Solubility of Zr(OH)4(am) and the Formation of Zr(IV) Carbonate Complexes in Carbonate Solutions Containing 0.1–5.0?mol·dm?3 NaNO3

Article abstract of DOI:10.1007/s10953-017-0599-6

The solubility of amorphous zirconium hydroxide [Zr(OH)₄(am)] was investigated in carbonate solutions containing various concentrations of sodium nitrate. The observed dependences of Zr(IV) solubility on the hydrogen ion concentration (pH_c

Full text of DOI:10.1007/s10953-017-0599-6

J Solution Chem
DOI 10.1007/s10953-017-0599-6
Solubility of Zr(OH)4(am) and the Formation of Zr(IV)
Carbonate Complexes in Carbonate Solutions Containing
0.1–5.0 molÁdm23 NaNO3
Taishi Kobayashi1 Takayuki Sasaki1
•
Received: 13 July 2016 / Accepted: 17 November 2016
Ó Springer Science+Business Media New York 2017
Abstract The solubility of amorphous zirconium hydroxide [Zr(OH)4(am)] was investi-
gated in carbonate solutions containing various concentrations of sodium nitrate. The
observed dependences of Zr(IV) solubility on the hydrogen ion concentration (pHc) and
carbonate concentration suggested the formation of ZrðCO3Þ4À, ZrðCO3Þ6À, and
4
5
Zr(OH)2ðCO3Þ2À as the dominant species in the neutral to weakly alkaline pH regions. The
2
solubility of Zr(IV) at certain pHc values and carbonate concentrations was observed to
increase slightly with increasing ionic strength, while the solid phase was determined to be
Zr(OH)4(am) at all ionic strengths by using thermal analysis. By applying the specific ion
interaction theory, the solubility data at different pHcs, carbonate concentrations, and ionic
strengths were analyzed to determine the formation constants of the Zr(IV) carbonate
complexes and their ion interaction coefficients. The obtained values explain well the
solubility data, which are discussed in comparison with those of analogous tetravalent
actinide carbonates.
Keywords Solubility Á Zr(OH)4(am) Á Carbonate Á Complex formation Á Ionic strength
1 Introduction
Determination of the solubility limit of radionuclides under geological conditions is
important for the safety assessment of radioactive waste disposal. Carbonate ions are
known to form strong complexes with radionuclides and are prevalent in underground
water. Although the solubility of some radionuclides, which behave as tetravalent metal
ions [M(IV)], is primarily controlled by the sparingly soluble solid phase amorphous
&
Taishi Kobayashi
kobayashi@nucleng.kyoto-u.ac.jp
1
Department of Nuclear Engineering, Graduate School of Engineering, Kyoto University,
Kyotodaigaku-katsura, Nishikyo, Kyoto, Japan
123

J Solution Chem
hydroxide, M(IV)(OH)4(am), complexation with carbonate ions potentially enhances the
apparent solubility of M(IV)(OH)4(am). A robust thermodynamic description of the
complexation with carbonate ions, based on their complexation constants, is therefore
required for a reliable prediction of the radionuclide’s solubility. Numerous studies have
investigated the carbonate complexes of tetravalent metal ions, and have been reviewed as
part of the Nuclear Energy Agency Thermochemical Database Project (NEA-TDB) [1–3].
Tetravalent zirconium is an element relevant to the safety assessment of radioactive
waste disposal, since it has a high yield in uranium fission products and Zr metal is used as
a fuel-cladding in light water reactors. Zr(IV) is also considered to be a chemical analog of
tetravalent actinides such as Th(IV), U(IV), Np(IV), and Pu(IV) [4–6]. The complexation
of Zr(IV) with carbonate ions has been the subject of few investigations. Among a limited
number of reports, several have suggested Zr(IV) carbonate complexes and their formation
constants [7–14], which have been recently reviewed by Brown et al. [2]. Dervin con-
ducted an extensive study on Zr(IV) carbonates using various techniques, including
cryoscopy, potentiometry, ion exchange, and solubility measurements. Based on the
experimental observations, they proposed the formation of binary Zr(IV) tetracarbonate
4À
Zr(CO3Þ4 as the dominant carbonate complex in solution. Solubility measurements of
Zr(IV) hydroxide in the presence of carbonate were conducted at a constant ionic strength
(I) of 1 molÁdm-3 in ammonium nitrate (NH4NO3) [7] and the results used to determine the
4À
formation constant of Zr(CO3Þ4 to be log10 bꢀ104 = 42.9 1.0 [2]. Malinko et al. con-
ducted potentiometric titrations and infrared spectroscopic measurements using mixtures of
0.01 and 0.4 molÁdm-3 Zr(SO4)2 with 0.2 molÁdm-3 Na2CO3 solutions at
4À
3À
,
I = 1.0 molÁdm-3
,
and suggested the presence of Zr(CO3Þ4
,
Zr(OH)(CO3Þ3
Zr(OH)2ðCO3Þ2À, and Zr(OH)3ðCO3ÞÀ to explain the experimental titration curves,
2
2À
4À
although only the successive complex formation constant from Zr(CO3Þ3 to Zr(CO3Þ4
was determined in the analysis [8]. Karlysheva et al. used Na2CO3 and ZrOCl2 in a molar
concentration ratio of 2:5 at I = 1.0 molÁdm-3 with a similar experimental method to that
of Malinko et al. to determine the successive complex formation constants from
2À
Zr(OH)2(CO3)(aq) to Zr(OH)2ðCO3Þ2 [9]. In a series of studies by Veyland et al.,
extensive work on the stoichiometries and coordination modes of Zr(IV) carbonate species
was carried out using potentiometric titration, nuclear magnetic resonance (NMR) spec-
troscopy, and electrospray ionization mass spectrometry (ESI-MS). Consequently,
4À
Zr(CO3Þ4 as a stable bidentate complex was proposed under 0.06–0.6 molÁdm-3 total
carbonate concentration [11–13]. Pouchon et al. measured the solubility of crystalline ZrO2
in the presence of 10-5 to 0.5 molÁdm-3 NaHCO3. Although two different chemical
4À
6À
models assuming the existence of Zr(CO3Þ4 or Zr(CO3Þ5 were considered to determine
each complex formation constant, the experimental data were rather limited in confirming
the chemical model [14].
4À
Considering the current knowledge, Zr(CO3Þ4 is one of the more robust Zr(IV) car-
bonate species observed in solution. It is likely, however, that it is not the only species to
2À
exist in the solutions, and other binary and ternary complexes such as Zr(CO3Þ3
,
Zr(OH)2(CO3)(aq), Zr(OH)(CO3Þ3À, and Zr(OH)2ðCO3Þ2À, are also involved in the Zr(IV)
3
2
carbonate system. Thermodynamic data on the binary and ternary complexes are still
necessary for a comprehensive description of the complexation abilities of Zr(IV) car-
bonates. In addition, the reported complex formation constants have only been obtained at
certain ionic strengths. In the context of the disposal of low level waste from a reprocessing
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J Solution Chem
plant (TRU waste), not only radionuclides in the waste but also zircaloy cladding waste
will come in contact with solutions with a wide range of sodium nitrate concentrations
[15–17]. The impact of this wide range of ionic strengths on radionuclide solubility is thus
an important issue for the safety assessment; however, information on the issue has not yet
been reported in the Zr(IV) carbonate system. In a review of Zr(IV) thermodynamic
constants, for instance, the ion interaction coefficient according to the specific ion inter-
4À
action theory (SIT) for Zr(CO3Þ4 could not be determined from the reported data, and
4À
could not be substituted by that of U(IV)(CO3Þ4 [2].
In the present study, we focus on Zr(IV) solubility in the presence of carbonate ions in a
range of dilute to concentrated NaNO3 solutions. The solubility was investigated across a
wide range of hydrogen ion concentration (pHc) values, total carbonate concentrations
([C]tot), and ionic strengths (I). The solid phase, after contact with the sample solution, was
examined by thermal analysis. Thermodynamic analysis of the soluble species revealed the
dominant soluble complexes present, and the formation constants of the Zr(IV) carbonate
complexes were determined by least-squares fitting analyses of the solubility data. The
obtained formation constants at different ionic strengths were corrected by using the SIT,
and the ion interaction parameters were determined and compared with those of the
tetravalent actinides.
2 Experimental Methods and Materials
2.1 Chemicals and Analytical Methods
All chemicals used were of reagent grade. ZrCl4 (C99.9%) was purchased from Sigma–
Aldrich. Deionized purified water (Milli-Q, Millipore) was used in all solution prepara-
tions. A 3.7 g sample of ZrCl4 was dissolved in 30 mL of purified water, and aliquots of
8 molÁdm-3 NaOH solution (Wako Pure Chemicals) were then added to the solution to
neutralize it and precipitate amorphous zirconium hydroxide [Zr(OH)4(am)]. The precip-
itate was washed with purified water several times and finally suspended in 50 mL of
purified water as a stock Zr(OH)4(am) suspension. The Zr(IV) concentration of the stock
solution suspension corresponds to 0.32 molÁdm-3 if the Zr(OH)4(am) was totally dis-
solved. The total carbonate concentration ([C]tot) was adjusted by adding an appropriate
amount of sodium bicarbonate (NaHCO3, Wako Pure Chemicals) to the sample solutions.
The free carbonate ion concentration ([CO23À]) was calculated from [C]tot and the disso-
ciation constants of carbonate and bicarbonate, assuming that the concentrations of the
Zr(IV) carbonate complexes were negligible compared to [C]tot.
A combination glass electrode (9615-10D, Horiba Ltd.) was used to measure the pHc.
The internal solution of the electrode was composed of aqueous sodium chloride (NaCl,
3.6 molÁdm-3) and sodium perchlorate (NaClO4, 0.4 molÁdm-3) (Wako Pure Chemicals).
The electrode was calibrated against standard pH buffer solutions of pH 4.01 and 6.86
(Horiba Ltd.) to obtain experimentally measured pH values (pHexp). Then, standard NaOH
solutions with pHc values of 11, 12, and 13 (Wako Pure Chemicals) at ionic strengths
I = 0.1, 0.5, 2.0, and 5.0 molÁdm-3 were prepared by adding appropriate amounts of
NaNO3. By measuring the pHexp values of the standard solutions at each ionic strength, the
‘‘A’’ and ‘‘B’’ values in the equation of pHc = A 9 pHexp ? B were determined to be 1.08
and -0.88 (I = 0.1 molÁdm-3), 1.04 and -0.20 (I = 0.5 molÁdm-3), 1.06 and -0.22
(I = 2.0 molÁdm-3), and 1.08 and -0.47 (I = 5.0 molÁdm-3). For the determination of
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pHc values of sample solutions, the pHexp values were corrected based on the above
equations. In the pHc determination of sample solutions in NaCl media, the same method
was adopted except the ionic strength of standard solutions was adjusted by NaCl.
2.2 Solubility Experiments
Sample solutions were prepared by an undersaturation approach and stored in an Ar glove
box (O2 \ 0.1 ppm) at 25 °C. An aliquot of NaHCO3 and HNO3 and/or NaOH solutions
was added to polypropylene tubes to prepare sample solutions of a specific pHc and [C]tot.
The pHc values ranged from 8 to 12, and the [C]tot ranged from 0.001 to 0.1 molÁdm-3
.
The ionic strength was fixed at I = 0.1, 0.5, 2.0 or 5.0 molÁdm-3 by adding appropriate
amounts of concentrated NaNO3 solution. A 0.3 mL aliquot of Zr(OH)4(am) stock sus-
pension was then added to the polypropylene tubes, such that the Zr(IV) concentration
corresponded to 0.01 molÁdm-3 if the solid phase was completely dissolved.
For comparison, several sample solutions were prepared in NaCl in the same manner.
The sample tubes were then left for a given aging time, up to 42 weeks, and occasionally
shaken by hand for a few minutes throughout the aging process. After the given aging time,
the pHc value of each sample solution was measured and the supernatant of the sample
solution was filtered through ultrafiltration membranes (Microcon NMWL 10 kDa, cor-
responding to pore sizes of approximately 3 nm, Millipore). After filtration, 30 lL of
HNO3 was added to the filtrate immediately to avoid any sorption of Zr(IV) species on the
sample tube throughout the solubility experiment. The filtrate was diluted in 0.1 molÁdm-3
HNO3 and measured by inductively coupled plasma mass spectrometry (ICP-MS;
ElanDRC II, PerkinElmer) to determine the Zr(IV) concentration. The detection limit of
Zr(IV) of the ICP-MS was about 10-8.5 molÁdm-3. For each measurement carried out by
ICP-MS, the standard error was within 10%, resulting in a Zr(IV) concentration error
of 0.1 in log10 units. After the solubility measurement, the supernatants of several sample
solutions were removed by centrifugation, and the solid phases were dried under atmo-
sphere at room temperature. Thermogravimetric analyses (TGA) and differential thermal
analyses (DTA) were performed under an N2 atmosphere to investigate the solid phases
using a thermal analyzer (DTG-60/60H, Shimadzu) at a heating rate of ?5 °CÁmin-1 to a
maximum temperature of 800 °C. Zr(OH)4(am) obtained from the stock suspension,
NaHCO3, and NaNO3 solutions were also investigated by TGA and DTA as references.
3 Results and Discussion
3.1 Zr(IV) Solubility in the Presence of Carbonate in 0.5 molÁdm23 NaNO3
Figure 1 shows the Zr(IV) solubility as a function of pHc at a constant ionic strength of
I = 0.5 molÁdm-3 NaNO3 in solutions with [C]tot = (0.015, 0.04, and 0.1) molÁdm-3. The
solubility values were obtained after ultrafiltration through 10 kDa membranes over an
aging period up to 42 weeks. Since the solubility results after 4, 8 and 42 weeks showed
similar values, it was assumed that a steady state was achieved within 4 weeks, similar to
the previous solubility studies with Zr(OH)4(am) where a steady state was confirmed
within several weeks [18–20]. Literature data on Zr(IV) solubility in the absence of car-
bonate at comparable ionic strengths are plotted in Fig. 1 for comparison [18, 19]. In the
presence of carbonate, the solubility of Zr(OH)4(am) has clearly increased, indicating the
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J Solution Chem
-2
-3
Zr(OH)4(am), [C]tot = 0
I = 0.5, NaClO4
Sasaki et al. 2006
I = 0.5, NaCl
Altmaier et al. 2008
-4
-5
-6
-7
-8
I = 0.5, NaNO3
[C]tot 4w 8w 42w
-9
0.015
0.04
0.1
-10
6
7
8
9
10
11
12
13
–log [H+]
Fig. 1 Solubility of Zr(IV) in the presence of 0.5 molÁdm-3 NaNO3 at [C]tot = (0.015, 0.04, and 0.1)
molÁdm-3 after ultrafiltration through 10 kDa membranes. The grey field in the figure represents the
detection limit of ICP-MS. The solid lines are calculated solubility curves discussed in Sect. 3.3.2
formation of Zr(IV) carbonate complexes. The solubility was observed to be independent
of pHc at 8 \ pHc \ 9, and, after this point, decreased with increasing pHc. The solubility
at around pHc 12 is on the order of 10-8 molÁdm-3, which was near the detection limit
level of the ICP-MS (indicated by the gray shading in the plot). Figure 2 shows the
solubility of Zr(IV) in the presence of carbonate at I = 0.5 molÁdm-3 NaNO3 as a function
of [C]tot under certain pHc conditions. At pHc 8.2, the slope was determined to be about 4
in the investigated [C]tot range, suggesting that four carbonates are mainly involved in the
dominant Zr(IV) carbonate complexes. The relationship between Zr(IV) solubility and
[C]tot is similar between pHc 8.2 and 10.9, while no significant relationship are observed at
pHc 11.7.
3.2 Effect of Ionic Strength on Zr(IV) Solubility in the Presence of Carbonate
The solubility of Zr(IV) in the presence of 0.015 molÁdm-3 [C]tot in 0.1–5.0 molÁdm-3
NaNO3 after 5 weeks aging and subsequent ultrafiltration through 10 kDa membranes are
plotted as a function of pHc in Fig. 3a. In the pHc range of 8–9, the Zr(IV) solubility
increases with ionic strength. The solubility at I = 5.0 is about 1.5 orders of magnitude
higher than that at I = 0.1 molÁdm-3 in the range of pHc 8–9, while, in contrast, little
difference was found between different ionic strengths at pHc [ 9. Figure 3b shows the
Zr(IV) solubility in the presence of 0.04 molÁdm-3 [C]tot in 0.1–5.0 molÁdm-3 NaNO3
after ultrafiltration through 10 kDa membranes after an aging period of 8 weeks, where a
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J Solution Chem
Fig. 2 Solubility of Zr(IV) in
0.5 molÁdm-3 NaNO3 as a
function of [C]tot after
ultrafiltration through 10 kDa
membranes. The grey field in the
figure represents the detection
limit of ICP-MS. The solid lines
are calculated solubility curves
discussed in Sect. 3.3.2
-2
-3
Slope 4
-4
-5
-6
-7
I = 0.5, NaNO3
pHc 8.2
-8
pHc 9.1
pHc 10.1
pHc 10.9
pHc 11.7
-9
-10
-3
-2
-1
0
log [C]tot
-2
(a) [C]tot = 0.015 mol·dm–3
(b) [C]tot = 0.04 mol·dm–3
Zr(OH)4(am)
I = 0.5, NaClO4
Sasaki et al. 2006
I = 0.5, NaCl
Altmaier et al. 2008
Zr(OH)4(am)
I = 0.5, NaClO4
Sasaki et al. 2006
I = 0.5, NaCl
Altmaier et al. 2008
-3
-4
-5
-6
-7
-8
-9
[C]tot = 0.015
[C]tot=0.04
I
NaNO3
I
NaNO3 NaCl
0.1
0.5
2.0
5.0
0.1
0.5
2.0
5.0
-10
6
7
8
9
10
11
12
13
6
7
8
9
10
11
12
13
–log [H+]
–log [H+]
Fig. 3 Solubility of Zr(IV) in the presence of 0.1–5.0 molÁdm-3 NaNO3 and NaCl with a 0.015 and
b 0.04 molÁdm-3 [C]tot after ultrafiltration through 10 kDa membranes. The grey field in the figure represents
the detection limit of ICP-MS. The solid lines are calculated solubility curves discussed in Sect. 3.3.2
123

J Solution Chem
similar trend of Zr(IV) solubility to that in 0.015 molÁdm-3 [C]tot is observed. In Fig. 3b,
the Zr(IV) solubility in the presence of 0.04 molÁdm-3 [C]tot in 0.1–5.0 molÁdm-3 NaCl is
also plotted, and it can be seen that a change in the ionic salt does not lead to a change in
Zr(IV) solubility. This observation can be considered to be reasonable, as the complexation
ability of NOÀ3 is as weak as that of Cl- [2], so NOÀ3 will have minimal influence on the
Zr(IV) carbonate system. In Fig. 4, the Zr(IV) solubilities at pHc 8.2 and
I = 0.1–5.0 molÁdm-3 NaNO3 are plotted as a function of [C]tot. Similar to the results at
I = 0.5 in Fig. 2, the slope of the graph of Zr(IV) solubility against [C]tot in increasingly
more concentrated NaNO3 solutions is observed to be about 4, suggesting that four car-
bonate ions are involved in the dominant species. However, in the case that conditions of
high ionic strength and [C]tot less than 0.01 molÁdm-3 were employed, the slope of the
graphs showed slightly lower values than those at low ionic strength, which suggests the
formation of an alternative or additional Zr(IV) carbonate complex.
The solid phases aged in the presence of carbonate in 0.1–5.0 molÁdm-3 NaNO3 at pHc
8 were investigated by TGA and DTA analyses, the results of which are shown in Fig. 7 in
Appendix 1. The solid phases showed endothermic peaks and weight losses, corresponding
only to the processes of dehydration of Zr(OH)4(am), and melting and decomposition of
residual NaNO3, so we can assume that the initial Zr(OH)4(am) solid phase was not
transformed under the experimental conditions employed.
Fig. 4 Solubility of Zr(IV) as a
function of [C]tot in (0.1, 0.5, 2.0,
and 5.0) molÁdm-3 NaNO3 at pHc
8.2 after ultrafiltration through
10 kDa membranes. The grey
field in the figure represents the
detection limit of ICP-MS. The
solid lines are calculated
-2
-3
Slope 4
-4
solubility curves discussed in
Sect. 3.3.2
-5
-6
-7
-8
pHc 8.2
I
NaNO3
0.1
0.5
2.0
5.0
-9
-10
-3
-2
-1
0
log [C]tot
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J Solution Chem
3.3 A Thermodynamic Model of Zr(IV) Solubility in the Na1–HCO3À–CO32À
–
NOÀ3 –H2O System
3.3.1 Ionic Strength Correction Method
The equilibrium reactions for the dissolution of Zr(OH)4(am) and the formation of the
4ÀxÀ2y
Zr(IV) carbonate complexes Zr(OHÞxðCO3Þy
can be described as:
ZrðOHÞ4ðamÞ ꢀ Zr4þ þ 4OHÀ
log10 Ksp ¼ ½Zr4þŠ½OHÀŠ4;
Zr4þ þ xOHÀ þ yCO32À ꢀ Zr(OHÞxðCO3Þy
ð1Þ
ð2Þ
ð3Þ
4ÀxÀ2y
.
4ÀxÀ2y
x
log10 b1xy ¼ ½Zr(OH)xðCO3Þy
Š ½Zr4þŠ½OHÀŠ ½CO22ÀŠy;
ð4Þ
where Ksp and b1xy represent the conditional solubility product and complex formation
constant at a certain molality-based ionic strength (Im), respectively. The Ksp and b1xy can
be written as follows, based on the SIT model [1]:
ꢀ
À
log10 Ksp ¼ log10 Ksp þ log10 cZr4þ þ 4 log10 cOH
È À
ÀÁ
É
ð5Þ
¼ log10 Ksꢀp þ 20D À e Zr4þ; NO3 þ 4eðOHÀ; NaþÞ Á Im
log10 b1xy ¼ log10 bꢀ1xy þ log10
c
À ðlog10 cZr4þ þ xlog10 cOH þ ylog10
c
Þ
À
CO23À
ZrðOHÞ ðCO3Þð4ÀxÀ2yÞ
x
y
n
o
2
¼ log10 bꢀ1xy þ ð4 À x À 2yÞ À16 À x À 4y D
e Zr(OH)xðCO3Þ4ÀxÀ2y;Naþ À e Zr4þ;NO3
ÀxeðOHÀ;NaþÞ À ye CO32À;Naþ Á Im
n ꢀ
ꢁ
À
ÀÁ
À
y
À
ÁÉ
ð6Þ
where Ksꢀp and b1ꢀxy are the solubility product and complex formation constant at I = 0;
eðZr(OH)xðCO3Þ4ÀxÀ2y; NaþÞ, eðZr4þ; NO3ÀÞ, eðOHÀ; NaþÞ, and eðCO23À; NaþÞ represent
y
the ion interaction coefficients for each species; and D is the Debye–Hu¨ckel term at 25 °C.
Under the conditions of the present study, the solubility of Zr(OH)4(am) ([Zr]tot) in the
presence of carbonate is described as a sum of the concentrations of hydrolysis species and
carbonate complexes:
h
i
X
X
Â
Ã
4ÀxÀ2y
½ZrŠ
¼
Zr(OH)4mÀm
þ
Zr(OH)xðCO3Þy
tot
m
x;y
,
!
ð7Þ
X
X
4
m
x
y
¼ Ksp ½OHÀŠ 1 þ
b1m0½OHÀŠ þ
b1xy½OHÀŠ ½CO23À
Š
m
x;y
where b1m0 is the hydrolysis constant. The concentration of carbonate ([CO23À]) can be
calculated from [C]tot and the dissociation constants of H2CO3(aq) and HCOÀ3 , provided
that [C]tot is much larger than [Zr]tot.
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J Solution Chem
4ÀxÀ2y
3.3.2 Aqueous Carbonate Complexes Zr(OHÞxðCO3Þy
in 0.1–5.0 molÁdm-3 NaNO3
(=1xy)
As Zr(IV) carbonate complexes can be binary or ternary, described as
Zr(OHÞ ðCO3Þ4ÀxÀ2y, many different complexes (1xy) are theoretically possible. Only
x
y
several complexes may contribute significantly, however, to the solubility of the com-
plexes under the investigated experimental conditions. The Zr(IV) tetracarbonate complex,
Zr(CO3Þ4À, which is denoted as (104) and is formed when the carbonate is in a large excess
4
with respect to Zr(IV), is considered to be one of the most robust species in the neutral pH
region [7, 8, 10–14]. In previous reports, potentiometric titration curves obtained with
[CO3]/[Zr(IV)] ratios of 1:2–60 could be best explained using the assumption that
4À
Zr(CO3Þ4 is the dominant species [7, 8, 12]. Infrared spectroscopic data indicated an
absorption peak characteristic of free carbonate when the [CO3]/[Zr(IV)] ratio exceeded
4À
4:1, which also suggests that Zr(CO3Þ4 is the complex preferentially formed [8]. Veyland
et al. adopted a direct detection method based on electrospray mass spectrometry and
4À
correlated the fragmentation spectra to Zr(CO3Þ4 [13]. In the present study, the slope of
Zr(IV) solubility against [C]tot is about 4 for [C]tot [ 0.01 molÁdm-3, suggesting the for-
mation of a complex incorporating mainly four carbonate ions. As the carbonate con-
centration condition was comparable to that used in the above mentioned studies, and
considering that the Zr(IV) concentration of the initial Zr(OH)4(am) at total dissolution
4À
was 0.01 molÁdm-3, we assumed Zr(CO3Þ4 to be one of the dominant species in our
system. The experimental plots near neutral pH region can be relatively well reproduced by
Zr(CO3Þ4À; however, the calculated solubilities at high pHc and high ionic strength tend to
4
deviate from the experimental plots, suggesting contributions of other carbonate
complexes.
The binary (105) species is one of the dominant species widely recognized in tetravalent
actinide carbonate systems [1, 3, 21–26]. For instance, the solubility of PuO2(am) in
relatively concentrated carbonate solutions ([C]tot [ 0.1 molÁdm-3) significantly increases
6À
with [C]tot and the solubility was interpreted based on Pu(CO3Þ5 with the aid of X-ray
absorption spectroscopy [25]. In the Zr(IV) carbonate system, Pouchon et al. assumed the
(104) or (105) species from the similarity of Zr(IV) and tetravalent actinides to explain the
solubility of cubic zirconia (c-ZrO2) in concentrated carbonate solutions [14]. Although the
slopes of 4 and 5 were rather close in Figs. 2 and 4, and it was difficult to clearly
distinguish the difference between (104) and (105) species in the present study; the (105)
species was included in the analysis based on the observations in tetravalent actinide
carbonate systems in the literature.
The ternary (122) species is another common species proposed to explain the solubility
of tetravalent actinides at low carbonate concentration less than [C]tot = 0.1 molÁdm-3
[1, 3, 21–25]. In the Zr(IV) carbonate system, Karlysheva et al. proposed the (122) species
to explain the titration curves observed for solutions of Na2CO3 containing ZrOCl2 in
Na2CO3:ZrOCl2 ratios of 1:2–5 [9]. In the present study, although only few points at
[C]tot \ 0.01 molÁdm-3 in Figs. 2 and 4 contributed the slope of Zr(IV) solubility against
[C]tot less than 4, the (122) species was also included in the analysis from the chemical
similarity of Zr(IV) and tetravalent actinides, similar to the case of the (105) species.
Based on Eqs. 5–7, the solubility data at different [C]tot and ionic strength were fitted,
4À
6À
2À
treating bꢀ104, bꢀ105, bꢀ122, e(Zr(CO3Þ4 , Na?), e(Zr(CO3Þ5 , Na?), and e(Zr(OH)2ðCO3Þ2
,
123

J Solution Chem
Na?) as free parameters. The solubility product of Zr(OH)4(am) (Ksꢀp), hydrolysis constant
(bꢀ1m0), and dissociation constants of carbonate and bicarbonate (K1ꢀ, K2ꢀ) at I = 0 were
taken from the literature [2, 18, 27], and used after correction by the SIT. The values for
e(Zr4?, NOÀ3 ), e(ZrOH3?, NO3À), e(Zr(OH)22?, NO3À), e(OH-, Na?), e(CO32À, Na?), and
e(HCOÀ3 , Na?) are 0.33, 0.26, 0.16, 0.04, -0.08, and 0.0, respectively [2]. As the values for
e(Zr(OH)þ3 , NOÀ3 ), e(Zr(OH)5À, Na?), and e(Zr(OH)26À, Na?) have not been reported in the
literature, they were then assumed to be 0 based on analyses in previous studies [18, 20].
The used and determined formation constants and ion interaction coefficients of SIT in
the analysis are summarized in Tables 1 and 2. The calculated log10 bꢀ104 value is in
agreement with that reported in the NEA-TDB Project (log10 bꢀ104 = 42.9 1.0) [2]. In
Table 3, the hydrolysis and carbonate complex formation constants are compared with
those of the corresponding tetravalent actinides. Comparing the log10 bꢀ104 values of Zr(IV)
with those for Np(IV) and Pu(IV), those for Zr(IV) are found to be higher by five orders of
magnitude.
4À
The obtained ion interaction coefficient value e(Zr(CO3Þ4 , Na?) = 0.64 0.06 is
higher than that reported by the NEA-TDB Project of -0.09 0.20, which was equated to
4À
4À
6À
e(U(CO3Þ4 , Na?) [2]. The large e(Zr(CO3Þ4 , Na?) and e(Zr(CO3Þ5 , Na?) values in this
study are a consequence of the minor effects of ionic strength on solubility under high
carbonate concentrations. In the case of the Th(IV) carbonate system, for instance, the
solubility increased more than two orders of magnitude when I was increased from 0.1 to
4.0 molÁdm-3 at pHc * 8 [22]. The results observed in this study indicate that a highly
negatively charged Zr(IV) carbonate complex is less stable at high ionic strength, com-
pared to the analogous Th(IV) complex. A larger impact of ionic strength than that in the
Table 1 Summary of the complex formation constants and solubility product in the Zr(IV)–carbonate
system (I = 0)
Reactions
Values
References
Zr(OH)4(am) … Zr4? ? 4OH-
Zr4? ? OH- … ZrOH3?
log10 Ksꢀp
log10 bꢀ110
log10 bꢀ120
log10 bꢀ130
log10 bꢀ140
log10 bꢀ150
log10 bꢀ160
-56.94
14.29
[18]
[27]
[27]
2þ
Zr4? ? 2OH- … Zr(OHÞ2
26.66
Zr4? ? 3OH- … Zr(OHÞþ3
Zr4? ? 4OH- … Zr(OH)4(aq)
Zr4? ? 5OH- … Zr(OHÞÀ5
35.85
43.12
46.52
48
[27]
[27]
[27]
[27]
2À
Zr4? ? 6OH- … Zr(OHÞ6
H2O ? CO2(aq) … H? ? HCO3À
HCOÀ3 … H? ? CO23À
log10 K1ꢀ
log10 K2ꢀ
log10 bꢀ105
-6.354
-10.329
41.6 0.2
43
[2]
[2]
6À
Zr4? ? 5CO23À … Zr(CO3Þ5
This study
[14]
log10 bꢀ104
42.4 0.1
42.9
This study
[2]
4À
Zr4? ? 4CO22À … Zr(CO3Þ4
42
[14]
log10 bꢀ122
46.9 0.1
This study
2À
Zr4? ? 2OH- ? 2 CO32À … Zr(OH)2ðCO3Þ2
123

J Solution Chem
Table 2 Summary of the ion
interaction coefficients of SIT
Values
References
e(Zr4?, NOÀ3 )
e(ZrOH3?, NOÀ3 )
0.33
0.26
0.16
[2]
[2]
[2]
2þ
e(Zr(OHÞ2 , NOÀ3 )
e(Zr(OH)þ3 , NOÀ3 )
e(Zr(OH)4(aq), NOÀ3 )
e(Zr(OHÞÀ5 , Na?)
0
0
0
0
–
–
–
–
2À
e(Zr(OHÞ6 , Na?)
e(CO23À, Na?)
e(HCOÀ3 , Na?)
-0.08
[2]
0.00
[2]
6À
e(Zr(CO3Þ5 , Na?)
0.95 0.18
This study
4À
e(Zr(CO3Þ4 , Na?)
0.64 0.06
-0.09
This study
[2]
2À
e(Zr(OH)2ðCO3Þ2 , Na?)
-0.01 0.04
This study
Table 3 Hydrolysis and carbonate complex formation constants of Zr(IV) and tetravalent actinides (I = 0)
Species (1xy)
log10 b1xy
4ÀxÀ2y
Zr(OHÞxðCO3Þy
Zr(IV)
Th(IV)
U(IV)
Np(IV)
Pu(IV)
(110)
(120)
(130)
(140)
(150)
(160)
(105)
(104)
(122)
14.29 [27]
26.66 [27]
35.85 [27]
43.12 [27]
46.52 [27]
48 [27]
12.2 [3]
23.0 [3]
32.7 [3]
39.1 [3]
13.46 [1]
14.55 [1]
28.35 [1]
14.6 [1]
28.6 [1]
39.7 [1]
47.8 [1]
46 [1]
47.7 [1]
41.6 0.2
42.4 0.1
46.9 0.1
31.0 [3]
36.8 [3]
34.0 [1]
37.84 [1]
38.91 [1]
43.17 [24]
35.65 [1]
37.0 [1]
35.12 [1]
41.3 [23]
44.76 [25]
Zr(IV) system was also expected [1, 3, 23–25] in other tetravalent actinide carbonate
systems. The dependence of formation constants on the ionic strength of tetravalent
actinide carbonate complexes has been discussed in the literature [28]; however, the trends
observed for ionic strength may differ among Zr(IV) and tetravalent actinides, especially
4À
6À
for highly negatively charged species like Zr(CO3Þ4 and Zr(CO3Þ5
.
Figures 5 and 6 present the differences in the solubility curves of Zr(IV) upon changes
in [C]tot (0.015, 0.04, and 0.1 molÁdm-3) with constant I (I = 0.5 molÁdm-3), as well as
with constant [C]tot (0.04 molÁdm-3) and changes in I (I = 0.1–5.0 molÁdm-3), as cal-
culated from the thermodynamic constants in Table 1 and the obtained ion interaction
coefficients in Table 2. The changes in solubility upon increases in NaNO3 concentration
are clearly described by the proposed carbonate complexes. As described above, in the
presence of 0.04 molÁdm-3 [C]tot, the impacts of ionic strength on the concentration of
4À
6À
Zr(CO3Þ4 and Zr(CO3Þ5 are observed to be limited when I [ 0.5 molÁdm-3
.
123

J Solution Chem
-2
-3
-4
-5
-6
-7
-8
-9
(104)
(104)
(105)
(122)
(105)
(122)
-10
-2
6
7
8
9
10
11
12
13
I = 0.5 (NaNO3)
–log [H+]
-3
-4
[C]tot = 0.1
[C]tot = 0.04
[C]tot = 0.015
(104)
-5
-6
(122)
-7
(105)
-8
-9
-10
6
7
8
9
10
11
12
13
–log [H+]
Fig. 5 Solubility curve and soluble species when [C]tot = (0.015, 0.04, and 0.1) molÁdm-3 at
I = 0.5 molÁdm-3. The plots show the experimental values, and the solid, dotted, broken, and bold curves
represent the (104), (105), (122) species and the Zr(IV) solubility, respectively
4 Conclusions
The solubility of amorphous zirconium hydroxide (Zr(OH)4(am)) was investigated in
carbonate solutions containing 0.1–5.0 molÁdm-3 sodium nitrate. The dependences of the
increase in Zr(IV) solubility on the hydrogen ion concentration (pHc) and carbonate
2À
concentration suggest the existence of Zr(CO3Þ4À, Zr(CO3Þ6À, and Zr(OH)2ðCO3Þ as the
4
5
2
dominant species in neutral to weakly alkaline pH regions. Thermal analysis suggested that
the solid phase was Zr(OH)4(am). The solubility data at different pHc values, carbonate
concentrations, and ionic strengths were analyzed using the SIT equation.
123

J Solution Chem
-2
-3
[C]tot = 0.04 mol·dm–3
I = 0.1
I = 0.5
I = 2.0
I = 5.0
(104)
-4
(104)
(122)
-5
-6
-7
-8
-9
(122)
(105)
(105)
-10
-2
(104)
(104)
-3
-4
(122)
(105)
(105)
-5
(122)
-6
-7
-8
-9
-10
6
7
8
9
10
11
12
13
6
7
8
9
10
11
12
13
-log[H+]
-log[H+]
Fig. 6 Solubility curve and soluble species when [C]tot = 0.04 molÁdm-3 and I = 0.1–5.0 molÁdm-3. The
plots show the experimental values, and the solid, dotted, broken, and bold curves represent the (104), (105),
(122) species and the Zr(IV) solubility, respectively
Acknowledgements This work has been supported in part by a grant from the Ministry of Economy, Trade
and Industry (METI). The authors would like to acknowledge and thank Drs. Xavier Gaona and Marcus
Altmaier of the Karlsruhe Institute of Technology for fruitful discussions.
Appendix 1
In the present study, the sample solutions were prepared using an undersaturation method.
The initial solid phase of Zr(OH)4(am) was placed into the sample solutions at specific pH,
[C]tot, and ionic strength. After aging of the sample solutions, the solid phases kept at pHc
123

J Solution Chem
8, [C]tot = 0.04 molÁdm-3, and I = (0.1, 0.5, 2.0 and 5.0) molÁdm-3 were investigated by
thermal analysis. The TGA and DTA curves are shown in Fig. 7, together with those of
Zr(OH)4(am), NaNO3, and NaHCO3. In the curves for NaNO3, an endothermic peak
around 310 °C represents the melting point, while the weight loss after 650 °C indicates
thermal decomposition. For NaHCO3, an endothermic peak and weight loss at 150 °C
shows a release of CO2 from the sample. For Zr(OH)4(am), an endothermic peak and
weight loss at around 100 °C represent the dehydration of Zr(OH)4(am) to ZrO2(s). The
solid phases that were in contact with the sample solutions showed endothermic peaks and
weight losses corresponding only to the processes of dehydration of Zr(OH)4(am) and
melting and decomposition of residual NaNO3. No indications of a Zr(IV) carbonate solid
compound were observed, so it was assumed that the initial Zr(OH)4(am) solid phase was
not transformed under the experimental conditions employed.
See Fig. 7.
Appendix 2: Experimental Solubility Data
See Tables 4, 5, 6, and 7.
100
NaNO3
I=5.0
90
I=2.0
Zr(OH)4(am)
I=0.5
80
70
60
50
I=0.1
NaHCO3
40
2
0
-2
Zr(OH)4(am)
NaHCO3
I=0.1
-4
-6
I=2.0
I=5.0
I=0.5
-8
NaNO3
-10
0
100
200
300
400
500
600
700
800
Temperature (ºC)
Fig. 7 TGA (upper) and DTA (lower) curves of Zr(IV) solid phases with 0.04 molÁdm-3 [C]tot at pHc 8 in
NaNO3 solutions of increasing concentration
123

J Solution Chem
Table 4 Solubility of Zr(IV) in the presence of 0.5 molÁdm-3 NaNO3 at [C]tot = (0.015, 0.04, and 0.1)
molÁdm-3 after ultrafiltration through 10 kDa membranes
Samples
[C]tot
Equilibration period
4 weeks
8 weeks
pHc
42 weeks
pHc
pHc
9.05
log10 [Zr]
log10 [Zr]
log10 [Zr]
ZCN-1
0.015
0.015
0.015
0.015
0.015
0.015
0.015
0.015
0.015
0.015
0.015
0.015
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.1
-5.79
-5.84
-6.05
-6.05
-6.17
-6.40
-6.82
-7.91
-8.85
-8.85
-8.85
-8.85
-3.52
-3.50
-3.55
-3.58
-3.63
-3.75
-4.59
-4.48
-5.44
-7.79
-8.85
-8.85
-2.56
-2.55
-2.58
-2.61
-2.62
-2.66
-2.75
-2.78
-3.31
-5.57
-7.29
-8.36
9.11
8.14
-5.49
-5.48
-5.48
-5.45
-5.51
-6.05
-6.78
-7.42
-7.70
-7.95
-7.98
-7.97
-3.70
-3.48
-3.50
-3.59
-3.62
-3.74
-4.34
ND
ZCN-2
9.12
9.28
ZCN-3
8.30
ZCN-4
9.32
8.43
ZCN-5
9.41
8.86
ZCN-6
9.57
9.61
ZCN-7
9.80
9.84
ZCN-8
10.17
10.38
10.97
11.31
11.65
8.54
10.21
10.43
11.00
11.34
11.68
8.70
ZCN-9
ZCN-10
ZCN-11
ZCN-12
ZCN-13
ZCN-14
ZCN-15
ZCN-16
ZCN-17
ZCN-18
ZCN-19
ZCN-20
ZCN-21
ZCN-22
ZCN-23
ZCN-24
ZCN-25
ZCN-26
ZCN-27
ZCN-28
ZCN-29
ZCN-30
ZCN-31
ZCN-32
ZCN-33
ZCN-34
ZCN-35
ZCN-36
8.70
8.29
8.84
8.48
8.97
9.24
9.75
-3.56
-3.59
-3.94
8.93
8.14
9.07
9.11
9.27
9.30
9.71
9.75
9.78
10.70
10.13
10.95
11.41
11.64
8.18
10.08
10.90
11.36
11.61
8.34
-5.02
-7.41
-7.89
-7.91
-2.47
-2.45
-2.47
-2.46
-2.43
-2.77
-2.66
-2.86
-3.23
-5.09
-7.15
-7.67
10.12
11.05
11.43
-4.82
-7.14
-7.53
0.1
8.45
8.64
0.1
8.61
8.34
0.1
8.75
8.50
0.1
8.93
9.00
0.1
9.12
9.20
0.1
9.41
9.46
0.1
9.66
9.70
0.1
10.01
10.67
11.34
11.65
10.04
10.71
11.36
11.71
0.1
0.1
0.1
123

J Solution Chem
Table 5 Solubility of Zr(IV) in
the presence of
0.1–5.0 molÁdm-3 NaNO3 at
[C]tot = 0.04 molÁdm-3 after
ultrafiltration through 10 kDa
membranes
Samples
I (NaNO3)
Equilibration period
4 weeks
8 weeks
pHc
8.50
pHc
log10 [Zr]
log10 [Zr]
ZCN-37
ZCN-38
ZCN-39
ZCN-40
ZCN-41
ZCN-42
ZCN-43
ZCN-44
ZCN-45
ZCN-46
ZCN-47
ZCN-48
ZCN-49
ZCN-50
ZCN-51
ZCN-52
ZCN-53
ZCN-54
ZCN-55
ZCN-56
ZCN-57
ZCN-58
ZCN-59
ZCN-60
ZCN-61
ZCN-62
ZCN-63
ZCN-64
ZCN-65
ZCN-66
ZCN-67
ZCN-68
ZCN-69
ZCN-70
ZCN-71
ZCN-72
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
2
8.24
-4.07
-4.03
-4.03
-4.06
-4.14
-4.21
-4.26
-4.45
-4.77
-6.28
-7.95
-7.95
-3.31
-3.29
-3.33
-3.23
-3.35
-3.45
-3.58
-3.78
-4.68
-6.78
-7.52
-8.65
-3.22
-3.20
-3.20
-3.22
-3.30
-3.47
-3.78
-4.01
-5.26
-7.65
-7.65
-7.65
-4.12
-4.09
-4.08
-4.11
-4.47
-4.20
-4.27
-4.36
-4.82
-6.15
-7.96
-8.44
-3.20
-2.90
-3.26
-3.25
-3.24
-3.37
-3.56
-3.76
-4.66
-6.54
-7.63
-8.09
-3.00
ND
8.52
8.69
8.80
8.91
9.02
9.15
9.37
9.69
10.34
11.17
11.41
8.28
8.41
8.59
8.64
8.75
8.95
9.17
9.39
9.83
10.50
10.99
11.44
8.19
8.23
8.30
8.47
8.67
8.89
9.19
9.40
9.86
10.80
11.17
11.40
8.65
8.19
8.87
7.65
9.05
7.91
9.38
9.70
10.32
11.17
11.39
8.44
7.88
8.06
8.69
8.37
8.97
9.18
9.40
9.83
10.50
11.01
11.46
7.77
7.88
8.39
8.15
8.71
8.91
9.18
9.41
9.85
10.79
11.19
11.38
2
2
2
2
2
2
2
2
2
2
2
5
5
5
-3.13
-3.14
-3.26
-3.40
-3.74
-4.00
-5.20
-7.35
-7.41
-7.21
5
5
5
5
5
5
5
5
5
123

J Solution Chem
Table 6 Solubility of Zr(IV) in the presence of 0.1–5.0 molÁdm-3 NaNO3 at [C]tot = 0.001–0.015 -
molÁdm-3 after ultrafiltration through 10 kDa membranes
Samples
I (NaNO3)
[C]tot
Equilibration period
2 weeks
5 weeks
pHc
pHc
8.18
log10 [Zr]
log10 [Zr]
ZCN-100
ZCN-101
ZCN-102
ZCN-103
ZCN-104
ZCN-105
ZCN-106
ZCN-107
ZCN-108
ZCN-109
ZCN-110
ZCN-111
ZCN-112
ZCN-113
ZCN-114
ZCN-115
ZCN-116
ZCN-117
ZCN-118
ZCN-119
ZCN-120
ZCN-121
ZCN-122
ZCN-123
ZCN-124
ZCN-125
ZCN-126
ZCN-127
0.1
0.1
0.1
0.1
2
0.015
0.015
0.015
0.015
0.015
0.015
0.015
0.015
0.015
0.015
0.015
0.015
0.001
0.002
0.004
0.008
0.001
0.002
0.004
0.008
0.001
0.002
0.004
0.008
0.001
0.002
0.004
0.008
-5.73
-5.76
-6.56
-8.82
-4.76
-4.69
-5.48
-7.87
-4.40
-4.51
-5.06
-7.24
-7.68
-7.59
-7.56
-6.41
-7.73
-7.49
-7.42
-6.21
-7.54
-7.65
-7.25
-5.61
-6.60
-6.59
-6.45
-5.31
8.46
8.93
9.73
11.03
8.38
8.65
9.44
10.88
8.10
8.72
9.09
10.78
8.36
7.90
8.24
8.48
8.22
8.22
8.27
8.31
8.03
8.12
8.20
8.29
8.24
8.17
8.21
8.35
-5.55
-5.50
-6.31
-7.74
-4.57
-4.56
-5.17
-7.21
-4.14
-4.23
-4.55
-7.19
-8.25
-8.48
-8.02
-6.96
-8.03
-8.29
-7.74
-6.34
-7.22
-7.39
-7.07
-5.78
-7.49
-7.14
-6.82
-5.28
8.82
9.63
10.92
7.86
8.42
9.28
10.75
7.58
8.55
8.91
10.60
8.41
7.69
8.22
8.41
7.23
7.78
8.11
8.20
7.41
7.46
7.74
8.08
7.21
7.40
8.09
8.23
2
2
2
5
5
5
5
0.1
0.1
0.1
0.1
0.5
0.5
0.5
0.5
2
2
2
2
5
5
5
5
123

J Solution Chem
Table 7 Solubility of Zr(IV) in
the presence of
Samples
I (NaCl)
[C]tot
Equilibration period
0.1–5.0 molÁdm-3 NaCl at
[C]tot = 0.04 molÁdm-3 after
ultrafiltration through 10 kDa
membranes
2 weeks
pHc
log10 [Zr]
ZCC-1
ZCC-2
ZCC-3
ZCC-4
ZCC-5
ZCC-6
ZCC-7
ZCC-8
ZCC-9
ZCC-10
ZCC-11
ZCC-12
ZCC-13
ZCC-14
ZCC-15
ZCC-16
ZCC-17
ZCC-18
ZCC-19
ZCC-20
0.1
0.1
0.1
0.1
0.1
0.5
0.5
0.5
0.5
0.5
2
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
0.04
7.69
8.04
8.81
9.84
9.97
7.73
8.18
8.73
9.33
9.93
7.82
7.78
8.48
9.11
9.78
7.92
8.17
8.03
8.65
9.46
-4.22
-4.19
-4.27
-5.19
-5.53
-3.43
-3.31
-3.61
-4.16
-5.10
-3.24
-3.19
-3.34
-3.73
-4.68
-3.10
-3.07
-3.20
-3.49
-4.32
2
2
2
2
5
5
5
5
5
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123