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.

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.

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.

• 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.

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.

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.

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.

• 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”.

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.

• 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”.

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)

• 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.

• 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 ]

• 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.

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.

Animation showing formation of primary and secondary dendrites

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.

Animations of dendratic growth