Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
Table of Contents
1 INTRODUCTION ..............................................................................................................................................1
2 RESEARCH OBJECTIVES ..............................................................................................................................5
3 LITERATURE REVIEW ..................................................................................................................................6
3.1 INTRODUCTION ..............................................................................................................................................6
3.2 TREATMENT OF MULTICOMPONENT DIFFUSION PROCESSES ..........................................................................6
3.2.1 Single Phase ..........................................................................................................................................6
3.2.2 Multiphase.............................................................................................................................................7
3.3 Thermodynamics of Ni-Cr-Al system........................................................................................................8
3.4 COATING LIFE PREDICTION ............................................................................................................................8
3.4.1 C.E. Campbell .......................................................................................................................................8
3.4.2 J.E. Morral ............................................................................................................................................9
3.4.3 M.A. Dayananda .................................................................................................................................10
3.4.4 J.A. Nesbitt ..........................................................................................................................................12
4 APPROACH USED ..........................................................................................................................................13
4.1 SEM/EDA ANALYSIS ..................................................................................................................................14
4.2 IMSL PROGRAM...........................................................................................................................................16
4.3 REPRODUCTION OF THERMODYNAMIC DIAGRAMS ........................................................................................18
4.4 MODIFICATION OF COSIM CODE .................................................................................................................19
5 RESULTS ..........................................................................................................................................................20
5.1 SEM/EDA ANALYSIS ..................................................................................................................................20
5.2 IMSL PROGRAM...........................................................................................................................................24
5.2.1 Input and Output .................................................................................................................................24
5.2.2 Diffusion Treatment.............................................................................................................................24
5.2.3 Initial Approximation ..........................................................................................................................25
5.2.4 Calculated profiles ..............................................................................................................................25
5.3 REPRODUCTION OF THERMODYNAMIC DIAGRAMS ........................................................................................28
6 DISCUSSION....................................................................................................................................................32
7 CONCLUSIONS ...............................................................................................................................................35
8 REFERENCES .................................................................................................................................................37
9 APPENDICES...................................................................................................................................................39
9.1 TABLES ........................................................................................................................................................39
9.2 SELECTED MICROGRAPHS ............................................................................................................................40
9.3 CONCENTRATION PROFILES .........................................................................................................................41
9.4 IMSL PROGRAM INPUT FILE .........................................................................................................................47
9.5 THERMO-CALC TDB FILE ............................................................................................................................50
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
1 Introduction
The gas turbine was not always at the forefront of aerospace propulsion, nor was it a factor in
power generation. In 1940, a committee put together by the National Academy of Sciences to
evaluate possibilities of gas turbines came to the following conclusion,
“In its present state, and even considering the improvements possible when adopting the
higher temperatures proposed for the immediate future, the gas turbine engine could
hardly be considered a feasible application to airplanes mainly because of the difficulty in
complying with the stringent weight requirements imposed by aeronautics.”1
Despite the committee’s educated recommendation, Frank Whittle proceeded with his
research into gas turbines, and on April 8, 1941, the first flight of the British jet fighter
Gloster E28 powered by a Whittle W-1 jet engine marked the beginning of this remarkable
technology.
Industrial gas turbines and jet aircraft engines have only one moving part, the common shaft
which has compressor blades and turbine blades, otherwise known as the hot section because
of the temperatures at which it operates. In order for these devices to have greater efficiency
and output/thrust, the temperature at which the combustion gas enters the hot section must be
as high as possible (Figure 1, Figure 2)
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Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
Figure 1 Output as a function of turbine inlet temperature2
Figure 2 Efficiency as a function of inlet
temperature2
A class of materials with corrosion/oxidation resistance and excellent mechanical properties at
high temperatures (creep, fatigue resistance), known as superalloys were developed to be used
in gas turbines. Today, the most common superalloys are Ni- and Co-based, consisting of an
FCC matrix (γ) with precipitates of FCC Ni3(Al,Ti) (γ') as seen in Figure 3.
γ′
γ
Figure 3 SEM micrograph of GTD-111 microstructure after 9000hrs. @ 940°C (2500x)
Other alloying elements include C, Cr, Mo, W, Ta, Zr, B, Re, Y, Nb all for the purpose of
enhancing high temperature longevity in one way or another.
During high temperature
service, these alloy systems develop at protective oxide layer (mainly Al2O3) on the exposed
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Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
surface which acts a protective barrier against further oxidation. The prolonged use of these
devices creates a requirement for greater protection.
The solution has been to coat the components exposed to the harshest environments (hot
section) with an Al-rich coating of similar structure to the base alloy. These MCrAlY (M=Ni
and/or Co) coatings consist again of an FCC matrix (γ), with BCC NiAl (β) precipitates
(Figure 4). These particles act as sources of Al for oxidation and the coating continues to
oxidize sacrificially to protect the expensive base alloy.
In this way, the coatings are
consumable, and at prescribed times are stripped and replaced. Another consequence of high
temperature service is the interdiffusion of elements between coating and base alloy to
eliminate gradients in chemical potential.
β
γ
Figure 4 Photomicrograph of GT-33 (NiCoCrAlY) coating microstructure after 343hrs. @ 1050°C (40x)
The art which requires science is in coating life prediction. The most common analysis tool is
to use an empirical relationship for β depletion in the coating.
The simplicity of this
measurement and the independence from first principles calculations make it attractive to
some, but make it difficult to use in different situations if diffusion in different phases
dominates the process at different temperatures.
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Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
It would be valuable to have an accurate model of coating degradation, capable of predicting
the effects of interdiffusion. This would enable users to run their machines, typically costing
between $10M and $30M to run to their fullest extent without the risk of catastrophic
oxidation of the blade alloys which cost anywhere from $500,000 to $3M per row to replace.
Area of interest containing
multiple rows of blades
Figure 5 Gas turbine schematic
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Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
2 Research Objectives
•
To model diffusion in the whole superalloy-coating system for a Ni-based superalloy
with MCrAlY overlay coating by back calculating diffusion parameters from
concentration profiles
•
To develop thermodynamic database for Ni-Cr-Al system for generating relevant
phase diagrams and for calculating the thermodynamic properties needed
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Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
3 Literature Review
3.1 Introduction
In order to determine how MCrAlY coatings degrade with time, both the thermodynamics and
the kinetics of the system must be known. It this can be done, an accurate description of the
system can be established and the dynamics of the operation of these devices can be
understood.
3.2 Treatment of Multicomponent Diffusion Processes
3.2.1 Single Phase
Onsager’s formalism of Fick’s laws for a multicomponent diffusion is described with (n-1)2
interdiffusion coefficients for an n-component system, and the flux of species i is expressed
by
n −1
~ ∂C j
J i = −∑ Dij
∂z
j =1
(1)
~
where D is the matrix of interdiffusion coefficients [(n-1) x (n-1)]. For example, in the
quaternary case, the flux of component i would be expressed as
~ ∂C
~ ∂C 2 ~ ∂C 3
J i = − Di1 1 − Di 2
− Di 3
∂z
∂z
∂z
(2)
In this case, the interdiffusion matrix would contain nine parameters, which in the general
case, may be concentration dependent. To evaluate these terms base on previous methods,
two diffusion couples must be prepared with a common composition in the diffusion zone
where the interdiffusion coefficients are to be evaluated3,4.
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Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
If it can be assumed that the elements of the diffusion matrix are constant with respect to
compositions, analytical solutions for isothermal systems are well established5-9, but if this
assumption is not valid, numerical methods must be employed.
3.2.2 Multiphase
Diffusion in multiphase systems is much more common and adds great complexity to the
problem. Second phase particles have been known to increase or decrease diffusivity of the
overall system depending on their magnitudes with respect to the matrix10. Along with being
sources or sinks of solute atoms, the fraction of these phases can also change during diffusion
processes to accommodate changing concentrations. Moreover, as demonstrated by Hopfe
and Morral11, diffusion paths in two phase regions of a multicomponent system have
discontinuities and are typically composed of straight lines, and can be ‘serpentine’ or ‘zigzag’ between subsequent regions. This is caused by the fact that the inequality
∂µ i
> 0 is not
∂C i
automatically held in mulcicomponent systems..
The calculation of effective mass transport properties for multiphase systems can be
incredibly complex, making the use of approximations very common.
One such
approximation involves multiplying the diffusivities of alloying elements in the matrix by a
so-called labyrinth factor10. Engstrom et al simulated the diffusion paths of several single
phase and multiphase superalloy couples. This was conducted assuming diffusion occurred
entirely within the matrix phase, and during each step in the simulation the volume fraction
and composition of the precipitates remained constant.
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Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
They simulated γ/γ+β, γ+β/γ+β and γ+β/γ+β+γ' and single phase diffusion couples simply
containing Ni, Cr and Al which showed, for example, how a γ/γ couple can exhibit the
behavior of forming γ' at the interface.
3.3 Thermodynamics of Ni-Cr-Al system
Thermodynamic databases usually constructed via the thermodynamic optimization (i.e.
CALPHAD12) method allow constructing a wide variety of phase diagram and property
diagrams. Huang and Chang13 published the thermodynamic description of the Ni-Cr-Al
system, which was re-worked into a corresponding THERMO-CALC14 compatible database.
In this work, they modeled the liquid(L), FCC(γ), BCC(α), and two ordered phases (γ' and β).
γ, L, and α are treated as substitutional solutions, while γ’ and β utilize several sublattices.
Binary compounds existing in the Ni-Cr-Al system were also included.
3.4 Coating Life Prediction
A coating is considered spent when it no longer serves its function; that is to produce a stable,
protective oxide. Since the protective oxide is Al2O3, a critical concentration of Al (usually
around 1wt%) is a logical choice for determining coating life. By calculating the time when
this level is reached, expensive shut downs for evaluation of components, and even more
expensive repairs can be reduced or ideally avoided. Most studies are conducted on either
interdiffusion or oxidation, but since the focus of this work is interdiffusion, this is where the
most time will be spent.
3.4.1 C.E. Campbell
Using diffusion couples of René-88/Ni, and René-88/Inconel 718 whose composition are
found in the appendix, Campbell et al15 compared the diffusion couples which were observed
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Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
using a CAMECA (Paris, France) microprobe with those calculated using DICTRA16
software. In order to generate accurate concentration profiles with DICTRA16, the Ni-Data
thermodynamic database17 was utilized in conjunction with the diffusion mobility data based
by Campbell et al18 to re-calculate the equilibrium using THERMO-CALC14 at each time
step.
This fundamental study of diffusion processes in superalloys used samples aged for 1000
hours at 1150°C followed by a water quench to produce a single phase structure. By using
these samples, the intricacies of multi-phase diffusion were avoided, but validation of the
mobility database18 was successful.
3.4.2 J.E. Morral
J.E. Morral has been involved with numerous studies into diffusion behaviour of Ni-Cr-Al
alloys. One such study investigated three types of boundaries found in Ni-Cr-Al diffusion
couples19 using the difference in equilibrium phases on either side of the interface to
distinguish between them (i.e. γ/γ+β Î 2-1 Î type 1). In 1994, Morral et al.20 used a piece
of software called “Profiler” to generate concentration profile of Al and Cr in several γ+β (NiCr-Al) diffusion couples. This work represented the first diffusion analysis conducted on a
pair of two phase alloys, rather than a single phase coupled to a two phase, and this generated
the first diffusion paths on this style of diffusion couple. Later, a similar study was conducted
using DICTRA16 software. It was assumed that diffusion only occurred in the matrix phase,
and the precipitates only act as sources or sinks. During each time step, only the composition
of the matrix changed, while the composition and volume fraction of the precipitates
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Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
remained constant.
Again, Morral et al. used these simulations to show the “zig-zag”
diffusion path demonstrated earlier by Hopfe and Morral11.
3.4.3 M.A. Dayananda
If it is assumed that the diffusion coefficients are independent of concentration or if the
concentration dependence is insignificant; an isothermal diffusion couple with minimal
changes in concentration can be assumed to have constant diffusion coefficients. It is based
on these assumptions that Dayananda explored average effective diffusion coefficients21-24 to
calculate ternary diffusion profiles. The analysis is based on the Botzmann-Matano method25
which yields the relation for diffusion coefficients as a function of composition
C′
D (C ' ) = −
1 ⎛ dz ⎞ ⎤
⎟ ⋅ (z − Z M )dC
⎜
2t ⎝ dC ⎠⎥⎦ C ′ C∫R
(3)
where t ≡ time, z ≡ position, ZM ≡ position of Matano interface, C ≡ concentration, CR ≡
concentration at left most point and C' ≡ concentration of interest.
From equation 3, the flux can be expressed as
dCi 1 C '
J i = − D (C ' )
=
( z − Z m )dCi
dz
2t C∫R
(4)
which can be equated to the ternary flux equation (2)
~ ∂C
~ ∂C
J i = − Di31 1 − Di32 2
∂z
∂z
(5)
Integrating the latter equation with respect to z yields,
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Richard Meguerian
z2
C1 ( z 2 )
∫ J dz = − ∫
C2 ( z2 )
∫
3
i1
i
z1
D dC1 −
TMS Outstanding Student Paper Contest 2005
McMaster University
C1 ( z1 )
Di32 dC 2 → J i ( z 2 − z1 ) = D i1 [C1 ( z1 ) − C1 ( z 2 )] + D i 2 [C 2 ( z1 ) − C 2 ( z 2 )]
3
3
(6)
C2 ( z1 )
This gives two equations (species 1 and 2) for the determination of four variables (diffusion
coefficients). The other two equations come from a modified version of Fick’s law based on
3
the assumption that the effective diffusion coefficients D ij are constant over the selected
composition range.
3
J i = − D i1
3 ∂C
∂C1
− Di2 2
∂z
∂z
(7)
If equation 7 is multiplied by (z - z0)n and integrated over the diffusion zone,
z2
∫ J (z − z
i
z1
0
)dz = − D
3
i1
C1 ( z 2 )
∫ (x − x )
0
C1 ( z 2 )
n
dC1 − D
3
i2
C2 ( z 2 )
∫ (x − x )
0
n
dC 2
(8)
C2 ( z 2 )
When n=0, we obtain the previous set of two equations, but if n=1, unique equations are
obtained and complete the system of equations, containing only easily calculated values
available from the concentration profiles. After calculation of the average effective diffusion
coefficient on both sides of the Matano interface, the average is taken and reported.
Dayananda has released a piece of software, MultiDiFlux which reads ternary concentration
profile to back calculate the effective interdiffusion coefficients over specific composition
ranges based on the method presented here.
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Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
3.4.4 J.A. Nesbitt
Coupling both oxidation and interdiffusion in overlay-coated turbine parts, Dr. Nesbitt’s
work26 allows the specification of oxidation, spallation and interdiffusion parameters along
with dimensions of the system in order to calculate ternary concentration profiles (Figure 6).
His software, entitled COSIM (Coating Oxidation and Substrate Interdiffusion Model), was
developed in the mid 1980s at NASA, but the source code was recently made available
publicly.
Figure 6 Sample COSIM output for a 250µm coating at 850°C (Coating: Ni-40Cr-9Cr, Alloy: Ni-20Cr4Al)
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Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
4 Approach Used
The calculation of accurate diffusion data is tedious, and requires many experiments. Based
on Onsager’s formalism, quaternary diffusion is expressed with three equations and nine
diffusion coefficients.
If it can be assumed that local equilibrium is maintained in the
direction parallel to the coating/substrate interface, then all diffusion takes place in the
direction normal this interface and the problem can be made one dimensional. This is valid
since the only diffusion parallel to the interface is due to the growth of the γ’ phase in the
matrix which can be considered slow with respect to the diffusion of atoms across the
coating/substrate interface. Moreover, if the partial molar volumes of each phase are assumed
to be equal15,18, then the average composition within a control volume can be used instead of
the matrix and/or precipitates.
Following this logic, mass transfer will be modeled using a set of “operative” diffusion
coefficients rather than phase-specific ones assuming that a representative sample is taken for
concentration measurements and that a reasonable averaging procedure is used. Although
these values will be different from the classical interdiffusion coefficients, they still relate
mass transport to fluxes and will therefore be useful in modeling processes between the
coating and substrate.
Fick’s second law can now be expressed as,
∂Ci
∂ 2 C1 ˆ ∂ 2 C 2 ˆ ∂ 2 C3
= Dˆ i1
+ Di 2
+ Di 3
∂t
∂z 2
∂z 2
∂z 2
(9)
where D̂ij are the operative diffusion coefficients and Ci represents the volume average
concentration of component i.
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Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
By collecting concentration profiles from available diffusion couples (Table 1), an
optimization can be carried out to calculate the operative diffusion coefficients.
Table 1 Samples available for diffusion analysis
NiCoCrAlY/Ni-base
Coating: GT-33
Alloy: DS GTD-111
Couple Mount No.
35C
1691
35E
2287
35F
3188
35H
1485
35I
1682
35J
1897
35N
1444
35O
1462
35P
1533
35Q
1643
35T
1423
35U
1453
35V
1524
CoCrAlY/Ni-base
Diffusion
Diffusion
Coating: GT-29
Temperature, time,
Alloy: GTD-111
°C(°F)
(hrs.)
Couple Mount No.
58C
1698
865 (1589)
1959
58E
2294
865 (1589)
8698
58F
3195
865 (1589)
17054
58H
1492
940 (1724)
492
58I
1689
940 (1724)
1980
58J
1904
940 (1724)
4512
58N
1451
990 (1814)
119
58O
1469
990 (1814)
324
58P
1540
990 (1814)
711
58Q
1650
990 (1814)
1338
58T
1430
1050 (1922)
187
58U
1460
1050 (1922)
343
58V
1531
1050 (1922)
736
4.1 SEM/EDA Analysis
The process of collecting concentration profiles was conducted on a Philips 515/Link EDA
scanning electron microscope (SEM) with LaB6 filament. The accelerating voltage was
20keV, and the filament current was set to 15µA.
In order to acquire accurate concentration profiles, a method was developed to take the
volume average composition at individual points along the direction of interest. By setting
the electron gun to scan a line perpendicular to the diffusion trajectory, rather than focusing
on a point while collecting an x-ray spectrum, the average over a volume equal to the length
of the scan (~500µm) by the interaction volume width (~1µm) and by the interaction volume
depth (~1µm) can be accurately acquired (Figure 7).
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Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
Alloy
Z1
Z2
Coating
Z3
Z4
Z5
Z6
Z7
Z8
Figure 7 Use of scan feature to collect average concentration profiles (green) for main trajectory (red)
over different position (z) values.
The length of the scan can be justified since the microstuctural features (γ′ precipitates) in the
alloy are on the order of 500nm and in the coating, β phase is essentially continuous.
Therefore, any scan length in the order of hundreds of microns is a representative sample.
Although the coating/alloy interface is easy to see on an etched sample (Figure 7), in order to
get optimal X-ray emission and measurement, the surface must be smooth to approximately
1µm. Therefore, using an etched sample is not practical. As seen in Figure 8, the original
interface can be observed by the increased porosity due to the alloy being grit blasted before
the application of the coating.
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Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
Original interface
Figure 8 SEM micrograph showing original coating/alloy interface by porosity from grit blasting (550x )
In order to ensure that accurate concentration profiles could be extracted from the X-ray
spectrums, a superalloy was solution treated to produce a single phase structure, and then sent
to an independent lab where turnings were analyzed for composition. These samples were
then used to standardize the SEM software (URSA 1.3). This ensures that the “matrix
effects” are taken into account rather than just pure elements standards generally used.
4.2 IMSL program
Once the concentration profiles have been obtained, an analysis was conducted to calculate
the operative diffusion coefficients. To carry out these calculations, a Fortran 90 compiler
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Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
was used with the IMSL Fortran Library by Visual Numerics27. Within this library, there
exists MOLCH, a robust subroutine which can be utilized to solve a system of partial
differential equations. This allows the calculation of concentration profiles at different times
and temperatures starting from specified initial conditions and operative diffusion coefficients
by solving the modified version of Fick’s second law for a substitutional solution.
∂C1
∂ 2 C1 ˆ ∂ 2 C 2 ˆ ∂ 2 C 3
ˆ
= D11
+ D12
+ D13
∂t
∂z 2
∂z 2
∂z 2
(10)
∂C 2
∂ 2 C1 ˆ ∂ 2 C 2 ˆ ∂ 2 C 3
ˆ
= D21
+ D22
+ D23
∂t
∂z 2
∂z 2
∂z 2
(11)
∂C3
∂ 2 C1 ˆ ∂ 2 C 2 ˆ ∂ 2 C3
= Dˆ 31
+ D32
+ D33
∂t
∂z 2
∂z 2
∂z 2
(12)
∂C 4
∂
= − (C1 + C 2 + C 3 )
∂t
∂t
(13)
This is conducted with zero-flux boundary conditions. After profiles are calculated at the
times and temperatures of the corresponding specimens, an analysis is conducted to determine
how close the calculations are to the experimental counterparts.
This comparison is
conducted with a non-linear least squares analysis in conjunctions with another IMSL
function (UNLSF) where appropriate changes are made to the operative diffusion matrix to
reduce the sum of the squares of the operative function (Equation 14).
calc
exp
⎛ C kji
( z kji ) − C kji
( z kji , Dˆ ) ⎞
⎜
⎟
∑∑∑
exp
⎜
⎟
C
(
z
)
∆
i =1 j =1 k =1
kji
kji
⎝
⎠
N
N i M ij
2
(14)
where N is the number of components, Ni is the number of profiles for component i, and Mi j
is a number of spatial points for j-th profile of the i-th component.
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Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
The minimization continues until the stopping criterion is met.
UNLSF utilizes the
Levenberg-Marquardt algorithm28 to evaluate the non-linear terms.
Is the
stopping
criterion
satisfied?
Change
D matrix
Initial
approximation
of the D matrix
(diagonal, etc.)
Solve system of
PDEs (modified
Fick’s 2nd law) for
conc. profiles from
initial profiles
Determine the
direction which
D components
are to be
changed
Compare
results with
experimental
counterparts
Figure 9 Iteration process for determining operative diffusion coefficients
4.3 Reproduction of thermodynamic diagrams
Phase diagrams can be generated based on published thermodynamic properties13 and
Thermo-Calc software package14. These properties were entered as a database of excess
Gibbs energy functions with standard states from a well-sourced reference by Dinsdale29. The
phases included in the analysis were: γ, γ', σ, β, L, α; and compounds: Al11Cr2, Al13Cr2,
Al3Ni, Al3Ni2, Al3Ni5, Al4Cr, Al8Cr5, Al9Cr4 and AlCr2.
A thermodynamic description of the Co-Cr-Al system is not readily available in literature like
the Ni-Cr-Al system, but is available for purchase17. This limited the evaluation to only Ni,
Cr and Al.
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Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
4.4 Modification of COSIM code
Due to the fact that the COSIM code is publicly available, it is possible, time permitting, to
modify the program to use operative diffusion coefficients. Following appropriate
modifications, it will simulate a gas turbine blade in service under a variety of conditions.
Using the determined operative diffusion coefficients, estimates of oxidation/spallation
parameters and the appropriate dimensions, coating lifetime can be estimated based on a
critical aluminum concentration in the coating.
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Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
5 Results
5.1 SEM/EDA Analysis
The calibration of distances on the SEM, although normally not an issue, was paramount for
this study, and had to be completed before the acquisition of concentration profiles. To
ensure that the stage micrometers were accurate in the plane of interest, a transmission
electron microscope (TEM) grid was attached to a representative sample with carbon tape and
observed on the SEM. Knowing the certified spacing of the grid and moving the sample stage
a specified distance using the stage micrometers, it was confirmed that the stage micrometers
offer the degree of accuracy required for this study.
Figure 10 SEM micrograph of grid used to
calibrate the stage micrometers (13.2x)
Figure 11 Higher magnification of Figure 10 showing
details of grid (424x)
This proved that as long as the surface being studied is parallel to the sample stage, and that
the stage tilt remains constant (30°), the micrometers are accurate. If either one of these
variables changes, the stage micrometers cannot be used. Controlling the stage tilt is a trivial
task, but small variations in height across the samples results in different take off angles
(TOA).
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Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
y
θ
e-
x
Sample
Sample stage
Figure 12 Effect of variation in height across sample
Although each sample had a slightly different TOA, the maximum deviation of any sample
was less than 10°. From Figure 12, it can be seen that
y=
x
cos(θ )
(15)
For and ideal case when θ = 0 D , y=x, but when θ = 10 D , y=1.015x, resulting in an error of
only ±1.5% for the maximum deviation in TOA.
The smallest spacing between spatial data points that was feasible using the stage micrometer
was 10µm. If higher resolution was needed, the electron gun had to be repositioned and
interpolation of distances from the monitor would be required. Since this was the case, most
differential distances were multiples of 10µm. At these increments, the small amount of play
in the stage micrometers becomes an issue. This is referred to as gear lash, and is unavoidable
with mechanical systems. It cannot be eliminated, only reduced. This was accomplished by
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Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
proceeding in the same direction between points to keep continuous pressure on the same side
of the gears. By doing this, the incremental change in position remains constant and accurate.
The EDA spectrums for each line scan were collected until the X-ray count has reached
200 000. This allowed for ample averaging from all points on the line and ensures an
adequate signal to noise (background) ratio.
To get accurate compositions, all elements that were known to be in the material were labeled
for quantitative analysis (Ni, Al, Cr, Co, Ti, W, Ta, Mo) in the EDA spectrum (Figure 13).
Figure 13 EDA spectrum for sample 1485 at a position 90µm from the original interface into the alloy.
The software was instructed to normalize results because all elements had been identified,
and the standard which was created earlier with the single phase sample was implemented.
A similar spectrum was acquired for each point on each sample, then quantitatively analyzed,
recorded, and repeated. After all data about a single diffusion couple was organized, a
concentration profile could be generated as seen in Figure 14.
22
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Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
Table 2 Truncated concentration data for diffusion couple 1462
80
Concentration (wt%)
70
60
50
Distance from
interface
Ni
-150
-110
-90
-70
-50
-40
-30
-20
10
20
30
40
50
70
90
110
150
200
300
500
Certified Composition
Position
8
7
6
5
4
3
2
1
9
10
11
12
13
14
15
16
17
18
19
20
Co
36.33
36.56
36.07
36.89
39.72
41.56
39.15
40.3
37.27
40.8
56.37
61.69
64.13
64.28
64.7
64.6
64.44
66.22
63.56
65.82
wt%
Cr
33.36
33.93
33.79
32.78
30.89
29.43
30.84
29.63
32.57
29.81
20.94
12.36
10.18
9.13
9.86
9.8
10.31
9.43
10.44
9.54
Al
18.15
19.03
19.24
19.58
16.77
15.07
17.29
16.18
20.06
17.63
9.02
11.65
11.37
11.67
12.34
12.09
12.5
10.99
12.83
11.53
Coating
10.43
9.43
9.25
8.85
11.03
12.12
10.23
11.81
7.4
9.17
7.13
4.82
4.48
3.58
3.34
3.56
3.08
3.44
3.06
3.35
Sample: 1462
Spectrum File Name
1462008
1462007
1462006
1462005
1462004
1462003
1462002
1462001
1462009
1462010
1462011
1462012
1462013
1462014
1462015
1462016
1462017
1462018
1462019
1462020
Alloy
Ni
Co
Cr
Al
40
30
20
10
0
-200
-100
0
100
200
300
Distance from original interface (µm)
Figure 14 Concentration profile for sample 1462
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Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
Despite the excellent correspondence with certified values as seen in Figure 14, this was not
always the case.
From other concentration profiles found in the appendix, Al and Cr
measurements show great deviation from expected values.
5.2 IMSL program
5.2.1 Input and Output
Upon running the executable, the user is prompted to enter the name of the input and output
files that the software will interface with. As seen in section “9.4 IMSL program input file”,
the format is simple and obvious. Any number of profiles with different times, temperature
and spatial coordinates are automatically read from this file. Along with this, the number of
components and identities of them are also read from the input file. This allows any number
of components to be analyzed.
After the optimization is complete, the software automatically outputs separate files for each
component, time and temperature found in the input file. Within each file is the original data
points (concentrations), experimental error, and calculated profiles for that time and
temperature. The files are named appropriately with species, temperature and time (i.e.
AlT990t1323.dat for Al @ 990°C, 1323hrs.) allowing quick checks to be performed on the
correspondence between calculated and experimental profiles.
5.2.2 Diffusion Treatment
Using the Arrhenius relation for diffusion coefficients, there are two variables to be taken into
account.
⎛ E ⎞
D = Do exp⎜ − act ⎟
⎝ RT ⎠
(16)
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Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
Do is the pre-exponential term and Eact is the activation energy. In the case of quaternary
diffusion, there are nine Do and nine Eact terms. These terms are treated as independent of
temperature and composition in this version of the software, but this could be changed in the
future if a relationship was desired.
The diffusion matrix must also be positive definite. Since MOLCH is unaware of the fact that
it is calculating diffusion profile, a check that the matrix is positive definite is carried out each
time a diffusion matrix is calculated. This is done by confirming that all eigenvalues are real
and positive. If a matrix fails this test, it is disregarded and the optimization continues.
5.2.3 Initial Approximation
Due to a great number of variables, it is possible that multiple minima of the objective
function exist. To find an area in the minimization space to begin the optimization, an initial
approximation of the solution is required. If the user does not have an approximation to
supply the software, the computer generates random values within bounds specified for
relevant terms and calculates the objective function (Equation 14). After a user-specified
number of random terms have been generated and the objective function is calculated, the
terms which produced the lowest value of the objective function is chosen as the starting point
for the non-linear least squares optimization.
5.2.4 Calculated profiles
As seen in Figure 15, the correspondence between calculated and experimental profiles for Co
is quite good after a typical optimization.
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Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
40
35
Concentration (wt%)
30
Cexp
Ccalc
25
20
15
10
5
-150
-100
-50
0
50
100
Distance from the original interface (µm)
Figure 15 Calculated and experimental Co profile for sample 1691
Cr and Al showed larger deviations between experimental and calculated profiles. In most
samples, the experimentally determined concentrations of Cr and Al were lower than the
expected and calculated ones.
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Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
25
Concentration (wt%)
Cexp
Ccalc
20
15
10
-150
-100
-50
0
50
100
Distance from the original interface (µm)
Figure 16 Calculated and experimental Cr profile for sample 1691
These results were typical of any optimization, although the exact values of diffusion
parameters could be quite different from one time to the next.
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Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
10
Concentration (wt%)
Cexp
Ccalc
5
0
-150
-100
-50
0
50
100
Distance from the original interface (µm)
Figure 17 Calculated and experimental Al profile for sample 1691
5.3 Reproduction of thermodynamic diagrams
A database of thermodynamic properties of the Ni-Cr-Al system and the code produced can
be seen in section “9.5 Thermo-Calc TDB File”.
The following are reproductions of
isothermal sections of the Ni-Cr-Al ternary phase diagram at temperatures corresponding to
the samples studied.
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Richard Meguerian
TMS Outstanding Student Paper Contest 2005
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γ
γ+γ'
β+
γ'
γ'
γ
γ'
α+
γ+
α+β
γ'
α+
β+
γ'
α+
β
α+
Figure 18 Ni-Cr-Al phase diagram at 865°C, with area of interest expanded
γ
γ+γ'
'
β+
γ
α+
γ'
γ'
α+
γ'
γ'
β+
α+β
γ+
α+
β
α+γ
Figure 19 Ni-Cr-Al phase diagram at 940°C, with area of interest expanded
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Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
γ
α+γ'
γ+γ'
β+
γ'
γ'
γ'
γ'
α+β
β+
γ+
β
α+
α+
α+γ
Figure 20 Ni-Cr-Al phase diagram at 990°C, with area of interest expanded
γ
γ+γ'
β+
γ'
γ'
α +β +γ
β
α+β
'
β+γ
α+β+γ
α+γ
Figure 21 Ni-Cr-Al phase diagram at 1050°C, with area of interest expanded
It should be noted that the β+γ two-phase region is not stable except in the 1050°C samples.
This explains why the formation of α and γ' can sometimes be observed at the alloy/coating
30
Tuesday, September 06, 2005
Richard Meguerian
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interface at lower temperatures. These diagrams must also not be taken as 100% accurate to
the actual system since the interactions of other elements, specifically Co has not been taken
into account, and it’s known that Co does not form all phases shown in the Ni-Cr-Al system.
31
Tuesday, September 06, 2005
Richard Meguerian
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6 Discussion
The discrepancy between calculated and experimental Al profiles can be explained by the fact
that the software uses the certified compositions of the coating and alloy as the concentration
profiles for t=0 while the acquired profiles do not coincide with this. Mass is conserved
during each time step because of the zero-flux boundaries imposed and expressed by Equation
17.
⎛ zn calculated
⎞
⎛ zn
⎞
⎜ C
⎟
⎜ C ( z )dz ⎟
=
(
z
)
dz
i
i
⎜ z∫
⎟
⎜∫
⎟
⎝1
⎠ ∀t >0 ⎝ z1
⎠ t =0
(17)
From the concentration profiles in the appendix, it is seen that there is significantly less Al in
the system than should be seen since the coating is 10 wt% Al and the alloy is 3 wt% Al.
Because of this, the computer cannot get an accurate match to the profiles.
To prove that discrepancies between the actual and experimental concentration profiles are
such a large source of error, the software was given the following initial conditions.
Alloy:
Al 1.4wt%
Cr 12wt%
Co 9.5wt%
Ni BAL
Coating:
Al 6wt%
Cr 17wt%
Co 30wt%
Ni BAL
These values correspond with the concentrations from the endpoints of acquired profiles
rather than the expected values. After the optimization was complete with these new initial
values, the discrepancies were greatly reduced (Figure 22 and Figure 23) for all profiles and
elements. This proved that the main source of the discrepancies for Al and Cr was the
erroneous EDA acquired concentration profiles, and that the method was implemented
correctly.
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Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
Concentration (wt%)
10
Cexp
Ccalc
5
0
-150
-100
-50
0
50
100
Distance from the original interface (µm)
Figure 22 Calculated and experimental Al profile for sample 1691 after initial conditions in optimization
were changed
Concentration (wt%)
25
Cexp
Ccalc
20
15
10
-150
-100
-50
0
50
100
Distance from the original interface (µm)
Figure 23 Calculated and experimental Cr profile for sample 1691 after initial conditions in optimization
were changed
33
Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
One explanation for the lower than expected Al and Cr concentrations may be the difficulty in
standardizing elements using samples with less than 5 wt%. Since the SEM/EDA method was
standardized using the same alloy which contains 4 wt% Al, calibration with a standard
coating containing 10 wt% Al would hopefully allow already collected spectrums to be reanalyzed to acquire more accurate concentration profiles.
Another aspect requiring attention is the fact that many solutions can be obtained from the
same input file depending on the initial approximation. This is because the minimization
space of 18 variables contains many local minima, and the quality of input data only adds to
this problem. The only way to improve the chances of finding the best solution from the
available data is to use a greater number of random approximations to increase the chances of
finding the global minimum. If relationships were found between Eact or Do values in their
respective matrices, then the number of variables could be reduced and possibly lead to a
unique solution.
Although many solutions can be obtained with greatly varying parameters, the calculated
profiles remain very similar and the value of the objective function remains fairly constant for
each optimization.
34
Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
7 Conclusions
This study has shown that it is possible to use the volume average composition of a
superalloy/MCrAlY coating to model diffusion processes. This was conducted with GTD111 alloy and GT-33 NiCoCrAlY coating for numerous times and temperature. It has further
proved that with accurate data, the method employed of non-linear least squares regression
can accurately reproduce concentration profiles. The creation of a new standards file for
evaluation of acquired spectrum may yield greatly improved correspondence between
experimental and calculated profiles. If this is not successful, the Al and Cr data could be
systematically modified to ensure that mass in conserved in the system. Consideration should
be given to the possibility of using EPMA (Electron Probe Micro Analysis) on these samples
to acquire more accurate concentration profiles if sufficient results cannot be obtained with
current data.
This will reduce scatter in the profiles, moreover, it could decrease the
ambiguity of solutions by decreasing, if not eliminating the non-uniqueness of the solution.
Although the non-uniqueness poses a problem when comparing the values of diffusion
parameters with literature, if one is only interested in duplicating concentration profiles, and
predicting profiles for different times and temperature, adequate results can be obtained
immediately after addressing the problems with the Al and Cr profiles.
Upon successful completion of current system, investigation should continue into other
alloy/coating systems to determine the effects of composition on diffusion and create a
coating life model for numerous alloys/coatings through the modification of the COSIM
software with relevant oxidation/spallation parameters.
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Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
A Ni-Cr-Al thermodynamic database has been developed which can be made available on the
McMaster University Materials Engineering Thermo-Calc server for use by all who use
Thermo-Calc and available upon request. To follow up on this, the interactions associated
with Co, although not currently available should be added when available to create a more
accurate description of the actual system.
36
Tuesday, September 06, 2005
Richard Meguerian
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McMaster University
8 References
1. John Golley. Genesis of the Jet, Frank Whittle and the Invention of the Jet Engine,
Airlife Publishing Ltd: 1996.
2. C.T.Sims; N.S.Stoloff; W.C.Hagel. Superalloys II, John Wiley & Sons, Inc.: 1987.
3. J.S.Kirkaldy. Canadian Journal of Physics 1958, 36, pp. 899-906.
4. J.S.Kirkaldy; D.J.Young. Diffusion in the Condensed State, The Institute of Metals,
London: 1987.
5. W.Jost. Diffusion in Solids, Liquids, Gases, Academic Press, New York: 1952.
6. J.S.Kirkaldy. Advances in Materials Research. Herman, H. [4], 55. 1970. New York,
Wiley.
7. P.K.Gupta and A.R.Cooper. Physica 54, 39. 1971.
8. M.S.Thompson and J.E.Morral. Acta Materialia 34, 339,2201. 1986.
9. F.J.J.van Loo, G.F.Bastin, and J.W.G.A.Vrolijk. Metallurgical and Materials
Transactions A 18A, 801. 1987.
10. A.Engström; J.E.Morral; J.Ägren. Acta Materialia 1997, 45, pp. 1189-99.
11. W.D.Hopfe; J.E.Morral. Acta Metallurgica Et Materialia 1994, 42, pp. 3887.
12. Kaufman, L.; Bernstein, H. Computer Calculation of Phase Diagrams, Academic Press:
New York, 1970.
13. W.Huang; Y.A.Chang. Intermetallics 1999, 7, pp. 863-74.
14. B.Sundman; B.Jansson; J-O Andersson. Calphad 1985, 9, pp. 153-90.
15. C.E.Campbell; J-C Zhao; M.F.Henry. Journal of Phase Equilibria and Diffusion 2004,
25, pp. 6-15.
16. J.-O Andersson; L.Höglund; B.Jönsson; J.Ägren. Fundamentals and Applications of
Ternary Diffusion, Pergamon Press: New York, 1990.
17. N.Saunders Superalloys 1996, 1996 TMS; pp. 101.
18. C.E.Campbell; W.J.Boettinger; U.R.Kattner. Acta Materialia 2002, 50, pp. 775-92.
19. Cheng Jin; J.E.Morral. Scripta Materialia 1997, 37, pp. 621-26.
37
Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
20. C.W.Yeung; W.D.Hopfe; J.E.Morral; A.D.Romig Jr. Materials Science Forum 1994,
163-165, pp. 189-94.
21. M.A.Dayananda; J.A.Nesbitt TMS-AIME Fall Meeting, Detroit, MI, 1984 pp. 195-230.
22. M.A.Dayananda. Metallurgical and Materials Transactions A 1983, 14A, pp. 1851-58.
23. C.W.Kim; M.A.Dayananda. Metallurgical and Materials Transactions A 1983, 14A, pp.
857-64.
24. M.A.Dayananda; C.W.Kim. Metallurgical and Materials Transactions A 1979, 10A, pp.
1333-39.
25. Matano, C. Japanese Journal of Physics 1932, 8, pp. 109.
26. J.A.Nesbitt. NASA/TM-2000-209271 2000.
27. Visual Numerics. IMSLTM Numerical Libraries Family of Products.
http://www.vni.com/products/imsl/index.html . 2004.
28. D.W.Marquardt. Journal of the Society for Industrial and Applied Mathematics 1963,
11, pp. 431-41.
29. A.T.Dinsdale. Calphad 1991, 15, pp. 317-425.
38
Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
9 Appendices
9.1 Tables
Table 3 Nominal composition of selected alloys and coatings
GTD 111
René-88
IN-718
GT-33
GT-29
Ni
BAL
BAL
BAL
32
--
C
0.1
0.03
0.008
---
Cr
14
16
19
21
29
Co
9.5
13
-BAL
BAL
Al
3
2.1
0.5
10
6
Composition wt%
Ti
Mo
W
4.9
1.5
3.8
3.7
4
4
0.9
3
--------
Nb
-0.7
5.1
---
Ta
2.8
-----
Zr
0.01
0.03
----
B
0.01
---0.0015
Y
--0.5
0.6
Table 4 Samples available for analysis
NiCoCrAlY/Ni-base
Coating: GT-33
Alloy: DS GTD-111
Mount
Couple No.
35C
1691
35E
2287
35F
3188
35H
1485
35I
1682
35J
1897
35N
1444
35O
1462
35P
1533
35Q
1643
35T
1423
35U
1453
35V
1524
CoCrAlY/Ni-base
Coating: GT-29
Alloy: GTD-111
Mount
Couple No.
58C
1698
58E
2294
58F
3195
58H
1492
58I
1689
58J
1904
58N
1451
58O
1469
58P
1540
58Q
1650
58T
1430
58U
1460
58V
1531
Diffusion
Temperature,
°C(°F)
Diffusion
time,
(hrs.)
865 (1589)
865 (1589)
865 (1589)
940 (1724)
940 (1724)
940 (1724)
990 (1814)
990 (1814)
990 (1814)
990 (1814)
1050 (1922)
1050 (1922)
1050 (1922)
1959
8698
17054
492
1980
4512
119
324
711
1338
187
343
736
39
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Richard Meguerian
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9.2 Selected Micrographs
Figure 24 Optical micrograph of sample 1691
Figure 25 Optical micrograph of sample 1897
40
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Richard Meguerian
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9.3 Concentration Profiles
80
Concentration (wt%)
70
60
50
Ni
Co
Cr
Al
40
30
20
10
0
-200
-100
0
100
200
Distance from original interface (µm)
Figure 26 Concentration profile for sample 1691
80
Concentration (wt%)
70
60
Ni
Co
Cr
Al
50
40
30
20
10
0
-200
-100
0
Distance from original interface (µm)
100
Figure 27 Concentration profile for sample 2287
41
Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
80
Concentration (wt%)
70
60
Ni
Co
Cr
Al
50
40
30
20
10
0
-200
-100
0
100
200
300
Distance from original interface (µm)
Figure 28 Concentration profile for sample 3188
80
Concentration (wt%)
70
60
Ni
Co
Cr
Al
50
40
30
20
10
0
-200
-100
0
100
200
Distance from original interface (µm)
Figure 29 Concentration profile for sample 1485
42
Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
70
Concentration (wt%)
60
Ni
Co
Cr
Al
50
40
30
20
10
0
-200
-100
0
100
Distance from original interface (µm)
200
Figure 30 Concentration profile for sample 1682
70
Concentration (wt%)
60
Ni
Co
Cr
Al
50
40
30
20
10
0
-200
-100
0
100
Distance from original interface (µm)
200
Figure 31 Concentration profile for sample 1897
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Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
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80
Concentration (wt%)
70
Ni
Co
Cr
Al
60
50
40
30
20
10
0
-200
-100
0
100
200
Distance from original interface (µm)
Figure 32 Concentration profile for sample 1444
80
Concentration (wt%)
70
60
50
Ni
Co
Cr
Al
40
30
20
10
0
-200
-100
0
100
200
300
Distance from original interface (µm)
Figure 33 Concentration profile for sample 1462
44
Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
70
Concentration (wt%)
60
Ni
Co
Cr
Al
50
40
30
20
10
0
-150
-50
50
150
250
Distance from original interface (µm)
Figure 34 Concentration profile for sample 1533
80
Concentration (wt%)
70
60
Ni
Co
Cr
Al
50
40
30
20
10
0
-200
-100
0
100
200
Distance from original interface (µm)
Figure 35 Concentration profile for sample 1423
45
Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
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80
Concentration (wt%)
70
60
Ni
Co
Cr
Al
50
40
30
20
10
0
-200
-100
0
100
200
Distance from original interface (µm)
Figure 36 Concentration profile for sample 1453
80
Concentration (wt%)
70
60
Ni
Co
Cr
Al
50
40
30
20
10
0
-200
-100
0
100
200
Distance from original interface (µm)
Figure 37 Concentration profile for sample 1524
46
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Richard Meguerian
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9.4 IMSL program input file
TEMPERATURE 990
TIME 324
CO
150 33.36 1
110 33.93 1
90 33.79 1
70 32.78 1
50 30.89 1
40 29.43 1
30 30.84 1
20 29.63 1
-10 32.57 1
-20 29.81 1
-30 20.94 1
-40 12.36 1
-50 10.18 1
-70 9.13 1
-90 9.86 1
-110 9.8 1
-150 10.31 1
-200 9.43 1
-300 10.44 1
-500 9.54 1
CR
150 18.15 1
110 9.03 1
90 19.24 1
70 19.58 1
50 16.77 1
40 15.07 1
30 17.29 1
20 16.18 1
-10 20.06 1
-20 17.63 1
-30 9.02 1
-40 11.65 1
-50 11.37 1
-70 11.67 1
-90 12.34 1
-110 12.09 1
-150 12.5 1
-200 10.99 1
-300 12.83 1
-500 11.53 1
AL
150 10.43 1
110 9.43 1
90 9.25 1
70 8.85 1
50 11.03 1
40 12.12 1
30 10.23 1
20 11.81 1
-10 7.4 1
-20 9.17 1
-30 7.13 1
-40 4.82 1
-50 4.48 1
-70 3.58 1
-90 3.34 1
-110 3.56 0.5
-150 3.08 0.5
-200 3.44 0.5
-300 3.06 0.5
-500 3.35 0.5
TEMPERATURE 940
TIME 492
CO
150 35.04 2
120 37.22 2
90 36.47 2
60 33.54 2
40 33.38 2
30 34.28 2
20 33.5 2
10 31.27 2
-10 36.2 2
-20 19.49 2
-30 12.31 2
-40 10.76 1
-60 10.45 1
-90 10.49 1
-120 9.8 1
-150 9.46 1
CR
150 18.22 1
120 20.23 1
90 20.17 1
60 17.57 1
40 18.05 1
30 19.02 1
20 18.78 1
10 15.81 1
-10 22.35 1
-20 8.19 1
-30 11.97 1
-40 12.42 1
-60 13.66 1
-90 13.34 1
-120 12.36 1
47
-150 12.05 1
AL
150 5.25 1
120 4.42 1
90 4.35 1
60 5.01 1
40 4.79 1
30 4.34 1
20 4.62 1
10 5.71 1
-10 2.08 1
-20 3.22 1
-30 2.06 1
-40 1.43 1
-60 1.27 1
-90 1.29 1
-120 1.35 1
-150 1.28 1
TEMPERATURE 1050
TIME 736
CO
150 26.92 1.5
100 27.08 1.5
70 28.45 1.5
50 28.51 1.5
30 27.95 1.5
20 28.59 1.5
10 31.6 1.5
-10 29.58 1.5
-20 30.44 1.5
-30 28.19 1.5
-60 19.28 1.5
-80 14.94 1.5
-100 10.88 1.5
-150 9.62 1.5
-200 9.87 1.5
CR
150 14.91 1
100 15.16 1
70 16.28 1
50 16.5 1
30 16.31 1
20 16.83 1
10 19.76 1
-10 19.67 1
-20 20.27 1
-30 20.01 1
-60 10.55 1
-80 9.6 1
Tuesday, September 06, 2005
Richard Meguerian
-100 9.85 1
-150 10.89 1
-200 12.14 1
AL
150 12.11 1
100 11.72 1
70 10.9 1
50 10.34 1
30 10.35 1
20 9.19 1
10 6.63 1
-10 6.04 1
-20 5.89 1
-30 5.84 1
-60 7.6 1
-80 6.67 1
-100 5.98 1
-150 4.89 1
-200 3.57 1
TEMPERATURE 865
TIME 1959
CO
90 32.6 2
60 32.21 2
40 36.26 2
30 33.94 2
20 31.87 2
10 31.19 2
-10 22.64 2
-20 12.08 2
-30 10.32 1
-40 10.72 1
-60 9.33 1
-90 9.53 1
-120 9.54 1
-150 9.85 1
CR
90 16.22 2
60 16.77 2
40 20.44 2
30 19 2
20 16.57
10 16.35 2
-10 11.88 2
-20 10.9 2
-30 12.24 2
-40 12.96 2
-60 12.7 2
-90 11.92 2
-120 12.33 2
-150 12.03 2
AL
TMS Outstanding Student Paper Contest 2005
McMaster University
-250 13.67 1
-300 13.04 1
90 7.92 1
60 7.67 1
40 5.4 1
30 6.25 1
20 7.14 1
10 7.17 1
-10 3.58 1
-20 2.87 1
-30 2.07 1
-40 1.79 1
-60 1.84 1
-90 1.86 1
-120 1.63 1
-150 1.71 1
TEMPERATURE 865
TIME 17054
CO
150 31.43 2
120 34.39 2
80 31.59 2
60 35.03 2
40 30.9 2
30 34.46 2
20 33.12 2
10 34.15 2
-10 37.83 2
-20 21.01 2
-30 12.19 1
-50 10.98 1
-80 8.94 1
-100 9.63 1
-130 9.07 1
-160 10.37 1
-200 10.75 1
-250 10.7 1
-300 10.57 1
CR
150 16.12 1
120 19.9 1
80 16.61 1
60 20.65 1
40 15.67 1
30 19.23 1
20 19.38 1
10 19.69 1
-10 23.97 1
-20 11.49 1
-30 11.74 1
-50 12.19 1
-80 10.27 1
-100 11.87 1
-130 14.43 1
-160 13.2 1
-200 13.34 1
48
AL
150 6.3 0.5
120 4.87 0.5
80 6.2 0.5
60 4.44 0.5
40 6.43 0.5
30 4.8 0.5
20 5.03 0.5
10 4.82 0.5
-10 2.46 0.5
-20 3.46 0.5
-30 2.52 0.5
-50 1.71 0.5
-80 1.55 0.5
-100 1.79 0.5
-130 1.47 0.5
-160 1.43 0.5
-200 1.49 0.5
-250 1.46 0.5
-300 1.55 0.5
TEMPERATURE 940
TIME 4512
CO
150 29.81 1.5
100 30.36 1.5
70 33.23 1.5
50 28.52 1.5
30 32.93 1.5
20 32.29 1.5
10 34.93 1.5
-10 35.56 1.5
-20 24.61 1.5
-30 13.98 1
-50 11.66 1
-70 9.92 1
-100 10.3 1
-150 10.45 1
CR
150 16.33 1
100 15.68 1
70 19.15 1
50 14.54 1
30 18.83 1
20 18.22 1
10 21.76 1
-10 22.68 1
-20 11.36 1
-30 12.96 1
-50 12.48 1
-70 11.96 1
-100 13.78 1
Tuesday, September 06, 2005
Richard Meguerian
-150 12.81 1
AL
150 5.69 0.5
100 5.73 0.5
70 4.41 0.5
50 6.47 0.5
30 4.17 0.5
20 4.31 0.5
10 3.18 0.5
-10 2.5 0.5
-20 3 0.5
-30 2.43 0.5
-50 1.66 0.5
-70 1.6 0.5
-100 1.25 0.5
-150 1.44 0.5
TEMPERATURE 990
TIME 119
CO
150 36.82 1.5
100 37.34 1.5
70 32.71 1.5
50 34.81 1.5
30 33.81 1.5
20 31.02 1.5
10 30.03 1.5
-10 32.54 1.5
-20 21.41 1
-30 12.06 1
-50 10.17 1
-70 10.58 1
-100 10.45 1
-150 8.94 1
CR
150 19.69 1
100 21.07 1
70 16.74 1
50 19.5 1
30 19.37 1
20 17.8 1
10 16.86 1
-10 21.87 1
-20 10.66 0.5
-30 12.37 0.5
-50 13.96 0.5
-70 13.33 0.5
-100 12.99 0.5
-150 10.47 0.5
AL
150 5.45 0.5
100 4.64 0.5
70 6.34 0.5
TMS Outstanding Student Paper Contest 2005
McMaster University
50 5 0.5
30 4.77 0.5
20 5.39 0.5
10 5.86 0.5
-10 2.49 0.5
-20 3.3 0.5
-30 2.28 0.5
-50 1.53 0.5
-70 1.41 0.5
-100 1.51 0.5
-150 1.48 0.5
TEMPERATURE 990
TIME 711
CO
100 31.5 1.5
70 32.24 1.5
50 31.33 1.5
30 31.65 1.5
20 30.07 1.5
10 32.48 1.5
-10 29.69 1.5
-20 22.6 1.5
-30 14.32 0.5
-50 11.07 0.5
-70 10.25 0.5
-100 9.88 0.5
-150 9.54 0.5
-200 10.8 0.5
CR
100 15.94 1
70 18.01 1
50 16.65 1
30 17.64 1
20 16.04 1
10 18.08 1
-10 16.13 1
-20 12.61 1
-30 9.82 1
-50 13.23 1
-70 13.18 1
-100 12.57 1
-150 11.32 1
-200 13.29 1
AL
100 6.68 0.5
70 5.46 0.5
50 6.01 0.5
30 5.7 0.5
20 6.07 0.5
10 4.68 0.5
-10 5.17 0.5
-20 3.29 0.5
-30 3 0.5
49
-50 1.72 0.5
-70 1.66 0.5
-100 1.46 0.5
-150 1.58 0.5
-200 1.62 0.5
TEMPERATURE 940
TIME 1980
CO
100 32.07 2
70 33.29 2
50 30.39 2
30 30.92 2
20 30.87 2
10 31.02 2
-10 32.11 2
-20 16.99 1
-30 13.28 1
-50 10.18 1
-70 10.35 1
-100 8.79 1
CR
100 17.52 1.5
70 18.25 1.5
50 15.93 1.5
30 16.39 1.5
20 16.54 1.5
10 16.97 1.5
-10 19.02 1.5
-20 9.57 1
-30 11.26 1
-50 13.35 1
-70 13.43 1
-100 10.76 1
AL
100 6.84 0.5
70 5.74 0.5
50 7.36 0.5
30 7.15 0.5
20 6.67 0.5
10 6.51 0.5
-10 4.19 0.5
-20 3.95 0.5
-30 2.65 0.5
-50 1.95 0.5
-70 1.87 0.5
-100 1.74 0.5
TEMPERATURE 865
TIME 8698
CO
150 36.47 2
120 32.65 2
Tuesday, September 06, 2005
Richard Meguerian
90 35.27 2
60 33.75 2
40 34.6 2
30 33.59 2
20 32.57 2
10 34.05 2
-10 38.68 2
-20 25.76 2
-30 16 2
-40 12.57 1
-80 10.71 1
CR
150 20.32 2
120 16.03 2
90 18.94 2
60 17.77 2
40 19.06 2
30 17.25 2
20 16.79 2
10 18.1 2
-10 24.01 2
-20 11.62 1
-30 11.55 1
-40 15.48 1
-80 13.31 1
AL
150 2.74 0.5
120 3.96 0.5
90 3.18 0.5
60 3.67 0.5
40 3.23 0.5
30 3.78 0.5
20 3.85 0.5
10 3.42 0.5
-10 1.4 0.5
-20 2.05 0.5
-30 1.76 0.25
-40 1.38 0.25
-80 0.94 0.25
TEMPERATURE 1050
TIME 187
CO
150 32.48 2
100 32.32 2
TMS Outstanding Student Paper Contest 2005
McMaster University
70 33.03 2
50 31.62 2
30 33.07 2
20 32.3 2
10 30.41 2
-10 30.84 2
-20 31.71 2
-30 26.37 2
-50 16.42 1
-70 11.93 1
-100 10.91 1
-150 10.34 1
150 31.01 2
100 33.67 2
70 30.15 2
50 30.32 2
30 32.67 2
20 32.49 2
10 31.42 2
-10 32.67 2
-20 33.48 2
-30 32.14 2
-50 30.33 2
-70 20.4 2
-100 13.21 1.5
-150 10.51 1.5
CR
150 17.19 2
100 17.68 2
70 18.66 2
50 17.26 2
30 18.45 2
20 18.96 2
10 16.83 2
-10 18.83 2
-20 20.29 2
-30 18.18 2
-50 11.12 2
-70 11.97 2
-100 13.36 2
-150 13.01 2
AL
150 3.88 0.5
100 3.74 0.5
70 2.85 0.5
50 3.49 0.5
30 2.96 0.5
20 3.01 0.5
10 3.6 0.5
-10 2.69 0.5
-20 1.85 0.5
-30 1.4 0.5
-50 1.94 0.5
-70 1.57 0.5
-100 1.09 0.25
-150 1.03 0.25
TEMPERATURE 1050
TIME 343
CO
CR
150 16.56 2
100 19.52 2
70 15.92 2
50 16.27 2
30 18.47 2
20 18.78 2
10 17.94 2
-10 19.59 2
-20 21.67 2
-30 20.1 2
-50 20.16 2
-70 10.46 2
-100 12.27 2
-150 13.92 2
AL
150 4.13 0.5
100 2.87 0.5
70 4.1 0.5
50 3.87 0.5
30 3.15 0.5
20 2.9 0.5
10 3.13 0.5
-10 2.55 0.5
-20 2.19 0.5
-30 2.53 0.5
-50 1.76 0.5
-70 2.29 0.5
-100 1.66 0.5
-150 1.12 0.5
9.5 Thermo-Calc TDB File
$ Database file written
$
ELEMENT VA
VACUUM
ELEMENT AL
FCC
ELEMENT CR
BCC
ELEMENT NI
FCC
5- 2-21
0.0000E+00
2.6982E+01
5.1996E+01
5.8690E+01
50
0.0000E+00
4.5400E+03
4.0500E+03
4.7870E+03
0.0000E+00!
2.8300E+01!
2.3543E+01!
2.9796E+01!
Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
FUNCTION GALFCC
2.98140E+02 -7976.15+137.093038*T-24.3671976*T*LN(T)
-.001884662*T**2-8.77664E-07*T**3+74092*T**(-1); 7.00000E+02 Y
-11276.24+223.048446*T-38.584296*T*LN(T)-.018531982*T**2
-5.764227E-06*T**3+74092*T**(-1); 9.33600E+02 Y
-11278.378+188.684153*T-31.748192*T*LN(T)-1.231E+28*T**(-9);
2.90000E+03 N !
FUNCTION GALHCP
2.98150E+02 +5481-1.8*T+GALFCC#;
6.00000E+03
N !
FUNCTION GALLIQ
2.98140E+02 +GALFCC#+11005.029-11.841867*T
+7.934E-20*T**7; 9.33470E+02 Y
+GALFCC#+10482.382-11.253974*T+1.231E+28*T**(-9); 2.90000E+03 N !
FUNCTION GALBCC
2.98140E+02 +GALFCC#+10083-4.813*T; 2.90000E+03 N !
FUNCTION GCRBCC
2.98140E+02 -8856.94+157.48*T-26.908*T*LN(T)
+.00189435*T**2-1.47721E-06*T**3+139250*T**(-1); 3.11500E+02 Y
-8856.94+157.48*T-26.908*T*LN(T)+.00189435*T**2-1.47721E-06*T**3
+139250*T**(-1); 2.18000E+03 Y
-34869.344+344.18*T-50*T*LN(T)-2.88526E+32*T**(-9); 6.00000E+03 N !
FUNCTION GCRHCP
2.98150E+02 +4438+GCRBCC#;
6.00000E+03
N !
FUNCTION GCRLIQ
2.98140E+02 +GCRBCC#+24335.955-11.420225*T
+2.37615E-21*T**7; 2.18000E+03 Y
+GCRBCC#+18409.36-8.563683*T+2.88526E+32*T**(-9); 6.00000E+03 N !
FUNCTION GCRFCC
2.98150E+02 +GCRBCC#+7284+.163*T;
6.00000E+03
N !
FUNCTION GNIFCC
2.98140E+02 -5179.159+117.854*T-22.096*T*LN(T)
-.0048407*T**2; 1.72800E+03 Y
-27840.655+279.135*T-43.1*T*LN(T)+1.12754E+31*T**(-9); 3.00000E+03 N
!
FUNCTION GNIHCP
2.98150E+02 +1046+1.2552*T+GNIFCC#;
6.00000E+03
N
!
FUNCTION GNILIQ
2.98140E+02 +GNIFCC#+16414.686-9.397*T
-3.82318E-21*T**7; 1.72800E+03 Y
+GNIFCC#+18290.88-10.537*T-1.12754E+31*T**(-9); 3.00000E+03 N !
FUNCTION GNIBCC
2.98140E+02 +GNIFCC#+8715.084-3.556*T; 3.00000E+03 N
!
FUNCTION UN_ASS
2.98140E+02 0.0 ; 3.00000E+02 N !
FUNCTION UALCR
2.98150E+02 7910;
6.00000E+03
N !
FUNCTION UCRNI
2.98140E+02 -3831; 3.00000E+03 N !
FUNCTION UALNI
2.98140E+02 -14556.4+2.945*T; 2.90000E+03 N !
TYPE_DEFINITION % SEQ *!
DEFINE_SYSTEM_DEFAULT SPECIE 2 !
DEFAULT_COMMAND DEF_SYS_ELEMENT VA !
TYPE_DEFINITION & GES A_P_D BCC MAGNETIC
PHASE BCC %& 1 1.0 !
CONSTITUENT BCC :AL,CR,NI : !
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
REF:0 !
PARAMETER
REF:0 !
PARAMETER
-1.0
4.00000E-01 !
G(BCC,AL;0) 2.98140E+02 +GALBCC#; 2.90000E+03 N REF:0 !
G(BCC,CR;0) 2.98150E+02 +GCRBCC#;
6.00000E+03
N REF:0 !
TC(BCC,CR;0) 2.98150E+02 -311.5;
6.00000E+03
N REF:0 !
BMAGN(BCC,CR;0) 2.98150E+02 -.01;
6.00000E+03
N REF:0 !
G(BCC,NI;0) 2.98140E+02 +GNIBCC#; 3.00000E+03 N REF:0 !
TC(BCC,NI;0) 2.98140E+02 575; 3.00000E+03 N REF:0 !
BMAGN(BCC,NI;0) 2.98140E+02 .85; 3.00000E+03 N REF:0 !
G(BCC,AL,CR;0) 2.98140E+02 -54900+10*T; 2.90000E+03 N REF:0 !
G(BCC,AL,CR,NI;0) 2.98140E+02 -100000; 2.90000E+03 N REF:0 !
G(BCC,AL,NI;0) 2.98140E+02 -50000+11*T; 2.90000E+03 N REF:0 !
G(BCC,CR,NI;0) 2.98140E+02 +17170-11.8199*T; 3.00000E+03 N
G(BCC,CR,NI;1)
TC(BCC,CR,NI;0)
2.98140E+02
2.98140E+02
51
+34418-11.8577*T;
2373;
3.00000E+03
3.00000E+03
N
N REF:0 !
Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
PARAMETER TC(BCC,CR,NI;1) 2.98140E+02 617; 3.00000E+03 N REF:0 !
PARAMETER BMAGN(BCC,CR,NI;0) 2.98140E+02 4; 3.00000E+03 N REF:0 !
PHASE AL11CR2 % 3 10
CONSTITUENT AL11CR2
1
2 !
:AL : AL : CR :
!
PARAMETER G(AL11CR2,AL:AL:CR;0) 2.98150E+02 -175500+25.805*T
+11*GALFCC#+2*GCRBCC#;
6.00000E+03
N REF:0 !
PHASE AL13CR2 % 2 13
CONSTITUENT AL13CR2
2 !
:AL : CR :
!
PARAMETER G(AL13CR2,AL:CR;0) 2.98150E+02
+2*GCRBCC#;
6.00000E+03
N REF:0 !
PHASE AL3NI1 % 2 .75
.25 !
CONSTITUENT AL3NI1 :AL : NI :
PARAMETER G(AL3NI1,AL:NI;0)
+.25*GNIFCC#;
6.00000E+03
PHASE AL3NI2 % 3 3
CONSTITUENT AL3NI2
-174405+22.2*T+13*GALFCC#
!
2.98150E+02
N REF:0 !
-40463+5.312*T+.75*GALFCC#
2
1 !
:AL : AL,NI% : NI,VA% :
!
PARAMETER G(AL3NI2,AL:AL:NI;0) 2.98150E+02 -41219+2.792*T+5*GALBCC#
+GNIBCC#;
6.00000E+03
N REF:0 !
PARAMETER G(AL3NI2,AL:NI:NI;0) 2.98150E+02 -428055+71.808*T+3*GALBCC#
+3*GNIBCC#;
6.00000E+03
N REF:0 !
PARAMETER G(AL3NI2,AL:AL:VA;0) 2.98150E+02 +30000-3*T+5*GALBCC#;
6.00000E+03
N REF:0 !
PARAMETER G(AL3NI2,AL:NI:VA;0) 2.98150E+02 -356836+66.079*T+3*GALBCC#
+2*GNIBCC#;
6.00000E+03
N REF:0 !
PARAMETER G(AL3NI2,AL:AL,NI:NI;0) 2.98150E+02 -38157;
6.00000E+03
REF:0 !
PARAMETER G(AL3NI2,AL:AL:NI,VA;0) 2.98150E+02 -23319;
6.00000E+03
REF:0 !
PARAMETER G(AL3NI2,AL:NI:NI,VA;0) 2.98150E+02 -23319;
6.00000E+03
REF:0 !
PARAMETER G(AL3NI2,AL:AL,NI:VA;0) 2.98150E+02 -38157;
6.00000E+03
REF:0 !
PHASE AL3NI5 % 2 .375
.625 !
CONSTITUENT AL3NI5 :AL : NI :
PARAMETER G(AL3NI5,AL:NI;0)
+.625*GNIFCC#;
6.00000E+03
PHASE AL4CR % 2 4
CONSTITUENT AL4CR
5 !
:AL : CR :
PARAMETER G(AL8CR5_H,AL:CR;0)
N
N
-54795+5.292*T+.375*GALFCC#
!
PARAMETER G(AL4CR,AL:CR;0) 2.98150E+02
+GCRBCC#;
6.00000E+03
N REF:0 !
PHASE AL8CR5_H % 2 8
CONSTITUENT AL8CR5_H
N
!
2.98150E+02
N REF:0 !
1 !
:AL : CR :
N
-89025+19.05*T+4*GALFCC#
!
2.98150E+02
52
-147732-58.5*T+8*GALFCC#
Tuesday, September 06, 2005
Richard Meguerian
+5*GCRBCC#;
TMS Outstanding Student Paper Contest 2005
McMaster University
6.00000E+03
PHASE AL8CR5_L % 2 8
CONSTITUENT AL8CR5_L
N REF:0 !
5 !
:AL : CR :
PARAMETER G(AL8CR5_L,AL:CR;0)
6.00000E+03
N REF:0 !
PHASE AL9CR4_H % 2 9
CONSTITUENT AL9CR4_H
!
2.98150E+02
4 !
:AL : CR :
!
PARAMETER G(AL9CR4_H,AL:CR;0) 2.98150E+02
+4*GCRBCC#;
6.00000E+03
N REF:0 !
PHASE AL9CR4_L % 2 9
CONSTITUENT AL9CR4_L
4 !
:AL : CR :
2 !
:AL : CR :
-230750+16.094*T+9*GALFCC#
!
PARAMETER G(ALCR2,AL:CR;0) 2.98150E+02
+2*GCRBCC#;
6.00000E+03
N REF:0 !
PHASE BETA % 2 1
CONSTITUENT BETA
-134433-56.16*T+9*GALFCC#
!
PARAMETER G(AL9CR4_L,AL:CR;0) 2.98150E+02
+4*GCRBCC#;
6.00000E+03
N REF:0 !
PHASE ALCR2 % 2 1
CONSTITUENT ALCR2
-229515+8*GALFCC#+5*GCRBCC#;
-32700-8.79*T+GALFCC#
1 !
:AL,CR,NI : CR,NI,VA :
!
PARAMETER G(BETA,AL:CR;0) 2.98140E+02 +GALBCC#+GCRBCC#; 2.90000E+03 N
REF:0 !
PARAMETER G(BETA,CR:CR;0) 2.98150E+02 +100+2*GCRBCC#;
6.00000E+03
N
REF:0 !
PARAMETER G(BETA,NI:CR;0) 2.98140E+02 +GCRBCC#+GNIBCC#+7000;
3.00000E+03 N REF:0 !
PARAMETER G(BETA,AL:NI;0) 2.98140E+02 +GALBCC#+GNIBCC#-152685+23.936*T;
3.00000E+03 N REF:0 !
PARAMETER G(BETA,CR:NI;0) 2.98140E+02 +GCRBCC#+GNIBCC#+7000;
3.00000E+03 N REF:0 !
PARAMETER G(BETA,NI:NI;0) 2.98140E+02 +2*GNIBCC#; 3.00000E+03 N REF:0 !
PARAMETER G(BETA,AL:VA;0) 2.98140E+02 +GALBCC#+10000-T; 2.90000E+03 N
REF:0 !
PARAMETER G(BETA,CR:VA;0) 2.98150E+02 +GCRBCC#+20000;
6.00000E+03
N
REF:0 !
PARAMETER G(BETA,NI:VA;0) 2.98140E+02 +GNIBCC#+162508-24.936*T;
3.00000E+03 N REF:0 !
PARAMETER G(BETA,AL,NI:CR;0) 2.98140E+02 -47306+4.909*T; 2.90000E+03
N REF:0 !
PARAMETER G(BETA,AL:CR,VA;0) 2.98140E+02 -10000; 2.90000E+03 N REF:0 !
PARAMETER G(BETA,AL:CR,NI;0) 2.98140E+02 -10000; 2.90000E+03 N REF:0 !
PARAMETER G(BETA,CR,NI:CR;0) 2.98140E+02 10000; 3.00000E+03 N REF:0 !
PARAMETER G(BETA,CR,NI:CR;1) 2.98150E+02 10000;
6.00000E+03
N REF:0 !
PARAMETER G(BETA,CR:CR,VA;0) 2.98150E+02 200000;
6.00000E+03
N
REF:0 !
PARAMETER G(BETA,CR:CR,NI;0) 2.98140E+02 10000; 3.00000E+03 N REF:0 !
PARAMETER G(BETA,CR:CR,NI;1) 2.98150E+02 10000;
6.00000E+03
N REF:0 !
PARAMETER G(BETA,NI:CR,VA;0) 2.98140E+02 200000; 3.00000E+03 N REF:0 !
PARAMETER G(BETA,NI:CR,NI;0) 2.98140E+02 10000; 3.00000E+03 N REF:0 !
53
Tuesday, September 06, 2005
Richard Meguerian
PARAMETER
PARAMETER
N REF:0 !
PARAMETER
N REF:0 !
PARAMETER
N REF:0 !
PARAMETER
PARAMETER
PARAMETER
N REF:0 !
PARAMETER
N REF:0 !
PARAMETER
N REF:0 !
PARAMETER
PARAMETER
TMS Outstanding Student Paper Contest 2005
McMaster University
G(BETA,NI:CR,NI;1)
G(BETA,AL,NI:NI;0)
2.98150E+02
2.98140E+02
10000;
6.00000E+03
N REF:0 !
-47306+4.909*T; 2.90000E+03
G(BETA,AL,CR:NI;0)
2.98140E+02
+28660-39.38*T;
G(BETA,AL:NI,VA;0)
2.98140E+02
-62755+29.622*T;
G(BETA,CR,NI:NI;0)
G(BETA,CR,NI:NI;1)
G(BETA,CR:NI,VA;0)
2.98140E+02
2.98150E+02
2.98140E+02
10000; 3.00000E+03 N REF:0 !
10000;
6.00000E+03
N REF:0 !
-62755+29.622*T; 3.00000E+03
G(BETA,NI:NI,VA;0)
2.98140E+02
-62755+29.622*T;
G(BETA,AL,NI:VA;0)
2.98140E+02
-47306+4.909*T;
G(BETA,CR,NI:VA;0)
G(BETA,CR,NI:VA;1)
2.98140E+02
2.98150E+02
10000;
10000;
PHASE DISORD % 1 1.0 !
CONSTITUENT DISORD :AL,CR,NI :
PARAMETER
PARAMETER
PARAMETER
PARAMETER
REF:0 !
PARAMETER
PARAMETER
REF:0 !
PARAMETER
REF:0 !
PARAMETER
PARAMETER
REF:0 !
PARAMETER
N REF:0 !
2.90000E+03
3.00000E+03
2.90000E+03
3.00000E+03 N REF:0 !
6.00000E+03
N REF:0 !
!
G(DISORD,AL;0) 2.98140E+02 +GALFCC#; 2.90000E+03 N REF:0 !
G(DISORD,CR;0) 2.98150E+02 +GCRFCC#;
6.00000E+03
N REF:0 !
G(DISORD,NI;0) 2.98140E+02 +GNIFCC#; 3.00000E+03 N REF:0 !
G(DISORD,AL,CR;0) 2.98140E+02 -45850+6*T; 2.90000E+03 N
G(DISORD,AL,CR,NI;0) 2.98140E+02 96489; 2.90000E+03 N REF:0 !
G(DISORD,AL,NI;0) 2.98140E+02 -16367+12*UALNI#; 2.90000E+03 N
G(DISORD,AL,NI;1)
2.98140E+02
+2023+39.894*T;
G(DISORD,AL,NI;2)
G(DISORD,CR,NI;0)
2.98140E+02
2.98140E+02
84175; 2.90000E+03 N REF:0 !
+8030-12.87*T; 3.00000E+03 N
G(DISORD,CR,NI;1)
2.98140E+02
+33080-16.0362*T;
TYPE_DEFINITION ' GES A_P_D FCC MAGNETIC
PHASE FCC %' 1 1.0 !
CONSTITUENT FCC :AL,CR,NI : !
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
REF:0 !
PARAMETER
REF:0 !
PARAMETER
PARAMETER
REF:0 !
PARAMETER
PARAMETER
PARAMETER
REF:0 !
PARAMETER
REF:0 !
2.90000E+03
-3.0
2.90000E+03
N
3.00000E+03
2.80000E-01 !
G(FCC,AL;0) 2.98140E+02 +GALFCC#; 2.90000E+03 N REF:0 !
G(FCC,CR;0) 2.98150E+02 +GCRFCC#;
6.00000E+03
N REF:0 !
TC(FCC,CR;0) 2.98150E+02 -1109;
6.00000E+03
N REF:0 !
BMAGN(FCC,CR;0) 2.98150E+02 -2.46;
6.00000E+03
N REF:0 !
G(FCC,NI;0) 2.98140E+02 +GNIFCC#; 3.00000E+03 N REF:0 !
TC(FCC,NI;0) 2.98140E+02 633; 3.00000E+03 N REF:0 !
BMAGN(FCC,NI;0) 2.98140E+02 .52; 3.00000E+03 N REF:0 !
G(FCC,AL,CR;0) 2.98140E+02 -45900+6*T; 2.90000E+03 N REF:0 !
G(FCC,AL,CR,NI;0) 2.98140E+02 -853+16.245*T; 2.90000E+03 N
G(FCC,AL,NI;0)
2.98140E+02
-168343+16*T;
2.90000E+03
N
G(FCC,AL,NI;1)
G(FCC,AL,NI;2)
2.98140E+02
2.98140E+02
34311; 2.90000E+03 N REF:0 !
+4162+27.29*T; 2.90000E+03 N
TC(FCC,AL,NI;0) 2.98140E+02 -1112; 2.90000E+03 N REF:0 !
TC(FCC,AL,NI;1) 2.98140E+02 1745; 2.90000E+03 N REF:0 !
G(FCC,CR,NI;0) 2.98140E+02 +8030-12.8801*T; 3.00000E+03 N
G(FCC,CR,NI;1)
2.98140E+02
54
+33080-16.0362*T;
3.00000E+03
N
Tuesday, September 06, 2005
Richard Meguerian
TMS Outstanding Student Paper Contest 2005
McMaster University
PARAMETER TC(FCC,CR,NI;0) 2.98140E+02 -3605; 3.00000E+03 N REF:0 !
PARAMETER BMAGN(FCC,CR,NI;0) 2.98140E+02 -1.91; 3.00000E+03 N REF:0 !
PHASE LIQUID % 1 1.0 !
CONSTITUENT LIQUID :AL,CR,NI :
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
N REF:0 !
PARAMETER
PARAMETER
N REF:0 !
PARAMETER
REF:0 !
PARAMETER
N REF:0 !
!
G(LIQUID,AL;0) 2.98140E+02 +GALLIQ#; 2.90000E+03 N REF:0 !
G(LIQUID,CR;0) 2.98150E+02 +GCRLIQ#;
6.00000E+03
N REF:0 !
G(LIQUID,NI;0) 2.98140E+02 +GNILIQ#; 3.00000E+03 N REF:0 !
G(LIQUID,AL,CR;0) 2.98140E+02 -29000; 2.90000E+03 N REF:0 !
G(LIQUID,AL,CR;1) 2.98140E+02 -11000; 2.90000E+03 N REF:0 !
G(LIQUID,AL,CR,NI;0) 2.98140E+02 8257; 2.90000E+03 N REF:0 !
G(LIQUID,AL,NI;0) 2.98140E+02 -197088+30.353*T; 3.00000E+03
G(LIQUID,AL,NI;1)
G(LIQUID,AL,NI;2)
2.98140E+02
2.98140E+02
5450; 2.90000E+03 N REF:0 !
+54624-11.383*T; 2.90000E+03
G(LIQUID,CR,NI;0)
2.98140E+02
+318-7.3318*T;
G(LIQUID,CR,NI;1)
2.98140E+02
+16941-6.3696*T;
3.00000E+03
N
3.00000E+03
$ THIS PHASE HAS A DISORDERED CONTRIBUTION FROM DISORD
TYPE_DEFINITION ( GES AMEND_PHASE_DESCRIPTION ORD DIS_PART DISORD,,,!
PHASE ORD %( 2 .75
.25 !
CONSTITUENT ORD :AL,CR,NI : AL,CR,NI : !
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
PARAMETER
G(ORD,AL:AL;0) 2.98140E+02 0.0 ; 2.90000E+03 N REF:0 !
G(ORD,CR:AL;0) 2.98140E+02 +3*UALCR#; 2.90000E+03 N REF:0 !
G(ORD,NI:AL;0) 2.98140E+02 +3*UALNI#; 2.90000E+03 N REF:0 !
G(ORD,AL:CR;0) 2.98140E+02 +3*UALCR#; 2.90000E+03 N REF:0 !
G(ORD,CR:CR;0)
2.98140E+02 0.0 ; 2.90000E+03 N REF:0 !
G(ORD,NI:CR;0) 2.98140E+02 +3*UCRNI#; 3.00000E+03 N REF:0 !
G(ORD,AL:NI;0) 2.98140E+02 +3*UALNI#; 2.90000E+03 N REF:0 !
G(ORD,CR:NI;0) 2.98140E+02 +3*UCRNI#; 3.00000E+03 N REF:0 !
G(ORD,NI:NI;0) 2.98140E+02 0.0 ; 3.00000E+03 N REF:0 !
G(ORD,AL,CR:*;0) 2.98140E+02 +6*UALCR#; 2.90000E+03 N REF:0 !
G(ORD,AL,NI:*;0) 2.98140E+02 +6*UALNI#; 2.90000E+03 N REF:0 !
G(ORD,CR,NI:*;0) 2.98140E+02 +6*UCRNI#; 3.00000E+03 N REF:0 !
PHASE SIGMA % 3 8
4
18 !
CONSTITUENT SIGMA :NI : CR : CR,NI :
!
PARAMETER G(SIGMA,NI:CR:CR;0) 2.98150E+02 +221157-227*T+8*GNIFCC#
+4*GCRBCC#+18*GCRBCC#;
6.00000E+03
N REF:0 !
PARAMETER G(SIGMA,NI:CR:NI;0) 2.98150E+02 +175400+8*GNIFCC#+4*GCRBCC#
+18*GCRBCC#;
6.00000E+03
N REF:0 !
LIST_OF_REFERENCES
NUMBER SOURCE
!
55
Tuesday, September 06, 2005