Activation Mechanism of the Cyclic Switchover Effect …
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is no polarization. These points belong to the polarization inversion boundary (PIB)
[5, 6]. On both sides of the PIB at the “conduction channel surface–electrolyte” interface, oppositely directed electrochemical processes take place: the anode processes
occur on the surface adjacent to the positive pole of the electric current source,
while the cathode processes are observed on the opposite side. The electrolyte loops
the ionic conduction channel. In this channel, the charge is transferred by both the
autochthonous ions of the electrolyte and the ions coming to the solution from the
crystalline lattice of the metal as a result of the exchange processes occurring at
the interface. In an electric field, the area of the most intense passage of ions into
the solution is the positively polarized surface which, by definition, is in the zone
affected by the anode processes. Therefore, the chemical reduction processes occur
on the negatively polarized surface [6]. The positively polarized section experiences
a growing with time narrowing of the conduction channel which almost completely
determines the point-contact resistance. It is obvious that the interruption of the direct
conduction must occur in the area of the maximum density of the anode current. This
area is in the zone of contact between the dendrite tip and the bulk counterelectrode
(“anvil”) characterized by the maximum anode polarization E max = U/ 2.
The explicit equation (1) implies a relation between the parameters of the process
of electrochemical dissolution and the material of the system. Parameters j 0 and
α are sensitive to material nature. In our experiments, we studied dendritic copper
point contacts during the cyclic switchover effect; therefore, we are going to use
the physicochemical characteristics of copper in our subsequent calculations. Equation (3) allows calculation of temporal dependence of the maximum density of the
anode current. Since the phenomenon under study is based on the Faraday processes,
this dependence can be used to find a correlation between the duration of the anode
reaction and the linear dimensions of the channel. Indeed, if we assume a 100%
current yield, the following expression holds true [11]
t =
k e j el
,
(4)
where δ is the thickness of the layer that gets dissolved; k e is the electrochemical
equivalent; j el is the current density; t is the duration of the process; γ is the density
of the material.
According to (4), determination of the thickness of the layer dissolved in the anode
process over a time τ with a monotonously changing current density (δ calc ) can be
reduced to calculating the following integral:
δ calc =
k e
γ
τ
0
j el dt.
(5)
As a result of the step dependence of the point-contact resistance on time of its
exposure to an electric field in the final phase of dissolution (Fig. 1), it is natural to
assume that the time τ at , i.e., the time of dissolution of a point contact to a size of
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is no polarization. These points belong to the polarization inversion boundary (PIB)
[5, 6]. On both sides of the PIB at the “conduction channel surface–electrolyte” interface, oppositely directed electrochemical processes take place: the anode processes
occur on the surface adjacent to the positive pole of the electric current source,
while the cathode processes are observed on the opposite side. The electrolyte loops
the ionic conduction channel. In this channel, the charge is transferred by both the
autochthonous ions of the electrolyte and the ions coming to the solution from the
crystalline lattice of the metal as a result of the exchange processes occurring at
the interface. In an electric field, the area of the most intense passage of ions into
the solution is the positively polarized surface which, by definition, is in the zone
affected by the anode processes. Therefore, the chemical reduction processes occur
on the negatively polarized surface [6]. The positively polarized section experiences
a growing with time narrowing of the conduction channel which almost completely
determines the point-contact resistance. It is obvious that the interruption of the direct
conduction must occur in the area of the maximum density of the anode current. This
area is in the zone of contact between the dendrite tip and the bulk counterelectrode
(“anvil”) characterized by the maximum anode polarization E max = U/ 2.
The explicit equation (1) implies a relation between the parameters of the process
of electrochemical dissolution and the material of the system. Parameters j 0 and
α are sensitive to material nature. In our experiments, we studied dendritic copper
point contacts during the cyclic switchover effect; therefore, we are going to use
the physicochemical characteristics of copper in our subsequent calculations. Equation (3) allows calculation of temporal dependence of the maximum density of the
anode current. Since the phenomenon under study is based on the Faraday processes,
this dependence can be used to find a correlation between the duration of the anode
reaction and the linear dimensions of the channel. Indeed, if we assume a 100%
current yield, the following expression holds true [11]
t =
k e j el
,
(4)
where δ is the thickness of the layer that gets dissolved; k e is the electrochemical
equivalent; j el is the current density; t is the duration of the process; γ is the density
of the material.
According to (4), determination of the thickness of the layer dissolved in the anode
process over a time τ with a monotonously changing current density (δ calc ) can be
reduced to calculating the following integral:
δ calc =
k e
γ
τ
0
j el dt.
(5)
As a result of the step dependence of the point-contact resistance on time of its
exposure to an electric field in the final phase of dissolution (Fig. 1), it is natural to
assume that the time τ at , i.e., the time of dissolution of a point contact to a size of