SOLID STATE CHEMISTRY
Key concepts, Handouts, supplemental information.
Reading in Zumdahl: Chapter 16
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This page: DESCRIBING CRYSTALLINE SOLIDS
 1-D lattices Planar Lattices Space Lattices Crystal systems Bravais Lattices Cubic Lattices

Basic concepts/terms.

Crystalline solids: highly regular arrangement of atoms, ions, molecules - periodic (repeating)
Amorphous solids: no repeating pattern, only short range order, extensively disordered - non crystalline (e.g. glasses)

We will focus on Crystalline solids :

- how do we describe them ? - lattices
- what types exist ? - metallic, ionic, extended covalent (or network), molecular.

- how can we study their structures ? - many ways, for example x-ray diffraction.

Crystallinity - have a repeating unit = unit cell

To define repeating unit use concept of a lattice

A lattice is "an infinite 1,2, or 3-D regular arrangement of points, each of which has identical surroundings".

Any periodic pattern can be described by placing lattice points at equivalent positions within each unit of the pattern.

To recover original pattern we add the motif to each lattice point.
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1-D lattices.  The regular pattern of wagons below can be described by placing a lattice point at the same place in each wagon.  The arrangement of dots is the lattice, which has a given repeat distance.  The motif is the wagon.  The pattern is recovered by stamping the motif on each lattice point.

2-D patterns: Planar lattices.

Consider each of the patterns below - what is the lattice and unit cell ?
Place lattice points at equivalent positions in the pattern, find smallest repeat unit that by translation, can cover all space.
All of these patterns have the same Planar Lattice.(square), but each has a different motif.

3-D Space Lattices.

Crystal structures repeat in 3 dimensions.  The motif can be single atoms or groups of atoms.  Again we assign lattice points to the atomic structure and produce a Space Lattice.

Space lattice + motif = Crystal Structure

There are 7 unique unit-cell shapes that can fill all 3-D space.  These are the 7 Crystal systems.

We define the size of the unit cell using lattice parameters (sometimes called lattice constants, or cell parameters).  These are 3 vectors, a, b, c.  The angles between these vectors are given by a (angle between b and c), b (angle between a and c), and g (angle between a and b).

Although there are only 7 crystal systems or shapes, there are 14 different crystal lattices, called Bravais Lattices.  (3 different cubic types, 2 different tetragonal types, 4 different orthorhombic types, 2 different monoclinic types, 1 rhombohedral, 1 hexagonal, 1 triclinic). See below.

Real crystals always possess one of these lattice types, but different crystalline compounds that have the same lattice can have different motifs and different lattice parameters (these depend upon the chemical formula and the sizes of the atoms in the unit cell).  We will only concern ourselves with the cubic lattices, though we will refer to the hexagonal lattice in passing.

Bravais Lattices

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Cubic Lattices.

3 types; Simple cubic (also called primitive cubic), lattice points only at corners.

Body Centered Cubic (BCC), lattice points at corners and in middle of cube.

Face Centered Cubic (FCC) lattice points at the corners and in the middle of each face.

How many lattice points and/or atoms "belong" to a unit cell ?
Corners: The points at the corner of the cell are shared by the surrounding unit cells, therefore each one is shared by 8 in total and is only "worth" 1/8 to each cell.

Faces : - these lattice points are shared by 2 cells, each one is "worth" 1/2 to each cell.

Body : - this is the sole possesion of that cell, worth 1.

Total number lattice points: primitive cubic = 8(1/8) = 1; FCC = 6x1/2 + 8(1/8) = 4; BCC = 8(1/8) + 1 = 2.

Now that we know how to describe crystalline solids, let us examine different types according to the nature of their bonding.  We will begin with metallic solids, followed by ionic solids, and extended covalent or framework solids.