Question

Define the following terms: crystalline solid, lattice point, unit cell, coordination number, closest packing.

Short answer

Crystalline solids have ordered patterns; lattice points indicate positions in these patterns; unit cells replicate patterns; coordination numbers count neighbors; closest packing maximizes space use.

Step-by-step solution

Understanding Crystalline Solid

A crystalline solid is a material with a structure composed of atoms, ions, or molecules arranged in a highly ordered repeating pattern extending in all three spatial dimensions. This structure results in well-defined geometric shapes and distinct melting points.

Defining Lattice Point

A lattice point is a position in a crystal lattice, a 3-dimensional grid-like structure, where atoms, ions, or molecules can be located. The entire crystal structure can be described by the arrangement of these lattice points.

Explaining Unit Cell

A unit cell is the smallest repeating unit of a crystal lattice that, when repeated in all spatial directions, creates the entire lattice. It defines the simplest geometric pattern from which the overall lattice structure can be derived.

Determining Coordination Number

The coordination number is the number of nearest-neighbor particles surrounding an atom, ion, or molecule in a crystal structure. It describes how many other particles each particle is in direct contact with.

Describing Closest Packing

Closest packing refers to the method of arranging particles in a crystal structure such that they occupy the largest possible fraction of available space. Common types include hexagonal closest packing and cubic closest packing, both maximizing density.

Key concepts

Lattice Point

In the world of crystalline solids, lattice points are fundamental. A lattice point is essentially a specific position in a crystal lattice where an atom, ion, or molecule resides. Imagine a 3-dimensional grid, like a crystalline city, where each intersection marks a lattice point laden with an atom. These points play a crucial role because the entire structure of a crystal can be traced by observing the arrangement of its lattice points. By determining how these points are organized, we can glean essential details about the material's properties and the symmetry of the crystal structure. Keeping this in mind helps when exploring more complex structures or analyzing the stability of the solid.

Unit Cell

The concept of a unit cell in crystalline structures is pivotal. Think of it as the fundamental building block of a crystal lattice. It is the smallest segment of the crystal that, when tessellated or repeated in three dimensions, can recreate the entire structure of the crystal. This makes the unit cell an invaluable tool for understanding the geometry of a crystal.

• A unit cell is defined by its edge lengths (a, b, and c) and the angles between them (α, β, and γ).
• This tiny repeating unit might contain different numbers and types of atoms, depending on the complexity of the crystal structure.

From the simplest cubic unit cells to more complex triclinic structures, understanding unit cells allows scientists to construct crystallographic models and analyze how molecules pack together in a crystal.

Coordination Number

Coordination number is a term that tells us about the local environment of a particle within a crystal. Essentially, it is the count of nearest neighbors around a particular atom, ion, or molecule. This is key to understanding the stability and geometry of the crystal. For some common crystal structures, such as:

• Face-centered cubic (FCC) - Coordination number is 12.
• Body-centered cubic (BCC) - Coordination number is 8.
• Simple cubic - Coordination number is 6.

By examining the coordination number, we gain insight into how densely particles are packed together and how they interact within the lattice. This allows for predictions about the material's physical properties, like density and melting point.

Closest Packing

The idea of closest packing in crystals focuses on how particles can be efficiently arranged in a structure to make the best use of space. When particles are packed as tightly as possible, they minimize empty space, leading to denser crystal formations. Two main types of closest packing are:

• Hexagonal closest packing (HCP) - Particles are stacked in a 3-layer repeating pattern (ABAB... sequence).
• Cubic closest packing (CCP) - Also known as face-centered cubic (FCC), follows a 3-layer ABCABC...sequence.

Both HCP and CCP achieve the maximum packing efficiency possible for spheres, filling approximately 74% of space. Understanding these packing arrangements helps explain why certain metals have specific properties and why some materials are more compressible than others.