Concept explainers
(a)
Draw the hexagonal crystal plane having Miller-Bravais indices of
(a)
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Show the hexagonal crystal plane having Miller-Bravais indices of
(b)
Draw the hexagonal crystal plane having Miller-Bravais indices of
(b)
Explanation of Solution
Show the hexagonal crystal plane having Miller-Bravais indices of
(c)
Draw the hexagonal crystal plane having Miller-Bravais indices of
(c)
Explanation of Solution
Show the hexagonal crystal plane having Miller-Bravais indices of
(d)
Draw the hexagonal crystal plane having Miller-Bravais indices of
(d)
Explanation of Solution
Show the hexagonal crystal plane having Miller-Bravais indices of
(e)
Draw the hexagonal crystal plane having Miller-Bravais indices of
(e)
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Show the hexagonal crystal plane having Miller-Bravais indices of
(f)
Draw the hexagonal crystal plane having Miller-Bravais indices of
(f)
Explanation of Solution
Show the hexagonal crystal plane having Miller-Bravais indices of
(g)
Draw the hexagonal crystal plane having Miller-Bravais indices of
(g)
Explanation of Solution
Show the hexagonal crystal plane having Miller-Bravais indices of
(h)
Draw the hexagonal crystal plane having Miller-Bravais indices of
(h)
Explanation of Solution
Show the hexagonal crystal plane having Miller-Bravais indices of
(i)
Draw the hexagonal crystal plane having Miller-Bravais indices of
(i)
Explanation of Solution
Show the hexagonal crystal plane having Miller-Bravais indices of
(j)
Draw the hexagonal crystal plane having Miller-Bravais indices of
(j)
Explanation of Solution
Show the hexagonal crystal plane having Miller-Bravais indices of
(k)
Draw the hexagonal crystal plane having Miller-Bravais indices of
(k)
Explanation of Solution
Show the hexagonal crystal plane having Miller-Bravais indices of
(l)
Draw the hexagonal crystal plane having Miller-Bravais indices of
(l)
Explanation of Solution
Show the hexagonal crystal plane having Miller-Bravais indices of
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Chapter 3 Solutions
Foundations of Materials Science and Engineering
- 7. Sketch within a cubic unit cell the following planes: (a) (011) (e) (717) (b) (112) (f) (122) (c) (102) (g) (723) (d) (131) (h) (013)arrow_forwardFind the total number of equivalent planes in the cubic structure (multiplicity factor) belonging to the following families: (a) {100} (b) (110} (c) {111) (d) (210)arrow_forwardVanadium has the Body-Centered Cubic (BCC) crystal structure shown in the figure below. The radius of the Vanadium atom is r= 0.132 nm. What is the planar density in atoms/nm2 in plane (200)? Plane (200) Select one: a. 10.76 b. 21.52 C. 16.19 d. 7.61 e. 3.80arrow_forward
- For the images shown below, which Miller indices for crystallographic planes are included? lu C. Z Select one or more: a. (111) b. (230) (211) d. (110) e. (100) b y X a/2 Z b Z 2b/3arrow_forwardQ1).Sketch the [102] direction in a simple cubic lattice h e h Q2). Find the Miller indices of the plane shown below e k 2/3 1 b Karrow_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_forward
- B) 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(c) Find dk for: (i) A simple cubic lattice (ii) A orthorhombic lattice (a + b± c, a = B = y= /2)arrow_forwardChromium (Cr) has the Body-Centered Cubic (BCC) crystal structure. The edge length is a 0.288 nm. What is the linear density in atoms/nm along direction [111P Select one: O a. 7.48 b. 3.18 c. 6.37 d. 4.50 O e. 4.01 Europium has the Body-Centered Cubic (BCC) crystal structure shown in the figure below The radius of the Europium atom is r= 0.204 nm. What is the planar density in atoms/nm im plane (200)2 Plare(200)arrow_forward
- Draw the plane direct and reciprocal lattice for: 3-1) a rectangular centered lattice with parameters a = 10nm, b = 14nm. 3-2) the rectangular lattice in (a) drawn as a primitive lattice.arrow_forwardQ4). Sketch the [112 2 ] plane in the outline of the hexagonal lattice below a Parrow_forward1. Many substances crystallize in a cubic structure. The unit cell for such crystals is a cube having an edge with a length equal to do. -Face diagonal a. What is the length, in terms of do, of the face diagonal, which runs diagonally across one face of the cube? (Hint: Use the Pythagorean theorem.) b. What is the length, again in terms of do. of the cube diagonal, which runs from one corner, through the center of the cube, to the opposite corner? (Hint: Make a right triangle having a face diagonal and an edge of the cube as its sides, with the hypotenuse equal to the cube diagonal, then use the Pythagorean theorem again.) 2. In an FCC structure, the centers of the atoms are found on the corners of the cubic unit cell and at the center of each face. The unit cell has an edge whose length is the distance from the center of one corner atom to the center of another corner atom on the same edge. The atoms on the diagonal of any face are touching. One of the faces of the unit cell is shown…arrow_forward
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