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And all for the want of a button And all for the want of a button! Tin has two allotropic forms - one is a hard crystalline white colored β-tin and the other is gray colored amorphous α-tin. White tin is hard solid and stable only above 13°C. Below that temperature, it slowly changes into soft gray tin.

There was a very strong argument for why Napoleon and the French were decimated in Russia in 1812. During the summer of 1812, Napoleon's French army numbered 600,000 strong. Just five months later, however, this once powerful army numbered fewer than 10,000. The quote, "And all for the want of a button" is similar to the old English nursery rhyme that states "And all for the want of a horseshoe nail". The quote gives a brief description of how Napoleon's great army was defeated. When Napoleon was deciding on his army's uniform, he chose to use tin buttons. When winter came, the extreme cold (−30° C) caused the tin buttons to turn into a crumbly amorphous gray powder. The soldiers were exposed to the freezing temperature of the Russian winter, and became defenseless in the fight against the Russians, eventually leading to the demise of the army.

Learning Objectives

After completing the topic, the student will be able to:

  • Describe general characteristics of solid state such as density, elasticity etc.
  • Understand the behavior of amorphous and crystalline solids.
  • Differentiate the characteristics of amorphous and crystalline solids.
  • Define the basic crystal parameters such as crystal lattice and unit cell.
  • Categorize the crystals based on physical and chemical properties and group the crystal based on lattice shape.
  • Distinguish the ionic, metallic and covalent (molecular) crystals.
  • List different unit cell structures and calculate the packing fraction of each unit cell.
  • Discuss the crystal defects such as point defects, linear defects and planar defects.
  • Understand the process of using X-ray diffraction to determine the structure of solids.
  • Calculate the unit cell lengths and densities of solids etc., by using Bragg's equation.
  • Calculate the lattice energy of a crystal and discuss the factors effecting lattice energy.
3-D geometric forms Five basic three dimensional geometric forms commonly found in solids

1. Dodecahedron
2. Icosahedron
3. Tetrahedron
4. Octahedron
5. Cube
Solids

A solid has a certain size and shape. Solids are the thickest forms of matter. All the molecules in a solid are tightly fitted together, so the molecules can't move around very much. Solids are made up of different parts or compounds. Unlike liquids or gases, solids retain the same shape. Examples: wood, rock, and metals. Other examples of solids are the computer, the desk, and the floor.

You can change the shape of solids, but not easily. You can change the shape of sheets of lumber by sawing it in half or burning it. How might you change the shape of a piece of gum? At room temperature and atmospheric pressure, many substances exist as solids. In the periodic table, there are two liquids and 11 gases; the remaining 96 elements are solids.

Solids have the property of retaining their shapes with or without a container. This occurs because solids have rigid structures. Solids differ from liquids in that the particles in liquids, while still stuck together, do have some freedom of motion. Solids differ from gases in that gas molecules really don't interact with each other much, flying all over the place. Based on the molecular or atomic arrangement solids are broadly classified into crystalline solids and amorphous solids. Crystalline solids are perfect solids but amorphous solids have liquid like properties.

Unit Cells Unit cell structres A crystal lattice may be imagined to be made up of a very large number of small units known as unit cells. A unit cell is a smallest repeating unit in a crystal lattice which when repeated again and again in different directions results in the crystal of the given substance. Shapes of crystals depends upon the length of intersecting edges i.e., a, b, c and also the angles (α, β and γ) between the edges.
Crystalline solids

Crystalline solid structures may be defined based on the attractive forces that hold them together or on the arrangement of the atoms in the crystals themselves. Crystal types are based on attractive forces. But there is more than one way to categorize a crystal. The two most common methods are to group them according to their crystalline structure and physical and chemical properties.

Crystals grouped by lattices (shapes)
A lattice is a regular arrangement of particles whether these are atoms, ions or molecules. Seven types of basic crystal structures are present. They are:

  1. Cubic or isometric:
    These are the crystal lattices with three equal axes, intersecting at right angles to each other.
  2. Tetragonal:
    These are similar to cubic crystals with two equal, horizontal axes at right angles and one axis longer or shorter than the other two axis and is perpendicular to the plane. They form the pyramids and prisms with this type of arrangement.
  3. Orthorhombic:
    In this type of crystals, the three axes are unequal and they intersect at right angles to each other. They form rhombic prisms or dipyramids.
  4. Trigonal or Rhombohedral:
    In this arrangement, the three axis are equal in length and the three axis will intersect at oblique angles.
  5. Monoclinic:
    In this arrangement, the three axes are unequal and two axes intersect at right angles while the third is inclined at an oblique angles to the plane of other two. They look like the skewed tetragonal crystals.
  6. Triclinic:
    In this type, the three axis are not equal and they intersect at oblique angles with each other.
  7. Hexagonal:
    These are the crystal lattices with three equal axes, intersecting at 60° angle in a horizontal lane and a fourth, longer or shorter axis, perpendicular to the plane of the other three.

The classification present above is a simplified view of crystal structures. In addition, the lattices can be primitive (only one lattice per unit cell) or non-primitive (more than one lattice per unit cell). Combining the 7 crystal systems with 2 lattice types yields the 14 Bravais lattices. Thus 14 types of arrangements are possible for crystals. These are explained in more detail under "crystal structures" later in this topic.

The Seven Crystal Systems