nickel {rotations}

Nickel electron backscatter diffraction data set

Description

This data set consists of electron backscatter diffraction (EBSD) data obtained by scanning a fixed 12.5 \mum-by-10 \mum nickel surface at individual locations spaced 0.2 \mum 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.

Usage

nickel

Format

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

Source

The data set was collected by the Ames Lab located in Ames, IA.

References

1. 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.

2. 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.

3. Stanfill, B., Genschel, U., & Heike, H. (2013). "Point estimation of the central orientation of random rotations". Technometrics, 55(4), pp. 524-535.

Examples

# 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))