Pergamon Solid State Communications, Vol. 101, No. 1, pp. 7-9, 1997

Copyright @ 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved

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PII:SOO38-1098(96)00550-9

ACOUSTIC PHONON MODE CONDENSATION IN NizMnGa COMPOUND

V. V. Kokorin, a V. A. Chernenko, a J. Pons, b C. Segu b and E. Cesari b

a Institute of Magnetism, 252680 Kiev, Ukraine b Universitat de les Illes Balears, E-07071 Palma de Mallorca, Spain

(Received 30 April 1996; accepted 17 September 1996 by H. Eschrig)

The structural changes as well as the anomalies displayed by some phys- ical properties in the temperature interval which precedes the marten- sitic transformation in NizMnGa compound have been studied. It is concluded that the TA2 soft phonon condensation at T = TI > TM (TM being the martensitic transformation temperature) is responsible for the behaviour mentioned above. Copyright @ 1996 Elsevier Science Ltd

Keywords: A. metals, C. crystal structure and symmetry, D. phase transition.

The existence of TA2 soft phonon mode (with both wave vector 4 and polarisation vector e parallel to (110) type directions) in NizMnGa compound was first reported in Ref [l]. The corresponding disper- sion curves w(q) were recently obtained by means of inelastic neutron scattering measurements [2], and a minimum on LO (q) curve for TA2 [ 5501 mode was de- tected at 50 = 0.33. The compound NizMnGa has L2t type ordered structure with a lattice parameter a = 0.582 nm; however, due to the small difference between the atomic scattering factors of the alloy components, this structure appears as a bee structure with a lat- tice parameter a0 = 0.291 nm in the X-ray diffraction spectra. In this case the relation 50 = l/3 : 27-r/a = 1/6.2n/ao will hold. Therefore the extra diffuse max- ima on X-ray diffraction patterns [1] are spaced from the basic reflections along < 110 > type directions by 0.165-r (T is the magnitude of the reciprocal lattice vector connecting the nearest main reflections along < 110 >). These diffuse maxima correspond to the wave vector with the minimum frequency w [2]. The intensity of X-ray extra maxima increases consider- ably during cooling [l], with simultaneous decrease of LO for the mentioned phonons [2]. From the above described situation, an anomalous behaviour of the physical properties in the temperature interval where significant softening of the phonon mode TA2 occurs can be anticipated. Despite LO does not reach a zero value [2], indeed, the possibility of the TA2 soft mode

condensation as a first order transformation exists. For instance, the surface phonon frequencies are always lower than those in the bulk; hence the free surface is a preferable site for the nucleation of the new phase [3]. In our case the local lattice regions where the atom dis- placements associated with the TA2 mode are frozen can be taken as the nucleation centers.

The goal of the present work is to investigate the structure and physical properties of the NizMnGa compound in the temperature interval where the fre- quency of the TA2 phonon mode takes its minima values.

Monocrystalline specimens of this compound with slightly changed composition in comparison to that used in [l, 21 were studied. The temperature depen- dence of elongation and internal friction (IF) and elas- tic modulus ( El) were studied. The IF and El spec- tra were measured in three-point bending configura- tion at a frequency v = 2 Hz. An oscillating applied stress (T = a0 exp i(2nvt) causes a strain of the spec- imen given by E = EO exp i(2nvt + 61, where 6 is the phase shift between the applied load and the bending strain response. The internal friction is obtained as tan 6 and the elastic modulus as El = (u,-,/Eo) cos b. X-ray and electron diffraction measurements were also performed.

Figure 1 shows the temperature dependence of the thermal expansion coefficient, 8, during cooling. Two minima of /3(T) can be observed at T = TI - 200 K

7

8 ACOUSTIC PHONON MODE CONDENSATION IN NizMnGa COMPOUND Vol. 101, No. 1

ON 180 220

TEMPERATURE (K)

Fig. I. Temperature dependence of the thermal expan- sion coefficient during cooling.

7 Z?

4: 0 2 0 x 3.0.

‘3.0 2 s

; B 6

s .2.0 g

g tl 2.0

. iz

P .I.0 a

. E

1.0 6

100 150 200 250

TEMPERATURE (K)

Fig. 2. Temperature dependence of internal friction (1) and elastic modulus (2) during heating.

and T = TM - 160 K. In Fig. 2 it can be seen that both the IF (curve 1) and modulus (curve 2) also dis- play two anomalies, namely, a IF maximum (and mod- ulus minimum) at T = TI preceding the IF maximum (and Et minimum) corresponding to the martensitic transformation at T = TM. The mentioned anomalies resulted to be reversible on cooling and heating the specimens.

The distribution of X-ray and electron diffuse scat- tering intensities in a temperature interval 150-300 K including T, and TM temperatures were studied. Typ- ical electron diffraction patterns are presented in Fig. 3. The diffuse X-ray and electron scattering observed at 300 K (Fig. 3a) is replaced by extra sharp reflections in the temperature interval TM < T < TI (Fig. 3b).

DISCUSSION

From Fig. 3, it can be seen that the cubic symmetry of the crystal lattice of the high temperature parent phase is kept unchanged even at temperature T < TI. The electron diffraction patterns of thin foils with other zone axes confirm this conclusion. The system of ex-

Fig. 3. Electron diffraction patterns obtained at (a) 300 K and (b) 195 K (< 100 > zone axis).

tra spots (Fig. 3b) indicates the multiplycation of the initial unit cell. In relation to the L2t structure the lat- tice parameter at T < TI becomes three times larger.

While at T > TI the atoms of the initial crystal lat- tice fluctuate around their equilibrium positions coin- ciding with the L21 crystal lattice positions, at T < TI

the equilibrium positions of atoms correspond to the initial lattice modulated by the static displacement waves corresponding to the TA2[550] (5 = 0.33) phonon mode. The evolution of diffuse intensity dis- tribution can be explained as follows. As a result of a TA2 soft mode existence in high temperature phase at T > TI, dynamic local regions are formed. The atoms belonging to these regions are displaced from their equilibrium positions in accordance with the given polarization and wave vectors of the soft vibration mode. When approaching to temperature TI an increasing in life mean-time and mean-size of these regions occurs. Therefore, during cooling the intensity of the diffuse maxima labeled by arrows in Fig. 3a increases and their width decrease. The size and life time of regions during phase transformation at T = TI become infinitely large, which corresponds

Vol. 101, No. 1 ACOUSTIC PHONON MODE CONDENSATION IN NizMnGa COMPOUND 9

to the appearance of the extra spots system (Fig. 3b). In summary, it is concluded that condensation of the The mean square displacement of atoms as a func- TA2 phonon mode with q f 0, which is manifested as

tion of frequency for Rw << kT can be expressed a premartensitic phase characterized by the multiply- (see, e. g., [4]): cation of the high temperature phase unit cell, takes

(%I2 - kT/NMw2(q), (1) place. Such kind of condensation is a relatively new phenomenon for metallic systems. The premartensitic

where 1 uq I * is the contribution of the phonon with phase is interpreted as intermediate between the par-

wave vector q and frequency w to the atom mean ent and martensite phases. The thermal expansion co-

square displacement, N is the number of atoms with efficient and elastic modulus minima at T = Tr are

mass A4 and k is the Boltzmann constant. As follows associated with the enhancement of the mean-square

from the above formula, the contribution of vibrations displacement of atoms at temperatures where the TA2

with q f 0 and w - 0 dominates, and hence the mode frequency is anomalously low.

amplitudes of the thermal vibrations of atoms increase Acknowledgements-V. A Chernenko is grateful to the

at temperatures where the lowest values of w for the Universitat de les Illes Balears for financing his stay at

TA2 mode occur. This increase in amplitude results the Departament de Fisica.

in the enlargement of the interatomic distances due to the anharmonic effects. As a result, a minimum of fi REFERENCES occurs (Fig. 1). The local decrease of elastic modulus (Fig. 2, curve 2) is also related to the increase of lattice 1. G. Fritsch, V V. Kokorin and A. Kempf, J. Phys. parameter. Condens. Matter 6, 107, (1994).

The maximum of tan 6 at T = fi (Fig. 2, curve 1) 2. A. Zheludev, S. M. Shapiro, P. Wochner, A. can arise from domain boundaries appearing during the formation of the low temperature premartensitic

Schwartz, M. Wall and L. E. Tanner, Phys. Rev. B, 51, 11310 (1995).

phase, which has a three times larger lattice parameter. 3. V. V. Kokorin, Phase Transitions, 54, 143 (1995). The motion of these boundaries under the oscillating 4. J. A. Reissland, Physics Phonons, p. 368. New applied stress is accompanied by an energy dissipation, York, London (1973). which is reflected in tan 6 behaviour. The nature of these boundaries is, at this moment, unclear.

The premartensitic phase which is formed at T = Tr exists in a relatively narrow temperature interval (TM < T < T,), and on further cooling it trans- forms martensitically, giving rise to the behaviour of the properties displayed in Figs 1 and 2 at T = TM. As follows from the low temperature electron microscopy observations, the martensitic transformation in this case results in the formation of tetragonal long-period structures.