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Unformatted text preview: Crystal Structure Spatial arrangement of atoms Controlled by types of bonds A way to organize crystal types:
1. 2. 3. 4. Covalent (repeat from before) Molecular (repeat from before) Metallic: "closest packing" three types Ionic best description of mineral structure: most common type of bond (1) Covalent Bonded Minerals Atoms need to be in specific arrangements Orbitals must overlap Required to share electrons Prevents close packing Typically hard and high melting points Diamond lattice Electrons shared: Highly oriented; directional Controls locations of atoms Fig. 35 (2) Molecular Crystals Discrete molecules packed in systematic way Molecules bonded internally with covalent/ionic bonds Molecules held together with van der Waals or Hydrogen bonds Example graphite and ice Graphite Covalent bonds Van der Waal forces Ice Covalent/hydrogen Hydrogen bond Fig. 312 (3) Metallic Bonding Atoms pack in regular arrangement to minimize open space All elements are identical size Three types: Hexagonal closest packing Cubic closest packing 2 types:
Face centered Body centered Metallic Bonding Assume spheres are in layers Different packing arrangement comes about because of the way that the spheres are stacked Hexagonal closest packing Hexagonal Every 3rd layer is aligned Means each atom has 12 nearest neighbors ABABAB stacking Symmetry is hexagonal } Hexagonal Facecentered Cubic closest packing facecentered cubic lattice 12 nearest neighbors Every 4th layer aligned ABCABCABC stacking Native metals are good examples If same size and charge, the native metals can form alloys e.g. silver and gold Bodycentered cubic packing E.g. Fe Atoms at nodes of body centered cubic lattice Arrangement has 8 (not 12) nearest neighbors Physical properties
Less dense than hexagonal or cubic packing Closely packed atoms so more dense then ionic bonded crystals Conduct electricity and malleable Body centered cubic lattice Unit cell w/8 nearest neighbors Open lattice, less dense packing 8 unit cells Fig. 42 (4) Ionic Bonding Oxygen most abundant anion making up earth Oxygen bonds mostly ionic Bonding characteristic of SiO is 50% ionic Other elements (Al, Fe, Mg, Ca, Na, K) are even higher percentages ionic bonds In mineralogy, we'll assume most bonds are ionic This simplification allows determining crystal structure particularly true of the silicate minerals No directionality of bonds Does not require overlapping orbitals Only consider geometry (e.g. packing) of atoms Similar to metallic bonds, but now different size spheres Pauling's Rules A set of rules to describe how ionic spheres can pack given assumptions Five rules: Coordination Principle Electrostatic Valency Principle Sharing of Polyhedral elements I Sharing of Polyhedral elements II Principle of Parsimony Coordination Principle (rule 1) Packing arrangement depends on size of ions Coordination number Number of ions surrounding central ion Usually cation surrounded by anions Common numbers are 12, 8, 6, 4, 3, 2 There can be others 11, 10... etc. Coordination Principle (rule 1) Coordination polyhedron Shape defined by anions coordinating around cation Depends on coordination number
8 = cube 6 = octahedron 4 = tetrahedron 3 = triangle 2 = line 12fold coordination 8fold coordination cube 6fold coordination octahedral 4fold coordination tetrahedral 3fold coordination triangle 2fold coordination line Fig 43 Coordination number depends on radius ratio, RR: RR = Rcation/Ranion These values are tabulated Most coordination is between oxygen (1.26) and common ions Effective radii are known for all ions (see appendix A) Possible to predict coordination between ions Ionic radius changes with coordination Some cations fit in more than one coordination Al3+ = 4 or 6 fold coordination Fe2+ and Mg2+ = 6 or 8 fold coordination Na+ and Ca2+ = 8 or 12 fold coordination Irregular numbers and shapes Irregularities caused by many factors Cations can coordinate with 5, 7, 9, 10 or 11 anions Shapes of regular coordination polyhedra may be distorted Often related to bonds being partially covalent, so directionality If strongly bonded, can form anions group: CO32, SO42, SiO44 Electrostatic valency principle (rule 2) Bonding capacity is proportional to: Called Electrostatic valence bond (evb) Evb = ion charge/CN Oxidation state (charge) Coordination number Two broad types: Uniform bond strengths Isodesmic Nonuniform bond strengths Anisodesmic & Mesodesmic Isodesmic Uniform bond strength Isodesmic = equal strength All bonds between cations and anions have same strength Anions tend to pack into highly symmetrical arrangements Typically isometric, tetragonal or hexagonal Typically oxides, fluorides, chlorides etc. Example: Halite
All bonds between each atom exactly the same strength Nonuniform bond strength Some bonds are stronger than others within an individual mineral Form anionic groups Commonly oxygen with small, high charge cations: C4+, S6+, P5+, Si4+ Anionic groups: CO34+, SO46+, PO45+, SiO44+ 2 kinds of nonuniform bonds Anisodesmic Some anioncation bonds take more than half the charge of the oxygen Soluble into cations and anionic groups E.g. calcite Also sulfates (SO42) and phosphates (PO43) Ca Ca2+ + CO32 strong weak evbCO = 4+/3 = 1 1/3; Means 2/3 charge remain on oxygen evbCaO = 2+/6 = 1/3; Means each oxygen is bonded with 2 Ca 6 fold coordination (not shown) Fig. 44 Mesodesmic Some anioncation bonds take exactly half of the anion charge Silica bonds with 4 oxygen Silica tetrahedron Arrangement of tetrahedron is basis of silicate mineral classification Allows polymerization Classification of silicate minerals evbSiO = 4+/4 = 1; Uses exactly charge of oxygen
4+ 2+ 2+ Two possibilities: (1) polymerization (2) other cations Very important to classification of silicate minerals Fig. 45 Sharing of polyhedral elements I (rule 3) Cations generally share only single anions Occasionally will share two anions point sharing Edge sharing Face sharing Never share 3 anions Reason for this is that cations have to be separated by sufficient distance Edge sharing Face sharing
a Point sharing Figure 4.6 Sharing of polyhedral elements II (rule 4) Highly charged cations are not placed near each other in a structure Like charge repel highly charge ions must be far apart Small cations (highly charge) have low coordination number Other cations bonded to anions have low charge and are large Use more than of anion charge E.g. CO32, PO43, SO44, Anhydrite Structure CaSO4 Sulfur (S6+) separated by long distances Fig. 48 Principle of Parsimony (rule 5) Parsimony = "stinginess" Number of fundamentally different sites for a mineral is small Typically fewer than 4 different coordination polyhedron (sites) for cations Means there are small integer ratios of elements in mineral formulas Amphiboles one of the least parsimonious minerals e.g., Hornblende: (Na,K)01Ca2(Mg, Fe2+, Fe3+, Al)5Si67.5Al20.5O22(OH)2 Examples of Pauling's rules Halite RR = Na/Cl = 1.16/1.81 = 0.64 Uniform isodesmic bonding (rule 2) Cubic closest packing Filling of octahedrons mean that Na+ polyhedron has to share edges (rule 3) Coordination number = 6 (rule 1) Simple structure (rule 5) Rule 4 doesn't apply no highly charge ions OK because Na small charge (+1) Layers of Cl parallel to (111) plane Edge sharing is ok, small charge on ions Fig. 47 Anhydrite CaSO4 Nonuniform anisodesmic bonding S6+ is tetrahedrally coordinated with 4 O2 Rule 2: evb = 1.5 on SO bonds, so there is 1/2 charge for bonding with Ca2+ CaO coordination usually 8 fold (rule 1) Rule 2: evb = 0.25 on CaO bonds Insufficient space for cubic coordination Ca coordination polyhedron distorted cube Must arrange 8 O around cations ...
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