d = distance between atoms n = an integer wavelength of the x-rays λ= of reflection = θ Can you think of a practical application of Bragg’s equation? Example problem: (make sure your calculator is in degrees!) X rays of wavelength 1.54 Å were used to analyze an aluminum crystal. A reflection was produced at = 19.3 degrees. Assuming n = 1, calculate the distance, d, between the planes of atoms producing θ this reflection. 3 types of Crystalline Solids: classified according to what type of component occupies the lattice points. (see table bleow) Classification of Solids: Atomic Solids Molecular Ionic Solids Solids Metallic Network Group 13 Components metal atoms non-metal group 13 discrete ions that occupy atoms atoms molecules lattice points Bonding delocalized directional London Dipole-Dipole Ionic covalent covalent Dispersion and/or (molecules) forces L. D. F. Properties range of hardness and hard, high very low low melting high melting melting points, melting point, melting poins points, points conductor insulator insulator Examples silver, iron, diamond solid argon is ice, dry ice NaCl, CaF2 another example What is the difference between solids and molecular solids? Packing in Metals: Model: Packing uniform, hard spheres to best use available space. This is called closest packing. Each atom has 12 nearest neighbors. (pictures on next pages) hexagonal closest packed (“aba”) closest packed (“abc”)
d = distance between atoms n = an integer λ= wavelength of the x-rays θ = of reflection Can you think of a practical application of Bragg’s equation? Example problem: (make sure your calculator is in degrees!) X rays of wavelength 1.54 Å were used to analyze an aluminum crystal. A reflection was produced at θ = 19.3 degrees. Assuming n = 1, calculate the distance, d, between the planes of atoms producing this reflection. 3 types of Crystalline Solids: classified according to what type of component occupies the lattice points. (see table bleow) Classification of Solids: Atomic Solids Molecular Solids Ionic Solids Metallic Network Group 13 Components that occupy lattice points metal atoms non-metal atoms group 13 atoms discrete molecules ions Bonding delocalized covalent directional covalent (molecules) London Dispersion forces Dipole-Dipole and/or L. D. F. Ionic Properties range of hardness and melting points, conductor hard, high melting point, insulator very low melting poins low melting points, insulator high melting points Examples silver, iron, diamond solid argon is another example ice, dry ice NaCl, CaF2 What is the difference between solids and molecular solids? Packing in Metals: Model: Packing uniform, hard spheres to best use available space. This is called closest packing. Each atom has 12 nearest neighbors. (pictures on next pages) hexagonal closest packed (“aba”) closest packed (“abc”)
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