CRYSTAL STRUCTURE

Atomic structure

Quantum theory & wave mechanics

Bohr atom

Electron orbits

Orbital shape, density, electron distribution

Interatomic bonds

Ionic bonds

Covalent bonds

Van der Waals bonds

Metallic bonds

Atomic bonding in solids

Ionic

Covalent

Molecular

Metallic

Hydrogen

Ionic crystals

Madelung constant

depends on the geometry of the crystal structure and is characteristic for a particular structure type

Example: NaCl structure: = 1.748

CsCl structure: = 1.763

zincblende structure: = 1.748

Madelung constant represents the Coulomb energy of an ion pair in a crystal relative to the Coulomb energy of an isolated ion pair

> 1 but not far

Penurunan Madelung constant sbb:

The energy of one ion of charge Zie in a crystal (ex NaCl) = summation of its interaction with the other j ions in the crystal

Ei =

nj

ij

j

ji

Ri

B

Ri

eeZZ

4

Ionic crystals are characterized by:

Strong infrared absorption

Transparency in the visible wavelength

Low electrical conductivity at low temp,but good electrical conductivity at high temp

Compounds of metal ions with group III anion are strongly ionic. Ex: NaCl, LiF

Compounds of metals with oxygen are largely ionic. Ex: MgO, Al2O3, ZrO2

Compounds with with higher atomic weight elements of group VI (S, Se, Te) which have lower electronegativity are increasingly less ionic.

Ionic bonds

The strength of ionic bonds increases as the valence increases.

The electron distribution in ions is nearly spherical

The interatomic bond (since it arises from coulombic forces) is nondirectional

Covalent crystals

A pair of electron is concentrated in the space between the atoms

Covalent crystals form when a repetitous structure can be built up consistently with the strong directional nature of the covalent bond

Examples:

C form 4 tetrahedral (covalent) bond

In methane, CH4: all the tetrahedral bonds are used up in forming a molecule so that no electron are available for forming additional covalent bonds. No covalent crystal can be built up

In diamond: covalent crystal is formed. Each C is surrounded by 4 other C atoms. The tetrahedral (fourfold) coordination doesnot allow dense packing

Covalent crystal (ex: diamond, SiC) Have high hardness High melting point Low electrical conductivity (when pure) at low

temp Formed between atoms of similar

electronegativity which are not close in electronic structure to inert gas config: C, Ge, S, Te etc

Molecular bond

In organic molecules, inert gases. Atoms are bound together in solid phase by means of weak vd waals forces: weak, compressible, low melting point, low boiling point.

These forces occur in all crystals and important only when other forces are absent

In ceramics: the bonding together of silicate sheet in clays.

Hydrogen bond crystal

In inorganic crystals

H ions form a rather strong bonds between two anions

Metal crystals

Crystal structures

The most stable crystal structures are those that have the densest packing of atoms; consistent with other requirements, such as the no of bons per atom, atom size and bond direction.

Crystal structures

Simple cubic

Close-packed cubic

Close-packed hexagonal

Simple cubic structure

48% void space (not very dense)

6 nearest neighbours

Typical structures with

anions forming simple cubic

5. Cesium chloride

structure

Formula = AX

e. g. CsCl, CsBr

Anions = simple cubic

Cations = fill all of

the cubic centres

CN = 8 for both

anions and cations

Close-packed cubic structure

26 void volume

12 nearest neighbours

Example of the most simple unit cell: face centered cubic

For fcc, there are two kinds of interstices: octahedral and tetrahedral

Close-packed hexagonal structure

Space lattice

32 permissible arrangements 14 different Bravais or space lattice, grouped into 6 system:

Triclinic

Monoclinic

Orthorhombic

Tetragonal

Hexagonal

cubic

Grouping of ions and Paulings Rules

For crystals having a large measure of ionic bond character (halides, oxides and silicates), the structure is (in large part) determined on the basis of how + and ions can be packed to maximize electrostatic attractive forces and minimize electrostatic repulsion. The stable array of ions in a crystal is the one with the lowest energy.

Ionic crystal structure Paulings Rules 1st rule

Coordination polyhedron of anions is formed about each cation (and vice versa)

Cation anion distance

Coordination number (CN) = the number of anions surrounding a cation

A given coordination is stable only when the ratio of cation to anion radius is greater than a critical value (#9)

Critical radius ratio govern the coordination of cation about anion (#9)

Since anions are larger than cations, crit radius ratio is determined by the coordination of anions about the cation cation coordination polyhedron.

Geometry would permit the structure to form with any one of a number of smaller coordination number. The most stable structure however always has the maximum permissible coordination number (#9).

Pauling,s 2nd Rule

Local electrical neutrality

The formal charge of cation divided by its CN = ionic bond strength (#10)

Example: Si, valence 4; tetrahedral coordination bond strength = 4/4 = 1

Al3+, octahedral coordination; bond strength = 3/6 = , regardless whether all coordinating anions are of the same species.

In a stable structure, the total strength of the bonds reaching an anion from all surrounding cations should be equal to the charge of the anion.

Example: SiO2 two bonds of strength 1 reached the shared O ion from the surrounding Si ions 2 x 1= 2 == valence of O.

Implying that in Si2O7 no additional cation may be bonded to the shared O

MgAl2O4 (spinel structure). Each O2- is surrounded by one Mg2+ which donate bond of strength 2/4 and three Al3+ which donate three bonds of strength 3/6: 2 == (1)(2/4) + (3)(3/6)

#10

Paulings 3rd rule

The separation of cations within the polyhedron decreases as the polyhedron successively shared corners, edges and faces and the repulsive interaction between cations accordingly increases

Pauling,s 4th rule

Polyhedron formed about cations of lowest CN and high charge tend to be linked by corner

--- the repulsive interaction between a pair of cations increases as the square of their charge and that the separation of caations within a coordinated polyhedron decreases as the CN becomes smaller

Pauling,s 5th rule

The number of different constituents in a structure tends to be small

--- follow from the difficulty encountered in efficiently packing into a single structure ions and coordination polyherda of different size.

Oxide structures

Rock salt

Wurtzite

Zincblende

Spinel

Corundum

Rutile

Cesium chloride

Fluorite

Antifluorite

Perovskite

Ilmenite

Derivative structures, mechanism

Substitution of different atoms

Omission of atoms

Addition of an atom to an unoccupied site (stuffing)

Distortion of an atomic array

Silicate structures

Radius ratio Si-O = 0.29 tetrahedral coordination (CN = 4)

Bond strength = 4/4 = 1 O may be coordinated with only two Si low CN of O makes silica not so dense

Silicates classification

are based on the number of shared O ions per [SiO4] tetrahedra (bridging oxygen). Silicates characteristics largely depend on the nature of the tetrahedral arrangement. Inversely, the characteristics and behaviour of silicates provide many clues to their internal structure.

Silicates classification

1. Independent silicates (orthosilicates)

2. Ring silicates (cyclosilicates)

3. Chain/linear silicates (polysilicates)

4. Layer/sheet silicates (phyllosilicates)

5. Framework silicates

Orthosilicates The silica tetrahedra do not share any O bonds

examples

Cyclosilicates the tetrahedra are joined forming ring, each tetrahedron shares two O with the adjacent tetrahedra. The rings are complex groups of (SiO3)3

-6 or (SiO3)6-12. Charges are balanced by

metal ions holding the rings together in a crystal structure.

examples

polysilicates a linear open structure of tetrahedra in which each tetrahedron share two O with its adjacent tetrahedra. In effect a giant negative ion is created with an indefinite number of tetrahdera, each carrying 2 negative charges. The chains are aligned and held together by metal ions other than silicon.

pyroxenes

Phyllosilicates are formed when each tetrahedron shares 3 O with other tetrahedra. The resulting giant negative ions extends imdefinitely in 2D. The sheet consists of (Si2O5)-2 units held together in stacks by metal ions.

Framework silicates the tetrahedra shares all of its 4 O with the other tetrahedra forming a framework structure extending in 3D. Al can substitute Si as the centre of the tetrahedra. If part of the [SiO4] tetrahedra are substituted by [AlO4]- tetrahedra, the corresponding minerals are termed aluminosilicates. As Al has 3 positive charges while the 4 O give 4 negative charges, the resultant tetrahedra has to be charge-balanced by a cation, usually of the alkali and alkaline-earth metals.

Silica, crystalline SiO2

Polymorphs: quartz, tridymite and cristobalite, each exist in two or three modif.

SiO2, silica are both monotropic and enantiotropic. and quartz are two stable form of silica showing enantiotropic behaviour.

and cristobalite are two metastable form of silica which are enantiotropic wrt one another but monotropic to the stable forms of and quartz.

enantiotropy

Type of polymorphism in which each phase posses a definite range of stability

It is a common type

Monotropy

One that posseses more than one crystalline form but where one form is stable over the whole temp range and the other form is merely metastable at all temp

Derivative structures, of silicates

Structures that are derived from a more simple one; by distortion or by substitution of different chemical species.

Examples: quartz, tridymite and cristobalite, all have low-temp structures that are distorted from the more symmetrical high-temp structures (Fig 2-32)

Examples; in stuffed silica structures in which Si4+ is replaced by Al3+.

LiAlSiO4, eucryptite, is a stuffed derivative of quartz

Clay minerals