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CHEMISTRY 221: Inorganic Chemistry (I)
The Structures of Simple Solids
Dr. Adnan S. Abu-Surrah
Professor of Inorganic & Materials Chemistry
Tel.: +974 4403 6839
E-mail: [email protected]
The Structures of Simple Solids
• The majority of inorganic compounds exist as solids and
comprise ordered arrays of atoms, ions, or molecules.
– Some of the simplest solids are the metals, the structures
in which metal centers interact through metallic bonding,
a type of bonding that can be described in two ways:
One view is that bonding occurs in metals when each
atom loses one or more electrons. The strength of the bonding results
from the combined attractions between all these freely moving electrons and
the resulting cations.
An alternative view is that metals are effectively
enormous molecules with a multitude of atomic orbitals that
overlap to produce molecular orbitals extending throughout the
The Structures of Simple Solids
 Thus, metals are malleable (easily deformed by the
application of pressure) and ductile (able to be drawn into a
wire) because the electrons can adjust rapidly to relocation of
the metal atom nuclei and there is no directionality in the
● They are lustrous because the electrons can respond,
almost freely to an incident wave of electromagnetic radiation
and reflect it.
The description of the structures of solids
The arrangement of atoms or ions in simple solid
structures can often be represented by different arrangements
of hard spheres.
The spheres used to describe metallic solids represent
neutral atoms because each cation is still surrounded by its full
complement of electrons.
The spheres used to describe ionic solids represent the
cations and anions because there has been a substantial transfer
of electrons from one type of atom to the other.
Crystal Lattices
• The ‘crystal lattice’ is the pattern formed by the points and used
to represent the positions of these repeating structural
– Lattice: a two or three dimensional array of objects with a well defined
• Unit cells: smallest repeating unit (imaginary parallel-sided
region) that through translation can recreate a lattice. (also
called the asymmetric unit)
Amorphous means a disordered array
Unit cells
A two-dimensional solid and two choices of a unit cell. The
entire crystal is reproduced by translational displacements
of either unit cell,
Two possible choices of repeating unit are shown but (b) would
be preferred to (a) because it is smaller.
Lattice and Units Cells
The relationship between the lattice parameters in three
dimensions as a result of the symmetry of the structure
gives rise to the seven crystal systems
Most common types:
Less common types:
The angles (a, b , g) and lengths (a,
b, c) used to define the size and
shape of a unit cell are the unit cell
parameters (the ‘lattice
Angle between b and c is a
Angle between a and c is b
Angle between a and b is g
(or rhombohedral)
Rules to determine number of lattice points in a
three-dimensional unit cell
1) A lattice point in the body of, that is fully
inside, a cell belongs entirely to that cell and
counts as 1.
2) A lattice point on a face is shared by two cells
and contributes 1/2 to the cell.
3) A lattice point on an edge is shared by four
cells and contributes 1/4.
4) A lattice point at a corner is shared by eight
cells that share the corner, and so contributes
The same process can be used to count the
number of atoms, ions, or molecules that the
unit cell contains.
Simple Cubic
denoted by the symbol P
The number of lattice
points is:
(8 x1/8 ) = 1.
Lattice points describing the translational symmetry
of a primitive cubic unit cell.
Body Centered Cubic (BCC)
denoted by the symbol I
The number of lattice
points is:
(1x1) + (8 x1/8 ) = 2.
Lattice points describing the translational
symmetry of a cubic unit cell.
Face Centered Cubic (FCC)
denoted by the symbol F
The number of lattice
points is:
(6x1/2) + (8 x 1/8) = 4
Lattice points describing the translational symmetry of a
face-centred cubic unit cell.
a = b = g = 90°
• Usually, the smaller cations will be found in the holes in the
anionic lattice, which are named after the local symmetry of
the hole
•i.e. six equivalent anions around the hole makes it
octahedral, four equivalent anions makes the hole
Crystal Lattices
Two main types of arrays:
• Open: occupies 68% of the space
• Close-packed: occupies 75% of the space
– Two types of close-packed arrays: hexagonal and cubic. (ABAB...
versus ABCABC... )
– Close-packed structures have layers of octahedral and tetrahedral
holes --
Cubic Close-Packed (ccp)
• first layer in a hexagonal arrangement of atoms or ions
• second layer over depressions in the first layer, over tetrahedral
• third layer over depressions in the second which are not over the
depressions in the first that the atoms in the second occupy, over
octahedral holes
• fourth layer is identical to the first
• fifth layer is identical to the second
• sixth layer is identical to the third
• face-centered-cubic, standing on its body diagonal, is camouflaged
by ccp
• C. N. = 12
Hexagonal Close-Packed (hcp)
- first layer in a hexagonal arrangement of atoms or ions
- second layer over depressions in the first layer, over tetrahedral
- odd numbered layers identical to the first
- even numbered layers identical to the second
- 12 nearest neighbors,
C. N. = 12
Examples in nature of Hexagonal Close Packing
Cubic and Hexagonal Close Packing
In one polytype, the spheres of the third layer lie directly above the
spheres of the first. This ABAB...pattern of layers, where A denotes
layers that have spheres directly above each other and likewise for B,
gives a structure with a hexagonal unit cell and hence is said to be
hexagonally close-packed (hcp).
In the second polytype, the spheres of the third layer are placed above
the gaps in the first layer. The second layer covers half the holes in the
first layer and the third layer lies above the remaining holes. This
arrangement results in an ABCABC...pattern. This pattern corresponds
to a structure with a cubic unit cell and hence it is termed cubic closepacked (ccp).
Because each ccp unit cell has a sphere at one corner and one at the
centre of each face, a ccp unit cell is sometimes referred to as facecentred cubic (fcc).
Cubic Close Packing
This pattern corresponds to a structure with a cubic unit
cell and hence it is termed cubic close-packed (ccp).
Holes in close-packed structures
Octahedral hole: rh = 0.414r
Tetrahedral hole: rh = 0.225r
Coordination Numbers:
Coordination Number: the number of nearest neighbors.
Hexagonal close-packing of sphere gives a
coordination number (CN) of 12 and leaves
interstitial sites capable of coordination numbers
6 or 4.
Structures of Metals
• In addition to ccp and hcp, metals also have simple cubic and
body-centered cubic structures.
• The CN of ccp or hcp = 12, simple or primitive cubic = 6, bodycentered cubic (bcc) = 8.
• Note that bcc is favored for Group 1 and 2 metals. This is due to
the weaker “electron sea” which prevents close-packing.
a regular array of organized cations
surrounded by delocalized sea of electrons.
Structures of Metals
Polytypes involving complex stacking arrangements of close-packed
layers occur for some metals.
a close-packed structure need not be either of the common ABAB...or
cobalt is an example of a metal that displays more complex
polytypism above 500 0C. The structure that results is a nearly
randomly stacked set ( ABACBABABC….
Nonclose-packed structures
A common nonclose-packed metal structure is body-centred
cubic; a primitive cubic structure is occasionally
encountered. Metals that have structures more complex
than those described so far can sometimes be regarded as
slightly distorted versions of simple structures.
One commonly adopted arrangement has the translational
symmetry of the body- centred cubic lattice and is known as the
body-centred cubic structure (cubic-I or bcc) in which a sphere
is at the centre of a cube with spheres at each corner (See Fig).
Polymorphism of metals
Polymorphism is a common consequence of the low directionality
of metallic bonding. At high temperatures a bcc structure is
common for metals that are close-packed at low temperatures on
account of the increased amplitude of atomic vibrations.
Iron, for example, shows several solid–solid phase transitions; a-Fe,
which is bcc, occurs up to 906°C, g-Fe, which is ccp, occurs up to
1401°C, and then a-Fe occurs again up to the melting point at
1530°C. The hcp polymorph, b-Fe, is formed at high pressures and
was to believed to be the form that exists at the Earth’s core.
Substitutional solid solution
Interstitial solid solution
Another lattice
Brass – up to 40% Zn in Cu
Bronze – a metal other than Zn or Ni in Cu
Stainless steel – over 12% Cr in Fe
Substitutional Solid Solutions -- conditions
• The atomic radii of the elements are within
15% of each other
• The crystal structures of the two pure metals
are the same
• The electropositive characteristics of the two
metals are similar
Interstitial Solid Solutions
• True compounds – simple whole number
ratios of atoms
• Solid solutions – small atoms distributed
randomly in the available holes in the lattice
Compounds with Particular Crystal Structures
The Structure of NaCl
 It is a fcc array of chloride ions as the packing layers.
 The sodium ions are in all the octahedral holes.
 The coordination number of both ions is 6.
 The unit cell has four net sodium ions and four chloride
 Other salts with this structure are: LiX, NaX, KX, RbX
where X = F, Cl, Br, I; also MgO, MgS, CaO, etc.
Rock Salt (NaCl) Structure
Rock Salt structure
(6,6) coordination
Face-centered cubic (fcc)
e.g. NaCl, LiCl, MgO, AgCl
CsCl Unit Cell--Contd--
lattice energy (Uo,
Ionic Bonding:
lattice energy, Uo,
•The energy that holds the arrangement of ions together is called the
lattice energy, Uo, and this may be determined experimentally or
•A lattice energy must always be exothermic.
•E.g.: Na+(g) + Cl-(g)  NaCl(s) Uo = -788 kJ/mol
Lattice energies are determined experimentally using a
Born-Haber cycle such as this one for NaCl. This approach
is based on Hess’s law and can be used to determine the
unknown lattice energy from known thermodynamic values.
Lattice Energy, Uo
DHfo = DHoie + DHosub + DHod + DHoea - Uo
where DHosub => heat of sublimation
- endothermic process
- always positive number
DHod=> bond dissociation energy
- endothermic process
- always positive number
where DHfo => standard state enthalpy of formation
- can be either endothermic or exothermic
- therefore, value may be positive or negative
Ionic Bonding -- Born-Haber cycle
Na(s)  Na(g)  Na+(g)
½ Cl2(g)  Cl(g)  Cl-(g)
Lattice Energy, Uo
DH°f = DH°sub + DH°ie + 1/2 DH°d + DH°ea - Uo
-411 = 109 + 496 + 1/2 (242) + (-349) - Uo
Uo = -788 kJ/mol
You must use the correct stoichiometry and signs to obtain the correct lattice energy.
Practice Born-Haber cycle analyses at:
Ionic Bonding
If we can predict the lattice energy, a Born-Haber cycle analysis can tell us
why certain compounds do not form. E.g. NaCl2
(DH°ie1 + DH°ie2)
Na(s)  Na(g)  Na+2(g)
Cl2(g)  2 Cl(g)  2Cl-(g)
DH°d DH°ea
Lattice Energy, Uo
DH°f = DH°sub + DH°ie1 + DH°ie2 + DH°d + DH°ea - Uo
DH°f = 109 + 496 + 4562 + 242 + 2*(-349) + -2180
DH°f = +2531 kJ/mol
This shows us that the formation of NaCl2 would be highly endothermic and very
unfavourable. Being able to predict lattice energies can help us to solve many
problems so we must learn some simple ways to do this.
K(g) + ½ Cl2(g)
Extrinsic defects are defects introduced into
a solid as a result of doping with an impurity
atom. Example is the introduction of As into
Si to modify the latter’s semi-conducting