Elastic constants of bcc CuAl-Ni alloys

We have measured the adiabatic elastic constants of two Cu-Al-Ni martensitic alloys using ultrasonic methods and we have compared the results to recent neutron-scattering experiments. It is shown that the elastic behavior of Cu-Al-Ni alloys follows the same trends exhibited by other Cu-based alloys; in particular, the TA2 long-wavelength acoustic modes are softer than all other modes. Disciplines Condensed Matter Physics | Metallurgy Comments This article is from Physical Review B 49 (1994): 9969–9972, doi:10.1103/PhysRevB.49.9969. Authors Lluís Mañosa, M. Jurado, Antoni Planes, Jerel L. Zarestky, Thomas A. Lograsso, and C. Stassis This article is available at Iowa State University Digital Repository: http://lib.dr.iastate.edu/ameslab_pubs/106 PHYSICAL REVIEW B VOLUME 49, NUMBER 14 Elastic constants of bcc Cu-Al-Ni alloys 1 APRIL 1994-II Ll. Manosa, M. Jurado, and A. Planes Departament d Estructura i Constituents de la Materia, Facultat de Fr'sica, Uniuersitat de Barcelona, Diagonal 647, E-08028 Barcelona, Catalonia, Spain J. Zarestky, T. Lograsso, and C. Stassis Ames Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 500II (Received 7 December 1993) We have measured the adiabatic elastic constants of two Cu-Al-Ni martensitic alloys using ultrasonic methods and we have compared the results to recent neutron-scattering experiments. It is shown that the elastic behavior of Cu-Al-Ni alloys follows the same trends exhibited by other Cu-based alloys; in particular, the TA2 long-wavelength acoustic modes are softer than all other modes.


I. INTRODUCTION
The stability of the bcc structure exhibited by a num- ber of metals and alloys has been the subject of continu- ous interest for many years.' Since the pioneer work of Zener' it has been acknowledged that a large entropy is the stabilizing factor for the bcc phase, since close- packed phases have lower energies.This large entropy has mostly a vibrational origin ' and is associated with a low transverse acoustic TA2 branch, and a low value of the elastic constant C'= (C"-C, z )/2.
On cooling, many of these bcc metals and alloys under- go a phase transition towards a close-packed structure.The transformation is first order, diffusionless, and is principally described by a shear; it is the martensitic transformation.
Typical examples of materials undergo- ing these transitions can be found in alkali metals, transi- tion metals, and many noble-metal-based alloys.Among them, the Cu-based alloys have received special interest because of their technologically important shape-memory properties, associated with the martensitic transformation.
In the last few years, considerable effort has been de- voted towards an understanding of the martensitic trans- formation.Several Landau-type models have been proposed ' that involve two coupled order parameters: a uniform strain and a phonon mode (shuffie).Also, computer simulation studies qualitatively describe the vibra- tional properties of bcc solids.' The development of these models has renewed the effort to determine the vi- brational and elastic properties of materials undergoing martensitic transformations.
In this paper we present experimental results on the elastic behavior of Cu-Al-Ni single crystals just above their transition temperatures M, .Samples for elastic-constant measurements were cut into a cubic shape (about 10-mm side) using a low-speed diamond saw, with faces parallel to the (110), (110), and   (001) planes.The samples were polished ffat to surface ir- regularities of about 2 pm and parallel to better than 10 rad.To remove stresses caused by the cutting pro- cess, samples were annealed for one hour at 1273 K and quenched into water at 298 K.The nominal transition temperatures were 260 and 220 K for Cuz 742Al, ,osNio»2 and Cu2 ~26Al»z2Nio»2 respectively.Elastic constants were determined using a pulse-echo ultrasonic method.Both X-cut and Y-cut transducers were used to generate and detect 10-MHz ultrasonic pulses.Acoustic coupling between sample and transduc- er is optimized using Dow resin 276-V9 and Nonaq stop- cock grease in the temperature ranges 210 -350 and 77 -270 K, respectively.Ultrasonic-pulse transit times were obtained using the phase-sensitive detection technique (MATEC, MBS-8000).'

III. EXPERIMENTAL RESULTS AND DISCUSSION
The velocity of ultrasonic waves has been measured along the [110] direction of the samples.The adiabatic second-order elastic constants at room temperature for the two crystals investigated are shown in Table I.The values correspond to an average over three independent runs, and the error is the maximum deviation from the mean value.We have double-checked the consistency of our data by measuring the velocity of ultrasonic waves along the [100] direction.From these measurements we have obtained C44 = 98.0 GPa, C» = 137 GPa for Cu2726A1, &z2Nio.&s2 and C44=96. 3GPa, C» =136 GPa for Cu2742Al, ,osNio, s2.These values are within 4% scatter coincident with those obtained from the data 0163-1829/94/49(14)/9969(4)/$06.00 49 9969 1994 The American Physical Society We have also measured the temperature dependence of the elastic constants close to the nominal martensitic transformation temperature, M, .Below M" the surface relief associated with the appearance of the martensitic domains breaks the acoustic coupling between the sample and transducer, causing the ultrasonic echoes to disappear.In Fig. 1 we have plotted typical examples for the relative change of the elastic constants with temperature, for the two samples investigated.
No anomalous behavior is found for CL and C44.they increase as the temperature is reduced.C' decreases as the temperature drops; that is, the material becomes softer for a (110) (110) shear.This behavior is common for all noble- metal alloys undergoing martensitic transformations.'   The decrease in C' when the temperature is reduced has been found to be linear, and the corresponding slopes are listed in Table I.
It is worth stressing that ultrasonic velocities could not be measured down to the nominal M, .Several degrees above M, a marked increase in echo attenuation oc- curred, accompanied by a change in slope in the curve of elastic constant versus temperature.
To investigate the origin of these anomalies we have performed highsensitivity calorimetry on the same samples used for ulee trasonic measurements.A magnified view of the temper- ature range just above M, is shown in Fig. 2 for Cup 726A1] ]$2Nio», the inset shows the complete ther- mogram.It is clear that the beginning of the anomalous behavior in C' (marked with an arrow in Fig. 1) coincides with the first thermal effect detected calorimetrically, corresponding to the transformation of a small amount of material.The occurrence of transformation of a small fraction (less than 1%) of the sample above I, is a typi- cal feature in bulky samples subjected to a quench.Inter- nal stresses are generated during the quench, that are re- tained in the sample and locally increase the transition temperature.A detailed study of this effect has already been reported on Cu«Zn-Al by one of us.'  It is instructive to compare the elastic behavior of Cu- Al-Ni with the behavior of other Cu-based martensitic alee loys.All the elastic constants and their temperature dependence are very similar to the values previously re- ported for Cu-A1-Pd, ' and Cu-A1-Be.' It is of special Cuq 96,Alo», Beo»2 (Ref.11), (d) Cuz 70A1, O, Pdo zz (Ref.16), (e) Cu&»Zno»Alo» (Ref. 19),and (f) Auo»Cu& 2oZn& 88 (Ref. 20).
The lines are the slopes at the origin computed using the values of C' measured ultrasonically.
interest to evaluate C' at M, .Values are given in Table I.
They coincide (within 3%%uo error) with the values found for Cu-A1-Be and Cu-Zn-A1.' Indeed, the present results for Cu-Al-Ni confirm our previous findings that C' at the transition temperature always takes similar values.A phenomenological explanation for this will be given else- where.' We finally compare present values of C' with inelastic neutron-scattering experiments carried out on the same crystals, performed at the High Flux Isotope Reactor (HFIR) at the Oak Ridge National Laboratory.We have used a 20' collirnator in order to be able to measure at low wave vectors.In Figs. 3(a) and 3(b) we present the origin of the TA2 branch for the two crystals investigated.The straight line is the slope at the origin computed using the values of C' given in Table I.A striking feature is that these slopes are lower than the ones obtained by extrapolation to zero frequency of the TA2 branch.To check whether this is a common feature for martensitic alloys, we have collected data for the TA2 branch and C' from the literature"' ' ' and have replotted them on the same scales in Figs.3(c) -3(f).Although in most cases no neutron data exist for q &0.2 it is clear that, within the combined experimental errors from neutron and ul- trasound experiments, the slope computed from C' is al- ways lower than the extrapolation of the phonon branch to q=0.These results show that the long-wavelength transverse acoustic modes are softer than all other modes.Anharmonic effects could be the source of this extra softening.Nevertheless, to our knowledge there is still no theoretical justification for this fact.
To conclude, we have measured the elastic constants of Cu-Al-Ni and their temperature dependence down to the martensitic transformation temperature.We have found that this alloy behaves similarly to other Cu-based mar- tensitic alloys.A comparison of phonon dispersion curves and ultrasonic measurements for a number of noble-metal-based alloys suggests that the longwavelength acoustic TA2 modes are softer than all other modes.

TABLE I .
Elastic constants C» at room temperature, their relative thermal variation I » = CIJ 'dC»ldT, and C' at the transition temperature M, . in TableI(C»=CI+C' -C").It must be mentioned that the present values for C» and C44 are very close to the ones reported by Hausch and Torok' for Cu2 744A1»O4Ni0, 48, but they reported C'=9. 4 GPa, which is larger than our values. presented