{"id":45,"date":"2007-08-28T10:08:28","date_gmt":"2007-08-28T08:08:28","guid":{"rendered":"http:\/\/www.lookingatnothing.com\/?p=45"},"modified":"2007-08-28T16:12:04","modified_gmt":"2007-08-28T14:12:04","slug":"impossible-angles-in-the-porod-relationship-an-open-question","status":"publish","type":"post","link":"https:\/\/lookingatnothing.com\/index.php\/archives\/45","title":{"rendered":"Impossible angles in the Porod relationship, an open question"},"content":{"rendered":"<p>The unbiquitous porod relationship, as published in many places, is often written as:<br \/>\n<em>lim I = K\/s^4.<\/em><\/p>\n<p>Here, <em>s<\/em> is the scattering vector, described by <em>s=2\/lambda sin(theta)<\/em> with <em>lambda<\/em> the radiation wavelength, and <em>theta<\/em> as half the scattering angle. <\/p>\n<p>Strangely, though, the limit in the porod relationship is often written as the limit when <em>s<\/em> becomes infinity. Looking at the description of <em>s<\/em>, however, one sees immediately that this is not possible, whilst the maximum value of <em>s<\/em> (with a constant wavelength) is <em>2\/lambda<\/em> for a scattering angle of 90 degrees. <\/p>\n<p>So how am I to read that porod relationship then? as a limit where <em>s<\/em> goes to <em>2\/lambda<\/em>, or where <em>s<\/em> goes to an unreachable infinity?<\/p>\n<p><strong>Addendum:<\/strong><br \/>\nTheoretically, the scattering vector $q$ or $s$ can indeed go to infinity, but only if the radiation wavelength approaches zero. Nevertheless, it remains interesting why the limit is not to <em>2\/lambda<\/em>, but instead is written as it goes to infinity.<\/p>\n","protected":false},"excerpt":{"rendered":"<div class=\"mh-excerpt\"><p>The unbiquitous porod relationship, as published in many places, is often written as: lim I = K\/s^4. Here, s is the scattering vector, described by <a class=\"mh-excerpt-more\" href=\"https:\/\/lookingatnothing.com\/index.php\/archives\/45\" title=\"Impossible angles in the Porod relationship, an open question\">[&#8230;]<\/a><\/p>\n<\/div>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"activitypub_content_warning":"","activitypub_content_visibility":"","activitypub_max_image_attachments":4,"activitypub_interaction_policy_quote":"anyone","activitypub_status":"","footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[],"tags":[],"class_list":["post-45","post","type-post","status-publish","format-standard","hentry"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p1gZ2v-J","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/lookingatnothing.com\/index.php\/wp-json\/wp\/v2\/posts\/45","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lookingatnothing.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lookingatnothing.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lookingatnothing.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/lookingatnothing.com\/index.php\/wp-json\/wp\/v2\/comments?post=45"}],"version-history":[{"count":0,"href":"https:\/\/lookingatnothing.com\/index.php\/wp-json\/wp\/v2\/posts\/45\/revisions"}],"wp:attachment":[{"href":"https:\/\/lookingatnothing.com\/index.php\/wp-json\/wp\/v2\/media?parent=45"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lookingatnothing.com\/index.php\/wp-json\/wp\/v2\/categories?post=45"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lookingatnothing.com\/index.php\/wp-json\/wp\/v2\/tags?post=45"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}