CHAPTER 4 Crystal Structure

CHAPTER 4Crystal StructureIntroduction to Mineralogy,Second editionWilliam D. NesseCopyright 2012, by Oxford University Press, Inc.

We can assume minerals to be made of orderly packing of atoms or rather ionsor molecules. Many mineral properties like symmetry, density etc are dependent on how theatoms or ions are packed We can approximate the atoms or ions in a metal to be rigid spherical balls Think of a box full of ping pongballs.The densest packing is one onwhich a layer of balls sit on thehollow between the balls in thelayer below.The two closest packing are: Hexagonal close packing(ABCABC) Cubic close packing (ABAB)Figure 4.1 Closest packing of spheres.Introduction to Mineralogy,Second editionWilliam D. NesseCopyright 2012, by Oxford University Press, Inc.

Some what less dense packing is bodycentered cubic packing, seen in Iron. Because they can be packed so closely,metals have high densityFigure 4.2 Body-centered cubic packing. (a) Bodycentered lattice (left) and with atoms at each lattice node (right). (b) Eight unit cells.Each sphere is in contact with eight neighbors.Introduction to Mineralogy,Second editionWilliam D. NesseCopyright 2012, by Oxford University Press, Inc.

Covalent and Molecular Bonds Covalent bonds are strong therefore covalent crystalsare strong and have high melting point Because atoms need to be placed in a specificorientation only, covalent crystals do not show a closepacking. The bonds in molecular crystals are weak, hence thesetend to be soft. The geometry of the structure isdetermined by the shape and charge distribution in themolecules (e.g., Hydrogen bond in water)Introduction to Mineralogy,Second editionWilliam D. NesseCopyright 2012, by Oxford University Press, Inc.

Ionic Bonds For minerals formed largely by ionic bonding,the ion geometry can be simply considered to bespherical Spherical ions will geometrically pack(coordinate) oppositely charged ions aroundthem as tightly as possible while maintainingcharge neutrality For a particular ion, the surrounding coordinationions define the apices of a polyhedron The number of surrounding ions is theCoordination NumberIntroduction to Mineralogy,Second editionWilliam D. NesseCopyright 2012, by Oxford University Press, Inc.

Pauling’s Rules of MineralStructureRule 1: A coordination polyhedronof anions is formed around eachcation, wherein:- the cation-anion distance isdetermined by the sum of theionic radii, and- the coordination number of thepolyhedron is determined by thecation/anion radius ratio (Ra:Rx)Linus Pauling

Radius Ratioof Cation andAnion (Rc/Ra),Coordinationnumber tionnumberPackinggeometry 1.012Corners of acuboctahedron(close packing)0.732-18Corners of acube0.4140.7326Corners of aoctahedron0.2250.4144Corners of atetrahedron0.1550.2253Corners of anequilateraltriangle 0.1552LinearFigure 4.3 Coordination polyhedra. Anions withradius Ra are shown with light shading, cations withradius Rc with dark. Left view shows cation andanions drawn to scale.Introduction to Mineralogy,Second editionWilliam D. NesseCopyright 2012, by Oxford University Press, Inc.

Pauling’s Rules of MineralStructureRule 2: The electrostatic valency principleThe strength of an ionic (electrostatic)bond (e.v.) between a cation and an anionis equal to the charge of the anion (z)divided by its coordination number (n):e.v. z/nIn a stable (neutral) structure, a chargebalance results between the cation and itspolyhedral anions with which it is bonded.

Charge Balanceof Ionic Bonds

Uniform Bond Strength Isodesmic: where all ionicbonds are of equal strength Anions tend to pack around thecation in highly symmetric andgenerally close packingarrangement Most of the minerals crystallizein highly symmetric systems likeisometric, tetragonal orhexagonal systems Oxides, Fluorides, Chlorides arecommon examplesFigure 4.4 Tetrahedral and octahedral sites in close-packed structures. A layer of anions (light) is shown with just four anions from anadjacent layer (dark).Introduction to Mineralogy,Second editionWilliam D. NesseCopyright 2012, by Oxford University Press, Inc.

Nonuniform Bond Strength Some anion-cation bonds are strongerthan others: cations forming strongerbonds are smaller and have a high charge– Ex: C4 , S6 , P5 , Si4 – These strongly charged cations from CO32-,SO44-, PO43-,SiO44- anionic groups Have lower symmetry, irregularcoordination polyhedraIntroduction to Mineralogy,Second editionWilliam D. NesseCopyright 2012, by Oxford University Press, Inc.

Formation of Anionic GroupsAnisodesmic Bonds results from high valence cations with electrostaticvalencies greater than half the valency of the polyhedral anions; otherbonds with those anions will be relatively weaker.Mesodesmic: anion-cation bond takes exactly half othe available anioncation chargeCarbonateAnisodesmicSulfate

Figure 4.5 Anisodesmic carbonate (CO3 2 ) group. Each O–C bond occupies 1.33 of the available –2 charge on oxygen; only two-thirds ofa charge on the oxygen is available to bond with other cations such as Ca2 .Introduction to Mineralogy,Second editionWilliam D. NesseCopyright 2012, by Oxford University Press, Inc.

Figure 4.6 Mesodesmic silicon tetrahedra.Introduction to Mineralogy,Second editionWilliam D. NesseCopyright 2012, by Oxford University Press, Inc.

Pauling’s Rules of MineralStructure Rule 3: Anion polyhedra that share edges orfaces decrease their stability due to bringingcations closer together; especially significant forhigh valency cations Rule 4: In structures with different types ofcations, those cations with high valency andsmall CN tend not to share polyhedra with eachother; when they do, polyhedra are deformed toaccommodate cation repulsion

Figure 4.7 Sharing anions between polyhedra.Introduction to Mineralogy,Second editionWilliam D. NesseCopyright 2012, by Oxford University Press, Inc.

Pauling’s Rules of MineralStructure Rule 5: The principle of parsimony : nature tendstowards simplicityBecause the number and types of different structuralsites tends to be limited, even in complex minerals,different ionic elements are forced to occupy the samestructural positions – leads to solid solution.

Figure 4.8 NaCl structure.Introduction to Mineralogy,Second editionWilliam D. NesseCopyright 2012, by Oxford University Press, Inc.

Figure 4.9 Anhydrite structure. Isolated SO4 2 groups are bonded laterally through Ca2 (dark spheres).Introduction to Mineralogy,Second editionWilliam D. NesseCopyright 2012, by Oxford University Press, Inc.

Sphere to scale:First layerobscures whateveris behindStick and ballPolyhedra: onlycoordinatepolyhedral are shownHybrid: polyhedraland stick and ball:anions are omittedMapped: Position of each atomis projected from a axis to theback wall of the unit cell.Numbers denote % distanceaway from the back wall of theunit cell.Figure 4.10 Illustration of olivine (Mg2SiO4) crystal structure viewed down the a axis. Each unit cell (outlined) contains four formula units.Introduction to Mineralogy,Second editionWilliam D. NesseCopyright 2012, by Oxford University Press, Inc.

Isostructural Minerals, Polymorphism Two minerals showing same type of crystal structure are calledisostructural: e.g., carbonate group: calcite, magnesite, siderite etcor halite (NaCl) and galena (PbS) Same chemical compound with different crystalline structure ordifferent minerals with the same chemical formula are calledpolymorphs. The phenomenon is Polymorphism and the collectionof minerals of the same formula is called a polymorphic group.e.g., (diamond and graphite), (Kyanite, Andalusite, Sillimanite) (see Table 4.4) One of the polymorphs is stable under a particular P,T condition,Generally higher P favors denser, more close packing Four types of Order-disorderPolytypismIntroduction to Mineralogy,Second editionWilliam D. NesseCopyright 2012, by Oxford University Press, Inc.

ReconstructivePolymorphism: Old bond isbroken and new ions arereassembled in new bondsExample: Diamond andGraphitePolymorphs do not convertfrom one to the other formFigure 4.11 Diamond and graphite stability fields.Introduction to Mineralogy,Second editionWilliam D. NesseCopyright 2012, by Oxford University Press, Inc.

Displacive Polymorphism: No breakingof structure – involves only bending ordistortion of crystal structureExample: α- quartz and β-quartz (highquartz) : automatic unquenchableconversion takes place at 573 C High T forms have higher symmetry Crystal form of High T form isretained on conversion but low Tforms show signs of internal strainFigure 4.12 Structures of α-quartz and β-quartz. Thetop view looks down the c axis, the bottom view is fromthe side. The unit cell is outlined.Introduction to Mineralogy,Second editionWilliam D. NesseCopyright 2012, by Oxford University Press, Inc.

Order-disorder Polymorphism: mineralstructure and composition remains thesame – only the cation distribution withinstructural sites change.Ex; K-Feldspars (KAlSi3O8): Containes 1Al for every 3 Si ions. In a disordered state, Al can be foundin any one of the four tetrahedral sites(High-Sanidine), In a maximum ordered state (low ormaximum microcline) , Al is found onlyin one of the Tetrahedral sites, the otherthree always occupied by Si High T favors more disordered state Rapid cooling prevents ordering henceSanidine is found only in volcanic rocksFigure 4.13 Order–disorder in K-feldspar (KAlSi3O8)polymorphs.Introduction to Mineralogy,Second editionWilliam D. NesseCopyright 2012, by Oxford University Press, Inc.

Polytypism: polymorphs differ only in stacking order. Typically seen in sheetsilicates like micas or clay minerals. Also in hexagonal vs Cubic ClosePacking as discussed earlier.Figure 4.14 Polytypism involves different patterns of stacking identical sheets. The symbols used here are adapted from those used inthe sheet silicates.Introduction to Mineralogy,Second editionWilliam D. NesseCopyright 2012, by Oxford University Press, Inc.

In a Solid Solution, one ion can substitute for the other inthe same mineral structure. For example Fe and replaceMg in Olivine (Fe,Mg)2SiO4 (Simple Substitution) The extreme compositions (e.g., Fe2SiO4 and Mg2SiO4 areknown as end members.The range of compositions produced by solid solution is calledSolid solution or Substitution Series.A series can be complete or continuous series where allintermediate range between the end members is possible.Or, incomplete series where only a restricted range ofcomposition is found.Three types: Substitution Solid Solution, Omission SolidSolution and Interstitial Solid SolutionSubstitution: Ions of similar charge and size can substituteeach other –usually size differing by less than 15% cansubstitute extensively. Elements are Diadochic if they canoccupy the same structural siteAt higher temp more solid solution but at lower temp solidsolution can unmix or exsolve.In a Coupled Substitution a double substitution takes place –one substitution increases charge so to maintain chargeneutrality another substitution takes place which decreasescharge. Ex: Plagioclase series – NaAlSi3O8 –CaAl2Si2O8Ca2 replaces Na (similar size but different charge) – andcharge balance is maintained by one Al3 replacing one Si4 Figure 4.15 Solid solution.

In Omission Substitution, charge balance ismaintained by leaving some cation sites vacant. In Pyrrhotite (FeS) Fe3 substitutes for Fe2 . To maintaincharge balance 3 Fe2 is replaced by 2 Fe3 , leaving onesite vacant Interstitial Substitution is opposite of Omissionsubstitution – extra ions are placed in normally vacantsites. Beryl (Al2Be3Si6O18) is a ring silicate where ions like K ,Rb , Cs etc are placed in the central hollow and isbalanced by replacing one Al3 by Si4 Introduction to Mineralogy,Second editionWilliam D. NesseCopyright 2012, by Oxford University Press, Inc.