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Z. [0 1 0]. [1 0 1]. Y. X. - 2 / 3 11. z. [111]. [001]. c. y. [120]. b. 1½0. [210]. x. a. [100]. For cubic: a = b = c = a o. Miller Indices. Miller Indices. Z. Z. Z. Y. Y. Y. X. X. X. (100). (110). (111). FAMÍLIA DE PLANOS {110} É paralelo à um eixo.

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  1. Z [0 1 0] [1 0 1] Y X

  2. -2/311 z [111] [001] c y [120] b 1½0 [210] x a [100] For cubic: a = b = c = ao

  3. Miller Indices

  4. Miller Indices

  5. Z Z Z Y Y Y X X X (100) (110) (111)

  6. FAMÍLIA DE PLANOS {110}É paralelo à um eixo

  7. FAMÍLIA DE PLANOS {111}Intercepta os 3 eixos

  8. Directions & Miller Indices in Hexagonal Structures [011] (0001) [210] [UVW] or [uvtw] (hkil) or (hk·l)

  9. Diamond Lattice (100) (110)

  10. Diamond Lattice (111)

  11. Spacing of Planes Cubic: Cubic: Tetragonal: Tetragonal: Hexagonal: Rhombohedral:

  12. Spacing of Planes Orthorhombic: Monoclinic: Triclinic:

  13. Reciprocal Lattice Unit cell: b1, b2, b3 Reciprocal lattice unit cell: b1*, b2*, b3* defined by: b3* B P C b3 b2 A O b1

  14. Reciprocal Lattice Like the real-space lattice, the reciprocal space lattice also has a translation vector, Kl: Where the length of R·K is equal to: The magnitude of the translation vector has the following relationship:

  15. Angles and Inner Planar Spacing is  to (hkl) plane. Therefore, the angle between (h1k1l1) and (h2k2l2) planes is the angle between the Kh1k1l1 and Kh2k2l2 vectors. Recall the dot product: Angles between reciprocal lattice vectors.

  16. Two Dimensional Lattice Wigner-Seitz Possible choices of primitive cell for a single 2D Bravais lattice.

  17. First Brillouin Zone If these lattice points now represent reciprocal lattice points, then the first Brillouin zone is just the Wigner-Seitz cell of the reciprocal lattice. b2* b1*

  18. DETERMINAÇÃO DA ESTRUTURA CRISTALINA POR DIFRAÇÃO DE RAIO X

  19. DIFRAÇÃO DE RAIOS XLEI DE BRAGG n= 2 dhkl.sen • É comprimento de onda N é um número inteiro de ondas d é a distância interplanar  O ângulo de incidência Válido para sistema cúbico dhkl= a (h2+k2+l2)1/2

  20. DISTÂNCIA INTERPLANAR (dhkl) • É uma função dos índices de Miller e do parâmetro de rede dhkl= a (h2+k2+l2)1/2

  21. TÉCNICAS DE DIFRAÇÃO • Técnica do pó: É bastante comum, o material a ser analisado encontra-se na forma de pó (partículas finas orientadas ao acaso) que são expostas à radiação x monocromática. O grande número de partículas com orientação diferente assegura que a lei de Bragg seja satisfeita para alguns planos cristalográficos

  22. O DIFRATOMÊTRO DE RAIOS X • T= fonte de raio X • S= amostra • C= detector • O= eixo no qual a amostra e o detector giram Amostra Fonte Detector

  23. DIFRATOGRAMA

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