In this article we will discuss about the solidification of polycrystalline materials with its schematic diagram.

A space lattice is formed by adding unit cells one after the other in three dimensions. It is possible to produce a macroscopic visible piece of a metal, formed by repetition of unit cells of crystal structure of that metal in three dimensions of 103 to 108 atomic diameters as illustrated schematically in Fig. 2.12. Such a piece is called a ‘single crystal’ of that metal.

The surface of the piece limits the stacking dimensions. Single crystals are quite common in naturally occurring minerals like galena, quartz, fluorite, etc. It is possible to grow such single crystals of metals in laboratory (the science of single crystal growth had become important since the development of semi-conductors, transistors, lasers, etc.).

The crystal axes in a single crystal are in the same direction everywhere, i.e., atoms are oriented in one direction only. There are no grains boundaries, the bounding surfaces are the only surfaces present. A turbine blade of single crystal of titanium has proved a great success.


If a pure liquid metal is cooled very slowly, then at its freezing temperature, solidification begins.

This process occurs in two stages:

(a) Nucleation,

(b) Growth of nuclei.


Suppose only one small particle of crystalline solid begins to form at a point within the liquid (under proper conditions). It is called nucleus (it is different than nucleus of an atom). It is a collection of many atoms, which is stable in the liquid. As more and more atoms transfer themselves to this growing solid, it becomes macroscopically large. This whole solid, thus formed is a single crystal, such as illustrated in Fig. 2.12.

Engineering materials usually contain many crystals, i.e., they are polycrystalline. The common process of melting, casting and freezing in a mould, by which nearly all metals and alloys (except from powder metallurgy, etc.) are made, solidify as polycrystalline material as schematically illustrated in Fig. 2.13. Nuclei of crystals appear simultaneously at many points (three of them are shown in Fig. 2.13 (a)), throughout the liquid.

At each of these sites, atoms from the liquid attach themselves to the crystal nucleus, giving up their energy of motion as latent heat of fusion and take up relatively definite atomic sites with respect to one another, thereby increasing the size of each growing dendrite (a tree like structure) as illustrated in Fig 2.13 (b) and (c).


Each solid dendrite has the same crystal structure as of the metal, but the orientation of crystal axes (is same in one dendrite), in different dendrites is usually random, and there is no coordination between different growing dendrites. Dendrites grow outwardly from each crystal-nucleus until they meet other growing dendrites Fig. 2.13 (c) from neighbouring nuclei. The remaining liquid crystallises in the space between the arms of dendrites until it solidifies completely. This result in a polycrystalline structure, one crystal from each nucleus as illustrated in Fig. 2.13 (d).

Each crystal of the polycrystalline solid is called a grain, and its interface with the neighbouring grain is a grain boundary. Grain refers to individual crystal in a macroscopic piece. Rather, grain and crystal are commonly used interchangeably.

Each grain inside the metal is joined to its neighbours at all points on its grain boundary, and the position of the grain boundary is determined by where the separate growing crystals happen to meet. The grains, thus, have generally irregular and uncrystallographic outlines. Flat crystal faces cannot form, when each grain takes up a shape dictated by the chance arrangement of neighbouring grains.


In a single phase (a phase is a physically-distinct, chemically homogeneous and mechanically separable region) solid such as a pure metal, these crystals have arrangements of similar atoms with same crystal structure in three dimensions bounded with grain boundaries.

One of the most useful aids in understanding the structures of metals is the picture (or a photograph of it, and then it is called photo-micrograph) of a sample of metal as observed through a microscope, called microstructure. Metal sample is polished and the etched surface is observed under a microscope.

It is able to reveal such features as the arrangement and size of grains, distribution of phases, the results of plastic deformation and the existence of impurities and flaws. The suitable chemical reagent, with slight chemical attack first reveals the grain boundaries.

Further etching produces shades which vary from one grain to the next, owing to the fact that etching reagent does not attack the metal surface evenly (same way) but along certain (Fig. 2.14) crystallographic planes.

Facets having the same orientation are then produced in each grain, and since each grain has a different orientation from that of its neighbours, one grain may reflect light into the objective of the microscope, and consequently appear light, while the adjacent grains reflect most of the light in other directions and appear darker (with different shades depending on the extent of such reflection of light).

At the grain boundaries, a difference in level may exist, or more commonly a groove may form. In either case, the incident light is not reflected back to the eye, and thus, the grain boundary is visible as a dark line. The microstructure is a two-dimensional picture. No fine-scale atomic details, such as the structure of a grain boundary, the existence of dislocations, are revealed because the resolving power (it is the ability of the microscope to separate distinctly two close objects) is too poor (resolution under best state cannot exceed 0.2 (µm).

Fig. 2.15 (a) illustrates a sketch relating the two dimensional microstructure of a metal to the underlying three dimensional arrangement. Fig. 2.15 (b) is a typical microstructure of a pure metal (though a solid solution also shows similar microstructure) showing the grains and the grain boundaries.

Atoms are arranged in a crystalline order in each grain, though there is a difference in orientation of atoms (20° or more) in the randomly distributed grains, but there is an area of mismatch, mostly consisting of large-angle grain boundaries In a pure metal, the crystal structure continues unchanged right up to the interface itself, and the grain boundary is a narrow transition region, not more than about two atoms thick, across which the atoms change over from the crystal sites of the one grain to those of the other.

Field-ion microscope has shown this. Atoms at the grain boundaries should be within the range of interatomic forces of the neighbouring grains. As interatomic forces are short-ranged, this transition layer can be only about 2 atoms thick. Atoms at grain boundary, sit in positions to make a balance of forces of attraction due to atoms of the neighbouring grains, and these sites are normally not the lattice sites of either grain.

Atoms on the grain boundary find it increasingly difficult to fit simultaneously on the lattice sites of adjoining grains due to the difference in orientation of the crystal axes in these grains. This is illustrated by models in Fig. 2.16 (a) and (b). Here nearly perfect crystals extend up to each other and touch at irregular points.

The boundary contains atoms that belong to both crystals, and atoms belonging to neither crystal. Fig. 2.16 (c) and (d) illustrate old model of grain boundary. Here two nearly perfect crystals extend up to a thin layer of atoms that has an amorphous structure and acts almost as a liquid boundary layer separating the almost perfect crystals.


Calculate the width of a large-angle boundary in copper if its grain boundary energy is 0.55 Jm-2. The latent heat of melting is 10 -20 J atom-1. (Assume the disorder in a boundary to be equal to that in the liquid).


As the disorder of atoms is just like that in the liquid, the energy of an atom in the liquid is more than an atom in the crystal. This excess energy is the energy of the boundary per atom, which is the latent heat of melting per atom. Let d m be the thickness of the boundary-

In general, a general grain boundary has five degrees of freedom; the three degrees specify orientation of one grain relative to the other (oriented along three axes X, Y and Z), and two degrees specify the orientation of boundary relative to one of the grains.

A single phase substitutional solid solution alloy (say, Fe-Cr) or a single phase interstitial solid solution alloy (low carbon steel having only ferrite) have microstructures as illustrated respectively in Fig. 2.17 (a) and (b), but they appear to be just like of a pure metal. Compare with Fig. 2.15 (b).

Similar grains with dark grain boundaries with slight difference in the shading of grains (due to difference in the orientation of atoms) are seen, Fig. 2.18 (a) illustrates schematic picture at atom level of a substitutional solid solution (80% Cu, 20% Ni). Compare it with Fig. 2.16 (a), In Fig. 2.18 (a), every grain has same crystal structure (as in Fig. 2.16 a), but some atoms of copper have been substituted by nickel atoms.

Fig. 2.18 (b) illustrates ferrite in which carbon forms interstitial solid solution. This too resembles Fig. 2.16 (a). Crystal structure is same in all the grains. The microstructures of a pure metal and the solid solution are similar and it is difficult to distinguish one from the other. Other methods could be used to distinguish. The colour of brass (70/30), a solid solution distinguishes it from pure metal copper.

As the atoms at the grain boundaries are displaced from the normal lattice sites, they have more energy. Thus, they are more reactive and can be displaced easily to rearrange to low energy positions.

Thus, a grain boundary shows:

1. A groove due to preferential attack of the etching chemical with these atoms at grain boundary, which appears as a dark line under microscope.

2. If a new phase is to form (due to lowering of temperature, if a phase transformation takes place), preferential formation of the new phase takes place at the grain boundary because high energy atoms here can rearrange easily into a new phase. The surface energy of grain boundary helps in the formation of new grains of new phase.

3. Preferential presence of impurity atoms in the metal at the grain boundaries, or the first fraction of atomic percent of the atoms of the alloying elements are also present at the grain boundaries. There are voids, dislocations, etc. present at the grain boundary and these incoming atoms can fit in here more comfortably without much elastic strains as compared to when they join the grain as a substitutional atom or interstitial atom (where they always cause large elastic distortions of the crystal lattice). They occupy those sites which increase the energy of the crystal to a minimum.

4. A grain boundary energy is usually of an order of magnitude of 600 mJ per m2, though it considerably depends on factors such as composition and orientation of grains.

5. Faster diffusion takes place here than though the grains as there arc voids present here to aid the diffusing atoms.

6. Grain boundaries are source and sink of the vacancies, i.e. vacancies can diffuse to them, or can be generated in the crystal lattice due to diffusion of vacancies from grain boundaries.

7. The non-crystalline nature of grain boundaries makes its viscosity to decrease continuously on heating as compared to crystalline grains, and the latter retain solid rigidity up to the melting point. Due to continuous lowering of viscosity, grain boundaries loose their strength at a lower temperature, particularly above it equicohesive temperature.

Thus fracture runs along the grain boundaries, resulting in intercrystalline fracture. At room temperatures, the grain boundaries, as a rule, are quite strong, and metals fail by transcrystalline nature, i.e., across the grains.

8. In high temperature applications, grain boundaries act like very viscous liquid, causing neighbouring grains to slide against each other under, the stress. This causes the creep of metals at high temperatures.

9. Grain boundaries strengthen the metals and alloys below equicohesive temperatures as these blocks the motion of dislocations. In coarse grains, pile-up contains more dislocations, which in turn causes higher stress concentrations in the neighbouring grain resulting easier yielding. Fine grained materials are stronger than coarse grained materials.

As a grain boundary has energy related with it, it tends to minimise its area in order to reduce its total energy, and thus, reduces the energy of the solid to make it more stable (a stable state has lower energy). This driving force for the reduction in grain boundary energy (interfacial energy) is called surface tension and is expressed as dynes/cm, or ergs/cm2, or Joules per square meter.

Normally the grain boundaries have irregular shapes. In order to decrease its energy, the grain boundary tries to straighten itself under the force of surface tension (a straight boundary has less length than an irregular shaped boundary, and thereby also the energy).

If a metal is heated in order to anneal it, the thermal energy helps the atoms to diffuse from one site to another. This jumping (diffusion) becomes easier under a force like surface tension as illustrated in Fig. 2.19. The atom X has lesser bonding in grain I and if it diffuses to site Y, the atom is bonded with two atoms of grain II. Heating the metal helps in the process of diffusion, and thereby in straightening the layer separating the crystals.

If three grain boundaries in a single-phase solid (an annealed pure metal, or a solid solution) intersect at a point as illustrated in Fig. 2.20. As a first approximation, the grain boundary energy of each grain boundary is assumed to be equal (neglecting the slight variation in energy due to orientation difference), because these boundaries are in between the grains of the same phase, i.e., the surface tensions are equal. As the surface tensions form a system of forces in equilibrium with a mechanical analogy to the triangle law of forces. Thus,

Thus, the grains meet at an angle of 120° to each other in ideal condition (in perfectly equilibrium and fully annealed condition) as illustrated in Fig. 2.17. If all boundaries meet at an angle of 120°, then the shape of the grain which when stacked over each other fill the space completely. This polyhedron is called tetra-kaidecahedron, which satisfies the conditions.