A comment on the paper of Prohászka on the origin of dislocations in dendrites

ACTA

1094

have

complete

generality,

METALLURGICA,

as follows.

The resolved

nobe + &(o -

where a, b, c are the direction

circuit

12, 1964

could

enclose

one or more additional

layers in the cooler tip.

shear stress acting on any slip system is given by 7 = oad -

VOL.

tial dislocation

no)qf

density resulting from the extra layer

to be proportional

cosines of the slip plane,

atomic

Proh&szka showed the poten-

to the square of the temperature

difference between the tip and the balance of the array, which was taken to be the melting point, T,.

If this

and d, t:, f those of the slip direction, relative to the stress axes. Since the slip direction lies in the slip

difference is of the order of a degree, the mechanism

plane, then ad + be + cf = 0, and substituting

could introduce

for cf

This temperature

leads to 7 = &(l + n)a(ad Thus

whatever

the value

maintained

be)

of n at any instant

the

relative values of resolved shear stress on various slip systems are given by the factors ad serves t,o indicate

be. This also

that sheet and strip rolling should

not differ, at least at the central plane. In connection

with the stability of various likely end

orientations

the (100) [OOl] texture

as I pointed

out previously,@J

rolling

direction

to produce

and this kind of instability small reductions [OOl],

which.

by rotation

about the

an (h k 0) [OOl] texture

can be seen even after very

by rolling.

although

can be destroyed,

The end point

unstable

itself,

is (110)

cannot

be

passed with slip confined to the primary and conjugate systems because it is only reached after lOOo/o reduction in thickness. by Dillamore failure from

densities about

In practice

and Roberts,

to maintain

cross-slip probably

the rolling

one pass to the next,

as suggested enhanced

direction

by

accurately

leads to other textures

before (110) [OOl] is reached.

Aluminium

Laboratories Ltd.

12,281

between

the closing interfaces

to keep temperature

closing the circuit.

because

between difference

must vanish, in order

gradients finite.

The exact’ tem-

perature at which closure is accomplished T,

be

across the

the tip and the first side, the temperature

of local requirements

will not be

of curvature

and

atomic kinetics; in fact, none of the growing array can be exactly

at T,,

partures from T,,

as assumed.

However,

and more particularly

the de-

at the point

of closure, around the loop, will be very small relative to the departure at a dendritic tip, growing freely in its own thermal field.

If a degree is a reasonable

for the latter, the differences

in temperature

figure around

the loop at closure may well be one or more orders of magnitude

smaller, because of large radii of curvature,

low normal growth velocities,‘2)

and the proximity

adjacent growing interphases.(3)

Thus, the number of

dislocations

that might be introduced

of

will be much

from the original

mechanism.

model, which is perhaps more attrac-

Gibson and Fort,ey have related situations.(4)

densities arise when arms dendritic

considered

arrays merge.

this, and other

D. R. Westinghouse

19, 1964.

however,

small separation

of two separate, misoriented,

1. I. L. DILLAMORE and W. T. ROBERTS, Acta Met. (1964). 2. G. E. G. TUCKER, J. Inst. Met. 82, 655 (1954). February

In the limit of vanishingly

tive, is that high dislocation

References

cannot,

tip advances

fourth side of the square, physically

An alternative

Banbur;y, Oxon,

* Received

difference

when a dendrite

lower than calculated

G. E. G. TUCKER

106/cm.2

HAMILTON

Research Laboratories

Pittsburgh 35, Pa. References 1. J. PROHKSZKA. Acta Met. 11. 125 (1963).

A comment on the paper of Proh6szka on the origin of dislocations in dendrites* Proh&szka(l) dislocation fact

has recently proposed

formation

in dendrites,

that the temperature

a mechanism based

upon

of the

at the tip of a growing

dendrite is always lower than elsewhere on the interface.(2) Because of this, and the contraction of the lattice on cooling, there are extra atomic layers in unit distance about the tip relative to other parts of a dendritic system. If, for example, branches of a continuous, monocrystalline, dendrite form three sides of a square, and if one of these sides ends in an advancing tin. then a line drawn across the fourth side of the

2. D. E. TEMPKI;, D&l. Akad. NW& &SdR 132, 1307 (1960). G. F. BOLLING and W. A. TILLER, J. A&. Phq.7. 32, 2587 (1961). 3. R. G. SEIDENSTICKER and D. H. HAMILTON, J. Appl. Phys. 34, 3113 (1963). 4. A. J. FORTEY and J. G. GIBSON, Acta Met. 6, 137 (1958). * Received

February

10, 1964.

Reply to comment by Hamilton on the origin of dislocations in dendrites* Hamilton(l) has commented on the mechanism of formation of dislocations proposed by the author in connection

with dendritic

crvstallisation.

It is rather