Constante de
Madelung
Canché Martín, Juan Alberto
Carrillo Romero, Enrique Mauricio
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Madelung Constant: A Comprehensive Guide with Examples and Applications, Study Guides, Projects, Research of Physics
A comprehensive overview of the madelung constant, a fundamental concept in solid-state physics and chemistry. It explores the calculation of the madelung constant for various crystal structures, including 1d ionic lines, 2d ionic lattices, and 3d structures like nacl and cscl. The document also delves into the concept of born-landé equation and its application in determining the energy of a crystal lattice. It includes illustrative examples, diagrams, and references to relevant resources, making it a valuable resource for students and researchers in related fields.
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2020/2021
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Constante de
Madelung
Canché Martín, Juan Alberto
Carrillo Romero, Enrique Mauricio
Tabla de contenidos 01 ¿Qué es la constante de Madelung? 04 Estructura NaCl (3D) 05 Estructura^ CsCl (3D) 03 Red iónica (2D) 02 Línea iónica (1D) 06 Generalización
Existen otros factores a considerar para evaluar la energía de una red como la mostrada por Max Born y Alfred Lande ¿Qué es? Ecuación de Born-Landé Constante de Madelung
Línea iónica (1D) Notemos que cada se tienen dos iones del mismo signo, de modo que se obtiene la siguiente serie: Imaginemos una línea iónica (por ejemplo de NaCl).
Red iónica (2D) Expandiendo cuadrados Expandiendo círculos
Red iónica (2D)
Red iónica (2D) Expandiendo círculos Promediando podemos ver que la serie intenta converger, pero muy lentamente. Al final el valor obtenido es
Estructura NaCl (FCC)
Estructura NaCl (FCC)
Estructura CsCl (BCC)
La constante de Madelung incrementa con relación al número de coordinación. Extra Las contribuciones de los vecinos más cercanos son las más importantes
Referencias Kittel, C. (1996) Introduction to Solid State Physics. 7th Edition, John & Wiley, New York. LibreTexts Chemistry (2024). Madelung Constants. Recuperado de https://chem.libretexts.org/Courses/Northern_Michigan_University/CH_215%3A_Chemistry_of_the Elements_Fall_2023/05%3A_Solids_and_Solid-State_Chemistry /5.11%3A_Lattice_Energy_-_Madelung_Constants Pfeifenberger, M. (2010). Berechnung der Madelung Konstante und des kritischen Radius von zweidimensionalen Kristallstrukturen, Recuperado de https://lampz.tugraz.at/~hadley/ss1/studentpresentations/2011/MadelungKonst2dim.pdf Roccatano, D. (2017). The calculation of the Madelung constant. Recuperado de https://daniloroccatano.blog/2017/10/27/calculation-of-the-madelung-constant/ Sankar, B. (2012). Direct Calculation Of Madelung Constant. Recuperado de http://parsek.yf.ttu.ee/~physics/SSP/msct_madelung.pdf Wolfram Mathworld (2024). Madelung Constants. Recuperado de https://mathworld.wolfram.com/MadelungConstants.html