Generating X-ray diffraction patterns from atomic coordinates

I have a list of atomic coordinates for a periodic system as a result of a molecular dynamics simulation. I want to use those coordinates and predict what it's 1D diffraction pattern looks like.The approach I am taking is to generate a 2D cross section and then radially integrate it to get the 1D pattern. To do so, I am using the following equation taken from the reference cited at the bottom (I know this is a very computationally slow approach but I want to understand the theory right before I get fancy with FFTs):I(ks) $\propto$ |F(q)|2 $\pro...Read more

Single slit diffraction - wave vs particle view

If monochromatic light is shot through a single slit onto a screen, we can analyze the pattern on the screen using wave properties. This analysis is done assuming the wavelength is constant.But with a particle view... there's uncertainty in the momentum after going through the slit... hence with DeBroglie's relation $p=\dfrac{h}{\lambda}$, uncertainty in the wavelength.So is there any contradiction here... the first analysis has no uncertainty in wavelength (allowing us to calculate minimums and maximums using the wavelength of light and the wi...Read more

Deriving formula for effect of slit width and multiplicity for multi-slit diffraction pattern

I have to derive formulas for the effect of slit width and slit multiplicity on a multi-slit diffraction diffraction pattern. The formulas I've been given are the typical ones, $d\sin\theta=m\lambda$,for the single slit pattern, where d is the slit width,$D\sin\theta = n\lambda$ for the double slit pattern, where D is the separation of the slits, and $L\tan\theta \approx L\sin\theta$ where L is the distance from the slit to the surface on which the pattern is being projected on.I'm absolutely stuck on how to change these to give what I want. Wo...Read more

How does the intensity not change when the width of the slit changes in single slit diffraction

The picture in the book by Resnick and Halliday shows as the width of the slit increases the width of the central maximum decreases and becomes flat as the slit width decreases,my concern is when the slit width decreases and the curve becomes flat in the first picture,the area under the central maximum graph increases keeping the intensity same,from where the extra energy is coming to cover the whole screen by the central maximum,in this case when the width decreases the amount of light entering the slit actually decreases,so when the area unde...Read more

single slit diffraction - $\sin\theta=n(\lambda)/b $ or $\sin\theta = (2n+1)(\lambda)/b$

I'm getting a contradiction as follows and am not sure how to resolve it:logic 1leads to the conclusion that the higher order minimas of single slit diffraction will be given by $b\sin\theta = n(\lambda)$ where $n = 1,2,3,\dots$ (this is given in textbooks)logic 2leads to the conclusion that the higher order minimas of single slit diffraction should be given by $b\sin\theta = (2n+1)\lambda$ where $n = 0,1,2,3,\ldots$(i.e. only for odd multiples of wavelength.I need to understand why logic 2 is wrong.logic 2: if we divide the slit into two equal...Read more

Secondary maximum in Fraunhofer/single-slit diffraction

Question: The angular position at which first minima is observed is $\theta=\pi/6$ rad for a slit of width $e$ and light of wavelength $\lambda$. The angular position at which secondary maximum is observed is = ?My attempt:For first minima, $e\sin\theta=\lambda...(i)$ Unfortunately, formula for maxima is not given in my book so I derived it on my own:For deriving second maximaConsider $2N$ wavelets all throughout the slit.Path difference between the $i$-th wavelet and $(N+i)$-th wavelet ($i\in [1,N]$) should be $\lambda$ for constructive inter...Read more

Diffraction by small holes

This is a follow-up to this question: What happens to waves when they hit smaller apertures than their wavelenghts?Hans Bethe wrote a paper in 1944, "Theory of Diffraction by Small Holes," Phys. Rev. 66, 163. I don't have access to the paper, but from descriptions online it sounds like he proved the following. Suppose a plane wave impinges on an absorbing sheet, and there is a hole in the sheet of diameter $d$, with $d<\lambda$. Let $P_0$ be the power incident on the hole, and $P$ the power diffracted through the hole. Then the transmission ...Read more

diffraction - When the gap size is less than the wavelength, the angle through which the wave is diffracted remains a maximum . What does this mean?

When the gap size is less than the wavelength, the angle through which the wave is diffracted remains a maximum while the intensity decreases as the gap getssmaller than the wavelength. I understand this statement except for this "the angle through which the wave is diffracted remains a maximum" part.Can someone please explain what they mean here?...Read more

diffraction - How do atoms scatter X-rays?

I am learning the theory behind X-ray diffraction but I have a question. According to the textbook I am using, X-ray tubes (in diffractometers) produce near monochromatic X-rays. In other words, they produce X-rays of nearly the same wavelength. Then, these X-rays interact with the electrons of atoms in a crystal lattice. The atom, in return, spherically emanates X-rays of the same wavelength as the X-rays from the diffractometer tube (elastic scattering). How exactly does elastic scattering work? Why do atoms accept incoming X-rays and then pr...Read more