Concept explainers
The Miller-Bravais direction indices of the
Answer to Problem 55AAP
The Miller-Bravais Direction indices of the vector OA is
The Miller-Bravais Direction indices of the vector OB is
The Miller-Bravais Direction indices of the vector OC is
The Miller-Bravais Direction indices of the vector OD is
The Miller-Bravais Direction indices of the vector OE is
The Miller-Bravais Direction indices of the vector OF is
Explanation of Solution
For finding the Miller-Bravais direction indices we need coordinates of intercept of the plane. By using the method of indices the intercept
Coordinate of intercept of the vectors OA is
Coordinate of intercept of the vectors OB is
Coordinate of intercept of the vectors OC is
Coordinate of intercept of the vectors OD is
Coordinate of intercept of the vectors OE is
Coordinate of intercept of the vectors OF is
By using these intercept we will find the Miller-Bravais direction indices.
Conclusion:
Direction vector originating at the centre of the lower basal plane and ending at the end point of the upper basal plane for a Hexagonal closed packed unit cell.
Figure-(1)
The given closed packing is Hexagonal closed packing and the direction vector of the planes are shown in figure-1. Here, the originating vector at the centre of the lower basal plane and ending at the end point of the upper basal plane for a Hexagonal closed packed unit cell is defined in the figure-1
Miller-Bravais direction Indices for the Direction vector are tabulated below.
Direction Vector | Co-ordinates of intercepts | Reciprocal of intercept | Direction indices |
OA | |||
OB | |||
OC | |||
OD | |||
OE | |||
OF |
The Miller-Bravais Direction indices of the vector OAis
The Miller-Bravais Direction indices of the vector OB is
The Miller-Bravais Direction indices of the vector OC is
The Miller-Bravais Direction indices of the vector OD is
The Miller-Bravais Direction indices of the vector OE is
The Miller-Bravais Direction indices of the vector OF is
Want to see more full solutions like this?
Chapter 3 Solutions
FOUND.OF MTRLS.SCI+ENGR.(LL)-W/CONNECT
- in cubic structure Write down the CORRECT direction that is perpendicular to the miller indices [001]arrow_forwardDetermine the indices for the directions in the cubic unit cell shown in the figure belowarrow_forwardDetermine the Miller indices of the cubic crystal plane that intersects the following position coordinates(points): (1, ½, 1), (½, 0, ¾), and (1, 0, ½). Sketch the plane, and show all steps and distances.arrow_forward
- Determine the possible crystal structure of Zinc Blende structure (ZnS), if the radii are as follows Zn+2 = 0.074 and S-2 = 0.184.arrow_forwardAre these statements True or False? CFRP and GFRP are examples of hybrid materials. Body diagonal in BCC structure has Miller indices of [111]. A closed packed triangular plane in FCC crystal has Miller indices of (111). The density of a material is determined exclusively by its atomic weight.arrow_forwardWhich of the following statement is correct about miller indices for planes and directions?a. Planes and their negatives are not identicalb. Planes and their multiples are identicalc. Directions and their negatives are identicald. Directions and their multiples are identicalarrow_forward
- Determine the Miller indices for the planes of the cubic unit cell shown in figure 2, according to the coordinate axis system shown.arrow_forwardDetermine the intercepts of a plane when the miller indices are (111) where h is negative.arrow_forwardWhat are the Miller indices of the planes ABC, BCED and BFGH; and directions BC,AB and BH in the figure below. Please be sure to include the X-Y-Z reference axes andshow the steps involved.arrow_forward
- Cite the indices of the direction that results from the intersection of the (001) and (121) planes within a cubic crystal.arrow_forwardDetermine the indices for the following crystallographic direction. Must show complete solution following the steps below, and use proper notation. Steps in defining the 3 directional indices 1. Vector repositioning (if necessary) to pass through origin. (needed in this case) 2. Read off projections in terms of unit cell dimensions a, b, and c 3. Adjust to smallest integer values 4. Enclose in square brackets, no commas → [u v w]arrow_forwardThe attached photo shows the Young’s modulus of a cubic single crystal as a function of orientation. where a1 a2 and a3 are the direction cosines between the direction hkl and [100], [010], and [001], respectively. For a certain crystal, E111 = 500 GPa and E100 = 90 GPa. Calculate Young’s modulus for this single crystal in the <110> directionarrow_forward
- Understanding Motor ControlsMechanical EngineeringISBN:9781337798686Author:Stephen L. HermanPublisher:Delmar Cengage Learning