課程名稱︰物理冶金
課程性質︰必修
課程教師︰楊哲人
開課學院：工學院
開課系所︰材料系
考試日期（年月日）︰102.11.21
考試時限（分鐘）：180 min
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.(a) In an actual crystal, because of the more complex spatial arrangement
of atoms, the dislocation are complicated and often difficult to vasualize.
However, two terms can be used to completely describe the dislocation. Point
out these two terms. (2%)
(b) Explain why the intersection of two perpendicular screw dislocations can
lead to the production of a row of vacancies. (2%)
(c) What is the dark-field image of transmission electron microcopy ? (2%)
2.(a) It is possible to make a dislocation loop all of whose segment are pure
screw dislocation. Briefly explain why.
(b) Explain how to create a screw-compoment kink on an edge dislocation. (4%)
3.(a) Construct a 100 standard stereographic projection of a cubic crystal.
In this projection, show the great circles for {100} and {110} planes, and
the poles for {100}, {110} and {111} planes.
(b) Use the stereographic projection construct in Problem 2(a) to consider the
following procedure. Rotate 100 standard stereographic projection about its
north-south axis to obtain a 1 0 1 standard projection, and draw a
corresponding figure showing the poles of {1 0 0}, {1 1 0} and {1 1 1} planes
whose zone axis is [1 0 1]. In this case, what is the north-south axis for
rotation ? How much angle is rotated along this axis ?
(c) On the assumption that the electron beam of a transmission electron
microscope is parallel to [1 0 1] in a simple cublc (cubic-P) crystal, draw
a sketch of electron fiddraction pattern (according to a proportional scale).
(10%)
4.(a) Explain how to create the scondary electrons and characteristic X-rays,
during the interaction of a high-energy beam of electrons and a metallic
specimen.
(b) Briefly explain why (1 1 0) plane is not a reflection plane in FCC
metals. (5%)
5. Claculate the magnitudes of 1/6 [-1 0 1 3] in terms of lattice parameters,
a and c of hexagonal crystal. (5%)
6. From X-ray diffractometry of a FCC metal, point out the indices of the
planes, which are connected with the first seven respective diffraction peaks
(from low angle to high angle). (5%)
7. A pure metal crystal belongs to the cubic crystal system. From X-ray
diffractometry measurement, it is known that the first seven diffraction
peaks occurs at sin^2(θ) = 0.137, 0.275 ,0.412, 0.551, 0.688, 0.826, 0.962.
What is the Bravais lattice ? Calculate and answer the question. (5%)
8. An intrinsic stacking fault in FCC metals can occur by condensation of
vacancies on a (-1 1 1) plane. The partial dislocation loop, surrounding
the stacking fault, forms. Give the Burgers vector for this partial
dislocation loop. Is this dislocation with pure edge, pure screw or mixed
characteristic ? why ? (5%)
9. It has been well known that the stacking sequence of the close-packed plane
(1 1 1) in the FCC metals is ABCABC...... If the movement of an atom on a B
plane by a ahear 1/2 [-2 1 1] relative to the neighboring C plane, can this
atom remain in the B plane stacking ? Why ? Give your reason. (5%)
10. The schematic diagram is for representation of the DEebye-Scherrer or
power camera method. In this powder method, the wavelength λ remains
constant and a variation of Bragg's angle θ is obtained. Specimen is assumed
to be simple cubic and the spacing between (h k l) planes is can be expressed
as d(hkl) = a / (N^1/2) where N = h^2 + k^2 + l^2, and a is lattice constant.
Derive a formula to relate Bragg's angle θ with N value. (5%)
11.(a) What kind of stress field is associated with the screw dislocation ?
(b) Explain why a dislocation cannot end inside a crystal. (5%)
12. The force is extered on a straight screw dislocation (with Burgers
vector, b) by a ahear stress τ, which is parallel to the dislocation line
along the slip plane as shown in the following figure. Assume that L is the
length of the dislocation; Δx is the dislocation moving along slip plane
through a distance; A is the area of the slip plane. Calculate the force per
unit length on the dislocation, and also indicate the direction of this
force. (5%) (附上講義75頁第一個圖)
13. In the above figure, take the orientation of the screw dislocation snd
than use Burgers circuit to determine the Burgers vector. (請畫在上圖) Is it
right-hand or left-hand screw dislocation ? What is the relationship between
the Burgers vector and the orientation of this dislocation ? (5%)
14.(a) When a dislocation moves on its slip plane from one side of a crystal
to the other, what information can be specified by its Burgers vector ?
(b) What is an extended dislocation ? (5%)
15. Electron diffraction patterns represent the information of a reciprocal
lattice for a corresponding real lattice. Give two key points for the
relationship between reciprocal lattice and real lattice. (5%)
16. Use the Burgers vector notation for dislocation reactions to illustrate
that in an FCC metal a total dislocation with Burgers vector 1/2 [1 1 0]
breaks down into a pair of Shockley partial dislocations on (1 -1 1)
planes. (5%)
17. Repeat the above question for that in an HCP metal a total dislocation
with Burgers vector 1/3 [2 -1 -1 0] breaks down into a pair of Shockley
partial dislocations on the basal plane. (5%)
18. The srain energy of a dislocation normally varies as the square of its
Burgers vector. Show that on the basal plane in a HCP crystal the
disslocation of a total dislocation in the above question is energetically
feasible. (Assume that the stacking fault energy is negligible.) (5%)
19. The following figure shows two pure screw dislocations, one of which
contains a kink and the other a jog. Take the positive direction of the
lines as shown by the arrows. Both the kinked segments and the jogged segment
are pure edge dislocations.
(a) Redraw the above kinked dislocation and ahow on your drawing the location
of the extra plane of atoms for both kinked segments.
(b) Repeat (a) for the jogged dislocation. (5%)
(附講義72頁下面、73頁上面的圖)
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