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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In X-Ray crystallography, if an object is composed of multiple electrons, how does the structure factor help us figure out the structure?
From one of my courses:
Structure factor of an object composed of a large number of electrons:
$$ F \left( s \right) = \sum_{j} 1e_{j} e^{2 \pi i s r_{j}} \tag{1} $$
Where $1e$ is the amplitude, $s$ ...
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How to enumerate all Miller indices in the unit cell?
Taking the unit cell of $\rm NaCl$ as an example, I want to compute the XRD pattern of its crystal structure. One step is to enumerate all miller indices within a limited sphere as follows:
$$\frac{1}{...
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Possibility of calculating phonon dispersion from crystal structure
Is it in principle possible to calculate the dispersion relation of phonons in a crystal from the crystal structure?
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Why 3 mmm and 4mmmm point group symmetry elements do not exist?
Why 3 mmm and 4mmmm point group symmetry elements do not exist? How we can say 3 mmm and 4mmmm are rather equivalent to 3m and 4mm respectively?
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Why a crystal lattice with short axes would have a diffraction pattern in which spots would appear far apart using Bragg's law?
With the aid of Bragg's law, explain why a crystal lattice with short axes would have a diffraction pattern in which spots would appear far apart?
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First brillouin zone propagation wave vector components in special surface cuts in cubic systems
I'm trying to figure out a context in an article about the allowed in plane propagation wave vector , in specific surface cuts or orientations such as (001) (110) (111) where the authors gave the ...
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Intuitive software for Peak Deconvolution?
I've seen many recommendations of different Peak Analysis software used to find peaks (whether they are Gaussian/Lorentizan/Voigt) in various spectrums (What software programs are recommended for ...
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Peaks possibility with structure factor for BCC and FCC
I have a doubt regarding what peaks are possible for BCC and FCC atoms. Say $n_{1}$, $n_{2}$ and $n_{3}$ are coordinates which are only integers such that for atom A, $n_{1}+n_{2}+n_{3}$ is odd and ...
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Relation between reciprocal vector and gradient of a plane $(hkl)$
Suppose we have a unit cell with lattice vector $\vec a_1,\;\vec a_2,\;and\;\vec a_3$ (crystallographic axes)
Consider $(hkl)$ plane. This plane makes an intercept of $\frac{1}{h}$ unit along $\vec ...
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How do you cut a single crystal into one of a different orientation?
I am reading about laser-cutting of single crystal wafers to produce wafers of a different orientation.
Is this as simple as cutting along the plane of the desired orientation? Meaning: with a 100 ...
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On describing fcc and bcc planes in a Cartesian system (simple cubic system)
Ashcroft and Mermin remark, at the bottom of page 91 that
As a general rule, face-centered and body-centered cubic Bravais lattice[s] are described in terms of a conventional cubic cell, i.e. as ...
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Formula for amplitude of X-ray diffraction through crystal
I’m an undergrad currently writing a report on a lab we’ve done using X-ray diffraction to look into the structure of crystals. We’ve been told that the structure factor of an element relates to the ...
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Are the Laue equations only satisfied when the reciprocal lattice point touches the Ewald sphere?
I've derived the Laue conditions from the requirements for constructive interference in a crystal lattice ( J. Drenth (2007), Principles of X-Ray Crystallography 3rd Edition ) and also then ...
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Freezing of soft modes
Displacive structural transitions are in most cases obtained by freezing soft modes (collective atomic vibrations fulfilling selected symmetry constrains) as thermodynamically parameters (temperature ...
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Intensity as a function of selected energy by a crystal monochromator simulation data is different from experimental data
As explained in the above, with a ray tracing Monte carlo simulation software, I record the intensity as a function of the energy I chose to select with a crystal monochromator after the beam has been ...
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Why is the Lattice of a crystal required to have at least as much symmetry as its motif?
I know that a crystal structure is formed by the addition of a motif to a lattice (crystal structure = lattice + motif). I also know that an arbitrary lattice will in general exhibit certain ...
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How to determine the interplanar distance from the Miller Indeces $(h k l)$ of different lattices
I know that for cubic unit cells, there is a simple correspondence between the interplanar distance and the Miller Indeces:
$d=\frac{1}{\sqrt{h^2 + k^2 + l^2}}$
What happens when we have more complex ...
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Order of Diffraction Bragg's law
Given the relation of Bragg's law $\sin\theta= \frac{n\lambda}{2d}$, this suggests that for a given wavelength $\lambda$ the order of diffraction is limited such that $\sin\theta$ is less than one. ...
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Number of unique lattice planes
According to my textbook:
The families of lattice planes are in one-to-one correspondence9
with the possible directions of reciprocal lattice vectors $G$, to which
they are normal. Further, the ...
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Why is Copper ($\rm Cu$) better than Molybdenum anode for X-Ray diffraction?
I work in a physics lab, and the project I am working on includes X-Ray (Bragg) diffraction using $\rm NaCl$ single crystal and powdered sample. My professor said that changing the anode of the X-Ray ...
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Relation between Fourier transforms and atomic form factors
I am currently trying to understand how the X-ray diffraction pattern relates to the Fourier transform of the atomic electron density function. I roughly understand the theory behind the diffraction ...
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Why does an electron diffraction pattern of a crystal come out to be visible in the reciprocal space?
I have been recently trying to understand electron diffraction patterns of crystals. What I am not able to visualise is the reason why a diffraction pattern of the reciprocal space is formed on the ...
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What are the correlations measured by a static structure factor?
The static structure factor is defined as:
$$S(\mathbf{q}) = \frac{1}{\sum_{j=1}^{N}f_j^2} \sum_{j=1}^{N} \sum_{k=1}^{N} f_{j} f_{k } \mathrm{e}^{-i \mathbf{q} \cdot (\mathbf{R}_j - \mathbf{R}_k)}$$
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Diffraction Centres in Bragg's Law and Young's Experiment
Image shows the famous Bragg's law as the condition of constructive interference in the XRD. In the image, it can seen that diffraction centres are atoms in the crystal lattice. However, when ...
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Number of Possible Primitive Vectors and Primitive cells in a Bravais Lattice
According to my Book Solid State Physics by Ashcroft and Mermin, given a 3-dimensional Bravais lattice, there are infinite sets of 3 primitive vectors that we can come up with that will span the ...
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Questions About Bragg's Law
Bragg's law is schematically shown on the picture:
Two parallel and plane waves are shown which propagate towards the crystal. For plane waves, wave fronts are flat planes perpendicular to the wave ...
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Why does Bragg's law consider only specular scattering for constructive interference?
My textbook only considers two-dimensional scattering, so I will stick to that. When explaining Bragg's law, it states that the incidence angle and the scattering angle must be equal so that all ...
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Deducing specific hkl directions from families of hkl directions
For a crystal I have families of equivalent directions < > and I'm trying to deduce specific directions.
The family of the main plane of diffraction of the crystal is <111>. <110> is ...
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Calculating the Miller Indices for the Crystal Structure of Graphite
I am currently completing a lab project on X-Ray Crystallography where I am investigating the crystal structure of graphite.
We are given this relation (1) between the lattice constant $a$ and the ...
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Why reflection occurs in crystals?
Why do reflections occur in crystals? Why not transmission only? How can atomic planes work as mirrors?
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Characteristic X rays
How do the atom in the target (in the x ray production experiment) go to the normal state if the accelerated electron (from the cathode) knocks a k-electron out the atom and L-electron jumps to fill ...
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How was the structure of DNA deduced using X-ray crystallography
The determination of DNA's double helix structure by Watson, Crick, and co-workers using X-ray crystallography is a well-known milestone in the development of biology. My question is, what was the ...
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Why X-ray imaging base on photon counting is more quick than traditional energy integral detector?
photon counting based on detector can be used to x-ray imaging in industrial pubilc security. In traditional, people often use energy integral scintillation detecor to imaing object through x-ray. The ...
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Phase transition detected using Raman spectra is not visible with XRD analysis
I am currently trying to analyse a paper in which perovskite material is pressurized and they observe the variation in structural properties using Synchrotron XRD and Raman Spectroscopy. Now the ...
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Can LeBail XRD method be used in order to get the position of atoms inside the unit cell?
I am reading this paper "Defect Perovskites Under Pressure: Structural Evolution of Cs2SnX6 (X = Cl, Br, I)" in which the authors perform Synchrotron XRD and Raman spectra analysis of ...
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Why is an equilateral triangle not a 2d unit cell?
An equilateral triangle obeys the crystallographic restriction theorem, but it is not a part of 2d crystal structure. What symmetry does it lack? Why can't it be a Bravais lattice?
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Questions about creating diffraction grating
I have a modern physics lab project this semester where we have to perform an experiment related to modern physics as a group of 3.
We choose https://aapt.scitation.org/doi/10.1119/1.5020051, an ...
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Determining Brillouin Zone for a crystal with multiple atoms
The Brillouin Zone (BZ) refers to a region of reciprocal space corresponding to the primitive cell. That is, a Brillouin Zone is a subset of the reciprocal space which contains all the information ...
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What is a physical explanation of scattering vector $q$?
I understand that $q = 4 \pi \sin\theta\,/\lambda$ in scattering theory. Also, $q = 2 \pi/k$, where $k$ is the wave vector. I have read the explanations that it is the momentum vector, the scattering ...
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Why does x ray diffraction take place in crystals as it seems to violate the law of conservation of energy?
I was reading through the explanation on x ray diffraction from crystals, but found the explanation troublesome.
The explanation given in a text book on x ray crystallography states that when an x ray ...
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What is the input of calculating signal noise ratio (SNR) and detective quantum efficiency (DQE) in estimation of imaging system?
In its definition, the signal noise ratio (SNR) is the ratio of the mean siganl to the standard deviation of the noise. However, for a given picture what is the noise? The detective quantum efficiency ...
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Production of X-Rays for crystallography
X-Ray diffraction is an important tool for determining the crystal structure of a sample. I believe that monochromatic X-Ray beams are necessary for this kind of experiments, since diffraction ...
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How can the waves interfere in X-ray diffraction?
This is the popular diagram surrounding the Bragg's law for X ray diffraction:
But what I seem to not be able to understand is when they say that the reflected waves interact constructively to create ...
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Why aren't there any $S_8$ or $S_{12}$ point groups in crystallography?
When considering improper rotations (roto-reflections), we can derive that if $n$ is odd, then $C_n$ and $\sigma_h$ (reflection plane normal to $C_n$ axis) must exist. Similarly, we can also derive ...
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What does it mean when people (physicists) say electron has a wavelength of $x$ unit of length physically?
When we discuss about the wavelength of em(electromagnetic) wave's wavelength,
It is meant we are talking about the tip to tip of the oscillation of electrical and magnetic field in physical space.
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Do neutrons change their wavelengths when diffracted?
Both neutrons and X-rays are used in diffraction. In XRD, the diffracted beam is of the same wavelength of the incident beam. The reason is that X-rays are EM waves which cause electrons to vibrate. ...
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What is the connection between reciprocal lattice vectors $\vec G$ and the Miller indices?
We know that a family of crystal planes with Miller indices $(hk\ell)$ is orthogonal to the reciprocal lattice vector $\vec G = h \vec b_1 + k \vec b_2 + \ell\vec b_3$. My question is the converse of ...
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How to interpret XRD results?
I am given several datapoints of XRD strain information. It comes from XRD measurement of a thin layer (100 nm) of semiconductor deposited on top of another semiconductor.
The result I'm given is ...
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bcc (100) and (200) planes and their xrd peaks
(a) I understand (100) lattice planes with an interplanar spacing of a if we assume it to be a bcc lattice of lattice parameter a. Then (200) planes have an interplanar spacing of a/2 but that would ...
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Is there a theoretical equation for the $d$-spacing for an amorphous solid or a metastable crystal?
So I am trying to study and compare two different samples (thin films) of the same material but with different cooling rates. I made one that was cooled slowly, allowing it to nucleate and crystallize ...
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