Equazione di Born-Landé

L'equazione di Born-Landé rappresenta un modo di calcolare l'energia reticolare di un composto ionico cristallino. Fu elaborata nel 1918^[1] da Max Born e Alfred Landé che proposero di tenere conto, oltre all'energia coulombiana derivata dalle interazioni elettrostatiche, del contributo delle interazioni repulsive a corto raggio tra gli ioni.^[2]

Derivazione

Applicando la legge di Coulomb è possibile calcolare l'energia potenziale legata alle interazioni fra gli ioni che costituiscono il reticolo cristallino. Sommando algebricamente i singoli contributi delle interazioni con uno ione preso come riferimento, e tenendo conto che la carica totale di un anione e un catione è pari a ze, dove z è la singola carica ed e la carica elementare, per una mole di ioni si perviene a

E=-{\frac {\alpha }{r}}\cdot {\frac {|z_{1}||z_{2}|N_{A}e^{2}}{4\pi \varepsilon _{0}}}

dove α è la costante di Madelung, N_A la costante di Avogadro, ε₀ la permettività del vuoto, r la distanza tra gli ioni.

Born e Landé suggerirono di inserire il termine repulsivo ${\frac {B}{r^{n}}}$ , dove B è una costante, r la distanza fra gli ioni, n il coefficiente di Born che assume valore compreso tra 5 e 12. Questo coefficiente può essere ricavato sperimentalmente da misure di comprimibilità oppure in modo teorico.^[3]

Quindi, l'espressione dell'energia reticolare (eq. di Born-Landè) diviene:

E=-{\frac {\alpha }{r}}\cdot {\frac {|z_{1}||z_{2}|N_{A}e^{2}}{4\pi \varepsilon _{0}}}+{\frac {B}{r^{n}}}

Ricavando il valore di B differenziando l'equazione precedente rispetto a dr, ovvero dall'espressione che fornisce il valore di r per il quale l’energia reticolare è minima, e sostituendo tale valore nell'equazione per il calcolo dell'energia reticolare, si ottiene infine l'equazione di Born-Landé nel punto di minimo della funzione

E(r_{\text{minimo}})=-|z_{1}||z_{2}|{\frac {\alpha }{r_{\text{minimo}}}}\left(1-{\frac {1}{n}}\right)\cdot {\frac {N_{A}e^{2}}{4\pi \varepsilon _{0}}}

Note

^ I.D. Brown, The chemical Bond in Inorganic Chemistry, IUCr monographs in crystallography, Oxford University Press, 2002, ISBN 0198508700
^ David Arthur Johnson, Metals and Chemical Change, Open University, Royal Society of Chemistry, 2002, ISBN 0854046658
^ Cotton, F. Albert; Wilkinson, Geoffrey; (1966). Advanced Inorganic Chemistry (2d Edn.) New York: Wiley-Interscience.

Voci correlate

Equazione di Kapustinskij

Collegamenti esterni

Energia Reticolare ed Equazione di Born-Landé (PDF) ^{[collegamento interrotto]}, su dpci.unipd.it.

Portale Chimica

Portale Fisica

Read other articles:

Orkney

Peta Letak Kepulauan Orkney Orkney merupakan nama kepulauan yang terletak di Laut Utara. Secara administratif Orkney merupakan sebuah kabupaten Skotlandia yang berstatus kepulauan. Pusat administrasinya berada di Kirkwall. Pulau ini memiliki luas wilayah 990 km² dengan memiliki jumlah penduduk 19.800 jiwa (2006). Subdivisi Pickaquoy Berstane and Work Warrenfield Lynnfield Brandyquoy Papdale Scapa and Kirkwall South West Shapinsay and Kirkwall Harbour Stromness North Stromness South, Gra...

Cowok Komersil

Cowok KomersilSelebaranSutradaraArizalDitulis olehArizalPemeranDoris Callebaute Debby Cynthia Dewi Alicia Djohar Marina Gardena Ade Irawan Bambang Irawan Rachmat Kartolo Nurnaningsih Yati Octavia Robby SugaraTanggal rilis1977Durasi108 menitNegaraIndonesiaIMDbInformasi di IMDb Cowok Komersial adalah film drama Indonesia yang dirilis pada tahun 1977. Film produksi PT Nusantara Film ini dibintangi antara lain oleh Doris Callebaute, Debby Cynthia Dewi, Alicia Djohar, Marina Gardena, Ade Irawan, B...

متحف حمص

متحف حمص معلومات عامة الدولة سوريا تعديل مصدري - تعديل متحف حمص يقع في وسط مدينة حمص في سوريا،[1] وفي أحد أهم شوارعها (شارع شكري القوتلي) وقد تم اختيار أحد أهم الأبنية ذات الطابع الفرنسي الجميل ليكون المتحف الوطني. بُني المبنى على ثلاث مراحل: * بُني الدور الأرضي عام...

Ecocrop

EcocropProduserOrganisasi Pangan dan Pertanian (Italia)BahasaInggrisAksesBiayaAkses terbukaCakupanDisiplinTaksonomi tumbuhanGeospasialsemua wilayahJumlah catatan2.300Tautan [gaez.fao.org/pages/ecocrop-find-plant Situs web] Ecocrop adalah basis data yang digunakan untuk menentukan kesesuaian suatu tanaman untuk lingkungan tertentu.[1] Dikembangkan oleh Organisasi Pangan dan Pertanian Perserikatan Bangsa-Bangsa (FAO), ini memberikan informasi yang memprediksi viabilitas tanaman di lokas...

Gunung Odae

Gunung OdaeNama KoreaHangul오대산 Hanja五臺山 Alih AksaraOdaesanMcCune–ReischauerOtaesan Odaesan (Gunung Odae) adalah gunung yang terletak dalam kawasan Taman Nasional Gunung Odae, mencakup wilayah Kabupaten Pyeongchang, Hongcheon dan pinggiran Gangneung, Provinsi Gangwon, Korea Selatan.[1] Taman Nasional Gunung Odae diresmikan pada tahun 1975. Terletak 90 km sebelah barat kota Gangneung, 140 km jauhnya di sebelah timur kota Seoul. Taman nasional ini ditandai dengan ...

UFC 97

UFC mixed martial arts event in 2009 UFC 97: RedemptionThe poster for UFC 97: RedemptionInformationPromotionUltimate Fighting ChampionshipDateApril 18, 2009VenueBell CentreCityMontreal, Quebec, CanadaAttendance21,451Total gate$4,900,000Buyrate650,000[1]Event chronology UFC Fight Night: Condit vs. Kampmann UFC 97: Redemption UFC 98: Evans vs. Machida UFC 97: Redemption (not to be confused with UFC 17: Redemption) was a mixed martial arts event held by the Ultimate Fighting Championship...

Russia–Transnistria relations

Bilateral relationsRussia-Transnistria relations Russia Transnistria Russia–Transnistria relations are the bilateral relations between the Pridnestrovian Moldavian Republic (Transnistria), an unrecognised breakaway state that is internationally recognised as part of Moldova, and the Russian Federation. Russia does not officially recognise the independence of Transnistria; nevertheless, Russia maintains special relations with Transnistria in the political, military, cultural, and economic sp...

2020 European Tour

Golf tour season 2020 European Tour seasonDuration28 November 2019 (2019-11-28) – 13 December 2020 (2020-12-13)Number of official events38[a]Most wins Christiaan Bezuidenhout (2) John Catlin (2) Rasmus Højgaard (2) Sam Horsfield (2)Race to Dubai Lee WestwoodGolfer of the Year Lee WestwoodPlayers' Player of the Year Lee WestwoodSir Henry Cotton Rookie of the Year Sami VälimäkiGraduate of the Year Antoine RoznerUK Swing Order of Merit Rasmus Højgaard�...

Данио-рерио

Данио-рерио Научная классификация Домен:ЭукариотыЦарство:ЖивотныеПодцарство:ЭуметазоиБез ранга:Двусторонне-симметричныеБез ранга:ВторичноротыеТип:ХордовыеПодтип:ПозвоночныеИнфратип:ЧелюстноротыеГруппа:Костные рыбыКласс:Лучепёрые рыбыПодкласс:Новопёрые рыбыИн�...

قائمة شركات الأنمي

لا يزال النص الموجود في هذه الصفحة في مرحلة الترجمة إلى العربية. إذا كنت تعرف اللغة المستعملة، لا تتردد في الترجمة. (أبريل 2019) جزء من سلسلة حولالأنمي والمانغا أنمي أنمي التاريخ الصناعة رسوم متحركة أصلية للشبكة رسوم متحركة أصلية للفيديو الترجمة الدبلجة الشركات أطول المسلسل�...

Metro de Astaná

Este artículo se refiere o está relacionado con una infraestructura de transporte público futura o en desarrollo. La información de este artículo puede cambiar frecuentemente. Por favor, no agregues datos especulativos y recuerda colocar referencias a fuentes fiables para dar más detalles. Metro de Astaná LugarUbicación Astaná, Kazajistán KazajistánDescripciónTipo MetroCaracterísticas técnicasLongitud red 45 kilómetros (2017)Estaciones 18Velocidad máxima 80 km/h (50 mi/h)Expl...

The Pirate's Dream

1940 film The Pirate's DreamItalian theatrical release posterDirected byMario MattoliWritten byMario MattoliVittorio MetzStenoProduced byLiborio CapitaniStarringErminio MacarioCinematographyAldo TontiEdited byMario SerandreiRelease date 20 October 1940 (1940-10-20) Running time75 minutesCountryItalyLanguageItalian The Pirate's Dream (Italian: Il pirata sono io!) is a 1940 Italian film directed by Mario Mattoli and starring Erminio Macario.[1] Plot The setting is Santa C...

¡Cu-Cut! incident

Assault conducted by Spanish officers due to a satirical cartoon The ¡Cu-Cut! incident, also known as La Cuartelada, was an assault conducted by Spanish officers on the Catalan satirical magazine ¡Cu-Cut! offices in Barcelona on November 25, 1905 in response to the publication of a satirical cartoon mocking the Spanish military.[1][2] Background Spanish military personnel had been a common target of ¡Cu-Cut!'s editors because the Spanish Army had become an outdated and defe...

Christ Church Lutheran (Minneapolis, Minnesota)

Historic church in Minnesota, United States United States historic placeChrist Church LutheranU.S. National Register of Historic PlacesU.S. National Historic Landmark Christ Church Lutheran viewed from the northeastLocation3244 34th Avenue South, Minneapolis, Minnesota 55406Coordinates44°56′37″N 93°13′24″W / 44.94361°N 93.22333°W / 44.94361; -93.22333Built1948–1949Built byKraus-Anderson, Inc.ArchitectEliel SaarinenArchitectural styleInternational Sty...

Renaisans Tinggi

Fresko karya Raffaello di Ruang Raffaello di dalam Istana Apostolik di Vatikan, atas perintah Paus Yulius II Penciptaan Adam, pemandangan dari atas langit-langit Kapel Sistina karya Michelangelo (sekitar tahun 1508-1512), atas perintah Paus Yulius II Perjamuan Terakhir, mural karya Leonardo da Vinci Dalam sejarah seni, Renaisans Tinggi merupakan periode singkat munculnya seni-seni artistik terbaik selama era Renaisans Italia, khususnya di Roma, Negara Kepausan, dan di Firenze. Kebanyakan seja...

Bologna Football Club 1909 2005-2006

Voce principale: Bologna Football Club 1909. Bologna FC 1909Stagione 2005-2006Sport calcio Squadra Bologna Allenatore Renzo Ulivieri[1], poi Andrea Mandorlini[2], poi Renzo Ulivieri Presidente Alfredo Cazzola Serie B8º posto Coppa ItaliaSecondo turno Maggiori presenzeCampionato: Pagliuca (42)Totale: Pagliuca (44) Miglior marcatoreCampionato: Bellucci (25)[3]Totale: Bellucci (26) StadioRenato Dall'Ara (38 462) Abbonati7 061 Maggior numero di spettatori1...

George M. Humphrey

American politician For other people named George M. Humphrey, see George M. Humphrey (disambiguation). This article's lead section may be too short to adequately summarize the key points. Please consider expanding the lead to provide an accessible overview of all important aspects of the article. (August 2021) George Humphrey55th United States Secretary of the TreasuryIn officeJanuary 21, 1953 – July 29, 1957PresidentDwight D. EisenhowerPreceded byJohn SnyderSucceeded byRobert B. ...

Tsar

Pour les articles homonymes, voir Tsar (homonymie). Nicolas II, dernier tsar de l'Empire russe. Siméon II, dernier tsar des Bulgares. Le titre de tsar est un titre royal ou impérial porté par les souverains de la Russie (de 1547 à 1917), de la Bulgarie (de 917 à 1018, de 1185 à 1422 et de 1908 à 1946) ou de la Serbie (de 1346 à 1371). Le tsarisme est une forme d'autocratie (plus tard de l'absolutisme) spécifique à la grande-principauté de Moscou (devenu par la suite le tsarat de R...

Osztopán

Village in Southern Transdanubia, HungaryOsztopán Stupan (in Croatian)VillageTallián Mansion in Osztopán Coat of armsLocation of Somogy county in HungaryOsztopánLocation of OsztopánCoordinates: 46°31′13″N 17°40′14″E / 46.52032°N 17.67068°E / 46.52032; 17.67068Country HungaryRegionSouthern TransdanubiaCountySomogyDistrictKaposvárRC DioceseKaposvárArea • Total22.83 km2 (8.81 sq mi)Population (2017) • Tot...

Associazione Calcio Novara 1967-1968

Voce principale: Novara Calcio. Associazione Calcio NovaraStagione 1967-1968Sport calcio Squadra Novara Allenatore Franco Giraudo affiancato da Giuseppe Molina come DT Camillo Achilli Presidente Francesco Plodari Serie B20º posto. Retrocesso in Serie C. Coppa ItaliaPrimo turno. Maggiori presenzeCampionato: Fumagalli (40) Miglior marcatoreCampionato: Calloni G., Milanesi (6) 1966-1967 1968-1969 Si invita a seguire il modello di voce Questa pagina raccoglie le informazioni riguardanti l'...