I. Goal:

1. To understand the basic operation of an xray diffractometer. To be able to describe the method's advantages in the study of materials.

2. To observe several diffraction patterns using this method:

a. to understand better the concept of Miller indices and diffraction directions

b. to understand how the concepts in part a can be applied in the study of polycrystalline films, epitaxial and single crystal films and textured samples.

3. To be able to distinguish among the following patterns:

a. The difference between a single crystal and polycrystalline (powder) sample

b. The difference between a polycrystalline sample and a textured sample.

c. The pattern for an epitaxial sample.

4. To understand the principles of sample alignment

4. Exercise-demonstration: Some advantages of high intensity xrays and four-circle diffractometers.

II. What you will need:

1. Your wam or glue account.

2. Access to an appropriate (or favorite) text editor.

3. EXCEL or any appropriate plotting program, capable of plotting in logarithmic scale.

At the end of this experiment, you will transfer the data to your account(s) in order to finish the analysis of the samples.

II. Procedure:

A. The procedure consists of:

1. A description of the xray diffractometer.

2.If available: measurement of a Si polycrystalline sample.

3. Measurement of a polycrystalline Cu sample : identification of peaks, d spacings and relative intensities.

a. Each group will analyze one sample, prepared using a different processing method.

b. At the end of the exercise, there will be an in-class discussion of the similarities and differences between the samples.

4. Measurement of an epitaxial film.

a. Alignment and calibration using a single crystal LAO sample.

b. Determination of the peaks present (or absent).

c. If time allows: measurement of a rocking curve contour.

Note: All of us will meet for the introduction and the lecture-demonstrations (goals 1, 4 and 5). The group will subdivide in subgroups of four for the measurements (subdivision TBD).

B. Steps:

1. The Xray diffractometer - summary.

The machine we will use in this exercise is a Rigaku 18kW rotating anode source. The machine ranges in power from 20kVx10mA to 300kVx60mA. This machine is capable of analyzing very small small samples and thin films. The source is a water-cooled Cu anode which emits X-rays with a wavelength of 1.54Å. The machine is equipped with a four-circle diffractometer, capable of making a 3-dimensional diffraction analysis of the sample. The four axes consist of the 2q arm and q or rocking curve axis, the f (w) or axial angle axis, and the c angle. In this exercise, the q and f axes are the same. Note that because of the extra axes and flight paths used, this machine does not have in general the angular range in more typical diffractometers.

A(n electron) current which excites a target produces entire xray spectrum corresponding to the particular target. This spectrum depends on the atomic structure of the particular target. This strongest lines of this "white radiation" spectrum can be separated with the use of a monochromator. Selection of this line is based on Bragg's law and depends on the structure of the monochromator used.

The width (or resolution) of the lines depends on the monochromator used and on the so-called "mosaicity"" of the crystal. The linewidth determines the degree of resolution one can achieve with the diffractometer. High resolution is useful in the analysis of small strains and/or small changes that occur as a result of a phase transformation. A lower resolution results in a higher beam intensity, which allows the study of very small samples. In analyzing small samples, one must compromise between intensity and resolution.

The monochromatized beam illuminates the sample. The diffracted beam is recorded either directly by a detector or with the use of an analyzer crystal. When an analyzer is used, the detector is oriented at the angle corresponding to the Bragg angle of the crystal used.

2. Calibration using a single crystal LAO sample. This operation will be performed at a power of 30kVx45mA. Observe the steps the instructor takes to set this power.

This part will serve as a demonstration of the operation of the machine. In order to save the data, the instructor types

newfile "name" (for better reference, we will name the files 310x01 where x=a, b, c, ...)

Sample alignment

a. The instructor will place a sample of LAO in the diffractometer. The sample will be moved to the angle position 2q = 1°, f = 0.5° (why?). Remember that the phi and theta axes coincide in the geometry used.

b. The LAO sample is a monocrystalline sample oriented along the (001) direction. This compound is cubic with a lattice spacing of 3.79Å. Based on your reading, what does this mean? Which diffraction lines would you expect to see?

c. The sample will be rocked about 0.5°, using the command,

dscan phi -5 5 50 2

(Note: the operating software varies from diffractometer to diffractometer. We will use only those commands we need to obtain our information. You will obtain further details on specific software if you work with a particular machine).

Where is the peak? Is it at 0.5°? If not, what does this mean?

d. (If the peak is _ 0.5°) The instructor will move to the highest intensity position by executing the command,

mv phi "maxvalue"

and will repeat the rocking curve taking smaller steps (eg, dscan phi -1 1 20 2).

e. Once the angle of maximum intensity is located, the instructor will "redefine" it as 1/2 (1°) by executing the command,

set phi 0.5°.

Why (use the figures again as guide)? This finishes the alignment of the sample.

Calibration:

f. Determine at which angle(s) one expects to see a diffraction peak based on the lattice parameter and the X-ray wavelength of 1.54Å. The instructor will now perform a diffraction scan in the vicinity of these angles by executing the command,

a2scan tth initangle finalangle phi initphi finalphi steps 2.

Note again the position of the maximum intensity in twotheta: this will be your calibration angle.

Note on calibration: the diffractometer may be slightly off-center and the angle will not coincide with the ideal ones as determined from Bragg's law. In order to correct for this, a (bulk) sample of known structure is measured. This ensures more accurate measurements of unknown or "treated" samples that deviate from the bulk value.

3. Measurement of a polycrystalline (powder) Si sample. We will use a Si standard to observe the pattern from a powder sample.

One can use standard to calibrate a particular diffractometer.

For this part, you will need the Si diffraction card for this measurement.

a. The instructor will mount a sample of Si on the four-circle diffractometer and will type the command

a2scan tth initangle finalangle phi initphi finalphi steps 2,

using the lowest observable angle as a guide (where can you obtain this?).

4. Measurement of a polycrystalline (textured) sample of Cu.

You will need the copy of the Cu diffraction card you looked up at the library.

The instructor will place a polycrystalline sample of Cu in the diffractometer.

a. Based on your card, and with the instructors aid, set up a scan to look at the observable peaks (note: in the particular configuration used, this machine does not measure beyond 70° due to the flight paths and chi arm). How many peaks do you expect to see? Mark down the scan number for the subgroups first file (important!).

One member of the group executes the command,

a2scan tth initangle finalangle phi initphi finalphi steps 2

b. Mark the positions of the peaks. Compare their relative intensity. How do these intensities compare with that expected from the card.

c. Note that the measurement above was done without aligning the sample in phi. Do need to do this with this sample? Why?

d. To get experimental proof of your answer above, move to 1° and 0.5°, and execute the rocking curve given in part 2 above (a second member of the group should execute the command). Note the scan number in your notebook.

e. Based on your result in d, decide if you need a broader or narrower rocking curve. A third member of the group will repeat the rocking curve based on your decision. Note the scan number in your notebook.

f. Describe your results in d and e. Compare it with the result for the LAO sample above.

(Optional: g. If the rocking curve has a shape that can be "centered", re-define the center as 0.5°. Repeat the scan in a above. Note any differences, similarities).

Subgroup 2 will repeat the procedure above, marking the appropriate scan numbers in their notebooks).

5. Measurement of an epitaxial film.

a. An epitaxial film is a single crystal grown on top of another single crystal. In this part, you will measure the diffraction pattern of a tetragonal ferroelectric film. The instructor will provide the lattice spacings. Based on these lattice spacings, which diffraction lines you expect to see and where? Make note of these.

b. Based on these, determine an appropriate diffraction scan with the instructors assistance (you may want to subdivide the scan in two). Make note of the regions of interest.

c. This is a single crystal sample. Align it with the instructor's help and follow the steps described in part 2. Note the scan numbers, the position of maximum intensity and any angle resetting you may need.

d. Once the sample is aligned, execute the command for the diffraction scan. Note the position of the peaks, and their relative intensities.

e. This sample is grown on LAO. Can you see the peak from LAO in your scan?

1. Please read the general instructions on the format of the report

2. Your results should include:

a. A table listing the positions (d-spacings) and relative intensity of the Si standard.

b. A table listing the positions (d-spacings) and relative intensity of the Cu textured sample corresponding to your group.

c. A Figure showing the Cu textured sample diffraction scan

d. A Figure showing the PLZT film diffraction scan

e. A short discussion on how your group's patterns differ from the other's.

3. Please include your group with your name.