{"id":3464,"date":"2025-07-21T14:53:48","date_gmt":"2025-07-21T12:53:48","guid":{"rendered":"https:\/\/kmplg.sk\/?page_id=3464"},"modified":"2025-08-15T13:31:45","modified_gmt":"2025-08-15T11:31:45","slug":"theocrystmin-teoreticke-zaklady","status":"publish","type":"page","link":"https:\/\/kmplg.sk\/?page_id=3464","title":{"rendered":"TheoCrystMin – Teoretick\u00e9 z\u00e1klady"},"content":{"rendered":"\n

Z\u00e1kladn\u00e9 inform\u00e1cie o projekte<\/a><\/p>\n\n\n\n

Teoretick\u00e9 z\u00e1klady<\/a><\/p>\n\n\n\n

Program BoVaToM<\/a><\/p>\n\n\n\n

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\u00davod<\/strong><\/h2>\n\n\n\n

V klasickej kry\u0161talografii a kry\u0161taloch\u00e9mii i\u00f3nov\u00fd model opisuje kry\u0161t\u00e1lov\u00fa \u0161trukt\u00faru ako s\u00fabor at\u00f3mov (i\u00f3nov) v \u0161pecifick\u00fdch kry\u0161talografick\u00fdch miestach, ktor\u00e9 s\u00fa fyzik\u00e1lnymi objektmi \u2013 nabit\u00fdmi sf\u00e9rami spojen\u00fdmi elektrostatick\u00fdmi interakciami (Born a Land\u00e9 1918; Madelung 1918; Born a Mayer 1932). Potenci\u00e1lna energia medzi at\u00f3mami sa vyjadrovala ako s\u00fa\u010det pr\u00ed\u0165a\u017eliv\u00e9ho Coulombovho potenci\u00e1lu at\u00f3mov s r\u00f4znymi a odpudiv\u00e9ho potenci\u00e1lu kr\u00e1tkeho dosahu subatom\u00e1rnych \u010dast\u00edc s rovnak\u00fdm n\u00e1bojom. Tento model bol \u00fa\u010dinn\u00fd pre anorganick\u00e9 zl\u00fa\u010deniny s jednoduch\u00fdmi \u0161trukt\u00farami, ale v zlo\u017eitej\u0161\u00edch \u0161trukt\u00farach narazil na \u0165a\u017ekosti (Brown 2006). Navy\u0161e, neskor\u0161\u00ed v\u00fdvoj v kvantovej mechanike odhalil, \u017ee spr\u00e1vny opis chemickej v\u00e4zby vy\u017eaduje rie\u0161enie Schr\u00f6dingerovej rovnice pre kry\u0161t\u00e1l. V\u00fdpo\u010dtov\u00e9 po\u017eiadavky na to s\u00fa v\u0161ak e\u0161te vy\u0161\u0161ie ako v pr\u00edpade klasick\u00e9ho i\u00f3nov\u00e9ho modelu a zlo\u017eitos\u0165 tohto pr\u00edstupu ho rob\u00ed takmer nepou\u017eite\u013en\u00fdm (Brown 2006). Preto potreba zjednodu\u0161enia a pou\u017eite\u013enosti viedla k v\u00fdvoju r\u00f4znych pr\u00edstupov k modelovaniu chemick\u00fdch v\u00e4zieb, vr\u00e1tane modelu symetrie (Niggli 1919), topologick\u00fdch modelov (Liebau 1985; Smith 1988) a modelu elektrostatick\u00e9ho mocenstva (Pauling 1929). Podrobnosti o ka\u017edom modeli n\u00e1jdete v Brown (2006).<\/p>\n\n\n\n

Klasick\u00e9 interpret\u00e1cie i\u00f3nov\u00fdch modelov maj\u00fa jasn\u00e9 limity v predikcii vlastnost\u00ed kry\u0161t\u00e1lovej \u0161trukt\u00fary. Okrem toho existuj\u00fa faktory, ktor\u00e9 nemo\u017eno do tejto interpret\u00e1cie zahrn\u00fa\u0165. Patria sem vn\u00fatorn\u00e1 \u0161trukt\u00fara at\u00f3mov\u00e9ho obalu a elektrostatick\u00e9 vlastnosti v\u00e4zieb, Jahn-Tellerova distorzia v d-prvkoch, kr\u00e1tkodob\u00e9 \u00fa\u010dinky susedn\u00fdch at\u00f3mov a dlhodob\u00e9 \u00fa\u010dinky celej \u0161trukt\u00fary (Ba\u010d\u00edk 2018; Bosi 2018; Ba\u010d\u00edk a Fridrichov\u00e1 2021). T\u00fdmto probl\u00e9mom sa mo\u017eno vyhn\u00fa\u0165, ak sa \u0161trukt\u00fara pova\u017euje za fyzik\u00e1lne pole. Bragg (1930) ako prv\u00fd poznamenal, \u017ee elektrostatick\u00fa interakciu medzi kati\u00f3nmi a ani\u00f3nmi mo\u017eno reprezentova\u0165 Faradayov\u00fdmi silo\u010diarami. T\u00e1to my\u0161lienka bola nesk\u00f4r plne presk\u00faman\u00e1 (Preiser et al. 1999). Elektrostatick\u00e9 pole sa m\u00f4\u017ee prirodzene rozdeli\u0165 na lokalizovan\u00e9 fragmenty, \u010d\u00edm sa vytvor\u00ed chemick\u00e1 v\u00e4zba, ktor\u00e1 poskytuje intuit\u00edvny sp\u00f4sob pochopenia a modelovania \u0161trukt\u00far a ich vlastnost\u00ed (Brown 2006). V\u0161etky Coulombove sily s dlh\u00fdm dosahom v kry\u0161t\u00e1li s\u00fa spr\u00e1vne op\u00edsan\u00e9 elektrostatick\u00fdmi tokmi v\u00e4zieb, \u010do znamen\u00e1, \u017ee Madelungovo pole molekuly alebo kry\u0161t\u00e1lu mo\u017eno reprezentova\u0165 ako sie\u0165 v\u00e4zieb (Beevers a Lipson 1932). V\u00e4zbov\u00e1 sie\u0165 teda pozost\u00e1va zo s\u00faboru at\u00f3mov spojen\u00fdch v\u00e4zbami. D\u00f4le\u017eit\u00fdmi vlastnos\u0165ami tejto siete s\u00fa mocenstvo at\u00f3mov a toky v\u00e4zieb. Tieto vlastnosti v kombin\u00e1cii so znalos\u0165ou topol\u00f3gie siete poskytuj\u00fa kompletn\u00fa reprezent\u00e1ciu vlastnost\u00ed Madelungovho po\u013ea, a teda aj mocenstva v\u00e4zieb s dlh\u00fdm dosahom v kry\u0161t\u00e1li (Brown 2006).<\/p>\n\n\n\n

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Financovan\u00e9 Eur\u00f3pskou \u00faniou z prostriedkov Pl\u00e1nu obnovy a odolnosti SR<\/h2>\n\n\n\n
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Z\u00e1kladn\u00e9 inform\u00e1cie o projekte Teoretick\u00e9 z\u00e1klady Program BoVaToM \u00davod V … <\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"ngg_post_thumbnail":0},"folder":[101],"yoast_head":"\nTheoCrystMin - Teoretick\u00e9 z\u00e1klady - Katedra mineral\u00f3gie, petrol\u00f3gie a lo\u017eiskovej geol\u00f3gie<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/kmplg.sk\/?page_id=3464\" \/>\n<meta property=\"og:locale\" content=\"sk_SK\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"TheoCrystMin - Teoretick\u00e9 z\u00e1klady - Katedra mineral\u00f3gie, petrol\u00f3gie a lo\u017eiskovej geol\u00f3gie\" \/>\n<meta property=\"og:description\" content=\"Z\u00e1kladn\u00e9 inform\u00e1cie o projekte Teoretick\u00e9 z\u00e1klady Program BoVaToM \u00davod V …\" \/>\n<meta property=\"og:url\" content=\"https:\/\/kmplg.sk\/?page_id=3464\" \/>\n<meta property=\"og:site_name\" content=\"Katedra mineral\u00f3gie, petrol\u00f3gie a lo\u017eiskovej geol\u00f3gie\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/kmplg\/\" \/>\n<meta property=\"article:modified_time\" content=\"2025-08-15T11:31:45+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/kmplg.sk\/wp-content\/uploads\/2025\/01\/POO-plagat-projektu-VA-OK-PB-dolnybanner-1024x160.jpg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Predpokladan\u00fd \u010das \u010d\u00edtania\" \/>\n\t<meta name=\"twitter:data1\" content=\"3 min\u00faty\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebSite\",\"@id\":\"https:\/\/kmplg.sk\/#website\",\"url\":\"https:\/\/kmplg.sk\/\",\"name\":\"Katedra mineral\u00f3gie, petrol\u00f3gie a lo\u017eiskovej geol\u00f3gie\",\"description\":\"Pr\u00edrodovedeck\u00e1 fakulta Univerzity Komensk\u00e9ho v Bratislave\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/kmplg.sk\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"sk-SK\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/kmplg.sk\/?page_id=3464\",\"url\":\"https:\/\/kmplg.sk\/?page_id=3464\",\"name\":\"TheoCrystMin - 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