Electromigration in polycrystalline and single crystal magnesium

I Phvs. Chem Sohds. 1975 Vol. 36. pp 10254031.

Pergamon Press

Printed in Great Bntain

ELECTROMIGRATION IN POLYCRYSTALLINE CRYSTAL MAGNESIUMt

Departments of

AND SINGLE

J. WOHLGEMUT@ Physics, Rensselaer Polytechnic Institute,Troy, NY 12181,U.S.A. (Received 25 March 1974)

Abstract-The electromigration of magnesium single and polycrystal samples was measured under the influence of a d.c. current density of approximately 6 x lo3A/cm*using the vacancyflux technique.The single crystal data were taken on samples with the c-axis of themetal making angles of 22”and 63”respectively with the cylindrical axis of the specimen. Accurate measurements of the longitudinal and transverse motion were made over a period of several weeks and used to c&date a value for the atom drift velocity, V,. The atom drift velocity is used to calculate Z*, the effective electromigration charge on the ion. All of the observed motion was directed toward the anode. The polycrystal runs yielded an average value of Z*/f = -2.03 kO.33. The single crystal runs resulted in an anisotropic drift velocity ratio of V.,/V.,, = 1.4. However, the product of diffusivity times resistivity is anisotropic by the same ratio as the atom drift velocity and the correlation factor f is nearly isotropic for magnesium. As a result Z* is isotropic and turns out to be -1.6.

1. INTRODUCTION In recent years there have been numerous investigations of electromigration in pure solid metals in the diffusion range [ I,21 but these have been for the most part either on polycrystalline specimens or cubic structures. Consequently the effect of crystalline anisotropic has been overlooked except for two investigations, conducted in this laboratory, on zine[3] and cadmium[4]. In both cases the results showed that the electromigration drive, as measured by the effective charge number, Z*, was highly anisotropic. (Z* is defined by FIeE where F is the driving force for electromigration, e the magnitude of the electron charge and E the applied electric field.) For each of these hexagonal metals the 2* in the basal plane is about double the Z* for motion down the c-axis. In view of the nearly isotropic behavior of electrical conductivity for these metals these results were somewhat unexpected. This study on magnesium was undertaken to broaden the experimental picture of the effect of crystalline anisotropy on electromigration and particularly to explore the phenomenon in an hexagonal metal with a c/a ratio close to the ideal ratio for close packing and a pronounced isotropy in all its properties. Of course, zinc and cadmium have c/a values far from the ideal and many of their parameters, particularly the elastic are highly anisotropic. At this point something should be said of the state of the theory for electromigration. Here there has been little progress beyond the basic application to the free electron metal. For this highly simplified model there appears to be fairly uniform agreement between three rather different approaches[5-71, at least as far as the influence of the so-called electron wind. The result has been formulated by Huntington[S], Z*=Z~_IZ~dNm* 2 pNdm*

tWork supported by the U.S.A.E.C. and NSF. SNOWat Waterloo University, Waterloo, Ontario, Canada.

where the Z’ is the valence of the moving ion and this term is believed to represent the electrostatic force of the field, although this interpretation is not universally accepted. The second term gives the effect of momentum exchange with charge carriers; Z is the valence of the lattice atoms, p.+/Ndis the incremental resistivity per moving atom and p/N is the normal resistivity per ion. The m * is the effective mass of the charge carrier so that the final term becomes positive if the carriers are in a “hole” band. Clearly the spherical Fermi surface, implicit in such a model, rules out any explanation of crystalline anisotropy effects. There have, however, been recently some extensions of the theory to real metals. First of these is that of Sorbello[8] who used specific pseudopotentials to apply the general procedure of Bosvieux and Friedel[7] to many real metals with uniformly gratifying results. The method demonstrates that forces are exerted by the “electron wind” against the moving ion and its neighbors but is not particularly suitable for explaining anisotropic effects. An alternative approach to real metals has been developed by Feit [9] who has applied second order perturbation theory to Bloch wave functions disturbed by the presence of the moving ion to calculate the wind effect, more along the ballistic lines initiated by Huntington[S] and Fiks[6]. Although this technique has not beed developed further to date, it holds promise of being applicable to the anisotropy problem. An initial step in its application requires that one knows the mean free path as a function of position on the Fermi surface and this calculation is being carried out by Chan and Huntington[lO] for zinc. Since electromigration appears as a net result of the action of the electron-type and hole-type carriers in opposition, it might appear that the effect should correlate strongly with the Hall effect. There is a correlation but actually the situation is too complex for both phenomenon to expect a close relation. In single crystals of non-cubic metals many of the physical properties depend upon the orientation of the

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crystal. Magnesium is a hexagonal metal with a c/a ratio of 1.6235, which is very nearly the hexagonal close-pack structure. The resistivity [ 1l] and diffusivity [ 121are both anisotropic with ratios PII/PL= O-83:4,/D, = 0.815.

(2)

Both ratios are independent of temperature in the range of interest for electromigration experiments. Atly and Stringer[l3] found that the Hall coefficient was isotropic for magnesium. An isotropic Hall coefficient implies isotropy for the density and mobility of the conduction electrons and holes, or compensation between these influences. Therefore, for magnesium one would expect that the anisotropy of Z* would depend primarily on the influence of the defect resistivity. The experimental technique used in this investigation is that of the “vacancy flux” metbod[2]. In this method one observes the dimensional changes of the specimen carrying a high current and infers from them what the defect flux pattern must have been, i.e., one knows V, the atom veIocity as a function of position. From the Nerst-Einstein relation V, = D*Z*eEIfkT and a knowledge of D*, the self-diffusivity as determined from tracer methods, one can then find Z*lf where f is the correlation coefficient for the self-diffusion process and k is the Boltzmann constant. In the next section the particular application of this method to magnesium is described. The third section gives the results and the final section discusses their significance.

from the manufactured rods. To grow single crystals, a four inch length was cut and etched in 10%HCI and 90% H,O until ah of the surface oxide was removed. The sample was then encased in a split graphite mold, which was placed inside an alumina tube. The alumina tube was put in a core would furnace and attached by means of a rubber hose to a mechanical fore pump and’an oil diffusion pump. The sample was heated under a dynamic vacuum until the temperature was approximately at the melting point, at which time the alumina tube was filled with helium to a pressure of 2Ibs. above atmospheric. A modified Bridgman technique was employed, where the temperature gradient moves through the sample instead of the sample moving through the gradient. The temperature gradient in the furnace .varied from 3”C/cm up to PC/cm. Near the melting point the rate of temperature decrease was between 3 and 4°C per minute. As long as the hole in the graphite mold was reamed smooth the magnesium crystals slid out easily. The crystals were etched with a solution of 5 grams citric acid and 95 cc of water, to expose the grain boundaries. If no grain boundaries were observed, a two inch long segment was cut from the sample using an acid string saw. The two ends that had been cut from the sample were analyzed by the back reflection Laue X-ray technique. The Laue pictures were compared to standard projections of the major axes and the angle between the cylindrical axis and the hexagonal axis was determined. Magnesium is a very reactive metal with a high vapor pressure at temperatures near its melting point. Therefore, the samples must be run in a clean atmosphere of inert gas. A standard two inch oil diffusion pump and a mechanical fore pump are the main components of the vacuum system. The inert gas used was UHP Argon (99999%). The experimental chamber is cylindrical with copper sides silver-soldered to steel ends. In the bottom plate there are feed troughs for the electrodes and water cooling, consisting of copper pipes sealed by Viton “0”-rings and electrically insulated with rubber gaskets. In the top there is a quartz plate for viewing the sample during the progress of an experiment. Figure 2 shows a diagram of the specimen mounting

2. EwEIUMl!.NTAL. F’ROCEDURE The vacancy flux technique was employed to measure the

electron&ration in magnesium.The particular ditIlculty of the experimentwas the maintenanceof this highly reactive element chemically unaltered at elevated temperatures for times as long as 2 or 3 weeks. As shown in Fig 1, the ends of the specimen are water cooled while the sample is heated by a 600A/cm’ d.c. current density to yield an almost parabolic temperature distribution along its length. During the experiment one measures the longitudinal motion of scratches, which have been spark etched on the surface of the sample, and also measures the changes in diameter. The motion of the surface scratches and the dilation of the diameter can be used to calculate the atom driit velocity and therefore, the effective charge number for electromigration, Z* (see Section 3). The magnesium was 999% pure, supplied by Leico Industries in the form of rods l/8” dia. Polycrystal samples were cut directly

u-

UHP wpon

ToEs

Fig. 1. Experimental chamber.

-Bon Copper tutxx wrylng

current and water

Fig. 2. Specimen mounting apparatus. apparatus. One copper electrode is fixed. The other grip rides on four ball-bearing wheels, while its bottom sits in a gallium indium eutectic ahoy bath and so is free to move parallel to the long axis of the sample allowing strain-free thermal expansion with good electric contact. The samples were etched in %% ethyl alcohol and 4% nitric acid to remove all impurities from the surface. Then marks approximately 100microns wide and 100microns deep were spark etched 1 mm apart on the surface. The samples were again cleaned in the same solution, rinsed in 50% acetone and 50%methanol and stored under benzene until used. Indium foil was placed around the sample inside of the grips to afford good electrical and thermal contact. The chamber could not be outgassed with the magnesium sample in place because this would cause the oxide layer on the magnesium surface to evaporate, so when the sample was heated to the experimental run temperature the magnesium itself evaporated. So the chamber was outgassed before the sample was mounted and re-evacuated with the diffusion pump but not outgassed after the sample was mounted. The temoerature of the sample was read with a Model 500HC Ircon Ra&ation Thermometer. The reactivity of magnesium causes the surface emittance to vary. To obtain accurate readings

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Electromigrationin polycrystallineand singlecrystalmagnesium with the pyrometer, a fine colloidal graphite dispersion called Aquadag was placed on the surface of the sample. Initially Aquadagwas placedon the sampleat the beginningof a run, but such samples elongated 20-30 microns per day and bumps appeared on parts of the surface coveredwiththe Aquadag.Antill et al.[ lo] discoveredthat placinga smallamount of carbon on the surface of a piece of magnesium and heating the sample to 500°C resulted in the same sort of sample expansion and surface cracking. It was their opinion that the carbon acted as a catalyst for breaking down the oxide on the magnesium surface. Therefore, the graphite dispersion cannot be on the surface of the magnesium during an experimental run. Another method of measuring the temperature must be employed so that the initial temperature of an experiment may be at least approximately known. The total length of the magnesium sample is a function of its temperature. From dummy samples painted with Aquadag, the relationship between thermal expansion and temperature of the hottest spot on the sample was found. The thermal expansion of the sample was used as the temperature indicator calibrated by heating the sample up to its experimental run temperature. Tests showed that, if the power supply was shut off and then turned back on again, the sample returned to the same temperature within the limits of the pyrometer. At the end of an experiment the power supply was shut off, the sample coated with Aquadag, the power turned on again and the temperature measured with the optical pyrometer. Then to calibrate the pyrometer, a melting point check was performed. Since the pyrometer can only be used at the end of an experimental run, the temperature variation of the sample cannot be directly measured. Dummy samples with Aquadag on the surface were run for several days while the temperature was monitored. These samples showed no temperature changes. During the actual runs the voltage across a standard resistor and the voltage across the grips were monitored. These remained constant so the current, voltage and resistance of the sample remained constant for the duration of a run. The overall length of the sample is another indicator of temperature change. Even wifh a constant temperature, however, the length of the sample may increase. At lower temperatures, where the reactivity of the magnesium is reduced and the other causes of expansion should be smaller, the length of the sample is constant. At higher temperatures, the temperature measured by the pyrometer at the end of the run agrees with the temperature obtained by the thermal expansion measured at the beginning of the run but not with the new length after.expansion during the run. These results support the hypothesis that the temperature is a constant during the course of an experiment All dimensional changes were measured with a Gaertner Traveling Microscope. The traveling microscope was mounted above the quartz window parallel to the specimen and was not moved for the duration of an experiment. The longitudinal motion of the surface scratches was measured to the nearest micron by rotation of the micrometer slide. Because the shape of a mark might change during the course of an experiment, measurements were taken on both edges of each mark. The diameter changes of the magnesium samples were measured with a bifilar micrometer eyepiece, which measures lengths perpendicular to the normal travel direction of the microscope. The focus was not changed over the course of an experiment so that the same point on the sample was measured each time. It would be simpler to take longitudinal and transverse data on the same sample at the same time, but to accomplish this the focus would have to be changed. Therefore, for more accurate results it was necessary to take transverse and logitudinal data separately. At low temperatures the samples lasted a long time so the longitudinal marker positions were recorded three separate times each day every day for several weeks and then the diameter measured three times each day at every mark for several more weeks. For high temperature runs the magnesium sample would not last long enough for both kinds of data to be taken on the same sample. Therefore, one sample had to be used for longitudinaldata and another sample at the same temperature for transverse data. There was no apparent discrepancy in the relationship between the longitudinal motion and the transverse motion between the two typ6.s of experimental runs.

3. RESULTS A. Polycrystalline electromigration The polycrystalline electromigration results were obtained from five diffbrent samples. Two samples were measured for longitudinal motion, two samples for diameter change and one sample was used for both kinds of measurement. In the longitudinal runs the marker velocities V,,,were determined from linear least squares fits of the marker displacement versus time plots at each marker position. Figure 3 is a plot of marker velocity versus marker position for sample No. 25P. Motion toward the fixed end or cathode is indicated by a negative marker velocity, while motion away from the fixed end or toward the anode is indicated by a positive marker velocity. The motion in the hottest region of the sample is toward the cathode. This sample elongated at a rate of 2 microns per day. The plot shows not only electromigration but includes, if measurable, thermomigration since there is a temperature gradient in the sample. It also includes any effects due to keeping magnesium at a high temperature. To measure the effects other than electromigration, a run was performed using ac current to heat the sample. Figure 4 is a plot of marker velocity (scaled to yield the same expansion of the movable end that was observed in sample No. 25P) versus marker position for sample No. 1T which was heated with ac current. The overall length expansion through the hottest region is the same sort of effect observed by Anti11 et al. [14]. Runs at lower temperatures (below 475°C) did not show this overall length expansion. The data from sample No. 1T are subtracted from the data for run No. 25P and the result is the velocity curve plotted in Fig. 5. The velocities taken from the smooth curve in Fig. 5 are those used in the calculations for the longitudinal runs. +3 +2

k-2 In -3 s-4 s

-5 -6

02

4

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12 14 16 16202224262630

PosItIon,mm Fig. 3. Marker velocity-sample 25P.

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Fig. 4. Marker velocity-sample IT.

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integral of the dilation of the radius expression[ 151 Va(x)= V(x)+:

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(4)

In our experiments the total volume change of the sample is zero, so the atom drift velocity can be the only cause of volume change. We define a quantity a, as the ratio of the longitudinal velocity to the atom drift velocity

mm

Fig. 5. Correctedmarkervelocity-sample 25P. In the transverse runs the time rate of change of the variations in dieter were determined from linear least squares fits of the diameter versus time plots. Figure 6 is a plot of the time rate of change of diameter versus position for sample No. 36P. This plot is not purely antisymmetric since it includes temperature dependent effects as well as the electromigration. The curve is broken down into symmetric and antisymmetric parts and the antisymmetric part is used to calculate the electromigration. The atom drift velocity, V., at a position X is related to the longitudinal velocity V at this position X and to the

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Fig. 6. Velocityof diameter-sample 36P.

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If all the motion were longitudinal, Q would equal 1 and if the distortion were isotropic, (Ywould equal l/3. If one uses this expression for OL, then it is possible to calculate cxZ*/f for longitudinal runs and (1 - e)Z*/f for transverse runs by means of equation 2. In our experiment the electric field is equal to the product of the applied dc current density times the resistivity of the magnesium sample at given temperatures from the Metals Handbook [ 161. The results for the polycrystalline runs are shown in Table 1. There was no indication of any temperature dependence of Z*/f so the values for each run are the weighted means over the temperature range of each sample. The average value for Z*/f for all the polycrystalline runs is -2.03 * 0.20. The error in temperature determination includes an instrumental error of *2.8”C, an error in temperature distribution of irZ.O”Cand an error due to standardization by melting point check of *2*8”C. The first two errors vary from mark to mark while the melting point error is constant for the duration of one run but varies from run to run. The temperature error leads to an uncertainty in

Table 1.Polycrystallineelectromigration Run No.

Longitudinaldata Temperaturerange (K)

25P 28P 37P

783-823 760-789 727-748

f.Yz* f -0.73?0.10 -0.74kO.13 -0.73 2 0.13

MeanValue of crz* = -0.73 + 0.07 f Transverse data Run No.

Temperature range (K)

3OP 36P 37P

735-848 730-770 727-748 MeanValueof~=-l.3O+-O~t9 Mean 7 = -2.03 rt 0.20 (Y= 0.36 2 0.03 Activation energy Q = 31.9C 1.0 (Kcal/mole) = 1.392 0.04 (eV/atom)

(1 - fY)z*

f -1.09t0.53 -1.3220.23 -1~43~0~51

Electromigration in polycrystalline and singlecrystalmagnesium

diffusivity of up to 17 per cent and an error in resistivity of 1 per cent. The error in atom velocity is a combination of the standard deviation of the least squares fit for each velocity and the error due to local deviation in the velocity versus position plot. The error in the longitudinal contribution to the atom drift velocity averaged around 10 per cent, while the error in the transverse contribution to the atom velocity was nearly 20 per cent. The error in current and cross sectional area led to a probable error of 2.7 per cent for the current density. At each marker position there is calculated a value of cyZ*/f or (1 - a)Z*/f and an absolute value of the error in either cyZ*/f or (1 - a)Z*/f. For each run all of these values are used to find a weighted mean for either aZ*/f or (I- a)Z*/f and a weighted error for each run. These are the values listed in Table 1.The final error is the error in the weighted mean calculated from the values from all of the runs. The results for the complete V, from the 6 runs have been plotted in Fig. 7 in the form In V./j vs (U-l. One expects that the slope of the best straight line through the points would agree closely with the activation energy for self-diffusion, if the defect resistivity is temperature independent. The slope of the actual line as shown in Fig. 7 is 31.9, I.0 kcal/mole to be compared with the value found by Shewmon and Rhines[l7] from diffusion measurements of 32.0 kcal/mole. Although the closeness of the agreement may be somewhat fortuitous, the evidence is clearthattheelectromigrationisprimarilyabulkprocess. B. Single crystal electromigration The single crystal electromigration results were taken

from three samples. Two 63”crystals were used. One gave transverse data while the other was run for longitudinal data. A 22” crystal was run and yielded both longitudinal and transverse data. The analysis of the data was exactly the same within experimental error for the single crystal runs as for the polycrystal runs. The single crystal results are given in Table 2. The value of Z*/f for the 63” crystal is 1.83 20.30, while the value for the 22” crystal is 2.00 z 0.28.

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VJ V,I,= 1.4 _‘0*25.

(7)

Using the diffusivity data found by Shewmon [ 121and the

63” Crystals Temperature range (K)

4s

748-786

6s

755-769

(I-a)Z*=1.02*0.22 I I

Mean -=1~83+0~30 2*(63’)

f

a!=o44~0~10

22”Crystals Run No.

Temperature range (K)

7s

740-776

(1 - a)Z*

I=

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740-776

f

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(cat /mole)

Within the accuracy of the experiment the observed anisotropy in Z*/f is not significant. Mullen’s[lI)] calculations show that, because magnesium has such a small anisotropy in diffusion, the differences in the correlation factor should be less than 2 per cent, which is considerably smaller than the errors in our data. Since our measurements show Z*/f isotropic, it follows Z* is isotropic. The atom drift velocity in the different directions is not isotropic. The measured ratio is

Run No.

Mean 2*0

I 70

Fig. 7. Polycrystalline data V./J vs (RT)-‘.

Table 2. Single crystal electromigration

7s

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= 2.00 kO.28

a = 0.39 ? 0.03

1.2250.25

I030

J. WOHLGEMUTH

resistivity data from the Metals Handbook[ll], obtains the ratio PlDl/Pllql=

1.39.

one

(8)

The velocities show effectively the same anisotropy as the product of resistivity and diffusivity. Since all of the experiments were performed with the same current density, j, all of the anisotropy in atom drift velocity is due to the anisotropy in resistivity and diffusivity and the electromigration interaction appears isotropic within the accuracy of the measurement. 4. DISCUSSION

The mass motion measured in this experiment was toward the anode and resulted in a negative value for Z*. The electron wind force dominates the sum of the electrostatic and hole wind forces. Magnesium is a two band metal and should have both electron- and hole-type carriers. Alty and Stringer[9] found that the Hall coefficient in magnesium is close to the Hall coefficient of a divalent free electron metal. For the Hall coefficient to be near the free electron value either the number of holes, the hole mobility or both must be smaller than the corresponding number or mobility of the electrons. Therefore, the electron wind should be larger than the hole wind. The electromigration experiments confirm this. Calculations by Mullen[ 181show that magnesium has a correlation factor of approximately 0.78. On this basis the value of Z* = -1.6. This is among one of the smaller negative values found for Z*. The presence of a hole current is a partial explanation but, since the Hall coefficient indicates a small hole influence, the situation is by no means clear. The electron wind term may itself be fairly small. The interaction between the activated complexes and the moving electrons may perhaps be weak so that magnesium has a small defect resistivity. Magnesium has the hexagonal close-packed structure with 12 nearest neighbors. Six of these nearest neighbors are in the basal plane and 6 are out of this plane but at essentially the same distance. Since nearest neighbor vacancy jumps probably dominate the diffusion process, most of the jumps in magnesium will be of the same length. The contiguration of the lattice ions around an ion jumping from one lattice site to another in the basal plane is different than the conftguration during a jump out of the basal plane. For magnesium this difference is small. At the saddle point the difference involves only a small angular shift in two of the “ring” neighbors. It appears that the small difference in surrounding structure will have very little effect on the interaction between the jumping ion and the electric field or the electron and hole winds, so that electromigration driving force may well be isotropic. In addition to giving the strength and anisotropy of Z* the vacancy flux method gives some information on the mechanisms for vacancy generation and annihilation through the behavior of (equation 4). It has been shown by Penney[l9] that a increases above its isotropic value of l/3 for specimens of large width-length ratio and of low plastic ductility. Because the magnesium samples were much longer than they were thick and because magnesium

is a soft metal, there should have been very little radial strain on the samples during electromigration. With no radial strain the deformations of the polycrystal samples should be nearly isotropic. The actual measured polycrystal value of (Y=0*36 agrees well with the perfectly isotropic value for isotropic deformation of a! = 0.33. While the dimensional changes are nearly isotropic in the hottest region of the sample, as one approaches the cold end a increases and appears to approach unity. As was previously stated, in the center of the sample there is no radial strain, but near the ends of the sample the colder magnesium may be rigid enough to prevent relative motion in the radial direction so the deformation is almost uniaxial. In this region, the marker motion is so small that is is impossible to calculate good values for the velocity. Several millimeters (or marks) from the onset of marker motion, the dimensional changes become isotropic. It is data from the isotropic region that have been used for all of the calculations. Magnesium oxide is denser than magnesium metal. Therefore, if magnesium on the surface of the sample is oxidized the volume would decrease and the magnesium oxide layer would squeeze the magnesium inside of it. This squeezing would cause the sample to elongate and indeed the samples at the higher temperature did elongate. Several samples, which showed large increases in length had isotropy factors, (Y,that were considerably larger on the anode side. This was a result of the radial strains caused by the oxide layer on the surface. Some of the magnesium samples had bumps grow on the surface. These bumps appeared to be magnesium that escaped through the protective oxide layer on the surface and eventually oxidized. A dirty atmosphere or a graphite dispersion on the surface increased the rate of the oxide surface breakdown and allowed the magnesium to escape and oxidize more rapidly. The surface marks on the sample caused the oxide layer to break down quicker. Since storing longer in benzene slowed the growth rate, it is possible that oil trapped in the marks during spark etching may have speeded up the oxide breakdown and that longer storage in benzene served better to clear out all residual oil. It is also possible that, because of the shape of the marks, the oxide layer near each mark was weaker than the layer over a smooth portion of the metal. 5. CONCLUSIONS The vacancy flux technique yielded an effective charge number Z* = -1.6 for the electromigration interaction for both polycrystalline specimens and single crystals. The anode directed mass motion agrees with the negative Hall coefficient. The small value for Z* may imply a weak interaction between the conduction electrons and the jumping ions. While the atom drift velocity is dependent upon the crystal orientation, this dependence results from the anisotropy in diffusivity and resistivity. The electromigration interaction and the effective charge Z* are isotropic. Acknowledgements-The

author wishes to thank Dr. H. B. Huntington for suggesting the subject of this work and for advice and encouragement during the course of the study.

Electromigration in polycrystahine and single crystal magnesium REFERENCE3

1. Pratt J. N. and Sellers R. G. R., EIecfrotransporl in Metals and Alloys in Diffusion and Defect Monograph Series, No. 2. Trans. Tech. SA-Riehen-Switzerland (1973). 2. Huntington H. B., Electron&ration, Encyclopedia of Chemical Technology, Supp. 2nd Ed., p. 278, Wiley, New York (1971). 3. Routbort J. L., Phys. Reu. 176,796 (1%8). 4. Alexander W. B., Z. /. Naturjorsche, %a, 18 (1973). 5. Huntington H. B. and Grone A. R., L Phys. Chem. Solids 20, 76 (1961). 6. Fiks V. B., Fiz. Tuerd, Tela. 1, 16 (1959)[English translation: Soviet ohvs.-solid state 5. 2549 W36411. 7. Bosvieux’C. and Friedel'J., J. khys:-Chem. Solids 23, 123 (1%2). 8. Sorbello R. S., J. Phys. Chem. Solids 34, 937 (1973). 9. Huntington H. B., Alexander W. B., Feit M. D. and Routbort

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J. L., Anisotro of Electromigration in Atom Transport in Solids and Liqu9yds, (Edited by A. Lodding and T. Lagerwall), Verlag der Zeitschrift fur Naturforschung, Tubingen (1971). 10. Chan W. C. and Huntington H. B., private communication. Il. Goens E. and Schmid E., Naturis. 19, 376 (1931). 12. Shewmon P. G., Trans. AIME, 206, 918 (1956). 13. Atly J. L. and Stringer J., Phys. Status Solidi 32,243 (1969). 14. Anti11J. E., Bennett M. J. and Chatfey G. H., Peakall K. A. and Warburton J. B., .r. Nuci. Materials 36, 1 (1970). 15. D’AmicoJ. F. and Huntington H. B., J. Phys. Chem. Solids 30, 2607 (1969). 16. Metals Handbook, 8th Edition, Vol. 1, Properties and Selection of Metals, Americal Societv for Metals (1961). 17. Shewmon P. G. and Rhines F. N., &arts. AIME‘200,‘1021 (1954). 18. Mullen J. G., Phys. Rev. 124, 1723(l%l). 19. Penney R. V., 1. Phys. Chem. Solids 25, 335 (1964).