The viscosity of the Cu47-Ti34-Zr11-Ni8 glass forming alloy was determined by beam bending experiments and by a noncontact oscillating drop technique. These viscosity data can be described with the Vogel-Fulcher-Tammann relation. Using the strong/fragile classification of glasses, Cu47-Ti34-Zr11-Ni8 is more fragile than the strong Zr-Ti-Cu-Ni-Be metallic glass formers

Glade, S. C.

Johnson, W. L.

English

S. C. Glade

W. L. Johnson

Crossref

Viscous flow of the Cu47Ti34Zr11Ni8 glass forming alloy

Caltech Authors - Main

JOURNAL OF APPLIED PHYSICS VOLUME 87, NUMBER 10 15 MAY 2000Viscous flow of the Cu47Ti34Zr11Ni8 glass forming alloy
S. C. Gladea) and W. L. Johnson
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, California 91125
~Received 20 December 1999; accepted for publication 18 February 2000!
The viscosity of the Cu47Ti34Zr11Ni8 glass forming alloy was determined by beam bending
experiments and by a noncontact oscillating drop technique. These viscosity data can be described
with the Vogel–Fulcher–Tammann relation. Using the strong/fragile classification of glasses,
Cu47Ti34Zr11Ni8 is more fragile than the strong Zr–Ti–Cu–Ni–Be metallic glass formers. © 2000
American Institute of Physics. @S0021-8979~00!07910-X#I. INTRODUCTION
A metallic glass was first obtained from the metallic
melt by Duwez et al. in 1961, using cooling rates on the
order of 106 K s21. In the early 1990s, new metallic glass
forming compositions were developed that form glasses with
much lower cooling rates, as low as 1 K s21 for the best glass
forming compositions. These alloys include La–Al–Ni,1
Zr–Ni–Al–Cu,2 Mg–Cu–Y,3 Zr–Ti–Cu–Ni–Be,4 and
Cu–Ti–Zr–Ni.5 Due to the improved stability against crys-
tallization of these alloys, thermophysical property measure-
ments in the amorphous solid and supercooled liquid that
were previously not possible can now be performed.
In this article, we report on a study of the viscosity of the
Cu47Ti34Zr11Ni8 glass forming alloy. After measuring the
viscosity with beam bending experiments and by a noncon-
tact oscillating drop technique, the data have been described
using a Vogel–Fulcher–Tammann ~VFT! relation. The tem-
perature dependent viscosity of Cu47Ti34Zr11Ni8 is then com-
pared to other glass formers.
II. EXPERIMENT
An alloy of nominal composition Cu47Ti34Zr11Ni8 was
prepared in an arc melter with a titanium gettered, ultrahigh
purity argon atmosphere, with elements of purities from
99.9% to 99.9999%. To obtain amorphous samples for the
beam bending experiments, pieces of the alloy were remelted
in quartz tubes with a radio frequency induction furnace and
then injection cast with ultrahigh purity argon into a copper
mold with dimensions 8 mm by 4 mm by 1 mm. Beams for
the beam bending experiments were made by cutting the 1
mm thick amorphous strip on a diamond saw. The beams had
cross sectional areas ranging from 0.25 to 0.8 mm2.
Viscosity for the amorphous solid and the supercooled
liquid was measured by three point beam bending experi-
ments using a thermomechanical analyzer ~Perkin–Elmer
TMA-7!. In these experiments, a constant load was applied
to the center of a beam of uniform cross section which was
supported on its ends. Heating the sample up ~at a heating
rate of 100 K s21 to 623 K and then at a heating rate of 50
K s21 to the desired temperature! and holding it isothermally
a!Author to whom correspondence should be addressed; electronic mail:
sglade@caltech.edu7240021-8979/2000/87(10)/7249/3/$17.00
Downloaded 12 Jan 2006 to 131.215.240.9. Redistribution subject toresulted in a deflection of the center of the beam. Viscosity
~in Pa s! at a given temperature is given by the equation6–8
h5
gL3
144Icn
S M1 5rAL8 D , ~1!
where g is the gravitational constant ~m s22!, L is the support
span length (5.0831023 m for our experiments!, Ic is the
cross sectional moment of inertia ~m4!, n is the midpoint
deflection rate ~m s21!, M is the applied load ~kg!, r is the
density of the sample ~kg m23!, and A is the cross sectional
area ~m2!. Loads ranging from 100 to 900 mN were used in
these experiments. This method can be used to measure vis-
cosities ranging from 107 to 1014 Pa s.
Viscosity measurements in the equilibrium liquid were
made for this alloy using a noncontact oscillating drop
technique.9 A noncontact technique offers the advantages of
possibly being able to access the undercooled liquid regime
and of avoiding contamination of the sample. These mea-
surements were made under microgravity conditions using
TEMPUS ~Tiegelfreies Elektromagnetisches Prozessieren
Unter Schwerelosigkeit, see Ref. 10!, an electromagnetic
processing facility that flew on board the National Aeronau-
tics and Space Administration’s ~NASA! space shuttle. By
measuring the damping of oscillations of the spherical
sample, the viscosity can be determined for the fundamental
surface oscillation mode n52 by
h5
3
20p
MG
R0
, ~2!
where M is the sample mass, G is the damping constant, and
R0 is the unperturbed sample radius.
III. RESULTS
For the thermomechanical analyzer ~TMA! experiments,
the samples were annealed until equilibrium was reached.
The data can be fit to a stretched exponential relaxation func-
tion
h~ t !5ha1heq~12e2~ t/t!
b
!, ~3!
where ha is the viscosity of the amorphous alloy before re-
laxation, heq is the equilibrium viscosity, t is time, t is the
average shear flow relaxation time, and b is a stretching9 © 2000 American Institute of Physics
 AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp
7250 J. Appl. Phys., Vol. 87, No. 10, 15 May 2000 S. C. Glade and W. L. Johnsonexponent. The equilibrium viscosity, when measured on a
long time scale, is equivalent to the viscosity of the super-
cooled liquid.11
The viscosity data for Cu47Ti34Zr11Ni8 are plotted in an
Arrhenius plot in Fig. 1. Viscosity could not be measured at
higher temperatures with the three point beam bending ex-
periments due to crystallization of the sample. These data
can be fit with a Vogel–Fulcher–Tammann ~VFT!
relation,12–14 an empirical equation that has been shown to fit
the temperature dependence of viscosity for glass forming
liquids.15 The VFT relation, in a modified form,16 is
h5h0expS D*T0T2T0D , ~4!
where D* is the fragility parameter and T0 is the VFT tem-
perature. h0 is the high temperature limit of viscosity, deter-
mined according to the relationship17
h05h/Va . ~5!
In this relation, h is Planck’s constant, and Va is the atomic
volume of the liquid. Va5M /(Nar), where M is the molar
mass ~60.87 g g atom21!, NA is Avogadro’s number, and r is
the density of the liquid ~;6 g cm23!. This gives a value for
h0 of 431025 Pa s.
A fit of the data with the VFT equation yields D*
512.0 and T05500 K.
IV. DISCUSSION
As a liquid is cooled below its melting point, if nucle-
ation and growth of crystalline phases is avoided, the viscos-
ity of the liquid increases until the liquid is frozen in a solid
form, i.e., a glass. For some liquids, such as silicate glasses,
the viscosity of the liquid follows an Arrhenius behavior;
FIG. 1. Arrhenius plot of the viscosity of Cu47Ti34Zr11Ni8 . Lower tempera-
ture viscosity of the amorphous solid and the supercooled liquid both before
reaching equilibrium ~s! and after reaching equilibrium ~d! were measured
with three point beam bending experiments. Higher temperature viscosity
was measured with the noncontact oscillating drop technique ~m!. The equi-
librium data are fit with the VFT relation ~dotted line!.Downloaded 12 Jan 2006 to 131.215.240.9. Redistribution subject tothese liquids are called ‘‘strong’’ liquids. Other liquids, such
as organic and ionic glasses, show a non-Arrhenius behavior
of viscosity; these liquids are called ‘‘fragile liquids.’’
Angell16 popularized this classification of strong and fragile
liquids. When the viscosity data are fit with the VFT relation,
strong liquids have fragility parameters of 100, while fragile
liquids have fragility parameters as low as 2. The fragility
parameter of Cu47Ti34Zr11Ni8 is 12.0. A comparison of
strong and fragile glass formers is in Fig. 2, an Arrhenius
plot normalized to the glass transition temperature Tg . Tg is
taken as the temperature at which the viscosity reaches a
value 1012 Pa s.
The fragility parameter is also a good indicator of the
glass forming ability of the system. Glass forming ability is
the ability to avoid nucleation when cooling the liquid from
the melt. The larger the fragility parameter, the better the
glass forming ability of the liquid. Glasses with large fragil-
ity parameters have sluggish kinetics in the supercooled liq-
uid regime, inhibiting crystallization of the liquid. A com-
parison of the critical cooling rates for glass formation and
the fragility parameters of a number of glass formers is given
in Table I.
TABLE I. Critical cooling rates and fragility parameters for a number of
glass formers. The data were taken from Refs. 18 and 19.
Critical cooling rate
~K s21! Fragility parameter
SiO2 731024 100
Zr46.75Ti8.25Cu7.5Ni10Be27.5 ,10 22.7
Zr41.2Ti13.8Cu12.8Ni10Be22.5 1 18.5
Pd48Ni32P20 ,10 16.6
Cu47Ti34Zr11Ni8 250 12.0
Pd77.5Cu6Si16.5 500 11.1
Au77.8Ge13.8Si8.4 ;105 8.4
FIG. 2. Arrhenius plot of viscosity data, normalized by the glass transition
temperature Tg . Tg is taken to be the temperature at which the viscosity is
1012 Pa s, commonly regarded as the viscosity at which a liquid becomes a
solid. SiO2 shows strong liquid behavior while o-terphenyl shows fragile
liquid behavior. Cu47Ti34Zr11Ni8 is more fragile than one of the best metallic
glass formers, Zr41.2Ti13.8Cu12.8Ni10Be22.5 . Data for the glass formers in this
plot were taken from Ref. 18. AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp
7251J. Appl. Phys., Vol. 87, No. 10, 15 May 2000 S. C. Glade and W. L. JohnsonV. CONCLUSIONS
The viscosity of Cu47Ti34Zr11Ni8 was measured in the
amorphous solid, the supercooled liquid, and the equilibrium
liquid states. The data are described well using the VFT re-
lation. The fragility parameter, a term in the VFT relation, is
a good indicator of the glass forming ability of glass forming
liquids.
ACKNOWLEDGMENTS
The authors thank T. A. Waniuk for his assistance
performing the beam bending experiments, R. Busch for
helpful discussions, and John Haygarth of Teledyne Wah-
Chang for providing material for the TEMPUS samples.
They also thank Team TEMPUS for helping make
the MSL-1 space shuttle flight experiments successful,
R. Hyers and G. Trapaga for the TEMPUS viscosity data,
and R. K. Wunderlich for his assistance with temperature
calculations. This work was supported by NASA ~Grant No.
4NAG8-1182!. S.C.G. acknowledges fellowship support
from NDSEG.Downloaded 12 Jan 2006 to 131.215.240.9. Redistribution subject to1 A. Inoue, T. Zhang, and T. Masumoto, Mater. Trans., JIM 31, 425 ~1990!.
2 T. Zhang, A. Inoue, and T. Masumoto, Mater. Trans., JIM 32, 1005
~1991!.
3 A. Inoue, A. Kato, T. Zhang, S. G. Kim, and T. Masumoto, Mater. Trans.,
JIM 32, 609 ~1991!.
4 A. Peker and W. L. Johnson, Appl. Phys. Lett. 63, 2342 ~1993!.
5 X. H. Lin and W. L. Johnson, J. Appl. Phys. 78, 6514 ~1995!.
6 F. T. Trouon, Proc. R. Soc. London 77, 426 ~1906!.
7 M. Reiner, in Rheology, edited by F. R. Eirich ~Academic, New York,
1956!, Vol. 1, p. 9.
8 H. E. Hagy, J. Am. Ceram. Soc. 46, 93 ~1963!.
9 I. Egry, J. Non-Cryst. Solids 250, 63 ~1999!.
10 J. Szekely, E. Schwartz, and R. Hyers, JOM 47, 50 ~1995!.
11 R. Busch and W. L. Johnson, Appl. Phys. Lett. 72, 2695 ~1998!.
12 H. Vogel, Phys. Z. 22, 645 ~1921!.
13 G. S. Fulcher, J. Am. Ceram. Soc. 8, 339 ~1925!.
14 G. Tamman and G. Hesse, Z. Anorg. Allg. Chem. 156, 245 ~1926!.
15 L. Battezzati and A. L. Greer, Acta Metall. Mater. 37, 1791 ~1989!.
16 C. A. Angell, Science 267, 1924 ~1995!.
17 S. Glasstone, K. J. Laidler, and H. Eyring, The Theory of Rate Processes
~McGraw-Hill, New York, 1941!.
18 T. A. Waniuk, R. Busch, A. Masuhr, and W. L. Johnson, Acta Mater. 46,
5229 ~1998!.
19 R. Busch, E. Bakke, and W. L. Johnson, Acta Metall. Mater. 46, 4725
~1998!. AIP license or copyright, see http://jap.aip.org/jap/copyright.jsp


Viscous flow of the Cu47-Ti34-Zr11-Ni8 glass forming alloy

https://authors.library.caltech.edu/1998/1/GLAjap00a.pdf

Viscous flow of the Cu47-Ti34-Zr11-Ni8 glass forming alloy

Abstract

Similar works

Full text

Available Versions

Crossref

Caltech Authors - Main