The results of phase equilibria investigation and characterization of the alloys in the Bi-Ga10Sb90 section of Ga-Bi-Sb system are presented in this paper. Phase diagram of the mentioned section has been calculated according to CALPHAD model, using Pandat software. In the frame of alloys characterization, structural, mechanical and electrical characteristics were determined using SEM-EDX analysis, microhardness and electroconductivity measurements

Balanović, Ljubiša

Manasijević, Dragan

Minic, D.

Mitovski, A.

Rangelov, I.

Talijan, Nadežda M.

Ćosović, Vladan

Živković, Dragana

English

 CER - Central Repository of the Institute of Chemistry;  Technology and Metallurgy

JOURNAL OF OPTOELECTRONICS AND ADVANCED MATERIALS, Vol. 12, No. 6, June 2010, p. 1262 - 1267 
 
Phase diagram investigation and characterization of 
alloys in Bi-Ga10Sb90 section of Ga-Bi-Sb system 
 
 
D. ŽIVKOVIĆa*, D. MINIĆb, D. MANASIJEVIĆa, N. TALIJANc, LJ. BALANOVIĆa,  
A. MITOVSKIa, V. ĆOSOVIĆc, I. RANGELOVa 
aUniversity of Belgrade, Technical Faculty, Bor (Serbia) 
bUniversity of Priština, Faculty of Technical Sciences, Kosovska Mitrovica (Serbia) 
cUniversity of Belgrade, Institute for Chemistry, Technology and Metallurgy, Belgrade (Serbia) 
   
   
 
The results of phase equilibria investigation and characterization of the alloys in the Bi-Ga10Sb90 section of Ga-Bi-Sb 
system are presented in this paper. Phase diagram of the mentioned section has been calculated according to CALPHAD 
model, using Pandat software. In the frame of alloys characterization, structural, mechanical and electrical characteristics 
were determined using SEM-EDX analysis, microhardness and electroconductivity measurements. 
 
(Received Aptil 22, 2010; accepted June 16, 2010) 
 
Keywords: Phase diagram, Characterization, Ternary alloys, Ga-Sb-Bi system 
 
 
 
1. Introduction 
 
Gallium-based alloys, especially multicomponent 
gallium antimonide- based alloys, have been a subject of 
different investigations for their wide application in 
electronics and other engineering practice. The knowledge 
of their phase diagram is important from theoretical and 
practical point of view, so main task in complete 
determination of such semiconducting materials is to 
investigate their thermodynamic properties and phase 
equilibria. 
 
 
 
Fig. 1. Ternary system Bi-Ga-Sb with signed – investigated 
section Bi-Ga10Sb90 [3] 
 
One of the interesting systems, among mentioned 
group of alloys, is the Bi-Ga-Sb system. This system has 
been thermodynamically analyzed in some sections, 
experimentally – using emf measurements [1] and Oelsen 
calorimetry [2,3], and analitically – using calculation 
procedures of thermodynamic predicting (general solution 
model, Hajra, Margules, Bale-Pelton) [4,5], but still not 
completely investigated, although some new results of 
phase equilibria of this system has been available in 
literature recently [6]. 
As a contribution to the completion of data concering 
Bi-Ga-Sb system, the results including phase diagram, 
structural, mechanical and electrical characteristics 
investigation in the section from Bi corner with molar ratio 
of Ga:Sb = 1:9, given in Fig.1, are presented in tis paper. 
 
 
2. Experimental  
 
The metals used for the preparation of selected 
samples were bismuth, gallium and antimony of 99.99% 
purity. Investigated compositions were with xBi equal to 0; 
0.1;0.3;0.5;0.7 and 0.9. 
 For experimental investigation used in this work, 
SEM-EDX analysis, microhardness and 
electroconductivity measurements were applied.  
Scanning Electron Microscopy (SEM) and Energy 
Dispersive X-ray Spectroscopy (EDX) analysis were 
performed on the electronic microscope Philips XL-300. 
The solution of (8M H2SO4 + 2g K2Cr2O7) was used as 
etching agens for structure development. 
Microhardness measurements were done using 
standard Vickers method, using 100g load in five points, 
taking average value.  
Electrical conductivity of investigated materials was 
measured using three series of measurements on the 
standard apparatus SIGMATEST 2.069 (Foerster) - eddy 
current instrument for measurements of electrical 
conductivity of non-ferromagnetic metals, based on 
complex impedance of the measuring probe with diameter 
of 8mm. 
All experiments were performed in an air atmosphere. 
Phase diagram investigation and characterization of alloys in Bi-Ga10Sb90 section of Ga-Bi-Sb system                1263 
 
3. Theoretical fundamentals 
 
The basics of CALPHAD method [7,8], used in this 
paper for the calculation of phase equilibria, is a 
constrained minimization of Gibbs energy for a given 
temperature, pressure and overall composition, which is 
compatible with all currently available software packages 
for the modelling of thermodynamic properties and phase 
diagrams of multicomponent systems. 
The molar Gibbs energy of a phaseφ can be 
considered as the sum of a number of different 
contributions: 
...+++++= φφφφφφ PmagEidrefm GGGGGG      (1) 
where φrefG   is the molar Gibbs energy of the weighted 
sum of the system constituents i (elements, species, 
compounds etc.) of the phaseφ  relative to the chosen 
reference state (typically the Stable Element Reference 
state ‐ SER), 
∑
=
⋅=
n
i
i
o
iref GxG
1
φφ                             (2) 
 
and its temperature dependence is given by 
 ( ) ( ) ∑+++=
i
n
iTdTcTbTaTG ln             (3) 
where a‐di are adjustable coefficients. 
In the case where the constituent in question is a 
stoichiometric compound, its contribution to the φrefG  is 
usually expressed by the Gibbs energy of formation 
relative to the chosen reference state, fG , 
∑
=
+⋅=
n
i
fi
o
iref GGxG
1
φφ                           (4) 
but, there is also a contribution to the Gibbs energy from 
ideal random mixing of the constituents on the crystal 
lattice, denoted φidG , 
( )∑
=
⋅=
n
i
iiid xxRTG
1
lnφ   , i=1,..,n              (5) 
 
for an n‐constituent system. 
φ
EG  is the excess Gibbs energy, which describes the 
influence of non‐ideal mixing behaviour on the 
thermodynamic properties of a solution phase and is given 
by the Muggianu extension of the Redlich‐Kister 
formalism [9,10] 
( )∑ ∑ ∑
≠ = = ≠≠ =
+−=
n
ji
ji
m
z
n
kji
kji
ijkkji
z
ji
z
jiE LxxxxxLxxG
1, 0 1,,
φ   z=0,...,m    (6) 
where the interaction parameters, describing the mutual 
interaction among constituents i and j, are denoted as zL. 
The liquid phase and solid solution phases are modeled in 
this way, but more complex phases, such as intermetallic 
compounds, are usually modeled using the compound 
energy formalism [11].  
4. Results and discussion 
 
In the first part of this paper, phase diagram 
calculation according to CALPHAD method [7,8], was 
done. Therefore, the phase stability equations compiled by 
Dinsdale [12] were used for the thermodynamic functions 
of the pure elements in their stable and metastable states, 
while starting binary thermodynamic data for the Bi–Ga, 
Bi-Sb and Ga-Sb subsystems were taken from Refs.[13-
15], respectively. The phases from mentioned binaries, 
considered for thermodynamic binary-based prediction 
with their crystallographic data, are listed in Table 1, while 
optimized unary and binary thermodynamic data used in 
this work are given in Appendix.  
 
Table 1. The phases considered for thermodynamic 
binary based prediction –their crystallographic data and 
database names 
 
Phase-
common 
name 
Prototype Pearson Symbol 
Space 
Group 
Thermodynami
c database 
name 
liquid    LIQUID 
(Bi)(Sb) αAs hR2 R3m RHOMBO_A7
(Ga) αGa oC8 Cmca ORTHORHOMBIC (ORT) 
GaSb ZnS cF 8 F43m ZINCBLENDE_B3 
 
Based on data presented in Table 1 and Appendix, 
following the CALPHAD procedure described in 
theoretical fundamentals and using Pandat Software, phase 
diagram of the investigated section Bi-Ga10Sb90 was 
obtained and shown in Fig. 2. Comparison with our 
previous DTA results on this system [3] was done and 
shown in the same figure, showing good agreement 
between experimental and calculated phase diagram.  
 
 
Fig. 2. Calculated phase diagram of the Bi-Ga10Sb90 
section (lines - this work) compared with DTA results  
                         (circles – Ref. [3]). 
 
In the second part of this work, characterization of the 
selected alloys in the Bi-Ga10Sb90 section in the Bi-Ga-
Sb system was done.  
1264                         D. Živković, D. Minić, D. Manasijević, N. Talijan, Lj. Balanović, A. Mitovski, V. Ćosović, I. Rangelov 
 
SEM-EDX analysis was used for structural analysis 
and determination of chemical composition of coexisting 
phases presented in the investigated section. The results 
obtained by SEM-EDX analysis, including SEM 
microphotographs and experimental determination of 
compositions, are given in Fig.3 and Table 3, respectively. 
 
 
(a)                                                                   (b) 
 
(c)                                                           (d) 
 
(e)                                               (f) 
Fig. 3. SEM microphotographs for the alloys with xBi equal to 0 (a); 0.1 (b); 0.3 (c); 0.5 (d); 0.7 (e); 0.9 (f) (1 – light gray phase 
RHOMBO-A7 (Bi); 2 – dark gray phase RHOMBO_A7 (Sb); 3 – black phase ZINCBLENDE_B3 (GaSb) ) 
 
Tab. 3. EDX results for: (a) experimental determination 
of compositions and(b) experimental composition of 
phases 
 
a 
Experimentally determined overall 
composition  
Alloy 
composition 
Bi Ga Sb 
Ga10Sb90 - 11.32 88.68 
Bi10Ga9Sb81 10.30 8.90 80.80 
Bi30Ga7Sb63 31.42 6.4 62.18 
Bi50Ga5Sb45 49.93 4.23 45.84 
Bi70Ga3Sb27 70.32 3.55 26.14 
Bi90Ga1Sb9 89.96 0.95 9.09 
 
 
 
 
b 
 
Experimentally determined 
compositions of phases 
[at.%] 
 
Experimentally 
determined 
overall 
composition  
Experimentally 
determined phases 
Bi Ga Sb 
10.30 at.%Bi 
8.90 at.% Ga 
80.80 at.%Sb 
RHOMBO_A7 (Bi)   
RHOMBO_A7 (Sb) 
ZINCBLENDE_B3 
(GaSb) 
77.3 
4.78 
 
2.07 
- 
48.56 
20.63 
95.22 
51.44 
49.93 at.%Bi  
4.23 at.% Ga 
45.84 at.%Sb 
RHOMBO_A7 (Bi) 
RHOMBO_A7 (Sb) 
ZINCBLENDE_B3 
(GaSb) 
77.3 
25.55 
 
4.51 
0.4 
49.5 
18.17 
74.05 
50.5 
 
 
 
Phase diagram investigation and characterization of alloys in Bi-Ga10Sb90 section of Ga-Bi-Sb system                1265 
 
Obtained SEM-EDX results confirmed experimentally 
overall alloys compositions and indicated to folowing 
phases present in the system (Fig. 3): black phase responds 
to GaSb (ZINCBLENDE_B3); while dark and light gray 
phases are related to Bi-Sb solid solution (RHOMBO_A7) 
rich on Sb and on Bi, respectively. 
The results of microhardness measurements are 
shown in Fig. 4, in the form of microhardness dependence 
on antimony composition. The microhardness values were 
measured for the light gray phase (RHOMBO_A7 – Bi-Sb 
solid solution rich on Bi) and was found to lie between 25 
and 59 HV corresponding to the applied load of 100 g. It 
may be noticed that microhardness values increases 
uniformly with bismuth content increase, following the 
relation: HV = -45.085xBi2 + 71.183xBi + 29.845.  
 
 
 
Fig. 4.  Microhardness vs. composition for chosen alloys 
in the Bi-Ga10Sb90 section 
 
 
The results of electrical conductivity measurements 
are presented in Table 4. As can be seen, the electrical 
conductivity was given for only two samples, because the 
other investigated samples didn’t show any response 
during measurement. 
 
Table 4.  Measured values of electrical conductivity for 
investigated Au-In-Sb alloys. 
 
xBi Electroconductivity (MS/m) 
0.5 0.4245 
0.7 1.1883 
 
 
5. Conclusions 
 
The Bi-Ga-Sb alloys from the section with molar ratio 
Ga:Sb = 1:9 has been investigated in order to determine 
the phase diagram and characterize selected samples. 
Phase diagram of the Bi-Ga10Sb90 section was calculated 
using CALPHAD approach and Pandat Software based on 
available optimized unary and binary thermodynamic 
parameters. Obtained diagram showed good agreement in 
comparison with experimental DTA results taken from 
literature. Structural and phase analysis has been done 
using SEM-EDX analysis, confirming experimentally 
overall alloys compositions and existence of three phases 
presented - black phase responding to GaSb 
(ZINCBLENDE_B3); as well as dark and light gray 
phases related to Bi-Sb solid solution (RHOMBO_A7) 
rich on Sb and on Bi, respectivelly. More, the values of 
microhardness and electroconductivity have been 
measured and presented in the paper. 
 
 
Acknowledgement 
 
This work was supported by Ministry of Science and 
Technology Development, Republic of Serbia (Project No. 
142043). Calculations were performed using PANDAT 
software. 
 
References 
 
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        B. Jansson, B. Sundman, Acta Metall. 34, 437 (1986). 
[12] A. T. Dinsdale, “SGTE unary database, version. 4.4”  
        ( www.sgte.org ) 
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        31(4), 438 (2007). 
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1266                         D. Živković, D. Minić, D. Manasijević, N. Talijan, Lj. Balanović, A. Mitovski, V. Ćosović, I. Rangelov 
 
Appendix   
 
Optimised unary and binary thermodynamic data for Bi-Ga-Sb system used in present study 
 
LIQUID 
CONSTITUENTS: BI,GA,SB 
G(LIQUID,BI;0)-H298(RHOMBO_A7,BI;0) = 
+3428.29+107.782416T-28.4096529Tln(T)+0.012338888T2-8.381598E-06T3-5.9549E-19T7 
(298.14<T<  544.54) 
[12] 
+41544.282-414.460769T+51.8556592Tln(T) -0.075311163T2+1.3499885E-05T3-3616168T-1 
(544.54<T<  800.00) 
[12] 
+290.595+161.738553T-35.9824Tln(T) +0.0074266T2-1.046E-06T3 
(800.00<T< 1200.00) 
[12] 
+3754.947+103.961021T-27.196Tln(T) 
(1200.00<T< 3000.00) 
[12] 
G(LIQUID,GA;0)-H298(ORT,GA;0) = 
+5491.298-18.073995T-7.017E-17T7+GHSERGA 
(200.00<T<  302.92) 
[12] 
+5666.455-18.681147T-1.645E+23T -9+GHSERGA 
(302.92<T< 4000.00) 
[12] 
G(LIQUID,SB;0)-H298(RHOMBO_A7,SB;0) = 
+10579.47+134.231525T-30.5130752Tln(T)+0.007748768T2-3.003415E-06T3+100625T-1-1.74847E-20T7 
(298.14<T<  903.78) 
[12] 
+8175.359+147.455986T-31.38Tln(T) 
(903.78<T< 2000.00) 
[12] 
L(LIQUID,BI,GA;0) = +8401.6+.996135T [13] 
L(LIQUID,BI,GA;1) = -560.9-2.43423T [13] 
L(LIQUID,BI,GA;2) = +754.8-0.682275T [13] 
L(LIQUID,BI,GA;3) = -1162.5 [13] 
L(LIQUID,BI,SB;0) = +2230+0.06T [14] 
L(LIQUID,GA,SB;0) = -13953.8+71.0787T-9.6232Tln(T) [15] 
L(LIQUID,GA,SB;1) = +1722.9-1.92588T [15] 
L(LIQUID,GA,SB;2) = 2128.3 [15] 
RHOMBO_A7 
CONSTITUENTS: BI,SB 
G(RHOMBO_A7,BI;0)-H298(RHOMBO_A7,BI;0) = +GHSERBI= 
-7817.776+128.418925T-28.4096529Tln(T)+12.338888E-3T2-8.381598E-6T3                                                          
(298.14<T< 544.55)                                                    
[12] 
30208.022-393.650351T+51.8556592Tln(T)-75.311163E-3T2+13.499885E-6T3 
 -3616168T -1+166.145E23T-9                                                         
 (544.55<T< 800.00) 
[12] 
-11045.664+182.548971T-35.9824Tln(T)+7.4266E-3T2-1.046E-6T3+166.145E23T-9                                                
(800.00<T< 1200.00)                                       
[12] 
-7581.312+124.77144T-27.196Tln(T)+166.145E23T-9          
(1200.00<T< 3000.00) 
[12] 
G(RHOMBO_A7,SB;0)-H298(RHOMBO_A7,SB;0) = +GHSERSB= 
-9242.858 + 156.154689T - 30.5130752Tln(T) + 7.748768E-3 T2
 
- 3.003415E-6 T3
 
+ 100625T-1 
(298.15 < T < 903.78) 
[12] 
-11738.83 + 169.485872T -31.38Tln(T) +1616.849E24 T-9                            
  
(903.78 < T < 2000.00) 
[12] 
L(RHOMBO_A7,BI,SB;0) =  +10150-6.3T [14] 
L(RHOMBO_A7,BI,SB;1) = 150 [14] 
ORT 
CONSTITUENTS: GA 
G(ORT,GA:VA;0)-H298(ORT,GA;0) = +GHSERGA= 
-21312.331 + 585.263691T - 108.2287832Tln(T) + 227.155636E-3T2 - 118.575257E-6 T3 + 439954T-1                   
(200.00 < T < 302.91) 
[12] 
-7055.643 + 132.73019T - 26.0692906Tln(T) + 0.1506E-3T2 - 0.040173E-6T3 - 118332T-1 + 164.547E21T-9           
 (302.91 < T < 4000.00) 
[12] 
Phase diagram investigation and characterization of alloys in Bi-Ga10Sb90 section of Ga-Bi-Sb system                1267 
 
ZINCBLENDE_B3 
CONSTITUENTS: GA : SB 
G(ZINCBLENDE_B3,GA:SB;0)-0.5 H298(ORT,GA;0)-0.5 H298(RHOMBO_A7,SB;0)=  
-21738.1-10.53764T+2.692876TLN(T)-0.00137791T2+0.5GHSERGA+0.5GHSERSB 
(200.00<T< 4000.00) 
[15] 
 
 
 
______________________________ 
*Corresponding author: dzivkovic@tf.bor.ac.yu; 
                                       dzmaca@yahoo.com 
 


Phase diagram investigation and characterization of alloys in Bi-Ga10Sb90 section of Ga-Bi-Sb system

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Phase diagram investigation and characterization of alloys in Bi-Ga10Sb90 section of Ga-Bi-Sb system

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