Difference between revisions of "Talk:Lattices"

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B.M. Mladek, B.M.;  
 
B.M. Mladek, B.M.;  
 
Mladek, B.M.; Fornleitner, J.;  Martinez-Veracoechea, F.C.; Dawid, A.; Frenkel, D. [http://pubs.rsc.org/en/content/articlehtml/2013/sm/c3sm50701g Procedure to construct a multi-scale coarse-grained model of DNA-coated colloids from experimental] ''Soft Matter'' '''2013''', 9, 7342-7355 [http://dx.doi.org/10.1039/C3SM50701G doi: 10.1039/C3SM50701G]
 
Mladek, B.M.; Fornleitner, J.;  Martinez-Veracoechea, F.C.; Dawid, A.; Frenkel, D. [http://pubs.rsc.org/en/content/articlehtml/2013/sm/c3sm50701g Procedure to construct a multi-scale coarse-grained model of DNA-coated colloids from experimental] ''Soft Matter'' '''2013''', 9, 7342-7355 [http://dx.doi.org/10.1039/C3SM50701G doi: 10.1039/C3SM50701G]
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==Extra math==
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A given real-space lattice will have dimensions:
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:<math>\left(a,b,c\right)</math>
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Such that the position of any particular cell within the infinite lattice is:
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:<math>\mathbf{r}_{hkl} = \left\langle ah,bk,cl\right\rangle </math>
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Where ''h'', ''k'', and ''l'' are indices.
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The corresponding inverse-space lattice would be:
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:<math>
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\mathbf{q}_{hkl} = 2\pi \left\langle \frac{h}{a} , \frac{k}{b} , \frac{l}{c}  \right\rangle
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</math>
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:<math>
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q_{hkl} = 2\pi \sqrt{ \left( \frac{h}{a} \right)^2 + \left( \frac{k}{b} \right)^2 + \left( \frac{l}{c} \right)^2 }
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</math>
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In the case where <math>a=b=c</math>:
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:<math>
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\begin{alignat}{2}
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q_{hkl} & = 2\pi \sqrt{ \left( \frac{h}{a} \right)^2 + \left( \frac{k}{a} \right)^2 + \left( \frac{l}{a} \right)^2 } \\
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    & = \frac{2\pi}{a} \sqrt{ h^2 + k^2 + l^2 }
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\end{alignat}
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</math>

Latest revision as of 18:51, 13 November 2016

To Do

Add structures reported in:

B.M. Mladek, B.M.; Mladek, B.M.; Fornleitner, J.; Martinez-Veracoechea, F.C.; Dawid, A.; Frenkel, D. Procedure to construct a multi-scale coarse-grained model of DNA-coated colloids from experimental Soft Matter 2013, 9, 7342-7355 doi: 10.1039/C3SM50701G


Extra math

A given real-space lattice will have dimensions:

Such that the position of any particular cell within the infinite lattice is:

Where h, k, and l are indices. The corresponding inverse-space lattice would be:

In the case where :