{"id":370788,"date":"2017-02-28T03:00:00","date_gmt":"2017-02-28T00:00:00","guid":{"rendered":"https:\/\/www.fyysika.ee\/?guid=7001adaa15c3b7a7c8fbc4a928b69564"},"modified":"2017-02-28T03:00:00","modified_gmt":"2017-02-28T00:00:00","slug":"visualising-higher-order-brillouin-zones-with-applications-3","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=370788","title":{"rendered":"Visualising higher order Brillouin zones with applications"},"content":{"rendered":"<p>A key concept in material science is the relationship between the Bravais lattice, the reciprocal<br \/>\nlattice and the resulting Brillouin zones (BZ). These zones are often complicated shapes that are<br \/>\nhard to construct and visualise without the use of sophisticated software, even by professional<br \/>\nscientists. We have used a simple sorting algorithm to construct BZ of any order for a chosen<br \/>\nBravais lattice that is easy to implement in any scientific programming language. The resulting<br \/>\nzones can then be visualised using freely available plotting software. This method has pedagogical<br \/>\nvalue for upper-level undergraduate students since, along with other computational methods, it can<br \/>\nbe used to illustrate how constant-energy surfaces combine with these zones to create van Hove<br \/>\nsingularities in the density of states. In this paper we apply our algorithm along with the<br \/>\nempirical pseudopotential method and the 2D equivalent of the tetrahedron method to show how they<br \/>\ncan be used in a simple soft&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A key concept in material science is the relationship between the Bravais lattice, the reciprocal<br \/>\nlattice and the resulting Brillouin zones (BZ). These zones are often complicated shapes that are<br \/>\nhard to construct and visualise without the use of sop&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[178],"tags":[],"class_list":{"0":"post-370788","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-rss-fuusikaharidus","7":"entry"},"_links":{"self":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/370788","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=370788"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/370788\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=370788"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=370788"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=370788"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}