Nucleation and Martensitic Transformation in Subjects of Small Dimensions
The existing models and schemes of the martensitic phase nucleation are considered in the review. Theoretical and experimental works devoted to the nucleation of the martensitic crystals in different metals are discussed and analysed. The parameters and processes of the martensitic transformation in...
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Інститут металофізики ім. Г.В. Курдюмова НАН України
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irk-123456789-984282016-04-15T03:02:08Z Nucleation and Martensitic Transformation in Subjects of Small Dimensions Lobodyuk, V.A. The existing models and schemes of the martensitic phase nucleation are considered in the review. Theoretical and experimental works devoted to the nucleation of the martensitic crystals in different metals are discussed and analysed. The parameters and processes of the martensitic transformation in such subjects of small dimensions as particles, porous materials, thin films, nanoparticles, and nanomaterials are also considered and discussed. В обзоре рассматриваются существующие модели и схемы зарождения мартенситных фаз, обсуждаются теоретические и экспериментальные работы, посвящённые зарождению кристаллов мартенсита в различных металлах. Рассматриваются и обсуждаются параметры и процессы мартенситного превращения в таких объектах малых размеров как частицы, порошковые материалы, тонкие плёнки, наночастицы и наноматериалы. В огляді розглядаються наявні моделі та схеми зародження мартенситних фаз, обговорюються теоретичні й експериментальні роботи, присвячені зародженню кристалів мартенситу в різних металах. Розглядаються й обговорюються параметри та процеси мартенситного перетворення у таких об’єктах малих розмірів як частинки, порошкові матеріяли, тонкі плівки, наночастинки та наноматеріяли. 2014 Article Nucleation and Martensitic Transformation in Subjects of Small Dimensions / V.A. Lobodyuk // Успехи физики металлов. — 2014. — Т. 15, № 4. — С. 173-212. — Бібліогр.: 72 назв. — англ. 1608-1021 PACS numbers: 61.50.Ks, 61.72.Bb, 61.72.Lk, 62.20.fg, 64.60.Q-, 81.07.Bc, 81.30.Kf http://dspace.nbuv.gov.ua/handle/123456789/98428 en Успехи физики металлов Інститут металофізики ім. Г.В. Курдюмова НАН України |
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The existing models and schemes of the martensitic phase nucleation are considered in the review. Theoretical and experimental works devoted to the nucleation of the martensitic crystals in different metals are discussed and analysed. The parameters and processes of the martensitic transformation in such subjects of small dimensions as particles, porous materials, thin films, nanoparticles, and nanomaterials are also considered and discussed. |
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Lobodyuk, V.A. |
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Lobodyuk, V.A. Nucleation and Martensitic Transformation in Subjects of Small Dimensions Успехи физики металлов |
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Lobodyuk, V.A. |
| author_sort |
Lobodyuk, V.A. |
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Nucleation and Martensitic Transformation in Subjects of Small Dimensions |
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Nucleation and Martensitic Transformation in Subjects of Small Dimensions |
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Nucleation and Martensitic Transformation in Subjects of Small Dimensions |
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Nucleation and Martensitic Transformation in Subjects of Small Dimensions |
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Nucleation and Martensitic Transformation in Subjects of Small Dimensions |
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nucleation and martensitic transformation in subjects of small dimensions |
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Інститут металофізики ім. Г.В. Курдюмова НАН України |
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Nucleation and Martensitic Transformation in Subjects of Small Dimensions / V.A. Lobodyuk // Успехи физики металлов. — 2014. — Т. 15, № 4. — С. 173-212. — Бібліогр.: 72 назв. — англ. |
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Успехи физики металлов |
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AT lobodyukva nucleationandmartensitictransformationinsubjectsofsmalldimensions |
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2025-07-07T06:30:06Z |
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1836968634885341184 |
| fulltext |
173
PACS numbers: 61.50.Ks, 61.72.Bb, 61.72.Lk, 62.20.fg, 64.60.Q-, 81.07.Bc, 81.30.Kf
Nucleation and Martensitic Transformation in Subjects
of Small Dimensions
V. A. Lobodyuk
G. V. Kurdyumov Institute for Metal Physics, N.A.S. of Ukraine,
36 Academician Vernadsky Blvd.,
UA-03680 Kyiv-142, Ukraine
The existing models and schemes of the martensitic phase nucleation are con-
sidered in the review. Theoretical and experimental works devoted to the nu-
cleation of the martensitic crystals in different metals are discussed and ana-
lysed. The parameters and processes of the martensitic transformation in
such subjects of small dimensions as particles, porous materials, thin films,
nanoparticles, and nanomaterials are also considered and discussed.
В огляді розглядаються наявні моделі та схеми зародження мартенсит-
них фаз, обговорюються теоретичні й експериментальні роботи, прис-
вячені зародженню кристалів мартенситу в різних металах. Розгляда-
ються й обговорюються параметри та процеси мартенситного перетво-
рення у таких об’єктах малих розмірів як частинки, порошкові матері-
яли, тонкі плівки, наночастинки та наноматеріяли.
В обзоре рассматриваются существующие модели и схемы зарождения
мартенситных фаз, обсуждаются теоретические и экспериментальные
работы, посвящённые зарождению кристаллов мартенсита в различных
металлах. Рассматриваются и обсуждаются параметры и процессы мар-
тенситного превращения в таких объектах малых размеров как частицы,
порошковые материалы, тонкие плёнки, наночастицы и наноматериалы.
Keywords: alloys, crystals, dimensions, nanoparticles, dislocation, nuclea-
tion, nucleus, martensitic transformation, martensite.
(Received September 26, 2014)
CONTENTS
1. Introduction
2. Nucleation of martensite
Успехи физ. мет. / Usp. Fiz. Met. 2014, т. 15, сс. 173–212
Îòòèñêè äîñòóïíû íåïîñðåäñòâåííî îò èçäàòåëÿ
Ôîòîêîïèðîâàíèå ðàçðåøåíî òîëüêî
â ñîîòâåòñòâèè ñ ëèöåíçèåé
2014 ÈÌÔ (Èíñòèòóò ìåòàëëîôèçèêè
èì. Ã. Â. Êóðäþìîâà ÍÀÍ Óêðàèíû)
Íàïå÷àòàíî â Óêðàèíå.
174 V. A. LOBODYUK
2.1. Theoretical aspects of nucleation of martensite
2.2. Experimental confirmation of presence of martensitic nuclei
3. Martensitic transformation in the subjects of small dimensions
3.1. Martensitic transformation in particles and inclusions
3.2. Martensitic transformation in powder materials
3.3. Martensitic transformation in thin films
3.4. Martensitic transformation in nanocrystals and nanomaterials
4. Conclusion
1. INTRODUCTION
Martensitic transformation (MT) in the subjects of small dimensions
takes place with essential peculiarities in comparison to massive
materials that is stipulated for so named ‘sized factor’. Considera-
tion of these peculiarities is needed to begin from problems of nu-
cleation of martensitic phase and martensitic crystals in parent
phase because beginning from nucleation and during future growth
of martensitic crystals these peculiarities arise, and they are condi-
tioned by own mechanism of martensitic transformation. This is
caused by considerable influence of transformation volume on pro-
ceeding of new phase nucleation processes and following phase
transformation [1].
Problems of nucleation of new phase during MT are sufficiently
difficult and least solved despite of many years investigations of
the nature and mechanism MT in metals and alloys which takes
place during lowering of temperature or under different external
influences (stress, deformation, magnetic field, irradiation) [2]. Ap-
parently, these problems are concerned with that besides some sup-
positions there are no reliable experimental results on the existence
and structure of martensitic nuclei.
There are some investigations devoted to consideration of models
and patterns of martensite crystal nucleation and following growth.
Theoretical studies of these processes also fulfilled. However, these
models and patterns are proposed for definite MT in definite alloys,
most often for MT in the Fe and Co alloys. Generalized models for
the whole types of MT did not elaborate and did not propose up to
now. Dislocation model of martensite phase nucleation in cobalt was
historically first [3]. Later some others for different types of MT
were proposed. Consideration of these models and schemes will be
made in the next section.
G. V. Kurdyumov presented principal statements about the na-
ture of martensitic transformations in fundamental work [4]. Mech-
anism and kinetic peculiarities of this type phase transformation
were also considered and discussed in this work. There were con-
cluded that, if MT proceeded without content changes, these trans-
NUCLEATION AND MARTENSITIC TRANSFORMATION IN SMALL DIMENSIONS 175
formations can be regarded as transitions in single component sys-
tems similarly polymorphic transformations in pure metals. Then,
as in case of other phase transitions, MT must take place due to
formation of nuclei and their following growth during change of
external conditions: temperature, pressure, radiation. This conclu-
sion gives possibility to use for consideration of MT basic postulates
used for crystallization of liquid of one-component system.
The principal existing views of the processes of martensitic phase
nucleus formation and future growth, different models of nucleus
formation will be considered and discussed in this review. Theoreti-
cal and experimental works devoted to these problems will be also
discussed. Martensitic transformations in the subjects of small di-
mensions as porous materials formed during aging particles, differ-
ent types of thin films, nanoparticles and nanomaterials will be dis-
cussed in connection with the peculiarities of MT and their great
practical interest. Latter stipulated for that structure and state of
these materials must result in many peculiarities in proceeding of
MT and in corresponding changing of properties that is often condi-
tioned by sized factor.
2. NUCLEATION OF MARTENSITE
2.1. Theoretical Aspects of Nucleation of Martensite
It was supposed that in structure of the parent phase small sections
with crystal structure of new (martensitic) phase could arise [4].
During decreasing of temperature lower than equilibrium tempera-
ture, these sections will serve as nuclei of new phase. Only nuclei
with sizes greater critical one will be grow. Critical size nucleus
which can grow is defined by the undercooling degree T T0 T,
where T0—equilibrium temperature of parent and martensitic phas-
es, T—current temperature. Essential amount of critical size nuclei
appear only under definite undercooling T T0 TM, where TM is
boundary of instability (temperature of beginning of martensitic
transformation Ms).
In the case of crystallization of liquid, amount of appearing in
time unit nuclei is defined by the following equation [5]:
I Kexp{U/(kT)}exp{Rm/(kT)}, (1)
where U—activation energy, Rm—formation work of nucleus capable
to grow, K—T-independent coefficient.
During MT, activation energy is small, therefore first multiplier
is near 1, and amount of nuclei is defined by the work of nuclei
formation Rm. Near equilibrium temperature, the work Rm is large
176 V. A. LOBODYUK
and quickly decreases with growing of deflection from T0. Only un-
der some undercooling and approaching to the metastable boundary
(in the case of MT to temperature Ms), it is possible of appearing of
noticeable number of nuclei [5]. Under holding at temperature be-
low Ms, the rate of nucleus formation decreases quickly, therefore
MT ceases. For next transformation, it is needed additional cooling
under which the growth of those nuclei proceeds, which were lesser
than critical sizes at higher temperature. Definite temperature be-
low Ms own size critical nucleus corresponds too.
Experimental results testify that dependences of nucleus number
and volume of martensitic phase on temperature have the same
(identical) view [4]. In this work, the idea about frozen concentra-
tion fluctuations of the solid solution in which MT takes place and
on dependence of the equilibrium temperature T0 on the concentra-
tion of elements advanced. Critical nucleus formation probability
depends on the concentration in definite areas. This probability is
greater in the area with concentration lower than average one and
is lesser in the areas with higher concentration. Such dependence is
essential particularly during initial stages of MT. Under transfor-
mation progress, the influence of appeared martensite on non-
transformed parts becomes more essential.
Existence up to the transformation beginning (higher T0) of defi-
nite number of new phase critical nuclei is supposed also in Ref.
[6]. However, the conditions and mechanism of their appearances
were not explained. In this work, MT is described in the following
way. Under cooling lower Ms, new nuclei arise autocatalytically
during transformation, their number depends on amount of marten-
site appeared at given temperature. During this process, a part of
already existing nuclei is spent on the arising of new portions of
martensite. Authors supposed that number nuclei ni existing in cm3
in moment of time t is determined by the equation:
nt (ni pf Nv)(1 f), (2)
where ni is a number of existing up to transformation nuclei, p—
autocatalytical factor determining the number of new arisen nuclei
in cm3 (this factor does not depend on the size of initial grain and
grows during temperate lowering), f—volume part of martensite,
Nv—a number of martensitic plates in unit volume. The expression
(ni pf Nv) determines a number of nuclei in 1 cm3, which can
grow in the time moment t. However, in this equation, the part of
nuclei that is spent during formation of martensite in present mo-
ment does not take into account. Autocatalytic factor stipulated
arising of elastic and plastic deformations during MT.
Many works devoted also to investigations of the autocatalytic
NUCLEATION AND MARTENSITIC TRANSFORMATION IN SMALL DIMENSIONS 177
effect during MT and to discovery nature of this effect. The results
of these works confirm important influence on the mechanism of
MT appearing during transformation deformations and distortions.
The rate of nucleation of new crystals in arbitrary moment of
time t is determined by the equation:
N (ni pf N)exp{Wa/(RT)}, (3)
where —oscillated lattice frequency (103 cm
1), Wa—increasing of
the free energy necessary for activation of the Avogadro nucleus
number [6]. Authors offered to rewrite this equation to next view:
N (ni N)(p 1)exp{Wa/(RT)}, (4)
where —average volume of the martensitic plate. It is follow from
this equation that, if (p 1) 0, the nuclei number in the unit
volume remains constant at each ni because of number expensed
during the nuclei transformation equals again to the arising one at
the expense of autocatalytic effect. In this case, nucleation velocity
does not depend on the reaction time. Therefore, real velocity will
not be to differ from actual initial nucleus velocity .N
The results of numerous investigations showed that number ex-
isting up to beginning of MT nuclei does not depend on the grain
sizes. It is follow from this that the boundaries do not appear the
places of the preferential nucleation of the new phase crystals, at
any rate at the initial transformation stages.
Growth of the preliminary existing nuclei during following cool-
ing lower martensitic point Ms is considered also in Refs. [7, 8].
Authors of Ref. [8] supposed that, in Fe alloys, these nuclei have
b.c.c. structure, their radius is equal to some tens nm. It is sup-
posed that semi-coherent nucleus boundary consists from some mul-
titude of parallel dislocation loops providing the tie of nucleus with
surrounding matrix. Following radial growth of nucleus takes place
by moving of edge dislocation component, arising new dislocation
loops at the boundary and their next transfer [8]. Nucleus thicken-
ing proceeds by the moving of screw dislocation component. Evalua-
tions fulfilled for MT in Fe–Ni–Mn alloy showed that time for-
mation of every next dislocation loop is decreased compared to time
of previously appeared loop.
At definite stage, nucleation growth proceeds only in radial di-
rection. As shown by evaluations, stress causing nucleus thickening
are proportional to relation of semi-thickness c to its radius r: c/r
[8]. Dependence of radial growth on stress is more complicated. For
this growth, dependence on derivative G/r is characteristic one;
here, G—free energy change during formation martensitic particle
178 V. A. LOBODYUK
(nucleus) by r radius. According to suggested model, velocity of ra-
dial growth depends on nucleus size and quickly increases during
martensitic crystal growth and own process of MT becomes as ex-
plosive process. Activation energy of nucleation of new dislocation
loop depends also on critical nucleus size and, according to fulfilled
evaluations for alloy Fe–29.3% Ni–0.2% Mn (wt.%) at 15C,
quickly decreases starting from r 60 nm. Nevertheless, it is diffi-
cult already to name this formation by martensitic nucleus.
Assumption about previously existing (higher T0) martensitic nu-
clei did not find any experimental confirmations. May be, their dis-
covery cannot be fulfilled by using modern experimental investiga-
tion methods. In addition, up to now, we have not clear definition:
what is martensitic nucleus?
In Ref. [9], next mechanism of martensitic nuclei formation at
transformation temperature was proposed. During MT, definite re-
construction takes place by means of the successive transformations
of defects existing in material at temperature Ms into some specific
defects forming martensitic nucleus. This defect may be group of
3–5 dislocations. Authors consider that proposed mechanism is in
accordance with heterogeneous character of MT, crystallography of
MT, in particular with orientation relationship of parent and mar-
tensitic phases, and with athermal character of martensitic trans-
fer. Like other phase transformation, own process of martensitic
nucleus formation takes place in some stages with changing of co-
herence level at interphase boundary from some maximum to mini-
mum value. Authors considered the mechanisms of nucleus for-
mation for martensitic transfer of type f.c.c. h.c.p. (hexagonal
close-packed structure), f.c.c. b.c.c. or other type of martensitic
lattice.
In the case of f.c.c. h.c.p. transformation, the origin of de-
fects, that during following reconstruction of the martensitic nu-
cleus forms takes place on neighbouring close-packed plane of par-
ent structure. These can be extraction-stacking faults. Their for-
mation takes place spontaneously and proceeds so that the defect
plane does not change own location at following stages (that is does
not rotate), that provides necessary orientation relationship of two
structures—parent and martensitic. Consideration of chemical (dif-
ference of free energies of parent and arising phases), deformation
and surface energy of nucleus shows that during reconstruction it
is energetically advantageously the splitting of the defect group ex-
isting in parent phase and appearing of defect consisting of the ex-
tracting stacking faults forming martensitic nucleus. Energy of de-
fect consisting of n planes can be written in the form:
nA(Gchem Edef) 2(n), (5)
NUCLEATION AND MARTENSITIC TRANSFORMATION IN SMALL DIMENSIONS 179
where A—density of atoms in close-packed planes in moles on surface
unity, a difference of chemical free energies of parent and arising
phases Gchem
and deformation energy E
def
determined as molar quanti-
ties, 2(n)—free energy of unity area of interphase boundary ‘parti-
cle–matrix’. According to classical Gibbs definition, quantities Gchem
and E
def
relate to volume properties and do not depend on nucleus size.
The whole differences between the ‘volume’ and the nucleus consist of
surface energy but can depend on defect thickness n. In this case,
the equation (5) describes general defect energy.
Fulfilled evaluations showed that if the defect energy becomes
negative nucleus formation takes place without barrier and process
proceeds by athermal manner. Temperature Ms of the beginning of
MT is determined by the biggest defect, which can transform, that
is by amount n—quantity of close-packed planes in nucleus. The
size of defect, which transforms in nucleus spontaneously for
FeCrNi alloys, can be obtained from equation (5), if we set 0:
*
chem def
2
( )
n
G E
. (6)
Evaluations showed that n* 7 for Fe–16% Cr–13% Ni (wt.%)
and n* 10 for Fe–18% Cr–12% Ni (wt.%). As during transferring
of one partial dislocation, the formation of two atom planes of
h.c.p. structure takes place the defect leading to rise of martensite
at Ms consists of 4 or 5 dislocations.
Besides perfect dislocations, which are dissociated into partial dis-
locations with formation of stacking faults, the special grain bounda-
ries, the boundaries of incoherent twins and inclusions can serve as
places of nucleation of martensitic crystals (of defects of crystal struc-
ture). Nucleation at these defects for the case of f.c.c. b.c.c. and oth-
er martensitic transformation types (b.c.c. f.c.c., b.c.c. h.c.p.)
was considered in [9]. The mechanism of formation of martensitic
nuclei in the case of these transitions is more complicated. Using
proposed in [10] hard sphere model for describing lattice defor-
mation taking place during MT the mechanism of appearing mar-
tensitic nucleus from defect authors [9] presented next manner.
Formation of martensitic nucleus proceeds by two shears. At first
(twinning) shear by the value af.c.c.112/6, some intermediate state
arises from f.c.c. structure with the structure similar to b.c.c. This
proceeds in the result of appearing some dilatation component
af.c.c.112/18 perpendicular to shear plane that brings to enlarging
by 5.4%. In this state, sequence of planes does not correspond to
terminal b.c.c. structure. To obtain this structure, it is needed sec-
ond shear by af.c.c.112/16 corresponding to shear in b.c.c. structure
by ab.c.c.110/8 on each plane and dilatation perpendicular shear
plane by 3.6%. As dilatation proceeds during these two shears, they
180 V. A. LOBODYUK
can be imaged as invariant plane deformations. The first shear by
mechanism of f.c.c. b.c.c. transition [10] can be obtained by
means of using group of Shockley partial dislocations arranged at
each third close-packed plane. The second shear from this scheme
needs to be changed. During the second shear, it is necessary to re-
construct atom configurations obtained in the first shear to b.c.c.
structure without rotation initial shear plane.
Scheme of f.c.c. b.c.c. reconstruction and sequence of shears in
proposed scheme are presented in (Fig. 1). There is screw disloca-
tion аf.c.c.[11 0]/2 situated perpendicular plane (111)f.c.c.. At the first
shear, dissociation of this dislocation takes place and then three
partial dislocations аf.c.c.[12 1]/18 and three partial dislocations
аf.c.c.[21 1 ]/18 arise as a result of transfer over three planes (Fig. 1,
b). Defect thickening takes place during following dissociation of
dislocation аf.c.c.[11 0]/2 and moving of arising partial dislocations.
In further reconstruction (second shear in plane (111 )f.c.c.
(011)b.c.c.), atoms occupy the positions corresponding to b.c.c. struc-
ture. Then due to relaxation at interphase boundary ‘nucleus–
parent phase’, new partial dislocations arise (Fig. 1, c). In the re-
sult, semi-coherent b.c.c. nucleus appears. Then in the final stage
(Fig. 1, d), nucleus arises with fully relaxed long-range deformation
fields caused by formed partial dislocations. In this (b.c.c.) state,
a b
c d
Fig. 1. Scheme of semi-coherent b.c.c. nucleus formation from screw dislo-
cation in f.c.c. structure [9]: a—screw dislocation af.c.c.[11 0]/2 in the ini-
tial f.c.c. structure; b—splitting of dislocation with formation of defect
and intermediate structure (on classification [10]); c—reconstruction of
defect to b.c.c. structure with formation of new partial dislocations on an
interphase boundary; d—imperfect structure arisen up during formation
in b.c.c. phase of new screw dislocations stipulating for relaxation of the
long-range deformation fields caused by appearance of partial dislocations
arisen on the stage (c).
NUCLEATION AND MARTENSITIC TRANSFORMATION IN SMALL DIMENSIONS 181
nucleus has the Kurdyumov–Sacks orientation relationship with
parent f.c.c. structure: (111)f.c.c.(101)b.c.c., [11 0]f.c.c.[111 ]b.c.c..
For spontaneous nucleation, it is needed to fulfil following condi-
tions: under increasing of nucleus thickness its energy decreases and
becomes equal nil or becomes negative in the case of dissociation of de-
fect of definite size. This condition is fulfilled not always, not to the
whole cases of MT. Based on using of experimental values of E
def
and
Gchem
for Fe–30 wt.% Ni alloy, evaluations of the defect thickness,
from which martensitic nucleus forms, give thickness of n
*
13 close-
packed planes. This is critical size of defect, which is necessary for ap-
pearance of nucleus that consists of 4–5 properly situated dislocations.
Thus, defects from which martensitic nucleus arises during f.c.c.
h.c.p. and f.c.c. b.c.c. transitions are practically identical. Depend-
ing on invariant lattice deformation taking place in initial stages of
transformation, martensitic crystals in the Fe alloys arise with habit
plane (111)f.c.c., (225)f.c.c. or (3 10 15)f.c.c..
It is proposed to consider formation of martensitic nucleus in
b.c.c. f.c.c. transition as dislocation dissociation process, which
takes place in reverse direction relatively to f.c.c. b.c.c. transi-
tion [9]. Dislocation аb.c.c.[11 1]/2 arranged in the (011)b.c.c. plane can
dissociate into partials by next scheme:
ab.c.c.[11 1]/2 ab.c.c.[01 1]/8 ab.c.c.[21 1]/4 ab.c.c.[01 1]/8.
Under dissociation of groups of these dislocations, the first shear
(homogeneous) is accomplish using partial dislocation ab.c.c.[01 1]/8.
The second shear by value af.c.c.[1 21 ]/18 takes place in plane
(101)b.c.c. becoming (111)f.c.c.. In addition, for obtaining final f.c.c.
structure, it is needed definite dilatation. In the result of relaxation
of long-range deformation fields, semi-coherent f.c.c. nucleus arises
with the interphase boundary structure similar to boundary struc-
ture of b.c.c. nucleus like that in (Fig. 1, d).
Experimental results of the investigations of MT in different al-
loys testify that b.c.c. f.c.c. transition proceeds very seldom. In-
deed, from b.c.c. state, the 9R-structures arise more often. These
structures with some approach can image as distorted f.c.c. struc-
tures having stacking faults in each third planes (111)f.c.c. (see, for
example, martensitic transitions in Cu–Al and Cu–Zn alloys).
In the case of b.c.c. h.c.p. transitions, which take place in Ti
alloy or in a number of noble-based alloys, for nucleation martensit-
ic mechanism, it can use previously considered mechanism for b.c.c.
f.c.c. transition. Partial dislocation аb.c.c.[21 1]/4 (this dislocation
corresponds to partial dislocation Shockley in f.c.c. structure
af.c.c.[112]/6) arisen during dissociation of dislocation аb.c.c.[11 1]/2
under moving across f.c.c. nucleus transfer it to h.c.p. structure.
182 V. A. LOBODYUK
Thus during b.c.c. h.c.p. transition, f.c.c. structure can consider
as intermediate structure. In new h.c.p. structure, stacking fault
plane is basal plane.
Under consideration f.c.c. f.c.t. transition, mechanism of aris-
ing of martensitic nucleus presented before can use if a minor te-
tragonal distortions in f.c.c. structure account [9]. In this case lat-
tice deformation takes place not in close-packed planes but in the
planes of {110}f.c.c. where dissociating defect situated.
Other types of martensitic transitions (transformation with for-
mation of the orthorhombic or tetragonal crystal structures) can be
obtained from considered higher if to introduce additional small
distortions in the structure of the arising phase. These distortions
appear in the result of ordering in the parent phase (long-range,
short-range order), anisotropy, and presence of insertion atoms of
other type or other reasons. As pointed, higher martensitic nuclei
can arise not only at individual dislocations and their groups but
also at sections of definite type of grain boundaries, some inclina-
tion boundaries, non-coherent twin boundaries, boundaries of parti-
cles (inclusions). At these boundaries, definite dislocation groups
with non-relaxed stress are present always or these boundaries,
their separate sections can image as such dislocation groups. It is
important so as the energy of these ‘defects’ did not increase the
total energy of nucleus. Definite confirmation of nucleation and
growth of martensitic crystals at these defects (boundaries, sub-
boundaries in Au–Cd alloy and twin boundaries in Fe–32.3 wt.% Ni
alloy) can find in [11, 12].
Conditions of growth of nucleus situated in defect plane are also
considered in Ref. [9]. Defect becomes instable in respect to nucleus
formation if energy of defect is
n|b|, (7)
where n—number of dislocations with Burgers vector b forming of
nucleus, —stresses that move dislocations.
Evaluations gave possibility to determine the size of defect form-
ing b.c.c. nucleus of critical size. In Fe–30 wt.% Ni, during spon-
taneous formation of nucleus at temperature Ms, number of disloca-
tions in defect is n 16.
Growth of martensitic nucleus proceeds in the plane of defect ar-
rangement and thickening—perpendicular to the plane of defect.
Thickening takes place in the result of appearing of new transfor-
mation dislocations the same type that forming initial defect.
Again, appeared dislocations have long-range deformation fields as
its function consists in change of form that takes place during
transformation.
NUCLEATION AND MARTENSITIC TRANSFORMATION IN SMALL DIMENSIONS 183
Calculations of energy change during these processes bring about
to conclusion that at nucleus growth continuous increase of disloca-
tion line must play principal role but not formation of new disloca-
tion loops that provides the lattice deformation during transfor-
mation as thermal activation of new loops is more difficult. Process
of thickening can take place by pole mechanism as in (Fig. 2). This
mechanism based on interaction transformation dislocations situat-
ed as a rule in a plane of close packing and dislocations of ‘forest’
that are always present in alloy. Dislocation of ‘forest’ has Burgers
vector with screw component perpendicular plane of defect and it
value is equal one interplanar distance. This dislocation will be act
as pole dislocation during spiral motion of transformation a disloca-
tion across successive close-packed planes and brings to thickening
of nucleus. The process of thickening can be shortly described by
the following way (see Fig. 2). Under crossing transformation dislo-
a b c
d e f
g h
Fig. 2. Thickening of nucleus by pole mechanism [9]: a—dislocation of trans-
formation bT and pole dislocation bp; b—interaction (crossing) of dislocations
bT and bp; c—formation of dislocation dipole; d—group of transformation dis-
locations limiting nucleus; e—crossing (interaction) of transformation dislo-
cations and pole dislocation and formation of dislocation dipole; f—
interaction of dislocation dipole; g—formation of single dipole; h—rotation
of dislocation dipole round pole dislocation stipulating nucleus thickening.
184 V. A. LOBODYUK
cation bТ (equal to аf.c.c.[12 1]/18) and pole dislocation bр (equal to
аf.c.c.[1 01]/2 (Fig. 2, а), threshold arises at transformation disloca-
tion (Fig. 2, b). During motion, the dipole of partial dislocations
reserves for itself (Fig. 2, c). The whole multitude of transfor-
mation dislocations at the nucleus front of critical size (Fig. 2, d) at
its motion intersects pole dislocation (Fig. 2, e) and forms dipole at
each plane. In the result of their interaction (Fig. 2, f), single dislo-
cation dipole arises connected to pole dislocation with the distance
between its dislocations equal to nucleus thickness. Under influence
of Bain deformation, pole dislocation transfers in dislocation with
Burgers vector bp within nucleus (Fig. 2, g). Transformation dislo-
cations rotate around pole dislocation (Fig. 2, h). During each evo-
lution, close-packed plane moves and nucleus thickens.
In the case of f.c.c. h.c.p. transition, the motion of transfor-
mation dislocation af.c.c.112/6 at every second close-packed plane
needs for thickening of nucleus. At this transition, the dipole (Fig.
2, g) begins to rotate only after its intersection with two inclination
lattice dislocations and arising so named ‘twofold pole’.
For heterogeneous nucleation, the dislocation model of martensit-
ic nucleus was proposed in [13, 14]. Authors of model [13] suppose
that martensitic nucleus is formed at dislocation line arisen in par-
ent phase (Fig. 3). There is not determined the value of Burgers
vector. It is needed for that some single dislocation with arbitrary
Burgers vector approximates by plane pile up creating the same
stress field. This arbitrariness was needed authors for account real
surface energy of nucleus. Authors presented nucleus in the form of
Fig. 3. Scheme of appearance of martensite on dislocation [13]. Nucleus
with discrete twins (a). Nucleus with monotonous distribution of twins (b).
NUCLEATION AND MARTENSITIC TRANSFORMATION IN SMALL DIMENSIONS 185
flattened out ellipsoid oriented definite manner. Evaluations of bar-
rier for heterogeneous nucleation at 250 K in Fe–29 wt.% Ni with
number dislocation in pile up equal 1 and surface energy 23 erg/cm2
showed that ratio of ellipsoid axes for minimal nucleus is less than
8. In the case of critical nucleus with amount of atoms near 1000,
ratio of ellipsoid axes is equal to 20. For realistic surface energy
200 erg/cm2, number of dislocations needed for appearing of the
martensitic nucleus is equal to 10. Unfortunately, authors propose
no mechanism providing following growth of nucleus and formation
of macroscopic martensitic crystal.
Formation of the martensitic nuclei during MP in steels is con-
sidered in [14]. It is accepted that martensitic nucleus has the form
of stretched ellipsoid. Energy change during nucleus formation has
appearance:
Etot Echem Edef Esurf, (8)
where Echem—difference of chemical energy of parent and new
phase, Edef—elastic energy arising in the result of crystal structure
discrepancy at interphase boundary, Esurf—energy of coherent inter-
phase boundary. After substitutions, they obtained:
Еtot 2а
2
16
3
(s/2)2ac2 f
4
3
a2c, (9)
where —surface energy per unit area, —shear modulus in austen-
ite, ‘c’ and ‘a’—semi-thickness and radius of ellipsoid (used c/a
0.03), f—difference of free energies of parent and martensitic
phase per unit volume. As solution, it is appeared that coherent de-
formation energy (calculated according to Eshelby elasticity theory)
is by 25 times greater than chemical free energy change that is crit-
ical nucleation barrier is too great for spontaneous formation of
martensite (under reasonable choice Echem). It is appeared also that
energy change is not very sensitive to the ratio c/a.
They imaged ellipsoidal nucleus as set of twins of different
thickness. Alteration of coherent deformation energy during nuclea-
tion formation can be minimized by changing thickness correlation.
Thus, consideration of different conditions of formation of marten-
sitic nucleus resulted in conclusion that critical nucleus must be
(most probably) thin twinned ellipsoid the orientation of which in
austenite is not very much critical if he is located in area of ‘mini-
mum energies’.
An energy needed for formation of nucleus, as shown in the per-
formed estimations, is sensible to , to the change of free energy
F, and to the amount of shear s (which is parallel to the plane of
ellipsoid). The critical sizes of (ellipsoid) nucleus also depend on
186 V. A. LOBODYUK
these parameters. The performed estimations result in the follow-
ings dependences:
crit
2
c
f
, (10)
2
crit 2
16 ( 2)
( )
s
a
f
. (11)
These equations are suitable only partly for the case of twinned nu-
cleus, as at their receipt energy of twin boundaries was not taken
into account. However, estimations show that influence of twin
boundaries on an energy change not very much substantial. The
main influence on energy barrier for formation of nucleus renders
superficial energy . So, change from 20 erg/sm2 to 200 erg/sm2
results in the increase of Emin from 14 eV to 1.4104 eV. Authors
supposed that nucleation on defects in austenite can substantially
decrease energy barrier to formation of nucleus because of interac-
tion of the deformation field of defect (dislocation) with the defor-
mation field of embryo. Therefore, in expression for energy change
(8), they added additional term Einter. Authors suggest examining a
nucleation on a dislocation loop for Poisson ratio 1/3
Еinter 2sabc. (12)
The carried out estimations of energy change in the case of nu-
cleation of martensite on defects (the dislocation loop) show that in
this case formation of martensitic nucleus takes place spontaneous-
ly, but nucleus must be twinned for it subsequent growth. For ap-
pearance of nucleus, some special orientations of dislocations or
their specific configurations are not needed. They are not structural
part of embryo. Authors give them a certain catalytic role. It is
marked that for further growth (thickening) of nucleus the partici-
pation of dislocations is not obligatory. The role of twinning of nu-
cleus consists of lowering of his general energy.
For confirmation of the model, authors [13] allude to the experi-
mental results of electron microscopic researches of MT in the de-
formed stainless steel of type 18/8 [15]. In this work, at a direct
supervision of processes of MT in the electron microscope, they did
find out the formation of the plates of -phases on crossing of two
strips of gliding at passing of the dislocation pile up. However, in
the work, only formation of already macroscopic (formed) plates of
-phase is given. Experimental evidences of existence of the real
martensitic nuclei or observations of the processes of the nucleus
formation of the new phase did not obtain. At crossing of two strips
of gliding, there are martensitic formations as long ellipsoids,
NUCLEATION AND MARTENSITIC TRANSFORMATION IN SMALL DIMENSIONS 187
which give reflexes of b.c.c. -phase. The size of less semi-axis of
ellipsoid is equal to a few ten of angstrom. The authors of work
named such formations as ‘elementary (?) martensite’. At further
growth, ellipsoids take shape of polyhedrons with a habitus (5 29 ).
Is it necessary to point out that martensitic crystals, arising up in
massive specimens, have a habitus {225} or {112}? Calculations
carried out in the work allowed estimating the number of disloca-
tions in a pile up, caused the formation of martensitic plate. As ap-
peared, the amount of dislocations in such pile up is equal to 22.
Using supposition about the thermally activated motion of dislo-
cations during formation of martensitic nucleus, as made in Ref.
[9], and equation determining activation energy for such nucleation:
subtr
a
W Q0
*
a
2E
V
n
b b
*V
b
G,
where Q0 is activation energy of moving of dislocation in absence of
driving force, a—is athermal stress, causing the motion of disloca-
tion, —is density of atoms on close-packed plane, b—Burgers vec-
tor of partial dislocation, which for f.c.c. b.c.c. transformation is
equal: a112/18, E—energy of coherent deformation, —surface
energy of interphase ‘austenite–martensite’ boundary, n—number
of atomic planes in nucleus, G—change of chemical free energy
per mole, V*—activating volume for motion of dislocation, in Ref.
[16] activation energy calculated at certain parameters (n 16) and
got values were compared to experimental one. As appeared with
the chosen parameters, the calculated and experimental values of
activation energy are enough well coincide in the wide interval of
temperatures (from 77 K to 203 K). In opinion of authors [16],
these results confirm applicability offered in [9] model for the anal-
ysis of processes of nucleation during martensitic transformation.
2.2. Experimental Confirmation of Presence of Martensitic Nuclei
Attempts to observe and identify martensitic embryos in different
materials (alloys based on iron, non-ferrous alloys) were undertaken
as early as 60th of past century [17, 18]. Their search began to be
conducted especially actively with development of methods of elec-
tron microscopy, which allows to find out different imperfect struc-
tures, set of type of the defects, their location, very small areas of
other phase. However, the electron-microscopy studies carried out
with many materials and obtained experimental results did not give
reliable confirmation of existence of martensitic nuclei. A question
remains opened: what one has to consider as martensitic nucleus?
Found out microstructure features in parent phase in the alloys of
188 V. A. LOBODYUK
Fe–Ni from 30 and 32.3 wt.% Ni [17, 18] at temperatures near Ms
are well enough possible to explain by appearance of very little
(thin) martensitic plates with the stretched dislocations or their
well-organized clusters [18] or by formation of twins in the marten-
site which at certain sections (orientations) can be accepted as mar-
tensitic nucleus.
Electron-microscopy investigations in situ (directly in an electron
microscope) on the search of martensitic nuclei in the thin-films of
alloy of Fe–27.6% Ni–0.08% V–0.05% C (wt.%) prepared from the
specimens preliminary deformed and then cooled to the necessary
temperature were conducted in Ref. [19]. Authors came to conclu-
sion that found out near the martensitic crystals dislocation for-
mations of type of ‘butterfly’ are martensitic nuclei. Such for-
mations result in appearance of interference bands on electron mi-
croscopy images. However, the same interference image may arise
up in the result of presence in the sample of martensitic lamina in-
clined to the surface of foil. A like microstructure images that is
appearance of interference bands ahead of growing martensitic
crystal in the alloy of Cu–Al–Ni observed in Ref. [20]. Interference
bands are well explained by the origin of moiré because of imposi-
tion of two crystals: thin martensitic plate inclined to the surface
of foil and area of parent phase. At some orientations, distinction
in the interplanar distances of parent and martensitic phases are
insignificant that results in appearance of moiré contrast before
growing martensitic crystal. Diffraction reflexes from such marten-
sitic plate get hardly because of small volume of this plate.
Authors of Ref. [19] revealed that, during small deformation,
long dislocation loops appear at first and then along some of them
dislocation clusters appear. The nuclei of martensite from which at
the subsequent cooling or deformation in an electron microscope
thin martensitic plates grow with high-density dislocations as a
substructure appear on such groups of defects. A large martensitic
plate consists of group of such thin plates. The performed calcula-
tion of diffraction pictures from areas with ‘nucleus’ brought au-
thors over to the conclusion that crystalline structure of ‘nuclei’ is
intermediate between parent (f.c.c.) and martensitic (b.c.c.) struc-
tures, has an orthorhombic lattice with parameters: a 0.251 nm,
b 0.410 nm, c 0.435 nm and angles: 90. What does
‘intermediate’ structure mean, for what it is needed, which is its
role in the proceeding of MT, and how it appears, authors did not
explain. This work presumably is unique, in which arising of some
‘intermediate’ phase (structures) during direct MT is reported. In
accordance with scheme suggested in [19], during martensitic tran-
sition, there is a shear [211 ]f.c.c./6 between three close-packed
planes but not two as in the case of formation of stacking fault. In
NUCLEATION AND MARTENSITIC TRANSFORMATION IN SMALL DIMENSIONS 189
case of formation of martensitic phase, shears in neighbouring nu-
clei take place in opposite directions.
Problems of nucleation of martensite and formation of nuclei of
martensitic -phase on crossings of micro shear bands, arising up in
the process of deformation in stainless steel 304 considered in [21].
In electron-microscopy investigations of the deformed samples, they
did find out areas, which on dark field images in reflexes of -
phase have the appearance of thin bands 5–7 nm in thick. The au-
thors of work consider them as the martensitic nuclei. Accordingly
to the conducted estimations, the stable nucleus of martensite con-
sists of 27 close-packed planes (type {111}f.c.c.), that corresponds his
thickness of 5.7 nm.
Based on the obtained experimental results, authors [21] came to
conclusion that martensitic nuclei arising up at different degrees
and types of deformation in the initial state have an identical base
structure: microstructure, geometry and crystallographic peculiari-
ties. It is important that, during the deformation, there were the
special great numbers of defects, located in planes {111} at the
shear of a112/6. On crossings of such defects, for example, mi-
croshear bands, stable elements appear with b.c.c. structure. The
process of formation of the special defects and formation of mar-
tensitic nucleus is schematically presented in Fig. 4. At creation of
scheme of reconstruction of f.c.c. structure into b.c.c. structure,
authors used supposition about two invariant plane deformations
(shears) from a model offered in [10]. Except for these two shears,
for the receipt of necessary structure, some dilatation is needed.
However, for formation of semi-coherent interphase boundary be-
a b
Fig. 4. Scheme of formation of specific defect at which a martensitic nu-
cleus arise [21]: a—crossing of defects and formation of stable nucleus of
martensite; b—irregular location (formation) of martensitic nucleus in a
wide micro shear band or at crossing twin defects.
190 V. A. LOBODYUK
tween the arising b.c.c. structure and the parent f.c.c. matrix, more
complicated invariant deformations of crystalline structure (lattice)
are required.
The analysis of electron microscopy images obtained in [21] al-
lows to conclude that there are the lens form plates of martensite
(b.c.c. -phase) but not nuclei are visible. They have a size near 1
m (see [21]) and the reflexes of martensitic phase are present on
diffractograms from areas with these plates. On dark field images
obtained in the reflexes of -phase, these plates are visible (‘shine’).
Therefore, in any way they are impossible to consider as nuclei: on
the presented microstructures are there, they formed crystals of
martensite, which give the diffraction picture of -phase. Interest-
ing model of the formation of martensite in almost equiatomic alloy
of Ti–50.3 at.% Ni is offered in Ref. [22]. At approaching to the
temperature of beginning of MT because of appearance of defor-
mation inhomogeneities there are distortions in the planes {110}B2.
They are consequence of dynamic displacements of atoms of Ti and
Ni in the alternating planes {110}B2 in the direction of 110B2. The
strongly diffused diffraction reflexes appear on the diffraction pic-
tures of B2-phase. Displacements of atoms of Ti and Ni result in
the formation of domains as very thin plates with the habitus
{110}B2. It is assumed that the structure of these domains oscillates
between the structures of high temperature and low temperature
phases. At decreasing in a temperature below than beginning of MT
from such domains, martensitic crystals grow.
Consideration of martensitic f.c.c. b.c.c. transformation in
elastically anisotropic crystals at a heterogeneous nucleation on dis-
locations resulted in a conclusion that a nucleus of new phase is not
one domain particle as it was usually accepted but compound self-
organized ensemble consisting of twin connected micro domains
[23]. Metastable martensitic nuclei on dislocation loops appear
higher than temperature of beginning of martensitic transfor-
mation. A twinning in a martensitic nucleus provides the decreas-
ing of total level of tensions because of accommodation of twin-
connected microdomains.
From estimations obtained on the basis of experimental investiga-
tions of the martensitic transformation in small particles, the num-
ber of originally existent places of origin of martensite makes from
105 to 107 on 1 cm3 [24].
Using the method of impulsive loading, the time of origin at
athermal MT in the alloys of Fe–Ni (–C) with the temperature of
beginning of martensitic transformation Ms 240
C was estimated
[25]. This time in preliminary deformed due to passing of shock
wave across the material makes less than 55 nanoseconds.
Simultaneously with the problem of the formation of martensitic
NUCLEATION AND MARTENSITIC TRANSFORMATION IN SMALL DIMENSIONS 191
nucleus, there is a problem of the state and structure of interphase
boundaries. At the initial stages, such boundaries apparently must
be coherent or partly coherent even in alloys with not thermoelastic
MT for decreasing of arising stress and facilitation of moving of
the interphase boundary. At the subsequent increase of nucleus and
formation of martensitic crystal, the coherences is violated, on
boundaries and in a crystal, dislocations appear. Formation prob-
lems, structure and state of interphase boundaries of crystals of
martensite in alloys with different character of martensitic transi-
tion are considered in detail in Ref. [26].
Numerous attempts to observe experimentally the defect struc-
ture of places of nucleation of the martensitic crystals in different
alloys both at cooling and at MT under influence of the applied
stress were undertaken. We already reported about not very suc-
cessful and reliable attempts to discover nuclei of martensitic phase
[11, 12]. By the use of methods of high-resolution electron micros-
copy, the formation of martensitic nucleus with orientation rela-
tionship with the parent phase of type of Kurdyumov–Sachs and
orientation of habitus (111)f.c.c.(011)b.c.c. was set in the alloys Fe–
23% Ni–3.8% Mn and Fe–9% Cr–1.1% C (wt.%) [27]. Growth of nu-
cleus took place in the direction of [101]f.c.c.[111]b.c.c.. The study of
crystalline structure allowed establishing its change from f.c.c. to
b.c.c. at transferring to central part of embryo. However, by the
conclusion of authors, transition to b.c.c. structure is not completed
in central part of nucleus. Generally, it is not clear because a crys-
talline structure for these alloys can be or f.c.c. (in a parent phase)
or b.c.c. (in a martensitic phase). Authors do not explain an inter-
mediate structure between f.c.c. and b.c.c. crystalline structure.
The obtained results testify about complication of problem. There
is not reliable determination what to consider as martensitic nucle-
us. What size and structure martensitic nucleus has? From what
size, it is already the martensitic crystal? The second question is
easier. Apparently, minimum nucleus having definite morphology
of new-phase crystal structure, giving corresponding diffraction
pattern, is already a martensitic crystal. However, questions re-
main, and new reliable experimental results and proper theoretical
calculations and models are needed.
A set of interesting and important results relating to the process-
es of origin of the martensitic phase and growth of the martensitic
crystals was obtained at use of the methods of electron microscopy.
The origin of martensitic - and -phases on dislocations under in-
fluence of the stress put to the thin films of the Cu–Al–Ni alloys
directly in an electron microscope is reported in Ref. [28]. Investi-
gation of processes MT in the Cu–Al–Ni alloys showed that growth
of martensitic crystals began from particles 2-phase or near-by
192 V. A. LOBODYUK
them, that is in those places where the concentration of Al in par-
ent phase became lower [29]. It related to that on formation of the
enriched by aluminium 2-particles Al concentration in the areas of
parent phase nearby particles decreases and the temperature of be-
ginning of MT becomes higher.
During the electron microscopy study of MT in thin films of Cu–
14.1% Al–5.0% Ni (wt.%) alloy, some special places of nucleation
of martensitic crystals (-phase) have not been found. Under influ-
ence of arising local stress, thin (a few m) martensitic plates begin
to grow from the edge of hole or appear in the areas of foil free of
defects–dislocations or their clusters, in any case, at this orienta-
tion of thin film [20]. New crystals appear nearby from before aris-
ing up. Sometimes, ahead of growing crystal moving of plane clus-
ters of dislocations is observed. In these areas, as microdiffraction
studies showed, no changes of crystalline structure yet take place, a
parent phase is preserved.
By the method of low-energy electron diffraction highly sensitive
to the structural peculiarities on the surface attempts to discover
the ‘frozen’ embryos of new phase in the single crystals of cobalt at
both the direct MT and the reverse one were undertaken [30, 31].
These attempts appeared unsuccessfully. It was observed no prefer-
able places of nucleation with the structure of arising at a change
of temperature new phase. On that ground, the authors of these
works deny the special role of surface in the nucleation of new
phase and in the processes of martensitic transformation. However,
numerous experimental researches of processes of MT show that the
first crystals of martensite arise up at first on the surface.
3. MARTENSITIC TRANSFORMATION IN THE SUBJECTS
OF SMALL DIMENSIONS
All subjects of small dimensions, in which the peculiarities of mar-
tensitic transformation will be considered, can be divided into the
followings basic groups: separate particles of different size and in-
clusions in massive materials, powder-like materials, thin-films (ob-
tained by thinning, high-rate quenching from the liquid state, depo-
sition), nanocrystals, and nanomaterials.
3.1. Martensitic Transformation in Particles and Inclusions
Martensitic transformation in particles and inclusions takes place
with some peculiarities conditioned by their dimensions. In particu-
lar, linear defects (dislocations) can absent in such objects and a
number of existing up to transformation and again arising nuclei of
NUCLEATION AND MARTENSITIC TRANSFORMATION IN SMALL DIMENSIONS 193
new phase can be restricted in connection with small size of the
particles.
Investigation of peculiarities of martensitic transformation in
monocrystalline spheroid particles of the size 0.1–0.3 mm in Fe–
(25.7–30.6) wt.% Ni alloys showed that during cooling martensite
does not arise in the monocrystalline state [32]. Transformation
takes place mainly as ‘explosion’ with formation of plenty of the
martensitic needles. However, transition interval stretches on the
wide area of temperatures. For example, in the Fe–30.6 wt.% Ni
alloy, transformation begins at 12°C and finished below 196°C. A
‘surface’ martensite arises only during the concentration of nickel
less than 30.6 wt.%. Martensitic phase appears as thin needles con-
siderably less in size as compared to arising in bulky single-
crystalline specimens. Degree of -transformations (volume of
martensitic phase) is substantially higher than in massive speci-
mens: an amount of not transforming parent phase after compres-
sion deformation is 1–5% only.
In the single crystal, the zero-defect particles of Cu–1.5 wt.% Fe
alloys containing 0–5 wt.% of Ni, the degree of MT depends on
nickel content in particles [33]. Particles of the diameter 0.002–0.2
m are obtained by extracting at the electropolishing of specimens
of these alloys after their thermomechanical treatment and addi-
tional annealing at 700°C. In the extracted particles, content of
nickel could attain 10–20 wt.%, but only at 5% of its initial con-
centration in an alloy. Electron microscopy investigations showed
that, at low nickel concentration, MT in the extracted particles
takes place completely and, as a result, from single-crystalline -
phases, twinned single crystalline -phase is formed. The minimum
volume of martensite contains, on estimations, 5000 atoms. At the
increase of nickel concentration, there is the partial or complete
stabilizing of parent phase in particles. Martensitic transformation
in particles, containing Ni, begins on the surface: needles (plates)
appear by the width of 3 nm. In partly transformed particles at the
further cooling, MT does not take place. As it was not found out
defects (dislocations) in the extracted particles, a conclusion is as
follows: in process preceding the MT in such particles, there is not
a necessity for defects. The nucleation of martensitic crystals in
these particles takes place not on defects.
Martensitic transformation in the particles of Fe located in Cu-
matrix does takes place with some peculiarities as compared to
transformation in the extracted particles of Fe. Under investiga-
tion of MT in the monocrystalline alloy of Cu–1.0 wt.% Fe, it was
shown that, during deformation directly in an electron microscope,
there is interaction of gliding dislocations with the Fe-particles
[34]. The MT begins only in the case of interaction of the primary
194 V. A. LOBODYUK
and secondary systems of gliding with a particle. The crystals of
martensite appear during 0.02 s after the beginning of growth.
Around particles, there are plenty of dislocations. Their appearance,
in opinion of authors, is conditioned by shear deformation at MT.
Amount of appearing martensite is determined by the size of parti-
cles and degree of deformation. It was shown that with the increase
of size of particles the degree of transformation (volume of marten-
site) grows. Figure 5 presents the dependences of amount of mar-
tensite (Fe) on the amount of the applied tensile stress.
Influence of size of particles on proceeding of MT was observed
in [35]. In this work, it was shown that in obtained by the method
of gas evaporation particles with a size 10–200 nm at a room tem-
perature the initial f.c.c. structure is saved, although in the mas-
sive state at 20°C, the h.c.p. phase exists. In particles, there are
one or two systems of twins on the planes {111}f.c.c.. In a number of
cases, plane defects (presumably stacking faults) found out; possi-
bly, they arose up because of proceeding of MT. However, in parti-
cles, dislocations are not found out. A conclusion is as follows: in
process, MT in such particles takes place without the stage of nu-
cleation, i.e., the nuclei of martensite is absent.
The size of particles influences also on the crystallography peculiar-
ities of MT. So, in the alloy of Cu–1.0 wt.% Fe, relationship of
Kurdyumov–Sachs between f.c.c. and b.c.c. structures during marten-
sitic transition in spherical particles preserves only at their diameter
less than 20 nm [36]. In particles with size more than 20 nm, deviation
from an exact orientation is observed because of rotating of particles
Fig. 5. Dependence of amount of martensite in the particles of different sizes
on the size of tensile stress [34]; 1—130 nm, 2—70 nm, 3—50 nm, 4—30 nm.
NUCLEATION AND MARTENSITIC TRANSFORMATION IN SMALL DIMENSIONS 195
on angle up to 4.2° as a result of shear by system of {111}111f.c.c. con-
ditioned by the mechanism of MT and slipping in Cu-matrix.
3.2. Martensitic Transformation in Powder Materials
The peculiarities of martensitic transformation in powder materials
are conditioned by a few reasons: by the sizes of particles (powder)
used at a subsequent compaction, conducting of the corresponding
deformation and thermal treatment that bring to certain structural
changes, which can influence on further phase transitions in these
materials.
Investigations of - and -transitions in compacted to-
gether with the oxide of aluminium powders of iron of different
purity showed that both the size of particles and number of cycles
of these transitions influence on the temperatures of these transi-
tions [37]. By decreasing of size of the particles below 70 m, tem-
perature of the first -transition rises (Fig. 6, a) substantially
regardless of purity of initial powder of iron. The size of particles
influences lesser on -transition temperature which lowering by
decreasing of radius of Fe particles. At the second cycle, transfor-
mation temperature increases for all sizes of particles (upper curve
in Fig. 6, a) and transition decreases a little (lower curve in
a b
Fig. 6. a—dependences of temperatures of the and transitions
on the size of particles at the first and second cycle in pressed Fe-powders
[37]. First cycle (curves 1, 2): ●— , ■— . Second cycle (curves 3,
4): ○— , □— . b—dependence of hysteresis value on average di-
ameter of Fe-powders particles [37]. 1—B-214, first cycle; 2—Atomet,
first cycle; 3—REP, first cycle; 4—B-214, second cycle; 5—Atomet, sec-
ond cycle; 6—REP, second cycle. Here, B-214 is high-purity Fe-powder;
Atomet is annealed sponge Fe-powder; REP is Fe-powder with spherical
particles.
196 V. A. LOBODYUK
Fig. 6, a). The hysteresis value of these transitions increases at de-
creasing of particle diameter (Fig. 6, b) and number of cycles.
Metallographic studies carried out in Ref. [37] allowed conclud-
ing about the influence of grain sizes, triple joints of grains and
surface size of grains on the processes of nucleation of new phase.
By authors’ opinion, nucleation of -phase proceeds on the grains
and their joints, especially triple. Into grains, more high energy is
required for nucleation. At decreasing of the indicated quantities,
the amount of suitable places for nucleation is substantially lower-
ing what results in growth of temperature of transition. The
increase of temperature of this transition during second cycle is re-
lated to the growth of the size of grains because of overheat and
more difficult nucleation. Decreasing of transition tempera-
ture is not explained by authors with microstructure peculiarities
but with distinction of the chemical composition of the particles of
different sizes. As this distinction is not very much, its influence is
insignificant. In addition, this transition takes place by the for-
mation of nuclei and their subsequent growth. Dependence of hyste-
resis value on the size of particles authors, naturally, also explains
by the microstructure peculiarities of the investigated materials:
decreasing of grain number at lowering of the size of particles and
easier nucleation during transition.
The fulfilled analysis of the kinetics of phase transitions in pow-
der-like materials showed that a key parameter determining kinetics
is a relation of the transformation time of the whole particle G to
the time N necessary for formation of nucleus: G/N [38]. This rela-
tion is in the following dependence on the particle size L: 1/L4.
Theory is suitable for a case when relation G/N is small and a few
nuclei are present in a particle only. Rate of nucleation is deter-
mined by the expression
N
N
( ) exp( )
N
J t t
,
where N is total amount of crystals in powder. It is assumed that
nucleation takes place on defects. Size N is determined by the fol-
lowing dependence
3
N 0
( )L L ,
where L0 is average distance between defects and is a measure of
nucleation velocity on one defect. Amount (L0/L)3 determines the
number of defects in a crystal, which a nucleation is possible on. If
L is comparable with L0, that is in the case of absence of defects, in
the crystal nucleation and, accordingly, phase transition is not im-
possible.
NUCLEATION AND MARTENSITIC TRANSFORMATION IN SMALL DIMENSIONS 197
Powder materials display the same properties as well as massive.
For example, in the alloys of NiTi, got hot pressing of powders of
Ni and Ti with the homogeneous distribution of pores measuring
50–200 m the same martensitic transformation takes place as well
as in standards got from the cast alloys [39]. In this alloy, a super-
elasticity conditioned by MT is fully reversed also. At high porosity
(40%) in the quasi-binary alloy of TiNi–TiPd obtained from pow-
ders, martensitic transformation proceeds in wide interval (250C)
because of large chemical heterogeneity [40]. In the cast alloy of the
same composition, this interval is only 30–40C.
3.3. Martensitic Transformation in Thin Films
There are a few methods of production of thin films, in thick less
than 100 m. Basic methods are as follow: chemical or electrolytic
thinning, evaporation by different methods, rapid quenching from
the liquid state. The state of films at the use of these methods can
substantially differ as a result of the influence of such factors, as
temperature, arising stress, influence of substrate (for example, at
evaporation), existing and appearing during production heterogene-
ities. The degree of influence of these factors is different and de-
termined by the conditions of the film production. We will consider
the peculiarities of MT in thin films, got different methods, sepa-
rately for each case.
Martensitic transformation in the films obtained by thinning.
Thinning by a chemical or electrolytic polish is more frequent than
all used for preparation of samples for electron microscopy investi-
gations. In this case, the influence of thickness on the peculiarities
of MT is conditioned by a few factors: dimensions, more essential
influence on the nucleation of martensite of present inhomogeneity,
substantial role of surface both in the processes of nucleation of the
new phase and during subsequent growth of crystals.
During investigations of MT peculiarities in the thin films of
Cu–14.1% Al–5.0% Ni (wt.%) alloy (Ms near-by room temperature),
it was set directly in an electron microscope that in areas high-
density dislocations a martensitic phase does not appear [20]. It can
be related to requirement of the special type of dislocations and
their specific configuration for formation of nucleus of martensite.
At the same time, some preferable places of nucleation of the mar-
tensitic crystals have not been observed. It was shown that under
influence of arising up during investigations stress the plate-like
crystals of martensite appear in thin films. As a rule, plates grow
from the edge of foil. Rate of the plate growth is not high: there
was, for example, moving of interphase boundary on 5 m during 5
sec. It should be noted that the substructure of the martensitic
198 V. A. LOBODYUK
crystals arises up on the earliest stages of his appearance, simulta-
neously with their formation and interphase boundaries are flat and
straight one. Growth of plate is accompanied by the appearance of
stress in parent phase that was set by the formation of dislocation
piles up in front of crystal and by moving of this pile up in the pro-
cess of growth of crystal.
During MT, there is a morphology change of the martensitic
crystals in thin films. If, in the massive samples of the alloys with
thermoelastic MT during cooling below Mn, there are needle-shaped
crystals, in thin films (for example, in CuAlNi, TiNi), a martensite
appears as thin plates with straight interphase boundaries [20, 41].
Plates grow or decrease during change of temperature or stress
state of the film practically without hysteresis. New plates, as a
rule, appear near arising first. After disappearance of plates be-
cause of reverse MT during repeated cooling, martensitic plates
growth in those places, which are at first direct MT. The authors of
work [41] observe the change of orientation of habitus with (334)B2
on (112)B2 at the sizes of plates lesser 10 nm.
The change of structure of interphase boundaries and substruc-
ture of martensitic plates during MT in thin films (thickness 30
m) of Fe–Ni–Co–Ti alloys observed [42]. Interphase boundaries be-
come bent (there are straight boundaries of crystals in the massive
specimens). Instead of high density of twins in the plates, there are
dislocations and more thin twins. In thinned samples, as authors of
the work mark, there is a change of orientation relationship be-
tween parent and martensitic phases. If, in the massive specimens,
there is nearly Nishiyama relationship, in thin films, in which mar-
tensite appears with dislocations, there is 5° deflection from this
orientation.
Martensitic transformation in films obtained by evaporation. In the
last decade for the obtaining of thin films, the different methods of
evaporations have obtained a wide application; among them, magne-
tron and thermal depositions are basic. Advantage of these methods
is possibility to obtain fully certain thicknesses of the films. There
are some failings, mainly, heterogeneity of composition, difficulty
of its control, complications with following heat treatment in the
case of its necessity. We will consider the basic peculiarities of MT
in the films obtained by means of these methods.
Investigations by electron-microscopy methods of the structural
and phase states arising up in the films of Cu–Al–Ni and Cu–Al–
Mn alloys (with Ms below 0°C) obtained with thermal deposition on
substrate of different type (copper, aluminium, glass) showed that
at this method already in the process of obtaining of films, there is
partial decomposition of high temperature b.c.c. -phases with for-
mation of mixture of b.c.c. -, f.c.c. - and f.c.c. 2-phases [43, 44].
NUCLEATION AND MARTENSITIC TRANSFORMATION IN SMALL DIMENSIONS 199
In such thin films (thickness 100 nm), high-temperature -phase
usually ordered at a room temperature is in the disordered state
that can be conditioned by the small size of grains (10–50 nm).
Martensitic transformation in films with such size of grains does
not take place. Heating to the high temperatures causes growth of
grains. At cooling, there is ordering of high temperature phase and
reversible MT. Partial decomposition of -phase with formation of
- and 2-phases proceeding in the process of deposition causes the
change of composition and increase of martensitic point. It is neces-
sary also to mark the change of morphology of martensite arising
up in such films. Instead of the usually observed needle-shaped
crystals in films obtained with thermal evaporation, martensite ap-
pears as thin plates, which form packages on more late stage of
transformation.
For the obtaining of thin films, the method of magnetron deposi-
tion is widely used also. It is possible to obtain films by this method
in thick from 0.5 m and higher and with high enough composition
homogeneity degree. However, quality and capacity (properties) of
these films substantially depend on the conditions of deposition
(temperature, velocity of evaporation, thickness, and kind of sub-
strate), composition of initial alloy and type of the following heat
treatment.
In the micromechanism of different type and assignment applied
in different areas, thin films obtained by the methods of magnetron
deposition of the Ti–Ni and Ti–Ni–Me (Me Cu, Fe, Co, Pd) alloys
are most often used. Alloying allows changing of temperature in-
tervals and hysteresis of the martensitic transitions. In the films
obtained by magnetron deposition of initial equiatomic alloys of Ti–
Ni, the concentration of Ni is always enhanced. Additional films of
Ti deposited on the target allow obtaining compositions with Ni in
the interval 45–53 at.% [45]. If deposition is fulfilled on cold sub-
strate, the films are obtained in the amorphous state and, only at
heating higher 500°C, crystallization takes place. A structure and
state substantially depend also on pressure of Ar in a chamber and
type of substrate. Most often glass, plates of copper or silicon use
as substrate.
At cooling of crystalline films of Ti–Ni alloys obtained by magne-
tron deposition, those phases appear that are in the massive state.
So, in the Ti–51.9 at.% Ni alloy after annealing at 500°C from the
ordered B2-phase with the lattice parameter aB2 0.3012 nm during
lowering of the temperature two phases arise: rhombohedral R-
phase (lattice parameter aR 0.3012 nm, rhombohedral angle
89.53
) and monoclinic M-phase (lattice parameters: a 0.2883
nm, b 0.4121 nm, c 0.4909 nm, 96.54
) [45, 46]. A rhombo-
hedral angle of R-phase depends on the temperature of annealing
200 V. A. LOBODYUK
and decreasing with lowering of the temperature. Thus, the parame-
ters of phases arising in the crystalline thin films substantially do
not differ from the parameters of these phases appearing in Ti–Ni
alloys of the same composition in the massive state.
In the Ti–51.3 at.% Ni alloy during annealing in the interval of
temperatures 300–500°C, sizes of grains are not changed (about 1
m) and there is formation of needle-shaped Ti3Ni4 particles [46].
Their size substantially depends on temperature and time of aging
and can run up to 460 nm after annealing at 500°C during 100 h.
The low-limit of these particles is observed after annealing at 400°C
during 1 h and reaches to 10 nm. As well as in the massive materi-
als, the particles of Ti3Ni4 are located in the {111)B2 planes along
directions 110B2. Increase of duration of annealing at 500°C in Ti–
51.9 at.% Ni results in the increase of the beginning temperatures
of formation R- and M-phases and temperatures of the reverse
transitions M B2 and R B2.
In the deposited films of Ti–43.9 at.% Ni alloy, transformation
at both cooling and heating takes place in two stages, through R-
phase [46]. The size of grains in such films changes from 0.5 m to
a few m. Annealing at 500°C during time, which does not exceed
10 h, changes the temperatures of B2 R M and M R B2
transitions. Dependences of temperature beginning of the direct MT
Ms in thin films of Ti–51.9 at.% Ni and Ti–43.9 at.% Ni alloys on
aging time at 500°C resulted in Fig. 7.
In the case of deposition on cold substrate (including room tem-
perature), the films of Ti–Ni alloys appear in the amorphous state.
During crystallization, the equilibrium state arises in alloys only in
Fig. 7. The dependence of temperature of beginning of the direct MT Ms
on annealing time at 500°C for alloys Ti–51,9 at.% Ni (○, ) and Ti–
43,9 at.% Ni (▲, ●) measured by methods of DSC (○, ▲) and by mechanical
tests (, ●) [46].
NUCLEATION AND MARTENSITIC TRANSFORMATION IN SMALL DIMENSIONS 201
the concentration interval 49.5–50.5 at.% of Ni. In Ti- or Ni-
enriched alloys, appearing state is not equilibrium. Therefore, dur-
ing crystallization of the amorphous thin films, excepting equilibri-
um equiatomic phase, non-equilibrium TiNi phases and states can
arise [46]. Their structure appears clearly during investigations by
the methods of high-resolution electron microscopy. For example, in
the Ti–48.3 at.% Ni alloy after annealing at 600°C during 1 h,
there were found very thin disc-like Ti-enriched particles having
0.5 nm thickness and 5–10 nm radius. Diffraction patterns from
these particles correspond to the crystalline structure of the high-
temperature B2-phase. Particles are located in the planes of {100}B2-
type along the directions [010]B2 and [001]B2, and bring to appear-
ance of streaks in these directions on the corresponding micro-
diffraction systems [47]. Disc-like particles are the result of for-
mation of Guinier–Preston zones. They appear on the boundaries of
crystalline domains arising during crystallization of amorphous
films. The spherical particles of Ti2Ni measured to 20 nm and dis-
tributed arbitrary in B2-phase are found out too. These particles
are partly coherent with a matrix [47].
If aging of the Ti-enriched films of the Ti–Ni (47.3 or 48.2 at.%
of Ni) or Ti–43.0% Ni–6.2% Cu (at.%) alloys obtained by deposi-
tion carried out at a crystallization temperature or below by 50°C,
thin (0.5–1.5 nm in thick) plate-like coherent with matrix particles
appear [48]. Their crystalline structure corresponds to b.c.t. lattice
with the high degree of tetragonality: c/a 1.1–1.4. Such plate-like
particles result in appearance around them fields of large elastic
deformations. By opinion of authors, such particles increase amount
of the reversible deformation conditioned by the martensitic trans-
formation.
The Guinier–Preston zones (seen as thin plate particles in a few
atomic layers thick) at the increase of temperature or duration of
annealing grow in a size, their number is increased also [49]. Zones
have influence on subsequent MT changing the microstructure of
martensitic plates-type of twins appearing in the plates of marten-
site. Correlation of widths of twin constituents is changed also in a
martensite.
In the martensite of the equiatomic Ti–Ni alloys (or near to them
by composition), the Guinier–Preston zones do not appear; there are
twins of a 011 type. However, in thin plates of martensite appear-
ing in the Ti–Ni alloys enriched by Ti appearance of twins is possi-
ble on a plane (111 ). At a sufficient width and number of the Guin-
ier–Preston zones, compound twinning in a martensite takes place
on a plane (001) [49].
Investigation of the MT parameters in deposited films of Ti–
50 at.% Ni alloy allowed to determined dependence of the trans-
202 V. A. LOBODYUK
formation temperatures on the thickness of film [50]. At thickness-
es less than 1 m, characteristic temperatures are lowered, but de-
creasing largely depends on the state of surface. In the case of pres-
ence of oxide film, there is decreasing of the transition tempera-
tures approximately on 50°C.
In deposited films of Ti–Ni–Cu alloys, those monoclinic and or-
thorhombic martensitic phases appear in the massive samples of
this composition [46]. The dependence of the characteristic trans-
formation temperatures on copper content is presented in Fig. 8.
The size of transformation hysteresis also depends on the concen-
tration of copper in these alloys. Such dependence manifests itself
most strongly in area of the single-phase B2 M transition. With
increase of Cu concentration from 0 to 9.5 at.%, the hysteresis at
this transformation is changed from 27 K to 9.5 K. In the range of
two-phase transitions, dependence of hysteresis on Cu concentration
in an alloy is substantially less.
Considering the MT peculiarities in thin films obtained magne-
tron deposition, influences of thickness on such transitions, and
their distinctions with the peculiarities of MT in used for deposition
massive specimens (alloys), it is always needed to take into account
the possibility of change the concentration of elements constituting
the alloy. For example, in [51], it was shown that at magnetron
deposition of Ti50.5Ni44.99Cu4.96 alloy on substrate with a temperature
below 100oC obtained films by 1.5–6.0 m thick had composition:
Ti47.5Ni47.5Cu5.0. In such alloy, instead of single B2 M phase tran-
sition MT during cooling proceeds through R-phase. At a room tem-
perature, there were found out the enriched by Cu particles of
Fig. 8. Dependence of peak temperatures of direct reverse MT measured
by the DSC method on Cu concentration in thin films of Ti–Ni–Cu alloys
[46]. B2 monoclinic: ■—austenitic phase, □—martensite phase;
В2 orthorhombic: ▲—austenitic phase, —martensite phase.
NUCLEATION AND MARTENSITIC TRANSFORMATION IN SMALL DIMENSIONS 203
Ti0.33Ni0.43Cu0.24 with a tetragonal structure (lattice parameters: a
0.31 nm, c 0.80 nm). Such particles appear as thin rectangles,
have a size of 100 nm in a long direction, semi-coherent interphase
boundary with B2 phase and orientation {100}B2. Arising as a result
of discrepancy on the interphase boundary of particles of Ti–(Ni
Cu)2 stress (deformations) brings to the increase of temperature of
the formation beginning of the phase arising before martensitic one
and appearance of preferable places of its heterogeneous origin. A
martensitic phase appears below 110°C as thin plates.
A size effect was also observed in deposited films of Ni–Mn–Sn
alloys in which the ferromagnetic shape memory effect takes place
in the massive state [52]. In these alloys, the influence of grain size
on proceeding of MT found out also. At the grain sizes lesser than
10.8 nm, transformation does not take place, an parent phase re-
mains stable at all temperatures. The observations showed that
growth of martensitic plates was stopped on the grain boundaries.
In the films of Cu–26.9% Al–5.5% Ni (at.%) alloy (thickness of
3 m) obtained by magnetron deposition on glass or Si(100) sub-
strate with the grain size of a few nanometres, the textured b.c.c.-
structure and three variants of the hexagonal structure coexist at a
room temperature (hexagonal structure in the copper-based alloys
presents usually as orthorhombic one) [53]. There are stacking
faults in a hexagonal phase. Crystal lattices of founded phases have
the followings parameters: ab.c.c. 0.298 nm, a2H 0.45 nm, b2H
0.52 nm, c2H 0.422 nm that is the same parameters as well as in
the massive alloys of this composition. A difference consists of that
all arising up in thin films phases are disordered. Another peculiar-
ity of the obtained films consists of that they are brittle one and
shape-memory effect (SME) absents in such films. After heating to
750°C and aging during 60 min in subsequent quenching to 20°C,
grain size is increased to 300 nm and martensite appears with 18R-
structure. The shape memory effect proceeds in this state. However,
recover of initial size and state at heating higher Af is only partial
that can be conditioned some deformation of martensitic phase at
loading in the process of SME investigations.
Martensitic transformation in films obtained by quenching from
liquid state. For the obtaining of thin films (ribbons), the method
of quenching from the liquid state (melt) is used sufficiently fre-
quently. By use this method, it is possible to obtain the cooling ve-
locity of 104–108 K/s and to obtain films of 40–100 m thick. Be-
cause of the high cooling rate, there is often amorphous state and a
small thickness stipulates the range of peculiarities in proceeding of
the phase (and martensitic) transformations after crystallization.
Stress arising during high-rate quenching results in essential
change of the imperfect structure: formation of high-density of dis-
204 V. A. LOBODYUK
locations and vacancies. In addition, during crystallization of the
amorphous films often there is a fine-grained structure. Such struc-
tural states render substantial influence on proceeding of martensit-
ic and other phase transitions in films obtained by the high-rate
quenching from the melt.
Already in the first works on investigations of MT peculiarities
in such samples, it was shown that, at the quenching rate of 107
K/s in foils of Au–50 at.% Cd alloy, the temperature of starting of
transition of the parent phase into martensitic one is decreased
and, for the starting of transformation, a tempering at room tem-
perature is required [54]. Authors explain the delay of MT at
quenching with formation of high concentration of vacancies anni-
hilating on dislocations where formation of nuclei of martensitic
phase can be. About influence of high concentration of vacancies
arising in films of Cu–11.7% Al–3.5% Ni (wt.%) alloy (obtained by
the velocity quenching 106 K/s from the liquid state) on the tem-
peratures of direct–reverse martensitic transformation it is also re-
ported in [55].
In the films of Cu–Sn alloys obtained by quenching from the liq-
uid state with rates of 106–107 K/s, MT arresting was not succeeded
[56]. It can be related to the change of the alloy composition at
quenching—by formation during quenching of extractions enriched
with Sn and as a result by increase of the temperature of beginning
of MT. The fulfilled electron-microscopy investigations showed that
in grains less than 1 m martensitic crystals (- and -phases) do
not appear. Morphology and substructure of crystals of martensite
arising in the films at this receipt method practically does not dif-
fer from such in crystals appearing in massive samples quenched by
ordinary speeds. Substantially smaller sizes of the crystals are ob-
served in the films obtained by high-rate quenching from the melt
and are conditioned by small sizes of grains and simultaneous for-
mation and growth of many martensitic plates during high-rate
cooling.
The method of the high-rate quenching from the melt was widely
used for obtaining of thin films (ribbons) of Ti–Ni and Ti–Ni–Me
(Me Cu, Fe, Co, Hf) alloys. Enhanced interest to these alloys is
conditioned not only the features of proceeding of the phase (and
martensitic including) transitions but also their practical wide use
as the alloys with unusual mechanical properties conditioned by
MT. We will consider only those peculiarities of MT in these films,
which are conditioned by the method of obtaining and by the influ-
ence of sizes (thicknesses) on these features.
At first, we will note two main peculiarities observed at the use
of the ultrafast quenching from melt: formation of films (ribbons)
of Ti–Ni and Ti–Ni–Cu alloys in the amorphous state and lowering
NUCLEATION AND MARTENSITIC TRANSFORMATION IN SMALL DIMENSIONS 205
of temperatures MT [57–59]. The amorphous state arises only at
certain conditions: quenching rates must be higher than 106 K/s
and concentrations of copper (entered in alloy instead of nickel)
more than 15 at.%. The change of temperatures and intervals of
the direct–reverse MT is conditioned not only a size factor but also
origin in the alloys of high concentration of vacancies at ultrafast
quenching. As electron-microscopy and diffraction investigations
showed, tempering in the interval 500–700°C of temperatures re-
sults in ordering of such vacancies and formation of the long-period
f.c.c. x-phase with the lattice parameter ax 1.58 nm [60, 61].
Investigations carried out using thin ribbons of Ti50Ni50xCux
(x 5–32 at.%) alloys obtained at rates of quenching from the liq-
uid state of 104–106 K/s allowed to define influence of the quench-
ing rate, composition and thickness on characteristic temperatures,
intervals and hysteresis of the martensitic transitions and also on
phase composition of appearing films [59, 62–64]. In this concen-
tration range as well as in the massive specimens of alloys of such
composition, the following phases appear b.c.c. B2, rhombohedral
R, monoclinic B19 and rhombic B19. Amount of one or other phase
is determined by composition, thickness of film and cooling temper-
ature.
Fig. 9. Temperature dependences of electrical resistance in Ti50Ni50xCux
alloys at x 10 (a), 15 (b), 25 (c) and 32 (d) at.%. Quenching rate (from
the liquid state) is 106 K/s in (a), (b)—lower graphs are for samples after
additional thinning [62].
206 V. A. LOBODYUK
In Figure 9, dependences of electrical resistance on a temperature
are presented for the ribbons of Ti–Ni–Cu alloys containing the dif-
ferent amount of copper. All mentioned phases appear only in the
alloy with 15 at.% Cu and there is the following sequence of phase
transitions: B2 R B19 B19. Fully amorphous state arises in
the alloys with copper concentration of 25 and 32 at.% that is con-
firmed by x-ray and microdiffraction researches. Crystallization
takes place because of heating higher 430
C and amorphous state
transfers to the crystalline B2 phase. It should be noted that addi-
tional thinning of the ribbons (thickness 40–100 m) to 5 m re-
sults in the substantial lowering of characteristic temperatures of
transformation (see Fig. 9). Morphology of martensitic crystals
changes also in the thinned ribbons. In place of trihedral pyramids
usually observed later in ribbons, the plates appear mainly that can
be caused by the change of the stress state during MT in thin films.
The rounded crystalline areas in which MT proceeds with certain
peculiarities appear during initial stages of crystallization: for-
mation of crystals of martensite begins not from boundaries as it
usually takes place in massive specimens but in a centre of rounded
area. It can be related both to concentration homogeneity in the
whole volume of alloy and on a boundary ‘crystalline area–
amorphous area’ and with relaxed state of these boundaries. Anoth-
er peculiarity of MT during the initial stages of crystallization is
noticeable influence of size factor: in crystalline areas with a diam-
eter less than 5–10 m, martensite crystals do not appear [65].
The use of high-resolution electron microscopy enabled to set the
structure of interphase boundaries between amorphous and marten-
sitic phases. With the ribbons of NiTi–Hf40 alloys, it was shown
that such boundaries are of high energy and have non-equilibrium
configuration [66]. Some parts of these boundaries are not direct,
have irregular configuration, other ones show up as zigzag lines.
Analysis performed by the method of energy dispersible spectrosco-
py showed that concentration of Ni and Ti in amorphous phase and
in martensite is different.
3.4. Martensitic Transformation in Nanocrystals and Nanomaterials
With martensitic transformation in little size subjects, for instance,
nanocrystals and nanoparticles, decision influence render such fac-
tors as proceeding of accommodation during transition, relaxation
of arising stress, presence or absence of different sort of defects
and, naturally, size factor, influencing above all things on possibil-
ity of the formation of nuclei of new (martensitic) phase and its
subsequent growth is demonstrated. The size of initial nanocrystals
determines dimensions of arising martensitic crystals and their sub-
NUCLEATION AND MARTENSITIC TRANSFORMATION IN SMALL DIMENSIONS 207
structure that can be related to the peculiarities of relaxation of
arising during MT stress determining the final microstructure of
the crystals.
During studying of MT in ultra-small powders of some Fe-based
alloys, it was ascertained that, at sizes 10–200 nm, the stabilization
of parent -phase took place and martensitic crystals did not appear
[67–70]. Critical size of nanocrystals for beginning of MT depends
on material and type of the MT—thermoelastic or going on with
large hysteresis. It caused by different character of proceeding of
accommodation processes during MT in rounded particles of inves-
tigated amorphous Fe–Ni, Fe–Ni–B and Ni–Ti–Cu alloys obtaining
by quenching from the liquid state. Martensitic transformation does
not take place in particles less than 100 nm in Fe–Ni and less than
15 nm in Ni–Ti–Cu alloys [69].
Critical size for different MT in nanocrystals (rounded nanoparti-
cles in an amorphous matrix) and nanocrystal binary almost
equiatomic Ni–Ti alloys differs: for B2 R and R B19 transfor-
mations in nanocrystals, they are 30 and 100 nm and, for the same
transitions in nanocrystal alloys, are 5 and 60 nm, respectively
[70]. Authors suppose that this distinction is caused by different in
size power barriers to these types of MT in this alloy and different
character proceeding during MT occurring. In particles with a di-
ameter less than 100 nm, one variant of twinned martensite appears
and at the sizes of particles more than 100 nm is observed two
twinned variants of martensite formally named ‘herringbone’ mar-
tensite [71]. According to the authors’ opinion, differences in mor-
phology are caused by different proceeding of accommodation pro-
cesses in the particles of different size. At herringbone morphology,
the processes of relaxation of deformation energy arising up during
transformation proceeds more easily. This relaxation takes place on
the additional boundaries of appearing ‘superfluous’ twins. Since
B2 R transition requires lesser transformation deformation, R-
phase appears in nanoparticles with a size up to 15 nm. B2-phase
remains fully in smaller nanograins.
4. CONCLUSION
In a review, two problems important for understanding of mecha-
nism and peculiarities of martensitic transformations are considered
and discussed: formation of nuclei of martensite crystals and pecu-
liarities of martensitic transition in the subjects of small dimen-
sions.
It is difficult to understand substantial difference of morphologi-
cal and structural peculiarities of martensitic phases in different
materials without consideration and accounting of the mechanism
208 V. A. LOBODYUK
of formation of the martensitic nuclei during change of external
conditions—temperature and applied stress. Such properties condi-
tioned by formation of martensitic phase determine strength, plas-
ticity, shape-memory effect, superelasticity, and superplasticity.
Structural states of parent and arising phases affect also the kinetic
peculiarity of the martensitic transformation.
In the review, models and schemes of martensitic nuclei proposed
by different authors are considered. They relate more frequently to
concrete materials and definite types of martensitic transitions—Fe-
based alloys or non-ferrous metals (mainly copper alloys) with
b.c.c. f.c.c., f.c.c. h.c.p., and b.c.c. orthorhombic transi-
tions. Unfortunately, it is necessary to note that there is no one of
works dealing with nucleus formation during MT, where clear defi-
nition of martensitic nucleus is considered. The questions arise as
follow: is nucleus a some formation with the special distribution of
atoms (different from the initial or arising states) or is needed to
account that nucleus is an area with a certain characteristic imper-
fect structure typical for each material ready to transform during
the change of external conditions—temperature and magnitude of
applied stress? Neither clear determinations nor exhaustive answers
are proposed in the considered works.
In a number of works, it is assumed existence of certain areas
with a structure similar to the structure of the phase appearing in
the parent one. Growth of the martensite crystals starts from these
areas. Areas can arise up because of change of temperature, for ex-
ample, during quenching or at decomposition of parent phase,
which are going on at quenching. Existence of such areas (with the
structure of new phase?) is indirectly confirmed, for example, in
carried out microstructure investigations with the CuAlNi alloys
[72]. Authors found out the presence of some own ‘memory’ of the
martensitic nuclei (some ready places): if, during the reverse trans-
formation, there is no overheating a specimen substantially higher
than temperature of the end of the reverse MT, during subsequent
repeated lowering of the temperature, martensitic crystals arise in
those places that at the first cooling. Thus, this can be concentra-
tion heterogeneity or certain kind of defects preserved during
changes of the temperature below 200°C. In a number of alloys, es-
pecially of copper-based, e.g., CuAlNi(Mn), CuZnAl, CuSn, in the
process of quenching, there are concentration changes (e.g., due to
formation of inclusions), which can result in the appearance of the
first martensite crystals in these places (see Ref. [29]).
Presence of the special type of dislocations, their determined dis-
tribution and interaction are assumed in the proposed dislocation
models of formation of the martensitic nuclei. There is both the
splitting of complete dislocations and the formation of partials at
NUCLEATION AND MARTENSITIC TRANSFORMATION IN SMALL DIMENSIONS 209
some conditions. Because of their moving, there is a change of the
crystal structure of the parent phase by the martensitic phase in
this area. An important condition for the further reconstruction
and proceeding of the phase transformation is a necessity of ap-
pearance of special interphase boundary with a certain structure
dividing the parent and appearing phases. An arising interphase
boundary must be coherent or consisting of coherent sections sepa-
rated by the dislocations. Only in this case, it will possess high mo-
bility, and growth of martensite crystal will be possible. However,
many moving boundaries appear only in the case of the thermoelas-
tic martensitic transformation.
Due to the lacks of the considered dislocation models of the nu-
cleation of the martensitic phase, it is necessary to take into ac-
count their discrepancy with the following experimental facts. It is
well known that additional annealing of the parent phase resulting
in lowering of density of dislocations in material stipulates its sta-
bilization that is considerable lowering of the temperature of the
MT starting proceeds. It is also possible the braking of MT and pre-
serving of the parent phase, though certain amount of dislocations
is retained after annealing. At the same time, the MT promotes
small deformations (5–15%). It is related presumably to the for-
mation of the certain-type dislocations located in the corresponding
planes during the process of deformations. However, deformations
higher 35–40%, at which the dislocations’ density and other defects
rise, substantially break martensitic transition in most alloys, in
which MT is possible at cooling. Thus, the role of dislocations in the
process of formation of nuclei of new phase and further proceeding
of MT is ambiguous enough. Apparently, for the starting of MT,
the special type of dislocations, their special location (in certain
crystallographic planes), possibility of splitting, moving, and inter-
action with other defects, including dislocations, is required.
In each proposed model, the mechanism of growth of appearing
nucleus and specific type of interphase boundary between the parent
and arising phases, which must possess high mobility for occurring
of further transformation, is required. However, such mechanism is
absent in many models.
Thus, in every case of the nucleation at MT, it is necessary to ex-
amine the type of initial crystal structure, transition conditions,
possible and necessary (for splitting) type of dislocations, mecha-
nism of their splitting and interaction during formation of marten-
sitic nucleus as well as mechanism of growth of the martensite
crystals taking into account the structure of the interphase bounda-
ry. Apparently, development of universal mechanism of formation
of nuclei for all types of MT is hardly possible in any event in near-
est future.
210 V. A. LOBODYUK
The problem of martensitic transformation in the subjects of
small dimensions is concerned with a question about the nucleation
of the martensite. The MT in these subjects is strongly dependent
on dimensions (thickness, diameter, size of the transformed vol-
ume), i.e., on the correlation of size of new-phase nucleus and di-
mensions of these subjects. In the subjects of small dimensions, the
MT can take place with some peculiarities in some cases. The stage
of nucleus formation at its some sizes is absent, or the number of
nuclei is limited. In small particles, dislocations and other defects
can be absent too. Since often there is no separating over grains in
such subjects, the influence of grain boundaries on the processes of
martensitic transition is absent. During MT in these materials, the
role of the surface increases considerably, but stress effect can be
absent or do not rise. The peculiarities of MT in subjects of small
sizes are following: decreasing of the transition temperatures,
change of the transformation intervals, value of the hysteresis, par-
tial proceeding of MT. Influence of inhomogeneity on transition is
increasing. Appearing martensite often has morphological peculiari-
ties as compared to the crystal forms of the martensite in bulky
specimens. The thin (sub)structure of the martensite crystals and
crystallography of transformation can also change, in particular,
the change of the mutual orientation of the parent and martensitic
phases takes place. Stabilization of the parent phase in most mate-
rials occurs at the sizes of 10–200 nm. A critical size depends on
material, in which there is the MT, type of transition, conditions of
occurring of the transformation, relaxation degree of arising stress.
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