Spouge's approximation - Revision history

en>Yobot: /* External links */WP:CHECKWIKI error fixes using AWB (10093)

2014-05-05T13:05:37Z

External links: WP:CHECKWIKI error fixes using AWB (10093)

← Older revision		Revision as of 15:05, 5 May 2014
Line 1:		Line 1:
	~~[[Image:Bubblerraft2.jpg\|right\|thumb\|200px\|Image of a bubble raft (bubble size ~1.5 mm) showing vacancies~~ and ~~an edge dislocation in the bottom right corner~~.]]		Hello and welcome. My name is Figures Wunder. To gather coins is what his family and him enjoy. My working day job is a meter reader. Puerto Rico is exactly where he and his wife live.<br><br>Feel free to visit my web-site; [http://test.ithink-now.org/content/think-f83d96d08fe71e25bf80a6cb59048a18 http://test.ithink-now.org/content/think-f83d96d08fe71e25bf80a6cb59048a18]

	'''Bubble rafts''' demonstrate materials' [[microstructure\|microstructural]] and atomic length-scale behavior by modelling the {111} plane of a close-packed crystal. A material's observable and measurable mechanical properties strongly depend on its atomic and microstructural configuration and characteristics. ~~This fact~~ is ~~intentionally ignored in [[continuum mechanics]], which assumes a material to have no underlying microstructure and be uniform and semi-infinite throughout.~~

	Bubble rafts assemble bubbles on a water surface, often with the help of [[amphiphilic]] soaps. These assembled bubbles act like atoms, diffusing, slipping, ripening, straining, and otherwise deforming in a way that models the behavior of the {111} plane of a close-packed crystal. The ideal (lowest energy) state of the assembly would undoubtedly be a perfectly regular single crystal, but just as in metals, the bubbles often form defects, grain boundaries, and multiple crystals.

	~~== History of bubble rafts ==~~

	The concept of bubble raft modelling was first presented in 1947 by Nobel Laureate Sir [[William Lawrence Bragg]] and [[John Nye (scientist)\|John Nye]] of [[Cambridge University]]'s [[Cavendish Laboratory]] in [[Proceedings of the Royal Society A]].[1] Legend claims that Bragg conceived of bubble raft models while pouring oil into his ~~lawn mower. He noticed that bubbles on the surface of the oil assembled into rafts resembling the {111} plane of close-packed crystals[2]. Nye~~ and Bragg later presented a method of generating and controlling bubbles on the surface of a glycerine-water-oleic acid-triethanolamine solution, in assemblies of 100,000 or more sub-millimeter sized bubbles. In their paper [1], they go on at length about the microstructural phenomena observed in bubble rafts and hypothesized in metals.

	~~==Relation to crystal lattices==~~
	~~In deforming a crystal lattice, one changes the energy and the interatomic potential felt by the atoms of the lattice. This interatomic potential~~ is ~~popularly (and mostly qualitatively) modeled using the [[Lennard-Jones potential]], which consists of~~ a ~~balance between attractive and repulsive forces between atoms~~.

	~~The "atoms" in Bubble Rafts also exhibit such attractive and repulsive forces:~~

	~~<math>U ( \rho ) = - \pi R^4 \rho_{solution} g \left ( \frac{\Beta}{\alpha} \right )^2 \mathit{A} K_0 (\alpha \rho) +~~

	~~\begin{cases} 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \rho \ge \ 2 \\ \pi R^4 \rho_{solution} g \left ( \frac{(2-\rho)^2}{\alpha^2} \right ) ~~~ \rho \le\ 2 \end{cases}~~

	~~</math> [2]~~

	~~The portion of the equation to the left of the plus sign~~ is ~~the attractive force,~~ and ~~the portion to the right represents the repulsive force~~.

	~~<math>U ( \rho )~~<~~/math~~> ~~is the interbubble potential~~

	<~~math~~>~~R</math> is the average bubble radius~~

	~~<math>\rho_{solution}</math> is the density of the solution from which the bubbles are formed~~

	~~<math>g</math> is the gravitational constant~~

	~~<math>\rho</math> is the ratio of the distance between bubbles~~ to ~~the bubble radius~~

	~~<math>\Beta</math> is the radius of ring contact~~

	~~<math> \alpha</math> is the ratio R/a of the bubble radius to the Laplace constant a, where~~

	~~<math> a^2 = \frac {T}{\rho_{solution} g}</math>~~

	~~<math>T</math> is the surface tension~~

	~~<math>A</math> is a constant dependent upon the boundary conditions of the calculation~~

	~~<math>K_0</math> is a zeroth~~-~~order modified [[Bessel function]] of the second kind[2]~~

	Bubble rafts can display numerous phenomena seen in the crystal lattice. This includes such things as point [[Crystallographic defect\|defect]]s (vacancies, substitutional impurities, interstitial atoms), [[dislocations]] (edge and screw) and [[Crystallite\|grains]]. It is even possible to replicate some microstructure treats such as [[annealing (metallurgy)\|annealing]]. The annealing process is simulated by stirring the bubble raft. This anneals out the dislocations ([[recovery (metallurgy)\|recovery]]) and promotes [[recrystallization (metallurgy)\|recrystallization]].

	~~[[Image:Dislocated Bubble.png\|centre\|thumb\|800px\|A bubble raft showing a close up of an edge dislocation.]]~~

	~~== References ==~~
	*{{cite journal\|last1=Bragg\|first1=Lawrance\|last2=Nye\|first2=J. F.\|year=1947\|title=A Dynamical Model of a Crystal Structure\|journal=Proc. R. Soc. Lond. A\|volume=190\|issue=1023\|pages=474-481\|url=http://~~web~~.~~mit~~.~~edu/mikejd/previously_online~~/~~aices_mit_2009~~/~~Bragg~~-~~bubble_raft.pdf}}~~
	*Laboratory Handout in MIT's 3.032: Mechanical Properties of Materials. [http://~~stellar~~.~~mit~~.~~edu~~/S/~~course/3/fa06/3.032/index.html]~~

	~~{{DEFAULTSORT:Bubble Rafts}}~~
	~~[[Category:Materials science]~~]

en>Addbot: Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q935210

2013-03-16T07:11:59Z

Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q935210

← Older revision		Revision as of 09:11, 16 March 2013
Line 1:		Line 1:
	~~Alyson Meagher~~ is the ~~title her parents gave her~~ but ~~she doesn~~'~~t like when individuals use her complete name~~. ~~Invoicing~~ is ~~my profession~~. ~~Ohio is exactly where my home~~ ~~psychic love readings~~ ([~~http:~~//~~srncomm.com~~/~~blog~~/~~2014~~/08/25/~~relieve-that-stress-find-~~a~~-new-hobby~~/ ~~http:~~//~~srncomm~~.~~com/~~]) is ~~but my husband wants us~~ to ~~transfer~~. ~~Playing badminton~~ is a ~~thing that he is totally addicted to~~.~~<br><br>My blog good [~~http://~~www~~.~~seekavideo~~.~~com~~/~~playlist~~/~~2199~~/~~video~~/ ~~accurate psychic predictions] (~~[http://~~203~~.~~250~~.78.~~160/zbxe~~/~~?document_srl=1792908 Test by click the "Remove Empty Lines" button and watch these blank lines between this text disappear~~.])		[[Image:Bubblerraft2.jpg\|right\|thumb\|200px\|Image of a bubble raft (bubble size ~1.5 mm) showing vacancies and an edge dislocation in the bottom right corner.]]

			'''Bubble rafts''' demonstrate materials' [[microstructure\|microstructural]] and atomic length-scale behavior by modelling the {111} plane of a close-packed crystal. A material's observable and measurable mechanical properties strongly depend on its atomic and microstructural configuration and characteristics. This fact is intentionally ignored in [[continuum mechanics]], which assumes a material to have no underlying microstructure and be uniform and semi-infinite throughout.

			Bubble rafts assemble bubbles on a water surface, often with the help of [[amphiphilic]] soaps. These assembled bubbles act like atoms, diffusing, slipping, ripening, straining, and otherwise deforming in a way that models the behavior of the {111} plane of a close-packed crystal. The ideal (lowest energy) state of the assembly would undoubtedly be a perfectly regular single crystal, but just as in metals, the bubbles often form defects, grain boundaries, and multiple crystals.

			== History of bubble rafts ==

			The concept of bubble raft modelling was first presented in 1947 by Nobel Laureate Sir [[William Lawrence Bragg]] and [[John Nye (scientist)\|John Nye]] of [[Cambridge University]]'s [[Cavendish Laboratory]] in [[Proceedings of the Royal Society A]].[1] Legend claims that Bragg conceived of bubble raft models while pouring oil into his lawn mower. He noticed that bubbles on the surface of the oil assembled into rafts resembling the {111} plane of close-packed crystals[2]. Nye and Bragg later presented a method of generating and controlling bubbles on the surface of a glycerine-water-oleic acid-triethanolamine solution, in assemblies of 100,000 or more sub-millimeter sized bubbles. In their paper [1], they go on at length about the microstructural phenomena observed in bubble rafts and hypothesized in metals.

			==Relation to crystal lattices==
			In deforming a crystal lattice, one changes the energy and the interatomic potential felt by the atoms of the lattice. This interatomic potential is popularly (and mostly qualitatively) modeled using the [[Lennard-Jones potential]], which consists of a balance between attractive and repulsive forces between atoms.

			The "atoms" in Bubble Rafts also exhibit such attractive and repulsive forces:

			<math>U ( \rho ) = - \pi R^4 \rho_{solution} g \left ( \frac{\Beta}{\alpha} \right )^2 \mathit{A} K_0 (\alpha \rho) +

			\begin{cases} 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \rho \ge \ 2 \\ \pi R^4 \rho_{solution} g \left ( \frac{(2-\rho)^2}{\alpha^2} \right ) ~~~ \rho \le\ 2 \end{cases}

			</math> [2]

			The portion of the equation to the left of the plus sign is the attractive force, and the portion to the right represents the repulsive force.

			<math>U ( \rho )</math> is the interbubble potential

			<math>R</math> is the average bubble radius

			<math>\rho_{solution}</math> is the density of the solution from which the bubbles are formed

			<math>g</math> is the gravitational constant

			<math>\rho</math> is the ratio of the distance between bubbles to the bubble radius

			<math>\Beta</math> is the radius of ring contact

			<math> \alpha</math> is the ratio R/a of the bubble radius to the Laplace constant a, where

			<math> a^2 = \frac {T}{\rho_{solution} g}</math>

			<math>T</math> is the surface tension

			<math>A</math> is a constant dependent upon the boundary conditions of the calculation

			<math>K_0</math> is a zeroth-order modified [[Bessel function]] of the second kind[2]

			Bubble rafts can display numerous phenomena seen in the crystal lattice. This includes such things as point [[Crystallographic defect\|defect]]s (vacancies, substitutional impurities, interstitial atoms), [[dislocations]] (edge and screw) and [[Crystallite\|grains]]. It is even possible to replicate some microstructure treats such as [[annealing (metallurgy)\|annealing]]. The annealing process is simulated by stirring the bubble raft. This anneals out the dislocations ([[recovery (metallurgy)\|recovery]]) and promotes [[recrystallization (metallurgy)\|recrystallization]].

			[[Image:Dislocated Bubble.png\|centre\|thumb\|800px\|A bubble raft showing a close up of an edge dislocation.]]

			== References ==
			*{{cite journal\|last1=Bragg\|first1=Lawrance\|last2=Nye\|first2=J. F.\|year=1947\|title=A Dynamical Model of a Crystal Structure\|journal=Proc. R. Soc. Lond. A\|volume=190\|issue=1023\|pages=474-481\|url=http://web.mit.edu/mikejd/previously_online/aices_mit_2009/Bragg-bubble_raft.pdf}}
			*Laboratory Handout in MIT's 3.032: Mechanical Properties of Materials. [http://stellar.mit.edu/S/course/3/fa06/3.032/index.html]

			{{DEFAULTSORT:Bubble Rafts}}
			[[Category:Materials science]]

en>FilipeS at 10:47, 9 May 2012

2012-05-09T10:47:35Z

New page

Alyson Meagher is the title her parents gave her but she doesn't like when individuals use her complete name. Invoicing is my profession. Ohio is exactly where my home psychic love readings ([http://srncomm.com/blog/2014/08/25/relieve-that-stress-find-a-new-hobby/ http://srncomm.com/]) is but my husband wants us to transfer. Playing badminton is a thing that he is totally addicted to.<br><br>My blog good [http://www.seekavideo.com/playlist/2199/video/ accurate psychic predictions] ([http://203.250.78.160/zbxe/?document_srl=1792908 Test by click the "Remove Empty Lines" button and watch these blank lines between this text disappear.])