Questions tagged [x-ray-crystallography]

X-ray crystallography encompasses the structural characterization of crystalline materials by means of X-rays. This is done most commonly by X-ray diffraction, which can be applied to monocrystalline materials or heterostructures, as well as to polycrystalline materials, where the later is referred to as powder X-ray diffraction.

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What is the interplanar distance? Bragg´s law [closed]

An X-ray (wavelength λ= 12.4 pm falls on a crystal) The incidence angle (Θ) is the same as the dispersion angle = 16.6 degrees. What is the interplanar distance if we observe the first order maximum? ...
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About Crystal Orientation

If I have (001), (101), (110) and (104) planes then what is its significance. I understand that they are miller indices referring to a plane. But what does these planes means in polycrystalline thin ...
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Bloch theorem for a semi-infinite crystal

How could we formulate the Bloch theorem for a semi-infinite crystal? For simplicity I suggest assuming that the crystal boundary is along one of its crystallographic planes. One could also assume a ...
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Diamond structure factor as product of FCC and BCC structure factors

I need help understanding why the step on this Wikipedia page is true. Why does the structure factor of the diamond lattice is the product of the structure factor of a BCC Lattice and a FCC lattice? ...
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X-ray intensity and the dependence of that intensity on the atomic position

I am currently studying the textbook, Solid-State Physics, Fluidics, and Analytical Techniques in Micro- and Nanotechnology, by Madou. In a section on X-Ray Intensity and Structure Factor $F(hkl)$, ...
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Bragg's law vs. Laue condition. Are they related?

Is the Bragg's law of reflection somehow related to the Laue condition of constructive interference in X-ray diffraction?
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Doubts with the Bragg's law of reflection

The Bragg's condition of constructive interference between two rays reflected from two parallel crystal planes separated by a distance $d$ is $$2d\sin\theta=n\lambda$$ where $\lambda$ is the common ...
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What causes the diffraction resolution limit of a protein crystal?

My question regards diffraction patterns and resolution limit of protein crystals. I understand that the inner symmetry (i.e. arrangement of the macromolecules) in a protein crystal determines how ...
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X-ray diffraction intensity and Laue equations

My textbook, Solid-State Physics, Fluidics, and Analytical Techniques in Micro- and Nanotechnology, by Madou, says the following in a section on X-Ray Intensity and Structure Factor $F(hkl)$: In ...
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113 views

Path difference between scattered x-rays

My textbook, Solid-State Physics, Fluidics, and Analytical Techniques in Micro- and Nanotechnology, by Madou, says the following in a section on X-Ray Intensity and Structure Factor $F(hkl)$: We ...
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Distance between miller planes for face centered cubic and body centered cubic?

Can someone confirm if this equation still applies to fcc and bcc crystals? $$ {\displaystyle d_{\ell mn}={\frac {a}{\sqrt {\ell ^{2}+m^{2}+n^{2}}}}}$$ If so, can someone outline a quick proof? I can ...
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Derivation of Laue equations

The Wikipedia article for the Laue equations presents them as follows: Let $\mathbf{a}\, ,\mathbf{b}\, ,\mathbf{c}$ be the primitive vectors of the crystal lattice $L$, whose atoms are located at ...
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Equivalent representations of path difference? (Laue equations and Bragg's law)

My textbook, Solid-State Physics, Fluidics, and Analytical Techniques in Micro- and Nanotechnology, by Madou, presents the following image and explanation in a section on x-ray diffraction and Laue ...
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What space group describes a 1-dimensional crystal with reflection symmetry along axis?

I'm trying to understand the symmetry of an effectively 1-dimensional system, but I'm confused about how the 1-dimensional ``line groups'' are classified. If you have a system along the $z$-axis which ...
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60 views

What did Feynman say about cesium chloride and body-centered cubic structure?

The slideshare.net slides Basic crystallography shows an illustration of (what looks like) the interleaved nature of the cesium and chlorine cubic arrangements in a CsCl crystal. The text on the ...
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X-ray diffraction by Debye-Scherrer Method

I was watching lectures by Dr. Steve Simon(Oxford) at Stanford. He said that in a Debye-Scherrer Method for measuring X-ray diffraction, you should calculate d(spacing between lattice planes) by $$d=\...
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What does the blue directions indicate?

This is with close reference to the X ray diffraction.I do not understand what it means to highlight a particular direction as blue when the incident light can diffract in all directions.Please help.
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Related to error propagation in crystallite size calculation from Scherrer formula

I am trying to calculate the error in crystallite size calculation from Scherrer formula $ t=kλ/β\cos\theta $ and I have calculated error propagation using the formula $\Delta t/t = \sqrt((\Delta\beta/...
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How to determine interplanar spacing for BCC/FCC crystals?

I have a query as to how interplanar spacing in fcc and bcc can be determined. In line with the known formula, $$d_{hkl} = \frac{a}{\sqrt{h^2+k^2+l^2}}$$ for a crystal with Miller indices (1 1 0), ...
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Is wavelength expressed in astronomical unit?

i have a question! is wavelength expressed in astronomical unit? I know that it is possible to express it, but is it done in books or questions?
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Which techniques to explore the stoichiometry of a thin film surface material?

I wonder what other technological approaches are feasible to get the ratio of elemental distribution in the surface near layer of a coated (silicon) wafer. The layer thickness will be from several ...
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I have calculated Crystalite size and it ranges 4 to 7 Aangstron. is it lying in nanoscale?

I calculated crystalite size using sharer equation and using most intense peak the value comes out in the range 4 to 7 Angstron. is it in nanoscale?
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What is the effect of dopant on the crystalite size?

Crystal size decreases with doping and then increases with increase in dopant concentration, why? the ionic radii of dopant is greater than the host atoms.
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For what choice of the basis atoms origin the Structure Factor is real?

I have a Cuprite Structure: Now, given that I described this structure as a Simple Cubic lattice with a 6 atoms basis, I have to choose the origin for these basis atoms such that the structure ...
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How is quadratic form of miller index useful?

I have seen that we have used the $h^2+k^2+l^2$ value for finding whether the lattice is BCC,FCC or simple cubic.Where is this factor coming from?Why can I not use the structure factor theorem ...
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Is the Compton effect observed during regular x-ray diffraction?

Here we have the standard set up to observe the compton effect. From what I understand, due to the particle like nature of light, when the x ray photons collide with the electrons in the scatterer ...
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Can faster sampling frequency solve the x-ray diffraction phase problem?

In the x-ray diffraction, only the intensity the light that hits the detector is captured while the phase of the light is not determined. The energy flux of the light is the Poynting vector. For a ...
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265 views

Extinction Rules In cubic lattices FCC and BCC

I was recently looking at structure factor of different cubic lattices BCC and FCC and came across something called the extinction rule which I am having a hard time visualizing. So and example is ...
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Intensity of x-ray difracted on a crystal

Suppose we have an X-ray tube R which emits X-rays of intensity $I_s(\lambda)$, obeying the Kramers' law. The X-rays then come to the cubic crystal K under the angle $\vartheta$, where diffraction ...
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Geiger Counter vs PIN Detector

I have noticed in many papers that test Moseley's law use PIN detectors instead of Geiger counters to measure the XRF spectrums of elements. Why is that? is it because Geiger counters signal also ...
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Why are experimental atomic scale images black and white?

XRay diffraction patterns are black and white. So are scanning electron microscope (SEM) images. Why is this so? At the time of measurement at the atomic level, do the atoms fail to absorb or emit ...
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Scattering on crystals beyond Ewald and Bragg

So I whenever we consider the diffraction and scatting using crystals, powders, basically anything crystalline in the lab using X-rays we get a bunch of theories and models. The most simple one would ...
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Elastic X-ray diffraction: Where does the Photon Momentum go to?

lately I was discussing the following situation. Let's suppose you are doing X-Ray diffraction experiments on a crystal. So what you basically do is shooting a high energy photon with a wave vector $k$...
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Origin of XRD Peak Asymmetry

I have been doing an introductory XRD experiment in which we measure the crystal spacing of a simple lattice (LiF) and as usual obtained data for intensity against two theta. Ideally the peaks should ...
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Can we call a hexagonal system with two different atoms as inversion symmetric?

Graphene is two-dimensional honeycomb crystal lattice with the two Carbon atoms in its unit cell. Clearly, it is inversion symmetric. But, suppose we have two different atoms in the hexagonal system ...
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299 views

Why is intensity decreasing for higher orders of Bragg (x-ray)diffraction?

Bragg diffraction for x-rays by a crystal structure is governed by $$ n\lambda=2dsin\theta ,$$ where $n$ is an integer and the diffraction order, $\lambda$ is the x-ray wavelength, $d$ the lattice ...
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X-ray frequency or crystal structure: which was known first?

In the classical Bragg setup, one can determine the distance between crystal layers if the wavelength of a characteristic line is known or the other way round, calculate the distance if the wavelength ...
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Structure Factor for diffraction patterns

im trying to figure out myself the use of Structure Factor for Diffraction patterns. I have the Structure Factor for a monoatomic lattice $S(\overline G)=\sum_{i=1}^n f e^{\overline G \cdot \...
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293 views

Comparison between X-ray diffraction and slit experiment

Most diagrams regarding X-ray diffraction suggest that after hitting an atom, X-ray would get reflected. But then the method results in an interference pattern which means X-ray get diffracted. I am ...
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Using Miller indices to determine interference from a particular plane in a crystal lattice

In terms of x-ray diffraction from crystals. I was wondering how you can use the miller indices to determine whether there will be constructive or destructive interference from a particular plane in ...
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How can I tell the cubic structure of different crystals?

So I have a couple of crystals I am analysing (LiF RbCl NaCl...) and I have the x ray diffraction patterns for them. How do I determine the different structures of these crystals as I need to ...
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190 views

Why the first peak in the X-ray diffraction of an amorphous solid has significantly high, in terms of intensity than the second peak?

In the XRD pattern of an amorphous solid we do not observe sharp peaks. Instead we see only diffused peaks. Why these peaks are diffused and more importantly why the first peak is significantly high ...
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Issues with Miller indices

I have read that to find the intercepts of a plane represented by Miller indices is to take the reciprocal of each index. However, I noticed that does not give the original plane if we had to reduce ...
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Phase Retrieval and Oversampling

In signal and image processing theory, it is known that taking the Fourier transform of a zero-padded image gives the oversampled Fourier transform of the image. And that oversampling is a necessary ...
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What causes Lorentzian broadening of X-ray diffraction peaks?

In X-ray diffraction, the pseudo-Voigt model is a combination of Gaussian and Lorentzian distributions, and is often used to model peaks. The form of the peak is often described as $V(x)$ = (1-$\...
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Why/when can the chemical structure of crystals be assumed to be diffraction gratings?

Why/when can the chemical structure of crystals be assumed to be diffraction gratings? Like how does one know a priori, whether the structure is like a diffraction grating, if one doesn't yet know ...
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How to determine the degree of how high a symmetry of high-symmetry points in the first Brillouin zone?

For exmple, we have a hexagonal lattice with hexagonal Brillouin zone, shown in the picture The points $\Gamma$, K, M and $\Lambda$ are high symmetry points. Now, $\Gamma$ point is the highest-...
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Meaning of crystal orientation

If I have a crystal, say (001)-oriented ABO3, what does the 001 imply, from an experimental perspective? I understand that the 001 is referring to a plane as described by Miller indices, but what is ...
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241 views

Miller indices and FCC structure - non-existent planes

Below is a copy from Kittel's Introduction to Solid State Physics, 8th edition, page 42. It is a picture to illustrate that in FCC structures (loosely said and exactly cited) "no reflections can ...
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SAXS: Why would a second order peak behave differently than first order?

What is the significance of a second order peak in SAXS and during an assembly of nanoparticles, why would it have a different shape over time: What are factors that are unique to first or second ...