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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Structure factor of FCC
I know that the structure factor of FCC in conventional basis is
\begin{equation}
S=1+e^{iπ(h+k)}+e^{iπ(l+k)}+e^{iπ(h+l)}
\end{equation}
Now if I change the basis to the primitive basis, the new ...
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How to get Miller indexes from a diffraction pattern?
Working with a single crystal, what is the first thing the diffractometer has access to? What is the output I see and what are the steps from this two levels of information?
If I'm correct, the output ...
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Book recommendation on X-ray diffraction
I am a mathematician with just high-school level of physics knowledge. I am studying the area of protein modelling and trying to understand how small angle x-ray scattering works. But I think my lack ...
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Is it possible to have a crystal structure where you are getting peaks of different intensities at different $2\theta$ values with same $hkl$ planes?
Is it possible to have a crystal structure. where you are getting peaks of different intensities at different 2thetha values with same h k l planes? What will you be calling that system to be a single ...
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Confusion between trigonal and hexagonal systems
I'm studying space groups.
It's quite clear (I think) why trigonal and hexagonal systems collapse in the same primitive Bravais lattice, while are different when we introduce non-primitive unit cells, ...
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Electron microscopy and Interatomic distances of miller planes
I am studying Transmission Electron Microscopy (TEM), and have been seeing in articles TEM images of different materials typically come accompanied by these diffraction patterns, caused by the ...
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How does the diffraction pattern of a 2-dimensional grating/lattice relate to the reciprocal lattice?
I am trying to understand the relationship between the diffraction pattern produced when shining light onto a 2D lattice and the reciprocal lattice of the direct lattice in question.
So suppose we ...
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How to compare XRD data from literature?
I'm a grad student. Trying to do a literature review this summer. My advisor is telling me to gather XRD data of my samples for my research, and I have. Unfortunately, I have no idea how to compare it/...
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How are 3 Principle Sections possible in a crystal even when there is only one optical axis and all must contain it?
While studying polarization in calcite crystals, I came across that there are 3 possible principle sections in the rhombohedral crystal. But the conditions are that each section must be perpendicular ...
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Are there multiple d-spacings due to a single diffraction plane in XRD?
The Bragg Law is
$$n \lambda=2d \sin(\theta) $$
Therefore, you can find the d-spacing of a given diffraction plane if you know the wavelength and angle by:
$$ d = \frac{n \lambda}{2 \sin \theta}$$
But ...
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How to find Euler angles for orientation of Single crystals with respect to Lab Frame?
I have a monoclinic C2 space group single crystal sample glued to a tenon plate. I know the surface normal direction and the edge plan of the crystal. Also, I know the XY plane of the tenon plate. How ...
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Small-Angle X-Ray Scattering of Bulk Polymers
Does anyone have any recommendations on how to get useful information from SAXS of polymers when the system is not dilute?
This is the type of data we're working with:
My understanding is that since ...
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2D primitive unit cells
The answer given says that 2 & 3 are primitive unit cells.How can a hexagon be a primitive unit cell.Can someone explain?
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Generating high symmetry unit cell from lower symmetry primitive cell
I'm trying to create a workflow where one step of the process is taking in a primitive cell of a crystal structure and produce a cell that has the highest possible symmetry (conventinal cell) ...
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Understanding Wyckoff Position of Apatite group
I was learning about Wyckoff position, and one of the simplest example was of $ZrO_{2}$. For Zr and O, the Wyckoff positions are 4a and 8c and belongs to space group Fm-3m. Now from the Wyckoff ...
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Finding the Bremsstrahlung in diffraction patterns of NaCl
I recently got the chance to measure the diffraction pattern of a NaCl crystal using the Bragg-Brentano method. I can see the peaks caused by the characteristic lines of the used X-ray tube (in this ...
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Unique lattice constant using X-ray diffraction
I recently learned about X-diffraction methods to analyse crystal lattices. One important law in this is the Bragg condition
$$\lambda = 2d\sin(\theta).$$
I understand that $d$ is the distance between ...
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What's the difference between X-ray crystallography and X-ray spectroscopy?
From my understanding, further evidence for the structures of molecules can be obtained from single crystal X-ray crystallography which involved irradiating a crystal with X-rays and looking at the ...
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Physical meaning of Laue's condition for diffraction from crystals
The Laue's condition for diffraction is that scattering vector is equal to reciprocal lattice vectors $\mathbf{G}$. But how can a 'particular vector' equal a set of vectors? The reciprocal lattice ...
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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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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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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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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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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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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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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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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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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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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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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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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 ...
