H.-J. Fecht
Ulm University, Faculty of Engineering, Albert-Einstein-Allee 47
89081 Ulm, Germany and
W.L. Johnson
California Institute of Technology, Keck Laboratories 138-78
Pasadena, CA, 91125, USA
Glasses are formed if upon cooling of a melt below the glass transition temperature crystal nucleation and growth are avoided. Recently, multi-component alloys with deep eutectic temperatures have been developed which allow the formation of a metallic glass during slow cooling of the melt. These so-called bulk metallic glasses or supermetals can be produced with several cubic centimeters dimensions and have excellent properties making them suitable as a superior engineering material.
Moreover, for these amorphous alloys crystallization can be avoided over a broad temperature / time window not accessible so far for metals. As such, the relevant thermodynamic properties of the metastable glassy and undercooled liquid states can be directly measured and modelled below and above the glass transition temperature, respectively. The obtained data give new insight into the fundamental aspects regarding the stability of undercooled liquids and the nature of the glass transition.
1. INTRODUCTION
Glasses have been manufactured from silica and related oxides for more than four thousand years. A glass is characterized by its lack of long range atomic order and exhibits a glass transition manifested by a change in the thermodynamic properties, such as specific heat and thermal expansion coefficient during heating or cooling
[1]
. From a theoretical point of
view the glass transition has been considered to be either a first order [2], second order [3] or third order phase transition [4]. For example, the entropy theory of Gibbs [3] concentrates on the stiffness of macromolecular polymer chains, whereas the free volume theories [2,5] relate to the atomic mobility in a certain volume. Apparently, related relaxation and transport processes depend on the cohesive energy and the type of chemical bond. Just considering the dynamical aspects the glass transition can be described as a localization phenomenon with power law singularities of relevant relaxation times and viscosity based on mode-coupling theories [6,7]. Further experimental results point to its kinetic nature [8].
Four decades ago the synthesis of glasses was extended to metallic systems
[9]. The first liquid-metal alloy vitrified by cooling was Au-Si requiring cooling rates as high as 10 5 - 10 6 K/sec in order to avoid heterogeneous (and homogeneous) nucleation. In general, these high cooling rates have been obtained by quenching the liquid alloys on a cold metallic substrate that generally limited the sample geometries to thin sheets of metal typically about 100 micrometers in thickness. Further attempts still required critical cooling rates in the range of 10 3 K/sec for eutectic Au-Pb-Sb alloys [10] or specific surface treatments by fluxing techniques [11].
4

Extending the range of chemical composition to more complex multicomponent alloys a second generation of metallic glasses has been derived recently.
Samples of bulk metallic glass (BMG) can be produced now with several cm 3 in volume by conventional casting techniques in a controlled atmosphere
[12,13,14]
. For a number of near-eutectic Pd- [15,16] and Zr- [17,18] based alloys a critical cooling rate R c
as low as 1 K/sec is sufficient now to obtain the required levels of undercooling (see Figure 1) and produce a bulk metallic glass. These materials have a relatively high reduced glass transition temperature t g
= T g
/ T m
of about 0.65.
10
10 10
Ni
10 8
10 6
10 4
Zr-Ni, Au-Si
10 2
0
10 0
Zr-Ti-Ni-Cu-Be
Pd-Ni-P
-2
10 -2
-4
10 -4
Oxide Glasses
0.3
0.4
0.5
0.6
0.7
t g
=T g
/T m
Figure 1.
Critical cooling rate R
C
in order to form a glass (avoid crystallization) as a function of the reduced glass transition temperature.
Figure 2 exhibits several shapes and geometries of the bulk metallic glass
Zr
41
Ti
14
Cu
12.5
Ni
10
Be
22.5
produced at cooling rates as low as 1 K/sec [19].
Figure 2.
Representation of a few examples of geometrical shapes obtained for the bulk metallic glass Zr
41
Ti
14
Cu
12.5
Ni
10
Be
22.5 in relation with a centimeter scale.
In addition, it is important to mention that these materials are sufficiently stable against crystallization in the highly undercooled liquid state up to about 100 K
5

above the glass transition temperature. This allows new insight into the dynamic and thermal properties of highly undercooled metallic liquids [20,21] and to prove theoretical concepts about the glass transition itself for metallic materials. The properties in the highly undercooled liquid state, which have not been accessible for metallic materials so far, include the temperature dependent thermodynamic properties, such as entropy, enthalpy and Gibbs free energy [22], volume (density)
[23] and viscosity [24,25].
2. LIQUID UNDERCOOLING
2.1
Nucleation Kinetics
A liquid can be cooled below its equilibrium melting point if appropriate kinetic measures are taken to control the onset of crystallization. The metastability of the undercooled liquid phase is finally terminated by the transformation to a solid phase, i.e. either a crystal or a glass.
The kinetics controlling the rate of crystal nucleation in undercooled liquids have generally been discussed in terms of classical nucleation theory [26,27,28].
Homogeneous nucleation provides an intrinsic limit to glass formation. Some metallic glasses have a reduced glass transition temperature T g
/ T m
high enough to avoid homogeneous nucleation and / or growth of post-critical nuclei [29]. The steady state homogeneous nucleation rate per unit volume is then simply the collision frequency of single atoms with clusters of critical size resulting in a steady state nucleation rate
Jv:
Jv = nv v exp
[
 G
A
/ kT
] exp
[
 G* / kT
]
(1) where nv = number of atoms per unit volume, v = a frequency factor equal to the
Debye-frequency 10 13
s
-1 ,  G
A
= activation energy for an atom addition to a cluster,
 and
 G* = 16   3 / 3  G 2 (2)
 = interfacial energy between the crystalline nucleus and liquid,  G = chemical driving force per unit volume. In general the prefactor in equation (1) can be lumped together and can be approximated as W = 10 30   cm -3 s -1 poise -1 .  , the liquid shear viscosity in poise, has been determined experimentally for Pd-Ni-P [30] and Zr-Ti-Ni-
Cu-Be alloys  31  and can be described accurately according to the free volume model.
In multi-component alloys the approximation for the average driving force of crystallization

G in general is only approximate since concentration fluctuations corresponding to the maximum driving force for nucleation determine the concentration of the nucleus to be formed. In the case of a binary alloy this process can satisfactorily be described by the parallel tangent rule

32

. For the formation of a solid solution with a small curvature of the free energy as a function of composition in a eutectic phase diagram this rule describes experimental results very well

33

. In comparison, the multi-component alloys described here crystallize to a phase mixture of a number of several different intermetallic compounds. Due to the nature of these
6

line compounds the deviation from chemical stoichiometry is rather small. As such, the above approximation for the formation of an intermetallic phase mixture is sufficiently accurate to account for the situation.
An alternative to the classical approach of postulating an a priori distribution of subcritical crystalline configurations has recently been suggested [34]. Here, it is assumed that nuclei of critical size are formed inside zones of density fluctuations of appropriate amplitudes by a diffusionless process. In these zones polytetrahedal liquid-like structural units form critical size crystalline nuclei resulting however in a similar nucleation barrier as in the classical approach.
The nucleation rate is a relatively steep function of temperature with a magnitude determined principally by the exponential term involving  G* and to a lesser degree by the prefactor term. Consequently, one of the most important factors in the analysis of the kinetics of crystallization at high undercooling is the Gibbs free energy difference per unit volume  G and its temperature dependence. According to classical thermodynamics  G(T) is a function of the heat capacity difference between metastable liquid and crystalline solid and the enthalpy of melting  f
as:
 G (T) =  f
 T / T +
T T
  c p
(T) dT - T
  c p
(T) / T dT (3)
T m
T m with  T = the temperature difference between the melting point, T m
, (the eutectic temperature) and  c p
(T) = the heat capacity difference between undercooled liquid and the corresponding crystalline solid. Here it becomes evident that the thermodynamic properties of the undercooled liquid and, in particular, the specific heat at high undercooling are an important measure for the tendency of crystallization or glass formation.
2.2
Crystal Growth Kinetics
The growth velocity u of the crystalline phase nucleated from the highly undercooled liquid is usually expressed as: u = f l -1 D eff
(1 - exp (-

G / kT)) (4)
Here, f corresponds to the fraction of atomic sites where atoms are added or removed at the liquid-crystal interface and is usually taken as f = 1. l is the average atomic diameter in the liquid and the effective diffusivity D eff
is generally assumed to be proportional to
 
, the reciprocal shear viscosity which has been measured for some of the alloys described here. On this basis, the time t x
which is required to crystallize a detectable sample volume can be described as [25,35,36]: t x
= (3 x /

I v
u 3 ) 1/4 (5)
The minimum in the nucleation time, i.e. the “nose of the TTT diagram”, corresponds to dt x
/ dT = 0.
7

3. GLASS FORMING ABILITY
To make a bulk glass, one must frustrate the process of crystallization. The phase diagrams of typical metallic glass-forming alloys are usually characterized by the formation of "deep" eutectics and thus by steeply plunging melting (liquidus) temperatures. The melting transition of a crystalline solid solution can be generally described by including the static atomic disorder in addition to the temperature induced dynamic disorder. Thus, the melting temperature (liquidus temperature) is decreasing more with increasing atomic size mismatch. Computer simulations [37,38] as well as analytical solutions [39] can be based on the elastic energy contribution due to atomic size mismatch and show an elastic instability of the crystal at an atomic size mismatch of about 15% [40] . In a simple model the uncertainty of atomic position w and thus the melting temperature T m
for a binary alloy depends on the atomic distance d
12
, concentrations c
1
and c
2
and atomic radii r
1
and r
2
[41]. The melting temperature
T m
therefore is proportional to:
T m
 x m
2 d 2
12
 1 – 4 (  r
12
) 2 / x m
2 d 2
12
 (6a) with (  r
12
) 2 = c
1 c
2
(r
1
- r
2
) 2 (6b) and x m
= 0.15 (for example for a bcc crystal structure) (6c)
These relationships can be extended to multi-component alloys and describe the reduction of the solidus / liquidus temperatures in a bulk metallic glass forming alloy as schematically indicated in Figure 3 for multiple atoms that are chemically different in size, valence etc.
T o
C
T go
T go
Glass
A Composition
B
Figure 3.
Schematic (pseudo)-ternary phase diagram of a glass forming alloy with solidus and liquidus temperatures as well as the polymorphous crystallization temperature T o
(equality of solid and liquid
Gibbs free enthalpy) and the isentropic glass transition temperatures T go [42].
8

For the particularly stable Zr-Ti-Cu-Ni-Be based bulk metallic glass the optimum concentration of easy glass formation is indicated in Figure 4. Under equilibrium conditions the crystalline phases shown in the quasi-ternary phase diagram are being formed. Crystallization of the bulk metallic glass just above the glass transition temperature leads to a nanocrystalline phase mixture with a volume density of about 10 16 to 10 18 particles per m 3 of an intermetallic compound with cubic. structure and an average diameter of 4 nm. By a combination of TEM, FIM, Xray and neutron diffraction analysis it has been found furthermore that the initial crystallization of this nanocrystalline phase is preceded by a liquid / liquid phase separation in the metastable undercooled liquid on a length scale of several nanometers.
Figure 4 . Isothermal cut below the glass transition temperature of the pseudo-ternary phase diagram of the Zr
41
Ti
14
Cu
12.5
Ni
10
Be
22.5
alloy containing several crystalline phases, which are formed under equilibrium conditions as well as the region of bulk metallic glass formation.
4.
THERMODYNAMIC FUNCTIONS OF METASTABLE LIQUIDS
A metastable phase, e.g. an undercooled liquid, can be in a true reversible equilibrium though the free energy is above that of the equilibrated stable (here the crystalline) phase [43]. It can be regarded as an extension of a stable equilibrium due to a change in temperature or pressure under the constraint that one or more of the stable phases are absent due to an effective kinetic hindrance in their formation. If applied to a bulk metallic glass forming liquid alloy its energetic state can be
9

determined in relationship to the more stable crystalline phase mixture based on equation (3).
4.1
Specific Heat Functions
From a theoretical point of view the existence of crystal-like clusters in the liquid is generally postulated [44,45]. These clusters give an additional contribution to the liquid heat capacity c reduce the contribution to the specific heat, thus explaining generally the decrease of c p l p l . With increasing temperature these clusters dissolve and
with temperature. For several liquid metals (In, Sn, Pb) c universal function of only two dimensionless parameters [46]. p l can be described by a
In the undercooled liquid region few data have been obtained due to the obvious experimental difficulties. The only data available over a wide temperature range have been measured using droplet emulsion samples for the pure metals Bi, In and Sn [47] and the bulk metallic glass forming liquid alloys
(Zr
41
Ti
13
)(Cu
13
Ni
10
)Be
23
[48] and Ni
40
Pd
40
P
20
[49,50]. In Figure 5 results of the specific heat measurements are shown. For the purpose of analyzing crystallization processes and glass formation it is generally sufficient to consider the difference in specific  c p
(T) between the undercooled liquid and the corresponding crystal as given in equation (3). For the sake of a better comparison these data are presented here as a function of the reduced melting (eutectic) temperature T / T m
.
Figure 5.
The crystal / liquid specific heat difference
 c p
as a function of undercooling for several metallic elements and bulk glass forming alloys together with the indication of the experimental data.
For the bulk metallic glass alloys the glass transition can be clearly distinguished and agrees well with other measurements of the diffusivity, viscosity and elastic constants. From Figure 5 it becomes evident that the specific heat increase of the bulk metallic glass forming alloys is considerably larger than that of pure metals, such as In, Sn and Bi. Whereas  c p
for metallic elements is generally close to zero at the melting temperature [51] a considerable increase of 7 - 10 J / g-atom K is observed for the deep eutectics.
10

For the specific heat increase near the eutectic composition, i.e. in the glass forming composition range, three possible contributions can be considered [52]:
(1) a change in the vibrational spectrum due to a change in the type of chemical bonding in general and during melting in particular,
(2) a decrease in non-random association between unlike atoms with increasing temperature and
(3) changes in configurational entropy from the multiplicity of atomic positions which also causes the temperature variation.
4.2
Thermodynamic Entropy Functions
From the specific heat data the thermodynamic functions of the undercooled liquid can be obtained as well. For example, the entropy difference

S between the undercooled liquid and the stable crystalline phase mixture is a valuable measure for the glass forming ability of a liquid with:
 S (T) =
T
  c p
/ T dT (7)
T m
Based on the specific heat data the entropy difference

S (T) is obtained and shown in Figure 6 for a typical metallic element (Indium) and the Pd- and Zr-based
BMG forming alloys. It is obvious that entropy is frozen out during undercooling.
Due to the smaller specific heat the enthalpy reduction for the elemental metal is much less than for the bulk glass with increasing undercooling.
Figure 6.
The crystal / liquid entropy differences for pure metals (for example Indium, dashed line) and bulk metallic glass forming alloys (solid line).
The entropy values are based on experimental results between 0.6 and 1.0 T /
T m
They can further be extrapolated below the experimentally determined range.
Consequently, an isentropic temperature is found at about 0 .
3 T m
for the metallic element (T
K e ) Indium and at about 0.6 T m
for the bulk metallic glass forming alloys
(T go
). The values for the isentropic crystal / liquid temperatures of 1/3 T m
and 2/3 T eut for a pure metal and a good glass forming alloy, respectively, are a common observation and not limited to the examples given here.
11

Kauzmann already pointed out that with progressive undercooling, the entropy of a liquid tends towards the entropy of the crystalline state as indicated by the increase of  c p
(T) during cooling [53,
54
].
Below the extrapolated isentropic temperature the entropy of the undercooled liquid would become less than that of the crystalline phase. Thus, one would be faced with the paradox that at temperatures below the isentropic temperature, the entropy of the ordered, thermodynamically most stable crystal would exceed that of the highly undercooled disordered liquid. This paradox situation can be generally avoided by two different solidification processes:
(a) either crystallization occurs when the homogeneous nucleation temperature
(between 0.55 and 0.6 T / T m
) is located above the isentropic temperature, such as for most elementary and binary metals or
(b) vitrification occurs when the homogeneous nucleation temperature is located below the ideal glass transition temperature T go
. The experimentally determined reduced glass transition temperature T g
is determined experimentally at T g
= 0.65 - 0.7 T / T m
and depends furthermore on the applied cooling rates and corresponding time scales (T g
= T go
for infinitely small temperature changes during heating or cooling). Thus for BMG alloys, the isentropic temperature sets a natural limit to the maximum level of undercooling and triggers the formation of the glass.
It is interesting to note further that a postulated density catastrophy would set in at temperatures below the entropic catastrophe temperature and thus can not account for the instability of the undercooled liquid at the glass transition [55].
4.3
Thermodynamic Gibbs Free Energy Functions
The resistance to crystallization and the improved tendency for glass formation of bulk metallic glasses is inherently coupled with a eutectic reaction and the related increase in the excess specific heat. From the measured  c p
(T) data and measured heats of fusion the thermodynamic Gibbs free energy functions were further calculated for several different Zr-based metallic glass forming alloys and are shown in Figure 7. The enthalpies of fusion and the specific heat data were determined by containerless processing methods under micro-gravity conditions by a newly developed method of containerless processing applicable to chemically hghly reactive materials [56,57]. In Figure 7  G(T) functions for several metallic glass forming alloys are shown including those processed in high precision microgravity experiments in recent space shuttle flights [58]:
Curve (1) Zr
64
Ni
36
with a critical cooling rate R c
> 10 5 K/sec
(2) Ti
(3) Zr
34
65
Zr
Al
11
7.5
Cu
Cu
47
Ni
17.5
8
Ni
10
(4) Zr
60
Al
10
Cu
18
Ni
9
Co
3
(5) Zr
57
Nb
5
Cu
15.4
Ni
12.6
Al
10 and
(6) Zr
41.2
Ti
13.8
Cu
12.5
Ni
10
Be
22.5 with R c

1K/sec.
Thus, with reduced driving force for crystallization the critical cooling rates R c are decreased considerably from 10 5 K/sec to 1 K/sec as shown in Figure 1.
Based on the above model (equations 4,5) the minimum time for crystallization of the
Zr
41
Ti
14
Cu
12.5
Ni
10
Be
22.5
alloy has been estimated to be t x
= 40 sec at a temperature of
895 K in good agreement with experimental results

25

and with the interfacial
12

tension treated as a fit parameter. The growth velocity and nucleation rate have a strong dependence on the driving force

G due to the exponential function.
This approach is strictly only valid for partitionless (polymorphous) crystallization. In the currently described situation primary crystallization occurs with compositional changes between undercooled liquid and crystal. In addition, most of these alloys exhibit a pronounced liquid / liquid phase separation which has been analyzed by appropriate neutron scattering methods
[59,60]
On the other hand, since the crystallization occurs basically to a mixture of intermetallic compounds with the character of a line compound and a composition not far from the average initial one
(see Figure 4) the uncertainty in the chemical composition of the crystalline nucleus to be formed is small and generally can be neglected.
Gibbs Free Energy Difference
4000
3000
2000
1
2
3
4
5
6 reduced
Kauzmann temperature
1000
0
0,3 0,4 0,5 0,6 0,7 0,8
Reduced Temperature T/T l
0,9 1,0
Figure 7.
Gibbs free energy difference (negative driving force for crystallization) between the undercooled liquid and the equilibrium intermetallic phase mixture for binary eutectic Zr-Ni (1) and multi-component Zr-based bulk metallic glass forming alloys (2) – (6).
Furthermore, with regard to the discussion above the arrows in Figure 7 indicate the isentropic temperatures T go
which are the lower limits for the experimentally determined reduced glass transition temperatures with

S (T go
) = - d

G(T) / dT = 0 (8)
From these data a clear trend becomes obvious, i.e. that the glass forming ability is improved with increased reduced glass transition temperature. This is a measure of the time spent in the supercooled liquid regime when cooling the liquid from the melt. Larger reduced glass transition temperatures indicate better glass forming ability; the temperature interval between the melting temperature and glass transition temperature is smaller decreasing the likelihood of crystallization.
5. CONCLUSIONS
13

The described alloys are representative for a new family of bulk metallic glass formers. These alloys are unique in allowing access to the highly undercooled metastable liquid state, the measurement of the thermodynamic and dynamic properties of different liquid and solid metastable states and the control of the crystallization and microstructure developing over a wide range of length scales.
Accurate control of the conditions of glass formation and crystallization sequences further will lead to the development of advanced engineering materials with particular shape design and improved physical and mechanical properties.
The different thermodynamic and kinetic conditions required for a bulk metallic glass to be formed at a critical cooling rate on the order of 1 K/sec can be summarized as follows:
(i) Deep eutectic temperatures and steeply plunging T o
-lines
due to a large negative enthalpy of mixing (more negative in the liquid than in the solid)
(ii)
Difference in atomic radii of more than 15% (elastic energy contribution in the crystalline phases due to local atomic-level strains)
(iii) Reduced driving force for crystallization

G (T)
(iv) High reduced glass transition temperature (t g
= T g
/ T m
= 0.65 – 0.70)
(v) Avoiding liquid / liquid phase separation (spinodal decomposition due to removal of entropic contributions to the free energy surface).
The application of this new class of structural amorphous materials has already been realized in the areas of sports goods due to the excellent elastic properties with a relatively low elastic modulus, high strength and the lack of cold working. In the near future, further applications are expected as a material for MEMS
(micro-electro-mechanical systems and devices) due to the lack of mechanical hysteresis and as a coating and thin film material due to its good mechanical and wear properties as well as the small coefficient of thermal expansion.
6. ACKNOWLEDGEMENTS
The financial support by the Deutsche Forschungsgemeinschaft (G.W. Leibniz program) and the collaboration with Drs. P. Desre, S. Glade, G. Wilde and R.
Wunderlich are gratefully acknowledged.
7.
REFERENCES
1. H.-J. Fecht, Mat. Trans. JIM, 36 (1995) 777
2. M.H. Cohen and G.S. Grest, Phys. Rev. B (1979) 1077
3. G. Adam and J.H. Gibbs, J. Chem. Phys. 43, (1965) 139
4. L.V. Woodcock, J. Chem. Soc. Faraday II 72, (1976) 1667
5. J. Jäckle, Rep. Prog. Phys. 49 (1986) 172
6. E. Leutheusser, Phys. Rev. A29 (1984) 2765
7. W. Götze and L. Sjögren, Z. Phys. B 65 (1987) 415
8. N.O. Birge and S.R. Nagel, Phys. Rev. Lett. 54 (1985) 2674
9. W. Clement, R.H. Willens and P. Duwez, Nature 187 (1960) 869
10. H.-J. Fecht, J.H. Perepezko, M.C. Lee and W.L. Johnson, J. Appl. Phys., 68 (1990) 4494
11. A.L. Drehman, A.L. Greer and D. Turnbull, Appl. Phys. Lett. 41 (1982) 7169
12. A. Peker and W.L. Johnson, Appl. Phys. Lett. 63 (1993) 23
13. W.L. Johnson, MRS Bulletin, October 1999, 42
14. R.K. Wunderlich and H.-J. Fecht, Metall. and Materials Transactions, 29A (1998) 1829
14

15. N. Nishiyama and A. Inoue, Mater. Trans. JIM, 37 (1996) 1531
16. R.B. Schwarz and Y. He, Mater. Sci. Forum, 235 (1997) 231
17. A. Inoue, T. Zhang and T. Masumoto, Mater. Trans. JIM 31 (1990)
18. H.-J. Fecht, Mat. Res. Soc. Symp. Proc. 455 (1997) 307
19. A. Peker, PhD dissertation, California Institute of Technology (1994)
20. H-J. Fecht, J. Mat. Sci. and Engg., A 133 (1991) 443 - 447.
21. D. Herlach, B. Cochrane, I. Egry, H.-J. Fecht and A.L. Greer, Int. Materials Reviews 38
(1993) 27
22. K. Samwer, H.-J. Fecht and W.L. Johnson: "Amorphization in Metallic Systems",
Review Article in Glassy Metals III, Topics in Applied Physics, Vol. 72, Beck /
Güntherodt editors, Springer Verlag (1994) 6
23. S. G. Klose, P. S. Frankwicz and H.-J. Fecht, Mat. Sci. Forum 179 (1995) 729
24. G. Wilde, G.P. Gorler, R. Willnecker and H.-J. Fecht, J. Appl. Phys. 87 (2000) 1141
25. A. Masuhr, T.A. Waniuk, R. Busch and W.L. Johnson, Phys. Rev. Lett. 82 (1999) 2290
26. D. Turnbull, J. Chem. Phys. 20 (1952) 411
27. D. Turnbull, Contemp. Phys., 10 (1969) 473
28. F. Spaepen and D. Turnbull, in Rapidly Quenched Metals, N.J. Grant and B.C. Giessen eds., MIT Press, Boston, (1976) 2055
29. K.F. Kelton, Acta Mater. 48 (2000) 1967
30. G. Wilde, PhD dissertation, Technical University Berlin (1996)
31 A. Mahsur, R. Busch and W.L. Johnson, J. Non-Cryst. Solids, 250 (1999) 566
32 . H.I. Aaronson, Lectures on the Theory of Phase Transformations, AMME (1975)
33 H-J. Fecht, Acta Mater., 39 (1991) 1003
34. P. Desré, A.R. Yavari and P. Hicter, Phil. Mag. B, 61, 1 (1990)
35. D.R. Uhlmann, J. Non-Cryst. Solids, 7 (1972) 337
36. H.A. Davies, Proc. Third Int. Conf. On Rapidly Quenched Metals, B. Cantor ed.,
Brigthon, Chameleon Press (1978) 1
37. L. Bocquet, J.P. Hansen, T. Biben and P. Madden, J. Phys.: Condens. Matter 4 (1992)
2375
38. M. Li and W.L. Johnson, Phys. Rev. Lett. 70 (1993) 1120
39. H.-J. Fecht, J. Mat. Sci. Engg., A179 (1994) 491
40. W. Hume-Rothery, The Structure of Metals and Alloys (The Institute of Metals, London)
1956, p. 101
41. A. Voronel, S. Rabinovich, A. Kisliuk, V. Steinberg and S. Sverbilova, Phys. Rev. Lett.
60 (1988) 2402
42. A. Sagel, PhD dissertation, Ulm University (1999)
43. H.-J. Fecht and J.H. Perepezko, Met. Trans. 20A (1989) 785
44. M. Hoch and T. Vernardikis, Ber. Bunsenges. Phys. Chem., 80 (1976) 770
45. T.E. Faber, An Introduction to the Theory of Liquid Metals, Cambridge Univ. Press,
Cambridge (1972)
46. T.W. Chapman, J. Mater. Sci. Engg., 1 (1966) 65
47. J H. Perepezko and J.S Paik, J. Non-Crystall. Solids 61&62 (1984) 113
48. H.-J. Fecht and R.K. Wunderlich, Mat. Sci. Engg. A178 (1994) 61.
49. G. Wilde, G.P. Görler, R. Willnecker, S. Klose and H.-J. Fecht, Mat. Sci. Forum Vols.
225-227 (1996) 101.
50. I.-R. Lu, G.P. Görler, H.-J. Fecht and R. Willnecker, J. Non-Cryst. Solids, (2000) in print
51. T. Iida and R.I.L. Guthrie, The Physical Properties of Liquid Metals Clarendon, Oxford
(1988)
52. H.S. Chen and D. Turnbull, J. Appl. Phys., 38 (1967) 3646
53. W. Kauzmann, Chem. Rev. 43 (1948) p. 219
54. H.-J. Fecht and W.L. Johnson, Nature 334 (1988) 50
55. J. L. Tallon, Nature 342 (1989) 658
56. H.-J. Fecht and W.L. Johnson, Review of Scientific Instruments, 62 (1991) 1299
57. R. Wunderlich, H.-J. Fecht and R. Willnecker, Appl. Phys. Lett. 62 (1993) 3111
15

58. S.C. Glade, R. Busch, D.S. Lee, W.L. Johnson, R.K. Wunderlich and H.-J. Fecht,
J. Appl. Phys. 87 (2000) 7242
59. M.P. Macht, N. Wanderka, A. Wiedenmann, H. Wollenberger, Q. Wei, S. Klose and H.-
J. Fecht, Mat. Sci. Forum Vols. 225-227 (1996) 6
60.
S. Schneider, P. Thiyagarajan and W.L. Johnson, Appl. Phys. Lett. 68 (1996) 49
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