Question

6. A single crystal, a. is made of grains with different crystallographic directions b. is formed as the result of interlocking unit cells without any interruption c. does not show polymorphism d. has isotropic properties 7. By increasing the temperature from room temperature to the melting point of iron, the sequence of polymorphic transformations of iron is a FCC-BCC-HCP b. FCC-BCC-FCC c. BCC-FCC-BCC d. BCC-FCC-HCP 8. The Miller indices for the crystallographic plane shown are a. (123) b. (336) c. (632) d. (636) 9. The relationship between the unit cell edge length (a) and atomic radius (R) for the BCC crystal structure is 2R a. a = 2 b. a = 2RV2 c. a = V3R d. a =** 10. The linear density for the FCC [110] direction can be expressed by a. LD: 10 = b. LD, 10 = 4R c. LD: 10 = 2 atoms d. LD,10 = 11. In polycrystalline materials, a. properties may/may not vary with the direction of measurement b. properties are independent of the direction of measurement c. all grains have texture d. bande 12. By increasing the cation to anion radius ratio in ceramics, a. the number of cations around anions increases b. the number of anions around cations increases c. unstable structures form d. charge on anions increases 13. Factors that affect the crystal structure of ceramics are a the number of ions and the ratio of atomic weights of ions b. the relative size of ions and the charge neutrality of the structure c. the charge neutrality of the structure and the number of cations in the unit cell d. the ratio of atomic weights of ions and the charge neutrality of the structure Page 2 of 7

Answer 1

6 B

7 C

8 C

explanation - the x-, y-, and z- intercepts are 1/3,2/3, and 1, the Miller indices are calculated as follows:

1. Take reciprocals: 3, 3/2, 1
2. Clear fractions {multiply by 2}: 6, 3, 2
3. Reduce to lowest terms (already there)

9 D

explanation - the length of the cell edge is represented by a. The direction from a corner of a cube to the farthest corner is called body diagonal (bd). The face diagonal (fd) is a line drawn from one vertex to the opposite corner of the same face. If the edge is a, then we have:

fd2=a2+a2=2a2

bd2=fd2+a2=a2+a2+a2

bd² = 3a²

Atoms along the body diagonal (bd) touch each other. Thus, the body diagonal has a length that is four times the radius of the atom, R.

bd=4R

so ,4R = 3^1/2a

10 A

explanation - LD = no of atoms centered on direction vector/ length of direction vector

2 atoms along diagonal 110 in the cube and legnth = 4R

so LD = 1atom/ 2R

11 B

12 B

13 B

(rest of the problems doesn't need any explanation as they are direct answers that you should remember!)