Lattice dynamics of the high temperature shape memory
alloy Nb-Ru
Shape memory materials (SMM) have the remarkable property of returning to their original shape after deformation, either by heating them to a temperature above the martensitic transformation (MT) temperature, or by unloading them when a stressinduced transformation has occurred1. A handful of metallic alloys exhibit this property. The most well-known and commercially developed material is the Ni-Ti alloy that was discovered in 1963 by Buehler et al. at the US Naval Ordnance Laboratory2. (This alloy was dubbed Nitinol as an acronym for NiTi Naval Ordnance Laboratory!). The 2 applications to technology are limited only by an engineer's inventiveness. Its uses range from the medical (stents) to the mechanical (automated window openings) to the inbetween: artificial sphincter muscles. Nitinol, and other commercially important shape memory alloys such as Cu-Zn-Al and Cu-Al-Ni, are useful up to temperatures of about 200°C. There is a technological need to develop new SMM for use at high temperatures
that could be applied to automobile and rocket engines, gas turbines and nuclear reactor environments. Only a few alloys exhibit Martensitic transformation and shape memory properties at elevated temperatures of > 500°C. These include the Ti alloys, TiPt and TiPd3 along with Ru alloys of NbTu4,5 and TaRu5,6. Surprisingly, the studies of these are somewhat limited, most probably due to the difficulties of making the standard type of bulk measurements such as resistivity, magnetic susceptibility, etc. at these very high temperatures.
All SMM exhibit martensitic transformations (MT), which are at the heart of the shape memory property. These extensively studied transitions are always first order and transverse atomic displacements play a major role7,8. Precursor effects are usually seen, but their strength varies amongst the different systems. In some cases the MT is preceded by a pre-martensitic phase, in which a modulation of the lattice is superimposed upon the high temperature parent phase structure. The role of phonons as precursors to the martensitic transformation has also been extensively studied in many systems9. The majority of the studies show some phonon softening, but it is most pronounced in systems that exhibit a pre-martensitic phase. This raises the question of whether the phonon softening is a precursor to the MT or the pre-martensitic phase.
In this paper we report the first studies on a single crystal of the equiatomic composition SMM, NbRu. The phase transitions in this compound have been studied for over 35 years3,4,6,10,11. Two structural transitions have been reported between room temperature and 1000°C. Above 900°C, in the β-phase, the crystal structure is theordered cubic, CsCl-type (!Pm3 m) with the Nb and Ru atoms occupying the corners and the center of the cube. In reality this has not been proven because the x-ray scatteringlengths of Nb and Ru are so similar that the superlattice peak intensities, corresponding to the differences in scattering lengths, are not observable. It was inferred from the similarity of the transformation with that occurring in TaRu alloy12. Below 900°C, the 3 crystal transforms to a tetragonal structure, called the β' phase. There is another transformation near 750°C to β"-phase, which is either orthorhombic or monoclinic. The shape memory effects are associated with the high temperature the β to β' transition5, which is first order, but with a surprisingly small amount of hysteresis. Earlier experiments claimed there was no hysteresis and the transitions can be considered as continuous, which contradicts a fundamental first order aspect of martensitic transformations. The first order nature of the β β' transition was reported in more recent experiments that claimed a coexistence of the β and β' phases over a 200°C temperature range12. The β'to β" transition was reported to be continuous, which is allowed by the symmetry of the two phases according to Landau theory.
We report on temperature dependent inelastic neutron scattering experiments in the β phase of single crystals of Nb50Ru50, specially grown for this experiment using a state-of-the-art image furnace. We measure the partial dispersion curves along two symmetry directions and determined the elastic constants of the cubic phase. The only branch that shows a dramatic temperature dependence is the [qq0]-TA2 branch corresponding to propagation along the [110] direction with perpendicular displacements along the [1-10] direction. This corresponds, in the limit of q 0, to the elastic constant C'=1/2(C11-C12). There is a general softening over nearly the entire branch as the MT is approached, but the branch never approaches zero. No modulation of the lattice was observed nor is there a particular q-value of the softening.
Experimental
The single crystal of Nb50Ru50 used in this experiment was grown at Brookhaven National Laboratory. High purity Nb and Ru were melted by using an arc-melting furnace under Ar gas atmosphere and then the melt was cast into rods. These cast polycrystalline rods of NbRu, 12mm in diameter and 120 mm in length, were used as feed rods. A floatingzone furnace equipped with two ellipsoidal mirrors and two 3.5 kW halogen lamps was used to grow the single crystals. The growth chamber was first evacuated to 10-6 torr and then filled with high purity (99.999%) Ar gas to a pressure of 1 bar. The crystal growth was carried out under Ar flow. The feed rod and the seed rod were counter-rotated to achieve 4 homogeneous heating of the floating zone and to promote the mixing of the elements in the zone, which is useful in maintaining steady growth. The shape of the solid-liquid interface of the seed rod was controlled by varying the rotation speed and traveling velocities between the feed rod and the seed rod, in order to grow large single crystals in the seed rod13. The growth velocity of the seed rod was 0.4mm/h and that of the feed rod was 0.1mm/h. The asgrown rod had a diameter of 6 mm and length of 210 mm. It was cut into 10 to 25 mmlength sections.
The many domains present in the low temperature phase at room temperature complicates the alignment and verification of the quality of the crystal. However, as the crystal is heated into the cubic-β phase, the domains disappear and a single uniform peak is observed in the rocking curve with width <0.3°.>
Scientific Products high temperature furnace with a maximum temperature of 1600°C. Temperature regulation was better than 1°C at the elevated temperatures. Some measurements were made with the temperature being scanned at a heating and cooling rate of ~12°C/min. The chosen scattering plane was (001), which allowed for observation of [110]-TA2 phonon branch. Most measurements were made in the (1,1,0) and (2,0,0) Brillouin zones.
All neutron experiments were performed on the BT9 thermal beam triple axis instrument at the NIST research reactor. Pyrolytic graphite (PG) was used as a monochromator, analyzer and filter placed after the analyzer. A fixed final energy of Ef=14.7 meV was chosen for the experiments. The collimation was either 40-40-40-80 or 40-20-20-40 depending upon the conflicting needs of intensity and resolution.
All neutron experiments were performed on the BT9 thermal beam triple axis instrument at the NIST research reactor. Pyrolytic graphite (PG) was used as a monochromator, analyzer and filter placed after the analyzer. A fixed final energy of Ef=14.7 meV was chosen for the experiments. The collimation was either 40-40-40-80 or 40-20-20-40 depending upon the conflicting needs of intensity and resolution.
Results
Phase transformations
Niobium and ruthenium, coincidently, have nearly identical neutron scattering lengths14: bNb=7.054, bRu=7.03. The ratio of the intensities of the superlattice reflections of the CsCl lattice [ (h+k+l)=odd], whose intensity is proportional to (bNb-bRu)2, compared to the fundamental bcc peaks [(h+k+l)=even],whose intensity is proportional to (bNb+bRu)2 is 3 x 10-6. This very small ratio makes it difficult to observe the superlattice 5 reflections. Also, since they have nearly the same number of electrons it is difficult to measure the superlattice peaks with x-rays and the earlier x-ray studies could not measure them12. However in our study of the parent phase we used two PG filters to eliminate any higher order neutrons and were able to observe a weak (1,0,0) Bragg peak intensity. This confirms the expected, though unproven, β-CsCl ( ! Pm3 m) symmetry of the high temperature cubic phase.
The early studies4 showed that two phase transformations take place as a function of temperature. The high temperature β phase is cubic and transforms on cooling into the reported tetragonal phase (β') near 900°C10 and another transition occurs near 750°C into the β" phase which is either orthorhombic or monoclinic10,12. Our measurements on a single crystal could not establish the definitive structure of the different phases but we could monitor the lattice parameters of the various phases by performing mesh scans about the two accessible Bragg peaks, (1,1,0) and (2,0,0). Figure 1 shows the intensity contours for the (1,1,0) and (2,0,0) Bragg peaks at temperatures in the three different phases and Table I lists the lattice parameters determined from these intensity contours.
The top row shows the peaks in the β-phase measured at 900°C at the appropriate positions using the cubic phase lattice parameter, a= 0.3176 nm. Upon cooling to 875°C into the β' phase field, the crystal splits up into domains as evidenced by the multiple spots observed in the second row. For the measurement about (2,0,0,) the change in the distance of the spots along the H direction corresponds to the change in the lattice parameters, whereas the change along the K direction corresponds to the relative orientation of the domains. The lattice parameters of the β' phase measured in this way are at=0.3106 nm and ct=0.3307 nm, which agree well with the high temperature x-ray measurements12. The third row are measurements at 600°C, where the symmetry is reported to be orthorhombic12 or monoclinic15. The lattice parameters determined in this phase are ao=0.3014nm, bo=0.3081nm, and co=0.3430nm. The values agree well with Ref. 12 and our results are more consistent with the reported orthorhombic structure for the β" phase rather than monoclinic.
Although these transitions are expected to be first order, the early studies4 of the resistivity and magnetic susceptibility showed very little hysteresis. (<10°c),>
Lattice dynamics and elastic constants
The primary purpose of this experiment is to investigate the phonon behavior of the parent phase of NbRu and to look for precursors to the martensitic transition. Since the crystal was oriented in the (HK0) scattering plane it was only possible to measure along the [100] and [110] symmetry directions. Figure 3 shows the dispersion curves for the TA modes and the partial dispersion of the LA modes measured at 1100°C. Table II lists the velocities of the LA and TA modes determined from the limiting slopes near the origin of reciprocal space. From these values the elastic constants, tabulated in Table III, are calculated using the formula:
where ρ is the density: 6.05 gms/cm3 and v is the limiting sound velocity. The anomalous branch is the [110]-TA2 branch with atomic displacements along the [-110] direction and the limiting slope corresponds to the elastic constant C'=1/2(C11-C12). The anisotropy factor A=C44/C'=4.8 is large, compared to harmonic lattices where it is unity. However, it is small compared to other shape memory alloys. For example, NiAl16 Ni2MnGa17, NiTi18, AuCd19 have values of A=23, 23, 2, and 14, respectively, for a given temperature 7 and composition..
This branch also shows a slight curvature near the middle of the Brillouin zone, which as shown below is very temperature dependent. Temperature dependent phonon branches: The only branch that shows any anomalous temperature dependence is the [110]- TA2 transverse acoustic mode. Figure 4 shows the dispersion of this branch measured at 910°C, just above the transformation temperature, and 1550°C, the maximum limit of the temperature range of the furnace. At the higher temperature the dispersion is nearly a normal sinusoidal shape. As the temperature is lowered there is a softening of the branch nearly out to the zone boundary. This is shown more dramatically in Figure 5, which shows only the low-q portion of the dispersion curve measured at several temperatures between 910°C and 1550°C. A gradual softening with temperature is observed, but nowhere does the energy approach zero as the transformation temperature is approached. Also, there is no particular q-vector that shows a stronger anomaly as observed in other SMM such as NiAl20 or Ni2MnGa21 alloys. These materials exhibit a pre-martensitic behavior which is a commensurate modulation of the cubic lattice. Figure 6 is a plot of the phonon energy squared vs temperature for several q-values near the zone center.
These all extrapolate to zero at temperatures well below the transformation temperature, TM = 900°C, with the larger q-values extrapolating to a lower temperature. The temperature dependence of the TA phonon propagating along the [001] direction was also measured. This corresponds to the C44 elastic constant in the limit of q~0. Only a weak softening (<10%) q="0.1">
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1. L. M. Schetky, Scientifi American 241, 82 (1979)
2. W. J. Buehler, J. V. Gilfrich and K. C. Weiley, J. Appl. Physics 34, 1467 (1963).
3. H. C. Donkersloot and J. H. N. VanVucht, J. Less Common Met. 20, 83 (1970).
4. B. K. Das, M. A. Schmerling and D. D. S. Lieberman, Mat. Sci. Eng. 6, 248 (1970).
5. R. W. Fonda, H. N. Jones and R. A. Vandermeer, Scripta Mat. 39, 1031 (1998).
6. M. A. Schmerling, B. K. Ds and D. S. Lieberman, Met. Trans. 1, 3273 (1970).
7. Z. Nishayama, Martensitic Transformations (Academic Press, NY, 1978).
8. Martensite, G. B. Olson and W. S. Owen, eds., (ASM International , Materials Park,
Ohio, 1992)
9. S. M. Shapiro in Magnetism and Structure in Functional Materials (Springer,
Heidleburg, 2005).
10. B. Das. And D. S. Lieberman, Acta Met. 23, 579 (1975).
11. B. Das, E. A. Stern and D. S. Lieberman, Acata Met. 24, 37 (1976).
12. B. H. Chen and H. F. Franzen, J. of Less-Common Met. 153, L13 (1989)
13 G. D. Gu, M. Hucker, Y. J. Kim, A. Li and A. R. Moodenbaugh, J. Crystal Growth
287,318 (2006)
14. Neutron News 3, 29 (1992).
15. R. W. Fonda, H. N. Jones and R. A. Vandermeer, Scripta Met. 39, 1359 (1998).
16. T. Davenport, L. Zhou and J. Trivisonno, Phys. Rev. B 59,3421 (1999).
17. J. Worgull, E. Petti, and J. Trivisonno, Phys. Rev. B 54, 15695 (1996).
18. O. Mercier, K. N. Melton, G. Gremaud, and J. Hagi, J. Appl. Phys. 51, 1833 (1980).
19. S. Zirinsky, Acta Metall. 4, 164 (1956).
20. S. M. Shapiro, B. X. Yang, Y. Noda, L. E. Tanner and D. Schryvers, Phys. Rev. B 44,
9301 (1991).
21, A. Zheludev, S. M. Shapiro, P. Wochner and L. E. Tanner, Phys. Rev B 54, 15045
(1996).
22. C. Zener, Phys. Rev. 71, 846 (1947).
23. H. Tietze, M. Müller, and B. Renker, J. Phys. C: Solids State Phys. 17, L529 (1984).
24. T. Ohba, S. M. Shapiro, S. Aoki and K. Otsuka, Jpn. J. Appl. Phys. 33, L1631 (1994).
25. H. G. Smith, Phys. Rev. Lett. 58, 1228 (1987).
26. M. Sato, B. H. Grier, S. M. Shapiro, and H. Miyajima, J. Phys. F: Met. Phys. 12,
2117 (1982).
27. G. L Zhao and B. N. Harmon, Phys. Rev. B 45, 2818 (1992).
28. A. D. Bruce and R. A. Cowley, Structural Phase Transitions (Taylor & Francis,
Cesar A Hernandez E
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