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Concept explainers
(a)
Show the cubic direction
(a)
![Check Mark](/static/check-mark.png)
Explanation of Solution
Show the cubic direction
Position coordinates:
For the cubic direction
Repeat distance:
For the cubic direction
(b)
Show the cubic direction
(b)
![Check Mark](/static/check-mark.png)
Explanation of Solution
Show the cubic direction
Position coordinates:
For the cubic direction
Repeat distance:
For the cubic direction
(c)
Show the cubic direction
(c)
![Check Mark](/static/check-mark.png)
Explanation of Solution
Show the cubic direction
Position coordinates:
For the cubic direction
Repeat distance:
For the cubic direction
(d)
The angle between the cubic directions
(d)
![Check Mark](/static/check-mark.png)
Answer to Problem 29AAP
The angle between the cubic directions
Explanation of Solution
Write the expression to calculate angle between the cubic directions
Here, Miller indices of the cubic plane 1 are
Conclusion:
Substitute 0 for
Thus, the angle between the cubic directions
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Chapter 3 Solutions
Foundations of Materials Science and Engineering
- Determine the indices for the directions shown in the following cubic unit cell. Part 1 Z We begin with Direction A. (a) What is the x coordinate of the vector tail (x₁)? (b) What is the x coordinate of the vector head (x2)? (c) What is the y coordinate of the vector tail (y₁)? (d) What is the y coordinate of the vector head (y2)? (e) What is the z coordinate of the vector tail (2₁)? (f) What is the z coordinate of the vector head (z₂)? Fractional entries should be expressed in decimal form. H +yarrow_forward1. Within a cubic unit cell, sketch the following directions: [110], [121], [0Ī2], [123], [103]arrow_forwardDraw the following direction vectors in an orthorhombic unitcell:[111],[201]and [2 ̄31]. with lattice parameters {1, 2, 3, 90, 90, 90}arrow_forward
- 6. Within a cubic unit cell, sketch the following directions: ( :)) (a) [110] (e) [771] (b) [121] (f) [722] (c) [072] (d) [133] (g) [123] (h) [103]arrow_forward(b) Draw the following direction vectors in a cubic unit cell: [212] and [101] Draw the following crystallographic planes in a cubic unit cell: (111) and (121) "oin 2/2 Page 1 of 2arrow_forwardB) Draw the following planes in the hexagonal crystal: (1) (1 0i ) (2) (ī010) (3) ( 0ī 11) (4) ( 0 1 o) C) Draw the following direction vectors in the cubic unit cell: (1) [111] (2) [011] (3) [110] (4) [112]arrow_forward
- (a) Derive linear density expressions for BCC [110] and [111] directions in terms of the atomic radius R and (b) compute linear density values for these same two directions for tungsten. (a) [110]: i [111]: i (b) [110]: i [111]: eTextbook and Media atom/R atom/R 1/m 1/marrow_forwardWithin a cubic unit cell, sketch the following directions: (a) [110] (b) [121] (c) [012] (d) [133]arrow_forwardwithin a orthorhombic unit cell, sketch the following: [123] and [133]arrow_forward
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