1. The mechanism of electro-crystallization

2. The crystallization under electrochemical conditions
The growth process of incomplete plane 未完成晶面的生长过程 The growth process of crystal nucleus on flat plane 已完成晶面上晶核的生长过程 The growth process of actual lattice plane 实际晶面的生长过程

3. The growth process of incomplete plane
The possible way：
I. Both electrochemical step and electro-crystallization are take place on the growing point.
II. The electrochemical step are take place on any position of the lattice plane, the metal ions form adsorpted atoms, the adsorpted atoms diffuse to the growth lines and points.
III. The absorped metal atoms form two or three dimensional atomic clusters.
Metal cation
Metal atom

4. The growth process of incomplete plane
The electrochemical step can take place in all the surface of the liquid electrode ,if the reaction only take place in the growing point ,there will be a big difference on the value of exchange current
on the whole solid electrode surface, it can take place electrochemical reaction i0
CHg2+ x10^3/(mol/L)
The exchange current on solid and liquid mercury electrode in 45% HClO4 solution
45% HCIO4 中固态液态汞电极上交换电流密度

5. The growth process of incomplete plane
If the rate of crystallization < electrochemical step，it is difficult to diffuse to the growing point. In this situation, the value of CMad >C0Mad .
The electronic exchange equilibrium is not damaged, Then the crystallization overpotential
If the rate of crystallization is fast, then the crystallization step can not cause the overpotential.

6. The growth process of incomplete plane
Through measuring the steady-state polarization curves on solid and liquid electrode of the same metal, we can determine whether the crystallization is the slow step.
on the liquid electrode, there is no crystallization.
ŋc/mV
solid electrode 10
liquid electrode 25 30
i/(uA/cm2)
Steady-state polarization curves measured on solid and liquid gallium electrode

7. The growth process of incomplete plane
Transient method: constant current polarization
1- the actual curve; 2-the calculated value caused by electrochemical polarization
ŋc/m 1
i0=4.5A/cm2
when i=300uA/cm2 ,the concentration polarization can ignore ,theoverpotential :
ŋ=RTI/Fi0 =1.6X 10-6
The actual is much large. 3 2 1 2
t/ms
The ŋ-t curve of the constant current polarization (Ag electrode; solution: HClO4)

8. Crystal nucleus formation and growth
On the flat plane, there is no growing point. if the crystals continue to grow, it needs crystal necleus. With radius r of the domed crystal nucleus (from circular foundation baseto a domed crystal necleus) as a case analysis to generate new critical condition of crystal nucleus and the nucleation rate. Increased surface free energy: ∆Gs = πr2σ Hemisphere crystal free energy change: ∆G本体 = πr3∆Gv ∆Gv = -nFŋ/V

9. Crystal nucleus formation and growth
∆G = ∆Gs + ∆G本体
=πr2σ πr3nFŋ/V
when r < rcritical, the free energy increase, it is unstable for the crystallization.
r临界= σv/nFŋ
∆G 临界=πσ3V2/(3n2F2ŋ2)
V成核= kexp(-∆G)
∝exp(-A/ŋ2 ) G
∆Gs
G临界 r
r 临界 ∆G
∆G本体

10. The growth process of actual lattice plane
The actual crystals contain a large number of dislocations(位错).
If the crystal growth around the dislocation line, the growth lines will not dispear.