**3. Growth processes**

The growth process is conceived as the sitting of further atoms on the stable nuclei which brings in the growth of individual crystal or a general growth in the mass of the solid as solidification proceeds *the latent heat of crystallisation* is liberated at the solid–liquid interface. *Zones of thermal supercooling* are generated in the liquid pool. Also, with the lowering of temperature the solubility of an alloying element in the liquid melt decreases. As a consequence, the solute is rejected at the solid–liquid interface. The equilibrium freezing temperature of the alloy is

continuously altered and a phenomenon known as *constitutional supercooling*, takes place. Both thermal and constitutional supercooling obstruct growth and alter the growth pattern.

#### **3.1 Plane-front growth**

Nucleation does not take place randomly in the metal/alloy melt throughout the liquid because in the actual case of solidification, and uniform lowering of temperature throughout the melt cannot be obtained. There exist a thermal gradient between the cool mould wall surface exposed to the ambience and the interior of the solidifying melt that would eventually form the casting. Therefore, in the practical case, nucleation is initiated at the mould surface and the growth of the solid phase proceed being directed towards the centre of the casting. This growth takes place in a preferred crystallographic direction as dictated by the characteristic of the solidifying crystal. For an example, in a cubic crystal the preferred crystallographic direction is <001>. With the aid of the temperature gradient, the grains oriented favourably grow at a faster rate than the others.

With the lapse of time, depending on the no of effective nuclei and the initial growth rate setup by the initial temperature gradient, the growth of the crystals in the lateral direction gets obstructed. This is because the laterally growing crystals impinge into each other restricting growth of the neighbouring crystals. Also any growth of any crystal ahead of the others, into the high temperature melt is inhibited due to the unfavourable temperature conditions. Such a situation gives rise to planar or plane front growth where in a seemingly plane interface proceeds into the melt causing growth [11]. The interface is plane macroscopically whereas in actual, it is a terraced structure microscopically. This is a typical condition leading to the formation of columnar grains which is often observed in cast ingots. These columnar grains grow in a direction opposite to the direction of heat-flow. This is illustrated in **Figure 3**.

The occurrence of planar growth giving rise to a columnar structure involves thermal condition present in **Figure 4**.

It is assumed, a positive temperature gradient exists at the solid–liquid interface. Here, the liberated latent heat of crystallisation is not enough to reverse the temperature gradient due to the freezing; i.e., a situation is not created when some pockets in the inside of the melt, away from the interface, are at relatively lower

**25**

**Figure 5.**

*Schematic presentation of generation of thermal undercooling.*

*Solidification of Metals and Alloys*

**3.2 Thermal super-cooling**

**Figure 4.**

solidified melt.

*DOI: http://dx.doi.org/10.5772/intechopen.94393*

*Schematic presentation of the thermal condition for plane front growth.*

temperature. This situation is favoured at slow cooling rates which ensure a stiff and positive temperature gradient. Under these conditions only, the interface assumes the shape of a seemingly plane surface a columnar grain-structure is favoured.

The thermal conditions get grossly distributed when sufficient accumulation of the liberated latent heat of crystallisation at the interface is experienced. The liberated heat now disturbs the thermal gradient. Though there is a positive thermal gradient due to the cold mould surface, the local evolution of latent heat produces a reverse temperature gradient at the interface. This is illustrated in **Figure 5**. Where a zone of thermal super cooling indicating pulls in the melt at the interface or adjacent to it at temperatures lower than the equilibrium temperature are witnessed. Obviously, growth does not occur due to the general advancement of the planefront but by preferential growth processes in these undercooled pulls in the melt. The planar growth pattern is disturbed as the minimum temperature in the liquid melt is not witnessed at the interface. Plane-front growth is hindered and growth occurs by other means. Depositions of further atoms on the surface of the nuclei may occur in regions of greater under cooling in preference to the interface. The thermal super cooling greatly influences the final structure of the

**Figure 3.** *Schematic presentation of planar growth giving rise to columnar dendrite.*

*Solidification of Metals and Alloys DOI: http://dx.doi.org/10.5772/intechopen.94393*

#### **Figure 4.**

*Casting Processes and Modelling of Metallic Materials*

favourably grow at a faster rate than the others.

growth pattern.

**3.1 Plane-front growth**

illustrated in **Figure 3**.

thermal condition present in **Figure 4**.

*Schematic presentation of planar growth giving rise to columnar dendrite.*

continuously altered and a phenomenon known as *constitutional supercooling*, takes place. Both thermal and constitutional supercooling obstruct growth and alter the

Nucleation does not take place randomly in the metal/alloy melt throughout the liquid because in the actual case of solidification, and uniform lowering of temperature throughout the melt cannot be obtained. There exist a thermal gradient between the cool mould wall surface exposed to the ambience and the interior of the solidifying melt that would eventually form the casting. Therefore, in the practical case, nucleation is initiated at the mould surface and the growth of the solid phase proceed being directed towards the centre of the casting. This growth takes place in a preferred crystallographic direction as dictated by the characteristic of the solidifying crystal. For an example, in a cubic crystal the preferred crystallographic direction is <001>. With the aid of the temperature gradient, the grains oriented

With the lapse of time, depending on the no of effective nuclei and the initial growth rate setup by the initial temperature gradient, the growth of the crystals in the lateral direction gets obstructed. This is because the laterally growing crystals impinge into each other restricting growth of the neighbouring crystals. Also any growth of any crystal ahead of the others, into the high temperature melt is inhibited due to the unfavourable temperature conditions. Such a situation gives rise to planar or plane front growth where in a seemingly plane interface proceeds into the melt causing growth [11]. The interface is plane macroscopically whereas in actual, it is a terraced structure microscopically. This is a typical condition leading to the formation of columnar grains which is often observed in cast ingots. These columnar grains grow in a direction opposite to the direction of heat-flow. This is

The occurrence of planar growth giving rise to a columnar structure involves

It is assumed, a positive temperature gradient exists at the solid–liquid interface. Here, the liberated latent heat of crystallisation is not enough to reverse the temperature gradient due to the freezing; i.e., a situation is not created when some pockets in the inside of the melt, away from the interface, are at relatively lower

**24**

**Figure 3.**

temperature. This situation is favoured at slow cooling rates which ensure a stiff and positive temperature gradient. Under these conditions only, the interface assumes the shape of a seemingly plane surface a columnar grain-structure is favoured.

#### **3.2 Thermal super-cooling**

The thermal conditions get grossly distributed when sufficient accumulation of the liberated latent heat of crystallisation at the interface is experienced. The liberated heat now disturbs the thermal gradient. Though there is a positive thermal gradient due to the cold mould surface, the local evolution of latent heat produces a reverse temperature gradient at the interface. This is illustrated in **Figure 5**. Where a zone of thermal super cooling indicating pulls in the melt at the interface or adjacent to it at temperatures lower than the equilibrium temperature are witnessed. Obviously, growth does not occur due to the general advancement of the planefront but by preferential growth processes in these undercooled pulls in the melt.

The planar growth pattern is disturbed as the minimum temperature in the liquid melt is not witnessed at the interface. Plane-front growth is hindered and growth occurs by other means. Depositions of further atoms on the surface of the nuclei may occur in regions of greater under cooling in preference to the interface. The thermal super cooling greatly influences the final structure of the solidified melt.

**Figure 5.** *Schematic presentation of generation of thermal undercooling.*

### **3.3 Constitutional super cooling**

Constitutional supercooling in an alloy is best illustrated in **Figure 6**.

The **Figure 6** presents the solidification and hence the phase changes in a simple binary alloy of 'A' and 'B'. Let us consider the alloy of Co. The initial alloy deposited from Co has a composition confirming to 'C1'. Obviously, 'C1' has a composition pertaining to 'B' which is less than that of the original alloy 'Co'. Therefore, as 'C1' is formed, the residual liquid gets slightly enriched in 'B'. Thus, as solidification proceeds 'B' is continuously rejected into the liquid. This rejection occurs at the solid–liquid interface throughout the process of freezing. A constitutional gradient is, thus, created in the liquid, solute 'B' being continuously rejected at the interface. The concentration of 'B' is maximum at the interface and gradually diminishes as one goes towards the interior of the liquid melt. This compositional variation is presented in **Figure 7(a)**. The change of composition brings in a corresponding change

**Figure 6.** *Phase diagram of a typical binary alloy.*

#### **Figure 7.**

*Schematic presentation of rejection of solute at the interface (7(a)) and change of equilibrium temperature (7(b)) as a consequence of the solute accumulation.*

**27**

*Solidification of Metals and Alloys*

**Figure 8.**

*DOI: http://dx.doi.org/10.5772/intechopen.94393*

in the equilibrium freezing temperature of the alloy as presented in **Figure 7(b)**. Each composition on the solute distribution curve has its corresponding equilibrium freezing temperature as it depends on the corresponding composition of an alloy. The relationship between the actual (existing) temperature gradient in the melt and the equilibrium freezing temperature as a consequence of alterations in the

*Schematic presentation of constitutional supercooling as a consequence of solute rejection at the interface and* 

**Figure 8** clearly illustrates, before the actual (existing) temperature falls considerably for growth to occur, there, is a pool of melt where considerable supercooling can be witnessed at points farther within the melt. In this pool of supercooled liquid conditions are more favourable for freezing than at the interface. This condition is

Alloys having Eutectic composition or containing appreciable amounts of eutectic constituents, undergo eutectic freezing. The alloy of eutectic composition solidifies at a single temperature to precipitate a mixture of two phases '' ''

b.Rod-like or globular solids of apparently discontinuous phase in the matrix of

It is the extent of undercooling and its relative location in the melt that immensely influence the mode of growth of the crystal in a solidifying melt. As suggested earlier, it can be a thermal undercooling or a constitutional undercooling. Different extents of undercooling may be found in a band of liquid adjoining the

interface or even in the inside of the melt depending on the following:

of different compositions, 'x' and 'y' [2]. Thus, two separate phases, of two different compositions are precipitated out at a single temperature as a consequence of freezing of an eutectic alloy. Here, unlike the growth of grains as in a solid solutions, each of the eutectic grains is formed by the simultaneous growth of two dissimilar phases in close association. The eutectic structure could be any

α

 β*and*

composition of the alloy-melt, is illustrated in **Figure 8**.

*the resultant alternation in the equilibrium freezing temperature.*

referred to as constitutional super-cooling.

**3.4 Freezing of eutectic alloys**

one of the following:

the other phase.

**3.5 Other growth modes**

a.Alternate laminates of the two,

*Solidification of Metals and Alloys DOI: http://dx.doi.org/10.5772/intechopen.94393*

#### **Figure 8.**

*Casting Processes and Modelling of Metallic Materials*

Constitutional supercooling in an alloy is best illustrated in **Figure 6**.

The **Figure 6** presents the solidification and hence the phase changes in a simple binary alloy of 'A' and 'B'. Let us consider the alloy of Co. The initial alloy deposited from Co has a composition confirming to 'C1'. Obviously, 'C1' has a composition pertaining to 'B' which is less than that of the original alloy 'Co'. Therefore, as 'C1' is formed, the residual liquid gets slightly enriched in 'B'. Thus, as solidification proceeds 'B' is continuously rejected into the liquid. This rejection occurs at the solid–liquid interface throughout the process of freezing. A constitutional gradient is, thus, created in the liquid, solute 'B' being continuously rejected at the interface. The concentration of 'B' is maximum at the interface and gradually diminishes as one goes towards the interior of the liquid melt. This compositional variation is presented in **Figure 7(a)**. The change of composition brings in a corresponding change

*Schematic presentation of rejection of solute at the interface (7(a)) and change of equilibrium temperature* 

**3.3 Constitutional super cooling**

**26**

**Figure 7.**

**Figure 6.**

*Phase diagram of a typical binary alloy.*

*(7(b)) as a consequence of the solute accumulation.*

*Schematic presentation of constitutional supercooling as a consequence of solute rejection at the interface and the resultant alternation in the equilibrium freezing temperature.*

in the equilibrium freezing temperature of the alloy as presented in **Figure 7(b)**. Each composition on the solute distribution curve has its corresponding equilibrium freezing temperature as it depends on the corresponding composition of an alloy.

The relationship between the actual (existing) temperature gradient in the melt and the equilibrium freezing temperature as a consequence of alterations in the composition of the alloy-melt, is illustrated in **Figure 8**.

**Figure 8** clearly illustrates, before the actual (existing) temperature falls considerably for growth to occur, there, is a pool of melt where considerable supercooling can be witnessed at points farther within the melt. In this pool of supercooled liquid conditions are more favourable for freezing than at the interface. This condition is referred to as constitutional super-cooling.

#### **3.4 Freezing of eutectic alloys**

Alloys having Eutectic composition or containing appreciable amounts of eutectic constituents, undergo eutectic freezing. The alloy of eutectic composition solidifies at a single temperature to precipitate a mixture of two phases '' '' α β *and* of different compositions, 'x' and 'y' [2]. Thus, two separate phases, of two different compositions are precipitated out at a single temperature as a consequence of freezing of an eutectic alloy. Here, unlike the growth of grains as in a solid solutions, each of the eutectic grains is formed by the simultaneous growth of two dissimilar phases in close association. The eutectic structure could be any one of the following:


#### **3.5 Other growth modes**

It is the extent of undercooling and its relative location in the melt that immensely influence the mode of growth of the crystal in a solidifying melt. As suggested earlier, it can be a thermal undercooling or a constitutional undercooling. Different extents of undercooling may be found in a band of liquid adjoining the interface or even in the inside of the melt depending on the following:

## i. Temperature gradient in the melt,


Depending on the extent of under cooling growth can be Dendritic Growth, Cellular Growth or growth due to independent nucleation.

Dentric crystalline growth takes place on solidification of a metal/alloy melt when the liquid–solid interface moves into supper cooled liquid at a temperature lower than that of the interface. This is illustrated in **Figures 5** and **6** wherein the thermal supercooling or the constitutional supercooling, as the case may be, generate pools in the liquid melt with temperature less than that at the interface. To understand dendritic growth it is important to realise that any protuberance on the solid face may tend to be stable and act as a centre for further growth in preference to other locations due to undercooling. The general advancement of the interface is retarded by the liberated lateral heat of crystallisation or by a solute barrier, but the local growth centres have the possibilities to grow into the zones of supercooling. This gives rise to dendritic growth. This is characterised by commercial alloys forming solid-solutions. It can be emphasised, under rapid solidification conditions non equilibrium condition of solid –liquid interface influence the dendritic characteristics to a great extent [12].

Primary axis of the dendrite is a result of preferred growth at the edge or corner of an existing crystallite. The projection develops into a needle, an then into a plate following the general direction of heat flow. This growth direction is usually associated with a particular crystallographic direction. Again, lateral growth of the primary crystal, needle or plate, is restricted by the liberation of latent heat of crystallisation or solute accumulations that had earlier restricted the growth of the original interface. However, the secondary or tertiary branches may grow by a similar mechanism that helped the formation of the primary stem. This is presented in **Figure 9** which depicts the branch like dendritic growth.

This unidirectional dendritic growth produces columnar dendritic structure.

In a pure metal dendritic growth is detected by interrupted freezing and decantation (once a portion freezes, it is separated from the liquid, i.e., the liquid is decanted from the freezing crystal). On the other hand, in alloys dendritic growth is revealed by the characteristic cored structure. Coring is resulted from the differential freezing processes. The centre of the dendrites are deficient in solute which are rejected to the interdendritic zone, as explained earlier.

**29**

**Figure 10.**

*Solidification of Metals and Alloys*

nucleations at points in the melt,

interior of the liquid-melt.

*3.6.1 Alloy constituents*

*3.6.2 Thermal conditions*

**3.6 The structure of the casting**

the crystallographic morphology of the casting.

*DOI: http://dx.doi.org/10.5772/intechopen.94393*

Dendritic growth may be associated by crystals growing independently on independently formed nuclei, elsewhere in the melt depending on the preventing thermal conditions. This independently growing crystal within the melt has an interface on its periphery. Thus, it is capable of growing in all directions generating an approximately equiaxial grain. With a less marked undercooling, when the undercooling is not enough to form dendrites, cellular growth may still take place. Thus, cellular growth precedes dendritic growth. The cellular substructure is produced as a cluster of hexagonal rods. These rods grow into the liquid and reject solute on their boundaries at the respective interfaces. After a certain level of undercooling is achieved by both thermal and the constitutional means, cellular growth gives way to dendritic growth. This proceeds by the preferential development of some of the cells. This intermediate, rod like structure is also referred to as *Fibrous Dendrites*.

As shown in **Figure 10** when the temperature gradient is very shallow or the rate of freezing is very rapid, the undercooling achieved may be sufficient to promote

distant from the main interface. In such an eventuality, the nuclei are free to grow in all directions on their periphery. An equiaxial grain structure, is thus, produced by independent nucleations. **Figure 10**, thus, exhibits the effect of increased undercooling (with the creation of different temperature gradient) on the mode of growth. It also shows the growth pattern with this different temperature gradients existing in the melt in the growth direction away from the mould wall into the

The alloy constitution (composition) decides whether the structure will be of a simple phase or eutectic grains or both. The alloy composition also indicates the tendency of the alloy to respond to constitutional supercooling. The extent of constitutional supercooling is certain to influence the growth pattern that decides

The thermal conditions to which the liquid melt/alloy is exposed during solidification, refer to both, the rate of cooling and the temperature distribution in the

*Schematic representation of the influence of undercooling on the growth pattern and grain morphology.*

Three factors have major influence on the casting structure.

**Figure 9.** *Schematic diagram showing the growth of a typical dendritic arm.*

## *Solidification of Metals and Alloys DOI: http://dx.doi.org/10.5772/intechopen.94393*

*Casting Processes and Modelling of Metallic Materials*

ii.The equilibrium freezing temperature and

Cellular Growth or growth due to independent nucleation.

iii.The nucleation temperature (which will also be dictated by heterogeneous

Depending on the extent of under cooling growth can be Dendritic Growth,

Dentric crystalline growth takes place on solidification of a metal/alloy melt when the liquid–solid interface moves into supper cooled liquid at a temperature lower than that of the interface. This is illustrated in **Figures 5** and **6** wherein the thermal supercooling or the constitutional supercooling, as the case may be, generate pools in the liquid melt with temperature less than that at the interface. To understand dendritic growth it is important to realise that any protuberance on the solid face may tend to be stable and act as a centre for further growth in preference to other locations due to undercooling. The general advancement of the interface is retarded by the liberated lateral heat of crystallisation or by a solute barrier, but the local growth centres have the possibilities to grow into the zones of supercooling. This gives rise to dendritic growth. This is characterised by commercial alloys forming solid-solutions. It can be emphasised, under rapid solidification conditions non equilibrium condition of solid –liquid interface influence the dendritic charac-

Primary axis of the dendrite is a result of preferred growth at the edge or corner

This unidirectional dendritic growth produces columnar dendritic structure. In a pure metal dendritic growth is detected by interrupted freezing and decantation (once a portion freezes, it is separated from the liquid, i.e., the liquid is decanted from the freezing crystal). On the other hand, in alloys dendritic growth is revealed by the characteristic cored structure. Coring is resulted from the differential freezing processes. The centre of the dendrites are deficient in solute which are

of an existing crystallite. The projection develops into a needle, an then into a plate following the general direction of heat flow. This growth direction is usually associated with a particular crystallographic direction. Again, lateral growth of the primary crystal, needle or plate, is restricted by the liberation of latent heat of crystallisation or solute accumulations that had earlier restricted the growth of the original interface. However, the secondary or tertiary branches may grow by a similar mechanism that helped the formation of the primary stem. This is presented

in **Figure 9** which depicts the branch like dendritic growth.

rejected to the interdendritic zone, as explained earlier.

*Schematic diagram showing the growth of a typical dendritic arm.*

i. Temperature gradient in the melt,

nucleation)

teristics to a great extent [12].

**28**

**Figure 9.**

Dendritic growth may be associated by crystals growing independently on independently formed nuclei, elsewhere in the melt depending on the preventing thermal conditions. This independently growing crystal within the melt has an interface on its periphery. Thus, it is capable of growing in all directions generating an approximately equiaxial grain. With a less marked undercooling, when the undercooling is not enough to form dendrites, cellular growth may still take place. Thus, cellular growth precedes dendritic growth. The cellular substructure is produced as a cluster of hexagonal rods. These rods grow into the liquid and reject solute on their boundaries at the respective interfaces. After a certain level of undercooling is achieved by both thermal and the constitutional means, cellular growth gives way to dendritic growth. This proceeds by the preferential development of some of the cells. This intermediate, rod like structure is also referred to as *Fibrous Dendrites*.

As shown in **Figure 10** when the temperature gradient is very shallow or the rate of freezing is very rapid, the undercooling achieved may be sufficient to promote nucleations at points in the melt,

distant from the main interface. In such an eventuality, the nuclei are free to grow in all directions on their periphery. An equiaxial grain structure, is thus, produced by independent nucleations. **Figure 10**, thus, exhibits the effect of increased undercooling (with the creation of different temperature gradient) on the mode of growth. It also shows the growth pattern with this different temperature gradients existing in the melt in the growth direction away from the mould wall into the interior of the liquid-melt.
