西安工业大学材料科学基础试题及答案分析 - 图文

第一章 固体材料的结构 Chapter 1. The Structure of Materials

作业1：原版教材第105页第17题

17. Identify the plane in an FCC metal formed by the intercepts 1,-1,-2. What is the normal to this plane?

Solution:

1) the intercepts of this plane are 1,-1,-2; 2) The reciprocals of this plane are 1,-1,-reciprocals of the intercepts. 3) clear fractions, 4) site planes in parentheses (221) 5) The directions and planes which have same miller indices are perpendicular to each other.

作业2：原版教材第105页第18题

18. Calculate the angle between [100] and [111] in Al.

Solution:

The crystal structure of Al is Fcc. We can calculate the angle between [100] and [111] as

??z o y 1,taking the 2x cos??

uu'?vv'?ww'u?v?w?u'?v'?w'222222?1?1?0?1?0?11?0?0?1?1?1z 222222?13

??54.73?

o y x

作业3：原版教材第105页第19题

19. Construct a coordinate system at the center of a cubic unit cell with the axes parallel to the 100 directions. Determine the tetrahedral angle, the angle between directions from the origin to two ends of any face diagonal. Solution:

111??? OA:,,???111?

222??111??? OB:,,???111?

222??s? co?1?1?1?1?1?112?12?12?12?12?12?2??

33?3?2

作业4：原版教材第105页第21题

21. Give the indices of the points, directions, and planes in the cubic cells shown in Figure HP3.1.

Solution:

The first step is to select an origin and orient the coordinate axes. We have elected to use the bottom back left corner of the cube as our origin. z As shown in the figure; 1; 21Point B has coordinate 0,1,; 2Point A has coordinate 0,0,Plane F: The intercepts of F are 1,1, Take reciprocals: 1,1,2; Clear fraction: 1,1,2; Cite them into parentheses: ?112? Plane E: The intercepts of E: ?,?,1 Taking reciprocals: 0,0,1

Plane E 2 A B D 1; 2y Plane F x 1 C ???Direction C: 2号坐标 1,1,0 1号坐标：1,0,1 ?011?

??(1) Determine the coordinates of two points

(2) Subtract the coordinates of the second point from those of the first point; (3) Cleat fractions from the difference to give indices in lowest integer vales, 0,1,1

????(4) write the indices in square brackets without commas: ?011?

??????201??? (5) negative integer values are indicated by placing a bar over the integer. D: ?1） The coordinates of points G and H are 0,0,2) plane L:

(1) determine the intercepts of plane L:?11; 0,,0 respectively; 32111,, 223(2) take the reciprocals of the intercepts: -2,2,3 (3) clear fractions: -2,2,3 (4) cite planes in parentheses, placing bars over negative ???

indices: ?223?

??

???3) plane K: ?1,1,???110? ??Plane K J 114) directions: I 1点：?,1, 2点：0,1,0 22 2-1:

G I 11??,0,???101? 22???Plane L H J 2点：0,0,1 1点：-1,1,0 ??????? 1-2: -1,1,-1 ?111???111?

????作业5：原版教材第106页第22题

22. Give the indices of the points, directions, and planes in the cubic cells shown in Figure HP3.2.

Solution:

11???? Plane E: 1,?,? 1,-2,-2 ??122?

22??1??? Plane F: ?,?,1?0,?2,1??021?

2??A Plane E C B plane F D

1,0 211 Point B: ,?,?1

22 Point A: 0,? Direction B D:

D点坐标：0,0,-1

11??? D-B: ?,?,0??1,1,0??110?

22?? Direction C：（1） 1，-1，0 （2） 0,0,?1 21??? （1）-（2） 1,?1,?2,?2,1??221?

2??

Point H: 1,1,1

I 11Point G: ,,0

22Direction I: (1) 0,0,H Plane K 1 (2) 1,1,1 2Plane L G J 1????? (1)- (2) ?1,?1,???221? 2?? Direction J: (1) 1,1,0 (2) 0,1,0 (1)- (2) 1,0,0??100? Plane L: ?,11,?0,2,2??011? 22????Plane K: 1,1,1??111?

??

作业6：

Use a calculation to verify that the atomic packing factor for the FCC structure is 0.74. Solution:

In an FCC, there are four lattice points per cell: if there is one atom per lattice point, there are also four atoms per cell. The volume of one atom is 4πr3/3 and the volume of the unit cell is a3: Packing factor = 4×4πr3/3 a3

Since for FCC unit cell, a=4r/2, packing factor =o.74

作业7：

用金属键原理解释金属的以下几个特征：良好的导电导热性、正的电阻温度系数、不透明和良好的延展性。 解答：

1）导电导热性：

金属中的自由电子在外加电场作用下，能够沿着电场方向作定向运动，具有导电性。金属中正离子振动和自由电子的运动均可传递热量（能），表现出良好的导热性。 2）正的电阻温度系数：

温度升高时，金属正离子的振动加剧，与自由电子的碰撞几率加大，对自由电子的定向运动阻力增大，故具有电的电阻温度系数。 3) 不透明：

金属中自由电子能够吸收并随后辐射出投射到金属表面的光能。故金属不透明，且具有光泽。

4） 延展性：

金属键没有方向性和饱和性，对原子也没有选择性。当受外力原子发生相对移动时，金属正离子仍包围在电子气之中。金属键不会受到破坏。 作业8：

算出fcc、bcc晶体中四面体间隙和八面体间隙 大小，用原子半径rA表示，并注明原子间隙位置。 解答：

bcc：八面体间隙：最小rB?置（

a?rA?0.154rA，位2411rA,（面中心及各边中心） ，，1），a?223 四面体间隙：（

11，，1） 24?a??a?rB???????rA?0.25rA，

?2??4? fcc：八面体间隙：体心处（

22111，，），222rB?4arA ?rA?0.414rA，a?22 四面体间隙：体对角线

1313处：（，，），4444rB?3a?rA?0.25rA 4

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