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The influence of some metal ions on the kinetics of dissolution of barium fluoride
Journal of Crystal Growth 102 (1990) 303—308 North-Holland
303
THE INFLUENCE OF SOME METAL IONS ON THE KINETICS OF DISSOLUTION OF BARIUM FLUORIDE S.M. HAMZA Chemistry Department, Faculty of Science, El-Menofia University, Shebin El-Kom, Egypt Received 5 September 1989; manuscript received in final form 16 November 1989
The influence of magnesium, calcium and strontium cations on the kinetics of dissolution of barium fluoride crystals has been studied in aqueous solutions using a constant-composition method at 25°C. The addition of metal ions even at relatively low 3) markedly retard the rates of dissolution. Moreover, the effect was enhanced as the relatives concentration (5 x 10—6 mol dm undersaturation decreased. The retardation effect of these additives has been attributed to the blocking of active sites by adsorption of metal ions at the crystal surfaces. Inhibition of dissolution by metal ions can be interpreted in terms of a Langmuir isotherm.
1. Introduction
using both Ultrapure (Alfa Chemical) and reagent grade (J.T. Baker) chemicals. Metal ion concentra-
Nature continuously conducts large scale precipitation and dissolution experiments in the atmosphere, in the soil and in natural waters [1]. Dissolution reactions are also very important in
tions were determined by atomic absorption spec-
technical and physiological systems. The dissolution of fluoride salts of the alkaline earths is of importance in view of their applications in many fields. Impurities play an important part in the theory of crystallization and dissolution in supersaturated or undersatuçated solutions. The factors that govern the mechanism of precipitation and
troscopy. Seed crystals of the barium fluoride were prepared by precipitation from a mixed solution of potassium fluoride and barium nitrate at 250 C. The seeds were washed with saturated solutions of the barium fluoride and allowed to age for at least one month at 250 C, until the specific surface area (SSA) reached a constant value 0.7 m2 g Dissolution experiments were made at 25 ± 0.10 C in a double-walled reaction cell 300 ml
dissolution of these fluoride salts are therefore of considerable interest, especially the influence of
capacity fitted with a Teflon lid. Nitrogen gas was first bubbled into a solution of the electrolyte at
foreign cations which may exert a marked effect on the rates of crystallization and dissolution either through adsorption at the surface of the crystals or by lattice substitution, In the present work, the constant-composition method [2] has been used to investigate the influence of magnesium, calcium and strontium ions on the dissolution of barium fluoride crystals over a range of undersaturation.
the temperature of the reaction for saturation with water vapour, and then into the reaction vessel throughout the experimental duration. At the beginning of each experiment the fluoride electrode was standardized by adding aliquots of potassium fluoride solution in the cell. Subsequently, undersaturated solutions of desired concentrations were prepared by slow addition of barium nitrate to potassium fluoride solutions. The ionic strength was maintained constant during the dissolution experiments by the addition of potassium nitrate (Ultrapure) solution. Aliquots of reaction mixture were withdrawn at regular time intervals and filtered through a 0.22 ~tm millipore. The filtrate was analysed for metals by atomic absorption
2. Experimental
Undersaturated solutions of barium fluoride were prepared in triply distilled, deionized water, 0022-0248/90/$03.50 © 1990
—
Elsevier Science Publishers B.V. (North-Holland)
S. M. Ham.a
304
/ Influence of metal tons on kinetics
ofdissolution ofbarium fluoride
spectroscopy (Perkin—Elmer model 503) in order to verify the constancy of the concentrations (±1.0%). The solid phases collected during the experiment were investigated by X-ray diffraction and by scanning electron microscopy.
using convential dissolution experiments in which the undersaturation is allowed to decrease. The crystallization and dissolution of divalent metal ion salts in general [11—141 are greatly inhibited by additives. In the present work, the rate of dissolution of barium fluoride was studied in the presence of magnesium calcium and strontium
3. Results and discussion
ions. The influence of added metal ions on the dissolution reactions are illustrated in fig. 1. From the rate profiles shown in fig. 1, the dissolution rates of barium fluoride in presence of metal ions
The concentrations of free-ion species in the solutions were calculated from mass-balance and electroneutrality expressions as described previously [3], using the thermodynamic equilibrium constants, K, for the various associated species [4—7]. Activity coefficients were calculated from the extended form of the Debye—Huckel equation proposed by Davies [81. The degree of relative undersaturation, o, for barium fluoride solutions may be defined by:
4.
([Ba2+
1/3
10[F
]~)
2~ J[F ~ 1/2 ([Ba
12) i/3 ,
(1)
([Ba2+]o[F]~) where [Ba2~], [F1
and [Ba2~1
0, [F-]0 are the concentrations of free barium and fluoride ions at i and at equilibrium, respectively, at the ionic strength of the experiments. The conditional solu2~1 bility product, K~ ([Ba at the 0[F~I~), was (1.27 ± 3 =dm3 saturation ionic 0.05) x 10 mol strength (0.378 mol dm3) [9]. The rate of dissolution, R, can be expressed in terms of the relative undersaturation by: Rate
=
dm/di
=
Ksa”.
—.
-~r
°
2 0
2.
(2)
in which m is the number of moles dissolved at time t, k a rate constant, s a function of the initial seed surface area and n is the apparent order of the reaction. Previous kinetic studies of the dissolution of barium fluoride indicate that at higher driving forces (relative undersaturation 0.15—0.20), the rate seems to he controlled by volume diffusion. whereas at low undersaturation (0.04—0.12), a surface controlled reaction predominates [101. The microscopic reversibility near equilibrium is especially interesting [11] since it is not possible to obtain reliable rate data under these conditions
1 2.
Mg2~
20
40
[ M2~]I1O-6 mol Fig 1.
60 dm3
Plots of rates of dissolution against [M2~
]
in the
presence of magnesium, calcium, and strontium, at undersaturation (a
=
0.1).
S.M. Hamza
/
Influence ofmetal ions sin kinetics of dissolution ofbarium fluoride
305
Table 1 Effect of additives on the rates of dissolution of barium fluoride crystals ~)
Expt.
T
102 a
Additive (106 moldm3)
No. 19 30
(10~ moldm 13.665 13.665
10 10
—
—
Mg
5
7.280 2.598
31
13.665
10
Mg
10
0.891
32 33
13.665 13.665
10 10
Mg Mg
20 30
0.691 0.600
34
13.665
10
Mg
40
0.470
35 36 37 38 39 40 41 42 43 44 45 46 47
13.665 13.665 13.665 13.665 13.665 13.665 13.665 13.968 13.968 13.968 13.968 13.968 13.968
10 10 10 10 10 10 10 8 8 8 8 8 8
Mg Ca Ca Ca Ca Ca Ca
50 5 10 20 30 40 50
Ca Ca Ca Ca Ca
5 10 20 30 40
0.425 3.029 1.680 1.090 0.690 0.540 0.503 4.780 1.614 1.072 0.594 0.415 0.309
48
13.968
8
Ca
50
0.262
49 50
14.272 14.272
6 6
—
—
Ca
5
2.140 0.471
51
14.272
6
52 53 54 55 56 57 58 59 60 61
14.272 14.272 14.272 14.272 13.665 13.665 13.665 13.665 13.665 13.665
6 6 6 6 10 10 10 10 10 10
Ca Ca
10 20
0.287 0.177
Ca Ca Ca Sr Sr
30 40 50 5 10
0.125 0.108 0.092 5.063 3.875
Sr
20
2.790
Sr Sr Sr
30 40 50
1.991 1.882 1.733
~° ~
11a
TF
=
3)
1:2, [KNO
—
Rate molmin~ m2) (10~
—
3, 50 mg seed. stirring speed 200 rpm. 1J
=
0.378 mol dm
(magnesium, calcium and strontium) decrease with successive additions of metal ions. It can be seen that the effectiveness of the inhibition is Mg> Ca > Sr. Experiments in the presence of metal ions, summarized in table 1, show that concentrations as low as 5 x iO~ mol dm3 for each additive
anionic sites and inhibit the dissolution when present at very low levels. The adsorption can be interpreted in terms of a Langmuir-type isotherm [12] leading to an equation of the form: R 0/(R0
(expts. 35, 41 and 61) reduced the dissolution rates by as much as 94.2%, 93.1% and 76.2% in the presence of magnesium, calcium and strontium, respectively. In general, inhibitors exert their influence through adsorption at active dissolution sites on the crystal surfaces. Cations may be adsorbed at
—
R)
=
(KLC)~.
(3)
in which R1 and R0 are the rates of dissolution in the presence and absence of inhibitor respectively, KL is the adsorption affinity and C is the additive concentration. Typical adsorption plots according to eq. (3) in fig. 2 confirm the applicability of this simple adsorption isotherm for all metal ions
S. M. Hamza
306
/
Influence of metal ion.s on kinetics ofdissolution ofbarium fluoride
~
2]
[M
1
~
Fig. 2. Langmuir adsorption isotherms. Plots of R
2~ 5/(R5
—
dm3 moH I in the presence of magnesium,
calcium and strontium.
R~)against [M
studied. The values of the adsorption affinity constants. K~ are 4.42 x 10~dm3 molt for magnesium, 4.25 x 1O’~dm3 mol for calcium and 3.08 x io~dm3 molt for strontium at the same relative undersaturation, a = 0.1. These values reflect the high adsorption affinity which is in the following order: Mg> Ca> Sr. The effect of the inhibitor may be described as the prevention or strong retardation of the nucleation of etch pits in areas around the adsorbed inhibitor molecules. Due to interaction with the inhibitor, lattice ions in these areas will be strongly attached to the crystal surface. If sufficient inhibitor molecules are adsorbed onto the surface, the whole crystal may be inactivated and no dissolution will occur. Prevention or retardation of dissolution may occur by preferential adsorption of the inhibitor molecules at the edges of the subcritical etch pits forming on the surface thus pre-
venting their development beyond the critical size [13]. On the assumption that the degree of inhibition may be affected by the degree of relative undersaturation, the dissolution of barium fluoride in the presence of calcium ions has been investigated at different undersaturations (0.1—0.06). In terms of the simple Langmuir equation, the values of the adsorption affinity constants are 4.25 x 1O~,4.41 x 10” and 4.63 x iO~dm3 mol at relative undersaturation, a = 0.1, 0.08 and 0.06, respectively (fig. 3). Plots of these values against a in fig. 4 show the striking increase in the kinetically derived adsorption affinity near equilibrium. A similar dependence of the degree of inhibition with change in the driving force has been observed for the influence of phosphonate and metal ions on the rate of dissolution and crystallization of divalent metal fluorides in aqueous solutions [11,14—
S. M. Hamza
/ Influence ofmetal ions
307
on kinetics of dissolution of barium fluoride
2
0
0
cci
5
10
1ca2]~ ~
Fig. 3. Langmuir adsorption isotherms. Plots of R
0/(R0
—
15 dm3
20
moH
2~ ]1 for different undersaturations, a
=
0.06. 0.08, 0.1.
R) against [Ca
16]. As noted for the crystallization of gypsum by
6
Weijnen, Marchée and Van Rosmalen [17], the effectiveness of the phosphonate as an inhibitor is dependent on the degree of supersaturation. The marked dependence upon a of the effectiveness of growth and dissolution inhibitors has important
.4
4 .
consequences in assessing the usefulness of inhibitors for industrial applications.
2
References
.
[1] W. Stumm and J.J. Morgan. Aquatic Chemistry (Wiley— lnterscience, New York, 1981). [2[ P.G. Koutsoukos, Z. Amjad, M.B. Tomson and G.H. Nancollas, J. Am. Chem. Soc. 102 (1980) 1553. [3] G.H. Nancollas. Interactions in Electrolyte Solutions
I
-0.1
-0.08
-0.06
-0.04
-0.02
0
(Elsevier, Amsterdam, 1966). [4] A.J. Ellis, J. Chem. Soc. (1963) 4300.
Fig. 4. Plots of adsorption affinities, KL against undersaturation ~.
[51G.L. 342.
Gardner and G.H. Nancollas. Dental Res. 55 (1976)
S. M. lIam:a
308 [6] Dl.
Stock and (/W.
/
Influence of metal ion.s on kinetics of dissolution of barium fluoride
Davies, Trans Faraday Soc. 44
[12] P. Koutsoukos, Z. Amjad and Gil. Nancollas, J. (‘olloid
(1948) 856. RE. Connick and M.S. Tsao. J. Am. (‘hem. Soc. 76 (1954) 5311. (‘.W. Davies. Ion Association (Butterworths. London. 1960). J.P. Barone, D. Svrjeck and Gil. Nancollas. J. Crystal Growth 62 (1983) 27. S.M. Hamza, 8th Chinese Conf. on Crystal Growth
Interface Sc). 83 (1981) 599. [13] G.M. van Rosmalen. M.P.C. Weijncn and J.A.M. Meiser. 36th Intern. Conf. CEBEDEAU. Liege. 1983. [14] S.M. Hamza and G.H. Nancollas, J. Chem. Soc.. Farada~ Trans. 1, 81(1985)1833. [15) SM. l-Iamza and GE!. Nancollas. Langmuir 1(1985) 573. [161 A. Ahul-Rahman, S.M. l-Iamza and Gil. Nancollas, in: Proc. 7th AIChE Annual Meeting, (‘hicago. IL. 1987. pp.
(CCCG-8), Guilin, China. 1988. [II] SM. Hamza. A. Ahdul-Rahman and Gil. Nancollas. J. Crystal Growth 73 (1985) 245.
36—41. [17] M.P.C. Weijncn. W.G.J. Marchée and G.M. van Rosmalen. Desalination 47 (1983) 81.
[7] [8] [9] [10]
303
THE INFLUENCE OF SOME METAL IONS ON THE KINETICS OF DISSOLUTION OF BARIUM FLUORIDE S.M. HAMZA Chemistry Department, Faculty of Science, El-Menofia University, Shebin El-Kom, Egypt Received 5 September 1989; manuscript received in final form 16 November 1989
The influence of magnesium, calcium and strontium cations on the kinetics of dissolution of barium fluoride crystals has been studied in aqueous solutions using a constant-composition method at 25°C. The addition of metal ions even at relatively low 3) markedly retard the rates of dissolution. Moreover, the effect was enhanced as the relatives concentration (5 x 10—6 mol dm undersaturation decreased. The retardation effect of these additives has been attributed to the blocking of active sites by adsorption of metal ions at the crystal surfaces. Inhibition of dissolution by metal ions can be interpreted in terms of a Langmuir isotherm.
1. Introduction
using both Ultrapure (Alfa Chemical) and reagent grade (J.T. Baker) chemicals. Metal ion concentra-
Nature continuously conducts large scale precipitation and dissolution experiments in the atmosphere, in the soil and in natural waters [1]. Dissolution reactions are also very important in
tions were determined by atomic absorption spec-
technical and physiological systems. The dissolution of fluoride salts of the alkaline earths is of importance in view of their applications in many fields. Impurities play an important part in the theory of crystallization and dissolution in supersaturated or undersatuçated solutions. The factors that govern the mechanism of precipitation and
troscopy. Seed crystals of the barium fluoride were prepared by precipitation from a mixed solution of potassium fluoride and barium nitrate at 250 C. The seeds were washed with saturated solutions of the barium fluoride and allowed to age for at least one month at 250 C, until the specific surface area (SSA) reached a constant value 0.7 m2 g Dissolution experiments were made at 25 ± 0.10 C in a double-walled reaction cell 300 ml
dissolution of these fluoride salts are therefore of considerable interest, especially the influence of
capacity fitted with a Teflon lid. Nitrogen gas was first bubbled into a solution of the electrolyte at
foreign cations which may exert a marked effect on the rates of crystallization and dissolution either through adsorption at the surface of the crystals or by lattice substitution, In the present work, the constant-composition method [2] has been used to investigate the influence of magnesium, calcium and strontium ions on the dissolution of barium fluoride crystals over a range of undersaturation.
the temperature of the reaction for saturation with water vapour, and then into the reaction vessel throughout the experimental duration. At the beginning of each experiment the fluoride electrode was standardized by adding aliquots of potassium fluoride solution in the cell. Subsequently, undersaturated solutions of desired concentrations were prepared by slow addition of barium nitrate to potassium fluoride solutions. The ionic strength was maintained constant during the dissolution experiments by the addition of potassium nitrate (Ultrapure) solution. Aliquots of reaction mixture were withdrawn at regular time intervals and filtered through a 0.22 ~tm millipore. The filtrate was analysed for metals by atomic absorption
2. Experimental
Undersaturated solutions of barium fluoride were prepared in triply distilled, deionized water, 0022-0248/90/$03.50 © 1990
—
Elsevier Science Publishers B.V. (North-Holland)
S. M. Ham.a
304
/ Influence of metal tons on kinetics
ofdissolution ofbarium fluoride
spectroscopy (Perkin—Elmer model 503) in order to verify the constancy of the concentrations (±1.0%). The solid phases collected during the experiment were investigated by X-ray diffraction and by scanning electron microscopy.
using convential dissolution experiments in which the undersaturation is allowed to decrease. The crystallization and dissolution of divalent metal ion salts in general [11—141 are greatly inhibited by additives. In the present work, the rate of dissolution of barium fluoride was studied in the presence of magnesium calcium and strontium
3. Results and discussion
ions. The influence of added metal ions on the dissolution reactions are illustrated in fig. 1. From the rate profiles shown in fig. 1, the dissolution rates of barium fluoride in presence of metal ions
The concentrations of free-ion species in the solutions were calculated from mass-balance and electroneutrality expressions as described previously [3], using the thermodynamic equilibrium constants, K, for the various associated species [4—7]. Activity coefficients were calculated from the extended form of the Debye—Huckel equation proposed by Davies [81. The degree of relative undersaturation, o, for barium fluoride solutions may be defined by:
4.
([Ba2+
1/3
10[F
]~)
2~ J[F ~ 1/2 ([Ba
12) i/3 ,
(1)
([Ba2+]o[F]~) where [Ba2~], [F1
and [Ba2~1
0, [F-]0 are the concentrations of free barium and fluoride ions at i and at equilibrium, respectively, at the ionic strength of the experiments. The conditional solu2~1 bility product, K~ ([Ba at the 0[F~I~), was (1.27 ± 3 =dm3 saturation ionic 0.05) x 10 mol strength (0.378 mol dm3) [9]. The rate of dissolution, R, can be expressed in terms of the relative undersaturation by: Rate
=
dm/di
=
Ksa”.
—.
-~r
°
2 0
2.
(2)
in which m is the number of moles dissolved at time t, k a rate constant, s a function of the initial seed surface area and n is the apparent order of the reaction. Previous kinetic studies of the dissolution of barium fluoride indicate that at higher driving forces (relative undersaturation 0.15—0.20), the rate seems to he controlled by volume diffusion. whereas at low undersaturation (0.04—0.12), a surface controlled reaction predominates [101. The microscopic reversibility near equilibrium is especially interesting [11] since it is not possible to obtain reliable rate data under these conditions
1 2.
Mg2~
20
40
[ M2~]I1O-6 mol Fig 1.
60 dm3
Plots of rates of dissolution against [M2~
]
in the
presence of magnesium, calcium, and strontium, at undersaturation (a
=
0.1).
S.M. Hamza
/
Influence ofmetal ions sin kinetics of dissolution ofbarium fluoride
305
Table 1 Effect of additives on the rates of dissolution of barium fluoride crystals ~)
Expt.
T
102 a
Additive (106 moldm3)
No. 19 30
(10~ moldm 13.665 13.665
10 10
—
—
Mg
5
7.280 2.598
31
13.665
10
Mg
10
0.891
32 33
13.665 13.665
10 10
Mg Mg
20 30
0.691 0.600
34
13.665
10
Mg
40
0.470
35 36 37 38 39 40 41 42 43 44 45 46 47
13.665 13.665 13.665 13.665 13.665 13.665 13.665 13.968 13.968 13.968 13.968 13.968 13.968
10 10 10 10 10 10 10 8 8 8 8 8 8
Mg Ca Ca Ca Ca Ca Ca
50 5 10 20 30 40 50
Ca Ca Ca Ca Ca
5 10 20 30 40
0.425 3.029 1.680 1.090 0.690 0.540 0.503 4.780 1.614 1.072 0.594 0.415 0.309
48
13.968
8
Ca
50
0.262
49 50
14.272 14.272
6 6
—
—
Ca
5
2.140 0.471
51
14.272
6
52 53 54 55 56 57 58 59 60 61
14.272 14.272 14.272 14.272 13.665 13.665 13.665 13.665 13.665 13.665
6 6 6 6 10 10 10 10 10 10
Ca Ca
10 20
0.287 0.177
Ca Ca Ca Sr Sr
30 40 50 5 10
0.125 0.108 0.092 5.063 3.875
Sr
20
2.790
Sr Sr Sr
30 40 50
1.991 1.882 1.733
~° ~
11a
TF
=
3)
1:2, [KNO
—
Rate molmin~ m2) (10~
—
3, 50 mg seed. stirring speed 200 rpm. 1J
=
0.378 mol dm
(magnesium, calcium and strontium) decrease with successive additions of metal ions. It can be seen that the effectiveness of the inhibition is Mg> Ca > Sr. Experiments in the presence of metal ions, summarized in table 1, show that concentrations as low as 5 x iO~ mol dm3 for each additive
anionic sites and inhibit the dissolution when present at very low levels. The adsorption can be interpreted in terms of a Langmuir-type isotherm [12] leading to an equation of the form: R 0/(R0
(expts. 35, 41 and 61) reduced the dissolution rates by as much as 94.2%, 93.1% and 76.2% in the presence of magnesium, calcium and strontium, respectively. In general, inhibitors exert their influence through adsorption at active dissolution sites on the crystal surfaces. Cations may be adsorbed at
—
R)
=
(KLC)~.
(3)
in which R1 and R0 are the rates of dissolution in the presence and absence of inhibitor respectively, KL is the adsorption affinity and C is the additive concentration. Typical adsorption plots according to eq. (3) in fig. 2 confirm the applicability of this simple adsorption isotherm for all metal ions
S. M. Hamza
306
/
Influence of metal ion.s on kinetics ofdissolution ofbarium fluoride
~
2]
[M
1
~
Fig. 2. Langmuir adsorption isotherms. Plots of R
2~ 5/(R5
—
dm3 moH I in the presence of magnesium,
calcium and strontium.
R~)against [M
studied. The values of the adsorption affinity constants. K~ are 4.42 x 10~dm3 molt for magnesium, 4.25 x 1O’~dm3 mol for calcium and 3.08 x io~dm3 molt for strontium at the same relative undersaturation, a = 0.1. These values reflect the high adsorption affinity which is in the following order: Mg> Ca> Sr. The effect of the inhibitor may be described as the prevention or strong retardation of the nucleation of etch pits in areas around the adsorbed inhibitor molecules. Due to interaction with the inhibitor, lattice ions in these areas will be strongly attached to the crystal surface. If sufficient inhibitor molecules are adsorbed onto the surface, the whole crystal may be inactivated and no dissolution will occur. Prevention or retardation of dissolution may occur by preferential adsorption of the inhibitor molecules at the edges of the subcritical etch pits forming on the surface thus pre-
venting their development beyond the critical size [13]. On the assumption that the degree of inhibition may be affected by the degree of relative undersaturation, the dissolution of barium fluoride in the presence of calcium ions has been investigated at different undersaturations (0.1—0.06). In terms of the simple Langmuir equation, the values of the adsorption affinity constants are 4.25 x 1O~,4.41 x 10” and 4.63 x iO~dm3 mol at relative undersaturation, a = 0.1, 0.08 and 0.06, respectively (fig. 3). Plots of these values against a in fig. 4 show the striking increase in the kinetically derived adsorption affinity near equilibrium. A similar dependence of the degree of inhibition with change in the driving force has been observed for the influence of phosphonate and metal ions on the rate of dissolution and crystallization of divalent metal fluorides in aqueous solutions [11,14—
S. M. Hamza
/ Influence ofmetal ions
307
on kinetics of dissolution of barium fluoride
2
0
0
cci
5
10
1ca2]~ ~
Fig. 3. Langmuir adsorption isotherms. Plots of R
0/(R0
—
15 dm3
20
moH
2~ ]1 for different undersaturations, a
=
0.06. 0.08, 0.1.
R) against [Ca
16]. As noted for the crystallization of gypsum by
6
Weijnen, Marchée and Van Rosmalen [17], the effectiveness of the phosphonate as an inhibitor is dependent on the degree of supersaturation. The marked dependence upon a of the effectiveness of growth and dissolution inhibitors has important
.4
4 .
consequences in assessing the usefulness of inhibitors for industrial applications.
2
References
.
[1] W. Stumm and J.J. Morgan. Aquatic Chemistry (Wiley— lnterscience, New York, 1981). [2[ P.G. Koutsoukos, Z. Amjad, M.B. Tomson and G.H. Nancollas, J. Am. Chem. Soc. 102 (1980) 1553. [3] G.H. Nancollas. Interactions in Electrolyte Solutions
I
-0.1
-0.08
-0.06
-0.04
-0.02
0
(Elsevier, Amsterdam, 1966). [4] A.J. Ellis, J. Chem. Soc. (1963) 4300.
Fig. 4. Plots of adsorption affinities, KL against undersaturation ~.
[51G.L. 342.
Gardner and G.H. Nancollas. Dental Res. 55 (1976)
S. M. lIam:a
308 [6] Dl.
Stock and (/W.
/
Influence of metal ion.s on kinetics of dissolution of barium fluoride
Davies, Trans Faraday Soc. 44
[12] P. Koutsoukos, Z. Amjad and Gil. Nancollas, J. (‘olloid
(1948) 856. RE. Connick and M.S. Tsao. J. Am. (‘hem. Soc. 76 (1954) 5311. (‘.W. Davies. Ion Association (Butterworths. London. 1960). J.P. Barone, D. Svrjeck and Gil. Nancollas. J. Crystal Growth 62 (1983) 27. S.M. Hamza, 8th Chinese Conf. on Crystal Growth
Interface Sc). 83 (1981) 599. [13] G.M. van Rosmalen. M.P.C. Weijncn and J.A.M. Meiser. 36th Intern. Conf. CEBEDEAU. Liege. 1983. [14] S.M. Hamza and G.H. Nancollas, J. Chem. Soc.. Farada~ Trans. 1, 81(1985)1833. [15) SM. l-Iamza and GE!. Nancollas. Langmuir 1(1985) 573. [161 A. Ahul-Rahman, S.M. l-Iamza and Gil. Nancollas, in: Proc. 7th AIChE Annual Meeting, (‘hicago. IL. 1987. pp.
(CCCG-8), Guilin, China. 1988. [II] SM. Hamza. A. Ahdul-Rahman and Gil. Nancollas. J. Crystal Growth 73 (1985) 245.
36—41. [17] M.P.C. Weijncn. W.G.J. Marchée and G.M. van Rosmalen. Desalination 47 (1983) 81.
[7] [8] [9] [10]