The Kirkendall effect

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Solomon Douglas
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1 The Kirkendall effect Comment: In all these analysis, we have derived the relations for interdiffusion coefficient only. We are not able to calculate the intrinsic diffusion coefficients yet! The first systematic study on solid state diffusion (diffusion of gold in solid lead) that was reported by Sir W. C. Roberts (1896). From then there was a common belief for a very long time that both the species in a binary diffusion couple will have the same diffusion rate. Depending on that possible atomic mechanism of diffusion was developed or other phenomena which were controlled by diffusion were explained. However, few times, researchers working on diffusion or oxidation noticed some strange behavior. W.C. Roberts-Austen, On the diffusion of metals, Phil. Trans. Roy. Soc. A187 (1896)

2 Pfiel s was studying oxidation of steel and noticed one strange behavior as explained below Pfiel reported: It had frequently been noticed that small particles of foreign matter (such as pieces of muffle) falling on the surface of oxidising iron were gradually buried. The scale grew up around these particles until they finally disappeared beneath the surface, but they could afterwards be found by breaking up the layer of scale. This was rather an indication that the oxide scale was growing from the oxide/air interface. Then only the muffle pieces could get buried. This further indicated that the diffusion rate of the species Fe and O were most probably not the same. L.B. Pfeil, The oxidation of iron and steel at high temperatures, J. Iron Steel 119 (1929)

3 To check this issue Kirkendall with his student Smigelkas designed a special experiment (published in 1947) They took a rectangular block of brass, which is a Cu-Zn alloy and wound with Mo wire Following, they electroplated the block with pure Cu Then this block was annealed at an elevated temperature for different times. To their surprise they found that Mo wires moved inside from its original position. With the increase in annealing time it moved even more.

If the diffusion rate of both the species are the same, then amount of Cu transferred from Cu towards brass and Zn transferred from brass towards Cu should be the same.

4 If the diffusion rate of both the species are the same, then amount of Cu transferred from Cu towards brass and Zn transferred from brass towards Cu should be the same. Then Mo should not move from its original position. Mo is actually inert to the system and moves depending on the volume of the material transferred. Since Mo wire moves towards brass, it indicates that Zn must be the faster diffusing species than Cu. Movement of markers from the initial position was parabolic with time. This indicates the diffusion controlled process.

5 In a diffusion couple it can be clarified further. If the diffusion rate of A and B are the same and the flux of A and B transfer is also the same, then there will be no difference in the total amount of material on either side of the Kirkendall marker plane. Note that we are neglecting any change in molar volume. On the other hand, if J B >J A, then the amount of material transferring from right to left is higher. The difference is compensated by the flow of the vacancies. It can be understood that since the loss of B is more than the gain of A, it will create vacancies. Vacancies are consumed at the interface interphase or grain boundaries. So there will be expansion in the left hand side and shrinkage in the right hand side. So we shall see the movement of the marker plane towards right hand side. In the diffusion couple, since ends are free to move, it can be seen as marker plane is stationary and ends of the couple move because of expansion or shrinkage.

6 Two main conclusions were drawn from the experiment conducted by Kirkendall and Smigelkas. 1. The rate of diffusion of zinc is much greater than that of copper in alpha brass. 2. When zinc diffuses more rapidly than copper in alpha brass, the interface shifts to compensate at least partially for the diffusion rate. Kirkendall with his student Smigelkas submitted the article for publication. However, the manuscript was rejected by renowned scientist R.F. Mehl. There was rumour that Kirkendall s promotion to associate professor position was rejected. Ultimately Mehl took the suggestion of one common friend and allowed it for publication on the condition that he can add his comments along with the work. 5 pages of article and 8 pages of critical comments!!! Comment that was included from Mehl: If verified, this Kirkendall effect would greatly modify not only the treatment of diffusion data but also the theory of mechanism of diffusion. It would, for example, be no longer possible to represent diffusion data in a substitutional solid solution by one coefficient, applying to both metal atoms since the separate coefficients are equal, but one would have to show two coefficients, one each for each of the two metal atoms.

7 Immediately after that L.S. Darken supported the work and published with extensive mathematical discussion. Mehl also with his student conducted the experiments in many other systems and ultimately accepted authenticity of the Kirkendall s work Kirkendall visited Mehl just before he died. Mehl heartily said sorry to Kirkendall. He added, I wish I had an effect which had my name like your Kirkendall Effect. Further reading: H. Nakajima, The discovery and acceptance of the Kirkendall effect: The result of a short research career, JOM 49 (1997) Hartley was first to publish work (1946) with the use of inert markers in organic systems, however, this work was not known by the scientists working on inorganic systems G.S. Hartley, Diffusion and swelling of high polymers, Part I: The swelling and solution of a high polymer solid considered as diffusion process, Trans. Faraday Soc. 46 (1946) 6-11 H.B. Huntington and F. Seitz, Mechanism for self diffusion in metallic copper, Phys. Rev. 61 (1942)

8 In the mean time, even before Kirkendall s work, there was argument going on between C. Zener and F. Seitz. Direct exchange mechanism Ring mechanism Clarence Zener proposed direct exchange mechanism, in which atoms will exchange position between them. In that case note that the atoms have to displace the neighboring atoms such that the activation energy required will be very high. Seitz calculated and showed that it is not possible since the activation energy required for direct exchange mechanism is ~25 ev/atom (2412 kj/mole ). This is much higher than the activation energy found experimentally.

9 Then Zener proposed the ring mechanism, as explained in the previous slide. Frederick Seitz again calculated the activation energy required as ~21 ev/atom (2026 kj/mole ) Following that Seitz from experimental results showed that activation energy could vary mostly in the range of kj/mole In 1942, Huntington and Seitz argued that substitutional diffusion occurs by vacancy mechanism However, their work during world war II was overlooked. Kirkendall s work also proved that diffusion in substitution diffusion must occur by vacancy mechanism. Vacancy mechanism H.B. Huntington and F. Seitz, Mechanism for self diffusion in metallic copper, Phys. Rev. 61 (1942)

Definition and description of different diffusion terms

Definition and description of different diffusion terms efore proceeding further, it is necessary to introduce different terms frequently used in diffusion studies. Many terms will be introduced, which