4.6 Some Methods of Estimation of Reaction Volume Effect 171
localized automorph with a hard central core and a loose periphery is most likely
to occur if an isotherm has a convex trajectory (Fig. 4.1k). It is to be noted that the
above phenomena can only occur in a relatively small quantity of solution, assum-
ing, of course, that after accessing the eutonic point in a congruent system the
replacement stops and excessive matter of the protocrystal remains preserved in
relics. If the amount of a solution is relatively great, the process is characterized by
a short sector of the isotherm and the system state is close to a stationary one, with
formation of an almost homogeneous structure of the replacement products.
The process becomes more complicated in presence of additional compounds
(Fig. 4.1c). The quantity A′ of a dissolved substance makes it possible to generate
a quantity M′ of an additional phase, which requires a quantity B′ of the dissolving
substance. This mechanism is represented by auxiliary dash–dot lines in A′OB
coordinates. At the same time, M′M
1
part of the extra phase would crystallize,
while the other part OM
1
would remain in the solution. Further dissolution of B
results in crystallization of the additional substance M, which proceeds until the dot
E
2
is attained; quantities of substances undergoing dissolving and salting-out
(B
1
and M
1
M
2
) can be readily estimated using BOM coordinates (see corresponding
auxiliary dash–dot lines). The total balance of the process is as follows: amount
B′ + B
1
of the protocrystal dissolves, and M′M
2
quantity of a new formation crystal-
lizes out. This formal conclusion is only a partial representation of the real process,
which becomes quite complicated due to salting-out followed by dissolution of
substance A according to the sector A′E
1
, as it was mentioned before.
This process, including a number of uncertainties caused by kinetic effects, is
shown in details in Fig. 4.5.
At the first stage (trajectory A
1
E
1
), the quantity of dissolving protocrystal B is
characterized by the sector OB
1
, while the amount of the new formation A is
described by the sector A
1
A
2
.
At the second stage the process proceeds along E
1
M
1
trajectory and its estima-
tion should be performed in A
1
OM coordinates. At this stage the substance A dis-
solves completely accompanied by continuous dissolution of the substance B and
initiating the salting-out of the substance M. The quantity of the substance M
undergoing salting-out ranges from M
5
M
6
to M
1
M
2
and depends upon the ratio
between the rate of replacement of the substance B and that of the substance A.
These sections are plotted on the abscissa as sectors OA
3
and A
4
A
5
, which are equal
to section A
1
A
2
; after that it is possible to draw the lines A
3
M
10
and A
4
M
8
, as well
as the lines M
10
M
2
and M
8
M
6
(E
1
A
5
, A
3
M
10
, and A
4
M
8
are parallel to OM, while
M
10
M
2
and M
8
M
6
are parallel to the abscissa). To reach the position M
1
it is neces-
sary to dissolve the main quantity B
1
B
2
of the substance B (thus precipitating M
1
M
3
amount of M) and an additional quantity, which is described by the interval B
1
B
6
–
B
3
B
4
(thus precipitating M
7
M
8
–M
1
M
4
quantity of M). Dissolution of the additional
part of B compensates the movement of the system toward the dot E
1
that is caused
by the replacement of the substance A.
The additional part of the substance B and a quantity of the substance M corre-
sponding to that part, and the additional ratios of B, M, and A cannot be estimated
precisely, as their reactions are prolonged, and so their volume effect changes in the