Abstract
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PHYSICAL CHEMISTRY
I. V. MELIKHOV, TSYU SYAO-SI, and M. S. MERKULOVA
INTERACTION OF A MICROIMPURITY WITH THE SURFACE OF CRYSTALS
(Presented by Academician V. I. Spitsyn on 22 II 1960)
In the present work we consider the processes that occur during the interaction of an impurity with the surface of a perfect real heteropolar crystal in contact with a solution.
The first stage of the interaction is the transition of the impurity into the Fölmer phase ($^{1,2}$) (layer $A$ ($^3$)) (secondary ionic and molecular adsorption). At the moment of this transition, or after displacement along the crystal surface in layer $A$, an impurity particle may find itself near a vacancy formed in the surface layer of the crystal (layer $S$), and may fill this vacancy (be primarily adsorbed). For definiteness we shall assume that the impurity fills cation vacancies.
It was noted by us earlier ($^3$) that the probability $W$ of the appearance in an adsorption center of layer $A$ of an impurity particle that can pass into the energetically homogeneous layer $S$ is determined by the equality
[
W=b_A\nu_A e^{-U_A/kT}p_{S+}AC_L,
\tag{1}
]
where $b_A$ is a constant; $\nu_A$ is the frequency of vibrations of the impurity particle in an adsorption center of layer $A$; $U_A$ is the activation energy for the transition of the impurity into layer $S$; $p_{S+}$ is the concentration of cation vacancies in layer $S$; $k$ is Boltzmann’s constant; $T$ is the temperature of the system; $A$ is the adsorption constant; $C_L$ is the concentration of impurity in the solution adjacent to the crystal surface. Of the activated impurity particles of layer $A$ located near cation vacancies of layer $S$, only a certain fraction $\varphi_A$ will pass into the surface layer of the crystal, since these vacancies can also be occupied by particles of the macrocomponent. The quantity $\varphi_A$ is equal to the ratio of the probabilities of activation of an impurity particle to the sum of the probabilities of activation of impurity and macrocomponent particles located near one vacancy:
[
\varphi_A=\frac{1}{1+(n-1)e^{-\Delta U/kT}C_{MA}},
\tag{2}
]
where $n$ is the number of adsorption centers from which direct displacement of particles into a vacancy of layer $S$ can occur; $\Delta U=U_{MA}-U_A$; $U_{MA}$ is the activation energy for the transition of the macrocomponent into layer $S$; $C_{MA}$ is the concentration of macrocomponent particles in layer $A$. The rate $V_S$ of transition of impurity particles into layer $S$ is determined by the equality
[
V_S=nb_A\nu_A e^{-U_A/kT}\varphi_A p_{S+}AC_L=M_Ap_{S+}C_L,
\tag{3}
]
where $M_A$ is a quantity independent of the amount of microimpurity in the system. Similarly, one can determine the rate $V_A$ of transition of impurity particles
from layer (S) to layer (A) and, using the condition of surface equilibrium (V_S = V_A), obtain the equality
[
C_S = M \frac{p_{S+}}{p_{A+}} C_L,
\tag{4}
]
where (C_S) is the equilibrium concentration of the microimpurity in layer (S); (M) is a constant for a given composition and temperature of the solution; (p_{A+}) is the concentration of cation vacancies in layer (A).
However, the surface of a perfect crystal containing an impurity cannot always be regarded as homogeneous. Impurity particles deform the structure of layer (S), and therefore the quantities (V_A) and (V_S) of the deformed surface regions may differ substantially from the corresponding characteristics of the undeformed layer (S) ((^{4,5})).
The impurity concentration in the deformed and undeformed parts of layer (S) may be determined by equality (4), and the total concentration (C_0) of the impurity in the surface layer of the crystal will be determined by the equality
[
C_0 =
\frac{M}{p_{A+}}
\left(
p_{S+}
+
\frac{M' m p'{S+}}{M p'}
\, p_{A+} C_0
\right)
C_L,
\tag{5}
]
where a prime is used to denote the previously indicated characteristics of the deformed regions of layer (S); (m) is the number of particles of the macrocomponent constituting the deformed region around each impurity particle. The quantity (m) in equality (5), to a first approximation, is equal to the number of nearest neighbors of the impurity particle in layer (S) ((^{6})) and does not depend on the concentration (C_0). The quantity (p'{S+}) is determined by the deformation and, probably, is also not a function of the amount of impurity in layer (S). The concentrations (p') may depend on (C_0), but only in the case where the conditions}), (p_{A+}), (p'_{A+
[
C_0 \sim p_{S+},
\tag{6}
]
[
A C_L \sim p_{A+} \sim p'_{A+}.
\tag{7}
]
are satisfied.
It is reasonable to suppose that condition (6) is satisfied at microconcentrations of the impurity in the system (the quantity (p_{S+}) is very small ((^{6}))). The concentration (p_{A+} \gg p_{S+}), since the structure of layer (A) is loosened by the adsorbed solvent, and the quantities (p_{A+}) and (p'_{A+}) may be considered independent of (C_0).
The relation between the quantities (p_{S+}) and (C_0) can be established by investigating the processes leading to neutralization of the charge of the crystal surface relative to the Fölmer phase and the solution. The charge of the surface of a pure crystal may change when the impurity passes into layer (S), if the charge of the impurity particles (Z) differs from the charge of the cations of the macrocomponent (Z_1) (an “impurity” charge appears), or if, under the influence of the impurity, the quantity (p_{S+}) and the concentration (p_{S-}) of anion vacancies in layer (S) change. The “impurity” charge and the charge of vacancies may be neutralized mutually or by adsorption of counterions from the solution. The condition of electroneutrality of the phase-boundary surface will have the form
[
p_{S+} + m p'{S+} C_0
=
(1-\alpha)\frac{Z-Z_1}{Z_1} C_0
+
\beta m p' C_0
+
a_0
+
p_{S-},
\tag{8}
]
where (\alpha) and (\beta) are the probabilities of neutralization by adsorption of the “impurity” charge and of the charge of vacancies formed in the deformed part of layer (S), respectively; (a_0 = p_{S_0+} - p_{S_0-}); (p_{S_0\pm}) is the concentration of cation ((+)) and anion ((-)) vacancies in layer (S) of a pure crystal.
From equalities (5), (8), assuming, following Koch and Wagner ((^{7})), that cation and anion vacancies interact according to the law of mass action,
[
K_S = (p_{S+} + m p'{S+} C_0)p,
\tag{9}
]
we obtain the relation
[
C_0 =
\frac{
M\left[
a_0+
\sqrt{
a_0^2+
4K_S
\frac{
1+\dfrac{M}{p_{A+}}\left[mp'{S+}(\Gamma-\beta)-R\right]C_L
}{
1+\dfrac{M}{p\,C_L mp'}{S+}\Gamma
}
}
\right]
}{
2p\left{
1+\dfrac{M}{p_{A+}}\left[mp'_{S+}(\Gamma-\beta)-R\right]C_L
\right}
},
\tag{10}
]
where (K_S) is a constant; (R=\dfrac{Z-Z_1}{Z_1}(1-\alpha)); (\Gamma=1-\dfrac{M'p_{A+}}{Mp'_{A+}}).
Let us consider particular cases in which relation (10) is simplified.
- The deformation of the layer (S) by the impurity is insignificant. In this case, at small amounts of impurity in the system the quantity (\dfrac{M'}{M}mp'_{S+}\Gamma C_L \ll 1), and relation (10) takes the form
[
C_0=
\frac{M'\left(a_0+\sqrt{a_0^2+4K_S}\right)C_L}{2p_{A+}}
=
\frac{Mp'{S0+}}{p\,C_L .}
\tag{11}
]
- The deformation of the layer (S) by the impurity is significant; the “impurity” charge is absent ((Z=Z_1)) or is completely neutralized by adsorption ((\alpha=1)); the charge of the cation vacancies arising near the impurity particles practically cannot be neutralized by adsorption ((\beta\to0)). In this case the concentration (C_0) is equal to
[
C_0=
\frac{Mp'{S0+}C_L}{
p\Gamma C_L\right]}\left[1+\dfrac{M}{p_{A+}}\,mp'_{S+
}.
\tag{12}
]
Fig. 1. Dependence of the amount of (\mathrm{InCl_3}) that has passed into the solid phase on the amount of macrocomponent (y) forming the precipitate. (a)—coprecipitation occurs at (C_{\mathrm{H}}=3.5\cdot10^{-7}) g/ml; (b)—at (C_{\mathrm{H}}=2\cdot10^{-6}) g/ml; (v)—at (C_{\mathrm{H}}=2\cdot10^{-5}) g/ml; (g)—at (C_{\mathrm{H}}=3.5\cdot10^{-7}) g/ml and Al is present in the solution at a concentration of (1\cdot10^{-4}) g/ml.
- The deformation of the layer (S) is significant; the “impurity” charge is completely neutralized by adsorption and by vacancies located near impurity particles in the deformed regions of the layer (S) ((mp'_{S+}\Gamma=R)). Then, at (\beta\simeq0),
[
C_0=
\frac{MC_L}{2p_{A+}}
\left[
a_0+
\sqrt{
a_0^2+
\frac{4K_S}{
1+\dfrac{M}{p_{A+}}mp'_{S+}C_L
}
}
\right].
\tag{13}
]
At (a_0=0), equality (13) is analogous to the formula obtained by Kelting and Wittom ({}^{(8)}) for the equilibrium concentration of an impurity in the bulk of the solid phase.
For an experimental verification of the theoretical ideas, we investigated the coprecipitation of microquantities of (\mathrm{InCl_3}) with NaCl crystals growing from stirred, weakly supersaturated solutions at (20^\circ). The method of investigation was described earlier ({}^{(9)}). The experimental results showed that (\mathrm{InCl_3}) passes into the solid phase in appreciable amounts (up to 0.2%), and the concentration of the microimpurity in NaCl crystals does not depend on the mass of the macrocomponent forming the precipitate or on considerable amounts of foreign polyvalent ions (Fig. 1), but changes somewhat when the pH of the medium is varied. In most experiments the acidity was maintained at (0.45\,N), since in an acid medium the adsorption of indium by the walls of the flask, which is very considerable in a neutral medium, is prevented. Microscopic examination of the precipitate showed that the growing NaCl crystals occlu-
occlude a certain amount of mother liquor, although a very small one. A study of the change in the weight of the precipitate after its ignition and melting showed that the occluded mother liquor amounts to less than 0.24% of the weight of the precipitate and can entrain less than 0.002% of indium. Evidently, InCl$_3$ is coprecipitated not by internal or secondary surface adsorption, but, apparently, forms solid solutions in NaCl crystals.
Fig. 2. Dependence of the concentration of InCl$3$ in NaCl crystals ($x/y$) on the concentration of the impurity in the initial solution ($C$ in g/ml)}
The study of the dependence of the impurity concentration in the solid phase on the initial concentration of the impurity in solution $C_{\mathrm{н}}$ (Fig. 2) showed that coprecipitation is described by the relation
[
\frac{x}{y}=\frac{A C_{\mathrm{н}}}{(1+B C_{\mathrm{н}})^{1/e}},
\tag{14}
]
where $x$ and $y$ are, respectively, the amounts of impurity and macrocomponent that have passed into the precipitate; $A$ and $B$ are constants: $A=0.01$; $B=400$.
From the theoretical analysis of the diffusion of the macrocomponent and of the impurity to the surface of the growing crystal it follows that, at $x=0.2\%$, the concentration $C_{\mathrm{н}}\simeq C_L$, and the impurity concentration in each layer $S$ deposited on the surface of a slowly growing crystal is the same and equal to $x/y=C_0$; therefore equality (14) is analogous to formula (13) for $a_0=0$.
Thus, the experimental data on the coprecipitation of InCl$_3$, as well as the previously published data on the coprecipitation of PbCl$_2$ and CdCl$_2$ ($^9$) with NaCl crystals, correspond to the theoretical concepts set forth above.
According to the theoretical concepts, the interaction of In with the surface of NaCl crystals can be represented as follows. Indium ions, which form complexes InCl$4'$ ($^{10}$) in a supersaturated NaCl solution, do not lose all of their addends on passing into layer $S$. One of them occupies the adsorption center of layer $A$ nearest to the impurity particle and neutralizes one of the “impurity” charges of each In ion. The second “impurity” charge is neutralized by a cation vacancy formed in the deformation zone around each impurity particle; consequently, the quantity $m p'$ are reasonable and correspond to the difference in the properties of the cations of the impurity and of the macrocomponent.}\Gamma=1$. Since, probably, $\Gamma\sim 1$ ($^{4,5}$), $m=4$ for NaCl crystals, $p_{S+}=6.5\cdot 10 e^{-\overline{W}'/kT}=0.25$, where $\overline{W}'$ is the work of formation of a vacancy in the deformed part of layer $S$ ($^6$), then $\overline{W}'\simeq 0.14$ eV. According to formulas (12) and (14), $p_{S0}^{+}=A/B=2.5\cdot 10^{-5}$. Using the value of $p_{S0}^{+}$ and the results of experimental studies ($^9$), we calculated the values of $\overline{W}'$ for the NaCl—PbCl$_2$ system: $\overline{W}'=0.20$ eV, and for the NaCl—CdCl$_2$ system: $\overline{W}'=0.29$ eV. The obtained values of $\overline{W
Moscow State University
named after M. V. Lomonosov
Received
20 II 1960
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