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K. E. HEUSLER and R. KNOEDLER. Max-Planck-Institut fur Metallforschung, Stuttgart, West Germany. Abstract-On the surface of iron deposited from a ferrous ...
Elcciroctimica Acia, 1970, Vol . 15, pp. 243 to 250 . Pergatnon Press . Printed In Northern Ireland

ELECTRON-MICROSCOPICAL STUDIES OF THE ELECTROCRYSTALLIZATION OF IRON* K . E . HEUSLER and R . KNOEDLER Max-Planck-Institut fur Metallforschung, Stuttgart, West Germany Abstract -O n the surface of iron deposited from a ferrous sulphate solution under potentiostatic conditions tetragonal and trigonal growth pyramids are formed . At low overvoltages the tetragonal pyramids, and at high overvoltages the trigonal pyramids, prevail . The respective tangents of the angles between the sides and the bases of the pyramids are proportional to the overvoltage . The distances of the growth steps at the sides of the tetragonal pyramids are inversely proportional to the overvoltage . The height of the growth steps is nearly equal to the height of the unit cell, taking into account the most probable texture of the iron deposit . On the assumption that the pyramids grow at screw dislocations, the specific edge energy of the growth steps is calculated. R6sut-Des pyramides de croissance tetragonales et trigonales se fotmet a la surface du fer au cours de la deposition a lectrolytique Bans une solution de FeS0 4 sous conditions potentiostatiques . Les pyramides tetragonales sont predominantes h des surtensions faibles, les pyramides trigonales A des surtensions fortes . La tangente de Tangle entre la face laterale et la base d'un pyramide est proportionnel A la surtension . Le distances des gradins de croissance aux faces laterales des pyramides sont inversement proportionnel h Is surtension . En consideration de la texture plus probable du fer electrodepose, ('hauteur des gradins de croissance cat pros de l'hauteur de la cellule el8mentaire . On a calcule l'energie specific du bord des gradins de croissance aver I'hypothese que lee pyramides se forment aux dislocations en vis . Zusammenfassung-Auf der Oberflache von Eisen, das aus einer Ferrosulfatl6sung unter potentiostatischen Bedingungen abgeschieden wurde, entstehen tetragonale and trigonale Wachstumspyramiden . Bei kleinen Uberspannungen ilberwogen die tetragonalen, bei grosen Uberspannungen die trigonalen Pyramiden . Der Tangens des Winkets zwischen Pyramidenseitenflache and -basis war jeweils proportional der Uberspannung . Der Abstand der Wachstumsstufen an den Seitenflachen der tetragonalen Pyramiden war umgekehrt proportional der Uberspannung . Die Hohe der Wachstumsstufen erwies sich unter Beriicksichtigung der wahrscheinlichsten Textur des Eisenniederschlags als ahnlich grol3 wie die Hohe der Elementarzelle . Unter der Annahme, dap die Pyramiden durch Kristallwachstum an Schraubenversetzungen entstehen, wurde die spezifische Randenergie der Wachstumsstufen berechnet .

of crystal surfaces produced by electrocrystallization has been extensively studied qualitatively .' Recently a growing interest has arisen in the quantitative interpretation of the morphology on the basis of the theory of crystal THE MORPHOLOGY

growth . 2

For the latter purpose it is desirable to use high resolution techniques

allowing the identification of very small structures such as growth steps of molecular heights . Electron microscopy has been shown to be a suitable method .3 Its disadvantage is that it cannot be used for direct observation of the surface during crystal growth . Therefore, changes of the surface morphology during the preparation of the samples for electron microscopy must be avoided by working quickly and by studying surfaces that recrystallize very slowly. With metals of the iron group, changes of the surface morphology are expected to be very slow in solutions of the metal salts and in vacuum, since the exchange cds and the rate of surface diffusion are small. Work on cobalt3 has already shown that changes of the surface morphology during preparation can be avoided . * Presented at the 19th meeting of CITCE, Detroit, September 1968 ; manuscript received 11 February 1969. 243



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Growth pyramids have been observed on cobalt surfaces and earlier on copper 4 and silvers The geometry of the pyramids on polycrystalline cobalt changes with overvoltage as expected from the theory of Burton, Cabrera, and Franks for crystal growth at screw dislocations, although the pyramids are often not quite regular, indicating complications due to intergrowth or twinning . The morphology of iron surfaces after depositing iron under potentiostatic conditions is discussed below. EXPERIMENTAL TECHNIQUE Iron electrodes were made by depositing iron several tenths of a mm thick on a platinum sheet of 2 cmz area . The solution was a de-aerated 1 . 6 M ferrous sulphate solution of pH 4, at 20 ° C. The cd was ca 30 mA/cms . The iron electrodes were polished in a 10 % solution of perchloric acid in glacial acetic acid at a current density of 0 .7 A/cm2 . Electron microscopical inspection showed the surface to be almost flat and without any structure . After the electrodes had been carefully washed in distilled water they were brought into a fresh, de-aerated ferrous sulphate solution of the same composition and pH as before at 20 ° C . A constant pd was applied using a potentiostat and a sce . An iron deposit was grown to the desired thickness on the polished iron surface-usually the thickness was 2 . 5 pm . immediately after a specimen was removed from the solution it was thoroughly rinsed with a jet of distilled water and quickly dried in vacuum . Replicas were made by evaporating carbon on to the surface . The carbon layer was cut with a knife and removed from the iron by dipping the specimen into hydrochloric acid, or, after being covered with collodion, it was stripped from the iron surface . The collodion was dissolved in butyl acetate before the replica was inspected in the microscope. For high contrast micrographs the replicas were shadowed with a gold-palladium alloy at an angle of 45°. Without shadowing the pictures showed little contrast, but a high resolution of 20-25 A was obtained . The replicas were investigated with a Siemens Elmiskop I electron microscope . Usually two pictures tilted 10° with respect to each other were taken for stereoscopic measurements. With a stereoscopic viewing apparatus the difference in height H between two points appearing at a parallax y and at a magnification M was calculated from? (1) H = y/2 M sin 0 . The statistical error of any single measurement was estimated to be fu < (±300 A) for measurements of heights and f < (± 9° ) for measurements of angles.8 In order to decrease the statistical errors, 10 to 20 measurements were taken for each of the points given in the figures . RESULTS On the major part of the iron surfaces, growth pyramids could be identified . The two types of pyramid shown in Figs . 1 and 2 have been observed . Each type of pyramid was confined to separate parts of the surface . The probability of finding one type of pyramid depended on the overvoltage . The pyramids shown in Fig. l are typical of those found at low overvoltages between 60 and 110 mV . At high overvoltages, between 150 and 200 mV, the pyramids shown in Fig . 2 were 5 to 10 times more abundant than the pyramids shown in Fig . 1 .

Fro . 1, Tetragonal growth pyramids on the surface of iron deposited and 20°C from a 1-6 M ferrous sulphate solution . The arrow points t of the metal beam used for shadowing .

= 155 mY direction

Fro . 2. Trigonal pyramids on the surface of iron deposited at 27 = 155 MV and 20§C from a 1-6 M ferrous sulphate solution, 2 44



Electron-microscopical studies of the electrocrystallization of iron

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Figure 1 is the positive of a picture taken from a replica which had been stripped from the iron surface with collodion, The side of the carbon layer that was in contact with the iron surface was partially covered with latex spheres of 0-365 ± 0-04 /Am diameter before shadowing. The metal beam used for shadowing produced a thick deposit in front of the spheres . Behind the spheres there are shadows appearing white in Fig . 1 . One therefore knows the direction of the metal beam . In the replica, planes with an upward slope when looking in the direction of the metal beam have been covered more densely with the metal and appear darker in the picture than the surfaces parallel to the plane of the sheet . The pyramids thus have formed depressions in the replica ; they have been protrusions on the original iron surface . The shadows behind spheres on a plane sloped downwards in the replica are longer than the shadows behind spheres on a plane sloped upwards. The lengths of the shadows on the dark and on the light planes do not differ much . The pyramids are therefore rather flat . For optimal accuracy of the quantitative stereoscopic measurements, it was necessary to grow all the deposits to the same thickness over the polished surfaces . The optimal thickness was ca 2 . 5 /Am . However, within the limits of accuracy, pyramids of a given type grown at a given overvoltage were found to be geometrically similar independent of the thickness of the deposit . Thin deposits exhibited many pyramids of small height . Thickening of the deposits resulted in a decreasing number of higher pyramids and in the intergrowth of the pyramids until the appearance of single, well developed pyramids became a rare occasion . The dimensions of both the very small and the heavily intergrown pyramids could not be measured stereoscopically with the desired accuracy . The range of overvoltages experimentally accessible for exact measurements of the dimensions of the pyramids was limited at low overvoltages by the formation of very flat pyramids yielding little contrast, and by the long times necessary to reach the optimal thickness due to the steep exponential decrease of ed when the overvoltage was diminished . The stationary polarization curves were found to follow Tafel lines with a slope of 33(±3) mV per decade of cd . At high overvoltages the current density for the deposition of iron became diffusion-limited . Still, the geometry of the pyramids was shown to be determined only by charge-transfer overvoltage, which changes very little, if the cd is close to the diffusion-limited cd . The tetragonal pyramids in Fig . 1 have almost square bases . At low overvoltages, deviations from a square base could hardly be detected . Sharp pyramid edges extended from the comers of the bases to the tops of the pyramids . At high overvoltages, as in Fig . 2, some of the pyramids seem to disintegrate into structures with a three-fold symmetry . Figure 2 shows well developed trigonal pyramids . From the stereo pictures it can be seen that the points of highest elevation above the plane of the sheet are always intersections of three different edges . These points are the tops of pyramids . Planes at a certain level below the tops of the pyramids are triangles . The projections of the sides of the pyramids usually appear to be quadrangles, because the pyramids grow together at edges parallel to the edges of the pyramids and not at a certain level below the top of the pyramids like the tetragonal pyramids . Neighbouring pyramids have the same crystallographic orientation in areas of the order of lOs ,tame. In Fig . 1 pyramid edges are observed only in two directions, and in Fig. 2 in three directions . The geometry of the pyramids was quantitatively investigated in the following way .

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HEusLHR

and R .

KNOEDLwL

The difference in height H between the top and one corner at the base of a pyramid was measured stereoscopically . Knowing the projected length b of the respective edge of the pyramid, an angle a" between the edge and the plane of the sheet was calculated from tan e = Hid. In general, the angle a" differs from the angle a between the edge and the base of the pyramid because there is an angle 99 between the directions normal to the sheet and to the base . The angle a can be obtained from the average of the angles a" measured at many different pyramids or from the mean of two angles measured in opposite directions from the top of one pyramid. The assumption is made that the apex of a pyramid moves normal to the base when a pyramid is growing . From the differences between the angles a" and a' the inclination w can be calculated . For tetragonal pyramids the inclination was w = 0 ± 2° at all overvoltages. For trigonal pyramids, inclinations between rp = 100 and q' = 20° were observed at overvoltages of 140-165 mV . The inclination did not clearly depend on overvoltage . For a comparison with the theory, the angle a between the sides and the base of a pyramid is essential. The relationship between the angles a and cc' are tan a = V2 tan a' for tetragonal pyramids and tan a = 2 tan a' for trigonal pyramids . Figure 3 shows that the tangents of the angle a are proportional to the overvoltage 27 . For the two types of pyramids the slopes d?7/d tan a are different : for tetragonal pyramids do fd tan a = 0 .725 ~= 0.02 V, and for trigonal pyramids dry/d tan a = 0.338 f 0 .01 V. The visible height Ho of the pyramids did not depend on overvoltage . At the chosen optimal thickness of the deposit the average height of the tetragonal pyramids was 05-

04-

0 a

005 010 Overvottage, V

Ftc . 3 .

1 015 020

Tangents of the pyramid angle a as a function of overvoltage. ∎, tetragonal pyramids ; o , trigonal pyramids .



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Ho = 0-28 + 0-10 ,um, and that of the trigonal pyramids He = 0 . 07 f 0.04 ,am . The tetragonal pyramids are relatively flat and their number per unit area is small . On the other hand, there is a relatively large number per unit area of steep trigonal pyramids . The average scatter around the most probable height was greater for trigonal than for tetragonal pyramids . This is apparently connected with the fact that intergrowth at the bases of the trigonal pyramids does not occur at a well defined level below the top of the pyramids, while the level of intergrowth is better defined for tetragonal pyramids . Since at constant height tan a varies linearly with the overvoltage ?1, the side lengths of the pyramid bases are reciprocal to the overvoltage . On a surface completely covered with pyramids the number of pyramids per unit area accordingly increased with overvoltage . Inspection of unshadowed replicas prepared for high resolution from iron samples grown at low overvoltages (n S 110 mV) revealed systems of parallel lines at high magnifications . The directions of the lines changed abruptly at the edges of the tetragonal pyramids, this type being the only one to occur at low overvoltages . The lines were parallel to the pyramid bases . The distances between the lines decreased with the overvoltage. Within the limits of accuracy the distances 1 changed linearly with the reciprocal overvoltage, as shown in Fig . 4 . A slope of d1/d?) 1 = 6 . 8 + 1 A - V can be calculated from the measurements . The distances I were shown to be independent of the thickness of the deposit .

5

10

Reciprocal overvoltage,

5

20

V -I

FIG . 4 . Step distances at tetragonal pyramids as a function of reciprocal overvoltage . DISCUSSION

The observed shapes of the pyramids and their dependence on overvoltage can be described by the theory of Burton, Cabrera, and Frank" for crystal growth at screw dislocations . According to the theory, a crystal may grow without two-dimensional nucleation by deposition of metal atoms at steps originating from the point of emergence of a screw dislocation . If the mean distance between kinks in the edge of a step is large compared to the distance of neighbouring metal atoms in the lattice, the specific edge energy will strongly depend on the crystallographic direction of the step in the surface . Then, steps of macroscopic length will only appear in certain



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closely packed directions of low specific edge energy . When metal atoms are incorporated at a long step, this step will laterally move away from the dislocation and a new step in another direction will develop . As soon as the length of the newly formed step becomes larger than a certain critical length, lateral growth also will start at this step . Finally, a stepped growth pyramid will appear with the screw dislocation in its centre. The constant distance of the steps at a pyramid grown at a given overvoltage is determined by the critical length of the two-dimensional nucleus . The critical length a c corresponds to the maximum of the free energy (2) AG = k 2aK - k1z Ft7 a2h/VM of a two-dimensional nucleus with height h, area A = kta2 and the length L = k2a of the circumference at the overvoltage 27, assuming that the steps have the same specific edge energy x in all the directions observed . In (2) the molar volume and the charge to deposit one mole of metal from the ions are VM and zF, respectively . From 2G/2a = 0 the maximal free energy of the nucleus is obtained, AGc

_ k22 K2 VM 4 kl zFrih

k2 2

(3)

whence _ k2 K VM a` 2 kl zFr7h i

(4)

The step distance I is given by l = k3ao, and the tangent of the pyramid angle a by h 2 kl zFr7h2 tan a l ky KY .

(5)

(6)

For square base pyramids the geometric constants are kt = 1 and k2 = 4, and for regular triangles kl = 1/j and k 2 = 3 . The constant k 3 depends on how the rate v of the lateral advance of a step increases from zero at the critical length a. to the rate v . corresponding to an infinite length of the step a -' cc. For low overvoltages, n c< RT/zF, Burton, Cabrera and Franke proposed the relation v = v, (1 - ac/a) . For overvoltages of several RTIzF their theory predicts a very steep exponential increase with (a - ac) of v towards v . . At the overvoltages used in the present experiments on iron the relation v = 0 for a S ac and v = vW for a > a. will be a good approximation . One obtains k3 = 4 for tetragonal pyramids, and k3 = 3A/-3f for trigonal pyramids . Using only the experimental results and (4), (5) and (6), the specific edge energy K and the step height h may be calculated for the tetragonal pyramids . One gets h = 9.4 + 1 A, and from 2 kl zF dl \ 2 `d tan al K (7) = kzks VM \d27_ 1 1 d7 j (2.2 f 0 .7) x 10-* ergs/cm . However, one has to consider that the step height cannot assume any arbitrary value . The step height must be equal to the height of the unit cell in the proper orientation multiplied by an integer . Unfortunately, no experimental data on the texture of iron deposited from nearly K =



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neutral perchlorate baths at 20°C are available . Pangarov' investigated the texture of iron deposited mostly at elevated temperatures from acid ferroammonium sulphate solutions with and without additions of potassium iodide . The orientation of the fibre axes was found to change with increasing overvoltages in the order [110], [112], [310], [111] . In addition, in the earlier work of Glocker and Kaupp10 a weak orientation along [100] had been observed with iron deposited from a hot acid ferrous chloride bath . At a given overvoltage, the texture may change with the composition of the adsorbed layer on the iron surface . The composition of the adsorbed layer is a function of the temperature and of the composition of the solution . Therefore there is no direct evidence regarding the texture of the deposits obtained from perchlorate baths . On the other hand, for theoretical reasons it is highly improbable that other orientations than those already observed will appear . Some information on the texture may be obtained from the symmetry of the growth pyramids . The symmetry of the pyramid bases is expected to agree with the symmetry of the two-dimensional nuclei on planes having the respective orientations . The four-fold symmetry of the tetragonal pyramids is compatible with several orientations corresponding to the texture axes [100], [110], and j112] . The heights of the unit cell in these directions are h11w1 = a0, h1n01 = V2 a0 , and h11121 = -V6 a0 , with a0 = 2-86 A. A comparison with the experimental result for the step height yields n[lool = 3-28 ± 0-35, n11101 = 2-32 ± 0-25, and n[1121 =1-34 ± 0 . 15 . Since values of n > 2 are theoretically very improbable,° and since the [100] orientations seems to occur only under rare circumstances, only the orientations [110] and [112] will be considered . Using the step heights 2h[11o] and h 11121 the specific edge energies K11101 = 1 . 6 X 10 -4 erg/cm and ic 111El = 1-2 x 10 -4 erg/cm are calculated from (6) . From the symmetry of the trigonal pyramids, it can be safely concluded that the pyramid axes are parallel to the [111] direction . The specific edge energy calculated in units of the possible step heights h[n1] = n11111 N/3 a0 is K11111 = n2[llll x 0 .25 X 10 -4 erg/cm. It was not possible to measure step distances at the trigonal pyramids ; the step distances apparently were smaller than the limit of resolution in the region of overvoltage corresponding to the occurrence of that type . Such a result is expected, if in agreement with the theory° n11111 c 2 . Then, the specific edge energy of steps at the trigonal pyramids will be smaller than that at the tetragonal pyramids . It is interesting to note that the disintegration of the tetragonal pyramids into trigonal pyramids, shown in its early stages in Fig . 1, seems to occur without change of texture . As a consequence, the angle between the axes of the trigonal and of the tetragonal pyramids should agree with the angle between the directions [111] and [110] or [112], which are 35° or 19 ° , respectively . Experimentally, an angle of 10 °-20° has been observed between the axes of the two types of pyramids . Thus, a [112] texture axis of the deposits would be consistent with all the experimental results of the present work . The texture axis will change only if the direction of the axes of the pyramids changes with respect to the normal direction of the sheet . This process has been observed with cobalt . 3 The overvoltages required to change the texture of the iron deposits may be much higher than the overvoltages at which the tetragonal pyramids disintegrate into trigonal pyramids . In order to explain the dependence of the texture on overvoltage Pangarov calculated the work of formation of two-dimensional nuclei on planes of different

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K . E . HEusLER and R. KNOEDLER

orientations . The orientation of the planes with minimal work of formation changed in the same order as the texture axes . Without further experimental proof this coincidence was taken as an indication that growth proceeded by two-dimensional nucleation of successive planes . However, growth by two-dimensional nucleation does not offer an explanation of the morphology of surfaces produced by electrodeposition of iron and cobalt . The present work has shown that the morphology can be understood from the theory of crystal growth at screw dislocations. Now, in order to explain the dependence of the texture on overvoltage a mechanism will be required by which the Burgers vector of the screw dislocations in the centre pyramids changes its direction with respect to the plane of the sheet. Acknowledgement-Financial acknowledged .

of

the

support by the "Arbeitsgemeinschaft Korrosion" is gratefully

REFERENCES 1, G . J. F[NcH, H . Wnn .n and L. YANG, Discuss . Faraday Soc . 1, 144 (1947) ; H . FtscBBR, Elektrolytische Abscheldung and Elektrokristallisation von Metallen . Springer, Berlin (1954) ; J . O'M . Bocr-ms and A. DAMJANOVtc, in Modern Aspects of Electrochemistry, No . 3, ed . J . O'M . Bocnrs and B . E . CONwAY, p . 293 . Butterworths, London (1964) . 2 . M . FLEtsem1ANN and H. R. TmRstc, in Advances in Electrochemistry and Electrochemical Engineering, ed . P. DELAHAY and C . W . TOBIAS, Vol . 3, p . 123 . Interscience, New York (1963) ; K . J . VErrER, Electrochemical Kinetics, p . 282 . Academic Press, New York (1967) . 3 . K . E . HEusLER and R . KNOEDLER, Ber . Bunserges . phys_ Chem . 11, 1085 (1967) . 4 . H . J . PICK, Nature, Land. 176, 963 (1955) ; H . SEtrER and H . FiscHER, Z. Elektrochem . Ber. Bunserges. phys . Chem . 63, 249 (1959) ; H . SErrER, H . FiscnER and L . ALBERT, Electrochim. Acta 2, 97 (1960) . 5 . R . KAtscHEw, E . BuDEwsKI and J. MALINOWSKI, Z. phys . Chem . (Leipzig) 204, 348 (1955) . 6 . W. K . BURTON, N. CABRERA and F . C . FRANK, Nature, Load. 163, 398, (1949) ; Proc . R. Soc . (Land.) A243, 299 (1951) . 7 . V . K . ZwoRVKnN, G . MORTON, E . G . RAMBERG, H . HLLLER, and A . W . VANCE, Electron Optics and the Electron Microscope . New York (1945) . 8 . R . J . GARRoD and J . F . NANKivELL, Br . J. appl. Phys. 9, 214 (1958) . 9 . N . A . PANGAROV and S . D . VrrovKA, Eiectrochim . Acta 11, 1719 (1966) . 10 . R . CLocKER and E . KAUPP, Z. Phys . 24,121 (1924).