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Comment on the paper “electrocrystallization of Ni, Co and Fe dendrites from aqueous solutions” by S. Tajima and M. Ogata
1559
Short communications Ekcaocbimica
Acta, 1970. Vol. 15 , pp. 1559 to 1560. Pergamon Press. Printed in Northern Ireland
COMMENT ON THE PAPER “ELECTROCRYSTALLIZATION OF Ni, Co AND Fe DENDRITES FROM AQUEOUS SOLUTIONS” BY S. TAJIMA AND M. OGATA” J. W. DIGGLE~ The Electrochemistry Laboratory, The University of Pennsylvania, Philadelphia,
Pa. 19104, U.S.A.
TAJIMA and Ogatal proposed that the forward propagation of dendrites (nickel was referred to specifically) occurs under a linear diffusion flux. This conclusion was reached by comparing the dendrite growth rate, expressed as cd, with the limiting linear diffusion cd il, the former being 2400 A/cm2 and the latter 1340 A/cm2. The difference between the two values was proposed as being due to a diffusion coefficient too small and a 6 value too large. However, there is an error in the calculation of il and correction reduces ilim to 1.34 A/cm2, so that linear diffusion to the dendrite tip cannot possibly account for the dendrite growth rate. In previous work done in this laboratory,2>3 the dendrite tip was proposed as being a place for sphericaldiffusion, since the tip radius r < 6. Under spherical diffusion, the limiting cd is
where co is the bulk concentration of diffusing ion (valid only where the dendrite length y > S). For the growth of nickel dendrites in 3 M NiC12 at 105”C, 2 x 96,500 Q(B)
=
x 0.69
x 10” r
x 3 x lO-3
A/C&.
If the propagation rate of the nickel dendrite, reported by Tajima and Ogata as 700 ,um/s, is taken to occur at the limiting spherical cd, then r = 166 A. The total overpotential under such conditions would be phenomenal, being given by
For a low i,, metal, under conditions where i + ilcsj, the first two terms would be large; the third term, (ie the Kelvin term) would probably be small in comparison (but not negligible). The work of Tajima and Ogata has shown that nickel dendrites propagate 100 times faster in the forward than in the side direction-a fact itself difficult to explain if the dendrite tip is taken to propagate under a linear diffusion flux. Only when the flux to the tip is greater than that to sides can the difference be accounted for, the tip * Manuscript received 23 April 1970. t Present address: Corporate Research Laboratories, Allied Chemical Corporation, Morristown, New Jersey 07960, U.S.A.
1560
Short communications
being under spherical flux and the sides under linear flux, the flux densities differing by at least two orders of magnitude. Further work in this laboratorys*d upon zinc dendrites has shown that only under spherical diffusive flux can the dendrite forward propagation rate be maintained; whether the dendritic deposition occurs under diffusion or activation control depends upon the value of i0 and the contribution of the Kelvin term to the total overpotential. A recent publication by Tajima and Ogata6 has appeared in which the error in their earlier paper1 is rectified. However, this later publications does little to rationalize dendritic growth in terms of a mechanism involving both ionics and electrodics. The statement is made that it is difficult to apply concepts of normal limiting cd to dendritic phenomena-this is true if concepts are restricted to linear diffusivity, but not if the diffusivity is spherical or parabolic in nature. Ackmwkdgemerzts-The author is grateful to Professor J. O’M. Bockris for many valuable discussions, and to the National Aeronautics and Space Administration (NsG-325) for financial aid. REFERENCES 1. S. TAJIMAand M. OGATA, Etectrochim. Acta 13, 1845 (1968). 2. J. BARTON and J. O’M. BOCKFUS,Proc. R. Sot. A268,485 (1962). 3. A. R, DESPIC, J. W. DIG~LE and J. O’M. BOCKRIS,J. electrochem. S’oc, 115, 507 (1968). 4. J. W. DIGGLE, J. O’M. BOCKRISand A. R. DESPIC, J. electrochem. Sot. 116,1503 (1969). 5. S. TAJIMAand M. OGATA, Electrochim. Acta 15,61 (1970).
Short communications Ekcaocbimica
Acta, 1970. Vol. 15 , pp. 1559 to 1560. Pergamon Press. Printed in Northern Ireland
COMMENT ON THE PAPER “ELECTROCRYSTALLIZATION OF Ni, Co AND Fe DENDRITES FROM AQUEOUS SOLUTIONS” BY S. TAJIMA AND M. OGATA” J. W. DIGGLE~ The Electrochemistry Laboratory, The University of Pennsylvania, Philadelphia,
Pa. 19104, U.S.A.
TAJIMA and Ogatal proposed that the forward propagation of dendrites (nickel was referred to specifically) occurs under a linear diffusion flux. This conclusion was reached by comparing the dendrite growth rate, expressed as cd, with the limiting linear diffusion cd il, the former being 2400 A/cm2 and the latter 1340 A/cm2. The difference between the two values was proposed as being due to a diffusion coefficient too small and a 6 value too large. However, there is an error in the calculation of il and correction reduces ilim to 1.34 A/cm2, so that linear diffusion to the dendrite tip cannot possibly account for the dendrite growth rate. In previous work done in this laboratory,2>3 the dendrite tip was proposed as being a place for sphericaldiffusion, since the tip radius r < 6. Under spherical diffusion, the limiting cd is
where co is the bulk concentration of diffusing ion (valid only where the dendrite length y > S). For the growth of nickel dendrites in 3 M NiC12 at 105”C, 2 x 96,500 Q(B)
=
x 0.69
x 10” r
x 3 x lO-3
A/C&.
If the propagation rate of the nickel dendrite, reported by Tajima and Ogata as 700 ,um/s, is taken to occur at the limiting spherical cd, then r = 166 A. The total overpotential under such conditions would be phenomenal, being given by
For a low i,, metal, under conditions where i + ilcsj, the first two terms would be large; the third term, (ie the Kelvin term) would probably be small in comparison (but not negligible). The work of Tajima and Ogata has shown that nickel dendrites propagate 100 times faster in the forward than in the side direction-a fact itself difficult to explain if the dendrite tip is taken to propagate under a linear diffusion flux. Only when the flux to the tip is greater than that to sides can the difference be accounted for, the tip * Manuscript received 23 April 1970. t Present address: Corporate Research Laboratories, Allied Chemical Corporation, Morristown, New Jersey 07960, U.S.A.
1560
Short communications
being under spherical flux and the sides under linear flux, the flux densities differing by at least two orders of magnitude. Further work in this laboratorys*d upon zinc dendrites has shown that only under spherical diffusive flux can the dendrite forward propagation rate be maintained; whether the dendritic deposition occurs under diffusion or activation control depends upon the value of i0 and the contribution of the Kelvin term to the total overpotential. A recent publication by Tajima and Ogata6 has appeared in which the error in their earlier paper1 is rectified. However, this later publications does little to rationalize dendritic growth in terms of a mechanism involving both ionics and electrodics. The statement is made that it is difficult to apply concepts of normal limiting cd to dendritic phenomena-this is true if concepts are restricted to linear diffusivity, but not if the diffusivity is spherical or parabolic in nature. Ackmwkdgemerzts-The author is grateful to Professor J. O’M. Bockris for many valuable discussions, and to the National Aeronautics and Space Administration (NsG-325) for financial aid. REFERENCES 1. S. TAJIMAand M. OGATA, Etectrochim. Acta 13, 1845 (1968). 2. J. BARTON and J. O’M. BOCKFUS,Proc. R. Sot. A268,485 (1962). 3. A. R, DESPIC, J. W. DIG~LE and J. O’M. BOCKRIS,J. electrochem. S’oc, 115, 507 (1968). 4. J. W. DIGGLE, J. O’M. BOCKRISand A. R. DESPIC, J. electrochem. Sot. 116,1503 (1969). 5. S. TAJIMAand M. OGATA, Electrochim. Acta 15,61 (1970).