Second test with answers[1]

8/7/2019 Second test with answers[1]

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MSE 3010 Fall 2001Second test, October 25th

MAX POSSIBLE SCORE 44 Points

1) Using the Wulff net and tracing paper that has been provided. Plot a pole at 30º N 50º Won a stereographic projection (on the tracing paper). Mark on the drawing the trace of this

pole. Plot another pole at 20º S and 30º E. Determine the angle between the two polesthat you have on your stereographic projection. Note that the north pole is at 90º N and 0ºE, the east pole is at 0º N and 90º E etc. 6 POINTS



Angle between poles is ~92 degrees.



2) Determine in order of increasing angle the line positions (2θ) and Miller indices (hkl) for the first three lines that are observable (not systematically absent due to lattice centering)from the following materials (assume that the radiation wavelength is 1.54056Å):( 9 POINTS)a) A simple cubic compound a = 8.26Å

hkl 100 d 8.26 2θθθθ 10.70hkl 110 d 5.84 2θθθθ==== 15.16

==== hkl 111 d 4.77 2θθθθ==== 18.59

b) A face centered cubic compound a = 8.26Å

hkl 100 d 8.26 absenthkl 110 d 5.84 absent==== hkl 111 d 4.77 2θθθθ==== 18.59hkl 200 d 4.13 2θθθθ==== 21.50hkl 210 d 3.69 absenthkl 211 d 3.37 absenthkl 220 d 2.92 2θθθθ==== 30.59

c) A primitive tetragonal phase a = 8.26, c = 8.00Å

hkl 100 d 8.26 2θθθθ 10.70hkl 001 d 8.00 2θθθθ 11.05hkl 110 d 5.84 2θθθθ==== 15.16

3) Make a scale drawing of the Ewald construction for (100) diffraction from a primitivecubic material a = 4.0Å assuming that the radiation wavelength is 1.00Å and keeping thea*-b* plane coincident with both the plane of the drawing and the plane of the incidentand diffracted beams. Use a ruler and compass to construct this drawing – do not do it

free hand!! Mark and label the reciprocal lattice points 100, 200, 010, 020, 110, and 220on this drawing. By how much would you have to rotate the crystal from the (100)diffraction condition to see (200) diffraction (you can do this by calculation you do nothave to measure from the drawing)? 8 POINTS





4) What is the smallest d-spacing reflection that you can measure using Cu K α (1.5418Å)radiation? 2 POINTS

0.77 Å

5) The limiting sphere for an experiment doubles in radius as the wavelength is halved.What happens to the maximum number of measurable reflections as the wavelength ishalved? (Does the number go up or down? If it does change, does the number double,

triple…???) 2 POINTS

The maximum number of measurable reflections increases by a factor of 8.

6) A cubic crystal with lattice constant 3.0Å contains two identical atoms per unit cell atpositions ¼,0,0 and 3/4,1/2,1/2.

a) Write down an expression for the structure factors of this crystal

F(hkl) = f exp(iππππh/2) + f exp(iπ(3π(3π(3π(3h/2+k+l)) = f exp(iππππh/2) [1 + exp(iπ(π(π(π(h++++k+l))]3 POINTS

b) What is the Bravais lattice for this material.

Body centered cubic 2 POINTS

c) Calculate values for the structure factors of the 100 and 220 reflections using the formfactor values given in the following table (note that you need to calculate the value of sinθ/λ for the reflections of interest and then look up the appropriate value of the formfactor in the table). 4 POINTS

(Sinθ)/λ f 0.0 30.00

0.05 29.390.1 27.920.15 26.140.20 24.330.25 22.540.30 20.770.35 19.130.40 17.420.50 14.51

For the (100) reflection sinθθθθ/λ λλ λ = 0.167, but reflection will be systematically absent!

For the (220) reflection sinθθθθ/λ λλ λ = 0.47, form factor will be approximately 14.5.

So F(220) = 14.5 x –1 x (1+1) = -29



7) Using the appended pages from the Hanawalt index, identify the phase in the sample that

was used to record the following diffraction data (indicate the PDF card number for thephase). 46-1045 8 POINTS

d/Å I4.25 163.34 100

2.46 92.28 82.24 42.13 61.98 41.82 131.67 41.66 21.54 91.45 21.38 6

1.375 71.372 51.288 21.256 3









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Second test with answers[1]