Acoustic phonon mode condensation in Ni2MnGa compound

Solid State Communications, Vol. 101, No. 1, pp. 7-9, 1997 Copyright @ 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 003%1098/97 $17.00+.00

Pergamon

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 physical properties in the temperature interval which precedes the martensitic 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 dispersion 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 detected 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 lattice 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 maxima 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 considerably during cooling [l], with simultaneous decrease of LOfor 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 LOdoes 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 displacements 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 frequency 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 dependence of elongation and internal friction (IF) and elastic modulus ( El) were studied. The IF and El spectra were measured in three-point bending configuration at a frequency v = 2 Hz. An oscillating applied stress (T = a0 exp i(2nvt) causes a strain of the specimen given by E = EOexp 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

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ACOUSTIC PHONON MODE CONDENSATION

ON

IN NizMnGa COMPOUND

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220

180

TEMPERATURE (K) Fig. I. Temperature dependence of the thermal expansion coefficient during cooling. 7 4: 2

0Z? 0 x 3.0.

‘3.0

; B

6

s g tl

2 s

2.0

P

1.0 100

150

g

.

iz

.I.0

a

.

E 6

250

200 TEMPERATURE

.2.0

(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 display two anomalies, namely, a IF maximum (and modulus 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 scattering intensities in a temperature interval 150-300 K including T, and TM temperatures were studied. Typical 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 lattice parameter at T < TI becomes three times larger. While at T > TI the atoms of the initial crystal lattice fluctuate around their equilibrium positions coinciding 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 distribution 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

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ACOUSTIC PHONON MODE CONDENSATION

to the appearance of the extra spots system (Fig. 3b). The mean square displacement of atoms as a function of frequency for Rw << kT can be expressed (see, e. g., [4]): (%I2 - kT/NMw2(q),

(1)

where 1uq I* is the contribution of the phonon with wave vector q and frequency w to the atom mean square displacement, N is the number of atoms with mass A4 and k is the Boltzmann constant. As follows from the above formula, the contribution of vibrations with q f 0 and w - 0 dominates, and hence the amplitudes of the thermal vibrations of atoms increase at temperatures where the lowest values of w for the TA2 mode occur. This increase in amplitude results in the enlargement of the interatomic distances due to the anharmonic effects. As a result, a minimum of fi occurs (Fig. 1). The local decrease of elastic modulus (Fig. 2, curve 2) is also related to the increase of lattice parameter. The maximum of tan 6 at T = fi (Fig. 2, curve 1) can arise from domain boundaries appearing during the formation of the low temperature premartensitic phase, which has a three times larger lattice parameter. The motion of these boundaries under the oscillating applied stress is accompanied by an energy dissipation, 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 transforms 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.

IN NizMnGa COMPOUND

9

In summary, it is concluded that condensation of the TA2 phonon mode with q f 0, which is manifested as

a premartensitic phase characterized by the multiplycation of the high temperature phase unit cell, takes place. Such kind of condensation is a relatively new phenomenon for metallic systems. The premartensitic phase is interpreted as intermediate between the parent and martensite phases. The thermal expansion coefficient and elastic modulus minima at T = Tr are associated with the enhancement of the mean-square displacement of atoms at temperatures where the TA2 mode frequency is anomalously low. Acknowledgements-V. A Chernenko is grateful to the Universitat de les Illes Balears for financing his stay at the Departament de Fisica. REFERENCES

1. G. Fritsch, V V. Kokorin and A. Kempf, J. Phys. Condens. Matter 6, 107, (1994). 2. A. Zheludev, S. M. Shapiro, P. Wochner, A. Schwartz, M. Wall and L. E. Tanner, Phys. Rev. B, 51, 11310 (1995). 3. V. V. Kokorin, Phase Transitions, 54, 143 (1995). 4. J. A. Reissland, Physics Phonons, p. 368. New York, London (1973).