Pergamon Sctipta Metallurgica et Materialia, Vol. 31, No. 2, pp. 203-208, 1994

Copyright ©1994 Elsevier Science Ltd Printed in the USA. All rights reserved

0956-716X/94 $6.00 + 00

UNIAXIAL STRESS D E P E N D E N C E OF T H E [ ~ 0 ] - T A 2 P H O N O N BRANCH IN Ni6oAho

Ling Ye, S. M. Shapiro, and Henry Chou Department of Physics, Brookhaven National Laboratory

Upton, NY 11973

(Rece ived F e b r u a r y 1, 1994) (Rev i sed March 30, 1994)

Over the past decade there have been extensive experimental and theoretical studies of Martensite t ransformations (MT)(1) in metallic alloys, aiming at a fundamental understanding of this transition. Much of the work has concentrated on precursor or premartensite effects prior to the actual phase transformation(2-4). Although the understanding has not yet converged, it is generally agreed that the strain fluctuations in the parent lattice are crucial for the occurrence of a MT. Many studies have focused on NixAll_x alloys, which undergo a MT for 60 < x < 64 from a CsCI structure parent (1~) phase to a low temperature martensite phase at transition temperature TM. For T > TM, a strongly temperature dependent phonon anomaly and temperature dependent diffuse scattering are observed by neutron scattering. In

1 . Ni62.sA137.5, an anomaly exists in the [ ~ 0 ] - T A 2 phonon branch at ~ = ~wMch becomes

more pronounced as the temperature is reduced toward TM = 85 K(2,3). At the same value, an elastic diffuse central peak is found near room temperature, whose intensity increases as temperature decreases, and reaches a maximum around TM. Below TM, a

1 new 7M martensite structure appears(5,6)with Bragg peaks occurring near ~ = 7 '

These precursors are commonly recognized as a consequence of the structural micro-modulation of the parent phase. That is, numerous internal strain centers caused by defects, impurities or internal stress serve as embryos that perturb the parent lattice. They couple to the homogeneous lattice strain and develop as arrays of coherent-strain embryos of the product phase which are embedded within the parent phase. Indeed, experimental observation of these local premartensite structures have been made by using high resolution electron microscopy on Ni62.sAI37.5(3,7,8), which shows a mosaic assembly of contiguous domains of 4-6 nm in diameter that perturb the cubic parent lattice. Within those domains the micromodulated structure appears as diffuse bands parallel to [ l l0]cplanes . In addition, both the wave vector, 4, of the [ ~ 0 ] - T A 2 anomalous phonon mode and the TM are composition and stress dependent. It was found(3) tha t as x varies from 50 to 64, the dip in the anomalous [ ~ 0 ] - T A 2 phonon mode gets more pronounced and ~ decreases as x increases, while TM increases.

Recently, Shapiro et al (9)performed a detailed investigation of the uniaxial stress dependence of the phonon behavior in the parent phase of Ni62.5A137.5. Their results

203

204 [~0]-TA2 PHONON BRANCH Vol. 31, No. 2

indicate that both the temperature and the uniaxial stress could dramatically affect the dispersion curve of the [ ~ 0 ] - T A 2 phonon branch. The applied stress leads to a shift of the phonon anomaly toward higher wavevector ~, and the linewidth of the phonon spectra increases as the stress increases. The latter was interpreted according to Clapp's localized soft mode theory(10) of nucleation in Martensite, as the possibility of a distribution of different phonon energies corresponding to different regions of the crystal where the shear strains are different.

Studies of precursor phenomena in Ni62.5A137.5 have demonstrated that applying uniaxial stress on NixAll .x alloys could "trigger" a NIT at higher temperature due to the martensite nucleation processes. In Ni62.5A137.5, the martensite transition temperature increases linearly from 85 to 300 K when a uniaxial stress was applied from 0 to 150 MPa. For x = 60 no MT occurs and this seems to be near the lower limit of composition where a MT occurs. In this work, we explore the possibility of inducing a MT in Ni60Al40 by applying a uniaxial stress. We mainly focus on the uniaxial stress dependence of the [ ~ 0 ] - T A 2 phonon mode and the associated elastic diffuse scattering as a function of applied stresses.

The Ni60A140 crystal used in this study is cubic in shape with dimensions about 3.6 x 3.6 x 3.6 mm3 in volume. Four of the six faces are perpendicular to the <110> directions, and the other two are perpendicular to the <001> directions. During experiments, the uniaxial stress is applied along the [001] direction and the scattering plane was perpendicular to this direction. The lattice parameter is .2867 nm and the crystal mosaic is about 30' in the stress-free condition at room temperature. The crystal mosaic increases with increasing stress.

A calibrated torque-wrench is used to apply a uniaxial stress to the sample by a clamp device, which consisted of an aluminium frame as a jig, and a steel screw compressing the crystal mounted in the jig. Contact areas between sample and both the screw and the frame are sealed with Pb films in order to smooth out the stress on the crystal. The clamp device could be enclosed in an aluminum can filled with helium gas and attached to the cold finger of a closed-cycle refrigerator. Changing the stress necessitated removing the sample from the refrigerator and changing the applied torque .

Inelastic neutron scattering measurements were carried at the High Flux Beam Reactor at Brookhaven National laboratory, on a triple axis spectrometer with fixed final neutron energy of 14.7 mev and collimations of 40'-20'-40'-40' between reactor- monochromator , monochromator - sample , sample-analyzer , and ana lyzer -de tec tor , respectively. Pyrolytic graphite (002) reflections were used for the mononchromator and the analyzer, and a PG filter was used after the sample to eliminate higher-order contaminat ion .

Measurements of the low energy part of the [ ~ 0 ] - T A 2 phonon branch were

performed along the [ 1 1 0] direction near the (1,1,0,) reciprocal lattice vector. Elastic

Vol. 31, No. 2 [~0]-TA2 PHONON BRANCH 205

diffuse scattering was mostly measured along the [1 1 0] direction at the (2,0,0)

reciprocal lattice vector in order to avoid the effects of the crystal mosaic. Measurements of the lattice parameter as a function of stress were obtained from longitudinal elastic scans through the (1,0,0) Bragg peak.

R e s u l t s a n d D i s c u s s i o n

The uniaxial stress dependence of the lattice parameter measured perpendicular to the applied stress at room temperature in Ni60A140 is shown in Fig. 1 and compared with the previous measurements(3) on Ni62.sA137.5. The lattice parameter increases linearly along [I00] with increasing stress along the [001] direction. However, its slope is considerably less than previously observed in the x = 62.5 alloy in this figure. A smaller slope of the stress dependence of lattice parameters indicates that it exhibits a "stiffer" behavior relative to Ni62.5AI37.5. These measurements can be compared with one of the reciprocal elastic modulus, S12, defined as the ratio of the strain measured along the direction perpendicular to the applied stress. The calculated 512 from our neutron data for x= 60 and 62.5 are 2.42 x 10-5/MPa and 6.25 x 10-5/MPa, respectively, which are greater by 22% of the neutron data compared with that calculated from elastic constant measurements using the ultrasonic technique(l 1,12). This difference could be resulted from the systematic error of two measurement techniques. For instance, the applied uniaxial stress might not distribute homogeneously on the entire sample, which would lead to an experimental error on the precisely determination of the lattice parameter under the stress.

2 . 8 8

o<

2 . 8 7

2.81

I " i - I

Ni6zsA137.1/ ~f

. . . . I . . . . I . . . I . . ,

5 0 100 150 200 o(MPa)

Fig. 1 A comparison of the uni- axial stress dependence of lattice parameters in Ni60AI40, measured in this work, and Ni62.sAI37.5 mea- sured in Ref. 3.

1000

800

c 600 E

I n

400

= 200

~, 2S0

QO 2 0 0 - e- 0

1 5 0 . m

1 0 0 .

T=295 K ~= 0.18 T= 10K

o = 0 MPa T ~ t ¢

t ot S

0=168 MPa ~

5 0. teeeee

0 C " I : 2

(a) (c) o = 0 MPa

(b) (d) o = 168 MPa

o

i s ~ 1 2 3 4 s 6 E (mev)

Fig. 2 Uniaxial stress and temperature depen- dences of the inelastic neutron spectre of anoma- lous [~0]-TA2 phonon mode with 4=0.18. (a) and (b) are measured at room temperature with stress of 0 and 168 MPa; (c) and (d) are measured at T=10K with stress of 0 and 168 MPa.

206 [~0]-TA2 PHONON BRANCH Voi. 31, No. 2

The [ ~ 0 ] - T A 2 phonon spectra with ~ = 0.18 with/without stress and two different temperatures are shown in Figure 2. At room temperature the dispersion curve is nearly stress independent but the phonon energy decreases with increasing applied stress and a lowering of the temperature. Figure 3 is a summary of the stress dependence of the low energy portion of the [ ~ 0 ] - T A 2 phonon dispersion curve. For reference the zero-stress, room temperature dispersion curve is also presented. It is seen that there is a decrease in the phonon energy with temperature and a minimum develops near ~ = 0.16 at T = 10K. Application of a stress causes a further reduction of the energy and the minimum becomes more well defined and shifts to a larger ~ = 0.19 at a = 168 MPa. This observation is similar to those in the transforming alloy, Ni62.sAI37.5, where the origin of the phonon anomaly has been shown to be due to a q- dependent electron-phonon interaction, arising, in part, from a nesting of the Fermi surface(13). Based on these calculations, the increase of ~ with increasing stress is due to an increase of the Fermi energy with stress, and the anomalous changes observed are due to the stress dependence of the electron-phonon coupling.

A >

E

Ul

. . . . I . . . . I . . . . I . . . . I . . . . I . . . .

MPa, 295K

P B 102 MPa, 10K

0 0.1 0 .2 0 .3

Fig. 3 Uniaxial stress dependence of the low-frequency part of the [r,~0]-TA2 phonon branch at T=10K and 295K with zero stress, and at T=10K with 102 and 168 MPa. Lines are guides to the eye.

In addition to the anomalous phonon behavior, there is a significant amount of elastic diffuse scattering along the [ ~ 0 ] direction which is both temperature and stress dependent. Figure 4a shows the stress dependence of this elastic diffuse scattering measured at T = 10 K and Fig. 4b is the temperature dependence measured at a constant stress, a = 168 MPa. Both show clearly that the diffuse scattering increases with increasing stress and decreasing temperature which reflects a developing of structural modula t ions in the parent phase due to the intensif ied strain and

Vol. 3 l, No. 2 [~0]-TA2 PHONON BRANCH 207

temperature induced nucleation of Martensite regions in the parent phase. The wavevector, ~, of the satellite shifts to larger values with increasing stress and ~ = 0.195 at 168 MPa, which is the same value where the phonon minimum occurs in the dispersion curve (Fig. 3). The temperature dependence of the maximum of the diffuse scattering is plotted for different stress in Fig. 5. It is clear that for the higher stress Imax diverges at low temperature. This, coupled with the phonon softening, suggests that a phase transition would occur if a higher stress could be achieved. Unfortunately, in our experiment the crystal fractured when we tried to increase the stress to 220 MPa.

E Soo

1=oo

ooo Q

NImAI ~ [2-r..~,0] AS: : 0 1,500

E (1) . . . . . . . . . . ; 0 MF;a," I~ " o io2 MPa, IOK X 168 MPa, 10K

1000 xx X

X X X X

X o o O O x X x O O X

~Oe~° °Oo o O X e e O o ~ R ~

e e o l o e e J

(b) x I o K x x Q 1 0 0 K

X • 295 K X

168 MPm × x ×

X X n o n T X X X m _ O [ ] X

4 0 0 1 0 o O O ~ U o X

' ~ A & A & A & A A & . A °o~B 0 l . . . . .

0.10 0.15 ' ' (T).J20 ' ' ' ~).25 0.30 ¢

Fig. 4 Uniaxial stress and temperature dependences of the elastic diffuse scatter-

ing measured along [~ ~ 0] direction. (a) is measured at T=10K with uniaxial stre- sses of 0, 102 and 168 MPa; (b) is mea- sured at 168 MPa with temperatures of 10, 100 and 295K.

1 2 0 0

8 0 0

j,.q I~

4 0 0

I I I I I . . .

.~ N 16°AI4° × 0MPa

o 102 MPa ~ • 168 MPa

i i i i i . . . . . . . . t . . . . i . . . . i . . . . J ' ' ' ' J i

0 100 200 ~00

T (K)

Fig. 5 Temperature dependences of the peak intensity of satellites measured

with uniaxial stresses of 0, 102 and 168 MPa.

In conclusion, both the [ ~ 0 ] - T A 2 phonon anomaly and the elastic structural modulations appearing as diffuse satellites are intensified with an increasing stress at low temperature, and the wavevector position ~ of the phonon anomaly, as well as the elastic central peak, shifts to a higher value as the stress increases. Even though no MT occurs for the maximum applied stress o = 168 MPa, a MT is likely to be induced at higher stress.

208 [~0]-TA2 PHONON BRANCH Vol. 31, No. 2

p, c k n o w l e d ~ e m e n t s

The authors appreciate the helpful discussions with P. Clapp, Y. Noda, J. Trivisonno and L. E. Tanner who also supplied the sample. This work is supported by the Division of Material Science, U.S. Department of Energy, under Contract No. DE-AC02-76CH0016.

R e f e r e n c e s

1. See Z. Nishiyama, Martensitic Transformations (Academic, New York, 1978) 2. S.M. Shapiro, B. X. Yang, G. Shirane, J. Z. Larese, L. E. Tanner and S. C. Moss, Phys.

Rev. Letters 62, 1298 (1988). 3. S.M. Shapiro, B. X. Yang, Y. Noda, L. E. Tanner and D. Schryvers, Phys. Rev. B44,

9301 (1991). 4. M. Liu, T. R. Finlayson, T. F. Smith and L. E. Tanner, Mater. Sci. Eng. A157, 225,

(1992). 5. V.V. Martynov, K. Enami, L. G. Khandros, S. Nenno and A. V, Tkachenko, Phys. Met.

Metall. 55, 136 (1983) 6. Y. Noda, S. M. Shapiro, G. Shirane, Y. Yamada and L. E. Tanner, Phys. Rev. B42,

10397 (1990). 7. L .E. Tanner, D. Schryvers and S. M. Shapiro, Mater. Sci. Eng. A127, 205, (1990). 8. SD. Schryvers and L. E. Tanner, Ultramicroscopy. 32, 241, (1990). 9. S .M. Shapiro, E. Svensson, C. Vettier and B. Hennion, Phys. Rev. B48, 13223

(1993). 10. P. C. Clapp, Phys. Status Solidi B 57, 561, (1973); Mater. Sci. Eng. A127, 189,

(1990). 11. L. Zhou, P. Comely and J. Trivisonno, Proce. IEEE Ultrasonic Symposium,

1309, (1990). 12. N. Rusovic and H. Warlimont, Phys. Status Solidi 44, 609, (1977). 13. G. L. Zhao and B. N. Harmon, Phys. Rev. B45, 2818 (1992)