TEM laboratory exercise 1

Transcription

1 TEM laboratory exercise 1 From the TEM investigation we get combined imaging, diffraction and chemical information. Some of the experimental results obtained from the present TEM laboratory exercise are summarised in the following text. During the 4 hours you are in the laboratory (not on the TEM) you should analyse the diffraction results (negatives of the diffraction patterns will be put on light boxes in the lab and are marked A, B, C etc) and answer the questions in the text. Imaging: The sample consists of a matrix with particles and precipitates. Diffraction: Image A, B and C show diffraction patterns from the same area of the matrix. One row of reflections is the same in all projections. The approximate angles read from the goniometer are listed in the table: X Y A (neg. number 1,2) B (neg. number 3,4) 5 3 C (neg. number 5,6) 30-4 Table 1. Tilting angles x, y of the sample holder A B C 1. What is the total angle tilted between zone axis A and B and zone axis A and C? (hint: imagine x and y as coordinates of a line or vector, and find the length of the line/vector.) A B: A C:

2 2. Measure the length of three vectors on (at least one) of the diffraction patterns marked A, B or C (R 1, R 2 and R 3 ) and calculate the corresponding d-values. Share your data with your fellow students so that you all have data from all the diffraction patterns (A, B and C). L = Kλ. Fill out R, L and d in table 2. R L d HKL A R 1 A R 2 A R 3 B R 1 B R 2 B R 3 C R 1 C R 2 C R 3 Table 2. Measured and calculated data from diffraction pattern A, B and C. 3. What are the vector relationships between R 1, R 2 and R 3 in A, B and C? A: B: C: In cubic unit cells the planar spacing for a given hkl plane is given by 1/d hkl = (1/a)(h 2 + k 2 + l 2 ) 1/2 Cubic unit cells have a give ratio between the same sets of planar distances. 4. Calculate the ratios between the following planes given by their Miller indices HKL for a cubic unit cell: d 100 /d 110 : d 100 /d 111 : d 110 /d 111 : d 110 /d 200 : d 111 /d 200 : d 111 /d 220 : d 200 /d 220 : d 200 /d 311 : d 220 /d 311 :

3 5. Do any of the ratios correspond to ratios between planes in A, B and C? 6. Is it possible to index the diffraction patterns (A, B or C) without any prior knowledge about the unit cell? If so, fill out the column HKL in table If the unit cell is cubic, what is the unit cell dimension a? a = 8. Is the answer you found in 7 in agreement with the cell dimension of Al? (The crystal data of Al can be found in the appendix.) 9. Make a drawing of the reciprocal unit cell of an FCC unit cell (as Al). What are the conditions for the allowed reflections? (hint: can be found in international tables..) 10. Find the zone axis of A, B and C and indicate the location of the planes in the reciprocal space. Are the angles found in 1 in agreement with the drawing?

4 Two diffraction patterns from a particle is marked D. EDS results from particles in the sample is shown in the appendix. D1 D2 11. How can one find the concentration from the net counts from an element? A literature search for structures with Al, Mn, Fe and Si gives the data for ICSD# Measure the length of three vectors in one of the diffraction patterns from a particle (D) and calculate the corresponding d values. D R 1 D R 2 D R 3 R L d hkl R 1 /R 2 R 1 /R 3 R 2 /R Find the ratios between the d values and compare them with the ratios found under 4. Index the diffraction pattern if possible. 14. Is the diffraction pattern consistent with the Al,Mn,Fe,Si phase described by the data in ICSD# What is the zone axis?

5 Appendix A: Summarised results from the FindIt data base of search for Al and Al, Mn, Fe, Si *data for ICSD # Chem Name Aluminium, Structured Al, Sum D(calc) 2.68 Al1 Title Stoichiometry of U Al4 Author(s) Tougait, O.;Noel, H., Reference Intermetallics (2004), 12, Unit Cell 4.056(1) 4.056(1) 4.056(1) , Vol : 66.73, Z 4, Space Group: F m -3 m, SG Number: 225, Cryst Sys: cubic, Pearson cf4, Atom # OX SITE x y z SOF H Al a *end for ICSD # Aluminium

6 Aluminum Iron Manganese Silicide (17/3.2/0.8/2) *data for ICSD #52623 Chem Name Aluminum Iron Manganese Silicide (17/3.2/0.8/2) Structured Al17 (Fe3.2 Mn0.8) Si2, Sum Al17 Fe3.2 Mn0.8 Si2 D(calc) 3.71 Title The crystal structure of ternary alpha-(al Fe Si) Author(s) Cooper, M., Reference Acta Crystallographica (1967), 23, Unit Cell 12.56(2) , Vol: , Z: 6 Space Group P m -3, SG Number 200, Cryst Sys: cubic, Pearson cp138 Comments In other domains other positions for Al7 ( ), Al8 ( ), and Al9 ( ) (and Si7, Si8, Si9) Both domains together yield as average space group IM3- The structure has been assigned a PDF number (calculated powder diffraction data): Atom # OX SITE x y z SOF H Fe j Mn j Fe k Mn k Al e Al h Al j Al k Al l Al l Al f Al j Al k Si e Si h Si j Si k Si l Si l Si f Si j Si k *end for ICSD #52623

7 Appendix B: EDS results from small and large particles in the matrix Quantitative Results part Element Line Net Counts Net Counts Atom % Atom % Al K / / Si K / / Mn K / / Mn L 0 +/ Fe K / / Fe L 29 +/ Total

8 Quantitative Results part(1) Element Net Net Counts Atom % Atom % Line Counts Al K / / Si K / / Cr K 227 +/ / Cr L 0 +/ Mn K / / Mn L 49 +/ Fe K / / Fe L 0 +/ Total

9 Quantitative Results storpart Element Net Net Counts Atom % Atom % Line Counts Al K / / Si K / / Cr K 114 +/ / Cr L 31 +/ Mn K / / Mn L 1 +/ Fe K / / Fe L 81 +/ Ni K 205 +/ / Ni L 0 +/ Cu K 390 +/ / Cu L 0 +/ Total

10 Quantitative Results storpart(1) Element Line Net Counts Net Counts Atom % Atom % Al K / / Si K / / Cr K 142 +/ / Cr L 0 +/ Mn K / / Mn L Fe K / / Fe L 0 +/ Cu K 343 +/ / Cu L 0 +/ Total

11 Quantitative Results storpart(2) Element Line Net Counts Net Counts Atom % Atom % Al K / / Si K / / Mn K / / Mn L Fe K / / Fe L 104 +/ Ni K 221 +/ / Ni L Cu K 468 +/ / Cu L 39 +/ Ag L / / Ag M 0 +/ Total