X-RAY DIFFRACTION - Physics 122B122.physics.ucdavis.edu/sites/default/files/files/X Ray Diffraction... · alkali halide crystals using x-ray diffraction methods. In the process of

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Carnegie Mellon University 33.340 Modern Physics Laboratory

X-RAY DIFFRACTION

Last revision: S. Garoff And B. Luokkala, 1/2012

I. OBJECTIVE The objective of this experiment is to measure the lattice constant and crystal structure of several alkali halide crystals using x-ray diffraction methods. In the process of measuring these crystal structures, you will become familiar with the principles of x-ray diffraction, the primary method of determining the atomic scale structure of condensed phases of matter. II. EXPERIMENTAL PRECAUTION X-rays are hazardous and the utmost care must be exercised when using the apparatus. You must receive safety training before you begin the experiment. NEVER EXPOSE ANY PART OF THE BODY TO THE DIRECT X-RAY BEAM. Always make sure that the shielding is in place before turning on the high voltage. Consult your instructor for the shielding requirements. Use the portable Geiger counter to measure background levels with the beam off. Then verify that all potential radiation leaks which could exist while the beam is on have been eliminated. III. CRYSTAL STRUCTURE Attached to the back of this handout are excerpts from Introduction to Solid State Physics by C. Kittel (8th and 3rd editions, Wiley & Sons) which will give you the needed background for the experiment. Go to the library for clearer versions of the figures. Study the following pages and answer the questions. A. 8th ed. pp 2-11: How is the structure of a crystal described by a lattice and a basis? B. 8th ed. pp 13-15: What are the structures of simple cubic, face-centered cubic, and body-centered cubic crystals? C. 8th ed. pp 11-13: How can we describe the orientation of planes and location of atoms using Miller indices? D. 3rd ed. pp 37-43 How can we detect Bragg diffracted beams using multi-wavelength or single wavelength sources? How can we detect Bragg diffracted beams from single crystal samples or powders? E. The derivation of the location of diffracted beams is an interesting application of the principles of interference of electromagnetic waves. You study the full derivation by getting Kittel from the reserve shelf in the library. The key result you need is that:

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( ) θλ sinl,k,hd2=

where λ is the wavelength of the X-rays, θ is the angle between the incident and scattered x-ray beams, and d(h,k,l) is the distance between planes with Miller indices (h,k,l). F. 3rd ed. pp 62-65 What is the structure factor? For FCC, BCC, and simple cubic, work out the angles for which there are absences due to the structure factor. IV. X-RAY TUBE SPECTRUM The total spectrum of x-ray radiation emitted by an x-ray tube consists of a discrete line spectrum, superimposed on a continuum (see fig 7 on p40 of the Kittel excerpt). The continuum results from Bremsstrahlung processes occurring when beam electrons scatter from nuclei of the atoms in the anode. Whereas, inelastic scattering of the beam electrons with bound electrons produce the discrete spectrum. If a beam electron transfers sufficient energy to eject an inner shell electron, the excited atom will emit members of its discrete x-ray line series as it returns to its ground state. The ejection of a bound electron can be viewed as the creation of a spin-1/2 hole. The x-ray tube used in this experiment has a Cu anode whose K wavelengths are Kα=1.5418Å, Kα1=1.540562Å, Kα2=1.544390 Å, Kβ1=1.392218Å. The Kα wavelength represents a weighted average where Kα1 receives twice the weight of the Kα2. In the experiment, the Kβ line is filtered out. V. THE EXPERIMENT Using the automated diffractometer, obtain θ-2θ scans of LiF, NaCl, KCl, and CsCl, Al powders.

All these materials are cubic. Be sure you know whether your plots are using θ or 2θ on the

abscissa.

Deduce the Miller indices of all the prominent peaks and find the structure and lattice constant of

each material. Estimate the angular errors due to the geometry of this method. Can you account

for the peak widths? What are the associated errors on the lattice constants? Look up the

structure and lattice constant of LiCl and LiBr (we cannot run these samples because the

hygroscopic and degrade very rapidly). How do the structures of this series of alkali halide

crystals compare?

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Use your time wisely: As scans are running on the machine and work on analysis as the scans are

running.

VI. HINT FOR INDEXING THE PATTERNS

For the Bragg peaks of cubic crystals, show that

sin2θ1

sin2θ2

=h1

2 + k12 + l1

2

h22 + k2

2 + l22 .

Now make master table in order of increasing h2 + k2 + l2 (which is the same thing as increasing

θ) for all values of h,k,l you may see in your experiment. Now see if you can match the ratios of

sin2θ i

sin2θ i+1

from your data to a column or row on your table. You need to keep in mind two things:

(a.) You do not know the index of your peak with the smallest θ. (b.) Different types of cubic

crystals have different "absences" as you showed in the questions you answered.

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Operating Procedure: Siemens D-500 X-ray Diffractometer

Figure 1. Apparatus Schematic

Radiation Background Checks and Surveys Before powering up the x-ray diffractometer, use the radiation survey meter to check the normal background radiation level. When the x-ray unit has been powered up, and high voltage is on, use the survey meter to confirm that radiation levels in the vicinity of the diffractometer cabinet remain at background level. Radiation levels in the lab and around the x-ray cabinet should be checked with the survey meter at the start of your work for the day, at least once during the course of your work, and just before you shut down at the end of your work. X-ray Use Log Book Sign-In Before beginning your work for the day, sign in on one of the sheets in the X-ray Use Log Book.

Diffractometer Cabinet and Interlocked Window

Main Power & X-ray High Voltage Control Panel

Detector HV & Control Panel

Goniometer Control Panel

MDI Databox Interface

Computer

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Starting up the Diffractometer and the MDI Databox Interface NOTE: The diffractometer and the MDI Databox Interface must be turned on BEFORE starting up and running the computer data acquisition software.

1. Turn on the water supply at the wall behind the diffractometer by rotating the yellow valve handle until it is parallel to the water pipe. (The water filter may drip a bit. Don’t be alarmed.)

2. Check that both the Current and Voltage knobs on the X-ray High Voltage Control Panel

are set to minimum (5mA and 10kV). The three square buttons on the Main Power panel have the following functions:

• The left-most (red) button is the Power Off button. • The middle (yellow) button is for Main Power, X-ray tube filament, and

diffractometer cabinet lighting • The right-most (green) button is the High Voltage Ready/On button

3. Press and release the middle (yellow) button. You will hear a brief warning buzz, which

should stop when the button is released and the water begins to flow. The diffractometer cabinet lights will come on, and the green light in the right-most square button will come on, indicating that the High Voltage is ready to be turned on (but don’t turn it on yet!).

4. Switch on the MDI Databox Interface (small box between diffractometer and computer).

Inserting and Positioning the Sample WARNING: Samples are to be inserted or removed from the holder only with the shutter closed and the High Voltage turned OFF. The samples are held in place by three pins on a triangular platform, at the center of the goniometer. See Figure 2 for sample holder details.

1. Open the interlocked window on the front of the x-ray diffractometer cabinet. 2. Carefully slide the sample all the way into the sample holder, in the center of the

goniometer, on top of the three pins, until the sample stops against the back of the holder. 3. Lock the sample into place by pressing up on the square pin in the center of the bottom of

the sample holder. 4. To release the sample, press up on both of the side tabs on the bottom of the holder.

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Insert Sample here

Figure 2. Sample Holder Details

release release lock

Manually synchronizing the goniometer angles

1. Locate the small toggle switch labeled Manual Control and Computer Control on the Detector HV and Control Panel (Figure 1), and set this switch to Manual Control.

2. Look through the diffractometer cabinet window and check the angle readings in the base of the goniometer, below the x-ray sample stage. The angle readings should be within the ranges 5˚ < θ < 65˚ and 10˚ < 2θ < 130˚. If either θ or 2θ is outside these limits, ask your instructor for assistance before proceeding.

3. At the Goniometer Control Panel press synchron, followed by 2θ/θ, followed by Manual. If the current setting for θ is above 40˚ , press and hold the small black button labeled with double left arrows (←) to bring θ into the range 20˚ < θ < 40˚. (If θ is below 20˚, use the right arrow button.) The press the STOP button.

4. To synchronize θ and 2θ, press synchron, followed by 2θ/θ, followed by set. The θ and 2θ motors will move until they read 20.000 and 40.000. If the synchron does not respond (red indicator light does not come on), try pressing the STOP button (below and to the left, on the same panel), and then press the synchron and set buttons again.

5. Flip the small toggle switch on the Detector Control panel from Manual Control to Computer Control.

Turning on and Setting High Voltage WARNING: Be sure that the current and voltage knobs are set to their fully counterclockwise positions (5 mA and 10 kV, respectively). Attempting to turn on the high voltage if either of these knobs is not at its minimum setting may result in complete system shutdown.

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1. Press and release the green-lighted square button on the High Voltage Control Panel.

You should hear a single loud click. The current and voltage meters on the control panel will fluctuate briefly, and then settle down to about 5 mA and 15 kV.

2. Slowly turn up the voltage control knob to the recommended setting of 40 kV. (Slowly means roughly 5 kV at a time, waiting for about 2 seconds in between increments to allow the voltage to stabilize.)

3. Slowly turn up the current control knob to the recommended setting of 30 mA. Opening and Closing the Shutter NOTE: The Automatik knob, on the lower right corner of the goniometer control panel, should be in the O position (off). Otherwise, the shutter may open automatically when the interlocked window is closed. The shutter is controlled by means of the buttons on the goniometer control panel, labeled open and shut. The shutter is interlocked to the leaded plexiglass cabinet window, in front of the diffractometer. When the window is opened, the shutter will close automatically. Be sure to open the shutter before starting a scan. Check the radiation levels in the lab and around the cabinet with the survey meter, to be sure that the levels are at typical background when the high voltage is on and the shutter is open. Alignment This unit does not require the user to perform any alignment procedure. Bypassing The user is not permitted to bypass the interlocks for any reason. A bypass procedure may only be performed by the Principal Investigator or an authorized x-ray service technician. Starting the Detector The detector power unit and associated electronics are located in the front panel, to the right of the Main Power Control Panel. In ordinary operation, the detector should be on and ready to go, as soon as the main power is turned on. Check to be sure that the LINE ON switch, at the far right corner of the panel, is in the ON position, and that the detector high voltage switch, labeled contr., is in the “up” position (down is off, and straight out is standby). The detector voltage should be set to 1000 volts, as indicated on the meter.

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Starting the data acquisition program and setting the detector angle

1. Start up the computer (if it isn’t already up and running). 2. Double-click on the MDI DataScan5 shortcut icon, on the computer’s Desktop. 3. When the DataScan5 window appears, click “Control” in the top menu bar, and choose

“Open MDI Databox Dialog” from the menu of options. 4. Type the current value of 2θ into the Detector Angle window, and click “Set.” 5. Click “Yes” to confirm the setting. Then close the dialog window.

Setting up a scan

1. Click “Scan” in the top menu bar, and choose “Routine scan” from the menu of options. 2. You can run one of the pre-programmed scans, or modify an existing scan by double-

clicking on one of them. 3. Set the starting and ending values for 2θ within the limits 10˚ ≤ 2θ ≤ 130˚. 4. The default increment for 2θ is 0.1 degree, but can be set as low as 0.01 degree for a

detailed scan over a narrow range of angles. 5. A dwell time of 1 or 2 seconds is typical, but may be set longer for better counting

statistics. Running a Scan

1. When you have set the desired scan parameters, click “Start Scan”. 2. You will be prompted to set the current goniometer angle. WARNING: the computer

will display the last angle reading of the last scan that was completed, and not necessarily the actual current angle. DO NOT CONTINUE until you have typed in the current angle reading for 2θ.

3. Double check to be sure that high voltage is on and the X-ray shutter is open. 4. Also double check to be sure that the proper current and voltage have been set on the x-

ray tube. Do not attempt to change current or voltage once the scan has begun. Voltage spikes may cause errors in communication between the controller and the computer, resulting in system hang-ups.

5. When you are sure that the system is ready to take data, click START SCAN. If all is well, after a delay of a few seconds, the scan information is transmitted to the Siemac V, and the scan will begin.

Saving Your Data When the scan is complete, do a right-click on one of the data points. Select “data points” from the pop-up menu, and save the data as a text file. The file will include a few lines of header information, followed by the actual data. The data are arranged in three columns: data point number, 2θ (decimal degrees), and the number of x-ray counts accumulated at each angle. The text file can be opened with Microsoft Excel, using the tab-delimited option.

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Removing or Changing Samples

1. Close the shutter. 2. Slowly turn the x-ray current knob down to minimum. 3. Slowly turn the x-ray voltage knob down to minimum. 4. Turn off the high voltage by pressing the square yellow power button. 5. Open the interlocked cabinet window to remove your sample. 6. To release the sample, press up on both of the side tabs on the bottom of the holder (see

Figure 2). 7. If you are running another sample, follow the procedures as already outlined above.

Shutting Down for the day If you are finished for the day, shut down the system as follows:

1. Save your last data set as a text file. Then close the DataScan window on the computer. 2. Turn off the MDI Databox Interface unit. 3. (If you haven’t done this already, reduce the X-ray current and voltage to minimum, and

press the yellow panel button to turn off the High Voltage supply.) Press the red POWER OFF button on the X-ray Main Power Control Panel to shut down the power.

4. Turn off the water supply at the wall, behind the diffractometer, by rotating the yellow valve handle until it is perpendicular to the water pipe.

5. Just in case you forgot at the beginning of the day, be sure to sign in on one of the sheets in the X-ray Use Log Book




























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X-RAY DIFFRACTION - Physics 122B122.physics.ucdavis.edu/sites/default/files/files/X Ray Diffraction... · alkali halide crystals using x-ray diffraction methods. In the process of