Introduction to Solid-State Physics – Lattices & Course Roadmap

Vocabulary flashcards cover key terms introduced in the opening lecture: course scope, bonding, lattice geometry (Bravais and beyond), 2-D and 3-D lattice types, electronic models, and foundational concepts like Bloch’s theorem and band structure.

Solid-State Physics

Branch of physics that studies the atomistic (microscopic) origin of macroscopic properties in solids.

Quantum Mechanics

Fundamental theory used to describe the behaviour of electrons in solids.

Electromagnetism

Classical field theory employed alongside quantum mechanics to model interactions in materials.

Valence Electrons

Outer-shell electrons of an atom that participate in chemical bonding and largely determine a solid’s properties.

Chemical Bond

Attractive interaction that binds atoms; can be covalent, ionic, metallic, hydrogen, etc.

Covalent Bond

Strong bond formed by sharing valence electrons between atoms.

Ionic Bond

Bond produced by electrostatic attraction between oppositely charged ions.

Hydrogen Bond

Relatively weak bond involving a hydrogen atom attracted to an electronegative atom in another molecule or site.

Bonding Energy

Energy required to separate bonded atoms to infinity; relates to lattice stability and vibrations.

Vibrations (Phonons)

Collective atomic displacements about equilibrium positions in a solid or molecule.

Lattice (general)

Ordered, periodic arrangement of points in space representing atomic positions.

Bravais Lattice

Infinite set of points R = n₁a₁ + n₂a₂ (+ n₃a₃) generated from three (or D) linearly independent primitive vectors with all integers nᵢ.

Primitive Vectors

Smallest set of independent vectors (a₁, a₂, a₃) that generate every point of a Bravais lattice via integer combinations.

Crystal Structure (Lattice with a Basis)

Bravais lattice plus a finite set of additional vectors {bᵢ}; each lattice point carries an identical basis producing complex motifs.

Basis

Collection of vectors (and associated atoms) attached to every Bravais lattice point, specifying internal arrangement within the unit cell.

Bravais Lattice Vector

Any vector connecting two lattice points; integer combination of primitive vectors. Multiples of such vectors are also lattice vectors.

Square Lattice

2-D Bravais lattice with |a₁| = |a₂| and a₁ ⟂ a₂.

Rectangular Lattice

2-D Bravais lattice with a₁ ⟂ a₂ but |a₁| ≠ |a₂|.

Triangular (Hexagonal 2-D) Lattice

2-D Bravais lattice generated by equal-length vectors forming 60° (or 120°) between them; densest circle packing.

Honeycomb Lattice

2-D non-Bravais lattice obtained from a triangular Bravais lattice plus a two-point basis; geometry of graphene.

Cubic Lattice

3-D Bravais lattice with |a₁| = |a₂| = |a₃| and all axes mutually perpendicular.

Tetragonal Lattice

3-D Bravais lattice: a₁ ⟂ a₂ ⟂ a₃, |a₁| = |a₂| ≠ |a₃|.

Orthorhombic Lattice

3-D Bravais lattice with all three axes perpendicular and of unequal length.

Hexagonal Lattice (3-D)

Bravais lattice with a 2-D triangular base (60°) and a third axis perpendicular to the base (|a₁| = |a₂| ≠ |a₃|).

Triclinic Lattice

Most general 3-D Bravais lattice: no constraints on lengths or angles; defined by 3 lengths + 3 angles.

Tight-Binding Model

Electronic model assuming electrons remain closely associated with atoms; useful for describing localized states.

Quasi-Free Electron Model

Model that treats electrons as nearly free particles weakly perturbed by the periodic lattice potential.

Bloch’s Theorem

Theorem stating that electronic wavefunctions in a periodic potential take the form of plane waves modulated by lattice periodicity.

Brillouin Zone

Primitive cell of reciprocal space derived from a Bravais lattice; fundamental domain for electron k-vectors.

Band Structure

Energy spectrum of electrons in a crystal, arising from periodic potential; determines transport and optical properties.

Reciprocal Lattice

Mathematical lattice in momentum space constructed from primitive vectors; central to X-ray diffraction and wave propagation analysis.

X-Ray Diffraction

Experimental technique that reveals atomic order; interpretation relies on reciprocal lattice and Bragg’s law.

Electronic Transport

Movement of charge carriers (electrons/holes) through a solid; linked to band structure and scattering.