termRip: Simulate termination ripples

In nanop: Tools for Nanoparticle Simulation and Calculation of PDF and Total Scattering Structure Function

Description

Function to simulate termination ripples in the PDF calculated as the Fourier transform of the total scattering function that arise due to the finite value of the upper integration limit Qmax.

Usage

		   
  termRip(pdf, Qmax, dr, maxR, maxRTermRip)

Arguments

pdf	numeric vector containing PDF.
Qmax	numeric indicating value of Qmax at which scattering function was truncated before calculating PDF as the Fourier transform.
dr	numeric indicating the step size in r.
maxR	numeric indicating the maximum value of r in G(r).
maxRTermRip	numeric indicating the maximum value of r in G(r) for which the ripples should be simulated.

Value

numeric vector of function values.

See Also

calcPDF, calcQDepPDF

Examples

## simulate a particle 
Cu <- createAtom("Cu")
part <- simPart(atoms=list(Cu), atomsShell=list(Cu), r=12, 
    rcore=10, latticep=4.08, latticepShell=3.89)

## calculate the PDF  
gr1 <- calcPDF(part, maxR=24, scatterLength=c(4.87, 7.97))
gr1 <- broadPDF(gr1, sigma=c(.01, .01), nAtomTypes=2) 
## normalization
gr1$gr <- 4*pi*gr1$r*gr1$gr

## calculate and substract the baseline term
gQSAS <- calcTotalScatt(part, type="neutron",  minQ=0.001, 
    maxQ=0.771, dQ=0.005, scatterLength=c(4.87, 7.97), 
    sigma=c(.01, .01))
gammaR <- calcQDepPDF(minR=0.01, maxR=24, dr=0.01, maxQ=.771, 
    minQ=0.001, verbose=50, 
    preTotalScat=list(Q=gQSAS$Q, gQ=gQSAS$gQ))
gr1$gr <- gr1$gr - gammaR$gr

plot(gr1$r, gr1$gr, type="l", xlim=c(0,10))
## simulate termination ripples
rvector <- gr1$r
gr1 <- termRip(gr1$gr, Qmax=11.881, dr=0.01, maxR=24, maxRTermRip=16)
## plot the PDF with simulated termination ripples:
lines(rvector, gr1, col=2)

#### compare with ripples due to finite value of Qmax:
## calculate scattering function
gQ <- calcTotalScatt(part, type="neutron", 
    scatterLength=c(4.87, 7.97),  sigma=c(.01, .01))
## set Qmax to a value between 11 and 13 at which scattering function reaches 
##  minimum:
t1 <- which(gQ$Q > 11)[1]
t2 <- which(gQ$Q > 13)[1]
cut <- gQ$Q[t1:t2][which(abs(gQ$gQ[t1:t2])
    ==min(abs(gQ$gQ[t1:t2]) ))[1]]
## calculate Q-dependent PDF
gr3 <- calcQDepPDF(minR=0.01, maxR=24, dr=0.01, minQ=.771, 
    maxQ=cut, verbose=50, preTotalScat=list(Q=gQ$Q, gQ=gQ$gQ))

## add Q-dependent PDF to plot:
lines(gr3$r, gr3$gr, col=4)
legend(5,7,c("PDF as returned by calcPDF", "PDF with simulated 
    termination ripples", "PDF as Fourier transform"), lty=1, 
    col=c(1,2,4))
	

Example output

DIM BASE 1 4 
DIM BASE 1 4 
Finished computing r= 0.5 
Finished computing r= 1 
Finished computing r= 1.5 
Finished computing r= 2 
Finished computing r= 2.5 
Finished computing r= 3 
Finished computing r= 3.5 
Finished computing r= 4 
Finished computing r= 4.5 
Finished computing r= 5 
Finished computing r= 5.5 
Finished computing r= 6 
Finished computing r= 6.5 
Finished computing r= 7 
Finished computing r= 7.5 
Finished computing r= 8 
Finished computing r= 8.5 
Finished computing r= 9 
Finished computing r= 9.5 
Finished computing r= 10 
Finished computing r= 10.5 
Finished computing r= 11 
Finished computing r= 11.5 
Finished computing r= 12 
Finished computing r= 12.5 
Finished computing r= 13 
Finished computing r= 13.5 
Finished computing r= 14 
Finished computing r= 14.5 
Finished computing r= 15 
Finished computing r= 15.5 
Finished computing r= 16 
Finished computing r= 16.5 
Finished computing r= 17 
Finished computing r= 17.5 
Finished computing r= 18 
Finished computing r= 18.5 
Finished computing r= 19 
Finished computing r= 19.5 
Finished computing r= 20 
Finished computing r= 20.5 
Finished computing r= 21 
Finished computing r= 21.5 
Finished computing r= 22 
Finished computing r= 22.5 
Finished computing r= 23 
Finished computing r= 23.5 
Finished computing r= 24 
Finished computing r= 0.5 
Finished computing r= 1 
Finished computing r= 1.5 
Finished computing r= 2 
Finished computing r= 2.5 
Finished computing r= 3 
Finished computing r= 3.5 
Finished computing r= 4 
Finished computing r= 4.5 
Finished computing r= 5 
Finished computing r= 5.5 
Finished computing r= 6 
Finished computing r= 6.5 
Finished computing r= 7 
Finished computing r= 7.5 
Finished computing r= 8 
Finished computing r= 8.5 
Finished computing r= 9 
Finished computing r= 9.5 
Finished computing r= 10 
Finished computing r= 10.5 
Finished computing r= 11 
Finished computing r= 11.5 
Finished computing r= 12 
Finished computing r= 12.5 
Finished computing r= 13 
Finished computing r= 13.5 
Finished computing r= 14 
Finished computing r= 14.5 
Finished computing r= 15 
Finished computing r= 15.5 
Finished computing r= 16 
Finished computing r= 16.5 
Finished computing r= 17 
Finished computing r= 17.5 
Finished computing r= 18 
Finished computing r= 18.5 
Finished computing r= 19 
Finished computing r= 19.5 
Finished computing r= 20 
Finished computing r= 20.5 
Finished computing r= 21 
Finished computing r= 21.5 
Finished computing r= 22 
Finished computing r= 22.5 
Finished computing r= 23 
Finished computing r= 23.5 
Finished computing r= 24 

nanop documentation built on May 2, 2019, 3:39 p.m.