SOLID-LIQUID INTERACTIONS

• Zero-order reactions have a constant rate. • This rate is independent of the concentration

of the reactants. • A first order reaction has a rate proportional

to the concentration of one of the reactants. • A common example of a first-order reaction is

the phenomenon of radioactive decay.

Zero-order reactions

• A 0-order reaction has a rate which is independent of the concentration of the reactant(s).

• Increasing the concentration of the reacting species will not speed up the rate of the reaction.

• In zero-order reactions a material that is required for the reaction to proceed,

• Such as a surface or a catalyst, is saturated by the reactants

• A reaction is zero order if concentration data are plotted versus time and the result is a straight line

First-order reactions

• A first-order reaction depends on the concentration of only one reactant

• (a unimolecular reaction). Other reactants can be present, but each will be zero-order.

• Solidification and melting are transformations between crystallographic and non-crystallographic states of a metal or alloy.

• These transformations are of course basic to such technological applications as

• Ingot casting, foundry casting, continuous casting, single-crystal growth for semiconductors,

• More recently directionally solidified composite alloys

• Another important and complex solidification and melting process, often neglected concerns the process of fusion welding.

• An understanding of the mechanism of solidification and how it is affected by

• Such parameters as temperature distribution, cooling rate and alloying,

• Is important in the control of mechanical properties of cast metals and fusion welds.

• The objective our lecture is to develop some of the basic concepts of solidification,

• Apply these to the practical processes of ingot casting, continuous casting and fusion welding.

• We then consider a few practical examples illustrating the casting of engineering alloys in the light of the theoreticalbackground.

THE NUCLEATION OF SOLIDS IN LIQUIDS

• The liquid to solid transformation occurring by a first order process is discontinuous:

• The liquid does not change gradually into solid as it does in the glass transition.

• Before a first order solidification process can begin,• A nucleus of the solid phase has to exist in the

liquid, • Freezing then takes place by the growth of the

nucleus into the melt.

• Solidification in this sense requires the simultaneous presence of both the solid and the liquid phases

• An important feature of crystalline solids is that

• At constant pressure they have a characteristic equilibrium freezing/melting temperature, Tm.

• The solid and the liquid phases can only be in thermodynamic equilibrium at this unique temperature.

• we can also say that at the equilibrium freezing temperature

• The free energies of the solid and liquid phases are equal.• At temperatures above Tm , the liquid has a lower free

energy than the solid, • And the liquid is therefore the stable phase.• At temperatures below Tm the solid has the lower free

energy and is therefore the stable phase.

• when a liquid reached to a temperature below its thermodynamic freezing temperature

• It not immediately and spontaneously crystallize• A certain degree of “undercooling’ or ‘super

cooling’ of the liquid is usually necessary before the freezing process starts.

• If the undercooling is actually measured, a time— temperature graph such as is shown in Figure 3.2 is obtained.

• The liquid first under cools an amount T, • At this temperature the solid nucleates: • Growth then proceeds with the evolution of

latent heat, • The temperature rises to equilibrium freezing

temperature• ( more accurately, to slightly below

equilibrium freezing temperature,

• Since a small under cooling is required to drive the process in the direction of solidification.

• When solidification is complete and no more latent heat is evolved,

• The temperature of the solid continues to fall.• From this description of the freezing process, two questions immediately arises.

• (1) what are crystal nuclei? and • (2) why do they appear only at temperatures

significantly less than the equilibrium freezing temperature?

• To answer these questions we again have to consider the

• i) Atomic structure of liquids and solids, • Ii) Thermodynamic energy requirements for the

formation of a small crystal of the solid phase in the bulk liquid phase.

Homogeneous Nucleation• Consider a certain volume of liquid being progressively cooled. • The atoms of the liquid are in a state of constant agitation,• Therefore, the liquid exhibits no permanent long range order, • It is probable that some atoms will cluster together momentarily

into small regions having the crystal structure of the solid phase (embryos).

• These small clusters, called embryos, are potential nuclei for the solidification process.

• We can determine if the embryos will become actual nuclei by considering the free energy changes involved in their formation.

• If GL and Gs are the free-energies per unit volume of the liquid and solid phases respectively,

• the difference between GL and Gs ( Delta Gv) provides a negative energy contribution at temperatures less than TE (see Figure 3.1).

• There is, however, a positive energy term due to the creation of the solid—liquid interface.

• Let gammaSL represent the (positive) energy per unit area of the surface dividing the solid embryo from the liquid.

• The change in free energy corresponding to the formation of a sphere of solid of radius r is then given by

• The important thing to notice about this equation is that the surface energy term varies as the square of the radius,

• whereas the volume free energy term varies as the cube.

• The change in free energy varies with the size of solid sphere in a manner shown in Figure 3.3.

• When the solid clusters are small the surface energy term predominates;

• when they are large the negative volume energy term predominates.

• At the temperature to which the diagram refers, i.e. some temperature less than Tm,

• A cluster is stable only when its radius is greater than r, the critical radius;

• The free energy of sub-critical clusters would have to increase if they were to grow,

• This is thermodynamically impossible.• Consequently, embryos of radius less than r*

disappear, • Nuclei of radius greater than r grow larger.• The critical radius can be found from the equation 4.4• By differentiating G with respect to r and setting the

derivative equal to zero.

• It can easily be shown by differentiation of Equation 4.4 that

• The above formulation tells us what size embryo is required to form a critical nucleus at any temperature,

• But it does not say whether embryos of that size actually exist in the liquid at that temperature.

• Intuitively, we would expect a range of embryo sizes in the liquid at any temperature, and

• We would further anticipate that at the higher the temperature the smaller would be the largest-size embryos

• Because of the increased amplitude of atomic vibrations at the higher temperatures.

• It is also reasonable to assume that the larger the volume of liquid, the greater is the probability of an embryo of critcal size existing.

• Figure 3.4 the larger the supper cooling the smaller the critical nucleus size.

• Figure 3.5 shows the expected form of the ‘relationship between the maximum embryo size and temperature,

• A relationship we could confirm if we were to follow the argument through mathematically

• By superimposing Figure 3.5 onto Figure 3.4, • The point of intersection of the curves represents the

temperature at which embryos become viable crystal nuclei.

• Figure 3.6 is, therefore, the temperature at which solid will nucleate spontaneously in the liquid,

• And is called the homogeneous nucleation temperature. • It has been found empirically that for simple liquids, such as liquid

metals, • The amount of undercooling required for homogeneous nucleation • Is an approximately constant fraction of the melting point

(expressed in K )• For each material, T – O.2O Tm. The basic reason for this large

barrier t:

• The basic reason for this large barrier nucleation is the great difference in structure between the solid and liquid phases,

• The solid consisting of a regular arrangement of atoms on a crystal lattice

• whereas the liquid is best described as amorphous. • DeltaT(critical) is obviously the maximum undercooling

attainable• Since by definition a liquid cannot be (slowly)

supercooled to a temperature less than T*

• For the high temperature metals Delta T amounts to several hundred degrees centigrade:

• The homogeneous nucleation temperature of pure iron, for instance, is approximately 300 K below its equilibrium freezing temperature.

• From Equation (3.3) it can be calculated that the critical size nucleus for homogeneous nucleation contains in the region of 300 atoms

• It is known that the presence of foreign solids in the liquid, or

• Even the walls of the container in which the liquid is held,

• may serve to nucleate the solid heterogeneously at a temperature considerably above the homogeneous nucleation temperature.

• Using the example of commercial steels cast into ingot moulds,

• we know from experience that • The solid nucleates in the vicinity of the mould walls at

a temperature of only a few degrees less than the equilibrium freezing temperature

• The mould walls serve to chill the liquid locally and• Thus permit small solid particles in suspension in the

liquid to act as heterogeneous nucleation centres for the freezing process.

• Solidification begins at the outside of the ingot and progresses inwards with time.

• The purest commercial metals and alloys always contain sufficient foreign bodies, or inclusions,

• To serve as heterogeneous nucleation catalysts even if the mould walls are themselves inert in this respect.

• Very rarely, and then only under the most careful experimental conditions, will a liquid supercool to its homogeneous nucleation temperature.