1d:T799,# Scattering factor for 1D gaussian atoms Given unit cell length, atomic number, B factor, occupancy and Miller index h, this function returns the corresponding value of the analytical scattering factor calculated as Fourier transform of the 1D gaussian atom. ```r scafac(h, a, Zj, occj, Bj = NULL, k = ksigma) ``` ## Arguments - `h`: Real numeric. One or more 1D Miller indices. h can also have non-integer values in between integer values. This enables plotting of scattering curves. - `a`: Real numeric. Length of 1D unit cell. - `Zj`: Integer numeric. Atomic number (e.g. Oxygen has Zj <- 8) - `occj`: Real numeric. Atomic occupancy, a real number between 0 and 1, where 0 means that the atom is missing in the crystal and 1 means that is present in all unit cells of the crystal. - `Bj`: Real numeric. This is the B factor associated with the thermal vibration of the atom. It is measured in squared angstroms and it is equal to 8*pi^2*sigma^2, where sigma is the gaussian atom width. - `k`: A real number. It controls the standard deviation of the gaussian function describing the atom and, thus, the shape of the associated peak. The standard deviation sigma is given by: `sigma = k * sqrt(Z)` ## Returns A real numeric. The value of the scattering factor at the sprcified Miller idex or corresponding real value. ## Examples ```r # Values for some Miller indices h <- 0:10 a <- 20 Zj <- 16 Bj <- 18 # Roughly corresponding to sigma 0.23 occj <- 1 fval <- scafac(h,a,Zj,occj,Bj) plot(h,fval,pch=16,xlab="Miller index",ylab="Scattering factor", ylim=c(0,16)) # Continuous resolution h <- seq(0,10,length=1000) fval <- scafac(h,a,Zj,occj,Bj) points(h,fval,type="l",col=2) # Scattering curve for a lighter atom Zj <- 8 fval <- scafac(h,a,Zj,occj,Bj) points(h,fval,type="l",col=3) # Scattering curve for the same atom, just with smaller Bj (colder) Bj <- 10 fval <- scafac(h,a,Zj,occj,Bj) points(h,fval,type="l",col=4) ```

scafac function