On the tetragonality of substitutional martensites

Scripta

METALLURGICA

Vol. 5, pp. 1 0 1 - 1 0 4 , 1 9 7 1 P r i n t e d in the U n i t e d S t a t e s

Pergamon

Press,

Inc.

ON THE TETRAGONALITY OF SUBSTITUTIONAL MARTENSITES

John W. Cahn and William Rosenberg Department of Metallurgy and Materials Science Massachusetts Institute of Technology Cambridge, Massachusetts

(Received

December

4,

1970)

It has become clear that even substitutional alloys of iron may form tetragonal

martensltes

(1,2,3,4,5).

Winchell and Spelch (6) recently proposed a model based on the trans-

formation of large compositional clusters, such as Ni3Ti groupings, in Fe-NirTi alloys.

Such a

model, while attractively plausible, does not lend itself to easy verification, since the tools for measuring the number of clusters containing more than two atoms are still limited to fieldion microscopy and possibly the Mossbauer effect.

Furthermore, it would be difficult on the

basis of the clustering model to explain the tetragonallty of binary iron-nlckel martensites (i). We propose instead that the observed tetragonallty of substitutional martensites is due primarily to anlsotropy of atomic pair correlations brought about by the transformation.

We

assume a Baln correspondence B which carries lattice points and the atoms on them in the austenlte to corresponding positions in the martenslte.

We are particularly interested in the

inverse Baln correspondence which tells us what a particular vector in the martensite was in the original austenlte:

~a " B-l~m

[21

The eight 1 / 2 ( [ i 1 1 ] ) near-neighbor vectors i n the martensite a l l o r i g i n a t e from i / 2 ( [ 1 1 0 ] ) vectors i n the austenite,

Hence we conclude that the f i r s t - n e i g h b o r Warren shmrt-range order parameters

in austenite and martensite are equal.

~m(I/2[lll]) = Sa(i/2[llO])

i01

[3]

102

TETRAGONALITY

OF

SUBSTITUTIONAL

MARTENSITES

Vol.

5, No.2

However, of the six second neighbors in the martensite, four ([i00], [T00], [010], [010] came from first neighbors in the austenite:

~m([100]) - aa(I/2[ll0])

[4]

while the remaining two ([001]) and ([001]) came from second neighbors:

am(J001]) = ~a([lO0])

[5]

Thus, unless first- and second-nelghbor correlations in the austenite are equal, the secondneighbor pair correlation will not be consistent with cubic symmetry:

am([lO0]) ~ am([O01])

[6]

Consider now a general i/2[h,k,~] position vector in the martenslte, where h, k and are all odd or all even.

Using the inverse Bain correspondence, this vector connects two

atoms that were separated by a i / 2 [ ~ ,

T'h-k ~] vector in the austenite.

is to be cubic, the various permutations of h, k and ~ must be equivalent.

If the martensite But only for h=k=£

are the various permutations from equivalent [h,h,o] positions in the austenite.

Martensite

originating from austenlte in which there is short-range order cannot have cubic symmetry. The symmetry for such martensite is tetragonal. only h and k.

This is readily seen by permuting

These vectors come from equivalent positions in the austenlte.

We have shown that short-range order in the austenlte leads to a martensite with tetragonal pair correlations.

The correlations are quantities that can be measured in both

phases and the relationships can be experimentally verified. different directions should preferably be measured separately.

For the martensite the = for If this is too difficult, the

average of the ='s at a given "distance" is predictable from the austenite a's, e.g.

=m([lO0]) = i/6~4aa(i/2[ii0]) + 2aa([100])}

[7]

The "degree of tetragonality" is directly proportional to the differences in shortrange order in the austenlte.

A popular measure of tetragonality is the fractional difference

between the c and a lattice parameter.

If the second neighbors are primarily responsible for

the tetragonallty, it would be directly proportional to

vol.

5,

No.

2

TETRAGONALITY

(cm - a

TM) =

OF

SUBSTITUTIONAL

MARTENSITES

103

k{~a([100]) - ~a(i/2[llO])}

[8]

This relation could be verified by altering composition and/or prior heat treatment, and measuring c-a a aswell

as the u's.

We have implicitly assumed that the transformation carries atoms to designated positions in the martenslte.

Any diffusion or deformation will alter the pair correlations.

If martensite is essentially a body centered cubic phase which is born with non-cubic correlations, the changes will be to reduce the tetragonallty. There are nonferrous martensites in which the Bain strain is not known with any certainty (7).

We would like to invert our suggestion for these cases and assume the correctness

of the ~ relation.

Then by studying martensite containing alloy elements that exhibit short-

range order, we may identify the Baln correspondence uniquely.

References i.

P. G. Winchell and M. Cohen, Trans. Quarterly 55, 347 (1962)

2.

Y. Honnorat, G. Henry, G[ Murray and J. Manenc, C. R. Acad. Sci. Paris 260, 2214 (1965)

3.

Y. Honnorat, G. Henry and J. Manenc, M~m. Sclent. Revue Metall. 60, 429 (1965)

4.

J. K. Abraham and J. S. Pascover, Trans. Metall. Soc. AIME 245, 759 (1969)

5.

J. K. Abraham, J. K. Jackson, and L. Leonard, Trans. Am. Soc. Metals 61, 233 (1968)

6.

P. G. Winchell and G. R. Speich, Acta Met. 18, 53 (1970)

7.

A. G. Crocker and N. D. H. Ross, Mechanism of Phase Transformation in Crystalline Solids, Institute of Metals Mono. #33, 176 (1969)