Besides permitting an accurate determination of the
ferromagnetic-to-paramagnetic phase transition temperature and the
characteristic temperatures for the beginning and end of the growth of
martensite (austenite) phase at the expense of austenite (martensite) phase
while cooling (heating), the results of an extensive ac susceptibility, sound
velocity and internal friction investigation of the thermoelastic martensitic
transformation in melt-quenched (site-disordered) Ni55Fe20Al25 alloy provide a
clear experimental evidence for the following. Irreversible thermoelastic
changes (thermal hysteresis) occur in the austenite phase in the premartensitic
regime. In the heating cycle, the system retains the "memory" of the initiation
and subsequent growth of the martensitic phase (at the expense of the parent
austenite phase) that had taken place during the cooling cycle in the
austenite-martensite phase coexistence region. We report and discuss these
novel findings in this communication.Comment: 5 figure

Otsuka K.

P. K. Mukhopadhyay

S. N. Kaul

English

arXiv

AC susceptibility, sound velocity, and internal friction study of the martensitic transformation in melt-quenched (site-disordered) Ni55Fe20Al25 alloy unravels the irreversible thermoelastic changes (thermal hysteresis) that occur in the austenite phase in the premartensitic regime. In the heating cycle, the system retains the "memory" of the initiation and subsequent growth of the martensitic phase (at the expense of the parent austenite phase) that had taken place during the cooling cycle in the austenite-martensite phase coexistence region. These and other findings are discussed in this communication

Mukhopadhyay, P. K.

Kaul, S. N.

Publications of the IAS Fellows

 1 
Dynamic elastic properties and magnetic susceptibility across the 
austenite-martensite transformation in site-disordered 
ferromagnetic Ni-Fe-Al alloy 
 
P. K. Mukhopadhyay1†a and S. N. Kaul2 
 
1LCMP, S. N. Bose National Center for Basic Sciences, Salt Lake, Kolkata – 700 098, India 
2School of Physics, University of Hyderabad, Central University P. O., Hyderabad – 500 046, 
Andhra Pradesh, India 
 
Besides permitting an accurate determination of the ferromagnetic-to-paramagnetic phase 
transition temperature and the characteristic temperatures for the beginning and end of the 
growth of martensite (austenite) phase at the expense of austenite (martensite) phase while 
cooling (heating), the results of an extensive ac susceptibility, sound velocity and internal 
friction investigation of the thermoelastic martensitic transformation in melt-quenched (site-
disordered) 252055 AlFeNi  alloy provide a clear experimental evidence for the following. 
Irreversible thermoelastic changes (thermal hysteresis) occur in the austenite phase in the 
premartensitic regime. In the heating cycle, the system retains the “memory” of the initiation and 
subsequent growth of the martensitic phase (at the expense of the parent austenite phase) that had 
taken place during the cooling cycle in the austenite-martensite phase coexistence region. We 
report and discuss these novel findings in this communication.  
 
                                                  
a
 author to whom correspondences may be addressed (email: pkm@bose.res.in) 
 2 
PACS Numbers: 62.40.+i, 72.55.+s, 75.40.Cx, 81.30.Kf  
 
        Thermoelastic martensitic transformation from face-centered-cubic (fcc) austenite (high-
temperature) phase to tetragonal martensite (low-temperature) phase in a new ternary 
ferromagnetic alloy system Ni-Fe-Al (“prepared” in different states of site disorder) has been 
recently reported1 based on the results of a detailed neutron diffraction (ND), electrical 
resistivity, )(Tρ , and magnetization, ),( HTM , studies. The effect of site disorder, in this alloy 
system, is to1 (i) promote ductility, (ii) narrow down the temperature range over which austenite 
and martensite phases coexist (and hence sharpen the martensitic phase transition) and (iii) shift 
the martensitic transition temperature to higher temperatures. In the melt-quenched sample of 
252055 AlFeNi  (henceforth referred to as  q-Fe20), which has the highest degree of site disorder, 
the thermoelastic martensitic phase transition is sharp and occurs near the Curie temperature 
KTC 225≅ . The martensitic transformation (MT) is evidenced by the thermal hysteresis 
exhibited by electrical resistivity as a function of temperature, )(Tρ , when a given
 
sample 
undergoes thermal cycling. An elaborate analysis of the )(Tρ  data yields1 the characteristic 
temperatures for the beginning, bMT  ( bAT ), and end, eMT  ( eAT ), of the growth of martensite 
(austenite) phase at the expense of austenite (martensite) phase while cooling (heating) as 
KT bM 260≅ , KT eM 150≅ , KT bA 170≅  and KT eA 280≅  for the q-Fe20  sample. These values 
for the characteristic temperatures are consistent with those deduced from the ND data. 
 
        Recognizing that the thermoelastic martensitic transformation causes the shape memory 
effect2-7 and the thermoelastic nature of MT is directly reflected4,5,8 in the elastic property 
measurements across the austenite-martensite phase transformation, extensive measurements of 
 3 
dynamic elastic properties, such as sound velocity and attenuation, of the sample q-Fe20  were 
undertaken, using the vibrating reed technique9-11. This sample undergoes1 a ferromagnetic (FM) 
to paramagnetic (PM) transition at KTC 225≅  (the Curie temperature), which falls within the 
temperature range over which MT occurs. Since the intrinsic magnetic susceptibility diverges at 
CTT =  and is extremely sensitive to any structural changes, the real ( '0χ ) and imaginary  ( ''0χ ) 
components of ac susceptibility were measured as well.  
 
        Starting with 99.99 % pure Ni, Fe and Al, taken in proper proportions, polycrystalline rods 
of 10 mm diameter and 100 mm length with nominal composition 252055 AlFeNi  were prepared 
by radio-frequency induction-melting technique. A portion of these rods was melt-quenched to 
form 2 mm wide and mµ30≈  thick crystalline ribbons. The details about the sample 
preparation and actual composition are furnished elsewhere12. Vibrating reed experiments were 
performed on an absolutely flat ribbon strip of length 25 mm, which forms the reed. In such 
experiments, one end of the reed is clamped firmly to the base plate of the cryostat while a 
flexural resonance is set up at the other (free) end by an electrostatic drive via an electrode 
placed near that end. Another matching electrode (biased at 45 volts and connected to the input 
of a lock-in amplifier), placed against the opposite face of the reed, picks up the oscillations by 
electrostatic coupling. The reference input to the lock-in amplifier comes from the same 
generator that feeds the drive electrode with sine wave amplitude variation, but locked to the 
second harmonic. At room temperature, the resonance curve is obtained by measuring the 
amplitude of vibration of the free end as a function of the driving frequency. From the resonance 
curve, so measured, the absolute value of internal friction, resQ νν /1 ∆=− , (where ν∆  is the 
width of the resonance curve between the points at which the amplitude has the value 2/maxA  
 4 
if maxA  is the maximum amplitude at the resonance frequency resν ) at room temperature is 
deduced as 31 105.6)7.293( −− == xKTQ . Subsequently, the resonance is phase-locked and 
tracked as the sample temperature is varied. The sound velocity, V, as a function of temperature 
is obtained from the fundamental (resonance) vibration frequency, ν , using the relation 
Vld 2)/875.1()34/( piν = , where d and l are the thickness and length of the sample reed. Note  
that we can measure only the relative changes in sound velocity, VV /δ , with respect to its value 
at room temperature because the unknown clamping yield causes a large uncertainty in the 
measurement of actual effective l. This is a standard problem with vibrating reed measurements. 
In the present experiments, the relative change in sound velocity and internal friction could not 
be resolved better than 100 ppm and 5 %, respectively. To highlight the changes that occur in 
)(1 TQ−  near the phase transitions and in the mixed-phase regime, the 1−Q  data taken at different 
temperatures have been normalized to the room temperature value 31 105.6)7.293( −− == xKTQ .  
 
        After compensating for the earth’s magnetic field, ac susceptibility, )(Tacχ , was measured 
at a driving magnetic field of rms amplitude Oehac 1=  and frequency Hz111=ν  over the 
temperature range 1.7 K to 300 K. The temperature variations of the real ( '0χ ) and imaginary  
( ''0χ ) components of ac susceptibility in the cooling (from 300 K to 1.7 K) and heating (from 
1.7 K to 300 K) cycles are depicted in figure 1. The thermal hysteresis in )('0 Tχ  and )(''0 Tχ , 
extending from KT eM 150≅  to KT eA 280≅ , is an experimental signature of the thermoelastic 
martensitic transformation. The characteristic temperature KT bM 260≅  ( KT bA 170≅ ) for the 
beginning of the growth of martensite (austenite) phase at the expense of austenite (martensite) 
 5 
phase while cooling (heating) corresponds to the temperature at which the cooling and heating 
curves bifurcate (the temperature at which )('0 Tχ  and )(''0 Tχ  exhibit a pronounced shoulder in 
the heating curve). These characteristic temperatures are in excellent agreement with those 
previously1 determined from )(Tρ  and ND data. The temperature range over which the 
martensite and austenite phases coexist extends from bMT  to eMT  on the cooling )('0 Tχ  or 
)(''0 Tχ  curve and from bAT  to eAT  on the heating curve. The Curie temperature, CT , is 
identified with the temperature corresponding to the dip in the temperature derivative of )('0 Tχ , 
dTTd /)('0χ , versus T curves. This ‘inflection-point’ (in )('0 Tχ ) method yields KTC 223=  
( KTC 225= ) in the cooling (heating) run. 
 
        Figure 2 displays the temperature variations of VV /δ  and 1−Q  for q-Fe20, measured at a 
drive voltage of 7.9 V, when the sample is cooled down to 190 K. As the sample temperature 
decreases, VV /δ  declines while 1−Q  increases. This decline (rise) in VV /δ  ( 1−Q ) signals 
phonon “softening” in the premartensitic regime. The rate of decline in VV /δ  or equivalently, 
increase in 1−Q  slows down as the on-set temperature for the growth of the martensitic phase, 
KT bM 260≅ , is approached while cooling. This feature is followed, at bMTT < , by an upturn 
(downturn) in VTV /)(δ  ( 1−Q (T)) at KTup 236≅  and subsequently by a sharp drop (rise) at 
KTrap 232≅ . The temperature upT  ( rapT ) marks the stage within the mixed-phase regime at 
which the volume fraction of the tetragonal martensitic phase grows at a slow pace (starts 
growing at a very rapid rate) at the expense of the parent cubic austenite phase while cooling. 
These values of upT  and rapT  tally quite well with those corresponding to the upturn and steep 
 6 
rise observed in )(Tρ  previously1 and in )('0 Tχ  or )(''0 Tχ  now (Fig.1). The resonance phase-
lock is completely lost when the temperature falls below K218  so much so that the reed stops 
oscillating and the matching electrode picks up only spurious signals. An attempt was made to 
induce vibrations in the reed by increasing the drive amplitude from the normal value of 5V rms 
to 15 V rms but without success. Since the drive force varies as the square of the driving 
amplitude, this increase in the drive amplitude corresponds to about 10 times larger driving 
force. Consistent with our earlier observations1 based on the )(Tρ  and ND results, this 
“stiffness” of the reed is indicative of a massive martensitic transformation at such temperatures 
in the q-Fe20 sample.  
 
        To investigate the martensitic transformation (MT) in greater detail, three different 
experiments covering (a) the premartensitic regime, (b) part of the mixed-phase regime, and (c) 
the entire temperature range over which MT occurs, have been carried out. In these experiments, 
before heating the sample back to room temperature, the sample is cooled down to the 
temperature *T , which lies (a) above KT bM 260≅  ( KT 265* ≅ ), (b) well below bMT  but not 
too deep into the austenite-martensite phase coexistence region ( upTKT ≅= 65.238* ), and (c) 
well below the temperature KT eM 150≅ , which marks the end of the martensitic transformation, 
( KT 130* ≅ ). The results of the experiments (a) – (c) are shown in figures 3 – 5, respectively. 
These results, when viewed in the light of the relation ρ/EV = , where E is the Young’s 
modulus and ρ  is the mass density, imply the following. When bMTT >*  (case (a), 
premartensitic regime), VV /δ  and 1−Q , measured at a drive voltage of 7.9 V, both exhibit 
thermal hysteresis (Fig.3). While cooling from 294.5 K , the parent austenite phase remains 
 7 
“elastically stiff ” in its KT 5.294=  state till the temperature 291.5 K is reached when the 
phonon “softening” starts and this process continues till KT 265* ≅ . On the other hand, in the 
heating cycle, the austenite phase in the “kinetically arrested” metastable state, corresponding to 
*TT = , persists till the temperature reaches the value KT 275≅  (which is close to the 
characteristic temperature KT eA 280≅ ) beyond which the elastic recovery towards the room 
temperature parent austenite phase gets started. The elastic recovery process is nearly complete 
at KT 5.294=  when the thermoelastic hysteresis tends to vanish. These results assert that in the 
premartensitic regime, the parent austenite phase undergoes changes similar to those occurring in 
the high-temperature high-crystallographic-symmetry phase prior to a first order phase transition. 
When bMup TTT <≅*  (case (b), Fig.4), the sample has barely entered into the two-phase regime 
and with temperature increasing from *T , the austenite phase does not recover fully to its room 
temperature elastic state even when eATT >  , instead the system retains partially the “memory” 
of the elastic state in the two-phase region. Consequently, unlike the major VV /δ - T and 1−Q - T 
thermal hysteresis loops (Fig.5), the minor VTV /)(δ  and )(1 TQ −  thermal hysteresis loops, 
taken at a drive voltage of 7.9 V, do not close at room temperature. By contrast when the sample 
is cooled down to eMTT <*  (case (c), Fig.5) and the thermal cycling interval embraces the entire 
temperature range over with the MT takes place, VTV /)(δ  and )(1 TQ −  data, taken at a drive 
voltage of 2.13 V, exhibit a rich structure (i.e., peaks, minima, change of slope, etc.) 
symptomatic of the thermoelastic processes occurring in the two-phase region. Note that, as was 
the case in the previous experimental run (Fig.2), in this run too, the resonance phase-lock is 
completely lost when the temperature falls below K218  during cooling but the resonance phase-
lock is automatically restored when the temperature exceeds 218 K in the heating cycle. From 
 8 
the temperatures corresponding to the peaks, minima and change of slope in the VTV /)(δ  and 
1−Q (T) curves marked in Fig.5, the following important observations can be made. (i) The 
characteristic temperatures bMT , eAT   and  CT  are more sharply defined in the sound velocity 
and internal friction data than in the )(Tρ  (reference 1) and )('0 Tχ  or  )(''0 Tχ  data (Fig.1). (ii) 
In the heating cycle, the system remembers the initiation (marked by the peak in VTV /)(δ or dip 
in )(1 TQ− at KTT bM 260== ) and subsequent growth (represented by the dip in VTV /)(δ or 
peak in )(1 TQ−  at KT 236= ) of the martensitic phase (at the expense of the parent austenite 
phase) that had occurred during the cooling cycle in the two-phase regime. (iii) In both cooling 
and heating cycles, VTV /)(δ  ( )(1 TQ − ) exhibits pronounced minima (peaks) corresponding to 
the Curie temperatures KTC 223=  and KTC 225= , obtained from the dTTd /)('0χ  data 
(Fig.1). 
 
        In short, we report the elastic anomalies associated with the austenite – martensite phase 
transitions as they manifest themselves in the sound velocity and attenuation data and establish 
correlations with the results obtained by other standard but indirect measuring techniques such as 
electrical resistivity and magnetic susceptibility. Detailed vibrating reed measurements on 
252055 AlFeNi  samples with varied degree of site disorder and the analyses of the results, so 
obtained, are in progress. 
 9 
REFERENCES 
     
 
1S. N. Kaul, B. A. D’Santhoshini, A. C. Abhyankar, L. Fernández Barquin and P. 
  Henry, Appl. Phys. Lett. 89, 093119 (2006). 
 
 
2G. Guenin, Phase Transitions 14, 165 (1989). 
 
 
3Shape Memory Materials, edited by K. Ostuka and C. M. Wayman (Cambridge 
  University, Cambridge, 1998). 
 
 
4S. M. Shapiro, B. X. Yang, Y. Noda, L. E. Tanner and D. Schryvers, Phys. Rev. B 44, 
  9301 (1991). 
 
 
5H. Morito, A. Fugita, K. Fukamichi, R. Kainuma, K. Ishida and K. Oikawa, Appl. Phys. 
  Lett. 83, 4993 (2003). 
 
 
6P. J. Brown, K. Ishida, R. Kainuma, T. Kanomata, K. –U. Meumann, K. Oikawa, B. 
  Ouladdiaf and K. R. A. Ziebeck, J. Phys.: Condens. Matter 17, 1301 (2005). 
 
 
7M. Zhang, E. Brück, F. R. de Boer and G. Wu, J. Phys. D: Appl. Phys. 38, 1361 (2005). 
 
 
8Z. Song, S. Kishimoto, J. Zhu and Y. Wang, Solid State Commun. 139, 235 (2006); 
  R. Kainuma, Y. Imano, W. Ito, Y. Sutou, H. Morito, S. Okamoto, O. Kitakami, K.  
  Oikawa, A. Fujita, T. Kanomata and K. Ishida, Nature Lett. 439, 957 (2006). 
 10 
 
 
9P. K. Mukhopadhyay and A. K. Raychaudhuri, J. Phys. C: Solid State 21, L385 (1988); 
  J. Appl. Phys. 67, 5235 (1990). 
 
10K. Balakrishnan, P. D. Babu, V. Ganesan, R. Srinivasan and S. N. Kaul, J. Magn. 
   Magn. Mater. 250, 110 (2002). 
 
11K. Balakrishnan and S. N. Kaul, Phys. Rev. B 65, 134412 (2002). 
 
12B. A. D’Santhoshini and S. N. Kaul, J. Phys.: Condens. Matter 15, 4903 (2003). 
 
 
 11 
FIGURE  CAPTIONS 
 
 
FIG. 1. Temperature variations of the real ( ) and imaginary  ( )  components of ac 
susceptibility in the cooling (open circles) and heating (continuous curves) cycles. The 
characteristic temperatures for the beginning,   ( ), and end,   ( ), of the growth of 
martensite (austenite) phase during cooling (heating) are indicated. 
 
 
FIG. 2. The temperature variations of sound velocity, VV /δ , and internal friction, 
1−Q
,  
measured at a drive voltage of 7.9 V, when the sample is cooled down to 190 K. The values 
of the temperatures marking the characteristic features in these curves are indicated. 
 
FIG. 3. The temperature variations of sound velocity, VV /δ , and internal friction, 
1−Q
,  
measured at a drive voltage of 7.9 V, when the sample undergoes thermal cycling between 
265 K and 294.5 K in the premartensitic regime. The values of the temperatures marking 
the characteristic features in these curves are indicated. 
 
 12 
FIG. 4. The temperature variations of sound velocity, VV /δ , and internal friction, 
1−Q
,  
measured at a drive voltage of 7.9 V, when the sample undergoes thermal cycling between 
238.5 K and 293 K. The values of the temperatures marking the characteristic features in 
these curves are indicated. 
 
FIG. 5. The temperature variations of sound velocity, VV /δ , and internal friction, 
1−Q
,  
measured at a drive voltage of 2.13 V, when the sample undergoes thermal cycling between 
130 K and 296 K. The values of the temperatures marking the characteristic features in 
these curves are indicated. 
 
 13 
 
 
                            
0
1
2
3
4
Cooling
Heating
219 K
 211 KQuenched
Ni55Fe20Al25
TAe= 280 KTAb= 170 K
TMe= 150 K
TMb= 260 K
 
 
 
T    ( K )
χχ  
0'
'  
 
 
 
 
( 1
0 
-
 
3  
e
m
u
 / 
gO
e
 )
χχ  
0'
 
 
 
 
 
( 1
0 
-
 
2  
e
m
u
 / 
gO
e
 )
T
up= 236 K
0 100 200 300
0.0
0.8
1.6
TAe= 280 K
TMb= 260 K
TMe= 150 K
T
Ab
= 170 K
 216 K
 
  
 206 K
 
 
 
 
 
                                                                FIG. 1.  
 
 
 
 
 
 14 
 
 
                           
0
2
4
6
8
10
12
220 240 260 280 300
1
10
100
218 K
  T
up= 236 K
231.5 K TMb= 260 K
T    (K)
Q
-
1
δδV
 / 
V 
   
( 1
0 
-
 
5 
)
Quenched
Ni55Fe20Al25
 
 
 
 
 
 
 
 
 
 
                                                            FIG. 2.  
 
 
 
 
 
 15 
 
 
                         
5.0
6.0
7.0
8.0
260 270 280 290 300
1.0
1.2
1.4
1.6
1.8
      291.5 K
      294.5 K
275 K
 265 K
TAe= 280 K
 
 
δδV
 / 
V 
   
( 1
0 
-
 
5 
)
Quenched
Ni55Fe20Al25
 
 
T > TMb= 260 K
 Cooling
 Heating
T     (K)
Q
-
1
  
 
 
 
 
 
 
                                                              FIG. 3.  
 
 
 
 
 
 16 
                              
3
4
5
6
7
8
240 260 280 300
1.0
1.5
2.0
2.5
Quenched
Ni55Fe20Al25 
247 K238.5 K
TMb= 260 K
275 K
TAe= 280 K
δδV
 / 
V 
   
( 1
0 
-
 
5 
)
 
 
Cooling
 Heating
 T    (K)
  
Q
-
1  
 
 
 
 
 
 
                                                                      FIG. 4.  
 
 
 
 
 
 
 17 
                              
0.0
0.3
0.6
0.9
225 250 275 300
0.1
1
10
 221 K
 275 K
 244 K
 277 K
 260 K
 236 K
 T
Ae
= 280 K
 TC= 225 K
 T
Mb
= 260 K
T     (K)
Q
-
1  
 
 
δδV
 / 
V 
 
 
 
( 1
0 
-
 
5 
)
 
Quenched
Ni55Fe20Al25
 
 
 240 K
 222 K
 236 K
 T
C
~ 225 K
Cooling
Heating
 
 
 
 
 
 
 
                                                                    FIG. 5.  


Dynamic elastic properties and magnetic susceptibility across the austenite-martensite transformation in site-disordered ferromagnetic Ni-Fe-Al alloy

Crossref

Dynamic elastic properties and magnetic susceptibility across the austenite-martensite transformation in site-disordered ferromagnetic Ni–Fe–Al alloy

Indian Academy of Sciences

 1 
Dynamic elastic properties and magnetic susceptibility across the 
austenite-martensite transformation in site-disordered 
ferromagnetic Ni-Fe-Al alloy 
 
P. K. Mukhopadhyay1†a and S. N. Kaul2 
 
1LCMP, S. N. Bose National Center for Basic Sciences, Salt Lake, Kolkata – 700 098, India 
2School of Physics, University of Hyderabad, Central University P. O., Hyderabad – 500 046, 
Andhra Pradesh, India 
 
Besides permitting an accurate determination of the ferromagnetic-to-paramagnetic phase 
transition temperature and the characteristic temperatures for the beginning and end of the 
growth of martensite (austenite) phase at the expense of austenite (martensite) phase while 
cooling (heating), the results of an extensive ac susceptibility, sound velocity and internal 
friction investigation of the thermoelastic martensitic transformation in melt-quenched (site-
disordered) 252055 AlFeNi  alloy provide a clear experimental evidence for the following. 
Irreversible thermoelastic changes (thermal hysteresis) occur in the austenite phase in the 
premartensitic regime. In the heating cycle, the system retains the “memory” of the initiation and 
subsequent growth of the martensitic phase (at the expense of the parent austenite phase) that had 
taken place during the cooling cycle in the austenite-martensite phase coexistence region. We 
report and discuss these novel findings in this communication.  
 
                                               
a author to whom correspondences may be addressed (email: pkm@bose.res.in) 
 2 
PACS Numbers: 62.40.+i, 72.55.+s, 75.40.Cx, 81.30.Kf  
 
        Thermoelastic martensitic transformation from face-centered-cubic (fcc) austenite (high-
temperature) phase to tetragonal martensite (low-temperature) phase in a new ternary 
ferromagnetic alloy system Ni-Fe-Al (“prepared” in different states of site disorder) has been 
recently reported1 based on the results of a detailed neutron diffraction (ND), electrical 
resistivity, )(Tρ , and magnetization, ),( HTM , studies. The effect of site disorder, in this alloy 
system, is to1 (i) promote ductili ty, (ii) narrow down the temperature range over which austenite 
and martensite phases coexist (and hence sharpen the martensitic phase transition) and (iii) shift 
the martensitic transition temperature to higher temperatures. In the melt-quenched sample of 
252055 AlFeNi  (henceforth referred to as  q-Fe20), which has the highest degree of site disorder, 
the thermoelastic martensitic phase transition is sharp and occurs near the Curie temperature 
KTC 225≅ . The martensitic transformation (MT) is evidenced by the thermal hysteresis 
exhibited by electrical resistivity as a function of temperature, )(Tρ , when a given sample 
undergoes thermal cycling. An elaborate analysis of the )(Tρ  data yields1 the characteristic 
temperatures for the beginning, bMT  ( bAT ), and end, eMT  ( eAT ), of the growth of martensite 
(austenite) phase at the expense of austenite (martensite) phase while cooling (heating) as 
KT bM 260≅ , KT eM 150≅ , KT bA 170≅  and KT eA 280≅  for the q-Fe20  sample. These values 
for the characteristic temperatures are consistent with those deduced from the ND data. 
 
        Recognizing that the thermoelastic martensitic transformation causes the shape memory 
effect2-7 and the thermoelastic nature of MT is directly reflected4,5,8 in the elastic property 
measurements across the austenite-martensite phase transformation, extensive measurements of 
 3 
dynamic elastic properties, such as sound velocity and attenuation, of the sample q-Fe20  were 
undertaken, using the vibrating reed technique9-11. This sample undergoes1 a ferromagnetic (FM) 
to paramagnetic (PM) transition at KTC 225≅  (the Curie temperature), which falls within the 
temperature range over which MT occurs. Since the intrinsic magnetic susceptibil ity diverges at 
CTT =  and is extremely sensitive to any structural changes, the real ( '0χ ) and imaginary  ( ''0χ ) 
components of ac susceptibility were measured as well.  
 
        Starting with 99.99 % pure Ni, Fe and Al, taken in proper proportions, polycrystalline rods 
of 10 mm diameter and 100 mm length with nominal composition 252055 AlFeNi  were prepared 
by radio-frequency induction-melting technique. A portion of these rods was melt-quenched to 
form 2 mm wide and mµ30≈  thick crystalline ribbons. The details about the sample 
preparation and actual composition are furnished elsewhere12. Vibrating reed experiments were 
performed on an absolutely flat ribbon strip of length 25 mm, which forms the reed. In such 
experiments, one end of the reed is clamped firmly to the base plate of the cryostat while a 
flexural resonance is set up at the other (free) end by an electrostatic drive via an electrode 
placed near that end. Another matching electrode (biased at 45 volts and connected to the input 
of a lock-in amplifier), placed against the opposite face of the reed, picks up the oscil lations by 
electrostatic coupling. The reference input to the lock-in amplifier comes from the same 
generator that feeds the drive electrode with sine wave amplitude variation, but locked to the 
second harmonic. At room temperature, the resonance curve is obtained by measuring the 
amplitude of vibration of the free end as a function of the driving frequency. From the resonance 
curve, so measured, the absolute value of internal friction, resQ νν /
1 ∆=− , (where ν∆  is the 
width of the resonance curve between the points at which the amplitude has the value 2/maxA  
 4 
if maxA  is the maximum ampli tude at the resonance frequency resν ) at room temperature is 
deduced as 31 105.6)7.293( −− == xKTQ . Subsequently, the resonance is phase-locked and 
tracked as the sample temperature is varied. The sound velocity, V, as a function of temperature 
is obtained from the fundamental (resonance) vibration frequency, ν , using the relation 
Vld 2)/875.1()34/( πν = , where d and l are the thickness and length of the sample reed. Note  
that we can measure only the relative changes in sound velocity, VV /δ , with respect to its value 
at room temperature because the unknown clamping yield causes a large uncertainty in the 
measurement of actual effective l. This is a standard problem with vibrating reed measurements. 
In the present experiments, the relative change in sound velocity and internal friction could not 
be resolved better than 100 ppm and 5 %, respectively. To highlight the changes that occur in 
)(1 TQ−  near the phase transitions and in the mixed-phase regime, the 1−Q  data taken at different 
temperatures have been normalized to the room temperature value 31 105.6)7.293( −− == xKTQ .  
 
        After compensating for the earth’s magnetic field, ac susceptibility, )(Tacχ , was measured 
at a driving magnetic field of rms amplitude Oehac 1=  and frequency Hz111=ν  over the 
temperature range 1.7 K to 300 K. The temperature variations of the real ( '0χ ) and imaginary  
( ''0χ ) components of ac susceptibili ty in the cooling (from 300 K to 1.7 K) and heating (from 
1.7 K to 300 K) cycles are depicted in figure 1. The thermal hysteresis in )('0 Tχ  and )(''0 Tχ , 
extending from KT eM 150≅  to KT eA 280≅ , is an experimental signature of the thermoelastic 
martensitic transformation. The characteristic temperature KT bM 260≅  ( KT bA 170≅ ) for the 
beginning of the growth of martensite (austenite) phase at the expense of austenite (martensite) 
 5 
phase while cooling (heating) corresponds to the temperature at which the cooling and heating 
curves bifurcate (the temperature at which )('0 Tχ  and )(''0 Tχ  exhibit a pronounced shoulder in 
the heating curve). These characteristic temperatures are in excellent agreement with those 
previously1 determined from )(Tρ  and ND data. The temperature range over which the 
martensite and austenite phases coexist extends from bMT  to eMT  on the cooling )('0 Tχ  or 
)(''0 Tχ  curve and from bAT  to eAT  on the heating curve. The Curie temperature, CT , is 
identified with the temperature corresponding to the dip in the temperature derivative of )('0 Tχ , 
dTTd /)('0χ , versus T curves. This ‘ inflection-point’ (in )('0 Tχ ) method yields KTC 223=  
( KTC 225= ) in the cooling (heating) run. 
 
        Figure 2 displays the temperature variations of VV /δ  and 1−Q  for q-Fe20, measured at a 
drive voltage of 7.9 V, when the sample is cooled down to 190 K. As the sample temperature 
decreases, VV /δ  declines while 1−Q  increases. This decline (rise) in VV /δ  ( 1−Q ) signals 
phonon “softening” in the premartensitic regime. The rate of decline in VV /δ  or equivalently, 
increase in 1−Q  slows down as the on-set temperature for the growth of the martensitic phase, 
KT bM 260≅ , is approached while cooling. This feature is followed, at bMTT < , by an upturn 
(downturn) in VTV /)(δ  ( 1−Q (T)) at KTup 236≅  and subsequently by a sharp drop (rise) at 
KTrap 232≅ . The temperature upT  ( rapT ) marks the stage within the mixed-phase regime at 
which the volume fraction of the tetragonal martensitic phase grows at a slow pace (starts 
growing at a very rapid rate) at the expense of the parent cubic austenite phase while cooling. 
These values of upT  and rapT  tally quite well with those corresponding to the upturn and steep 
 6 
rise observed in )(Tρ  previously1 and in )('0 Tχ  or )(''0 Tχ  now (Fig.1). The resonance phase-
lock is completely lost when the temperature falls below K218  so much so that the reed stops 
oscillating and the matching electrode picks up only spurious signals. An attempt was made to 
induce vibrations in the reed by increasing the drive amplitude from the normal value of 5V rms 
to 15 V rms but without success. Since the drive force varies as the square of the driving 
amplitude, this increase in the drive amplitude corresponds to about 10 times larger driving 
force. Consistent with our earlier observations1 based on the )(Tρ  and ND results, this 
“stiffness” of the reed is indicative of a massive martensitic transformation at such temperatures 
in the q-Fe20 sample.  
 
        To investigate the martensitic transformation (MT) in greater detail, three different 
experiments covering (a) the premartensitic regime, (b) part of the mixed-phase regime, and (c) 
the entire temperature range over which MT occurs, have been carried out. In these experiments, 
before heating the sample back to room temperature, the sample is cooled down to the 
temperature *T , which lies (a) above KT bM 260≅  ( KT 265
* ≅ ), (b) well below bMT  but not 
too deep into the austenite-martensite phase coexistence region ( upTKT ≅= 65.238
* ), and (c) 
well below the temperature KT eM 150≅ , which marks the end of the martensitic transformation, 
( KT 130* ≅ ). The results of the experiments (a) – (c) are shown in figures 3 – 5, respectively. 
These results, when viewed in the light of the relation ρ/EV = , where E is the Young’s 
modulus and ρ  is the mass density, imply the following. When bMTT >*  (case (a), 
premartensitic regime), VV /δ  and 1−Q , measured at a drive voltage of 7.9 V, both exhibit 
thermal hysteresis (Fig.3). While cooling from 294.5 K , the parent austenite phase remains 
 7 
“elasticall y stiff ” in its KT 5.294=  state till the temperature 291.5 K is reached when the 
phonon “softening” starts and this process continues til l KT 265* ≅ . On the other hand, in the 
heating cycle, the austenite phase in the “kineticall y arrested” metastable state, corresponding to 
*TT = , persists till the temperature reaches the value KT 275≅  (which is close to the 
characteristic temperature KT eA 280≅ ) beyond which the elastic recovery towards the room 
temperature parent austenite phase gets started. The elastic recovery process is nearly complete 
at KT 5.294=  when the thermoelastic hysteresis tends to vanish. These results assert that in the 
premartensitic regime, the parent austenite phase undergoes changes similar to those occurring in 
the high-temperature high-crystallographic-symmetry phase prior to a first order phase transition. 
When bMup TTT <≅
*  (case (b), Fig.4), the sample has barely entered into the two-phase regime 
and with temperature increasing from *T , the austenite phase does not recover fully to its room 
temperature elastic state even when eATT >  , instead the system retains partially the “memory” 
of the elastic state in the two-phase region. Consequently, unlike the major VV /δ - T and 1−Q - T 
thermal hysteresis loops (Fig.5), the minor VTV /)(δ  and )(1 TQ −  thermal hysteresis loops, 
taken at a drive voltage of 7.9 V, do not close at room temperature. By contrast when the sample 
is cooled down to eMTT <
*  (case (c), Fig.5) and the thermal cycling interval embraces the entire 
temperature range over with the MT takes place, VTV /)(δ  and )(1 TQ −  data, taken at a drive 
voltage of 2.13 V, exhibit a rich structure (i.e., peaks, minima, change of slope, etc.) 
symptomatic of the thermoelastic processes occurring in the two-phase region. Note that, as was 
the case in the previous experimental run (Fig.2), in this run too, the resonance phase-lock is 
completely lost when the temperature falls below K218  during cooling but the resonance phase-
lock is automatically restored when the temperature exceeds 218 K in the heating cycle. From 
 8 
the temperatures corresponding to the peaks, minima and change of slope in the VTV /)(δ  and 
1−Q (T) curves marked in Fig.5, the following important observations can be made. (i) The 
characteristic temperatures bMT , eAT   and  CT  are more sharply defined in the sound velocity 
and internal friction data than in the )(Tρ  (reference 1) and )('0 Tχ  or  )(''0 Tχ  data (Fig.1). (ii ) 
In the heating cycle, the system remembers the initiation (marked by the peak in VTV /)(δ or dip 
in )(1 TQ− at KTT bM 260== ) and subsequent growth (represented by the dip in VTV /)(δ or 
peak in )(1 TQ−  at KT 236= ) of the martensitic phase (at the expense of the parent austenite 
phase) that had occurred during the cooling cycle in the two-phase regime. (iii ) In both cooling 
and heating cycles, VTV /)(δ  ( )(1 TQ − ) exhibits pronounced minima (peaks) corresponding to 
the Curie temperatures KTC 223=  and KTC 225= , obtained from the dTTd /)('0χ  data 
(Fig.1). 
 
        In short, we report the elastic anomalies associated with the austenite – martensite phase 
transitions as they manifest themselves in the sound velocity and attenuation data and establi sh 
correlations with the results obtained by other standard but indirect measuring techniques such as 
electrical resistivity and magnetic susceptibil ity. Detailed vibrating reed measurements on 
252055 AlFeNi  samples with varied degree of site disorder and the analyses of the results, so 
obtained, are in progress. 
 9 
REFERENCES 
     
 1S. N. Kaul, B. A. D’Santhoshini, A. C. Abhyankar, L. Fernández Barquin and P. 
  Henry, Appl. Phys. Lett. 89, 093119 (2006). 
 
 2G. Guenin, Phase Transitions 14, 165 (1989). 
 
 3Shape Memory Materials, edited by K. Ostuka and C. M. Wayman (Cambridge 
  University, Cambridge, 1998). 
 
 4S. M. Shapiro, B. X. Yang, Y. Noda, L. E. Tanner and D. Schryvers, Phys. Rev. B 44, 
  9301 (1991). 
 
 5H. Morito, A. Fugita, K. Fukamichi, R. Kainuma, K. Ishida and K. Oikawa, Appl. Phys. 
  Lett. 83, 4993 (2003). 
 
 6P. J. Brown, K. Ishida, R. Kainuma, T. Kanomata, K. –U. Meumann, K. Oikawa, B. 
  Ouladdiaf and K. R. A. Ziebeck, J. Phys.: Condens. Matter 17, 1301 (2005). 
 
 7M. Zhang, E. Brück, F. R. de Boer and G. Wu, J. Phys. D: Appl. Phys. 38, 1361 (2005). 
 
 8Z. Song, S. Kishimoto, J. Zhu and Y. Wang, Solid State Commun. 139, 235 (2006); 
  R. Kainuma, Y. Imano, W. Ito, Y. Sutou, H. Morito, S. Okamoto, O. Kitakami, K.  
  Oikawa, A. Fujita, T. Kanomata and K. Ishida, Nature Lett. 439, 957 (2006). 
 10 
 
 9P. K. Mukhopadhyay and A. K. Raychaudhuri, J. Phys. C: Solid State 21, L385 (1988); 
  J. Appl. Phys. 67, 5235 (1990). 
 
10K. Balakrishnan, P. D. Babu, V. Ganesan, R. Srinivasan and S. N. Kaul, J. Magn. 
   Magn. Mater. 250, 110 (2002). 
 
11K. Balakrishnan and S. N. Kaul, Phys. Rev. B 65, 134412 (2002). 
 
12B. A. D’Santhoshini and S. N. Kaul, J. Phys.: Condens. Matter 15, 4903 (2003). 
 
 
 11 
FIGURE  CAPTIONS 
 
 
FIG. 1. Temperature variations of the real ( ) and imaginary  ( )  components of ac 
susceptibility in the cooling (open circles) and heating (continuous curves) cycles. The 
characteristic temperatures for the beginning,   ( ), and end,   ( ), of the growth of 
martensite (austenite) phase during cooling (heating) are indicated. 
 
 
FIG. 2. The temperature variations of sound velocity, VV /δ , and internal friction, 
1−Q ,  
measured at a drive voltage of 7.9 V, when the sample is cooled down to 190 K. The values 
of the temperatures marking the characteristic features in these curves are indicated. 
 
FIG. 3. The temperature variations of sound velocity, VV /δ , and internal friction, 
1−Q ,  
measured at a drive voltage of 7.9 V, when the sample undergoes thermal cycling between 
265 K and 294.5 K in the premartensitic regime. The values of the temperatures marking 
the characteristic features in these curves are indicated. 
 
 12 
FIG. 4. The temperature variations of sound velocity, VV /δ , and internal friction, 
1−Q ,  
measured at a drive voltage of 7.9 V, when the sample undergoes thermal cycling between 
238.5 K and 293 K. The values of the temperatures marking the characteristic features in 
these curves are indicated. 
 
FIG. 5. The temperature variations of sound velocity, VV /δ , and internal friction, 
1−Q ,  
measured at a drive voltage of 2.13 V, when the sample undergoes thermal cycling between 
130 K and 296 K. The values of the temperatures marking the characteristic features in 
these curves are indicated. 
 
 13 
 
 
                            
0
1
2
3
4
Cooling
Heating
219 K 211 KQuenched
Ni
55
Fe
20
Al
25
T
Ae
= 280 K
T
Ab
= 170 K
T
Me
= 150 K
T
Mb
= 260 K
 
 
 
T    ( K )
χχ  
0
''   
  
 (
 1
0
 -
 3
 e
m
u
 /
 g
O
e 
)
χχ  
0'
   
  
( 
1
0 
- 
2
 e
m
u
 /
 g
O
e 
)
T
up
= 236 K
0 100 200 300
0.0
0.8
1.6
T
Ae
= 280 K
T
Mb
= 260 K
T
Me
= 150 K
T
Ab
= 170 K
 216 K
 
  
 206 K
 
 
 
 
 
                                                                FIG. 1.  
 
 
 
 
 
 14 
 
 
                           
0
2
4
6
8
10
12
220 240 260 280 300
1
10
100
218 K
  T
up
= 236 K
231.5 K TMb= 260 K
T    (K)
Q
-1
δδV
 /
 V
  
  (
 1
0
 -
 5
 )
Quenched
Ni
55
Fe
20
Al
25
 
 
 
 
 
 
 
 
 
 
                                                            FIG. 2.  
 
 
 
 
 
 15 
 
 
                         
5.0
6.0
7.0
8.0
260 270 280 290 300
1.0
1.2
1.4
1.6
1.8
      291.5 K
      294.5 K
275 K
 265 K
T
Ae
= 280 K
 
 
δδV
 /
 V
  
  (
 1
0
 -
 5
 )
Quenched
Ni
55
Fe
20
Al
25
 
 
T > T
Mb
= 260 K
 Cooling
 Heating
T     (K)
Q
-1
  
 
 
 
 
 
 
                                                              FIG. 3.  
 
 
 
 
 
 16 
                              
3
4
5
6
7
8
240 260 280 300
1.0
1.5
2.0
2.5
Quenched
Ni
55
Fe
20
Al
25
 
247 K238.5 K
T
Mb
= 260 K
275 K
T
Ae
= 280 K
δδV
 /
 V
  
  (
 1
0
 -
 5
 )
 
 
Cooling
 Heating
 T    (K)
  Q
-1
  
 
 
 
 
 
                                                                      FIG. 4.  
 
 
 
 
 
 
 17 
                              
0.0
0.3
0.6
0.9
225 250 275 300
0.1
1
10
 221 K
 275 K
 244 K
 277 K
 260 K
 236 K
 T
Ae
= 280 K
 T
C
= 225 K
 T
Mb
= 260 K
T     (K)
Q
-1
  
 
δδV
 / 
V
   
 (
 1
0
 -
 5
 )
 
Quenched
Ni
55
Fe
20
Al
25
 
 
 240 K
 222 K
 236 K
 T
C
~ 225 K
Cooling
Heating
 
 
 
 
 
 
 
                                                                    FIG. 5.  


http://repository.ias.ac.in/29810/1/361.pdf

Dynamic elastic properties and magnetic susceptibility across the
  austenite-martensite transformation in site-disordered ferromagnetic Ni-Fe-Al
  alloy

Dynamic elastic properties and magnetic susceptibility across the austenite-martensite transformation in site-disordered ferromagnetic Ni-Fe-Al alloy

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