International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B. ch. 2.3, p. 240   | 1 | 2 |

Table 2.3.2.3 

M. G. Rossmanna* and E. Arnoldb

aDepartment of Biological Sciences, Purdue University, West Lafayette, Indiana 47907, USA, and  bCABM & Rutgers University, 679 Hoes Lane, Piscataway, New Jersey 08854-5638, USA
Correspondence e-mail:  mgr@indiana.bio.purdue.edu

Table 2.3.2.3| top | pdf |
Position of Harker sections within a Patterson

Symmetry elementForm of [P(x, y, z)]
(a) Harker planes
Axes parallel to the b axis:  
 (i) 2, 3, [\bar{3}], 4, [\bar{4}], 6, [\bar{6}] [P(x, 0, z)]
 (ii) [2_{1}], [4_{2}], [6_{3}] [P(x, {1 \over 2}, z)]
 (iii) [3_{1}], [3_{2}], [6_{2}], [6_{4}] [P(x, {1 \over 3}, z)]
 (iv) [4_{1}], [4_{3}] [P(x, {1 \over 4}, z)]
 (v) [6_{1}], [6_{5}] [P(x, {1 \over 6}, z)]
(b) Harker lines
Planes perpendicular to the b axis:  
 (i) Reflection planes [P(0, y, 0)]
 (ii) Glide plane, [\hbox{glide} = {1 \over 2}a] [P({1 \over 2}, y, 0)]
 (iii) Glide plane, [\hbox{glide} = {1 \over 2}c] [P(0, y, {1 \over 2})]
 (iv) Glide plane, [\hbox{glide} = {1 \over 2} (a + c)] [P({1 \over 2}, y, {1 \over 2})]
 (v) Glide plane, [\hbox{glide} = {1 \over 4} (a + c)] [P({1 \over 4}, y, {1 \over 4})]
 (vi) Glide plane, [\hbox{glide} = {1 \over 4} (3a + c)] [P({3 \over 4}, y, {1 \over 4})]
(c) Special Harker planes
Axes parallel to or containing body diagonal (111), valid for cubic space groups only:[\matrix{& & \hbox{Equation of plane}\hfill\cr && lx + my + nz - p = 0\hfill\cr \hbox{(i)}\hfill & 3\hfill & l = m = n = \cos\ 54.73561^{\circ} = 0.57735\hfill\cr & & p = 0\hfill\cr \hbox{(ii)}\hfill & 3_{1}\hfill & l = m = n = \cos\ 54.73561^{\circ} = 0.57735\hfill\cr & & p = \sqrt{3}/3\hfill}]Rhombohedral threefold axes produce analogous Harker planes whose description will depend on the interaxial angle.