Mechanical (Brinell hardness test) and electrical properties of some selected ternary Ag-Ge-In alloys have been investigated in this study. By using obtained results for properties and ANOVA analysis it is suggested mathematical model for calculation properties for every composition of alloys. Microstructures of alloys have been carried out by using optical microscopy and scanning electron microscopy (SEM). Phases presented in microstructures have been detected by x-ray diffraction (XRD) analysis and compositions by energy dispersive spectrometry (EDS). Experimentally determined results are compared with calculated data. Calculation of isothermal section at 25 °C was carried out by using optimized thermodynamic parameters for the constitutive binary systems. Good overall agreement between experimental and calculated values was obtained.
Alloying presents an important and a time consuming task for researchers all over word. Since the properties of materials can be change by adding other elements it is encouraging to study different alloys in way to get alloys with good properties. In our group we are focusing on Ge alloys and their properties (Premovic
All ternary and three binary samples with total masses of about 3 g were prepared from high purity (99.999 at.%) Ag, Ge, and In produced by Alfa Aesar (Germany). Samples were melted in an induction furnace under high-purity argon atmosphere and slowly cooled to the room temperature. The average weight loss of the samples during induction melting was about 0.5 mass%. Such prepared samples are subjected to all experimental tests.
The compositions of samples and coexisting phases were determined by using JEOL JSM-6460 scanning electron microscope with energy dispersive spectroscopy (EDS) (Oxford Instruments X-act). Powder XRD data for phase identification of samples were recorded on a D2 PHASER (Bruker, Karlsruhe, Germany) powder diffractometer equipped with a dynamic scintillation detector and ceramic X-ray Cu tube (KFL-Cu-2K) in a 2θ range from 10° to 75° with a step size of 0.02°. The patterns were analyzed using the Topas 4.2 software, ICDD databases PDF2. Hardnesses of the samples were measured using Brinell hardness tester INNOVATEST, model NEXUS 3001. Electrical conductivity measurements were carried out using Foerster SIGMATEST 2.069 eddy current instrument.
The isothermal section at 25 °C of the Ag-Ge-In ternary system has been thermodynamically predicted using optimized thermodynamic parameters for the constitutive binary systems. Optimized thermodynamic parameters are used from Wang
Crystal structure data for the solid phases of the Ag-Ge-In system
Thermodynamic database name | Phase | Pearson symbol | Space group | Lattice parameters (Å) |
Ref. | |
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FCC_A1 | (Ag) | 4.0861 | Jette and Foote ( |
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DIAMOND_A4 | (Ge) | 5.65675 | Cooper ( |
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TETRAG_A6 | (In) | 3.2523 | 4.9461 | Ridley ( |
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BCC_A2 | β(Ag_{3}In) | 4.144(4) | Campbell |
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HCP_A3 | ζ(Ag_{3}In) | 2.961(2) | 4.778(4) | Campbell |
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CUIN_GAMMA | γ(Ag_{2}In) | 9.887(4) | Campbell |
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AGIN2 | AgIn_{2} | 6.881(4) | 5.620(4) | Havinga |
Predicted isothermal section of the ternary Ag-Ge-In system at 25 °C with marked compositions of the studied samples.
Compositions of the selected alloy samples lie along three vertical sections red squares Ag-Ge_{50}In_{50}, orange squares Ge-Ag_{50}In_{50} and violet squares In-Ag_{50}Ge_{50}. Eight different phase regions are calculated at isothermal section at 25 °C. Four are two-phase regions (Ge)+AgIn_{2}, (Ge)+γ(Ag_{2}In), (Ge)+ζ(Ag_{3}In) and (Ge)+(Ag) and another four are three-phase regions (Ge)+AgIn_{2}+(In), (Ge)+AgIn_{2}+γ(Ag_{2}In), (Ge)+ζ(Ag_{3}In)+γ(Ag_{2}In), and (Ge)+ζ(Ag_{3}In)+(Ag). From eight predicted phase regions four are experimentally confirmed by EDS and XRD analyses.
EDS and XRD results confirmed existence of same phases. In microstructures of samples 3, 9, and 13 three phases (Ge), AgIn_{2} and γ(Ag_{2}In) are detected. According to the calculated phase diagram
SEM micrographs of some samples: a) sample 3, b) sample 4 and c) sample 5.
SEM micrograph of sample 3, given on
LOM micrographs of some samples: a) sample 9, b) sample 13, and c) sample 14.
Samples 9 and 13, have a same phases in microstructure. Detected phases are marked at the microstructures in
Twelve ternary samples and three binary (marked on
Brinell hardness of the investigated Ag-Ge-In alloys with overall compositions along cross-sections: a) Ag-Ge50In50, b) Ge-Ag50In50, and c) In-Ag50Ge50.
By using this measurement and mathematical model, mathematical equation for calculation of Brinell hardness, were proposed. In order to define a mathematical model for the dependence of Brinell hardness vs composition for ternary alloys the Design Expert v.9.0.3.1 software package was used. Out of a possible canonical or Scheffe model (Cornell,
High value of F parameter (F=65.88) and small p, (p<0,0001) shows that in the Analysis of variance (ANOVA) chosen model is satisfactory. The final equation of the predictive model in terms of actual components is:
Two-dimensional contour diagrams for Brinell hardness of alloys in ternary Ag-Ge-In system, calculated based on Eq. (
Calculated iso-lines of Brinell hardness in ternary Ag-Ge-In system.
On same samples electrical conductivity were measurements in four points.
Calculated iso-lines of electric conductivity defined in ternary Ag-Ge-In system.
By using same procedure as for description of Brinell hardness mathematical equation for calculation of electrical conductivity, were proposed. Chosen mathematical model was Special Quartic. High value of F parameter (F=34.11) and small p, (p<0,0001) shows that in the Analysis of variance (ANOVA) chosen model is satisfactory. The final equation of the predictive model in terms of actual components is:
Iso-lines contour plot of electric conductivity defined by Eq. (
Electrical conductivity of the investigated Ag-Ge-In alloys with overall compositions along cross-sections: a) Ag-Ge50In50, b) In-Ag50Ge50, and c) Ge-Ag50In50.
Some characteristic alloys with different composition were experimentally tested with SEM-EDS, XRD, LOM, Brinell hardness test and electrical conductivity test. By using thermodynamic data set, isothermal section at 25 °C was calculated and eight different phase fields were predicted. By prepared samples four of eight phase region were confirmed with EDS and XRD results.
With SEM and LOM microstructures of tested alloys were observed. All samples are tested with Brinell hardness test and electrical conductivity and results were used for predicting a mathematical model for calculation of those properties along all composition range.
This work has been supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia (Grant No. OI172037).