Powder x-ray diffraction study of the thermoelastic martensitic transition in Ni
2
Mn
1.05
Ga
0.95
Rajeev Ranjan,
1
S. Banik,
2
S. R. Barman,
2
U. Kumar,
3
P. K. Mukhopadhyay,
3
and Dhananjai Pandey
1
1
School of Materials Science and Technology, Institute of Technology, Banaras Hindu University, Varanasi-221005, India
2
UGC-DAE Consortium for Scientific Research, University Campus, Khandwa Road, Indore, 452017, Madhya Pradesh, India
3
LCMP, S. N. Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake, Kolkata, 700098, West Bengal, India
Received 24 January 2006; revised manuscript received 8 November 2006; published 29 December 2006
Results of temperature-dependent magnetic susceptibility and powder x-ray diffraction XRD measure-
ments on Ni
2
Mn
1.05
Ga
0.95
and Ni
2.13
Mn
0.87
Ga magnetic shape memory alloys are compared. The transforma-
tion behavior of these two alloys is found to be entirely different. Detailed LeBail and Rietveld analyses of
powder XRD data of Ni
2
Mn
1.05
Ga
0.95
alloy show that the martensite phase belongs to the Pnnm space group
with 7M modulation. The limits of the supercooled austenite and the superheated martensite phases have been
determined by Rietveld analysis of powder XRD data recorded at close temperature intervals. It is shown that
the martensite and the austenite phases coexist over 30 K temperature range around the martensitic transition
temperature. The transformation strains during cooling in 001, 010, and 100 directions are found to be
-4%, +1.6%, and 2.1%, respectively, while the volume change is only 0.06%.
DOI: 10.1103/PhysRevB.74.224443 PACS numbers: 75.50.Cc, 64.70.Kb, 81.30.Kf
I. INTRODUCTION
Currently there is enormous interest in the Ni-Mn-Ga
magnetic shape memory alloy SMA system close to its
stochiometric composition, i.e., Ni
2
MnGa, because of its
unique magnetoelastic properties.
1
Observation of magnetic-
field-induced strains of 10% in this alloy system
2
makes it
technologically much more promising for magnetomechani-
cal actuator devices than other materials presently being used
commercially. For example, the well known Tb-Dy-Fe alloy
system Terfenol-D exhibits magnetostrictive strains of
about 0.1% only. Similarly, the present day piezoelectric ce-
ramics exhibit maximum strains up to 0.2%.
3
The crystal
structure of the parent austenite phase in the stoichiometric
Ni
2
MnGa compound is known to be cubic in the Fm3
¯
m
space group with L2
1
Heusler atomic order.
1
It shows fer-
romagnetic ordering on cooling below T
C
370 K.
1
On fur-
ther cooling, it exhibits a premartensitic phase transition
around 250 K, which has been attributed to the coupling of a
soft transverse acoustic TA
2
phonon at q = 1/3,1/3,0 with
the homogeneous deformation associated with Zener elastic
constant c' = c
11
- c
12
/2.
4–6
Finally, on cooling below T
m
=210 K, it undergoes a thermoelastic martensitic phase
transition.
1
Electronic structure calculations show a peak in
the density of states at the Fermi level, which splits due to
the redistribution of the electrons around the Fermi level in
the martensite phase.
7
The number of the martensite phases, their structures, and
the sequence of their occurrence in the Ni-Mn-Ga system
depend on the stoichiometry.
8–11
Chernenko et al.
8
have clas-
sified Ni-Mn-Ga ferromagnetic shape memory alloys into
three groups based on their martensitic transition tempera-
tures. Group I alloys, which are nearly stoichiometric, ex-
hibit low martensitic transition temperatures as compared to
the Curie temperature. This group of alloys also shows a
premartensitic transition. Group II alloys have martensitic
transition around room temperature but still below Curie
temperature. These alloys usually exhibit stress and ther-
mally induced intermartensitic transition also. Giant
magnetic-field-induced strain is a common feature of these
alloys. The group III alloys exhibit martensitic transition
above the Curie temperature.
The three well-known martensite phases in this alloy sys-
tem are traditionally referred to as 5M,7M, and nonmodu-
lated or NM phases. The 5M and 7M phases correspond to
five-layer and seven-layer modulations of the 110
A
planes
in 11
¯
0
A
direction, where the subscript A stands for the
austenite phase.
12
The proposed modulations are based on
the observation of the number of extra diffraction spots be-
tween the two parent phase spots along reciprocal lattice
rows parallel to one of the 110
A
directions on the electron
diffraction patterns
10,13
and single-crystal x-ray oscillation
photographs.
11–13
The cubic lattice has been reported to be
distorted tetragonally with c / a 1 in the 5M phase,
1
orthor-
hombically in the 7M Refs. 1 and 12 and tetragonally with
c / a 1 for the NM phase.
14
The difference in the martensitic
transition temperatures and the magnetoelastic properties of
the three groups of alloys in the Ni-Mn-Ga system is be-
lieved to be due to the difference in the crystal structure of
the martensite phases.
15,16
There is therefore considerable in-
terest in understanding the structure of the Ni-Mn-Ga alloy
system as a function of composition.
The splitting of the austenite 220 and the 400 peaks into
two or three peaks has generally been interpreted in terms of
“tetragonal”
1,17
or “orthorhombic”
13,17
distortions with 5M
or 7M modulations, respectively. Wedel et al.
14
have as-
signed I4/ mmm and Fmmm space groups to the so-called
tetragonally and orthorhombically distorted martensites. Nei-
ther of these two space groups has, however, been tested by
comparing the observed and the calculated diffracted inten-
sities for the martensite phases. Recently, an attempt
17
has
been made to index the x-ray diffraction XRD peaks of the
martensites of an alloy composition of the group II using
these two space groups. However, a perusal of the hkl Miller
indices given in this work
17
clearly shows that these are not
consistent with the I- and F-centered lattices. The only space
group that has been tested by comparing the calculated and
observed intensities is Pnnm for the premartensite and mar-
PHYSICAL REVIEW B 74, 224443 2006
1098-0121/2006/7422/2244438 ©2006 The American Physical Society 224443-1