1/28 lec 7

Water arranges in an ordered pattern, resulting in a void in its structure.
This void causes water to have a larger volume, leading to it being less dense than ice.
As pressure increases:
- Water molecules tend to come closer together.
- Water forms an extensive network structure, maintaining its liquid state under increased pressure.

Water has a tetrahedral arrangement of molecules, which can lead to voids.
Increasing pressure at a constant temperature still favors the liquid state of water, which is more complex than the solid state.
The compact arrangement of molecules in liquid water makes it less dense than solid ice, explaining why ice floats.

Carbon dioxide, unlike water, does not exhibit a similar network structure when solidified, leading to a different behavior under pressure.

The melting of crystalline solids occurs when the ordered structure is disrupted by heat, breaking intermolecular forces while maintaining the same melting temperature.
Crystalline solids have specific terms to describe their structure:
- Crystal Lattice: Highly ordered 3D arrangement of particles in a crystal.
- Unit Cell: The smallest repeating unit that maintains the crystal structure, defined by dimensions (length $a$, $b$, $c$) and angles between them.

Simple / Primitive Cubic: Equal edge lengths and angles, simplest form.
Body-Centered Cubic: Atoms are located at the corners and one in the center, leading to 8 atoms at the corners contributing rac{1}{8} each.
Face-Centered Cubic: Atoms at the corners and one atom centered on each face, contributing rac{1}{2} each face atom.

Nature aims to minimize voids in structures to achieve lower energy states.
Atom packing arrangements can lead to different types of voids, such as:
- Tetrahedral Holes: Formed when four atoms come together.
- Octahedral Holes: Formed when six atoms are arranged in a specific manner.

Coordination number refers to the number of atoms that a given atom is in contact with. Examples include:
- For simple cubic, the central atom is in contact with 6 atoms.
- Body Centered: 12 atoms.
- Face Centered: Coordination number is 12, including involvement of atoms in corners and faces.

Atoms positioned in unit cells contribute differently based on their location:
- Corner: rac{1}{8} of the atom within the unit.
- Face: rac{1}{2}.
- Center: 1 whole atom.
For face-centered cubic crystals, 6 face atoms contribute half and 8 corner atoms contribute a total of 1, yielding a total of 4 atoms.

Ionic Solids: Formed from complete ionic charge formation; they have well-defined arrangements in the unit cell with concepts such as octahedral and tetrahedral voids based on the arrangement of cations and anions.
The ratio of ionic sizes influences the arrangement of atoms in a solid.
Molecular Solids: They start with molecule formation and develop into solid structure.

The relative size between cations and anions determines the void types they will occupy:
- Radius ratio of $0.22 - 0.4$: Cation occupies tetrahedral holes.
- Radius ratio of $0.4 - 0.7$: Cation occupies octahedral holes.
Cation and anion interactions reflect their size difference in multiple structures.

The study involves understanding the impact of structure on properties of materials like water and other solids, focusing on their lattice arrangements, melting behaviors, and void characteristics.
The specific arrangements lead to defined coordination numbers and define the characteristics of different types of solids.
Adopting configurations that minimize voids aids in achieving lower energy states, reflecting the inherent tendencies of atomic structures to stabilize.