II Stage Mineralogy DM Sherman, University of Bristol
2001/2002
Bonding and the Structures of Minerals
Stage II Mineralogy University of Bristol
Types of Chemical Bonds
Covalent Metallic Ionic Van der Waals Hydrogen Bond
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Stage II Mineralogy DM Sherman, University of Bristol
2001/2002
Covalent Bonds
Formed between atoms of similar electronegativity. Atoms are held together by sharing electrons. Sulphide (sulfide) minerals. Most organic compounds.
Metallic Bond
Extreme example of covalent bond: electrons are delocalized throughout the crystal. Formed between metal atoms of similar electronegativity and with weakly held electrons. Can form between metal atoms in sulfide minerals.
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Stage II Mineralogy DM Sherman, University of Bristol
2001/2002
Ionic Bonds
Formed between atoms of very different electronegativity. The less electronegative atom completely donates one or more electron to the more electronegative atom. The resulting ions are held together by the electrostatic attraction. Most important for bonding between oxygen and Mg, Si,Al, Na, K. Hence, the primary bonding type in silicate and oxide minerals.
Example of an Ionic Bond: MgO
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Stage II Mineralogy DM Sherman, University of Bristol
2001/2002
Chemical Bonds in Minerals
Very Ionic: Mg-O Ca-O Na-O K-O Partially Covalent: Al-O Si-O Fe-S Ti-O Very Covalent: C-O as in (CO3)2S-O as in (SO4)2S-S as in S22-)
Stable Ionic Structures
F = q aq b r2
Attractive force between cations and anions (F < 0). Repulsive cation-cation and anion-anion forces (F > 0). Most stable structure will minimize the total potential energy.
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Stage II Mineralogy DM Sherman, University of Bristol
2001/2002
Ionic Radii (Shannon, 1976)
Paulings Rules for Ionic Structures
Rule 1: The coordination number of a cation A by an anion B will be determined by the radius ratio of the ions A and B: RA/RB < 0.16 0.16 > RA/RB < 0.41 0.41 > RA/RB < 0.73 0.73 > RA/RB < 1.00 1.0 > RA/RB 3-fold coord. 4-fold coord. 6-fold coord. 8-fold coord. 12-fold coord.
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Stage II Mineralogy DM Sherman, University of Bristol
2001/2002
Basis of Rule 1 (Octahedral Example)...
Important Coordination Polyhedra
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Stage II Mineralogy DM Sherman, University of Bristol
2001/2002
Note: Representation of Coordination Polyhedra..
Polyhedral Scheme Ball and Stick Scheme
In the scheme, polyhedral the vertices represent oxygens will the center of the polyhedron is the metal ion.
Example: B1-B2 structures
B1 structure has cations in 6-fold coordination. B2 structure has cations in 8-fold coordination. R(Na)/R(Cl) = 0.69 and R(K)/R(Cl) = 0.99.
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Stage II Mineralogy DM Sherman, University of Bristol
2001/2002
Paulings Rules for Ionic Structures(Cont).
Rule 2:An ionic structure will be stable to the extent that the sum of the strengths* of the electrostatic bonds that reach an anion from its coordination of cations will equal the charge on the anion. This is the electrostatic valency principle. (*The strength of a bond from each cation is its charge/coordination number).
Example of Paulings Rule 2:
Oxygens are never bonded to more than two tetrahedrally coordinated Si4+:
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Stage II Mineralogy DM Sherman, University of Bristol
2001/2002
Paulings Rules for Ionic Structures
Rule 3: The sharing of edges and faces by coordination polyhedra decreases the stability of a structure. Edge-sharing
Corner-sharing Face-sharing
Rule 3 Example: Rutile vs. Anatase
There are two polymorphs of TiO2. Rutile is more stable (by 6 kJ/mole) than anatase because there is less edge-sharing in the structure. Anatase Rutile
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Stage II Mineralogy DM Sherman, University of Bristol
2001/2002
Paulings Rules for Ionic Structures
Example: Low Albite NaAlSi3O8
Rule 4: In structures with more than one cation, those of high valency and small coordination number tend not to share polyhedron elements with each other.
Paulings Rules for Ionic Structures
Rule 5: the number of different kinds of sites in a stable crystal structure tends to be small. Hornblende NaCa2(Mg,Fe,Al)5[(Al,Si)4O11]2(OH)2 There are four octahedral sites, one 12-fold site and two tetrahedral sites.
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Stage II Mineralogy DM Sherman, University of Bristol
2001/2002
Breakdown of Paulings Rules
In very covalent compounds (e.g., sulfides). At high pressures and temperatures. A phase transition will occur when G = U -TS + PV < 0. Paulings rules only tell us the sign of U. At high pressure a dense structure may be favoured if PV < U . At high temperature a high entropy structure may be favoured if TS > U)
Example: Strange Sulfide Structures...
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Stage II Mineralogy DM Sherman, University of Bristol
2001/2002
Example: High Pressure SiO2 Polymorphs
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