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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Minimum distance for two parallel beam to interfere effectively

Following is an illustration of two parallel monochromatic beams interfering in Bragg's law experiment. For these two rays to interfere, what is the minimum distance OF required? I understand that the ...
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What is the difference between the X-ray diffraction and neutron diffraction?

In the Kittel book, I have read that the ionic form of $\text{KCl}$ contains $\text{K}^+$ and $\text{Cl}^-$, having equal number of electrons. Looking at the statement in figure that while doing the ...
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The wavelength of the probing wave and the interatomic distance relation

I have often seen this statement in different texts that the wavelength of the probing wave should nearly be of the same order as the interatomic distance of the structure to be probed for the best ...
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Reciprocal Lattice

I am just getting started with solid state physics. To get the information about the crystal lattice, about it's structure we use the method of X-ray diffraction. Now as X-ray diffraction is not the ...
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Using visible light to get (weak) diffraction information about crystals?

If a crystal has diameter roughly 0.25mm containing unit cells (say cubes) of about 1 angstrom on a side, there are about 2.5 million unit cells in the diameter of the crystal. Bragg's law (n$\lambda =...
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How does Bragg assigned $(h,k,l)$ values to planes in his paper?

I'm reading a Paper by Sir Lawrence Bragg on X-Ray Crystallography. I came across a paragraph which I don't understand after reading many times : In the structural diagrams of sodium chloride on the ...
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What happens to the X-ray diffraction (XRD) pattern if we use laser as a incident beam?

In X-ray diffraction (XRD) pattern we use X-ray because it has the wavelength of the same order as that of the inter-planar separation. Now if instead of X-rays I use laser light, then how it will ...
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What happens to the XRD pattern of a crystalline structure upon cooling?

Suppose you have a XRD pattern of some crystal which is crystalline in nature. Now if you are cooling the crystal to say up to the temperature of a liquid nitrogen then how does the XRD pattern gets ...
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Why "identity" is selected as "generator" in the Int. Tables of Crystallography?

In chapter 8.3.5 of the Int. Tables for Cryst. Vol A it is stated that “in group theory, a set of generators of a group is a set of group elements such that each group element may be obtained as an ...
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What's the difference between inelastic X-rays scattering and Raman scattering?

In solids, inelastic scattering of X-rays can produce or absorb a phonon, which is equivalent to saying that solid ends up in excited vibrational level ( or if it was in a vibrational level to begin ...
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X ray diffraction to determine crystal structure: Certain Fourier components must be zero?

In Phillip Hofmanns introduction to solid state physics, we derive that the intensity of the diffracted X-rays incident on a crystal will take the form $$I(\vec{K})\propto \left|\int_V \rho(\vec{r})e^{...
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Lattice periodicity and Brilliouin zone

I was reading this paper and found the following statement (top of right column, pg 3). In particular, the frequencies of the silicon 2 × 1 surface reconstruction can be identified at ($k_x$, $k_y$) = ...
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No solution to Bragg's law?

Bragg's Law provides a description for the diffraction peaks we observe when x-rays are incident on a crystal structure. We observe these diffraction peaks because the wavelength of the incident x-...
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How to understand what is happening in this freshman X-ray scattering diagram?

In this Yale chemistry course I am taking on YouTube, I am stuck on something at 21:36 in the lecture. I am trying to understand the diagram Professor McBride is using to explain how X-Rays scatter ...
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Resolution power of the Bragg law

A physical system that follows the Bragg law of diffraction, for example an electron scatter, shows interference patterns at some angle that follows the equation $nλ = 2d\sin(θ).$ Usually just the ...
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Why does the kinematic theory of diffraction for crystals predict the reflectivity will grow larger than 1?

Kinematic diffraction for perfect crystals is based on a few assumptions (neglecting multiple scattering, far field, etc.) some of which become less valid as the crystal thickness is increased. ...
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What is the Maximum Number of Electrons per Angstrom Cubed? [closed]

Upon some reading, it has come to my knowledge that electron density is measured in number per Angstrom cubed. I assume, since electrons take up 'space', that there is some sort of maximal number of ...
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Why does $P21/c$ space group have $2/m$ point group symmetry?

In wikipedia, it says $P21/c$ has $2/m$ symmetry. https://en.wikipedia.org/wiki/Monoclinic_crystal_system But in its space group diagram, there is no 2-fold rotation or mirror planes http://img.chem....
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What is the unit and dimension of a matrix operator in quantum mechanics?

Let us consider the higher order Born approximation that explains multiple scattering. The well-known Born expansion leads to the expression for transition "matrix" or "T-matrix" ...
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Can Bragg's spectrometer be used to determine wavelength of EM wave other than X-rays?

I have read that Bragg's spectrometer is used to study crystals using X rays. It is also used to determine the wavelength of X-rays . My question is that can it be used to determine wavelength of any ...
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Is X-ray scattering just measuring a correlation function?

In my textbook it says that X rays measures the density-density correlation function. If the scattering is elastic, we get the equal time correlation function. They mention that intensity of the ...
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Misconceptions related to Von Lau formulation of X-ray diffraction by a crystal

When we shine an X-ray beam on a crystal, according to Van Laue formulation, for a sharp intensity peak to be observed on the screen there is a specific direction $\mathbf{\hat{n}}$, in which for all ...
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Can a single atom be a unit cell?

I was reading a pdf online and it's author said Consider the bcc lattice with single atoms at each lattice point, its unit cell can be reduced to two identical atoms. Atom 1 is at 000 and atom 2 is ...
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Confusion regarding calculation of Miller indices for planes

Let's calculate the Miller indices of the yellow plane. The intercepts are $(2,2,1)$ . Taking the reciprocals we get $1/2,1/2,1$ . Clearing the fractions I get the indices as $(1,1,2)$. Why then does ...
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Miller indices of a BCC structure

The miller indices of the middle plane is $(2,0,0)$ and it's easy to see why it's so but I've read that one should reduce the Miller indices down to lower integers so the miller Indices of this middle ...
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Thermo Fischer: Phenom Pharos Desktop SEM

Does anyone know which "Thermo Fischer: Phenom Pharos Desktop SEM" generation is displayed in this picture. I have used this microscope during an experiment and I'm looking for the datasheet ...
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What is meant by "a plane wave that has the periodicity of a Bravais lattice"?

I'm reading through Ashcroft & Mermin's chapter on reciprocal lattices and am confused about this sentence: Consider a set of points R constituting a Bravais lattice, and a plane wave, e^{i k*r}. ...
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What does it mean to assign group operations to distinct sets for space groups?

I am trying to understand space groups in crystallography. In Internation tables for crystallography, for a nonsymmorphic space group, they list some symmetry operations. 8 of them are listed under ...
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What are the best resources for Crystallography?

I am undertaking a module in nanosurfaces and I was unaware that I would require some knowledge in Crystallography. The information that I must know regarding this area are Miller indices, Symmetries, ...
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Is structure factor depends on how to choose unit cell?

Consider FCC lattice, let lattice vectors are $$ \vec{a}_1=a\hat{x}, \quad \vec{a}_2=a\hat{y}, \quad \vec{a}_3=a\hat{z} $$ then basis are $(000),(\dfrac{1}{2}00),(0\dfrac{1}{2}0),(00\dfrac{1}{2})$, ...
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Quantify/visualize atomic clusters in multi-component crystalline materials

Let's say we have a material $AB$. Is it possible to detect atomic clusters of A atoms experimentally? The size of clusters in question: 2 atoms (nearest neighbour (nn) pairs), 3 atoms (nn triangles), ...
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Determining $\mathbf{a}^*$, $\mathbf{b}^*$, and $\mathbf{c}^*$ for reciprocal unit cell [closed]

We are given a unit cell with $a=4$ angstroms, $b = 6$ angstroms, and $c=8$ angstroms. $\alpha=\beta= 90^{\circ}$, $\gamma= 120^{\circ}$. I would like to find $\mathbf{a}^*$, $\mathbf{b}^{*}$, and $\...
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How is a non-primitive unit cell/lattice helpful?

I am starting with the basics of X-ray crystallography, and I have encountered something I'm not able to rationalize. As I understand it, the unit cell is the smallest parallelepiped enclosing the (a?)...
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Can I distinguish hexagonal close packing (HCP) from face centred cubic (FCC) arrangement based on Fourier transform

First of all I would say that I'm not a physicist, but I have recently been given the task of distinguishing a hexagonal close packing (HCP) from a face centred cubic (FCC) arrangement in a set of 3D ...
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What is an example of an actual crystal with a primitive cell containing more than one atom?

By definition, a primitive cell contains only one lattice point but may contain more than one atom. What is an example of a real crystal that has a primitive cell with more than one atom per cell? I ...
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Xray diffraction [closed]

why to diffraction, the spacing between the scatterers and the wavelength should be similar in size, For example in xray diffraction to determine crystal structure? If it not similar what does happen?
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Can X-ray diffraction be applied to liquids, gasses or non-crystalline materials?

I learned that X-ray diffraction happens due to the periodic arrangement of atoms in a crystalline material, so can X-ray diffraction studies be done on liquids and non-crystalline materials?
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How do I find Miller indices for a plane whose intercepts are fractions of the lattice constant?

[I'm talking with respect to cubic lattices alone.] For instance, if a plane has $x,y,z$ intercepts $a/2,a/2,a/2$ (where $a$ is the lattice constant) the miller index would be $[2\space2\space2]$. The ...
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Why is Bragg diffraction small-angle for thicker layers and/or larger molecules or unit cells? And wide-angle for small or shallow crystals?

It is easy to find equations that quantify this on the internet, but not an explanation as to why... Also, does this apply to electrons and neutrons? Or just X-ray reflection/diffraction?
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X- Ray diffraction confusion

In X-Ray diffraction experiment how the reflected rays superimpose as we know reflected rays are parallel. As we can see in the image
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Why does the scattering wave vector and reciprocal lattice vector have to be the same?

In Introduction to Solid state physics 8th edition by Charles Kittel. The scattering amplitude is defined as, $$F=\int dV n_G exp[i(\bf{G-\Delta k}).\bf{r}]$$ where G is the reciprocal lattice vector ...
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How can we represent P4mm space group?

I understand that P4mm belongs to Tetragonal system. But how do we decide along which axis should we perform these symmetry operations? According to my professor the axis along which we should do the ...
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1answer
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Having trouble understanding interplanar spacing using miller indices

We know that two parallel planes have the same Miller indices so we can have an infinite number of parallel planes close to one another all of which have the same Miller indices. But it's claimed that ...
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37 views

How will the X ray diffraction pattern change if the crystal changes its lattice structure

A text says: An X - ray diffraction experiment is carried out on a crystalline solid having FCC structure at room temperature. The solid undergoes a phase transformation on cooling and shows ...
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Can we draw a $(hkl)$ plane and the corresponding $\vec{G}$ vector in one diagram?

The reciprocal lattice vector $\vec{G}=h\vec{b}_1++k\vec{b}_2+l\vec{b}_3$ is perpendicular to the family of planes described by the Miller indices $(hkl)$. This means that if $\hat{n}$ be the unit ...
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Relation between $(hkl)$ indices and the integers $m_i$ in $\vec{G}=\sum_i m_i\vec{b}_i$?

Can somebody explain how to establish the connection between Miller indices $(h,k,l)$ of a crystal plane and the triplet of integers $(m_1,m_2,m_3)$ that appear in the linear combination $$\vec{G}=...
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37 views

Why only even integers occur in reflection indices of $\rm KCl$?

I was reading kittel and came across this .Its mentioned that since scattering factors of k+ and cl- are almost same the entire crystal appears to be a simple cubic crystal of constant $a/2$. but how ...
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Interplanar distance in FCC and BCC

Interplanar cystal spacing of cubic crystal families is defined as $$d_{hkl} = \frac{a}{\sqrt{h^2+k^2+l^2}}.$$ This source says that the interplanar spacing of the $(111)$ plane in FCC is $\frac{a}{\...
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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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55 views

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 ...