Experimental phase equilibrium study
Isothermal study (sample preparation and characterisation methods)
Diffusion couple
Methods of sample preparation of metal alloys
Raw materials in desired ratios are melted in hightemperature furnaces in protective gas atmosphere
(Ar, He) or in vacuum.
Arc-melting
Consumable and non-consumable electrode
Upper electrode (cathode) is water cooled Cu pole inlaid with W head, the lower
electrode (anode) is metal to be melted. A water cooled Cu platform is not only a
crucible for melted alloy but also part of positive electrode. Under inert gas or vacuum
an electric arc forms an ion plasma. The electric current passing through the electrode
melts the anode metals. Alloys are usually melted several times to ensure homogeneity.
Vacuum:
Positive: To avoid oxidation, impurity
removal, high temperatures
Negative: component evaporation
Inert gas atmosphere:
Positive: To avoid oxidation,
impurity removal, less
component evaporation
Negative: temperature is lower
Induction melting
Induction heating is heating of electrically conducting
object by electromagnetic induction through heat
generated in the object by eddy currents. An inductor
consists of electromagnet and an electronic oscillator that
passes a high-frequency alternating current through
electromagnet. The rapidly alternating magnetic field
penetrates the object generating electric current. Electric
current flowing through the resistance of material heat it
by Joule heating.
Heating process is short and high temperature can be obtained rapidly.
Natural stirring effect originating from induction current helps to homogenise alloys.
Melting process can be carried out in inert gas or vacuum atmosphere.
High-frequency induction melting is suitable for
variety of alloys. Compared with arc melting it
allows to prepare samples that contain volatile
components such as Mn, Sb, Pb. Crucibles are used
(Al2O3, graphite).
Another way is to put a mixture of starting metals
in a quartz ampoule, which is then evacuated and
encapsulated.
Using master alloys (Ni-40%B prepared by arc
melting). M.P. B is 2092°C, M.P. Ni-40%B is 1020°C.
Scheme for induction melting of alloys containing
elements of very diverse boiling points.
Powder metallurgy method
For alloys with oxidizable or volatile components or that may undergo severe
compositional segregation during solidification powder metallurgical methods are
better than high-temperature melting.
PM process consists from three steps: powder pulverisation, die compaction and
sintering. Compaction is performed at room temperature and sintering occurs at elevated
temperature and atmospheric pressure under carefully controlled atmosphere
composition (usually in protective atmosphere). Temperature of sintering is below
melting point of major constituent. In some cases minor constituent can form a liquid
phase; such cases are described as liquid phase sintering.
Non-equilibrium condition could occur during sintering. As a result, liquid phase can
appear at temperature lower than solidus. This liquid phase leads to overgrowth of
crystals and compositional segregation. Further homogenisation treatment is required.
Other techniques: hot isostatic pressing, spark plasma sintering
Homogenisation heat treatment
To accurately establish a phase diagram, it is important to reach equilibrium
state. During solidification from liquid non-equilibrium structures are easily
generated. Powder metallurgy sample are also require homogenisation
because sintering is short and it is non-equilibrium process.
Homogenisation heat treatment involves putting samples into furnace at high
temperature below the solidus temperature for an extended period of time.
The samples then quenched from elevated temperature to the room
temperature to freeze the phases stable at elevated temperature for analysis.
Homogenisation achieved through diffusion, thus annealing
temperature and diffusion are two important factors.
Analysis of quenched samples to construct isothermal section
(Static Method)
The success of quenching method depends
on preservation of high temperature
equilibrated phases at room temperature.
The method is appropriate for sluggish
phase transformations. One limitation is
difficulty to determine phase
transformation accurately. Another
problem is that quenched sample may not
represent the equilibrium state.
Characterisation methods
Composition of sample is controlled by chemical analysis (i.e. ICP-OES) or EPMA
XRD
Identification of phases present in the
sample, quantitative determination of
phase amounts, lattice parameters and
grain sizes by Rietveld analysis
Determination of crystal structure of a
new phase
XRD
Lattice parameter method to determine phase boundary
Binary system: different trends of lattice
parameters vs. solute concentration
Determination of ternary phase diagram using lattice parameter
method: a. isothermal section A-rich corner; b. variation of lattice
parameter of phase a along the tie-line; c. not along the tie-line; d
– variation of lattice parameters of a along the line being across
two phase and three phase region
The basic process of crystal structure identification is as follows.
Single phase diffraction is easier to index. Diffraction pattern is matched with all known
phases in the database. When the structure match is not found, the basic lattice group is
then estimated and used to match the peak positions and intensities. When pattern is
indexed, lattice parameters, molecular formula and space group are then determined.
Finally Rietveld refinement to modify the crystal structure and calculation of credence
factor are performed.
Metallography
Small samples are inlaid in polymer resin, mechanically ground and then polished
Optical microscopy: to determine number of phases, invariant reaction type, volume
fraction, homogeneity, surface contamination
Scanning electron microscopy (SEM) often coupled with energy dispersive X-ray
microanalysis (EDX):
To determine invariant reaction type, to distinguish phases by different contrast ( BSE)
and determine phase composition by EDX, to determine phase structure (EBSD), SE is
used for surface topology
TEM can detect fine precipitates
Electron probe microanalysis (EPMA) is similar to SEM with wavelength dispersive
spectrometers (WDS) attached.
EPMA is mainly used to measure composition of phases in two-phase or threephase regions and then establish the boundary of single phase regions
Example: phase relations in Al-Cr-Ti system at 1473 K
70Al-27Ti-3Cr
54Al-34Ti-12Cr
60Al-20Ti-20Cr
54Al-34Ti-12Cr
50Al-25Ti-25Cr
M. Kriegel et al. 2013
52Al-33Ti-15Cr
Combination of static and dynamic methods
1570 K U4: L+g-TiAl t+b
1354 K g-TiAl+bt+C14
In-situ measurements
To study phase equilibria directly at temperature of interest using hot-stage
microscopy, high temperature in-situ XRD. The advantages are
1. No complications from quenching
2. More straight forward interpretation of the results
3. Study in a continuous temperature range.
4. The disadvantage is less availability of such equipment, more difficult
experiments and potentially greater evaporation, oxidation.
In situ high temperature experiments are essential to study complex phase
equilibria in narrow temperature range.
Combinations of several methods
DTA-TG
DTA-TG-EGA Evolved Gas Analysis
Analysis of chemical composition of the evolved gas by means of spectroscopic methods
Coupling with FT-IR (Fourier transform infrared spectroscopy):
Determination of specific bands (e.g. C=O, CH3, etc.)
Coupling with mass-spectroscopy (detailed analysis of complex gas mixture)
Diffusion couple
The use of diffusion couples in phase diagram studies is based on the assumption
of local equilibrium at the phase interface in the diffusion zone. This means that
very thin layer adjacent to interface is in equilibrium with neighboring layer on the
other side of interface.
Chemical potentials of components vary continuously in the product layer of the
reaction zone and has the same value at both sides of interphase interface. Since
diffusion takes place if there is thermodynamic potential gradient, the total system
where diffusion occur is not in equilibrium. Local equilibrium is established and
maintained at the interfaces in the diffusion zone, which means that diffusion is
very slow compared with the rate of reaction to form a new phase.
Binary system
Single phase product layers separated by
parallel interfaces in sequence according
to phase diagram.
Ternary system
Two-phase area and single phase
area are possible.
f=C+2-P
T, P=fixed f=C-P f=1 to change composition P=1 for C=2 and P=2 for C=3
Preparation of diffusion couple
The bonding faces of the couple components are ground and polished flat, clamped
together and annealed at the temperature of interest. Depending upon initial
materials protective atmosphere can be used (vacuum and inert gas). After heat
treatment quenching of sample is desirable in order to freeze the high temperature
equilibrium.
Other plating techniques include plasma spraying and chemical vapour deposition
(CVD) . These techniques are suitable for metals and non-metals. Thermal
evaporation, electron beam evaporation or laser evaporation can be used to deposit
second component onto a bulk substrate.
Analytical techniques: EPMA. Standard metallographic procedure can be used to
prepare bulk multiphase couples for EPMA.
The measured concentration can be used to define tie-lines in the equilibrium
phase diagram
Example: binary system Cu-Zn
Fick‘s law – width of the layer ~ to t (time)
Zn atoms diffuse much faster than Cu
atoms. This explains why the intermetallic
phases form on the Cu side of original Cu-Zn
interface. This also explains the formation of
voids in g and e phases since Zn atoms are
moving towards the centre of the couple
faster than Cu atoms moving to Zn side.
Ternary system
The diffusion zone morphology developed in ternary couple depends on number,
structure and topological arrangement of newly formed phases and the resulting
microstructure can be visualized using the diffusion path . Diffusion path is the line in a
ternary isotherm representing the locus of average composition in planes parallel to the
original interface throughout the diffusion zone. Diffusion path must fulfill the law of
conservation of mass. Diffusion path should cross the straight line between end-members
of the reaction couple (mass balance line) at least once.
If phases are separated by planar interphases, the diffusion path crosses the two phase
region parallel to tie-line. However wavy interfaces or isolated precipitates can also form
at or near a phase interface.
Kirkaldy formulated a number of rules, which relates composition of the reaction zone to
the phase diagram. The reaction path involves a time-independent sequence of
intermediate layers. The plot give information about order of product layers, their
morphology and composition.
Diffusion path in ternary system (scheme)
a) Reaction zone structure in hypothetical couple A/Z of the A-B-C system b) Corresponding
diffusion path on the isotherm of the ternary system.
Dashed line parallel to tie-line in a two-phase region represents straight interface between single
phases (g-h). A solid line crossing tie-lines represents locally equilibrated two-phase zone (b-c, j-k, l-m).
Solid line entering two-phase region and returning back to single phase region (d-e-f-g )represents
region of isolated precipitates. A dashed lines crossing the three-phase region represent interface
between two phase and one phase layers (i-j) or two two-phase layers with one common phase (k-l).
Example: Ni-Cr-Ti system
Isothermal section at 850°C
Since a semi-infinite diffusion couple follows a
unique diffusion path, very often a large number of
couples should be studied experimentally to
construct a ternary isotherm.
Example: Ag-Fe-Ti system at 850°C
Fe60Ti40
Determination of phase equilibria for ternary system A-B-C
using two-phase alloys as end-members of diffusion couple
a. Schematic isothermal section; b. Schematic view of a possible reaction zone in
diffusion couple P/Q
Schematic view of reaction zones and diffusion path after
different annealing times
a. Initial „sandwich“ sample b. Reaction zone morphology for different annealing time;
c. Diffusion path for various annealing times
Microstructure of sandwich sample V/Ni foil/Cr after annealing at 1150°C
16 h annealing
Phase diagram of Ni-Cr-V system at 1150°C
49 h allealing
Possible sources of error
Possible melting in the diffusion couple, poor adhesion at the interfaces, and
accelerated reaction rate due to defects may complicate the interpretation of
diffusion couple experiments.
Difficulties associated with phase boundary concentrations in the reaction zone
(uncertainty of EPMA), difficulties to measure composition at the interface, X-ray
absorption and fluorescence effects.
Errors arising from formation quasi-equilibrated diffusion zone.
Sometimes certain phases seems to be missing when investigated by
microscopic or microprobe analysis. One of the reasons for absence of an
equilibrium phase can be presence of barrier layer at the interface such as oxide
films or presence of impurities. Segregation of impurities can make nucleation of
a certain phase difficult or cause metastable phase formation.
The fact that equilibrium phase is not identified can be explained by slow growth
kinetics (example Ti-Al couple indicates only TiAl3 at 625°C , while at 800°C
Ti3Al/TiAl/TAl2/TiAl3 are found).
Stabilisation by impurities (example Nb/Ni annealed at 1100°C NbNi3/m-Nb7Ni6
/Nb4Ni2N are forming).
Formation of volatile reaction product affects diffusion path. Example Mo-Si-N
system annealed at 1300°C Mo/Si3N4: dense Si3N4 – Mo3Si forms; porous Si3N4 –
MoSi2 and Mo5Si3 form. In first case N2 forming due to reaction can not escape
easily, while in the second case it can. Thus pressure of nitrogen determines
activity of Si at metal/ceramic interface.