Skip to main content
SpringerLink
Log in
Book cover

Crystal Structure Determination

The Role of the Cosine Seminvariants

  • Book
  • © 1972

Overview

Authors:
  1. Herbert A. Hauptman

    1. Mathematical Biophysics Department, Medical Foundation of Buffalo, Buffalo, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (13 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  3. Techniques of Implementation

    1. Front Matter

      Pages 185-186
      Download chapter PDF

    2. The Calculation of the Cosine Seminvariants

      • Herbert A. Hauptman
      Pages 187-209

    3. Using Calculated Cosines to Determine Values of Initial Phases

      • Herbert A. Hauptman
      Pages 211-225

    4. The Tangent Techniques

      • Herbert A. Hauptman
      Pages 227-249

  4. The Applications

    1. Front Matter

      Pages 251-251
      Download chapter PDF

    2. Two Androstane Derivatives; Least-Squares Analysis of the Cosine Invariants

      • Herbert A. Hauptman
      Pages 253-282

    3. The Estradiol·Urea Complex and 6α-Fluorocortisol; Two-Dimensional Invariants

      • Herbert A. Hauptman
      Pages 283-306

    4. Hexestrol; Quadruples

      • Charles Weeks
      Pages 307-326

    5. 9α-Fluorocortisol; Pairs

      • Herbert A. Hauptman
      Pages 327-359

    6. Valinomycin; Strong Enantiomorph Discrimination

      • Herbert A. Hauptman
      Pages 361-384

    7. 9-t-Butyl-9,10-Dihydroanthracene; Modified Tangent Procedure

      • Herbert A. Hauptman
      Pages 385-395

  5. Back Matter

    Pages 397-407
    Download chapter PDF
Back to top

Keywords

About this book

The central theme of this monograph is that the cosine seminvariants are the key to crystal structures. The cosine seminvariants are the cosines of those linear combinations of the phases (the so-called structure seminvariants) whose values, for a given functional form for the geometric structure factor, are uniquely determined by the crystal structure alone and are there­ fore independent of the choice of permissible origin. It follows that the cosine seminvariants themselves are uniquely determined, in general, by the observed magnitudes of the normalized structure factors. The values of the cosine seminvariants in turn lead unambiguously to the values of the individual phases and thus to the crystal structure by means of the E-map (Fourier synthesis). It is this property of the cosine seminvariants, that they serve to link the observed magnitudes with the desired phases of the normalized structure factors, which accounts for their importance and explains the emphasis which is here placed on their role.

Authors and Affiliations

  • Mathematical Biophysics Department, Medical Foundation of Buffalo, Buffalo, USA

    Herbert A. Hauptman

Bibliographic Information

  • Book Title: Crystal Structure Determination

  • Book Subtitle: The Role of the Cosine Seminvariants

  • Authors: Herbert A. Hauptman

  • DOI: https://doi.org/10.1007/978-1-4684-9954-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1972

  • Softcover ISBN: 978-1-4684-9956-8Published: 16 December 2012

  • eBook ISBN: 978-1-4684-9954-4Published: 17 April 2013

  • Edition Number: 1

  • Number of Pages: XII, 407

  • Number of Illustrations: 4 b/w illustrations

  • Topics: Crystallography and Scattering Methods, Mathematical Applications in the Physical Sciences

Publish with us

Policies and ethics

Back to top

Search

Navigation