilicates - cyclosilicates - chain silicates - sheet silicates - Framework silicates
RECAP CHAP. 1 Physical properties: - Habit: euhedral, subhedral, anhedral - Morphology: granular, tabular, prismatic - Transparency: transparent, translucent, opaque - Luster, Metallic, submetallic, adamantine, resinous, vitreous, earthy - Color - Streak: color of powder on a porcelain plate - Tenacity: brittle, sectile, ductile - Cleavage and fractures - Density in g/cm 3 or specific gravity (Wa/(Wa-Ww)) - Hardness: Moh s scale: talc<gypsum<calcite<fluorite<apatite<orthoclase< quartz< topaz< corundum< diamond - Others: taste, acid test, electric conductivity, radioactivity, magnetism, fluorescence, pleochroism
CONTENT CHAPTER 2 (2 LECTURES) Atomic arrangements Ionic radius and coordination number Pauling s rule
CLOSE-PACKING One layer A
CLOSE-PACKING One layer Two layers: 2 possibilities A A
Two layers: 2 possibilities AB
Three layers: 2 possibilities A C A C hcp Hexagonal close-packed ccp or fcc (Cubic close-packed)
Three layers: 2 possibilities hcp Hexagonal close-packed ccp or fcc (Cubic close-packed)
Three layers: 2 possibilities X layers: 3 possibilities - ABABA : hcp - ABCABCA..: ccp - Nothing regular: it s not periodic hcp Hexagonal close-packed ccp or fcc (Cubic close-packed)
Definition: A unit cell of a mineral is the smallest undivisible unit of a mineral that possesses the symmetry and properties of the mineral. hcp Hexagonal close-packed ccp or fcc (Cubic close-packed)
ccp or fcc (Cubic close-packed) Rotating view toward top view C-layer A-layer Notice that every face of the cube has an atom at every face center face-centered cubic (fcc) B-layer A-layer
ccp or fcc (Cubic close-packed) Rotating view toward top view Notice that every face of the cube has an atom at every face center face-centered cubic (fcc)
ccp or fcc (Cubic close-packed) Rotating view toward top view Notice that every face of the cube has an atom at every face center face-centered cubic (fcc)
ccp or fcc (Cubic close-packed) Rotating view toward top view Notice that every face of the cube has an atom at every face center face-centered cubic (fcc)
IONIC RADIUS AND COORDINATION Anions and cations have different sizes and valences, and both will defined the way that they pack. 1Å = 10-10 m
Definition: The coordination number or CN is the number of closest neighbors of opposite charge around an ion. It can range from 2 to 12 in ionic structures. These structures are called coordination polyhedron. Halite Cl Na Cl Cl Cl
An ideal close-packing of sphere for a given CN, can only be achieved for a specific ratio of ionic radii between the anions and the cations.
Rx/Rz = IR cation/ IR anion. Rx/Rz C.N. Type 1.0 12 1.0-0.732 8 Cubic Hexagonal or Cubic Closest Packing 0.732-0.414 6 Octahedral 0.414-0.225 4 Tetrahedral (ex.: SiO 4 4- ) 0.225-0.155 3 Triangular <0.155 2 Linear
Rx/Rz = IR cation/ IR anion. Rx/Rz C.N. Type 1.0 12 1.0-0.732 8 Cubic Hexagonal or Cubic Closest Packing 0.732-0.414 6 Octahedral 0.414-0.225 4 Tetrahedral (ex.: SiO 4 4- ) 0.225-0.155 3 Triangular <0.155 2 Linear Cat ion C.N. (with Oxygen) Coord. Polyhedron Ionic Radius, Å K + 8-12 cubic to closest 1.51 (8) - 1.64 (12) Na + 8-6 cubic to 1.18 (8) - 1.02 (6) Ca +2 8-6 octahedral 1.12 (8) - 1.00 (6) Mn +2 6 0.83 Fe +2 6 0.78 Mg +2 6 0.72 Octahedral Fe +3 6 0.65 Ti +4 6 0.61 Al +3 6 0.54 Al +3 4 0.39 Si +4 4 0.26 Tetrahedral P +5 4 0.17 S +6 4 0.12 C +4 3 Triangular 0.08
PAULING S RULES Rule #1: Around every cation, a coordination polyhedron of anions forms, in which the cation-anion distance is determined by the radius sums, and the coordination number is determined by the radius ratio. Linus Pauling
Rule #2: The Electrostatic Valency (e.v.) Principle The strength of an ionic (electrostatic) bond (electrostatic valency e.v.) between a cation and an anion is equal to the charge of the ion (z) divided by its coordination number (n): e.v. = z/cn In a stable (neutral) structure, a charge balance results between the cation and its polyhedral anions with which it is bonded. Example: Halite (NaCl), Na + has CN=6 and z=+1 each Cl- contributes a charge of -1/6 to the Na + 6 x -1/6 = -1 vs. z(na)=+1 NEUTRALITY IS ACHIEVED
Formation of anionic groups If electronegativity of anion and cation differs by 2.0 or more, the group will be ionic Carbonate Sulfate C has valence (+4); C.N = 3 e.v.= 4/3 Charge remaining on each O: (-2)+(4/3) Charge total: 3*(-2/3)=(-2) S has valence (+6), C.N = 4 e.v.= 3/2 Charge remaining on each O: (-2)+(3/2) Charge total: 4*(-1/2)=(-2)
Rule #3: Shared edges, and particularly faces of two anion polyhedra in a crystal structure decreases its stability. Rule #4: In a crystal structure containing several cations, those of high valency and small coordination number tend not to share polyhedral elements. Rules 1 to 4 maximize the cation - anion attractions and minimize the anion-anion and cation-cation repulsions.
Rule #3: Shared edges, and particularly faces of two anion polyhedra in a crystal structure decreases its stability. Rule #4: In a crystal structure containing several cations, those of high valency and small coordination number tend not to share polyhedral elements. Rules 1 to 4 maximize the cation - anion attractions and minimize the anion-anion and cation-cation repulsions. Rule #5: The principle of parsimony The number of different kinds of constituents in a crystal tends to be small.
NEXT TIME Reading: Chap. 14-5 Chap. 2-3 Lab: Physical properties of minerals