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# L19 - SUMMARY FROM LAST CLASS Miller indices A set of...

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Dr. P. Lucas U of A MSE 110 Miller indices SUMMARY FROM LAST CLASS A set of atomic planes entirely defines a crystal structure and we can identify these planes based on their orientation in the unit cell using the Miller indices . The plane orientation is specified by the intercept with each axes of the unit cell. This defines a set of Miller indices (hkl) determined as follow: Find an origin for which the plane intercepts all axes. Except for parallel axes. Find the intercepts on the three axes in fraction of the cell parameter. Except for parallel axes where intercept is . Determine the reciprocal of these numbers. Reduce the reciprocals to the smallest integers having the same ratio. Cite the three integers in parenthesis placing bars over negative indices. Using Bragg’s equation λ = 2d sin θ a set of d-spacings is obtained from the θ values on the XRD pattern. Each d correspond to a plane of orientation (hkl) . 2 2 2 ) ( l k h a d hkl + + = For a cubic cell, the geometric relationship between a , d and (hkl) is By inspection, we can calculate a and obtain the set of (hkl) for each d-spacing. This determines the structure entirely. a , d and (hkl) from all known minerals are compiled in a database.

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Dr. P. Lucas U of A MSE 110 Thermodynamics: INTRO TO THERMODYNAMICS What characterizes a system (a solid, a liquid, a gas or a mixture) when it is at equilibrium (when it doesn’t evolve anymore). Thermodynamics is the study of equilibrium states. It is powerful because it allows you to predict if a reaction or a process will take place, the direction of the process or the reaction, and the amount of energy transferred. Processes: melting, vaporization… Reactions: Na + Cl 2 Æ NaCl In order to characterize the thermodynamic state of a system we will need to introduce new variables: The enthalpy H : characterize the heat transferred during a process.
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