Received: 16 June 2023
Revised: 21 September 2023
Accepted: 21 September 2023
DOI: 10.1111/jace.19523
RESEARCH ARTICLE
Experimental and thermodynamic modeling study of phase
equilibria in the PbO–NiO–SiO2 system
Hamed Abdeyazdan
Pyrometallurgy Innovation Centre
(PYROSEARCH), School of Chemical
Engineering, The University of
Queensland, Brisbane, Queensland,
Australia
Correspondence
Hamed Abdeyazdan, Pyrometallurgy
Innovation Centre (PYROSEARCH),
School of Chemical Engineering, Room
342, 1016 Banksia Bldg, Long Pocket
Campus, 80 Meiers Rd, Indooroopilly, The
University of Queensland, Brisbane, QLD
4072, Australia.
Email: h.abdeyazdan@uq.edu.au
Funding information
Australian Research Council Linkage
program, Grant/Award Number:
LP180100028)
Maksym Shevchenko
Evgueni Jak
Abstract
An integrated experimental and thermodynamic modeling investigation of the
phase equilibria in the PbO–NiO–SiO2 system in air and also in equilibrium
with liquid metal has been undertaken to better characterize the chemical reactions taking place in the Ni-containing Pb processing slags. New experimental
phase equilibria data at 720◦ C–1740◦ C were obtained for this system using hightemperature equilibration of synthetic mixtures with predetermined compositions in sealed silica ampoules or in Au/Pt–Ir foils, a rapid quenching technique,
and electron probe x-ray microanalysis of the equilibrated phase compositions.
Phase equilibria and liquidus isotherms in the quartz/tridymite/cristobalite
(SiO2 ), olivine (Ni2 SiO4 ), monoxide (NiO), Ni-barysilite (Pb8 NiSi6 O21 ), massicot
(PbO), and di-lead silicate (Pb2 SiO4 ) primary phase fields were revealed and the
extent of the high-SiO2 two-liquid immiscibility gap in equilibrium with cristobalite was determined. New experimental data were used in the development of a
thermodynamic database describing this ternary system. Also, modeling revision
of the NiO–SiO2 binary system was conducted, resulting in a smaller miscibility
gap in ternary systems that was closer to the experimental results.
KEYWORDS
lead oxide, liquidus, Ni recycling, nickel oxide, PbO–NiO–SiO2 , phase equilibria, silica, slag
1
INTRODUCTION
Characterizing phase equilibria and chemical reactions
taking place in Ni-containing Pb processing slags is
important for optimizing recycling of Ni metal. Through
the pyrometallurgical processes, Pb-smelting reactors are
potentially considered for recycling a range of valuable
minor elements including Ni metal,1 as both Pb and Ni
represent major elements in the battery design sector and
may mutually contaminate when the recycled batteries
of different kinds are dealt with simultaneously. There is
however a lack of accurate phase equilibria information for
the oxide subsystems containing Ni oxide.
Phase equilibria studies of the minor elements in nonferrous metallurgy are broadly focused on copper smelting
and converting processes. There are a range of investigations for distribution of Ni2–6 and other minor elements,
for example, Au, Ag, Co, Bi, Sn, Sb, and so forth7–16
between slag-matte/metal in the Cu–Fe–O–S–Si system.
For the Pb–Fe–O–S–Si system however, there are only limited investigations available for distribution of Au and Ag,17
as well as Sn and Sb.18 No information was found for
distribution of Ni in the Pb-processing slag-matte/metal
equilibrium in the literature. Liquidus studies of the minor
elements-containing ternary and quaternary systems are
limited to a few investigations on the metal systems
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the
original work is properly cited.
© 2023 The Authors. Journal of the American Ceramic Society published by Wiley Periodicals LLC on behalf of American Ceramic Society.
J Am Ceram Soc. 2024;107:1383–1407.
wileyonlinelibrary.com/journal/jace
1383
1384
ABDEYAZDAN et al.
containing Cu and Ni19–21 and PbO-based oxide systems
containing SnO/SnO2 .22
While PbO–NiO–SiO2 is the key oxide subsystem to be
investigated for better characterizing the Ni recycling in
Pb smelters, there is no phase equilibria information for
this system in the literature. Importantly, the NiO–SiO2
binary system has been reviewed by Prostakova23 in 2013.
In this study, new phase equilibria data at 720◦ C–1740◦ C
were obtained for the PbO–NiO–SiO2 system in air and
also in equilibrium with liquid metal. The results were
used for optimization of the parameters in a thermodynamic database that describes the broader, more complex
system.
2
EXPERIMENTAL METHODOLOGY
The experimental technique and apparatus used in this
study have been detailed in previous publications.24–26
The initial chemical mixtures were prepared by blending
selected proportions of high-purity powders of PbO, NiO,
and Ni metal (99.9 wt.% purity), and SiO2 (99.9 wt.% purity,
pre-dried at 400◦ C for 1 h before mixing), supplied by Alfa
Aesar. The Pb3 O4 powder was prepared by oxidation of
PbO powder in an MgO crucible in air for 24 h at 450◦ C. To
reduce the extent of lead oxide vaporization, a master slag
of Pb4 Si6 O16 composition was prepared by mixing appropriate ratio of Pb3 O4 and dried SiO2 powders, and heating
initially for 2 h at 600◦ C and then a further 2 h at 900◦ C in
Pt crucible in air. Excess oxygen from Pb3 O4 was released
to atmosphere during heating, so that the final master slag
contained only Pb2+ ; direct use of PbO reagent was avoided
to protect the Pt substrate from accidental destruction due
to local reducing conditions, observed in a previous study
by the authors.22 The composition of the initial mixtures is
given in Table 1.
The mixtures were pelletized and divided into 0.2–0.3 g
samples for the experiments. The initial compositions were
selected to ensure that the liquid slag was in equilibrium
with at least one crystalline phase, and the crystalline
solid phase(s) fraction in the final sample at the equilibration temperature was preferably approximately 10 vol%
and not greater than 50 vol% to promote the retention
of the liquid as an amorphous phase during quenching.
The substrates used for equilibration were (i) vacuumsealed silica ampoules (99.9% purity, 5–10 cm long, 1.3 cm
outer diameter, supplied by Lianyungang Guoyi Quartz
Products Co., Ltd.) for high-SiO2 mixtures that were in
equilibrium with tridymite and cristobalite at the target
temperature; and (ii) Au and Pt–Ir foils for low-SiO2 mixtures, which were in equilibrium with olivine, barysilite,
massicot, or monoxide at the experimental temperature.
TA B L E 1
The composition of the initial mixtures in wt%.
Mixture
name
Pb3 O4
NiO
Pb4 Si6 O16
SiO2
Ni
PN1
90.9
9.1
–
–
–
PNS1
–
34.8
48.7
16.5
–
PNS2
63.1
9.9
27.0
–
–
PNS3
36.0
9.9
54.1
–
–
PNS4
–
–
80.4
10.7
8.9
PNS5
–
9.4
47.2
27.6
15.7
PNS5a
–
11.0
36.2
37.0
15.7
PNS6
–
15.5
84.5
–
–
PNS7
–
16.4
35.1
33.6
14.9
PNS7a
–
18.7
26.1
40.3
14.9
PNS8
–
26.9
19.2
38.5
15.4
PNS9
85.9
3.0
11.1
–
–
PNS10
15.2
5.1
79.8
–
–
PNS11
53.6
2.6
43.8
–
–
PNS12
66.4
2.3
31.3
–
–
PNS13
34.0
2.9
63.1
–
–
PNS14
–
–
91.8
4.8
3.4
PNS15
–
27.6
31.3
26.1
14.9
PNS16
–
23.1
36.6
25.4
14.9
PNS16a
–
23.8
38.0
24.1
14.1
PNS17
–
13.4
24.4
46.5
15.7
PNS18
–
6.4
32.0
45.6
16.0
PNS20
51.1
0.5
48.4
–
–
NiSi0
–
53.8
–
46.2
–
NiSi1
–
70.0
–
30.0
–
NiSi2
–
41.1
–
58.9
–
Au foils were used for low-temperature (T < 1000◦ C) and
Pt–Ir foils were used for high-temperature (T > 1000◦ C)
experiments.
The experiments were conducted in a high-temperature
vertical tube resistance PYROX furnace using lanthanum
chromite heating elements under air or argon atmosphere.
The samples were suspended in the center of the uniform
hot zone of the furnace on a Kanthal (Fe–Cr–Al alloy)
wire (0.7 or 1 mm diameter), with 15–20 cm platinum wire
added to the Kanthal wire for T > 1450◦ C to avoid failure
at high temperatures. Where there was no risk of excessive evaporation of lead oxide (i.e., sealed ampoules or low
temperatures), the samples were first pre-melted at 20◦ C–
50◦ C above the target temperature for 5 min to support
the formation of a homogeneous liquid. Otherwise, when
the rate of lead oxide evaporation was high (i.e., low-SiO2
slags in the monoxide primary phase field), preheatings
were avoided, and the equilibration times minimized to
0.2–0.5 h.
Substrate
Mixture
name
Pre-melt
Atmosphere T, ◦ C
Au foil
PNS12
Air
760
Au foil
Au foil
3
4
PNS13
PNS11
PNS11
Air
Air
Air
Au foil
PNS9
Air
Au foil
Au foil
Au foil
PtIr foil
6
7
8
9
PNS6
PNS10
PNS10
PNS10
Air
Air
Air
Air
Liquid slag + monoxide (NiO) + olivine (Ni2 SiO4 )
5
Liquid slag + monoxide (NiO) + massicot (PbO)
Au foil
2
1150
–
950
950
830
800
760
850
Liquid slag + monoxide (NiO) + barysilite (Pb8 NiSi6 O21 )
1
–
–
–
–
–
700
720
–
700
Pre-cool
T, ◦ C
1100
1000
900
800
800
750
750
735
720
Final equilibration
T, ◦ C
5
5
17
72
5
168
17
72
17
Time,
h
41.8 ± 0.23
0.07 ± 0.04
0.01 ± 0.01
51.7 ± 0.28
0.00 ± 0.00
33.5 ± 0.10
Olivine
0.01 ± 0.01
33.7 ± 0.07
Olivine
Monoxide
0.19 ± 0.11
Slag
44.7 ± 0.24
52.0 ± 0.24
Olivine
0.22 ± 0.06
0.57 ± 0.22
0.01 ± 0.01
0.51 ± 0.16
33.9 ± 0.16
Monoxide
Monoxide
45.6 ± 0.23
Slag
0.04 ± 0.03
52.3 ± 0.25
Olivine
33.6 ± 0.28
Monoxide
Slag
46.1 ± 0.22
0.52 ± 0.13
52.7 ± 0.20
0.50 ± 0.23
Slag
100.0 ± 0.02
0.00 ± 0.00
Massicot
Barysilite
0.15 ± 0.01
39.9 ± 0.12
Monoxide
85.4 ± 0.31
53.5 ± 0.44
0.94
Slag
14.1 ± 0.33
0.73
51.9 ± 0.37
Barysilite
0.11 ± 0.09
47.1 ± 0.44
0.00
39.9 ± 0.50
Monoxide
Monoxide
0.15
53.5 ± 0.52
33.5 ± 0.31
Slag
53.5 ± 0.23
65.9 ± 0.28
40.0 ± 0.15
Barysilite
Slag
67.6 ± 0.16
0.26 ± 0.03
31.9 ± 0.16
0.14 ± 0.02
Monoxide
66.4 ± 0.24
33.6 ± 0.24
Di-lead silicate
Slag
73.5 ± 0.22
0.85 ± 0.62
26.1 ± 0.21
0.31 ± 0.18
PbO/Pb
Monoxide
SiO2 /Si
Slag
Phase
Composition, mol.%
Experimental conditions and measured compositions of the condensed phases for PbO–NiO–SiO2 system in air/argon atmosphere.
Liquid slag + monoxide (NiO) + di-lead silicate (Pb2 SiO4 )
No.
TA B L E 2
(Continues)
66.5 ± 0.10
99.9 ± 0.04
5.5 ± 0.35
66.3 ± 0.07
99.6 ± 0.16
3.3 ± 0.14
66.1 ± 0.16
98.9 ± 0.38
2.1 ± 0.11
66.3 ± 0.26
99.0 ± 0.36
1.3 ± 0.11
0.01 ± 0.02
99.7 ± 0.10
0.44 ± 0.14
6.6 ± 0.17
98.3
1.0 ± 0.17
6.6 ± 0.03
99.9
0.56 ± 0.12
6.5 ± 0.12
99.6 ± 0.06
0.45 ± 0.07
0.01 ± 0.01
98.8 ± 0.79
0.39 ± 0.10
NiO/Ni
ABDEYAZDAN et al.
1385
PtIr foil
11
PNS1
PNS6
Mixture
name
Air
Air
–
–
Pre-melt
Atmosphere T, ◦ C
–
–
Pre-cool
T, ◦ C
1450
1200
Final equilibration
T, ◦ C
SiO2
ampoule
SiO2
ampoule
SiO2
ampoule
SiO2
ampoule
PNS16a
PNS4
PNS14
PNS14
Au foil
Au foil
Au foil
16
17
18
PNS11
PNS9
PNS11
Liquid slag + monoxide (NiO)
15
14
13
12
Air
Air
Air
Air
ampoule
Argon
ampoule
Argon
ampoule
Argon
920
–
850
1550
1150
950
950
–
–
–
1480
–
–
–
900
900
800
1530
1100
900
800
Liquid slag + olivine (Ni2 SiO4 ) + quartz/tridymite/cristobalite (SiO2 ) + Pb–Ni metal
PtIr foil
Substrate
(Continued)
10
No.
TA B L E 2
5
2
17
17
5
72
168
2
3
Time,
h
0.03 ± 0.02
0.00 ± 0.00
Monoxide
0.03
98.5 ± 0.53
37.9 ± 0.21
100.0
0.35 ± 0.28
60.5 ± 0.20
Quartz
Pb metal
34.0 ± 0.09
0.04 ± 0.02
0.04
75.5 ± 5.8
0.05 ± 0.03
12.1 ± 0.08
0.01 ± 0.00
0.01
1.0 ± 0.27
99.9
0.77 ± 1.4
0.03 ± 0.03
60.6 ± 0.26
33.2 ± 0.09
99.8
0.01 ± 0.03
Tridymite
Pb metal
Ni metal
Olivine
Cristobalite
Ni metal
0.40 ± 0.19
63.4 ± 0.15
0.12 ± 0.03
0.03 ± 0.03
Monoxide
Monoxide
35.3 ± 0.13
Slag
0.13 ± 0.10
87.4 ± 0.30
11.7 ± 0.25
Monoxide
Slag
62.9 ± 0.26
0.26 ± 0.02
36.3 ± 0.26
0.03 ± 0.04
Slag
Slag
Slag
61.8 ± 0.10
95.8 ± 0.62
33.9 ± 0.20
0.01 ± 0.01
100 ± 0.01
0.25 ± 0.18
Tridymite
Pb metal
Olivine
0.04
33.9
Olivine
Slag
39.4 ± 0.23
0.03 ± 0.02
59.7 ± 0.22
33.9 ± 0.27
Olivine
Slag
22.2 ± 0.16
0.02 ± 0.03
58.3 ± 0.26
33.2 ± 0.23
0.01 ± 0.02
33.4 ± 0.22
Olivine
Olivine
0.05 ± 0.03
0.00 ± 0.00
Monoxide
Slag
38.1 ± 0.29
53.8 ± 0.27
Composition, mol.%
PbO/Pb
SiO2 /Si
Slag
Phase
(Continues)
99.9 ± 0.04
1.4 ± 0.12
99.5 ± 0.22
0.87 ± 0.15
99.7 ± 0.05
0.83 ± 0.11
99.0 ± 0.28
0.24*
66.8 ± 0.10
27.4 ± 0.27
99.9 ± 0.05
23.7 ± 5.5
0.05*
66.0 ± 0.20
4.1 ± 0.08
4.0 ± 0.77
0.00
66.1
1.5 ± 0.09
1.1 ± 0.34
0.00
66.1 ± 0.28
0.85 ± 0.09
100.0 ± 0.02
66.8 ± 0.25
19.4 ± 0.17
66.6 ± 0.21
100.0 ± 0.03
8.1 ± 0.14
NiO/Ni
1386
ABDEYAZDAN et al.
Au foil
Au foil
Au foil
PrIr foil
PtIr foil
PtIr foil
PtIr foil
PrIr foil
PtIr foil
PtIr foil
PtIr foil
PtIr foil
PtIr foil
PtIr foil
PtIr foil
PtIr foil
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
Substrate
(Continued)
19
No.
TA B L E 2
PNS2
PNS2
PNS3
PNS3
PNS3
PNS3
PNS3
PNS2
PN1
PNS3
PNS2
PNS2
PN1
PNS3
PNS2
PN1
Mixture
name
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
Air
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
Pre-melt
Atmosphere T, ◦ C
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
Pre-cool
T, ◦ C
1300
1300
1300
1300
1200
1200
1200
1200
1200
1100
1100
1100
1100
1000
1000
1000
Final equilibration
T, ◦ C
0.25
0.25
1
1
0.5
0.5
0.5
0.25
0.2
1
0.5
0.5
0.4
3
2
1
Time,
h
2.7 ± 0.22
99.7 ± 0.16
97.3 ± 0.24
99.7 ± 0.05
0.22 ± 0.05
0.03 ± 0.03
62.6 ± 0.46
0.03 ± 0.03
29.6 ± 0.41
0.00 ± 0.00
Monoxide
Monoxide
0.00 ± 0.00
68.8 ± 0.41
Slag
0.05 ± 0.03
23.7 ± 0.20
Monoxide
0.00 ± 0.00
49.8 ± 0.56
Slag
0.05 ± 0.03
40.2 ± 0.48
Monoxide
0.00 ± 0.00
46.8 ± 0.55
Slag
0.09 ± 0.08
42.8 ± 0.54
Monoxide
0.02 ± 0.05
42.3 ± 0.04
Slag
0.09 ± 0.08
50.0 ± 0.09
Monoxide
0.02 ± 0.05
44.6 ± 0.15
Slag
0.09 ± 0.08
47.9 ± 0.32
Monoxide
0.02 ± 0.05
46.7 ± 0.08
45.8 ± 0.16
Slag
0.05 ± 0.03
0.02 ± 0.04
Monoxide
Slag
68.6 ± 0.90
26.5 ± 0.84
Slag
–
4.5 ± 0.25
95.5 ± 0.23
Monoxide
99.9 ± 0.12
0.08 ± 0.04
–
0.04 ± 0.08
Monoxide
Slag
(Continues)
100.0 ± 0.03
7.7 ± 0.25
100.0 ± 0.03
7.5 ± 0.30
99.9 ± 0.03
9.9 ± 0.16
99.9 ± 0.03
10.4 ± 0.08
99.9 ± 0.14
7.7 ± 0.05
99.9 ± 0.14
7.5 ± 0.17
99.9 ± 0.14
7.5 ± 0.09
99.9 ± 0.05
4.8 ± 0.15
4.4 ± 0.12
99.7 ± 0.06
0.18 ± 0.03
54.0 ± 0.32
Monoxide
3.1 ± 0.09
41.6 ± 0.27
Slag
3.1 ± 0.12
99.7 ± 0.06
0.09 ± 0.06
69.5 ± 0.23
27.4 ± 0.22
Monoxide
2.8 ± 0.11
Slag
71.2 ± 0.28
0.18 ± 0.03
25.7 ± 0.33
0.09 ± 0.06
Slag
–
0.32 ± 0.11
–
Monoxide
0.18 ± 0.10
Monoxide
Slag
99.6 ± 0.23
56.0 ± 0.59
41.2 ± 0.55
0.18 ± 0.14
Slag
1.9 ± 0.13
99.9 ± 0.10
70.5 ± 0.34
0.09 ± 0.10
27.6 ± 0.33
0.04 ± 0.03
1.7 ± 0.22
99.8 ± 0.06
98.3 ± 0.24
0.09 ± 0.04
Monoxide
–
NiO/Ni
Slag
–
Monoxide
Composition, mol.%
PbO/Pb
SiO2 /Si
Slag
Phase
ABDEYAZDAN et al.
1387
closed
Ir wire
closed
PtIr foil
closed
PtIr foil
NiSi1
PNS1
PNS3
PNS3
PNS3
PNS6
Mixture
name
Air
Air
Air
Air
Air
Air
PtIr foil
PNS1
Air
–
–
–
45
44
43
ampoule
SiO2
ampoule
SiO2
ampoule
SiO2
PNS5
PNS5
PNS4
Argon
ampoule
Argon
ampoule
Argon
ampoule
1550
1510
1180
–
–
–
1540
1500
1150
1450
1400
2
2
4
2
6
38.8 ± 0.11
0.02 ± 0.02
36.3 ± 0.26
0.02 ± 0.02
32.5 ± 0.26
0.02 ± 0.02
18.0 ± 0.15
0.03 ± 0.02
45.4 ± 0.10
0.04 ± 0.07
47.5 ± 0.25
0.04 ± 0.07
51.5 ± 0.23
0.04 ± 0.07
53.4 ± 0.15
0.03 ± 0.04
Monoxide
71.8 ± 1.9
0.06 ± 0.02
18.4 ± 0.09
0.29 ± 0.64
0.01 ± 0.02
65.6 ± 0.16
Pb metal
Ni metal
2.0 ± 0.45
16.7 ± 0.14
0.02 ± 0.01
1.9 ± 0.29
68.9 ± 0.22
99.9 ± 0.07
0.02 ± 0.03
Cristobalite
Ni metal
Ni metal
Slag
0.02 ± 0.03
0.00
99.8
Cristobalite
Slag
0.07
32.7 ± 0.19
99.9
Tridymite
62.1 ± 0.19
99.7
Tridymite
Slag
33.2 ± 0.23
Olivine
0.01
19.5 ± 0.10
0.02 ± 0.03
62.9 ± 0.23
Slag
0.01 ± 0.01
0.02 ± 0.02
33.2 ± 0.1
99.8 ± 0.13
22.5 ± 0.16
64.0 ± 0.16
–
Monoxide
Slag
–
39.3 ± 0.21
0.03 ± 0.03
Slag
Monoxide
Slag
Monoxide
Slag
Monoxide
Slag
Olivine
1450
0.03 ± 0.02
0.00 ± 0.00
Monoxide
Slag
34.5 ± 0.60
53.8 ± 0.65
Composition, mol.%
PbO/Pb
SiO2 /Si
Slag
Phase
Tridymite
Air
0.5
0.33
0.33
0.33
0.33
2
Time,
h
ampoule
PNS1
1700
1550
1400
1400
1400
1300
Final equilibration
T, ◦ C
+ hole
SiO2
–
–
–
–
–
–
Pre-cool
T, ◦ C
Liquid slag + tridymite/cristobalite (SiO2 ) + Pb–Ni metal (optional)
42
41
1710
–
–
–
–
–
Pre-melt
Atmosphere T, ◦ C
Liquid slag + olivine (Ni2 SiO4 ) + tridymite (SiO2 )
40
39
38
PtIr foil
closed
PtIr foil
36
37
PtIr foil
Substrate
(Continued)
35
No.
TA B L E 2
(Continues)
98.1 ± 0.29
0.12*
14.3 ± 0.19
98.0 ± 0.45
0.19
16.0 ± 0.16
99.9 ± 0.03
27.9 ± 1.6
0.07*
5.2 ± 0.11
0.27*
66.8 ± 0.25
17.6 ± 0.14
0.16*
66.8 ± 0.1
13.5 ± 0.18
99.97 ± 0.03
60.7 ± 0.21
99.9 ± 0.03
28.6 ± 0.17
99.9 ± 0.08
16.0 ± 0.11
99.9 ± 0.08
16.2 ± 0.13
99.9 ± 0.08
15.8 ± 0.10
100.0 ± 0.02
11.7 ± 0.13
NiO/Ni
1388
ABDEYAZDAN et al.
ampoule
SiO2
ampoule
SiO2
ampoule
SiO2
ampoule
SiO2
ampoule
SiO2
ampoule
SiO2
ampoule
SiO2
Substrate
(Continued)
NiSi0
PNS17
PNS18
PNS5a
PNS8
PNS7
PNS7
Mixture
name
Air
ampoule
Argon
ampoule
Argon
ampoule
Argon
ampoule
Argon
ampoule
Argon
Argon
1682
1645
1620
1615
1610
1615
1560
Pre-melt
Atmosphere T, ◦ C
–
–
–
–
–
–
–
Pre-cool
T, ◦ C
55
54
53
Ir wire
ampoule
SiO2
ampoule
SiO2
NiSi1
PNS15
PNS16
Air
ampoule
Argon
ampoule
Argon
1670
1590
1570
–
1520
1500
Liquid slag + monoxide (NiO) + cristobalite (SiO2 ) + Pb–Ni metal (optional)
52
51
50
49
48
47
46
No.
TA B L E 2
1655
1560
1540
1680
1630
1600
1600
1600
1600
1550
Final equilibration
T, ◦ C
0.8
4
4
0.4
3
3
3
2
2
2
Time,
h
0.59 ± 0.27
10.9 ± 0.18
0.02 ± 0.00
0.41 ± 0.10
7.2 ± 0.11
0.00 ± 0.00
59.7 ± 0.24
99.6 ± 0.03
0.03 ± 0.03
50.6 ± 0.44
Ni metal
Cristobalite
Ni metal
0.42 ± 0.06
13.0 ± 0.16
0.01 ± 0.01
0.79 ± 0.09
11.3 ± 0.16
0.01 ± 0.01
1.0 ± 0.26
0.00 ± 0.00
66.3 ± 0.45
99.7 ± 0.03
0.03 ± 0.04
79.3 ± 0.21
99.9 ± 0.04
0.05 ± 0.05
Ni metal
Cristobalite
Ni metal
Cristobalite
Ni metal
12.2 ± 0.12
0.01 ± 0.01
0.04 ± 0.03
1.0 ± 0.05
99.5 ± 0.04
0.00 ± 0.00
Cristobalite
Ni metal
–
0.01 ± 0.01
99.0
Monoxide
Cristobalite
–
–
44.0 ± 0.31
Slag
Slag
54.9 ± 0.25
1.3 ± 0.12
0.00 ± 0.00
Ni metal
0.00 ± 0.00
0.01 ± 0.02
99.9 ± 0.02
Cristobalite
Monoxide
13.4 ± 0.13
0.01 ± 0.01
57.5 ± 0.19
–
0.00 ± 0.00
99.0
Monoxide
Slag
Cristobalite
–
0.11 ± 0.06
0.04 ± 0.05
Ni metal
Slag
45.1 ± 0.17
10.0 ± 0.54
0.01 ± 0.01
55.6 ± 0.97
99.2 ± 0.01
Slag
Cristobalite
Slag
Slag
0.11
99.3
Cristobalite
Slag
Slag
0.03
13.9 ± 0.48
99.6
55.8 ± 0.58
Composition, mol.%
PbO/Pb
SiO2 /Si
Cristobalite
Slag
Phase
(Continues)
1.0*
99.99 ± 0.01
56.0 ± 0.31
99.0 ± 0.05
0.50*
100.0 ± 0.01
32.9 ± 0.29
98.7 ± 0.12
0.06*
100.0 ± 0.01
29.2 ± 0.19
1.0*
54.9 ± 0.17
99.8 ± 0.08
0.81*
34.4 ± 1.0
99.0 ± 0.26
0.13*
9.4 ± 0.13
99.2 ± 0.09
0.30*
20.6 ± 0.39
99.6 ± 0.06
0.41*
42.2 ± 0.41
99.6 ± 0.11
0.42*
29.3 ± 0.27
99.4 ± 0.27
0.35*
30.3 ± 0.61
NiO/Ni
ABDEYAZDAN et al.
1389
Substrate
(Continued)
Mixture
name
Ir wire
ampoule
SiO2
ampoule
SiO2
Au foil
PNS20
NiSi2
NiSi0
PNS8
Argon
Air
Air
Air
ampoule
780
–
1705
650
–
–
–
Pre-cool
T, ◦ C
730
1740
1703
1660
Final equilibration
T, ◦ C
120
1
0.4
2
Time,
h
6.3 ± 0.06
0.12 ± 0.10
2.0 ± 0.21
51.9 ± 0.38
0.9*
1.3 ± 0.16
53.2 ± 0.22
99.6 ± 0.10
0.51*
3.3 ± 0.17
38.7 ± 0.72
NiO/Ni
Zn ). Real solubility of NiO in
53.4 ± 0.32
40.3 ± 0.32
Barysilite
62
58.0 ± 0.21
41.9 ± 0.21
–
Slag2
Slag
–
48.1 ± 0.38
98.0 ± 0.21
Slag1
61
99.1
Cristobalite
–
–
Slag 1
–
0.02 ± 0.02
Ni metal
98.7 ± 0.16
0.40 ± 0.11
99.5
Cristobalite
46.8 ± 0.22
0.01
95.7 ± 0.21
Slag 2
6.3 ± 0.19
0.99 ± 0.05
55.0 ± 0.68
Composition, mol.%
PbO/Pb
SiO2 /Si
Slag 2
Slag 1
Phase
*NiO in quartz/tridymite/cristobalite is an artefact of secondary x-ray fluorescence, similar to other elements with high energy of characteristic lines (e.g., Fe, Cu
quartz/tridymite/cristobalite is expected to be <0.1%.
59
Slag + barysilite
58
Slag 1 + slag 2
57
56
1675
Pre-melt
Atmosphere T, ◦ C
Slag 1 + slag 2 + cristobalite (SiO2 ) + Pb–Ni metal
No.
TA B L E 2
1390
ABDEYAZDAN et al.
ABDEYAZDAN et al.
1391
(A)
(B)
(C)
(D)
(E)
(F)
F I G U R E 1 Back-scattered electron micrographs of typical phase assemblages in the PbO–NiO–SiO2 system illustrating: (A) liquid slag,
monoxide (NiO), and barysilite (Pb8 NiSi6 O21 ) equilibrium at 735◦ C; (B) liquid slag, monoxide, and olivine (Ni2 SiO4 ) equilibrium at 800◦ C; (C)
liquid slag, monoxide, and massicot (PbO) equilibrium at 800◦ C; (D) liquid slag, tridymite (SiO2 ), olivine, and Pb metal equilibrium at 900◦ C;
(E) liquid slag, tridymite, Ni metal, and Pb metal equilibrium at 1150◦ C; and (F) liquid slag 1, liquid slag 2, cristobalite (SiO2 ), and Ni metal
equilibrium at 1660◦ C. The labels indicate the experiment number, sample name, and experimental temperature as given in Table 2.
Following equilibration, the samples were rapidly
quenched in calcium chloride brine at −20◦ C, washed with
water and ethanol, dried, and mounted in epoxy resin.
Polished cross-sections were prepared using conventional
metallographic techniques. The samples were examined
using optical microscopy and then carbon-coated. The
compositions of the phases were measured using electron
probe x-ray microanalysis (EPMA) (JEOL 8200 L EPMA;
Japan Electron Optics Ltd.). The EPMA was operated with
a probe current of 20 nA and acceleration voltage of 15 kV.
The Duncumb–Philibert atomic number, absorption, and
fluorescence correction (ZAF correction) was applied.
1392
ABDEYAZDAN et al.
F I G U R E 2 Phase diagram of the
NiO–SiO2 system with new experimental
results at 1655◦ C–1740◦ C and lines estimated
using the thermodynamic database,
compared to previous model.23
(A)
(B)
(D)
(C)
F I G U R E 3 Calculated excess functions: (A) enthalpy, (B) entropy, (C) Gibbs energy, (D) heat capacity of mixing of the hypothetical
supercooled single liquid in the NiO–SiO2 system at 1700◦ C relative to pure supercooled liquid components, compared to previous model.23
Wollastonite (CaSiO3 ) and Ni metal (supplied by Charles
M. Taylor Co.) and PbO–SiOO2 K456 glass (71.4 wt.%
PbO, supplied by NIST) standards were used for Si, Ni,
and Pb calibration of the EPMA, respectively. The equilibrated samples were checked for Fe and Al impurities from
the Kanthal wires; measurements in the areas containing
these elements were rejected. Only the concentrations of
metal cations were measured with EPMA. According to
literature and authors’ previous studies,27–29 all cations in
this system (Pb2+ , Ni2+ , Si4+ ) were expected to have the
same valences in slag regardless of conditions being oxidizing (air) or reducing (equilibrium with metal). Therefore,
the results from both conditions can be presented on
the same liquidus phase diagram. The presence of Pb–Ni
ABDEYAZDAN et al.
TA B L E 3
1393
Thermodynamic parameters of the PbO–NiO–SiO2 system optimized in the present study (J/mol).
Excess parameters in liquid slag
Excess interaction
parameters
Value, J/mol
Model
0
Δ𝑔Pb
2+ ,Ni2+
12 970.4 +17.3636 T
MQM (site)
9,0,1
𝑞Si
4+ ,Pb2+ ,Ni2+
3,0,1
𝑞Si
4+ ,Pb2+ ,Ni2+
3,0,2
𝑞Si
4+ ,Pb2+ ,Ni2+
1,0,1
𝑞Si
4+ ,Pb2+ ,Ni2+
0,0,1
𝑞Si
4+ ,Pb2+ ,Ni2+
0
Δ𝑔Si
4+ ,Ni2+
3,0
𝑞Si
4+ ,Ni2+
7,0
𝑞Si
4+ ,Ni2+
0,1
𝑞Si
4+ ,Ni2+
9,0
𝑞Si
4+ ,Ni2+
0
Δ𝑔Si
4+ ,Pb2+
0,1
𝑞Si4+ ,Pb2+
0,2
𝑞Si
4+ ,Pb2+
1,0
𝑞Si
4+ ,Pb2+
2,0
𝑞Si
4+ ,Pb2+
3,0
𝑞Si
4+ ,Pb2+
5,0
𝑞Si4+ ,Pb2+
7,0
𝑞Si
4+ ,Pb2+
9,0
𝑞Si4+ ,Pb2+
11,0
𝑞Si
4+ ,Pb2+
13,0
𝑞Si
4+ ,Pb2+
15,0
𝑞Si
4+ ,Pb2+
12 970.4
MQM (pair)
−5230 −12.552 T
MQM (pair)
−12 970.4
MQM (pair)
−101 252.8 +62.76 T
MQM (pair)
−6694.4 +1.6736 T
MQM (pair)
−3305.36 +7.9496 T
MQM (site)
73 638.4
MQM (site)
299 867.28 –121.336 T
MQM (site)
7322
MQM (site)
10 627.36
Bragg–Williams
−19 939.4 −0.901 T
MQM (pair)
−7860.1
MQM (pair)
6599.9
MQM (pair
−5966.4
MQM (pair)
17 714.5
MQM (pair)
20 138.4
MQM (pair)
−1186.9
MQM (pair)
−2448.9
MQM (pair)
6461.7
MQM (pair)
−1925.8
MQM (pair)
−2081.9
MQM (pair)
12 627.2
MQM (pair)
Excess parameters in liquid metal
Excess interaction
parameters
Value, J/mol
Model
0
Δ𝑔Ni,O
−299 574.4 −2.9288 T
MQM (pair)
1,0
𝑞Ni,O
8,0
𝑞Ni,O
0,1
𝑞Ni,O
0,2
𝑞Ni,O
0
𝐿Pb,Si
0
Δ𝑔Pb,O
1,0
𝑞Pb,O
3,0
𝑞Pb,O
0,1
𝑞Pb,O
0,0,1
𝑞Pb,O,Ni
0
𝐿Ni,Pb
1
𝐿Ni,Pb
2
𝐿Ni,Pb
3
𝐿Ni,Pb
0
Δ𝑔Ni,Si
0
Δ𝑔Si,O
1,0
𝑞Si,O
23 430.4 +1.6736 T
MQM (pair)
33 890.4 −10.46 T
MQM (pair)
20 920
MQM (pair)
92 048 −16.736 T
MQM (pair)
17 154.4
Bragg–Williams
−336 937.52 +80.835 T −8.24248 Tln(T)
MQM (pair)
175 728 −75.312 T
MQM (pair)
−105 855.2 +54.392 T
MQM (pair)
41 840
MQM (pair)
29 288
MQM (pair)
14 470.553 −3.104133 T
Bragg–Williams
2685.23 −0.25543 T
Bragg–Williams
−8680.7633 +5.87333 T
Bragg–Williams
−580.57
Bragg–Williams
−44 936.16 +6.94544 T
MQM (pair)
−342 878.8 +17.9912 T
MQM (pair)
41 840
MQM (pair)
(Continues)
1394
TA B L E 3
ABDEYAZDAN et al.
(Continued)
Excess parameters in solid (FCC) metal
Excess interaction
parameters
Value, J/mol
Model
0
𝐿Ni,Si
−238 488 +50.208 T
Bragg–Williams
1
𝐿Ni,Si
0
𝐿Ni,Pb
−28 451.2
Bragg–Williams
19 691.39 +36.05 T
Bragg–Williams
Endmember in liquid slag
Endmember
ΔH𝟎 298 , J/mol
S𝟎 298 , J/mol K
Temperature
range, K
Cp (T), J/mol K
SiO2
−906 244.805
43.730
0–50
0.0003T3 −8.03274×10−6 T4 +6.14328×10−8 T5
50–298.15
−1.58728+0.130883T+0.000801T2
−4.05645×10−6 T3 +5.54804×10−9 T4
298.15–3500
−209.89−0.155843T+9.22876×10−6 T2
−1 384 359.64T−2 −2886.8039T−1
+11.663394T0.5 +2130.928475T−0.5
3500–4000
82.8079
0–50
0.0161T2 +7.15644×10−5 T3
−1.08544×10−5 T4 +1.16012×10−7 T5
50–400
−5.90711+0.618113T−0.003429T2
+9.98691×10-6 T3 −1.04244×10-8 T4
400–4000
64.9984
0–50
1.92258×10−5 T3 +9.62836×10−8 T4
50–298.15
−6.43526+0.150407T+0.000996T2
−4.91334×10−6 T3 +6.04796×10−9 T4
298.15–600
−142.44945+0.64610016T+3 531 493T−2
−0.000511168T2
600–4000
71
PbO
NiO
−200 875.5642
−202 570.045
75.4
42.78
Endmember in liquid
metal
Endmember
ΔH0 298 , J/mol
S0 298 , J/mol K
Temperature
range, K
Cp (T), J/mol K
Ni
18 253.76059
42.41963
0–50
0.007T+3.48508×10−5 T3 −3.87456×10−7 T4
+5.32392×10−9 T5
50–298.15
−11.3231+0.375198T−0.001541T−2
+2.95524×10−6 T3 −2.13808×10−9 T4
298.15–1728
22.096+0.0096814T+1.60574×10−19 T6
1728–5000
43.1
0–298.15
0.171588T−0.000273T−2
298.15–600.65
24.5242+0.007318T+1.4637×10−6 T−2
+2.52605×10−17 T6
600.65–1200
32.4914−0.003092T
1200–5000
18.9641+0.005766T−5.88864×10−7 T2
+5 393 509.8T−2
Pb
O
Si
4672.912535
130 747.228
50 200.00062
72.53827
32.3
48.61229
5000
33.2876
0–298.15
0.000433T2 −7.75504×10−7 T3
298.15–2990
24.5+0.001968T+7.76287×10−7 T2
−645 034.4T−2
2990–5000
36.2
0–1685
22.8092+0.003871T−352 992.8T−2
1685–5000
27.196
(Continues)
ABDEYAZDAN et al.
TA B L E 3
1395
(Continued)
Endmember in liquid slag
Temperature
range, K
ΔH𝟎 298 , J/mol
S𝟎 298 , J/mol K
Endmember
ΔH0 298 , J/mol
S0 298 , J/mol K
Temperature
range, K
Cp (T), J/mol K
Ni
1839.06979
33.02261
0–50
0.007T+3.48508×10−5 T3 −3.87456×10−7 T4
+5.32392×10−9 T5
50–298.15
−11.3231+0.375198T−0.001541T2
+2.95524×10−6 T3 −2.13808×10−9 T4
298.15–1728
22.096+0.009681T
1728–3000
43.1−1.01479×1033 T−10
3000–5000
43.0828
0–50
0.041198T2 −0.000780T3 −2.72169×10−6 T4
+1.04927×10−7 T5
50–298.15
25.1899+8.49961×10−5 T+1.94497×10−5 T2
−10009.3586T−2
298.15–600.65
24.5242+0.007318T+1.4637×10−6 T2
600.65–1200
32.4914−0.003092−7.2508×1027 T−10
1200–5000
18.9641+0.005766T-5.88864×10−7 T2
+5 393 509.8T−2 −7.2508×1027 T−10
5000
33.2876
24.5+0.001968T+7.76287×10−7 T2
−645 034.4T−2
Endmember
Cp (T), J/mol K
Endmember in solid
(FCC) metal
(D = 0.52, TC = 633,
p = .28)
Pb
0
64.78505
O
129 747.228
29.2
0–2000
2000–5000
31.3807
Si
50 999.99806
40.61963
0–1687
22.8318+0.003826T+2.1312×10−8 T2
−353 334T−2
1687–3600
27.196+3.78 332×1032 T−10
3600–5000
27.197
0
0
Compound
ΔH 298 , J/mol
S 298 , J/mol K
Temperature
range, K
Cp (T), J/mol K
SiO2_ Quartz(l)
−910 700
41.46
0–50
0.000122017T3 −1.51256×10−6 T4
50–298.15
−3.5035+0.16874T+0.00048566T2
−2.96634×10−6 T3 +4.20792×10−9 T4
298.15–373
80.012−3 546 684T−2 −240.276T−0.5
+491 568 369T−3
373–848.02
80.012+0.00844T−3 546 684T−2
−4.52127×10−5 T2 +6.0550446×10−8 T3
−240.276T−0.5 +491 568 369T−3
848.02–3000
80.012−3 546 684T−2 −240.276T−0.5
+491 568 369T−3
0–50
0.000122017T3 −1.51256×10−6 T4
50–298.15
−3.5035+0.16874T+0.00048566T2
−2.96634×10−6 T3 +4.20792×10−9 T4
298.15–3000
80.012−3 546 684T−2 −240.276T−0.5
+491568369T−3
0–50
0.0003T3 −8.03274×10−6 T4 +6.14328×10−8 T5
50–298.15
−1.587+0.13088T+0.000801248T2
−4.05645×10−6 T3 +5.54804×10−9 T4
298.15–3000
75.3727−5 958 095T−2 +958 246 123T−3
SiO2_ Quartz(h)
SiO2_ Tridymite(h)
−908 627
−907 045
44.2068
45.5237
(Continues)
1396
TA B L E 3
ABDEYAZDAN et al.
(Continued)
Endmember in liquid slag
Endmember
ΔH𝟎 298 , J/mol
S𝟎 298 , J/mol K
Temperature
range, K
Cp (T), J/mol K
SiO2_ Cristobalite(h)
−906 377
46.0288
0–50
0.0003T3 −8.03274×10−6 T4 +6.14328×10−8 T5
50–298.15
−1.587+0.13088T+0.000801248T2
−4.05645×10−6 T3 +5.54804×10−9 T4
298.15–3000
83.5136−2 455 360T−2 −374.693T−0.5
+280 072 194T−3
0–50
1.91456×10−5 T3 +9.62837×10−8 T4
50–298.15
−6.4443 +0.15074T+0.0009913T2
−4.97177×10−6 T3 +6.00761×10−9 T4
298.15–2230
514.27+0.39759T+5 035 500T−2
−3.4982×10−5 T2 −68 525T−1 −24.001T−0.5
0–50
0.28711T−0.000778629T2 +2.5234×10−5 T3
50–298.15
−13.19+0.57007T+0.000197912T2
−1.95592×10−6 T3
298.15–3000
214.997−4 944 530T−2 −1030.75T−0.5
+623 705 000T−3
0–50
0.0155T2 +8.727016×10−5 T3 −1.153202×10−5 T4
+1.223595×10−7 T5
50–298.15
5.401+0.16529T+0.00144058T2
−1.352167×10−5 T3 +4.12124×10−8 T4
−4.425483×10−11 T5
298.15–1159
47.639+0.012255T−45 546 016T−3
−65.75326T−0.5
1159–3000
64.998−120 000T−2 −7 826 793 210T−3
0–50
0.0160264T2 +2.434455×10−5 T3
−8.428563×10−6 T4 +8.541893×10−8 T5
50–298.15
5.028+0.25756T−0.000225791T2
−2.078854×10−6 T3 +7.11424×10−9 T4
−7.259215×10−12 T5
298.15–1159
47.639+0.012255T−45 546 016T−3
−65.75326T−0.5
1159–3000
64.998−120 000T−2 −7 826 793 210T−3
0–50
0.001109T3 −2.82901×10−5 T4 +2×10−7 T5
50–298.15
−1.9176+0.591015T−0.00141064T2
+1.66112×10−6 T3 −3.6643×10−10 T4
298.15–1200
−35.227−0.13966T+9.6807T0.5
NiO
−237 393
42.6585
(D = 0.933, TN = 523,
p = .28)
Ni2 SiO4
−1 394 775
128.3
(D = 0.75, TN = 29.15,
p = .28)
PbO_litharge_(red)(l)
PbO_massicot_
(yellow) (h)
PbSiO3
Pb2 SiO4
Pb3 Si2 O7 _Pb_
barysilite
−219 268
−218 062
−1 149 128
−1 369 422
−2 518 645
67.14
68.699
110.688
184
294.588
1200–3000
132.5303
0–50
0.0025585T3 −7.21063×10−5 T4 +5.6×10−7 T5
50–298.15
6.297+0.846782T−0.00187134T2
+1.52262×10−6 T3 +5.46982×10−10 T4
298.15–1200
−24.98−0.17976T+12.475T0.5
0–50
0.0036675T3 −0.0001004T4 +7.6×10−7 T5
50–298.15
4.3796+1.437796T−0.003282T2
+3.18374×10−6 T3 +1.80552×10−10 T4
298.15–1200
−60.207−0.31942T+22.1557T0.5
(Continues)
ABDEYAZDAN et al.
TA B L E 3
1397
(Continued)
Endmember in liquid slag
Endmember
ΔH𝟎 298 , J/mol
S𝟎 298 , J/mol K
Temperature
range, K
Pb5 SiO7
−2 007 200
408.72
0–50
0.0480792T2 +0.00263153T3 −9.7392×10−5 T4
+8.16257×10−7 T5
50–298.15
21.381+1.61947T−0.00254871T2
−4.713942×10−6 T3 +2.18897×10−8 T4
−2.17776×10−11 T5
298.15–1400
76.9129−0.1478776T+13.98408T0.5
0–50
0.080132T2 +0.00779722T3 −0.000258462T4
+2.107095×10−6 T5
50–298.15
44.0312+3.82816T−0.006743T2
−5.82641×10−6 T3 +3.72121×10−8 T4
−3.62961×10−11 T5
298.15–1300
57.142−0.57953T+43.733316T0.5
0–50
0.00957222T3 −0.000257277T4 +1.92×10−6 T5
50–298.15
−1.5202+4.20836T−0.0083939T2
+4.71795×10−6 T3 +5.635854×10−9 T4
298.15–1200
323.402−0.52057T+5 035 500T−2
−3.4982×10−5 T2 +39.6718T0.5 −68 525T−1
Pb11 Si3 O17
Pb8 NiSi6 O21
−5 204 405
−7 587 000
895.5
854
Cp (T), J/mol K
Note: MQM (site): modified quasichemical model expressed as polynomial in terms of site fractions; MQM (pair): modified quasichemical model expressed as
polynomial in pair fractions.
T A B L E 4 The invariant reactions in the NiO–SiO2 , PbO–NiO, and PbO–NiO–SiO2 systems calculated by FactSage using the database
developed in the present study.
Reaction
L2 = L1 + SiO2 (cristobalite), monotectic
Tmodel ,
◦
C
1703
mol.%, liquid
PbO
NiO
SiO2
0
1.7
98.3
0
53.3
46.7
L = NiO (monoxide) + SiO2 (cristobalite)
1655
0
55.5
44.5
NiO (monoxide)+ SiO2 (cristobalite) = Ni2 SiO4 (olivine)
1551
11.9
32.3
55.8
L = NiO (monoxide) + PbO (massicot)
883
99.20
0.80
0
L + NiO (monoxide) = Pb8 NiSi6 O21 (barysilite), saddle point
783
56.3
0.90
42.8
L + NiO (monoxide) = Pb8 NiSi6 O21 (barysilite) + Ni2 SiO4 (olivine)
767
50.6
0.99
48.4
L = Pb8 NiSi6 O21 (barysilite) + Ni2 SiO4 (olivine) + PbSiO3
758
49.4
0.91
49.7
L + Pb8 NiSi6 O21 (barysilite) = NiO (monoxide) + Pb2 SiO4
738
67.5
0.50
32.0
L + PbO (massicot) = Pb5 SiO7
733
79.1
0
20.9
L + PbO (massicot) = NiO (monoxide) + Pb5 SiO7
731
78.7
0.36
20.9
L = SiO2 (quartz) + PbSiO3
728
77.1
0.36
22.6
L + Pb5 SiO7 = Pb11 Si3 O17
726
77.3
0
22.7
L = SiO2 (quartz) + Ni2 SiO4 (olivine) + PbSiO3
725
40.6
0.62
58.8
L + Pb5 SiO7 = Pb11 Si3 O17 + NiO (monoxide)
724
77.1
0.36
22.6
L = PbSiO3 + Pb2 SiO4
720
59.5
0
40.5
L = Pb8 NiSi6 O21 (barysilite) + PbSiO3 + Pb2 SiO4
720
59.5
0.08
40.5
L = Pb2 SiO4 + Pb11 Si3 O17
719
74.1
0
25.9
L = NiO (monoxide) + Pb2 SiO4 + Pb11 Si3 O17
718
73.8
0.37
25.9
1398
ABDEYAZDAN et al.
F I G U R E 4 Calculated (A) enthalpy and
(B) entropy of melting of the NiO monoxide to
liquid, and (C) heat capacity of solid and
supercooled liquid NiO, compared to
literature.55–60
(A)
(B)
(C)
metal (liquid or solid) would provide additional information on thermodynamic behavior of the system (slag-metal
distributions). However, the Pb-rich liquid metal is corrosive to the available metallic substrates (Au or Pt–Ir),
and therefore this option was only used for experiments
in SiO2 ampoules (quartz/tridymite/cristobalite primary
phase fields).
Achievement of equilibrium in the samples was ensured
by using the four-point test approach26,30 : (i) variation of
equilibration time, (ii) assessment of the compositional
homogeneity of phases by EPMA, (iii) approaching the
final equilibrium point from different starting conditions,
and (iv) consideration of reactions specific to this system that may affect the achievement of equilibrium or
ABDEYAZDAN et al.
1399
to expected from the initial bulk mixtures were accepted.
Also, formation of certain solids (e.g., olivine Ni2 SiO4
from monoxide NiO + cristobalite SiO2 , or any solids at
low temperatures from viscous slags) could be problematic due to small thermodynamic driving force, therefore equilibration was followed from the pre-annealing
of sample at the temperature higher or lower than the
target equilibration temperature, to exclude potential
metastability.
(A)
(B)
F I G U R E 5 Calculated (A) enthalpy and (B) entropy of melting
of the Ni2 SiO4 olivine to liquid (metastable relative to monoxide and
cristobalite), compared to literature for the Ni2 SiO4 ,49,54 Mn2 SiO4 ,50
Fe2 SiO4 ,51,52 Co2 SiO4 ,49 and Mg2 SiO4 53 olivine–liquid transitions.
3
The experimental study was conducted parallel with a
thermodynamic database development describing the system. The database was used in conjunction with the
FactSage 7.2 thermodynamic package31 to assist the selection of sample compositions used in the experimental
study. As new experimental data were obtained, the thermodynamic parameters were progressively optimized and
incorporated in the revised database.
The slag phase was described using a modified Quasichemical formalism32–35 that combines the Gibbs energy
parameters of three types: (i) the Bragg–Williams model,
a polynomial in terms of pure component concentrations
for the random mixing configurational entropy; (ii) the
Quasichemical model, which assumes the formation of
A–A, B–B, A–B pairs with the Gibbs free energies that are
a polynomial function of the overall composition; and (iii)
the Quasichemical model, which assumes the formation
of pairs with the Gibbs free energy that are polynomial
functions of pair fractions. The binary parameters were
extrapolated into the corresponding ternary system using
a geometric formalism with the Toop (asymmetrical)
approach,36,37 where the acidic component SiO2 was
placed at the top apex of the Toop model triangle, while
the basic PbO and NiO were placed at its base.
4
4.1
F I G U R E 6 Calculated heat capacity of Ni2 SiO4 olivine and
supercooled liquid, compared to literature for liquid Ni2 SiO4 ,54
Mn2 SiO4 ,50 and Fe2 SiO4 .51
reduce the accuracy. Among the latter reactions, the one
of primary concern was evaporation of lead oxide. Several separate areas were tested in each sample in open
substrate, and if any areas were found to contain unreasonably reduced PbO concentration, they were rejected, while
those with gradient-free slag and PbO concentrations close
THERMODYNAMIC MODELING
RESULTS AND DISCUSSION
Experimental results
Figure 1 shows micrographs of the quenched PbO–
NiO–SiO2 samples at selected temperatures and bulk
compositions illustrating the phase assemblages observed
on equilibration. Examples of microstructures are presented for liquid slag–monoxide–barysilite equilibrium
at 735◦ C in Figure 1A liquid slag–monoxide–olivine at
800◦ C in Figure 1B, liquid slag–monoxide–massicot at
800◦ C in Figure 1C and liquid slag–tridymite–Ni metal–Pb
metal equilibrium at 1150◦ C in Figure 1E. Note that, Ni
oxide has a very steep liquidus at low temperature and
1400
ABDEYAZDAN et al.
F I G U R E 7 Liquidus projection of the PbO–NiO–SiO2 system according to the new experimental results at 720◦ C–1703◦ C in air or in
equilibrium with liquid metal (as given in Table 2), and estimated with the thermodynamic database, where; PS = PbSiO3 ,
P8NS6 = Pb8 NiSi6 O21 , P2S = Pb2 SiO4 , P11S3 = Pb11 Si3 O17 , P5S = Pb5 SiO7 , and N2S = Ni2 SiO4 . The experimental points shown with crossline
markers indicate the liquid slag composition at the target temperature.
the viscosity of slag is quite high. Therefore, NiO has
low chance to recrystalize into bigger regular-shaped
particles and predominantly stays as conglomerate of the
original mixture particles (Figure 1A–C). So, in the case
of barysilite, it formed after NiO particles were already
present, and so that is why NiO particles are included
in large barysilite particles. The experimental results
for the ternary PbO–NiO–SiO2 liquidus are given in
Table 2.
4.2
Thermodynamic modeling results
The updated thermodynamic parameters of quartz,
tridymite, and cristobalite (SiO2 ), monoxide (NiO),
olivine (Ni2 SiO4 ), litharge and massicot (PbO), lead
silicates (PbSiO3 , Pb2 SiO4 , Pb11 Si3 O17 , Pb5 SiO7 ), and the
parameters of the binary PbO–SiOO2 liquids were taken
from the parallel studies at PyroSearch,38 ensuring physically reasonable description of these phases down to 0 K
and improved description of heat capacities of liquid slag
endmembers. The NiO–SiO2 binary system published
before23 was reviewed in the present study as the models of
binaries have changed significantly since 2013. Therefore,
new optimization was required, supported particularly
by experiments at higher temperatures (1655◦ C–1740◦ C)
to reach previously unstudied phase assemblages—two
immiscible liquids and monoxide primary phase field.
The melting point of NiO is increased from 1955◦ C
to 1990◦ C in the new version of the model. Both values
ABDEYAZDAN et al.
1401
F I G U R E 8 Details of the high-PbO region of the liquidus projection of the PbO–NiO–SiO2 system according to the new experimental
results at 720◦ C–1703◦ C in air or in equilibrium with liquid metal (as given in Table 2) and estimated with the thermodynamic database. The
phase boundaries and liquidus isotherms are estimated using the thermodynamic database, where; PS = PbSiO3 , P8NS6 = Pb8 NiSi6 O21 ,
P2S = Pb2 SiO4 , P11S3 = Pb11 Si3 O17 , and P5S = Pb5 SiO7 . The experimental points shown with crossline markers give the liquid slag
composition at the target temperature.
appear in the literature.39–42 There is uncertainty due to
the probable mechanism of NiO melting with decomposition to Ni–NiO metal + O2 gas, which may result into
underestimated “true” congruent melting point of NiO.
The updated database calculation shows that if O2 loss is
considered, then NiO melts with decomposition to Ni–O
metal + O2 at 1970◦ C under 1 atm O2 and at 1947◦ C in air
(0.21 atm O2 ). Therefore, no contradiction to literature is
introduced by the increased Tmelt (NiO), as the observed
melting points with O2 loss might vary depending on the
atmosphere. The phase equilibria in the multicomponent
slags (particularly the slope of liquidus of NiO when combined with SiO2 , CaO, MgO, Al2 O3 , Fe2 O3 ) should be the
main criteria to selecting the “true” congruent Tmelt (NiO),
and the new value (1990◦ C) improves the description of
those phase equilibria (to be published elsewhere).
The new optimization and review of this system resulted
in improved binary and ternary miscibility gap description. In particular, (a) the monoxide (NiO) liquidus at
1700◦ C has improved; (b) the monoxide-cristobalite eutectic has increased from 1650◦ C to 1655◦ C, in agreement
with the new experiments; (c) the monotectic temperature
has increased from 1675◦ C to 1703◦ C and the composition of the high-SiO2 liquid changed to more SiO2 -rich,
also supported by the experiments of the present study
(Figure 2). The enthalpy of mixing of the NiO–SiO2 liquid
is modeled to be positive, responsible for the miscibility
gap (Figure 3). The difference from the previous model23
is more smooth shape of thermodynamic functions of
mixing, resulting in a miscibility gap that is disappearing more readily on addition of the third component
(PbO).
1402
ABDEYAZDAN et al.
F I G U R E 9 An isothermal section of the calculated phase diagram using the database developed in this study along with the
experimental results at 1100◦ C, where N2S = Ni2 SiO4 . The experimental points shown with crossline markers indicate the liquid slag
composition at the target temperature.
The thermodynamic properties of solid and supercooled liquid NiO were revised to make them more
consistent with the Third Law and avoiding the Kauzmann Paradox43,44 (Figure 4). The heat capacity of
supercooled liquid NiO was increased from 67 to 71 J/mol
K above 600 K. The value of 67 J/mol K is believed to be
mistakenly assigned by45 similar to molten FeO (the only
chemically similar oxide with low melting point for which
actual calorimetric data exist). However, that value by
Coughlin et al.46 was actually 68.2 J/mol K, and not for
FeO but for Fe0.947 O, which gives over 70 J/mol K when
normalized to two atoms instead of 1.947 per formula.
In addition, partial heat capacities of all divalent oxides
measured in slags by Stebbins et al.47 and Lange and
Navrotsky48 were all above 80 J/mol K, which gives more
probability in favor of higher values for supercooled
liquid NiO.
There is limited information in literature on thermodynamic functions of melting for the Ni2 SiO4 olivine.
Sugawara and Akaogi49 measured the enthalpies of cooling
of liquids along the CaMg0.5 AlSi2 O7 –Ni2 SiO4 composition
line to room temperature by drop calorimetry, and extrapolated that to the enthalpy of metastable melting of pure
Ni2 SiO4 to be 221 kJ/mol, and the entropy of melting
115 J/mol K. This value seems to be overestimated, as it
poorly compares to the entropies of melting of all other
related olivines—Mn2 SiO4 ,50 Fe2 SiO4 ,51,52 Co2 SiO4 ,49 and
Mg2 SiO4 .53 The present thermodynamic model fits qualitatively all these values (Figure 5). Its difference from
the previous model23 is Third-Law consistency—tendency
ABDEYAZDAN et al.
1403
(A)
(B)
F I G U R E 1 0 Phase diagram of the NiO–PbO system with new
experimental results at 1000◦ C–1200◦ C and lines estimated using
the thermodynamic database, (A) phase diagram at 800◦ C–2000◦ C,
and (B) a closer view at 850◦ C–1250◦ C.
F I G U R E 1 1 Composition of Ni–Pb liquid metal in
equilibrium with quartz/tridymite/cristobalite, liquid slag, and
olivine or solid (fcc) Ni metal: experimental results at 800◦ C–1660◦ C
and lines calculated with the new thermodynamic database. The
labels legend is as given in Figure 7.
of the entropies of both solid and supercooled liquid to
near-zero values at absolute zero temperature. This is
achieved by a consistently higher heat capacity of the
supercooled liquid compared to solid (Figure 6), which
is more in agreement with available literature for liquid
Ni2 SiO4 54 (estimated), and chemically related Mn2 SiO4 50
and Fe2 SiO4 51 (directly measured).
The parameters for the PbO–NiO binary, PbO–NiO–
SiO2 ternary liquid were introduced for the first time based
on the experimental results of the present study. Several
ternary parameters with high powers on SiO2 were needed
to describe the shape of the miscibility gap correctly. These
were needed presumably due to lack of binary parameters
with powers higher than 15, which did not allow sufficiently accurate description of the binary systems NiO–
1,0,1
0,0,1
SiO2 and PbO–SiOO2 . The 𝑞Si
4+ ,Pb2+ ,Ni2+ and 𝑞Si4+ ,Pb2+ ,Ni2+
parameters work in the central part of the diagram and
describe the monoxide, olivine, and tridymite liquidus.
Note that their values have been significantly reduced
compared to our earlier attempts before reoptimization
of the NiO–SiO2 binary and NiO melting point. Also, the
Pb8 NiSi6 O21 solid phase was added to the database as a stoichiometric compound. The thermodynamic parameters
are given in Table 3. The PbO–NiO–SiO2 phase diagrams
calculated using the database developed in this study along
with the experimental results are shown in Figures 7 and 8.
Also, an isothermal section of the calculated phase diagram with the experimental points at 1100◦ C is given in
Figure 9. In these figures, the experimental points indicate
the liquid slag composition at the target temperature.
As can be seen in Figures 7 and 8, the phase equilibria
and liquidus isotherms in the quartz/tridymite/cristobalite
(SiO2 ), olivine (Ni2 SiO4 ), monoxide (NiO), Ni-barysilite
(Pb8 NiSi6 O21 ), massicot (PbO), and di-lead silicate
(Pb2 SiO4 ) primary phase fields have been measured, and
the extent of the high-SiO2 two-liquid immiscibility gap
in equilibrium with cristobalite has been determined. The
invariant reactions of the system calculated by FactSage
using the database developed in the present study is given
in Table 4.
The NiO–PbO phase diagram calculated using the
database developed in this study and along with the
present experimental results is shown in Figure 10. Only
the low-temperature part of it has been studied (due to high
volatility of PbO and low viscosity that prevents successful
quenching above 1200◦ C).
For metallurgical processes, it is important to consider
the slag–metal equilibria. In this system, the PbO–NiO–
SiO2 slag coexists with Pb–Ni–O metal of variable composition: the Pb/(Pb+Ni) ratio can change over the whole
range from 0% to 100%, while O is limited to less than
1 mol.% in metal. Another feature of this system is presence of miscibility gap in the liquid Pb–Ni binary system,
1404
ABDEYAZDAN et al.
(A)
(C)
(B)
F I G U R E 1 2 Phase diagram of the Ni–Pb system in equilibrium with quartz/tridymite/cristobalite, liquid slag or olivine (A), a closer
view to the eutectic point at high-Pb side of the phase diagram (B), and solubility of oxygen in the liquid metal (C), estimated using the
thermodynamic database.
which is only slightly affected by the presence of minor
oxygen. Therefore, Figures 11 and 12 show the dependence
of metal composition and phase assemblage (one liquid,
two immiscible liquids, liquid + solid, etc.) on the slag
composition and temperature projected on various axes.
The measured mol.% Pb/(Pb+Ni) ratios in metal are presented as a function of mol.% PbO/(PbO+NiO) in slag for
a series of quartz/tridymite/cristobalite isotherms (800◦ C–
1600◦ C) in Figure 11. At low temperatures (<1163◦ C), the
highest %Ni that can be dissolved in liquid Pb-rich metal
is limited by olivine (Ni2 SiO4 ) liquidus that limits %NiO
in slag. At 1163◦ C–1350◦ C, solid Ni (fcc) forms on addition of NiO to PbO–SiOO2 slag before olivine liquidus
is reached. A monotectic is reached in the Ni–Pb system at 1350◦ C, with formation of a second Ni-rich liquid
metal (Figure 12).
5
CONCLUSIONS
This study presents the first systematic study of liquidus
in the PbO–NiO–SiO2 system and its Ni-containing sub-
systems, as well as compositions of the metal (Ni–Pb
liquid or Ni (fcc) solid) in equilibrium with some of
the slags. Volatilization of PbO was a major issue limiting the temperatures that could be studied to only
1200◦ C in the PbO-rich corner, but the low-PbO compositions could be studied up to 1740◦ C. The experimental
phase equilibria and liquidus data were measured in
the quartz/tridymite/cristobalite, olivine, monoxide, Nibarysilite, massicot, and di-lead silicate primary phase
fields and the extent of the high-SiO2 two-liquid immiscibility gap in equilibrium with cristobalite was determined.
Further, only one ternary phase, Pb8 NiSi6 O21 barysilite,
was found in the system. Through the thermodynamic
modeling of the system, the parameters for the PbO–NiO
binary and PbO–NiO–SiO2 ternary liquid were introduced
for the first time based on the present results. Also, the
NiO–SiO2 binary system was reviewed, which lead to
improved binary and ternary miscibility gap description,
and the Pb8 NiSi6 O21 solid phase was added to the database
as a stoichiometric compound. The results of the study
are merged into the multicomponent (Pb–Zn–Cu–Fe–Ca–
Si–O–Al–Mg–Cr–As–Sn–Sb–Bi–Ag–Au–Ni–Co–Na) mul-
ABDEYAZDAN et al.
1405
tiphase thermodynamic database, and will allow accurate
predictions of Ni impurities in PbO–SiOO2 -rich slags and
Pb impurities in NiO-rich slags, both of which are expected
to become more common in the industry due to increased
proportion of low-grade feeds and recycling (particularly
of batteries).
AC K N OW L E D G M E N T S
The authors would like to thank Australian Research
Council Linkage program (LP180100028), and consortium
of lead producers: Aurubis, Boliden, Kazzinc Ltd., Glencore, Nyrstar, Peñoles, and Umicore for the financial
support for this study. The authors are very grateful to
Prof. Peter Hayes for initiating and contributing in this
research program. The authors would like to thank Mrs.
Suping Huang, Mrs. Samaneh Ashjaa, and Mrs. Marina
Chernishova for assistance in the experiments, Ms. Mika
Sato for taking part in the high-temperature study of
the NiO–SiO2 system, and also the staff at the Centre
for Microscopy and Microanalysis (CMM), University of
Queensland for technical support.
ORCID
Hamed Abdeyazdan
7063
Maksym Shevchenko
9336
https://orcid.org/0000-0001-7408https://orcid.org/0000-0002-9420-
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How to cite this article: Abdeyazdan H,
Shevchenko M, Jak E. Experimental and
thermodynamic modeling study of phase equilibria
in the PbO–NiO–SiO2 system. J Am Ceram Soc.
2024;107:1383–1407.
https://doi.org/10.1111/jace.19523