I have 3 Crystalline-related Questions?

Question

1.) Why is there no base-centered cubic lattice listed with the Bravais lattices?

2.) Under what conditions does the triclinic system reduce to the hexagonal system?

3.) Under what conditions does the monoclinic syste reduce to the orthorhombic system?

Answer 1

1 perhaps you mean body centered, but the answer is the same. There are no unique faces in a cubic crystal so the primitive translation vector is the same. the term base centered is meaningful for tetragonal structures.

2. triclinic is the most general case where a, b,c, and the angles alpha, beta and gamma are unrestrained by symmetry. The conventional setting is c axis unique so a=b, alpha=beta=90, gamma=120.

3 in monoclinic crystals one angle is not 90. A monoclinic crystal becomes orthorhombic when alpha=beta=gamma=90. There are many examples of monoclinic-orthorhombic phase transitions.