Define these terms: crystalline solid, lattice point, unit cell, coordination number.

When we hear the term 'lattice point', it may evoke the idea of a mathematical grid or pattern. Indeed, in the context of crystalline solids, a lattice point is precisely that—a specific location within the crystal structure where the patterns of atoms or molecules repeat symmetrically. Imagine a crystal as a 3D chessboard, where each square's intersection point would be equivalent to a lattice point.

Lattice points serve as the foundation for the entire crystal structure. When you visualize these points collectively, they form a perfect map for where the atoms or ions are systematically arranged within the solid. However, it's crucial to note that lattice points are not the atoms themselves, but more like the placeholders for where atoms 'should be' in the repeating pattern that constitutes the crystal.

The concept of a 'unit cell' takes the lattice points one step further, defining the smallest repeating 'block' that gives the crystal its structure and properties. Think of it as the building block of crystals, similar to a LEGO piece, which when repeated, constructs an entire LEGO sculpture. Each corner of this 'LEGO piece' corresponds to a lattice point, and by repeating the pattern of the unit cell throughout three-dimensional space, you recreate the full crystal lattice.

Unit cells are vital to understanding the properties of the material, such as its density, because the arrangement of atoms within the unit cell determines how closely packed the atoms are throughout the solid. Crystals can have different types of unit cells, which gives rise to various crystal systems in nature, such as cubic, tetragonal, orthorhombic, and more.

The 'coordination number' is a term that might seem complex at first, but it's essentially a measure of how sociable an atom is within a crystal structure. It tells you how many other atoms or ions an atom is directly touching. These nearest neighbors are immediate to an atom in the lattice and play a key role in determining the stability and structure of the crystal.

For instance, in a simple cubic structure, each corner atom touches only the adjacent ones—giving it a coordination number of 4. This number can vary widely depending on the crystal structure, and it's a cornerstone concept in understanding how different elements bond and interact in solid form. It affects physical properties like melting point and hardness, since materials where atoms have a high coordination number tend to be denser and more closely packed.

A 'crystal lattice structure' is a concept that brings together the lattice points, unit cells, and coordination numbers into one harmonious whole. It represents the grand three-dimensional arrangement of the entire crystal—much like how a blueprint defines the detailed layout of a building. Each point on the lattice is a reflection of the systematic and periodic structure that is characteristic of crystalline solids.

In this grand design, the angles between the lattice points and the distances between them are not arbitrary—they are governed by the intrinsic nature of the chemical bonds and the type of particles that make up the crystal. Varying these angles and distances leads to different crystal lattice structures, and therefore, to different physical and chemical properties. It is the study of these lattice structures that forms the basis for material sciences, chemistry, and solid-state physics, enabling us to engineer new materials and understand the fundamental nature of the solid state.