DENDRITIC GROWTH

DENDRITIC GROWTH IN PURE METALSA dendritic crystalline growth occurs when the

liquid-solid interface moves into a super cooled liquid whose temperature falls in advance of interface.

Fig (a) represents a region containing a liquid-solid interface and that the heat is flowing away from the interface in both directions.

And heat is being removed through both the solid and super cooled liquid.

Fig(a) Temperature inversion during freezing

Heat of fusion released at the interface.Therefore the temperature of the interface usually

raises above the both solid and liquid.Under these conditions the temperature drops as one

moves from the interface into the solid because of heat flow direction.

The resulting temperature contour shown in fig(a), is known as temperature inversion.

When the temperature falls in the liquid in advance of the interface the latter become unstable.

In the presence of any small perturbation, cells may grow out from the general interface into the liquid.

Fig. (b) Schematic representation of 1st stage of dendritic growth.

Formation secondary BranchesSecondary branches forms on the primary cell and

possibly with tertiary branches forming on the secondary ones.

The resulting structure may also become quite complicated.

Resulting branched crystal often has the appearance of a miniature pine tree.

Therefore this is called a dendrite after the Greek word dendrites meaning “ of a tree.”

The reasons for the branched growth of a crystal into a liquid whose temperature falls in advance of the interface is not hard to understand.

Whenever a small section of the interface finds itself ahead of the surrounding surface, it will be in contact with liquid at a lower temperature.

It growth velocity will be increased relative to the surrounding surface which is in contact with liquid at a higher temperature.

With development of each cell there is release of a quantity of heat (Latent heat of fusion).

This heat raises the temperature of the liquid adjacent to any given cell and retards the formation of other similar projections on the general interface.

The net result is that number of cells of almost equal spacing are formed.

Cells will grow parallel to each other as shown in fig(b).

The directions in which these cells grow is crystallographic and is known as dendritic growth direction.

The branches or cells shown in fig(b) are first order or primary in nature .

How secondary branches may form from primary once will now be considered.

For this purpose consider a fig.(c).

fig.(c)Secondary dendrite arms form because there is a falling temperature gradient starting at a point close to primary arm and moving to a point midway between the primary arms. Thus,

Where section aa represents the general interface.Notice that in this fig.(c) the direction of dendritic

growth is assumed to be normal to the general interface.

Once the cells have formed, growth at the general interface will be slow because here super cooling is small.

At section bb, on the other hand the average temperature of the liquid is by definition lower than at aa.

Fig.(c) Formation of secondary arms on primary arms

How we were at this section at points in the liquid close to the cell wall the temperature will be higher than midway between the cells (TA>TB).

Because the latent heat of fusion released at the cells.There is, therefore, a decreasing temperature gradient

not only in front of primary cells, but also in direction perpendicular to the primary branches.

This temperature gradient is responsible for the formation of secondary branches.

Reason of formation of secondary branches is same as of primary branches.

Similarly, tertiary branches will form from the secondary branches if the space is available for their growth.