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It organizes the work into: space-group page basics (Schönflies vs. International symbolism, crystal systems, Bravais lattices, and point groups), space-group notation with Wyckoff sites (screw rotations, glide planes, and symmorphic vs. nonsymmorphic groups), and additional topics such as origin settings, group–subgroup relations, and diffraction conditions. Examples include space group I4/mmm for BaFe2As2 and selection rules like h+k+l even.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/physics-590-proposed-plan-international-tables-of-crystallography/511941/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/physics-590-proposed-plan-international-tables-of-crystallography/511941.png","ImageObject",300,407,{"name":42,"@type":43},"Logic","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-02","2026-10-06",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",7,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What are the main parts of the proposed plan for studying International Tables of Crystallography space group pages?","Question",{"text":63,"@type":64},"The plan is divided into three areas: basics of space-group pages (symbolism and fundamental symmetry concepts), space group notation with Wyckoff sites, and additional topics such as origin settings, group–subgroup relationships, and diffraction conditions.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How does the document compare Schönflies notation with International notation?",{"text":68,"@type":64},"It highlights that space-group symbolism can be expressed using Schönflies forms versus International notation, and uses tables of symmetry operations to connect improper rotations, roto-inversions, and other elements across the two systems.",{"name":70,"@type":61,"acceptedAnswer":71},"What selection rule example is given for diffraction indices in the document?",{"text":72,"@type":64},"For the example discussed, the indices satisfy the condition h+k+l equals an even integer (2n), connected to the example space group and diffraction conditions.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},511941,1791496727,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & 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Crystallography”  \nGordie Miller  \nProposed Plan  \n(1) Basic information on the “Space Group” pages  \n• Recognizing the symbolism (Schönflies vs. International)  \n• Crystal systems; Bravais lattices; Crystallographic point groups  \n(2) Space group notation and Wyckoff sites  \n• Screw rotations and glide planes; symmorphic vs. nonsymmorphic groups  \n• Crystal composition and site (point) symmetry  \n(3) Other information  \n• Origin settings (diamond)  \n• Group-subgroup relationships (solid-solid phase transitions)  \n• Diffraction conditions  \nOnline References  \nInternational Tables for Crystallography ([http://it.iucr.org/](http://it.iucr.org/)) Bilbao Crystallographic Server ([www.cryst.ehu.es](www.cryst.ehu.es))  \n(Comprehensive resources for all space groups)  \nWhat can we learn from the International Tables?  \nBaFe2As2  \nSpace Group: I4/mmm  \nLattice Constants: a = 3.963(1) Å  \nc = 13.046(2) Å  \nAsymmetric Unit:  \nBa (2a): 0 0 0  \nFe (4d): ½ 0 ¼  \nAs (4e): 0 0 0.3544(2)  \n• Publication  \n• ICSD (Inorganic Crystal Structure Database)  \n• CSD (Cambridge Structural Database  \n– organics)  \nIntensity (Arb. Units)  \n(013)  \n(004)  \n(002) (011)  \n(hkl) Indices  \nh + k + l = even integer (2n)  \n(112) (200) (116)  \n(015)  \n(213)  \n(215) (028)  \n2θ (Cu Kα)  \n2  \nTypical Space Group Pages…  \nSymbolism  \nPreferred for Molecules Crystals  \n\n| Symmetry Operation |  | Schönflies Notation |  | International Notation |  |\n| --- | --- | --- | --- | --- | --- |\n| Proper Rotations (by 2􀟨/􀝊) Identity |  | 􀜥􀯡 􀜥2, 􀜥3, 􀜥4,… 􀜧 |  | 􀝊  2, 3, 4,… \u003Cbr>1 |  |\n| Improper Rotations Inversion (x,y,z) → (–x,–y,–z) |  | 􀜵􀯡 = 􀟪ℎ ∙ 􀜥􀯡 􀜵3, 􀜵4, 􀜵5,…  |  | 􀝊ത = ത1 ത1 /􀝉􀝉 | ∙ 􀝊  ത3, ത4, ത5,… \u003Cbr>ൠ = ത2\u003Cbr>Roto-Inversions |\n|  |  | 􀝅 = 􀜵2 􀟪ℎ\u003Cbr>􀟪􀯩 , 􀟪􀯗 | ൠ = 􀜵1\u003Cbr>Roto-Reflections |  |  |\n| Reflections | ⊥ Prin. Axis 􀁟􀁟 Prin. Axis |  |  |  |  |\n\nOrientation  \nRotations:  \nAxis Direction  \nReflections:  \n⊥ plane  \nComparing 􀡿 􀫝 and ഥ􀫝:  \n􀣌 􀢎 ഥ􀫚  \n􀡿􀫝 =  \n􀡿􀫛􀫝 = 􀡯􀫛  \n􀡿􀫜􀫝 =  \n􀡿􀫝􀫝 = 􀡱  \nഥ􀫝 =  \nഥ􀫝􀫛 = 􀫛  \nഥ􀫝􀫜 =  \nഥ􀫝􀫝 = 􀫚  \nSymbolism: Point Groups – Subgroups of 􀡻 􀫜 Group of the Sphere  \nSchönflies International  \nPractice:  \n\n| Type | Symbol |  |  | Features |\n| --- | --- | --- | --- | --- |\n| Nonaxial | 􀜥1\u003Cbr>􀜥􀯜 | 1\u003Cbr>ത1 |  | No symmetry\u003Cbr>Inversion |\n| Uniaxial\u003Cbr>One 􀝊-fold principal axis\u003Cbr>| 􀜥􀯡􀜵2􀯡􀜥􀯦\u003Cbr>􀜥􀯡ℎ\u003Cbr>􀜥􀯡􀯩 |  􀝊 \u003Cbr>2􀝊􀝊ത\u003Cbr>􀝉􀝊Τ􀝉 2􀝊􀝊􀝉􀝉􀝊􀝉 | 􀝊 even\u003Cbr>􀝊 odd\u003Cbr>􀝊 even\u003Cbr>􀝊 odd\u003Cbr>􀝊 even\u003Cbr>􀝊 odd | One 􀜥􀯡 axis\u003Cbr>One 􀜵2􀯡 axis\u003Cbr>One mirror plane\u003Cbr>One 􀜥􀯡 axis + ⊥ mirror plane One 􀜥􀯡 axis\u003Cbr>+ 􀝊 || mirror planes |\n| Dihedral\u003Cbr>One 􀝊-fold principal axis\u003Cbr>+ ⊥ 􀜥2 ’s  | 􀜦􀯡\u003Cbr>􀜦􀯡ℎ\u003Cbr>􀜦􀯡􀯗 | 􀝊22 􀝊2\u003Cbr>􀝊Τ􀝉􀝉􀝉 2􀝊􀝉2\u003Cbr>\u003Cbr>2􀝊2􀝉􀝊ത􀝉 | 􀝊 even\u003Cbr>􀝊 odd\u003Cbr>􀝊 even\u003Cbr>􀝊 odd\u003Cbr>􀝊 even\u003Cbr>􀝊 odd | One 􀜥􀯡 axis + 􀝊 ⊥ 􀜥2 axes\u003Cbr>One 􀜥􀯡 axis + 􀝊 ⊥ 􀜥2 axes + ⊥ mirror plane\u003Cbr>One 􀜥􀯡 axis + 􀝊 ⊥ 􀜥2 axes + 􀝊 || mirror planes |\n| Polyhedral\u003Cbr>Multiple 􀜥3 axes | 􀜶 , 􀜶ℎ , 􀜶􀯗􀜱 , 􀜱 ℎ\u003Cbr>􀜫 , 􀜫ℎ | 23, 􀝉 ത3, 4 ത3􀝉 432, 􀝉 ത3􀝉 532, ത5ത3􀝉 |  | Tetrahedral: 4 􀜥3 axes\u003Cbr>Octahedral: 4 􀜥3 axes + 3 􀜥4 axes\u003Cbr>Icosahedral: 10 􀜥3 axes + 6 􀜥5 axes |\n\n􀜥2􀯩 =  \n􀜥3ℎ =􀜦 2ℎ =􀜦 3􀯗 =ത3 = 4Τ􀝉 =  \nത6􀝉2 =ത42􀝉 =  \nSymbolism: Crystal Systems  \nOnly 5 rotational symmetries are compatible with a lattice (translational symmetry):  \nC1 C2 (2π/2) C3 (2π/3) C4 (2π/4) C6 (2π/6)  \n\n| Crystal System | Minimum Symmetry | Primitive Unit Cell |\n| --- | --- | --- |\n| Triclinic | None | a 􀁺 b 􀁺 c; 􀁄 􀁺 􀁅 􀁺 􀁊 |\n| Monoclinic | One 2-fold axis (b-axis) | a 􀁺 b 􀁺 c; 􀁄 = 􀁊 = 90 􀁱 , 􀁅 􀁺 90 􀁱 |\n| Orthorhombic | Three orthogonal 2-fold axes | a 􀁺 b 􀁺 c; 􀁄 = 􀁅 = 􀁊 = 90 􀁱 |\n| Tetragonal | One 4-fold axis (c-axis) | a = b 􀁺 c; 􀁄 = 􀁅 = 􀁊 = 90 􀁱 |\n| Cubic | Four 3-fold axes | a = b = c; 􀁄 = 􀁅 = 􀁊 = 90 􀁱 |\n| Trigonal | One 3-fold axis | a = b = c; 􀁄 = 􀁅 = 􀁊\u003Cbr>a = b 􀁺 c; 􀁄 = 􀁅 = 90 􀁱 , 􀁊 = 120 􀁱 |\n| Hexagonal | One 6-fold axis (c-axis) | a = b 􀁺 c; 􀁄 = 􀁅 = 90 􀁱 , 􀁊 = 120 􀁱 |\n\n(rhombohedral)  \na  \n􀁄 = angle between b and c  \n􀁅 = angle between a and c  \n􀁊 = angle between a and b  \nSymbolism: Crystal Systems → ","cbCaibJUdQw20VcX","https://ap.wps.com/l/cbCaibJUdQw20VcX","pdf",2445315,"English","# Proposed Plan\n## Basic information on the “Space Group” pages\n## Space group notation and Wyckoff sites\n## Other information\n## Online References\n## What can we learn from the International Tables?\n# Symbolism and Practice\n## Symmetry Operation Notation\n## Symmetry: Point Groups and Subgroups\n## Practice: Crystal Systems\n## Crystal Systems to Bravais Lattices\n## Crystal Systems to Crystallographic Point Groups","[{\"question\":\"What are the main parts of the proposed plan for studying International Tables of Crystallography space group pages?\",\"answer\":\"The plan is divided into three areas: basics of space-group pages (symbolism and fundamental symmetry concepts), space group notation with Wyckoff sites, and additional topics such as origin settings, group–subgroup relationships, and diffraction conditions.\"},{\"question\":\"How does the document compare Schönflies notation with International notation?\",\"answer\":\"It highlights that space-group symbolism can be expressed using Schönflies forms versus International notation, and uses tables of symmetry operations to connect improper rotations, roto-inversions, and other elements across the two systems.\"},{\"question\":\"What selection rule example is given for diffraction indices in the document?\",\"answer\":\"For the example discussed, the indices satisfy the condition h+k+l equals an even integer (2n), connected to the example space group and diffraction conditions.\"}]","Physics 590 - Proposed Plan - International Tables of Crystallography | PDF",1791262540]