find XRD peaks • rigakuXRD

Objective: Finding all the XRD peaks can be difficult, if the peaks are not prominent. Let us explore an algorithm, which eliminates areas, where fitting for a peak is not possible, and other areas, where fitting for a peak is straight-forward.

library(rigakuXRD)
library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
library(ggplot2)
# Loading the date
filename = xrd.getSampleFiles()[1]
d = xrd.read.ASC(filename)

Plot different ranges, the following plot shows at least 6 peaks that should be found:

d = data.frame(th = d$theta, I = d$I)
plot(d, log='y', col='red')

Region

d %>%
  filter(th>36 & th < 42) %>%
  ggplot(aes(th, I)) + 
  geom_point(col='red') + 
  theme_bw()

  d1 = d %>% filter(th>36 & th<43)
  p = xrd.peakEstimate(d1$th, d1$I, verbose=TRUE)

  fit <- NULL
  try(fit <-
        nls(data = d1,
            I ~ b + A*exp(-(th-t)^2/(2*s*s)),
            start = list(b=p$b0, A = p$A0, 
                         t=p$th0, s=p$s0))
  ); # does not stop in case of error
  summary(fit) 
#> 
#> Formula: I ~ b + A * exp(-(th - t)^2/(2 * s * s))
#> 
#> Parameters:
#>    Estimate Std. Error t value Pr(>|t|)    
#> b 8.464e+02  1.946e+00  435.01   <2e-16 ***
#> A 4.492e+02  8.155e+00   55.08   <2e-16 ***
#> t 3.822e+01  5.668e-03 6743.22   <2e-16 ***
#> s 2.743e-01  5.912e-03   46.40   <2e-16 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error: 45.76 on 695 degrees of freedom
#> 
#> Number of iterations to convergence: 9 
#> Achieved convergence tolerance: 2.843e-06