An accurate knowledge of the electron source point is essential for the interpretation of electron backscatter diffraction patterns. With the increasing adaptation of high angular resolution electron backscatter diffraction, HR EBSD, , for strain measurement, it has become even more important. To achieve the 1 part in 10000 precision possible in HR EBSD where a pattern from a strained part of a crystal (or grain) is compared with that from an unstrained region, the relative positions of the electron source points for the two patterns has to be known to better than 1 part in 1000. When patterns are recorded at the higher resolution of conventional cameras used for EBSD detection, 1000×1000 pixels for example, this corresponds to determining the relative positions of the pattern centre to better than 1 pixel and any change in source point to recording screen distance with equivalent precision.
EBSD Pattern Centre
One EBSD camera pixel typically captures an area of 35μmx35μm on the specimen surface.The distance between the two pattern centres is normally assumed to be that calculated from the x and y shifts generated by the SEM scan generator. However, even though the SEM can move the e-beam by just a few nano metres per step, there are errors in the true step size due to small differences, on a day to day basis, of the actual accelerating voltage and of the scan coil and electron lens power supplies. Fortunately, these errors only become large enough to influence EBSD work at lower magnifications and when large area scans are attempted. For example in a scan of 500ìm x500ìm with a 10μm step and an error in the beam step size due to the above causes of only 0.1μm, the error after 30 steps would be enough to result in a detectable difference between the measured strain and the true strain. By the end of each line of the scan the error would result in a serious discrepancy of the measured strain.
Scanning errors also contribute to this problem. The specimen is normally tilted by 600 to 700 from the horizontal. This means a rectangular beam scan on a horizontal specimen distorts into a trapezium on a tilted sample with the upper scan line being shorter than the lower scan line. (The upper scan line for a tilted specimen is actually the last line of the scan). Thus unless the SEM manufacturers have taken this distortion specifically into account, the assumed beam shift will be different from the actual for all scan lines other than that at the centre. Another consequence of the tilted sample is that at very low magnifications the scan from top to bottom may be skewed as a consequence of the different paths taken by the electrons passing through the objective lens. These errors apply equally to standard EBSD experiments as well as to HR EBSD but they are more important in HR EBSD as they can give rise to anomalously large strain values. In conventional EBSD the errors are manifest only in distorting the image. Grain size and grain shape measurement errors will thus be introduced, but unless the scan shape is known the errors pass unnoticed.
Figure 1. Schematic of single aperture nose cone with prototype design
Figure 2. Left, Geometry associated with single aperture nose cone. Right, Projection associated with single aperture nose cone
We have recently investigated an attachment developed by BLGVantage that can detect and allow correction of the major errors caused by the above scanning problems. Its design is based on a concentric double aperture system originally developed by Venables et al. , but modified by offsetting the forward aperture to optimise the specific geometry needed in EBSD to maximise contrast in the patterns. A schematic is shown in Figure 1 and a photograph of a typical assembly is shown to the right.
With the e-beam positioned at point BP1 on the specimen the cast shadow of the aperture appears as a circle on the phosphor screen with centre at SC1. The centre of the shadow can be found by analysis of the shadow perimeter. The points BP1, the centre of the aperture, AC, and SC1, all fall on a straight line, as does the projection of these points onto the phosphor screen, PC1, CC, SC1. The projection of the e- beam onto the screen is of course the diffraction pattern centre.
As the e-beam moves across the sample to SP2, the shadow circle centre moves in the opposite sense so that a new line can be drawn on the phosphor connecting the three points, PC2, CC and SC2. It follows that if the point CC is known and the shadow circle centre determined then the pattern centre can be found. The geometry is shown in Figure 2 (left). In the figure, D is the distance aperture to phosphor screen and Z, the e-.beam to screen distance. Then
(SC – CC) / (SC – PC ) = D / Z
From which the tracking of the movement of pattern centre PC can be found, provided D Z and CC are known. All three parameters D, Z and CC are found in a calibration experiment. The value of Z is found through the equation
Z = Rc D / (Ra – Rc)
Here, Rc is the radius of the shadow circle and Ra the radius of the aperture. Again if D and Ra are known, Z can be determined because Rc is a measured quantity. The terms D and Ra are manufacturing parameters. The point CC has to be determined by calibration. In fact, all three parameters can be determined in the same calibration procedure as shown next and we do not need to rely on high manufacturing tolerances.
The e-beam is positioned at two or more points on the sample surface and the shadow circle centres determined. At each point the points PC have to be determined. Two methods to do this have been investigated. One was to place two or more steel ball bearings between the e-beam position and the phosphor screen, (Dingley and Biggin 1984). The spheres cast elliptical shadows on the screen the major axes of which all intersect at the pattern centre. Z is then found through the equation
Where a & b are the major and minor axes of the ellipse and d, the distance ellipse centre to pattern centre. The PC and Z values can be found using this method with an accuracy of around 1 pixel.
The calibration only has to be done once. When finished and tested as in Figure 3 the balls are removed and EBSD work for orientation and phase studies proceeds as normal. When HR EBSD is to be used, then to minimize scanning errors, the aperture shadow radius and centre are measured at each point of the scan. This is fully automated as is the calculation from these measurements of the PC and specimen to screen distance.
Figure 3. Between pattern centre and specimen to screen distance as determined by Balls method and back calculation from aperture shadow
The authors wish to thank the Interface Analysis centre at the University of Bristol for use of one of their SEMs to test this application.