Dendritic growth in pure metals

1.  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.
DENDRITIC GROWTH IN PURE
METALS

2. Fig(a)
Temperature
inversion
during
freezing

3.  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.

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

5.  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.”
Formation secondary Branches

6.  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.

7.  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).

8.  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).

9. 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,

10.  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.

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

12.  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.

13.  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.