Thermochemical study of tetravalent metal sulfate tetrahydrates: A4+(SO4)2(H2O)4 (A4+?=?Zr, Ce, U)

Article abstract of DOI:10.1016/j.jssc.2019.04.030

The syntheses, characterization, and calorimetric measurements of enthalpies of formation of four tetravalent metal sulfate tetrahydrates (A⁴⁺(SO₄)₂(H₂O)₄ (A⁴⁺ = Zr, Ce, U): α-Zr(SO₄)₂(H₂O)₄, α-Ce(SO₄)₂(H₂O)₄, β-Ce(SO₄)₂(H₂O)₄, and β-U(SO₄)₂(H₂O)₄)are reported. Direct calorimetric measurements showed that the formation enthalpies of these compounds from the corresponding oxides correlate with the eightfold coordination radius of the tetravalent cations. An energetic slope change is observed between the α- (Fddd)and β- (Pnma)forms and is consistent with previously reported studies.

Full text of DOI:10.1016/j.jssc.2019.04.030

Accepted Manuscript
4+
Thermochemical study of tetravalent metal sulfate tetrahydrates: A (SO ) (H O)
4
4
2
2
4+
(A
￿ ꢀ￿ =rZ CeZ U)
Lei =hangZ Haylie L. LobeckZ Ewa A. DzikZ Ginger E. SigmonZ Peter C. Burns
PII:
S0022-4596(19)30207-5
https://doi.org/10.1016/j.jssc.2019.04.030
YJSSC 20731
DOI:
Reference:
To appear in: Journal of Solid State Chemistry
Received Date: 16 January 2019
Revised Date: 29 March 2019
Accepted Date: 22 April 2019
Please cite this article as: L. =hangZ H.L. LobeckZ E.A. DzikZ G.E. SigmonZ P.C. BurnsZ Thermochemical
4+
4+
study of tetravalent metal sulfate tetrahydrates: A (SO ) (H O) (A ￿ ꢀ￿ =rZ CeZ JU o) uZ rnal of Solid
4
2
2
4
State Chemistry (2019)Z doi: https://doi.org/10.1016/j.jssc.2019.04.030.
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ACCEPTED MANUSCRIPT
Thermochemical Study of Tetravalent Metal Sulfate Tetrahydrates:
4
+
4+
A (SO ) (H O) (A = Zr, Ce, U)
4
2
2
4
a,*
a
a
a
a,b
Lei Zhang , Haylie L. Lobeck , Ewa A. Dzik , Ginger E. Sigmon , and Peter C. Burns
a
Department of Civil and Environmental Engineering and Earth Sciences, University of Notre
Dame, Notre Dame, IN 46556
b
Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, IN 46556
Abstract
The syntheses, characterization, and calorimetric measurements of enthalpies of formation of
4
+
4+
four tetravalent metal sulfate tetrahydrates (A (SO ) (H O) (A = Zr, Ce, U): α-
4
2
2
4
Zr(SO ) (H O) , α-Ce(SO ) (H O) , β-Ce(SO ) (H O) , and β-U(SO ) (H O) ) are reported.
4
2
2
4
4 2
2
4
4 2
2
4
4 2
2
4
Direct calorimetric measurements showed that the formation enthalpies of these compounds
from the corresponding oxides correlate with the eightfold coordination radius of the tetravalent
cations. An energetic slope change is observed between the α- (Fddd) and β- (Pnma) forms and
is consistent with previously reported studies.
Keywords: zirconium sulfate tetrahydrate; cerium sulfate tetrahydrate; uranium sulfate
tetrahydrate; calorimetry.
Corresponding Author
*
E-mail: lzhang12@nd.edu
1

ACCEPTED MANUSCRIPT
Declarations of interest: none.
Graphical Abstract
-
-
-
-
-
-
-
-
380
400
420
440
460
480
500
α
β
-form (Fddd)
-form (Pnma)
α
β
Hf Zr
Ce
Pu Np
U
Th
520
0
.80
0.84
0.88
0.92
0.96
1.00
1.04
1.08
Eightfold Coordination Radius of A4+
(Å)
1
. Introduction
4
+
4+
Our interest in the tetravalent metal sulfates, A (SO ) (H O) (A = Zr, Ce, U), emphasizes
4
2
2
4
understanding the trends in coordination chemistry and thermodynamic stability of compounds
4
+
containing 4f and 5f electrons. A (SO ) (H O) crystallizes as α- (Fddd) and β- (Pnma) forms
4
2
2
4
4
+
with identical stoichiometry and closely related structures. In both, A O
4 2 4
(H O) square
antiprisms share O vertices with four SO tetrahedra, resulting in heteropolyhedral sheets that are
4
connected to each other by hydrogen bonds. Both structures are illustrated in Figure 1, where it is
apparent that the sheets of polyhedra are parallel to (001) (α-form) and (100) (β-form). These
4
+
two polymorphs differ primarily in the local coordination environment about the tetravalent A ;
specifically, the arrangement of SO tetrahedra about the cation as shown in Figure 1.
4
2

ACCEPTED MANUSCRIPT
a)
b)
Fig. 1. Polyhedral representation of crystal structures of α- (Fddd) and β- (Pnma) polymorphs of
4
+
A (SO ) (H O) . a) Crystal structure of α-Zr(SO ) (H O) . b) Crystal structure of β-
4
2
2
4
4 2
2
4
U(SO
4
)
2
(H
2
4
O) . Green, dark green, and yellow polyhedra represent zirconium, uranium, and
sulfur atoms, respectively.
According to the literature, only Ce(SO ) (H O) and Pu(SO ) (H O) occur in both α- and β-
4
2
2
4
4 2
2
4
1
-3
forms. Zr(SO ) (H O) and Hf(SO ) (H O) crystallize in Fddd, and are isostructural to α-
4
2
2
4
4 2
2
4
4
, 5
Pu(SO ) (H O) ; U(SO ) (H O) and Np(SO ) (H O) crystallize in Pnma and are isostructural
4
2
2
4
4 2
2
4
4 2
2
4
6
, 7
to β-Pu(SO ) (H O) . No structure has been reported for Th(SO ) (H O) .
4
2
2
4
4 2
2
4
4
+
A (SO
4
)
2
(H
2
4
O) compounds are usually synthesized by hydrothermal reactions or slow
4
+
evaporation of saturated A (SO
4
)
2
solutions with different H
2
SO
4
concentrations at various
temperatures of crystallization. Bĕhounekite, orthorhombic U(SO
4
)
2
(H O) , is the first reported
2
4
8
natural sulfate of U(IV). It is known from one site in the Jáchymov ore district, Czech Republic,
where crystallization of U(IV) minerals may have been triggered by reduction of U(VI) in mine
3

ACCEPTED MANUSCRIPT
4 2 2 4
water accompanied by oxidation of As. The structure of bĕhounekite is that of β-U(SO ) (H O)
6
by Kierkegaard.
Besides tetravalent actinide sulfate tetrahydrates, the tetravalent actinide (IV) sulfate system
presents considerable stoichiometric and structural complexity. New compounds in the An(IV)-
2
-
4+
SO4 systems other than An (SO ) (H O) (where An = U, Np, Pu) have been reported recently,
4 2
2
4
9
,
10
10
12
12
3
including:
Na [Th (SO
[U (SO
Cs Np(SO
Th(SO ) (H O) ·2H O;
Na [Th (SO ) (H O) ]·3H O;
4
2
2
7
2
10
2
4 9
2
2
2
10
11
2
2
4
)
5
(H
]·6H
(H
2
2
O)
3
]·H
2
O;
Cs
2
Th(SO
4
)
3
(H
2
O)
2
;
U(SO
Cs [U
; Rb
4
)
2
(H
(SO
(SO
2
O)
(H
(H
7
·2H
2
O;
];
O)
12
12
K
8
2
4
)
8
O;
Rb
8
[U
2
(SO
4
)
8
]·2.5H
2
O;
8
2
4
)
3
2
O)
2
1
3
3
3
2
4
)
3
2
O)·H
2
O; Na10Pu
2
(SO
4
)
9
(H O)
2
4
; K
8
Pu
2
(SO
4
)
8
(H
2
O)
5
8
Pu
2
4
)
8
2
4
;
3
and Cs Pu(SO ) (H O) . The variety of the structural conformations of these An(IV) sulfate
4
4 4
2
2
complexes is fascinating and further work is needed to map their energetic landscape.
4
+
Here we explore the impact of specific tetravalent cations on the stability of A (SO ) (H O)
4
4
2
2
compounds that crystallize in α- and/or β-forms. We have synthesized and characterized
4
+
4+
A (SO ) (H O) (A = Zr, Ce, and U), and performed direct thermochemical studies to measure
4
2
2
4
their standard heats of formation.
2
. Materials and Methods
2
.1 Synthesis
α-Zr(SO ) (H O) , space group Fddd: Zr(OH) powder was prepared by dissolving
4
2
2
4
4
ZrO(NO ) ·xH O (Aldrich) in deionized H O, followed by addition of NH OH until the pH was
3
2
2
2
4
in the range of 9 to 10. Zr(OH) precipitated out of the resulting solution immediately and was
4
2
recovered by filtration and washed with deionized H O multiple times until the decant solution
4
pH was 7. The powder was then left to dry in air. 200 mg of Zr(OH) powder was then dissolved
4

ACCEPTED MANUSCRIPT
in 1M H (SO ) to produce a saturated Zr(SO ) solution, which was heated at 90 °C for 7 days
2
4 2
4 2
in a sealed Teflon-lined stainless-steel Parr reaction vessel. Subsequent to heating, the
concentrated solution was left open to air to slowly evaporate. Several months later, pure opaque
white hexagonal crystals of α-Zr(SO
α-Ce(SO (H O) , space group Fddd: Ce(OH)
Ce(NO ·xH O (Aldrich) in deionized H O, and adjusting the pH into the range of 9 to 10 by
adding NH OH. Ce(OH) precipitated immediately and was recovered by filtration and washed
4 2 2 4
) (H O) formed.
4
)
2
2
4
4
powder was prepared by dissolving
3
)
4
2
2
4
4
with deionized H O multiple times until the decant solution pH was 7. The powder was then left
2
to dry in air. 200 mg of Ce(OH) powder was dissolved in 1M H (SO ) to produce a saturated
4
2
4 2
Ce(SO ) solution, which was heated in a sealed Teflon-lined stainless-steel Parr reaction vessel
4
2
at 90 °C for a week. The cooled concentrated solution was then left open to air to allow for slow
evaporation. One month later, yellow needle shaped crystals formed that were later determined
to be α-Ce(SO ) (H O) .
4
2
2
4
β-Ce(SO ) (H O) , space group Pnma: Dry Ce(OH) powder was prepared as for the
4
2
2
4
4
synthesis of α-Ce(SO ) (H O) . 200 mg of Ce(OH) was then dissolved in 1M H (SO ) to make
4
2
2
4
4
2
4 2
a saturated Ce(SO
temperature. Several months later, yellow needle-shaped crystals of β-Ce(SO
β-U(SO (H O) , space group Pnma: 0.1 g of UO (CH COO) ·2H O was dissolved in 0.97
mL of concentrated H SO , followed by addition of 1 mL of deionized H O. The solution was
4
)
2
solution that was then left open to air for slow evaporation at room
4
)
2
(H O) formed.
2
4
4
)
2
2
4
2
3
2
2
2
4
2
then combined with 0.064 mL of N-(3-aminopropyl)-2-pyrrolidinone (Sigma-Aldrich) to aid in
the reduction of U. The solution was heated at 165 °C for 24 hrs in a sealed Teflon-lined
stainless-steel Parr reaction vessel. The cooled solution was then transferred to a closed vial.
About two weeks later, green tetragonal bipyramid crystals of pure β-U(SO ) (H O) formed.
4
2
2
4
5

ACCEPTED MANUSCRIPT
2
.2 Characterization
4
+
Crystals of A (SO ) (H O) were collected by filtering and washing with deionized H O
4
2
2
4
2
several times and were left to dry in air. β-U(SO ) (H O) was washed using ethanol as we noted
4
2
2
4
that it is soluble in water. The dried crystals were ground using an agate mortar and pestle and
their powder X-ray diffraction patterns were collected using a Bruker D8 Advance diffractometer.
The patterns were collected from 5 to 90 ° (2θ) using CuKα X-radiation and a step width of 0.02°
every second. Purity and identity of the compounds were confirmed by comparison with the
corresponding patterns from the PDF+4 database. Powder patterns are in the SI (fig. S1).
Zr, Ce, U, and S contents were analyzed by inductively coupled plasma optical emission
spectroscopy (ICP-OES). ICP-OES samples were prepared by dissolving 10 mg of crystals in
3 3
concentrated HNO (15.9M), and subsequent dilutions were made in a 5% HNO matrix.
Elemental analyses were performed on a Perkin Elmer Optima 8000 instrument with 165 – 800
nm coverage and resolution of approximately 0.01 nm for multi-elemental analysis. Seven
calibration standards were prepared ranging from 0.1 – 20 ppm for zirconium, cerium, uranium,
and sulfur analysis and a 0.5 ppm Y internal standard was added to each sample, blank, and
standard to monitor instrumental drift. Calculated concentrations of each element in the samples
were based on calibration coefficients of 0.99% or higher.
Thermogravimetric analyses were performed using about 10 mg of crystals in a Metler Toledo
TGA-DCS1 coupled with differential scanning calorimetry. The crystals were heated from room
2
temperature to 900 °C at a heating rate of 5 °C /min under N . The water content of each
compound was calculated using the measured mass loss, see Fig. S2 in SI.
6

ACCEPTED MANUSCRIPT
2
.3 Calorimetry
The enthalpies of drop solution of A (SO ) (H O) (A = Zr, Ce, and U) were measured
4
+
4+
4
2
2
4
using a Setaram AlexSYS 1000 high temperature Tian-Calvet calorimeter. The calorimeter was
14-16
calibrated against the well-known heat content value of 5 mg of α-Al O .
The crystals of
2
3
compound were ground and pressed into small pellets 1.6 mm in diameter that were then
dropped from room temperature into molten sodium molybdate oxide solvent at 700 °C. Pure
oxygen gas was flushed through the calorimetric assembly at 43 mL/min and bubbled through
the molten solvent at 5 mL/min, to facilitate the dissolution process and to provide an oxidizing
atmosphere to ensure that all uranium oxidized to U(VI). This methodology has been
successfully utilized to study the enthalpy of formation of many uranium materials containing
1
7-21
U(IV) and/or U(VI),
such as uranium dioxide solid solutions and uranium minerals.
Formation enthalpies from oxides, ∆Hf, ox and from elements, ∆Hf, el were calculated from
measured drop solution enthalpies ∆HDS by thermochemical cycles listed in Tables 1 and 2.
Table 1. Reactions and thermodynamic cycles used to calculate enthalpies of formation of
4
+
A (SO
4
)
2
(H
2
O)
4
(A = Zr, Ce) at 25 °C from oxides and from the elements in kJ/mol.
Reaction
∆H (kJ/mol)
4
+
2-
(
1) A(SO ) (H O)
→ A
+ 2SO4
+ 4H O
∆H = ∆H (A(SO ) (H O) )
4
2
2
4(c, 25 °C)
(sln, 700 °C)
(sln, 700 °C)
2
(g,
1
DS
4 2
2
4
700 °C)
2
-
4+
2-
16
16
(
2) AO2(c, 25 °C) + 2Mo
2
O
7
(sln, 700 °C) → A (sln, 700 °C) + 4MoO
4
(sln, 700 °C)
∆H
∆H
∆H
∆H
∆H
2
3
4
5
6
2
= ∆HDS(AO )
2
4
-
2-
2-
(sln, 700 °C)
(
(
(
(
3) SO3(g, 25 °C) + 2MoO
(sln, 700 °C) → SO
4
(sln, 700 °C) + Mo
2
O
7
3
= ∆HDS(SO )
22
4) H
2
O
(l, 25 °C) → H
2
O
(g, 700 °C)
= ∆Hheat content(H
2
O) = 69
5) AO2(c, 25 °C) + 2SO3(g, 25 °C) + 4H
2
O
(l, 25 °C) → A(SO
4
)
2
(H
2
O)4(c, 25 °C)
= ∆Hf, ox = -∆H
1
+ ∆H + 2∆H + 4∆H
2
3 4
22
6) A(c, 25 °C) + O2(g, 25 °C) → AO2(c, 25 °C)
2
= ∆Hf, el(AO )
2
2
(
7) S(c, 25 °C) + 3/2O2(g, 25 °C) → SO3(g, 25 °C)
∆H = ∆Hf, el(SO3)
7
7

ACCEPTED MANUSCRIPT
2
2
(
(
2
8) H2(g, 25 °C) + 1/2O2(g, 25 °C)→ H O
∆H = ∆H (H O)
8 f, el 2
2
(l, 25 °C)
9) A(c, 25 °C) + 2S(c, 25 °C) + 4H2(g, 25 °C) + 6O2(g, 25 °C) → A(SO ) (H O)
∆H = ∆H (A(SO ) (H O) ) = ∆H + ∆H +
9 4 2 2 4 5 6
4 2
2
4 (c,
f, el
∆H + 4∆H8
2
5 °C)
7
Table 2. Reactions and thermodynamic cycles used to calculate enthalpies of formation of the
U(SO (H O) at 25 °C from oxides and from the elements in kJ/mol.
4
)
2
2
4
Reaction
∆H (kJ/mol)
2
-
6+
(
1) U(SO ) (H O)
+ 1/2O2(g, 700 °C) + Mo O7
→ U
∆H = ∆H (U(SO ) (H O) )
4
2
2
4(c, 25 °C)
2
(sln, 700 °C)
(sln,
1
DS
4 2
2
4
2
-
2-
7
00 °C) + 2SO
4
(sln, 700 °C) + 2MoO
4
(sln, 700 °C) + 4H
2
O
(g, 700 °C)
6+
2
-
16
(
2) UO2(c, 25 °C) + 1/2O2(g, 700 °C) + 3Mo
2
O
7
(sln, 700 °C) → U (sln, 700 °C)
+
∆H
2
2
= ∆HDS(UO )
2
-
6
MoO4
(sln, 700 °C)
2
-
2-
2-
16
(
(
(
(
(
(
(
2
3) SO3(g, 25 °C) + 2MoO4
→ SO4
+ Mo O7
∆H = ∆H (SO )
(sln, 700 °C)
(sln, 700 °C)
2
(sln, 700 °C)
4(c, 25 °C)
3
DS
3
22
4) H O
→ H O
∆H = ∆H
(H O) = 69
heat content 2
2
(l, 25 °C)
2
(g, 700 °C)
4
5) UO2(c, 25 °C) + 2SO3(g, 25 °C) + 4H O
→ U(SO ) (H O)
∆H = ∆H = -∆H + ∆H + 2∆H + 4∆H
5 f, ox 1 2 3 4
2
(l, 25 °C)
4 2
2
2
2
6) U(c, 25 °C) + O2(g, 25 °C) → UO2(c, 25 °C)
7) S(c, 25 °C) + 3/2O2(g, 25 °C) → SO3(g, 25 °C)
8) H2(g, 25 °C) + 1/2O2(g, 25 °C)→ H O
∆H = ∆Hf, el(UO2)
6
22
∆H = ∆Hf, el(SO3)
7
2
2
∆H = ∆H (H O)
2
(l, 25 °C)
8
f, el
2
9) U(c, 25 °C) + 2S(c, 25 °C) + 4H2(g, 25 °C) + 6O2(g, 25 °C) → U(SO ) (H O)
∆H = ∆H (U(SO ) (H O) ) = ∆H + ∆H
9 4 2 2 4 5 6
4 2
2
4 (c,
f, el
+
2∆H + 4∆H8
5 °C)
7
3
. Results
4
+
All PXRD patterns of A (SO
α- (Fddd) or β- (Pnma), as shown in Figure S1. Both polymorphs of Ce(SO
synthesized separately, as were α-Zr(SO ) (H O) and β-U(SO ) (H O) . No β-form of
4
)
2
(H
2
O)
4
were indexed to either of the orthorhombic structures,
4
)
2
(H O) were
2
4
4
2
2
4
4 2
2
4
4 2 2 4 4 2 2 4
Zr(SO ) (H O) nor α-form U(SO ) (H O) have been reported. The purity of each compound
was confirmed within the limits of detection of X-ray powder diffractometry.
8

ACCEPTED MANUSCRIPT
4
+
Chemical analysis produced A to S ratios of 1:2, as listed in Table S1. Despite the slight
deviation from the ideal ratio, due to the lack of secondary phases (as confirmed by PXRD) and
other cations, we will use the formula of A(SO ) (H O) for the interpretation of TGA data. TGA
4
2
2
x
confirmed that the compounds studied were all tetrahydrates. The decomposition of the
A(SO ) (H O) compounds occurred in three stages: first the endothermic dehydration to
4
2
2
4
A(SO ) ; followed by the continuous loss of SO ; and finally, decomposition to AO and SO
4
2
3
2
3
(for U it was U
3
O
8
4 2 2 4
). As shown in Fig. S2, TGA for α-Zr(SO ) (H O) shows the weight loss to
Zr(SO ) is 20 wt% calculated, and 20 wt% observed; while its weight loss to ZrO is 65 wt%
4
2
2
calculated, and 65 wt% observed. The weight loss of α-Ce(SO ) (H O) to Ce O(SO ) (500 –
4
2
2
4
2
4 3
1
7
00 °C) is 28 wt% calculated, and 27 wt% observed. On the other hand, the weight loss of β-
Ce(SO ) (H O) to Ce O(SO ) (500 – 700 °C) is also 28 wt% calculated, and 28 wt% observed;
4
2
2
4
2
4 3
while its weight loss to CeO
2
is 57 wt% calculated, and 57 wt% observed. The weight loss of β-
U(SO ) (H O) to U O is 44 wt% calculated, and 43 wt% observed. We will use the ideal
4
2
2
4
3
8
chemical formula A(SO ) (H O) for the thermochemical calculations.
4
2
2
4
Table 3 lists the drop solution enthalpies (also in Table S2-S4), ∆H , formation enthalpies
DS
4
+
from oxides, ∆Hf, ox, and from elements, ∆H , for each A (SO ) (H O) compound. Note that
f, el
the formation enthalpy from oxides of α-Zr(SO
SO , and H O.
4 2
2
4
4 2 2 4 2
) (H O) was calculated from monoclinic ZrO ,
3
2
4
+
Table 3. Enthalpies of formation of A (SO ) (H O) (A = Zr, Ce, U) from oxides, and from
4
2
2
4
elements.
Compound
∆HDS
∆Hf, ox
∆Hf, el
9

ACCEPTED MANUSCRIPT
α-Zr(SO ) (H O)
4
320.75 ± 9.64 (8)
400.63 ± 2.97 (5)
391.76 ± 9.33 (8)
197.36 ± 2.46 (8)
-432.65 ± 12.68
-3467.97 ± 12.87
-3481.08 ± 8.98
-3472.21 ± 12.60
-3484.78 ± 9.02
4
2
2
α-Ce(SO
β-Ce(SO
β-U(SO
4
)
2
(H
(H
(H
2
O)
O)
O)
4
-457.66 ± 8.74
-448.79 ± 12.43
-465.16 ± 8.85
4
)
2
2
4
4
)
2
2
4
Note: Value is the mean of the number of experiments indicated in parentheses. Error is two standard deviation of
the mean.
4 2 2 4
∆Hf, el(α-Zr(SO ) (H O) ) was previously determined by calorimetric measurements of its
2
3
enthalpy of solution in 3.0 mol/L HCl to be -3469.3 ± 2.7 kJ/mol, which agrees well with the
value determined here, -3467.97 ± 12.87 kJ/mol. The newly measured ∆H (β-U(SO ) (H O) )
f, el
4 2
2
4
value (-3484.78 ± 9.02 kJ/mol) is consistent with that (-3483.2 ± 6.3 kJ/mol) selected in the
Update on the Chemical Thermodynamics of Uranium, Neptunium, Plutonium, Americium, and
2
4
Technetium, 2003. The direct calorimetric measurements reported here require only small
amounts of materials and produce consistent thermochemical data comparing well to other
techniques. This method is thus especially useful when applied to transuranic materials, for
which small sample sizes are essential.
4
. Discussion
4
+
Enthalpies of formation of A (SO ) (H O) compounds from stable binary compounds, in this
4 2 2 4
case the oxides, were calculated and are listed in Table 3. All enthalpies of formation from
oxides (less than -400 kJ/mol) indicate the very exothermic reaction of the formation of
4
+
A (SO ) (H O) . This is also consistent with the requirement of a temperature exceeding 700 °C
4
2
2
4
for their complete decomposition to oxides as shown by TGA.
In both the α- and β- forms of the orthorhombic modifications of A (SO
the tetravalent atoms are surrounded by eight oxygen atoms, forming square antiprisms that are
4
+
4 2 2 4
) (H O) compounds,
1
0

ACCEPTED MANUSCRIPT
linked through SO
4
tetrahedra to form electroneutral sheets that are connected by hydrogen
bonds. Thus, it is reasonable to compare the determined values with the formation enthalpies
from AO with eight-coordinated oxygen atoms. Both CeO and UO are fluorite structured, but
2
2
2
∆
Hf, ox(α-Zr(SO ) (H O) ) is calculated from monoclinic ZrO , in which Zr is coordinated by
4 2 2 4 2
seven oxygen atoms. Therefore, the ∆Hf, ox(α-Zr(SO ) (H O) , 8-CN) is recalculated from
4 2
2
4
tetragonal ZrO2,
∆H
f, ox(α-Zr(SO
4
)
2
(H
2
O)
4
, 8-CN) = ∆Hf, ox(α-Zr(SO
4
)
2
(H
2
O)
4
) - ∆Hm→t(ZrO
2
)
(1)
2
5
∆
Hm→t(ZrO ) has been reported to be 5.4 ± 0.3 kJ/mol, and ∆H (α-Zr(SO ) (H O) , 8-CN) =
2 f, ox 4 2 2 4
-438.05 ± 12.68 kJ/mol.
∆
Hf, (α-Hf(SO ) (H O) ) was previously determined by isothermal calorimetric
el
4 2
2
4
2
6
measurements in 3.15 mol/L HCl to be -3492.8 ± 3.3 kJ/mol, and its ∆Hf, ox(α-Hf(SO
4 2 2 4
) (H O) )
from monoclinic HfO , SO , and H O is calculated to be -440.5 ± 3.8 kJ/mol. Similar to the case
2
3
2
of ∆Hf, ox(α-Zr(SO ) (H O) , 8-CN), ∆H (α-Hf(SO ) (H O) , 8-CN) is recalculated from
4 2
2
4
f, ox
4 2
2
4
2
tetragonal HfO ,
∆
Hf, ox(α-Hf(SO ) (H O) , 8-CN) = ∆H (α-Hf(SO ) (H O) ) - ∆Hm→t(HfO2)
(2)
4 2
2
4
f, ox
4 2
2
4
2
7
∆H
2 4 2 2 4
m→t(HfO ) has been reported to be 7.7 ± 0.6 kJ/mol, therefore ∆Hf, ox(α-Hf(SO ) (H O) , 8-
CN) = -448.2 ± 3.9 kJ/mol.
1
1

ACCEPTED MANUSCRIPT
Formation enthalpies from oxides as a function of the tetravalent cation radius in eightfold
2
8
coordination are shown in Figure 2, and indicate a substantial thermodynamic stability with
respect to oxides as they all have very negative values,
AO2(c, 8-CN, 25 °C) + 2SO3(g, 25 °C) + 4H O
= A(SO ) (H O)
4(c, α- or β- form, 25 °C)
(3)
2
(l, 25 °C)
4 2
2
4
+
Comparing the enthalpies of formation of polymorphs of A (SO ) (H O) provides insight into
4
2
2
4
their relative stability. Since the reaction involves the same amount of SO gas, AO are all
3
2
coordinated with eight oxygens, and the α- and β- forms are structurally related, the difference in
entropy of reaction (3) will be negligible. Therefore, the Gibbs free energy ∆Gf, ox will parallel
the enthalpy ∆Hf, ox. As shown in Figure 2, overall the stability increases as the tetravalent cation
radii increases. The energy slope changes between the α- and β- forms. As the tetravalent cation
4
+
radii becomes larger than approximately 0.98 Å (equal to an A -O distance of 2.36 Å), the β-
4
+
forms of A (SO ) (H O) become energetically more favorable than the α- form. This is
4
2
2
4
consistent with reported observations, as summarized in Table 4, that U (1.0 Å) and Np (0.98 Å)
only form the β- form, Zr (0.84 Å) and Hf (0.83 Å) only form the α- form, and Ce (0.97 Å) and
Pu (0.96 Å) can form both polymorphs. As for Th (1.05 Å), the Th-O bond length is large
enough that a nine-fold or ten-fold O coordination is preferred, thus neither alpha or beta forms
2
9
of the sulfate tetrahydrate has been reported. Indeed, Th
3
(SO
O contain Th coordinated by 9 oxygens; and in Th(SO
coordinated by 10 oxygens.
4
)
6
(H
2
O)
6
·H
2
O
and
2
9
30
Th(SO
4
)
2
(H
2
O)
7
·2H
2
4
)
2
(H
2
O)
8
Th is
1
2

ACCEPTED MANUSCRIPT
-
-
-
-
-
-
-
-
380
400
420
440
460
480
500
α-form (Fddd)
β-form (Pnma)
α
β
Hf Zr
Ce
Pu Np
U
Th
520
0
.80
0.84
0.88
0.92
0.96
1.00
1.04
1.08
4
+
Eightfold Coordination Radius of A (Å)
Fig. 2 Formation enthalpies from oxides of α- (Fddd) and β- (Pnma) polymorphs of
A(SO ) (H O) versus eightfold coordination radius of the tetravalent cations. Note: ∆Hf, ox(α-
4
2
2
4
2
6
Hf(SO ) (H O) , 8-CN) is recalculated from ∆H (α-Hf(SO ) (H O) ).
4
2
2
4
f, el
4 2
2
4
Table 4. Summary of some A(IV) sulfate compounds.
8
-coordinate A(IV)
Compound
CN
(avg) A-O (Å)
Reference
2
8
radius (Å)
0.83
5
α-Hf(SO ) (H O)
8
8
2.19(6)
2.18(1)
Yankova, 2014
4
2
2
4
4
α-Zr(SO ) (H O)
0.84
Singer, 1959
4
2
2
4
1
3

ACCEPTED MANUSCRIPT
3
α-Pu(SO ) (H O)
8
8
0.96
0.96
0.97
0.97
0.98
1.0
2.32(3)
2.33(3)
2.32(4)
2.33(3)
2.33(3)
2.40(2)
2.43(9)
2.45(5)
2.52(4)
Wilson, 2011
4
2
2
4
2
β-Pu(SO
α-Ce(SO
β-Ce(SO
β-Np(SO
β-U(SO ) (H O)
4
)
2
(H
(H
(H
(H
2
O)
4
Jayadevan, 1982
1
)
2
2
O)
4
8
Casari, 2007
4
1
)
2
2
O)
4
8
Casari, 2007
4
7
4
)
2
2
O)
4
8
Charushnikova, 2000
6
8
Kierkegaard, 1956
4
2
2
4
2
9
Th
Th(SO
Th(SO ) (H O)
3
(SO
4
)
6
(H
2
O)
6
·H
2
O
9
1.09
1.09
1.13
Wilson, 2008
1
0
4
)
2
(H O)
2
7
·2H
2
O
9
Albrecht, 2011
30
10
Habash, 1983
4
2
2
8
The actinide sulfate compounds exhibit richer chemistry than their lanthanide counterparts.
There are many more An(IV), An(V), and An(VI) sulfate compounds reported and they show
complex structures with or without the incorporation of counter cations for charge balance.
Numerous actinide sulfate monomers, dimers, chains, sheets, and frameworks have been
3
1, 32
reported.
Further calorimetric studies of these complex compounds are being carried out in
our group, in order to understand the energy landscape of the actinide sulfate materials.
5
. Conclusions
4
+
A (SO ) (H O) (A = Zr, Ce, U) with α- (Fddd) and/or β- (Pnma) forms have been
4
2
2
4
synthesized and characterized, and their thermochemical properties have been measured by high
temperature oxide melt drop solution calorimetry. The thermodynamic stabilities of these two
polymorphs show a correlation with the eightfold coordination radius of the tetravalent cations
with an energetic transition around a radius of 0.98 Å. More comprehensive calorimetric studies
are planned of the actinide sulfate materials to improve our knowledge of their rich chemistry.
Acknowledgements
1
4

ACCEPTED MANUSCRIPT
This research was supported by the Chemical Sciences, Geosciences and Biosciences Division,
Office of Basic Energy Science, Office of Science, U.S. Department of Energy, grant no. DE-
FG02-07ER15880. Calorimetry, PXRD, and TGA data were collected at the Materials
Characterization Facility in the Center for Sustainable Energy (ND Energy) at the University of
Notre Dame. ICP-OES data were collected at the Center for Environmental Science and
Technology (CEST) at the University of Notre Dame.
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