17
Materials Chemistry and Physics, 10 (1984) 425-441 425 HYDROTHERMAL PHASE EQUILIBRIA IN Ln 0 -H O-CO 2-3-2-2 SYSTEMS FOR Tm, Yb AND Lu T.R.N. KUTTY Materials Research Laboratory. Indian Institute of Science, Bangalore 560 012 (India) IFTIQHAR MOHAMED and J.A.K. TAREEN Mineralosical Institute. University of Mysore, Manasa Gangotri, Mysore 570 006 (India) Received 3 November 1983 : accepted 20 December 1983 SUMMARY Phase diagrams for Tm203-H20-C02. Yb203-H20-CO2 and Lu203-H20-CO2 systems at 650 and 1300 bars have been investigated in the tempe- rature range of lOO-8OO'C. The phase diagrams are far more complex than those for the lighter lanthanides. The stable phases are Ln(OHj3, Ln2(C03j3.3H20 (tengerite phase), orthorhombic-LnOHC03, hexagonal-Ln202C03, LnOOH and cubic-Ln 0 2 3' Ln(OH) 3 is stable only at very low partial pressures of CO2. Additional phases stabilised are Ln20(OHj2C03 and Ln6(OH)4(C03)7 which are absent in lighter lanthanide systems. Other phases, isolated in the presence of minor alkali impurities. are Ln602(0H)8(C03)3. Ln4(OH)6(C03)3 and Ln1207(OH)lo(C03)6. The chemical equilibria prevailing in these hydrothermal systems may be best explained on the basis of the four-fold classification of lanthanides. INTRODUCTION The hydrothermal method is a psomising technique for the growth of more perfect single crystals of cubic lanthanide oxides. HOW- ever uncertainty still prevails on the lanthanide oxide-lanthanide hydroxide phase boundaries due to the possible contamination of CO2 in the fluid phase. Investigations on hydrothermal phase equilibria in ternary heterogeneous systems: Ln203-H20-CO2 (Ln = lanthanide) are also pertinent to the crystal growth of lanthanide hydroxides and carbonates as well as for the synthesis of carbonate minerals 0254-0584/84/$3.00 0 Elsevier Sequoia/Printedin The Netherlands

Hydrothermal phase equilibria in Ln2O3-H2O-CO2 systems I. The lighter lanthanides

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Materials Chemistry and Physics, 10 (1984) 425-441 425

HYDROTHERMAL PHASE EQUILIBRIA IN Ln 0 -H O-CO 2-3-2-2

SYSTEMS FOR Tm,

Yb AND Lu

T.R.N. KUTTY

Materials Research Laboratory. Indian Institute of Science, Bangalore 560 012 (India)

IFTIQHAR MOHAMED and J.A.K. TAREEN

Mineralosical Institute. University of Mysore, Manasa Gangotri,

Mysore 570 006 (India)

Received 3 November 1983 : accepted 20 December 1983

SUMMARY

Phase diagrams for Tm203-H20-C02. Yb203-H20-CO2 and Lu203-H20-CO2

systems at 650 and 1300 bars have been investigated in the tempe-

rature range of lOO-8OO'C. The phase diagrams are far more complex

than those for the lighter lanthanides. The stable phases are

Ln(OHj3, Ln2(C03j3.3H20 (tengerite phase), orthorhombic-LnOHC03,

hexagonal-Ln202C03, LnOOH and cubic-Ln 0 2 3'

Ln(OH) 3 is stable only

at very low partial pressures of CO2. Additional phases stabilised

are Ln20(OHj2C03 and Ln6(OH)4(C03)7 which are absent in lighter

lanthanide systems. Other phases, isolated in the presence of

minor alkali impurities. are Ln602(0H)8(C03)3. Ln4(OH)6(C03)3 and

Ln1207(OH)lo(C03)6. The chemical equilibria prevailing in these

hydrothermal systems may be best explained on the basis of the

four-fold classification of lanthanides.

INTRODUCTION

The hydrothermal method is a psomising technique for the growth

of more perfect single crystals of cubic lanthanide oxides. HOW-

ever uncertainty still prevails on the lanthanide oxide-lanthanide

hydroxide phase boundaries due to the possible contamination of CO2

in the fluid phase. Investigations on hydrothermal phase equilibria

in ternary heterogeneous systems: Ln203-H20-CO2 (Ln = lanthanide)

are also pertinent to the crystal growth of lanthanide hydroxides

and carbonates as well as for the synthesis of carbonate minerals

0254-0584/84/$3.00 0 Elsevier Sequoia/Printedin The Netherlands

426

containing lanthanides. Some of these phases have interesting

optomagnetic properties [l-3]. Several solid phases have been

reported in these ternary ststems both from hydrothermal experi-

ments [4-121 as well as experiments carried out at low temperature

and one atmosphere pressure [13-181. Some of these phases are

found to be isostructural with minerals like bastnaesite, ancylite,

lanthanite and tengerite. Hydrothermal experiments conducted by

many of the previous workers contained solubility modifying salts

(mineralisers), with the intention of growing larger single cry-

stals. AS such, these experiments did not represent true 3-compo-

nent systems. Besides, no systematic approach was made to demar-

cate the phase boundaries and thus construct the phase diagrams.

The present authors have reported the phase equilibria in

Ln203-H20-CO2 systems for lighter lanthanides [19-201. Extending

the work to heavier lanthanides, we have noticed considerable

differences in the equilibration of stable phases. New phases are

found in the case of Tm, Yb and Lu systems. This paper deals with

the phase diagrams and characterisation of solid phases isolated

from Ln203-H20-CO2 where Ln = Tm, Yb and Lu.

EXPERIMENTAL

Tm203 (Koch-Light Laboratories, U.K.) Yb203 (Fluka A.G., Switzer-

land) and Lu203 (Sigma Chemical Co., U.S.A.) were of 99.99 percent

purity. Details of hydrothermal experiments and the maintenance

of a known mole fraction of C02(Xco ) in the fluid phase were

presented in the earlier publicatiois [9-12, 19-201. The equili-

brated phases were isolated and characterised by chemical analyses

based on microgravimetry. The products obtained after every hydro-

thermal run were identified by X-ray powder diffraction patterns

using a Philips PW 1041 diffractometer. Standard patterns of pure

phases of lighter lanthanides and X-ray data reported in the lite-

rature were used for identification. Infrared absorption spectra

were taken with a Perkin-Elmer 597 spectrometer. Morphological

observations were carried out with a Hitachi S 450 scanning

electron microscope. Equilibrated fluid phase compositions were

also monitored by chemical analyses.

427

in Fig.1. There are eight

1

RESULTS AND DISCUSSSON

Tm203-K2o_co2 system

An isobaric phase diagram of Tm203-H20-CO2 with varying partial

pressures of CO2 has been completed from 72 experimental points.

The T-Xco2 diagram at 650 bars is shown

800

i

. _____l/_

700 - %03

l 0 0 l o

Fig. 1. T-Xc0 2

diagram for the Tm203-H20-CO2 system at 650 bars.

stable phases which are common to the Gd 0 2 3-H20-CO2system, reported

earlier [203. The phases not isolated from lighter lanthanides

are Tm6(OA)4(C03)7 and Tm20fORf2CO3. The isobaric phase diagram

at 1300 bars exhibited the same set of stable phases, except that

the area of Tm(OHj3 and TmOOH are shifted to lower XC0 values.

There are eight triple-points which are invariant at 2

constant

T and P for 3-component systems. The low temperature triple-point

is around 160~~~ involving Tm(OHj3, Tm2(C03)3.3H20 and TmOOH. The

high temperature triple-point is Tm00H-Tm202C03-Tm203. Similar to

428

the phase diagrams of lighter lanthanides [19-201 the field of tri-

hydroxide is restricted to a narrow range of XC0 (up to 0.01). 2

Around 160~~ Tm(OH), converts to TmOOH and further to Tm o at 2 3

630°C in the C02-free system. As the XC0 value is increased, 2

TmOOH coexists with TmOHCO 3, Tm20(OH)2C03 and Tm202C03. At lower

temperatures, Tm(OH) 3 transforms to Tm2(C03J33H20, which is iso-

structural with the mineral tengerite [7, 181. The phase equiva-

lent to lanthanite, Ln2(C03)3.8H20, is not stabilised under hydro-

thermal conditions, though Dexpert et al. [lS, 171 have reported --

this phase from 1 atm experiments. Tm2(C03j3. 3H20 converts to

orthorombic-TmOHCO 3'

isostructural with ancylite. There is no

hydrothermal stability for hexagonal-TmOHC03 (bastnaesite-like

phase) which is prevalent in lanthanides lighter than Gd. At

higher xCO2 values ( O.l), TIII~(CO~)~.~H~O and TmOHC03 convert to

Tm6(OH)4(C03) 7. At low CO2 concentrations, TmOHCO 3

transforms to

Tm20(0H)2C03. The phase boundaries between Tm6(OH)4(C03)7, TmOHC03

and Tm20(0H)2C03are very sensitive to small variations in X co2

values and minor temperature fluctuations. The reason is evident

from isothermal sections (Fig.2). The boundaries marked with

dashed-lines are tentative, though the diagram is constructed from

data points of highest reproducibility. Within the boundary of

Tm20(OH12C03 and TmOHC03, two more phases could be isolated:

Tm602(OHlS (C0313 and Tm4(OH)6(C03)3. These phases could only be

sparingly reproduced and were found to depend on alkali ion conta-

mination in parts per million concentrations. Since these phases

may not be stable in the highly pure Tm 0 2 3-H20-C02 system, they are

not shown in Fig.1. At the higher temperature part of the T-XC0

diagram, 2

hexagonal-Tm202C03 is replaced by cubic-Tm203.

Tm202C03 has a wider range of stability as the Xc0 value approa- 2

ches 1.0 (H20-free systems).

Figures 2A to 2C show the isothermal section of Tm 0 -H20-CO 2 3 2

at 650 bars. At 150°C, Tm(OHJ3, Tm2(C0313.3H20, TmOHC03 and

Tm6(OH14(C0317 are the stable phases. Tm202C03 is barely stable

under H 0 free conditions. 2

At 350°C, these phases are replaced by

TmOOH, Tm20(0Hj2C03 and Tm202C03 (Fig.2B). At 625'C Tm202C03 and

Tm203 are the only stable phases (Fig.2C). It is evident from

Figs. 2A and 2B that the isothermal stability fieid of TmOHC03,

Tm20(OH)2C03 and Tm2(C03)3.3H20 are very narrow, so that slight

429

/ Tm,tC03)33H20\h 1

Tm203 Tm202C03 CO2 -u..n

!03 TmzO$

A”L-

(B) L :03 CO2

Tm202a3 CO2 Tm203 -

Fig.2. Ternary diagrams for Tm 0 -H20-CO 2 3 2

at 650 bars.

compositional differences in the starting material will alter the

coexisting solid phases. The tie-lines between TmOHCO 3, Tm20(0H)s

CO3 and Tm6(OH)4(C03), overlap consideraly. Hence the demarcation

of the boundaries between these phases (Fig.11 turns out to be

difficult.

yb20_3-K202 system

The isobaric T-XC0 diagram for this system at 650 bars is shown 2

in Fig.3. It compares very well, in most features, with that of

the Tm203-H20-CO2 system; the stable phases are also identical.

The striking difference is that YbOHCO 3 has a very limited stabi-

lity. It is difficult practically to maintain a narrow range in

YbOOH

Yb202C03 - II

Fig.3. T-XCO

2

diagram for the Yb203-H20-CO2 system (650 bars).

%$e~:lues ; therefore, YbOHC03 is a

for all practical purposes.

Ln6(OH)4(C0317 extends to lower X co2

non-existant phase in this

The stability field of

values. However, a new phase,

with the composition Yb1207(OH)10(C03)6 is found to be stable when

Xco2 is around 0.02 with a temperature range of 230-29O'C. The

stabilisation of this phase could not be attributed to any definite

impurity. Isolation of the other sparingly stabilised phases,

Yb602(0H)9(C03)3 and Yb4(OH)6(C03)3, could be achieved only in the

presence of alkali halides or alkali hydroxides in low concentra-

tions, as in the case of the Tm-system.

(OH) lo(C03)6 were not isolated in the Tm

is that the stability region of YbOOH is

The YbOOH-Yb203 boundary shows a minimum

Phases similar to Yb120j

system. Another difference

extended to X co2

= 0.1.

in the middle range of

vb203 “b202C03

Fig.4. Isothermal ternary sections for Yb203-H20-CO2 (1300 bars).

X co2 -

The isothermal sections (Fig.41 show the corresponding

differences at 625OC; a wider range of existence for Yb203 but not

for Yb202C03 (compare with Fig.2).

&!$03-H~o-co2 system

The stable phases

The phase diagram is

lity fields of Lu(OH

in this system are indicated in Figs. 5 and 6.

similar to that of the Yb-system. The stabi-

3 and LuOOH are restricted to lower tempera-

tures and limited compositional range. Correspondingly lowered is

the temperature of formation of Lu203. The appearance range of

LUOHCO 3

is more limited than that of YbOHCO 3'

Due to the narrow

stability of LuOOH, direct conversion of Lu202C03 to Lu203 takes

place if XC0 is greater than 0.2. Due to these differences, the 2

432

Xc02

Fig.5. T-%02

diagram for the Lu203-H20-CO2 system 1650 bars).

isothermal sections presented in Fig.6 are identical to those in

Fig.4. The polynuclear carbonate phases Lu602fOHf8(C0313 and

Lu4(OH)6(C03)3 are also found in this system when minor alkali ion

impurities are present. However, Lu 0 (OH) lo(co3)6

could not be 12 7

detected.

General Considerations

The following chemical equilibria are invol

considered above.

(i) Temperature dependent equilibria :

Ln2 ICOj) 3. 3H20 = Ln20(0H)2C03 + 2CO2 +

2LnOHC03 * Ln20(0H)2C03 + CO2

Ln20(0H12C03 = Ln202C03 * H20

LnfOHf 3 = LnOOH * H20

ved in the systems

2H20 (3.1

(2)

(3)

(4)

L"zo3 L"f12c03 co2

Lu203 CO2

Fig.6. Ternary diagrams for Lu203-H20-CO 2 (1300 bars).

2LnOOH = Ln203 + El20

(ii) %O

dependent equilibria :

2

2Ln(OHj3 + 3C02 = Ln2(C03)3.3H20

3Ln20(OHj2C03 + 4C02 + 0.5H20 = Lng(OIi)4(CO3)7

2LnOOH + CO2 = Ln20(0H12C03

(iii) Temperature and Xco2 dependent equilibria :

Ln2 (CO31 3. 3H20 = 2LnOHC03 + 2H20 + CO2

LnOOH + CO 2

= Ll-i202C03 + H20

LnOOH + CO 2

= LnOHC03

Ln6(OHj4(C03)7 = 3Ln202C03 + 4C02 + 2H20

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

434

Ln202C03 = Ln203 + CO2 (13)

Hydrothermal phase diagrams are simple for lighter lanthanides

with fewer stable phases. The complexity increases towards heavier

lanthanides; the stabilisation of several polynuclear carbonate

phases is noticed, with overlapping compositional fields of stabi-

lity which are sparingly reproducible. The compound Ln2(0H);t3_XJ

(C03)x.nH20, where 2.35X21 for La - Eu and 1.52X51 for Gd - Lu,

has been synthesised by Caro et al [14], -- through precipitation at

23OC under low CO2 pressure (10 -2

bar). Under hydrothermal condi-

tions these phases are not stable for lighter lanthanides. In Tm

to Lu systems, Ln6(OH)4(C03)7 can be considered as the limiting

case where x = 2.3. Ln4(0H)6(C03)3 can be treated as per the

formula of Caro et al [14] with x = 1.5. When x = 2, the stable --

compound is LnOHC03. Chai and Mroczkowski [B] have reported

Ln2(OH)4C03 (where Ln = Y or Er), i.e. with x = 1, from hydro-

thermal systems using6M.NH4Cl as the hydrothermal fluid. There is

strong influence of dissolved compounds (mineralisers) on hydro-

thermal fluids by modifying the equilibria in Ln203-H20-CO2 systems.

Ln2(OH)4C03 is not stabilised under mineraliser-free conditions.

The systematic variations in the stability of carbonate phases

in Ln203-H20-CO2 systems are not correlatable with the decreasing

ionic radii and consequent change in basicity of the lanthanides.

This is evident from the hydrothermally stable carbonate phases in

various lanthanide systems (Table 1). Among the heavier lantha-

nides, identical features are noticed only in the case of Tm, Yb

and Lu, indicating better coherency in hydrothermal chemistry for

these three elements, compared to the rest of the heavier lantha-

nides. It also brings out the limitation of classifying the

lanthanides as lighter and heavier members in correlating the

chemical behaviour. Better correlation is seen when a 4-fold

classification of lanthanides is considered.

Charactexisation of carbonate phases .-

Table 2 gives the chemical composition of phases not common in

lighter lanthanide systems but found only for Tm. Yb and Lu systems.

The molecular formulae calculated are given in the last column.

The agreement between the observed Ln203, II20 and CO2 contents and

the calculated (not presented) is reasonably good in all cases.

Table

1.

Hydrothermally

Stable

Carbonate

Phases

in Ln203-H20-CO2

systems

(100

- 950°C)

System

Ln202C03

hexagonal

LnOHCO

3 Ln2(C03)3.3H20

rhombkc

LnOHCO

3

Ln

6 (O

H)

4 (C

30j)

7

Ln20(OH)2C03

La203-H20-CO2

X

X

Pr203-H20-CO2

X

X

Nd203-H20-CO2

X

X

Sm2o3 -H20-co2

X

X

X

Eu203-H20-CO2

X

X

X

Gd203-A20-CO2

X

X

X

X

Tb203 -H20-CO2

X

X

X

Er203-H20-CO2

X

X

X

Tm203-H20-CO2

X

X

X

X

X

Yb203-H20-CO2

X

X

X

X

X

Lu203-H20-CO2

X

X

X

X

X

X = isolated

phases

436

Table 2. Chemical Composition of Newer Phases (wt 0)

Ln Ln203 H2° =O2 Formula assigned

Ln4(OH)6(C03) 3

Tm 77.10 2.40

Yb 77.55 2.35

LU 77.60 2.35

Tm 86.00 4.02

Yb 86.21 4.00

LU 86.50 3.91

Yb 86.92 3.30

20.50

20.10

20.05

10.01

9.83

9.62

9.84

Tm 85.10 5.31 9.68

Yb 85.33 5.18 9.57

LU 85.45 5.20 9.41

Tm 80.53 5.57 13.87

Yb 80.85 5.45 13.65

LU 81.12 5.68 13.51

The phase purity of the analysed samples was confirmed by X-ray

powder patterns, morphological studies and by infrared spectra.

Unit cell contents derived from X-ray powder patterns for the

phases identical to those from the Gd203-H20-CO2 system could be

identified and indexed by comparison. X-ray patterns of

Ln20(0H)2C03 and Ln6(OH)4(C03)7, where Ln - Tm, Yb and Lu, are

indexed in terms of monoclinic and orthorhombic unit cells.

respectively (Table 3). The reported X-ray data of Christensen

[6,7], for Y20(0Hj2C03 is found to be useful in indexi.ng the

patterns of Ln20(0H)2C03. The unit cell parameters for those two

phases are plotted against the ionic radii in Fig.7, which shows

good correlative variation. The X-ray powder patterns of Ln602(0H)6-

(C03) 3' Ln4(OH)6(C03)3 and Ln120,(OH)10(C03)6 are found to be

different from the above phases (Table 3).

Morphological observations with SEM indicated orthorhombic

symmetry for Ln6(OH)4(C03)7 with well developed domal faces.

Ln20(OH12C03 crystals are monoclinic pinacoids with penetration

type twinning. Yb1207(OH) lo(C03)6 are triclinic with well

developed prism faces. Ln602(OH)8(C03)3 has hexagonal plate

morphology; its higher symmetry is also indicated from the fewer

number of X-ray reflections in the powder patterns. Ln4(oH)6(C03) 3

has thick cylindrical morphology with corroded surfaces and rounded

corners. The crystals fozm clusters and generally indicate forma-

tion via recrystallisation of a precursor gel.

Table

3.

X-Ray

Powder

Data

of Newer

Phases

(Representative

Examples)

a = 6.195

9

Tm6(0H)4(C03),

97.50

a=

5.118

g

-

-

=

b

"A

6

Yb120,(OH~o-

Tm602(0H)8

Tm4(0Hj6

= 5.914

b = 5.988

2

(C03

) 6

(CO

31

3

c =

13.158

g

(CO

31

3

c = 9.398

%

d(g)

I

hkl

d(%

I

hkl

d(g)

I

dt%

I

d(g)

I

6.212

vvs

100

4.288

ms

110

3.200

S

014

2.987

ms

020

2.750

S

210

2.696

W

015

2.571

W

204

2.363

m

234

2.257

ms

124

2.151

ms

220

1.952

S

224

1.920

W

304

1.885

m

108

1.801

W

133

1.164

VW

034

1.722

ms

108

1.675

W

231

1.650

VW

231

1.616

W

028

1.599

W

128

6.003

W

010

4.701

vvs

002

3.874

ms

110

3.694

vvw

012

2.987

S

020

2.526

ms

022

2.471

S

004

2.262

VW

122

2.102

m

212

1.941

m

220

1.850

S

130

1.831

ms

032

1.794

S

015

L.706

m

300

1.678

m

301

1.562

VW

230

1.497

mw

040

1.428

mw

042

1.334

m

206

1.2755

m

400

1.249

VW

332

12.02

17

7.19

30

6.345

73

6.110

30

4.913

43

4.160

30

4.092

17

4.003

35

3.913

39

3.815

26

3.722

13

3.591

22

3.48

52

3.178

100

3.058

19

2.968

17

2!958

17

2.614

30

2.731

17

12.1

4.982

4.268

4.009

3.913

3.022

2.618

1.852

1.583

15 other

lines

29

9.92

20

30

9.02

98

29

6.071

100

43

5.212

37

43

5.037

13

100

4.982

15

43

4.772

10

36

4.646

95

21

4.538

6

4.228

20

4.101

17

4.018

13

3.930

20

3.769

20

3.722

22

3.655

11

3.583

10

3.415

11

3.336

16

23 other

lines

438

h

V

OQ 0

v

0a

no

oa (60

9.39

I 9.36

9.33

5.99

i 5.96

J-

. 1 I .

Tm 0.87 0::6

6.20

i 6.15

Ionic radii, 1

Fig.7. Unit cell parameters varsus ionic radii for (a)

(a) Ln20(0H)2C03 and (b) Ln6(0H)4(C03) 7- The scale on left-hand

side (Y-axis) corresponds to dotted-lines.

The infrared absorption spectra could be used to distinguish

different phases. The free-state point-symmetry (D3h) of carbonate

ion is never preserved in these solids. The site symmetry is

lowered to Cs or C2" so that the designation of Gatehouse et al. --

[21] is more useful for the absorption bands. Hexagonal Ln202C03

(Ln = Tm, Yb, Lu) exhibits infrared spectra similar to that of

vaterite (IJ - CaC03) [16]. Orthorhombic-LnOHC03 with aragonite

type structure [14] shows OH stretching bands split into two compo-

(4

(e)

I \\ I I I I I I 1 3wo 1600 1200 600

Wavenumber Ccrf?~

Flg.8. Infrared absorption spectra of (a) Yb20(OH)2C03,

(bt Lu6(OH)4(C03)7. (cl Yb1207(OH)10(C03)6, (d) Tm602(OH)8(C0313

and (e) Tm4(OH)6 (CO3) 3.

nents (Fig.Eo, with the corresponding multiplicity in the OH

librational mode. v4 and V 1 of carbonate ions are clearly split

into two bands with V -1 4

- vl% 100 cm . According to Nakamoto et al _I

[22] and Fujita et al [23], this indicates the unidentate nature

of the carbonate ion. The v2 band (totally symmetric stretch) has

a clear identity, which, in the free carbonate ion, is infrared

inactive. Deformational mode (v61r in-plane bending mode (v,) and

440

out-of-plane deformation (V6) are split into three components each.

Turcotte et al. [13] have indicated that the splitting of non- --

degenerate bands is due to the presence of more than one kind of

site in the crystal. giving rise to non-equivalent carbonate groups

in the lattice. The splitting in these non-degenerate modes thus

indicates differently oriented carbonate groups, with respect to

crystallographic symmetry axes.

The spectra of other carbonate phases, like Ln6(OH)4(C03)7 and

Ln20(OH)2C03, differ considerably in the extent of.splitting in the

OR (stretching and librational) and carbonate bands (Fi.g.8). It

may be noticed that the spectra of Yb 1207(OH)lo(C03)6, Lu602(OHj4

(C03j3 and Lu~(OH)~(CO~)~ are very complex due to bridging through

anions, as proposed by Christensen [6].

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