PHD
  1. Inorganic chemistry  1.1. Coordination chemistry  1.1.1. Ligand field theory  1.1.2. Crystal field theory  1.1.3. Molecular Orbital Theory for Coordination Compounds  1.1.4. Stability of Coordination Compounds  1.1.5. Electronic spectra of coordination compounds  1.1.6. Isomerism in Coordination Compounds  1.1.7. Kinetics and mechanism of coordination reactions  1.2. Organometallic Chemistry  1.2.1. Metal Carbonyls  1.2.2. Metal alkyl and aryl  1.2.3. Fischer and Schrock carbonaceans  1.2.4. Oxidative Addition and Reductive Elimination  1.2.5. Metal Hydrides  1.2.6. Catalysis by organometallic compounds  1.2.7. Metallocenes and Sandwich Complexes  1.2.8. CH activation  1.3. Solid state chemistry  1.3.1. Crystal structures and lattices  1.3.2. Band theory and electrical properties  1.3.3. Defects in the crystal  1.3.4. Synthesis of solid state materials  1.3.5. Magnetic and optical properties of solids  1.3.6. Superconductivity  1.3.7. Solid state ionics  1.4. Bio-inorganic chemistry  1.4.1. Metalloproteins and enzymes  1.4.2. Metal ion transport and storage  1.4.3. The role of metals in medicine  1.4.4. Bioinspired catalysis  1.4.5. Metal–DNA interactions  1.4.6. Metal Complexes in Medical Science  1.5. Lanthanides and Actinides  1.5.1. Electronic configuration and oxidation states in lanthanides and actinides  1.5.2. Spectral and Magnetic Properties in Lanthanides and Actinides  1.5.3. Separation and Extraction of Lanthanides and Actinides  1.5.4. Coordination chemistry of f-block elements  1.6. Main Group Chemistry  1.6.1. Chemistry of boron compounds  1.6.2. Chemistry of Silicon and Germanium Compounds  1.6.3. Chemistry of Phosphorus and Sulfur Compounds  1.6.4. Organosilicon chemistry  1.6.5. Noble Gas Chemistry
  2. Organic chemistry  2.1. Reaction mechanism  2.1.1. Nucleophilic substitution reactions  2.1.2. Electrophilic addition and substitution reactions  2.1.3. Elimination reactions  2.1.4. Rearrangement reactions  2.1.5. Radical reactions  2.1.6. Pericyclic Reactions  2.1.7. Photochemical reactions  2.2. Stereoscopic  2.2.1. Chirality and optical activity  2.2.2. Structural analysis  2.2.3. Stereoelectronic effects  2.2.4. Asymmetric synthesis  2.2.5. Dynamic Stereochemistry  2.3. Organometallic Chemistry in Organic Synthesis  2.3.1. Organolithium and organomagnesium reagents  2.3.2. Transition metal catalyzed coupling reactions  2.3.3. Palladium-catalyzed reactions  2.3.4. Olefin Metathesis  2.3.5. Gold and silver catalysis  2.4. Natural products chemistry  2.4.1. Alkaloids and terpenoids  2.4.2. Steroids and Flavonoids  2.4.3. Total synthesis of natural products  2.4.4. Biosynthesis of natural products  2.5. Supramolecular Chemistry  2.5.1. Host-Guest Chemistry  2.5.2. Self-assembly and molecular recognition  2.5.3. Supramolecular Catalysis  2.5.4. Molecular Machines
  3. Physical Chemistry  3.1. Thermodynamics  3.1.1. Laws of Thermodynamics  3.1.2. Chemical Potential and Equilibrium  3.1.3. Statistical thermodynamics  3.1.4. Non-equilibrium thermodynamics  3.2. Quantum Chemistry  3.2.1. Schrödinger equation and its applications  3.2.2. Molecular orbital theory  3.2.3. Density functional theory  3.2.4. Post-Hartree–Fock methods  3.3. Chemical kinetics  3.3.1. Reaction rate theory  3.3.2. Mechanism and rate laws  3.3.3. Catalysis and enzyme kinetics  3.3.4. Reaction dynamics  3.4. Spectroscopy and molecular structure  3.4.1. Infrared Spectroscopy  3.4.2. UV-visible spectroscopy  3.4.3. Nuclear Magnetic Resonance Spectroscopy  3.4.4. Mass Spectrometry  3.4.5. Raman Spectroscopy  3.5. Surface and Colloid Chemistry  3.5.1. Absorption and Catalysis  3.5.2. Surfactants and micelles  3.5.3. Colloidal Stability  3.5.4. Nanomaterials and Interfaces
  4. Analytical chemistry  4.1. Chromatography  4.1.1. Gas Chromatography  4.1.2. High Performance Liquid Chromatography  4.1.3. Thin Layer Chromatography  4.1.4. Ion Chromatography  4.2. Electroanalytical techniques  4.2.1. Voltammetry and Polarography  4.2.2. Conductometry and potentiometry  4.2.3. Colometry  4.3. Spectroscopic Methods  4.3.1. Atomic absorption spectroscopy  4.3.2. Fluorescence Spectroscopy  4.3.3. X-ray diffraction  4.3.4. Electron paramagnetic resonance spectroscopy  4.4. Chemometrics  4.4.1. Data processing and statistical methods  4.4.2. Multidisciplinary analysis  4.4.3. Machine Learning in Analytical Chemistry
  5. Theoretical and Computational Chemistry  5.1. Molecular dynamics simulation  5.2. Quantum chemistry methods  5.3. Computational drug design  5.4. Machine Learning in Chemistry  5.5. Ab initio molecular dynamics
  6. Biophysics and Medicinal Chemistry  6.1. Drug discovery and design  6.2. Enzyme kinetics and inhibition  6.3. Chemical biology approach  6.4. Protein-ligand interactions  6.5. Bioorthogonal chemistry
  7. Materials chemistry  7.1. Polymer chemistry  7.1.1. Polymerization mechanism  7.1.2. Functional Polymers  7.1.3. Biodegradable Polymer  7.1.4. Conducting and semiconducting polymers  7.2. Nano Chemistry  7.2.1. Nanoparticles and nanostructures  7.2.2. Carbon-based nanomaterials  7.2.3. Quantum dots  7.3. Energy and Environmental Chemistry  7.3.1. Battery and Fuel Cell Chemistry  7.3.2. Green chemistry and sustainable materials  7.3.3. Photocatalysis

PHD → Inorganic chemistry → Solid state chemistry ↓


Crystal structures and lattices


In the fascinating world of solid state chemistry, one of the fundamental concepts is crystal structure. Understanding crystal structures is essential for anyone delving into the chemistry and physics of solids. Crystal structures define the ordered arrangement of atoms, ions, or molecules in a crystalline substance and significantly affect the physical properties of the substance.

Introduction to crystals

A crystal is a solid material whose atoms are arranged in a highly ordered, repetitive pattern spanning all three spatial dimensions. The repeating unit in this ordered structure is known as the unit cell, the smallest part of the crystal lattice that, when repeated, recreates the entire crystal structure.

The study of the formation of crystals and crystal lattices falls under the field of crystallography, which uses a variety of techniques to determine the arrangement of atoms within a solid.

Unit cells and lattices

A unit cell is defined by its lattice parameters, which are the lengths of the edges of the cell and the angles between them. The most straightforward examples of a unit cell are those of the cubic lattice, where the angles between the edges are 90 degrees, and the length of each edge is equal.

Type of mesh                | Length of edges | interaxial angle
Simple Cube                 | a = b = c       | α = β = γ = 90°
Body-centered cubic (BCC)   | a = b = c       | α = β = γ = 90°
Face-centered cubic (fcc)   | a = b = c       | α = β = γ = 90°

Different materials can crystallize in different lattice systems, which are broadly classified into seven crystal systems:

- Cube
- Quadrilateral
- Orthorhombic
- Hexagonal
- Rhomboid
- Monoclinic
- Triclinic

Seven crystal systems

Each of these crystal systems has its own distinctive features:

  • Cubic: Characterized by three perpendicular axes of equal length. Example: Sodium chloride (NaCl). 
       Oh Oh
  O------O 
  | O-----O
   Oh Oh
  • Tetragonal: Similar to a cube but with one axis longer. Example: white tin (Sn). 
       Oh Oh
  O------O 
  | O-----O
   Oh Oh
  • Orthorhombic: All three axes are of different length. Example: Sulfur (S). 
       Oh Oh
  O------O 
  | O-----O
   Oh Oh
  • Hexagonal: Two axes of equal length at 120° and a third axis perpendicular to the plane of the other two. Example: graphite. 
         Oh Oh
    Oh Oh
   O-------O 
   | O-----O
    Oh Oh
  • Rhombus: Also called triangular. All axes are of equal length and all angles are equal but not 90°. Example: Calcite (CaCO3). 
         Oh Oh
    Oh Oh
   O------O 
   | O----O
    Oh Oh
  • Monoclinic: Axes of unequal length, with two angles at 90° and one angle just off. Example: gypsum (CaSO4·2H2O). 
       Oh Oh
  Oh Oh
 O-------O 
 | O-----O
  Oh Oh
  • Triclinic: The least symmetrical. All sides and angles are different. Example: Potassium dichromate (K2Cr2O7). 
       Oh Oh
  Oh Oh
 O------O 
 | O----O
  Oh Oh

Close packing in a crystal

In nature, many crystalline structures form through a process called close packing. Close packing involves arranging spheres (representing atoms) in such a way that they occupy the maximum possible space with the least empty volume.

Types of close packing

  • Hexagonal close-packed (HCP): This arrangement can be represented as a repeating ABAB pattern. Each atom is surrounded by 12 other atoms. Example: Magnesium (Mg). 
    Layer A: oooo
Layer B:  ooo
Layer A: oooo
  • Face-centered cubic (FCC): This system is also known as cubic close-packed (CCP) and follows the pattern ABCABC. This is the structure of many metals such as aluminum (Al). 
    Layer A: oooo
Layer B:  ooo
Layer C: oooo

Cubic crystal structures

Many everyday metals and alloys crystallize in cubic structures because of their symmetry and simplicity.

Simple Cube (SC)

In the simple cubic structure, the atoms are located at each corner of the cube. It has a cubic primitive (or net) of one atom per unit cell.

Body-Centered Cubic (BCC)

In the BCC structure, atoms are found at all eight corners as well as one atom at the center of the cube. Iron (Fe) is a classic example of this. This arrangement provides more effective packing than the simple cube.

Face-centered cubic (FCC)

In the FCC structure, atoms are located at each corner and the centre of all the cube faces. This arrangement gives it high packing efficiency and is found in metals such as copper (Cu).

Understanding Coordination Number and Atomic Packing Factor

The coordination number is the number of nearest neighbors surrounding an atom in a crystal structure. The atomic packing factor (APF) is the fraction of the volume in a crystal structure that is occupied by atoms.

Cubic structures and their properties

Below are the properties of simple, body-centered and face-centered cubic structures:

Structure type            | Coordination number | Atomic packing factor
Simple cube               | 6                   | 0.52
Body-Centered Cubic (BCC) | 8                   | 0.68
Face-Centered Cubic (FCC) | 12                  | 0.74

Illustration of crystal structures

Consider a simple cubic structure represented visually in a grid, where there is an atom at each corner of the cube:

,
,
,
,
,

In short, the study of crystal structures and lattices provides deep insights into the physical properties of materials, affecting everything from electrical conductivity to mechanical strength. The orderly arrangement of atoms, the regularity of lattice structures, and the beauty of crystallographic systems play a key role in defining the characteristics of the materials we encounter in both nature and industry.

Conclusion

Exploring crystal structures and lattices is crucial in understanding the chemical and physical behaviour of materials. From simple cubes to complex polygons, each arrangement reveals the complexities and beauty of solid matter. As we delve deeper into solid state chemistry, these fundamental concepts pave the way towards innovation and discovery in materials science.


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Crystal structures and lattices

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