Dr. Kimberly Kurtis

School of Civil Engineering Georgia Institute of Technology Atlanta, Georgia

Portland Cement Hydration

3CaO•SiO2

2CaO•SiO2

3CaO•Al2O3

4CaO•Al2O3•Fe2O3

CaCO3 (limestone)

2SiO2•Al2O3 (clay, shale)

Fe2O3 (iron oxide)

SiO2 (silica sand)

~ 1450oC

Clinker

Finished interground

cement

Cement Composition

Gypsum +

CaO•SO3•2H2O

Kiln
Cement Composition

+ impurities (K, Na, Mg, etc)

• the presence and 

substitution (e.g., Na+ for 

Ca2+) of impurities can lead 

to polymorphism, structural 

“holes”, and greater reactivity

Cement Hydration

Hydration - chemical combination of cement and water

Two primary mechanisms:

Through solution - involves dissolution of anhydrous compounds to their ionic 

constituents, formation of hydrates in solution, and eventual precipitation due 

to their low solubility

Topochemical - or solid-state hydration - reactions take place directly at the 

surface of the anhydrous cement compounds without going into solution
Cement Hydration

When water is added to cement, what happens?

• Dissolution of cement grains

• Growing ionic concentration in “water” (now a solution)

• Formation of compounds in solution

• After reaching a saturation concentration, compounds precipitate out 

as solids (“hydration products”)

• In later stages, products form on or very near the surface of the 

anhydrous cement

Al+3

Al+3

Al+3

Ca+2

Ca+2

Ca+2

OHOHOHSiOSiOCement Hydration
Cement Hydration

Taylor, Cement Chemistry

Cement Hydration

C4AF 4%

C3A 7%

C2S 32%

C3S 54%

C4AF 0%

C3A 17%

C2S 30%

C3S 52%

Image Credit: Bentz at NIST
Cement Hydration

Because the hydration rates of the 4 key phases 

vary considerably, properties like

• time to stiffening

• setting time

• hardening rate

will vary with cement composition.

Cement Hydration

Taylor, Cement Chemistry
Cement Hydration

0 20 40 60 80 100

Time (days)

0

10

20

30

40

50

Compressive Strength (MPa)

2,000

4,000

6,000

8,000

10,000

0

60

70

Compressive Strength (psi)

C3A+CSH2

C4AF+CSH2

C2S

C3S

Compressive Strength development in pastes of 

pure cement compounds (Mindess et al, 2003)

 Hydrates & hardens rapidly

 Responsible for initial set and early strength

Tricalcium silicate 

(alite)

C3S

Properties of Hydrated Cement Compounds
 Hydrates & hardens slowly

 Contributes to later age strength (beyond 7 days)

Dicalcium silicate 

(belite)

C2S

 Hydrates & hardens rapidly

 Responsible for initial set and early strength

Tricalcium silicate 

(alite)

C3S

Properties of Hydrated Cement Compounds

 Liberates a large amount of heat during first few 

days

 Contributes slightly to early strength development

 Cements with low %-ages are more resistant to 

sulfates

C Tricalcium aluminate 3A

 Hydrates & hardens slowly

 Contributes to later age strength (beyond 7 days)

Dicalcium silicate 

(belite)

C2S

 Hydrates & hardens rapidly

 Responsible for initial set and early strength

Tricalcium silicate 

(alite)

C3S

Properties of Hydrated Cement Compounds
 Reduces clinkering temperature

 Hydrates rapidly but contributes little to strength

 Colour of hydrated cement (gray) due to ferrite 

hydrates

Tetracalcium

aluminoferrite

(ferrite)

C4AF

 Liberates a large amount of heat during first few 

days

 Contributes slightly to early strength development

 Cements with low %-ages are more resistant to 

sulfates

C Tricalcium aluminate 3A

 Hydrates & hardens slowly

 Contributes to later age strength (beyond 7 days)

Dicalcium silicate 

(belite)

C2S

 Hydrates & hardens rapidly

 Responsible for initial set and early strength

Tricalcium silicate 

(alite)

C3S

Properties of Hydrated Cement Compounds
0 5 30 1 2 6 1 2 7 28 90

Minutes Hours Days

Amount

0 5 30 1 2 6 1 2 7 28 90

Minutes Hours Days

Amount

Porosity

CH

Ettringite
0 5 30 1 2 6 1 2 7 28 90

Minutes Hours Days

Amount

Porosity

CH

Ettringite

C-S-H

0 5 30 1 2 6 1 2 7 28 90

Minutes Hours Days

Amount

Porosity

CH

Ettringite

C-S-H

C-(A,F)-H
0 5 30 1 2 6 1 2 7 28 90

Minutes Hours Days

Amount

Porosity

CH

Ettringite

C-S-H

C-(A,F)-H

Monosulfate

Cement Hydration

•Is the chemical combination of cement and water to form hydration 

products

•Takes time

•May not proceed to 100% completion

Formation of hydration products over time leads to:

•Stiffening (loss of workability)

•Setting (solidification)

•Hardening (strength gain)

Let’s look at the hydration reactions in more detail...
Hydration of the Calcium Silicates

2C3S + 7H → C3S2H8 + 3CH ∆H=-500J/g

2C2S + 7H → C3S2H8 + CH ∆H=-250J/g

•Both produce C-S-H and CH as reaction products

•C2S produces less CH (important for durability in sulfate rich 

environments)

•More heat is evolved during C3S hydration

•C3S hydration is more rapid, contributing to early age strength 

(2-3h to 14 days)

•C2S hydration occurs more slowly to contributing to strength 

after ~7-14 days.

Hydration of the Calcium Silicates

Like most chemical reactions, the rate of cement 

hydration is influenced by temperature.
C-S-H

•Calcium silicate hydrate

•C/S varies between 1.1-2; ~1.5 is typical

•H is even more variable

•Structure ranges from poorly crystalline to 

amorphous - highly variable and poorly 

understood

•Occupies 50-60% of the solid volume of the 

hydrated cement paste (hcp)

•Huge surface area (100-700 m2/g)

•Strength due to covalent/ionic bonding 

(~65%) and Van der Waals bonding (~35%) 

within the complex structure

•Primary strength-giving phase in portland 

cement concrete

image credit: Dr. Eric Lachowski, S.Y. 

Hong, and F.P. Glasser via Concrete 

Microscopy Library at UIUC

C-S-H

The structure of C-S-H is poorly understood.

16 hr. C3S paste

wet dry

SH2O = 200 m2/g

SN2 = 5-50 m2/g

Sneutrons= 50 m2/g

Variations in surface area, 

depending on technique used 
C-S-H

Figure credit: M&M text

Some other models for C-S-H

Adapted from 

Powers (1960’s) Feldman and 

Sereda (1970)

Munich model,

Wittman (1979)

Colloid model

Figure credit: M&M text
Microscopical Evidence 

Fine, fibrillar structure, 

similar to Power’s model

(typical of Ca/Si>1.5)

Foil-like structure, similar to 

Feldman-Sereda model

(typical of lower Ca/Si)

Figure credit: 

Richardson, in 

Structure and 

Performance of 

Cements, Bensted 

and Barnes (Eds), 

Spon 2002.

Calcium silicate sheets

Some other models for C-S-H

Clay-like structure

Aluminosilicate sheets
Some other models for C-S-H

Original Image

High X-ray 

Absorption by Ca

Low X-ray 

Absorption by Ca

Ca Map

345eV

347eV

517eV

E. Gartner, K.E. Kurtis, and P.J.M. Monteiro, Cement and Concrete Research, May 2000, V30 (5):817-822.

Some other models for C-S-H

At low C/S, C-S-H resembles tobermorite 

At high C/S, C-S-H resembles jennite 

Higher C/S ratios are obtained 

by 3 principle mechanisms.

SiO2 bridging 

tetrahedra SiO2 pairing

tetrahedra

Tobermorite (C/S~0.8)

CaO sheet

Long single 

silicate chains Composite layer

structure

1 Replacement of bridging

tetrahedra for interlayer calcium.

Tobermorite-like C-S-H(I)

2 Replacement of H on Si-OH 

with interlayer calcium.

Jennite-like C-S-H

3 Replacement of silicate chains 

with hydroxyls, producing Ca-OH.

Ca-OH

Jennite-like

environments

5 A
Summary of Models for C-S-H

Table 6: Summary of models for the structure of C-S-H. 

Name of Model Primary Experimental 

Basis 

Type of Model Selected Characteristics of Model 

 

Powers Water sorption Colloid All products are gel 

 Volume of pores Particle radius, 5 nm 

 Gel pore volume, 28% 

 

Taylor X-ray Imperfect Atomic structure of C-S-H 

 TGA Tobomerite 

 Jennite 

 

Brunauer Water Sorption 2-3 layers Structure changes upon drying 

Feldman-Sereda Nitrogen sorption Layers Crumpled and folded layers with 

 Length vs. RH interlayer water reversibly 

 Modulus vs. RH removed upon drying 

 Weight vs. RH 

 

Wittmann Modulus vs. RH Colloid Structure not defined 

 

 

Jennings Density vs. RH Colloid Fractal: density and surface area 

 Composition vs. RH depend on length scale 

 Surface area 

Inner vs. Outer Product C-S-H

Outer product (early) C-S-H/ 

groundmass

• forms during early hydration

• C-S-H forms away from the 

cement particle surface, filling 

water-filled space

• higher porosity

• contains high levels of 

impurities

• probably admixed with nanoscale C4AŠH12
Inner vs. Outer Product C-S-H

Inner product (late) C-S-H/ 

phenograins

• forms during later hydration, when 

the process is diffusion controlled

• C-S-H grows inwards and 

outwards from the C-S-H “barrier”

• C-S-H formed takes shape of 

cement grains

• lower porosity, more dense

• fewer impurities

• more resistant to physical change 

on drying

• more abundant as hydration ↑ or 

as w/c ↓

C3S Hydration

1 Day 3 Days

28 Days
CH

•Calcium hydroxide or Ca(OH)2

•Definite stoichiometry

• Variable morphology - from large, 

hexagonal prisms to thin, elongated 

crystals

•Size of the crystals depends on the 

amount of space available

•Occupies 20-25% of the solid volume 

in the hcp

•Much lower surface area than C-S-H

•Does not contribute much to strength

•Keeps the pore solution alkaline (pH 

12.4-13.5)

Hydration of the Calcium Aluminates

•Reaction of C3A with water occurs very quickly and liberates 

much heat - “Flash Set”

•Gypsum (CŠH2) is added to the cement to control the 

hydration of C3A

C3A + 3CŠH2 + 26H → C6AŠ3H32 ∆H=-1350J/g

Dormant Period Setting
Role of Gypsum

Role of Gypsum
Hydration of the Calcium Aluminates

When more C3A remains, 

C6AŠ3H32 + 2C3A + 4H → 3C4AŠH12

•Reaction of C4AF occurs more slowly

C4AF + 2CH + 14H → C4(A,F) H13 + (A,F)H3

Hydration of the Calcium Aluminates

•Reaction of C4AF (ferrite) phase are slower and evolve less 

heat than C3A

• Also heavily retarded by gypsum

C4AF + 3CŠH2 + 21H  C6(A,F)Š3H32 + (F,A)H3

C4AF + C6(A,F) Š3H32  3C4(A,F)ŠH12 + (F,A)H3

•Products of C4AF are more resistant to sulfate attack than 

those of C3A hydration
Hydration of the Calcium Aluminates

C6AŠ3H32 (Ettringite, Aft)

• Needle-like morphology

• Needles interlock, take up much water

• contributes to stiffening of mixture

• some early strength

Hydration of the Calcium Aluminates

Ettringite crystal structure as part of a 

single column projection where A=Al, 

C=Ca, H=O of an OH group, W=O of 

an H2O molecule. Hydrogen atoms 

have been omitted, as are the H2O 

molecules attached to the calcium 

atoms lying in the central vertical line 

of the figure. (based on Taylor, 1997)

W W

W

W

W

W

W

W

H H

C

H H H

A

C C

W

W

W

W

W

W

A

H H H

C

H H

A

c/2 = 1.075nm

W W

H

H

C C
Hydration of the Calcium Aluminates

Ettringite stability in 

alkaline environments as 

a function of pH and 

sulfate ion concentration. 

(adapted from Hampson

and Bailey, 1982)

.

- 2

- 3

- 4

- 5

11 12 13

Ettringite

Hydrogarnet

Al-Hydroxide Portlandite

Gypsum

pH

log(SO

4

2- )

Log [SO4

-2]

Hydration of the Calcium Aluminates

C4AŠH12 (monosulfate, Afm) 

• hexagonal plate morphology arranged 

in “rosettes” during early hydration

• become more “platey” with continued 

hydration

• can contain impurities

• vulnerable to sulfate attack
Calcium Aluminates and 

Calcium Sulfoaluminates

•Includes ettringite, monosulfate hydration, 

calcium aluminate hydrates, and ferric-aluminum 

hydroxide gels

•Comprise 15-20% of solid volume of hcp

•Do not contribute much to strength

•Formation of ettringite, in particular, does 

influence setting time

•High heat of hydration for C3A can be favorable 

or unfavorable, depending upon application

Hydrated Cement Paste (hcp)
Hydrated Cement Paste (hcp)

Hydrated Cement Paste (hcp)
Formation of hydration 

products over time leads to:

•Stiffening (loss of workability)

•Setting (solidification)

•Hardening (strength gain)

Cement Hydration

, sulfate attack
Heat of Hydration

• Cement hydration is exothermic

• Concrete is an insulator

Heat of hydration can be:

- detrimental (thermal gradients --> cracking)

- helpful (heat provides activation energy when 

concreting in cold weather; higher early strength)

Heat of Hydration

Heat evolution can be used to map the progress of 

hydration:

(1) Initial dissolution of solids (increasing ionic concentration)

(2) Induction period

(3) Acceleration

(4) Deceleration

(5) Steady state
• Popular model for describing hydration during the acceleration 

periods (Stages 2&3)

-ln(1-α)=[k(t-to)]m 

or when α is small, α=kt

m 

Where α is degree of hydration

t is time of hydration, where to corresponds to the length of induction period

k is a rate constant for a nucleation-controlled process

m = [(p/s)+q], where p= 1 for1D growth (needles/fibers)

m ~ 1-3 for C3S 2 for 2D (sheets/plates)

3 for 3D isotropic growth (sphere) 

s=1 for interface or phase-boundary-controlled growth

=2 for diffusion-controlled growth

and q=0 for no nucleation (nucleation saturation)

1 for continuous nucleation at a constant rate

Cement Hydration: Avrami Model*

* Avrami, M. J. Phys. Chem., 7, 1103 (1938), 8, 212 (1940).

• k, then, is a combined rate constant, 

accounting for rate of nucleation, rate of 

product growth, and other factors not 

accounted for (e.g., changing diffusion 

coefficients)

• Can calculate the rate constant k from 

calorimetry data and the Avrami equation: 

-ln(1-α)=[k(t-to)]m 

• when modeling as a function of time 

rather than degree of hydration:

dα/dt=Amkm (t-to)m-1exp{-[k(t-to)]m}

Where A is a preexponential factor.

Cement Hydration: Avrami Model

Figure credit: Gartner et al, in Structure 

and Performance of Cements, Bensted 

Thomas and Jennings, Chem. Mat., and Barnes (Eds), Spon 2002.

11:1907-14, 1999.
Cement Hydration: Avrami Model

•Can also determine the activation energy (Ea) for the reaction, which 

can be used to assess the temperature-dependence of the reaction: 

k(T)=A exp(-Ea/RT)

Where T is absolute temperature (K), R is gas constant, 

Thomas and Jennings, Chem. Mat., 

11:1907-14, 1999.

Cement Hydration: Jander Equation*

• In the deceleration period, the Jander equation for diffusion 

controlled processes has been used to model the reaction of 

cement during this period:

[1-(1-α)1/3]

2 = kD

Where kD is the rate constant for diffusion controlled 

processes.

* Jelenic, Adv. Cem. Tech. Gosh (Ed), p.397, Pergamon, 1987.

Bezjak and Jelenic, Cem. Conc. Res., 10:553, 1980.
Cement Hydration: Simple Kinetic Models

• Can estimate α based upon the available water-filled porosity (φw):

where k1 is analogous to a first-order rate constant and depends on the 

specific cement composition, particle size distribution, curing 

temperature, etc. 

• This approach, based upon first order "physical" kinetics and described 

by Bentz*, assumes hydration rate is simply proportional to the volume 

fraction of this water-filled porosity

• Other models** relate the kinetics of hydration to the changing radius of 

an idealized cement particle or particle distribution

*D. P. Bentz, “Influence of Water-to-Cement Ratio on Hydration Kinetics: Simple Models Based on Spatial Considerations”

at http://ciks.cbt.nist.gov/~garbocz/hydration_rates/index.html

**J.M. Pommersheim, J.R. Clifton, Mathematical modeling of tricalcium silicate hydration. Cem Concr Res 9 (1979) 765-770.

T. Knudsen, The dispersion model for hydration of portland cement 1. General concepts, Cem Concr Res 14 (1984) 622-630.

B. Osbaeck, V. Johansen, Particle size distribution and rate of strength development of portland cement. J Am Ceram Soc 72 (2) (1989) 197-201.

Cement Hydration: Simple Kinetic Models

Substituting 

into Powers equation for water-filled porosity

the result can be integrated and solved with the boundary 

condition that α(0)=0 to yield:

(the minimum function assures that α<1)

• Although derived from a different perspective, the above is 

similar in form to kinetics equations often derived 

considering nucleation and growth kinetics for cement 

hydration (so-called Avrami behavior) 

ƒexp is the volumetric expansion 

coefficient for the "solid" cement 

hydration products relative to the cement

reacted (often taken to be =1.15),

CS is the chemical shrinkage per gram o

cement (often taken to be 0.07 mL/g)
Heat of Hydration

For the usual portland cement:

• ~ 1/2 total heat is evolved in 1-3 days

• 3/4 at 7 days

• 83-91% at 180 days

Heat of Hydration

The RATE of heat evolution is related to 

• cement composition

• cement fineness

• cement content

• casting temperature

The total heat evolved is related to

• cement composition

• degree of hydration

• cement content
Heat of Hydration

Heat of Hydration: Influence of Cement 

Composition
Heat of Hydration: Influence of Cement 

Composition

Heat of Hydration: Influence of Cement Composition

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 6 12 18 24 30 36 42 48 54 60 66 72

Age (h)

Heat evolved (mW/g)

0

50

100

150

200

250

Cement 1 

Cement 2

Cement 3

Cement 4

Cement 5

Cumulative Rate evolution (J/g)

C4AF 11 9.1 8.6 12.2 10

C3A 4 7.5 10.1 7.1 9

C2S 16 19 7.9 20.6 26

C3S 59 55.9 62.9 50.4 42

Cement 

5

Cement 

4

Cement 

3

Cement 

2

Cement 

1
Heat of Hydration: Influence of Cement 

Fineness

Heat of Hydration: Influence of Ambient 

Temperature
Estimating Heat of Hydration

Verbeck and Foster estimated that the overall heat of 

hydration of a cement is near the sum of the heats of 

hydration of the individual components.

H = aA + bB + cC + dD

H3days= 240(C3S) + 50(C2S) + 880(C3A) + 290(C4AF) J/g

H1yr= 490(C3S) + 225(C2S) + 1160(C3A) + 375(C4AF) J/g

A,B,C,D are % by wt of C3S, C2S, C3A, C4AF

a,b,c,d are coefficients representing the 

contribution of 1% of the corresponding 

compound to the heat of hydration