4.3 Examples of common crystal structures (NaCl, CsCl, diamond, etc.)

Crystal structures are the building blocks of solid materials. They determine how atoms arrange themselves in repeating patterns, shaping a material's properties. Understanding common structures like NaCl, CsCl, and diamond helps us grasp why materials behave the way they do.

These examples showcase different atomic arrangements and bonding types. By studying them, we can predict how new materials might form and behave. This knowledge is crucial for designing everything from stronger metals to more efficient semiconductors.

Crystal Structures and Unit Cells

Crystal Systems and Lattices

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• Seven crystal systems characterize repeating unit cells
  • Cubic, tetragonal, orthorhombic, hexagonal, trigonal, monoclilic, triclinic
• Common crystal structures include face-centered cubic (FCC), body-centered cubic (BCC), hexagonal close-packed (HCP), and diamond cubic
• Bravais lattices describe 14 unique three-dimensional lattice point arrangements
  • Form the basis for all crystal structures
  • Examples include primitive cubic, body-centered cubic, face-centered cubic

Key Structural Characteristics

• Coordination number defines nearest neighbors for each atom in a crystal structure
  • Differentiates various crystal structures
  • Examples: FCC has coordination number 12, BCC has 8
• Packing efficiency measures percentage of space occupied by atoms in a unit cell
  • Varies among crystal structures
  • Influences material properties (density, mechanical strength)
  • FCC and HCP have highest packing efficiency (~74%)

Atomic Arrangements in Common Structures

Sodium Chloride (NaCl) Structure

• Based on face-centered cubic (FCC) lattice
  • Alternating Na+ and Cl- ions occupy lattice points and octahedral holes
• Coordination number 6:6
  • Each ion surrounded by six nearest neighbors of opposite charge
• Highly symmetrical structure
  • Contributes to its stability and ionic bonding characteristics

Cesium Chloride (CsCl) Structure

• Simple cubic lattice of one ion type
  • Other ion type occupies central position of each cube
• Coordination number 8:8
  • Each ion surrounded by eight nearest neighbors of opposite charge
• Higher coordination number than NaCl
  • Results in different properties (higher melting point, different cleavage planes)

Diamond and Related Structures

• Diamond structure based on FCC lattice
  • Carbon atoms occupy lattice points and tetrahedral interstitial sites
  • Coordination number 4
• Each carbon atom forms four covalent bonds in tetrahedral arrangement
  • Creates three-dimensional network
  • Contributes to diamond's extreme hardness
• Zinc blende structure similar to diamond
  • Alternating atom types occupy lattice sites
  • Common in compound semiconductors (GaAs, ZnS)

Properties of Crystal Structures

Factors Influencing Stability and Properties

• Atomic size ratios, electronegativity differences, and bonding types affect stability and mechanical properties
• Close-packed structures (FCC, HCP) generally have higher densities and packing efficiencies
  • Compared to more open structures like BCC or diamond cubic
• Crystal structure symmetry impacts physical properties
  • Optical, electrical, and thermal characteristics vary with symmetry
• Anisotropy more pronounced in lower-symmetry crystal structures
  • Compared to highly symmetric ones like cubic systems
  • Example: graphite shows strong anisotropy in electrical conductivity

Bonding and Structure Relationships

• Interstitial sites and their sizes influence diffusion rates and impurity accommodation
  • Example: carbon atoms in interstitial sites of iron (steel formation)
• Ionic bonding structures (NaCl, CsCl) typically have higher melting points and brittleness
  • Compared to covalent (diamond) or metallic bonding structures
• Electronic band structure strongly influenced by crystal structure and bonding type
  • Determines electrical and optical properties
  • Example: silicon's diamond structure contributes to its semiconductor properties

Predicting Crystal Structures

Rules and Principles for Structure Prediction

• Radius ratio rule compares relative sizes of cations and anions
  • Predicts coordination number and structure of ionic compounds
• Pauling's rules guide prediction of ionic compound crystal structures
  • Include radius ratio rule, electrostatic valence principle, principle of maximum symmetry
• Octet rule and VSEPR theory predict local coordination and overall structure of covalent compounds
  • Example: tetrahedral arrangement in methane (CH4)

Factors Affecting Structure Formation

• Metallic element crystal structure influenced by atomic size, valence electron count, and temperature
  • Example: iron transitions from BCC to FCC at high temperatures
• Electronegativity difference indicates degree of ionic or covalent character in bonding
  • Influences resulting crystal structure
• Polymorphism considers multiple possible crystal structures for a substance
  • External factors like temperature and pressure affect preferred structure
  • Example: carbon exists as graphite or diamond depending on pressure and temperature

Advanced Prediction Methods

• Density functional theory (DFT) calculations predict and compare stability of different possible crystal structures
  • Used for complex compounds or under extreme conditions
• Machine learning algorithms increasingly applied to crystal structure prediction
  • Analyze large databases of known structures to predict new ones