Mechanical and electrical properties of the ternary Ag-Ge-In alloys

Aleksandar Marković^a, Duško Minić^a, Milena Premović^a,*, Dragan Manasijević^b

^aUniversity of Priština, Faculty of Technical Science, Kneza Miloša 7, 40000 Kos. Mitrovica, Serbia

^bUniversity of Belgrade, Technical Faculty in Bor, VJ 12, 19210 Bor, Serbia

(*Corresponding author: milena.premovic@gmail.com)

1. INTRODUCTIONTOP

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 et al., 2014; Premovic et al., 2015; Premovic et al., 2016; Premovic et al., 2017a; Premovic et al., 2017b) due to the technical importance of the systems based on Ge (Chen et al., 2006; Raoux and Wuttig, 2009) and their special application as a phase change memory material (PCM materials) (Lacaita and Wouters, 2008; Ou et al., 2011; Ielmini and Lacaita, 2011; Nemec et al., 2012). Electrical and mechanical properties of ternary Ag-Ge-In system have not been investigated before. The reason for this study is experimental investigation of electrical and mechanical properties of the ternary Ag-Ge-In alloys at room temperature (≈25 °C). Phase equilibria in the ternary Ag-Ge-In system have been experimentally investigated before by our group Milisavljevic et al. (2018). Milisavljevic et al. (2018) have been experimentally investigated ternary alloys from three vertical sections Ag-GeIn, Ge-AgIn, and In-AgGe and two isothermal sections at 200 and 400 °C. By combining experimental results and thermodynamic parameters for the constitutive binary systems proposed in the literature (Chevalier, 1989; Kroupa et al., 2007; Wang et al., 2011) reliable thermodynamic data set has been proposed by Milisavljevic et al. (2018). Thermodynamic data set proposed by Milisavljevic et al. (2018) has been used in our study for the calculation of isothermal section at 25 °C. In the current study phase equilibria of the isothermal section at 25 °C have been investigated by using scanning electron microscopy (SEM) with energy dispersive spectrometry (EDS) and x-ray diffraction (XRD). Ternary Ag-Ge-In alloys have been tested with Brinell hardness test and test for electrical conductivity. Experimental results of Brinell hardness and electrical conductivity have been used for obtaining mathematical model for estimation of those properties for every composition of alloys at room temperature (≈25 °C). Obtained results aimed to provide better insight into properties of alloys which should contribute to further expansion of their application possibilities.

2. MATERIALS AND METHODSTOP

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.

3. RESULTS AND DISCUSSIONTOP

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 et al. (2011) for the Ag-Ge binary system, Kroupa et al. (2007) for the Ag-In binary system and from Chevalier (1989) for the Ge-In binary system. Based on the literature information for binary sub-systems crystallographic data for solid phases in the ternary Ag-Ge-In system are summarized and presented in Table 1 (Jette and Foote, 1935; Cooper, 1962; Ridley, 1965; Campbell et al., 1970; Havinga et al., 1972).

Table 1. 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.
				a=b	c
FCC_A1	(Ag)	cF4	Fm m	4.0861		Jette and Foote (1935)
DIAMOND_A4	(Ge)	cF8	Fd m	5.65675		Cooper (1962)
TETRAG_A6	(In)	tI2	I4/mmm	3.2523	4.9461	Ridley (1965)
BCC_A2	β(Ag3In)	cP2	Pm m	4.144(4)		Campbell et al. (1970)
HCP_A3	ζ(Ag3In)	hP2	P63/mmc	2.961(2)	4.778(4)	Campbell et al. (1970)
CUIN_GAMMA	γ(Ag2In)	cP52	P 3m	9.887(4)		Campbell et al. (1970)
AGIN2	AgIn2	tI12	I4/mcm	6.881(4)	5.620(4)	Havinga et al. (1972)

Figure 1 presents calculated isothermal section of the Ag-Ge-In ternary system at 25 °C. Selected alloys samples experimental investigated are also marked on Fig. 1.

Compositions of the selected alloy samples lie along three vertical sections red squares Ag-Ge₅₀In₅₀, orange squares Ge-Ag₅₀In₅₀ and violet squares In-Ag₅₀Ge₅₀. Eight different phase regions are calculated at isothermal section at 25 °C. Four are two-phase regions (Ge)+AgIn₂, (Ge)+γ(Ag₂In), (Ge)+ζ(Ag₃In) and (Ge)+(Ag) and another four are three-phase regions (Ge)+AgIn₂+(In), (Ge)+AgIn₂+γ(Ag₂In), (Ge)+ζ(Ag₃In)+γ(Ag₂In), and (Ge)+ζ(Ag₃In)+(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), AgIn₂ and γ(Ag₂In) are detected. According to the calculated phase diagram Fig. 1 it is visible that examined samples 3, 9, and 13 belongs to the same three phase region (Ge)+AgIn₂+γ(Ag₂In), and by experiments same phases are experimentally detected. Samples 4 and 5, detected two phases. Sample 4, by calculation belongs to the two-phase region (Ge)+ζ(Ag₃In), same phase region are experimentally detected by EDS and XRD tests. Sample 5, detected another two-phase region (Ge)+(Ag), same phase region as predicted by calculation. Last tested sample 14, according to the calculation belong to the three-phase region (Ge)+AgIn₂+(In), by experiments same phases are detected. Three SEM micrographs of selected samples 3, 4 and 5 are given in Fig. 2.

SEM micrograph of sample 3, given on Fig. 2.a, have three phases in equilibrium. Dark phase is (Ge) solid solution, gray phase is intermetallic compound AgIn₂, and light gray phase is γ(Ag₂In) intermetallic compound. Sample 4 is from (Ge)+ζ(Ag₃In) two-phase region and on SEM micrograph (see Fig. 2.b), (Ge) solid solution is dark phase and ζ(Ag₃In) intermetallic compound gray phase. Last microstructure on Fig. 2 is for sample 5, and two phases are detected, dark phase is (Ge) solid solution and gray phase (Ag) solid solution. Figure 3 presents a three LOM micrographs of selected samples 9, 13 and 14.

Samples 9 and 13, have a same phases in microstructure. Detected phases are marked at the microstructures in Fig. 3a, sample 9, and Fig. 3b, sample 13, with related name of the phase. Three phases Ge, AgIn₂ and γ(Ag₂In) are visible in the microstructures. Figure 3c, presents a microstructure of the sample 14, and three phases are visible. Phases are (Ge), (In), and AgIn₂.

3.1. Mechanical propertiesTOP

Twelve ternary samples and three binary (marked on Fig. 1) are experimentally tested with Brinell hardness test. Hardness of alloys were measured at three different position on the samples. Based on obtained results mine value of three measurements were calculated and given graphic form in Fig. 4. For easier visualization of the results mine value as a function of compositions are presented in graphic form in Fig. 4. Figure 4a presents hardness of alloys by increasing of the silver composition. With increasing of silver hardness of alloys increase to the point where silver is 0.4 mol in alloys, by adding more silver hardness of alloys decries. Figure 4b presents behaviors of hardness by increasing of germanium composition. From experimental results it is visible that by adding of the germanium, hardness of alloys decries to the alloys with 0.6 mol of Ge, while alloys with 0.8 mol of Ge hardness start to increase. Figure 4c presents hardness of alloys with increasing of indium and results shows that by adding indium, hardness decries.

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, 2002; Lazić, 2004; Kolarević et al., 2011) that meet the requirements of adequacy a Special Quartic model was recommended, Eq. (1):

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. (2), is shown in Fig. 5.

3.2. Electrical propertiesTOP

On same samples electrical conductivity were measurements in four points. Figure 6, presents graphic correlation between electrical conductivity and mole fraction of components for the all investigated samples. Electrical conductivity of alloys was measured at four different point and main value based on those four results were presented in Fig. 6 and used for graphic presentation and future calculation.

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. (3) is shown in Fig. 7.

4. CONCLUSIONSTOP

ACKNOWLEDGEMENTSTOP

This work has been supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia (Grant No. OI172037).

REFERENCESTOP