Thermodynamics of Cement Hydration

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UNIVERSITY OF ABERDEEN
DEPARTMENT OF CHEMISTRY




Thermodynamics of Cement Hydration
by
Thomas Matschei
Dipl.-Ing., Bauhaus University Weimar



A Thesis presented for the degree of
Doctor of Philosophy
at the University of Aberdeen


Aberdeen, 06 December 2007


Declaration



This Thesis is submitted to the University of Aberdeen for the degree of Doctor of Philosophy. It is
a record of the research carried out by the author, under the supervision of Professor F.P. Glasser. It
has not been submitted for any previous degree or award, and is believed to be wholly original,
except where due acknowledgement is made.




Thomas Matschei
Aberdeen, December 2007





Abstract 3


Abstract
The application of thermodynamic methods to cement science is not new. About 80 years ago,
Bogue wrote a series of equations describing the relationship between clinker raw meal chemical
composition and the mineralogy of the finished clinker. These enabled the amounts of minerals to
be calculated from a bulk chemical composition. Fundamental to the equations was a precise
description of the high temperature equilibrium achieved during clinkering. Bogue admitted four
oxide components into the calculation; lime, alumina, silica and ferric oxide and assumed that
equilibrium was attained (or very nearly attained) during clinkering. This approach, which is, with
modifications, still a widely used tool to quantify cement clinkering, was one of the main
motivations of this work. Thus the overall aim of this Thesis is to provide a generic toolkit, which
enables the quantification of cement hydration.
The use of thermodynamic methods in cement hydration was often doubted, as the water-cement
system was considered to be too complex. Furthermore metastable features occur, e.g. C-S-H,
which lead to the conclusion cement hydration is a “non-equilibrium” process. Nevertheless
pioneering works, by Damidot and Glasser, as well as from other groups e.g. Reardon et al. and
Berner et al. prove that cement hydration follows the basic principles of physical chemistry by
minimisation of the free energy of an isochemical system. Hence these studies demonstrated the
usefulness of thermodynamic equilibrium models in cement hydration. However the success and
the accuracy of these predictions are strongly linked to a reliable thermodynamic database,
including the standard state properties of the aqueous species and the cement hydrates.
Whereas the thermodynamic properties of the aqueous ions are well described in the literature, the
dataset for cement hydrates is incomplete or inconsistent, or both. Thus the main goal of this Thesis
was to develop a consistent thermodynamic database, which enables the assessment of the
constitution of hydrated Portland cements. Because hydrated concretes are exposed to different
service temperatures, data were obtained in the range ~1°C to 99°C. The database is developed for
commonly-encountered cement substances including C-S-H, Ca(OH)
2
, selected AFm, AFt and
hydrogarnet compositions as well as solid solutions. Literature data were critically assessed and
completed with own experiments. The tabulated thermodynamic properties were derived by a
harmonisation of the available data.
The new database enables the hydrate mineralogy to be calculated from the bulk chemical
composition of the system: most solid assemblages, the persistence of C-S-H and failure to
nucleate siliceous hydrogarnet apart, correspond closely to equilibrium. This realisation means that
hydrate assemblages can be controlled. The development of a thermodynamic approach also
enables a fresh look at how mineralogical changes occur as a function of cement composition as
well as in response to environmentally-conditioned reactions.
According to a literature review the constitution of the AFm phase in Portland cement is very
sensitive with respect to its chemical environment. Except for limited replacement of sulfate by
hydroxide, AFm phases do not form solid solutions and, from the mineralogical standpoint, behave
as separate phases. Therefore, in dependence of the bulk chemical composition, many hydrated
cements will contain mixtures of AFm phases rather than a single AFm solid solution. Relative to
previous databases, sulfate-AFm is shown to have a definite range of stability at 25°C thus
removing long-standing disagreement with theory about its persistence in hydrated cement pastes.
Carbonate is shown to interact strongly with AFm and displaces OH
-
and SO
4
2-
at species activities
Abstract 4


commonly-encountered in cement systems across a broad range of temperatures ≤50°C. Many of
the predicted reactions were confirmed by focussed experiments and literature studies.
Possible anion substitutions in the AFt phase were investigated. Non-ideal thermodynamic models
for SO
4
-CO
3
-AFt and ettringite-thaumasite solid solutions were derived from solubility
experiments. Whereas at 25°C only minor anion substitution is likely, low temperatures tend to
stabilise carbonate substituted AFt phases. Possible pathways of thaumasite formation were
developed. It was concluded that there is no single route of thaumasite formation, but several
pathways for thaumasite formation may occur simultaneously.
Limestone, mainly consisting of calcite, is a permitted additive to Portland cements up to a 5 wt.-%
limit under EN 197. The final chapter, on the impact of calcite addition upon cement hydration,
enables a quantitative approach to its interaction with cement phases and prediction of space filling
properties of pastes. The distribution of sulfate in AFt and AFm is much affected by the presence of
carbonate. In the presence of portlandite the stabilisation of carboaluminate results in changes of
the amounts of both portlandite and AFt: specimen calculations are presented to quantify these
changes. Calculations of the specific volume of solids as a function of calcite addition suggest that
the space filling ability of the paste is optimised when the calcite content is adjusted to maximise
the AFt content. Additional calculations show how sulfate and carbonate distribution are affected
by temperature. Carboaluminates become increasingly unstable at elevated temperatures, ≥ 50°C,
whereas carbonate substitution in AFt is favoured at low temperatures in the presence of calcite.
The resulting consequences of thermal cycles on the space filling properties of hydrated cements
are discussed.

Keywords: thermodynamics, thermodynamic data, modelling, cement hydration, AFm, AFt, sulfate,
carbonate

Acknowledgement 5



Acknowledgement


Several people contributed to the successful completion of this Thesis,
to whom I am grateful and indebted:

Professor Fred Glasser for his excellent supervision of this project during my time in Aberdeen. I
am most grateful for the advice and support he gave me throughout the duration of this Thesis. I
enjoyed our long-lasting, motivating and academically stimulating discussions, mainly related to
cement -surely one of the most fascinating manmade materials of this world-, but also to several
other aspects of “daily life”.
Dr. Barbara Lothenbach, EMPA Dűbendorf, my Thesis co-supervisor, for invaluable assistance
with questions about thermodynamic modelling and guidance with GEMS-PSI. Her enthusiasm
contributed to the completion of the database and related applications.
My industrial advisors, Dr. Ellis Gartner, Lafarge Central Research, France, and Dr. Duncan
Herfort, Aalborg Portland Group, Denmark, for stimulating discussions and guidance during this
work.
Nanocem, a research network of European cement producers and academic institutions, for funding
this work and for giving me the opportunity to present and discuss the results at several intern
meetings as well as at international conferences. Special thanks to Professor Karen Scrivener,
representing members of Nanocem and the Nanocem steering-committee, for valuable discussions
and helpful critics during the preparation of publications related to this Thesis. I would like to
thank Marie-Alix Dalang-Secrétan for her help with administration throughout this project and for
assistance with the preparation of the Workshop “Thermodynamic Modelling”.
Dr. Dmitrii Kulik, PSI, Switzerland, for troubleshooting and assistance with GEMS-PSI and for
helpful advice during the preparation of the thermodynamic database. In that respect I would also
like to thank Dr. John Gisby, NPL, UK, for his comments.
The staff of the Chemistry Department, University of Aberdeen, for technical assistance. I would
like to thank Professor Jőrg Feldmann and his TESLA-team for invaluable guidance and
introduction in “analytical methods for civil engineers” as well as for giving me the opportunity to
participate in “various” group meetings. Thanks to Professor Donald Macphee for inspiring
discussions about cement science, especially with respect to thaumasite formation. I enjoyed the
refreshing discussions with the recently formed “cement-group” as well as with my colleagues
from office “G 85”.
The staff at EMPA Dűbendorf, for great technical and intellectual support during my stay in
Switzerland.
I would like to thank my examiners, Professor Denis Damidot, Ecole des Mines de Douai, France,
and Professor Donald Macphee, University of Aberdeen, for critically reviewing this work.






















Finally, special thanks go to


Kristina,… for her infinite patience with this “cement guy”

my friends, whose support I appreciated throughout the years

ein besonderes Dankeschőn gebűhrt meiner Familie in Deutschland, insbesondere meinen Eltern,
Grosseltern, sowie allen Verwandten, die mich űber Jahre hinweg trotz mancher privater
Rűckschläge uneigennűtzig mit viel Geduld und Aufmunterung unterstűtzt und einen
entscheidenden Anteil am erfolgreichen Abschluss dieser Arbeit haben
.


Table of contents 7



Abstract .............................................................................................................................3
Acknowledgement................................................................................................................5
1. Introduction..............................................................................................................10
2. Status of database development..............................................................................11
3. Analytical methods...................................................................................................12
3.1.

Preparation of samples..........................................................................................................12

3.2.

X-ray diffraction....................................................................................................................12

3.3.

Thermal analysis...................................................................................................................12

3.4.

Microscopic examinations.....................................................................................................13

3.5.

Analysis of solutions.............................................................................................................13

3.5.1

Calcium, aluminium and sodium...........................................................................................13

3.5.2

Sulfate ...............................................................................................................................13

3.5.3

Silicon ...............................................................................................................................14

3.5.4

Carbon ...............................................................................................................................14

3.5.5

Measurement of pH...............................................................................................................14

4. Development of a thermodynamic database for cement hydrates......................15
4.1.

Synthesis of relevant cement hydrates..................................................................................15

4.1.1

Hydrogarnet...........................................................................................................................15

4.1.2

AFm phases...........................................................................................................................16

4.1.3

AFt phases.............................................................................................................................17

4.2.

Solubility determinations......................................................................................................18

4.3.

Methods used to derive and manipulate thermodynamic data..............................................19

4.3.1

Software and standard databases...........................................................................................19

4.3.2

Estimation of heat capacity...................................................................................................19

4.3.3

Solubility based estimation of standard molar thermodynamic properties...........................21

4.3.4

Thermodynamics of solid solutions and the use of Lippmann phase diagrams....................23

4.4.

Results...................................................................................................................................27

4.4.1

Hydrogarnet...........................................................................................................................27

4.4.2

AFm phases...........................................................................................................................30

4.4.3

AFt phases.............................................................................................................................41

4.4.4

C-S-H ...............................................................................................................................44

4.5.

Discussion.............................................................................................................................46

4.5.1

Data accuracy........................................................................................................................46

4.5.2

Relations between equilibrium and kinetics..........................................................................48

4.5.3

Applications of the database..................................................................................................49

4.6.

Concluding remarks..............................................................................................................52

Table of contents 8


5. The AFm phase in Portland cement.......................................................................53
5.1.

Literature review...................................................................................................................53

5.1.1

General remarks on the structure and formation of AFm phases..........................................53

5.1.2

Stability of AFm phases........................................................................................................54

5.1.3

Solid solutions between AFm phases....................................................................................56

5.1.4

Summary and conclusions from the literature.......................................................................59

5.2.

Preparation of solid solutions................................................................................................61

5.3.

Formation of AFm phases and AFm solid solutions.............................................................62

5.3.1

Monosulfoaluminate-hydroxy-AFm solid solutions.............................................................62

5.3.2

Monosulfoaluminate-monocarboaluminate...........................................................................73

5.3.3

Monocarboaluminate-hydroxy-AFm.....................................................................................74

5.4.

Ternary phase relations between sulfate-, carbonate- and hydroxy-AFm.............................75

5.4.1

Metastable phase assemblages at 25°C.................................................................................75

5.4.2

Stable phase assemblages at 25°C.........................................................................................76

5.5.

Discussion of the results........................................................................................................78

5.5.1

Extent of solid solution.........................................................................................................78

5.5.2

Transformation mechanisms.................................................................................................79

5.5.3

Solubility data and its interpretation.....................................................................................79

5.6.

Conclusions...........................................................................................................................80

6. The AFt phase in Portland cement.........................................................................82
6.1.

State of the art of science......................................................................................................82

6.1.1

General remarks on the structure and composition of AFt....................................................82

6.1.2

Solid solutions between AFt phases......................................................................................83

6.1.3

The formation of thaumasite and related solid solutions.......................................................84

6.2.

Solid solutions between sulfate- and carbonate-AFt.............................................................87

6.2.1

Synthesis of solid solutions and investigations of the solid phase........................................87

6.2.2

Thermodynamic modelling of the solid solution formation..................................................88

6.3.

Investigations on thaumasite.................................................................................................92

6.3.1

The need for investigations...................................................................................................92

6.3.2

Synthesis of thaumasite.........................................................................................................92

6.3.3

The temperature-dependent stability of thaumasite in aqueous solutions.............................94

6.3.4

Solid solution formation between ettringite and thaumasite...............................................100

6.4.

Formation of thaumasite and ettringite solid solutions in hydrated cements......................104

6.4.1

Carbonate substitution in SO
4
-AFt at 25°C.........................................................................104

6.4.2

Phase assemblages including thaumasite and related solid solutions..................................106

6.5.

Discussion...........................................................................................................................112

6.5.1

Interpretation of phase diagrams.........................................................................................112

6.5.2

Formation of AFt solid solutions.........................................................................................112

6.5.3

Pathways of thaumasite formation......................................................................................114

Table of contents 9


7. The influence of limestone addition on cement hydration.................................116
7.1.

Literature review.................................................................................................................116

7.1.1

Limestone addition to Portland cement...............................................................................116

7.1.2

Influence of temperature on the mineralogy of hydrated (limestone blended) Portland
cement: 25°C and above......................................................................................................118

7.2.

Implications of limestone addition to cement hydration.....................................................121

7.2.1

Experiments on the role of carbonate and sulfate on C
3
A hydration..................................121

7.2.2

Phase relations between AFt-AFm phases relevant to Portland cements at 25°C...............124

7.2.3

“Reactive” vs. “filler” calcite..............................................................................................128

7.2.4

Quantification of phases......................................................................................................131

7.2.5

Space filling by cement paste solids....................................................................................133

7.2.6

Composition of the aqueous phase......................................................................................135

7.3.

Applicability to Portland cement systems...........................................................................136

7.3.1

Experimental validation of phase changes..........................................................................136

7.3.2

Space filling vs. engineering properties..............................................................................139

7.4.

The role of temperature on Portland cement hydration.......................................................142

7.4.1

Thermally induced mineralogy changes..............................................................................142

7.4.2

Space filling vs. temperature...............................................................................................148

7.4.3

Experimental verification of thermally induced phase changes..........................................151

7.4.4

Summary.............................................................................................................................160

7.5.

Discussion...........................................................................................................................161

7.5.1

Limitations of the methodology and of the database...........................................................161

7.5.2

Kinetic factors: availability of sulfate, carbonate and alumina in the course of hydration.166

7.5.3

Volume changes..................................................................................................................168

7.5.4

Thermally induced phase changes.......................................................................................169

8. Summary and conclusions.....................................................................................171
8.1.

Thermodynamic quantification of cement hydration..........................................................171

8.2.

Implications for cement hydration......................................................................................172

References.........................................................................................................................174
Abbreviations...................................................................................................................187
Nomenclature in cement chemistry................................................................................................187

Abbreviations used in calculations.................................................................................................187

Other abbreviations........................................................................................................................188

Figures and Tables...........................................................................................................189
Figures ......................................................................................................................................189

Tables ......................................................................................................................................194

Appendix .........................................................................................................................195

Introduction 10


1. Introduction
One of the unsolved problems in the application of Portland cement is to quantify the performance
lifetimes of concrete constructions. The problem affects nuclear waste containments and,
increasingly, long-lived infrastructure developments where quantification has failed to keep pace
with the expectation of stakeholders.
Although a wealth of empirical evidence on the performance of historic concretes information on
their formulation is available, emplacement and exposure history is often incomplete and,
moreover, the nature of cements supplied today will almost certainly have changed since the
original construction. Empirical studies and historic examples have however yielded much useful
qualitative information on the aggressivity of various service environments. Numerous tests and
test methods have been used as indicators of durability but they do not yield generic conclusions
and their predictive capabilities are limited. As a consequence, designers of long-lived
constructions have at present to rely on received wisdom, as interpreted by experts and
incorporated into codes of practice.
The changing nature of cements is also of concern. Cement producers are under pressure to lower
the specific energy requirements of cement production and reduce gaseous emissions. These goals
are presently addressed by a combination of methods; partly by optimisation of process technology,
including the use of alternative fuels and raw materials (the effect of which are beyond the scope of
this study), and partly by reliance on supplementary cement materials to lessen the need for energy-
rich cement. Although the use of supplementary materials is generally regarded as beneficial in
terms of strength and durability as, for example highlighted by developments in cement and
concrete standards, long term performance is not fully understood. Supplementary materials
presently in use include industrial by-products such as slag, fly ash, silica fume, etc. as well as
natural materials, e.g. ground limestone, natural pozzolanic and semi-synthetic pozzolans such as
metakaolin. Each of these materials has a complex but distinctive chemistry, mineralogy and
granulometry. Moreover, each type of material ranges in composition and performance. Studies of
their behaviour in blended cements under controlled conditions are confined to selected
compositions and short term (1-5 years) laboratory measurements, perhaps supplemented by
observations on actual constructions, for which conditions may not be well controlled.
The complexity of blended cement systems and the wide-ranging nature of supplementary
cementing materials have meant that guesses -sometimes well informed- have to be made at the
outset about what aspects of behaviour should be studied. But the number and complexity of the
resulting systems are such that results are often confined to measurement of a few of the many
parameters affecting performance. Arguably the most serious question arising from the results of
empirical testing is how to extend or extrapolate the results to other compositions and formulations,
or to conditions other than those measured, or both. At present one cannot address these issues,
except qualitatively.
If quantification of performance is to be achieved, a new paradigm is needed and a key to the
development of a successful paradigm must be to concentrate on generic approaches.
Thermodynamics provides a consistent framework for the analysis of complex systems. Given an
adequate database to support calculations, its strength lies in its generic nature; user-defined
compositions and conditions can be selected for calculation. This realisation is not new although
previous attempts to apply thermodynamics have had only limited success.
Introduction 11


From an industrial point of view it could be argued that thermodynamic approaches to cement
durability are too theoretical and the calculations too difficult to perform. However, the latter is no
longer true: geochemists, faced by similar problems of treating complex systems, have developed
and validated computer-based protocols capable of being implemented on a PC. Thus reliable
protocols are available, many of which are in the public domain. Furthermore these protocols often
couple to other modules, for example, enabling mass to be conserved in the course of reaction
while maintaining a system of balanced equations. Selected physical properties can also be
calculated, for example by enabling the specific volumes occupied by the constituent solid phases
of mixtures to be tabulated.
Thermodynamics is most readily applied to isochemical systems, i.e., to systems having a constant
composition, whereas many cement deterioration reactions involve transport of species into or out
of the matrix (or both). But computer-based calculations also enable more complex conditions to be
imposed on the system.
It is not argued that the primary output achieved by application of thermodynamic methods
necessarily enables the durability and performance of cements and concretes to be quantified. But it
is believed that, in the search for quantification, a sound quantitative understanding of cement paste
mineralogy and of the ability to calculate features and processes arising from the interaction of
cement with potentially aggressive agents introduced from the environment, with additional
possibilities for calculating physical functions and the introduction of kinetic variables, constitutes
a great step forward. Other necessary links to develop integrated models of cement performance
will be anticipated in the discussion.
2. Status of database development
After years of development, Babushkin et al. published the first reasonably comprehensive
compilation of thermodynamic data for cement substances. Their book [12] also gives numerous
application examples but, as these are pre-computer, the examples selected for calculation tend to
be rather simplistic and at first sight, do not afford significant advance over empirical conclusions.
However a serious problem is that referenced data in this compilation have proved difficult if not
impossible to trace to source.
Other databases adding to our knowledge of cement substances have been produced subsequently,
e.g., by Atkins et al. [9][10][21], Damidot [44], Reardon [158][159], Lothenbach and Winnefeld
[125] by the Lawrence Livermore National Laboratory [38] and by ANDRA, the French National
Agency for Radioactive Waste Management [30]. Studies of phase equilibria, cited subsequently in
the text, have also added data on the thermodynamic properties of specific substances.
Experimental studies have shown that temperature is an important parameter with respect to the
formation of phase assemblages in the course of cement hydration. Pioneering calculations by
Damidot et al. [43][44][45][46][47][48][49] disclosed that thermodynamics enables to understand
phase transitions due to temperature changes as well as due to changes of the chemical
composition. Returning to the present state of development of performance-based thermodynamic
models, calculation is handicapped by lack of a consistent database applicable to a wide range of
temperature and cement compositions. Thus the aim of this work was to make progress towards the
development of a database which is sufficiently reliable and inclusive to sustain and support
calculations as well as experiments.
Analytical methods 12


3. Analytical methods
A programme of the acquisition of thermodynamic data was undertaken. This involved synthesis,
characterisation, analysis and data integration. New data were obtained through synthesis of phase
pure substances with subsequent solubility measurements. Focussed experiments were designed to
substantiate calculated results in the course of application of the database.
3.1.
Preparation of samples
Cement hydrates are generally very sensitive to decomposition by carbonation. Therefore many
syntheses and solubility experiments must be performed under N
2
-atmosphere to minimise access
of atmospheric CO
2
. Generally, if not stated otherwise, the synthesised solids, aged and stored in
inert HDPE or PTFE ware, have been vacuum-filtered with Whatman #540 filter paper and washed
several times with ultra pure degassed water to remove alkalis, if present. Subsequently the solids
were dried over saturated CaCl
2
solution at 37% r.h. for 2 weeks. Immediately before X-ray
analysis a light disaggregation of the dried solids was necessary, using an agate mortar, to obtain a
homogeneous powder.
Solutions were obtained by filtration of 15 ml aliquots (30 ml for carbon determination) of the
excess solution through a 0.22 μm alkali-resistant MF-millipore membrane syringe filter unit. Part
of the solution (10 ml) was acidified with 1 ml 0.1 M HCl for cation analysis; the remainder was
used to measure pH and determine anions, e.g. sulfate or carbonate. Solutions awaiting analysis
were stored briefly in polypropylene (PP) centrifuge tubes.
3.2.
X-ray diffraction
Mineralogical examination of the dried solid was made by X-ray diffractometry (XRD) using a
P
ANALYTICAL
X’P
ERT
P
RO
diffractometer with CuKα-radiation at room temperature, ~25°C; the
angular scan was between 5-80° 2θ with a step size of 0.02 and a count time of 1 s per step.
To characterise products of the temperature-dependent reactions in cementitious systems (chapter
7) a B
RUKER
D8
ADVANCE
powder diffractometer was used for X-ray analysis. XRD-data of the
samples have been collected using CuKα radiation at room temperature, ~25°C. The angular range
was set between 5-40° 2θ with a step size of 0.04 and a count time of 2 s per step. Powder samples
were filled sideways to the sample holder to minimise preferred orientation effects, particularly
important for samples containing platy crystals, e.g. AFm and/or portlandite.
3.3.
Thermal analysis
A simultaneous TGA-SDTA apparatus TGA/SDTA

851 by M
ETTLER
-T
OLEDO INC
. was used for
thermal analysis. Simultaneous TGA/SDTA collects complex thermo- and differential-thermo-
gravimetric weight changes (TGA and DTG) as well as thermal effects (DTA) during heating of
the sample. In the current investigations thermal analysis was used to determine the state of
hydration of the investigated solids. Furthermore significant weight losses during thermal
decomposition may be used for identification and distinction of the solids in phase mixtures. The
observed temperature range was between 30°C to 980°C; the rate of heating was 10°C/min. All
measurements were done in N
2
-atmosphere.
Analytical methods 13


3.4.
Microscopic examinations
An environmental scanning electron microscope (ESEM) FEI XL 30 was used for microscopic
observations. In contrast to ordinary SEMs, no additional sample preparation, e.g. coating, was
necessary and samples could be investigated in a defined gas atmosphere. Thus the possibilities of
experimental artefact formation, e.g. changes of morphology due to coating and dehydration, were
reduced. In the current work the GSE (gaseous secondary electron) or BSE (back scatter electron)
detectors were used for observations in a low vacuum water vapour atmosphere (pressure: ~1
Torr). The acceleration voltage was 10 to 25 kV depending on the investigated sample.
3.5.
Analysis of solutions
3.5.1 Calcium, aluminium and sodium
Aqueous calcium, aluminium and sodium were analysed by atomic absorption spectrometry using a
V
ARIAN
S
PECTR
AA 10 flame AAS. A nitrous oxide / acetylene flame was used for calcium and
aluminium and an air / acetylene flame for sodium. Calcium was measured at a wavelength of
422.7 nm. Aluminium was determined at a wavelength of 309.3 nm whereas sodium was analysed
at 589 nm. Standards were prepared from 1000 mg/l T
ITRISOL
(VWR chemicals). A linear
calibration curve for calcium was obtained in the range from 0 - 5 mg Ca
2+
/l and for sodium from
0 - 2.5 mg Na
+
/l; 2500 mg K
+
/l, as analytical grade KCl, was added to suppress ionisation. Due to
minor sodium impurities in KCl the analytical limit of detection of sodium was ~0.5 mg Na
+
/l. For
calcium and sodium analysis samples were diluted with 2500 mg K
+
/l solution to suppress
ionisation prior to analysis. Aluminium was usually measured in undiluted samples; no further
suppressing agents were added. Standards for aqueous aluminium calibration were prepared in the
range between 0-100 mg Al
3+
/l. High calcium concentrations (~400 mg Ca
2+
/l) may interfere with
aluminium determinations. To evaluate this matrix effect, a standard of 40 mg Al
3+
/l was diluted by
a factor of 2 with a saturated Ca(OH)
2
-solution (initial concentration 850 mg Ca
2+
/l). The
subsequently measured Al
3+
concentration, 17.4 mg/l, was slightly lower than the theoretical
reference value of 20 mg/l. A sensitivity analysis has shown that the analytical errors from this
slight depression do not significantly affect the subsequent thermodynamic calculations.
3.5.2 Sulfate
Aqueous sulfate concentrations were determined by ion chromatography with a D
IONEX
DX-120
IC. An ion exchange analytical column I
ON
P
AC
AS 4A 4mm equipped with a guard column was
fitted for sulfate analysis. The analyte was injected into a 25 μl sample loop; the applied pressure
was set between 1000-1100 psi (67-74 bars). The eluent used was 1.8 mM Na
2
CO
3
/ l.7 mM
NaHCO
3
. The eluent conductivity was suppressed by an ASRS Ultra self regenerating suppressor
with deionised water (> 18 MΩ cm) regenerant. The chromatograph had a linear calibration in the
range 0-10 mg SO
4
2-
/l and standards were prepared from 1000 mg SO
4
2-
/l T
ITRISOL
solution. The
achieved detection limit was ~0.25 mg SO
4
2-
/l at a background activity of ~14 μS. Due to low SO
4
2-

concentrations, most measurements were taken on undiluted samples and the mean value of three
independent analyses used to minimise the analytical error.
Analytical methods 14


3.5.3 Silicon
A spectrophotometric method based on the molybdenum blue method was adopted to determine the
silicon concentration: Ramachandran and Gupta

[156]. A C
AMSPEC
301 spectrophotometer was
used for the measurements. The optimum wavelength for silicon determination was 810 nm.
Standards were prepared from 1000 mg Si
4+
/l T
ITRISOL
solution. A linear calibration was achieved
in the range from 0 to 5 mg Si
4+
/l.
3.5.4 Carbon
Carbon was analysed using a LABTOC Analyser by PPM. Ultra-violet-promoted persulphate
oxidation is used to determine the contamination of dissolved organics present in the sample. The
content of total inorganic carbon (TIC) was determined as difference from the concentrations of
total carbon (TC) and total organic carbon (TOC) present in the solution. TC was first determined
as the sum of TIC- and TOC-content. In a second step, TOC was determined from the catalytically
oxidised CO
2
. Inorganic carbonates were automatically removed by sample pre-treatment using an
acid sparge. A sample with reagent was then injected in to the reaction vessel, the vessel being
continuously sparged by a carrier gas (typically nitrogen), to liberate any CO
2
gas generated
through oxidation. The resulting evolved CO
2
is delivered to an infrared detection system. The CO
2

plot is integrated and compared against a calibration curve to determine the reportable value. The
detection limit for a reliable TIC measurement using this method is ~ 1 mg/l; problems arose due to
the low concentrations of TIC in the solutions. In most cases the concentrations of carbon in
solution were lower than the limit of detection. Thus it was decided to estimate the values with the
help of thermodynamic calculations based on assumed equilibria with phases with known
thermodynamic properties, e.g. calcite.
3.5.5 Measurement of pH
The pH was measured by a M
ETTLER
T
OLEDO
system equipped with a combination pH electrode
I
N
L
AB
413 for simultaneous determination of pH and temperature of the solution. The pH-meter
was calibrated with a 3-point calibration with pH 4.01, 7.00 and 9.21 buffers (at 25°C).
Additionally calibration was checked with a saturated Ca(OH)
2
solution (pH~12.48 at 25°C) as an
external buffer. The pH was automatically corrected by the pH-meter for the measured
temperature. To minimise carbonation effects, the pH was measured immediately after filtration of
the sample solutions.
Development of a thermodynamic database for cement hydrates 15


4. Development of a thermodynamic database for cement hydrates
A thermodynamic database will include many substances for which standard compilations already
provide adequate data: it is not necessary to start totally afresh. For example, the thermodynamic
properties of water and of many aqueous ions and complexes are well known. Database
development focussing on cements is therefore mainly concerned with the properties of solids that
are abundant in cements but uncommon or absent in nature. Thus a comprehensive database can be
compiled by focussing on relatively few substances.
4.1.
Synthesis of relevant cement hydrates
The synthesis of the relevant cement hydrates required several solid precursors. These were made
from analytical grade (AR) reagents. C
3
A was prepared from a 3:1 molar ratio of CaCO
3
and
Al
2
O
3
. The Al
2
O
3
had a high fineness, d
max
< 10 μm, to enhance its reactivity. To eliminate
adsorbed water, the Al
2
O
3
and the CaCO
3
were dried previously at 950°C or 100°C overnight,
respectively. The starting materials were mixed to a homogeneous paste with water in an agate
mortar. A sufficient viscosity was necessary to avoid segregation. Afterwards the mixture was
dried for 2 hours at 50°C. Then it was placed in a platinum crucible and heated to 950°C in a
muffle furnace to decarbonate the CaCO
3
. After 4 hours the temperature was increased to 1400°C
for another 6 hours. Then the sintered material was cooled down, ground to a fineness < 75 μm and
reheated to 1400°C for 6-10 hours. This procedure was repeated at least four times. Afterwards the
material was checked for purity by XRD. No significant impurities e.g. free lime, CaO, were found
following the described procedure.
Lime, CaO, was obtained from decarbonation of analytical grade CaCO
3
at 900°C overnight. The
purity was checked by XRD and showed no impurities. Due to its sensitivity to hydration and
carbonation only freshly prepared CaO was used.
Anhydrite, CaSO
4
, was used as sulfate source in the experiments. It was prepared by dehydration of
gypsum in a muffle furnace at 750°C for 5 hours.
4.1.1 Hydrogarnet
“Hydrogarnet” is usually defined in the cement literature as the silicon-free composition
Ca
3
Al
2
(OH)
12
. However silicon is a main constituent of Portland and blended Portland cements and
the existence of solid solution between katoite, Ca
3
Al
2
(OH)
12
, and grossularite, Ca
3
Al
2
Si
3
O
12
, is
well-known both in the laboratory and from natural occurrences. Siliceous hydrogarnet thus
impacts significantly on silicon distribution in cements. To enable thermodynamic calculations,
two different compositions were synthesised. Ca
3
Al
2
(OH)
12
was prepared by mixing previously
synthesised C
3
A with boiling water and subsequent ageing at 105°C in sealed PTFE bottles for 7
days. A siliceous composition was also prepared with the target composition Ca
3
Al
2
SiO
4
(OH)
8
,
starting

from stoichiometric amounts of

CaO, Na
2
Si
2
O
5
⋅2H
2
O, NaAlO
2
and water. A slurry of
Na
2
Si
2
O
5
⋅2H
2
O and NaAlO
2
was prepared with an appropriate amount of water. In a separate
operation, CaO was suspended in boiling ultra pure water and the slurry containing mixed
Na
2
Si
2
O
5
⋅2H
2
O, NaAlO
2
added. Subsequently the preparation was aged for 4 weeks with periodic
agitation at 105°C in sealed PTFE bottles until filtration.
Development of a thermodynamic database for cement hydrates 16


Fig. 4.1: Estimation of the silicon-content of siliceous hydrogarnet; data marked PDF are from the Powder
Diffraction File. Data not marked were obtained in the course of the title study (solid compounds). The
composition of the synthesised solid solution (open diamond) is estimated by fitting to the curve shown by a
dashed line.
A literature review showed that the synthesis and characterisation of siliceous hydrogarnet is more
complicated than the silicon-free variant. Jappy, et al. [95] synthesised hydrogrossular solid
solutions Ca
3
Al
2
(SiO
4
)
3-x
(OH)
4x
and encountered two different hydrogarnet phases in most
preparations. A miscibility gap was postulated to exist at low silica substitutions. However in the
title study, one synthesis yielded a single hydrogarnet phase. According to subsequent XRD
analysis this solid solution had a lower silicon-content than the target composition,
Ca
3
Al
2
SiO
4
(OH)
8
. Its silicon-content was estimated assuming a linear relation of the unit cell lattice
parameter between C
3
AH
6
(a
0
~12.58 Å, PDF 24-217) and grossular, Ca
3
Al
2
(SiO
4
)
3
(a
0
~11.85 Å,
PDF 39-368). The unit cell size of the synthetic (a
0
= ~12.39 Å) was calculated by refining its
XRD-pattern by least squares minimisation on 14 reflections with the software C
ELREF
using
silicon, a
0
= 5.4308 Å as an internal standard (see Fig. 4.1). Accordingly, its formula was corrected
to Ca
3
Al
2
(SiO
4
)
0.8
(OH)
8.8
. The XRD-pattern also contained reflections attributed to C-S-H and most
of the “missing” silica and part of the alumina are believed to be present as minor C-S-H impurity.
4.1.2 AFm phases
Although the stability relations of the AFm phases are known to be sensitive to temperature, few
relevant data are available. To enable an estimation of thermodynamic data, the following
preparation route yielded suitable material. “Monosulfoaluminate”, Ca
4
Al
2
(SO
4
)(OH)
12
∙6H
2
O,
becomes more stable at temperatures > ~40°C. So a 1:1 molar mixture of C
3
A and CaSO
4
was
suspended at 100°C in initially ultra pure water and thereafter kept at 85°C for 7 days to synthesise
phase pure monosulfoaluminate.
“Monocarboaluminate”, Ca
4
Al
2
(CO
3
)(OH)
12
∙5H
2
O, was prepared by mixing C
3
A and CaCO
3
in a
1:1 molar ratio with previously degassed ultra pure water at 25°C and stored with agitation in
HDPE-bottles for 14 days until filtration at 25°C. A second source of monocarboaluminate was
prepared by mixing stoichiometric amounts of CaO, CaCO
3
and gibbsite (Al(OH)
3
) with a 0.1 M
KOH solution. The suspension was agitated periodically and stored at 50°C for 4 weeks, with
subsequent washing.
0
1
2
3
11.8 11.9 12 12.1 12.2 12.3 12.4 12.5 12.6
Unit cell size [Å]
Garnet silicon content [mol]
grossular (C
3
AS
3; PDF 1-74-1087
)
C
3
AH
6 (PDF 24-217)
sil. hydrogarnet (C
3
AS
1.25
H
3.5; PDF 45-1447
)
hibbschit e (C
3
AS
2
H
2; PDF 1-73-1654
)
sil. hydrogarnet (C
3
AS
0.8
H
4.4
)
hibbschit e (C
3
AS
2.3
D
1.4; PDF 1-84-2016
)
hibbschit e (C
3
AS
2
H
2; PDF 31-250
)
Development of a thermodynamic database for cement hydrates 17


“Hemicarboaluminate”, Ca
4
Al
2
(CO
3
)
0.5
(OH)
13
∙5.5H
2
O, was made by addition of C
3
A, CaCO
3
and
CaO in stoichiometric quantities to previously degassed ultra pure water at 25°C and stored in
HDPE-bottles to achieve a successful synthesis. The mixture was aged with stirring for 14 days
before filtration.
C
4
AH
x
, Ca
4
Al
2
(OH)
14
⋅xH
2
O, was synthesised according to the method of Atkins et al. [9]. C
3
A was
mixed with CaO in a 1:1 molar ratio at 5°C using degassed ultra pure water (w/s ~ 10). Afterwards
the preparation was stirred for 72 hours and periodically agitated, still at 5°C. After 3 weeks at 5°C
the solid was vacuum filtered under N
2
-atmosphere.
Several methods for the preparation of strätlingite, Ca
2
Al
2
SiO
2
(OH)
10
⋅3H
2
O are described in the
literature (e.g. sol-gel, preparation from glasses, etc.). These routes were pursued but the best
preparations were obtained by starting from a stoichiometric mix of CaO, Na
2
Si
2
O
5
⋅2H
2
O, NaAlO
2

and water (w/s ~ 10) at 25°C. First, all chemicals were separately suspended in ultra pure water at
25°C. The slurry containing sodium aluminate solution was added to the previously prepared
portlandite solution with stirring. Finally the sodium silicate solution was added and the resulting
suspension stirred for 4 weeks at 25°C prior to filtration. HDPE-bottles were used in all stages of
the preparation. Unlike other cement hydrates, which are uniformly white, the strätlingite
preparation had a pale bluish colour.
4.1.3 AFt phases
The preparation and determination of the solubility of SO
4
-AFt, ettringite, has been the subject of
numerous investigations [8][9][147][192]. The literature data show generally good agreement and
it was therefore concentrated on its less well characterised carbonate analogue, CO
3
-AFt or
“tricarboaluminate”, Ca
6
Al
2
(CO
3
)
3
(OH)
12
⋅26H
2
O, which was synthesised using a modification of
the method of Carlson and Berman [36] by precipitation from a stoichiometric mixture of CaO,
NaAlO
2
and Na
2
CO
3
in a 10% w/v sucrose solution. The previously-prepared slurries of sodium
aluminate and sodium carbonate were added to the sucrose-portlandite mixture (total w/s ~ 10),
stirred for 3 days and periodically agitated at 25°C until filtration after ~ 2 weeks.
Development of a thermodynamic database for cement hydrates 18


4.2.
Solubility determinations

Solubility determinations were made at various temperatures between 5°C and 105°C. Two series
of reaction mixtures were prepared to derive solubility data for katoite, Ca
3
Al
2
(OH)
12
. In the
experiment from undersaturation, previously synthesised dry Ca
3
Al
2
(OH)
12
powder was redispersed
in water (water/solid-ratio ~ 30) at 25°C and then stored in HDPE-bottles (at temperatures < 70°C)
or PTFE-bottles (at temperatures ≥ 70°C) isothermally at well-spaced intervals between 5°C to
105°C prior to analysis. In a second series, a slurry of Ca
3
Al
2
(OH)
12
, prepared from C
3
A as
described at 105°C, was divided into several samples with the aid of a syringe. The sample bottles
(HDPE or PTFE) were then filled with boiled water, sealed under N
2
-atmosphere and slowly
cooled to the desired temperature and held for ~ 4 weeks prior to analysis. The water/solid mass-
ratio of the second set of samples was deliberately set to ~ 1000 to enable direct comparison with
the results of Wells et al. [193], which were also obtained at this ratio.
Experiments were conducted from both super- and undersaturation for monosulfoaluminate,
monocarboaluminate and hemicarboaluminate at temperatures between 5°C and 110°C. Stoichio-
metric mixtures of C
3
A with either CaSO
4
or CaO and CaCO
3
(see paragraph 4.1) were used at
various temperatures in experiments from supersaturation (water/solid-ratio ~ 30). Solubilities from
undersaturation were determined by redispersing previously synthesised and characterised single
phase solids in ultra pure degassed water (water/solid-ratio ~ 30). The samples were analysed after
4 - 6 weeks reaction time in both cases. Additionally a second dataset for hemicarboaluminate at
25°C was generated by reaction of monocarboaluminate with synthetic C
4
AH
13
(previously
prepared at 5°C) at a 1:1 molar ratio (water/solid-ratio ~ 30): complete reaction at 25°C required ~
3 weeks.
The synthesis of siliceous hydrogarnet, strätlingite and the second source of monocarboaluminate
required the addition of alkalis and synthesis was thus achieved at high aqueous pH. Most of the
alkalis could be removed by flushing the filtrates several times with ultra pure degassed water prior
to drying. Residual alkali contents are commented subsequently. Solubilities determined from
undersaturation were obtained by redispersing powders of each mineral in ultra pure, degassed
water (water/solid-ratio ~ 30) and undertaking analyses at well-spaced time intervals.
Development of a thermodynamic database for cement hydrates 19


4.3.
Methods used to derive and manipulate thermodynamic data
4.3.1 Software and standard databases
Chemical thermodynamic modelling consists of calculating the chemical speciation (i.e. amounts
or concentrations of chemical components in all phases present in equilibrium state) from total bulk
composition of the system and thermodynamic data for components. In the GEM (Gibbs free
energy minimisation) method and GEMS-PSI code [109], the total Gibbs energy of the system is
minimised at given temperature and pressure; accordingly, for each component, the standard molar
Gibbs energy at the temperature of interest must be provided. Calculations require a database of
thermodynamic properties of components (substances), a correct statement of the problem, and a
solver of chemical equilibria. In this work GEMS-PSI [109] was used - a software package
including a GEM solver, a built-in thermodynamic database [93] and a graphical user interface for
easy extension of the thermodynamic database to user-defined “projects”. This was convenient
because not all cement minerals are included in standard databases such as Nagra-PSI [93] supplied
within GEMS-PSI package. This database was initially designed in “logK format” for application
to codes that use law of mass action algorithms at standard conditions (1bar and 25°C); to include it
in GEMS, the logK values were converted into standard molar Gibbs energies and merged with the
slop98.dat database [96][172], which was originally developed for the SUPCRT92 code [96]. For
aqueous species, this dataset is based on the HKF (Helgeson-Kirkham-Flowers) equation of state
which can be used to calculate temperature and pressure corrections up to 1000°C and 5 kbar; the
necessary parameters for aqueous species relevant for cementitious systems are given in [172][179]
and are summarised in Table A.1. The heat capacity coefficients needed for temperature
corrections for most of the minerals in the GEMS databases are also given in the slop98.dat dataset.
The database, included in the current software package, GEMS version 2.2, is documented in [184]
and is in the public domain
[93][96][172]. Raw data for minerals obtained in the title study have
been converted into standard molar thermodynamic properties and added to the GEMS-PSI
database in order to perform modelling calculations. Temperature corrections for thermodynamic
properties of condensed substances (e.g. minerals) used in GEMS are based on the well known
standard integration of the heat capacity function (e.g. [143]) as discussed below.
4.3.2 Estimation of heat capacity
The heat capacity function for solids (at constant pressure) was calculated according to Eq. 4.1
where a
0
, a
1
, a
2
and a
3
are empirically derived, temperature independent parameters characteristic of
each solid.

5.0
3
2
210
o
TaTaTaaCp
−−
+++=

(4.1)
The heat capacities can be measured experimentally or, as was done here, estimated by using a
reference reaction with a solid having a known heat capacity and similar structure. As shown by
Helgeson et al. [89], this principle was successfully applied to estimate the heat capacity of silicate
minerals by formulating a reaction involving a structurally-related mineral of known heat capacity.
Gu et al. [86] used a similar approach to predict equilibrium constants for reactions related to
aqueous species. Nevertheless, Helgeson et al. [89] pointed out that this method has limitations due
to the differing thermodynamic properties of “water”, variously bound loosely as hydrate water or
structurally, as OH-groups. To minimise errors associated with the varying strengths of bonding for
“water”, care was taken to formulate reference reactions so as not to involve “free” water as a
substituent in reactions unless appropriate to do so. Table 4.1 shows the coefficients to determine
the heat capacity of reference solids to estimate heat capacity data of the relevant cement hydrates.
Development of a thermodynamic database for cement hydrates 20


Table 4.1: Standard molar thermodynamic properties of cement hydrates at 25°C, 1 bar
Phase log K
S0
Δ
f
G
0

Δ
f
H
0
S
0
a
0
a
1
a
2
a
3

II
Ref

[kJ/mol]

[kJ/mol] [J/(mol⋅K] [J/(mol⋅K)] [J/(mol⋅K
2
)] [J⋅K/mol] [J/(mol⋅K
0.5
)] [cm
3
/mol
]

hydrogarnet
C
3
AH
6
-20.84 -5010.1 -5540 419 292
I
0.561
I
0 0 150
t.s.
C
3
AS
0.8
H
4.4
-29.87 -5368.0 -5855 369 109 0.631 -1.95e+06 2560 143
t.s.

AFt
C
6
AsH
32
-44.90 -15205.9 -17535 1900 1939
I
0.789
I
0 0 707 [123]
C
6
AcH
32
-46.50 -14565.7 -16792 1858 2042 0.558 -7.78e+06 0 650
t.s.

AFm
C
4
AsH
12
-29.26 -7778.5 -8750 821 594
I
1.168
I
0 0 309
t.s.

C
4
AcH
11
-31.47 -7337.5 -8250 657 618 0.982 -2.59e+06 0 262
t.s.

C
4
Ac
0.5
H
12
-29.13 -7336.0 -8270 713 664 1.014 -1.30e+06 -800 285
t.s.

C
4
AH
13
-25.40 -7326.6 -8300 708 711 1.047 0 -1600 274
t.s.

C
2
AH
8
-13.56 -4812.8 -5433 438 392 0.714 0 -800 184
t.s.

C
2
ASH
8
-19.70 -5705.1 -6360 546 438 0.749 -1.13e+06 -800 216
t.s.

C-S-H
jennite-type
(C
1.67
SH
2.1
)
-13.17 -2480.8 -2723 140 210 0.120 -3.07e+06 0 78
III
[123]
tobermorite -
type
(C
0.83
SH
1.3
)
-8.0 -1744.4 -1916 80 85 0.160 0 0 59
III
[123]
supplementary data
water (H
2
O) -237.2 -286 70 75 0 0 0 18 [93]
CAH
10
-7.50 -4622.4 -5320 501 151 1.113 0 3200 194
t.s.

SiO
2
(amorph) -848.9 -903 41 47 0.034 -1.13e+06 0 29
IV
[104]
gypsum (CaSO
4
⋅2H
2
O) -1797.8 -2023 194 91 0.318 0 0 75
IV
[93]
anhydrite (CaSO
4
) -1322.1 -1435 107 70 0.099 0 0 46
IV
[93]
portlandite (Ca(OH)
2
) -897.0 -985 83 187 -0.022 0 -1600 33
IV
[93]
lime (CaO) -604.0 -635 39 49 0.004 -6.53e+05 0 17
IV
[93]
calcite (CaCO
3
) -1129.2 -1207 93 105 0.022 -2.59e+06 0 37
IV
[93]
gibbsite (Al(OH)
3
) -1151.0 -1289 70 36 0.191 0 0 32
IV
[93]
clinker phases
C
3
S -2784.3 -2931 169 209 0.036 -4.25e+06 0 73 [12]
β-C
2
S -2193.2 -2308 128 152 0.037 -3.03e+06 0 52 [12]

C
3
A -3382.3 -3561 205 261 0.019 -5.06e+06 0 89 [12]

C
4
AF -4786.5 -5080 326 374 0.073 0 0 130 [12]

t.s. - data obtained in title study


I
see Ederova et al. [57]
II
calculated from unit cell parameters given in Taylor [180] if not
stated otherwise
III
see Lothenbach et al. [123]
IV
see GEMS-PSI-dataset [93][184]
Development of a thermodynamic database for cement hydrates 21


Table 4.2: Reference reactions used to estimate unknown heat capacities of cement minerals
Phase Formula and reference reaction

Siliceous
hydrogarnet
Ca
3
Al
2
(SiO
4
)
0.8
(OH)
8.8
+ 1.6 Ca(OH)
2
 Ca
3
Al
2
(OH)
12
+ 0.8SiO
2
+ 1.6CaO
Monocarboaluminate
Ca
4
Al
2
(CO
3
)(OH)
12
∙5H
2
O + 0.5CaSO
4
⋅2H
2
O + 0.5CaSO
4
 Ca
4
Al
2
(SO
4
)(OH)
12
∙6H
2
O +
CaCO
3

Hemicarboaluminate
Ca
4
Al
2
(CO
3
)
0.5
(OH)
13
∙5.5H
2
O + 0.25CaSO
4
⋅2H
2
O + 0.75CaSO
4
 Ca
4
Al
2
(SO
4
)(OH)
12
∙6H
2
O +
0.5CaCO
3
+ 0.5Ca(OH)
2

Hydroxy-AFm Ca
4
Al
2
(OH)
14
∙6H
2
O + CaSO
4
 Ca
4
Al
2
(SO
4
)(OH)
12
∙6H
2
O + Ca(OH)
2

C
2
AH
8
2Ca
2
Al
2
(OH)
10
∙3H
2
O + CaSO
4
 Ca
4
Al
2
(SO
4
)(OH)
12
∙6H
2
O + Ca(OH)
2
+ 2Al(OH)
3

CAH
10
CaAl
2
(OH)
8
⋅2H
2
O + CaSO
4
+ 2Ca(OH)
2
 Ca
4
Al
2
(SO
4
)(OH)
12
∙6H
2
O
Strätlingite
2Ca
2
Al
2
SiO
2
(OH)
10
⋅3H
2
O + CaSO
4
 Ca
4
Al
2
(SO
4
)(OH)
12
∙6H
2
O + 2SiO
2
+ Ca(OH)
2
+
2Al(OH)
3

Tricarboaluminate Ca
6
Al
2
(CO
3
)
3
(OH)
12
∙26H
2
O + 3CaSO
4
 Ca
6
Al
2
(SO
4
)
3
(OH)
12
∙26H
2
O + 3CaCO
3


The coefficients of the heat capacity function (Eq. 4.1) of the relevant cement hydrates were
calculated according to reference reactions given in Table 4.2. Experimentally-determined heat
capacities by Ederova and Satava [57] and data from the built-in GEMS database [93][184] were
used as the basis for the estimation of the unknown coefficients (see Table 4.1). Analogue
structures were used in the calculations, e.g. for “unknown” AFm phases monosulfoaluminate was
used as the model. Assuming the reference reaction Eq. 4.2; Eq. 4.3 shows the principle way of
calculating the necessary coefficient, a
n,A,
for component A with the aid of the known coefficients
a
n,B
and a
n,C
with y moles of component B and z moles of component C.
A  yB + zC
(4.2)
a
n,A
= y⋅a
n,B
+ z⋅a
n,C

(4.3)

Table 4.1 summarises the resulting coefficients and estimated standard heat capacities at 25°C and
1 bar pressure calculated from Eq. 4.1.

4.3.3 Solubility based estimation of standard molar thermodynamic properties
Explanation of the basic principles of the formulation, calculation and manipulation of solubility
products is given in textbooks [143]. In this Thesis, activity coefficients of the relevant species
were calculated using the extended Debye-Hűckel Eq. 4.4:

bI
IB1
IAz
log
i
2
i
i
+
α+


(4.4)
where γ
i
is the activity coefficient of ion i, A and B are Debye-Hűckel solvent parameters dependent
on the dielectric constant of water and temperature, z
i
is the ionic charge, α
i
is a parameter
dependent on the size of ion, i, taken from [93][184]; b is a semi-empirical parameter (~0.064 at
25°C) and I is the effective ionic strength. Aqueous ion activities and speciation were calculated
using the GEMS database appropriate to the particular calculation. Finally, temperature-dependent
solubility products were calculated from the activities obtained according to the dissolution
reactions in Table 4.3.
Development of a thermodynamic database for cement hydrates 22


Table 4.3: Dissolution reactions used to calculate solubility products
The Gibbs energy of reaction Δ
r
G
0
T
at temperature T was computed using Eq. 4.5:

T
0
Tr
KlnRTG −=Δ
(4.5)
where R = 8.31451 J/(molK) is the universal gas constant and K
T
is a thermodynamic equilibrium
constant (=equilibrium solubility product) at a given temperature.
From the solubility products calculated at each temperature, the standard molar thermodynamic
properties of each solid were computed with the help of GEMS-PSI using the built-in three-term
temperature extrapolation [106][108] to obtain a temperature-dependent “logK” function, which
was fitted to the previously calculated solubility products. This function was estimated using Eq.
4.6 and the relationships shown in Eqns. 4.6 to 4.12.

TlnATAAKlog
3
1
20T
++=

(4.6)
and

[
]
)Tln1(CpS
R
4343.0
A
0
0
0
T
r
0
0
Tr
0
+Δ−Δ⋅=
(4.7)

)TCpH(
R
4343.0
A
0
0
0
T
r
0
0
Tr2
Δ−Δ⋅−=
(4.8)

0
0
T
r3
Cp
R
4343.0
A Δ⋅=
(4.9)

0
0
0
T
r
0
0
Tr
0
Tr
T
T
lnCpSS Δ+Δ=Δ
(4.10)

)TT(CpHH
0
0
0
T
r
0
0
T
r
0
Tr
−Δ+Δ=Δ
(4.11)

0
Tr
0
Tr
0
Tr
STHG Δ−Δ=Δ
(4.12)
Mineral Dissolution reaction
C
3
AH
6
Ca
3
Al
2
(OH)
12


3Ca
2+
+2AlO
2
-
+ 4OH
-
+ 4H
2
O
Siliceous hydrogarnet Ca
3
Al
2
(SiO
4
)
0.8
(OH)
8.8


3Ca
2+
+2AlO
2
-
+ 0.8HSiO
3
-
+ 3.2OH
-
+ 2.4H
2
O
Monosulfoaluminate Ca
4
Al
2
(SO
4
)(OH)
12
∙6H
2
O → 4Ca
2+
+2AlO
2
-
+ SO
4
2-
+ 4OH
-
+ 10H
2
O
Monocarboaluminate Ca
4
Al
2
(CO
3
)(OH)
12
∙5H
2
O → 4Ca
2+
+2AlO
2
-
+ CO
3
2-
+ 4OH
-
+ 9H
2
O
Hemicarboaluminate Ca
4
Al
2
(CO
3
)
0.5
(OH)
13
∙5.5H
2
O → 4Ca
2+
+2AlO
2
-
+ 0.5CO
3
2-
+ 5OH
-
+ 9.5H
2
O
C
4
AH
13
Ca
4
Al
2
(OH)
14
∙6H
2
O → 4Ca
2+
+2AlO
2
-
+ 6OH
-
+ 10H
2
O
C
2
AH
8
Ca
2
Al
2
(OH)
10
∙3H
2
O → 2Ca
2+
+2AlO
2
-
+ 2OH
-
+ 7H
2
O
CAH
10
CaAl
2
(OH)
8
∙6H
2
O → Ca
2+
+2AlO
2
-
+ 10H
2
O
Strätlingite Ca
2
Al
2
SiO
2
(OH)
10
⋅3H
2
O

2Ca
2+
+2AlO
2
-
+ HSiO
3
-
+ OH
-
+7H
2
O
Tricarboaluminate (CO
3
-AFt) Ca
6
Al
2
(CO
3
)
3
(OH)
12
∙26H
2
O

6Ca
2+
+2AlO
2
-
+ 3CO
3
2-
+ 4OH
-
+ 30H
2
O
Ettringite (SO
4
-AFt) Ca
6
Al
2
(SO
4
)
3
(OH)
12
∙26H
2
O → 6Ca
2+
+2AlO
2
-
+ 3SO
4
2-
+ 4OH
-
+ 30H
2
O
Jennite-type C-S-H Ca
1.67
SiO
2
(OH)
3.33
⋅0.43H
2
O

1.67Ca
2+
+ HSiO
3
-
+ 2.33OH
-
+ 0.43H
2
O
Tobermorite-type C-S-H Ca
0.83
SiO
2
(OH)
1.67
⋅0.5H
2
O

0.83Ca
2+
+ HSiO
3
-
+ 0.67OH
-
+ 0.5H
2
O
Development of a thermodynamic database for cement hydrates 23


The heat capacity effect of reaction, Δ
r
Cp
0
T
= Δ
r
Cp
0
T
0

= Δa
o
, was assumed to be constant over the
temperature range 0-100°C. Two parameters were adjusted to obtain a best visual fit to the
experimental data:
1) Δ
r
G
0
T
at the reference state (25°C and 1 bar pressure) was estimated according to Eq. 4.5 using
the experimentally-derived solubility product at 25°C.
2.) Δ
r
H
0
T
at the reference state was estimated to obtain the best visual fit between extrapolated
solubility products according to Eq. 4.6 and calculated solubility products from experimentally-
derived solubilities.
Δ
r
S
0
T
was subsequently calculated using Eq. 4.12. Then the related standard molar thermodynamic
properties were calculated according to dissolution reactions given in Table 4.3 using standard state
properties of the aqueous species Table A.1 and the earlier estimated parameters Δ
r
G
0
T,
Δ
r
H
0
T
and
Δ
r
S
0
T
. Combined with previously estimated Cp(T) coefficients (Table 4.1) and the known HKF
parameters of the aqueous species, the individual temperature dependency of Cp(T) was
subsequently calculated for each hydrate phase. Thus, in a final step, the solubility products were
recalculated by GEMS using built-in parts of the S
UPCRT
92 program [96] to derive temperature-
dependent values. Differences arising between the first approach, using the three-term temperature
extrapolation with assumed constant Δ
r
Cp
0
T,
and the second calculation, taking into account
temperature-dependent heat capacity coefficients according to Table 4.1 and using values from the
GEMS standard database [93][184], are marginal and lie within limits of other errors over the
temperature range 0 to ~100°C [106].
To check the internal consistency of the thermodynamic database, the experimentally-derived
solubility data were predicted using the derived thermodynamic database and the observed phase
assemblages. This seems like a circular argument and indeed is not intended to prove that the data
are correct, only to demonstrate that internal self-consistency was achieved. Generally the best
agreement between recalculated and experimental solubility data of AFm, AFt and hydrogarnet
phases was observed by suppressing the formation of gibbsite in the computations. The
experimentally-derived solubility data for each phase are also listed in the appendix A of this
Thesis, leaving the reader free to perform other calculations, if desired.
4.3.4 Thermodynamics of solid solutions and the use of Lippmann phase diagrams
Solid solutions are frequently encountered in cementitious systems. The molar Gibbs free energy
ΔG
ss
of a solution between different end members i can be calculated according to Eq. 4.13:

M
0
if
i
iss
GGXG Δ+Δ=Δ

(4.13)

)KlnKlnX(RTGGG
ssiiexidM
−=Δ+Δ=Δ

(4.14)



iiid
XlnXRTG
(4.15)


γ=Δ
iiex
lnXRTG
(4.16)
Development of a thermodynamic database for cement hydrates 24


The first term of Eq. 4.13 describes the free energy of a mechanical mixture of the end members i
of the solid solution and is calculated using the mole fraction X
i
= n
i
/Σn
i
(n
i
is the mole amount of
the end member i; ΣX
i
= 1) and Δ
f
G
i
0
- the standard molar Gibbs energy of formation of end
member i. The second term of Eq. 4.13 expresses the molar Gibbs energy of mixing, ΔG
M
for a
given composition of the solid solution series and is computed according to Eq. 4.14 as the sum of
the Gibbs energy of mixing of an ideal solid solution, ΔG
id
, and the excess Gibbs energy of mixing,
ΔG
ex
, for the solid solution. ΔG
id
is calculated as described in Eq. 4.15 (with R, the universal gas
constant, and T as the temperature of interest). The excess Gibbs energy of mixing, ΔG
ex
, is only
needed to compute thermodynamic properties of non-ideal solid solutions and can be calculated
according to Eq. 4.16, where γ
i
is the activity coefficient of the end member i. In the case of an
ideal solid solution, all γ
i
equal 1 and thus ΔG
ex
= 0. In the title study, an ideal solid solution model
(ΔG
ex
= 0) was used to describe the thermodynamic properties of single phase calcium-silicate-
hydrate (C-S-H). A more detailed explanation of this solid solution model can be found in [104].
As shown in Eq. 4.14, ΔG
M
can be calculated independently, from the deviation of a linear function
of the sum of the partial solubility products K
i
of the end members i of the solid solution and the
actually calculated solubility product K
ss
of the solid solution at stoichiometric saturation as
described by Glynn [80].
Several cementitious phases form non-ideal solid solutions, but only over a limited range of
compositions. Hence, miscibility gaps will be observed. In the case of non-ideal mixing the Gibbs
energy of the solid solution, ΔG
ss
, is calculated with Eq. 4.13 and the activity coefficients γ
i
≠ 1 and
the excess Gibbs energy of mixing, ΔG
ex
, of a binary solid solution are calculated according to Eq.
4.17:

)lnXlnX(RTG
2211ex
γ+γ=Δ
(4.17)
where X
1
= n
1
/(n
1
+n
2
) and X
2
= n
2
/(n
1
+n
2
) (n
1
and n
2
are the amounts of end members; X
1
+X
2
=1).
The GEMS-PSI code has several built-in functions for non-ideal solid solutions [105]. In this
Thesis, a semi-empirical model first suggested by Guggenheim and later developed by Redlich and
Kister [80][81][82] was used to estimate the excess Gibbs free energy function of non-ideal binary
solid solutions (Eq. 4.18):

...))XX(a)XX(aa(RTXXG
2
212211021ex
+−+−+=Δ
(4.18)
The empirical interaction parameters a
0
, a
1
, … are dimensionless. As shown by Glynn [81],
knowledge of two fitting parameters a
0
and a
1
is sufficient to estimate the excess Gibbs energy
function with reasonable accuracy. The activity coefficients γ
i
of the end members i can be derived
by fitting a
0
and a
1
to Eq. 4.18 and estimated according to Eqns. 4.19 and 4.20:

[
]
)XX3(aaXln
2110
2
21
−+=γ
(4.19)

[
]
)XX3(aaXln
1210
2
12
−−=γ
(4.20)
In the title study, the software MBSSAS [81] was used to derive the fitting parameters a
0
and a
1

based on experimentally-observed compositional boundaries of the miscibility gap in the binary
solid solution series. A detailed description of MBSSAS is given in [81]: Kersten [101] applied a
similar approach to estimate thermodynamic data for C-S-H.
Development of a thermodynamic database for cement hydrates 25


Lippmann phase diagrams
Lippmann [120][121][122] developed a mathematical algorithm to construct phase diagrams to
display all possible equilibrium states of a binary solid solution B
1-x
C
x
A and its related aqueous
phase composition. The diagrams are based on the law of mass action equilibrium according to
Eqns. 4.21 and 4.22 ([81][82]):

BABABA
XK]A][B[ γ=
−+

(4.21)


CACACA
XK]A][C[ γ=
−+

(4.22)

where [A
-
], [B
+
], [C
+
] are the aqueous activities of the ionic species A
-
, B
+
and C
+
; K
BA
and K
CA
are
the solubility products of the end members BA and CA of the binary solid solution series; X
BA
and
X
CA
are the mole fractions of BA and CA in the solid and γ
BA
and γ
CA
are the activity coefficients
of the BA and CA members of the solid solution series; γ
BA
and γ
CA
are calculated according to
Eqns. 4.19 and 4.20 respectively, with X
1
= X
BA
and X
2
= X
CA
.
To enable the construction of this phase diagram Lippmann [121] introduced the “total solubility
product” ΣΠ as sum of Eqns. 4.23 and 4.24 and it is expressed as follows:

])C[]B]([A[
++−
+=Π


(4.23)
or
CACACABABABAsd,eq
XKXK γ+γ=Π


(4.24)
Eq. 4.24 is used to derive the
solidus
curve of a Lippmann diagram in dependence of the solid-
phase composition of the solid solution series.
To enable a complete description of the binary solid solution aqueous solution (SSAS) system a
mathematical function needs to be derived to relate the aqueous composition to the “total solubility
product” ΣΠ. Thus Lippmann [121] derived the
solutus
-equation according Eq. 4.25:








γ
+
γ


CACA
aq,C
BABA
aq,B
sl,eq
K
X
K
X
1

(4.25)
where X
B,aq
and X
C,aq
are the “aqueous activity fractions” [82][121] of the substitutable species B
+

and C
+
calculated according to Eqns. 4.26 and 4.27:



γ
=
+
=
++
+
sd,eq
BABABA
aq,B
XK
]C[]B[
]B[
X

(4.26)



γ
=
+
=
++
+
sd,eq
CACACA
aq,C
XK
]C[]B[
]C[
X

(4.27)
As stated by Glynn [81] the activity coefficients γ
BA
and γ
CA
are dependent on the solid-phase
composition (compare with Eqns. 4.19 and 4.20) and therefore are not a function of the aqueous
phase composition except in the case of an ideal solid solution with γ
BA
= γ
CA
= 1.
Development of a thermodynamic database for cement hydrates 26


To enable the construction of a Lippmann phase diagram the dimensionless parameters a
0
and a
1

have to be derived to calculate the activity coefficients γ
BA
and γ
CA
according to Eqns. 4.19 and
4.20. Glynn [81] developed the software MBSSAS which uses the previously described
mathematical relations to calculate thermodynamic equilibrium states of binary SSAS systems and
to construct Lippmann phase diagrams. In dependence of the input parameters, MBSSAS is able to
calculate the fitting parameters a
0
and a
1
or computes the location of miscibility gaps if the fitting
parameters are estimated. In cement science MBSSAS was applied by Kersten [101] to estimate
thermodynamic data for C-S-H. Further information about the software and possible applications
are given in [80][81][82][101][105].
In the current work MBSSAS was used to calculate the fitting parameters based on experimentally-
estimated compositional boundaries of the miscibility gap in different binary solid solution series.
Lippmann diagrams were used to refine the parameters a
0
and a
1
to experimentally-derived
solubility data. A more detailed description and an example of the use of Lippmann phase diagrams
will be given in chapter 5.3.1.
Development of a thermodynamic database for cement hydrates 27


6 8 10 12 14 16 18 20 22 24 26 28 30 32

[2
Θ
Cuk
α
]
500 counts
all main peaks hydrogarnet (C
3
AH
6
)
Mc - Monocarboaluminate
Intensity
5 degC
25 degC
105 degC
Mc
C
2
AH
8
Mc
4.4.
Results
Table 4.1 (chapter 4.3.2) summarises all thermodynamic data obtained in this study as well as
thermodynamic data of supplementary phases needed to estimate the data of the cement hydrates.
The following paragraphs explain in detail the determination of standard molar thermodynamic
properties of the individual cement hydrates.
4.4.1 Hydrogarnet
C
3
AH
6
, Ca
3
Al
2
(OH)
12

As shown in Fig. 4.2, no significant changes of mineralogy occurred in the temperature range from
25°C to 105°C amongst the solid samples commencing from undersaturation: C
3
AH
6
was the only
crystalline phase detected by XRD. However at 5°C small amounts of C
2
AH
8
and monocarboalu-
minate were present. Whereas the formation of monocarboaluminate is an artefact, probably due to
CO
2
contamination of the sample during preparation, formation of C
2
AH
8
seems to be favoured at
low temperatures. Table A.2 (appendix A) shows the results of the solubility experiments for
C
3
AH
6
; the solubilities of calcium and aluminium remain little-changed over the range studied.
Thus the observed decrease of pH with rising temperature results mainly from the temperature-
dependent change of the ion product of water. The mean aqueous ratios of Ca:Al, ~ 3 : 2, indicate
congruent dissolution; comparable solubilities derived from super- and undersaturation are very
similar. No significant solubility changes occurred between 28 and 84 days, suggesting that a
steady state was reached within 28 days.
Fig. 4.3 shows the evolution of calculated solubility products using solubility data from different
sources including those obtained in the title study. In the low temperature range, from 0°C to 50°C,
considerable data scatter is obvious. Although apparently comparable experimental conditions were
used, older solubility data published by Wells et al. [155][193] and by D’Ans et al. [51][52] differ
significantly from those obtained in the title study. Possible reasons for the disagreement with
Wells et al. are discussed in chapter 4.5. On the other hand, the solubility products calculated from
other available literature sources
[8][9][32][35][139][162] agree well with the dataset within
analytical accuracies.
Fig. 4.2: Comparison of XRD-patterns of C
3
AH
6
following annealing at 5°C, 25°C and 105°C (approach
from undersaturation)
Development of a thermodynamic database for cement hydrates 28



The resulting standard molar thermodynamic properties of C
3
AH
6
are summarised in Table 4.1.
The data agree well with those reported by Babushkin et al. [12] (Δ
f
G
0
= -5014.1 kJ/mol, Δ
f
H
0
=
-5548 kJ/mol) as well as with experimentally-determined Δ
f
H
0
by Berman [23] (Δ
f
H
0
~ -5561
kJ/mol) and Schönitz et al. [168] (Δ
f
H
0
~ -5551.5 kJ/mol): all lie within the expected range of
analytical errors.
Fig. 4.4 shows the recalculated temperature-dependence of calcium and aluminium solubilities
from C
3
AH
6
redispersed in pure water using the experimental conditions described in paragraph
4.3.3. The calculated data show good agreement with averaged measured concentrations.
Consideration of other solubility data (see Fig. 4.3), especially values at lower temperatures, results
in slightly lower concentrations compared to the data obtained in this Thesis. Hydrogarnet was
predicted as the only stable CaO-Al
2
O
3
-H
2
O solid at this composition over the temperature range
from 5 to 100°C at 1 bar pressure.
Siliceous hydrogarnet, Ca
3
Al
2
(SiO
4
)
0.8
(OH)
8.8

As shown in Fig. 4.5, phase pure siliceous hydrogarnet could not be synthesised using the
procedure described in 4.1.1. Small amounts of a C-S-H phase, coprecipitated during the initial
synthesis of siliceous hydrogarnet, persisted at all temperatures between 5°C to 85°C despite three
dispersions in the course of solubility experiments. As noted in section 4.1.1, it is likely that the
siliceous hydrogarnet had a lower silicon-content than the target. Thus provisional solubility
products were calculated using the composition estimated from XRD data, Ca
3
Al
2
(SiO
4
)
0.8
(OH)
8.8
.
Table A.3 shows provisional solubility data for the siliceous hydrogarnet. Comparison with the
C
3
AH
6
data shows that silica substitution leads to a significant reduction of solubility, indicating
stabilisation of the hydrogarnet phase by silica substitution. The calculated solubility products of
siliceous hydrogarnet are considerably lower than those of C
3
AH
6
.

Fig. 4.3: Calculated solubility products of C
3
AH
6
from
solubility experiments (lines show calculated results