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An electric field influence on dendritic growth
Journal
of Crystal
Growth
12 (1972) 309-315
AN ELECTRIC
,T North-Holland
Publishing
FIELD INFLUENCE
Co.
ON DENDRITIC
GROWTH
CORNELIAMOTOC Polyterhnical Received
Institute,
IO July
Bucharest,
1971; revised
Romania manuscript
received
15 November
1971
The dendritic growth of ammonium chloride on muscovite mica and glass substrates was studied: firstly under regular conditions and then under electric fields. The dendrites developed under regular conditions disclosed features of the substrate surface structure. In the presence of dc fields, crystalline needles were obtained which grew in the field direction; after the field was removed the needles developed branches from their bulk; shortly afterwards the branches detached themselves from the needles and the regular dendritic growth went on. When the dc fields were perpendicular to the growth chamber, the crystallization was stopped for quite a while; it started after the field removal and went on at a high rate, the dendritic branches detaching from the central stems. Under an ac field the dendritic growth was directed parallel to the field which also thickened the central stems. The effects may be explained by considering changes in the surface free energy induced by the electric field.
1. Introduction There has been reported a large amount of work on dendritic growth; most of the papers deal with the growth kinetics and with the dependence of the dimensions of the central stem tips on the growth condibetween the directions of the tions’ 3’). Connections branches and the crystallographic directions have also been discussed3*4). The influence of an electric field on dendritic growth has been less studied, mostly on ice5g6). This paper reports studies of dendritic growth of ammonium chloride from water solution on glass and muscovite mica substrates; the growth was studied with and without ac/dc electric fields.
2. Experimental Water solutions of ammonium chloride saturated at 35 “C were poured into a closed glass chamber (1 cm wide, 8 cm long, 0.05-O. 1 cm high) and cooled on a thermostated stage microscope to different temperatures ranging from 19 “C to 26 “C. In order to study epitaxial dendritic growth, a mica substrate was introduced in the growth chamber. 2.1. GROWTH
IN THE ABSENCE OF AN ELECTRIC FIELD
As dendritic growth on amorphous substrates is well known, there will be reported only the results
obtained using mica substrates, in which case an epitaxial dendritic growth is expected. In the absence of an electric field, the growth directions of ammonium chloride dendrites are connected to the mica crystallographic directions. The dendrites are parallel to the directions contained in the substrate surface plane: (OlO), (llO), and (li0); still the direction distribution of the dendrites is not uniform; most of them are parallel to (010) and this eventually agrees with the already reported differences between (010) and (1 lo), (li0) mica directions. The secondary branches are perpendicular to the central stems. A 0.05 cm high chamber brought up an interesting feature of the epitaxial growth. The crystallization in stems and perpendicularly attached branches is stopped when the saturation concentration is reached; then the branches set on changing orientation exhibit the tendency to form parallel to (1 lo), eventually detaching themselves from the central stems. This is clearly indicated by figs. I a and 1b (taken 20 min afterwards) and fig. lc (another 10 min). The phenomenon is accompanied by the thickening of the central stems and branches; it may be interpreted as a recrystallization aimed at a really stable epitaxial structure. Other remarkable cryststallized patterns are reported which were obtained by decanting ammonium chloride
CORNELIA
(b)
(4 Fig.
1.
(a) Dendritic
MOTOC
growth
on muscovite
mica;
solutions on mica surfaces. Fast growth of dendrites is likely to reveal the surface structure or defects on mica surfaces. Dendrites grow with the central stems perpendicular or parallel to the (010) direction; the branches are not always directed perpendicularly to the central stem or parallel to some crystallographic directions on the mica surface. The most frequent angles between the branches and the central stems are 72” or 48”, showing no relation with the hexagonal structure of the mica cleavage plane (fig. 2). A bidimensional lattice with 72” angles is thus formed. We recall that the pentagonal symmetry on mica surfaces has already been reported by Allpress and Sanders7). (Thin metallic films consisting of pentagonal polyhedra as well as triangular, quadrangular and hexagonal have been obtained on mica.) There is a hint that 72” angles characteristic for the pentagonal structure are likely to appear on a mica substrate, the superficial, planes of with are “twisted” by 13’. This assumption accepted, the central stems and branches would independently stick to the two “twisted” planes.
(b) is taken
20 min afterwards;
(c) follows
after
10 min.
As knownin muscovite mica there are distortions and tilts of surface oxygen network from the hexagonal. These distortions are primarily due to misfit between the tetrahedral and octahedrallayers. In muscovite mica a considerable contraction of the tetrahedral layer to fit the octahedral layer has to be taken into account. This fitting together of different sized layers may be accomplished by a rotation of 13” of the basal 0 triads as has been pointed outsB9). The difference between the 13” rotation of basal 0 triads and the 12” rotation assumed in this paper in order to explain the unorthodox angles between the central stem and dendrite branches is rather puzzling; some errors might well account for it. 2.2, GROWTH
IN THE
PRESENCE
OF AN
ELECTRIC
FIELD
Direct and alternating electric fields were applied perpendicular or parallel to the growth chamber; the electrodes were not, of course, immersed in the solction. When dc fields were applied parallel to the growth chamber, the crystallization resulted in needles parallel to the field direction. After field removal, from the very
AN
Fig.
ELECTRIC
2.
Epitaxial
FIELD
growth
INFLUENCE
of dendrites
ON
DENDRITIC
on miscovite
mica;
GROWTH
311
AT = 10 ‘C
bulk of the needle, branches rapidly developed and in a very short time the regular dendritic growth occurred. Remarkably, the branches do not start growing simultaneously all along the needle, but gradually toward the tip. Fig. 3 shows one of the needles grown in a 6600 V/cm field at AT = 11 “C which developed branches after the field was taken off. Such needles were obtained on both mica and glass substrates. With dc fields set perpendicularly to the growth chamber, the crystallization was remarkably inhibited. As an example, under fields higher than 6000 V/cm no
Fig. 3. Needle grown on muscovite electric field; AT = 11 “C.
mica
substrate
in a dc
crystallization was obtained from a supersaturated (AT = 14 “C) ammonium chloride solution during 1 hr. The growth started a few minutes after the field was switched off; a period of induction seemed to be necessary for the nucleatin and growth to start. The dendrites developed rapidly and uniformly in the whole sample (fig. 4) displaying some peculiarities : they detached themselves from the central stem; this effect, obtained on glass substrates, had been also obtained on mica substrates with no electric field. In both cases it followed shortly after the growth was stopped. Fig. 5 shows this effect for ammonium chloride dendrites; the solution was supersaturated at AT = 11 “C and subjected to a 6600 V/cm dc field. Careful examination of these dendrites obtained
312
CORNELIA
Fig.
Fig.
5.
4.
Branches
Dendritic
detaching
growth
after
themselves
field removal
from
central
from solutions previously subjected to high electric fields perpendicular to the growth chamber revealed branches grown in the field direction. Gradually the branches changed orientation reclining into the chamber plane (fig. 6). AC fields (50 Hz) ranging from 200 V/cm to 2 x IO4 V/cm were also used. When lower than 700 V/cm they did not show any influence on the orientated grown
MOTOC
obtained
stems,
on glass substrate;
obtained
AT = 14 ‘C.
on glass substrate;
AT = 11 “C.
dendrites on either mica or glass substrates. Electric fields higher 700 V/cm and perpendicular to the growth chamber thickened the central stems as well as the first dendritic branches. This permits revealing of the main dislocation of the dendrite, as shown in fig. 7 for ammonium chloride crystals grown on a mica substrate. (Similar effect are obtained on glass). Fig. 7, which shows a pattern of hexagonally grown dendrites
AN
ELECTRIC
Fig.
Fig.
7.
6.
Dendrites
FIELD
Dendritic
grown
INFLUENCE
growth
after
ON
field removal
on mica in an ac electric
besides the one directed on (OIO), proves again that the dendritic crystallization ennablas us to indicate crystal defects. When the fields were higher than IO4 V/cm, the dendrites exhibited the tendency to grow in the field direction on both glass and mica substrates. Under alternating fields no needles were formed. On mica substrates
DENDRITIC
(glass
GROWTH
313
substrate).
field (AT = 10 ?C; 1000 V/cm).
alternating fields of more than 2 x IO4 V/cm increased the nucleation rate in ammonium halide solutions; growth nuclei appeared in the whole solution; they were dendritic stars, both regular (triangular, quadrangular and hexagonal) and irregular (pentagonal). Some nuclei appear on the steps of the mica surface; the dendrites thus formed have only little connection
314
CORNELIA
Fig. 8.
Dendrites
MOTOC
grown on mica under an ac electric field (2 x lo4 V/cm; AT = 10 “C).
with the crystallographic directions of the mica substrate. In fig. 8 ammonium chloride dendrites grown on mica in 2 x lo4 V/cm are shown. 3. Discussion As is known, when the temperature gradient in the liquid at the interface is negative, tree-like growth forms are obtained, the central stem and branches extending in a well-defined crystallographic direction. When the temperature gradient is positive the branches are indistinct and the central stem has no uniquely defined crystallographic direction. In our experiments both cases were found: needles or dendrites with thick central stems under electric fields, and dendritic growth forms without electric field. These results are qualitatively similar to the electric field growth of ice crystals from vapour phase reported by Bartlett et al.‘). These two experimentally revealed cases may be qualitatively explained by examining the morphological stability of a dendrite growing in the presence and absence of an electric field. Let us examine the morphological stability of a dendrite; we shall let aside the tip region and for the remaining part of the dendrite we shall proceed the way we should do with a circular cylinder.
As has been shown by Coriell and Parker”‘“), any perturbation of the circular shape of the cylinder can be represented by a linear combination of harmonic perturbations. In the most simple case, the radius of the perturbed cylinder is given by r = R+6
exp (ik@),
where R is the unperturbed radius. It has been shown that the rate of growth perturbation is
SCD s
D(k-
= R2(C-
1) C,)
(C - C,)IX2’ R2
G,--
F
D, F k2(k+1)
of the @
k(k+,)
I
,
where D and D, are the volume and respectively surface diffusion coefficients, G, the concentration gradient at the precipitate-matrix interface, Sz the atomic volume of the precipitate Co the equilibrium concentration in the medium adjacent to the precipitate and CR = Co+ Co T/R (where r is the capillarity constant for the correction of equilibrium composition for interface curvature). i$@/S@ is composed of three terms: the first depends on the concentration gradient and is destabilizing: it favours the growth of the perturbation. The second and the third terms are proportional to the capillarity
AN
constant,
ELECTRIC
i.e. to the surface free energy;
FIELD
INFLUENCE
they favour the
decay of a perturbation. Then, if it is assumed that in the presence of an electric field the surface free energy is enhanced, an accidental perturbation would rapidly decay if the electric field is strong enough to compensate the destabilizing effect of the concentration gradient. Accordingly, when strong electric fields are employed, needles are expected to grow instead of dendrites. When the electric field is removed, the surface free energy would then be lowered and the destabilizing factor would prevail; any perturbation would grow and the needle would begin to develop branches from its bulk. As shown by the fig. 3, branches develop from these periodic accidental perturbations; finally the crystallization is similar to the well-known dendritic growth. There are certainly polarization effects, associated with the tendency of the induced dipoles to orientate in the field direction. Besides, the hydration effects have to be taken into account because the electric field changes the shape of the hydration sphere into an ellipsoidal one. There are really difficulties in deciding to what extent these effects influence the growth in the presence of an electric field. A most remarkable thing is that the dc field retards and prevents the crystallization; this effect may be ascribed to the orientation of dipoles in the field
ON
DENDRITIC
direction,
GROWTH
the formation
of clusters
315 or of the growth
nuclei being thus prevented. The detaching of the dendrite branches which grow from the solution previously subjected to a dc field is likely to be an electrostatic effect, as it has been observed on glass substrates only after an electric field was applied. In alternate fields habit changes are not produced. The effects are explained by assuming that the enhancement of nucleation occurred as a result of changing the orientation of the induced dipoles. As it has been shown in fig. 8, on mica surface the enhancement of nucleation produced regular and irregular dendritic stars. References 1) J. J. Gilman, The Art and Science of Growing Crystals (Wiley, New York, 1963) pp. 123, 182, 297, 334. 2) G. R. Kotler and L. A. Tarshis, J. Crystal Growth 3,4 (1968) 603. 3) M. E. Billig and P. J. Holmes, Acta Cryst. 8 (1955) 353. 4) D. R. Hamilton and R. G. Seidensticker, J. Appl. Phys. 31 (1960) 1165. 5) J. T. Bartlett, A. van der Heuvel and B. J. Mason, Z. Angew. Math. Phys. 14 (1963) 599. 6) P. R. Camp and F. C. Barter, Nature 200 (1963) 350. 7) J. G. Allpress and J. V. Sanders, Surface Sci. 7 (1967) 1. 8) E. w. Radoslovich, Acta Cryst. 13 (1960) 919. 9) J. D. Birke and R. Tettenhorst, Mineral. Mag. 36 (282) (1968) 883. 10) S. R. Coriell and R. L. Parker, J. Appl. Phys. 37 (1966) 1548. 11) S. R. Coriell and R. L. Parker, in: Crysfal Growfh, Ed. H. S. Peiser (Pergamon, Oxford, 1967) p. 703.
of Crystal
Growth
12 (1972) 309-315
AN ELECTRIC
,T North-Holland
Publishing
FIELD INFLUENCE
Co.
ON DENDRITIC
GROWTH
CORNELIAMOTOC Polyterhnical Received
Institute,
IO July
Bucharest,
1971; revised
Romania manuscript
received
15 November
1971
The dendritic growth of ammonium chloride on muscovite mica and glass substrates was studied: firstly under regular conditions and then under electric fields. The dendrites developed under regular conditions disclosed features of the substrate surface structure. In the presence of dc fields, crystalline needles were obtained which grew in the field direction; after the field was removed the needles developed branches from their bulk; shortly afterwards the branches detached themselves from the needles and the regular dendritic growth went on. When the dc fields were perpendicular to the growth chamber, the crystallization was stopped for quite a while; it started after the field removal and went on at a high rate, the dendritic branches detaching from the central stems. Under an ac field the dendritic growth was directed parallel to the field which also thickened the central stems. The effects may be explained by considering changes in the surface free energy induced by the electric field.
1. Introduction There has been reported a large amount of work on dendritic growth; most of the papers deal with the growth kinetics and with the dependence of the dimensions of the central stem tips on the growth condibetween the directions of the tions’ 3’). Connections branches and the crystallographic directions have also been discussed3*4). The influence of an electric field on dendritic growth has been less studied, mostly on ice5g6). This paper reports studies of dendritic growth of ammonium chloride from water solution on glass and muscovite mica substrates; the growth was studied with and without ac/dc electric fields.
2. Experimental Water solutions of ammonium chloride saturated at 35 “C were poured into a closed glass chamber (1 cm wide, 8 cm long, 0.05-O. 1 cm high) and cooled on a thermostated stage microscope to different temperatures ranging from 19 “C to 26 “C. In order to study epitaxial dendritic growth, a mica substrate was introduced in the growth chamber. 2.1. GROWTH
IN THE ABSENCE OF AN ELECTRIC FIELD
As dendritic growth on amorphous substrates is well known, there will be reported only the results
obtained using mica substrates, in which case an epitaxial dendritic growth is expected. In the absence of an electric field, the growth directions of ammonium chloride dendrites are connected to the mica crystallographic directions. The dendrites are parallel to the directions contained in the substrate surface plane: (OlO), (llO), and (li0); still the direction distribution of the dendrites is not uniform; most of them are parallel to (010) and this eventually agrees with the already reported differences between (010) and (1 lo), (li0) mica directions. The secondary branches are perpendicular to the central stems. A 0.05 cm high chamber brought up an interesting feature of the epitaxial growth. The crystallization in stems and perpendicularly attached branches is stopped when the saturation concentration is reached; then the branches set on changing orientation exhibit the tendency to form parallel to (1 lo), eventually detaching themselves from the central stems. This is clearly indicated by figs. I a and 1b (taken 20 min afterwards) and fig. lc (another 10 min). The phenomenon is accompanied by the thickening of the central stems and branches; it may be interpreted as a recrystallization aimed at a really stable epitaxial structure. Other remarkable cryststallized patterns are reported which were obtained by decanting ammonium chloride
CORNELIA
(b)
(4 Fig.
1.
(a) Dendritic
MOTOC
growth
on muscovite
mica;
solutions on mica surfaces. Fast growth of dendrites is likely to reveal the surface structure or defects on mica surfaces. Dendrites grow with the central stems perpendicular or parallel to the (010) direction; the branches are not always directed perpendicularly to the central stem or parallel to some crystallographic directions on the mica surface. The most frequent angles between the branches and the central stems are 72” or 48”, showing no relation with the hexagonal structure of the mica cleavage plane (fig. 2). A bidimensional lattice with 72” angles is thus formed. We recall that the pentagonal symmetry on mica surfaces has already been reported by Allpress and Sanders7). (Thin metallic films consisting of pentagonal polyhedra as well as triangular, quadrangular and hexagonal have been obtained on mica.) There is a hint that 72” angles characteristic for the pentagonal structure are likely to appear on a mica substrate, the superficial, planes of with are “twisted” by 13’. This assumption accepted, the central stems and branches would independently stick to the two “twisted” planes.
(b) is taken
20 min afterwards;
(c) follows
after
10 min.
As knownin muscovite mica there are distortions and tilts of surface oxygen network from the hexagonal. These distortions are primarily due to misfit between the tetrahedral and octahedrallayers. In muscovite mica a considerable contraction of the tetrahedral layer to fit the octahedral layer has to be taken into account. This fitting together of different sized layers may be accomplished by a rotation of 13” of the basal 0 triads as has been pointed outsB9). The difference between the 13” rotation of basal 0 triads and the 12” rotation assumed in this paper in order to explain the unorthodox angles between the central stem and dendrite branches is rather puzzling; some errors might well account for it. 2.2, GROWTH
IN THE
PRESENCE
OF AN
ELECTRIC
FIELD
Direct and alternating electric fields were applied perpendicular or parallel to the growth chamber; the electrodes were not, of course, immersed in the solction. When dc fields were applied parallel to the growth chamber, the crystallization resulted in needles parallel to the field direction. After field removal, from the very
AN
Fig.
ELECTRIC
2.
Epitaxial
FIELD
growth
INFLUENCE
of dendrites
ON
DENDRITIC
on miscovite
mica;
GROWTH
311
AT = 10 ‘C
bulk of the needle, branches rapidly developed and in a very short time the regular dendritic growth occurred. Remarkably, the branches do not start growing simultaneously all along the needle, but gradually toward the tip. Fig. 3 shows one of the needles grown in a 6600 V/cm field at AT = 11 “C which developed branches after the field was taken off. Such needles were obtained on both mica and glass substrates. With dc fields set perpendicularly to the growth chamber, the crystallization was remarkably inhibited. As an example, under fields higher than 6000 V/cm no
Fig. 3. Needle grown on muscovite electric field; AT = 11 “C.
mica
substrate
in a dc
crystallization was obtained from a supersaturated (AT = 14 “C) ammonium chloride solution during 1 hr. The growth started a few minutes after the field was switched off; a period of induction seemed to be necessary for the nucleatin and growth to start. The dendrites developed rapidly and uniformly in the whole sample (fig. 4) displaying some peculiarities : they detached themselves from the central stem; this effect, obtained on glass substrates, had been also obtained on mica substrates with no electric field. In both cases it followed shortly after the growth was stopped. Fig. 5 shows this effect for ammonium chloride dendrites; the solution was supersaturated at AT = 11 “C and subjected to a 6600 V/cm dc field. Careful examination of these dendrites obtained
312
CORNELIA
Fig.
Fig.
5.
4.
Branches
Dendritic
detaching
growth
after
themselves
field removal
from
central
from solutions previously subjected to high electric fields perpendicular to the growth chamber revealed branches grown in the field direction. Gradually the branches changed orientation reclining into the chamber plane (fig. 6). AC fields (50 Hz) ranging from 200 V/cm to 2 x IO4 V/cm were also used. When lower than 700 V/cm they did not show any influence on the orientated grown
MOTOC
obtained
stems,
on glass substrate;
obtained
AT = 14 ‘C.
on glass substrate;
AT = 11 “C.
dendrites on either mica or glass substrates. Electric fields higher 700 V/cm and perpendicular to the growth chamber thickened the central stems as well as the first dendritic branches. This permits revealing of the main dislocation of the dendrite, as shown in fig. 7 for ammonium chloride crystals grown on a mica substrate. (Similar effect are obtained on glass). Fig. 7, which shows a pattern of hexagonally grown dendrites
AN
ELECTRIC
Fig.
Fig.
7.
6.
Dendrites
FIELD
Dendritic
grown
INFLUENCE
growth
after
ON
field removal
on mica in an ac electric
besides the one directed on (OIO), proves again that the dendritic crystallization ennablas us to indicate crystal defects. When the fields were higher than IO4 V/cm, the dendrites exhibited the tendency to grow in the field direction on both glass and mica substrates. Under alternating fields no needles were formed. On mica substrates
DENDRITIC
(glass
GROWTH
313
substrate).
field (AT = 10 ?C; 1000 V/cm).
alternating fields of more than 2 x IO4 V/cm increased the nucleation rate in ammonium halide solutions; growth nuclei appeared in the whole solution; they were dendritic stars, both regular (triangular, quadrangular and hexagonal) and irregular (pentagonal). Some nuclei appear on the steps of the mica surface; the dendrites thus formed have only little connection
314
CORNELIA
Fig. 8.
Dendrites
MOTOC
grown on mica under an ac electric field (2 x lo4 V/cm; AT = 10 “C).
with the crystallographic directions of the mica substrate. In fig. 8 ammonium chloride dendrites grown on mica in 2 x lo4 V/cm are shown. 3. Discussion As is known, when the temperature gradient in the liquid at the interface is negative, tree-like growth forms are obtained, the central stem and branches extending in a well-defined crystallographic direction. When the temperature gradient is positive the branches are indistinct and the central stem has no uniquely defined crystallographic direction. In our experiments both cases were found: needles or dendrites with thick central stems under electric fields, and dendritic growth forms without electric field. These results are qualitatively similar to the electric field growth of ice crystals from vapour phase reported by Bartlett et al.‘). These two experimentally revealed cases may be qualitatively explained by examining the morphological stability of a dendrite growing in the presence and absence of an electric field. Let us examine the morphological stability of a dendrite; we shall let aside the tip region and for the remaining part of the dendrite we shall proceed the way we should do with a circular cylinder.
As has been shown by Coriell and Parker”‘“), any perturbation of the circular shape of the cylinder can be represented by a linear combination of harmonic perturbations. In the most simple case, the radius of the perturbed cylinder is given by r = R+6
exp (ik@),
where R is the unperturbed radius. It has been shown that the rate of growth perturbation is
SCD s
D(k-
= R2(C-
1) C,)
(C - C,)IX2’ R2
G,--
F
D, F k2(k+1)
of the @
k(k+,)
I
,
where D and D, are the volume and respectively surface diffusion coefficients, G, the concentration gradient at the precipitate-matrix interface, Sz the atomic volume of the precipitate Co the equilibrium concentration in the medium adjacent to the precipitate and CR = Co+ Co T/R (where r is the capillarity constant for the correction of equilibrium composition for interface curvature). i$@/S@ is composed of three terms: the first depends on the concentration gradient and is destabilizing: it favours the growth of the perturbation. The second and the third terms are proportional to the capillarity
AN
constant,
ELECTRIC
i.e. to the surface free energy;
FIELD
INFLUENCE
they favour the
decay of a perturbation. Then, if it is assumed that in the presence of an electric field the surface free energy is enhanced, an accidental perturbation would rapidly decay if the electric field is strong enough to compensate the destabilizing effect of the concentration gradient. Accordingly, when strong electric fields are employed, needles are expected to grow instead of dendrites. When the electric field is removed, the surface free energy would then be lowered and the destabilizing factor would prevail; any perturbation would grow and the needle would begin to develop branches from its bulk. As shown by the fig. 3, branches develop from these periodic accidental perturbations; finally the crystallization is similar to the well-known dendritic growth. There are certainly polarization effects, associated with the tendency of the induced dipoles to orientate in the field direction. Besides, the hydration effects have to be taken into account because the electric field changes the shape of the hydration sphere into an ellipsoidal one. There are really difficulties in deciding to what extent these effects influence the growth in the presence of an electric field. A most remarkable thing is that the dc field retards and prevents the crystallization; this effect may be ascribed to the orientation of dipoles in the field
ON
DENDRITIC
direction,
GROWTH
the formation
of clusters
315 or of the growth
nuclei being thus prevented. The detaching of the dendrite branches which grow from the solution previously subjected to a dc field is likely to be an electrostatic effect, as it has been observed on glass substrates only after an electric field was applied. In alternate fields habit changes are not produced. The effects are explained by assuming that the enhancement of nucleation occurred as a result of changing the orientation of the induced dipoles. As it has been shown in fig. 8, on mica surface the enhancement of nucleation produced regular and irregular dendritic stars. References 1) J. J. Gilman, The Art and Science of Growing Crystals (Wiley, New York, 1963) pp. 123, 182, 297, 334. 2) G. R. Kotler and L. A. Tarshis, J. Crystal Growth 3,4 (1968) 603. 3) M. E. Billig and P. J. Holmes, Acta Cryst. 8 (1955) 353. 4) D. R. Hamilton and R. G. Seidensticker, J. Appl. Phys. 31 (1960) 1165. 5) J. T. Bartlett, A. van der Heuvel and B. J. Mason, Z. Angew. Math. Phys. 14 (1963) 599. 6) P. R. Camp and F. C. Barter, Nature 200 (1963) 350. 7) J. G. Allpress and J. V. Sanders, Surface Sci. 7 (1967) 1. 8) E. w. Radoslovich, Acta Cryst. 13 (1960) 919. 9) J. D. Birke and R. Tettenhorst, Mineral. Mag. 36 (282) (1968) 883. 10) S. R. Coriell and R. L. Parker, J. Appl. Phys. 37 (1966) 1548. 11) S. R. Coriell and R. L. Parker, in: Crysfal Growfh, Ed. H. S. Peiser (Pergamon, Oxford, 1967) p. 703.