Textbook 12.6

THE SOLID STATE: STRUCTURE, PROPERTIES, AND BONDING

Structural Features of Solids

• Crystalline Solids

  • Have well-defined shapes.

  • Particles (atoms, molecules, ions) are arranged in an orderly manner.

  • Example minerals: Wulfenite, Barite, Beryl, Quartz.

• Amorphous Solids

  • Have poorly defined shapes.

  • Particles lack a consistent arrangement.

The Crystal Lattice and the Unit Cell

• Crystals consist of tightly packed particles in a 3-D array.

• Crystal Lattice

  • Formed from identical spheres positioned at lattice points.

  • Each point has identical surroundings.

• Unit Cell

  • Fundamental building block of the crystal structure.

  • When the unit cell repeats in 3D, it forms the complete crystal.

  • Examples of analogies: checkerboard, tiled floor.

Types of Cubic Unit Cells

• There are 7 crystal systems and several types of unit cells; focus on the cubic system.

• Coordination Number: Number of nearest neighbors of a particle in a crystal.

1. Simple Cubic Unit Cell:

   • 8 corner particles; coordination number = 6.

   • Contains 1 total particle.

2. Body-Centered Cubic Unit Cell:

   • 8 corner particles + 1 in the center; coordination number = 8.

   • Total of 2 particles.

3. Face-Centered Cubic Unit Cell:

   • 8 corner particles + 6 face-centered particles; coordination number = 12.

   • Total of 4 particles.

Packing Efficiency

• Packing Efficiency: Percentage of unit cell volume occupied by spheres.

1. Simple Cubic (52%):

   • Inefficient packing due to gaps between layers.

2. Body-Centered Cubic (68%):

   • Improved packing by aligning layers above gaps.

3. Cubic and Hexagonal Closest Packing (74%):

   • Efficient arrangements with high packing efficiency.

   • Coordination number: 12 for both configurations.

Tools for Studying Crystal Structures

• X-Ray Diffraction Analysis:

  • Diffraction of x-rays helps to determine distances and angles in crystal lattices.

  • Bragg's equation relates to the spacing of crystal layers.

• Scanning Tunneling Microscopy:

  • Allows observation of surfaces at the atomic scale.

  • Generates 3D maps based on electron tunneling near surfaces.

Types and Properties of Crystalline Solids

1. Atomic Solids

   • Formed by noble gases with weak dispersion forces.

   • Low melting and boiling points.

2. Molecular Solids

   • Formed by molecules; physical properties vary by intermolecular forces (dipole-dipole, H bonding).

   • Generally higher melting points than atomic solids.

3. Ionic Solids

   • Comprise cations and anions with high melting points due to strong ionic bonds.

   • Low conductivity in solid state, but conduct when melted.

4. Metallic Solids

   • Exhibit metallic bonding and delocalized electrons, providing high conductivity and malleability.

5. Network Covalent Solids

   • Atoms covalently bonded in a network; very high melting points, varying conductivity.

Amorphous Solids

• Noncrystalline materials with some ordered regions, like rubber or glass.

• Formed by rapid cooling from a molten state, preventing crystallization.

Bonding in Solids: Molecular Orbital Band Theory

• Band theory explains the behavior of metals and conductivity based on the formation of valence and conduction bands.

• Valence Band: Lower energy orbitals occupied by valence electrons.

• Conduction Band: Higher energy orbitals; electrons can easily transition to this band, allowing conductivity in metals.

Summary of Section 12.6

• Crystalline solids have repeated unit cells in their structure.

• Unit cell types include simple, body-centered, and face-centered cubic; highest packing is in face-centered and hexagonal packing.

• X-ray diffraction provides crystal data and atomic measurements.

• Different types of solids exhibit varying physical properties driven by their unique bonding and structure.