Structure of Materials

Explore the structure of crystalline and non crystalline materials, including liquid crystals, and introduce short and long range order with primitive lattice, lattice constant, interaction angle, and point groups.

Learn to describe 2D and 3D crystal lattices using lattice constants, basis vectors, and primitive cells, and see how translational order and cubic systems influence symmetry.

Explore crystallographic directions in cubic crystal systems using Miller indices, with four vectors u v w, and learn to identify crystal graphically equivalent directions and close-packed directions.

Explore crystallographic planes and their Miller indices, learn how to find intercepts, apply the inverse to define planes, and visualize plane families with practical examples.

Explore the body-centered cubic structure, with eight nearest neighbors and two atoms per unit cell, derive a = 4R/√3, and calculate the atomic packing factor about 0.61.

Explore the face-centered cubic (fcc) structure, with corner and face-centered atoms, 12 nearest neighbors, and a packing factor around 0.74 that makes it a close-packed arrangement.

Compare simple cubic, bcc, and fcc structures using a handy table that highlights primitive versus conventional unit cells, coordination numbers, distances, and close packed planes and directions.

Explore close packed directions and planes, identifying vectors like one-zero-zero and one-one-one in fcc and simple cubic lattices, and explain plane packing density using pi r^2 cross sections and 0.969.

Explore the planar density of the (100) plane in a simple cubic structure by counting atoms in the plane and comparing the density to a close-packed criterion.

Explore the planar density of the (110) plane in a bcc structure by counting atoms per plane. Calculate plane spacing to assess close packing and implications for dislocations and diffusion.

Analyze the planar density of the (111) plane in the FCC structure, identify it as the close-packed plane, and relate atom counts and hexagonal symmetry to diffusion defects.

This lecture shows how the pair distribution function measures short-range order in amorphous and polymer materials, links peak integrals to coordination numbers, and assesses translational order via peak patterns.

Identify simple cubic, fcc, and the remaining structure, enumerate atoms per cell and nearest neighbors, compute lattice parameters, and determine planar density and close-packed directions.

Explore how temperature and free energy balance create 0d point defects in crystals, including vacancies, substitution impurities, and interstitials.

Explain how vacancies attain equilibrium concentration in crystals by balancing energy penalties with entropy gains, using Arrhenius behavior, formation energy, and entropy changes.

Learn Kroger-Vink notation for intrinsic point defects in ionic crystals, including Schottky and Frankel defects, vacancies and interstitials, and how charge neutrality and mass balance govern descriptions.

Explore how impurities form extrinsic defects in crystals using Kroger-Vink notation, balancing charge and mass with vacancies and interstitials in the host lattice.

Explore one-dimensional line defects in crystals by examining edge and screw dislocations, their dislocation cores, Burgers vectors, and Burgers circuits to distinguish translation from rotation in crystal structure.

Draw Burgers circuits with the s.f. rh convention and right-hand rule; identify Burgers vector and note edge dislocations perpendicular to T, screw dislocations parallel to T.

Explore edge and screw dislocations, using Burgers vectors and the right-hand rule to draw circuits around a dislocation. Learn how dislocation density influences mechanical properties.

Investigate 2-D defects, including grain boundaries, surfaces, phase and twin boundaries, and stacking faults, and 3-D defects like pores and cracks, and their impact on mechanical properties.

Solve a practice crystallography exam problem by identifying the conventional unit cell and closed-packed directions in FCC, then determine plane intercepts and origin shifts to analyze interplanar geometry.