80.161.145.8 at 21:31, 5 January 2015

2015-01-05T21:31:03Z

en>Spinningspark: /* Impact on frequency response */ correct sign

2014-02-13T14:02:41Z

Impact on frequency response: correct sign

en>Chetvorno: Added to introduction date of discovery and discoverer, and importance of Miller capacitance in limiting the bandwidth of active devices

2014-01-14T20:26:18Z

Added to introduction date of discovery and discoverer, and importance of Miller capacitance in limiting the bandwidth of active devices

← Older revision		Revision as of 22:26, 14 January 2014
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	The ~~author~~ is ~~[http~~://~~www~~.~~sexualhealth~~.~~com/std~~-~~testing~~-~~windows/ called Irwin~~]~~. He~~ [~~http~~:~~//www~~.~~ddaybeauty~~.~~com/node/14766 home std test kit] used~~ to ~~be unemployed but now he~~ is a ~~computer operator but his marketing never arrives~~. ~~The over~~ the ~~counter std test preferred [http~~:~~//Www~~.~~strangecosmos.com~~/~~content/item/170784.html pastime]~~ for ~~my kids~~ [~~http~~://~~phpfoxdev~~.~~azurewebsites~~.~~net~~/~~index~~.~~php?do=/profile~~-~~44231/info/ home std test kit~~] ~~and me~~ is ~~to perform baseball~~ and I'~~m trying std testing at home to make it a profession~~. ~~For~~ a ~~while she's been in South Dakota~~.<br><br>~~Check out my web site;~~ [~~http:~~//~~www.xn~~--~~80aeerfhjjg1bv8c.xn~~--~~p1ai~~/~~%D0%A1%D0%BE%D0%B4%D0%B5%D1%80%D0%B6%D0%B0%D0%BD%D0%B8%D0%B5~~/~~cures~~-~~yeast~~-~~infection-tips-use-now www~~.~~домашнийвкус~~.xn-~~-p1ai~~]		In [[crystallography]], '''atomic packing factor''' (APF) or '''packing fraction''' is the fraction of volume in a [[crystal structure]] that is occupied by [[atom]]s. It is dimensionless and always less than unity. By convention, the APF of a crystal structure is determined by assuming that atoms are rigid spheres. The radius of the spheres is taken to be the maximal value such that the atoms do not overlap. For one-component crystals (those that contain only one type of atom), the APF is represented mathematically by

			:<math>\mathrm{APF} = \frac{N_\mathrm{atoms} V_\mathrm{atom}}{V_\mathrm{unit cell}}</math>

			where ''N<sub>atoms</sub>'' is the number of atoms in the unit cell, ''V<sub>atom</sub>'' is the volume of an atom, and ''V<sub>unit cell</sub>'' is the volume occupied by the unit cell. It can be proven mathematically that for one-component structures, the most dense arrangement of atoms has an APF of about 0.74. For multiple-component structures, the APF can exceed 0.74.

			==Worked out example==
			===Body-centered cubic crystal structure===
			[[File:CCC crystal cell (opaque).svg\|right\|thumb\|BCC structure]]

			The [[Unit cell\|primitive unit cell]] for the [[body-centered cubic]]
			(BCC) crystal structure contains several fractions taken from nine
			atoms: one on each corner of the cube and one atom in the center.
			Because the volume of each corner atom is shared between adjacent cells,
			each BCC cell contains two atoms.

			Each corner atom touches the center atom. A line that is drawn from one
			corner of the cube through the center and to the other corner passes
			through 4''r'', where ''r'' is the radius of an atom. By geometry, the
			length of the diagonal is ''a''√3. Therefore, the length of each side of
			the BCC structure can be related to the radius of the atom by

			:<math>a = \frac{4r}{\sqrt{3}}.</math>

			Knowing this and the formula for the [[volume of a sphere]], it becomes
			possible to calculate the APF as follows:

			:<math>\mathrm{APF} = \frac{N_\mathrm{atoms}
			V_\mathrm{atom}}{V_\mathrm{crystal}} = \frac{2 (4/3)\pi
			r^3}{(4r/\sqrt{3})^3}</math>

			<!-- extra blank line for legibility of mathematical notation -->

			:::<math>= \frac{\pi\sqrt{3}}{8} \approx 0.68.\,\!</math>

			===Hexagonal close-packed crystal structure===
			[[File:Hexagonal close packed.svg\|right\|thumb\|HCP structure]]

			For the [[Hexagonal crystal system\|hexagonal close-packed]] (HCP)
			structure the derivation is similar. Here the unit cell is a hexagonal
			prism containing six atoms. Let ''a'' be the side length of its base and
			''c'' be its height. Then:

			:<math>a = 2r</math>

			<!-- extra blank line for legibility of mathematical notation -->

			:<math>c = \sqrt{\frac{2}{3}}(4r).</math>

			It is then possible to calculate the APF as follows:

			:<math>\mathrm{APF} = \frac{N_\mathrm{atoms}\cdot
			V_\mathrm{atom}}{V_\mathrm{crystal}} = \frac{6\cdot (4/3)\pi
			r^3}{[(3\sqrt{3})/2](a^2)(c)}</math>

			<!-- extra blank line for legibility of mathematical notation -->

			:::<math>= \frac{6 (4/3)\pi
			r^3}{[(3\sqrt{3})/2](2r)^2(\sqrt{\frac{2}{3}})(4r)} = \frac{6 (4/3)\pi
			r^3}{[(3\sqrt{3})/2](\sqrt{\frac{2}{3}})(16r^3)}</math>

			:::<math>= \frac{\pi}{\sqrt{18}} \approx 0.74.\,\!</math>

			==APF of common structures==
			By similar procedures, the ideal atomic packing factors of all crystal structures can be found. The common ones are collected here as reference, rounded to the nearest hundredth.

			g৳
			* [[Hexagonal crystal system\|Hexagonal close-packed]]: 0.74
			* [[Face-centered cubic]]: 0.74
			* [[Diamond cubic]]: 0.34

			==See also==
			*[[Crystal]]


			==References==
			# {{cite book
			\| author = Schaffer, Saxena, Antolovich, Sanders, and Warner
			\| year = 1999
			\| title = The Science and Design of Engineering Materials
			\| edition = Second Edition
			\| pages = 81–88
			\| publisher = WCB/McGraw-Hill
			\| location = New York
			}}
			# {{cite book
			\| author = Callister, W.
			\| title = Materials Science and Engineering
			\| year = 2002
			\| edition = Sixth Edition
			\| publisher = John Wiley and Sons
			\| pages = 105–114
			\| location = San Francisco
			}}
			[[Category:Crystallography]]

en>Glenn: +da

2012-07-15T20:47:46Z

+da

New page

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Miller effect - Revision history

80.161.145.8 at 21:31, 5 January 2015

en>Spinningspark: /* Impact on frequency response */ correct sign

en>Chetvorno: Added to introduction date of discovery and discoverer, and importance of Miller capacitance in limiting the bandwidth of active devices

en>Glenn: +da