Space group is the most common space group among organic molecular crystals

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction

Solid State Physics, Ch Symmetry and the classification of crystals

Problem

Space group

P2_1/c

is the most common space group among organic molecular crystals. Read the symbol

P\,2_1/c

character by character, taking

b

as the unique axis. In the standard setting the

2_1

axis runs parallel to

b

through the line

x=0

z=\tfrac14

, and the

c

-glide plane is perpendicular to

b

y=\tfrac14

. ((a)) State what

P

2_1

and

c

each mean, giving the translation associated with the screw axis and with the glide plane. ((b)) Using the stated locations, write the screw and the glide as maps of fractional coordinates

(x,y,z)

. Compose them and show that the result is an inversion through the origin. What does this imply about the space group's centrosymmetry? ((c)) List the four general positions generated from

(x,y,z)

, reducing each coordinate modulo whole lattice translations.

Browse the problem library