Table Of ContentButterworths Monographs in Materials
The intention is to publish a series
of definitive monographs written
by internationally recognized
authorities in subjects at the
interface of the research interests
of the academic materials scientist
and the industrial materials
engineer.
Series editorial panel
M. Ashby FRS R. Kiessling
University of Cambridge Sveriges Mekanforbund, Stockholm
J. Charles H. Suzuki
University of Cambridge Tokyo Institute of Technology
A. G. Evans I. Tamura
University of California, Berkeley Kyoto University
M. C. Flemings G. Thomas
Massachusetts Institute of Technology University of California, Berkeley
R.I.Jaffee
Electric Power Research Institute,
Palo Alto, California
Already published
Amorphous metallic alloys
Control and analysis in iron and
steel making
Die casting metallurgy
Introduction to the physical
metallurgy of welding
Metals resources and energy
Forthcoming titles
Continuous casting of aluminium
Energy dispersive X-ray analysis of
materials
Mechanical properties of ceramics
Metallurgy of high speed steels
Microorganisms and metal recovery
Powder metallurgy of superalloys
Residual stresses in metals
Butterworths Monographs in Metals
Eutectic Solidification Processing
Crystalline and Glassy Alloys
Roy Elliott BSC, PHD
Lecturer, Metallurgy Department, University of
Manchester, England
Butterworths
London Boston Durban Singapore Sydney Toronto Wellington
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First published, 1983
©Butterworths & Co (Publishers) Ltd., 1983
British Library Cataloguing in Publication Data
Elliott, Roy
Eutectic solidification processing. -
(Butterworths monographs in materials)
1. Alloys - Metallurgy 2. Eutectics
I. Title
669'.94 TN690
ISBN 0-^08-10714-6
Library of Congress Cataloguing in Publication Data
Elliott, Roy, Ph. D.
Eutectic solidification processing.
(Butterworths monographs in materials)
Includes bibliographical references and index.
1. Eutectic alloys. 2. Solidification. I. Title.
II. Series.
TN690.E536 1983 669'.94 83-7464
ISBN 0-408-10714-6
Typeset by Illustrated Arts, Sutton, Surrey
Printed and bound by Robert Hartnoll Ltd., Bodmin, Cornwall.
Preface
This book is based on the author's twenty years experience of teaching, research and
industrial practice and describes solidification theory and its application to commer-
cial processing of components with desired properties. The underlying theme is an
analysis of the different paths taken by the liquid-solid transformation as the cooling
rate increases and a description of the structure and properties of the solid formed,
ranging from equilibrium to metastable phase formation in castings, to metallic glass
formation in splat quenched ribbons. Within this framework, current models of the
nucleation and growth of eutectic and primary phases are analysed critically and used
to explain how cast microstructures are formed. Extensive coverage of Al casting
alloys and all types of cast iron includes specifications, inoculants (types, mechanism
and procedure), modification practice, heat treatment and structure-property
relationships. Primary phase formation is considered in terms of the solidification of
a dendritic array leading to explanations for founding characteristics, spacing-
property relationships and segregation behaviour. For the latter, the dependence of
the extent of segregation on solidification conditions is explained and the practice of
segregation prevention during solidification, its removal during heat treatment and
the importance of fluid flow in producing macroscopic segregation in large ingots and
ways of minimizing this defect are described. The concept of the coupled zone in
eutectic solidification is explained and used to define the solidification conditions
required to grow in-situ composites. Sources of microstructural instability are
described and the properties of in-situ composites, particularly the high temperature
mechanical properties required for gas turbine components, are considered. Finally,
a brief account is given of the various types of metallic glasses, their fabrication,
important properties and potential uses.
Parts of this text form the basis of the author's undergraduate solidification
course in the University of Manchester. Frequent reference is made to original
research papers in order to explain the foundation upon which our understanding of
solidification is built. It is hoped that the text is sufficiently critical in parts to be of use
to research students and industrial alloy developers. However, an attempt has been
made to relate theory and practice throughout the text. It is hoped that this is suffi-
ciently evident to attract practising foundrymen to some of the more academic
aspects of the subject.
Roy Elliott
Manchester
Acknowledgements
I am indebted to learned societies, publishing houses and friends who have
given their permission for the use of copyright material to illustrate this text. Each
individual contribution is acknowledged in the appropriate figure caption. Micro-
graphs which are not acknowledged have been produced by myself or by my
colleagues in collaborative research. Thanks are due to all my colleagues, especially
Professors G. A. Chadwick, Κ. M. Entwistle, Α. Hellawell, W. Kurz and R. W.
Smith and Doctors Ο. A. Atasoy, D. Driver, F. Η. Hayes, J. D. Hunt, H. Jones, A.
Moore and F. Yilmaz.
R. Elliott
Manchester
Chapter 1
The liquid-solid transformation in
alloys close to the eutectic composition
Introduction
Robert Ransome, an agricultural machinery manufacturer in Ipswich at the
turn of the eighteenth century, discovered white or chilled cast iron accidentally
when one of his moulds split during casting. The iron in the mould spilled out and
cooled quickly (chilled) producing a stronger, harder, more wear resistant alloy than
when it had been left to cool in the mould. Ransome capitalized on his discovery by
redesigning his mould to have an upper surface of sand and a lower one of iron and
produced a ploughshare with a hard skin on one side. The soft upper side was worn
away during working, continuously exposing a hard sharp edge and eliminating the
need for constant sharpening. Approximately a hundred years later, it was realized
that a similar modification could be achieved in aluminium-silicon casting alloys,
either by chilling or by adding small amounts of sodium. Pacz wrote of the modified
alloy, Tr now the alloy be cast, it will be found that the fracture instead of being
coarse, dark and glassy is fine grained, light and dense. The physical properties have
undergone a most remarkable change, the tensile strength rising from a point
between 23 000 and 27 000 lbs in" 2 [160 - 190 Ν mm' 2] from 15 000 to 18 000 lbs
in"2 [105 - 125 Ν mm - 2] and the elongation to a point between 3.5 and 6.5% from
0.25 to 0.5%Just as World War I was the stimulant necessary for the development
of high-strength cast irons by inoculation, so World War II was the inspiration for
one of the most important innovations in metallurgy. The production of nodular cast
iron by magnesium treatment has been ascribed to the shortage of chromium in the
USA during the war. This method, pioneered by International Nickel, and the
cerium method discovered by Morrogh and Williams, were announced at a historic
American Foundryman's Congress at Philadelphia in 1948. It is only now that the full
potential of these alloys is being realized. The 1950s saw considerable advances in
our understanding of the solidification of single-phase alloys. Chalmers and co-
workers used directional solidification techniques to obtain the control necessary to
quantitatively define liquid-solid interface characteristics. They introduced the con-
cept of constitutional undercooling to explain the origin of the cellular and cellular-
dendritic structures that exert such an influence on the properties of cast alloys. They
also demonstrated the considerable influence that small amounts of impurity have on
the microstructure. Hunt and Jackson built upon this understanding to produce a
ι
2 The liquid-solid transformation in alloys close to the eutectic composition
comprehensive analysis of eutectic solidification in 1966. Soon Mollard and Flemings
demonstrated that directional solidification with a high Glv ratio (where G is the
temperature gradient in the liquid at the interface and ν is the growth velocity) could
be used to produce a eutectic structure without primary phase over a range of
compositions about the eutectic. This initiated the extensive search, that continues
today, for in-situ composites and has produced many alloys with outstanding high-
temperature properties. In 1960, Duwez was the first to demonstrate that high-
velocity solidification could result in metallic glass formation. The realization that
iron- and nickel-bearing glasses were ferromagnetic and that metallic glasses were
strong and plastically deformable at room temperature triggered an extensive study
of this new class of material in the 1980s.
These are just a few of the many milestones in the development of the science
and technology of the solidification of alloys close to the eutectic composition. In the
following chapters, we shall follow these developments and show that control over
composition, trace impurities, heat flow and cooling rate, and nucleation and growth
leads to a wide range of solidification structures. Accompanying these different
structures is an equally broad spectrum of physical, chemical and mechanical proper-
ties. The main characteristics of the liquid-solid transformation are introduced in
Chapter 1.
Thermodynamic criterion for liquid-solid equilibrium in
a metal
Thermodynamics is most effective in equilibrium situations and is used in
conjunction with experimental data to define equilibrium phase diagrams and to
provide information concerning the characteristics of the liquid-solid interface at
equilibrium. Although solidification is a non-equilibrium process, theories of the
transformation assume constrained equilibrium in which thermodynamics is applied
locally to individual processes, assuming that other processes proceed at a negligible
rate. Thermodynamics considers the free energy of a system: it is a property that
decreases spontaneously but cannot increase without applied work. The Gibbs free
energy is defined as
G = H-TS = E+ PV -TS (1.1)
where Η is the enthalpy, Τ the absolute temperature, Ρ the pressure, V the volume
and S the entropy. The Helmholtz free energy is defined as
F = E - TS (1.2)
where E is the internal energy. The difference between these two free energies is
small for free-energy changes at atmospheric pressure. We shall first consider
equilibrium in a pure metal. Figure 1.1 shows the change in free energy with tempera-
ture of the solid and liquid phases of a metal according to equation (1.1). The phase
with the lowest free energy (solid at temperatures < T and liquid at temperatures
e
> r) exists at equilibrium over the appropriate temperature range and the two
e
The liquid-solid transformation in alloys close to the eutectic composition 3
^ Liquid
v.
\
•ß a
Temperature
Figure 1.1 The variation of molar free energy with temperature for a metal
phases (solid and liquid) coexist in equilibrium with equal free energies at a single
temperature, Γ . This equilibrium temperature varies with pressure according to a
ε
Clapeyron-type equation
*L=T AX
(1.3)
ΔΡ AH e
where AT is the change in equilibrium temperature caused by a pressure change ΔΡ;
e
Δ V is the difference in molar volume between liquid and solid phases and AH is the
difference in their enthalpies. The volume of a liquid metal is usually greater than
that of the solid (bismuth and gallium are exceptions) so the equilibrium temperature
increases as the pressure rises. However, the effect is quite small and the dependence
is only significant when large pressure changes are involved. For example, large
pressure changes can be produced by cavitation in a liquid metal and lead to an
increased nucleation rate during solidification due to the rise in equilibrium tempera-
ture. The equilibrium temperature also varies with the curvature of the interface
separating the two phases in equilibrium according to the equation
(1.4)
where γ is the interfacial free energy, V is the molar volume of the solid and r and
s x
r are the principal radii of curvature of the interface. This effect becomes of signifi-
2
cance when the radii of curvature fall below 10~ 5 cm.
4 The liquid-solid transformation in alloys close to the eutectic composition
The liquid-solid transformation in a metal
The solid phase α can form when a liquid metal is cooled below Γ α in Figure
6
1.1. The driving force promoting this reaction is the difference between the free
energy of the two phases, AG . This increases as the temperature of the liquid
V
decreases (undercooling increases) and at any temperature Γ below is given by
AG, = Gj - G = AH - Τ AS (1.5)
s
where
J*
AH= AH- T" AC dT (1.6)
f p
and
AS=AS- jT"eACy (1.7)
{ p
The exact temperature dependence of AG, can be calculated if the heat capacities of
the liquid and solid phases are known as a function of temperature. This data is not
always available and the driving force can be approximated 1 by
AG, = ^ AT (1.8)
* e
The value of the latent heat of fusion of a typical metal, such as Cu, is 13 kJ mole" 1,
hence AG, for the solidification of Cu increases from zero at 1356 Κ to 13 kJ mole -1
at temperatures close to absolute zero. The solidification of a liquid metal is pro-
moted by heat removal and is initiated by nucleation and completed by the growth of
the nuclei into the remaining liquid. The rate of solidification is limited just below
T by the small driving force for nucleation, and at much lower temperatures by
e
reduced diffusion rates in the liquid phase. Nucleation proceeds at a maximum rate
at an intermediate temperature (~0.66Γ for homogeneous nucleation and at a much
6
higher temperature for heterogeneous nucleation, which is promoted by impurities
in most casting processes). If the liquid is cooled rapidly below this temperature and
below Γ α in Figure 1.1 without nucleating solid a, it is possible for a metastable solid
6
β to form at a faster rate than oc, even though its free energy is higher and thus the
driving force necessary for its formation is less than that for oc. The metastable solid
phase β may be subsequently transformed to the stable phase oc depending on the
nucleation and growth characteristics of the α-phase. If the liquid phase is cooled
very quickly, solidification may be avoided and the liquid or glass, if the viscosity is
high enough, can remain indefinitely as the metastable phase. Glass formation in
metals requires an exceptionally high cooling rate (> ΙΟ 9 Κ s"1). The tendency for
glass formation is greater in non-metals than in metals and in chalcogens than in
metalloids.
The liquid-solid transformation in alloys close to the eutectic composition 5
Thermodynamic criterion for equilibrium in alloys
The different paths described on page 4 for the liquid-solid transformation in
a metal occur in alloys. However, the presence of solute can influence both the
occurrence and mechanism of a particular transformation. For example, it is shown
later that glass formation occurs more readily in alloys than in the parent metals.
Whereas the criterion for equilibrium at T for a metal is satisfied when the free
e
energy of the solid and liquid phases are equal, in the case of an alloy, the composi-
tion of the phases in equilibrium is different. The criterion for equilibrium is that the
chemical potential μ of any component is identical in all phases. That is, in binary
alloy liquid-solid equilibrium, the chemical potential of component A in solid and
liquid phases is equal (μ,, Α = /x A) and likewise for component Β (μ,, Β = μ Β). The
s 5
chemical potential measures the activity of a component in a given phase and is the
change in free energy of the whole system, G\ when an infinitesimal addition of one
of the components is made reversibly
(1.9)
The molar free energy G = G'/(n + n) is related to the chemical potential by the
A B
equations
(1.10)
and
(1.11)
where N is the mole fraction of component B. Equations (1.10) and (1.11) form the
B
basis of the tangent construction which is used in conjunction with free-energy curves
for determining the composition of phases in equilibrium. This is illustrated in Figure
1.2 where a tangent drawn to a molar free energy curve at a chosen composition
intercepts the N = 0 vertical axis at μΑ and the N = 1 vertical axis at μΒ. When a
B B
common tangent is drawn to two free-energy curves as in Figure 1.2, the chemical
potential of component A in solid and liquid phases is equal, as is that of component
B. This is the criterion for equilibrium between solid and liquid phases, and the com-
position at the points of tangency defines the composition of the solid phase C and of
s
the liquid phase C in equilibrium at the temperature considered. The free-energy
x
curve for solid- and liquid-alloy phases can be determined as a function of tempera-
ture by experiment and the shape of the curve can be explained in terms of solution
theory. The simplest model considers the interaction of nearest-neighbour pairs of
atoms. The free-energy change on mixing components A and Β to give an alloy of
concentration N is given by2
B
G(N) = \NZN{\ - N)(2V - V )
B B B AB BB
enthalpy of solution
RT[N In N + (1 - N) In (1 - N )]
B B B B (1.12)
entropy of solution
