Graduate
  1. Physical Chemistry  1.1. Thermodynamics  1.1.1. Laws of Thermodynamics  1.1.2. Enthalpy and heat capacity  1.1.3. Entropy and free energy  1.1.4. Phase Equilibrium  1.1.5. Statistical thermodynamics  1.1.6. Thermodynamic cycle  1.1.7. Fugacity and activity  1.2. Quantum Chemistry  1.2.1. Principles of quantum mechanics  1.2.2. Schrödinger Equation  1.2.3. Particle in a box  1.2.4. Operators and eigenvalues  1.2.5. Atomic orbitals  1.2.6. Molecular orbital theory  1.2.7. Perturbation theory  1.2.8. Valence bond theory  1.2.9. Hybridization and chemical bonding  1.3. Chemical kinetics  1.3.1. Rate laws and reaction mechanisms  1.3.2. Collision theory  1.3.3. Transition state theory  1.3.4. Enzyme Kinetics  1.3.5. Chain Reactions and Polymerization  1.3.6. Photochemical reactions  1.4. Statistical mechanics  1.4.1. Partitioning functions  1.4.2. Molecular distribution functions  1.4.3. Boltzmann Distribution  1.4.4. Bose–Einstein and Fermi–Dirac statistics  1.5. Spectroscopy  1.5.1. Rotational Spectroscopy  1.5.2. Vibrational Spectroscopy  1.5.3. Electronic Spectroscopy  1.5.4. Nuclear magnetic resonance spectroscopy  1.5.5. Mass Spectrometry  1.5.6. Raman Spectroscopy  1.5.7. Electron paramagnetic resonance spectroscopy  1.6. Surface and colloidal chemistry  1.6.1. Absorption isotherm  1.6.2. Surface tension and wetting  1.6.3. Colloidal Stability  1.6.4. Catalysis  1.6.5. Emulsions and micelles  1.7. Electrochemistry  1.7.1. Nernst equation  1.7.2. Electrochemical cells  1.7.3. Conductivity and mobility  1.7.4. War  1.7.5. Fuel cells  1.7.6. Electrolysis
  2. Organic chemistry  2.1. Reaction mechanism  2.1.1. Nucleophilic substitution reactions  2.1.2. Electrophilic addition reactions  2.1.3. Elimination reactions  2.1.4. Rearrangement reactions  2.1.5. Radical reactions  2.1.6. Pericyclic reactions  2.2. Spectroscopy and structural determination  2.2.1. UV-Vis Spectroscopy  2.2.2. IR Spectroscopy  2.2.3. NMR Spectroscopy  2.2.4. Mass Spectrometry  2.2.5. X-ray crystallography  2.3. Stereoscopic  2.3.1. Chirality and optical activity  2.3.2. Structural analysis  2.3.3. Geometrical isomerism  2.3.4. Dynamic Stereochemistry  2.4. Organometallic Chemistry  2.4.1. Organolithium and organomagnesium reagents  2.4.2. Palladium-catalyzed cross-coupling reactions  2.4.3. Transition Metal Complexes  2.4.4. Metal–carbon bond  2.5. Polymer chemistry  2.5.1. Polymerization mechanism  2.5.2. Polymer Characteristics  2.5.3. Biodegradable Polymer  2.5.4. Conducting polymer  2.5.5. Supramolecular polymers  2.6. Medicinal chemistry  2.6.1. Drug design and development  2.6.2. Pharmacokinetics and pharmacodynamics  2.6.3. Structure-activity relationships  2.6.4. Molecular docking and drug screening
  3. Inorganic chemistry  3.1. Coordination chemistry  3.1.1. Crystal field theory  3.1.2. Ligand field theory  3.1.3. Spectrochemical Series  3.1.4. Chelation and stability  3.2. Organometallic Chemistry  3.2.1. Metal Carbonyls  3.2.2. Catalysis by organometallic complexes  3.2.3. Metallocenes  3.3. Bio-inorganic chemistry  3.3.1. Metalloproteins and enzymes  3.3.2. The role of metals in biological systems  3.3.3. Metal ion transport and storage  3.4. Solid state chemistry  3.4.1. Crystal Structures  3.4.2. Band theory of solids  3.4.3. Superconductors  3.4.4. Defects in the crystal  3.5. Lanthanides and Actinides  3.5.1. Electronic configuration in lanthanides and actinides  3.5.2. Coordination chemistry of the lanthanides  3.5.3. Magnetic Properties of Lanthanides
  4. Analytical chemistry  4.1. Chromatography  4.1.1. Gas Chromatography  4.1.2. High Performance Liquid Chromatography  4.1.3. Thin Layer Chromatography  4.2. Spectroscopic Techniques  4.2.1. Atomic absorption spectroscopy  4.2.2. X-ray diffraction  4.2.3. Inductively coupled plasma spectroscopy  4.3. Electroanalytical methods  4.3.1. Potentiometry  4.3.2. Voltammetry  4.3.3. Colometry  4.4. Mass Spectrometry  4.4.1. Ionization Technique  4.4.2. Fragmentation Pattern  4.5. Chemometrics  4.5.1. Multidisciplinary analysis  4.5.2. Machine Learning in Chemistry
  5. Theoretical and Computational Chemistry  5.1. Molecular dynamics simulation  5.1.1. Force fields and energy minimization  5.1.2. Monte Carlo simulation in molecular dynamics simulations  5.2. Quantum chemical methods  5.2.1. Hartree–Fock theory  5.2.2. Density functional theory  5.2.3. Semi-empirical methods  5.3. Computational drug design  5.3.1. Molecular Docking  5.3.2. QSAR Modeling  5.3.3. Virtual Screening
  6. Biochemistry  6.1. Enzyme Kinetics  6.1.1. Michaelis-Menten kinetics  6.1.2. Inhibition mechanism  6.2. Metabolism and Bioenergetics  6.2.1. Glycolysis  6.2.2. Citric acid cycle  6.2.3. Electron transport chain  6.3. molecular Biology  6.3.1. DNA replication and repair  6.3.2. Protein synthesis  6.3.3. Gene Regulation  6.4. Structural Biochemistry  6.4.1. Protein Folding  6.4.2. Membrane Biophysics
  7. Environmental Chemistry  7.1. Atmospheric Chemistry  7.1.1. Greenhouse gases  7.1.2. Ozone depletion  7.1.3. Air pollutants and smoke  7.2. Water Chemistry  7.2.1. pH and water hardness  7.2.2. Wastewater treatment  7.2.3. Aquatic Chemistry  7.3. Soil Chemistry  7.3.1. Heavy metal contamination  7.3.2. Soil pH and Buffering  7.3.3. Nutrient cycling  7.4. Toxicology and Chemical Safety  7.4.1. Toxicokinetics  7.4.2. Risk Assessment in Toxicology and Chemical Safety in Environmental Chemistry  7.4.3. Effects of pollutants on the environment

Graduate → Inorganic chemistry → Solid state chemistry ↓


Crystal Structures


In solid state chemistry, crystal structures represent the ordered arrangement of atoms within a substance. Understanding these structures is important for explaining many physical properties of substances, such as conductivity, magnetism, and optical properties. In inorganic chemistry, these crystal structures are particularly important because they help understand the structure and functionality of metals, ceramics, minerals, and other inorganic compounds.

Basic concepts

Crystalline solids are defined by the periodic arrangement of atoms, ions, or molecules in a three-dimensional lattice. The smallest repeating unit of this structure is called a unit cell. The arrangement of the unit cells forms the entire crystal, providing information about the structure and possible properties of the solid.

Unit cell

The unit cell is the building block of the crystal structure. It is defined by its lattice parameters, which are the lengths of the cell edges (a, b, c) and the angles between them (α, β, γ). These cells are repeated in a pattern to fill the space without overlapping.

A B

Types of unit cell

There are several different types of unit cells that form the basis of crystal structures:

  • Simple Cubic (SC): There is one atom at each corner of the cube. The simple cubic structure is the simplest but is rarely seen.
  • Body-centered cubic (BCC): Similar to SC, but with an extra atom at the center of the cube. An example of this is iron at low temperatures.
  • Face-centered cubic (FCC): An atom is located at each corner and the center of all faces of the cube. Common in metals such as aluminum, copper, and gold.
  • Hexagonal close-packed (HCP): Atoms are closely packed in a hexagonal arrangement. Examples include magnesium and titanium.

Text example of a simple cube structure

Simple Cubic Structure:
 
Corner Atom
(0,0,0) -------------------*------------------- (A,0,0)
 ,
 ,
 ,
 ,
 ,
 ,
 ,
 ,
 ,
 ,
 ,
 ,
 ,
 ,
(0,0,a) -------------------*------------------- (a,0,a)

Cubic crystal system

The cubic crystal system is one of the most common and important crystal systems. It has three equal axes that intersect at 90 degree angles. Within the cubic system, we have three main types:

  • Simple Cubic (SC): This system is not very efficient in space utilization. The packing efficiency or the fraction of volume filled by atoms is about 52%.
  • Body-centered cubic (BCC): Packing efficiency is higher than SC, about 68%, due to the central atom.
  • Face-centered cubic (FCC): This is the most efficient of the cubic types, with a packing efficiency of about 74%.

This view shows a body-centered cubic structure, with the corner atoms colored in blue and the central atom colored in red.

Hexagonal crystal system

Another widely studied crystal system is the hexagonal system, which has two equal axes perpendicular to each other and a third axis of a different length that intersects them both at 90 degrees. Its traditional example is the hexagonal close-packed (HCP) structure.

Text example of hexagonal close-packed structure

Upper layer:
 
atom 1 atom 2 atom 3
 
  ,
   ,
 
lower layer:
 
     atom 4 atom 5 atom 6
  
      ,
       ,
  
(Base floor view)

Coordination number

The coordination number is an important concept in understanding crystal structures. It refers to the number of nearest neighbouring atoms surrounding a central atom. It varies with the type of crystal structure:

  • The coordination number for Sc is 6.
  • The coordination number for bcc is 8.
  • The coordination number for fcc and hcp is 12.

Visualization of crystal structures

Visualizing crystal structures can be challenging. However, by analyzing lattice symmetry and repeating patterns, the complex nature of these structures can be better understood. Here, symmetry leads to unique properties that directly impact the functionality of the material.

Let us consider the cubic structure of diamond, in which the carbon atoms are covalently bonded in a tetrahedral geometry.

Polymorphism and allotropy

Polymorphism refers to the ability of a substance to exist in more than one crystal structure. This phenomenon is important in materials science and has an impact on physical properties, such as melting point and solubility. Allotropy is a similar concept, but it is restricted to elemental entities.

A classic example of this is carbon, which can form either graphite or diamond depending on its bonding and structure. Graphite has a layer structure with weak forces between the layers, while diamond has a tetrahedrally bonded structure resulting in hardness.

Applications of crystal structures

Understanding crystal structures is important in many technological applications. For example, the semiconductor industry relies heavily on crystal structure knowledge for the development of materials such as silicon and gallium arsenide. Similarly, the pharmaceutical industry evaluates crystal structures for drug design and manufacturing.

The discovery of new crystal structures is driving innovations in materials science, leading to the development of superconductors, catalysts, and novel structural materials with advanced properties.

Conclusion

In summary, crystal structures in solid state chemistry are fundamental to understanding a wide range of physical properties and technological applications. By analyzing the geometric arrangement of atoms and the resulting symmetry, scientists can predict and optimize the physical properties needed for specific uses.


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Crystal Structures

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