Viscosity of chalcogenide materials
1
2
2
Petr KOŠTÁL , Jaroslav BARTÁK , Jiří MÁLEK
1
Department of Inorganic Technology, University of Pardubice, Doubravice 41, Pardubice 532 10, Czech Republic
2
Department of Physical Chemistry, University of Pardubice, Studentská 573, Pardubice 532 10, Czech Republic
E-mail: [email protected]
Measuring methods
Penetration method
η – viscosity, F – applied force,
r – radius of indenter, h – penetration
depth, t – time of penetration
F
r
107.5-1013.5 Pa.s
Introduction
Extrapolation of viscosity data
Chalcogenide materials have been widely studied since 1960s.
Their unique electrical and optical properties designate them as
suitable materials for various interesting applications. One of the
most important physical parameters of each material is viscosity.
Knowledge of viscous behavior is essential for technology and
production of glassy materials. Furthermore, viscosity is in direct
connection with structural relaxation of glass and with crystal growth
in undercooled melt. Structural relaxation is very slow rearrangement
of thermodynamically unstable glass toward equilibrium. This
process is in fact very slow flow of material and hence it is influenced
by viscosity. Cold crystallization process is influenced by diffusion
which is determined also by viscosity.
Why?
study of crystallization and lack of data in region of melt
indenter
Se
sample
Vogel-Fulcher-Tammann
VFT
Avramov-Milchev
AM
14
14
Lower annealing point
12
10
Dilatometric softening point
log (/Pa.s)
Deformation range
log (/Pa.s)
104 - 1010 Pa.s
plate
8
Littleton softening point
6
sample
4
plate
Forming range
Flow point
log (/Pa.s)
Viscosity glass transition
10
10
12
Parallel-plate method
F
Mauro–Yue–Ellison–Gupta–Allan
MYEGA
Selenium
14
12
As2Se3
Equations
Transformation range
h
Model systems
As2S3
Important physical parameter
h
η – viscosity, F – applied force,
r – radius of indenter, h – penetration
depth, dh/dt – penetration rate
Where?
low region of undercooled melt
8
6
4
2
8
0
-2
6
1,0
1,5
2,0
2,5
3,0
3,5
-1
1000/T [K ]
4
experimental data
VFT fit
MYEGA fit
AM fit
2
Working point
0
2
η – viscosity, F – applied force,
dh/dt – deformation rate, V – sample
volume, h – sample height
Melting point
-2
1,5
0
2,0
2,5
Temperature
Rotating cylinder method
3,0
3,5
1000/T [K -1]
As2S3
Structural relaxation
100.5-101.5 Pa.s
14
12
12
η – viscosity, r1 – radius of inner cylinder,
r0 – radius of outer cylinder, M – moment of force,
h – height of the column of sliding melt, ω– angular
velocity
r0
h
η – viscosity, G – instantaneous shear modulus, τ – relaxation time
Crystallization
log (/Pa.s)
s
a
m
p
l
e
10
Eη – apparent activation energy of viscous flow, Δh* – activation energy from
Tool-Moynihan-Narayaswamy model
r1
8
log (/Pa.s)
10
8
6
4
2
0
6
-2
1,0
1,2
1,4
4
1,6
1,8
2,0
2,2
-1
1000/T [K ]
experimental data
our data
VFT fit
MYEGA fit
AM fit
2
Experimental data
0
Viscosity of selenium
16
log (/Pa.s)
10
8
1,0
1,2
1,4
B
log  = A +
T - T0
A
B
T0
1,8
2,0
2,2
As2Se3
-3.97 ± 0.07
1195 ± 20
227 ± 1
Literature
12
12
10
Selenium viscosity data
8
S. Dobinski, J. Wesolowski, Bl int Acad polon Sci Let Part A 7 (1937) 7.
M. Cukierman, D. R. Uhlmann, J Non-Cryst Solids 12 (1973) 199.
K. M. Khalilov, B. B. Kuliev, Fiz Tverd Tela+ 7 (1965) 2847.
K. Ueberreiter, H. J. Orthmann, Kolloid Z 123 (1951) 84.
M. Kunugi, R. Ota, T. Yamate, J Soc Mater Sci Jpn 15 (1966) 567.
S. U. Dzhalilov, S. O. Orudzheva, Zh Fiz Khim+ 60 (1966) 2130.
R. C. Keezer, M. W. Bailey, Mater Res Bull 2 (1967) 185.
D. E. Harrison, J Chem Phys 41 (1964) 844.
J. Shanelova, PhD thesis, Pardubice (2001).
G. Faivre, J. Gardissat, Macromolecules 19 (1986) 1988.
6
4
2
literature data
our data
VFT fit
0
-2
E. Jenckel, Z Elektrochem 43 (1937) 796.
K. M. Khalilov, Izv An Azerb SSR 6 (1959) 67.
K. Bernatz, I. Echeverria, S. Simon, D. Plazek, J. Non-Cryst. Solids 307 (2002) 790.
F. Q. Yang, J. C. M. Li, J Non-Cryst Solids 212 (1997) 136.
S. V. Nemilov, G. T. Petrovskii, J Appl Chem-USSR+ 36 (1963) 977.
T. Shirai, S. Hamada, K. Kobayaski, J Chem Soc Jpn 84 (1963) 968.
H. Krebs, W. Morsch, Z Anorg Allg Chem 263 (1950) 305.
S. Hamada, N. Yoshida, S. T., B Chem Soc Jpn 42 (1969) 1025.
C. M. Roland, P. G. Santangelo, D. J. Plazek, K. M. Bernatz, J Chem Phys 111 (1999), 9337.
P. Koštál, J. Málek, J Non-Cryst Solids 356 (2010) 2803.
As2S3 viscosity data
J. Malek, Thermochim Acta, 311 (1998) 183.
S.V. Nemilov, Fiz Chim Stekla, 5 (1979) 398-409.
S.V. Nemilov, Solid State Phys, 6 (1964) 1375-1379.
S. Tsuchihashi, Y. Kawamoto, J Non-Cryst Solids, 5 (1971) 286.
A.S. Tverjanovich, D.Y. Somov, Neorg Mater, 32 (1996) 1149.
S. Suzuki, Y. Kamiya, Y. Suzuki, T. Kobayashi, J Soc Mater Sci Jpn, 21 (1972) 143.
N.E. Zhukina, G.M. Orlova, G.A. Chalabjan, Fiz Chim Stekla, 5 (1979) 223.
G.Z. Vinogradova, S.A. Dembovskii, T.N. Kuzmina, A.P. Chernov, Zh Neorg Chim, 12 (1967) 3240.
A.P. Chernov, S.A. Dembovskii, V.I. Machova, Izv Akad Nauk SSSR Neorg Mater, 6 (1970) 823.
G. Chaussemy, J. Fornazero, J.M. Mackowski, J Non-Cryst Solids, 58 (1983) 219.
As2Se3 viscosity data
1,5
1,6
1000/T [K -1]
2,0
2,5
3,0
3,5
1000/T [K-1]
M. Kunugi, R. Ota, M. Suzuki, J Soc Mater Sci Jpn, 19 (1970) 145.
S.V. Nemilov, G.T. Petrovskii, J Appl Chem-USSR, 36 (1963) 977.
J. Malek, J. Shanelova, J Non-Cryst Solids, 351 (2005) 3458.
D.W. Henderson, D.G. Ast, J Non-Cryst Solids, 64 (1984) 43.
B.T. Kolomiets, V.P. Pozdnev, Sov Phys-Sol State, 2 (1960) 28.
10
8
log (/Pa.s)
12
0,8
log (/Pa.s)
14
-2
UR – reduced rate of crystal growth, ΔG – Gibbs energy accompanying transformation,
u – crystal growth rate, η –viscosity, ΔT – undercooling (Tm – T), Tm – temperature of melting,
T – temperature, ΔHm – enthalpy of melting
6
4
2
0
6
-2
1,0
1,2
4
1,4
1,6
1,8
2,0
2,2
-1
1000/T [K ]
2
A.P. Chernov, S.A. Dembovskii, V.I. Machova, Izv Akad Nauk SSSR Neorg Mater, 6 (1970) 823.
G.M. Orlova, S.S. Udalov, E.N. Manachova, Fiz Chim Stekla, 11 (1985) 215.
P.J. Webber, J.A. Savage, J Mater Sci, 16 (1981) 763.
A. Kadoun, G. Chaussemy, J. Fornazero, J.M. Mackowski, J Non-Cryst Solids, 57 (1983) 101.
A.S. Tverjanovich, I. Skorobogatova, Fiz Chim Stekla, 16 (1990) 369.
experimental data
VFT fit
MYEGA fit
AM fit
0
Viscosity equations
Vogel-Fulcher-Tammann equation according to Mauro et al.
H. Vogel, Phys Z 22 (1921) 645.
G. Tammann, W. Hesse, Z Anorg Allg Chem 156 (1926) 245.
I. Avramov, A. Milchev, J Non-Cryst Solids 104 (1988) 253.
G. S. Fulcher, J Am Ceram Soc 8 (1925) 339.
J. C. Mauro, Y. Yue, A. J. Ellison, P. K. Gupta, D. C. Allan, PNAS 106 (2009) 19780.
Acknowledgment
∞
m
T12
-3.97 ± 0.07
64.4 ± 0.6
301.9 ± 0.1
The authors thank to project CZ.1.07/2.3.00/20.0254 “ReAdMat Research Team for Advanced Non-Crystalline Materials”
cofinanced by the European Social Fund and the state budget of the
Czech Republic.
-2
0,8
1,0
1,2
1,4
1,6
1,8
2,0
2,2
2,4
1000/T [K -1]
Experimental viscosity data for given systems were fitted by
mentioned equations in the regions of undercooled melts and glasses.
Inset figures show extrapolations of fits to region of melt with no
fixation. Major figures show these extrapolations with fixed
parameter log ∞(T→∞) to -5 (according to Angell plot).
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