Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Bending of a Bimetallic Beam due to the Kirkendall Effect



William J. Boettinger, Geoffrey B. McFadden


The time dependent bending of single phase and two phase bimetal strips due to interdiffusion is computed. The model couples simple beam theory and diffusion, the bending being due to the creation and /annihilation of vacancies necessitated by unequal lattice diffusion rates of the two metals. The single phase problem employs a Fourier method for the diffusion analysis that results in beam curvature that is initially proportional to time and which reaches a steady state value at long time. The two phase results, which involve a moving interphase interface employs an error function solution for the diffusion analysis to model early times. This analysis results in linear behavior at early time, only if the original interface is centered in the beam. In general the curvature goes as the square root of time at early times. The single phase results are also compared to the results of Daruka et al., Acta Mater (1996) 44: 4981-4993
Journal of Phase Equilibria and Diffusion


Kirkendall Effect, Bending, Diffusion


Boettinger, W. and McFadden, G. (2010), Bending of a Bimetallic Beam due to the Kirkendall Effect, Journal of Phase Equilibria and Diffusion, [online], (Accessed June 22, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created January 1, 2010, Updated November 10, 2018