MIT材料科学与工程系【本科生课程】3.60.材料的对称性,结构,性能和张量.pdf

Symmetry, Structure, and Tensor Properties of Materials As taught in: Fall 2005 Crystal structure of the cuprate compound Bi Sr CaCu O or Bi2212, showing the 2 2 2 8+δ copper (purple)–oxygen (black) layer responsible for superconductivity. (Image courtesy of Lawrence Berkeley Laboratory.) Instructors: Prof. Bernhardt Wuensch MIT Course Number: 3.60 Level: Graduate Course Description This course covers the derivation of symmetry theory; lattices, point groups, space groups, and their properties; use of symmetry in tensor representation of crystal properties, including anisotropy and representation surfaces; and applications to piezoelectricity and elasticity. Syllabus Course Meeting Times Lectures: Two sessions / week, 1.5 hours / lecture Course Overview This course covers the derivation of symmetry theory; lattices, point groups, space groups, and their properties; use of symmetry in tensor representation of crystal properties, including anisotropy and representation surfaces; and applications to piezoelectricity and elasticity. Prerequisites The only prerequisites for this course are familiarity with linear algebra and matrix mathematics. Course concepts are developed from first principles using basic geometry. Textbook There is no required textbook. Students are expected to read handouts as listed in the readings section. Grading A students grade is based entirely upon an equal weighting of the three quizzes. Students are encouraged to turn in their homework assignments for correction and feedback, but the assignments do not contribute to the course grade. Calendar LEC # TOPICS KEY DATES Part 1. Crystallography and Symmetry 1 Introduction to Crystallography 2 Crystalline Structure and Geometry Problem set 1 due 3 Translation, Rotation, Periodicity P