Buy article online - an online subscription or single-article purchase is required to access this article.
Download citation
Download citation
link to html
This paper is an extension of a previous treatment of `twins by merohedry' with full lattice coincidence [Σ = 1, Klapper & Hahn (2010). Acta Cryst. A66, 327–346] to `twins by reticular merohedry' with partial lattice coincidence (Σ > 1). Again, the sets of symmetrically equivalent reflections {hkl} are considered as sets of equivalent faces (face forms) {hkl}, and the behaviour of the oriented eigensymmetries of these forms under the action of a twin operation is used to determine the X-ray reflection sets, the intensities of which are affected or not affected by the twinning. The following cases are treated: rhombohedral obverse/reverse Σ3 twins, cubic Σ3 (spinel) twins, tetragonal Σ5 twins (twin elements m′(120), 2′[{\overline 2}10]) and hexagonal Σ7 twins (m′(12{\overline 3}0), 2′[2{\overline 1}0]). For each case the twin laws for all relevant point groups are defined, and the twin diffraction cases A (intensity of twin-related reflection sets not affected), B1 (intensity affected), B2 (intensity affected only by anomalous scattering) and S (single, i.e. non-coincident reflection sets) are derived for all twin laws. A special treatment is provided for the cubic Σ3 twins, where the cubic face forms first have to be split into up to four rhombohedral subforms with a threefold axis along one of the four cube 〈111〉 directions, here [111]. These subforms exhibit different twin diffraction cases analogous to those derived for the rhombohedral obverse/reverse Σ3 twins. A complete list of the split forms and their diffraction cases for all cubic point groups and all Σ3 twin elements is given. The application to crystal structure determination of crystals twinned by reticular merohedry and to X-ray topographic mapping of twin domains is discussed.

Subscribe to Acta Crystallographica Section A: Foundations and Advances

The full text of this article is available to subscribers to the journal.

If you have already registered and are using a computer listed in your registration details, please email support@iucr.org for assistance.

Buy online

You may purchase this article in PDF and/or HTML formats. For purchasers in the European Community who do not have a VAT number, VAT will be added at the local rate. Payments to the IUCr are handled by WorldPay, who will accept payment by credit card in several currencies. To purchase the article, please complete the form below (fields marked * are required), and then click on `Continue'.
E-mail address* 
Repeat e-mail address* 
(for error checking) 

Format*   PDF (US $40)
   HTML (US $40)
   PDF+HTML (US $50)
In order for VAT to be shown for your country javascript needs to be enabled.

VAT number 
(non-UK EC countries only) 
Country* 
 

Terms and conditions of use
Contact us

Follow Acta Cryst. A
Sign up for e-alerts
Follow Acta Cryst. on Twitter
Follow us on facebook
Sign up for RSS feeds