Introduction to Crystallography and Solid State Chemistry

Posted on May 10, 2024 in Chemistry

Crystal Defects

Types of Crystal Defects

  1. Vacancy Defects: Lattice sites that are unoccupied in a crystal. When a neighboring atom moves to occupy the vacant site, the vacancy moves in the opposite direction.
  2. Interstitial Defects: Atoms occupying sites in the crystal structure where atoms are not usually present. These configurations are generally high energy, but small atoms (impurities) can sometimes occupy interstices without high energy (e.g., hydrogen in palladium).
  3. Substitutional Defects: Occur when an original atom in the lattice site is replaced by a different type of atom. The foreign atom occupies the lattice site, not an interstitial position. Depending on the size of the substituted atom, neighboring atoms may be in tension or compression.
  4. Frenkel Defects: In ionic materials, a smaller ion (cation) displaces a larger ion (anion) and occupies intermolecular space. This creates a vacancy defect at the cation’s original position and an interstitial defect at its new position. This is also referred to as a dislocation defect. The substance’s density remains constant. This occurs when anions and cations have a significant size difference (e.g., ZnS and AgCl).
  5. Schottky Defects: Vacancy defects found in ionic solids. To maintain electrical neutrality, an equal number of anions and cations are absent. This decreases the substance’s density. Cations and anions are nearly identical in size in this defect.

Bragg’s Law and X-ray Diffraction

Bragg’s Law

Bragg’s Law is a fundamental principle in crystallography that explains how X-rays are diffracted by a crystal lattice. It describes the conditions for constructive interference of X-rays scattered by crystal lattice planes.

  • When X-rays strike a crystal lattice at a particular angle, they undergo constructive interference if the path length difference between waves scattered by adjacent crystal planes is a whole number of wavelengths.
  • By analyzing the diffraction pattern produced when X-rays interact with a crystal, scientists can deduce the arrangement of atoms in the crystal lattice.

X-ray Diffraction (XRD)

XRD is a powerful non-destructive technique used for analyzing the atomic and molecular structure of a crystal. There are two main types:

  1. Powder X-ray Diffraction (PXRD): The sample is in the form of a fine powder of a bulk crystalline material. It provides information about the phase (polymorph) and crystallinity of the material.
  2. Single-crystal X-ray Diffraction (SCXRD): This technique provides the structure within a single crystal, which does not necessarily represent the bulk of the material. With SCXRD data, the exact atomic positions can be observed, and thus bond lengths and angles can be determined.

Laws of Crystallography

Crystallography is the branch of science that deals with the arrangement and bonding of atoms in crystalline solids, as well as the geometric structure of crystal lattices. It is based on three fundamental laws:

  1. Law of Constancy of Interfacial Angle (Steno’s Law): Under the same physical conditions, the angle between corresponding faces on various crystals of the same substance is constant. This means that even if the size or shape of the crystal changes, the angles between the faces remain the same.
  2. Law of Constancy of Symmetry: All crystals of a substance have the same symmetry elements, including planes of symmetry, axes of symmetry, and the center of symmetry.
  3. Law of Rational Indices (Hauy’s Law): The ratio of intercepts of the different faces of a crystal with the three axes is constant and can be expressed by rational numbers. The intercepts of any face of the crystal along the crystallographic axes are either equal to unit intercepts (a, b, c) or simple whole number multiples of them (na, n1b, n2c), where n, n1, and n2 are called Weiss indices.

Types of Solids

  1. Ionic Solids: Composed of positive and negative ions held together by strong electrostatic attractions. Many ionic crystals have high melting points due to the strong attractions between the ions.
  2. Metallic Solids: Formed by metal atoms held together by metallic bonding. This bonding gives rise to properties like high thermal and electrical conductivity, metallic luster, and malleability.
  3. Molecular Solids: Composed of molecules held together by forces with polar attraction. Small nonpolar molecules, such as H2 and N2, form molecular solids.
  4. Covalent Solids: Atoms in these solids are held together by a network of covalent bonds. These bonds are relatively strong, resulting in good hardness and high melting points.