Quality metrics

One method of obtaining more information from diffraction patterns is the calculation of quality metrics to evaluate how well a sample is diffracting. The following paragraphs give the definition of common quality metrics and summarize some of their applications published in the literature.


From an EBSD point of view, quality is a parameter that quantifies the crystallographic uniformity within the interaction volume. Different features of a diffraction pattern can be evaluated to assess its quality: intensity, contrast, sharpness of Kikuchi bands, noise level, etc. As such, different quality metrics can be designed to highlight these features for each diffraction pattern in a mapping. The metrics evaluate the quality of a diffraction pattern by calculating a numerical value representing the amount, strength or intensity of one or many specific features. An interesting parallel can be made between different quality metrics obtained from diffraction patterns and the different electron signals found in modern SEMs, namely secondary (upper or lower detector) and backscattered electrons detector (low and high angle). Electron signals give different ways of evaluating the interaction of the electron beams with the sample, whereas quality metrics offer a similar evaluation of the diffraction of the primary electrons with the crystallographic structure.

Quality metrics are complementary information to the crystallographic orientation obtained by pattern indexing. Other applications of quality metrics will be detailed in this section. They include examples for:

  • evaluating the strain level
  • discriminating crystallographically similar phases
  • estimating the accuracy of the measurements.

Then we shall give the formal definition and current understanding of several quality metrics that will be used later in this work.

Area of use

When a crystal is deformed, the dimensions of its lattice are distorted. This non-uniformity in the lattice leads to a greater distribution of the angles at which a crystallographic plane diffracts. Effectively, the Kossel cones emanating from the sample have a greater variation. On the diffraction pattern, this is manifested by blurring the Kikuchi bands edges [1], [2]. Furthermore, from the Bloch waves theory, this distortion inhibits the propagation of the Bloch waves resulting in a decrease in contrast of the Kikuchi bands. Wilkinson and Dingley [1] observed this phenomenon by comparing the intensity profile of the Kikuchi band of specific planes from undeformed and strained specimens. Although they found that specimen contamination in the SEM was a significant source of error, the Kikuchi band contrast and sharpness were found to decrease as the amount of deformation increased. A similar study was performed by Keller et al. [2] using the Image quality value calculated by the TSL software. The image quality is a measure of the Kikuchi bands’ intensities which is linked with the sharpness of the bands. Their measurements of the strain fields around an AlGaAs layer inside a GaAs matrix correlates with their finite element predictions. These two examples show that quality metrics based on the Kikuchi band profile or total intensity can evaluate the amount of deformation.

The analysis of the microstructure of commercial steels is a common application for EBSD. Although diffraction patterns of ferrite grains (body centered cubic crystal structure) can easily be differentiated from retained austenite grains (face centered cubic), EBSD is incapable of separating martensite or bainite regions from the ferrite grains. Martensite or bainite are obtained by rapid cooling from the austenite phase leaving the carbon atoms (soluble in the austenite phase) trapped inside a body centered cubic crystal structure. This result is the formation of a metastable body centered tetragonal structure. The c/a ratio of the tetragonal lattice is very close to unity [3] and is therefore very close to a cubic lattice. This slight variation of the c/a ratio is undetectable in normal EBSD operating conditions. The crystal structure of martensite, bainite and ferrite are indistinguishable from one another.

However, the dislocation density of bainite or martensite is higher than that of ferrite. [4] The higher dislocation density deteriorates the quality of the diffraction pattern due to the higher lattice distortion. On average, diffraction patterns of ferrite therefore have a higher quality than those of bainite and martensite. This principle was verified via nano and microhardness measurements by Wu et al. [5]. The separation of bainite from martensite is more complex since the difference in their dislocation densities is smaller. Ryde concludes that the discrimination between these two phases could only be performed by “analyzing the directions of the carbide precipitates with a high resolution microscope”. [3]

Szabo and Szalai [6], Wu et al. [5], Ryde [3], and Petrov et al. [4] used a quality metric related to the average intensity of the Kikuchi bands to successfully segment the ferrite from the martensite in duplex or TRIP-assisted steels. They used different methods to achieve the segmentation, but each of them consist of assigning the pixels with a quality lower than a threshold value to martensite and the others to ferrite. The quality metric was either the image quality as calculated by the TSL OIM software, the band contrast as calculated by the Oxford HKL Channel 5 software or the band slope also calculated from Oxford’s software. The band contrast is said to be closely related to the image quality. The band slope is related to the “slope of the intensity change between the background of the pattern and the band”[3].

As mentioned by Wu et al. [5], the effect of grain boundaries on phase segmentation must be taken into account. As with martensite or bainite, diffraction patterns near or at grain boundaries also have a lower quality. Wu et al. proposed a normalizing method combined with a multi-peak model for evaluating the area fraction of the different phases. The accuracy of the technique is, however, influenced by the presence of residual strain which would lower the quality of certain regions. Petrov et al. did a similar study to Wu et al. on a TRIP-assisted steel. They compared their EBSD results with optical micrographs and magnetic measurements. The area fractions of the retained austenite, bainite and ferrite calculated for these techniques were in good agreement with each other. They attributed the discrepancies to the variability in the size of the observed areas (largest for the magnetic measurements and smallest for EBSD). Finally, Ryde used the average image quality inside each grain to separate the martensite from the ferrite grains. This method was in good agreement with the microstructure observation. For the same sample, he also found that the band slope gave a better discrimination than the image quality.

The use of quality metrics for phase discrimination in steels was also studied by Wright and Nowell [7] as well as the effect of quality metrics on grain boundaries determination and strain measurements. Aside from Image quality, they looked at the variation of the average, standard deviation and entropy of the diffraction patterns as originally proposed by Tao [8]. Their observations on an Al-Cu, extruded copper and steel samples showed that the image quality is the best quality metric to differentiate grain boundaries and strain while the pattern intensity average provides better phase contrast. The authors also noted an important point about quality metrics: their dependence on the crystallographic orientation. Two grains of the same phase and with the same strain level can have two different values of a quality metric. This difference is due to the variation of the Kikuchi bands’ intensity from one set of crystallographic planes to another. However, this difference is “generally much smaller than the one due to phase, grain boundaries or strain” [7].

  1. Wilkinson, A. J., & Dingley, D. J. (1991). Quantitative deformation studies using electron backscatter patterns. Acta Metallurgica Et Materialia, 39(12), 3047-3055.
  2. Keller, R. R., Roshko, A., Geiss, R. H., Bertness, K. A., & Quinn, T. P. (2004). EBSD measurement of strains in GaAs due to oxidation of buried AlGaAs layers. Microelectronic Engineering, 75(1), 96-102.
  3. Ryde, L. (2006). Application of EBSD to analysis of microstructure in commercial steels. Materials Science and Technology, 22(11), 1297-1306.
  4. Petrov, R., Kestens, L., Wasilkowska, A., & Houbaert, Y. (2007). Microstructure and texture of a lightly deformed {trip}-assisted steel characterized by means of the EBSD technique. Materials Science and Engineering A, 447(1-2), 285-297.
  5. Wu, J., Wray, P. J., Garcia, C. I., Hua, M., & Deardo, A. J. (2005). Image quality analysis: A new method of characterizing microstructures. ISIJ International, 45(2), 254-262.
  6. Szab{\'o}, P. J., & Szalai, I. (2005). Effect of monotonic and cyclic deformation on the {iq}-maps of austenitic stainless steel. Materials Science Forum, 473-474, 267-272.
  7. Wright, S. I., & Nowell, M. M. (2006). EBSD image quality mapping. Microscopy Microanalysis, 12, 72-84.
  8. Tao, X. (2003). An EBSD study on mapping of small orientation differences in lattice mismatched heterostructures. (Unpublished doctoral dissertation). Lehigh University, .