- Email: [email protected]
Thermodynamic evaluation of the Mo-rich corner of the Mo-Hf-C system including O impurities
Accepted Manuscript Thermodynamic evaluation of the Mo-rich corner of the Mo-Hf-C system including O impurities D. Lang, E. Povoden-Karadeniz, J. Schatte, W. Knabl, H. Clemens, S. Primig PII:
S0925-8388(16)33364-3
DOI:
10.1016/j.jallcom.2016.10.227
Reference:
JALCOM 39394
To appear in:
Journal of Alloys and Compounds
Received Date: 8 May 2016 Revised Date:
19 October 2016
Accepted Date: 25 October 2016
Please cite this article as: D. Lang, E. Povoden-Karadeniz, J. Schatte, W. Knabl, H. Clemens, S. Primig, Thermodynamic evaluation of the Mo-rich corner of the Mo-Hf-C system including O impurities, Journal of Alloys and Compounds (2016), doi: 10.1016/j.jallcom.2016.10.227. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Thermodynamic evaluation of the Mo-rich corner of the MoHf-C system including O impurities D. Langa,b,1*, E. Povoden-Karadenizc, J. Schatted, W. Knabld, H. Clemensa, S. Primiga,2
3 4 a
Department of Physical Metallurgy and Materials Testing, Montanuniversitaet Leoben, A-8700 Leoben, Austria
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b
Christian Doppler Laboratory Early Stages of Precipitation, Montanuniversitaet Leoben, A-8700 Leoben, Austria
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c
Institute of Materials Science and Technology, TU Wien, A-1060, Vienna, Austria
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d
PLANSEE SE, A-6600 Reutte, Austria
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1
now at PLANSEE SE, A-8940 Liezen, Austria
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2
now at School of Materials Science & Engineering, UNSW Sydney, NSW 2052 Sydney, Australia
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* David Lang Corresponding author Department of Physical Metallurgy and Materials Testing, Christian Doppler Laboratory Early Stages of Precipitation, Montanuniversität Leoben, Franz-Josef Straße 18, A-8700 Leoben, Austria Now at Plansee SE, Werkstraße 14, A-8940 Liezen, Austria e-Mail: [email protected]
21 22 23 24
Erwin Povoden-Karadeniz Institute of Materials Science and Technology, TU Wien, Getreidemarkt 9, A-1060, Vienna, Austria e-Mail: [email protected]
25 26 27
Jürgen Schatte Plansee SE, Metallwerk-Plansee-Straße 71, A-6600 Reutte, Austria e-Mail: [email protected]
28 29 30
Wolfram Knabl Plansee SE, Metallwerk-Plansee-Straße 71, A-6600 Reutte, Austria e-Mail: [email protected]
31 32 33 34 35 36 37 38 39
Helmut Clemens Department of Physical Metallurgy and Materials Testing, Montanuniversität Leoben, Franz-Josef Straße 18, A-8700 Leoben, Austria e-Mail: [email protected]
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Sophie Primig Department of Physical Metallurgy and Materials Testing, Montanuniversität Leoben, Franz-Josef Straße 18, A-8700 Leoben, Austria Now at School of Materials Science & Engineering, UNSW Sydney, NSW 2052 Sydney, Australia e-Mail: [email protected]
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Abstract
2
In this paper the phase fractions of (Hf,Mo)C and (Mo,Hf)2C carbide phases are
3
investigated experimentally in the low Hf and C alloyed composition range of
4
technological Mo-Hf-C applications. Furthermore, solubilities of Hf and C in body
5
centered cubic Mo-base solid solution (Mo-bcc) are evaluated with consideration of
6
the presence of O-impurities. The results, together with thermodynamic stability data
7
from first-principles analysis, are taken into account in thermodynamic model
8
descriptions of the solid alloy and carbide phases. The presented modeling considers
9
O solubility in Mo-bcc and (Hf,Mo)C, as well as the role of O impurities in MHC, a Mo-
10
Hf-C alloy with a nominal composition of 0.65 at.% Hf and 0.65 at.% C, is discussed.
11
Finally, a typical application of the optimized thermodynamic database for the
12
prediction of phase stabilities in MHC is presented.
13
Keywords:
14
Refractory, Molybdenum- hafnium- carbon; MHC, Carbide, Thermodynamic,
15
Modeling
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1. Introduction
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Precipitation of HfC in Mo-base alloys has been studied since the 1960s and they
3
have a great potential to improve the mechanical properties at elevated
4
temperatures. A typical composition around 0.65 at.% Hf and 0.65 at.% C, named
5
MHC alloy, has been established. This composition exhibits an optimum balance
6
between processability and mechanical properties. Additionally, this alloy has a
7
sufficiently large window for solid solution heat treatment in the single-phase body
8
centered cubic Mo matrix at high temperatures and it is able to form ~1 vol.%
9
strength increasing face centered cubic (fcc) HfC nanoparticles [1–8].
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For an optimized alloy design of MHC, which includes thermo-mechanical processing
11
and heat treatments, detailed knowledge of the ternary Mo-Hf-C system, especially in
12
the Mo-rich corner, is inevitable. For instance, the C- and Hf solubilities in body
13
centered cubic Mo-base solid solution (Mo-bcc) control the carbide precipitation
14
behavior in MHC during technological heat treatments as a function of temperature.
15
The thermodynamic database for such predictions is obtained by CALPHAD-
16
optimized phase descriptions, representing molar Gibbs energies of phases as a
17
function of temperature and alloy composition. The thermodynamic model
18
descriptions of the constituent binary subsystems, Mo-Hf, Hf-C, and Mo-C are
19
combined and ternary excess Gibbs energy parameters need to be optimized to be
20
able to reproduce experimental equilibrium phase boundaries and relative phase
21
fractions in MHC in thermodynamic calculations. Whereas complete thermodynamic
22
descriptions of the constituent binaries are available in the literature [9–11], there has
23
still no thermodynamic description of the Mo-Hf-C system been published. However,
24
experimental phase diagrams, isothermal sections at 1400°C, 1700°C and 2000°C
25
are available [12–14]. The redrawn isothermal sections for 2000°C and 1400°C are
26
shown in Figs. 1a and 1b. Furthermore, reports on phase stabilities and compositions
27
in particular regions of the Mo-Hf-C system are given by Zakharov and Savitsky [15]
28
and the behavior of the HfC-HfO, HfC-Mo2C and HfC-MoC systems are described in
29
Refs [16–18]. Unfortunately, these early experimental studies reveal a considerable
30
inconsistency among each other. One research group suggested significant solubility
31
of Hf in Mo2C [12,13], whereas the other studies reported only low solubility [15]. Up
32
to now, MHC research has not been focused on a critical discussion of these
33
discrepancies [19,20]. It is clear that the experimental differences will result in a
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ACCEPTED MANUSCRIPT tremendous difference of the competing (Mo,Hf)2C / (Hf,Mo)C stabilities, i.e. the
2
relative equilibrium phase fractions present in the MHC alloy composition.
3
This means that the important questions for an optimized MHC alloy design cannot
4
be answered unambiguously with the existing experimental phase stabilities.
5
Therefore, a set of key experiments, using optical light microscopy (OLM), scanning
6
electron microscopy (SEM) and atom probe tomography (APT) were performed in
7
order to determine the relative phase stabilities at different temperatures in selected
8
MHC alloys. By means of APT measurements of the carbide phases of as-sintered
9
MHC Lang et al. [21] recently revealed that ~1 at.% Hf is dissolved in the Mo2C-
10
phase and that ~2 at.% Mo and a significant amount of ~4.5 at.% O are soluble in the
11
HfC-phase. It was pointed out by first-principles calculations that especially Mo and O
12
influences the energy of formation of HfC. It is increased by Mo and decreased by O
13
towards higher negative values. Based on these new findings and additionally
14
published [21] phase stabilities and compositions of (Mo,Hf)2C and (Hf,Mo)C,
15
CALPHAD-descriptions of MHC-relevant phases of the Mo-Hf-C system were
16
constructed. Furthermore, O impurities cannot be avoided during powder
17
metallurgically (PM) processing of Mo-Hf-C alloys. Thus, the extension of Mo-Hf-C to
18
Mo-Hf-C-O of our new thermodynamic database is discussed in the framework of
19
MHC application.
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2. Experimental procedures
2
PM processed MHC was used for the experimental investigation of the phase
3
stabilities at different temperatures. Therefore, molybdenum powder, HfH2- powder
4
and carbon black were mixed and cold isostatically pressed. Afterwards, the MHC
5
green compact was sintered in hydrogen atmosphere at temperatures above ~0.8·TM
6
(TM=2893 K is the melting point of Mo [22]). A detailed description of the powder
7
metallurgical processing route of refractory metals is given in [23].
8
Three as-sintered MHC samples were annealed at 1600°C for 20 h, 2000°C for 5 h
9
and at 2300°C for 5 h in a H 2-tubular furnace in order to obtain conditions near
10
equilibrium. Subsequently, the samples were quenched with a cooling rate of
11
~425 K/min by switching off the furnace. Furthermore, the surface layers of the
12
samples were removed in order to avoid decarburized areas and to ensure
13
homogeneous compositions of the annealed samples. The chemical compositions of
14
these samples are shown in Table 1. The C contents were determined with
15
combustion analysis (CA) with a Leco TCH 600. The O contents were determined
16
with carrier gas hot extraction (CGHE) using a Leco CS 230 and the Hf and Mo
17
contents were determined with inductively coupled plasma-optical emission
18
spectroscopy (ICP-OS) employing an iCAP 6500 DUO. Minor traces of W, Zr and Ti
19
were also detected by means of ICP-OS in all the samples.
20
For scanning electron microscopy (SEM) and optical light microscopy (OLM)
21
investigations the samples were ground, polished and etched as described in detail
22
in [24–26]. The volume fractions of the different phases in the near equilibrium
23
conditions were analyzed with Adobe Photoshop Version 12.0 by setting color
24
threshold values. Non-automatically selected areas were added manually to the
25
phase selection.
26
The residual Hf content in solid solution in Mo-bcc was determined with APT
27
measurements. Therefore, rod-like samples were pre-polished in a two-step process
28
as described in [27] using direct voltage of 10-14 V for the first polishing step and 5-
29
7 V for the second [21]. Additionally, the needle-shaped samples were sharpened by
30
annular milling using the focused ion beam (FIB) preparation technique with 30 kV
31
acceleration voltage in a FEI Versa 3D DualBeam workstation. Finally, the
32
specimens were cleaned with the FIB using 5 kV and 2 kV in order to reduce the
33
implantation of Ga+ ions [21,28]. Subsequently, the samples were measured with a
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with a pulse fraction of 15% and a target evaporation rate of 1%. Furthermore, the
3
datasets were analyzed with the IVAS 3.6.6 software.
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3. Thermodynamic modeling
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Optimized thermodynamic descriptions of the phases, Mo solid solution (Mo-bcc),
3
(Mo,Hf)2C (M2C) and (Hf,Mo)C (MC) in the ternary Mo-Hf-C system based on
4
experimental phase stabilities and compositions are presented. For the ternary
5
extensions of Mo-bcc, M2C and MC phases, the same thermodynamic sublattice
6
formulas were chosen as in the constituent binaries: (Hf,Mo)(Va)3 bcc ,
7
(Hf,Mo)2(C,Va) hcp and (Hf,Mo)(C,Va) fcc, where Va stands for vacancies. The
8
common description of molar Gibbs energies of these phases Φ reads, using
9
CALPHAD formulations: s1 s 2 s1 GmΦ = °G (φ, Hf : C ) yHf yC + °G (φ, Mo : C ) yMo yCs 2
10
s1 s1 s1 s1 + aRT ( yHf ln yHf + yMo ln yMo )
+bRT ( yCs 2 ln yCs 2 + (1 − yCs 2 ) ln(1 − yCs 2 )) + E GmΦ
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(Eq. 1)
In Equation 1, a and b denote the number of moles of atoms in the substitutional
12
metal sublattice (s1) and interstitial sublattice (s2), respectively. y is the fraction of
13
element i in a sublattice, and °G(φ,i:Va) is the Gibbs energy of one mole formula of
14
compound φ, with all the sites of the substitutional lattice filled up by element i, and
15
empty interstitial sublattice, i.e. pure metal i, while °G(φ,i:C) represents the Gibbse
16
energy of stoichiometric carbide compound iaCb. The site fraction of vacant sites on
17
s2 = 1 − yCs 2 . the interstitial sublattice is defined as yVa
18
RT-terms define contributions of ideal entropy of mixing to the Gibbs energy. EGmΦ
19
describes excess Gibbs energy of non-ideal mixing,
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s 2 2 s1 s1 ν ν φ yC ∑ ( yi − y j ) Li , j:C ν=0 E Φ Gm = ∑∑ yis1 y sj1 2 s2 i j >i s1 s1 ν ν φ + yVa ∑ ( yi − y j ) Li , j:Va ν=0
,
(Eq. 2)
2 ν s2 s1 + yCs 2 yVa y ( yCs 2 − yVas 2 ) ν Lφi:C ,Va ∑i i ∑ ν=0
21
Where νL are linearly temperature-dependent parameters with interaction exponents
22
ν. L-parameters describe excess interaction energies between i, j metallic atoms on 8
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the substitutional sublattice, or C,Va on the interstitial sublattice. Extensions of phase
2
descriptions
3
(Hf,Mo)(C,O,Va) fcc, considering O solubility on the small interstitial sites only.
O
read
(Hf,Mo)(Va,O)3
bcc,
(Hf,Mo)2(C,O,Va)
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and
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4. Results and Discussion
2
4.1
Experimental investigation of MHC samples annealed at different temperatures
3
SEM images of the MHC microstructures after annealing for 20 h at 1600°C (in the
5
following termed as: SA16), 5 h at 2000°C (SA20) an d 5 h at 2300°C (SA23) are
6
shown in Fig. 2 in back scattered electron (BSE) contrast in different magnifications.
7
It can be observed that HfO2, Mo2C and plate-like HfC are present in the
8
microstructure of SA16 (Figs. 2a and 2b). While HfO2 particles and Mo2C layers are
9
still present in the microstructure of SA20 (Figs. 2c and 2d) and SA23 (Figs. 2e and
10
2f) a change in the HfC population can be observed for both conditions. By
11
increasing the annealing temperature the HfC-phase becomes less frequent in SA20
12
and it vanishes, with exception of a few scattered particles, in SA23. In both
13
conditions residual pores can be observed, however, due to electrolytical polishing
14
they appear larger than their real size [21,24].
15
The Hf content in the bcc solid solution was analyzed with at least four APT
16
measurements for each condition. SA16 reveals 0.03 ± 0.01 at.% Hf in solid solution,
17
SA20 0.24 ± 0.03 at.% and SA23 contains 0.47 ± 0.02 at.% Hf. As mentioned in
18
previous studies [9,11], no C is in solid solution in all three samples, but the Hf
19
content changed significantly between the different annealing temperatures.
20
Additionally, it was reported that the C solubility in Mo decreases with increasing Hf
21
content in solid solution in the ternary Mo-Hf-C system [29]. For a comparable as-
22
sintered MHC material a Hf content of 0.10-0.15 at.% in solid solution was reported
23
[30]. This material was also sintered above ~0.8·TM.
24
Compared to HfC (-209.4 kJ·mol-1) and Mo2C (-50.3 kJ·mol-1), HfO2 (-1072.8 kJ·mol-
25
1
26
Thus, it is assumed that all the O available in the system forms HfO2 during the sinter
27
process. The distribution of Hf and C in the different phases of MHC can then be
28
roughly estimated on the basis of the overall chemical composition (Table 1) and the
29
APT measurements. Therefore, it is assumed that HfC has a stoichiometric
30
composition with an atomic ratio of Hf:C=1 and the slight dissolution of Hf in Mo2C is
31
neglected [12,13,15,17]. Then, the only Hf sources are the Mo-rich bcc matrix, HfO2
32
and HfC and the only C sources are HfC and Mo2C. The estimated distribution
33
considering these circumstances is shown in Table 2. After subtracting Hf in the Mo-
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) has by far the highest negative energy of formation in the MHC alloy [9,10,31].
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2
means of ICP-OS, ~0.45 at.% Hf remains, forming large HfC in SA16, ~0.28 at.% in
3
SA20 and none in SA23. Consequently, the same amount of C is consumed by HfC
4
in each condition, and the residual C forms Mo2C. These considerations are
5
consistent with the observed microstructures in Fig. 2 suggesting that HfC is
6
completely dissolved in SA23.
7
The plate-like HfC particles of SA16 and SA20 were analyzed in the SEM in detail for
8
quantitative determination of their volume fraction. The length and the thickness of
9
these carbides were measured in grains oriented near [001] direction of the matrix,
10
where the carbides are aligned edge-on or face-on as reported in [7,24,30]. For SA16
11
the obtained distribution of length and thickness of HfC is shown in Figs. 3a and 3b,
12
respectively. A mean length of 1.02 ± 0.40 µm and a mean thickness of 76 ± 24 nm
13
of these carbides is determined. The length in SA 16 is slightly larger than reported
14
by Pöhl et al. [32] and has its origin in the different sample treatment. For the
15
calculation of the mean particle volume of HfC a square cuboidal shape was used
16
[25]. The difference between the highest (100 nm) and the lowest (52 nm)
17
thicknesses was evenly distributed on the 24 classes of the length distribution and
18
with the mean value of each class, the total volume of all particles in the length
19
distribution is calculated (Fig. 3c). Afterwards, a volume fraction of ~0.71 vol.% HfC
20
was determined for SA16 at a sufficient large image, as shown in Fig. 3d, by
21
multiplying the number of HfC particles (marked in red color) with the mean volume
22
of one particle in relation to the information volume. The information depth at an
23
acceleration voltage of 20 kV is approximately 1 µm for backscattered electron
24
contrast [33]. The same procedure was done for SA20. For this condition a mean
25
particle length of 0.76 ± 0.30 µm and a mean thickness of 67 ± 40 nm are measured.
26
The determined volume fraction of HfC is 0.13 vol.%. In Table 3 the estimated
27
volume fractions of the different phases in MHC, which are based on the estimated
28
distribution of Hf and C (Table 2), are compared to the measured volume fractions. It
29
can be seen that the volume fraction of HfC in SA16 is in good agreement with the
30
estimated volume fraction. However, in comparison the measured volume fraction for
31
HfC in SA20 is too low. As mentioned above HfC dissolves with increasing
32
temperature (Figs. 2c and 2d for SA20). At higher magnifications small and,
33
therefore, barely detectable HfC can be seen. Thus, it is suggested that this deviation
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2
small and partially dissolved HfC- particles.
3
Furthermore, the volume fractions of HfO2 particles and Mo2C layers at the grain
4
boundaries were determined at four OLM images for each condition. An example for
5
the color etched microstructures is shown in Figs. 4a, 4c and 4e for SA16, SA20 and
6
SA23, respectively. In these images Mo2C at the grain boundaries is shown in white
7
color, whereas HfO2 particles show a grey contrast [25]. Due to the used
8
magnification HfC particles cannot be observed. The volume fraction of Mo2C and
9
HfO2 particles were analyzed separately for all the specimens as shown in Figs. 4b,
10
4d and 4f. In these images Mo2C is shown red. For SA16 a mean volume fraction of
11
0.92 ± 0.19 vol.% Mo2C is determined and for HfO2 0.50 ± 0.12 vol.% was obtained.
12
In SA20 for Mo2C a mean volume fraction of 1.16 ± 0.18 vol.% was detected and
13
0.38 ± 0.06 vol.% in case of HfO2. In SA23 for Mo2C a mean value of
14
1.75 ± 0.16 vol.% was revealed and 0.53 ± 0.10 vol.% for HfO2. Again these values
15
are in good agreement with the estimated volume fractions, which are based on the
16
overall chemical composition and the APT measurements, and can be seen in Table
17
3.
18
Based on these experimental results it can be concluded that the solvus temperature
19
of HfC is somewhere between 2100°C and 2300°C. Furt hermore, the results of SA23
20
affirm that the cooling rate of ~425 K/min was sufficient to suppress the volume
21
diffusion of Hf [34], but not that of C [35], because no C was measured in solid
22
solution by APT as it is reported in Ref. [30]. C containing Mo alloys strongly tend to
23
decarburization at high temperatures and long annealing times [4,8], making a setup
24
for full equilibrium experiments difficult. On one hand, sufficiently large sample sizes
25
are needed to obtain an unaltered composition in the core of the sample. On the
26
other hand, quenching of such sample sizes for full equilibrium determination
27
requires a special furnace design equipped with a dropping mechanism able to
28
anneal the samples for long times at very high temperatures in an inert atmosphere.
29
However, for the investigation conducted in this study such a special furnace was not
30
available.
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Thermodynamic considerations based on experimental key data: M2C
2
APT studies of (Mo,Hf)2C in an MHC alloy exhibiting 0.65 at.% Hf and 0.85 at.% C
3
revealed only a small content of ~1 at.% of Hf in the hexagonal (hcp) carbide
4
structure [21]. In other words, the stabilization of the M2C-phase by Hf is only weak.
5
Considering these experimental results in the modeling at full extent, the calculated
6
phase fraction of M2C in MHC is too low at elevated temperatures, i.e., below the
7
experimental detection limit. This discrepancy cannot be solved by any adjustment of
8
ternary model parameters. Indeed, it can be argued that Hf solubilities in Mo-bcc or
9
C-Va interactions in this phase would also contribute indirectly to the stability of M2C
10
in MHC. Of course this ability was tested, and absurd high interaction parameters of
11
several millions of Joules would be required. Another question may be the effect of O
12
impurities in M2C on its stability. However, no solubility of O has been found in this
13
carbide [21]. Actually, a search in the forming binary Mo-C system needs to be done
14
in order to obtain a solution of this problem [9]. As mentioned above, the system
15
description is complete and predicted phase boundaries fit the experimental data
16
well. This is also true for the reproduction of formation enthalpy of pure Mo2C hcp
17
phase. No proper argument for adjusting the CALPHAD-assessed enthalpy of Mo2C
18
exists. On the other hand, entropy and heat capacity (Cp) data of Mo2C, which are
19
also critical for a more reliable thermodynamic description of the high-temperature
20
stability of the phase, are lacking. Taking this into account, the Gibbs energy
21
description of Mo2C was adjusted to produce a slightly higher Cp of Mo2C than
22
calculated using the thermodynamic assessment of Andersson [9]. Additionally, the
23
entropy of formation of Mo2C was also re-assessed slightly. The according re-
24
optimized parameter for the molar Gibbs energy of hcp compound (Mo)(C)0.5 reads
25
G(hcp)=-24150-3.6125·T-0.3·T·ln(T)-163000·T-1
26
+G(Mo-bcc)+0.5·G(graphite),
27
compared to Andersson´s original parameter for hcp (Mo)2(C),
28
G(hcp)=2·(-24150)+2· (-3.625)·T+2·(-163000·T-1)+2·G(Mo-bcc)+G(graphite).
29
The change of B·T results in a molar entropy difference of 0.0083 J/molK. Adding
30
C·T(ln)T to the Gibbs energy polynomial influences excess Cp of the phase. The
31
comparison of the re-calculated Cp of this work with Andersson´s assessment [9] is
32
shown in Fig. 5 using MatCalc [36] thermodynamic and kinetic phase transformation
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(Eq. 3)
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(Eq. 4)
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2
conveniently used for simple thermodynamic property and phase fractions vs.
3
temperature plots. Calculated phase diagrams of this study are shown using Thermo-
4
Calc [37], version 2015b.
5
The C solubility in pure Mo-bcc requires some re-consideration because Mo alloys
6
tend to decarburization as already mentioned above [3,8]. Especially long term
7
annealing treatments with small sample sizes at high temperatures could cause a
8
tremendous problem in the homogeneity of the composition. Therefore, most
9
literature references [3,4,8] used C rods and methane enriched argon gas during
10
annealing to avoid this effect. It is likely that also previous experiments suffered by
11
this phenomenon, assumingly leading to an over-estimation of the single Mo-bcc
12
phase region in the construction of the experimental binary Mo-C phase diagram. We
13
believe that the theoretic (i.e. true equilibrium) Mo-bcc/Mo2C and Mo-bcc/liquid phase
14
boundary will lie to the left of Andersson´s suggestions [9], as shown in the re-
15
evaluation in Fig. 6. The suggested deviation is realized by adding excess interaction
16
energy parameters, 0L and 1L to the original bcc description in the Mo-C system,
17
obeying the formulation for non-ideal mixing of equation 2. A combination of 0th and
18
1st order interaction instead of a single parameter was chosen in order to keep the
19
effect
20
Mo2C/Mo2C+bcc small.
21
Only by combining these slight refinements, the temperature-dependent parameters
22
of Mo2C, i.e. entropic and heat capacity contributions to the Gibbs energy with a
23
smaller C solubility in Mo-bcc, the experimental high-temperature phase stability of
24
M2C in MHC is reproduced satisfactorily. In the thermodynamic parameter
25
optimization of M2C the fact of higher experimental “near equilibrium” Mo2C-phase
26
fractions than theoretic full equilibrium fractions at elevated temperatures is
27
considered. A lower weighting of experimental Mo2C-stabilities relative to measured
28
fractions of HfC is used.
29
4.3
30
The experimentally observed stability of Mo-containing MC-phase clearly showed
31
smaller deviations
32
parameter optimization of temperature-dependent 0L to 3L interactions according to
33
Eq. 2, with 0L=1L=2L=-50000+17T, led to satisfactorily reproduction of experimental
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experimental
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and
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Thermodynamic considerations based on experimental key data: MC
among different
researchers
14
[12–15,29]. Straight-forward
ACCEPTED MANUSCRIPT solubility of Mo in the carbide [12,13] and associated phase boundary between Mo-
2
bcc and MC in the isopleth section Mo-HfC [15] as shown in Fig. 7a. For comparison
3
purpose experimental data points from Zakharov and Savitskiy were added to Fig. 7a
4
[15]. The figure reveals a narrow phase field of stable M2C-phase, which the
5
experimental plot [15] does not contain. Clearly, the optimized M2C-description
6
cannot avoid this theoretic feature. In addition, the calculated HfC-solubility in Mo-bcc
7
is smaller than the experiment proposes. Once again, these differences between
8
experiment and theory can be explained by some C loss during isothermal heat
9
treatments: The experimental plot will expectedly deviate from the exact Mo-HfC line
10
and in accordance we may account for the C-loss, replacing the condition x(Hf)-
11
x(C)=0 by x(Hf)-x(C)=0.001. The “C-loss simulation” plot is presented in Fig. 7b. In
12
Fig. 7b the effective decrease of the 3-phase equilibrium field Mo-bcc+MC+M2C in
13
Mo-HfC1-δ is seen.
14
The studies of Zakharov [15] comprise an additional group of ternary experimental
15
phase diagram data, which need to be taken into account in the parameter
16
optimization of Mo-bcc and carbide phases. Ternary parameters, summarized in
17
Table 4, have been optimized together to obtain the least squares of error between
18
calculated and selected experimental phase boundaries [8-11] and newly measured
19
relative phase fractions and phase compositions. Unary parameters G(HF-HCP),
20
G(MO-BCC) and G(C-GRAPHITE) were taken from Dinsdale [38].The reproduction
21
of phase boundaries in the Mo-rich corner of the Mo-Hf-C system is presented in Fig.
22
8. Taking our isothermal experimental results into account, the experimental MC
23
solvus temperature of SA samples lies between 2100°C and 2300°C. Calculating for
24
MHC composition and considering complete binding of O to HfO2 and negligible O
25
solubility in Mo-bcc and M2C, the calculated MC solvus temperature is too low (Table
26
5). Lang et al. [21] found a surprisingly high amount of O of ~4.4 at.% dissolved in
27
MC. This stabilizes the phase towards a higher dissolution temperature. In order to
28
determine this effect, the structural formula for O-containing MC is defined.
29
Additionally, model parameters of metastable Hf-O compound and interaction
30
between O and Va on interstitial sites of (Hf,Mo)(O,Va) fcc-phase are optimized with
31
experimentally determined O content in MC, as well as first-principles enthalpies of
32
formation. The comparison of CALPHAD-assessed enthalpies of O containing MC
33
with enthalpies at 0 K [21] is shown in Fig. 9. The first-principles calculations are
34
based on 64 atoms in HfC, i.e. 32 Hf atoms and 32 C atoms without Mo and O. For
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ACCEPTED MANUSCRIPT the substitution of Hf by Mo and C by O different compositions of the MC carbide are
2
simulated. Mo increases the energy of formation and O decreases it towards higher
3
negative values [21]. Furthermore, model parameters of Mo-bcc containing O, partly
4
replacing Va or C on the interstitial sites, are optimized by the experiments of
5
Srivastava and Seigle [39]. Therefore, the Gibbs energy of metastable Mo:O end-
6
member and interaction of O and Va on interstitial sites are adjusted.
7
With these refinements and including oxide Gibbs energies [31] in the extended Mo-
8
Hf-C-O database, the MC-stability is expanded towards higher temperature. This can
9
be seen in the calculated solvi of O containing MC (Table 5) and the equilibrium
10
phase fractions versus temperature plots in Fig. 10a for SA16 (high C, high O) and
11
SA20 (low C, low O), indicating that O impurities play a significant role for process
12
and alloying optimization of MHC. The modeled O solubilities in carbide phases and
13
Mo-bcc are shown in Fig. 10b. The closing figure, Fig. 11, indicates the strong
14
potential of the established thermodynamic database for systematic adjustment of
15
alloying in MHC. Here, one can read out for a specific alloying of Hf, how a change of
16
the Hf/C ratio will affect the competition of M2C versus MC stabilization as a function
17
of temperature.
18
4.4
19
Calculated phase fractions as shown in Table 6 reproduce experimental temperature-
20
dependent phase stabilities rather well. However, equilibrium Mo2C is expected to be
21
almost dissolved at 2300°C, whereas almost 2 vol.% were found experimentally in
22
SA23 as shown in Table 3. This difference between equilibrium calculation and
23
experimental measurement supports incomplete quenching of C in the experiment.
24
Table 7 represents calculated equilibrium phase compositions of MHC at the three
25
experimental temperatures. Comparison with Table 2 reveals a consistent amount of
26
Hf dissolved in Mo-bcc. C and O contents in Mo-bcc increase as a function of
27
temperature, whereas dissolved Mo in MC shows the opposite behavior to our
28
modeling. The calculated Mo content in MC at 1600°C is considerably larger than the
29
measured value [20]. On the other hand, the theoretic high-temperature solubility is
30
close to the experimental data. The increasing deviation of calculated versus
31
measured solubilities towards lower temperatures may reflect non-equilibrium
32
conditions in the experiment due to the slow diffusion of Mo. In contrast to MC only
33
slight O solubility in M2C is suggested. Figure 10 reveals the strong influence of the C
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CALPHAD-based calculated phase stabilities in MHC
16
ACCEPTED MANUSCRIPT content in MHC on the dissolution temperature of MC. SA16 contains the highest C
2
content of the studied samples, resulting in a 51°C lower solvus temperature than
3
SA20. The O content of SA16 is also higher than in SA20, but does not reverse the C
4
effect of the decrease of MC phase fraction relative to M2C.
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ACCEPTED MANUSCRIPT
5. Conclusions
2
A technologically applicable CALPHAD- database for Mo-Hf-C alloys lying in the Mo-
3
rich corner of the ternary system has been established. These alloys tend to
4
considerable changes of relative phase stabilities in case of only slight variations of
5
composition, for instance by impurities of O. Presented experimental results on HfC
6
and Mo2C phase stabilities in MHC complement existing, and partly contradictory,
7
phase diagram data and contribute to the consistency of the presented
8
thermodynamic modeling and optimization of the Mo-Hf-C system with O addition.
9
The new database is feasible to reproduce the delicate relative stabilities of M2C /
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MC in MHC and to optimize heat treatments for improved alloy design.
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References
2 3 4
[1]
N.N. Morgunova, Effect of titanium, zirconium, and hafnium on the properties of molybdenum alloyed with carbon, Met. Sci. Heat Treat. 8 (1966) 1001–1005. doi:10.1007/BF00653001.
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[2]
I.S. Malashenko, Y.A. Kashtalyan, N.P. Vashchilo, V.Y. Naumenko, A.D. Vasilev, Hardening of molybdenum by microadditions of hafnium and HfC carbide, Strength Mater. 6 (1974) 850–855. doi:10.1007/BF01528328.
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P.L. Raffo, Exploratory study of mechanical properties and heat treatment of molybdenum- hafnium- carbon alloys - unpublished report from the Lewis research center, 1969.
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[12] V.N. Eremenko, S. V. Shabanova, T.Y. Velikanova, Structure of alloys and the phase equilibrium diagram of the Hf-Mo-C system VI. Isothermal section of the Hf-Mo-C system at 1400°C, Sov. Powder Metall. Met. Ceram. 16 (1977) 772– 777. doi:10.1007/BF00793585.
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[13] V. Eremenko, S. Shabanova, T.Y. Velikanova, Structure of alloys and the phase equilibrium diagram of the system Hf-Mo-C - V. Isothermal section of the
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system Hf-Mo-C at 1700°C, Sov. Powder Metall. Met. Ceram. 16 (1977) 772– 777. doi:10.1007/BF00791473. [14] V.N. Eremenko, T.Y. Velikanova, S. V. Shabanova, Investigation of alloys of the ternary hafnium-molybdenum-carbon system, in: Vysokotemp. Karbidy, Naukova Dumka, Kiew, 1975: pp. 90–96.
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[15] A. Zakharov, E. Savitskiy, Investigation of the molybdenum rich range of the phase diagram of the ternary Mo-Hf-C system, Russ. Metall. 4 (1969) 144–148.
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[16] E. Rudy, H. Nowotny, F. Benesovsky, R. Kieffer, A. Neckel, Über Hafniumkarbid enthaltende Karbidsysteme, Monatshefte Für Chemie. 91 (1960) 176–187. doi:10.1007/BF00903181.
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[17] H. Nowotny, R. Kieffer, F. Benesovsky, C. Brukl, E. Rudy, Die Teilsysteme von HfC mit TiC, ZrC, VC, NbC, TaC, Cr3C2, Mo2C (MoC), WC und UC, Monatshefte Für Chemie. 90 (1959) 669–679. doi:10.1007/BF00902392.
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[18] H. Nowotny, F. Benesovsky, E. Rudy, Hochschmelzende Systeme mit Hafniumkarbid und -nitrid, Monatshefte Für Chemie. 91 (1960) 348–356. doi:10.1007/BF00901755.
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[19] J. Wadsworth, A reevaluation of the mechanical properties of molybdenumand tungsten-based alloys containing hafnium and carbon, Metall. Trans. A. 14 (1983) 285–294. doi:10.1007/BF02651625.
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[20] J. Wadsworth, W.D. Klopp, The influence of the atomic ratios of hafnium to carbon on high-temperature strength in molybdenum and tungsten alloys, in: Phys. Metall. Technol. Molybdenum Its Alloy. Proc. a Symp. Held Amax Mater. Res. Cent., Ann Arbor, Michigan, 1985: pp. 127–133.
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[21] D. Lang, C. Pöhl, D. Holec, J. Schatte, E. Povoden-Karadeniz, W. Knabl, et al., On the chemistry of the carbides in a molybdenum base Mo-Hf-C alloy produced by powder metallurgy, J. Alloys Compd. 654 (2016) 445–454. doi:10.1016/j.jallcom.2015.09.126.
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[22] C.K. Gupta, Extractive Metallurgy of Molybdenum, CRC Press, Boca Raton, 1992. https://books.google.com/books?id=6V7oPjy_0IwC&pgis=1 (accessed January 18, 2016).
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[23] G. Leichtfried, Refractory metals, in: P. Beiss, R. Ruthardt, H. Warlimont (Eds.), Powder Metall. Data. Refract. Hard Intermet. Mater., Springer-Verlag, Berlin/Heidelberg, 2002: pp. 4–27. doi:10.1007/b83029.
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[24] D. Lang, J. Schatte, H. Clemens, S. Primig, Elektrolytisches Polieren vs. Vibrationspolieren: Entwicklung einer Präparationsmethode zur EBSD- Analyse der Mo- Basislegierung MHC, in: S. Mayer, M. Panzenböck, H. Clemens (Eds.), 14. Int. Metallogr., Leoben, 2014: pp. 44–46.
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ACCEPTED MANUSCRIPT [25] C. Pöhl, J. Schatte, H. Leitner, Metallographic characterization of the molybdenum based alloy MHC by a color etching technique, Mater. Charact. 77 (2013) 63–69. doi:10.1016/j.matchar.2013.01.001.
4 5
[26] R. Hasson, Metallography of molybdenum in color, Microscope. 16 (1968) 329–334.
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[27] M.K. Miller, A. Cerezo, M.G. Hetherington, G.D.W. Smith, Appendix A: specimen preparation, in: Atom Probe F. Ion Microsc., 2nd ed., Oxford University Press Inc., New York, 2006: pp. 476–483.
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[28] K. Thompson, D. Lawrence, D.J. Larson, J.D. Olson, T.F. Kelly, B. Gorman, In situ site-specific specimen preparation for atom probe tomography., Ultramicroscopy. 107 (n.d.) 131–9. doi:10.1016/j.ultramic.2006.06.008.
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[29] L. Rokhlin, N. Kolchugina, T. Dobatkina, E. Semenova, Carbon – Hafnium – Molybdenum, in: G. Effenberg, S. Ilyenko (Eds.), Refract. Met. Syst. Phase Diagrams, Crystallogr. Thermodyn. Data, Springer Berlin Heidelberg, Berlin, Heidelberg, 2010: pp. 409–428. doi:10.1007/978-3-642-02700-0_27.
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[30] C. Pöhl, D. Lang, J. Schatte, H. Leitner, Strain induced decomposition and precipitation of carbides in a molybdenum–hafnium–carbon alloy, J. Alloys Compd. 579 (2013) 422–431. doi:10.1016/j.jallcom.2013.06.086.
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[31] C. Wang, M. Zinkevich, F. Aldinger, The Zirconia-Hafnia System: DTA Measurements and Thermodynamic Calculations, J. Am. Ceram. Soc. 89 (2006) 3751–3758. doi:10.1111/j.1551-2916.2006.01286.x.
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[32] C. Pöhl, D. Lang, J. Schatte, H. Leitner, Strengthening mechanisms of the molybdenum-base alloy MHC, in: L.S. Sigl, H. Kestler, J. Wagner (Eds.), 18th Plansee Semin. - Int. Conf. Refract. Hard Mater., Reutte, Austria, 2013: pp. 61–70.
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[33] D. Drouin, A.R. Counture, D. Joly, N. Poirier-Demers, H. Demers, Casino monte carlo simulation of electron trajectory in solids, (2016). http://www.gel.usherbrooke.ca/casino/.
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[34] Y. Bhatt, L. Kumar, R. Patil, G. Kale, S. Garg, Diffusion studies in Hf–Mo, Zr– Mo, Cr–Nb, Cr–Ta and Th–Re systems above 1900 K, J. Alloys Compd. 302 (2000) 177–186. doi:10.1016/S0925-8388(00)00678-2.
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[35] P.S. Rudman, The solubility limit and diffusivity of carbon in molybdenum, Trans. Metall. Soc. AIME. 239 (1967) 1949–1954.
34 35 36 37
[36] E. Kozeschnik, B. Buchmayr, MatCalc - A simulation tool for multicomponent thermodynamics, diffusion and phase transformations, in: H. Cerjak, H.K.D.H. Bhaddeshia (Eds.), Math. Model. Weld Phenom. 5, IOM Communications Ltd, London, 2001: pp. 349–361.
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ACCEPTED MANUSCRIPT [37] B. Jansson, M. Schalin, M. Selleby, B. Sundman, The Thermo-Calc database system, in: C.W. Bale, G.A. Irons (Eds.), Comput. Softw. Chem. Extr. Metall., Metallurgical Society of CIM, Quebec, 1993: pp. 57–71.
4 5
[38] A.T. Dinsdale, SGTE data for pure elements, Calphad. 15 (1991) 317–425. doi:10.1016/0364-5916(91)90030-N.
6 7 8
[39] S.C. Srivastava, L.L. Seigle, Solubility and thermodynamic properties of oxygen in solid molybdenum, Metall. Trans. 5 (1974) 49–52. doi:10.1007/BF02642925.
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ACCEPTED MANUSCRIPT 1
Figure captions
2
Fig. 1: Experimental phase diagrams of the Mo-Hf-C system at a) 2273 K and b)
3
1673 K, redrawn from [12,14]. Dotted lines represent modeled phase boundaries
4
derived in this work.
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Fig. 2: SEM images of electrolytically polished MHC microstructures in two different
7
magnifications of the three different annealed conditions in BSE contrast. (a) and (b)
8
1600°C for 20h (SA16). (c) and (d) 2000°C for 5h (S A20).(e) and (f) 2300°C or 5 h
9
(SA23).
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6
10
Fig. 3: Investigation of large HfC after annealing for 20 h at 1600°C: (a) length
12
distribution; (b) thickness distribution; (c) volume distribution calculated on base of (a)
13
and (b). (d) SEM image of the electrolytically polished MHC microstructure in BSE
14
contrast. Counted HfC are shown red. The particle distribution is based on a log-
15
normal function.
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Fig. 4: OLM images of color etched MHC microstructures after annealing for (a) 20 h
18
at 1600°C, (c) 5h at 2000°C and (e) 5 h at 2300°C [ 25,26]. Mo2C particles are shown
19
in white and HfO2 in grey. (b), (d) and (f) Separated phases. Mo2C is shown red, HfO2
20
in grey.
21
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17
Fig. 5: Evaluated heat capacity Cp of the Mo2C-phase, compared with a previous
23
description (dashed curve) [9].
24
AC C
22
25
Fig. 6: Evaluated C-solubilities in Mo-bcc solid solution, compared with previous
26
assessment (dashed line) [9].
27
23
ACCEPTED MANUSCRIPT 1 Fig. 7: (a) Isopleth section Mo-HfC. For comparison purpose experimental data points
3
from Zakharov and Savitskiy [15] were added. (b) Mo-HfC1-δ section with simulation
4
of constant loss of C-fraction δ, realized by the condition x(Hf)-x(C)≠0 (see text). The
5
hdp phase region is significantly decreasing. The phase diagram starts at 0.186
6
mass percent of HfC1-δ (0.1 at.% Hf) where x(C) equals 0.
7
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Fig. 8: Comparison of previous experimental results in the Mo-rich corner of the Mo-
9
Hf-C system [15] with calculations using our CALPHAD optimization at 2373 K and
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8
1523 K. Bold lines represent phase boundaries, thin straight tielines mark two phases
11
equilibria.
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Fig. 9: Evaluated enthalpies of formation of MC containing 0, 1, 2, 3 Mo atoms and
14
each 0, 1, 2 or 3 Oxygen atoms by CALPHAD and first-principles analysis [21]. The
15
calculations are based on 64 atoms in the HfC, i.e. 32 Hf atoms and 32 C atoms for
16
HfC without Mo and O. By substitution of Hf by Mo and C by O different compositions
17
of the MC carbide are simulated. Mo increases the energy of formation and O
18
decreases it towards higher negative values [21].
19
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Fig. 10: (a) Equilibrium phase fractions as function of temperature in MHC; (b) O solubility in
21
MC, M2C and Mo-bcc in SA16 and SA20. Note the difference of O solubilities is too small
22
between both conditions to be discernable.
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Fig. 11: Predicted phase stabilities as function of C and Hf contents in MHC. At
25
x(Hf)/x(C)=1 and x(Hf)/x(C)=0.5 the single phase Mo ss (ss stands for solid solution)
26
expands towards higher C-contents. At x(Hf)/x(C)=0.5 the M2C-phase is stabilized
27
towards higher C contents, whereas at x(Hf)/x(C)=1.5 this phase does not form. At
28
x(Hf)/x(C)=1 the Mo2C is only stabilized in a narrow C composition range.
24
ACCEPTED MANUSCRIPT 1
TABLES
2 3 4 5 6
Table 1 Overall chemical composition in at.% of the investigated MHC samples after sintering and annealing for 20 h at 1600°C and for 5 h at 200 0°C and 2300°C in hydrogen atmosphere (RSD = relative standard deviation). SA20
SA23
Mo
balance
balance
balance
Testing procedure, accuracy at 1 g testing material ICP-OS, ± 1 ppm or <5% RSD
Hf
0.65
0.65
0.65
ICP-OS, ± 1 ppm or <5% RSD
C
0.85
0.74
0.77
CA, ± 2-3 ppm or <5% RSD
O
0.34
0.28
0.36
CGHE, ± 2-3 ppm or <5% RSD
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SA16
7
Table 2 On the basis of the overall chemical composition and APT measurements estimated Hf and C distribution in the phases of the MHC samples after annealing for 20 h at 1600°C and for 5 h at 2000°C and 2300°C (at.%) in hydrogen atmosphere.
Hf in solid solution
Hf in HfC C in HfC C in Mo2C
SA23
0.03
0.24
0.47
0.17
0.14
0.18
0.45
0.27
0.00
0.45
0.27
0.00
0.40
0.47
0.77
Table 3 On the basis of the overall chemical composition and APT measurements estimated distribution of phases in MHC samples compared to the measured distribution after annealing for 20 h at 1600°C and for 5 h at 2000°C and 2300°C in hydrogen atmosphere.
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13 14 15 16 17
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Hf in HfO2
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SA16
Phase
SA20
SA23
estimated
measured
estimated
measured
estimated
measured
mol.% vol.%
vol.%
mol.% vol.%
vol.%
mol.% vol.%
vol.%
HfC
0.90
0.74
Mo2C
1.20
HfO2
0.51
0.71
0.54
0.45
0.13
0.00
0.00
0.94 0.92±0.19
1.41
1.11
1.16±0.18
2.31
1.81 1.75±0.16
0.39 0.50±0.12
0.42
0.32
0.38±0.06
0.54
0.41 0.53±0.10
18
1
0.00
ACCEPTED MANUSCRIPT
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PHASE FCC_A1, Crystal structure: face-centered cubic, space group Fm-3m Sublattice description: (HF,MO)1(C,VA)1 End-member compound energies: G(FCC_A1,MO:C) -7500-8.5*T-0.35*T*LN(T) -750000*T**(-1)+G(MO-BCC)+G(C-GRAPHITE) Interaction parameters: 0L(FCC_A1,HF,MO:C) -50000+17*T 1L(FCC_A1,HF,MO:C) -50000+17*T 2L(FCC_A1,HF,MO:C) -50000+17*T
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Table 4 Optimized CALPHAD sublattice descriptions and model parameters of the Mo-Hf-C system.
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PHASE BCC_A2 Crystal structure: body-centered cubic, space group Im-3m Sublattice description: (HF,MO)1(C,VA)3 End-member compound energies: G(BCC_A2,MO:C;0) +300000-65*T-0.1*T*LN(T) +G(MO-BCC)+3*G(C-GRAPHITE) Interaction parameters: 0L(BCC_A2,MO:C,VA) -25000 1L(BCC_A2,MO:C,VA) -10000 0L(BCC_A2,HF,MO:C) +200000 1L(BCC_A2,HF,MO:C) -200000 2L(BCC_A2,HF,MO:C) +200000
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PHASE HCP_A3 Crystal structure: hexagonally close-packed, space group P63/mmc Sublattice description: (HF,MO)1(C,VA)0.5 End-member compound energies: G(HCP_A3,MO:C) -24150-3.6125*T-0.3*T*LN(T) -163000*T**(-1)+G(MO-BCC)+0.5*G(C-GRAPHITE) Interaction parameters: 0L(HCP_A3,HF,MO:C;0) +6200-10*T 1L(HCP_A3,HF,MO:C;1) -6200+10*T 2L(HCP_A3,HF,MO:C;2) +6200-10*T 0L(HCP_A3,HF,MO:C,VA;0) -5000+50*T
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SA16 SA20 SA23
(Hf,Mo)1(C,O,Va)1 2133 2184 2133.5
Table 6 With CALPHAD calculated equilibrium phase contents in MHC samples of the studied compositions from Table 1 annealed at 1600°C, 2000° C and 2300°C based on the optimized database. The term ss stands for solid solution. Compare with experimental results, Table 3.
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bcc ss MC M2C HfO2
vol.% (mol.%) SA16 SA20 SA23 97.68 (97.46) 98.47 (98.44) 99.23 (99.45) 0.72 (0.96) 0.31 (0.38) 0.88 (1.07) 0.65 (0.77) 0.007 (0.0083) 0.38 (0.51) 0.3 (0.40) 0.4 (0.54)
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at% Hf at.% Mo at.% C at.% O SA16 SA20 SA23 SA16 SA20 SA23 SA16 SA20 SA23 SA16 SA20 SA23
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bcc 0.08 0.32 0.47 99.8 99.32 98.76 0.085 0.36 0.77 5E-08 4E-06 5E-05 ss MC 41.07 45.92 11.7 4.93 47.18 45.54 0.44 3.6 M2C 0.72 2.81 3.72 70.05 69.89 69.27 29.23 27.3 26.85 3E-05 4E-03 0.17
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ACCEPTED MANUSCRIPT Highlights: Evaluation of the Mo-rich corner of the ternary Mo-Hf-C system.
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Reoptimization of the thermodynamics of Mo2C and HfC.
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O impurities have a significant influence on the phase stability of HfC
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S0925-8388(16)33364-3
DOI:
10.1016/j.jallcom.2016.10.227
Reference:
JALCOM 39394
To appear in:
Journal of Alloys and Compounds
Received Date: 8 May 2016 Revised Date:
19 October 2016
Accepted Date: 25 October 2016
Please cite this article as: D. Lang, E. Povoden-Karadeniz, J. Schatte, W. Knabl, H. Clemens, S. Primig, Thermodynamic evaluation of the Mo-rich corner of the Mo-Hf-C system including O impurities, Journal of Alloys and Compounds (2016), doi: 10.1016/j.jallcom.2016.10.227. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Thermodynamic evaluation of the Mo-rich corner of the MoHf-C system including O impurities D. Langa,b,1*, E. Povoden-Karadenizc, J. Schatted, W. Knabld, H. Clemensa, S. Primiga,2
3 4 a
Department of Physical Metallurgy and Materials Testing, Montanuniversitaet Leoben, A-8700 Leoben, Austria
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b
Christian Doppler Laboratory Early Stages of Precipitation, Montanuniversitaet Leoben, A-8700 Leoben, Austria
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c
Institute of Materials Science and Technology, TU Wien, A-1060, Vienna, Austria
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d
PLANSEE SE, A-6600 Reutte, Austria
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1
now at PLANSEE SE, A-8940 Liezen, Austria
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2
now at School of Materials Science & Engineering, UNSW Sydney, NSW 2052 Sydney, Australia
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* David Lang Corresponding author Department of Physical Metallurgy and Materials Testing, Christian Doppler Laboratory Early Stages of Precipitation, Montanuniversität Leoben, Franz-Josef Straße 18, A-8700 Leoben, Austria Now at Plansee SE, Werkstraße 14, A-8940 Liezen, Austria e-Mail: [email protected]
21 22 23 24
Erwin Povoden-Karadeniz Institute of Materials Science and Technology, TU Wien, Getreidemarkt 9, A-1060, Vienna, Austria e-Mail: [email protected]
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Jürgen Schatte Plansee SE, Metallwerk-Plansee-Straße 71, A-6600 Reutte, Austria e-Mail: [email protected]
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Wolfram Knabl Plansee SE, Metallwerk-Plansee-Straße 71, A-6600 Reutte, Austria e-Mail: [email protected]
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Helmut Clemens Department of Physical Metallurgy and Materials Testing, Montanuniversität Leoben, Franz-Josef Straße 18, A-8700 Leoben, Austria e-Mail: [email protected]
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Sophie Primig Department of Physical Metallurgy and Materials Testing, Montanuniversität Leoben, Franz-Josef Straße 18, A-8700 Leoben, Austria Now at School of Materials Science & Engineering, UNSW Sydney, NSW 2052 Sydney, Australia e-Mail: [email protected]
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Abstract
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In this paper the phase fractions of (Hf,Mo)C and (Mo,Hf)2C carbide phases are
3
investigated experimentally in the low Hf and C alloyed composition range of
4
technological Mo-Hf-C applications. Furthermore, solubilities of Hf and C in body
5
centered cubic Mo-base solid solution (Mo-bcc) are evaluated with consideration of
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the presence of O-impurities. The results, together with thermodynamic stability data
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from first-principles analysis, are taken into account in thermodynamic model
8
descriptions of the solid alloy and carbide phases. The presented modeling considers
9
O solubility in Mo-bcc and (Hf,Mo)C, as well as the role of O impurities in MHC, a Mo-
10
Hf-C alloy with a nominal composition of 0.65 at.% Hf and 0.65 at.% C, is discussed.
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Finally, a typical application of the optimized thermodynamic database for the
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prediction of phase stabilities in MHC is presented.
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Keywords:
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Refractory, Molybdenum- hafnium- carbon; MHC, Carbide, Thermodynamic,
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Modeling
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1. Introduction
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Precipitation of HfC in Mo-base alloys has been studied since the 1960s and they
3
have a great potential to improve the mechanical properties at elevated
4
temperatures. A typical composition around 0.65 at.% Hf and 0.65 at.% C, named
5
MHC alloy, has been established. This composition exhibits an optimum balance
6
between processability and mechanical properties. Additionally, this alloy has a
7
sufficiently large window for solid solution heat treatment in the single-phase body
8
centered cubic Mo matrix at high temperatures and it is able to form ~1 vol.%
9
strength increasing face centered cubic (fcc) HfC nanoparticles [1–8].
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For an optimized alloy design of MHC, which includes thermo-mechanical processing
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and heat treatments, detailed knowledge of the ternary Mo-Hf-C system, especially in
12
the Mo-rich corner, is inevitable. For instance, the C- and Hf solubilities in body
13
centered cubic Mo-base solid solution (Mo-bcc) control the carbide precipitation
14
behavior in MHC during technological heat treatments as a function of temperature.
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The thermodynamic database for such predictions is obtained by CALPHAD-
16
optimized phase descriptions, representing molar Gibbs energies of phases as a
17
function of temperature and alloy composition. The thermodynamic model
18
descriptions of the constituent binary subsystems, Mo-Hf, Hf-C, and Mo-C are
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combined and ternary excess Gibbs energy parameters need to be optimized to be
20
able to reproduce experimental equilibrium phase boundaries and relative phase
21
fractions in MHC in thermodynamic calculations. Whereas complete thermodynamic
22
descriptions of the constituent binaries are available in the literature [9–11], there has
23
still no thermodynamic description of the Mo-Hf-C system been published. However,
24
experimental phase diagrams, isothermal sections at 1400°C, 1700°C and 2000°C
25
are available [12–14]. The redrawn isothermal sections for 2000°C and 1400°C are
26
shown in Figs. 1a and 1b. Furthermore, reports on phase stabilities and compositions
27
in particular regions of the Mo-Hf-C system are given by Zakharov and Savitsky [15]
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and the behavior of the HfC-HfO, HfC-Mo2C and HfC-MoC systems are described in
29
Refs [16–18]. Unfortunately, these early experimental studies reveal a considerable
30
inconsistency among each other. One research group suggested significant solubility
31
of Hf in Mo2C [12,13], whereas the other studies reported only low solubility [15]. Up
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to now, MHC research has not been focused on a critical discussion of these
33
discrepancies [19,20]. It is clear that the experimental differences will result in a
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relative equilibrium phase fractions present in the MHC alloy composition.
3
This means that the important questions for an optimized MHC alloy design cannot
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be answered unambiguously with the existing experimental phase stabilities.
5
Therefore, a set of key experiments, using optical light microscopy (OLM), scanning
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electron microscopy (SEM) and atom probe tomography (APT) were performed in
7
order to determine the relative phase stabilities at different temperatures in selected
8
MHC alloys. By means of APT measurements of the carbide phases of as-sintered
9
MHC Lang et al. [21] recently revealed that ~1 at.% Hf is dissolved in the Mo2C-
10
phase and that ~2 at.% Mo and a significant amount of ~4.5 at.% O are soluble in the
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HfC-phase. It was pointed out by first-principles calculations that especially Mo and O
12
influences the energy of formation of HfC. It is increased by Mo and decreased by O
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towards higher negative values. Based on these new findings and additionally
14
published [21] phase stabilities and compositions of (Mo,Hf)2C and (Hf,Mo)C,
15
CALPHAD-descriptions of MHC-relevant phases of the Mo-Hf-C system were
16
constructed. Furthermore, O impurities cannot be avoided during powder
17
metallurgically (PM) processing of Mo-Hf-C alloys. Thus, the extension of Mo-Hf-C to
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Mo-Hf-C-O of our new thermodynamic database is discussed in the framework of
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MHC application.
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2. Experimental procedures
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PM processed MHC was used for the experimental investigation of the phase
3
stabilities at different temperatures. Therefore, molybdenum powder, HfH2- powder
4
and carbon black were mixed and cold isostatically pressed. Afterwards, the MHC
5
green compact was sintered in hydrogen atmosphere at temperatures above ~0.8·TM
6
(TM=2893 K is the melting point of Mo [22]). A detailed description of the powder
7
metallurgical processing route of refractory metals is given in [23].
8
Three as-sintered MHC samples were annealed at 1600°C for 20 h, 2000°C for 5 h
9
and at 2300°C for 5 h in a H 2-tubular furnace in order to obtain conditions near
10
equilibrium. Subsequently, the samples were quenched with a cooling rate of
11
~425 K/min by switching off the furnace. Furthermore, the surface layers of the
12
samples were removed in order to avoid decarburized areas and to ensure
13
homogeneous compositions of the annealed samples. The chemical compositions of
14
these samples are shown in Table 1. The C contents were determined with
15
combustion analysis (CA) with a Leco TCH 600. The O contents were determined
16
with carrier gas hot extraction (CGHE) using a Leco CS 230 and the Hf and Mo
17
contents were determined with inductively coupled plasma-optical emission
18
spectroscopy (ICP-OS) employing an iCAP 6500 DUO. Minor traces of W, Zr and Ti
19
were also detected by means of ICP-OS in all the samples.
20
For scanning electron microscopy (SEM) and optical light microscopy (OLM)
21
investigations the samples were ground, polished and etched as described in detail
22
in [24–26]. The volume fractions of the different phases in the near equilibrium
23
conditions were analyzed with Adobe Photoshop Version 12.0 by setting color
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threshold values. Non-automatically selected areas were added manually to the
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phase selection.
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The residual Hf content in solid solution in Mo-bcc was determined with APT
27
measurements. Therefore, rod-like samples were pre-polished in a two-step process
28
as described in [27] using direct voltage of 10-14 V for the first polishing step and 5-
29
7 V for the second [21]. Additionally, the needle-shaped samples were sharpened by
30
annular milling using the focused ion beam (FIB) preparation technique with 30 kV
31
acceleration voltage in a FEI Versa 3D DualBeam workstation. Finally, the
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specimens were cleaned with the FIB using 5 kV and 2 kV in order to reduce the
33
implantation of Ga+ ions [21,28]. Subsequently, the samples were measured with a
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with a pulse fraction of 15% and a target evaporation rate of 1%. Furthermore, the
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datasets were analyzed with the IVAS 3.6.6 software.
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3. Thermodynamic modeling
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Optimized thermodynamic descriptions of the phases, Mo solid solution (Mo-bcc),
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(Mo,Hf)2C (M2C) and (Hf,Mo)C (MC) in the ternary Mo-Hf-C system based on
4
experimental phase stabilities and compositions are presented. For the ternary
5
extensions of Mo-bcc, M2C and MC phases, the same thermodynamic sublattice
6
formulas were chosen as in the constituent binaries: (Hf,Mo)(Va)3 bcc ,
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(Hf,Mo)2(C,Va) hcp and (Hf,Mo)(C,Va) fcc, where Va stands for vacancies. The
8
common description of molar Gibbs energies of these phases Φ reads, using
9
CALPHAD formulations: s1 s 2 s1 GmΦ = °G (φ, Hf : C ) yHf yC + °G (φ, Mo : C ) yMo yCs 2
10
s1 s1 s1 s1 + aRT ( yHf ln yHf + yMo ln yMo )
+bRT ( yCs 2 ln yCs 2 + (1 − yCs 2 ) ln(1 − yCs 2 )) + E GmΦ
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(Eq. 1)
In Equation 1, a and b denote the number of moles of atoms in the substitutional
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metal sublattice (s1) and interstitial sublattice (s2), respectively. y is the fraction of
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element i in a sublattice, and °G(φ,i:Va) is the Gibbs energy of one mole formula of
14
compound φ, with all the sites of the substitutional lattice filled up by element i, and
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empty interstitial sublattice, i.e. pure metal i, while °G(φ,i:C) represents the Gibbse
16
energy of stoichiometric carbide compound iaCb. The site fraction of vacant sites on
17
s2 = 1 − yCs 2 . the interstitial sublattice is defined as yVa
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RT-terms define contributions of ideal entropy of mixing to the Gibbs energy. EGmΦ
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describes excess Gibbs energy of non-ideal mixing,
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s 2 2 s1 s1 ν ν φ yC ∑ ( yi − y j ) Li , j:C ν=0 E Φ Gm = ∑∑ yis1 y sj1 2 s2 i j >i s1 s1 ν ν φ + yVa ∑ ( yi − y j ) Li , j:Va ν=0
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(Eq. 2)
2 ν s2 s1 + yCs 2 yVa y ( yCs 2 − yVas 2 ) ν Lφi:C ,Va ∑i i ∑ ν=0
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Where νL are linearly temperature-dependent parameters with interaction exponents
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ν. L-parameters describe excess interaction energies between i, j metallic atoms on 8
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the substitutional sublattice, or C,Va on the interstitial sublattice. Extensions of phase
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descriptions
3
(Hf,Mo)(C,O,Va) fcc, considering O solubility on the small interstitial sites only.
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(Hf,Mo)2(C,O,Va)
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4. Results and Discussion
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4.1
Experimental investigation of MHC samples annealed at different temperatures
3
SEM images of the MHC microstructures after annealing for 20 h at 1600°C (in the
5
following termed as: SA16), 5 h at 2000°C (SA20) an d 5 h at 2300°C (SA23) are
6
shown in Fig. 2 in back scattered electron (BSE) contrast in different magnifications.
7
It can be observed that HfO2, Mo2C and plate-like HfC are present in the
8
microstructure of SA16 (Figs. 2a and 2b). While HfO2 particles and Mo2C layers are
9
still present in the microstructure of SA20 (Figs. 2c and 2d) and SA23 (Figs. 2e and
10
2f) a change in the HfC population can be observed for both conditions. By
11
increasing the annealing temperature the HfC-phase becomes less frequent in SA20
12
and it vanishes, with exception of a few scattered particles, in SA23. In both
13
conditions residual pores can be observed, however, due to electrolytical polishing
14
they appear larger than their real size [21,24].
15
The Hf content in the bcc solid solution was analyzed with at least four APT
16
measurements for each condition. SA16 reveals 0.03 ± 0.01 at.% Hf in solid solution,
17
SA20 0.24 ± 0.03 at.% and SA23 contains 0.47 ± 0.02 at.% Hf. As mentioned in
18
previous studies [9,11], no C is in solid solution in all three samples, but the Hf
19
content changed significantly between the different annealing temperatures.
20
Additionally, it was reported that the C solubility in Mo decreases with increasing Hf
21
content in solid solution in the ternary Mo-Hf-C system [29]. For a comparable as-
22
sintered MHC material a Hf content of 0.10-0.15 at.% in solid solution was reported
23
[30]. This material was also sintered above ~0.8·TM.
24
Compared to HfC (-209.4 kJ·mol-1) and Mo2C (-50.3 kJ·mol-1), HfO2 (-1072.8 kJ·mol-
25
1
26
Thus, it is assumed that all the O available in the system forms HfO2 during the sinter
27
process. The distribution of Hf and C in the different phases of MHC can then be
28
roughly estimated on the basis of the overall chemical composition (Table 1) and the
29
APT measurements. Therefore, it is assumed that HfC has a stoichiometric
30
composition with an atomic ratio of Hf:C=1 and the slight dissolution of Hf in Mo2C is
31
neglected [12,13,15,17]. Then, the only Hf sources are the Mo-rich bcc matrix, HfO2
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and HfC and the only C sources are HfC and Mo2C. The estimated distribution
33
considering these circumstances is shown in Table 2. After subtracting Hf in the Mo-
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means of ICP-OS, ~0.45 at.% Hf remains, forming large HfC in SA16, ~0.28 at.% in
3
SA20 and none in SA23. Consequently, the same amount of C is consumed by HfC
4
in each condition, and the residual C forms Mo2C. These considerations are
5
consistent with the observed microstructures in Fig. 2 suggesting that HfC is
6
completely dissolved in SA23.
7
The plate-like HfC particles of SA16 and SA20 were analyzed in the SEM in detail for
8
quantitative determination of their volume fraction. The length and the thickness of
9
these carbides were measured in grains oriented near [001] direction of the matrix,
10
where the carbides are aligned edge-on or face-on as reported in [7,24,30]. For SA16
11
the obtained distribution of length and thickness of HfC is shown in Figs. 3a and 3b,
12
respectively. A mean length of 1.02 ± 0.40 µm and a mean thickness of 76 ± 24 nm
13
of these carbides is determined. The length in SA 16 is slightly larger than reported
14
by Pöhl et al. [32] and has its origin in the different sample treatment. For the
15
calculation of the mean particle volume of HfC a square cuboidal shape was used
16
[25]. The difference between the highest (100 nm) and the lowest (52 nm)
17
thicknesses was evenly distributed on the 24 classes of the length distribution and
18
with the mean value of each class, the total volume of all particles in the length
19
distribution is calculated (Fig. 3c). Afterwards, a volume fraction of ~0.71 vol.% HfC
20
was determined for SA16 at a sufficient large image, as shown in Fig. 3d, by
21
multiplying the number of HfC particles (marked in red color) with the mean volume
22
of one particle in relation to the information volume. The information depth at an
23
acceleration voltage of 20 kV is approximately 1 µm for backscattered electron
24
contrast [33]. The same procedure was done for SA20. For this condition a mean
25
particle length of 0.76 ± 0.30 µm and a mean thickness of 67 ± 40 nm are measured.
26
The determined volume fraction of HfC is 0.13 vol.%. In Table 3 the estimated
27
volume fractions of the different phases in MHC, which are based on the estimated
28
distribution of Hf and C (Table 2), are compared to the measured volume fractions. It
29
can be seen that the volume fraction of HfC in SA16 is in good agreement with the
30
estimated volume fraction. However, in comparison the measured volume fraction for
31
HfC in SA20 is too low. As mentioned above HfC dissolves with increasing
32
temperature (Figs. 2c and 2d for SA20). At higher magnifications small and,
33
therefore, barely detectable HfC can be seen. Thus, it is suggested that this deviation
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small and partially dissolved HfC- particles.
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Furthermore, the volume fractions of HfO2 particles and Mo2C layers at the grain
4
boundaries were determined at four OLM images for each condition. An example for
5
the color etched microstructures is shown in Figs. 4a, 4c and 4e for SA16, SA20 and
6
SA23, respectively. In these images Mo2C at the grain boundaries is shown in white
7
color, whereas HfO2 particles show a grey contrast [25]. Due to the used
8
magnification HfC particles cannot be observed. The volume fraction of Mo2C and
9
HfO2 particles were analyzed separately for all the specimens as shown in Figs. 4b,
10
4d and 4f. In these images Mo2C is shown red. For SA16 a mean volume fraction of
11
0.92 ± 0.19 vol.% Mo2C is determined and for HfO2 0.50 ± 0.12 vol.% was obtained.
12
In SA20 for Mo2C a mean volume fraction of 1.16 ± 0.18 vol.% was detected and
13
0.38 ± 0.06 vol.% in case of HfO2. In SA23 for Mo2C a mean value of
14
1.75 ± 0.16 vol.% was revealed and 0.53 ± 0.10 vol.% for HfO2. Again these values
15
are in good agreement with the estimated volume fractions, which are based on the
16
overall chemical composition and the APT measurements, and can be seen in Table
17
3.
18
Based on these experimental results it can be concluded that the solvus temperature
19
of HfC is somewhere between 2100°C and 2300°C. Furt hermore, the results of SA23
20
affirm that the cooling rate of ~425 K/min was sufficient to suppress the volume
21
diffusion of Hf [34], but not that of C [35], because no C was measured in solid
22
solution by APT as it is reported in Ref. [30]. C containing Mo alloys strongly tend to
23
decarburization at high temperatures and long annealing times [4,8], making a setup
24
for full equilibrium experiments difficult. On one hand, sufficiently large sample sizes
25
are needed to obtain an unaltered composition in the core of the sample. On the
26
other hand, quenching of such sample sizes for full equilibrium determination
27
requires a special furnace design equipped with a dropping mechanism able to
28
anneal the samples for long times at very high temperatures in an inert atmosphere.
29
However, for the investigation conducted in this study such a special furnace was not
30
available.
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Thermodynamic considerations based on experimental key data: M2C
2
APT studies of (Mo,Hf)2C in an MHC alloy exhibiting 0.65 at.% Hf and 0.85 at.% C
3
revealed only a small content of ~1 at.% of Hf in the hexagonal (hcp) carbide
4
structure [21]. In other words, the stabilization of the M2C-phase by Hf is only weak.
5
Considering these experimental results in the modeling at full extent, the calculated
6
phase fraction of M2C in MHC is too low at elevated temperatures, i.e., below the
7
experimental detection limit. This discrepancy cannot be solved by any adjustment of
8
ternary model parameters. Indeed, it can be argued that Hf solubilities in Mo-bcc or
9
C-Va interactions in this phase would also contribute indirectly to the stability of M2C
10
in MHC. Of course this ability was tested, and absurd high interaction parameters of
11
several millions of Joules would be required. Another question may be the effect of O
12
impurities in M2C on its stability. However, no solubility of O has been found in this
13
carbide [21]. Actually, a search in the forming binary Mo-C system needs to be done
14
in order to obtain a solution of this problem [9]. As mentioned above, the system
15
description is complete and predicted phase boundaries fit the experimental data
16
well. This is also true for the reproduction of formation enthalpy of pure Mo2C hcp
17
phase. No proper argument for adjusting the CALPHAD-assessed enthalpy of Mo2C
18
exists. On the other hand, entropy and heat capacity (Cp) data of Mo2C, which are
19
also critical for a more reliable thermodynamic description of the high-temperature
20
stability of the phase, are lacking. Taking this into account, the Gibbs energy
21
description of Mo2C was adjusted to produce a slightly higher Cp of Mo2C than
22
calculated using the thermodynamic assessment of Andersson [9]. Additionally, the
23
entropy of formation of Mo2C was also re-assessed slightly. The according re-
24
optimized parameter for the molar Gibbs energy of hcp compound (Mo)(C)0.5 reads
25
G(hcp)=-24150-3.6125·T-0.3·T·ln(T)-163000·T-1
26
+G(Mo-bcc)+0.5·G(graphite),
27
compared to Andersson´s original parameter for hcp (Mo)2(C),
28
G(hcp)=2·(-24150)+2· (-3.625)·T+2·(-163000·T-1)+2·G(Mo-bcc)+G(graphite).
29
The change of B·T results in a molar entropy difference of 0.0083 J/molK. Adding
30
C·T(ln)T to the Gibbs energy polynomial influences excess Cp of the phase. The
31
comparison of the re-calculated Cp of this work with Andersson´s assessment [9] is
32
shown in Fig. 5 using MatCalc [36] thermodynamic and kinetic phase transformation
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(Eq. 3)
13
(Eq. 4)
ACCEPTED MANUSCRIPT software, version 6.00. Matcalc contains full CALPHAD functionality and can be
2
conveniently used for simple thermodynamic property and phase fractions vs.
3
temperature plots. Calculated phase diagrams of this study are shown using Thermo-
4
Calc [37], version 2015b.
5
The C solubility in pure Mo-bcc requires some re-consideration because Mo alloys
6
tend to decarburization as already mentioned above [3,8]. Especially long term
7
annealing treatments with small sample sizes at high temperatures could cause a
8
tremendous problem in the homogeneity of the composition. Therefore, most
9
literature references [3,4,8] used C rods and methane enriched argon gas during
10
annealing to avoid this effect. It is likely that also previous experiments suffered by
11
this phenomenon, assumingly leading to an over-estimation of the single Mo-bcc
12
phase region in the construction of the experimental binary Mo-C phase diagram. We
13
believe that the theoretic (i.e. true equilibrium) Mo-bcc/Mo2C and Mo-bcc/liquid phase
14
boundary will lie to the left of Andersson´s suggestions [9], as shown in the re-
15
evaluation in Fig. 6. The suggested deviation is realized by adding excess interaction
16
energy parameters, 0L and 1L to the original bcc description in the Mo-C system,
17
obeying the formulation for non-ideal mixing of equation 2. A combination of 0th and
18
1st order interaction instead of a single parameter was chosen in order to keep the
19
effect
20
Mo2C/Mo2C+bcc small.
21
Only by combining these slight refinements, the temperature-dependent parameters
22
of Mo2C, i.e. entropic and heat capacity contributions to the Gibbs energy with a
23
smaller C solubility in Mo-bcc, the experimental high-temperature phase stability of
24
M2C in MHC is reproduced satisfactorily. In the thermodynamic parameter
25
optimization of M2C the fact of higher experimental “near equilibrium” Mo2C-phase
26
fractions than theoretic full equilibrium fractions at elevated temperatures is
27
considered. A lower weighting of experimental Mo2C-stabilities relative to measured
28
fractions of HfC is used.
29
4.3
30
The experimentally observed stability of Mo-containing MC-phase clearly showed
31
smaller deviations
32
parameter optimization of temperature-dependent 0L to 3L interactions according to
33
Eq. 2, with 0L=1L=2L=-50000+17T, led to satisfactorily reproduction of experimental
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experimental
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boundaries
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and
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Thermodynamic considerations based on experimental key data: MC
among different
researchers
14
[12–15,29]. Straight-forward
ACCEPTED MANUSCRIPT solubility of Mo in the carbide [12,13] and associated phase boundary between Mo-
2
bcc and MC in the isopleth section Mo-HfC [15] as shown in Fig. 7a. For comparison
3
purpose experimental data points from Zakharov and Savitskiy were added to Fig. 7a
4
[15]. The figure reveals a narrow phase field of stable M2C-phase, which the
5
experimental plot [15] does not contain. Clearly, the optimized M2C-description
6
cannot avoid this theoretic feature. In addition, the calculated HfC-solubility in Mo-bcc
7
is smaller than the experiment proposes. Once again, these differences between
8
experiment and theory can be explained by some C loss during isothermal heat
9
treatments: The experimental plot will expectedly deviate from the exact Mo-HfC line
10
and in accordance we may account for the C-loss, replacing the condition x(Hf)-
11
x(C)=0 by x(Hf)-x(C)=0.001. The “C-loss simulation” plot is presented in Fig. 7b. In
12
Fig. 7b the effective decrease of the 3-phase equilibrium field Mo-bcc+MC+M2C in
13
Mo-HfC1-δ is seen.
14
The studies of Zakharov [15] comprise an additional group of ternary experimental
15
phase diagram data, which need to be taken into account in the parameter
16
optimization of Mo-bcc and carbide phases. Ternary parameters, summarized in
17
Table 4, have been optimized together to obtain the least squares of error between
18
calculated and selected experimental phase boundaries [8-11] and newly measured
19
relative phase fractions and phase compositions. Unary parameters G(HF-HCP),
20
G(MO-BCC) and G(C-GRAPHITE) were taken from Dinsdale [38].The reproduction
21
of phase boundaries in the Mo-rich corner of the Mo-Hf-C system is presented in Fig.
22
8. Taking our isothermal experimental results into account, the experimental MC
23
solvus temperature of SA samples lies between 2100°C and 2300°C. Calculating for
24
MHC composition and considering complete binding of O to HfO2 and negligible O
25
solubility in Mo-bcc and M2C, the calculated MC solvus temperature is too low (Table
26
5). Lang et al. [21] found a surprisingly high amount of O of ~4.4 at.% dissolved in
27
MC. This stabilizes the phase towards a higher dissolution temperature. In order to
28
determine this effect, the structural formula for O-containing MC is defined.
29
Additionally, model parameters of metastable Hf-O compound and interaction
30
between O and Va on interstitial sites of (Hf,Mo)(O,Va) fcc-phase are optimized with
31
experimentally determined O content in MC, as well as first-principles enthalpies of
32
formation. The comparison of CALPHAD-assessed enthalpies of O containing MC
33
with enthalpies at 0 K [21] is shown in Fig. 9. The first-principles calculations are
34
based on 64 atoms in HfC, i.e. 32 Hf atoms and 32 C atoms without Mo and O. For
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ACCEPTED MANUSCRIPT the substitution of Hf by Mo and C by O different compositions of the MC carbide are
2
simulated. Mo increases the energy of formation and O decreases it towards higher
3
negative values [21]. Furthermore, model parameters of Mo-bcc containing O, partly
4
replacing Va or C on the interstitial sites, are optimized by the experiments of
5
Srivastava and Seigle [39]. Therefore, the Gibbs energy of metastable Mo:O end-
6
member and interaction of O and Va on interstitial sites are adjusted.
7
With these refinements and including oxide Gibbs energies [31] in the extended Mo-
8
Hf-C-O database, the MC-stability is expanded towards higher temperature. This can
9
be seen in the calculated solvi of O containing MC (Table 5) and the equilibrium
10
phase fractions versus temperature plots in Fig. 10a for SA16 (high C, high O) and
11
SA20 (low C, low O), indicating that O impurities play a significant role for process
12
and alloying optimization of MHC. The modeled O solubilities in carbide phases and
13
Mo-bcc are shown in Fig. 10b. The closing figure, Fig. 11, indicates the strong
14
potential of the established thermodynamic database for systematic adjustment of
15
alloying in MHC. Here, one can read out for a specific alloying of Hf, how a change of
16
the Hf/C ratio will affect the competition of M2C versus MC stabilization as a function
17
of temperature.
18
4.4
19
Calculated phase fractions as shown in Table 6 reproduce experimental temperature-
20
dependent phase stabilities rather well. However, equilibrium Mo2C is expected to be
21
almost dissolved at 2300°C, whereas almost 2 vol.% were found experimentally in
22
SA23 as shown in Table 3. This difference between equilibrium calculation and
23
experimental measurement supports incomplete quenching of C in the experiment.
24
Table 7 represents calculated equilibrium phase compositions of MHC at the three
25
experimental temperatures. Comparison with Table 2 reveals a consistent amount of
26
Hf dissolved in Mo-bcc. C and O contents in Mo-bcc increase as a function of
27
temperature, whereas dissolved Mo in MC shows the opposite behavior to our
28
modeling. The calculated Mo content in MC at 1600°C is considerably larger than the
29
measured value [20]. On the other hand, the theoretic high-temperature solubility is
30
close to the experimental data. The increasing deviation of calculated versus
31
measured solubilities towards lower temperatures may reflect non-equilibrium
32
conditions in the experiment due to the slow diffusion of Mo. In contrast to MC only
33
slight O solubility in M2C is suggested. Figure 10 reveals the strong influence of the C
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CALPHAD-based calculated phase stabilities in MHC
16
ACCEPTED MANUSCRIPT content in MHC on the dissolution temperature of MC. SA16 contains the highest C
2
content of the studied samples, resulting in a 51°C lower solvus temperature than
3
SA20. The O content of SA16 is also higher than in SA20, but does not reverse the C
4
effect of the decrease of MC phase fraction relative to M2C.
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ACCEPTED MANUSCRIPT
5. Conclusions
2
A technologically applicable CALPHAD- database for Mo-Hf-C alloys lying in the Mo-
3
rich corner of the ternary system has been established. These alloys tend to
4
considerable changes of relative phase stabilities in case of only slight variations of
5
composition, for instance by impurities of O. Presented experimental results on HfC
6
and Mo2C phase stabilities in MHC complement existing, and partly contradictory,
7
phase diagram data and contribute to the consistency of the presented
8
thermodynamic modeling and optimization of the Mo-Hf-C system with O addition.
9
The new database is feasible to reproduce the delicate relative stabilities of M2C /
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MC in MHC and to optimize heat treatments for improved alloy design.
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References
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[1]
N.N. Morgunova, Effect of titanium, zirconium, and hafnium on the properties of molybdenum alloyed with carbon, Met. Sci. Heat Treat. 8 (1966) 1001–1005. doi:10.1007/BF00653001.
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system Hf-Mo-C at 1700°C, Sov. Powder Metall. Met. Ceram. 16 (1977) 772– 777. doi:10.1007/BF00791473. [14] V.N. Eremenko, T.Y. Velikanova, S. V. Shabanova, Investigation of alloys of the ternary hafnium-molybdenum-carbon system, in: Vysokotemp. Karbidy, Naukova Dumka, Kiew, 1975: pp. 90–96.
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[22] C.K. Gupta, Extractive Metallurgy of Molybdenum, CRC Press, Boca Raton, 1992. https://books.google.com/books?id=6V7oPjy_0IwC&pgis=1 (accessed January 18, 2016).
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[23] G. Leichtfried, Refractory metals, in: P. Beiss, R. Ruthardt, H. Warlimont (Eds.), Powder Metall. Data. Refract. Hard Intermet. Mater., Springer-Verlag, Berlin/Heidelberg, 2002: pp. 4–27. doi:10.1007/b83029.
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[24] D. Lang, J. Schatte, H. Clemens, S. Primig, Elektrolytisches Polieren vs. Vibrationspolieren: Entwicklung einer Präparationsmethode zur EBSD- Analyse der Mo- Basislegierung MHC, in: S. Mayer, M. Panzenböck, H. Clemens (Eds.), 14. Int. Metallogr., Leoben, 2014: pp. 44–46.
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[26] R. Hasson, Metallography of molybdenum in color, Microscope. 16 (1968) 329–334.
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[27] M.K. Miller, A. Cerezo, M.G. Hetherington, G.D.W. Smith, Appendix A: specimen preparation, in: Atom Probe F. Ion Microsc., 2nd ed., Oxford University Press Inc., New York, 2006: pp. 476–483.
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[29] L. Rokhlin, N. Kolchugina, T. Dobatkina, E. Semenova, Carbon – Hafnium – Molybdenum, in: G. Effenberg, S. Ilyenko (Eds.), Refract. Met. Syst. Phase Diagrams, Crystallogr. Thermodyn. Data, Springer Berlin Heidelberg, Berlin, Heidelberg, 2010: pp. 409–428. doi:10.1007/978-3-642-02700-0_27.
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[32] C. Pöhl, D. Lang, J. Schatte, H. Leitner, Strengthening mechanisms of the molybdenum-base alloy MHC, in: L.S. Sigl, H. Kestler, J. Wagner (Eds.), 18th Plansee Semin. - Int. Conf. Refract. Hard Mater., Reutte, Austria, 2013: pp. 61–70.
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[34] Y. Bhatt, L. Kumar, R. Patil, G. Kale, S. Garg, Diffusion studies in Hf–Mo, Zr– Mo, Cr–Nb, Cr–Ta and Th–Re systems above 1900 K, J. Alloys Compd. 302 (2000) 177–186. doi:10.1016/S0925-8388(00)00678-2.
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[35] P.S. Rudman, The solubility limit and diffusivity of carbon in molybdenum, Trans. Metall. Soc. AIME. 239 (1967) 1949–1954.
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[36] E. Kozeschnik, B. Buchmayr, MatCalc - A simulation tool for multicomponent thermodynamics, diffusion and phase transformations, in: H. Cerjak, H.K.D.H. Bhaddeshia (Eds.), Math. Model. Weld Phenom. 5, IOM Communications Ltd, London, 2001: pp. 349–361.
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4 5
[38] A.T. Dinsdale, SGTE data for pure elements, Calphad. 15 (1991) 317–425. doi:10.1016/0364-5916(91)90030-N.
6 7 8
[39] S.C. Srivastava, L.L. Seigle, Solubility and thermodynamic properties of oxygen in solid molybdenum, Metall. Trans. 5 (1974) 49–52. doi:10.1007/BF02642925.
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ACCEPTED MANUSCRIPT 1
Figure captions
2
Fig. 1: Experimental phase diagrams of the Mo-Hf-C system at a) 2273 K and b)
3
1673 K, redrawn from [12,14]. Dotted lines represent modeled phase boundaries
4
derived in this work.
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Fig. 2: SEM images of electrolytically polished MHC microstructures in two different
7
magnifications of the three different annealed conditions in BSE contrast. (a) and (b)
8
1600°C for 20h (SA16). (c) and (d) 2000°C for 5h (S A20).(e) and (f) 2300°C or 5 h
9
(SA23).
SC
6
10
Fig. 3: Investigation of large HfC after annealing for 20 h at 1600°C: (a) length
12
distribution; (b) thickness distribution; (c) volume distribution calculated on base of (a)
13
and (b). (d) SEM image of the electrolytically polished MHC microstructure in BSE
14
contrast. Counted HfC are shown red. The particle distribution is based on a log-
15
normal function.
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Fig. 4: OLM images of color etched MHC microstructures after annealing for (a) 20 h
18
at 1600°C, (c) 5h at 2000°C and (e) 5 h at 2300°C [ 25,26]. Mo2C particles are shown
19
in white and HfO2 in grey. (b), (d) and (f) Separated phases. Mo2C is shown red, HfO2
20
in grey.
21
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17
Fig. 5: Evaluated heat capacity Cp of the Mo2C-phase, compared with a previous
23
description (dashed curve) [9].
24
AC C
22
25
Fig. 6: Evaluated C-solubilities in Mo-bcc solid solution, compared with previous
26
assessment (dashed line) [9].
27
23
ACCEPTED MANUSCRIPT 1 Fig. 7: (a) Isopleth section Mo-HfC. For comparison purpose experimental data points
3
from Zakharov and Savitskiy [15] were added. (b) Mo-HfC1-δ section with simulation
4
of constant loss of C-fraction δ, realized by the condition x(Hf)-x(C)≠0 (see text). The
5
hdp phase region is significantly decreasing. The phase diagram starts at 0.186
6
mass percent of HfC1-δ (0.1 at.% Hf) where x(C) equals 0.
7
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Fig. 8: Comparison of previous experimental results in the Mo-rich corner of the Mo-
9
Hf-C system [15] with calculations using our CALPHAD optimization at 2373 K and
SC
8
1523 K. Bold lines represent phase boundaries, thin straight tielines mark two phases
11
equilibria.
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Fig. 9: Evaluated enthalpies of formation of MC containing 0, 1, 2, 3 Mo atoms and
14
each 0, 1, 2 or 3 Oxygen atoms by CALPHAD and first-principles analysis [21]. The
15
calculations are based on 64 atoms in the HfC, i.e. 32 Hf atoms and 32 C atoms for
16
HfC without Mo and O. By substitution of Hf by Mo and C by O different compositions
17
of the MC carbide are simulated. Mo increases the energy of formation and O
18
decreases it towards higher negative values [21].
19
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13
Fig. 10: (a) Equilibrium phase fractions as function of temperature in MHC; (b) O solubility in
21
MC, M2C and Mo-bcc in SA16 and SA20. Note the difference of O solubilities is too small
22
between both conditions to be discernable.
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Fig. 11: Predicted phase stabilities as function of C and Hf contents in MHC. At
25
x(Hf)/x(C)=1 and x(Hf)/x(C)=0.5 the single phase Mo ss (ss stands for solid solution)
26
expands towards higher C-contents. At x(Hf)/x(C)=0.5 the M2C-phase is stabilized
27
towards higher C contents, whereas at x(Hf)/x(C)=1.5 this phase does not form. At
28
x(Hf)/x(C)=1 the Mo2C is only stabilized in a narrow C composition range.
24
ACCEPTED MANUSCRIPT 1
TABLES
2 3 4 5 6
Table 1 Overall chemical composition in at.% of the investigated MHC samples after sintering and annealing for 20 h at 1600°C and for 5 h at 200 0°C and 2300°C in hydrogen atmosphere (RSD = relative standard deviation). SA20
SA23
Mo
balance
balance
balance
Testing procedure, accuracy at 1 g testing material ICP-OS, ± 1 ppm or <5% RSD
Hf
0.65
0.65
0.65
ICP-OS, ± 1 ppm or <5% RSD
C
0.85
0.74
0.77
CA, ± 2-3 ppm or <5% RSD
O
0.34
0.28
0.36
CGHE, ± 2-3 ppm or <5% RSD
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SA16
7
Table 2 On the basis of the overall chemical composition and APT measurements estimated Hf and C distribution in the phases of the MHC samples after annealing for 20 h at 1600°C and for 5 h at 2000°C and 2300°C (at.%) in hydrogen atmosphere.
Hf in solid solution
Hf in HfC C in HfC C in Mo2C
SA23
0.03
0.24
0.47
0.17
0.14
0.18
0.45
0.27
0.00
0.45
0.27
0.00
0.40
0.47
0.77
Table 3 On the basis of the overall chemical composition and APT measurements estimated distribution of phases in MHC samples compared to the measured distribution after annealing for 20 h at 1600°C and for 5 h at 2000°C and 2300°C in hydrogen atmosphere.
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13 14 15 16 17
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Hf in HfO2
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8 9 10 11
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Phase
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estimated
measured
estimated
measured
estimated
measured
mol.% vol.%
vol.%
mol.% vol.%
vol.%
mol.% vol.%
vol.%
HfC
0.90
0.74
Mo2C
1.20
HfO2
0.51
0.71
0.54
0.45
0.13
0.00
0.00
0.94 0.92±0.19
1.41
1.11
1.16±0.18
2.31
1.81 1.75±0.16
0.39 0.50±0.12
0.42
0.32
0.38±0.06
0.54
0.41 0.53±0.10
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PHASE FCC_A1, Crystal structure: face-centered cubic, space group Fm-3m Sublattice description: (HF,MO)1(C,VA)1 End-member compound energies: G(FCC_A1,MO:C) -7500-8.5*T-0.35*T*LN(T) -750000*T**(-1)+G(MO-BCC)+G(C-GRAPHITE) Interaction parameters: 0L(FCC_A1,HF,MO:C) -50000+17*T 1L(FCC_A1,HF,MO:C) -50000+17*T 2L(FCC_A1,HF,MO:C) -50000+17*T
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PHASE BCC_A2 Crystal structure: body-centered cubic, space group Im-3m Sublattice description: (HF,MO)1(C,VA)3 End-member compound energies: G(BCC_A2,MO:C;0) +300000-65*T-0.1*T*LN(T) +G(MO-BCC)+3*G(C-GRAPHITE) Interaction parameters: 0L(BCC_A2,MO:C,VA) -25000 1L(BCC_A2,MO:C,VA) -10000 0L(BCC_A2,HF,MO:C) +200000 1L(BCC_A2,HF,MO:C) -200000 2L(BCC_A2,HF,MO:C) +200000
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PHASE HCP_A3 Crystal structure: hexagonally close-packed, space group P63/mmc Sublattice description: (HF,MO)1(C,VA)0.5 End-member compound energies: G(HCP_A3,MO:C) -24150-3.6125*T-0.3*T*LN(T) -163000*T**(-1)+G(MO-BCC)+0.5*G(C-GRAPHITE) Interaction parameters: 0L(HCP_A3,HF,MO:C;0) +6200-10*T 1L(HCP_A3,HF,MO:C;1) -6200+10*T 2L(HCP_A3,HF,MO:C;2) +6200-10*T 0L(HCP_A3,HF,MO:C,VA;0) -5000+50*T
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SA16 SA20 SA23
(Hf,Mo)1(C,O,Va)1 2133 2184 2133.5
Table 6 With CALPHAD calculated equilibrium phase contents in MHC samples of the studied compositions from Table 1 annealed at 1600°C, 2000° C and 2300°C based on the optimized database. The term ss stands for solid solution. Compare with experimental results, Table 3.
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bcc ss MC M2C HfO2
vol.% (mol.%) SA16 SA20 SA23 97.68 (97.46) 98.47 (98.44) 99.23 (99.45) 0.72 (0.96) 0.31 (0.38) 0.88 (1.07) 0.65 (0.77) 0.007 (0.0083) 0.38 (0.51) 0.3 (0.40) 0.4 (0.54)
M AN U
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Table 7 With CALPHAD calculated equilibrium phase compositions in MHC samples of the studied composition from Table 1 based on the optimized database. The term ss stands for solid solution.
TE D
10 11 12 13
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at% Hf at.% Mo at.% C at.% O SA16 SA20 SA23 SA16 SA20 SA23 SA16 SA20 SA23 SA16 SA20 SA23
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bcc 0.08 0.32 0.47 99.8 99.32 98.76 0.085 0.36 0.77 5E-08 4E-06 5E-05 ss MC 41.07 45.92 11.7 4.93 47.18 45.54 0.44 3.6 M2C 0.72 2.81 3.72 70.05 69.89 69.27 29.23 27.3 26.85 3E-05 4E-03 0.17
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ACCEPTED MANUSCRIPT Highlights: Evaluation of the Mo-rich corner of the ternary Mo-Hf-C system.
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Reoptimization of the thermodynamics of Mo2C and HfC.
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O impurities have a significant influence on the phase stability of HfC
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