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"HEAT-AND-BEAT" or "SHAKE-AND-BAKE“
Solid state reactions
At least one of the reactants and one of the products are solid
Reactions in a lattice of atoms
Atomic mobility
No mobility without defects – perfect crystal = no chemistry
High temperatures
Reactions on the interphase between phases
Microstructure - crystallite size, shape, defects
Diffusion controls the reaction rate
Direct Reactions of Solids
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Reaction Types
Solid - solid synthesis - addition A + B  AB
MgO(s) + Al2O3(s)  MgAl2O4(s)
MgO(s) + SiO2(s)  MgSiO3(s) or Mg2SiO4(s)
Solid - solid synthesis – exchange, metathesis AB + C  AC + B
CaCO3(s) + SiO2(s)  CaSiO3(s) + CO2(g)
Ge(s) + 2 MoO3(s)  GeO2(s) + 2 MoO2(s)
Solid - solid synthesis – exchange and addition
PbSO4 + ZrO2 + K2CO3  K2SO4 + PbZrO3 + CO2
Solid - solid synthesis - dissociation AB  A + B
Ca3SiO5(s)  Ca2SiO4(s) + CaO(s)
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Reaction Types
Solid - solid synthesis - addition A + B  AB
MgO(s) + Al2O3(s)  MgAl2O4(s)
MgO(s) + SiO2(s)  MgSiO3(s) or Mg2SiO4(s)
Solid - solid synthesis – exchange, metathesis AB + C  AC + B
CaCO3(s) + SiO2(s)  CaSiO3(s) + CO2(g)
Ge(s) + 2 MoO3(s)  GeO2(s) + 2 MoO2(s)
Solid - solid synthesis - dissociation AB  A + B
Ca3SiO5(s)  Ca2SiO4(s) + CaO(s)
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Reaction Types
Solid – gas synthesis A + B  AB
2 Fe3O4(s) + 1/2 O2(g) 3 Fe2O3(s)
2 SiCl4(g) + 4 H2(g) + Mo(s) MoSi2(s) + 8 HCl(g)
High temperature corrosion of metals in air
Solid – gas dissociation AB  A + B
CaCO3(s)  CaO(s) + CO2(g)
Al4Si4O10(OH)8(s) Al4(Si4O10)O4(s) + 4 H2O(g)
Kaolinite Metakaolinite
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Reaction Types
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Reaction Types
Other classes than oxides
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Reaction Types
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Experimental Considerations
Powder Mixing Method
Precise weighing for exact stoichiometry
Mixing (components, dopants, additives)
Milling or grinding (ball mill, mortar)
Compaction (pelleting, organic binders)
Calcination @ high temperature (> 1000 °C)
Firing/grinding cycles
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Planetary ball mill
Planetary ball mill
Rotation and counter-wise spining
Milling
Rotation speed: up to 400 rpm
Milling jars: alumina, YSZ, tungsten
carbide, agate
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Milling
Atritor mill
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Compaction - Pressing
Hydraulic Uniaxial Press
Maximum pressure: 120 MPa
Warm Isostatic Press
Max. pressure: 400 MPa
Max. temperature: 80 oC
Volume: 2,5 l
Hot press
Max. temperature: 1250 °C
Max. pressure: 100 MPa
Max. diameter: 25 mm
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Calcination
Tube Furnace
in air and in controled atmosphere
Maximum temperature: 1450 oC or 1600 °C
Furnace-tube diameter: up to 75 mm
Vacuum Furnace
in vacuum or Ar, N2, O2 atmosphere
Maximum temperature: 1200 °C
Chamber Dimensions: 150x200x250 mm3
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Direct Reactions of Solids
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Experimental Considerations
 Reagents
Drying, fine grain powders for maximum SA, surface activation (Mo + H2),
in situ decomposition (CO3
2-, OH-, O2
2-, C2O4
2-) for intimate mixing,
precursor reagents, homogenization, organic solvents, grinding, ball milling,
ultrasonication
 Prior decomposition
Initial cycle at lower temperature to prevent spillage or volatilization, frequent
cycles of heating, cooling, grinding, boost SA. Overcoming sintering, grain
growth, fresh surfaces. Pelleting, hot pressing, enhanced contact area increases
rate and extent of reaction
 Container Materials
Chemically inert crucibles, boats, ampoules (open, sealed, welded)
Noble metals: Au, Ag, Pt, Ni, Rh, Ir, Nb, Ta, Mo, W
Refractories: alumina, zirconia, silica, BN, graphite
Reactivities with containers at high temperatures needs to be carefully evaluated
for each system, pelleting minimizes contact with container, sacrificial pellet
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Experimental Considerations
 Controlled atmosphere
oxidizing, reducing, inert or vacuum.
Unstable oxidation states, preferential component
volatilization if T is too high, composition
dependent atmosphere (O2, NH3, H2S, …)
 Heating Program
Slow or fast heating, cooling, holding at a set point
temperature. Furnaces, RF, microwave, lasers, ion
or electron beam
Tammann’s rule: Tr  2/3 Tm
Factors Influencing Direct Reactions of
Solids
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Direct Reactions of Solids
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Direct Reactions of Solids
Silicanumber of
cubes
edge length SA, m2/g
1 1 cm 6.10-4
103 1 mm 6.10-3
1012 1 m 6
1021 1 nm 6000
Consider 1 g of a material, density 1.0 g/cm3 , cubic crystallites
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Direct Reactions of Solids
Contact area
not in reaction rate expression
for product layer thickness, x,
versus time:
dx/dt = k/x
But for a constant product volume (V = x A) : x ~ 1/Acontact
and furthermore Acontact ~ 1/dparticle
Thus particle sizes and surface area inextricably connected and obviously
x ~ d
and SA particle size affect the interfacial thickness
x
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Direct Reactions of Solids
Direct Reactions of Solids
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Reaction Paths between Two Solids
gas phase diffusion
volume diffusion
interface diffusion
surface diffusion
A
B
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Direct Reactions of Solids
(A)x[By]Oz Stoichiometric formula of spinel
(A) occupy 1/8 Td
[B] occupy 1/2 Oh
ccp array of O2Derive
the stoichiometric formula of spinel
(A)x[By]Oz
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The Spinel Structure: (A)[B2]O4
fcc array of O2- ions, A occupies 1/8 of the
tetrahedral and B 1/2 of the octahedral holes
 normal spinel: AB2O4
Co3O4, GeNi2O4, WNa2O4
 inverse spinel: B[AB]O4
Fe3O4: Fe3+[Fe2+Fe3+]O4, TiMg2O4, NiLi2F4
 basis structure for several
magnetic materials
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The Spinel Structure: MgAl2O4
(A)[B2]O4
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The Spinel Structure: MgAl2O4
I II
I II
• = Mg
x = O
= Al
(A)[B2]O4
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Direct Reactions of Solids
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Model for a classical solid-solid reaction (below melting point !):
Planar interface between two crystals
MgO + Al2O3  MgAl2O4 (Spinel)
Phase 1:
nucleation
Phase 2:
growth of nuclei
MgO Al2O3 MgO Al2O3
Direct Reactions of Solids
MgAl2O4
x
dx/dt = k/x
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Direct Reactions of Solids
 Structural differences between reactants and products,
major structural reorganization in forming product spinel
MgO ccp O2-, Mg2+ in Oh sites
Al2O3 hcp O2-, Al3+ in 2/3 Oh sites
MgAl2O4 ccp O2-, Mg2+ 1/8 Td, Al3+ 1/2 Oh
Making and breaking many strong bonds (mainly ionic), high temperature process
as D(Mg2+) and D(Al3+) large for small highly charged cations
Long range counter-diffusion of Mg2+ and Al3+ cations across interface, usually
RDS (= rate determining step), requires ionic conductivity, substitutional or
interstitial hopping of cations from site to site to effect mass transport
Nucleation of product spinel at interface, ions diffuse across thickening interface,
oxide ion reorganization at nucleation site
 Decreasing rate as spinel product layer thickens
Parabolic rate law: dx/dt = k/x
x2 = kt
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Direct Reactions of Solids
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Reaction Mechanism
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Pt = the value of a property at time t
P0 = the value of a property at the beginning
Pe = the value of a property at the end
Direct Reactions of Solids
e.g. Pt = mass loss, x, ……
– the molar fraction of the reacted product at a time t
k(T) – the rate constant of the process
General kinetic expression
Reaction rate
Rate constant
Reaction order
Experimentally evaluate at different t
Fit data into a g() = k(T)t expression to obtain k(T) and the type of mechanism
model
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Direct Reactions of Solids
Decreasing reaction rate as spinel product layer (x) thickens
Here  = x
Parabolic rate law:
dx/dt = k/x
x2 = kt
MgO Al2O3
MgAl2O4
x
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Avrami Plot
α,Fractionreacted
Conversion is
50% Complete
is the time
required for
50% conversion
| Incubation Time |
t, Time (s)
α =1 exp[(kt)n]
k = rate constant
n = exponent
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Direct Reactions of Solids
Perform the measurements in a range of temperatures T
use Arrhenius equation to evaluate the activation energy Ea
k(T) = k0 exp(Ea/RT)
FractionTransformed
135 C
120 C
80 C
Time, s
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Cation Diffusion in LaCoO3
La2O3 CoO
DCo >> DLa
Rate-determining step:
Diffusion of Co cations
Marker experiments
LaCoO3
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Growth Kinetics of LaCoO3
Parabolic rate law valid = diffusion controlled process
x2 = kt
In air
1673 K
1573 K
1478 K
1370 K
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Growth Kinetics of LaCoO3
EA = (250 ± 10) kJ mol-1
k(T) = k0 exp(Ea/RT)
log k = log k0  Ea/RT
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Nucleation
Homogeneous nucleation
Liquid melt to crystalline solid
Cluster formation
Gv = driving force for solidification (negative)
below the equilibrium melting temperature, Tm
T = undercooling, Hv = enthalpy of solidification (negative)
Small clusters of crystallized solid form in a melt because of the random
motion of atoms within the liquid
Driving force is opposed by the increase in energy due to the creation of a
new solid-liquid interface
SL = the solid/liquid interfacial energy
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r: radius of spheric seed
r*: critical radius
GN: total free energy change
Gs: surface free energy change
Gv: volume free energy change
GN = 4r2SL + 4/3r3GV
Nucleation
G
G
N
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Critical Radius r*
The critical radius r* = the radius at which GN is maximum
The energy barrier to homogeneous nucleation
The temperature-dependence
r* = 1/T G*r = 1/T2
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Nucleation
a nucleus
stable for r >r*
the stable nucleus continues to grow
a sub-critical cluster
unstable for r < r*
the cluster re-dissolves
Increasing r
G > 0
Increasing r
G < 0
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Nucleation rate n
Liquid to solid
GN = thermodynamic barrier to nucleation
GD = kinetic barrier to diffusion across the liquid/nucleus interface
Assume, that solid phase nucleates as spherical clusters of radius r
GN = the net (excess) free energy change for a single nucleus
GN = GS + 4/3r3GV
GS = 4r2SL surface free energy change positive
4/3r3GV volume free energy change negative, l to s lowers the energy
Nucleation rate n
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Heterogeneous Nucleation
Nuclei can form at preferential sites:
flask wall, impurities, catalysts, …..
The energy barrier to nucleation, G*, is substantially
reduced
The critical nucleus size, r* is the same for both
heterogeneous and homogeneous nucleation
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Heterogeneous Nucleation
a solid cluster forming on a wall:
• the newly created interfaces (i.e. solid-liquid and solid-wall)
• the destroyed interface (liquid-wall)
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Heterogeneous Nucleation
 = wetting angle
Shape factor S()
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Wetting Angle
Force equilibrium
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Heterogeneous Nucleation
The critical radius r* is the same for both homogeneous and
heterogeneous nucleation
The volume of a critical nucleus and G* can be significantly
smaller for heterogeneous nucleation due to the shape factor,
depending on the wetting angle, 
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Direct Reactions of Solids
Solidification
G = 4/3  r3 Gv +4  r2 SL
– Volume free energy + surface energy
One solid phase changing to another
G = 4/3  r3 Gv +4  r2 SL + 4/3  r3 
– Volume energy + surface energy + strain energy
– the new solid does not take up the same volume as the old solid
– a misfit strain energy term, Gs = V 
αβ = the α/β interfacial energy
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Nucleation
Transformation from liquid
to solid phase requires:
•Nucleation of new phase
•Growth of new phase
Nucleation depends on:
•driving force toward equilibrium – cooling of a melt
increases as we move to lower temperatures
•diffusion of atoms into clusters
increases at higher temperatures
Combination of these two terms (multiplication)
determines the total nucleation rate
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Nucleation rate I
Nucleation rate [m-3 s-1] I = β n*
n* = the steady-state population of critical nuclei (m-3)
n0 = the number of potential
nucleation sites per unit volume
G* = the critical free energy of
nucleation
β = the rate at which atoms join critical nuclei (s-1), thereby
making them stable, a diffusion-dependent term
 = temperature independent term incorporating vibrational frequency and the
area to which atoms can join the critical nucleus
Q = an activation energy for atomic migration
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Nucleation rate I
n* = the steady-state population of critical nuclei (m-3)
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Nucleation
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Nucleation vs. Growth
Growth
Rate
Nucleatio
n Rate
Overall
Transformation
Rate
Temperature
Rate
Equilibrium transformation temperature
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Undercooling – cooling below the melting point
relations between undercooling, nucleation rate and growth rate of the nuclei
large undercooling: many small nuclei
(spontaneous nucleation)
growth rate small - high viscosity, slow diffusion
small undercooling: few (evtl. small) nuclei
growth rate high – fast diffusion close to the m.p.
Nucleation vs. Crystal Growth
(solution or melt)
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Nucleation vs. Crystal Growth
Rate of nucleation
Rate of growth
Ta = small undercooling, slow cooling
rate
Fast growth, slow nucleation = Few
coarse crystals
Tb = larger undercooling, rapid
cooling rate
Rapid nucleation, slow growth =
many fine-grained crystals
Tc = very rapid cooling
Nearly no nucleation = glass
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Direct Reactions of Solids
Topotactic reactions
More specific, require interfacial and bulk crystalline structural similarity,
lattice matching
Topotaxy: involves lock-and-key ideas of self-assembly, molecule recognition,
host-guest inclusion, clearly requires available space or creates space in the
process of adsorption, injection, intercalation etc.
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Direct Reactions of Solids
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Direct Reactions of Solids
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Direct Reactions of Solids
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Direct Reactions of Solids
Atoms located in (111) and (100) crystal planes for spherical
and cuboid particles
Model particles = fcc structure of Pt 4 nm size
Dark grey = atoms located in (111)-surface
Light orange = the (100) face
Surface Facet Reactivity
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Electron tomography and electron
energy loss spectroscopy (EELS)
map the valency of the Ce ions in
CeO2x nanocrystals in 3D.
A facet-dependent reduction
shell at the surface; {111} facets
show a low surface reduction,
whereas at {001} surface facets,
the cerium ions are more reduced.
Work function of different crystal planes
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Direct Reactions of Solids
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Self-Sustained High-Temperature
Synthesis (SHS)
Mixing
Metal powders (Ti, Zr, Cr, Mo, W, ....) + other reactants
Pressing into pellets
Ignition by energy pulse (W wire)
S.S. reactor, under Ar
Exothermic reaction
Byproduct removal
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Self-Propagating Metathesis
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Self-Propagating Metathesis
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Combustion Synthesis
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Examples
Combustion Synthesis
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Combustion Synthesis
Reaction front propagation: glycine-iron nitrate
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Self-Propagating Metathesis
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Examples
Combustion Synthesis
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Yttrium Iron Garnet (YIG) Y3Fe5O12
Metal nitrates (MN) = oxidants
• Y(NO3)3·6H2O
• Fe(NO3)3·9H2O
Citric acid monohydrate (CA) = fuel
Solution in water Y:Fe = 3:5
The solution evaporated at 85 C
stirrred until viscous gel
Increasing the temperature up to 250  C
ignition of the gel
MN/CA ratio controls the size
Solution Combustion Synthesis
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Fusion-Crystallization from Glass
Glass is a non-equilibrium, non-crystalline
condensed state of matter that exhibits a
glass transition. The structure of glasses is
similar to that of their parent supercooled
liquids (SCL), and they spontaneously relax
toward the SCL state. Their ultimate fate, in
the limit of infinite time, is to crystallize.
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Fusion-Crystallization from Glass
Mixing powders
Melting to glass: single phase, homogeneous
(T, C), amorphous
Temperature limits:
• mp of reagents
• volatility of reagents
Nucleation agent
Homogeneous nucleation, few crystal seeds
Slow transport of precursors to seed
Lowest possible crystallization temperature
Crystallizing a glass above its glass
transition
Metastable phases accessible, often
impossible to prepare by other methods
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Fusion-Crystallization from Glass
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Fusion-Crystallization from Glass
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Cements
5600 BC - the floor of a villa in Serbia, a red lime binder (calcium oxide). Lime obtained by
burning gypsum, limestone or chalk
2589-2566 BC - Egypt, the Great Pyramid of Cheops, gypsum-derived binders
800 BC the Greeks, 300 BC the Romans, limestone-derived cements became widespread
Vitruvius, De Architectura
the Appian Way, the Coliseum, the Pantheon
cements based on a mixture of natural and synthetic aluminosilicates with lime - pozzolan
1756 John Smeaton, lighthouse, a pozzolanic binder from lime, volcanic ash and copper slag,
able to withstand the harsh coastal environment
1824 Joseph Aspdin, Leeds, England, developed and patented Portland cement.
Portland cement - made by heating at 1450°C chalk, shale, and clay or limestone in a kiln to
form a partially fused mixture – clinker, which is then finely ground with gypsum
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Cements
Hydraulic cements - materials that set and harden by reacting with water, produce an adhesive
matrix, combined with other materials, are used to form structural composite materials.
Non-hydraulic cements - lime and gypsum plasters, set by drying out, must be kept dry, gain
strength slowly by absorption of CO2 to form calcium carbonate through carbonatation
Concrete - a mixture of cement (binding agent) and water with aggregate (varying amounts of
coarse and fine sand and stone). Consumption of concrete - 2.5 tonnes per person per year.
Mortar - used to bind bricks together, made from cement but with finer grade of added materials.
Portland cement
Component Formula Phase wt%
Tricalcium silicate C3S Ca3SiO5 Alite 50-70
Β-dicalcium silicate C2S Ca2SiO4 Belite 15-30
Tricalcium aluminate C2A Ca3Al2O6 Aluminate 5-10
Tetracalcium aluminoferrite C4AF Ca2(Al/Fe)O5 Ferrite 5-15
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S SiO2 C CaO
A Al2O3 F Fe2O3
T TiO2 M MgO
K K2O N Na2O
H H2O
CO2
SO3
Chemical Cement Nomenclature