Pattern size
The term “size” is often used in different ways. Rarely the absolute size of the image is actually meant, but often and misleadingly the image resolution, i.e. the number of pixels with which a signal is described.
In the case of EBSD, however, the size of a pattern actually means the angular range that appears on the image. Hence the explicit emphasis on wide-angle Kikuchi patterns that can be analyzed in CALM or also during pattern indexing.
Depending on the application, this captured sector can then additionally be stored in an image either with high angular resolution (for so-called HR-EBSD investigations), or highly binned with low angular resolution per pixel (for common standard orientation measurements).
Only perfect patterns can provide an optimal determination of the lattice parameters. However, even from simulated patterns the used lattice parameters is not perfectly extractable in a simple way. There are several reasons why not.
The “optimum” pattern quality
The optimum pattern quality also depends on the application. For standard orientation measurements, this usually means the signal with which the phase and crystal orientation can just be determined. For misorientations to be derived, this is no longer sufficient, since the smallest changes must be detected.
In contrast, for lattice parameter determination it describes the best possible signal-to-noise ratio with little effort in order to be able to use low band intensities.
A high image resolution seems very logical to increase measurement accuracy in Kikuchi patterns. But this is only apparently benefitial, because
- Kikuchi band edges will not get sharper by using higher resolution images.
- The position of the Bragg angle is not obvious as, for example, in X-ray diffraction by peak maxima.
CALM uses the extrema positon of the 1st derivative of the band profile to estimate the Bragg angle. - The 1st derivatives deliver different lattice parameters for each band.
Lattice parameter distribution derived from about 200 bands discovered in a simulated Kikuchi pattern of FeSi (ao=4.485Å). For this analysis even perfectly symmetric profiles from the master pattern were used (PC and all traces are perfectly known).
Nevertheless, Δa/a shows a spread. The derived bandwidths are systematically too narrow ( Δa/a>0).
With decreasing θ, Δa/a often increases so that only bands between 2°< θ <4.5° (black dots) are considered.
It follows a mean lattice parameter of a= 4.57Å and a double standard deviation of 2σ=±0.04Å.
Band edges are so blurred that moderately binnned patterns do not give significantly worse results compared to their high-resolution counterparts.
If one additionally considers the difficulties associated with experimental imaging, the tendency for image distortion is significantly higher with high-resolution images due to the longer acquisition times and possible static charging, not to mention the expected contamination from the longer dwell time and thus further blurring of the signal.
Therefore, binned patterns, e.g. averaged 400×300 pixel patterns, are often more suitable than high-resolved but noisy Kikuchi patterns.