{"id":658,"date":"2021-11-19T06:20:42","date_gmt":"2021-11-19T06:20:42","guid":{"rendered":"http:\/\/www.calm-ebsd.com\/?page_id=658"},"modified":"2021-12-09T12:25:45","modified_gmt":"2021-12-09T12:25:45","slug":"possible-solutions","status":"publish","type":"page","link":"https:\/\/www.calm-ebsd.com\/index.php\/solution\/possible-solutions\/","title":{"rendered":"(Im)possible solutions"},"content":{"rendered":"\n<p>The <strong>derivation of<\/strong> the <strong>crystal lattice and<\/strong> the assignment of a <strong>Bravais lattice type<\/strong> <strong>has<\/strong> objective <strong>limits<\/strong>. <br><strong>In general<\/strong>, due to measurement and imaging errors, <strong>the approximation of pseudosymmetric lattice types is the rule<\/strong>.<br>So there is always the danger to consider a higher symmetric lattice as solution.<\/p>\n\n\n\n<p>The <strong>first reason<\/strong> for this is that from a <strong>purely metrological<\/strong> point of view alone, angles of exactly 90\u00b0, for example, will never result. The same applies of course to special ratios between basis vectors.<\/p>\n\n\n\n<p>The <strong>second reason<\/strong> is that the symmetry of a crystal structure imposes certain requirements on the metric of the crystal lattice, but <strong>crystal symmetry cannot be inferred from the crystal lattice metric<\/strong>. <br>Unfortunately, in the past years, mostly due to carelessness, <strong>description errors of crystal lattices<\/strong> have crept in [1].<br><em>For example, for orthorhombic lattices is assumed that a, b and c must be different, but actually no conditions at all are put to the lengths [2]. This means that also for an orthorhombic phase a = b = c can occur.<\/em><br><em>The following table shows that<strong> up to orthorhombic<\/strong> <strong>no conditions<\/strong> are defined <strong>for the length ratios<\/strong> of the basis vectors.<\/em><\/p>\n\n\n\n<hr class=\"wp-block-separator is-style-wide\"\/>\n\n\n\n<div class=\"wp-block-media-text alignwide is-stacked-on-mobile is-vertically-aligned-bottom\" style=\"grid-template-columns:35% auto\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" width=\"455\" height=\"338\" src=\"http:\/\/www.calm-ebsd.com\/wp-content\/uploads\/2021\/12\/LatticeDefinition.png\" alt=\"\" class=\"wp-image-1585 size-full\" srcset=\"https:\/\/www.calm-ebsd.com\/wp-content\/uploads\/2021\/12\/LatticeDefinition.png 455w, https:\/\/www.calm-ebsd.com\/wp-content\/uploads\/2021\/12\/LatticeDefinition-300x223.png 300w, https:\/\/www.calm-ebsd.com\/wp-content\/uploads\/2021\/12\/LatticeDefinition-360x267.png 360w\" sizes=\"(max-width: 455px) 100vw, 455px\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<p style=\"font-size:14px\"><em>Definition of the conditions for lattice parameter ratios and angles of different translation lattice .<\/em><\/p>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator is-style-wide\"\/>\n\n\n\n<p>Once derived lattice parameters plus agreed uncertainties describe a high-symmetric lattice, it is not clear whether the remaining deviations are due to measurement or imaging errors or really exist, i.e. the lattice is possibly not so high-symmetric but described by one of the other solution presented.<\/p>\n\n\n\n<p>But again: Even with practically non-existing deviations it follows that e.g. a phase with cubic lattice metric does not necessarily have cubic symmetry. It is merely very probable.<\/p>\n\n\n\n<p>Therefore, <strong>CALM always lists<\/strong> a <strong>triclinic<\/strong> lattice description (aP),<strong> but<\/strong> additionally <strong>also<\/strong> possible <strong>higher-symmetric solutions<\/strong>.<\/p>\n\n\n\n<p style=\"font-size:14px\">[1] Nespolo, M.: The ash heap of crystallography: restoring forgotten basic knowledge. <em>J. Appl. Cryst., <\/em><strong>2015<\/strong><em>, 48<\/em>, 1290-1298<br>[2] Hahn, T,: International Tables for Crystallography, Vol.A (2005), 5<sup>th<\/sup> ed., Springer,Table 3.1.2.1, p.44<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The derivation of the crystal lattice and the assignment of a Bravais lattice type has objective limits. In general, due to measurement and imaging errors, the approximation of pseudosymmetric lattice types is the rule.So there is always the danger to <a href=\"https:\/\/www.calm-ebsd.com\/index.php\/solution\/possible-solutions\/\" class=\"read-more\">Read More &#8230;<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"parent":1043,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/www.calm-ebsd.com\/index.php\/wp-json\/wp\/v2\/pages\/658"}],"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=658"}],"version-history":[{"count":22,"href":"https:\/\/www.calm-ebsd.com\/index.php\/wp-json\/wp\/v2\/pages\/658\/revisions"}],"predecessor-version":[{"id":1592,"href":"https:\/\/www.calm-ebsd.com\/index.php\/wp-json\/wp\/v2\/pages\/658\/revisions\/1592"}],"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=658"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}