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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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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How to find the plane from which X-ray diffraction will occur for a FCC crystal? [closed]

I don't have any teacher to go to, This is not a homework problem. While going through a paper A question went as $\rm KCl $ has the $\rm NaCl $ type structure which is FCC with two-atom basis, one ...
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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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What is meant by the symmetry group of a crystal?

When we talk about the symmetry group of a crystal, does it mean the set of transformation under which a unit cell is taken to itself? For example, if we have a two-dimensional hexagonal lattice, can ...
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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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X-Ray Diffraction pattern peak tailing

I have recently been working with Rietiveld refinement on powder X-Ray Diffraction (XRD) patterns by using the GSAS2 (General Structure Analysis System) program where, one of the steps, is to produce ...
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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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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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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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Thickness-dependence of diffraction intensity in single-scattering regime?

Is the thickness of a sample related to the intensity of x-ray diffraction? seems to ask about the thickness-scaling of diffraction intensity in crystallography, but in the body it refers only to ...
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Expression for differential solid angle in terms of wave vector?

I have been reading this book " High resolution x-ray scattering from thin films to lateral nano structures " by Pietsch et.al. In the last line of page number $63$ the author replaces the ...
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Intuitively explained, how are lattice planes defined?

I understand that the symmetry in a diffraction pattern is used to define the unit cell parameters (i.e. the unit cell), and the miller indices are reciprocal of the lattice planes that intersect with ...
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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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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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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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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 now ...
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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 the ...
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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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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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1answer
102 views

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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1answer
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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?