{"id":641,"date":"2021-11-19T05:22:26","date_gmt":"2021-11-19T05:22:26","guid":{"rendered":"http:\/\/www.calm-ebsd.com\/?page_id=641"},"modified":"2021-12-27T12:36:47","modified_gmt":"2021-12-27T12:36:47","slug":"aspects-to-consider","status":"publish","type":"page","link":"https:\/\/www.calm-ebsd.com\/index.php\/solution\/aspects-to-consider\/","title":{"rendered":"Basis vector setup"},"content":{"rendered":"\n<p>Unfortunately, a <strong>lattice description<\/strong> with and without knowledge of structure and symmetry<strong> is not uniform<\/strong>. <\/p>\n\n\n\n<p style=\"font-size:22px\">No crystal structure data available (e.g. CALM)<\/p>\n\n\n\n<p>If one determines only the lattice parameters, e.g. by means of XRD, then the recommendation for <strong>triclinic<\/strong> applies:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\begin{align*}\na \\leq b \\leq c \\quad \\textrm{and} \\quad \\alpha, \\beta, \\gamma &gt;90\\degree\n\\end{align*}<\/pre><\/div>\n\n\n\n<p>For <strong>monoclinic<\/strong>  the <strong>physical axes setup<\/strong> is <strong>valid<\/strong>:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\begin{align*}\na\\leq b \\quad \\textrm{and} \\quad \\gamma&gt;90\\degree\n\\end{align*}<\/pre><\/div>\n\n\n\n<p>although more common is still the mineralogic axes setup with \u03b2 different from 90\u00b0.<\/p>\n\n\n\n<p>The internationally accepted recommendation for <strong>orthorhombic<\/strong> is:<\/p>\n\n\n\n<div class=\"wp-block-katex-display-block katex-eq\" data-katex-display=\"true\"><pre>\\begin{align*}\na\\leq b\\leq c\n\\end{align*}<\/pre><\/div>\n\n\n\n<p>For all higher-symmetric crystal systems no rules are required since there are no reasonable axes permutations. <\/p>\n\n\n\n<p>The reason for these rules is that a phase search in tables (Hanawalt or Fink index) or databases can be significantly shortened [1]. <br>In addition, (phase-specific) information such as the lattice parameter ratios a \/ b : 1 : c \/ b are then unambiguous.<\/p>\n\n\n\n<p style=\"font-size:22px\">Data from crystal structure databases<\/p>\n\n\n\n<p>However, <strong>if<\/strong> the <strong>crystal structure<\/strong> of a phase <strong>is known<\/strong>, <strong>the upper rules are obsolete<\/strong>.<\/p>\n\n\n\n<p>Then the <strong>definition<\/strong> of axes and angle definition <strong>follows<\/strong> the alignment of the symmetry elements, as specified in the <strong>standard settings<\/strong> of the space-group types <strong>in the International Tables for Crystallography (Vol. A)<\/strong>.<\/p>\n\n\n\n<p><span class=\"has-inline-color has-navy-blue-color\">Since also <strong>in CALM<\/strong> only the crystal lattice is determined, this means that the rules listed above are followed. <br>Thus, even for correctly described lattices of low-symmetry phases, there <strong>will inevitably be differences from <\/strong>their <strong>descriptions<\/strong> listed <strong>in databases<\/strong>.<\/span> <\/p>\n\n\n\n<p><em>Thus, for orthorhombic phases, a, b and c can be interchanged arbitrarily, while the output in CALM will always show:<\/em><br><em>a &lt; b &lt; c.<\/em><\/p>\n\n\n\n<p style=\"font-size:14px\">[1] Faber, J.; Weth, C. &amp; Jenkins, R.:PCSIWIN: A Windows-Based Index Program with Hanawalt, Fink and Alphabetic Search Capabilities for Use with the ICDD Powder Diffraction File (PDF), <em>Mater. Sci. Forum, <em><strong>378-381<\/strong><\/em> <\/em>(2001), 106-111<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Unfortunately, a lattice description with and without knowledge of structure and symmetry is not uniform. No crystal structure data available (e.g. CALM) If one determines only the lattice parameters, e.g. by means of XRD, then the recommendation for triclinic applies: <a href=\"https:\/\/www.calm-ebsd.com\/index.php\/solution\/aspects-to-consider\/\" class=\"read-more\">Read More &#8230;<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"parent":1043,"menu_order":2,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/www.calm-ebsd.com\/index.php\/wp-json\/wp\/v2\/pages\/641"}],"collection":[{"href":"https:\/\/www.calm-ebsd.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.calm-ebsd.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.calm-ebsd.com\/index.php\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.calm-ebsd.com\/index.php\/wp-json\/wp\/v2\/comments?post=641"}],"version-history":[{"count":18,"href":"https:\/\/www.calm-ebsd.com\/index.php\/wp-json\/wp\/v2\/pages\/641\/revisions"}],"predecessor-version":[{"id":1809,"href":"https:\/\/www.calm-ebsd.com\/index.php\/wp-json\/wp\/v2\/pages\/641\/revisions\/1809"}],"up":[{"embeddable":true,"href":"https:\/\/www.calm-ebsd.com\/index.php\/wp-json\/wp\/v2\/pages\/1043"}],"wp:attachment":[{"href":"https:\/\/www.calm-ebsd.com\/index.php\/wp-json\/wp\/v2\/media?parent=641"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}