Dendritic crystal growth occurs when a liquid-solid interface moves into supercooled liquid. Heat is released at the interface, causing a temperature inversion where the interface is hotter than the surrounding liquid and solid. Small perturbations at the interface can then grow out into the liquid, forming branched crystal structures that resemble trees, hence the term "dendrite." Secondary and tertiary branches form on the primary branches as the temperature gradient causes further crystalline growth perpendicular to the initial branches.

1. DENDRITIC GROWTH

2. DENDRITIC GROWTH IN PURE
METALS
A 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.

3. Fig(a) Temperature
inversion during
freezing

4. 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.

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

6. Formation secondary Branches
Secondary 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.”

7. 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.

8. 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).

9. 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).

10. 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,

11. 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.

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

13. 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.

14. 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.