Noncontact modulation calorimetry using electromagnetic heating and radiative heat loss under ultrahigh-vacuum conditions has been applied to levitated solid, liquid, and metastable liquid samples. This experiment requires a reduced gravity environment over an extended period of time and allows the measurement of several thermophysical properties, such as the enthalpy of fusion and crystallization, specific heat, total hemispherical emissivity, and effective thermal conductivity with high precision as a function of temperature. From the results on eutectic glass forming Zr-based alloys thermodynamic functions are obtained which describe the glass-forming ability of these alloys

Fecht, H.-J.

Johnson, W. L.

Lee, D. S.

Wunderlich, R. K.

English

Caltech Authors - Main

PHYSICAL REVIEW B 1 JANUARY 1997-IVOLUME 55, NUMBER 1Noncontact modulation calorimetry of metallic liquids in low Earth orbit
R. K. Wunderlich
Technical University Berlin, Metalphysics and Technology, Hardenbergstrasse 36, PN 2-3 10623 Berlin, Germany
D. S. Lee* and W. L. Johnson
California Institute of Technology, Keck Laboratory of Engineering Materials 138-78, Pasadena, California 91125
H.-J. Fecht
Technical University Berlin, Metalphysics and Technology, Hardenbergstrasse 36, PN 2-3 10623 Berlin, Germany
~Received 29 July 1996!
Noncontact modulation calorimetry using electromagnetic heating and radiative heat loss under ultrahigh-
vacuum conditions has been applied to levitated solid, liquid, and metastable liquid samples. This experiment
requires a reduced gravity environment over an extended period of time and allows the measurement of several
thermophysical properties, such as the enthalpy of fusion and crystallization, specific heat, total hemispherical
emissivity, and effective thermal conductivity with high precision as a function of temperature. From the
results on eutectic glass forming Zr-based alloys thermodynamic functions are obtained which describe the
glass-forming ability of these alloys. @S0163-1829~97!02302-3#Precision measurements of the specific heat of stable and
undercooled melts are of fundamental interest regarding the
ultimate thermodynamic stability of undercooled melts and
nonequilibrium crystals against vitrification and
amorphization,1 formation of associate structures in the
melt,2 the thermodynamic contribution to nucleation
kinetics,3 and thus the glass-forming ability of a material. In
particular, Zr-based alloys have attracted considerable atten-
tion due to their glass-forming ability on rapid cooling,4
solid-state amorphization reactions,5 and, as base alloys of
the recently discovered bulk glass formers.6,7
However, investigations of the thermophysical properties
of the chemically reactive liquid metallic specimen at el-
evated temperatures are usually hampered using conven-
tional techniques due to exothermic reactions with the con-
tainer walls. Therefore, a containerless method has been
developed which allows one to alleviate these problems.8,9
Due to insufficient temperature and positioning control of
the samples of interest in an earth laboratory under UHV
conditions the experiments have been performed in the space
shuttle Columbia during the recent International Micrograv-
ity Laboratory 2 ~IML-2! mission using the containerless
electromagnetic processing ~TEMPUS! device.10 The ab-
sence of excessive heating and fluid flow associated with
levitation under 1 g conditions assures quiescent sample con-
ditions in an ultraclean environment ~,1028 Torr base pres-
sure! and precise modeling of the thermal balance.
Here, a metallic 8 mm diameter specimen ~as an example
Zr64Ni36! is heated by a 400 kHz radio frequency dipole field
and positioned in the center of the heating coil by a 200 kHz
quadrupole field. Temperature is measured by a high preci-
sion, ,0.1 K, well calibrated two-color InAs pyrometer.
The different frequency and geometry of the heating and
positioning fields allows separation of the total power input
into additive components from heater and positioner, P tot
5PH1PPPos . The specimen equilibrium temperature T0 , is
given by P tot5As«T0
4 with « total hemispherical emissivity,550163-1829/97/55~1!/26~4!/$10.00A surface area and s Stefan-Bolzmann constant. Induction
heating of the levitated specimen can be discussed by
analytical11,12 and numerical methods including the induced
force and fluid-flow fields.13 The rate of Joule heat generated
by the heater field is given as
PH53pR~T !r~T !F~x !L IH
2 5GH~T !IH
2 ~1!
with R(T), r(T), and IH corresponding to radius, resistiv-
ity, and heater oscillating circuit current, respectively. The
geometry factor L describes the relative position of heating
coils and specimen. F(x) accounts for the skin effect in a
spherical sample with x5R(T)/d(T) and d skin depth.
F(x) is given in terms of analytical functions.11,14 GH(T)
defines the temperature-dependent heater coupling coeffi-
cient.
For heat-capacity measurements a sinusoidal modulation
of heater current is applied, IH5IH01Imsin(vt), resulting in
a heater power input:
PH~ t !5GH~T !@IH0
2 1 12 Im
2 12IH0Imsin~vmt !
1 12 Im
2 sin~2vmt !# ~2!
and a steady state temperature response of the specimen
given by
T~ t !5T01DTav1DTm~v!sin~vt1f1!
1DTav~2v!sin~2vt1f2!. ~3!
For each modulation frequency the heat capacity CP of the
specimen is connected with the amplitude of temperature
modulation by15
CP5 f ~v ,t1 ,t2!
Pm~v!
DTm~v!v
. ~4!
Pm(v) amplitude of power modulation at frequency
v f (v ,t1 ,t2) represents a correction function accounting
for the effects of radiative heat loss with external relaxation26 © 1997 The American Physical Society
55 27BRIEF REPORTSFIG. 1. Temperature-time profile of Zr64Ni36
specimen as processed in microgravity experi-
ment. Inset shows temperature decay to equilib-
rium ~a!, FFT-filtered signal ~b! and logarithmic
plot ~c! for t1 evaluation.time t1 and finite thermal conductivity with internal relax-
ation time t2. For DTav /T0!1 the increase in the average
temperature is given by
DTav5DPav
t1
CP
. ~5!
t1 is determined from measurements of temperature relax-
ation to equilibrium following a change in input power as
t15~CP/4 A s « T0
3!, ~6!
allowing direct determination of « from t1 and CP measure-
ments. For spherical symmetry and thermal conductivity k
the internal relaxation time is given by8
t25~3CP/4p3kR !. ~7!
Due to the widely different time scales of radiative heat loss
and internal thermal conductance the low-frequency re-
sponse of DTm(v) is dominated by t1, while the high-
frequency response is determined by t2. Adiabatic condi-
tions are characterized by vt1/10.1.10vt2 and
f (v ,t1 ,t2)'1, equivalent to DTm(v)v5const. As such,
measurements of the frequency dependence of DTm(v) al-
low identification of the adiabatic regime.
Figure 1 shows a typical experimental sequence per-
formed in the space experiment on a Zr64Ni36 specimen. The
enthalpy of fusion is determined from the duration of the
isothermal melting ~1! and recalescence plateau ~5! at low
undercooling. The specific heat is obtained from modulation
experiments and from the increase in the average tempera-
ture upon application of heating power modulation ~2!. The
total hemispherical emissivity is obtained from t1 measure-
ments ~3!. Variation of the modulation frequency allows de-
termination of an internal relaxation time ~4!, and an average
value of the specific heat in the undercooled melt is obtained
from measurements of the duration of the isothermal recale-
scence plateau as a function of undercooling ~5!. The inset
shows the evaluation of the external relaxation time from
temperature decay to equilibrium.
Quantitative evaluation of specific-heat values requires
knowledge of the power component P(v) and of the correc-tion function f (v ,t1 ,t2). From Eq. ~2!, P~v! and DPav are
given in terms of heater current as
P~v!52GH~T !IH0Im , Pav5 12 GH~T !Im
2
. ~8!
In situ calibration experiments performed at Tc5Tm240 K
where the specific heat is known independently from high-
temperature differential scanning calorimetry ~DSC! mea-
surements provide GH(Tc). The modulation frequency was
chosen such as to guarantee adiabatic conditions. The corre-
sponding reference experiments were performed on identical
solid 8 mm diameter spheres in a ground based experiment
shown in Fig. 2 indicating an adiabatic regime for modula-
tion frequencies in the range 0.05–0.2 Hz with an internal
relaxation time t250.18 s. From Eq. ~7! a thermal conduc-
tivity of 0.25 W/cm K was obtained for the solid state in very
good agreement with the Wiedemann-Franz law and a mea-
sured resistivity of 128 mV cm at Tc .
Describing the temperature dependence of GH(T) re-
quires knowledge of the temperature dependence of resistiv-
ity and specimen radius including the change at Tm . The
resistivity was determined in situ from measurements of the
temperature dependence of the oscillating circuit current and
FIG. 2. Correction function f (v ,t1 ,t2! as function of modula-
tion frequency.
28 55BRIEF REPORTScalibration with a specimen of known resistivity.16 An upper
limit of 3% for the volume change on melting could be in-
ferred from analysis of video images of the specimen during
processing in the TEMPUS facility in accordance with re-
cently measured values for a similar glass forming alloy.17
With these data the coupling function GH(T) has been ob-
tained. By far, the main contribution to the temperature de-
pendence of GH(T) arises from the resistivity change at
Tm . As such GH(T) is rather insensitive to precise knowl-
edge of the absolute temperature within 610 K. The advan-
tage of modulation calorimetry calibration as compared to
pulse heating experiments is that no knowledge of the emis-
sivity is required and that it can be performed independently
of the presence of a second heating field.
Figure 3 shows a recording of a modulation experiment at
v50.08 Hz for a liquid specimen at T051420 K. The driv-
ing heater current is shown on the left-hand ordinate. Open
circles represent measured values sampled at 1 Hz allowing
precise, 60.7°, determination of the relative phase between
heater current and temperature response. The additional
high-frequency modulation in the temperature signal arises
from sample movement in the potential well of the position-
ing field with eigenfrequencies near 1.2 Hz. The smooth
curve represents a vL50.8 Hz low pass fast-Fourier trans-
form ~FFT! filter. Fourier analysis of the temperature re-
sponse reveals the presence of the 2v modulation component
according to Eq. ~3!. The amplitude of temperature modula-
tion at frequency v was obtained from the FFT-filtered curve
after ~i! correction for the transfer function of the low pass
filter and ~ii! subtracting the contribution of the 2v compo-
nent with proper phase resulting in a relative accuracy of 0.2
K for DTm determination.
Adiabatic conditions in the liquid modulation experiments
were verified by measurements of the phase shift between
heater current and temperature. At T051430 K values of
f1522.5 mod p/4 and 23.4 mod p/4 were obtained for
vm50.08 and 0.10 Hz, respectively. With a measured exter-
nal relaxation time of ~22.161! s this phase shift allows
evaluation of the internal relaxation time as ~0.2460.03! s
indicating 12 f (v ,t1 ,t2)<131022. From Eq. ~7! a corre-
sponding effective thermal conductivity of 0.25 W/K cm is
obtained. For comparison, application of the Wiedemann-
Franz law with a measured resistivity of 155 mV cm ~Ref.
FIG. 3. Modulation experiment with liquid ZrNi specimen for
vm50.08 Hz. Heater current shown on left ordinate. Temperature
response shown on right ordinate.16! results in a thermal conductivity of 0.19 W/cm s and
t250.32 s. This apparent increase in the measured effective
thermal conductivity is due to the effect of electromagnetic
stirring of the liquid and may serve to distinguish different
fluid-flow models.
Table I exhibits specific heat values obtained by modula-
tion calorimetry and those obtained from measurements of
DTav and t1. The good agreement between cp values at dif-
ferent modulation frequencies indicates the absence of ef-
fects caused by transient internal temperature gradients. Val-
ues of the total hemispherical emissivity «H are shown in the
last column with the liquid values exhibiting a ArT tempera-
ture dependence.
Determination of the thermodynamic functions requires
knowledge of the enthalpy of fusion which can be obtained
from the power balance pertaining to the isothermal melting
or solidification plateau. Input power is given by the rate of
crystallization enthalpy release and by the combined action
of heating and positioning fields while output is determined
by purely radiative heat loss. Figure 4 shows temperature
and heater current of a recalescence event at low undercool-
ing, DTu'10 K, used for the evaluation of the enthalpy of
crystallization. The heating efficiency of the positioner field,
GPos(T), can be evaluated from modulation measurements at
Tc with temperature scaling similar to GH(T).18 The change
in heater current shown in Fig. 4 results from the resistivity
change at Tm and was used to scale GH(Tm ,t) and
GPos(Tm ,t) as a function of time between liquid and solid
values. As solidification proceeds rapidly on the surface of
the droplet the emissivity during solidification was taken to
correspond to that of the solid at Tc . We thus obtain DHf
5(14.460.4) kJ mol 21 including a contribution of 0.45 kJ
mol21 from heating the undercooled melt by DTu'10 K.
Knowledge of DHf allows determination of the average spe-
cific heat in the temperature interval DTu from measure-
ments of the duration of the isothermal recalescence plateau
as a function of undercooling.19 The resulting specific-heat
values of Zr64Ni36 obtained in this experiment are summa-
rized in Fig. 5. The lower curve represents crystalline values
obtained by conventional DSC measurements, while the up-
per curve represents data in the stable and undercooled melt
with a maximum undercooling of 80 K. Squares represent
TABLE I. Specific heat of Zr 64Ni36. ~mod!: results obtained by
modulation calorimetry; ~av!: results obtained from DTav and t1
measurements.
T0~°C!
vm
~Hz!
cp ~mod!
~J mol21
K21!
cp ~av!
~J mol21
K21!
t1
~s! « tot
1215 0.05 43.760.8 43.062 18.261 0.38
1160 0.08 44.561.2 43.064 21.861 0.36
0.10 43.261 43.562
1038 0.05 43.961 41.262 30.060.6 0.34
0.08 44.261 43.962
1008 0.05 44.061 44.762 33.061 0.33
0.10 44.661 45.762
980 0.05 45.561.2 36.962 0.32
960 0.08 32.061 32.061 30.861 0.30
solid, Tc
55 29BRIEF REPORTSdata obtained by modulation calorimetry, while the full
circles represent the average specific heat in the undercooled
melt showing an increase of the liquid specific heat with
decreasing temperature typical for glass-forming alloys.
Liquid specific-heat data were linearly extrapolated for an
estimate of the thermodynamic functions in the undercooled
melt according to
cP
1 ~T !5~55.0228.031023 T! J mol21 K21. ~9!
From the Kauzmann stability criterion, DS1,x(Tg0)50, the
reduced glass transition temperature Tg05Tm /Tg was ob-
tained as Tg050.51 which places the ZrNi binary eutectic at
an intermediate position between the bulk glass formers with
Tg05(0.6460.3) and a typical extrapolated value of Tg0
50.32 for pure metals.20 The value of Tg0 thus obtained is in
good agreement with recent model calculations21 for this sys-
tem, Tg050.49, and an upper limit of Tg050.50 obtained
FIG. 4. Recalescence event. Left ordinate: temperature; right
ordinate: rf-heater generator current.from crystallization of rapidly quenched splats.22 Further-
more, the driving force for crystallization, DG1,x(T)/DHf ,
of the binary ZrNi eutectic in comparison with a pure metal20
at a critical undercooling Tu50.5 (11Tg0) corresponds to
0.22 and 0.32, respectively, equivalent to at least five orders
of magnitude difference in critical cooling rates for glass
formation.
We acknowledge stimulating discussions with Professor
G. Frohberg ~TU-Berlin!, Professor William Hofmeister
~Vanderbilt University!, and Dr. G. Loho¨fer ~DLR Cologne!
and the excellent support of the MUSC team at DLR Co-
logne. R.K.W. and H.J.F. acknowledge financial support
from DARA ~Grant No. 50 WM 94-31-4!, D.S.L. and W.L.J.
from NASA ~Grant No. NAG8-954/NAG9-1192!.
FIG. 5. Specific heat of Zr64Ni36. Lower curve crystalline solid.
Upper curve liquid; full squares: values obtained by modulation
calorimetry, full circles: values of the average specific heat in the
undercooled regime.*Present address: Amorphous Technologies International, 27722 El
Lazo, Laguna Niguel, CA 92656.
1H. J. Fecht and W. L. Johnson, Nature ~London! 334, 50 ~1988!.
2F. Sommer, Z. Metallkd. 73, 77 ~1982!.
3D. Turnbull, J. Chem. Phys. 20, 411 ~1952!; F. Spaepen, Acta
Metall. 23, 729 ~1975!.
4K. H. J. Buschow, B. H. Verbeek, and A. G. Dirks, J. Phys. D 14,
1087 ~1981!.
5W. L. Johnson, Prog. Mater. Sci. 30, 81 ~1986!.
6A. Peker and W. L. Johnson, Appl. Phys. Lett. 63, 2342 ~1993!.
7A. Inoue, T. Zhang, N. Nishiyama, K. Ohba, and T. Masumoto,
Mater. Trans. JIM 35, 1234 ~1993!.
8H.-J. Fecht and W. L. Johnson, Rev. Sci. Instrum. 62, 1299
~1991!.
9R. K. Wunderlich, R. Willnecker, and H.-J. Fecht, Appl. Phys.
Lett. 62, 3111 ~1993!.
10Team TEMPUS, in Materials and Fluids Under Low Gravity,
edited by L. Ratke, H. Walter, and B. Feuerbacher, Springer
Lecture Notes in Physics ~Springer, Berlin, 1995!.
11E. Fromm and H. Jehn, Z. Metallkd. 58, 366 ~1967!.12G. Loho¨fer, Int. J. Eng. Sci. 32, 107 ~1994!.
13 J. H. Zhong, B. Li, and J. Szekely, Acta Astron. 29, 305 ~1993!.
14B. Q. Li, Int. J. Eng. Sci. 31, 201 ~1993!.
15Y. A. Krafmakher, High Temp. High Pressures 24, 145 ~1992!.
16G. Loho¨fer ~unpublished!.
17H.-J. Fecht, S. G. Klose, and M. P. Macht, in Proceedings of the
2nd Pacific Rim International Conference on Advanced Materi-
als and Processing, edited by K. S. Shin, J. K. Yoon, and S. J.
Kim ~The Korean Institute of Metals and Materials, Seoul,
1995!, p. 2155.
18R. K. Wunderlich and H.-J. Fecht, Int. J. Thermophys. ~to be
published!.
19A. J. Rulison and W. K. Rhim, Rev. Sci. Instrum. 65, 695
~1994!.
20H.-J. Fecht, Mater. Trans. JIM 36, 777 ~1995!.
21T. Aihara, Jr., K. Aoki, and T. Masumoto, Mater. Trans. JIM 36,
399 ~1995!.
22Z. Altounian, Tu Guo-hua, and J. O. Strom-Olsen, J. Appl. Phys.
54, 3111 ~1983!.


Noncontact modulation calorimetry of metallic liquids in low Earth orbit

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Noncontact modulation calorimetry of metallic liquids in low Earth orbit

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