Structure of Crystalline Solids

Effect of IMF’s on Phase Solids• Kinetic energy overcome by intermolecular forces • Does not flow

C60 molecule

• Retains own shape Allotropes of Carbon

• Virtually incompressible • No to little diffusion Network-Covalent solid

Molecular solid

Solid Structures 1. Crystalline solid = solid in which atoms or ions are held in simple, regular geometric patters. (NaCl) Has a definite m.p. 2. Amorphous solid = solid in which the arrangement of particles lacks an ordered internal structure (glass)

Bonding in Solids •There are four general types of solids: • Metallic solids share a network of highly delocalized electrons. • Ionic solids are sets of cations and anions mutually attracted to one another.

m.p. occurs over a range

Bonding in Solids •There are four general types of solids: • Covalent-network solids are joined by an extensive network of covalent bonds. • Molecular solids are discrete molecules that are linked to one another only by van der Waals forces.

Attractions in Crystal Structures In crystals, atoms or ions pack themselves so as to maximize the attractions and minimize repulsions between the ions.

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Crystal Lattices One can deduce the pattern in a crystalline solid by thinking of the substance as a lattice of repeating shapes formed by the atoms in the crystal.

Crystal Lattices The individual shapes of the lattice, then, form "tiles," or unit cells, that must fill the entire space of the substance. Unit cell = the smallest repeating internal unit that has the symmetry characteristic of the solid.

Crystal Lattices • In a crystal lattice, each point of a repeating geometric pattern is called a lattice point.

•Because of the order in a crystal, we can focus on the repeating pattern of lattice point arrangement called the unit cell.

Crystal Lattices • Crystallography has identified seven basic three-dimensional lattices: – Cubic – Tetragonal – Orthorhombic – Rhombohedral – Hexagonal – Monoclinic – Triclinic

William Lawrence Bragg (1913) Discovered that the nuclei of atoms or ions (2-20Å) diffract x-rays and form a pattern on photo film that can be analyzed to deduce the geometric arrangements of atoms in the crystalline structure. This process is called X-ray Crystallography

X-ray crystallography passes polarized x-rays through a pure crystalline solid to determine its geometric arrangement of atoms

Diffraction Pattern from which the now famous DNA alpha helix structure was determined

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Crystal Lattices

Crystal Lattices Once one places atoms within a unit cell, the structure of the compound can be seen by bonding the atoms to one another across unit cells.

• Within each major lattice type, additional unit cells are generated by placing lattice points in the center of the unit cell or on the faces of the unit cell. • This has given rise to over 23 unit cells derived from the 7 basic lattices

Metallic Structure

Let’s draw the three cubic unit cells together: Simple Cubic (primitive) - SC Body-Centered Cubic - BCC Face-Centered Cubic - FCC

The structures of many metals conform to one of the cubic unit cells.

Units Cells for Metals

Cubic Structures One can determine how many atoms are within each unit cell which lattice points the atoms occupy.

Hexagonal Unit Cell

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Each atom in a unit cell has a coordination number Coordination number = The number of particles immediately surrounding a particle in a crystalline structure

Close Packing The atoms in a crystal pack as close together as they can based on the respective sizes of the atoms.

Looking at the simple cubic unit cell: Notice, this is not the best arrangement because there is a lot of empty space that could bring atoms closer together, resulting in lower energies.

Number of Atoms per Unit Cell Unit Cell Type SC BCC FCC

Net Number Atoms 1 2 4

One model used to describe the unit cells is the close packing of spheres. We have already made the assumption that metal atoms are spherical. Therefore, the minimal energy arrangement possible is the one with the closest packing of atoms.

The most efficient arrangement of a metallic solid is made up of layers of atoms surrounded by six other atoms stacked upon one another.

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If the spheres of the 3rd layer are in line with the 1st layer, the result is called Hexagonal Close Packing (ABAB)

A B A Gives rise to: Hexagonal Unit Cell NOT Cubic

Alloys

If the spheres of the 1st, 2nd & 3rd layers are all arranged differently, the result is Cubic Close Packing (ABCA)

A B C A Gives rise to: FaceCentered Cubic Unit Cell

Alloys

• Alloys are combinations of two or more elements, the majority of which are metals. • Adding a second (or third) element changes the properties of the mixture to suit different purposes.

• In substitutional alloys, a second element takes the place of a metal atom. • In interstitial alloys, a second element fills a space in the lattice of metal atoms.

Metallic Bonding • In elemental samples of nonmetals and metalloids, atoms generally bond to each other covalently. • Metals, however, have a scarcity of valence electrons; instead, they form large groups of atoms that share electrons among them.

Metallic Solids • One can think of a metal, therefore, as a group of cations suspended in a sea of electrons. • The electrical and thermal conductivity, ductility, and malleability of metals is explained by this model.

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Ionic Solids

Ionic Solids

• In ionic solids, the lattice comprises alternately charged ions. • Ionic solids have very high melting and boiling points and are quintessential crystals.

Simple Ionic Compounds The relative size of Cs to Cl prevents either ion from being more isolated within a closer packing from other like charged ions therefore resulting in a primitive cubic cell.

Determining Empirical Formulas • We can determine the empirical formula of an ionic solid if we know its unit cell geometry by determining how many ions of each element fall within the unit cell.

The differentsized ions in an ionic compound minimize the distance between oppositely charged ions while keeping like-charged ions away from each other.

Simple Ionic Compounds However, when chlorine bonds with sodium, the smaller size of the sodium atom results in a face centered cubic unit cell for sodium chloride.

For example, what are the empirical formulas for ionic these compounds? (a) Green: chlorine; Gray: cesium (b) Yellow: sulfur; Gray: zinc (c) Green: calcium; Gray: fluorine (a)

(b)

(c)

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Molecular Solids • The physical properties of molecular solids are governed by van der Waals forces. • The individual units of these solids are discrete molecules.

Covalent-Network and Molecular Solids • Graphite is an example of a molecular solid, in which atoms are held together with van der Waals forces. – They tend to be softer and have lower melting points.

Covalent-Network and Molecular Solids • Diamonds are an example of a covalent-network solid, in which atoms are covalently bonded to each other. – They tend to be hard and have high melting points.

You have seen only the three unit cells having a cubic geometrical arrangement. Think of the complexity as you move into the rhombus and polygonal geometries giving rise to some of the other 23 unit cell geometries.

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