High Temperatures-High Pressures, Vol. 38, pp. 63–78
Reprints available directly from the publisher
Photocopying permitted by license only
©2009 Old City Publishing, Inc.
Published by license under the OCP Science imprint,
a member of the Old City Publishing Group
DSC investigation of binary iron-nickel alloys
Andrzej J. Panas1,∗ and Dagmara Panas2
1 Institute
of Aviation Technology, Military University of Technology,
Kaliskiego 2, 00-908 Warsaw, Poland
2 Institute of Experimental Physics, Warsaw University, Hoża 69,
00-861 Warsaw, Poland
Received: October 13, 2008. Accepted: December 1, 2008.
Differential scanning calorimetry (DSC) measurements on a range of
binary iron-nickel (Fe-Ni) alloys, including invar, are reported. The study
was conducted to verify and supplement existing knowledge of thermophysical properties of Fe-Ni alloys with a focus on magnetic phase
transition. There were 11 investigated samples altogether, spanning nickel
contents from 10 to 72 wt%. The measurements were performed within a
range from 253 K to 870 K applying power compensation DSC apparatus.
A specially developed thermal program with linear steps interrupted by
isotherms was used enabling investigations on both heating and cooling.
Specific heat at constant pressure as a function of temperature was obtained
using the three-curve method. The collected DSC data were processed
using B-spline approximation procedures. The obtained thermal characteristics are reported altogether with the identified characteristic temperatures
of the observed phase transitions. Results of supplementary density measurements are provided as well. The study revealed inconsistency in the
literature data concerning Curie temperature.
Keywords: Differential scanning calorimetry, specific heat, phase transitions, binary
alloys, invar, B-spline approximation.
1 INTRODUCTION
Binary alloys composed of iron and nickel, including invar type compositions, provide a widely used material in industry and technology. Investigating
their properties is an important part of engineering process as it enables us to
understand and predict their basic behavior in different circumstances, all the
∗ Corresponding author: E-mail: [email protected]
63
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64
A. J. Panas and D. Panas
more for the fact that there is no consistent theoretical model for explaining
invar-type anomalies [1].
For this study it was decided to compare specific heat capacity of 11 types
of seasoned alloys, varying in nickel content. A subset of this group consisted
of invar alloys. Systematic investigations over a certain composition range are
of exceptional value, especially when performed with improved techniques
and high thermal resolution (comp. ex. [2]), as such an analysis can provide
insight on how the composition influences the behavior of a given material.
Additionally, samples that have been stored for over 15 years, which is the
case here, are rarely under investigation.
It is a commonly accepted fact that DSC techniques allow for high thermal
resolution measurements. However, the experiments are rarely performed on
cooling over a wide temperature interval [3] and it creates severe limitations
when materials with temperature dichotomy between direct and inverse phase
transition are studied. This is the case of many binary alloys, including ironnickel ones [4]. Additionally, collecting specific heat data in a single wide
temperature range scan often results in curve distortion.
Consequently, a modified version of DSC procedure was employed. Continuous data collecting over the whole temperature range [5] was substituted
with step-executed scans over subintervals and the procedure was performed
on both heating and cooling [6].
An important part of the study is useful description of collected information. Well-approximated data are both more compact than raw results and
substantially more reliable than averaged table values. In the present case
we decided to post-process the data with the use of B-splines [6,7]. Splines
exhibit unique features that predestine them for implementation in thermophysical data processing as they enable to model not only continuous courses
but also discontinuities of any order [8].
In this paper complete obtained results are presented graphically and a table
with approximation results is provided for future reference.
2 MATERIALS AND METHODS
2.1 Specimens
The set of samples consisted of 11 binary iron-nickel alloys most of which came
from the same manufacturer. These materials had been studied previously for
the thermal expansivity [2]. The investigated compositions are provided in
Table 1 (for a more detailed structural specification see [2]). The components
had been mixed and afterwards melted in an induction furnace, next forged
at a temperature of about 1270 K, and finally rolled and faced (except for
samples Fe58Ni42 and Fe63Ni37). All then had been subjected to annealing.
The material pieces left after cutting out dilatometric samples had been stored
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65
DSC investigation of binary iron-nickel alloys
Sample
name
Fe90Ni10
Fe80Ni20
Fe70Ni30
Fe66Ni34
Fe64Ni36
Fe63Ni37
Fe60Ni40
Fe58Ni42
Fe50Ni50
Fe40Ni60
Fe28Ni72
Structure/vol%
after annealing
Nickel
Nickel
Density ± std.
3
content/wt% content/at% Mass [mg] dev. [Mg/m ] α (bcc) γ (fcc)
10
19.83
29.2
33.7
35.45
37
39.12
41.18
50
60
71.5
8.94
17.93
26.7
30.98
32.66
34.15
36.2
38.21
46.9
56.98
68.9
165.685
149.85
155.165
165.395
194.14
139.305
163.63
135.265
156.440
162.630
183.335
8.44 ± 0.21
8.38 ± 0.14
8.23 ± 0.12
8.27 ± 0.32
8.03 ± 0.13
8.03 ± 0.14
8.12 ± 0.07
8.1 ± 0.12
8.24 ± 0.03
7.72 ± 0.13
7.81 ± 0.15
100
70
15
0
0
–
0
0
–
0
0
0
30
85
100
100
–
100
100
–
100
100
TABLE 1
Specification of investigated Fe-Ni specimens.
at room temperature and normal pressure since 1988. In 2006 DSC specimens
were machined and investigated.
All DSC samples were disk shaped, of approximately 5 mm diameter and
1 mm thickness. Before and after measurements the specimens were weighted
with a MettlerToledo AT261DR microbalance. The same balance equipped
with a density measurement kit was employed for density determination. In
these measurements distilled water was used as the reference liquid. The
results of gravimetric investigations, with density results corrected for the
ambient temperature changes, are listed in Table 1. For microcalorimetric
studies the samples were encapsulated in aluminium sample pans (of mass
around 26.5 mg), provided by the DSC equipment manufacturer.
2.2 Experimental procedure
Microcalorimetric investigations were carried out with the use of power compensation [3] Perkin-Elmer Pyris 1 DSC equipped with Intracooler 1 system.
The core idea of the scanning operation is to change the temperature of a sample linearly over time while monitoring heat influx in relation to the reference
material. Pressure in the measuring chamber is kept constant. Knowing: the
heat capacity of the reference material cref , the mass ratio, the heat flux consumption of the reference Href and the sample Hsample , we are able to tell the
specific heat capacity of tested material applying the formula [5]
csample (T ) = cref (T ) ·
mref
Hsample (T )
·
msample
Href (T )
(1)
where T stands for the temperature. In an experiment, however, it is impossible to achieve continuous readings and data collecting must be digitized.
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66
A. J. Panas and D. Panas
Consequently, obtained specific heat is just some average approximation of
actual value, and its accuracy is influenced by the temperature interval and
heating speed.
When performing single scan specific heat DSC investigations over a wide
temperature range the problem of cp (T ) curve distortion usually arises [9].
To address it a special procedure can be applied of scanning in consecutive
steps [6]. After each step some time is left for the sample to reach equilibrium
in isothermal operation mode of the instrument. Such a subinterval-executed
procedure is repeated on heating or cooling. This way the investigated specific
heat capacity can be asserted more reliably than in a continuous mode.
As was shown in [6], after proper calibration of DSC apparatus the literature
value [3,6] of 2% of the overall accuracy of measurements can be reached,
both on heating and cooling. The results of test measurements done on a Cu
specimen comply within 0.9% with the appropriate literature data [10] up to
873 K and within 1.2% up to 930 K [6].
2.3 Data acquisition and pre-processing
The instrument was calibrated with indium and zinc and the process was optimized for heating/cooling rates of 10 K/min. The extrapolation of calibration
characteristics below 429.55 K (In) and above 692.65 K (Zn) was verified with
additional test measurements performed on a Cu specimen. The heat capacity results comply with the data provided by White and Minges [10] within
1.1%. The thermal program was composed of two multiple step scan cycles
followed by a single scan cycle (see Figure 1). The measurements were performed within a range from 253 to 873 K. Sampling frequency was adjusted
to 1 Hz. A dynamic dehydrated N2 atmosphere with a flow rate of 20 mL per
minute was employed.
Specific heat results were obtained using a ratio method, also referred to as
‘three-curve method’, described in the section above [3]. The baseline run was
performed on empty instrument cells and the reference run with a sapphire
FIGURE 1
Illustration of the applied heating-cooling cycling program of 10 K/min. DSC measurements.
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DSC investigation of binary iron-nickel alloys
67
60.33 mg specimen, put in a sample cell. In both cases the basic thermal program was the same as in the main measurements. The specific heat data were
then prepared for presentation and further analysis by truncating every single
scan results by 43 starting points, as the first moments of heating/cooling after
isothermal period do not render reliable information. Next, both the raw heat
flux and the specific heat data were thoroughly examined in a search for any
characteristic points to provide starting data for the following approximation.
2.4 Approximation
The approximation procedure was conducted with the use of automated data
analysis tool, the paradigm of which was the B-spline analysis. B-splines [8]
are recurrently defined functions that can be correspondingly represented as
piecewise polynomials. As they form a functional basis, the signal can be
decomposed and approximated by a set of such functions.
The huge advantage of splines over i.e. simple polynomials is that they can
well model discontinuities. Approximation procedure involves defining knot
points, thus separating the signals into subintervals. Each subinterval has its
own set of corresponding polynomials assigned, so within this interval the
approximate of a signal and its derivatives are continuous. However, on the
knot points the derivatives do not need to be continuous.
The specific heat data were numerically processed applying similar procedures as described in [6] and [7]. B-splines employed in this study were of 4th
order. Knot points were selected so as to comply with the physical interpretation of the data, i.e. discontinuities within 1st or 2nd derivative were allowed
only in apparent transition points.
The data from heating and cooling of the second cycle were pooled together
and served as a basis for approximation (barring specimen Fe80Ni20, for
which heating and cooling needed to be treated separately). Second cycle was
chosen because the corresponding results appeared to be free from typical
DSC first run “contamination”.
3 RESULTS AND DISCUSSION
2nd cycle DSC specific heat results are presented in figures from 2 to 13,
altogether with the corresponding spline approximates. Because most of the
diagrams (the exception are Figures 3 and 4) show overlapped heating and
cooling experimental data it should be explained that characteristic distortions
at about 490 K, 575 K and between 700 K and 760 K appeared only on cooling.
They were identified as to be of instrumental character and were ignored during
accommodation of spline basis.
The numerical data are listed in Tables from 2 to 5. The details concerning
B-spline representations are not presented, as the appropriate information can
be obtained from the smoothed data provided in tables.
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68
A. J. Panas and D. Panas
FIGURE 2
Comparison between the measured specific heat data (points) and the spline approximate (solid
line) for Fe90Ni10 specimen.
FIGURE 3
Comparison between the measured specific heat data on heating (points) and the appropriate
spline approximate (solid line) for Fe80Ni20 specimen.
FIGURE 4
Comparison between the measured specific heat data on cooling (points) and the appropriate
spline approximate (solid line) for Fe80Ni20 specimen.
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DSC investigation of binary iron-nickel alloys
69
FIGURE 5
Comparison between the measured specific heat data (points) and the spline approximate (solid
line) for Fe70Ni30 specimen.
FIGURE 6
Comparison between the measured specific heat data (points) and the spline approximate (solid
line) for Fe66Ni34 specimen.
FIGURE 7
Comparison between the measured specific heat data (points) and the spline approximate (solid
line) for Fe64Ni36 specimen.
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70
A. J. Panas and D. Panas
FIGURE 8
Comparison between the measured specific heat data (points) and the spline approximate (solid
line) for Fe63Ni37 specimen.
FIGURE 9
Comparison between the measured specific heat data (points) and the spline approximate (solid
line) for Fe60Ni40 specimen.
FIGURE 10
Comparison between the measured specific heat data (points) and the spline approximate (solid
line) for Fe70Ni30 specimen.
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DSC investigation of binary iron-nickel alloys
71
FIGURE 11
Comparison between the measured specific heat data (points) and the spline approximate (solid
line) for Fe50Ni50 specimen.
FIGURE 12
Comparison between the measured specific heat data (points) and the spline approximate (solid
line) for Fe40Ni60 specimen.
FIGURE 13
Comparison between the measured specific heat data (points) and the spline approximate (solid
line) for Fe28Ni72 specimen.
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72
A. J. Panas and D. Panas
Fe90Ni10
Fe80Ni20 (on cooling) Fe80Ni20 (on heating)
temp.
[K]
s.h.c.
[J/g/K]
temp.
[K]
s.h.c.
[J/g/K]
temp.
[K]
s.h.c.
[J/g/K]
258
278
298
318
338
358
378
398
418
438
458
478
498
518
538
558
578
598
618
638
658
678
698
718
738
758
778
798
818
838
858
868.5
0.4301
0.43943
0.44822
0.45653
0.46442
0.47196
0.47919
0.48618
0.49298
0.49965
0.50626
0.51285
0.51948
0.52622
0.53312
0.54023
0.54763
0.55536
0.56348
0.57205
0.58113
0.59078
0.60105
0.612
0.6237
0.63619
0.64954
0.66385
0.67935
0.6963
0.71495
0.72549
258
278
298
318
338
358
378
398
418
428
439
448
455
460.8
468
478
498
518
538
558
578
598
618
638
658
678
698
718
738
758
778
798
818
838
854.2
858
864
0.429041
0.440045
0.453962
0.488709
0.513299
0.524559
0.534409
0.554853
0.597898
0.631865
0.659182
0.635861
0.596415
0.5599
0.518473
0.500237
0.512611
0.520714
0.526291
0.531133
0.536129
0.54136
0.546876
0.552728
0.558967
0.565642
0.572805
0.580506
0.588796
0.597725
0.607343
0.617702
0.628852
0.640844
0.671921
0.705563
0.727665
258
278
298
318
338
358
378
398
418
438
458
478
498
518
538
558
578
598
618
638
658
678
698
718
738
758
778
798
818
838
858
864
866
867.7
868.6
0.432232
0.441223
0.449641
0.457551
0.465019
0.472111
0.478891
0.485425
0.491779
0.498018
0.504208
0.510414
0.516702
0.523136
0.529783
0.536708
0.543976
0.551654
0.559805
0.568497
0.577793
0.587761
0.598465
0.60997
0.622333
0.635047
0.64673
0.655927
0.661915
0.677767
0.729257
0.79592
0.850333
0.901899
0.943672
TABLE 2
Approximation results for specimens: Fe90Ni10, Fe80Ni20.
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73
DSC investigation of binary iron-nickel alloys
Fe70Ni30
Fe66Ni34
Fe64Ni36
temp.
[K]
s.h.c.
[J/g/K]
temp.
[K]
s.h.c.
[J/g/K]
temp.
[K]
s.h.c.
[J/g/K]
258
278
298
318
338
358
378
398
418
438
458
478
498
518
538
558
578
598
618
638
658
678
698
718
738
758
778
798
818
838
858
0.466502
0.475408
0.482829
0.488935
0.493894
0.497877
0.501051
0.503586
0.505652
0.507417
0.509051
0.510699
0.51239
0.514118
0.51588
0.517669
0.51948
0.521307
0.523145
0.52499
0.526834
0.528674
0.530504
0.532318
0.534111
0.535878
0.537613
0.539312
0.540968
0.542576
0.544131
258
278
298
318
338
358
378
398
418
438
447.1
458
478
498
518
538
558
578
598
618
638
658
678
698
718
738
758
778
798
818
838
858
0.460668
0.472706
0.481681
0.490334
0.498423
0.505705
0.511936
0.516875
0.520279
0.521911
0.522064
0.521858
0.52069
0.519015
0.517441
0.516501
0.516246
0.516533
0.51722
0.518162
0.51927
0.520524
0.521909
0.523411
0.525015
0.526705
0.528467
0.530287
0.532149
0.534038
0.53594
0.53784
258
278
298
318
338
358
378
398
418
438
458
470.3
478
498
518
538
558
578
598
618
638
658
678
698
718
738
758
778
798
818
838
858
0.458057
0.469544
0.479893
0.489239
0.497714
0.505453
0.51259
0.519258
0.525589
0.53128
0.535012
0.53571
0.53544
0.532819
0.528608
0.524291
0.521221
0.519609
0.519089
0.519288
0.519851
0.520627
0.521596
0.522741
0.524044
0.525489
0.527056
0.52873
0.530491
0.532324
0.53421
0.536132
TABLE 3
Approximation results for specimens: Fe70Ni30, Fe66Ni34, Fe64Ni36.
Commenting the choice of the 2nd cycle it should be mentioned that examining raw DSC data we did not observe any differences between results from
the first and second cycle showing effects of irreversible property change due
to first heating. Worth pointing is also the fact that results for all specimens
except Fe80Ni20 from heating and cooling overlapped each other.
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74
A. J. Panas and D. Panas
Fe63Ni37
Fe60Ni40
Fe58Ni42
temp.
[K]
s.h.c.
[J/g/K]
temp.
[K]
s.h.c.
[J/g/K]
temp.
[K]
s.h.c.
[J/g/K]
258
278
298
318
338
358
378
398
418
438
458
478
499.7
518
538
558
578
598
618
638
658
678
698
718
738
758
778
798
818
838
858
0.456614
0.467568
0.477764
0.487269
0.496151
0.504478
0.512317
0.519735
0.526802
0.53357
0.539788
0.544903
0.54844
0.540227
0.530638
0.526183
0.524482
0.523597
0.523149
0.523096
0.523391
0.523991
0.524851
0.525926
0.527173
0.528547
0.530002
0.531496
0.532982
0.534418
0.535757
258
278
298
318
338
358
378
398
418
438
458
478
498
518
538
559.1
578
598
618
638
658
678
698
718
738
758
778
798
818
838
858
0.450336
0.461174
0.471463
0.481236
0.490527
0.499368
0.507795
0.515839
0.523535
0.530915
0.538014
0.544864
0.551498
0.557951
0.56425
0.568199
0.564674
0.554838
0.542202
0.534256
0.53042
0.528845
0.528046
0.52774
0.527888
0.528454
0.529399
0.530686
0.532279
0.534138
0.536227
258
278
298
318
338
358
378
398
418
438
458
478
498
518
538
558
578
603.1
618
638
658
678
698
718
738
758
778
798
818
838
858
0.449731
0.460558
0.470867
0.480702
0.490109
0.49913
0.50781
0.516192
0.524322
0.532242
0.539997
0.547632
0.555189
0.562705
0.57006
0.577003
0.583277
0.589684
0.573342
0.556865
0.547019
0.541853
0.539414
0.538257
0.538045
0.538586
0.539692
0.541171
0.542834
0.544489
0.545948
TABLE 4
Approximation results for specimens: Fe63Ni37, Fe60Ni40, Fe58Ni42.
As can be seen in Figures 3 and 4, Fe80Ni20 behaved differently on heating
and cooling. It indicates that the position of transition point between α and
γ phase depends on the direction of temperature changes. This observation
confirms literature data [1]. The phenomenon is not observed in Fe90Ni10
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75
DSC investigation of binary iron-nickel alloys
Fe50Ni50
Fe40Ni60
Fe28Ni72
temp.
[K]
s.h.c.
[J/g/K]
temp.
[K]
s.h.c.
[J/g/K]
temp.
[K]
s.h.c.
[J/g/K]
258
278
298
318
338
358
378
398
418
438
458
478
498
518
538
558
578
598
618
638
658
678
698
718
738
757
768
778
798
818
838
858
0.432774
0.442476
0.451678
0.460432
0.468791
0.476805
0.484527
0.492009
0.499303
0.50646
0.513532
0.520572
0.527631
0.534762
0.542015
0.549443
0.557099
0.565033
0.573297
0.581944
0.591026
0.600594
0.6107
0.621396
0.632746
0.651031
0.621309
0.585941
0.567918
0.56442
0.563594
0.559332
258
278
298
318
338
358
378
398
418
438
458
478
498
518
538
558
578
598
618
638
658
678
698
718
738
758
778
798
818
838
848.5
858
0.426017
0.43453
0.442661
0.450445
0.457918
0.465117
0.472077
0.478835
0.485427
0.491888
0.498255
0.504563
0.510849
0.51715
0.523499
0.529935
0.536492
0.543208
0.550117
0.557257
0.564662
0.572369
0.580415
0.588834
0.597664
0.607416
0.622468
0.649071
0.693491
0.761991
0.808295
0.633757
258
278
298
318
338
358
378
398
418
438
458
478
498
518
538
558
578
598
618
638
658
678
698
718
738
758
778
798
818
838
858
868.6
0.415146
0.422887
0.430338
0.437523
0.444467
0.451192
0.457722
0.464083
0.470297
0.476389
0.482382
0.488301
0.494168
0.50001
0.505848
0.511707
0.517612
0.523585
0.529651
0.535834
0.542158
0.548646
0.555324
0.56262
0.571983
0.585023
0.603349
0.628568
0.66229
0.706123
0.761676
0.791538
TABLE 5
Approximation results for specimens: Fe50Ni50, Fe40Ni60, Fe28Ni72.
as the α − γ transition temperature exceeds the maximum temperature of
measurements [1].
As can be observed in Figures 9 and 11, there are no distinct thermal
hysteresis effects such as were revealed in dilatometric measurements for
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A. J. Panas and D. Panas
Fe60Ni40 and Fe50Ni50 [2]. However, as was noted in [6], dilatometric data
are usually more sensitive to thermal stimuli than specific heat data when 2nd
order phase transitions are concerned.
Figure 14 illustrates gradual changes of the specific heat curves and evolution of the characteristic temperature within the range of the invar anomaly
Fe-Ni compositions. It was arbitrarily decided to indicate the characteristic
temperature as the maximum of cp (T ) characteristic. The identified characteristic points, if such appear for a given specimen, are put into Tables 2–5
and indicated by underlining.
Figure 15 illustrates how characteristic points established in this study
relate to literature data. As can be seen, obtained temperatures comply with
the Curie point data presented in [1] and [11], yet it is not the case when the
FIGURE 14
Comparison between selected results of DSC investigations – approximates for specific heat
temperature curves – showing the evolution of the characteristic temperature (circles).
FIGURE 15
Characteristic points from present study (black crosses) compared with Curie point temperature
curves from literature [1,4,11].
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DSC investigation of binary iron-nickel alloys
77
phase diagram from [4] is considered. Although there is no consistence within
the referenced literature, after comparing the discussed DSC results with the
dilatometric data [2] it could be concluded that the characteristic points that
appear throughout specimens from Fe66Ni34 to Fe40Ni60 (Figures 14, 15)
can be related to the Curie transition.
As it concerns the density results (Table 1) they do not strictly comply with
a mixing rule. It can be easily noticed when the Fe and Ni density values
provided in [12] are considered.
4 CONCLUSIONS
Systematic DSC investigations of eleven Fe-Ni alloys ranging in composition
from 10 wt% to 72 wt% were performed over the temperature range from 253 K
to 873 K. The attention was focussed on specific heat and its dependence on
temperature. During measurements a special thermal program was applied that
enabled to gather precise specific heat data both from heating and cooling. This
made thermal cycling investigation possible. Raw 2nd heating-cooling cycle
results were post-processed applying B-spline approximation procedures. As a
result representative specific heat thermal characteristics have been obtained.
The present studies compliment dilatometric investigations of the same
alloys (comp. [2]). Newly obtained DSC results comply with theoretical
expectations derived from dilatometric data analysis.
Our study revealed inconsistency in the literature data concerning magnetic
phase transition phenomena. Characteristic temperatures identified as Curie
point temperatures agree with information provided in [1] and [11]. The data
from [4] for alloys of Ni contents below about 43 at.% seems to be disputable.
ACKNOWLEDGMENT
This research is performed within the frame of GW-HB/647 MUT grant
program.
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