2021 Fundamentals of Crystallography

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Academic unit or major
Undergraduate major in Materials Science and Engineering
Nakamura Yoshio  Fujii Toshiyuki 
Course component(s)
Lecture    (対面)
Day/Period(Room No.)
Tue5-6(W331)  Fri5-6(W331)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
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Course description and aims

This course focuses on the fundamentals of crystallography. We will start from the indexing of directions and planes in lattices, the crystal systems, and the Bravais lattice. This course also covers the principles and applications of stereographic projections and their application to the cubic system.

Through lectures and exercise problems, the course enables students to understand the basic concepts of crystallography.

Student learning outcomes

At the end of this course, students will be able to:
1) Understand the concept of lattice and the general rules of lattice directions and planes.
2) Acquire the ability to handle stereographic projections of the cubic system.


lattice, crystal structure, crystal systems, Miller index, interplanar distance, coordination number, packing efficiency, zone, reciprocal lattice, stenographic projection, Wulff net

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

Attendance is taken in every class.
Towards the end of class, students are given exercise problems related to what is taught on that day to solve.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Lattice and crystal structure Learn crystal structures in materials
Class 2 Lattice lines and planes, Miller index Learn indices of directions and planes in a lattice
Class 3 Directions and planes of hexagonal lattice Learn indices of directions and planes in the hexagonal structure
Class 4 Interplanar distance, interplanar angle, interatomic distance Learn interplanar distance, interplanar angle, and interatomic distance
Class 5 Coordination number, packing efficiency Learn the packing efficiency of the cubic structures
Class 6 Zones, zone axis and the zone law Learn the relationship between zone and zone axis
Class 7 Achievement evaluation and general practice (1) Understand the basic things of lattice and crystal structure
Class 8 Crystal symmetry Learn the crystal symmetry of the cubic structure
Class 9 The stereographic projection Learn the method of the stereographic projection
Class 10 The Wulff net Draw the Wulff net for the stereographic projection
Class 11 Trace analysis Learn the trace analysis using the stereographic projection
Class 12 Standard stereographic projection of cubic crystals Draw the standard stereographic projection of the cubic crystal
Class 13 Application of stereographic projection (1) Draw the stereographic projection of the cubic crystal
Class 14 Application of stereographic projection (2) Learn the applications of the stereographic projection

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.


Course materials are provided during class.

Reference books, course materials, etc.

C. S. Barrett,"Structure of Metals, 2nd edition", McGraw-Hill.
A. Kelly, G. W. Groves and P. Kidd,"Crystallography and Crystal Defects, Revised Edition", John Wiley & Sons, Ltd,.

Assessment criteria and methods

Students’ course scores are based on exercise problems (20%) and midterm exams (30%) and final exams (50%).

Related courses

  • MAT.M401 : Applied Diffraction Crystallography in Metals and Alloys
  • MAT.M303 : Lattice Defects and Dislocation

Prerequisites (i.e., required knowledge, skills, courses, etc.)

No prerequisites.

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