- Dendritic crystal growth occurs when a liquid-solid interface moves into a supercooled liquid. Heat is removed from the interface into both the solid and liquid. - Undercooling of the liquid allows the formation of spikes at the interface that grow faster than the surrounding interface. This leads to the formation of branched, tree-like dendritic structures. - Secondary and tertiary branches can form from primary branches/spikes. The branching occurs due to temperature gradients that arise from the release of heat at the interface.

1. Dendrite:
• The term "dendrite" comes from
the Greek word dendron, which means "tree".
• A dendrite is a crystal with a tree like
branching structure.
• Dendritic crystal growth is very common and
illustrated by snowflake formation
and frost patterns on a window.

2. Dendritic Growth
• This growth occurs when the liquid solid interface
moves into a ‘super cooled liquid ’. whose
temperature decreases in advance of the interface.
• The figure shows a region containing a liquid solid
interface and heat is flowing away from the interface
in both directions.

3. Dendritic Growth
• That is the heat is being removed through
both the solid and the super cooled liquid.
• Because of the heat of fusion released at the
interface, the temperature of the interface
usually rises above that of both the liquid and
solid.

4. •Under these conditions , the temperature drops as one
moves from the interface into the solid because this is the
heat flow direction.
It also falls off into the liquid because there is a natural flow
of heat from the interface into the super cooled liquid.
The figure is called ‘ Temperature Inversion ‘ diagram.

5. Dendritic Growth
• Let’s consider the case where the
temperature of the liquid-solid interface
decreases in advance of the interface.
• The temperature gradient of this type may
be achieved by considerable under cooling.
When sufficient under cooling has been
achieved the temperature of the liquid
would be sufficiently below the equilibrium
freezing point.

6. Dendritic Growth
• Whenever a small section of interface find
itself ahead of surrounding surface, it will be
in contact with the liquid metal at a lower
temperature.
• Its growth velocity will be increased relative to
the surrounding surface (which is in contact
with liquid at high temp) and formation is
expected.

7.  The temperature of interface would be higher
either liquid or solid. It is due to the release of heat of
fusion at the interface.
 Figure shows a region containing a liquid-solid
interface ,and formation of primary dendrites.

8. • It becomes more interesting when secondary
and in some cases tertiary branches grow
from primary spikes. The resulting branched
crystal looks like a small pine tree & therefore
it is named as dendrite meaning “of a tree”.

9. Reason:
• The reason of such crystal growth is,
• Whenever a section of interface is ahead of
it’s surroundings, it will be in contact with the
liquid metal in a low temperature it will grow
faster as compared to surrounding liquid
which is
in contact with a liquid at a higher
temperature.

10. • Such situation gives rise to the formation of
spikes which seem to shoot out the interface.
• The formation of each spike releases the heat
of fusion which increases the temperature in
immediate vicinity of each spike which retards
the formation of furthers spike.
• This explains the equal spacing between these
spikes which grow parallel to each other. The
direction in which these spikes grow is
crystallographic which is termed as “dentritic
growth direction”.

11. Dendratic growth direction depends upon the
crystal structure of a metal.
• Crystal structure dendratic growth
direction
F.C.C (100)
B.C.C (100)
H.C.P (10-10)
B.C.T (110)

12. • The branches in Figure are of first order or
primary in nature, however secondary
branches may from the primary ones will now
be considered as shown in Fig. where “aa”
represents the general interface.

13. • Once the spikes have formed growth of
general interface will be slow because here
the supper cooling is small.
• At section “bb” on the other hand the average
temperature of the liquid is lower than at “aa”
due to the release of latent heat of fusion at
the spikes, the temperature TA (at the spikes )
will be higher as compared to TB (between the
spikes ). [ TA >TB ]

14. • So there is a decreasing temp. gradient, not
only infront of the primary cells but also in the
direction perpendicular to the primary cells.
• This temp. gradient is responsible for the
formation of secondary branches.
• Which forms at more or less regular intervals
along the primary branches.

15.  Since the secondary branches form for the same
basic reason as the primary branches form.
 Figure shows the dendritic growth of crystal
showing primary and secondary branches.

16. Animation showing formation of
primary and secondary dendrites

17. Important Note:
• Dendritic growth occurs in freezing of pure metals,
when the interface is allowed to move forward into
sufficiently super cooled liquid.
• In metals of relatively low purity, it is almost
impossible to obtain enough thermal super cooling ,
so the entire freezing process is not dendritic unless
heat is constantly removed from the liquid.
• In the absence of cooling from outside, a very large
super cooling is required for complete dendritic
freezing in pure metals.

18. Animations of dendratic growth