MSE 27000 Atomistic Materials Science

Credits and Contact Hours: 3 credits. Weekly Schedule for 15 weeks: three 50 minute lectures.

Instructors or Course Coordinators: Alejandro Strachan and John Blendell.

Textbook: Richard J.D. Tilley, “Crystals and Crystal Structures,” 1st edition, 2006, Wiley, New York.

Specific Course Information

  1. Catalog Description: Introductory course with an atomistic viewpoint on material properties. Three primary class sections: bonding, crystallography and statistical mechanics.  Bonding topics include introduction to quantum mechanics, emphasis on understanding of metallic, ionic and covalent bonding. Crystallography topics include crystal descriptions and symmetry principles. Statistical mechanics development with application to electronic and thermodynamic properties.
  2. Prerequisites: MA 26100, Corequisites: MSE 23000 and MA 26500.
  3. Course Status: MSE 27000 is a required course.

Specific Goals for the Course

1. All Students

A. Understand the origins of metallic, covalent and ionic bonding.

  • Schrödinger’s Equation and its solution for simple situations.
  • Origin of cohesive energies and relationship with elastic constants.
  • Descriptions of metallic, covalent and ionic bonding.

B. Understand how symmetry in materials leads to crystal structure.

  • Be able to identify symmetry elements, such as mirror planes, rotation axes, glide planes and screw axes.
  • Identity the underlying symmetry elements in specific crystallographic point and space groups.

C. To be able to describe crystal classes, crystal directions and lattice planes.

  • Describe crystal directions and lattice planes using Miller indices.
  • Describe unit cells and lattices.

D. Understand the origin of statistical expressions of population occupancy.

  • Show how different assumptions about the character of a population lead to different occupancies of energy levels.
  • Correlate statistical distributions of occupied energy levels with internal energy, entropy and free energy.

2. Most Students

A. Have an understanding of the underlying origins of bonding.

  • Show how solution of the Schrödinger  Equation for the hydrogen atom can be expanded to atoms with more than one proton, leading to the periodic table of the elements.
  • Understand the origin of cohesive energy in ionic crystals.
  • Understand how wave function overlaps lead to molecular orbitals and covalent bonding, and why these bonds are both direction and strong.
  • Understand how state splitting provides an intuitive understanding of crystal bands and metallic bonding.

B. Understand how particular combinations of crystal symmetry lead to specific point and space groups.

C. Utilize the stereographic projection to relate planes and directions in a crystal.

D. Understand how statistical descriptions of energy states lead to material properties such as heat capacity and specific heat.

3. Some Students

A. Be able to utilize the information in the International Tables of Crystallography to create models of a crystal structure.

B. Correlate the existence of anisotropy in materials with specific bonding characteristics.

C. Correlate changes in temperature with changes in thermodynamic quantities.

Relation of Course to Student Outcomes:

(MSE-1, ABET-a) an ability to apply knowledge of mathematics, science, and engineering to problems in materials engineering.

Topics Covered: Symmetry of point groups, Lattice definition, Atomic positions in structure, x-ray diffraction, Crystal structure basics, Miller indices and lattice directions, Rotations-mirrors-inversion, Interstitial sites, 1D-2D-3D lattices, Bravais lattices, Property symmetries, Schroendger equation, Atomic structure, Band theory , Electron orbitals, Atomistic simulations.