The Physical–Chemical Model of Nanoscaled Metal Component Formation …
271
N (t) = J
t
0
exp
−α J u
2
P τ
3
dτ.
(17)
The mean square of nucleus S o (t) is equal to N
−1
(t) or
S o (t) = J
−1
⎧
⎨
⎩
t
0
exp
−α J u
2
P τ
3
dτ
⎫
⎬
⎭
−1
.
(18)
It is necessary to determine the mean square of nuclei at the final stages X (t) ∝ 1.
In this case (17) and (18) could be reduced to
N = J
2
3
0.893
α u
2
P
1
3
; S o = J
−
2
3
α u
2
P
1
3
0.893
.
(19)
Using the expression (19) for the mean square of nuclei, the mean linear size of
crystallite r XY in the plane of graphite surface may be expressed as
r XY ≈
S o ≈
u P
J
1
3 .
(20)
By substitution of (12) and (14) to (20) one can obtain
r XY ≈
V C g Salt-Oxide
sin θ
1
3 ·
1 − exp
−
G Salt-Oxide
RT
1
3
× exp
16π
9kT
σ
3
ψ(θ )
( g Salt-Oxide ) 2
9kT
16 σ 3 ψ(θ )
1
6
.
(21)
It should be emphasized that (21) corresponds to the point of time, when metal
salt totally transformed into metal oxide at graphite surface.
Let us define the parameters of (21) influencing on the mean size of metal oxide
crystallite, which is formed at graphite surface.
The limiting wetting angle θ characterizes the state of graphite supporter surface.
The limiting wetting angle is determined, firstly, by the type of graphite material and,
secondly, by the type of oxidant that activates the graphite supporter surface before
its impregnation by the metal salt. Parameters g Salt-Oxide ; G Salt-Oxide and their
temperature dependences, coefficient of the interphase tension σ is the parameters
that are determined by the type of salt being used. Temperature T is the external
parameter of the thermolysis.
To analyze the type of salt influence on the oxide phase properties, it is necessary
to use not only (21) characterizing the final state of the oxide phase but also (12) and
(14), which define the kinetics of phase formation.
271
N (t) = J
t
0
exp
−α J u
2
P τ
3
dτ.
(17)
The mean square of nucleus S o (t) is equal to N
−1
(t) or
S o (t) = J
−1
⎧
⎨
⎩
t
0
exp
−α J u
2
P τ
3
dτ
⎫
⎬
⎭
−1
.
(18)
It is necessary to determine the mean square of nuclei at the final stages X (t) ∝ 1.
In this case (17) and (18) could be reduced to
N = J
2
3
0.893
α u
2
P
1
3
; S o = J
−
2
3
α u
2
P
1
3
0.893
.
(19)
Using the expression (19) for the mean square of nuclei, the mean linear size of
crystallite r XY in the plane of graphite surface may be expressed as
r XY ≈
S o ≈
u P
J
1
3 .
(20)
By substitution of (12) and (14) to (20) one can obtain
r XY ≈
V C g Salt-Oxide
sin θ
1
3 ·
1 − exp
−
G Salt-Oxide
RT
1
3
× exp
16π
9kT
σ
3
ψ(θ )
( g Salt-Oxide ) 2
9kT
16 σ 3 ψ(θ )
1
6
.
(21)
It should be emphasized that (21) corresponds to the point of time, when metal
salt totally transformed into metal oxide at graphite surface.
Let us define the parameters of (21) influencing on the mean size of metal oxide
crystallite, which is formed at graphite surface.
The limiting wetting angle θ characterizes the state of graphite supporter surface.
The limiting wetting angle is determined, firstly, by the type of graphite material and,
secondly, by the type of oxidant that activates the graphite supporter surface before
its impregnation by the metal salt. Parameters g Salt-Oxide ; G Salt-Oxide and their
temperature dependences, coefficient of the interphase tension σ is the parameters
that are determined by the type of salt being used. Temperature T is the external
parameter of the thermolysis.
To analyze the type of salt influence on the oxide phase properties, it is necessary
to use not only (21) characterizing the final state of the oxide phase but also (12) and
(14), which define the kinetics of phase formation.