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UNIVERSITY OF OSLO

Faculty of Mathematics and Natural Sciences

Exam in MENA3100 – Characterization of materials

Day of exam: 8th

June 2017

Exam hours: 14:30–18:30

This examination paper consists of 7 pages including the periodic table.

Permitted materials: Electronic calculator of accepted type, ruler, pair of

compasses, eraser

Make sure that your copy of this examination paper is complete before answering.

Upon censoring all sub exercises will be weighted equally. We reserve the right to

do some adjustments.

Exercise 1

a) Deduce Braggs’ law geometrically taking a primitive cubic lattice and (001) planes as

a starting point.

b) The cubic close packed (ccp) structure can be described with a cubic face centered

(fcc) lattice. With the above deduction as a starting point, show why reflections from

(001) are extinct for such an lattice.

Figure 1a) below shows the unit cell of NaCl. Cl- is located at the lattice points and

Na+ fills the octahedral holes. In figure 1b) you see several unit cells projected along the

[110] direction. The (111) plane, oriented perpendicular to the paper plane, has also been

drawn.

Figure 1a): The unit cell of sodium chloride. The larger spheres represent Cl-, and

the smaller Na+. Figure 1b): Several unit cells seen along the [110] zone axis. The position

of the (111) plains are indicated. The origin is in the center of the figure.

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c) For an element that crystalizes with cubic close packing, the reflection arising from

diffraction from the (111) plane is the strongest. Based on figure 1b), what can you

state about the relative intensity of the 111 reflection of NaCl. Will it be different

from that of a crystal that only has atoms at the lattice points?

Figure 2 shows a diffractogram of sodium chloride, NaCl, recorded using

monochromated CuKα1-radiation. The peak positions and the corresponding d-values are

given in table 1.

Figure 2: Diffractogram of sodium chloride recorded with CuK1-radiation.

Table 1: 2θ peak positions from figure 2 with the corresponding d-values.

2θ/o d/Å

27.372 3.257

31.710 2.821

45.454 1.995

53.876 1.701

56.484 1.629

66.241 1.411

73.082 1.294

75.307 1.262

84.013 1.152

d) Index (give the hkl-values) for the first five reflexes (those with the largest 2θ values)

and find the unit cell dimension, a, of NaCl.

Seltin is an alternative to ordinary table salt (NaCl) containing less sodium since

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some NaCl is replaced with KCl. KCl also have the NaCl type structure. The diffractogram

of Seltin is shown in Figure 3 below.

Figure 3: X-ray diffractogram of the product Seltin with main ingredients NaCl and KCl.

e) Has KCl got a larger or a smaller unit cell than NaCl? Give arguments for your

answer.

Exercise 2

Seltin, which is a mixture of sodium chloride and potassium chloride, is depicted in

Figure 4. The images are recorded in a scanning electron microscope using secondary

electrons. Image a) has been recorded in a high vacuum mode while image b) is recorded in a

low vacuum mode where water vapour is present in the specimen chamber. (Pressure being

60 Pa.)

Figure 4: Seltin depicted with secondary electrons (SE). a) Image recorded in a high

vacuum mode. b) Image recorded in a low vacuum mode.

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a) Discuss the reasons why the images look so different.

b) The image in Figure 5 has been recorded using back scattered electrons (BSE) (in

compositional mode, Compo). Is the crystal marked A NaCl or KCl? Give arguments

for your answer.

Figure 5: Seltin (NaCl and KCl) depicted using back scattered electrons. x indicates

the position of the electron beam during an EDS analysis. See the text for A.

c) We record an X-ray spectrum (EDS-analysis) while the electron beam is located in

the positon marked as x in Figure 5. In addition to chlorine, the spectrum shows both

sodium and potassium. One of the two is dominating. Does this imply that the crystal

we have analyzed actually contain ions of the other alkali metal? Argue for your

answer.

d) Describe the process behind the creation of characteristic X-rays.

Exercise 3

a) Make a drawing of a SAD pattern, free of choice, from NaCl. Index three reflections,

not located along the same row of reflections, and state which zone axis you have

drawn.

b) Where are the SAD apertures and the objective apertures located along the optical

pathway in a TEM.

c) How does one obtain TEM bright field (BF) and a dark field (DF) images. What kind

of contrast do they show?

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Exercise 4

Figure 6 and 7 are examples of electron energy loss spectra (EELS) of NaCl and

KCl, respectively, and show some of the characteristic signals one can observe.

a) What do the peaks A and B in Figure 6 represent and which effect does the specimen

thickness have on the signals?

b) What does the edges named Cl-L2,3 and K-L2,3 in Figure 7 represent?

Figure 6: Low loss EELS-spectrum of NaCl.

Figure 7: EELS-spectrum of KCl from 0–400 eV. The intensity in the spectrum is

generally dropping towards the right. In order to see details in the spectrum the Y-axis is re-

scaled after ~150 eV. The K-L2,3 edge is located at 293,6 eV and the Cl-L2,3 edge at 200,0 eV.

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Figure 8 shows the result of an analysis of KCl with the use of XPS where both photo- and

Auger electrons have been recorded.

Figure 8: XPS spectrum from the analysis of KCl with a monochomated Al Kα radiation.

c) What is the physical mechanism behind the creation of photo- and Auger-electrons?

Which of the peaks in Figure 8 are associated with the Auger-electrons?

d) What is the origin of the background in the XPS spectra? Why does the background

increase towards higher binding (lower kinetic) energies?

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Appendix 1