A Caltech Library Service

l. The Crystal Structure of Trimesic Acid. II. Topics in Crystallographic Calculations


Duchamp, David James (1965) l. The Crystal Structure of Trimesic Acid. II. Topics in Crystallographic Calculations. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/JGPC-Y356.


I. Trimesic acid (1, 3, 5-benzenetricarboxylic acid) crystallizes with a monoclinic unit cell of dimensions a = 26.52 A, b = 16.42 A, c = 26.55 A, and β = 91.53° with 48 molecules /unit cell. Extinctions indicated a space group of Cc or C2/c; a satisfactory structure was obtained in the latter with 6 molecules/asymmetric unit - C54O36H36 with a formula weight of 1261 g. Of approximately 12,000 independent reflections within the CuKα sphere, intensities of 11,563 were recorded visually from equi-inclination Weissenberg photographs.

The structure was solved by packing considerations aided by molecular transforms and two- and three-dimensional Patterson functions. Hydrogen positions were found on difference maps. A total of 978 parameters were refined by least squares; these included hydrogen parameters and anisotropic temperature factors for the C and O atoms. The final R factor was 0.0675; the final "goodness of fit" was 1.49. All calculations were carried out on the Caltech IBM 7040-7094 computer using the CRYRM Crystallographic Computing System.

The six independent molecules fall into two groups of three nearly parallel molecules. All molecules are connected by carboxylto- carboxyl hydrogen bond pairs to form a continuous array of sixmolecule rings with a chicken-wire appearance. These arrays bend to assume two orientations, forming pleated sheets. Arrays in different orientations interpenetrate - three molecules in one orientation passing through the holes of three parallel arrays in the alternate orientation - to produce a completely interlocking network. One third of the carboxyl hydrogen atoms were found to be disordered.

II. Optical transforms as related to x-ray diffraction patterns are discussed with reference to the theory of Fraunhofer diffraction.

The use of a systems approach in crystallographic computing is discussed with special emphasis on the way in which this has been done at the California Institute of Technology.

An efficient manner of calculating Fourier and Patterson maps on a digital computer is presented. Expressions for the calculation of to-scale maps for standard sections and for general-plane sections are developed; space-group-specific expressions in a form suitable for computers are given for all space groups except the hexagonal ones.

Expressions for the calculation of settings for an Eulerian-cradle diffractometer are developed for both the general triclinic case and the orthogonal case.

Photographic materials on pp. 4, 6, 10, and 20 are essential and will not reproduce clearly on Xerox copies. Photographic copies should be ordered.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Chemistry)
Degree Grantor:California Institute of Technology
Division:Chemistry and Chemical Engineering
Major Option:Chemistry
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Marsh, Richard Edward
Thesis Committee:
  • Unknown, Unknown
Defense Date:14 May 1965
Funding AgencyGrant Number
Record Number:CaltechTHESIS:03192015-081930753
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8791
Deposited By: Benjamin Perez
Deposited On:19 Mar 2015 15:43
Last Modified:20 Feb 2024 22:55

Thesis Files

PDF - Final Version
See Usage Policy.


Repository Staff Only: item control page