Lattice:HCP - Revision history

KevinYager: /* Reciprocal-space Peaks */

2014-11-10T22:31:17Z

‎Reciprocal-space Peaks

2014-11-10T22:31:07Z

‎Particle Positions (Cartesian coordinates)

2014-10-14T15:45:51Z

‎Symmetry

2014-10-14T15:29:02Z

‎See Also

2014-10-14T15:26:20Z

‎Particle Positions (basis vectors)

2014-10-14T15:20:52Z

‎Canonical HCP

2014-10-14T15:14:16Z

2014-10-14T15:14:06Z

‎Nano

2014-10-14T15:05:54Z

‎Canonical HCP

2014-10-14T15:03:07Z

‎Canonical HCP

@@ Line 37: / Line 37: @@
 ===[[Reciprocal-space]] Peaks===
 * Allowed reflections:
-* <math>l</math> even
+** <math>l</math> even
-* <math>h+2k \neq 3 n</math>
+** <math>h+2k \neq 3 n</math>
 * Peak positions:
 *: <math>q_{hkl}=2\pi\left( \frac{(h^2 + hk + k^2)^2}{a^2} + \frac{l^2}{c^2} \right)^{1/2}</math>

@@ Line 34: / Line 34: @@
 ====Particle B: inner====
 * <math>\left(\frac{a}{3}+\frac{b}{6},\frac{\sqrt{3}b}{6},\frac{c}{2} \right)</math>
 ===Examples===

@@ Line 12: / Line 12: @@
 ** 'inner' particles: <math>1</math>
 ** 'corner' particles: <math>1</math>
 * Dimensionality: <math>d=3</math>

← Older revision		Revision as of 15:29, 14 October 2014
Line 50:		Line 50:
	==See Also==		==See Also==
	* [http://en.wikipedia.org/wiki/Close-packing_of_equal_spheres Wikipedia: Close-packing of equal spheres]		* [http://en.wikipedia.org/wiki/Close-packing_of_equal_spheres Wikipedia: Close-packing of equal spheres]
		+	* [[Lattice:AlB2]]

@@ Line 24: / Line 24: @@
 ====Particle B: inner====
 * <math> 1 \, \mathrm{inner} \, \times \, 1 = 2</math>
-** <math>\left(\frac{1}{3},\frac{1}{3},\frac{1}{2} \right), </math>
+** <math>\left(\frac{1}{3},\frac{1}{3},\frac{1}{2} \right) </math>
 ===Examples===

@@ Line 6: / Line 6: @@
 \frac{c}{a} = 2 \sqrt{ \frac{2}{3} } = \frac{2\sqrt{6}}{3} \approx 1.633
 </math>
 ===Examples===
 ====Elemental====
 : 4. [http://en.wikipedia.org/wiki/Beryllium Beryllium (Be)] (''a'' = ''b'' = 2.290 Å, ''c'' = 3.588, ''c''/''a'' = 1.567)
 : 27. [http://en.wikipedia.org/wiki/Cobalt Cobalt (Co)] (''a'' = ''b'' = 2.5071 Å, ''c'' = 4.0695, ''c''/''a'' = 1.623)

← Older revision		Revision as of 15:14, 14 October 2014
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−	'''HCP''' ('''Hexagonal close-packed''') is a [[Lattice:Hexagonal\|hexagonal]] [[Lattices\|lattice]]. It is notable (along with [[Lattice:FCC\|~~FACC~~]]) because it achieves the densest possible packing of spheres. It thus arises naturally in many atomic crystals, as well as in colloidal crystals and nanoparticles [[superlattice]]s.	+	'''HCP''' ('''Hexagonal close-packed''') is a [[Lattice:Hexagonal\|hexagonal]] [[Lattices\|lattice]]. It is notable (along with [[Lattice:FCC\|FCC]]) because it achieves the densest possible packing of spheres. It thus arises naturally in many atomic crystals, as well as in colloidal crystals and nanoparticles [[superlattice]]s.

	==Canonical HCP==		==Canonical HCP==

@@ Line 17: / Line 17: @@
 ====Nano====
-* TBD
+* Gold nanoparticles
 ==See Also==
 * [http://en.wikipedia.org/wiki/Close-packing_of_equal_spheres Wikipedia: Close-packing of equal spheres]

@@ Line 4: / Line 4: @@
 In the canonical HCP, the ratio between the ''a'' and ''c'' distances is:
 :<math>
-\frac{c}{a} = 2 \sqrt{ \frac{2}{3} } \approx 1.633
+\frac{c}{a} = 2 \sqrt{ \frac{2}{3} } = \frac{2\sqrt{6}}{3} \approx 1.633
 </math>