Crystal Planes amp; Indices Wells College AdvancedWebmail 晶面amp；指标威尔斯学院先进的网络邮件.pptVIP

Crystal Planes Indices Crystals often have polyhedral shapes bounded by flat faces; this is a consequence of the periodicity of its internal arrangement. Take a 2-D distribution of lattice points; choose any two (e.g. A B) and pass a line through those points; can pass parallel lines through every other lattice point (N.B. in 3-D need 3 points not on the same line). Have generated a set of equivalent equidistant planes. Because these planes pass equally through the lattice points, what is generated corresponds to the stacking of layers. The faces of crystals arrive from those planes which most favor the growth of the crystal (i.e. molecules add more easily on some faces than on others). Crystal Planes Indices The orientation of a set of parallel planes can be specified by means of intercepts through the axes of the coordinate system (i.e. the unit cell edges). It is customary to specify the orientations by means of indices, which are proportional to the reciprocals of the intercepts. Here the intercept, using fractional coordinates, along the a axis is at 1, and at ? along the b axis. So, the index would be: 1 2. a b Crystal Planes Indicies The figure to the right shows a unit cell with a set of parallel planes. plane I intercepts at 2/3 1/2 ∞ (i.e. the plane is parallel to the c axis); the reciprocals are 3/2 2 0. plane II intercepts at 1/3 1/4 ∞ ; the reciprocals are 3 4 0. The orientation of the planes is of interest to us. Notice that we can multiply the first set of reciprocals by a common factor (x2) to obtain integers (3 4 0), which are identical to the second plane; that is, these two planes are parallel and part of the same set. (3 4 0): These 3 numbers (h k l) are called the Miller indices. Note that they reveal the number of planes that pass across each axis. Law of Rational Indices: the indices of the faces of a crystal are usually small integers, seldom greater than 3 (Hauy, 1784). b a II I 2/3 a 1/2 b Two Methods for Determining Miller In