nickel | R Documentation |
This data set consists of electron backscatter diffraction (EBSD) data obtained by scanning a fixed 12.5 μm-by-10 μm nickel surface at individual locations spaced 0.2 μm apart. This scan was repeated 14 times for each of the 3,449 locations yielding a total of 48,286 observations. Every observation corresponds to the orientation, expressed as a rotation matrix, of a cubic crystal on the metal surface at a particular location. Be aware that there are missing values and erroneous scans at some locations and scans. See Bingham et al. (2009) and Bingham et al. (2010) for more details and analysis.
nickel
A data frame with 48,286 rows and the following 13 columns:
xpos
location x position
ypos
location y position
location
Location number for easy reference
rep
Replicate scan identifier
V1
First element of x-axis describing crystal orientation at corresponding location
V2
Second element of x-axis describing crystal orientation at corresponding location
V3
Third element of x-axis describing crystal orientation at corresponding location
V4
First element of y-axis describing crystal orientation at corresponding location
V5
Second element of y-axis describing crystal orientation at corresponding location
V6
Third element of y-axis describing crystal orientation at corresponding location
V7
First element of z-axis describing crystal orientation at corresponding location
V8
Second element of z-axis describing crystal orientation at corresponding location
V9
Third element of z-axis describing crystal orientation at corresponding location
The data set was collected by the Ames Lab located in Ames, IA.
Bingham, M. A., Nordman, D., & Vardeman, S. (2009). "Modeling and inference for measured crystal orientations and a tractable class of symmetric distributions for rotations in three dimensions." Journal of the American Statistical Association, 104(488), pp. 1385-1397.
Bingham, M. A., Lograsso, B. K., & Laabs, F. C. (2010). "A statistical analysis of the variation in measured crystal orientations obtained through electron backscatter diffraction." Ultramicroscopy, 110(10), pp. 1312-1319.
Stanfill, B., Genschel, U., & Heike, H. (2013). "Point estimation of the central orientation of random rotations". Technometrics, 55(4), pp. 524-535.
# Subset the data to include only the first scan Rep1 <- subset(nickel, rep == 1) # Get a rough idea of how the grain map looks by plotting the first # element of the rotation matrix at each location ggplot2::qplot(xpos, ypos, data = Rep1, colour = V1, size = I(2)) # Focus in on a particular location, for example location 698 Rs <- subset(nickel, location == 698) # Translate the Rs data.frame into an object of class 'SO3' Rs <- as.SO3(Rs[,5:13]) # Some observations are not rotations, remove them Rs <- Rs[is.SO3(Rs),] # Estimate the central orientation with the average mean(Rs) # Re-estimate central orientation robustly median(Rs) # Visualize the location, there appears to be two groups plot(Rs, col = c(1, 2, 3))
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