Microscopy 101
Table 1: SAED results for 20 cm camera length. Au d-spacing
Area # 201 202 203 204 205 206 207 208 209 210
Avg=
Std Dev= Rel Err %=
Measured Au d111
2.3730 2.3656 2.3620 2.3620 2.3620 2.3584 2.3620 2.3584 2.3332 2.3296 2.3566 0.0139 0.59%
(Å)
2.3544 Å %∆
0.79 0.48 0.32 0.32 0.32 0.17 0.32 0.17 0.90 1.05
Cam Len (cm)
27.254 27.299 27.316 27.352 27.371 27.384 27.364 27.420 27.717 27.751 27.423 0.171
0.62%
Table 2: SAED Results for 25 cm camera length. Au d-spacing
Area # 401 402 403 404 405 406 407 408 409 410
Avg=
Std Dev= Rel Err %=
Measured Au d111
2.3578 2.3550 2.3578 2.3521 2.3521 2.3492 2.3521 2.3464 2.3464 2.3521 2.3521 0.0040 0.17%
Cam Len (cm) Cal (Å−1
10 Avg=
Std Dev= Rel Err %=
28.221 27.848 27.897 27.910 27.990 27.875 27.856 28.046 27.918 27.242 27.880 0.251
(Å)
2.3544 Å %∆
0.14 0.03 0.14 0.10 0.10 0.22 0.10 0.34 0.34 0.10
Cam Len (cm)
34.595 34.616 34.605 34.661 34.715 34.693 34.691 34.737 34.732 34.727 34.677 0.055
0.16%
Table 3: Calibration reproducibility (20 cm) check. Area #
1 2 3 4 5 6 7 8 9
1.2719×10−3 1.2899×10−3 1.2864×10−3 1.2868×10−3 1.2837×10−3 1.2881×10−3 1.2892×10−3 1.2805×10−3 1.2868×10−3 1.3186×10−3 1.2882×10−3 1.19×10−5
0.90% 0.93% 2020 July •
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Cal (Å−1
DiffTools Au Calibrator Factor Results /pix)
×10−3 1.3174 1.3158 1.3152 1.3130 1.3111 1.3116 1.3115 1.3090 1.2949 1.2943 1.3094 0.0082 0.62%
err % %∆ From Avg %∆ From Old 0.10 0.09 0.08 0.11 0.11 0.07 0.12 0.10 0.10 0.11
0.61 0.49 0.44 0.28 0.13 0.17 0.16 0.03 1.11 1.15
0.82 0.70 0.65 0.48 0.34 0.37 0.37 0.18 0.90 0.95
Cal (Å−1
DiffTools Au Calibrator Factor Results /pix)
×10−3 1.0370 1.0373 1.0366 1.0357 1.0337 1.0348 1.0347 1.0339 1.0335 1.0333 1.0351 0.0015 0.15%
err % 0.13 0.09 0.10 0.17 0.12 0.09 0.12 0.10 0.10 0.08
0.19 0.22 0.15 0.06 0.13 0.02 0.03 0.11 0.15 0.17
%∆ From Avg
%∆ From Old
0.13 0.15 0.09 0.00 0.19 0.09 0.10 0.17 0.21 0.23
For the 20 and 25 cm camera lengths, Δd111
/pix) err % R2 0.11% 0.99999 0.12% 0.99999 0.09% 0.99999 0.10% 0.99999 0.10% 0.99999 0.09% 0.99999 0.10% 0.99999 0.10% 0.99999 0.10% 0.99999 0.12% 0.99999
and 0.0012, respectively. Since the calibration factor, CL
are 0.0015 , will
decrease as the camera length increases, the error associated with positioning of the peak will improve for a given (hkl), as the tables show. Equation 4 indicates two things should be done experimentally to improve the measurement of a sample’s lattice parameters: the highest camera length and the largest reciprocal lattice vector, that is, largest possible index in the pattern, should be used. However, care must be exercised in using too high a camera length because then fewer peaks are available to determine the calibration factor in the linear fit- ting routine, resulting in a higher uncertainty. Error in “Z” height positioning. Part 1 of this series of
articles emphasized the importance of having the sample at the correct height with the microscope at standard focus and IL1 grabbing the back focal plane. How critical are these param- eters? To investigate, a series of ten SAED patterns at different “Z” height positions were acquired, and the Au111
d-spacings and 51
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