Editing Kirkendall effect (section)

==Kirkendall porosity==
One important consideration deriving from Kirkendall's work is the presence of [[Porosity|pores]] formed during diffusion. These voids act as sinks for vacancies, and when enough accumulate, they can become substantial and expand in an attempt to restore equilibrium. Porosity occurs due to the difference in diffusion rate of the two species.<ref name=porosity>{{cite journal |last=Seitz |first=F. |title=On the porosity observed in the Kirkendall effect |journal=Acta Metallurgica |date=May 1953 |volume=1 |issue=3 |pages=355–369 |doi=10.1016/0001-6160(53)90112-6}}</ref>

Pores in metals have ramifications for mechanical, thermal, and electrical properties, and thus control over their formation is often desired. The equation<ref name=equation>{{cite journal |last=Son |first=Yoon-Ho |author2=J. E. Morral |title=The Effect of Composition on Marker Movement and Kirkendall Porosity in Ternary Alloys |journal=Metallurgical Transactions A |date=November 1989 |volume=20A |issue=11 |pages=2299–2303 |doi=10.1007/BF02666665 |bibcode=1989MTA....20.2299S |s2cid=137088474}}</ref>
<math display="block">
 X^K = (a_1 \Delta C_1^\circ + a_2 \Delta C_2^\circ + \dots + a_{n-1} \Delta C_{n-1}^\circ)\sqrt{t},
</math>
where <math>X^K</math> is the distance moved by a marker, <math>a</math> is a coefficient determined by intrinsic diffusivities of the materials, and <math>\Delta C^\circ</math> is a concentration difference between components, has proven to be an effective model for mitigating Kirkendall porosity. Controlling annealing temperature is another method of reducing or eliminating porosity. Kirkendall porosity typically occurs at a set temperature in a system, so [[Annealing (metallurgy)|annealing]] can be performed at lower temperatures for longer times to avoid formation of pores.<ref>{{cite journal |last=Cogan |first=S. F. |author2=S. Kwon |author3=J. D. Klein |author4=R. M. Rose |title=Fabrication of Large Diameter External-Diffusion Processed Nb<sub>3</sub>Sn Composites |journal=IEEE Transactions on Magnetics |date=May 1983 |volume=Mag-19 |issue=3 |pages=1139–1142 |doi=10.1109/tmag.1983.1062517 |bibcode=1983ITM....19.1139C }}<!--|accessdate=28 April 2013--></ref>