The corundum crystal structure, found for Al2O3, consists of an HCP arrangement of O2- ions; the Al3+ ions occupy octahedral positions.
(a) What fraction of the available octahedral positions are filled with Al3+ ions?
(b) Ketch two close-packed O2\u2013planes stacked in an AB sequence, and note octahedral positions that will be filled with the Al3+ ions.<\/p>\n\n\n\n
The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n The corundum (\u03b1-Al\u2082O\u2083) structure consists of an hcp (hexagonal close-packed)<\/strong> arrangement of O\u00b2\u207b ions. In an hcp unit cell, there is one octahedral site per anion (O\u00b2\u207b)<\/strong>. Given the chemical formula Al\u2082O\u2083<\/strong>, for every 3 oxygen ions, there are 2 aluminum ions. Therefore:<\/p>\n\n\n\n So, the fraction of octahedral sites filled<\/strong> is:<\/p>\n\n\n\n $$ Answer: (a) 2\/3 of the octahedral positions are filled.<\/strong><\/p>\n\n\n\n In the hcp structure, oxygen anions form a hexagonal close-packed arrangement<\/strong>, with alternating layers labeled A and B<\/strong>. Each oxygen layer is a flat sheet of spheres (O\u00b2\u207b ions), and the stacking sequence alternates ABAB\u2026<\/p>\n\n\n\n Octahedral positions<\/strong> are located:<\/p>\n\n\n\n In corundum:<\/p>\n\n\n\n Corundum (\u03b1-Al\u2082O\u2083) adopts a crystal structure based on a hexagonal close-packed (hcp)<\/strong> lattice of O\u00b2\u207b ions. In this configuration, the oxide ions form alternating layers of close-packed spheres (A and B layers). Between these layers, there are interstitial voids<\/strong>, specifically octahedral and tetrahedral sites<\/strong>, where cations can reside. The Al\u00b3\u207a ions in corundum occupy only the octahedral<\/strong> positions.<\/p>\n\n\n\n Each O\u00b2\u207b ion in an hcp lattice contributes one octahedral site, so in total, there are as many octahedral sites as there are O\u00b2\u207b ions<\/strong>. Given the stoichiometry of Al\u2082O\u2083, for every three O\u00b2\u207b ions, two Al\u00b3\u207a ions are needed to maintain charge neutrality. Therefore, only 2\/3 of the available octahedral sites are occupied<\/strong> by Al\u00b3\u207a ions. This partial occupancy is crucial because it determines the overall symmetry and physical properties of the crystal.<\/p>\n\n\n\n The arrangement of the Al\u00b3\u207a ions is not random; instead, it follows an ordered pattern<\/strong>, which minimizes electrostatic repulsion and ensures structural stability. This results in the distortion of the ideal hcp lattice and leads to the rhombohedral unit cell characteristic of the corundum structure<\/strong>.<\/p>\n\n\n\n When sketching the structure, two O\u00b2\u207b layers in AB sequence can be drawn as alternating triangles. Between these layers, some of the octahedral voids formed by the staggered triangles are filled with Al\u00b3\u207a ions, specifically 2 out of every 3 available voids. This selective filling and ordered placement of Al\u00b3\u207a ions are key features that define the unique mechanical hardness and chemical stability of Al\u2082O\u2083.<\/p>\n","protected":false},"excerpt":{"rendered":" The corundum crystal structure, found for Al2O3, consists of an HCP arrangement of O2- ions; the Al3+ ions occupy octahedral positions.(a) What fraction of the available octahedral positions are filled with Al3+ ions?(b) Ketch two close-packed O2\u2013planes stacked in an AB sequence, and note octahedral positions that will be filled with the Al3+ ions. The […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-211069","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/211069","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=211069"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/211069\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=211069"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=211069"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=211069"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}(a) Fraction of Octahedral Positions Filled by Al\u00b3\u207a Ions<\/strong><\/h3>\n\n\n\n
\n
\\text{Fraction} = \\frac{\\text{Number of Al}^{3+}}{\\text{Number of octahedral sites}} = \\frac{2}{3}
$$<\/p>\n\n\n\n
\n\n\n\n(b) Diagram Description and Explanation<\/strong><\/h3>\n\n\n\n
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\n\n\n\nExplanation (300 words)<\/strong><\/h3>\n\n\n\n