Example:Particle spacing from peak position - Revision history

KevinYager: /* See Also */

2014-12-01T14:45:18Z

‎See Also

KevinYager at 14:43, 1 December 2014

2014-12-01T14:43:48Z

KevinYager: /* FCC 111 */

2014-09-02T18:40:57Z

‎FCC 111

KevinYager: /* FCC 111 */

2014-09-02T18:38:17Z

‎FCC 111

KevinYager: /* BCC 110 */

2014-09-02T18:36:50Z

‎BCC 110

KevinYager: /* BCC 110 */

2014-09-02T18:31:57Z

‎BCC 110

KevinYager at 18:28, 2 September 2014

2014-09-02T18:28:01Z

KevinYager: Created page with "Consider a cubic unit cell (SC, Lattice:BCC, Lattice:FCC). Note that in general: : $\begin{alignat}{2} \left( \frac{1}{d_{hkl}} \right )^2 = \left(\frac{h}{a}\rig..."$

2014-09-02T18:25:16Z

Created page with "Consider a cubic unit cell (SC, Lattice:BCC, Lattice:FCC). Note that in general: :<math> \begin{alignat}{2} \left( \frac{1}{d_{hkl}} \right )^2 = \left(\frac{h}{a}\rig..."

New page

Consider a cubic unit cell (SC, [[Lattice:BCC]], [[Lattice:FCC]]). Note that in general:
:<math>
\begin{alignat}{2}
\left( \frac{1}{d_{hkl}} \right )^2 = \left(\frac{h}{a}\right)^2 + \left(\frac{k}{b}\right)^2 + \left(\frac{l}{c}\right)^2
\end{alignat}
</math>

[[Q value|Since]] <math>q=2 \pi / d</math>, and since <math>a=b=c</math>, the realspace spacing of planes is:
:<math>
\begin{alignat}{2}
d_{hkl}
& = \frac{a}{\sqrt{ h^2 + k^2 + l^2 }}
\end{alignat}
</math>

← Older revision		Revision as of 14:45, 1 December 2014
Line 79:		Line 79:

	==See Also==		==See Also==
−	Weidman, M.C.; [[Yager, K.G.]], Tisdale, W.A. [http://pubs.acs.org/doi/abs/10.1021/cm503626s Interparticle Spacing and Structural Ordering in Superlattice PbS Nanocrystal Solids Undergoing Ligand Exchange] ''Chemistry of Materials'' '''2015''' [http://dx.doi.org/10.1021/cm503626s doi: 10.1021/cm503626s]	+	* Weidman, M.C.; [[Yager, K.G.]], Tisdale, W.A. [http://pubs.acs.org/doi/abs/10.1021/cm503626s Interparticle Spacing and Structural Ordering in Superlattice PbS Nanocrystal Solids Undergoing Ligand Exchange] ''Chemistry of Materials'' '''2015''' [http://dx.doi.org/10.1021/cm503626s doi: 10.1021/cm503626s]

← Older revision		Revision as of 14:43, 1 December 2014
Line 77:		Line 77:
	===Comparison===		===Comparison===
	Notice that the BCC 110 and FCC 111 have the same 'conversion factor' from ''q''-position into particle-particle distance. Thus, even without knowing which unit cell the particles are packing into, one can perform the conversion, provided one is confident about the peak being either the BCC 110 or the FCC 111.		Notice that the BCC 110 and FCC 111 have the same 'conversion factor' from ''q''-position into particle-particle distance. Thus, even without knowing which unit cell the particles are packing into, one can perform the conversion, provided one is confident about the peak being either the BCC 110 or the FCC 111.
		+
		+	==See Also==
		+	Weidman, M.C.; [[Yager, K.G.]], Tisdale, W.A. [http://pubs.acs.org/doi/abs/10.1021/cm503626s Interparticle Spacing and Structural Ordering in Superlattice PbS Nanocrystal Solids Undergoing Ligand Exchange] ''Chemistry of Materials'' '''2015''' [http://dx.doi.org/10.1021/cm503626s doi: 10.1021/cm503626s]

← Older revision		Revision as of 18:40, 2 September 2014
Line 74:		Line 74:
	\end{alignat}		\end{alignat}
	</math>		</math>
		+
		+	===Comparison===
		+	Notice that the BCC 110 and FCC 111 have the same 'conversion factor' from ''q''-position into particle-particle distance. Thus, even without knowing which unit cell the particles are packing into, one can perform the conversion, provided one is confident about the peak being either the BCC 110 or the FCC 111.

@@ Line 66: / Line 66: @@
 </math>
 Or:
 \begin{alignat}{2}
-d_{110}
+d_{111}
-   & = \frac{a}{\sqrt{ 2 }} \\
+   & = \frac{a}{\sqrt{ 3 }} \\
-   & = \frac{ 2 d_{nn} / \sqrt{3} }{\sqrt{ 2 }} \\
+   & = \frac{ 2 d_{nn} / \sqrt{2} }{\sqrt{ 3 }} \\
    & = \frac{ 2 d_{nn} }{\sqrt{ 6 }} \\
 \end{alignat}
 </math>

@@ Line 23: / Line 23: @@
 </math>
 [[Lattice:BCC|Note that for BCC]], the particle-particle distance is given by:
-:<math>d_{nn}=\frac{ \sqrt{3}a }{2}</math>
+:<math>d_{nn} = \sqrt{3}a /2</math>
 So we expect:
 :<math>
@@ Line 31: / Line 31: @@
    & = \frac{ \sqrt{3} d_{110} \sqrt{2} }{2} \\
    & = \frac{ \sqrt{6} d_{110}  }{2} \\
-   & = \frac{ \sqrt{6} (2 \pi / q_{110}  }{2} \\
+   & = \frac{ \sqrt{6} (2 \pi / q_{110} ) }{2} \\
    & = \frac{ \pi \sqrt{6}  }{q_{110}} \\
 \end{alignat}
 </math>

@@ Line 1: / Line 1: @@
-Consider a cubic unit cell (SC, [[Lattice:BCC]], [[Lattice:FCC]]). Note that in general:
+Consider the case of trying to measure the particle-particle spacing from the ''q''-value of a particular peak. The interpretation of the ''q'' value of course depends upon the packing of the particles; i.e. the [[unit cell]]. Consider a cubic unit cell ([[Lattice:SC|SC]], [[Lattice:BCC|BCC]], [[Lattice:FCC|FCC]]). Note that in general:
 :<math>
 \begin{alignat}{2}
@@ Line 11: / Line 11: @@
 d_{hkl}
    & = \frac{a}{\sqrt{ h^2 + k^2 + l^2 }}
 \end{alignat}
 </math>

Example:Particle spacing from peak position - Revision history

KevinYager: /* See Also */

KevinYager at 14:43, 1 December 2014

KevinYager: /* FCC 111 */

KevinYager: /* FCC 111 */

KevinYager: /* BCC 110 */

KevinYager: /* BCC 110 */

KevinYager at 18:28, 2 September 2014

KevinYager: Created page with "Consider a cubic unit cell (SC, Lattice:BCC, Lattice:FCC). Note that in general: : \begin{alignat}{2} \left( \frac{1}{d_{hkl}} \right )^2 = \left(\frac{h}{a}\rig..."

KevinYager: Created page with "Consider a cubic unit cell (SC, Lattice:BCC, Lattice:FCC). Note that in general: : $\begin{alignat}{2} \left( \frac{1}{d_{hkl}} \right )^2 = \left(\frac{h}{a}\rig..."$