PHASE AND STRUCTURAL TRANSFORMATIONS

UDC 669.14.018.8:669.017.3

COOPERATIVE MECHANISM OF THE s-PHASE � FERRITE

TRANSFORMATION IN STAINLESS STEEL 05Kh22AG15N8M2F

AND HARDENABILITY OF STEELS

V. S. Kraposhin,1 A. I. Plokhikh,1 A. L. Talis,2 M. V. Kostina,3 and S. O. Muradyan3

Translated from Metallovedenie i Termicheskaya Obrabotka Metallov, No. 12, pp. 3 – 6, December, 2013.

The geometric mechanism of cooperative transformation of �-phase into bcc-ferrite observed in some

austenitic stainless steels is considered. This mechanism is used to explain the elevation of the hardenability of

steels upon the introduction of alloying elements.

Key words: stainless steels, structure, phase transformations, coordination polyhedrons.

INTRODUCTION

We have studied the relations between the structural

transformations and mechanical properties of a new cast

stainless steel based on the Fe – Cr – Mn – Ni – Mo system

(with an approximate composition of 0.5 C, 22 Cr, 15 Mn,

8 Ni, 2 Mo, 0.5 N, 0.2 V (in wt.%) in [1]. It turned out that a

�-phase in an amount of 12 – 13 vol.% formed between den-

drites of the austenite matrix in the structure of the cast steel

as a product of solidification of the retained melt. The re-

gions of the �-phase were enriched with ferrite-forming ele-

ments (28 – 29% Cr, 2.8% Mo) and depleted of austen-

ite-forming elements (12% Mn, 3.5% Ni). Annealing of this

steel in the range of 1100 – 1200°C causes formation of fer-

rite in the place of the regions of the �-phase (in a certain

sense, it may be called �-ferrite though its does not form

from a liquid phase). The shape of the ferrite regions after

such annealing is the same as it has been observed in the

metal of the dendrite arm spacing in cast condition [1]. It is

enough to hold the metal for only several minutes at 1100°C

for ferrite to appear in the place of the �-phase. The transfor-

mation of the �-phase into ferrite is accompanied by lower-

ing of the hardness of the metal in the dendrite spacing (from

900 to 400 HV ) and growth in the ductility and in the impact

toughness of the steel as a whole. A similar transformation

has also been observed in steel 10Kh18N10T; a ferrite border

appeared around regions of the �-phase already after 5 min

of holding at 1050°C [2]. The � � � transformation ob-

served in [1, 2] resembles the in-situ transformation of car-

bides in some chromium-alloyed steels [3]: ferrite forms at

the place of particles of the initial �-phase and preserves

their size and shape and an approximately the same chemical

composition as the �-phase. The transformation develops

rapidly, and this circumstance also speaks in favor of its co-

operative nature. However, the conventional approach to the

description of a cooperative transformation as a shear one

does not work due to the great difference in the number of at-

oms per elementary cell (30 and 2 respectively).

In our previous works [4 – 7] we described the transfor-

mation as a mutual reconstruction of the coordination poly-

hedrons of the corresponding crystal structures.

In the present work we made an attempt to explain the

mechanism of the rapid �-phase � ferrite transformation us-

ing the earlier-developed approach and basing ourselves on

the special features of the crystal structures of the phases.

RESULTS AND DISCUSSION

Model of the s � d Transformation

If we consider the structure of an elementary cell of the

�-phase, i.e., the coordinate polyhedrons forming the former

and the method of their combination into the structure, in-

Metal Science and Heat Treatment, Vol. 55, Nos. 11 – 12, March, 2014 (Russian Original Nos. 11 – 12, November – December, 2013)

639

0026-0673/14/1112-0639 © 2014 Springer Science + Business Media New York

1N. É. Bauman Moscow State Technical University, Moscow, Rus-

sia (e-mail: kraposhin@gmail.com).2

A. N. Nesmeyanov Institute of Organoelement Compounds

(INEOS) of the Russian Academy of Sciences, Moscow, Russia.3

A. A. Baikov Institute for Metallurgy and Materials Science

(IMET) of the Russian Academy of Sciences, Moscow, Russia.

stead of the sizes and shapes of the �-phase particles, we will

be able to suggest a model of the � � � transformation. Fi-

gure 1 presents a plan of the structure of the �-phase in plane

(001), i.e., perpendicularly to the tetragonal axis c [2].

The crystal structure of the �-phase can be represented as

a division of its space into Frank – Kasper 14-vertex polyhe-

drons. The polyhedrons are united over a common 6th-order

axis into rods (Fig. 2); the vertex of each polyhedron located

on the axis centers the volume of the neighbor polyhedron.

The infinite crystal structure of the �-phase forms due to par-

allel packing of the rods over a symmetry axis of order 4 (the

c-axis in Fig. 3). In such a representation of the structure of

the �-phase is similar to the structures of phase A15 (Cr3Si)

and �-phase (a high-pressure phase of titanium and zirco-

nium), the crystal space of which is also determined by pack-

ing of parallel rods formed by 14-vertex polyhedrons. The

three structural types differ in the kind of union of the rods in

directions perpendicular to the axes of the rods. The variants

of such union determine the formation of structures with cu-

bic (A15), hexagonal (�-phase) or tetragonal (�-phase) lat-

tices. In accordance with the mechanism of polymorphic

(martensitic) transformations between fcc-, bcc-, and

hp-phases suggested in [3 – 5] these transformations are im-

plemented by reconstruction of the coordination polyhedrons

of the partners through intermediate configurations coincid-

ing with the structures of phase A15 [3, 4] or �-phase [5].

The 14-vertex rhombododecahedron of a bcc-lattice is recon-

structed into a 14-vertex Frank – Kasper polyhedron (Fig. 4)

and the 12-vertex cubooctahedron of the fcc- or hp-packing

is reconstructed into a 12-vertex Frank – Kasper polyhedron,

i.e., an icosahedron (Fig. 5). The possibility of the transfor-

mation is determined by the fact that the intermediate config-

uration A15 is an intersection of the meshes of 12-vertex and

14-vertex Frank – Kasper polyhedrons. In addition, it has

been shown in [6, 7] that the rods in structure A15 may be

described as three-dimensional projections of the rods of a

four-dimensional analog of the icosahedron, i.e., a {3,3,5}

polytope, which in turn is a substructure of an eight-dimen-

sional lattice E8

[8]. The symmetry of E8

is much richer than

the crystallographic one, and thus describes the local (not

crystallographic!) transformations presented in Figs. 4 and 5.

These transformations may be implemented successively in

the whole of the infinite structure. Though it is hard to imag-

ine an eight-dimensional space, we may consider an analogy

with three-dimensional Euclidean space. In a three-dimen-

sional space a cubic lattice (any) contains two-dimensional

quadratic, rectangular and triangular lattices and, corre-

spondingly, two-dimensional sections over (100), (110) and

(111) as substructures. Similarly, an infinite eight-dimen-

640 V. S. Kraposhin et al.

A

A

D

E

B

C

Fig. 1. Scheme of the lattice of �-phase in the Fe – Cr system [2];

the nodes are filled as follows: A, B ) positions of Fe; C, D ) positions

of Cr; E ) Fe, Cr (statistically).

Fig. 2. A rod of a 14-vertex

Frank – Kasper configuration.

à

b

Fig. 3. Division of the structure of �-phase into rods consisting of

14-vertex Frank – Kasper configurations: a) isometry; b ) tetragonal

axis c is arranged vertically in the plane of the figure.

sional lattice E8

contains substructures of infinite three-di-

mensional bcc- and fcc-lattices, i.e., we are dealing with in-

tersections of an eight-dimensional lattice by a three-dimen-

sional Euclidean space. From the standpoint of physics,

propagation of the mentioned local reconstructions of coor-

dination polyhedrons to the macroscopic volume of a crystal

is describable in the language of a model [9], where marten-

sitic transformation is treated as propagation of a transforma-

tion wave controlled by superposition of longitudinal (or

quasi-longitudinal) wave beams. The successions of phase

transformations with participation of �-phase observed in the

steel studied due to solidification and high-temperature an-

nealing are obviously connected with the special features of

its crystal structure.

Solidification is accompanied by formation of austenite

dendrites, the space between which is filled with a � + �

phase mixture. The author of [10] was the first to suggest that

tetrahedrons in a metallic melt obey a helicoidal union. It is

shown in [11] that the main features of melting of any metal

(the low volume effect of melting up to a negative one, the

absolute value of the latent melting heat) are explainable un-

der the assumption that the tetrahedral helicoids in liquid

metal are united into icosahedral helicoids, while the

icosahedrons themselves appear in the melt as a result of re-

construction (at the melting point) of the coordination poly-

hedron of the solid crystalline metal into an icosahedron or

into a Frank – Kasper 14-vertex configuration. According to

the authors of [12], the symmetry of such spirals in a liquid is

again determined by the symmetry of the eight-dimensional

lattice E8, i.e., by the presence of nonintegral rotary axes of

symmetry of orders 30�11 (a helicoid of tetrahedrons) and

15�4 (a helicoid of icosahedrons) with angles of rotation of

132° and 96° respectively. It is the presence of �-phase in the

Fe – Cr system which allows us to expect that the presence

of chromium in the steel will stabilize the existence of

14-vertex Frank – Kasper polyhedrons not only in the solid

state but also in the liquid state.

In accordance with data of neutron diffraction [14], posi-

tions A and B in the structure of the �-phase of the binary

Fe – Cr system (Fig. 1) are occupied exceptionally by Fe

atoms, positions C and E are occupied exceptionally by Cr

atoms, and positions D are occupied statistically by atoms of

both types. The formation of a �-phase upon solidification of

the liquid of the dendrite spacing is caused by accumulation

of chromium and other alloying elements in it. During

high-temperature annealing at 1100 – 1200°C the regions of

the �-phase are depleted of chromium [1].The content of

chromium atoms becomes insufficient for filling all the C, E

and D positions prescribed by the crystal chemistry of the

�-phase; in the absence of chromium the 14-vertex Frank –

Kasper polyhedron is destabilized and reconstructed into a

14-vertex rhombododecahedron of a bcc-phase, i.e., the

� � � transformation proceeds by the scheme presented in

Fig. 4. The coordinate polyhedrons may be treated as some

architectural construction in which atoms of different chemi-

cal nature play the role of articulated joints (with different

properties); in this “mechanical” sense we are dealing with

destabilization of the Frank – Kasper coordination polyhe-

dron. Even little changes in the proportion of the numbers

(and positions) of chromium and iron atoms in a cell of the

�-phase can violate considerably the balance of forces in the

coordination polyhedron, because the distance between

Cooperative Mechanism of the s-Phase � Ferrite Transformation in Stainless Steel 05Kh22AG15N8M2F 641

à

b

Fig. 4. Reconstruction of a 14-vertex rhombododecahedron of a

bcc-lattice (a) into a 14-vertex Frank – Kasper polyhedron (b ):

b ) one of the third-order axes of the cubic lattice is directed verti-

cally in the plane of the figure and has become a six-order axis of

Frank – Kasper polyhedrons.

Fig. 5. Rotation of triangular faces (111) reconstructs a cuboocta-

hedron of an fcc-lattice (green) into an icosahedron (the blue lines

and vertexes) with the same number of vertexes.

atomic layers (over axis c) in the structure of the �-phase of

the Fe – Cr system is 22.8 pm, which is much less than the

distances in the Fe – Fe iron lattice (24.8 pm) or Cr – Cr

chromium lattice (24.9 pm). In the process of a high-tempe-

rature hold the concentration of chromium in the �-phase de-

creases, the rhombododecahedron destabilizes, and a � � �

transformation develops by the mechanism multiple

microtwinning suggested in [14]. Reconstruction of the coor-

dination polyhedron (“mechanical destabilization”) may be

initiated by the difference in the coefficients of temperature

expansion of the Fe – Fe and Fe – Cr interatomic bonds.

This standpoint may be used to explain the growth in the

hardenability of a steel when it is alloyed with chromium.

Cooling of the austenite should be accompanied by transfor-

mation of the cubooctahedron of fcc-austenite (12 vertexes)

into a rhombododecahedron of bcc-ferrite (14 vertexes). The

intermediate configurations of this cooling-caused transition

are 12- and 14-vertex Frank – Kasper polyhedrons. The pres-

ence of �-phase in the Fe – Cr system (rods of 14-vertex

polyhedrons) indicates “mechanical” stabilization of the

14-vertex Frank – Kasper polyhedron upon occupation of

some of the vertexes with chromium. The life time of this

14-vertex configuration increases, which is perceived in an

experiment as a shift of the C-curve to the right, i.e., the

hardenability of the steel increases. There is no need to ex-

plain that such a scheme is suitable for other alloying ele-

ments, because a �-phase exists in iron alloys with Mo, V, W,

etc. These systems also contain a �-phase (Fe7W

6, Fe

7Mo

6);

though it has a rhombohedral lattice, the symmetry of the lat-

tice is not important. It is important that the structure of the

�-phase is formed by parallel rods of 14-vertex Frank –

Kasper polyhedrons, just like the structure of the �-phase.

CONCLUSIONS

1. The transformation of retained �-phase in some

austenitic stainless steels into bcc-ferrite may be described as

a cooperative reconstruction of 14-vertex Frank – Kasper co-

ordination polyhedrons of the �-phase into a 14-vertex

rhombododecahedron of a bcc-phase. Such description coin-

cides with the model suggested by us earlier for martensitic

transformation in steels.

2. The presence of retained �-phase in austenitic steels

and its cooperative transformation into ferrite allows us to

explain the growth in the hardenability of steels under the ac-

tion of alloying components by stabilization (increase in the

lifetime) of the intermediate Frank – Kasper polyhedron

upon occupation of its vertexes by atoms of the alloying

component.

The work has been performed with financial support

of the Russian Foundation for Basic Research (Grant

11-02-00296).

REFERENCES

1. M. V. Kostina, S. O. Muradyan, M. S. Khadyev, and A. A. Kor-

neev, “Phase transformations in corrosion-resistant high-chro-

mium nitrogen-containing steel,” Izv. Ross. Akad. Nauk,

Metally, No. 5, 33 – 48 (2011).

2. A. M. Parshin, Structure, Strength and Radiation Damage of

Corrosion-Resistant Steels and Alloys [in Russian], Metallur-

giya, Chelyabinsk (1988), 656 p.

3. E. Gudremon, Special Steels, Vol. 1 [Russian translation],

Metallurgiya, Moscow (1966), 736 p.

4. V. S. Kraposhin, A. L. Talis, and M. N. Pankova, “Polytope

topological approach to description of martensitic transforma-

tion,” Metalloved. Term. Obrab. Met., No. 8, 23 – 28 (1999).

5. V. S. Kraposhin, M. N. Pankova, A. L. Talis, and Yu. A. Frei-

man, “An application of a polytope (4D-polyhedron) concept

for the description of polymorphic transition: iron martensite

and solid oxygen,” J. Phys. IV France, 112, 119 – 122 (2003).

6. V. S. Kraposhin, A. L. Talis, and Y. Wang, “A geometrical

model of polymorphic transformations in titanium and zirco-

nium,” Metalloved. Term. Obrab. Met., No. 9, 8 – 16 (2005).

7. V. S. Kraposhin, A. L. Talis, and Y. J. Wang, “Description of

polymorphic transformations of Ti and Zr in the framework of

the algebraic geometry,” Mater. Sci. Eng. A, 438 – 440, 85 – 89

(2006).

8. L. Schubert, Crystal Structures of Bicomponent Phases [Rus-

sian translation], Metallurgiya, Moscow (1971), 536 p.

9. M. P. Kashchenko and V. G. Chashchina, “A dynamic model of

supersonic growth of martensite crystals,” Usp. Fiz. Nauk,

181(4), 345 – 364 (2011).

10. J. D. Bernal, “The structure of liquids,” Proc. Roy. Soc., 280,

299 – 322 (1964).

11. V. S. Kraposhin, A. L. Talis, and M. I. Samoylovitch, “Axial

(helical) substructures determined by the root lattice E8 as gen-

erating clusters of the condensed phases,” J. Non-Cryst. Solids,

353, 3279 – 3284 (2007).

12. M. I. Samoylovitch and A. L. Talis, “Special classes of helicoids

with crystallographic, quasi-crystallographic, and noninteger

axes,” Dokl. Ross. Akad. Nauk, 414, 30 – 35 (20070.

13. B. G. Bergman and D. P. Shoemaker, “The determination of the

crystal structure of the sigma phase in the Fe – Cr and the

Fe – Mo systems,” Acta Crystallogr., 7, 857 – 865 (1954).

14. V. Kraposhin, I. Jakovleva, L. Karkina, et al., “Microtwinning

as a common mechanism for the martensitic and pearlitic trans-

formations,” J. Alloys Comp. (2011), accepted for publication,

http:��dx.doi.org�10.1016� j.jallcom.2011.10.102.

642 V. S. Kraposhin et al.