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Diffusion in Copper and Copper Alloys. Part I. Volume and Surface Self-Diffusion in Copper

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Diffusion in Copper and Copper Alloys. Part I. Volume and Surface Self-Diffusion in Copper Diffusion in Copper and Copper Alloys. Part I. Volume and Surface Self-Diffusion in Copper Cite as: Journal of Physical and Chemical Reference Data 2, 643 (1973); https://doi.org/10.1063/1.3253129 Published Online: 29 October 2009 Daniel B. Butrymowicz, John R. Manning, and Michael E. Read ARTICLES YOU MAY BE INTERESTED IN Diffusion in Copper and Copper Alloys, Part II. Copper-Silver and Copper-Gold Systems Journal of Physical and Chemical Reference Data 3, 527 (1974); https:// doi.org/10.1063/1.3253145 Diffusion in copper and copper alloys. Part III. Diffusion in systems involving elements of the groups IA, IIA, IIIB, IVB, VB, VIB, and VIIB Journal of Physical and Chemical Reference Data 4, 177 (1975); https://doi.org/10.1063/1.555516 Diffusion in copper and copper alloys part IV. Diffusion in systems involving elements of group VIII Journal of Physical and Chemical Reference Data 5, 103 (1976); https://doi.org/10.1063/1.555528 Journal of Physical and Chemical Reference Data 2, 643 (1973); https://doi.org/10.1063/1.3253129 2, 643 © 1973 The U. S. Secretary of Commerce on behalf of the United States. Diffusion in Copper and Copper Alloys Part I. Volume and Surface Self-Diffusion in Copper DanielB. Butrymowicz:, John R. Manning, and Michael E. Read Institute for Materials Research, National Bureau of Standards, Washington, D. C. 20234 A survey, comparison, and critical analysis is presented of data compiled fr.om t~e sci~nt~c literature concerning copper self-di1fusion. Topics include volume diffusion, dislocat1o~ PI~ diffus~on, surface diffusion, sintering, electromigration, thermomigration, pressure effect on diffuSlO~, st~am~nhanced diffusion nuclear magnetic resonance measurements of solid state diffusion and diffUSion m molten copper. An extensive bibliography is presented along with ligures, tabular presentation of data, and discussion of results. Key words: Copper; diffusion; electromigration; liquid copper diliusion; nuclear m~e~lC resoulW"". and diffusion; pressure effects on diffusion; self-diffusion; sintering; surface diffUSiOn; thermo­ migration. Contents present purposes to review this subject in several pa~ts. Copper self-diffusion is treated in this first part. AttentIon Page is focused on copper diffusion itself, rather than on forma­ 1. Introduction________ 643 tion and annealing of crystal defects. Also, emphasis is on 2. CU"'-)CU (Volume Diffusion)______________ 645 the direct experiwt;uLal n~:;ult:;, with diffusion theory heing 2.1. High Temperature Range_____________ 645 discussed only where it aids in selecting among conflicting 2.2. Low Temperature Range-Possible Cur- data or in predicting and interpreting experimental results. vature in log D vs T-l PIoL_____ __ _ _ 647 The primary quantities of interest for diffusion are the 3. Dislocation Pipe Diffusion_________________ 648 diffusion coefficient, D, and the activation energy for 4. Surface Diffusion_ _ ___ __ _ __ __ _ __ __ __ __ _ __ 649 diffusion, Q. The diffusion coefficient is defined hy the 5. Copper Sintering_________________________ 650 equation 6. J£lectromigration_ __ _ __ __ 651 7. Thermomigration______________ 652 J= -D«(Jc/iJx), (1) 8. Pressure Effects__________________________ 652 where iJc/ iJx is the concentration gradient of the diffusing 9. Strain-Enhanced Diffusion ____ - ------- __ -.:. - 652 species along a direcLiull (:Ii) uf illten~5t and the diffusion 10. Nuclear Magnetic Resonance Measurements of flux, ], is the amount of diffusing species crossing unit area Diffusion_ -- ------ ---- ------ - --- - __ - -_ 652 normal to the x-axis per unit time. D itself is a constant of n. Molten Copper______ __ _ __ _ __ _ __ _ __ _ __ __ _ _ 652 proportionality and usually is expressed in units of cm2js. 12. References ______ - _______ - __ _ __ _ __ __ __ _ __ 653 Experimentally, D is usually found to depend exponentially on temperature according to an Arrhenius type equation, 1. Introduction D-Du exp ( Q/RT). (2) Copper and copper alloys are important commercial Thus, a straight line is usually obtained when log D is materials which often are used at temperatures where dif­ plotted as a function of T-l. Here T is the absolute tem­ fusion proce:SSe5 :strongly affect their properties. Signi£.c~nt perature, Do and Q are experimentally mea:;un::u cun::;Lants changes in mechanical and electrical properties can occur which can be determined from the intercept and the slope through surface alloying, compositional changes at inter­ of that line, and R is the universal gas constant (1.987 faces, and interface degradation resulting directly from cal K-I mol-l = 8.314 J. K-I·mol-l). diffusion. Many metallurgical processes such as creep, The quantity Q in eq (2) is usually found expressed in precipitation, ageing, and corrosion are diffusion-limited. the literature in units of kcal/mol, or in units of kcal Other important diffusion effects include homogenization alone (with the mole understood). Usually Q can be deter­ of alloys, electromigration effects on copper components mined to only two or three significant figures and has a in electrical circuits, diffusional breakdown of protective value between 10,000 and 100,000 cal/mol. Thus, when films, permeability of thin-walled tubing, and diffusion Q is expressed directly in terms of cal/mol, as is sometimes bonding. found in the literature, the las t few zeros before the decimal Because of the strong practical and scientific interest are not significant figures. A second type of unit for Qfre­ in diffusion involving copper and its alloys, references to quently found in the literature is the electron volt or elec­ this topic in the literature are very numerous. In view of tron volt per atom. When this unit is reported, it is under­ the large body of data to be reported, it is convenient for stood that R in eq (2) is replaced by Boltzmann's constant 23 5 Coprri!;ht © 1973 by the U.s. Secretary of Commerce OD behalf of the UDit~ States. '!?ia k (equal to 1.3806X10- J·K-l or 8.617X10- eV·K-I). copyright wiII be assigned to tho American Institute of Physico and the Ameneon Chemlcal 3oGl~lY. lQ ",,",buUl .u X"''iU~ll$ .~4\,"!i.uts ."'p.v-d.~~\.i.Qn o'b.-ould.1x> o..d.d..::OGQ.od.. One fundamental distinction which can be made between 643 J. Ph.ys. Chem. Ref. D<afa, Vol. 2, No.3, 1973 644 BUTRYMOWICZ, MANNING, AND READ different types of diffusion measurements is that between Because of the accuracy of tracer techniques, such re­ volume diffusion, where atoms move through parts of the sults are emphasized in this review wherever possible. material having regular crystal structure, and short circuit However, results applicable to volume diffusion from other diffusion processes, where the atoms move along easier methods such as nuclear magnetic resonance and sintering diffusion paths such as surfaces, grain boundaries or disloca­ also are reviewed. Other volume diffusion phenomena tions. Both types of data are collected in the present which are discussed include diffusion in an electric field review. (electromigration), diffusion in a temperature gradient Volume diffusion normally is found to have an appreci­ (thermomigration), effects from hydrostatic pressure, dif­ ably higher activation energy than short circuit diffusion; fusion in strained crystals, and self-diffusion in molten hut, beoause of the many volume diffusion paths available, copper. volume diffusion normally dominates at high temperatures. ·In choosing among various tracer results for reliability, Short circuit diffusioIL usually becomes the predominant the internal consistency and reproducibility of the data means of mass transport at lower temperatures, however. are .considered important. It is expected that the experi. Since copper has a face-centered cubic structure, volume mental points, expressed as log D, should fall very nearly diffusion in copper is isotropic, and D is independent of the on a straight line when plotted as a function of T-l, as diffusion direction. By contrast, surface diffusion and other given by eq (2). The degree of scatter from a line drawn types of short circuit diffusion should not be expected through the experimental points is usually as.sumed to to be isotropic, since the surface structure and particular provide a good indication of the accuracy of the data. directions of easy diffusion paths can introduce significant Such a line usually will not be well-established if only a anisotropic effects. Grain boundary diffu5ion may be 5ig- . few luea::suremenls in a limiled ltauptralure range are nificant in. polycrystalline material and tends to increase reported. For this reason, data taken at many different the net measured diffusion, especially when measurements temperatures and over a wide temperature range usually are made at temperature!'! below (2/~)Tm, whflrfl T.,. i!'! are r:onsidereil morfl n!'>flfnl llnil llrfl more easily evaluated. the melting p()int. For this reason, single crystal results are Diffusion of copper on copper surfaces can be measured considered more reliable as measurements of volume by measuring the change in shape of the copper surface diffusion. or· by introducing radioactive tracer atoms on the surface. The most accurate method of measuring volume diffusion In both cases, possible volume diffusion effects on the is by radioactive-tracer-sectioning techniques. Here a thin results must be taken into account. The surface diffusion layer of radioactive tracer atoms is deposited on the surface coefficient, Ds, is defined from eq (1) but with the change of a homogeneous crystal and diffusion is allowed to pro­ that c is concentration per unit area and J represents flux ceed for time t. The specimen is then sectioned into slices across a line on the surface normal to the flux. Reviews parallel to the surface and the specific activity, c, of each of experimental surface diffusion techniques have been slice is measured.
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