•Solid state chemistry is the study of the principles and concepts underlying the synthesis, structure, bonding, reactivity, and physical properties of solid state materials.

•A subdiscipline of Chemistry, which primarily involves the study of extended solids (Materials formed under ultrahigh pressure).

•Except helium*, all substances form a solid if sufficiently cooled at 1 atm.

•Majority of solids exist in crystalline form – where the atoms, molecules, or ions are arranged in a regular repeating fashion.

Solid State Chemistry

•The primary focus will be on the structures of metals, ionic solids, and extended covalent structures, where extended bonding arrangements dominate.

•The properties of solids are related to its structure and bonding.

•In order to understand or modify the properties of a solid, we need to know the structure of the material.

•Crystal structures are usually determined by X-ray crystallography technique.

•Structures of many inorganic compounds may be initiallydescribed in terms of simple packing of spheres.

Brief History and Notable Contributions from Solid State Chemistry

•X-ray crystallography in the early 1900s by William Bragg.•Zeolite and platinum-based catalysts for petroleum processing in the 1950s.•High purity silicon, a core component of microelectronic devices in the 1960s•Microwave dielectrics (Wireless communications) in the 1970s and colossal magnetoresistive•High temperature superconductivity in the 1980s•Giant and colossal magnetoresistive (CMR) materials in the 1990s•Nano-, energy storage and generation and functional materials in the 2000s

Introduction

•Solids are substances characterised by

•i. definite shape

•ii. definite volume

•iii. non-compressibility

•iv. very slow diffusion

•v. rigidity and

• vi. mechanical strength.

•The atoms, molecules or ions in solids are closely packed and cannot move randomly.

•They are held together by strong forces (Intermolecular, interatomic, ionic forces).

•Solids can be either crystalline or amorphous.

•A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an ordered pattern extending in all three spatial dimensions.

Examples of large crystals - snowflakes, diamonds, graphite and table salt.

Most inorganic solids are not crystals but polycrystals, i.e. many microscopic crystals fused together into a single solid.

Examples: most metals, rocks, ceramics, and ice. A third category of solids is amorphous solids, where the atoms have no periodic structure. They have completely random particle arrangement.

Examples: glass, wax, and many plastics.

Crystal Particles Attractive forces Melting point

Other properties

Ionic Positive and negative ions

Electrostatic attractions

High Hard, brittle, good electrical conductor in molten state

Molecular Polar molecules

London force and dipole-dipole attraction

Low non-conductor or extremely poor conductor of electricity in liquid state

Molecular Non-polar molecules

London force Low Soft conductor

Quasicrystals (Dan Shechtman)

A quasicrystal consists of arrays of atoms that are ordered but not strictly periodic.They have many attributes in common with ordinary crystals, such as displaying a discrete pattern in x-ray diffraction, and the ability to form shapes with smooth, flat faces.Quasicrystals are most famous for their ability to show five-fold symmetry, which is impossible for an ordinary periodic crystal

The material Ho-Mg-Zn forms quasicrystals, which can take on the macroscopic shape of a dodecahedron.

Amorphous Crystalline

Random particle arrangement Regular geometry

Do not have sharp M.Pts Sharp M.Pt

Isotropic Anisotropic

No cleavage planes Cleavage planes

No symmetry Crystal symmetry

Crystalline versus Amorphous solids

Charge-Dipole Interactions

Dipole-Dipole Interactions

1/r2

1/r3

Intermolecular interactions

London Dispersion Interactions

Hydrogen Bonding Interactions

Intermolecular interactions

Crystal Structure

A crystal is a solid substance having a definite geometrical shape with flat faces and sharp edges.

Crystallography deals with geometry, properties and structures of crystalline compounds.

Fundamental laws of crystallography

i.Law of constancy of interfacial angles- The shape and size of the crystals may vary with crystallization conditions, but the interfacial angles ( Angle between the two intersecting faces) remain constant.

Law of rational indices

All faces cut a given axis at distances from the origin, which bear a simple ratio to one another

Miller indices of a given crystal face are inversely proportional to the intercepts of that face on the various axes.

When a face intersects

i.all crystallographic axes, it has Miller Indices (hkl).

ii. two crystallographic axes and parallel to the third, has Miller Indices (0kl), (h0l), (hk0).

iii. one crystallographic axis and parallel to others two, has Miller Indices (h00), (00l), (0k0).

Find intercepts along axes → 2:3:1Take reciprocal → 1/2:1/3:1Convert to smallest integers in the same ratio → 3:2:6 Enclose in parenthesis → (326)

(2,0,0)

(0,3,0)

(0,0,1)

Miller Indices for planes

Intercepts → 1 Plane → (100)Family → {100} → 3

Intercepts → 1 1 Plane → (110)Family → {110} → 6

Intercepts → 1 1 1Plane → (111)Family → {111} → 8(Octahedral plane)

It is possible to choose along the three coordinates unit distances from the origin (a, b and c), which may or may not be of same length, such that the ratio of the three intercepts of any plane in the crystal is given by (ha:kb:lc), where h, k and l are integral numbers.

Say for a plane that makes intercepts 2a, 2b & 3c respectively, then the ratio of the intercepts in terms of the standard is 2:2:3. The coefficients of a,b & c are known as Weiss indices.

Miller indices are obtained by taking the reciprocal of Weiss indices and multiplying throughout by the least common multiple to obtain integral values.

Miller indices

Positions within the unit cell are specified in terms of translations along the three lattice vectors, e.g. the atoms in a bcc unit cell are at (0,0,0) and (½,½,½). Lattice planes are indexed by their intercepts of the coordinate axes. Lattice planes are identified by their Miller indices, (h k l). To obtain the indices of a lattice plane, the reciprocals of the intercepts are taken, and the set of smallest integers giving the same ratio between them is determined. These are the Miller indices for the lattice plane, usually represented as (h k l).

Miller indices

Tetrahedron inscribed inside a cube with bounding planes belonging to the

{111} family

8 planes of {111} family forming a regular octahedron

The (111) planes:

Law of symmetry

All crystals of the same subtance possess the same elements of symmetry

Three main types of symmetry

Plane of symmetry

Axis of symmetry

Centre of symmetry

Axes of Symmetry:Proper axes of rotation (Cn)Rotation with respect to a line (axis of symmetry) which molecules rotate.•Cn is a rotation of (360/n)°, where n is the order of the axis.•C2 = 180° rotation, C3 = 120° rotation, C4 = 90° rotation, C5 = 72° rotation, C6 = 60° rotation…•Each rotation brings you to the indistinguishable state for original

Planes and Reflection (σ)

Molecules contain mirror planes, the symmetry element iscalled a mirror plane or plane of symmetry.•σh(horizontal): plane perpendicular to principal axis•σd(dihedral), σv(vertical): plane colinear with principal axis•σv: Vertical, parallel to principal axis•σd: σ parallel to Cn and bisecting two C2' axes

Inversion, Center of Inversion (i)A center of symmetry: A point at the center of the molecule. (x,y,z) → (-x,-y,-z).Center of inversion can only be in a molecule. It is not necessary to have an atomin the center (e.g. benzene).Tetrahedrons, triangles, and pentagons don't have a center of inversion symmetry

Ru(CO)6C2H6

SymmetrySymmetry is useful when it comes to describing the shapes of both individual molecules and regular repeating structures.Point symmetry - is the symmetry possessedby a single object that describes the repetitionof identical parts of the object.Symmetry operations – are actions such asrotating an object or molecule.Symmetry elements – are the rotationalaxes, mirror planes, etc., possessed by objectsSchoenflies (or Schönflies) notation Sn: one of two conventions commonly used to describe point groups used in spectroscopy.Herman-Mauguin – can describe the point symmetry of individual molecules, and also therelationship of different atoms to one anotherin space (space symmetry). Hermann–Mauguin notationdescribe the space group of a crystal lattice and is used in crystallography.

n

CRYSTAL STRUCTURE

•Atoms and ions will be viewed as hard spheres. In the case of pure metals, the packing pattern often provides the greatest spatial efficiency (closest packing).

•Ionic crystals can often be viewed as a close-packed arrangement of the larger ions, with the smaller ions placed in the “holes” of the structure.

• Crystals contain highly ordered molecules or atoms held together by non-covalent interactions

• NaCl . has the cubic structure

• Crystal lattice is a highly ordered three dimensional structure, formed by its constituent atom or molecules or ions

• An infinite set of points (represent the constituents of the crystal) repeated regularly along a line (1D), in a plane (2D) or along the three coordinates in space(3D).

• Unit cell is the smallest building unit in space of crystal which when repeated over and over again in 3 dimensions results in a space lattice of the crystalline substance.

CRYSTAL STRUCTURE

A crystalline solid possesses rigid and long-range order. In a crystalline solid, atoms, molecules or ions occupy specific (predictable) positions.

An amorphous solid does not possess a well-defined arrangement and long-range molecular order.

A unit cell is the basic repeating structural unit of a crystalline solid.

Unit Cell

latticepoint

Unit cells in 3-dimensions

At lattice points:

• Atoms

• Molecules

• Ions

The simplest repeating unit in a crystal is called a unit cell. Each unit cell is defined in terms of lattice points the points in space about which the particles are free to vibrate in a crystal. The structures of the unit cell for a variety of salts are shown below.

Types of Crystal Structure

1. Cubic- sodium chloride

2. Tetragonal- urea

3. Hexagonal - iodoform

4. Rhombic- iodine

5. Monoclinic- sucrose

6. Triclinic- boric acid

7. Trigonal

Unit cell in 3D lattice is characterised by the lengths a, b and c and the angles α, β and γ. Collectively known as unit cell parameters.A total of seven crystal lattices are constructed from these parameters.

Bravais Lattices

1. End-centred

i. Monoclinic

ii. orthorombic

2. Face-centred

i. Cubic (NaCl)

ii. Orthorombic

3. Body-centred

i. Cubic tetragonal

ii. Orthorombic

Total of 14 possible types of unit cells

For drugs, only 3 types:

1. Triclinic

2. Monoclinic

3. Orthorombic

The unit cell is the simplest repeating unit in the crystal.

Opposite faces of a unit cell are parallel.

The edge of the unit cell connects equivalent points.

Three types of crystal structure

Shared by 8 unit cells

Shared by 2 unit cells

When silver crystallizes, it forms face-centered cubic cells. The unit cell edge length is 408.7 pm. Calculate the density of silver.

d = mV

V = a3 = (408.7 pm)3 = 6.83 x 10-23 cm3

atoms/unit cell in a face-centered cubic cell

m = 4 Ag atoms107.9 g

mole Agx

1 mole Ag

6.022 x 1023 atomsx = 7.17 x 10-22

d = mV

7.17 x 10-22 g

6.83 x 10-23 cm3= = ___________________

Extra distance = BC + CD = 2d sin = n (Bragg Equation)

X rays of wavelength 0.154 nm are diffracted from a crystal at an angle of 14.170. Assuming that n = 1, what is the distance (in pm) between layers in the crystal?

n = 2d sin n = 1 = 14.170 = 0.154 nm = 154 pm

d =n

2sin=

1 x 154 pm

2 x sin14.17= ____________

Types of SolidsIonic Crystals or Solids• Lattice points occupied by cations and anions• Held together by electrostatic attraction• Hard, brittle, high melting point• Poor conductor of heat and electricity

CsCl ZnS CaF2

Types of SolidsMolecular Crystals or Solids• Lattice points occupied by molecules• Held together by intermolecular forces• Soft, low melting point• Poor conductor of heat and electricity

Types of SolidsNetwork or covalent Crystals or Solids• Lattice points occupied by atoms• Held together by covalent bonds• Hard, high melting point• Poor conductor of heat and electricity

diamond graphite

carbonatoms

Types of SolidsMetallic Crystals or Solids• Lattice points occupied by metal atoms• Held together by metallic bond• Soft to hard, low to high melting point• Good conductor of heat and electricity

Cross Section of a Metallic Crystal

nucleus &inner shell e-

mobile “sea”of e-

Types of Crystals

Types of Crystals and General Properties

Radius ratios, coordination numbers, and coordination environment for both the cations and anions for four representative AB-type ionic lattices.

Different types of Lattice planes

Interplanar spacing

Extended Covalent ArraysSeveral elements for covalently bonded solids at room temperature, including B, C, Si, Ge, P, As, Se, Te.

Unit cell of C (diamond).All C-C bond length are identical (1.54 Å).Covalent C-C bonds are strong and therigid 3D network of atoms give diamondthe hardest substance known and it alsohas a high melting point.

Unit cell of C (graphite).All C-C bond length are identical (1.42 A).Two dimensional layers of carbon atoms ina hexagonal layer.The distance between layers is 3.40 A.

Covalent Network Crystals

A covalent network crystal is composed of atoms or groups of atoms arranged into a crystal lattice held together by an interlocking pair of covalent bonds.Covalent bonds, the sharing of one or more pairs of electrons in a region of overlap between two or more atoms, are directional interactions as opposed to ionic and metallic bonds that are nondirectional.These interactions are directional in nature.Compounds that form covalent network crystals include SiO2, C, Si, BN.

Metallic CrystalsThe structure of metals may be visualized as a lattice of cations held together by a Fermi sea (“of electrons”).The electrons are no longer associated with any particular cation.Valence electrons are delocalized about the lattice of cations.This type of electron movement enables high conductivity typically associated with metals.

Ionic crystalsIonic bonds are nondirectional – the electrostatic forces dominate.Many salts form ionic crystals NaCl, CsCl, CaF2, KNO3, and NH4Cl.

Na+

Cl-

Ionic bonding inNaCl

An amorphous solid does not possess a well-defined arrangement and long-range molecular order.

A glass is an optically transparent fusion product of inorganic materials that has cooled to a rigid state without crystallizing

Crystallinequartz (SiO2)

Non-crystallinequartz glass

Formula Cation : anionCoordination

Type and number of holes occupied

Examples:Cubic close packing

Examples: Hexagonalclose packing

MX •6:6

•4:4

•All octahedral

•Half tetrahedral; everyalternate site occupied

•Sodium chloride: NaCl,FeO, MnS, TiC•Zinc blende: ZnS,CuCl, γ-AgI

•Nickel arsenide:NiAs, FeS, NiS•Wurtzite: ZnS,β-AgI

MX2 •8:4•6:3

•All tetrahedral•Half octahedral; alternate layers have fully occupied sites

•Fluorite: CaF2, ThO2, ZrO2, CeO2

•Cadmium chloride: CdCl2

•None•Cadmium iodide:CdI2

MX3 6:2 One-third octahedral; alternate pairs of layershave two-thirds of theoctahedral sites occupied.

Bismuth iodide:BiI3, FeCl3, TiCl3,VCl3.

M2X3 6:4 Two-thirds octahedral Corundum: α-Al2O3, α-Fe2O3,V2O3, Ti2O3, α-Cr2O3

ABO3 Two-thirds octahedral Ilmenite: Fe2O3

AB2O4 One-eighth tetrahedraland one-half octahedral

Olivine: Mg2SiO4

Structures related to close-packed arrangements of anions

Lattice Packing

• Elemental Cu and Ni each uses fcc packing and both have very similar lattice parameters (e.g. internuclear distances).

• If we heat the two elements to melting and then mix together and cool slowly, the fcc packing is retained, but with a random placement of the two elements.

• Known as a solid solution ≈ alloy.

Lattice Packing

• Elemental Cu and Au each uses fcc packing but have very different lattice parameters (Au >> Cu).

• Upon reaction (melt and cool) yields a specifically ordered arrangement = an intermetallic compound, which may not conform to oxidation state rules.

HCP

•In ionic crystals, ions pack themselves so as to maximize the attractions and minimize repulsions between the ions.•A more efficient packing improves these interactions.•Placing a sphere in the crevice or depression between two others gives improved packing efficiency.

hexagonal closepacked (hcp)ABABABSpace Group:P63/mmc

cubic closepacked (ccp)ABCABCSpace Group:Fm3m

A ccp structure has a fcc unit cell.

Different Types of Crystal Lattices

Close Packing

Holes in Close Packed Crystals

There are two types of holes created by a close-packed arrangement. Octahedral holes lie within two staggered triangular planes of atoms.

Holes in Close Packed Crystals

The coordination number of an atom occupying an octahedral hole is 6.For n atoms in a close-packed structure, there are n octahedral holes.

Octahedral Holes

The green atoms are in a cubic close-packed arrangement. The small orange spheres show the position of octahedral holes in the unit cell. Each hole has a coordination number of 6.

Octahedral Holes

The size of the octahedral hole = 0.414 rwhere r is the radius of the cubic close-packed atom or ion.

Holes in Close Packed Crystals

Tetrahedral holes are formed by a planar triangle of atoms, with a 4th atom covering the indentation in the center. The resulting hole has a coordination number of 4.

Tetrahedral Holes

The orange spheres show atoms in a cubic close-packed arrangement. The small white spheres behind each corner indicate the location of the tetrahedral holes.

Tetrahedral Holes

For a close-packed crystal of n atoms, there are 2n tetrahedral holes.

The size of the tetrahedral holes = 0.225 rwhere r is the radius of the close-packed atom or ion.

Atoms/Unit Cell

For atoms in a cubic unit cell:Atoms in corners are ⅛ within the cell

For atoms in a cubic unit cell:Atoms on faces are ½ within the cell

For atoms in a cubic unit cell:

Atoms in corners are ⅛ within the cellAtoms on faces are ½ within the cellAtoms on edges are ¼ within the cell

# of Atoms/Unit Cell

For atoms in a cubic unit cell:

Atoms on faces are ½ within the cell

# of Atoms/Unit Cell

A face-centered cubic unit cell contains a total of 4 atoms: 1 from the corners, and 3 from the faces.

# of Atoms/Unit Cell

For atoms in a cubic unit cell:

Atoms in corners are ⅛ within the cell Atoms on faces are ½ within the cell Atoms on edges are ¼ within the cell

Other Metallic Crystal Structures

Body-centered cubic unit cells have an atom in the center of the cube as well as one in each corner. The packing efficiency is 68%, and the coordination number = 8.

Other Metallic Crystal Structures

Simple cubic (or primitive cubic) unit cells are relatively rare. The atoms occupy the corners of a cube. The coordination number is 6, and the packing efficiency is only 52.4%.

Polymorphism

Many metals exhibit different crystal structures with changes in pressure and temperature. Typically, denser forms occur at higher pressures.

Higher temperatures often cause close-packed structures to become body-center cubic structures due to atomic vibrations.

Atomic Radii of Metals

Metallic radii are defined as half the internuclear distance as determined by X-ray crystallography. However, this distance varies with coordination number of the atom; increasing with increasing coordination number.

Atomic Radii of Metals

Goldschmidt radii correct all metallic radii for a coordination number of 12.

Coord # Relative radius 12 1.000 8 0.97 6 0.96 4 0.88

Most Common MX Structures

NaCl structureNa+ in fcc latticeCl- in Oh “holes”

CsCl structureCl- in simple cubic latticeCs+ in cubic “hole”

Zinc blende (ZnS) structureS-2 in fcc latticeZn+2 in alternating Td “holes”

Most Common MX2 Structures

Rutile (TiO2) structureTi+2 in body centered cubic latticeOxygens in lower symmetry array.

Fluorite (CaF2) structureCa+2 in fcc latticeF- in all Td “holes”

Common Crystal Types

1. The Rock Salt (NaCl) structure-

The coordination number is 6 for both ions.

Common Crystal Types

2. The CsCl structure-Chloride ions occupy the

corners of a cube, with a cesium ion in the center (called a cubic hole) or vice versa. Both ions have a coordination number of 8, with the two ions fairly similar in size.

Common Crystal Types

3. The Zinc-blende or Sphalerite structure-Anions (S2-) ions are in a face-centered

cubic arrangement, with cations (Zn2+) in half of the tetrahedral holes.

Common Crystal Types

4. The Fluorite (CaF2) and Antifluorite structuresA face-centered cubic arrangement of Ca2+

ions with F- ions in all of the tetrahedral holes.

Common Crystal Types

4. The Fluorite (CaF2) and Antifluorite structuresThe antifluorite structure reverses the

positions of the cations and anions. An example is K2O.

The rock-salt crystal structure. Each atom has six nearest neighbors, with octahedral geometry.

rNa= 0.102 nm ; rCl= 0.181 nmrNa/rCl= 0.564

cations (Na+) prefer octahedral sites

MgO and FeO also have the NaCl structure

AX Crystal Structures

∴Since 0.732 < 0.939 < 1.0, cubic sites preferred. So each Cs+has 8 neighbor Cl-

AX–Type Crystal Structures include NaCl, CsCl, and zinc blende

AX2Crystal StructuresFluorite structure

Calcium Fluorite (CaF2)Cations in cubic sitesUO2,ThO2, ZrO2, CeO2

Antifluorite structure –positions of cations and anions reversed

ABX3Crystal StructuresPerovskite structure Ex: complex oxide BaTiO3

SPINELSClass of minerals of general formula A2+B3+

2O2-4

Crystallise in the cubic (isometric) crystal system, with the oxide anions arranged in a cubic close-packed lattice and the cations A and B occupying some or all of the octahedral and tetrahedral sites in the lattice. A and B can be divalent, trivalent, or quadrivalent cations, including magnesium, zinc, iron, manganese, aluminium, chromium, titanium, and silicon. Although the anion is normally oxide, the analogous thiospinel structure includes the rest of the chalcogenides. A and B can also be the same metal under different charges, as is the case with magnetite, Fe3O4 (as Fe2+Fe3+

2O2-4), which is the most abundant member of the Spinel

group.Spinels are grouped in series by the B cation.

A common example of a normal spinel is MgAl2O4.Mg2+ Al3+ O2-

Spinel is the name given to the mineral MgAl2O4. It has a common structural arrangement shared by many oxides of the transition metals with formula AB2O4.

In the normal pattern the oxygens form a cubic close packed (ABCABC or face centred) array and the Mg(II) and Al(III) sit in tetrahedral (1/8 occupied) and octahedral (1/2 occupied) sites in the lattice, giving a Unit Cell with 8 Mg's, 16 Al's and 32 O's.

An inverse spinel is an alternative arrangement where the divalent ions swap with half of the trivalent ions so that the M(II) now occupy octahedral sitesi.e. B(AB)O4. NiFe2O4

In this case Ni(II) is octahedral and half of the Fe(III) are tetrahedral.

Complexes that share this structure include a number of 1st row TM oxides and sulfides.

Spinel (AB2O4) structures

Normal Spinel: MgAl2O4

Similar structures include FeCr2O4, Mn3O4, FeCr2S4, ZnAl2S4 and ZnCr2Se4

Inverse Spinel Co3O4

Examples of inverse spinel structures include Fe3O4, TiMn2O4, TiFe2O4, TiZn2O4 & SnZn2O4

Examples of partially inverse spinel structures include MgFe2O4, MnFe2O4 and NiAl2O4  

Normal spinel structures are usually cubic close-packed oxides with one octahedral and two tetrahedral sites per oxide. The tetrahedral points are smaller than the octahedral points. B3+ ions occupy the octahedral holes because of a charge factor, but can only occupy half of the octahedral holes. A2+ ions occupy 1/8 of the tetrahedral holes. A common example of a normal spinel is MgAl2O4.

Inverse spinel structures however are different in the cation distribution, in that all of the A cations and half of the B cations occupy octahedral sites, while the other half of the B cations occupy tetrahedral sites. A common example of an inverse spinel is Fe3O4, if the Fe2+ (A2+) ions are d6 high-spin and the Fe3+ (B3+) ions are d5 high-spin.

Spinels

Spinel

Magnetite is another compound with mixed-valent iron atoms . It has the AB2X4 spinel structure

Magnetite has the empirical formula Fe3O4 , or Fe2+(Fe3+O2)2 , “ferrous ferrite” . Its formula as a spinel would be Fe3+

tetFe2+octFe3+

octO4 , where "tet" and "oct" stand for tetrahedral and octahedral coordinations by the oxide anions . In the above model , the blue spheres represent the tetrahedral iron(III) cations , and the red spheres are the octahedrally coordinated iron(II) and (III) cations . The oxide anions are shown as the green spheres . Because of the fortuitous inverse nature of the magnetite structure , ferrous and ferric cations are both in the similar octahedral coordination by oxides . In "normal" spinels , such as the mineral spinel itself (magnesium aluminate) , the A cation is tetrahedral and the M cations are both octahedral :

This close-packed spheres representation provides a wider view of the spinel structure , showing the regular packing order of the tetrahedral and octahedral cations among the anions .

Point defects in non-ionic and ionic solids occur in different ways, as described by following chart:

(i) Stoichiometric Defects : Also called intrinsic or thermodynamic defects. Due to this defects the stoichiometry (i.e., the ratio of cations and anions as per the chemical formula) of the solid is not disturbed.Non-ionic solids show following defects:(A) Vacancy Defects : This defect arises due to a vacancy created in the lattice site. This results in decrease in density of the substance. Generally, this defect arises on heating of a substance.(B) Interstitial Defect : When some atoms or molecules occupy the interstitial site, this is called interstitial defects. Due to this defect density of the substances increases.

Ionic solids have following defects instead of the above two defects because they must maintain electrical neutrality.(C) Frenkel Defect : Also called dislocation defect because in this defect cation (smaller ion) is dislocated from its normal site to an interstitial site. Thus vacancy defect arises at the original site while interstitial defect at the new location. Due to this defect there is no change in the density of substance. This defect is shown by the ionic compounds having large difference in the size of ions. For example— ZnS, AgCl, AgBr, AgI, etc.(D) Schottky Defect : Basically it is a vacancy defect but in this case number of missing cations and anions are equal so that electrical neutrality of the substance is maintained. Like vacancy defect, Schottky defect also decreases the density of the substance. There is one Schottky defect per ions. This defect is shown by the ionic compounds having cations and anions of almost similar size. For example—NaCl, KCl, CsCl, AgBr, etc.

Schottky defect of crystalsEqual number of cations and anions are missing from lattice sites. Electrical neutrality is maintained. Decreases density of the material.Schottky defects are found in NaCl, KCl, KBr etc.

Frenkel Defect-An ion missing from the lattice occupies any interstitial void.Electrical neutrality and stoichiometry remains same.Density is not affected.This defect are found in AgCl, AgBr etc.This defect are found in AgCl, AgBr etc.