Crystallography Part 1 - Lecture Notes Review

A set of concise Q&A flashcards covering the key concepts from Crystallography Part 1 lecture notes.

What is crystallography?

The study of crystals (a division of mineralogy covering geometrical, physical, and chemical aspects).

From which Greek words is the term crystallography derived?

Kryos (Κρύος) meaning cold or frost and Grafo (Γράφω) meaning describe.

Crystallography is a division of which broader field?

Mineralogy.

Name the three branches of crystallography mentioned.

Geometrical Crystallography, Physical Crystallography, Chemical Crystallography.

What does Geometrical Crystallography study?

The morphology of crystals and their geometric shapes.

What does Physical Crystallography study?

The relationship between crystal geometry and its physical properties.

What does Chemical Crystallography study?

The relationship between crystal geometry and its chemical properties.

What is a crystal?

A solid with a regular polyhedral shape reflecting long-range internal order and symmetry.

What is meant by 3D periodic arrangements of atoms?

Crystals comprise 3D periodic arrangements of atoms in space.

Which materials are crystalline?

Metals, non-metallic minerals, many ceramics, semiconductors, some polymers, and proteins.

What is the difference between crystalline and amorphous materials?

Crystalline have long-range periodic order; amorphous lack periodic packing (e.g., volcanic glass, plastics).

What controls the external shape of a mineral?

The regular arrangement of atoms in a crystal.

What is a lattice?

A 3D translationally periodic arrangement of points in space.

Do lattice points represent atoms in a lattice?

No; they describe translation symmetry, not necessarily atoms.

What is a motif in crystallography?

The fundamental part of a symmetric design that, when repeated, creates the whole pattern; an atom or group of atoms at each lattice point.

What does the equation Crystal = Lattice + Motif mean?

A crystal is formed by a lattice with a motif attached at each lattice point.

What is a translation operation?

An operation that generates a pattern of regular identical intervals; can occur in 1D, 2D, or 3D.

What is a Unit Cell?

The basic small volume of a crystal that, when periodically repeated, generates the entire pattern.

In how many dimensions can unit cells be translated?

One, two, or three dimensions.

Do different arrangements of unit cells produce different crystal shapes?

Yes.

Is the Unit Cell unique?

No; a unit cell is not unique.

What rule must the unit cell satisfy to be correct?

It must represent the symmetry of the whole crystal.

What are the criteria for choosing the edges of a unit cell?

Edges should coincide with lattice symmetry, be related by lattice symmetry, and be the smallest cell containing all elements.

What is the relationship between unit cell symmetry and crystal symmetry?

Unit cells have at least as much symmetry as the crystal (internal order ≥ external order).

What is the typical shape of a Crystal Unit in 3D?

A parallelepiped with lattice points at the corners.

What are the lattice parameters?

The lengths a, b, c and angles α, β, γ.

What are Primitive and Non-Primitive unit cells?

Primitive (P) has lattice points only at corners; Non-Primitive may have additional lattice points (I, F, C).

What does an axis of symmetry represent?

A line through the center around which the crystal can be rotated to look the same after a definite rotation.

What are the five 2D plane lattices?

Square, Rectangle (Primitive P), Oblique, Diamond (Rectangle Centered C), Hexagonal (rhombus).

What is a Space Lattice?

The 3D array formed by the axes a, b, c and the associated unit cell in three dimensions.

What is the angle between the a and b axes in a space lattice?

Gamma (γ) – the angle between a and b.

What is a Polar Axis in crystallography?

An axis of symmetry that joins two different end elements (e.g., a face and a vertex); symbols include A2p, A3p, etc.; no mirror plane perpendicular to it.

What is a Plane of Symmetry?

A mirror plane; a two-dimensional surface that divides the crystal into two mirror-image halves; symbol is m.

What is Centre of Symmetry?

A point such that every line through it has opposite points equidistant on opposite sides; many crystals have a centre of symmetry even without planes or axes.