Solidification of Metals: Structure and Energetics | Metallurgy

In this article we will discuss about:- 1. Introduction to Solidification 2. Structure of Crystalline Solid 3. Energetics 4. Smooth or Stable Interface-Growth 5. Temperature Inversion and Dendritic Growth 6. Dendritic Growth.

Introduction to Solidification:

A metallurgist is called upon to economically produce the required shape of an object, and which has the required properties. In almost all metals and alloys, the material at some point in its processing is a liquid. The liquid solidifies as it cools below its freezing temperature.

The metal parts may be allowed to solidify into either their final shapes, called castings (where the cast structure is controlled properly to correspond to the required properties) or produce some other shapes, called ingots, which on subsequent change to required shape (by plastic deformation) also obtain simultaneously the required structure corresponding to the required properties.

The structure produced by solidification, particularly the grain size and the grain shape, affects to a large extent the properties of the products, particularly the castings. It is thus, essential to understand the mechanism of transformation of liquid metal to solid metal, i.e., the process of solidification.

Structure of Crystalline Solid:

When a pure crystalline metal melts, practically all its properties change sharply by finite amounts. The most characteristic property of the solid, that is, the rigidity, (as measured by its resistance to shear stress) changes to the most characteristic property of the liquids called fluidity, where resistance to shear stress is almost negligible.

The viscosity changes by a factor of 10¹⁸Pa s. This probably is due to several orders of magnitude faster atomic diffusion in liquids than in solids. The changes in other properties may not be so drastic. For example, there is an increase of 2 to 6 percent volume, when most metals melt (some metals like bismuth and gallium, which have crystal structures of low coordination number, contract on melting).

This small change in volume means that atoms in liquids have almost same distance of separation as atoms in solids; the coordination number is almost identical. (But the characteristic of all liquid metals is that all of them have almost same coordination number irrespective of the fact whether the solid metal had close-packed structure or open-structure).

This fact is further confirmed as the latent heat of melting is only about 3 to 4 percent of the corresponding latent heat of vapourisation (in which the atoms are pulled apart completely). This thus leads to the conclusion that bonding of atoms in solid and liquid phases are probably similar. The fact that the liquids are isotropic is clear indication that they lack extended lattice structure and long-range ordered arrangement of atoms, which are characteristics of crystalline solids.

X-ray diffraction studies and electron microscopy have revealed the picture of the crystalline solid as atoms arranged in three dimensions in a definite pattern over long distances, i.e., there is a complete long-range order in the arrangement of atoms (ignoring the defects like vacancies and dislocations, etc.). Fig. 5.1 (a) illustrates schematic picture of a crystalline solid.

The structure of the liquid metals is essentially indeterminant. However, x-ray diffraction studies have come out with some picture of it. Atoms in a liquid are arranged in an ordered manner over short-distances, but lack long-range order. This probably is due to the presence of increased structural defects like vacancies, interstitialcies, dislocations, etc., which are the characteristics of the liquid phase.

These defects probably are also responsible for much higher atomic diffusion rates in liquids. This faster motion of atoms also results in the typical ever-changing structure of the liquids, i.e., an order of atoms, existing at one position in space, changes continuously with time. For example, look at Fig. 5.1 (b), there is short-range order of atoms, i.e., ordered arrangement of atoms is present over very short distances at a moment.

Due to intense thermal motion of atoms, short range order is dynamically unstable. Clusters of large number of atoms having regular arrangement may appear, may exist for a while, but then fall apart to appear again at some other place in the liquid. Thus, at a moment, there may be clusters (of atoms) of different sizes, which change in size the next moment.

As the temperature of liquid approaches the freezing point, the degree of short-range order increases. The size of clusters of atoms in which atoms are packed in the same order as in solid crystal increases. The larger size clusters may become nuclei when they attain a definite size.

Liquid phase may be pictured as a dense gas in which atoms are held together by attractive forces between the atoms. But the presences of the characteristic structural defects control the properties of the liquids, and are responsible for very fast atomic diffusion in liquids.

This is demonstrated by the fact that electrical and thermal conductivities of all liquid metals try to attain a common value; even the coordination number of all liquid metals is almost the same. In solids, the physical properties are controlled by the forces of bonding between the atoms.

The x-ray diffraction studies on liquids also confirm another important characteristic of liquids, i.e., the presence of gaps, or holes (as proposed by Eyring as hole theory of liquids) in liquids. The atoms can move into the hole, and the vacant site in turn may be occupied by another atom, and so on.

Thus, the holes in the liquid structure provide a flow mechanism in which only a few atoms need to move simultaneously, and thus provide low energy paths-by which atoms can be displaced. The presence of holes accounts for the fluidity of the liquids, their low viscosity, greater thermal expansion, and change in density, etc.

Energetics of Solidification:

At any temperature, the thermodynamically stable state is the one which has the lowest free energy and consequently, any other state tends to change to the stable form. The equilibrium temperature for transition between two states is the temperature at which they have the same free energy.

Let us take a simple case of pure liquid metal transforming to solid crystal of pure metal X as:

A crystalline solid has lower internal energy and high degree of order, or lower entropy as compared to the liquid-phase, i.e., liquid has higher internal energy (equal to heat of fusion) and higher entropy due to its more random structure.

The result is that with the increase of temperature, the free-energy curve for the liquid phase falls more steeply (in a more negative sense) than the free energy curve of solid-phase as illustrated in Fig. 5.2. At the T_m, the equilibrium melting point, the free energies of both the phases are equal. Solidification does not occur as (free energy change), ∆g = 0, even when kept for indefinite time.

Above T_m, the liquid has a lower free energy than the crystalline solid X, i.e., liquid is more stable. The solidification reaction cannot occur under such conditions as the free energy change, ∆g for the reaction 5.1 is positive. Below T_m, the free energy of the crystalline solid X, is less than the liquid phase. The free energy change for the reaction 5.1 is negative,

Thus, below T_m, the solidification can occur spontaneously. The Fig. 5.2 also illustrates that at just below T_m, the magnitude of Ag, the free energy change is very small, and the solidification occurs very slowly, but at much lower temperature than T_m, that is, at large supercooling, the magnitude of ∆g is quite large, and thus, solidification occurs at a fast rate.

The variation of ∆g with temperature can be derived as follows:

If E_x and E_l are internal energies and S_x and S_l are the entropies of the solid and the liquid respectively, then at some temperature, T, of solidification, below T_m:

It has been assumed that entropy and internal energies do not vary with minor changes in the temperature. Also, E_x – E_l = ∆h, is the enthalpy of the change (heat of the reaction), or latent heat of freezing per unit volume of the product. Thus, ∆S = ∆h/T_m. Putting it in equation (5.3),

where, T is the temperature of solidification below T_m, and ∆T is the amount of supercooling.

Smooth or Stable Interface-Growth of Solidification:

When the liquid ahead of the solid-liquid interface has positive temperature gradient that means heat is being lost by its flow from right to the left, Fig. 5.13 (a). Latent heat of fusion is removed by conduction through the solid. The temperature gradient is linear and perpendicular to the interface. Under these conditions, “smooth interface” is stable, which moves into liquid almost as a unit.

The interface may have steps, some of which have dense-packed planes and some of them have loose-packed planes as indicated in Fig. 5.14. The most advanced portions of the solid interface correspond to the loose- packed planes i.e., high accommodation factor surfaces, while most retarded correspond to slow growing i.e., low accommodation factor surfaces.

As there is rising temperature ahead of the interface, those portions which are most advanced are in contact with hotter liquid than those portions to the rear. But the rate of growth is also a function of the degree of undercooling. Thus, a last-growing plane is in contact with hotter liquid, while a slow growing plane is in contact with cooler liquid. When both these factors balance, an interface is obtained which grows at a constant speed as it takes the similar shape after sometime (dotted line in Fig. 5.14).

Temperature Inversion and Dendritic Growth of Solidification:

Whenever there is temperature inversion, i.e., the temperature falls in the liquid ahead of the interface, a very important type of crystalline growth occurs, called the dendritic growth. ‘Dendrite’ is the Greek word for tree, as the growth is treelike projections that form on the solid surface. It takes place when the supercooling is large.

The smooth-interface is then unstable because any part of the interface that grows ahead of the remainder is in a region of liquid metal at a lower temperature, and therefore of more rapid growth. The result is a ‘spike’ (Fig. 5.15 d) that grows out into the liquid. It remains isolated because the released latent heat (of spike) raises the temperature of the immediately surrounding liquid and thus, retards the formation of other similar projections on the general interface in the immediate vicinity of a given spike.

Thus, a number of spikes of almost equal spacing are formed which grow parallel to each other, Fig. 5.15 (d).These spikes grow in certain crystallographic direction called dendritic growth direction, which depends on the crystal structure of the metal as given in Table 5.2.

These first spikes as shown in Fig. 5.15 (d) are called primary arms of dendrites. Now, the average temperature of the liquid at section YY is lesser than average temperature at section XX. Also at section YY, T₁ is greater than T₂ because of the latent heat released by the formation of two neighbouring primary arms.

Thus, again, there is temperature inversion in direction perpendicular to primary arms, the right conditions for the formation of secondary arms, Fig. 5.15 (e). As the temperature inversion is responsible for their formation, they also form at more or less regular intervals perpendicular to the primary arms.

Their growth directions are equivalent crystallographically. Actually in cubic metals, the dendritic arms are perpendicular to each other as these can form along all the <100> directions. Based on the similar arguments, tertiary arms form on secondary arms. As the dendrites grow in length, they also grow in thickness. Each dendrite is a single crystal ultimately after solidification of the metal.

The size of the dendrites is normally characterized by measuring the distance between the secondary dendrite arms. If the casting freezes rapidly, there is less time available to conduct the heat, additional dendrite arms develop and grow assisted by with the evolution of the latent heat. The finer and more extensive dendritic network conducts more efficiently the latent heat to the supercooled liquid.

The secondary dendrite arm spacing or SDAS is reduced when the casting freezes more rapidly as illustrated in Fig. 5.29 (a) for some alloys, and is given by:

SDAS = ktⁿ

where, n and k are constants depending on the composition of the metal. The effect of SDAS on the properties of aluminium alloys is shown in Fig. 5.29 (b).

Dendritic Growth in Pure Metals:

The driving force for dendritic growth is the temperature inversion, i.e., the liquid ahead of the solid-liquid interface should be in sufficient supercooled state as illustrated in Fig. 5.15 (c). This figure can be used to understand the development of such temperature gradient.

If the liquid metal has been supercooled to a large extent so that its temperature is well below the equilibrium freezing temperature, and that heat is conducted from the right to left, i.e., through the solid, the heat of fusion which is released at the interface, raises its temperature above both the liquid and the solid.

This results in the temperature distribution as illustrated in Fig. 5.15 (c), i.e., the temperature falls from the interface into the solid as it is the heat-conduction direction, and also from interface into liquid because there is natural flow of released latent heat of fusion from the interface to the liquid. Thus, temperature inversion is developed.

Pure metals can be supercooled only by the process of thermal supercooling. But to get complete dendritic freezing in pure metals, a very large supercooling of at least about 100°C is needed to counteract the effect of latent heat of fusion released as the dendrites grow, and still maintain a supercooled liquid ahead.

But it is difficult to obtain such large thermal supercooling in relatively pure metals in practice as heterogeneous nucleation takes place in them. Usually, 10 percent of pure metal may solidify dendritically, but by then the heat of fusion overcomes the thermal supercooling, and the negative temperature gradient becomes the positive temperature gradient. Further solidification occurs by ‘smooth interface’ growth, i.e., the contour of the interface, produced by dendritic growth, and is maintained for it to grow at a constant speed.

The dendritic fraction in a pure metal is given by:

fraction, f = C . ∆T/∆H_f

where, C is the specific heat of the liquid.

Dendritic growth is quite commonly observed in alloys.

Alloys can have- (i) Thermal supercooling, (ii) Constitutional supercoiling, but the latter plays a significant role in resulting dendritic freezing. The driving force for dendritic freezing is the large amount of supercooled liquid layer ahead of the interface. Normally, the effect of thermal supercooling is easily wiped off by the heat of fusion evolved, and thus, the constitutionally supercooled layer (‘x’ in Fig. 5.19) should be large to obtain dendritic freezing.

If the supercooled region is small, then long spikes of the dendrites cannot grow due to limited depth of this region. Under these conditions, dome-shaped growth-cells, Fig. 5.20 (a) are formed. The cells are usually hexagonal in shape, 5.20 (b). The centre of each cell (G) is the growing point.

The rejection of solute at such points sets up lateral concentration gradient that causes diffusion of solute towards the cell walls. This lowers the liquids temperature of the liquid ahead of the cell-walls, and thus, stabilizes the shape of the surface. The cell walls contain a higher concentration of solute than the cell centres. Fig. 5.20 (b). This is called microsegregation. As T₁ > T₂ but solute content at T₁ is less than at T₂, the freezing occurs uniformly over the entire surface maintaining its shape.