Fundamentals of crystal chemistry Mineralogy Carleton College

Crystal Chemistry As we have been discussing for the last week, crystals, and thus minerals, are made up of a 3-dimensional array of atoms arranged in an orderly fashion.

Crystal Chemistry Now we will explore what these atoms are and how they interact with one another to determine the physical and structural properties of crystals.

Crystal chemistry We can better understand the wide variety of different mineral species and the variations exhibited by individual mineral species by recognizing the gross chemical features of the Earth and especially of the crust.

Composition of the crust

Crystal chemistry While Oxygen comprises almost half of the crust by weight, it occupies almost 94% by volume!

Crystal chemistry This is directly reflected in minerals as well. Oxygen is the most dominant anion in crustal minerals, and as you would predict from the numbers, the silicate minerals make up the bulk of the crustal rocks.

Crystal chemistry The Earth's crust, on an atomic scale consists essentially of a close packing of oxygen anions with interstitial metal cations, chiefly Silicon.

Crystal chemistry In addition to the silicate minerals, the crust also contains significant amounts of other oxygen compounds such as the oxide and carbonate minerals.

Chemical Bonding The chemical and physical properties of crystals depend almost entirely on the forces that bind the atoms together in a crystal structure. Forces known collectively as chemical bonds.

Chemical Bonding Chemical bonding depends on the electronic structure of the atoms involved, in particular the valence electrons in the outermost shells, and on the size of the ion or atom.

Chemical Bonding In general we recognize 4 different types of chemical bonds, although as we will see, all bond types are transitional from one type to another.

Types of Chemical Bonds Ionic Covalent Metallic Van der Waals Hydrogen Bond

Ionic Bonds –There is a tendency for atoms to lose or gain electrons and become ions in order to achieve the stable electronic configuration with completely filled outer electron shells.

Ionic Bonds –Positively charged ions are called cations and negatively charged ions are called anions.

Ionic Bonds –These ions can achieve various values of electronic charge depending on the number of electrons gained or lost.

Ionic Bonds Electron charges  +1 monovalent cations  +2 divalent cations  +3 trivalent cations  +4 tetravalent cations  +5 pentavalent cations  -1 monovalent anions  -2 divalent anions

Ionic Bonds For example, Na has one electron in its outermost shell. It will tend to give up this electron to become Na +1 ion.

Ionic Bonds Similarly, Cl has 7 electrons in its outermost shell and would like to gain an electron to become Cl -1 ion.

Ionic Bonds Once these atoms become Na +1 and Cl -1, the force of attraction betweenthe oppositely charged ions results in an ionic bond.

Ionic Bonds

Formed between atoms of very different electronegativity The less electronnegativity atom completely donates one or more electron to the more elctronegative atom. The resulatin ions are held together by electronstatic attaraction

Ionic Bonds Most important for bonding between oxygen and Mg, Si, Al, Na, K Hence, the primary bonding type in silicate and oxide minerals

Ionic Bonds Ionic bonds are non-directional in nature, that is the attractive forces occur form all directions.

Ionic Bonds Crystals made of ionically bonded atoms tend to have the following properties:

Ionic Bonds Dissolve easily in polar solvents like water (H2O is a polar solvent because the hydrogen ions occur on one side the water molecule and give it a slight positive charge while the other side of the water molecule has a slight negative charge).

Ionic Bonds Tend to form crystals with high symmetry. Moderate hardness and density. High melting temperatures. Generally poor conductors of heat and electricity (they are good materials for thermal and electrical insulation).

Covalent Bonds Elements near the right hand side of the periodic table tend to bond to each other by covalent bonds to form molecules that are found in crystal structures. For example Si and O form an SiO4 -4 molecule that can bind to other atoms or molecules either covalently or ionically.

Covalent Bonds Carbon has four electrons in its outer shell and needs 4 more to achieve the stable electronic configuration. So a Carbon atom can share electrons with 4 other Carbon atoms to form covalent bonds. This results in compounds like diamond or graphite that are held together by strong covalent bonds between Carbon atoms.

Covalent Bonds In reality, bonding between atoms usually does not take place as pure covalent or pure ionic bonds, but rather as a mixture of bond types. The amount of each type is determined by the electronegativity difference between the atoms involved.

Covalent Bonds Covalent bonds can also be thought of as shared electron bonds. Covalent bonds develop when atoms can achieve the a stable outer shell electron configuration by sharing electrons with another atom. This results in each of the atoms having a stable electronic configuration part of the time.

Covalent Bonds Formed between atoms of similar electronegativity Atoms are held together by “Sharing electrons” Sulfide minerals Most organic compounds

Covalent Bonds

Covalent bonds are very strong directional bonds, that is they occur along the zone where they electrons are shared.

Covalent Bonds Covalently bonded crystals have the following properties: –Relatively insoluble in polar solvents like water. –High melting temperatures. –Generally form crystals structures of low symmetry. –Tend to have high hardness. –Generally poor conductors of heat and electricity.

Covalent Bonds In reality, bonding between atoms usually does not take place as pure covalent or pure ionic bonds, but rather as a mixture of bond types. The amount of each type is determined by the electronegativity difference between the atoms involved.

Covalent Bonds For example, consultation of electronegativity chart above shows Cl with a value of 3.16 and Na with a value of The electronegativity difference is 2.3, suggesting that only 80% of the bonding in NaCl is ionic. Even looking a larger electronegativity difference like for NaF, the bonding would by only about 90% ionic. Bonding between Oxygen atoms or between Carbon atoms, where the electronegativity difference is 0, would result in pure covalent bonds.

Electronegativity

Covalent Bonds

Chemical Bonds in Minerals

Metallic Bonds None of the bond types discussed so far result in materials that can easily conduct electricity. Pure metals however, do conduct electricity easily and therefore must be bonded in a different way.

Metallic Bonds

This is the metallic bond, where positively charge atomic nuclei share electrons in their electron clouds freely. In a sense, each atom is sharing electrons freely with other atoms, and some of the electrons are free to move from atom to atom.

Metallic Bonds Since some of the electrons are free to move, metallically bonded materials have high electrical conductivity.

Metallic Bonds Pure metals appear to bind in this way. When crystals are formed with metallic bonds they have the following properties:

Metallic Bonds Low to Moderate hardness. Usually very malleable and ductile. Good thermal and electrical conductors. Soluble only in acids. Crystals with high symmetry.

Residual Bonds Residual bonds are weak bonds that involve the attraction of partially charged atoms or molecules. These partial charges are created when electrons become concentrated on one side of an atom or molecule to satisfy ionic or covalent bonds.

Residual Bonds This sometimes creates a polar atom or molecule which has a concentration of negative charges on one side and a concentration of positive charges on the other side.

Residual Bonds When residual bonds occur in a crystal structure, they generally form planes or zones of easy cleavage because of the weakness of the residual bond.

Residual Bonds Two special cases are discussed here. – Hydrogen Bonds –van der Waals

Residual Bonds Hydrogen Bonds - These occur in the special case of hydrogen, because H has only one electron. When Hydrogen gives up this electron to become H +1 ion or shares its single electron with another atom in a covalent bond, the positively charged nucleus of the hydrogen atom is exposed, giving that end of the H ion a residual +1 charge.

Residual Bonds

This is what causes the H 2 O molecule to be a polar molecule seen here.

Residual Bonds Similarly, an OH -1 molecule, common in sheet silicate minerals like micas and clay minerals, although possessing a -1 charge will have exposed H nuclei that can bond to other negative residual charges forming a weak hydrogen bond. Layers of OH -1 molecules in the sheet silicates result in the easy cleavage along the {001} planes.

Residual Bonds van der Waals Bonds are also residual bonds that result from polarization of atoms or molecules. In the mineral graphite, the C atoms are held together by strong covalent bonds, that result in concentrations of positive and negative charges at either end of the C atoms. Bonding between sheets takes place as a result of the slight attraction between these residual charges from one sheet to another.

Residual Bonds

Mixture of Bonds in Crystals Since most crystals are complex mixtures of atoms, there will likely be more than one bond type in complex crystals. Thus, except in very simple compounds properties such as hardness, cleavage, solution rate, and growth rate may be directional, as discussed in a previous lecture.

Stable Ionic Structure Between an pair of oppositely charged ions there is an attractive force, that is proportional to the products of their charges and inversely proportional to the square of the distance between their centers. (Coulomb’s Law)

Stable Ionic Structure F = K qi, qj/ r 2 Where F = Coulomb force (bond strength) K = proportionality constant Q = point charges of ions I and j R = distance between ion I and j

Coordination Coordination Principles - As ions bond to each other, they gather in an arrangement such that they are symmetrically clustered.

Coordination The convention is chosen such that cations lie at the center of coordination, with anions residing as nearest neighbors. The number of anions that form this polyhedron around thecation is known as the coordination number (C.N.).

Coordination C.N. = 4 C.N. = 6 (octahedral)

Coordination The geometry of the first coordination shell (nearest neighbors) is related to the relative size of the atomic radii. Relative sizes can be expressed as the Radius Ratio. R = R A / R B Where: R A = Radius of cations R B = Radius of anions

Coordination Example: Potassium and oxygen R A = 1.33Å, R B =1.40Å, R A / R B KO = 0.95

Coordination Example: Silica and oxygen R A = 0.42Å, R A =1.40Å, R A / R B SiO = 0.30

Coordination When coordinating identically sized spheres there are several possible ways of packing so as to create contact between the spheres. 1.C.N. =12 –a. Hexagonal Closest Packing (HCP) –b. Cubic Closest Packing (CCP)

Coordination 2. Cubic Packing where the C.N. = 8 (cubic coordination)

Coordination 3. For relative R values less than 0.732, the 6 C.N. (or octahedral coordination) is the preferred packing arrangement. The limiting value for the interior of octahedrally coordinated anions (relative size of 1) is in the range of R =

Coordination 4. Tetrahedral coordination is the next smallest interior space with R = Triangular coordination is next smallest space with R = Linear coordination is smallest where R< 0.155

Ionic Radii

Radius Ratio R A /R B Where A is radius of Cation and B is radius of anion.

Pauling’s Rules for Ionic Structures Rule 1: The coordination number of a cation A by an anion B will be determined by the radius ration of the ions A and B

Basis for Rule 1 (Octahedral example)

Cos 30 o = 0.5 / ( x) x = 0.5 / Cos 30 o  = 0.5 /  =  0.5 x =  x= 0.155

Basis for Rule 1 (Octahedral example)

(1 + x) 2 = x = √2 = X = 0.414

Pauling’s 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 coordinatio of cations will equal the charges on the anion. This is the electrostatic valency principle. (* The strength of a bond from each cation is its charge/coordination number)

Pauling’s Rule for Ionic Structures Rule 3: The sharing of edges and faces by coordination polyhedra decreases the stablity of a structure.

Pauling’s Rules for Ionic Structures Rule 4: In Structures with more than one cation, those of high valency and small coordination number tend not share polyhedron elements with each other.

Pauling’s Rules for Ionic Structures Rule 5: The number of different kinds of sites in a stable structure tends to be small. Hornblende NaCa 2 (Mg,Fe,Al) 5 [(Al,Si) 4 O 11 ](OH) 2