Methods of phase equilibrium study in ceramic materials
Control of oxygen partial pressure
Examples of using phase diagram for ceramic materials
Al2O3-GdAlO3 DSE
Al2O3-YAG-ZrO2 DSE
Al2O3-YAG DSE
Al2O3-GdAlO3-ZrO2 DSE
Experimental methods to construct phase diagrams for ceramics
Sample preparation
Solid state reactions
Starting materials are oxide
mixtures and/or oxy-salts (e.g.
carbonates).
When heated oxy-salts
decompose forming oxides and
gas products released from
sample.
The starting powders are mixed
together by grinding in agate
mortar with small amount of
acetone or alcohol. Automated
milling can be also used.
Co-precipitation
(for slow-reacting oxide system)
Starting materials are salts (e.g. nitrates ,
dissolved in water or mineral acids).
Elemental analysis should be done to
control composition (ICP-OES). NH4OH is
used for precipitation of hydroxides.
After drying to remove most of the
water, the samples are calcined to form
oxide mixture.
Other sol-gel methods including organic
substances. Pyrolysis is necessary to
destroy organic materials.
The mixed powders are pressed into pellets and heat treated at desired
temperatures. Pt-crucibles or foil packets are recommended.
Sample characterisation: XRD, SEM/EDX, EPMA
Experimental methods to construct phase diagrams for ceramics
Furnaces:
Ni-Cr heating elements up to 1200°C, SiC – up to 1600°C, MoSi2 – up to 1800,
ZrO2 – up to 2050°C in air
C (graphite) heating elements in vacuum or inert atmosphere - up to 3000°C.
Temperature control – Pt/Pt-Rh thermocouple, pyrometer at high temperature
> 1700°C
Scheme of vertical quench furnace
Modification of quench furnace to
control atmosphere
Experimental methods to construct phase diagrams for ceramics
Oxygen partial pressure control
When heated under isothermal
condition M/MOx mixture will exchange
oxygen with the carrier gas until
equilibrium pO2 is established according
to the following reaction
Scheme of using metal/metal-oxide buffers to control oxygen partial pressure
Buffer gas mixtures
pO2 depends on CO/CO2 ratio and temperature
Phase and compositional analysis
Visual inspection can provide information if the sample was melted or partially melted, if
there was reaction with crucibles. Cracking or crumbling may signify unquenchable
transition.
Optical microscopy in polarized light can be helpful in identification small amounts of second
phase. It can be confirmed if equilibrium conditions were achieved.
(1) immersion method (powdered sample is immersed in the liquid with known refractive
index ; crystal optical properties and refractive indices can be determined); (2) thin section
method (morphological structure, melting and crystallisation behaviour); (3) polished section
method in reflecting light microscope.
X-ray diffraction is the most common method to determine phase assemblage of
ceramic system. Phase fractions, lattice parameters and grain sizes can be determined
by Rietveld analysis. The corresponding software generate theoretical diffraction
pattern based on atom positions and site occupancies. This way X-ray pattern of the
solid solutions can be fitted. Every peak should be assigned to a phase and indexed.
Electron microscopy SEM/EDX and EPMA play important role in construction of phase
diagrams in combination with XRD.
Microstructure investigation can identify if sample was equilibrated, partially melted.
Phase compositions can be determined by EDX or EPMA. Quantitative analysis requires
relatively large grains, larger than sampling volume of electron beam. EPMA require to
use standards, which are the best if they are similar to the system under study.
Example: Ga2O3-In2O3-SnO2 system
XRD can be used to determine
phase compositions:
XRD for single phase samples to
plot unit cell volume vs.
composition
b. (Ga1-xInx)2O3
c. (Ga1-xInx)4Sn2O10
Graphs are used to determine
phase composition for two
phase sample (p) and threephase sample (q)
Lattice parameters can be
calculated using Rietveld
analysis
Identification of a new phase
Compositional analysis using EPMA is necessary to prepare phase pure sample.
Single –crystal X-ray diffraction is preferred method for structure determination,
but Rietveld analysis using XRD powder diffraction or neutron powder diffraction
data are increasingly applied for structure determination especially if single
crystals are not available.
Single crystals for XRD should be ~0.2-0.5 mm. Such crystals can not grown by
solid state reactions; growing from the melt is necessary. If the liquidus
temperature is too high then suitable flux can be used (flux is a substance which
form homogeneous flux from which desired phase can grow). Flux-grown crystals
should be chemically analysed to identify possible contamination.
Rietveld analysis requires a starting model that include lattice parameters, correct
space group and approximate atom positions. Alternatively, unit-cell information
can be also obtained using electron diffraction data obtained for polycrystalline
samples using a transmission electron microscopy (TEM).
Thermal analysis DTA-TGA
For ceramic materials DTA is also used to study melting, crystallisation, chemical
reactions and polymorphic transformations. Heating rate normally used for ceramic
materials is 10 K/min. Lower heating rate can result in broad shallow peak difficult to
interpret. Faster heating will result in narrow peaks but may not represent
equilibrium temperature of transformation. Pt-crucibles are usually recommended
to study ceramic materials up to 1700°C. To study transformations at higher
temperatures W-crucibles can be used.
Crucibles with lids or sealed crucibles can be used to avoid contamination of sample
(e.g. La2O3 by C from the vitreous carbon furnace protection tube) or in case of foam
formation to keep liquid inside the crucible (e.g. MgO-Al2O3 system). When sealed
crucibles are used, influence of pressure should be considered.
In case of ceramics the samples are usually not melted before DTA and do not have
fine eutectic microstructure. The heat treated sample of eutectic composition can
have large grains of phases. That is why peaks on heating can be not so sharp as
expected for eutectic reaction.
Eu2O3-Al2O3 system:
sample 24%Eu2O3-76%Al2O3
XRD Al2O3+EuAlO3 (EAP)
Example: ZrO2-Eu2O3
Sample #2 66.67%ZrO2-33.33%Eu2O3
(Eu2Zr2O7)
Tcor=2128 K ( HTXRD (lit.) 1997 or 2273 K)
Sample #4 20%ZrO2-80%Eu2O3
Tcor=2155 K
XRD 1873 K
SEM/EDX heat treatment 1773 K, then 1923 K
TGA: thermogravimetric analysis
TGA measure mass loss or gain with temperature and/or oxygen partial pressure.
TGA can be used to investigate red/ox reactions in M/Oxide system and
decomposition reactions accompanied by gas formation (e.g. CaCO3CaO+CO2 (gas))
Calculated phase diagram of the Mn-O system
778°C 3Mn2O3  2aMn3O4+0.5O2
1167°C aMn3O4  bMn3O4
1458°C bMn3O4  3MnO+0.5O2
pO2=10-2 bar
Thermogravimetric analysis. Example Fe-O system
Calculated potential diagram
of the Fe-O system
Experiment of Kitayama et al. (2004):
Fe2O3 was equilibrated at 1100°C (1373 K) using
various gas mixtures CO2/H2 and CO2/O2. WT is total
weight gain from reference state (logpO2=-15 pure Fe)
to Fe2O3 1 bar of O2. WO2 is weight gain from reference
state of pure Fe to present p(O2). XRD is widely used in
conjunction with TGA to identify phases before and
after mass change.
Coulometric titration
After heating in vacuum the
chamber is sealed and sample is
equilibrated. According to Nernst
equation:
E is measured potential, pO2 is
oxygen partial pressure inside the
chamber, pO2 ref – outside the
chamber.
After recording of pO2 oxygen is
admitted or removed by driving of
current though YSZ (oxygen sensor).
The amount of oxygen pumped is
recorded (dx) and sample is
equilibrated again. This way partial
oxygen pressure is recorded as
function of oxygen content.
Plateaus correspond to
decomposition of phase.
High-temperature X-ray diffraction and other in-situ methods
HT-XRD is very useful tool to identify phases that cannot be retained upon quenching and
to study reactions under varying temperature and oxygen partial pressure conditions.
The technique is often used in conjunction with DTA, which provide more accurate
measurement of the transition temperature. Diffraction data can be collected at
temperature below and above transition temperature to provide information about
structure of phases. HT-XRD also can be used to determine transformations which can
not be detected by DTA.
High temperature diffractometers with volume heating are now commercially available
with heating up to 1200 °C. Custom-built system allow measurements under control
atmosphere up to 1600°C.
Thermo-microscopy (hot-stage microscopy) can be conducted in dynamic or isothermal
modes to monitor a variety of physical changes such as melting, crystallisation,
decomposition, oxidation and even crystal transformations.
In-situ measurement of electric, dielectric and magnetic properties can be helpful to
identify phase transitions which can not be found using DTA. Because the electric
properties are highly dependent on microstructure and defect chemistry they are usually
used in combination with other in-situ methods.
Directionally solidified eutectic ceramic oxides - in situ composites
Melt growth composites prepared by unidirectional solidification of oxides have
advantages compared with sintered oxides or ceramic matrix composites. Al2O3-based DSE
with minimum interphase spacing and free of large defects showed excellent mechanical
properties up to temperature close to melting point as well as outstanding microstructural
stability and corrosion resistance. DSE ceramic oxides present important advantages for
high temperature structural applications. Also DSE present interest for optical, electronic
and magnetic applications. The main functional applications are aimed at:
The used of DSE oxides is envisaged for a new
generation of gas turbines operating with inlet
temperatures as high as 1700°C. The
applications could be vanes, hollow non-cooled
nozzles, eventually turbine blades and in the
combustion chamber, liner panels.
Oxide eutectic systems
Al2O3-based eutectics presents interest because of outstanding creep resistance of
sapphire along the c-axis in combination with other oxide properties create new family
of ceramic matrix composites with exceptional thermo-mechanical properties. In
particular, binary, pseudo-binary and ternary eutectics in the system Al2O3-ZrO2-Y2O3
were explored in detail following phase diagram for this system experimentally studied
by Lakiza and Lopato (1997). This includes Al2O3/Y3Al5O12 (YAG) , Al2O3/ZrO2 and Al2O3/
ZrO2(Y2O3) DSE. The addition of Y2O3 to Al2O3/ZrO2 leads to pseudo-binary eutectic in
which different ZrO2 polymorphs (monoclinic, tetragonal or cubic zirconia) could be
obtained by changing Y2O3 content. Ternary eutectic Al2O3/YAG/YSZ further improve
excellent mechanical properties of their binary counterparts. In addition rare-earth
aluminate-sapphire Al2O3/RE2O3-Al2O3 are eutectic composites made up by sapphire in
combination with perovskite REAlO3 for Sm, Eu, Gd or garnet RE3Al5O12 for Y, Yb, Lu.
Al2O3/YAG DSE
Al2O3/YAG/ZrO2 DSE
Oxide eutectic systems
Al2O3/GdAlO3 DSE
Al2O3/GdAlO3/ZrO2 s.s. (F)
MgAl2O4/MgO – MgO crystalline fibers embedded into spinel matrix, MgAl2O4/Mg2SiO4 MgAl2O4 fibers within Mg2SiO4 matrix
ZrO2-based eutectics - NiAl2O4/YSZ is highly ordered colonies of YSZ fibers in hexagonal
arrangement embedded in NiAl2O4 single crystal matrix and Ni nano-particles produced by
reduction of NiAl2O4. Lamellar NiO/YSZ, CaSZ/CaZrO3 well-aligned lamellae, fibrous
MgO/MgSZ is hexagonal array of MgO fibers embedded within a MgSZ single crystal matrix,
lamellar NiO/CaO, NiO/Y2O3, NiO/Gd2O3 and fibrous NiO in NiAl2O4.
Microstructure and crystallography
TE
DT
T0
Crucial point leading to specific microstructure is coupled growth of two
(binary) or three (ternary) phased from the melt. Coupled eutectic growth
T
avoiding dendrites is complex process implicating numerous phenomena.
Lamellar growth is considered for simplicity. Lamellae grow unidirectionally
l
side by side and perpendicular to the planar growth front (solid/liquid
interface). If phases grow separately then long range diffusion is necessary At the point of three phase junction the
curvature of solid phases in contact with
to insure solute transport in the direction of growth. Solid phase a will
liquid (solid/liquid interface) is determined
reject in the liquid atoms corresponding to phase b and vice-versa
by condition of mechanical equilibrium of
(diffusion coupling) thus leading to a diffusion flux parallel to growth
the interface forces a/b – gab, a/liq – ga
front. The eutectic growth is largely governed by diffusive mass
b/liq –gb known as capillarity effect.
transport.
These two phenomena diffusion (through the mean solute undercooling) and capillarity (through the mean curvature
undercooling) are the main factors contributing to DT (undercooling ) T0<TE. Another consequence of these two factors
is lamellar spacing l varies as a function of growth rate V.
Microstructure and crystallography
Eutectic behaves like pure chemical substance. Due to latent heat (enthalpy of fusion)
phase change from liquid to solid occurs with “thermal arrest” solidification time. High
latent heat (e.g. Al2O3) may effect kinetics of undercooling which depends on growth rate
V. This is the third contribution to DT0.
DT0=TE-T0=DTC+DTs+DTK, where temperature gradient DTC=-miDCC is due to concentration
gradient, DTs=2g/(rDSm) is due to interface curvature and DTK is due to kinetics (mi is
liquidus slope, DCC concentration gradient dependent on diffusion coefficient D and
growth rate V, g- is solid-liquid surface energy, r- radius and DSm melting entropy).
Another important factor is materials characteristics, essentially the marked tendency of
the two phases to grow under specific crystallographic orientations.
Finally, due to effects of the various parameters, such as coefficient of diffusion D of solute
in liquid phase, coupled eutectic growth under given growth rate V can be obtained if
thermal gradient (GT) in the ceramic ingot attains a sufficient value GT/V> (GT/V) critical
Consequently in the Bridgman furnace, where temperature gradient is smaller than in
floating-zone method, a lower growth rate leads to coupled eutectic growth.
Coupled growth produces regular eutectic growing near extremum conditions . The
structure can self-adapt to local growth instability by branching, i.e. mechanism in which
lamellae or rod can change growth direction. Two materials characteristics can hinder this
adaption: 1) one or both phases grow in preferred directions – this makes change of
growth direction difficult and leads to irregular spacing; 2) materials composition departs
from eutectic, which leads to producing single phase dendrites or cells. The presence of
dendrites or cells depends on growth rate, solidification thermal gradient and
concentration gradient: V, GT and DC control planar growth.
Microstructure and crystallography
The symmetric eutectic coupled zone over phase diagram (n is growth rate)
Growth rate dependence Al2O3/YAG
a
Morphology and microstructure vs. the solidification rate.
a. 5 mm/h; b. 20 mm/h; c. 30 mm/h.
Change of composition in the range 76.3-86.3% Al2O3 (eutectic
81.3%Al2O3) does not influence microstructure.
c
b
Composition dependence Al2O3/GdAlO3: a. 73%Al2O3; b. 76%Al2O3 (eutectic); c. 77%Al2O3
a
Microstructure
Homogeneous microstructures are produced in coupled eutectic growth conditions,
while uncoupled growth leads to development of colonies or dendrites. Other
important aspects are the grain size and shape of eutectic domains and relative
crystallographic orientations as well as morphology and nature of eutectic domains.
The presence of eutectic grains is a consequence of
adaptation of eutectic structure to small instabilities
in solidification front and grain size is governed by
growth conditions and eutectic ability to
accommodate growth fluctuations. The small size of
eutectic grains imposes limits in application. Regular
structures which consist of non-faceted phases either
single crystal rods or lamellae embedded in matrix
are found in some DSE. In simplest case of isotropic
surface energy rods are predicted when volume
fraction of minor phase is less then 28% and lamellar
when it is more than 28%. Regular microstructure are
rather exception in oxide DSE due to strong tendency
of most oxides to grow along certain crystallographic
planes. It should be noted that eutectic grains are
absent in irregular eutectics.
NiO/YSZ DSE
Scheme of simplest regular eutectics
found in DSE
Microstructure
The microstructure is irregular when entropy of fusion DS f is high, because growth
interface can not easily deviate from certain crystal orientation and faceted phases
are produced. A special case of irregular microstructure was found in DSE oxides
where the phases are continuously entangled in three-dimensional interpenetrating
network (TDI). TDI microstructure is a homogeneous and fine dispersion of phases
free of grain boundaries. The absence of grain boundaries together with excellent
bonding between phases lead to extraordinary mechanical properties as well as high
temperature stability and corrosion resistance.
The TDI are found in faceted Al2O3/non-faceted YSZ
DSE grown at low growth rate and in faceted Al2O3 /
faceted YAG DSE grown in wide range of growth rate .
The domains Al2O3/YAG exhibit sharp angle facets
(morphology known as Chinese Script). The same
morphology of continuous networks of two singlecrystal phases is observed in sections perpendicular to
solidification direction and parallel to the growth
direction. It should be noted that phases are not
elongated in growth directions, but perfectly similar in
shape and size in both sections. The phases
interpenetrate without grain boundaries, pores or
colonies.
SEM micrograph showing threedimensional microstructure of
the Al2O3-GAP eutectic
composite The growth direction
is shown by vertical arrow.
Microstructures
Microstructure of binary DSE Al2O3 and garnet or perovskite are shown. In each case continuous
network of single phases are observed Al2O3 (dark) and perovskite or garnet (bright). The domain
mean size (length of shortest axis) is similar in Al2O3/EAG(Er3Al5O12) and Al2O3/GAP(GdAlO3), but much
larger in Al2O3/YAG. Also Al2O3/EAG and Al2O3/GAP exhibit curved interfaces, while Al2O3-YAG exhibits
faceted interfaces.
From left to right:
Al2O3/YAG, Al2O3/EAG
and Al2O3/GAP
Typical microstructures of ternary eutectics Al2O3/RE aluminate/YSZ are shown in figure.
Morphology of garnet type phase depends of rare earth and ZrO2. The Al2O3/YAG/ZrO2 DSE
exhibits fine microstructure with smooth interfaces contrary to coarser microstructure with
large planar interfaces and sharp angles in Al2O3/YAG. ZrO2 grows at interfaces between Al2O3
and YAG, while in other cases ZrO2 dispersed grains are observed in Al2O3.
From left to right:
Al2O3/YAG/ZrO2,
Al2O3/EAG /ZrO2 and
Al2O3/GAP/ZrO2
Crystallography
Aligned eutectic microstructure grow by unidirectional solidification usually consists
of single crystal phases grown preferentially along well-defined crystallographic
directions. These directions are not necessarily the directions of easy growth of the
isolated phases but correspond to minimum of interfacial energy configuration
between phases. The perfect crystal lattices of each phase are related by orientation
relationships which are unique in most systems and produce well defined interface
planes corresponding to dense atomic arrangements in the correspondent phases.
Electron diffraction studies performed in TEM on thin plates cut perpendicularly to
solidification axis reveal growth directions and corresponding well-defined
crystallographic directions.
Methods of DSE production
Bridgman method – growing bulk samples of large size. Melt
is contained in Mo, W or Ir crucibles heated by resistance
heater or radio-frequency induction through graphite
susceptor. Unidirectional solidification is achieved by slow
pulling the crucible off the hot zone. The apparent
temperature gradient <100 K/cm, growth rate V should be
less 100 mm/h to avoid cellular growth, l > 10mm.
Czochralsky method. Contact between crucible and growth
material is avoided since the eutectic is pulled out from the
melt pool. Thick rods 6 mm diameter can be grown by this
method.
Melt zone methods: fiber crystal growth from free melt
meniscus i.e. melting zone . Floating zone (FZ), pedestal
growth (PG) are crucible-less methods in which small sample
volume is melted by laser, radio-frequency or lamp mirror
furnaces. Temperature gradients are 10000 K/cm. Al2O3/YAG
DSE grown by laser-heated floating-zone method presents
interface spacing less 1 mm. Other growth-from-meniscus
methods are edge-defined film growth (EFG) and micropulling down (m-P) give thermal gradients 1000 K/cm.
Solidified sample is pulled out at high growth rate from liquid
pool feed by capillaries though the shaping dies.
Floating zone method
EFG
m-P