All Questions
Tagged with lattices crystallography
16 questions
8
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2
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2k
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Why are there only 14 types of Bravais lattices and not 28 when there are 7 types of unit cells and each can have four variations?
As the title suggests, I can't understand why certain kinds of variations (like Face-centred or Body-centred) are restricted to certain types of unit cells. An orthorhombic unit cell has Primitive, ...
- 337
1
vote
1
answer
5k
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Radius ratio of octahedral interstitial site in BCC lithium
Problem
Determine the minimum radius of an atom that will just fit into (a) the tetrahedral interstitial site in FCC nickel and (b) the octahedral interstitial site in BCC lithium.
Solution
(a) For ...
- 284
1
vote
0
answers
37
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HCP and hexagonal primitive cell [duplicate]
There are 14 types of Bravais lattices one of them is hexagonal which is just present as primitive cell ie the basis are at its corners , now when I read about hexagonal closed packing I came to know ...
- 29
3
votes
1
answer
1k
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Whats the difference between unit cell and motif?
The definition in my material is that motif and unit cells are both a repeating unit, but whereas motif is with respect to 2D lattice the unit cell is with respect to 3D lattice. But I can't find ...
- 230
4
votes
1
answer
6k
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Finding the atomic packing factor (APF) of Sodium Chloride and other FCC ionic compounds
For a piece of coursework I am doing, I need to calculate the atomic packing factor of some ionic compounds. I have had no formal teaching in this area, so what I know comes from information I have ...
- 41
2
votes
2
answers
2k
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Conventional unit cell for a hexagonal crystal system
The figure shows a unit cell of a hexagonal crystal system. Drawn in bold, is the unit cell. The lightly shaded one is a unit cell as well and has a six fold symmetry along an axis, hence is more ...
- 313
1
vote
1
answer
2k
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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 ...
- 113
4
votes
2
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929
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Is there a standard scholarly reference for lattice constants of crystals of the elements?
I need to discuss the lattice constants of bulk crystals of several metal and semiconductor elements. I can find plenty of tables and numbers that are probably "close enough" but for a paper ...
- 5,997
6
votes
3
answers
10k
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Converting fractional coordinates into cartesian coordinates for crystallography
So let's say for a given molecule I have the volume of a unit cell, the shape of the unit cell (monoclinic, cubic, etc), the cell angles alpha, beta, and gamma, the cell lengths a,b, and c, and a list ...
0
votes
0
answers
125
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What is meant by "rotation about an axis that passes through a lattice point"?
I am currently studying Introduction to Solid State Physics, 8th edition, by Charles Kittel. In the section Fundamental Types of Lattices of chapter 1, the author says the following:
Crystal lattices ...
- 1,103
0
votes
2
answers
980
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Sketching lattice points, primitive axes, primitive cell, and basis of atoms
I am currently studying Introduction to Solid State Physics, 8th edition, by Kittel. Chapter 1 provides the following figure and accompanying explanations:
It also says the following:
An ideal ...
- 1,103
8
votes
0
answers
4k
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What are the limitations of the Born-Lande' equation?
The Born-Lande' equation is used to theoretically calculate the lattice energy, $\Delta U$, of ionic compounds. It is often cited as such in literature,
$$\Delta U = -\frac{k_Az_1z_2Me^2}{4 \pi \...
- 111
1
vote
1
answer
867
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Does a unit cell have to contain a whole number of atoms?
I was given this problem recently to compute the number of ions in a unit cell of ferrous oxide $\ce{FeO}$. The data given was:
Side length $a = \pu{5 Å}$
Density $d = \pu{4 g/cc}$
Using the formula ...
- 6,338
5
votes
1
answer
3k
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How do the three Miller indices (hkl) denote planes orthogonal to the reciprocal lattice vector?
The Wikipedia page for Miller indices defines Miller indices as follows:
There are two equivalent ways to define the meaning of the Miller indices: via a point in the reciprocal lattice, or as the ...
- 1,103
2
votes
1
answer
430
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Do we really have technology with the resolution to distinguish between layers of single atoms of materials?
My textbook, Solid-State Physics, Fluidics, and Analytical Techniques in Micro- and Nanotechnology, by Madou, says the following:
X-ray analysis reveals the symmetries of crystals (lattice type), ...
- 1,103
3
votes
1
answer
185
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Does a molecule need to be placed symmetrically in the unit cell?
I was watching an OCW by MIT (3.091X) on solid state. My previous notion of lattice point and unit cell got shattered after this example.
Where are the unit cell and lattice points in this picture?
...
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