Microscopy 101
analyses in the TEM has been taught the derivation for the camera constant,
λLdD= (1)
from Bragg’s law, where λ is the wavelength of the electrons, L is the camera length, d is the d-spacing of a reflection, and D is the distance on the pattern from the transmitted beam to that reflection. Students are taught that we don’t know either the accelerating voltage or the camera length accurately, but we do know the product of these two parameters for a known mate- rial. To determine λL, use a known material such as gold to measure the distance on the pattern from the (000) to a known reflection with a known d-spacing and multiply the two values. For digital images, λL can be measured in units of nm⋅pixels or Å⋅pixels. For example, if the size of the pixel elements of the camera is known, then λL can be converted to units of nm⋅cm. Soſtware packages universally calculate a precise relativistic wavelength for the accelerating voltage used and then calcu- late the actual camera length for the nominal camera length used. An easy way that soſtware packages calibrate the cam- era length is to superimpose a simulated ring pattern of the standard known material on top of an experimental ring pat- tern and adjust the camera length until the pattern matches, as shown in Figure 1B. DiffTools offers a gold calibration tool that works in the traditional method, where the reciprocals of the known d-spacings are plotted against the measured radius of the rings and fitted with a straight line as shown in Fig- ure 2. From equation (1), the slope of the line is the calibra- tion factor for the image in units of reciprocal d-spacing per pixel and is simply the reciprocal of the camera constant, λL. Tis approach has the benefit of giving a relative error associ- ated with the fit, which gives an indication of the reliability for the calibration. Tis method will be used below to determine the reproducibility of the microscope for measuring SAED
patterns using the polycrystalline gold sample. Note: for DM users, only the diameter of a single ring from a polycrystal- line sample or the distance of a known reflection from a spot pattern from a single crystal pattern is used to calibrate DM (Figure 3A). Notice that DiffTools calibrates the diffraction pattern in units of Å−1
, whereas units of nm−1 were chosen for
DM. Differentiating this way allows the user to know which calibration factor was used, DiffTools or DMs. If desired, the values determined by DiffTools can be used to replace the DM calibration values so that the confidence of the calibration fac- tor is known. To do this, take the reciprocal of the calibration, divide by the relativistic wavelength, λ(Å), and multiply by the camera pixel size in mm to get the value in camera length with units of mm. Tis is the value that can be used in the edit box of Figure 3B for changing the calibration manually in DM. Notice the slight discrepancy in calibration values between DiffTools (1.0320×10−3
Å-1 /pixel) and DM (0.010259 nm-1 /pixel), which is
a difference of 0.59%. DiffTools should be better because it sam- ples the entire intensity of the rings and more than just one ring.
Can SAED Results Be Trusted? Lattice parameter. Aſter all of this, it is fair to ask several
questions. How reliable is the calibration factor that is used to analyze a SAED pattern? How reliable are the measurements? How reproducible is a measurement? How oſten does the micro- scope require calibration? In preparing this article, a series of SAED patterns from a polycrystalline gold calibration stan- dard sample were collected at two nominal camera lengths, 20 and 25 cm. Prior to each SAED pattern, the sample was moved to a random area, the “Z” position adjusted to the standard focus position, IL1 focused, the pattern centered on the cross- hair, and then the long exposure and short exposure patterns acquired. Using calibration values that had been taken well over two years previously, DiffTools was used to calibrate the cam- era length, find the center of the pattern, perform a rotational
Figure 2: Screen capture of the Gold Calibration results from DiffTools. The slope of the line is the calibration factor measured in Å−1
⋅pixels−1
, which is the reciprocal
of the camera constant. With the accelerating voltage and pixel resolution of the camera known, the camera length for the microscope is calculated. In this example, the nominal 25 cm camera length is actually 34.8 cm.
2020 July •
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