{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T18:58:52Z","timestamp":1785437932804,"version":"3.56.0"},"reference-count":68,"publisher":"International Union of Crystallography (IUCr)","issue":"3","license":[{"start":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T00:00:00Z","timestamp":1776902400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode"},{"start":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T00:00:00Z","timestamp":1776902400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode"}],"funder":[{"DOI":"10.13039\/501100012163","name":"Universit\u00e4t Innsbruck","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100012163","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["iucr.org","wiley.com","iucrj.org"],"crossmark-restriction":true},"short-container-title":["Acta Crystallogr A Found Adv","Acta Crystallogr A","Acta Crystallogr A Found Crystallogr","Acta Cryst A","Acta Cryst A Found Adv","Acta Cryst Sect A","Acta Cryst Sect A Found Adv","Acta Crystallogr Sect A","Acta Crystallogr Sect A Found Adv","Acta Crystallogr Sect A Found Crystallogr"],"accepted":{"date-parts":[[2026,4,3]]},"published-print":{"date-parts":[[2026,5,1]]},"abstract":"<jats:p>\n                    Polytypes can occur in many inorganic and organic compounds alike. In the most basic scenario, different polytypes of a compound are based on translationally equivalent layers and two equivalent arrangements of adjacent layers. This means there are only two distinct stacking vectors,\n                    <jats:bold>t<\/jats:bold>\n                    <jats:sub>1<\/jats:sub>\n                    and\n                    <jats:bold>t<\/jats:bold>\n                    <jats:sub>2<\/jats:sub>\n                    . For this particular situation, we have enumerated the number of principally different polytypes for a given number\n                    <jats:italic>m<\/jats:italic>\n                    of layers in the stacking sequence, under the assumption of the validity of four constraints: (i) periodicity, (ii) exchangeability, (iii) reversibility and (iv) simplicity. Different results are obtained when the reversibility constraint is overturned, a factor that depends on the polar or non-polar character of the underlying layers. The results of this theoretical study have been applied to derive the existing polytypes up to\n                    <jats:italic>m<\/jats:italic>\n                    = 6 for two different polysomes of the family of so-called silico-ferrites of calcium and aluminium (SFCA and SFCA-I, respectively). These phases are of considerable interest to the steel industry, as they represent the primary constituents of the matrix in iron-ore sinters. Finally, the impact of polytypism on the powder diffraction patterns of the SFCAs was investigated and the influence of stacking disorder on the diffractograms was analysed. The resulting collection of simulated powder diffraction patterns may serve as a reference database for the identification of polytype effects in industrial sinters.\n                  <\/jats:p>","DOI":"10.1107\/s2053273326003505","type":"journal-article","created":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T11:51:07Z","timestamp":1776167467000},"page":"145-162","update-policy":"https:\/\/doi.org\/10.1107\/cm_01","source":"Crossref","is-referenced-by-count":0,"title":["Glass bead games: enumeration of possible polytypes based on two stacking vectors and applications to the iron-ore sinter phases SFCA and SFCA-I"],"prefix":"10.1107","volume":"82","author":[{"given":"Michael Francesco","family":"Salzmann","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/054pv6659","id-type":"ROR","asserted-by":"publisher"}],"department":["Institute of Mineralogy and Petrography"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0652-7984","authenticated-orcid":true,"given":"Volker","family":"Kahlenberg","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/054pv6659","id-type":"ROR","asserted-by":"publisher"}],"department":["Institute of Mineralogy and Petrography"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7652-1166","authenticated-orcid":true,"given":"Hannes","family":"Kr\u00fcger","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/054pv6659","id-type":"ROR","asserted-by":"publisher"}],"department":["Institute of Mineralogy and Petrography"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7000-6200","authenticated-orcid":true,"given":"Tim","family":"Netzer","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/054pv6659","id-type":"ROR","asserted-by":"publisher"}],"department":["Institute of Mathematics"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"329","published-online":{"date-parts":[[2026,4,23]]},"reference":[{"key":"cam5016_bb2","doi-asserted-by":"crossref","first-page":"1797","DOI":"10.1134\/S0022476623100013","volume":"64","author":"Aksenov","year":"2023","journal-title":"J. Struct. Chem."},{"key":"cam5016_bb3","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1524\/zkri.2006.221.1.15","volume":"221","author":"Aroyo","year":"2006","journal-title":"Z. Kristallogr."},{"key":"cam5016_bb4","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1524\/zkri.1912.50.1.33","volume":"50","author":"Baumhauer","year":"1912","journal-title":"Z. Kristallogr."},{"key":"cam5016_bb5","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1524\/zkri.1915.55.1.249","volume":"55","author":"Baumhauer","year":"1915","journal-title":"Z. Kristallogr."},{"key":"cam5016_bb6","doi-asserted-by":"crossref","first-page":"536","DOI":"10.1107\/S0108768112037457","volume":"68","author":"Britton","year":"2012","journal-title":"Acta Cryst. B"},{"key":"cam5016_bb7","doi-asserted-by":"crossref","unstructured":"Cheung, R. (2006). Editor. Silicon Carbide Micro Electromechanical Systems for Harsh Environments, pp. 1-17. London: Imperial College Press.","DOI":"10.1142\/9781860949098_0001"},{"key":"cam5016_bb8","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1127\/njma\/175\/1999\/153","volume":"175","author":"Christiansen","year":"1999","journal-title":"njma"},{"key":"cam5016_bb9","doi-asserted-by":"crossref","first-page":"548","DOI":"10.1007\/BF00311025","volume":"15","author":"Christy","year":"1988","journal-title":"Phys. Chem. Miner."},{"key":"cam5016_bb10","first-page":"121","volume":"28","author":"Cocco","year":"1959","journal-title":"Period. Mineral."},{"key":"cam5016_bb11","first-page":"1","volume":"9","author":"Cook","year":"2019","journal-title":"Minerals"},{"key":"cam5016_bb12","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1107\/S0365110X56001625","volume":"9","author":"Dornberger-Schiff","year":"1956","journal-title":"Acta Cryst."},{"key":"cam5016_bb13","first-page":"1","volume":"9","author":"Dornberger-Schiff","year":"1964","journal-title":"Abh. Dtsch. Akad. Wiss. Berl. Kl. Chem. Geol. Biol."},{"key":"cam5016_bb14","doi-asserted-by":"crossref","first-page":"1027","DOI":"10.1002\/crat.19790140903","volume":"14","author":"Dornberger-Schiff","year":"1979","journal-title":"Krist. Tech."},{"key":"cam5016_bb15","doi-asserted-by":"crossref","first-page":"1035","DOI":"10.1002\/crat.19720070907","volume":"7","author":"Dornberger-Schiff","year":"1972","journal-title":"Cryst. Res. Technol."},{"key":"cam5016_bb16","doi-asserted-by":"crossref","first-page":"752","DOI":"10.1107\/S0365110X55002351","volume":"8","author":"Dornberger-Schiff","year":"1955","journal-title":"Acta Cryst."},{"key":"cam5016_bb17","doi-asserted-by":"crossref","first-page":"989","DOI":"10.1039\/b821274k","volume":"11","author":"Duggirala","year":"2009","journal-title":"CrystEngComm"},{"key":"cam5016_bb18","doi-asserted-by":"crossref","first-page":"1661","DOI":"10.1107\/S0567740868004814","volume":"24","author":"\u010eurovi\u010d","year":"1968","journal-title":"Acta Cryst. B"},{"key":"cam5016_bb19","doi-asserted-by":"crossref","unstructured":"\u010eurovi\u0107, S. (1997). Fundamentals of OD Theory. EMU Notes in Mineralogy, Vol. 1, edited by S. Merlino, pp. 3-28. Budapest: E\u00f6tv\u00f6s University Press.","DOI":"10.1180\/EMU-notes.1.1"},{"key":"cam5016_bb20","unstructured":"\u010eurovi\u010d, S. (1999). International Tables for Crystallography, Vol. C, edited by A. C. J. Wilson & E. Prince, pp. 752-765. Dordrecht: Kluwer Academic Publishers."},{"key":"cam5016_bb21","doi-asserted-by":"crossref","first-page":"15","DOI":"10.3406\/bulmi.1986.7913","volume":"109","author":"\u010eurovi\u0107","year":"1986","journal-title":"Bull. Min\u00e9ral."},{"key":"cam5016_bb22","first-page":"285","volume":"2","author":"Fine","year":"1958","journal-title":"Ill. J. Math."},{"key":"cam5016_bb23","doi-asserted-by":"crossref","first-page":"550","DOI":"10.1107\/S205252062500914X","volume":"81","author":"Fr\u00f6schl","year":"2025","journal-title":"Acta Cryst. B"},{"key":"cam5016_bb24","unstructured":"Grell, H., Krause, C. & Grell, J. (1988). Tables of the 80 Plane Space Groups in Three Dimensions. Berlin: Institut f\u00fcr Informatik und Rechentechnik, Akademie der Wissenschaften der DDR."},{"key":"cam5016_bb25","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1107\/S0108767384000842","volume":"40","author":"Guinier","year":"1984","journal-title":"Acta Cryst. A"},{"key":"cam5016_bb26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1127\/njma\/161\/1989\/1","volume":"161","author":"Hamilton","year":"1989","journal-title":"njma"},{"key":"cam5016_bb27","unstructured":"Hardy, G. H. & Wright, E. M. (1979). An Introduction to the Theory of Numbers, 5th ed. Oxford: Clarendon Press."},{"key":"cam5016_bb28","doi-asserted-by":"crossref","first-page":"e3","DOI":"10.1107\/S2053273324099960","volume":"80","author":"Hinrichsen","year":"2024","journal-title":"Acta Cryst. A"},{"key":"cam5016_bb29","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1524\/zkri.1981.155.1-2.121","volume":"155","author":"Iglesias","year":"1981","journal-title":"Z. Kristallogr."},{"key":"cam5016_bb30","doi-asserted-by":"crossref","first-page":"1126","DOI":"10.1107\/S2052520619014380","volume":"75","author":"Kahlenberg","year":"2019","journal-title":"Acta Cryst. B"},{"key":"cam5016_bb31","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/s00269-021-01148-4","volume":"48","author":"Kahlenberg","year":"2021","journal-title":"Phys. Chem. Miner."},{"key":"cam5016_bb32","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/s00710-020-00730-y","volume":"115","author":"Kahlenberg","year":"2021","journal-title":"Miner. Petrol."},{"key":"cam5016_bb33","first-page":"024","volume":"120","author":"Kahlenberg","year":"2025","journal-title":"J. Miner. Petrological Sci."},{"key":"cam5016_bb34","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1107\/S0021889801011852","volume":"34","author":"Kroumova","year":"2001","journal-title":"J. Appl. Cryst."},{"key":"cam5016_bb35","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1515\/zkri-2018-2071","volume":"233","author":"Larvor","year":"2018","journal-title":"Z. Kristallogr."},{"key":"cam5016_bb36","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1007\/s00710-015-0411-5","volume":"110","author":"Liles","year":"2016","journal-title":"Miner. Petrol."},{"key":"cam5016_bb37","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1107\/S0108767389010950","volume":"46","author":"Mardix","year":"1990","journal-title":"Acta Cryst. A"},{"key":"cam5016_bb38","first-page":"69","volume":"59","author":"Merlino","year":"1990","journal-title":"Period. Mineral."},{"key":"cam5016_bb39","doi-asserted-by":"crossref","unstructured":"Merlino, S. (1997). OD Approach in Minerals: Examples and Applications. EMU Notes in Mineralogy, Vol. 1, edited by S. Merlino, pp. 29-54. Budapest: E\u00f6tv\u00f6s University Press.","DOI":"10.1180\/EMU-notes.1.2"},{"key":"cam5016_bb40","doi-asserted-by":"crossref","first-page":"1613","DOI":"10.2138\/am-1999-1015","volume":"84","author":"Merlino","year":"1999","journal-title":"Am. Mineral."},{"key":"cam5016_bb41","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1127\/0935-1221\/2003\/0015-0267","volume":"15","author":"Merlino","year":"2003","journal-title":"Eur. J. Mineral."},{"key":"cam5016_bb42","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1524\/zkri.1998.213.10.513","volume":"231","author":"Merlino","year":"1998","journal-title":"Z. Kristallogr."},{"key":"cam5016_bb47","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1127\/0935-1221\/2008\/0020-1778","volume":"20","author":"Mo\u00eblo","year":"2008","journal-title":"Eur. J. Mineral."},{"key":"cam5016_bb48","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1127\/0077-7757\/2003\/0178-0307","volume":"178","author":"Mumme","year":"2003","journal-title":"njma"},{"key":"cam5016_bb49","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1127\/njma\/173\/1998\/93","volume":"173","author":"Mumme","year":"1998","journal-title":"njma"},{"key":"cam5016_bb50","doi-asserted-by":"crossref","unstructured":"Neder, R. B. & Proffen, T. (2008). Diffuse Scattering and Defect Structure Simulations: a Cook Book Using the Program DISCUS. New York: Oxford University Press Inc.","DOI":"10.1093\/acprof:oso\/9780199233694.001.0001"},{"key":"cam5016_bb51","unstructured":"Neder, R. B. & Proffen, T. (2025). Discus Simulation Package, version 6.19.00. https:\/\/tproffen.github.io\/DiffuseCode\/."},{"key":"cam5016_bb52","unstructured":"Nespolo, M. (2026). OD Structures and Polytypes. https:\/\/www.crystallography.fr\/mathcryst\/OD_structures.htm."},{"key":"cam5016_bb53","doi-asserted-by":"crossref","unstructured":"Nespolo, M., Takeda, H. & Ferraris, G. (1997). Crystallography of Mica Polytypes. EMU Notes in Mineralogy, Vol. 1, edited by S. Merlino, pp. 81-118. Budapest: E\u00f6tv\u00f6s University Press.","DOI":"10.1180\/EMU-notes.1.4"},{"key":"cam5016_bb54","doi-asserted-by":"crossref","first-page":"2157","DOI":"10.2355\/isijinternational.ISIJINT-2018-203","volume":"58","author":"Nicol","year":"2018","journal-title":"ISIJ Int."},{"key":"cam5016_bb55","unstructured":"OEIS Foundation Inc.(2025). The On-Line Encyclopedia of Integer Sequences. https:\/\/oeis.org."},{"key":"cam5016_bb56","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1007\/BF00309314","volume":"10","author":"Ohashi","year":"1984","journal-title":"Phys. Chem. Miner."},{"key":"cam5016_bb57","doi-asserted-by":"crossref","first-page":"3001","DOI":"10.1107\/S0567740882010681","volume":"38","author":"Pa\u0142osz","year":"1982","journal-title":"Acta Cryst. B"},{"key":"cam5016_bb58","doi-asserted-by":"crossref","first-page":"2272","DOI":"10.2138\/am-2022-8284","volume":"107","author":"Pekov","year":"2022","journal-title":"Am. Mineral."},{"key":"cam5016_bb59","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1515\/zkri-2014-1737","volume":"229","author":"Pet\u0159\u00ed\u010dek","year":"2014","journal-title":"Z. Kristallogr."},{"key":"cam5016_bb60","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/BF02546665","volume":"68","author":"P\u00f3lya","year":"1937","journal-title":"Acta Math."},{"key":"cam5016_bb61","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1107\/S002188989600934X","volume":"30","author":"Proffen","year":"1997","journal-title":"J. Appl. Cryst."},{"key":"cam5016_bb62","doi-asserted-by":"crossref","first-page":"838","DOI":"10.1107\/S0021889899004860","volume":"32","author":"Proffen","year":"1999","journal-title":"J. Appl. Cryst."},{"key":"cam5016_bb63","doi-asserted-by":"crossref","first-page":"433","DOI":"10.2307\/2370675","volume":"49","author":"Redfield","year":"1927","journal-title":"Am. J. Math."},{"key":"cam5016_bb64","doi-asserted-by":"crossref","first-page":"1900164","DOI":"10.1002\/crat.201900164","volume":"55","author":"Rotter","year":"2020","journal-title":"Cryst. Res. Technol."},{"key":"cam5016_bb65","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1007\/s00710-024-00874-1","volume":"118","author":"Salzmann","year":"2024","journal-title":"Miner. Petrol."},{"key":"cam5016_bb66","doi-asserted-by":"crossref","first-page":"929","DOI":"10.1007\/s11663-004-0087-4","volume":"35","author":"Scarlett","year":"2004","journal-title":"Metall. Mater. Trans. B"},{"key":"cam5016_bb68","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1107\/S0021889802022112","volume":"36","author":"Spek","year":"2003","journal-title":"J. Appl. Cryst."},{"key":"cam5016_bb69","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/0025-5408(76)90064-7","volume":"11","author":"Terhell","year":"1976","journal-title":"Mater. Res. Bull."},{"key":"cam5016_bb70","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/S1463-0184(00)00046-0","volume":"3","author":"Timofeeva","year":"2000","journal-title":"Cryst. Eng."},{"key":"cam5016_bb71","doi-asserted-by":"crossref","first-page":"1344","DOI":"10.1007\/s11663-012-9740-5","volume":"43","author":"Webster","year":"2012","journal-title":"Metall. Mater. Trans. B"},{"key":"cam5016_bb72","unstructured":"Welberry, T. R. (2004). Diffuse X-ray Scattering and Models of Disorder. New York: Oxford University Press Inc."},{"key":"cam5016_bb74","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1016\/0898-1221(88)90247-7","volume":"16","author":"Zvyagin","year":"1988","journal-title":"Comput. Math. Appl."},{"key":"cam5016_bb75","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1524\/zkri.218.3.210.20747","volume":"218","author":"Zvyagin","year":"2003","journal-title":"Z. Kristallogr."}],"container-title":["Acta Crystallographica Section A Foundations and Advances"],"original-title":[],"link":[{"URL":"https:\/\/journals.iucr.org\/a\/issues\/2026\/03\/00\/cam5016\/cam5016.pdf","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.iucr.org\/a\/issues\/2026\/03\/00\/cam5016\/cam5016.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T07:35:23Z","timestamp":1778830523000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.iucr.org\/paper?S2053273326003505"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,23]]},"references-count":68,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2026,5]]}},"alternative-id":["S2053273326003505"],"URL":"https:\/\/doi.org\/10.1107\/s2053273326003505","relation":{"is-supplemented-by":[{"id-type":"doi","id":"10.1107\/S2053273326003505\/cam5016sup1.zip","asserted-by":"subject"},{"id-type":"doi","id":"10.1107\/S2053273326003505\/cam5016sup2.zip","asserted-by":"subject"}]},"ISSN":["2053-2733"],"issn-type":[{"value":"2053-2733","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,23]]},"assertion":[{"value":"Acta Crystallographica Section A: Foundations and Advances","order":0,"name":"journal","label":"Publication","explanation":{"URL":"https:\/\/journals.iucr.org\/a"},"group":{"name":"general","label":"General"}},{"value":"research papers","order":1,"name":"content_type","label":"Content type","explanation":{"URL":"https:\/\/journals.iucr.org\/a\/services\/notesforauthors.html"},"group":{"name":"general","label":"General"}},{"value":"Available","URL":"https:\/\/scripts.iucr.org\/cgi-bin\/citedin?cam5016","order":2,"name":"article_metrics","label":"Article metrics","group":{"name":"general","label":"General"}},{"value":"Yes","order":0,"name":"peer_reviewed","label":"Peer reviewed","group":{"name":"peer_review","label":"Peer review"}},{"value":"Single blind","order":1,"name":"review_process","label":"Review process","group":{"name":"peer_review","label":"Peer review"}},{"value":"16 December 2025","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication history"}},{"value":"3 April 2026","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication history"}},{"value":"23 April 2026","order":2,"name":"published_online","label":"Published online","group":{"name":"publication_history","label":"Publication history"}},{"value":"This article has supporting information","name":"supplementary_materials","label":"Supplementary materials","explanation":{"URL":"https:\/\/scripts.iucr.org\/cgi-bin\/sendsup?cam5016"}},{"value":"\u00a9 2026 Michael Francesco Salzmann\n                      et al.","order":0,"name":"copyright","label":"Copyright","explanation":{"URL":"https:\/\/journals.iucr.org\/services\/copyrightpolicy.html"},"group":{"name":"copyright_and_licencing","label":"Copyright and licencing"}},{"value":"Creative Commons Attribution (CC-BY)","order":1,"name":"license","label":"Licence","explanation":{"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode"},"group":{"name":"copyright_and_licencing","label":"Copyright and licencing"}}]}}