Effect of Chemical Composition on the Microstructure, Hardness and Electrical Conductivity Profiles of the Ag-Bi-Ge Alloys

Marković, Aleksandar; Minić, Duško; Premović, Milena; Manasijević, Dragan; Guresić, Dejan; Kolarevi, Milan

doi:10.1590/1980-5373-MR-2019-0372

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Articles • Mat. Res. 22 (6) • 2019 • https://doi.org/10.1590/1980-5373-MR-2019-0372 copy

Effect of Chemical Composition on the Microstructure, Hardness and Electrical Conductivity Profiles of the Ag-Bi-Ge Alloys

Authorship SCIMAGO INSTITUTIONS RANKINGS

Microstructure, hardness and electrical properties of the selected ternary Ag-Bi-Ge alloys were investigated in this study. Isothermal sections of the Ag-Bi-Ge system at 25, 100 and 500 °C have been extrapolated using optimized thermodynamic parameters from literature and experimentally investigated. Performed experiments were optical microscopy, scanning electron microscopy (SEM) and energy dispersive spectrometry (EDS), X-ray powder diffraction (XRD), hardness measurements by Brinell method and electrical conductivity measurements. EDS results were compared with predicted phase equilibria and good overall agreement between experimental and calculated values was obtained. XRD results were also in agreement with predicted phase equilibria. Hardness and electrical conductivity of selected alloys were measured and by using appropriated mathematical model these properties were predicted in the whole composition range.

Keywords:
Phase equilibrium; hardness; electrical conductivity; mathematical model

Thermodynamic database name	Phase	Pearson symbol	Space group	Lattice parameters (Å)		Ref.
Thermodynamic database name	Phase	Pearson symbol	Space group	a=b	c
FCC_A1	(Ag)	cF4	Fm 3 m	4.0861		[21]
DIAMOND_A4	(Ge)	cF8	Fd 3 m	5.65675		[22]
RHOMBO_A7	(Bi)	hR2	R 3 m	4.535±.002	11.814±.006	[23]

N	Composition of samples x(at. %)	Determined phases		Compositions of phases x(at. %)			Lattice parameters l(10^-10m)
N	Composition of samples x(at. %)	EDS	XRD	Ag	Bi	Ge	a=b=c
	7.89 Ag	L		10.77±0.2	86.41±0.2	2.82±0.1
1	50.80 Bi	(Ge)	(Ge)	0.80±0.1	1.30±0.1	97.9±0.3	5.6532±0.0006
	41.31 Ge
	22.71 Ag	L		29.09±0.3	66.37±0.1	4.54±0.6
2	51.68 Bi	(Ge)	(Ge)	0.92±0.3	1.01±0.2	98.07±0.1	5.6538±0.0007
	25.61 Ge
	26.83 Ag	L		42.48±0.4	51.39±0.1	6.13±0.2
3	33.04 Bi	(Ge)	(Ge)	0.5±0.1	0.89±0.1	98.61±0.1	5.6552±0.0003
	40.13 Ge
	42.06 Ag	L		60.17±0.5	31.29±0.3	8.54±0.3
4	9.57 Bi	(Ge)	(Ge)	0.73±0.2	0.89±0.4	98.38±0.2	5.6549±0.0001
	48.37 Ge	(Ag)	(Ag)	91.67±0.3	1.73±0.5	6.6±0.1	4.1023±0.0005

	59.97 Ag	L		62.85±0.3	28.85±0.4	8.3±0.1
5	19.97 Bi	(Ge)	(Ge)	0.98±0.5	1.13±0.5	97.89±0.2	5.6532±0.0004
	20.06 Ge	(Ag)	(Ag)	90.02±0.4	2.73±0.1	7.25±0.2	4.1029±0.0003
	77.06 Ag	L		60.18±0.2	36.48±0.2	3.34±0.1
6	19.53 Bi	(Ag)	(Ag)	93.73±0.3	3.28±0.2	2.99±0.1	4.1019±0.0002

N	Composition of samples x(at. %)	Determined phases		Compositions of phases x(at. %)			Lattice parameters 1(10^-10m)
N	Composition of samples x(at. %)	EDS	XRD	Ag	Bi	Ge	a=b	c
	62.03 Ag	(Ag)	(Ag)	98.05±0.3	0.75±0.4	1.2±0.2	4.0891±0.0003
7	22.81 Bi	(Bi)	(Bi)	0.05±0.2	98.92±0.1	1.03±0.5	4.5356±0.0002	11.8153±0.0002
	15.16 Ge	(Ge)	(Ge)	0.08±0.1	0.12±0.2	99.8±0.1	5.6563±0.0007
	55.23 Ag	(Ag)	(Ag)	98.03±0.1	1.02±0.2	0.95±0.2	4.0892±0.0006
8	18.65 Bi	(Bi)	(Bi)	0.80±0.1	98.71±0.1	0.49±0.2	4.5358±0.0005	11.8155±0.0007
	26.12 Ge	(Ge)	(Ge)	0.80±0.6	1.20±0.3	98.00±0.3	5.6543±0.0002
	32.80 Ag	(Ag)	(Ag)	98.32±0.2	0.87±0.4	0.81±0.1	4.0879±0.0008
9	18.62 Bi	(Bi)	(Bi)	0.31±0.2	99.07±0.5	0.62±0.5	4.5353±0.0003	11.8148±0.0005
	48.58 Ge	(Ge)	(Ge)	0.30±0.5	0.52±0.3	99.18±0.2	5.6559±0.0002
	32.18 Ag	(Ag)	(Ag)	98.25±0.4	1.08±0.3	0.67±0.3	4.0885±0.0005
10	34.60 Bi	(Bi)	(Bi)	0.51±0.4	99.03±0.2	0.46±0.5	4.5353±0.0001	11.8150±0.0008
	33.22 Ge	(Ge)	(Ge)	0.71±0.3	0.58±0.4	98.71±0.2	5.6551±0.0007
	9.33 Ag	(Ag)	(Ag)	98.72±0.2	0.18±0.2	1.1±0.1	4.0873±0.0005
11	32.22 Bi	(Bi)	(Bi)	0.51±0.1	98.31±0.2	1.18±0.2	4.5359±0.0002	11.8163±0.0002
	58.45 Ge	(Ge)	(Ge)	0.82±0.2	0.13±0.1	99.05±0.3	5.6556±0.0003
	7.28 Ag	(Ag)	(Ag)	98.31±0.1	0.92±0.2	0.77±0.5	4.0880±0.0001
12	65.86 Bi	(Bi)	(Bi)	0.81±0.3	98.52±0.2	0.67±0.2	4.5357±0.0004	11.8161±0.0001
	26.86 Ge	(Ge)	(Ge)	0.52±0.1	0.71±0.1	98.77±0.3	5.6552±0.0002

N.	Mole fraction of components			Value (MN/m²)			Mean value (MN/m²)
N.	x(Ag)	x(Bi)	x(Ge)	1	2	3	Mean value (MN/m²)
B1	0	0.5	0.5	117.4	124.2	122.6	121.4
13	0.2	0.4	0.4	56.2	59.0	86.8	67.3
14	0.4	0.3	0.3	61.0	103.1	67.4	77.16
15	0.6	0.2	0.2	66.6	52.2	72.4	63.73
16	0.8	0.1	0.1	113.5	62.8	61.0	79.1
	1	0	0		24.5
B2	0.5	0	0.5	94	89.6	94.2	92.6
17	0.4	0.2	0.4	41.7	28.8	50.2	40.23
18	0.3	0.4	0.3	48.8	74.6	65.0	62.8
19	0.2	0.6	0.2	55.5	71.5	84.1	70.36
20	0.1	0.8	0.1	26.5	47.4	49.6	41.16
	0	1	0		94.2
B3	0.5	0.5	0	60.6	63.4	64.1	62.7
21	0.4	0.4	0.2	38.4	59.6	32.1	43.36
22	0.3	0.3	0.4	66.2	78.3	116.0	86.83
23	0.2	0.2	0.6	83.2	71.5	104.7	86.46
24	0.1	0.1	0.8	98.8	184.4	146.9	143.46
	0	0	1				366.74

Source	Sum of Squares	df	Mean Square	F Value	p-value Prob > F
Model	114986.00	9	12776.22	30.364	< 0.0001	significant
A-Bi	22494.41	1	22494.41	53.460	< 0.0001
B-Ag	52810.26	1	52810.26	125.509	< 0.0001
AB	15837.80	1	15837.80	37.640	< 0.0001
A^2	8148.49	1	8148.49	19.366	< 0.0001
B^2	19216.99	1	19216.99	45.671	< 0.0001
A^2B	4647.81	1	4647.81	11.046	0.0020
A^3	4798.99	1	4798.99	11.405	0.0017
A^3B	2521.65	1	2521.65	5.993	0.0191
A^4	3672.15	1	3672.15	8.727	0.0054
Residual	15989.22	38	420.77
Lack of Fit	5026.74	8	628.34	1.720	0.1346	not significant
Pure Error	10962.49	30	365.42
Cor Total	130975.22	47

Std. Dev.	20.51	R-Squared	0.8779
Mean	81.28	Adj R-Squared	0.8490
C.V. %	25.24	Pred R-Squared	0.8056
PRESS	25460.59	Adeq Precision	36.3541

Component	Coefficient Estimate	df	Standard Error	95% CI Low	95% CI High
Intercept	363.92	1	18.53	326.41	401.42
A-Bi	-2699.99	1	369.27	-3447.55	-1952.44
B-Ag	-746.90	1	66.67	-881.86	-611.93
AB	4120.80	1	671.67	2761.08	5480.53
A^2	11154.09	1	2534.65	6022.97	16285.22
B^2	406.52	1	60.15	284.75	528.30
A^2B	-14252.95	1	4288.47	-22934.50	-5571.39
A^3	-18185.14	1	5384.73	-29085.94	-7284.33
A^3B	15446.10	1	6309.54	2673.10	28219.11
A^4	9460.05	1	3202.25	2977.44	15942.65

Mole fraction of components			Value (MN/m²)			Mean value (MN/m²)
x(Ag)	x(Bi)	x(Ge)	1	2	3
0.333	0.333	0.333	54.1	73.6	63.5	63.73
0.6	0.2	0.2	54.6	70.9	65.1	63.53
0.2	0.6	0.2	62.2	60.4	78.5	67.03
0.2	0.2	0.6	98.7	74.4	82.3	85.13

Point #	Predicted Mean	Predicted Median	Observed	Std Dev	n	SE pred	95% PI low	Data mena	95% PI high
1	63.405	63.405	-	20.5127	3	12.637	37.822	63.733	88.988
2	64.513	64.513	66.6	20.5127	3	14.228	35.710	63.533	93.316
3	59.862	59.862	55.5	20.5127	3	13.433	32.668	67.033	87.056
4	82.140	82.140	83.2	20.5127	3	14.228	53.337	85.133	110.943

N	Mole fraction of components			Value (MS /m)				Mean value (MS/m)
N	x(Ag)	x(Bi)	x(Ge)	1	2	3	4	Mean value (MS/m)
B1	0	0.5	0.5	1.24	1.012	1.12	1.355	1.124
13	0.2	0.4	0.4	0.3328	0.3057	0.3079	0.3051	0.3129
14	0.4	0.3	0.3	0.6459	0.6746	0.6472	0.6633	0.6578
15	0.6	0.2	0.2	1.013	1.136	1.064	1.144	1.089
16	0.8	0.1	0.1	1.908	1.951	1.984	1.899	1.936
	1	0	0		62
B2	0.5	0	0.5	10.186	10.328	10.164	10.378	10.264
17	0.4	0.2	0.4	0.4676	0.4653	0.4802	0.4782	0.4728
18	0.3	0.4	0.3	0.8375	0.8358	0.83	0.6975	0.8002
19	0.2	0.6	0.2	1.842	1.8126	1.8288	1.8226	1.8265
20	0.1	0.8	0.1	0.9636	0.9689	0.9824	0.9795	0.9736
	0	1	0		0.867
B3	0.5	0.5	0	3.314	3.244	3.268	3.242	3.267
21	0.4	0.4	0.2	1.055	1.041	1.052	1.047	1.049
22	0.3	0.3	0.4	0.4982	0.4835	0.4944	0.4978	0.4935
23	0.2	0.2	0.6	0.3059	0.3047	0.3056	0.3083	0.306
24	0.1	0.1	0.8	0.8639	0.869	0.8744	0.7807	0.847
	0	0	1					1.344

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