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Thermodynamic description, hardness and electrical conductivity of the Bi–Ni–Zn system: Experiment and modeling
Journal of Alloys and Compounds 825 (2020) 154156
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Thermodynamic description, hardness and electrical conductivity of the BieNieZn system: Experiment and modeling Milena Premovic a, b, *, Dusko Minic a, Yong Du b, Milan Kolarevic c, Milan Milosavljevic a University of Pristina, Faculty of Technical Science, Kneza Milosa 7, 38220, Kos. Mitrovica, Serbia State Key Laboratory of Powder Metallurgy, Central South University Changsha, China c Faculty of Mechanical Engineering, University of Kragujevac, Kraljevo, Serbia a
b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 October 2019 Received in revised form 10 January 2020 Accepted 2 February 2020 Available online xxx
Selected ternary systems are chosen due to the significant interest of nickel alloys in the different industry such as electronic, chemical, automotive, marine etc. Chosen ternary system up to this paper has not been studied. The ternary system BieNieZn has been experimentally and analytically tested. Temperatures of phase transformation were determined by differential thermal analysis (DTA) on 12 ternary samples. Obtained results by DTA test were compared with calculated vertical sections BieNiZn, NieBiZn and ZneBiNi. Hardness and electrical conductivity were measured for some alloys. By using experimental results of hardness and electrical conductivity tests, mathematical model has been proposed for calculation of those properties along all composition ranges. Composition of alloys and phases in alloys annealed at 400 and 700 C were determined by scanning electron microscopy (SEM) with energy dispersive spectrometry (EDS). Obtained results by EDS were compared with calculated isothermal sections at 400 and 700 C. X-ray powder diffraction (XRD) tests were used for phase identification in all ternary samples. Used analytical method was Calphad method. Calculation of phase diagrams (three vertical sections and two isothermal sections) was performed by using thermodynamic parameters for constitutive binary systems. Good agreements between calculated phase diagrams and experimental data have been reached without introducing ternary thermodynamic parameters. Based on this conclusion liquidus projection and invariant reaction were calculated without additional experimental tests. © 2020 Elsevier B.V. All rights reserved.
Keywords: Bi-Ni-Zn system Phase diagrams Liquidus projection Experiment tests
1. Introduction Nickel and nickel-based alloys are widely used in different industries [1e4], such as electronic, chemical, automotive, marine etc. Alloys are used for making vessels, pipes, heat exchangers, pumps, impellers, valves [5], alkaline batteries, gas engines and turbines [6], optical mirrors [7,8], equipment for food industry, chemical industry, petrochemical industry, as well as for galvanic coating of steel objects and other type of equipment. Due to the significant applications of alloys it is highly necessary to study Nibased alloys. Up to now a lot of binary alloys were studied but typically applicable alloys consist of more elements, it is therefore necessary to study systems which consist of three, four and more
* Corresponding author.University of Pristina, Faculty of Technical Science, Kneza Milosa 7, 38220, Kos. Mitrovica, Serbia. E-mail address: [email protected] (M. Premovic). https://doi.org/10.1016/j.jallcom.2020.154156 0925-8388/© 2020 Elsevier B.V. All rights reserved.
elements. Ternary systems based on Bi-Ni [9e12] were studied in past but still some of the ternaries were not tested. Chosen system in our study is BieNieZn since there is no study related to it. The focus of this study is on experimental investigation of phase equilibria in a ternary BieNieZn system. The ternary BieNieZn system has not been experimentally investigated before. In the present study, three series of the samples prepared for experimental investigation. The as-cast samples from three vertical sections were investigated using differential thermal analysis (DTA), electrical conductivity and hardness test. The samples annealed at 400 and 700 C were studied by means of scanning electron microscopy (SEM) together with energy dispersive spectrometry (EDS) and X-ray diffraction analysis (XRD) with samples in a powder form. In parallel with that, phase diagrams of the investigated ternary system BieNieZn were calculated by using thermodynamic parameters for the constitutive binary systems reported in literature [13e17]. The calculated results that include phase diagrams of the
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M. Premovic et al. / Journal of Alloys and Compounds 825 (2020) 154156
experimentally investigated sections, liquidus projection and invariant reactions were compared with the obtained experimental results and a close mutual agreement was observed.
As a summary based on literature data in the ternary BieNieZn system ten solid phases should appears and one liquid phase. Constructed thermodynamic dataset based on literature [13e17] has been used in our calculation of isothermal sections, vertical sections and liquidus projection.
2. Thermodynamic calculation Calculated phase diagram of constitutive binary systems for ternary BieNieZn system are shown in Fig. 1. Optimized thermodynamic parameters for those binaries are taken from literature [13e17]. Binary BieNi system has been tested by Vassilev et al. [13,14], Dinsdale et al. [15] and thermodynamic data presented in their study are used in our calculation. Fig. 1 a. Presents calculated BieNi phase diagram. Binary phase diagram consists of five phases L, (Ni), (Bi), BiNi and Bi3Ni. The binary BieZn system was calculated by using thermodynamic data given by Malakhov [16]. Calculated phase diagram is presented on Fig. 1 b. Calculated phase diagram consist of three phases Liquid phase (L), solid solutions (Bi) and (Zn). The binary NieZn system was calculated by using thermodynamic data given by Xu et al. [17] and presented on Fig. 1 c). Calculated phase diagram consists of Liquid phase L, and seven solid phases (Ni), b, b1, g, d, NiZn3 and (Zn). Based on the literature information for binary sub-systems crystallographic data for phases in the ternary BieNieZn system are summarized and presented in Table 1 [18e27].
3. Experimental procedure The ternary samples were prepared by using high purity (99.999 atomic%) elements Bi, Ni and Zn produced by Alfa Aesar (Germany). Samples were measured in different molar ration and the total masses of the ternary alloy samples were about 3 g. Weighed masses of the pure metals were arc-melted under a high purity argon atmosphere using a non-consumable tungsten electrode. Obtained samples were re-melted six times in order to improve homogeneity and then slowly cooling to room temperature. The average weight loss of the samples during melting was about 0.5% of the total weight. Such prepared samples were divided into four groups. Samples from first and second group were subjected to the SEM-EDS test. Samples from third group for measurement of mechanical and electrical properties. Samples from fourth group for DTA tests. All samples from 1st, 2nd and 3rd group were firstly tested by XRD. Device for XRD test was D2 PHASER, Bruker, Germany powder diffractometer equipped with a dynamic scintillation detector and
Fig. 1. Calculated binary phase diagrams a) BieNi system [13e15], b) BieZn system [16], and c) NieZn system [17].
M. Premovic et al. / Journal of Alloys and Compounds 825 (2020) 154156
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Table 1 Considered phase, their crystallographic data and database names for the phases of the ternary BieNieZn systems. Thermodynamic database name
Phase
Pearson symbol
Space group
Lattice parameters (Å) a
LIQUID RHOMBO_A7
Liquid (Bi)
e hR2
e R3m
4.535 (2)
FCC_A1
(Ni)
cF4
3.5243
HCP_ZN BI3NI BINI BCC_B2
(Zn) Bi3Ni BiNi
hP2 oP16 mC64 cP2
Fm3m P63/mmc Pnma F12/m1
NiZnL GAMMA DELTA NiZn3
b b1 g d NiZn3
tP2 cI52 mC50 oA276
ceramic x-ray Cu tube (KFL-Cu-2 K). XRD patterns were recorded in a 2q range from 10 to 75 with a step size of 0.02 and patterns were analysed using the Topas 4.2 software, ICDD databases PDF2 (2013). Samples from 1st and 2nd group were put into quartz glass ampoules, sealed under vacuum and annealed at 400 and 700 C temperatures for six weeks, respectively. After annealing samples were quenched into ice water in order to preserve the equilibrium compositions. Those samples were subjected to the SEM-EDS and XRD test. Used device for SEM-EDS analysis was JEOL JSM-6460 scanning electron microscope with energy dispersive spectroscopy (EDS) (Oxford Instruments X-act). The selected samples for SEMeEDS analysis were firstly ground using sand paper, then polished using diamond paste, and finally cleaned in an ultrasonic bath. The overall compositions of annealed samples were determined by mapping the entire polished surface of the samples. In contrast, the compositions of the observed coexisting phases were determined by examining the surface of the same phase in different parts of the sample. Samples from third group were divided into two parts. One part of the samples were powdered and subjected to the XRD test. Other part were sealed in the polymer, grinded by using sand paper, then polished using diamond paste, and finally cleaned in an ultrasonic bath. Such prepared samples were tested by using Brinell hardness tester and electrical conductivity test. Electrical conductivity measurements were carried out using Foerster SIGMATEST 2.069 eddy instrument. Hardness of the samples was measured using Brinell hardness tester INNOVATEST, model NEXUS 3001 with indenter diameter of 1 mm and the pressing load 98,07 N. Samples from last group were used for phase transition temperature determination which were measured by DTA method. The DTA measurements were performed on a DTG-60H (Shimadzu). Alumina crucibles were used and measurements were performed under flowing argon atmosphere. Samples weighing between 20 and 30 mg were investigated at a heating rate of 5 C/min with three cycles of heating and cooling. The sample masses and heating rates were determined by analysis of one sample at different testing conditions. The temperatures determined in this study were taken from the second and third heating cycles because the temperatures detected were close to each other. The temperatures from the first cycle were omitted due to deviations from the temperatures recorded in the second and third cycles. The phase transition temperatures were determined from the DTA results as described previously [28,29]. The liquidus temperatures were evaluated from the peak maximum and the temperatures of the invariant reactions were determined from the real onset of the corresponding peaks above the melting point. The reference material was empty alumina crucible. The overall uncertainty of the determined phase transformation temperatures was estimated to be ±1 C.
Pm3m P4/mmm I43m C12/m1 Abm2
2.665 8.879 14.124 2.908
b
11.814 (6)
[18]
4.947 11.483 21.429
[20] [21] [22] [23]
3.190
[24] [24,25]
7.65 12.499
[26] [27]
[19] 4.0998 8.1621
2.747 8.941 13.37 33.326
Ref. c
7.47 8.869
4. Results and discussion 4.1. Experimental results of phase equilibria at 400 and 700 C Six ternary samples annealed at 400 C were analysed using SEMeEDS and XRD method. Results of test are summarized in Table 2. By using the EDS analyzer, the compositions of the samples and the compositions of the observed phases were determined. Based on the determined compositions of the phases and the obtained XRD patterns, it was found that sample 1 contains (Ni) and BiNi as co-existing phases. Fig. 2, presents XRD pattern of sample 1. Sample 2 has (Ni), BiNi and b1 as co-existing phases, while sample 3 has Bi3Ni, BiNi and b1 phases. Fig. 3 presents SEM microstructure of sample 3, on which three phases are clearly visible. On microstructure of sample 3, Bi3Ni compound rich with bismuth and appears as a light gray phase, BiNi phase as a gray phase and b1 phase as a dark phase. Samples 4 and 5 have same co-existing phases NiZn3, L and b1, while in sample 6, co-existing phases are L, (Zn) and d. XRD results are obtained by comparing XRD patterns of samples 1 to 6 with literature crystal information files [19e22,24,26]. For the purpose of determining a phase equilibria at 700 C, seven ternary alloy samples were prepared and tested by SEM-EDS and XRD. The results of the SEMeEDS and XRD are summarized in Table 3. Based on the determined compositions of the phases and XRD results, it was found that samples 1 and 2 contains two same phases L and (Ni), sample 3 has (Ni), L and b1 phases, sample 4 has L and b1 phases, samples 5 has phases NiZn3, L and b, sample 6 has L and NiZn3 and sample 7 has L and g co-existing phases. XRD results are obtained by comparing XRD patterns of samples 1 to 7 with literature crystal information files [19,23e25,27]. Fig. 4 presents XRD pattern of sample 1 as one illustration. While Fig. 5 presents SEM microstructure of sample 5, Bi36.07Ni23.73Zn40.20. From Fig. 5, three phases are visible in microstructur b phase as a dark phase, NiZn3 phase as a gray phase and L phase as a light gray phase. 4.2. Experimental results of DTA studied Twelve ternary samples from three different vertical section were used for DTA tests. Composition of tested samples were checked with EDS method. Summary of DTA and EDS results are presented in Table 4. By apperance of peaks on DTA curve temperatures of phase transformation are organized in Table 4 as a ternary reactions, monovariant and Liquidus. On DTA curves sharp peaks are usually
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Table 2 EDS and XRD results of the ternary BieNieZn samples annealed at 400 C for six weeks. N.
1
2
3
4
5
6
Composition of samples x (at. %)
16.33 Bi 73.95 Ni 9.72 Zn 17.11 Bi 58.84 Ni 24.05 Zn 34.04 Bi 44.26 Ni 21.70 Zn 28.06 Bi 27.54 Ni 44.40 Zn 48.24 Bi 20.02 Ni 31.74 Zn 23.54 Bi 3.26 Ni 73.20 Zn
Determined phases
Compositions of phases x (at.%)
EDS
XRD
Bi
Ni
Zn
(Ni) BiNi
(Ni) BiNi
1.51 ± 0.01 50.29 ± 0.03
82.65 ± 0.01 49.23 ± 0.02
15.84 ± 0.05 0.48 ± 0.04
(Ni) BiNi b1 Bi3Ni BiNi b1 NiZn3 L b1 NiZn3 L b1 L (Zn)
(Ni) BiNi b1 Bi3Ni BiNi b1 NiZn3 e b1 NiZn3 e b1 e (Zn)
d
d
1.93 ± 0.01 50.30 ± 0.02 0.28 ± 0.07 74.59 ± 0.05 49.41 ± 0.03 0.69 ± 0.01 0.28 ± 0.07 94.34 ± 0.04 0.69 ± 0.03 1.51 ± 0.07 94.34 ± 0.05 0.71 ± 0.01 64.50 ± 0.02 1.31 ± 0.04 0.89 ± 0.05
72.2 ± 0.03 48.67 ± 0.04 53.04 ± 0.05 24.55 ± 0.05 49.70 ± 0.07 51.73 ± 0.02 27.97 ± 0.01 2.51 ± 0.01 48.41 ± 0.05 28.1 ± 0.03 3.25 ± 0.08 46.91 ± 0.02 0.46 ± 0.01 0.73 ± 0.03 9.79 ± 0.03
25.87 ± 0.01 1.03 ± 0.01 46.68 ± 0.02 0.86 ± 0.05 0.89 ± 0.06 47.58 ± 0.07 71.75 ± 0.01 3.15 ± 0.02 50.90 ± 0.03 70.39 ± 0.05 2.41 ± 0.06 52.38 ± 0.04 35.04 ± 0.03 97.96 ± 0.05 89.32 ± 0.08
Fig. 2. XRD pattern of sample 1, Bi16.33Ni73.95Zn9.72.
related to the reaction transformation since during transformation large energy is released. In our study temperatures from sharp peaks are read as a real onset and located in column named ternary reactions. By grouping detected temperatures of ternary invariant reactions, it can be concluded that eight reactions appear in the ternary system. Just by DTA results it is hard to comment which reaction appears. More detail is commented in next part of text by consulting calculated vertical sections. Other peaks on DTA curves are usually broad with small energies and those transformation are related to the transformation in liquid state. Last peak on DTA curve is usually transformation of all phases in liquid state. Above this temperature just one phase exists and it is Liquid phase. In our study last peaks are marked as Liquidus transformation and are related to the transformation of all phases into liquid state. Those temperatures are listed in last column of Table 4. Peaks detected in-between ternary reaction and liquidus are related to the monovariant phase transformation. Some DTA heating curves are presented on Fig. 6. Fig. 6a presents, DTA heating curve of sample Bi20.11Ni39.80Zn40.09. With sample Bi20.11Ni39.80Zn40.09 four phase transformation are recorded. First transformation is recorded at 268.3 C and it should be related to the reaction transformation, while other peaks at 342.8, 753.8 and 953.1 C monovariants and liquid transformation. Fig. 6b) presents, DTA heating curve of sample Bi40.89Ni20.71Zn38.40. By this sample four peaks are recorded, in this case first three peaks at 260.1, 647.3 and 851.9 C are sharp and shoud be related to the reactions temperatures while last peak is brode and last one recorded so it belong to the liquid transfomation. Fig. 6c) presents DTA curve of sample Bi29.17Ni29.48Zn41.35 and four peaks are visible on curve. First two peaks are reaction transformation at temperatures 275.7 and 647.3 C. Last detcted temperature at 947.1 C shoud be liquid temperature while paek at 836.4 C is monovariant transformation.
4.3. Calculation of phase diagrams
Fig. 3. SEM microstructure of sample 3, Bi34.04Ni44.26Zn21.70.
Experimentally obtained results presented in previous part are compared with calculated phase diagrams. Calculation of phase diagrams were performed by using Pandat software and thermodynamic dataset constructed based on binary constitutive systems. Constructed thermodynamic dataset is based on literature information from Refs. [13e17].
M. Premovic et al. / Journal of Alloys and Compounds 825 (2020) 154156
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Table 3 EDS and XRD results of the ternary BieNieZn samples annealed at 700 C for six weeks. N.
1
2
3
4
5
6
7
Composition of samples x (at. %)
21.68 Bi 71.27 Ni 7.05 Zn 31.15 Bi 51.25 Ni 17.60 Zn 41.86 Bi 37.77 Ni 20.37 Zn 43.01 Bi 30.06 Ni 26.93 Zn 36.07 Bi 23.73 Ni 40.20 Zn 22.71 Bi 19.34 Ni 57.95 Zn 21.89 Bi 12.93 Ni 65.18 Zn
Determined phases
Compositions of phases x (at. %)
EDS
XRD
Bi
Ni
Zn
(Ni) L
(Ni) e
3.36 ± 0.07 80.77 ± 0.01
88.00 ± 0.02 18.32 ± 0.01
8.64 ± 0.04 0.91 ± 0.03
(Ni) L
(Ni) e
1.13 ± 0.02 81.38 ± 0.05
71.58 ± 0.05 16.91 ± 0.07
27.29 ± 0.05 1.71 ± 0.07
(Ni) L b1 L b1
(Ni) e b1 e b1
0.48 ± 0.04 82.21 ± 0.02 0.48 ± 0.03 82.21 ± 0.07 1.31 ± 0.01
66.95 15.57 53.13 11.33 50.31
L NiZn3
e NiZn3
83.03 ± 0.05 0.71 ± 0.02 0.69 ± 0.08 82.61 ± 0.02 0.87 ± 0.01
5.58 ± 0.01 29.22 ± 0.07 43.43 ± 0.04 2.48 ± 0.03 24.74 ± 0.02
11.39 70.07 55.88 14.91 74.39
65.53 ± 0.03 0.92 ± 0.04
1.25 ± 0.01 18.61 ± 0.07
33.22 ± 0.03 80.47 ± 0.07
b
b
L NiZn3
e NiZn3
L
e
g
g
Fig. 4. XRD pattern of sample 1, Bi21.68Ni71.27Zn7.05.
Fig. 5. SEM microstructure of sample 5, Bi36.07Ni23.73Zn40.20.
± ± ± ± ±
0.03 0.08 0.01 0.05 0.02
32.57 ± 0.06 2.22 ± 0.03 46.39 ± 0.01 6.46 ± 0.07 48.38 ± 0.05 ± ± ± ± ±
0.02 0.08 0.03 0.01 0.04
EDS results givin in Tables 2 and 3 are compared with caluclated isothermal sections at 400 and 700 C. Fig. 7 presents comparison of the calculated isothermal section at 400 C and the EDS results in Table 2. The obtained experimental results are marked with the same symbol but in different color. Different color is used in order to make a distinction between the EDS composition of different samples. Calculated isothermal section consists of 16 different phase regions. From those 16 regions two are single phase region, L and (Ni) phase regions, seven are two-phase regions and seven three-phase regions. From 16 predicted phase regions five are experimentally confirmed, four three-phase regions and one two-phase region. Composition of sample 1 is located in the (Ni)þBiNi two-phase region, sample 2 in (Ni)þBiNiþb1 three-phase region, sample 3 in Bi3Ni þ BiNiþb1 three-phase region, sample 4 and 5 in NiZn3þLþb1 three-phase region and sample 6 in Lþ(Zn)þd threephase region. By comparing compositions of the detected phases for sample 1 to 6 determined by EDS and the related calculated phase compositions it can be noticed that they are in a fairly close agreement. In generall it can be also said that a close overall agreement between the results of calculations and the experiments was obtained. The EDS results given in Table 3 are compared with the calculated isothermal section at 700 C. Fig. 8, presents comparison of the calculated phase diagram and the EDS results. Calculated isothermal section at 700 C, consists of sixteen phase regions. Calculated phase regions are: three single phase regions, L rich with bismuth, L phase rich with zinc and (Ni) solid solution, eight two phase regions ((Ni)þL, (Ni)þb1, Lþb1, Lþb, L þ NiZn3, Lþg, L’þL00 and Lþg) and five three-phase regions ((Ni)þ Lþb1, b1þLþb, L þ NiZn3þb, L þ NiZn3þg and L’þgþL”). Six of sixteen calculated phase regions are experimentally confirmed. From which four are two-phase regions (Ni)þL (samples 1 and 2), Lþb1 (sample 4), L þ NiZn3 (sample 6) and Lþg (sample 7) and two are three phase regions (Ni)þLþb1 (samples 3) and L þ NiZn3þb (sample 5) were experimentally verified. Comparison of EDS results given in Table 3 and calculated isothermal section at 700 C show a very good overall agreement. Experimentally determined composition of phases agree well with calculated composition of phases. In general for both isothermal studies EDS experimental results
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M. Premovic et al. / Journal of Alloys and Compounds 825 (2020) 154156
Table 4 Phase transition temperatures of the studied alloys from the ternary BieNieZn system determined by DTA at pressure p ¼ 0.1 MPa. Temperatures of phase transformation (oC)a
Composition (at.%) nominal Vertical section BieNi50Zn50 Bi20Ni40Zn40 Bi40Ni30Zn30 Bi60Ni20Zn20 Bi80Ni10Zn10 Vertical section NieBi50Zn50 Bi40Ni20Zn40 Bi30Ni40Zn30 Bi20Ni60Zn20 Bi10Ni80Zn10 Vertical section ZneBi50Ni50 Bi40Ni40Zn20 Bi30Ni30Zn40 Bi20Ni20Zn60 Bi10Ni10Zn80 a
EDS
Ternary reactions
monovariant
Liquidus
Bi20.11Ni39.80Zn40.09 Bi38.78Ni30.18Zn31.04 Bi61.07Ni20.56Zn18.37 Bi79.52Ni10.03Zn10.45
268.3 274.8 271.8 273.1
342.8/753.8 322.1/726.1 722.1 711.9
953.1 943.8 907.3
Bi40.89Ni20.71Zn38.40 Bi29.76Ni39.61Zn30.63 Bi19.18Ni59.73Zn21.09 Bi9.13Ni79.15Zn11.72
260.1/647.3/851.9 265.1/463.1/806.3 498.3
970.8
Bi41.08Ni39.81Zn19.11 Bi29.17Ni29.48Zn41.35 Bi19.81Ni20.52Zn59.67 Bi11.01Ni9.13Zn79.86
453.1/485.7/794.1 275.7/647.3 277.4 249.1/493.3
919.7
591.8
836.4
1218.3 1315.7 1054.3 947.1 863.1 812.4
Temperatures in table are organized by consulting calculated vertical sections.
Fig. 6. DTA curves of some samples.
did not detected significant solubility than is expected and also ternary compounds are not detected. As a next step, temperature of phase transformations summarized in Table 4 are compared with calculated vertical sectiions and presented in Fig. 9. As can be seen in Fig. 9, good overall agreement between the calculated vertical sections and the DTA results was achieved. By comparing the calculated and the experimentally determined temperatures, it is clear that the highest detected temperatures correspond to the liquidus temperatures. Calculated vertical section BieNiZn is slightly simpler in comparison with calculated NieBiZn and ZneBiNi vertical sections. From Fig. 9a, it is clear that first detected peak at all samples is related to the ternary eutectic reaction L/b1þBi3Niþ(Bi). Calculated temperature of ternary eutectic reaction is 269.06 C while experimental value are in range from 265.1 to the 274.8 C. Other detected temperatures are relatet to the monovariant phase transformation while last peaks are related to the liquidus temperature.
Fig. 9b, presents NieBiZn vertical section compared with DTA results. By DTA results of sample Bi40.89Ni20.71Zn38.40 temperature of three invariant reaction were detected, L þ NiZn3/b1þ(Bi) (calculated at 269.09 C), Lþb/NiZn3þb1 (calculated at 641.38 C) and L’/L”þNiZn3þb (calculated at 842.38 C). The experimentally determined temperatures are 260.1, 647.3 and 851.9, respectively which are close to the calculated one. With sample Bi29.76Ni39.61Zn30.63 temperatures of L/b1þBi3Niþ(Bi) (calculated at 269.06 C), L þ BiNi/b1þBi3Ni (calculated at 464.06 C) and bþ(Ni)/Lþb1 (calculated at 804.50 C) invariant reactions are detected. Detected temperatures are 265.1, 463.1 and 806.3 respectively. First detected peak on sample Bi19.18Ni59.73Zn21.09 is realted to the invariant reaction Lþ(Ni)/ b1þBiNi at temperature 498.3 C while calculated temperature is 492.29 C. Second detected temperature on same samples is realted to the liquidus temperature. Two peaks are detected with sample Bi9.13Ni79.15Zn11.72 where first is monovariant phase transformation and second is liquidus temperature. Fig. 9c, presents ZneBiNi vertical section compared with DTA
M. Premovic et al. / Journal of Alloys and Compounds 825 (2020) 154156
7
Fig. 7. Calculated isothermal section at 400 C compared with EDS results given in Table 2.
Fig. 8. Calculated isothermal section at 700 C compared with EDS results given in Table 3.
results. Sample Bi41.08Ni39.81Zn19.11 (Table 4), detected four temperature, by comparison it can be concluded that firts temperature at 453.1 C is related to the L þ BiNi/b1þBi3Ni ternary reaction which is calculated at 464.06 C. Second recorded temperature at 485.7 C is related to the Lþ(Ni)/b1þBiNi reaction (calculated at 492.29 C). Reaction bþ(Ni)/Lþb1 (calculated at 804.50 C) is determined with same sample at 794.1 C while peak at 1054.3 C is liquidus temperature. Sample Bi29.17Ni29.48Zn41.35 recorded four transformations. First is at 275.7 C and it is related to the L þ NiZn3/b1þ(Bi) reaction (calculated at 269.09 C), second detected transformation at 647.3 C is related to the Lþb/NiZn3þb1 reaction (calculated at 641.38 C) and other two experimental temperatures are monovarian and liquidus transformation, respectively. Reaction L þ NiZn3/(Bi)þg (calculated at 268.53 C) is detected with sample Bi19.81Ni20.52Zn59.67 to be 277.4 C (first detected temperature) while second peak is liquidus
temperature. Last tested sample from ZneBiNi vertical section is Bi11.01Ni9.13Zn79.86. With this sample two reactions are confirmed (Bi)þg/Lþd (calculated at 260.72 C) and L’þg/L”þd (calculated at 485.22 C), at temperatures 249.1 and 493.3 C, respectively. In general, it can be said that the experimentally determined temperatures of phase transformations support the results of the calculations quite well. Based on the presented results, it can be safely assumed that it is not necessary to introduce new parameters to describe the ternary BieNieZn system. Therefore, the applied thermodynamic dataset was further used for the calculation of a liquidus projection and invariant reactions. Fig. 10, presents prediction of liquidus projection of the ternary BieNieZn system, with magnified bismuth and zinc rich part. Predicted liquidus projection has ten fields of primary crystallization and field of miscibility gap. Twelve invariant reactions were
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M. Premovic et al. / Journal of Alloys and Compounds 825 (2020) 154156
Fig. 9. Calculated vertical sections of the ternary BieNieZn system compared with DTA experimental results: a) BieNiZn, b) NieBiZn and c) ZneBiNi.
Fig. 10. Prediction of liquidus projection of the ternary BieNieZn system with. Magnified Bi and Zn rich part.
predicted and details are given in Table 5. Three reactions are E-type (eutectic) and nine are U-type (univariant) reactions. E1 reaction L’/L”þNiZn3þb and E2 reaction L’/(Zn)þL”þd are monotectic reaction, while E3 reaction
L/b1þBi3Niþ(Bi) is ternary eutectic reaction. U2 and U9 reactions are solid transition reactions, and all others are liquid transition reactions. Eight of twelve predicted invariant reactions are experimentally confirmed.
M. Premovic et al. / Journal of Alloys and Compounds 825 (2020) 154156
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Table 5 Predicted invariant reaction of the ternary BieNieZn system. T (ºC) Reactions
Typea
Phase
0
843.49 L’þNiZn3/L”þg
U1
L NiZn3 L00
842.38 L’/L”þNiZn3þb
E1
L0 L00 NiZn3
804.50 bþ(Ni)/Lþb1
U2
641.38 Lþb/NiZn3þb1
U3
Composition of reaction in mole fraction Bi
Ni
Zn
0.080793
0.179583
0.739624
0.092703
0.280723
0.626574
0.747760
0.182174
0.070066
0.864691
0.053503
0.081806
0.858813
0.137497
0.003690
0.015942
0.010758
0.973300
0.873735
0.123334
0.002931
0.007396
0.002386
0.990219
0.989336
0.006521
0.004143
0.989255
0.006738
0.004007
0.986164
0.000147
0.013689
0.950883
8.064510E-008
0.049117
g
b В (Ni) L b1 L
b
492.29 Lþ(Ni)/b1þBiNi
U4
485.22 L’þg/L”þd
U5
464.06 L þ BiNi/b1þBi3Ni
U6
416.93 L’/(Zn)þL”þd
E2
269.09 L þ NiZn3/b1þ(Bi)
U7
269.06 L/b1þBi3Niþ(Bi)
E3
268.53 L þ NiZn3/(Bi)þg 260.72 (Bi)þg/Lþd
U8
NiZn3 b1 L (Ni) b1 BiNi L0
g L00
d L BiNi b1 Bi3Ni L’ (Zn) L00
d L NiZn3 b1 (Bi) L b1 Bi3Ni (Bi) L NiZn3 (Bi)
g U9
(Bi)
g L
d a
U-univariant reaction, E-eutectic reaction, number from 1 to 9 depend on temperature decrease.
As a next step, hardness and electrical properties were measured on nineteen as-cast ternary alloys samples and three binary samples. Based on obtained experimental results mathematical model for calculation of those properties along all composition range is proposed. Development of mathematical model is utilized in software Desig Expert v.9.0.3.1. Hardness of alloys were tested by Brinell method in three point. Results of hardenss tests are given in Table 6 [30,31], together with alloy composition and calculated fraction of a phases. According to the results given in Table 6, Brinell hardness is strongly dependent on alloys compositions and fraction of the phases. Samples marked with numbers from 1 to 5, have same three phases in microstructure Bi3Niþb1þ(Bi), fraction of those three phases changes with compositions of alloys. In samples from number 1 to 5 wt of bismuth increases and relation of phase fractions of Bi3Ni, b1 and (Bi) phase changes according with bismuth increasement. Fraction of (Bi) phase increase with bismuth increasement according to this change hardness of alloys increase. Samples from number 6 to 11, have increasement of nickel weight and those alloys lie along NieBiZn vertical section. According to the calculated phase fraction each of alloys belongs to different phase region, six phase regions, from which three are three-phase and three are two-phase regions. It can be noticed that hardness of
alloys increases as content of nick increase in alloys. Drastic increasement in hardness is detected in Bi12.5Ni75Zn12.5 alloy (sample 11) since in this alloy (Ni) phase is detected in fraction of 75.1% and BiNi 24.9% and both of the phases have a high hardness. Samples from number 12 to 17 lie along ZneBiNi vertical section and content of the zinc increase in those alloys from 12 to 17, respectively. In alloys 12 and 13 same three phases appears, but in different ration. In sample 12 there is more BiNi phase then in sample 13. This results that hardness of alloy 12 is higher than alloy 13. For samples 14 to 17, content of zinc increase and phase regions changes from samples. Those changes of sample compositions result in hardness increasement. Fig. 6, presents graphical presentation of hardness depending on alloy composition. In Fig. 11 calculated phase regions are marked. From Fig. 11a it can be concluded that in alloys from vertical section BieNiZn, all alloys have same three phases in equilibrium and hardness increase with bismuth content. Fig. 11b shows hardness of alloys from vertical section NieBiZn, and increasement in hardness is noticed with increasement of nickel. Fig. 11c, is for alloys from Zn vertical section. Hardness of alloys from number 12 to 17, is changing with content of zinc. Firstly hardness decrease and then increase with content of zinc. In general can be concluded that ternary alloys which are rich
10
M. Premovic et al. / Journal of Alloys and Compounds 825 (2020) 154156
Table 6 Compositions of the investigated samples with calculated phase fractions at room temperature and related Brinell hardness values. N.
B1 1 2 3 4 5 Bi B2 6 7 8 9 10 11 Ni B3 12 13 14 15 16 17 Zn
Alloy nominal composition (at.%) Bi
Ni
Zn
0 0.05 0.2 0.4 0.6 0.8 1 0.5 0.45 0.4 0.325 0.25 0.2 0.125
0.5 0.475 0.4 0.3 0.2 0.1
0.5 0.475 0.4 0.3 0.2 0.1
0 0.1 0.2 0.35 0.5 0.6 0.75 1 0.5 0.45 0.4 0.35 0.275 0.175 0.05
0.5 0.45 0.4 0.325 0.25 0.2 0.125
0.5 0.45 0.4 0.35 0.275 0.175 0.05
0 0.1 0.2 0.3 0.45 0.65 0.9 1
Calculated fraction of a phase (%)
100% b1 4.8% (Bi), 0.3%Bi3Ni, 94.9% b1 19.8% (Bi), 0.3% Bi3Ni, 79.9% b1 39.9% (Bi), 0.2% Bi3Ni, 59.9% b1 59.9% (Bi), 0.1% Bi3Ni, 40.0% b1 80.0% (Bi), 0.1% Bi3Ni, 19.9% b1 100.0% (Bi) 50.1% (Bi), 49.9% (Zn) 45.0% (Bi), 55.0% g 40.0% (Bi), 49.0% NiZn3, 11.0% b1 24.9% (Bi), 10.2% Bi3Ni, 64.9% b1 50.2% b1, 49.8% BiNi 31.6% (Ni), 28.5% b1, 39.9% BiNi 75.1% (Ni), 24.9% BiNi 100% (Ni) 99.9% BiNi, 0.1% (Ni) 19.6% Bi3Ni, 20.1% b1, 60.3% BiNi 40.1% Bi3Ni, 40.1% b1, 19.8% BiNi 19.9% (Bi), 20.2% Bi3Ni, 59.9% b1 27.5% (Bi), 42.8% NiZn3, 29.7% b1 17.5% (Bi), 5.7% g, 76.8% NiZn3 5.0% (Bi), 45.0% d, 50% (Zn) 100% (Zn)
Measured value (MN/m2)
Mean value (MN/m2)
1
2
3
14.9 28.7 32.1 45.3 62.8 73.1
15.2 29.1 35.7 47.1 61.3 71.8
16.6 25.6 37.1 47.1 64.3 74.5
61.6 23.2 52.6 53.3 75.9 94.2 150.3
62.4 27.0 54.5 59.3 77.3 89.3 155.1
61.8 25.3 47.4 56.4 69.8 96.1 147.8
150.8 81.8 61.5 65.5 72.4 93.1 139.7
147.1 87.5 51.2 62.3 69.6 92.8 135.9
148.9 83.9 55.5 65.8 77.0 90.7 141.7
15.5 27.8 34.9 46.5 62.8 73.0 94.2 61.9 25.2 51.5 56.3 74.3 93.2 151.1 700 148.9 84.4 56.1 64.5 73.0 92.2 139.1 412
ref
[30] [31]
[30]
[30]
Fig. 11. Graphical presentation of Brinell hardness dependence of composition and phase fraction: a) vertical section BieNiZn, b) vertical section NieBiZn and c) vertical section ZneBiNi.
M. Premovic et al. / Journal of Alloys and Compounds 825 (2020) 154156
with Ni have high hardness. This is especially related to the alloy sample 11, where (Ni) solid solution appear in content of 75.1%. Based on experimental hardness value, appropriated mathematical model has been developed in way to predict hardness of ternary alloys over all ternary composition range. By utilizing experimentally determined values of hardness given in Table 6 and software Desig Expert v.9.0.3.1 mathematical model of the dependence of the Brinell hardness on composition for the BieNieZn alloys was developed. Out of a possible canonical or Scheffe model [32e34] that meet the requirements of adequacy is recommended Special Cubic Mixture model:
Table 8 R-squared and other statistics after the ANOVA. Std. Dev.
1.2972
R-Squared
0.9453
Mean C.V. % PRESS
9.4304 13.7559 102.3201
Adj R-Squared Pred R-Squared Adeq Precision
0.9270 0.8151 31.4695
Table 9 Estimation of parameters for Special Cubic Mixture model of Brinell hardness in ternary BieNieZn system. Component
Coefficient Estimate
df
Standard Error
95% CI Low
95% CI High
A-Bi BeNi CeZn AB AC BC ABC
10.16078 25.57761 19.01072 26.57603 31.03244 73.27272 91.66989
1 1 1 1 1 1 1
1.15144 1.19263 1.03875 5.52956 5.41095 5.37188 30.46797
7.74171 23.07198 16.82839 38.19322 42.40041 84.55863 27.65907
12.57986 28.08323 21.19305 14.95885 19.66446 61.98681 155.68071
y ¼ b1 X1 þ b2 X2 þ b3 X3 þ b12 X1 X2 þ b13 X1 X3 þ b23 X2 X3 þ b123 X1 X2 X3
(1)
The Analysis of variance (ANOVA) implies that the model is significant. However, the diagnosis of the statistical properties of the assumed model found that the distribution of residuals is not normal and that it is necessary to transform the mathematical model in order to meet the conditions of normality. Similar adjustment of mathematical model are introduced in study of ternary Bi-Ge-Sb, Al-Cu-Sb [35] and AleAg-Ga [36] systems. The Box-Cox diagnostics [37,38] recommends the „Square Root“ transformation for the variance stabilization. In this case, ANOVA confirms the adequacy of the Model (Table 7). The F-value of the Model is 51.80 and it implies that the model is significant. In this case, all model terms are significant. R-squared and other statistics after the ANOVA have appropriate values which confirm the justification of the choice of the adopted mathematical model (Table 8). The “Pred R-Squared” of 0.8151 is in reasonable agreement with the “Adj R-Squared” of 0.9270 i.e. the difference is less than 0.2. “Adeq Precision” measures the signal to noise ratio. A ratio of 31.4695 is greater than 4 and indicates an adequate signal. Estimation of individual regression coefficients, Standard error and 95% confidence interval are shown in Table 9. The final equation of the predictive model in Terms of Actual Components is: Sqrt(HB) ¼ 10.16078(Bi)þ25.57761(Ni)þ19.01072(Zn)26.57603(Bi)x(Ni)-31.03244(Bi)x(Zn)-73.27272(Ni)x(Zn)þ 91.66989(Bi)x(Ni)x(Zn) (2) The diagnosis of the statistical properties of the assumed model found that the distribution of residuals are normal. After the applied Box-Cox procedure, the value of l is 0.50, the optimum value of l is 0.27 and the 95% confidence interval for l (Low C.I. ¼ 0.01, High C.I. ¼ 0.55) contains the value 0.50. Iso-lines contour plot for Brinell hardness of alloys defined by equation (2) is shown in Fig. 12. On same alloys as for hardness measurement, electrical conductivity was mesured. Electrical conductivity were mesured in
11
Fig. 12. Calculated iso-lines of Brinell hardness in ternary BieNieZn system with R2 ¼ 0.9453.
four point in one sample and results of tests are given in Table 10. In table are also given composition on samples, calculated fractions of phases and mean value of electrical conductivity [31,39]. Mean value of electrical conductivity of samples from 1 to 5, decries with increasement of bismuth content. Those results are also connected with changes of (Bi), Bi3Ni and b1 phase fractions in
Table 7 ANOVA for Special Cubic Mixture model. Source
Sum of Squares
df
Mean Square
F Value
p-value Prob > F
Model Linear Mixture AB AC BC ABC Residual Cor Total
523.018 82.886 38.872 55.350 313.088 15.234 30.291 553.309
6 2 1 1 1 1 18 24
87.1697 41.4429 38.8717 55.3504 313.0881 15.2336 1.6828
51.8000 24.6272 23.0993 32.8916 186.0507 9.0525
2.19559E-10 7.04638E-06 0.000141479 1.94744E-05 6.25258E-11 0.007540847
significant
12
M. Premovic et al. / Journal of Alloys and Compounds 825 (2020) 154156
Table 10 Compositions of the investigated samples with calculated phase fractions at room temperature and related electrical conductivity values. N.
B1 1 2 3 4 5 Bi B2 6 7 8 9 10 11 Ni B3 12 13 14 15 16 17 Zn
Alloy nominal composition (at.%) Bi
Ni
Zn
0 0.05 0.2 0.4 0.6 0.8 1 0.5 0.45 0.4 0.325 0.25 0.2 0.125
0.5 0.475 0.4 0.3 0.2 0.1
0.5 0.475 0.4 0.3 0.2 0.1
0 0.1 0.2 0.35 0.5 0.6 0.75 1 .5 0.45 0.4 0.35 0.275 0.175 0.05
0.5 0.45 0.4 0.325 0.25 0.2 0.125
0.5 0.45 0.4 0.35 0.275 0.175 0.05
0 0.1 0.2 0.3 0.45 0.65 0.9 1
Calculated fraction of a phase (%)
100% b1 4.8% (Bi), 0.3%Bi3Ni, 94.9% b1 19.8% (Bi), 0.3% Bi3Ni, 79.9% b1 39.9% (Bi), 0.2% Bi3Ni, 59.9% b1 59.9% (Bi), 0.1% Bi3Ni, 40.0% b1 80.0% (Bi), 0.1% Bi3Ni, 19.9% b1 100.0% (Bi) 50.1% (Bi), 49.9% (Zn) 45.0% (Bi), 55.0% g 40.0% (Bi), 49.0% NiZn3, 11.0% b1 24.9% (Bi), 10.2% Bi3Ni, 64.9% b1 50.2% b1, 49.8% BiNi 31.6% (Ni), 28.5% b1, 39.9% BiNi 75.1% (Ni), 24.9% BiNi 100% (Ni) 99.9% BiNi, 0.1% (Ni) 19.6% Bi3Ni, 20.1% b1, 60.3% BiNi 40.1% Bi3Ni, 40.1% b1, 19.8% BiNi 19.9% (Bi), 20.2% Bi3Ni, 59.9% b1 27.5% (Bi), 42.8% NiZn3, 29.7% b1 17.5% (Bi), 5.7% g, 76.8% NiZn3 5.0% (Bi) 45.0% d, 50% (Zn) 100% (Zn)
alloys. Electrical conductivity for alloys from NieBiZn vertical section, have trends to increases with nickel content until 0.35 mol of nickel, then decrease with 0.5 mol of nickel and again increase. This small drop of electrical conductivity can be related to the content of b1 and BiNi phases in sample. Similar trend can be noticed for electrical conductivity of ternary alloys from ZneBiNi vertical section. So electrical conductivity increases until 0.3 mol of zinc and then in alloy with 0.45 mol of zinc decries to 0.8705 MS/m, and after sample 15, electrical conductivity drastically increases. Decries of electrical conductivity of sample 15, can be explained by high content of (Bi) phase and occurrence of NiZn3 phase, similar electrical conductivity is detected with sample 7, which have same three phases in equilibrium as sample 15. As a next step mean value of electrical conductivity depending on sample composition, together with calculated phases are given on Fig. 13. By using experimental value of electrical conductivity appropriated mathematical model has been proposed for calculation of electrical conductivity along all composition range for ternary alloys. The Model summary statistics are suggested a Quadratic Mixture model for the dependence of the electrical conductivity on the composition for the BieNieZn alloys
y ¼ b1 X1 þ b2 X2 þ b3 X3 þ b12 X1 X2 þ b13 X1 X3 þ b23 X2 X3
(3)
The Analysis of variance (ANOVA) implies that the model is significant. However, the diagnosis of the statistical properties of the assumed model found that the distribution of residuals is not normal and that it is necessary to transform the mathematical model in order to meet the conditions of normality. The Box-Cox diagnostics [37,38] recommends the „Square Root” transformation for the variance stabilization.The Model summary statistics for „Square Root“ model transformation are suggested Quadratic Mixture model. In this case, ANOVA confirms the adequacy of the Model. High F value of model (F ¼ 47.74) and low value of probability (p < 0.0001) indicate that the model is significant (Table 11). The coefficient of determination (R-Squared ¼ 0.926) and others statistic of models have a satisfactory value, which confirms the
Measured value (MS/m)
Mean value (MS/m)
1
2
3
4
2.9083 2.1800 1.9038 1.5981 1.2381 0.8561
2.9089 2.1875 1.9078 1.5920 1.2398 0.8426
2.9090 2.1809 1.9076 1.5923 1.2365 0.8389
2.9069 2.1890 1.9067 1.5909 1.2389 0.7919
1.956 0.7982 0.8654 1.8365 1.5902 2.4751 4.9080
1.864 0.7998 0.8646 1.8398 1.5909 2.4719 4.9087
1.902 0.7952 0.8633 1.8322 1.5902 2.4728 4.9028
e 0.8005 0.8644 1.8398 1.5971 2.4789 4.9078
2.1090 0.9325 1.2890 1.7898 0.8669 4.9310 7.0918
2.1078 0.9342 1.2890 1.7809 0.8666 4.9309 7.0976
2.1098 0.9147 1.2867 1.7894 0.8707 4.9320 7.0971
2.1068 0.9228 1.2867 1.7856 0.8780 4.9318 7.0987
2.9082 2.1843 1.9064 1.5933 1.2383 0.8324 0.77 1.907 0.7984 0.8644 1.8371 1.5921 2.4747 4.9068 14.0 2.1083 0.9260 1.2878 1.7864 0.8705 4.9314 7.0963 17.0
ref
[39] [31]
[39]
[39]
validity of the adopted mathematical model (Table 12). The “Pred RSquared” of 0.8451 is in reasonable agreement with the “Adj RSquared” of 0.9069 i.e. the difference is less than 0.2. “Adeq Precision” measures the signal to noise ratio. A ratio of 23.66 is greater than 4 and indicates an adequate signal. Estimation of individual regression coefficients, Standard error and 95% confidence interval are shown in Table 13. The final equation of the predictive model in Terms of Actual Components is: Sqrt(s) ¼ 0.96214(Bi)þ3.66805(Ni)þ3.81946(Zn)3.47829(Bi)x(Ni)-4.3371(Bi)x(Zn)-7.97561(Ni)x(Zn)
(4)
After transformation of the model, the response variance is stabilized, the distribution of the response variable is closer to the normal distribution, and the fit of the model to the data is improved. After the applied Box-Cox procedure, the value of l is 0.50, the optimum value of l is 0.19 and the 95% confidence interval for l (Low C.I. ¼ -0.26, High C.I. ¼ 0.53) contains the value 0.50, so the use of a „Square Root“ transformation is indicated. Iso-lines contour plot for Electrical conductivity of alloys defined by equation (4) is shown in Fig. 14. In general proposed mathematical models are significant for prediction of those two properties along all composition range. Improvement of models is necessary by including experiment of properties at different temperatures which will lead to proposed more general model for calculation of properties allong all composition and temperature ranges. But proposed mathematical model in this study are starting point and necessary for future development of model since up to this paper there is no similar studies related to the BieNieZn system. 5. Conclusion Alloys from ternary BieNieZn system are experimentally and analytically tested for the first time. Experimental results of DTA test were compared with calculated vertical sections. By DTA test temperature of eight invariant reactions have been determined,
M. Premovic et al. / Journal of Alloys and Compounds 825 (2020) 154156
13
Fig. 13. Graphical presentation of electrical conductivity dependence of composition and phase fraction: a) vertical section BieNiZn, b) vertical section NieBiZn and, c) vertical section ZneBiNi.
Table 11 ANOVA for Quadratic Mixture model. Source
Sum of Squares
df
Mean Square
F Value
p-value Prob > F
Model Linear Mixture AB AC BC Residual Cor Total
16.0551 7.7379 0.9885 1.6164 5.1105 1.2778 17.3329
5 2 1 1 1 19 24
3.2110 3.8689 0.9885 1.6164 5.1105 0.0673
47.7438 57.5264 14.6973 24.0346 75.9868
4.17338E-10 8.69033E-09 0.001120171 9.88751E-05 4.57756E-08
Table 12 R-squared and other statistics after the ANOVA. Std. Dev.
0.2593
R-Squared
0.9263
Mean C.V. % PRESS
1.5544 16.6840 2.6845
Adj R-Squared Pred R-Squared Adeq Precision
0.9069 0.8451 23.6602
temperatures of other phase transformation and liquidus temperature. Comparison of DTA results and calculated vertical section shows good agreement between calculated and experimentally determined temperatures of phase transformation. Furder annealed alloys at 400 and 700 C were prepared in way to
significant
Table 13 Estimation of parameters for Quadratic Mixture model of Electrical conductivity in ternary BieNieZn system. Component
Coefficient Estimate
df
Standard Error
95% CI Low
95% CI High
A-Bi BeNi CeZn AB AC BC
0.9621 3.6680 3.8195 3.4783 4.3371 7.9756
1 1 1 1 1 1
0.2267 0.2359 0.2045 0.9073 0.8847 0.9149
0.4876 3.1743 3.3913 5.3773 6.1887 9.8906
1.4367 4.1618 4.2476 1.5793 2.4855 6.0606
14
M. Premovic et al. / Journal of Alloys and Compounds 825 (2020) 154156
Fig. 14. Calculated iso-lines of Electrical conductivity in ternary BieNieZn system with R2 ¼ 0.9263.
determined isothermal sections at chosen temperatures. Existence of the phase were detected with XRD test and composition of detected phases have been determined with EDS test. EDS tests did not detected new compound or even large solubility of third element into intermetallic compounds r solid solution. According to this results it can be concluded that it is not necessary to introduce new thermodynamic parameters for description of the phase diagrams of the ternary BieNieZn system. Based on this conclusion liquidus projection were predicted and twelve invariant reaction were predicted from which eight are experimentally confirmed by DTA test. Experimentally detected temperatures of invariant reaction are in close agreement with calculated temperatures. In next step Brinell hardness and electrical conductivity have been mesured on seventeen ternary samples. Properties of ternary alloys are conected with microstructural changes. Phase presented in microstructure of samples were determined with XRD. Furder by using experimental results of hardness and electrical conductivity one mathematical model has been proposed in way to predict those properties along all ternary composition range. Declaration of competing interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work has been supported by the National Natural Science Foundation of China of China (project No. 414010049) and the Ministry of Education, Science and Technological Development of the Republic of Serbia (Grant No. OI172037). References [1] S. Semboshi, S. Sato, A. Iwase, T. Takasugi, Discontinuous precipitates in agehardening Cu-Ni-Si alloys, Mater. Char. 115 (2016) 39e45, https://doi.org/ 10.1016/j.matchar.2016.03.017. [2] J. Lei, H. Xie, S. Tao, R. Zhang, Z. Lu, Microstructure and selection of grain boundary phase of Cu-Ni-Si ternary alloys, Rare Met. Mater. Eng. 44 (12) (2015) 3050e3054, https://doi.org/10.1016/S1875-5372(16)60049-8.
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Vizdal, Atlas of Phase Diagrams for the Lead-Free Soldering, COST 531 (Lead-free Soders), vol. 1, © COST office, 2008, ISBN 978-80-86292-28- 1 (Printed in the Czech Republic). [16] D.V. Malakhov, Thermodynamic assessment of the Bi-Zn system, Calphad 24 (2000) 1e14, https://doi.org/10.1016/S0364-5916(00)00011-0. [17] K. Xu, S. Liu, Y. Du, L. Dreval, G. Cai, Z. Jin, Thermodynamic investigation of the Mg-Ni-Zn system by experiments and calculations and its application, J. Alloys Compd. 784 (2019) 769e787, https://doi.org/10.1016/j.jallcom.2018.12.377. [18] P. Cucka, C.S. Barrett, The crystal structure of Bi and of solid solutions of Pb, Sn, Sb and Te in Bi, Acta Crystallogr. 15 (1962) 865e872, https://doi.org/10.1107/ S0365110X62002297. [19] E.A. Owen, E.L. Yates, X-ray measurement of the thermal expansion of pure nickel, Philos. Mag. A 7 (21) (1936) 809e819, https://doi.org/10.1080/ 14786443608561628. [20] N. Ridley, Densities of some indium solid solutions, J. Less Common. Met. 8 (1965) 354e357, https://doi.org/10.1016/0022-5088(65)90071-8. [21] E.L. Martinez Pineiro, B.L. Ruiz Herrera, R. Escudero, L. Bucio, Possible coexistence of superconductivity and magnetism in intermetallic NiBi3, Solid State Commun. 151 (2011) 425e429, https://doi.org/10.1016/j.ssc.2011.01.005. [22] M. Ruck, Die Kristallstruktur von BiNi: eine komplexe Ausdünnungsvariante des InNi2-. Typs, Z. Anorg. Allg. Chem. 625 (1999) 2050e2054, https://doi.org/ 10.1080/14786443608561628. [23] W. Heike, J. Schramm, O. Vaupel, The system nickel-zinc, Metallwirtschaft, Metallwissenschaft, Metalltechnik 15 (1936) 655e662. [24] R.P. Anantatmula, D.B. Masson, Thermodynamic properties of solid NieZn alloys by atomic absorption, Metall. Trans. 5 (1974) 605e613, https:// doi.org/10.1007/BF02644656. [25] A. Johansson, H. Ljung, S. Westman, X-ray and neutron diffraction studies on G-Ni,Zn and G-Fe,Zn, Acta Chem. Scand. 22 (1968) 2743e2753, https:// doi.org/10.3891/acta.chem.scand.22-2743. [26] J.K. Critchley, S. Denton, The crystal structure of d-NieZn, J. Inst. Met. 99 (1971) 26e27. [27] G. Nover, K. Schubert, The crystal structure of NiZn3.r, J. Less Common Met. 75 (1980) 51e63, https://doi.org/10.1016/0022-5088(80)90368-9. [28] P. Fima, A. Gazda, Thermal analysis of selected Sn-Ag-Cu alloys, J. Therm. Anal. Calorim. 112 (2013) 731e737, https://doi.org/10.1007/s10973-012-2583-0. [29] W.J. Boettinger, U.R. Kattner, K.W. Moon, J.H. Perepezko, in: DTA and HeatFlux DSC Measurements of Alloy Melting and Freezing (NIST Recommended Practice Guide, Special Publication 960-15, NIST, 2006, https://doi.org/ 10.6028/NBS.SP.960-15. [30] accessed date, https://periodictable.com/Properties/A/BrinellHardness.v.html. (Accessed 10 September 2019). [31] Dusko M. Mini c, Milena M. Premovi c, Dragana T. Zivkovi c, Dragan M. Manasijevi c, Mirjana Z. Dimi c, Zvonko R. Petrovi c, Smiljana M. Markovi c, Structural, mechanical and electrical properties of alloys in ternary Ag-Bi-Zn
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system, Rev Metal Madrid 51 (2) (2015), e042, https://doi.org/10.3989/ revmetalm.042. Cornell, Experiments with Mixtures, third ed., John Wiley&Sons, Inc, New York, 2002. Design of Experiments in Chemical Engineering, Wilez-VCH Verlag Lazi c Z, GmbH&Co.KGaA, Weiheim, 2004. M. Kolarevi c, M. Vuki cevi c, B. Radi cevi c, M. Bjeli c, V. Grkovi c, A methodology for forming the regression model of ternary system, in: The Seventh Triennial International Conference Heavy Machinery HM 2011, Faculty of Mechanical Engineering, Proceedings, Vrnja cka Banja 1e6, 2011, 29 june-2 july. M. Premovic, D. Mini c, M. Kolarevic, D. Manasijevic, D. Zivkovi c, Al Djordjevic, D. Milisavljevic, Electrical properties of ternary Bi-Ge-Sb and Al-Cu-Sb alloys,
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Rev. Metal. (Madr.) 53 (3) (2017), e098. [36] M. Premovic, M. Tomovic, D. Minic, D. Manasijevic, D. Zivkovic, V. Cosovic, V. Grkovic, A. Ðordjevic, Determination of 200 0C isothermal section of Al-AgGa phase diagram by microanalysis, X-ray diffraction, hardness and electrical conductivity measurements, J. Mater. Eng. Perform. 26 (2017) 2491e2501. [37] G. Box, N. Draper, Response Surfaces, Mixtures, and Ridge Analyses, second ed., John Wiley & Sons, Inc, New Jersey, 2006, 2nd ed. [38] R.H. Myers, D.C. Montgomery, C.M. Anderson-Cook, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, third ed., John Wiley & Sons, Inc, New Jersey, 2009, p. 704. [39] accessed date, https://periodictable.com/Properties/A/ElectricalConductivity. v.html. (Accessed 13 September 2019).
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Thermodynamic description, hardness and electrical conductivity of the BieNieZn system: Experiment and modeling Milena Premovic a, b, *, Dusko Minic a, Yong Du b, Milan Kolarevic c, Milan Milosavljevic a University of Pristina, Faculty of Technical Science, Kneza Milosa 7, 38220, Kos. Mitrovica, Serbia State Key Laboratory of Powder Metallurgy, Central South University Changsha, China c Faculty of Mechanical Engineering, University of Kragujevac, Kraljevo, Serbia a
b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 October 2019 Received in revised form 10 January 2020 Accepted 2 February 2020 Available online xxx
Selected ternary systems are chosen due to the significant interest of nickel alloys in the different industry such as electronic, chemical, automotive, marine etc. Chosen ternary system up to this paper has not been studied. The ternary system BieNieZn has been experimentally and analytically tested. Temperatures of phase transformation were determined by differential thermal analysis (DTA) on 12 ternary samples. Obtained results by DTA test were compared with calculated vertical sections BieNiZn, NieBiZn and ZneBiNi. Hardness and electrical conductivity were measured for some alloys. By using experimental results of hardness and electrical conductivity tests, mathematical model has been proposed for calculation of those properties along all composition ranges. Composition of alloys and phases in alloys annealed at 400 and 700 C were determined by scanning electron microscopy (SEM) with energy dispersive spectrometry (EDS). Obtained results by EDS were compared with calculated isothermal sections at 400 and 700 C. X-ray powder diffraction (XRD) tests were used for phase identification in all ternary samples. Used analytical method was Calphad method. Calculation of phase diagrams (three vertical sections and two isothermal sections) was performed by using thermodynamic parameters for constitutive binary systems. Good agreements between calculated phase diagrams and experimental data have been reached without introducing ternary thermodynamic parameters. Based on this conclusion liquidus projection and invariant reaction were calculated without additional experimental tests. © 2020 Elsevier B.V. All rights reserved.
Keywords: Bi-Ni-Zn system Phase diagrams Liquidus projection Experiment tests
1. Introduction Nickel and nickel-based alloys are widely used in different industries [1e4], such as electronic, chemical, automotive, marine etc. Alloys are used for making vessels, pipes, heat exchangers, pumps, impellers, valves [5], alkaline batteries, gas engines and turbines [6], optical mirrors [7,8], equipment for food industry, chemical industry, petrochemical industry, as well as for galvanic coating of steel objects and other type of equipment. Due to the significant applications of alloys it is highly necessary to study Nibased alloys. Up to now a lot of binary alloys were studied but typically applicable alloys consist of more elements, it is therefore necessary to study systems which consist of three, four and more
* Corresponding author.University of Pristina, Faculty of Technical Science, Kneza Milosa 7, 38220, Kos. Mitrovica, Serbia. E-mail address: [email protected] (M. Premovic). https://doi.org/10.1016/j.jallcom.2020.154156 0925-8388/© 2020 Elsevier B.V. All rights reserved.
elements. Ternary systems based on Bi-Ni [9e12] were studied in past but still some of the ternaries were not tested. Chosen system in our study is BieNieZn since there is no study related to it. The focus of this study is on experimental investigation of phase equilibria in a ternary BieNieZn system. The ternary BieNieZn system has not been experimentally investigated before. In the present study, three series of the samples prepared for experimental investigation. The as-cast samples from three vertical sections were investigated using differential thermal analysis (DTA), electrical conductivity and hardness test. The samples annealed at 400 and 700 C were studied by means of scanning electron microscopy (SEM) together with energy dispersive spectrometry (EDS) and X-ray diffraction analysis (XRD) with samples in a powder form. In parallel with that, phase diagrams of the investigated ternary system BieNieZn were calculated by using thermodynamic parameters for the constitutive binary systems reported in literature [13e17]. The calculated results that include phase diagrams of the
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experimentally investigated sections, liquidus projection and invariant reactions were compared with the obtained experimental results and a close mutual agreement was observed.
As a summary based on literature data in the ternary BieNieZn system ten solid phases should appears and one liquid phase. Constructed thermodynamic dataset based on literature [13e17] has been used in our calculation of isothermal sections, vertical sections and liquidus projection.
2. Thermodynamic calculation Calculated phase diagram of constitutive binary systems for ternary BieNieZn system are shown in Fig. 1. Optimized thermodynamic parameters for those binaries are taken from literature [13e17]. Binary BieNi system has been tested by Vassilev et al. [13,14], Dinsdale et al. [15] and thermodynamic data presented in their study are used in our calculation. Fig. 1 a. Presents calculated BieNi phase diagram. Binary phase diagram consists of five phases L, (Ni), (Bi), BiNi and Bi3Ni. The binary BieZn system was calculated by using thermodynamic data given by Malakhov [16]. Calculated phase diagram is presented on Fig. 1 b. Calculated phase diagram consist of three phases Liquid phase (L), solid solutions (Bi) and (Zn). The binary NieZn system was calculated by using thermodynamic data given by Xu et al. [17] and presented on Fig. 1 c). Calculated phase diagram consists of Liquid phase L, and seven solid phases (Ni), b, b1, g, d, NiZn3 and (Zn). Based on the literature information for binary sub-systems crystallographic data for phases in the ternary BieNieZn system are summarized and presented in Table 1 [18e27].
3. Experimental procedure The ternary samples were prepared by using high purity (99.999 atomic%) elements Bi, Ni and Zn produced by Alfa Aesar (Germany). Samples were measured in different molar ration and the total masses of the ternary alloy samples were about 3 g. Weighed masses of the pure metals were arc-melted under a high purity argon atmosphere using a non-consumable tungsten electrode. Obtained samples were re-melted six times in order to improve homogeneity and then slowly cooling to room temperature. The average weight loss of the samples during melting was about 0.5% of the total weight. Such prepared samples were divided into four groups. Samples from first and second group were subjected to the SEM-EDS test. Samples from third group for measurement of mechanical and electrical properties. Samples from fourth group for DTA tests. All samples from 1st, 2nd and 3rd group were firstly tested by XRD. Device for XRD test was D2 PHASER, Bruker, Germany powder diffractometer equipped with a dynamic scintillation detector and
Fig. 1. Calculated binary phase diagrams a) BieNi system [13e15], b) BieZn system [16], and c) NieZn system [17].
M. Premovic et al. / Journal of Alloys and Compounds 825 (2020) 154156
3
Table 1 Considered phase, their crystallographic data and database names for the phases of the ternary BieNieZn systems. Thermodynamic database name
Phase
Pearson symbol
Space group
Lattice parameters (Å) a
LIQUID RHOMBO_A7
Liquid (Bi)
e hR2
e R3m
4.535 (2)
FCC_A1
(Ni)
cF4
3.5243
HCP_ZN BI3NI BINI BCC_B2
(Zn) Bi3Ni BiNi
hP2 oP16 mC64 cP2
Fm3m P63/mmc Pnma F12/m1
NiZnL GAMMA DELTA NiZn3
b b1 g d NiZn3
tP2 cI52 mC50 oA276
ceramic x-ray Cu tube (KFL-Cu-2 K). XRD patterns were recorded in a 2q range from 10 to 75 with a step size of 0.02 and patterns were analysed using the Topas 4.2 software, ICDD databases PDF2 (2013). Samples from 1st and 2nd group were put into quartz glass ampoules, sealed under vacuum and annealed at 400 and 700 C temperatures for six weeks, respectively. After annealing samples were quenched into ice water in order to preserve the equilibrium compositions. Those samples were subjected to the SEM-EDS and XRD test. Used device for SEM-EDS analysis was JEOL JSM-6460 scanning electron microscope with energy dispersive spectroscopy (EDS) (Oxford Instruments X-act). The selected samples for SEMeEDS analysis were firstly ground using sand paper, then polished using diamond paste, and finally cleaned in an ultrasonic bath. The overall compositions of annealed samples were determined by mapping the entire polished surface of the samples. In contrast, the compositions of the observed coexisting phases were determined by examining the surface of the same phase in different parts of the sample. Samples from third group were divided into two parts. One part of the samples were powdered and subjected to the XRD test. Other part were sealed in the polymer, grinded by using sand paper, then polished using diamond paste, and finally cleaned in an ultrasonic bath. Such prepared samples were tested by using Brinell hardness tester and electrical conductivity test. Electrical conductivity measurements were carried out using Foerster SIGMATEST 2.069 eddy instrument. Hardness of the samples was measured using Brinell hardness tester INNOVATEST, model NEXUS 3001 with indenter diameter of 1 mm and the pressing load 98,07 N. Samples from last group were used for phase transition temperature determination which were measured by DTA method. The DTA measurements were performed on a DTG-60H (Shimadzu). Alumina crucibles were used and measurements were performed under flowing argon atmosphere. Samples weighing between 20 and 30 mg were investigated at a heating rate of 5 C/min with three cycles of heating and cooling. The sample masses and heating rates were determined by analysis of one sample at different testing conditions. The temperatures determined in this study were taken from the second and third heating cycles because the temperatures detected were close to each other. The temperatures from the first cycle were omitted due to deviations from the temperatures recorded in the second and third cycles. The phase transition temperatures were determined from the DTA results as described previously [28,29]. The liquidus temperatures were evaluated from the peak maximum and the temperatures of the invariant reactions were determined from the real onset of the corresponding peaks above the melting point. The reference material was empty alumina crucible. The overall uncertainty of the determined phase transformation temperatures was estimated to be ±1 C.
Pm3m P4/mmm I43m C12/m1 Abm2
2.665 8.879 14.124 2.908
b
11.814 (6)
[18]
4.947 11.483 21.429
[20] [21] [22] [23]
3.190
[24] [24,25]
7.65 12.499
[26] [27]
[19] 4.0998 8.1621
2.747 8.941 13.37 33.326
Ref. c
7.47 8.869
4. Results and discussion 4.1. Experimental results of phase equilibria at 400 and 700 C Six ternary samples annealed at 400 C were analysed using SEMeEDS and XRD method. Results of test are summarized in Table 2. By using the EDS analyzer, the compositions of the samples and the compositions of the observed phases were determined. Based on the determined compositions of the phases and the obtained XRD patterns, it was found that sample 1 contains (Ni) and BiNi as co-existing phases. Fig. 2, presents XRD pattern of sample 1. Sample 2 has (Ni), BiNi and b1 as co-existing phases, while sample 3 has Bi3Ni, BiNi and b1 phases. Fig. 3 presents SEM microstructure of sample 3, on which three phases are clearly visible. On microstructure of sample 3, Bi3Ni compound rich with bismuth and appears as a light gray phase, BiNi phase as a gray phase and b1 phase as a dark phase. Samples 4 and 5 have same co-existing phases NiZn3, L and b1, while in sample 6, co-existing phases are L, (Zn) and d. XRD results are obtained by comparing XRD patterns of samples 1 to 6 with literature crystal information files [19e22,24,26]. For the purpose of determining a phase equilibria at 700 C, seven ternary alloy samples were prepared and tested by SEM-EDS and XRD. The results of the SEMeEDS and XRD are summarized in Table 3. Based on the determined compositions of the phases and XRD results, it was found that samples 1 and 2 contains two same phases L and (Ni), sample 3 has (Ni), L and b1 phases, sample 4 has L and b1 phases, samples 5 has phases NiZn3, L and b, sample 6 has L and NiZn3 and sample 7 has L and g co-existing phases. XRD results are obtained by comparing XRD patterns of samples 1 to 7 with literature crystal information files [19,23e25,27]. Fig. 4 presents XRD pattern of sample 1 as one illustration. While Fig. 5 presents SEM microstructure of sample 5, Bi36.07Ni23.73Zn40.20. From Fig. 5, three phases are visible in microstructur b phase as a dark phase, NiZn3 phase as a gray phase and L phase as a light gray phase. 4.2. Experimental results of DTA studied Twelve ternary samples from three different vertical section were used for DTA tests. Composition of tested samples were checked with EDS method. Summary of DTA and EDS results are presented in Table 4. By apperance of peaks on DTA curve temperatures of phase transformation are organized in Table 4 as a ternary reactions, monovariant and Liquidus. On DTA curves sharp peaks are usually
4
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Table 2 EDS and XRD results of the ternary BieNieZn samples annealed at 400 C for six weeks. N.
1
2
3
4
5
6
Composition of samples x (at. %)
16.33 Bi 73.95 Ni 9.72 Zn 17.11 Bi 58.84 Ni 24.05 Zn 34.04 Bi 44.26 Ni 21.70 Zn 28.06 Bi 27.54 Ni 44.40 Zn 48.24 Bi 20.02 Ni 31.74 Zn 23.54 Bi 3.26 Ni 73.20 Zn
Determined phases
Compositions of phases x (at.%)
EDS
XRD
Bi
Ni
Zn
(Ni) BiNi
(Ni) BiNi
1.51 ± 0.01 50.29 ± 0.03
82.65 ± 0.01 49.23 ± 0.02
15.84 ± 0.05 0.48 ± 0.04
(Ni) BiNi b1 Bi3Ni BiNi b1 NiZn3 L b1 NiZn3 L b1 L (Zn)
(Ni) BiNi b1 Bi3Ni BiNi b1 NiZn3 e b1 NiZn3 e b1 e (Zn)
d
d
1.93 ± 0.01 50.30 ± 0.02 0.28 ± 0.07 74.59 ± 0.05 49.41 ± 0.03 0.69 ± 0.01 0.28 ± 0.07 94.34 ± 0.04 0.69 ± 0.03 1.51 ± 0.07 94.34 ± 0.05 0.71 ± 0.01 64.50 ± 0.02 1.31 ± 0.04 0.89 ± 0.05
72.2 ± 0.03 48.67 ± 0.04 53.04 ± 0.05 24.55 ± 0.05 49.70 ± 0.07 51.73 ± 0.02 27.97 ± 0.01 2.51 ± 0.01 48.41 ± 0.05 28.1 ± 0.03 3.25 ± 0.08 46.91 ± 0.02 0.46 ± 0.01 0.73 ± 0.03 9.79 ± 0.03
25.87 ± 0.01 1.03 ± 0.01 46.68 ± 0.02 0.86 ± 0.05 0.89 ± 0.06 47.58 ± 0.07 71.75 ± 0.01 3.15 ± 0.02 50.90 ± 0.03 70.39 ± 0.05 2.41 ± 0.06 52.38 ± 0.04 35.04 ± 0.03 97.96 ± 0.05 89.32 ± 0.08
Fig. 2. XRD pattern of sample 1, Bi16.33Ni73.95Zn9.72.
related to the reaction transformation since during transformation large energy is released. In our study temperatures from sharp peaks are read as a real onset and located in column named ternary reactions. By grouping detected temperatures of ternary invariant reactions, it can be concluded that eight reactions appear in the ternary system. Just by DTA results it is hard to comment which reaction appears. More detail is commented in next part of text by consulting calculated vertical sections. Other peaks on DTA curves are usually broad with small energies and those transformation are related to the transformation in liquid state. Last peak on DTA curve is usually transformation of all phases in liquid state. Above this temperature just one phase exists and it is Liquid phase. In our study last peaks are marked as Liquidus transformation and are related to the transformation of all phases into liquid state. Those temperatures are listed in last column of Table 4. Peaks detected in-between ternary reaction and liquidus are related to the monovariant phase transformation. Some DTA heating curves are presented on Fig. 6. Fig. 6a presents, DTA heating curve of sample Bi20.11Ni39.80Zn40.09. With sample Bi20.11Ni39.80Zn40.09 four phase transformation are recorded. First transformation is recorded at 268.3 C and it should be related to the reaction transformation, while other peaks at 342.8, 753.8 and 953.1 C monovariants and liquid transformation. Fig. 6b) presents, DTA heating curve of sample Bi40.89Ni20.71Zn38.40. By this sample four peaks are recorded, in this case first three peaks at 260.1, 647.3 and 851.9 C are sharp and shoud be related to the reactions temperatures while last peak is brode and last one recorded so it belong to the liquid transfomation. Fig. 6c) presents DTA curve of sample Bi29.17Ni29.48Zn41.35 and four peaks are visible on curve. First two peaks are reaction transformation at temperatures 275.7 and 647.3 C. Last detcted temperature at 947.1 C shoud be liquid temperature while paek at 836.4 C is monovariant transformation.
4.3. Calculation of phase diagrams
Fig. 3. SEM microstructure of sample 3, Bi34.04Ni44.26Zn21.70.
Experimentally obtained results presented in previous part are compared with calculated phase diagrams. Calculation of phase diagrams were performed by using Pandat software and thermodynamic dataset constructed based on binary constitutive systems. Constructed thermodynamic dataset is based on literature information from Refs. [13e17].
M. Premovic et al. / Journal of Alloys and Compounds 825 (2020) 154156
5
Table 3 EDS and XRD results of the ternary BieNieZn samples annealed at 700 C for six weeks. N.
1
2
3
4
5
6
7
Composition of samples x (at. %)
21.68 Bi 71.27 Ni 7.05 Zn 31.15 Bi 51.25 Ni 17.60 Zn 41.86 Bi 37.77 Ni 20.37 Zn 43.01 Bi 30.06 Ni 26.93 Zn 36.07 Bi 23.73 Ni 40.20 Zn 22.71 Bi 19.34 Ni 57.95 Zn 21.89 Bi 12.93 Ni 65.18 Zn
Determined phases
Compositions of phases x (at. %)
EDS
XRD
Bi
Ni
Zn
(Ni) L
(Ni) e
3.36 ± 0.07 80.77 ± 0.01
88.00 ± 0.02 18.32 ± 0.01
8.64 ± 0.04 0.91 ± 0.03
(Ni) L
(Ni) e
1.13 ± 0.02 81.38 ± 0.05
71.58 ± 0.05 16.91 ± 0.07
27.29 ± 0.05 1.71 ± 0.07
(Ni) L b1 L b1
(Ni) e b1 e b1
0.48 ± 0.04 82.21 ± 0.02 0.48 ± 0.03 82.21 ± 0.07 1.31 ± 0.01
66.95 15.57 53.13 11.33 50.31
L NiZn3
e NiZn3
83.03 ± 0.05 0.71 ± 0.02 0.69 ± 0.08 82.61 ± 0.02 0.87 ± 0.01
5.58 ± 0.01 29.22 ± 0.07 43.43 ± 0.04 2.48 ± 0.03 24.74 ± 0.02
11.39 70.07 55.88 14.91 74.39
65.53 ± 0.03 0.92 ± 0.04
1.25 ± 0.01 18.61 ± 0.07
33.22 ± 0.03 80.47 ± 0.07
b
b
L NiZn3
e NiZn3
L
e
g
g
Fig. 4. XRD pattern of sample 1, Bi21.68Ni71.27Zn7.05.
Fig. 5. SEM microstructure of sample 5, Bi36.07Ni23.73Zn40.20.
± ± ± ± ±
0.03 0.08 0.01 0.05 0.02
32.57 ± 0.06 2.22 ± 0.03 46.39 ± 0.01 6.46 ± 0.07 48.38 ± 0.05 ± ± ± ± ±
0.02 0.08 0.03 0.01 0.04
EDS results givin in Tables 2 and 3 are compared with caluclated isothermal sections at 400 and 700 C. Fig. 7 presents comparison of the calculated isothermal section at 400 C and the EDS results in Table 2. The obtained experimental results are marked with the same symbol but in different color. Different color is used in order to make a distinction between the EDS composition of different samples. Calculated isothermal section consists of 16 different phase regions. From those 16 regions two are single phase region, L and (Ni) phase regions, seven are two-phase regions and seven three-phase regions. From 16 predicted phase regions five are experimentally confirmed, four three-phase regions and one two-phase region. Composition of sample 1 is located in the (Ni)þBiNi two-phase region, sample 2 in (Ni)þBiNiþb1 three-phase region, sample 3 in Bi3Ni þ BiNiþb1 three-phase region, sample 4 and 5 in NiZn3þLþb1 three-phase region and sample 6 in Lþ(Zn)þd threephase region. By comparing compositions of the detected phases for sample 1 to 6 determined by EDS and the related calculated phase compositions it can be noticed that they are in a fairly close agreement. In generall it can be also said that a close overall agreement between the results of calculations and the experiments was obtained. The EDS results given in Table 3 are compared with the calculated isothermal section at 700 C. Fig. 8, presents comparison of the calculated phase diagram and the EDS results. Calculated isothermal section at 700 C, consists of sixteen phase regions. Calculated phase regions are: three single phase regions, L rich with bismuth, L phase rich with zinc and (Ni) solid solution, eight two phase regions ((Ni)þL, (Ni)þb1, Lþb1, Lþb, L þ NiZn3, Lþg, L’þL00 and Lþg) and five three-phase regions ((Ni)þ Lþb1, b1þLþb, L þ NiZn3þb, L þ NiZn3þg and L’þgþL”). Six of sixteen calculated phase regions are experimentally confirmed. From which four are two-phase regions (Ni)þL (samples 1 and 2), Lþb1 (sample 4), L þ NiZn3 (sample 6) and Lþg (sample 7) and two are three phase regions (Ni)þLþb1 (samples 3) and L þ NiZn3þb (sample 5) were experimentally verified. Comparison of EDS results given in Table 3 and calculated isothermal section at 700 C show a very good overall agreement. Experimentally determined composition of phases agree well with calculated composition of phases. In general for both isothermal studies EDS experimental results
6
M. Premovic et al. / Journal of Alloys and Compounds 825 (2020) 154156
Table 4 Phase transition temperatures of the studied alloys from the ternary BieNieZn system determined by DTA at pressure p ¼ 0.1 MPa. Temperatures of phase transformation (oC)a
Composition (at.%) nominal Vertical section BieNi50Zn50 Bi20Ni40Zn40 Bi40Ni30Zn30 Bi60Ni20Zn20 Bi80Ni10Zn10 Vertical section NieBi50Zn50 Bi40Ni20Zn40 Bi30Ni40Zn30 Bi20Ni60Zn20 Bi10Ni80Zn10 Vertical section ZneBi50Ni50 Bi40Ni40Zn20 Bi30Ni30Zn40 Bi20Ni20Zn60 Bi10Ni10Zn80 a
EDS
Ternary reactions
monovariant
Liquidus
Bi20.11Ni39.80Zn40.09 Bi38.78Ni30.18Zn31.04 Bi61.07Ni20.56Zn18.37 Bi79.52Ni10.03Zn10.45
268.3 274.8 271.8 273.1
342.8/753.8 322.1/726.1 722.1 711.9
953.1 943.8 907.3
Bi40.89Ni20.71Zn38.40 Bi29.76Ni39.61Zn30.63 Bi19.18Ni59.73Zn21.09 Bi9.13Ni79.15Zn11.72
260.1/647.3/851.9 265.1/463.1/806.3 498.3
970.8
Bi41.08Ni39.81Zn19.11 Bi29.17Ni29.48Zn41.35 Bi19.81Ni20.52Zn59.67 Bi11.01Ni9.13Zn79.86
453.1/485.7/794.1 275.7/647.3 277.4 249.1/493.3
919.7
591.8
836.4
1218.3 1315.7 1054.3 947.1 863.1 812.4
Temperatures in table are organized by consulting calculated vertical sections.
Fig. 6. DTA curves of some samples.
did not detected significant solubility than is expected and also ternary compounds are not detected. As a next step, temperature of phase transformations summarized in Table 4 are compared with calculated vertical sectiions and presented in Fig. 9. As can be seen in Fig. 9, good overall agreement between the calculated vertical sections and the DTA results was achieved. By comparing the calculated and the experimentally determined temperatures, it is clear that the highest detected temperatures correspond to the liquidus temperatures. Calculated vertical section BieNiZn is slightly simpler in comparison with calculated NieBiZn and ZneBiNi vertical sections. From Fig. 9a, it is clear that first detected peak at all samples is related to the ternary eutectic reaction L/b1þBi3Niþ(Bi). Calculated temperature of ternary eutectic reaction is 269.06 C while experimental value are in range from 265.1 to the 274.8 C. Other detected temperatures are relatet to the monovariant phase transformation while last peaks are related to the liquidus temperature.
Fig. 9b, presents NieBiZn vertical section compared with DTA results. By DTA results of sample Bi40.89Ni20.71Zn38.40 temperature of three invariant reaction were detected, L þ NiZn3/b1þ(Bi) (calculated at 269.09 C), Lþb/NiZn3þb1 (calculated at 641.38 C) and L’/L”þNiZn3þb (calculated at 842.38 C). The experimentally determined temperatures are 260.1, 647.3 and 851.9, respectively which are close to the calculated one. With sample Bi29.76Ni39.61Zn30.63 temperatures of L/b1þBi3Niþ(Bi) (calculated at 269.06 C), L þ BiNi/b1þBi3Ni (calculated at 464.06 C) and bþ(Ni)/Lþb1 (calculated at 804.50 C) invariant reactions are detected. Detected temperatures are 265.1, 463.1 and 806.3 respectively. First detected peak on sample Bi19.18Ni59.73Zn21.09 is realted to the invariant reaction Lþ(Ni)/ b1þBiNi at temperature 498.3 C while calculated temperature is 492.29 C. Second detected temperature on same samples is realted to the liquidus temperature. Two peaks are detected with sample Bi9.13Ni79.15Zn11.72 where first is monovariant phase transformation and second is liquidus temperature. Fig. 9c, presents ZneBiNi vertical section compared with DTA
M. Premovic et al. / Journal of Alloys and Compounds 825 (2020) 154156
7
Fig. 7. Calculated isothermal section at 400 C compared with EDS results given in Table 2.
Fig. 8. Calculated isothermal section at 700 C compared with EDS results given in Table 3.
results. Sample Bi41.08Ni39.81Zn19.11 (Table 4), detected four temperature, by comparison it can be concluded that firts temperature at 453.1 C is related to the L þ BiNi/b1þBi3Ni ternary reaction which is calculated at 464.06 C. Second recorded temperature at 485.7 C is related to the Lþ(Ni)/b1þBiNi reaction (calculated at 492.29 C). Reaction bþ(Ni)/Lþb1 (calculated at 804.50 C) is determined with same sample at 794.1 C while peak at 1054.3 C is liquidus temperature. Sample Bi29.17Ni29.48Zn41.35 recorded four transformations. First is at 275.7 C and it is related to the L þ NiZn3/b1þ(Bi) reaction (calculated at 269.09 C), second detected transformation at 647.3 C is related to the Lþb/NiZn3þb1 reaction (calculated at 641.38 C) and other two experimental temperatures are monovarian and liquidus transformation, respectively. Reaction L þ NiZn3/(Bi)þg (calculated at 268.53 C) is detected with sample Bi19.81Ni20.52Zn59.67 to be 277.4 C (first detected temperature) while second peak is liquidus
temperature. Last tested sample from ZneBiNi vertical section is Bi11.01Ni9.13Zn79.86. With this sample two reactions are confirmed (Bi)þg/Lþd (calculated at 260.72 C) and L’þg/L”þd (calculated at 485.22 C), at temperatures 249.1 and 493.3 C, respectively. In general, it can be said that the experimentally determined temperatures of phase transformations support the results of the calculations quite well. Based on the presented results, it can be safely assumed that it is not necessary to introduce new parameters to describe the ternary BieNieZn system. Therefore, the applied thermodynamic dataset was further used for the calculation of a liquidus projection and invariant reactions. Fig. 10, presents prediction of liquidus projection of the ternary BieNieZn system, with magnified bismuth and zinc rich part. Predicted liquidus projection has ten fields of primary crystallization and field of miscibility gap. Twelve invariant reactions were
8
M. Premovic et al. / Journal of Alloys and Compounds 825 (2020) 154156
Fig. 9. Calculated vertical sections of the ternary BieNieZn system compared with DTA experimental results: a) BieNiZn, b) NieBiZn and c) ZneBiNi.
Fig. 10. Prediction of liquidus projection of the ternary BieNieZn system with. Magnified Bi and Zn rich part.
predicted and details are given in Table 5. Three reactions are E-type (eutectic) and nine are U-type (univariant) reactions. E1 reaction L’/L”þNiZn3þb and E2 reaction L’/(Zn)þL”þd are monotectic reaction, while E3 reaction
L/b1þBi3Niþ(Bi) is ternary eutectic reaction. U2 and U9 reactions are solid transition reactions, and all others are liquid transition reactions. Eight of twelve predicted invariant reactions are experimentally confirmed.
M. Premovic et al. / Journal of Alloys and Compounds 825 (2020) 154156
9
Table 5 Predicted invariant reaction of the ternary BieNieZn system. T (ºC) Reactions
Typea
Phase
0
843.49 L’þNiZn3/L”þg
U1
L NiZn3 L00
842.38 L’/L”þNiZn3þb
E1
L0 L00 NiZn3
804.50 bþ(Ni)/Lþb1
U2
641.38 Lþb/NiZn3þb1
U3
Composition of reaction in mole fraction Bi
Ni
Zn
0.080793
0.179583
0.739624
0.092703
0.280723
0.626574
0.747760
0.182174
0.070066
0.864691
0.053503
0.081806
0.858813
0.137497
0.003690
0.015942
0.010758
0.973300
0.873735
0.123334
0.002931
0.007396
0.002386
0.990219
0.989336
0.006521
0.004143
0.989255
0.006738
0.004007
0.986164
0.000147
0.013689
0.950883
8.064510E-008
0.049117
g
b В (Ni) L b1 L
b
492.29 Lþ(Ni)/b1þBiNi
U4
485.22 L’þg/L”þd
U5
464.06 L þ BiNi/b1þBi3Ni
U6
416.93 L’/(Zn)þL”þd
E2
269.09 L þ NiZn3/b1þ(Bi)
U7
269.06 L/b1þBi3Niþ(Bi)
E3
268.53 L þ NiZn3/(Bi)þg 260.72 (Bi)þg/Lþd
U8
NiZn3 b1 L (Ni) b1 BiNi L0
g L00
d L BiNi b1 Bi3Ni L’ (Zn) L00
d L NiZn3 b1 (Bi) L b1 Bi3Ni (Bi) L NiZn3 (Bi)
g U9
(Bi)
g L
d a
U-univariant reaction, E-eutectic reaction, number from 1 to 9 depend on temperature decrease.
As a next step, hardness and electrical properties were measured on nineteen as-cast ternary alloys samples and three binary samples. Based on obtained experimental results mathematical model for calculation of those properties along all composition range is proposed. Development of mathematical model is utilized in software Desig Expert v.9.0.3.1. Hardness of alloys were tested by Brinell method in three point. Results of hardenss tests are given in Table 6 [30,31], together with alloy composition and calculated fraction of a phases. According to the results given in Table 6, Brinell hardness is strongly dependent on alloys compositions and fraction of the phases. Samples marked with numbers from 1 to 5, have same three phases in microstructure Bi3Niþb1þ(Bi), fraction of those three phases changes with compositions of alloys. In samples from number 1 to 5 wt of bismuth increases and relation of phase fractions of Bi3Ni, b1 and (Bi) phase changes according with bismuth increasement. Fraction of (Bi) phase increase with bismuth increasement according to this change hardness of alloys increase. Samples from number 6 to 11, have increasement of nickel weight and those alloys lie along NieBiZn vertical section. According to the calculated phase fraction each of alloys belongs to different phase region, six phase regions, from which three are three-phase and three are two-phase regions. It can be noticed that hardness of
alloys increases as content of nick increase in alloys. Drastic increasement in hardness is detected in Bi12.5Ni75Zn12.5 alloy (sample 11) since in this alloy (Ni) phase is detected in fraction of 75.1% and BiNi 24.9% and both of the phases have a high hardness. Samples from number 12 to 17 lie along ZneBiNi vertical section and content of the zinc increase in those alloys from 12 to 17, respectively. In alloys 12 and 13 same three phases appears, but in different ration. In sample 12 there is more BiNi phase then in sample 13. This results that hardness of alloy 12 is higher than alloy 13. For samples 14 to 17, content of zinc increase and phase regions changes from samples. Those changes of sample compositions result in hardness increasement. Fig. 6, presents graphical presentation of hardness depending on alloy composition. In Fig. 11 calculated phase regions are marked. From Fig. 11a it can be concluded that in alloys from vertical section BieNiZn, all alloys have same three phases in equilibrium and hardness increase with bismuth content. Fig. 11b shows hardness of alloys from vertical section NieBiZn, and increasement in hardness is noticed with increasement of nickel. Fig. 11c, is for alloys from Zn vertical section. Hardness of alloys from number 12 to 17, is changing with content of zinc. Firstly hardness decrease and then increase with content of zinc. In general can be concluded that ternary alloys which are rich
10
M. Premovic et al. / Journal of Alloys and Compounds 825 (2020) 154156
Table 6 Compositions of the investigated samples with calculated phase fractions at room temperature and related Brinell hardness values. N.
B1 1 2 3 4 5 Bi B2 6 7 8 9 10 11 Ni B3 12 13 14 15 16 17 Zn
Alloy nominal composition (at.%) Bi
Ni
Zn
0 0.05 0.2 0.4 0.6 0.8 1 0.5 0.45 0.4 0.325 0.25 0.2 0.125
0.5 0.475 0.4 0.3 0.2 0.1
0.5 0.475 0.4 0.3 0.2 0.1
0 0.1 0.2 0.35 0.5 0.6 0.75 1 0.5 0.45 0.4 0.35 0.275 0.175 0.05
0.5 0.45 0.4 0.325 0.25 0.2 0.125
0.5 0.45 0.4 0.35 0.275 0.175 0.05
0 0.1 0.2 0.3 0.45 0.65 0.9 1
Calculated fraction of a phase (%)
100% b1 4.8% (Bi), 0.3%Bi3Ni, 94.9% b1 19.8% (Bi), 0.3% Bi3Ni, 79.9% b1 39.9% (Bi), 0.2% Bi3Ni, 59.9% b1 59.9% (Bi), 0.1% Bi3Ni, 40.0% b1 80.0% (Bi), 0.1% Bi3Ni, 19.9% b1 100.0% (Bi) 50.1% (Bi), 49.9% (Zn) 45.0% (Bi), 55.0% g 40.0% (Bi), 49.0% NiZn3, 11.0% b1 24.9% (Bi), 10.2% Bi3Ni, 64.9% b1 50.2% b1, 49.8% BiNi 31.6% (Ni), 28.5% b1, 39.9% BiNi 75.1% (Ni), 24.9% BiNi 100% (Ni) 99.9% BiNi, 0.1% (Ni) 19.6% Bi3Ni, 20.1% b1, 60.3% BiNi 40.1% Bi3Ni, 40.1% b1, 19.8% BiNi 19.9% (Bi), 20.2% Bi3Ni, 59.9% b1 27.5% (Bi), 42.8% NiZn3, 29.7% b1 17.5% (Bi), 5.7% g, 76.8% NiZn3 5.0% (Bi), 45.0% d, 50% (Zn) 100% (Zn)
Measured value (MN/m2)
Mean value (MN/m2)
1
2
3
14.9 28.7 32.1 45.3 62.8 73.1
15.2 29.1 35.7 47.1 61.3 71.8
16.6 25.6 37.1 47.1 64.3 74.5
61.6 23.2 52.6 53.3 75.9 94.2 150.3
62.4 27.0 54.5 59.3 77.3 89.3 155.1
61.8 25.3 47.4 56.4 69.8 96.1 147.8
150.8 81.8 61.5 65.5 72.4 93.1 139.7
147.1 87.5 51.2 62.3 69.6 92.8 135.9
148.9 83.9 55.5 65.8 77.0 90.7 141.7
15.5 27.8 34.9 46.5 62.8 73.0 94.2 61.9 25.2 51.5 56.3 74.3 93.2 151.1 700 148.9 84.4 56.1 64.5 73.0 92.2 139.1 412
ref
[30] [31]
[30]
[30]
Fig. 11. Graphical presentation of Brinell hardness dependence of composition and phase fraction: a) vertical section BieNiZn, b) vertical section NieBiZn and c) vertical section ZneBiNi.
M. Premovic et al. / Journal of Alloys and Compounds 825 (2020) 154156
with Ni have high hardness. This is especially related to the alloy sample 11, where (Ni) solid solution appear in content of 75.1%. Based on experimental hardness value, appropriated mathematical model has been developed in way to predict hardness of ternary alloys over all ternary composition range. By utilizing experimentally determined values of hardness given in Table 6 and software Desig Expert v.9.0.3.1 mathematical model of the dependence of the Brinell hardness on composition for the BieNieZn alloys was developed. Out of a possible canonical or Scheffe model [32e34] that meet the requirements of adequacy is recommended Special Cubic Mixture model:
Table 8 R-squared and other statistics after the ANOVA. Std. Dev.
1.2972
R-Squared
0.9453
Mean C.V. % PRESS
9.4304 13.7559 102.3201
Adj R-Squared Pred R-Squared Adeq Precision
0.9270 0.8151 31.4695
Table 9 Estimation of parameters for Special Cubic Mixture model of Brinell hardness in ternary BieNieZn system. Component
Coefficient Estimate
df
Standard Error
95% CI Low
95% CI High
A-Bi BeNi CeZn AB AC BC ABC
10.16078 25.57761 19.01072 26.57603 31.03244 73.27272 91.66989
1 1 1 1 1 1 1
1.15144 1.19263 1.03875 5.52956 5.41095 5.37188 30.46797
7.74171 23.07198 16.82839 38.19322 42.40041 84.55863 27.65907
12.57986 28.08323 21.19305 14.95885 19.66446 61.98681 155.68071
y ¼ b1 X1 þ b2 X2 þ b3 X3 þ b12 X1 X2 þ b13 X1 X3 þ b23 X2 X3 þ b123 X1 X2 X3
(1)
The Analysis of variance (ANOVA) implies that the model is significant. However, the diagnosis of the statistical properties of the assumed model found that the distribution of residuals is not normal and that it is necessary to transform the mathematical model in order to meet the conditions of normality. Similar adjustment of mathematical model are introduced in study of ternary Bi-Ge-Sb, Al-Cu-Sb [35] and AleAg-Ga [36] systems. The Box-Cox diagnostics [37,38] recommends the „Square Root“ transformation for the variance stabilization. In this case, ANOVA confirms the adequacy of the Model (Table 7). The F-value of the Model is 51.80 and it implies that the model is significant. In this case, all model terms are significant. R-squared and other statistics after the ANOVA have appropriate values which confirm the justification of the choice of the adopted mathematical model (Table 8). The “Pred R-Squared” of 0.8151 is in reasonable agreement with the “Adj R-Squared” of 0.9270 i.e. the difference is less than 0.2. “Adeq Precision” measures the signal to noise ratio. A ratio of 31.4695 is greater than 4 and indicates an adequate signal. Estimation of individual regression coefficients, Standard error and 95% confidence interval are shown in Table 9. The final equation of the predictive model in Terms of Actual Components is: Sqrt(HB) ¼ 10.16078(Bi)þ25.57761(Ni)þ19.01072(Zn)26.57603(Bi)x(Ni)-31.03244(Bi)x(Zn)-73.27272(Ni)x(Zn)þ 91.66989(Bi)x(Ni)x(Zn) (2) The diagnosis of the statistical properties of the assumed model found that the distribution of residuals are normal. After the applied Box-Cox procedure, the value of l is 0.50, the optimum value of l is 0.27 and the 95% confidence interval for l (Low C.I. ¼ 0.01, High C.I. ¼ 0.55) contains the value 0.50. Iso-lines contour plot for Brinell hardness of alloys defined by equation (2) is shown in Fig. 12. On same alloys as for hardness measurement, electrical conductivity was mesured. Electrical conductivity were mesured in
11
Fig. 12. Calculated iso-lines of Brinell hardness in ternary BieNieZn system with R2 ¼ 0.9453.
four point in one sample and results of tests are given in Table 10. In table are also given composition on samples, calculated fractions of phases and mean value of electrical conductivity [31,39]. Mean value of electrical conductivity of samples from 1 to 5, decries with increasement of bismuth content. Those results are also connected with changes of (Bi), Bi3Ni and b1 phase fractions in
Table 7 ANOVA for Special Cubic Mixture model. Source
Sum of Squares
df
Mean Square
F Value
p-value Prob > F
Model Linear Mixture AB AC BC ABC Residual Cor Total
523.018 82.886 38.872 55.350 313.088 15.234 30.291 553.309
6 2 1 1 1 1 18 24
87.1697 41.4429 38.8717 55.3504 313.0881 15.2336 1.6828
51.8000 24.6272 23.0993 32.8916 186.0507 9.0525
2.19559E-10 7.04638E-06 0.000141479 1.94744E-05 6.25258E-11 0.007540847
significant
12
M. Premovic et al. / Journal of Alloys and Compounds 825 (2020) 154156
Table 10 Compositions of the investigated samples with calculated phase fractions at room temperature and related electrical conductivity values. N.
B1 1 2 3 4 5 Bi B2 6 7 8 9 10 11 Ni B3 12 13 14 15 16 17 Zn
Alloy nominal composition (at.%) Bi
Ni
Zn
0 0.05 0.2 0.4 0.6 0.8 1 0.5 0.45 0.4 0.325 0.25 0.2 0.125
0.5 0.475 0.4 0.3 0.2 0.1
0.5 0.475 0.4 0.3 0.2 0.1
0 0.1 0.2 0.35 0.5 0.6 0.75 1 .5 0.45 0.4 0.35 0.275 0.175 0.05
0.5 0.45 0.4 0.325 0.25 0.2 0.125
0.5 0.45 0.4 0.35 0.275 0.175 0.05
0 0.1 0.2 0.3 0.45 0.65 0.9 1
Calculated fraction of a phase (%)
100% b1 4.8% (Bi), 0.3%Bi3Ni, 94.9% b1 19.8% (Bi), 0.3% Bi3Ni, 79.9% b1 39.9% (Bi), 0.2% Bi3Ni, 59.9% b1 59.9% (Bi), 0.1% Bi3Ni, 40.0% b1 80.0% (Bi), 0.1% Bi3Ni, 19.9% b1 100.0% (Bi) 50.1% (Bi), 49.9% (Zn) 45.0% (Bi), 55.0% g 40.0% (Bi), 49.0% NiZn3, 11.0% b1 24.9% (Bi), 10.2% Bi3Ni, 64.9% b1 50.2% b1, 49.8% BiNi 31.6% (Ni), 28.5% b1, 39.9% BiNi 75.1% (Ni), 24.9% BiNi 100% (Ni) 99.9% BiNi, 0.1% (Ni) 19.6% Bi3Ni, 20.1% b1, 60.3% BiNi 40.1% Bi3Ni, 40.1% b1, 19.8% BiNi 19.9% (Bi), 20.2% Bi3Ni, 59.9% b1 27.5% (Bi), 42.8% NiZn3, 29.7% b1 17.5% (Bi), 5.7% g, 76.8% NiZn3 5.0% (Bi) 45.0% d, 50% (Zn) 100% (Zn)
alloys. Electrical conductivity for alloys from NieBiZn vertical section, have trends to increases with nickel content until 0.35 mol of nickel, then decrease with 0.5 mol of nickel and again increase. This small drop of electrical conductivity can be related to the content of b1 and BiNi phases in sample. Similar trend can be noticed for electrical conductivity of ternary alloys from ZneBiNi vertical section. So electrical conductivity increases until 0.3 mol of zinc and then in alloy with 0.45 mol of zinc decries to 0.8705 MS/m, and after sample 15, electrical conductivity drastically increases. Decries of electrical conductivity of sample 15, can be explained by high content of (Bi) phase and occurrence of NiZn3 phase, similar electrical conductivity is detected with sample 7, which have same three phases in equilibrium as sample 15. As a next step mean value of electrical conductivity depending on sample composition, together with calculated phases are given on Fig. 13. By using experimental value of electrical conductivity appropriated mathematical model has been proposed for calculation of electrical conductivity along all composition range for ternary alloys. The Model summary statistics are suggested a Quadratic Mixture model for the dependence of the electrical conductivity on the composition for the BieNieZn alloys
y ¼ b1 X1 þ b2 X2 þ b3 X3 þ b12 X1 X2 þ b13 X1 X3 þ b23 X2 X3
(3)
The Analysis of variance (ANOVA) implies that the model is significant. However, the diagnosis of the statistical properties of the assumed model found that the distribution of residuals is not normal and that it is necessary to transform the mathematical model in order to meet the conditions of normality. The Box-Cox diagnostics [37,38] recommends the „Square Root” transformation for the variance stabilization.The Model summary statistics for „Square Root“ model transformation are suggested Quadratic Mixture model. In this case, ANOVA confirms the adequacy of the Model. High F value of model (F ¼ 47.74) and low value of probability (p < 0.0001) indicate that the model is significant (Table 11). The coefficient of determination (R-Squared ¼ 0.926) and others statistic of models have a satisfactory value, which confirms the
Measured value (MS/m)
Mean value (MS/m)
1
2
3
4
2.9083 2.1800 1.9038 1.5981 1.2381 0.8561
2.9089 2.1875 1.9078 1.5920 1.2398 0.8426
2.9090 2.1809 1.9076 1.5923 1.2365 0.8389
2.9069 2.1890 1.9067 1.5909 1.2389 0.7919
1.956 0.7982 0.8654 1.8365 1.5902 2.4751 4.9080
1.864 0.7998 0.8646 1.8398 1.5909 2.4719 4.9087
1.902 0.7952 0.8633 1.8322 1.5902 2.4728 4.9028
e 0.8005 0.8644 1.8398 1.5971 2.4789 4.9078
2.1090 0.9325 1.2890 1.7898 0.8669 4.9310 7.0918
2.1078 0.9342 1.2890 1.7809 0.8666 4.9309 7.0976
2.1098 0.9147 1.2867 1.7894 0.8707 4.9320 7.0971
2.1068 0.9228 1.2867 1.7856 0.8780 4.9318 7.0987
2.9082 2.1843 1.9064 1.5933 1.2383 0.8324 0.77 1.907 0.7984 0.8644 1.8371 1.5921 2.4747 4.9068 14.0 2.1083 0.9260 1.2878 1.7864 0.8705 4.9314 7.0963 17.0
ref
[39] [31]
[39]
[39]
validity of the adopted mathematical model (Table 12). The “Pred RSquared” of 0.8451 is in reasonable agreement with the “Adj RSquared” of 0.9069 i.e. the difference is less than 0.2. “Adeq Precision” measures the signal to noise ratio. A ratio of 23.66 is greater than 4 and indicates an adequate signal. Estimation of individual regression coefficients, Standard error and 95% confidence interval are shown in Table 13. The final equation of the predictive model in Terms of Actual Components is: Sqrt(s) ¼ 0.96214(Bi)þ3.66805(Ni)þ3.81946(Zn)3.47829(Bi)x(Ni)-4.3371(Bi)x(Zn)-7.97561(Ni)x(Zn)
(4)
After transformation of the model, the response variance is stabilized, the distribution of the response variable is closer to the normal distribution, and the fit of the model to the data is improved. After the applied Box-Cox procedure, the value of l is 0.50, the optimum value of l is 0.19 and the 95% confidence interval for l (Low C.I. ¼ -0.26, High C.I. ¼ 0.53) contains the value 0.50, so the use of a „Square Root“ transformation is indicated. Iso-lines contour plot for Electrical conductivity of alloys defined by equation (4) is shown in Fig. 14. In general proposed mathematical models are significant for prediction of those two properties along all composition range. Improvement of models is necessary by including experiment of properties at different temperatures which will lead to proposed more general model for calculation of properties allong all composition and temperature ranges. But proposed mathematical model in this study are starting point and necessary for future development of model since up to this paper there is no similar studies related to the BieNieZn system. 5. Conclusion Alloys from ternary BieNieZn system are experimentally and analytically tested for the first time. Experimental results of DTA test were compared with calculated vertical sections. By DTA test temperature of eight invariant reactions have been determined,
M. Premovic et al. / Journal of Alloys and Compounds 825 (2020) 154156
13
Fig. 13. Graphical presentation of electrical conductivity dependence of composition and phase fraction: a) vertical section BieNiZn, b) vertical section NieBiZn and, c) vertical section ZneBiNi.
Table 11 ANOVA for Quadratic Mixture model. Source
Sum of Squares
df
Mean Square
F Value
p-value Prob > F
Model Linear Mixture AB AC BC Residual Cor Total
16.0551 7.7379 0.9885 1.6164 5.1105 1.2778 17.3329
5 2 1 1 1 19 24
3.2110 3.8689 0.9885 1.6164 5.1105 0.0673
47.7438 57.5264 14.6973 24.0346 75.9868
4.17338E-10 8.69033E-09 0.001120171 9.88751E-05 4.57756E-08
Table 12 R-squared and other statistics after the ANOVA. Std. Dev.
0.2593
R-Squared
0.9263
Mean C.V. % PRESS
1.5544 16.6840 2.6845
Adj R-Squared Pred R-Squared Adeq Precision
0.9069 0.8451 23.6602
temperatures of other phase transformation and liquidus temperature. Comparison of DTA results and calculated vertical section shows good agreement between calculated and experimentally determined temperatures of phase transformation. Furder annealed alloys at 400 and 700 C were prepared in way to
significant
Table 13 Estimation of parameters for Quadratic Mixture model of Electrical conductivity in ternary BieNieZn system. Component
Coefficient Estimate
df
Standard Error
95% CI Low
95% CI High
A-Bi BeNi CeZn AB AC BC
0.9621 3.6680 3.8195 3.4783 4.3371 7.9756
1 1 1 1 1 1
0.2267 0.2359 0.2045 0.9073 0.8847 0.9149
0.4876 3.1743 3.3913 5.3773 6.1887 9.8906
1.4367 4.1618 4.2476 1.5793 2.4855 6.0606
14
M. Premovic et al. / Journal of Alloys and Compounds 825 (2020) 154156
Fig. 14. Calculated iso-lines of Electrical conductivity in ternary BieNieZn system with R2 ¼ 0.9263.
determined isothermal sections at chosen temperatures. Existence of the phase were detected with XRD test and composition of detected phases have been determined with EDS test. EDS tests did not detected new compound or even large solubility of third element into intermetallic compounds r solid solution. According to this results it can be concluded that it is not necessary to introduce new thermodynamic parameters for description of the phase diagrams of the ternary BieNieZn system. Based on this conclusion liquidus projection were predicted and twelve invariant reaction were predicted from which eight are experimentally confirmed by DTA test. Experimentally detected temperatures of invariant reaction are in close agreement with calculated temperatures. In next step Brinell hardness and electrical conductivity have been mesured on seventeen ternary samples. Properties of ternary alloys are conected with microstructural changes. Phase presented in microstructure of samples were determined with XRD. Furder by using experimental results of hardness and electrical conductivity one mathematical model has been proposed in way to predict those properties along all ternary composition range. Declaration of competing interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This work has been supported by the National Natural Science Foundation of China of China (project No. 414010049) and the Ministry of Education, Science and Technological Development of the Republic of Serbia (Grant No. OI172037). References [1] S. Semboshi, S. Sato, A. Iwase, T. Takasugi, Discontinuous precipitates in agehardening Cu-Ni-Si alloys, Mater. Char. 115 (2016) 39e45, https://doi.org/ 10.1016/j.matchar.2016.03.017. [2] J. Lei, H. Xie, S. Tao, R. Zhang, Z. Lu, Microstructure and selection of grain boundary phase of Cu-Ni-Si ternary alloys, Rare Met. Mater. Eng. 44 (12) (2015) 3050e3054, https://doi.org/10.1016/S1875-5372(16)60049-8.
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