Localized Soft Modes Research Articles

Transformation of soft localized modes in glasses under pressure

Experimentally observed narrowing of spectral holes in a glass under hydrostatic pressure confirms our theoretical finding that the external pressure, in addition to increasing the frequencies of soft localized modes, also reduces their number. This occurs because the majority of soft localized modes in glasses is shown to have a negative cubic anharmonicity. For that reason the applied pressure not only enhances the stiffness of these modes, but also transforms a fraction of them into tunneling two-level systems, whereas the simultaneous reverse transformations of some other two-level systems into soft localized modes are less numerous.

Soft Modes in Confined Nematic Liquid Crystals

Collective fluctuations of the liquid-crystalline order in two model geometries with a domain-like equilibrium configuration are analyzed within the Landau-de Gennes theory. The wetting-induced heterophase structure is characterized by a localized soft mode corresponding to fluctuations of the position of the interface between the two phases. In a very thin hybrid cell, the soft mode is associated with a structural transition from the configuration with a step-like profile of the tilt angle to the usual bent structure. This slowdown is exhibited by the lowest director mode. In both geometries the critical behavior is expected to be observable by the evanescent light wave scattering.

Molecular dynamics simulation of martensitic transformations in NiAI

Both thermally induced and stress-induced coherent nucleation and growth of an L10 martensitic phase have been examined and analyzed at the atomic level in molecular dynamics (MD) computer simulations of an ordered B2 NiAl lattice array using embedded atom method (EAM) interatomic potentials. Both heterogeneous and homogeneous nucleation are observed, the latter requiring an applied stress. The heterogeneous process occurs at ledge corners on stepped free surfaces and can be analyzed in terms of localized soft modes. The homogeneous nucleation can be understood as resulting from a strain spinodal instability which produces a morphology reminiscent of chemical spinodal decomposition. Self-accommodating martensite variants appear very early in the growth process, and all interfaces remain coherent with no detectable presence of dislocations in these early stages.

Hybridization-induced electron self-trapping in soft local structures in non-metallic solids

A new type of electron self-trapping is described, which can occur even if the bare single-electron energy level is independent of the surrounding local atomic configuration coordinates. Such a self-trapping can be realized in soft local structures in non-metallic solids, e.g., semiconductors. Hybridization of states in the interband gap is decisive for the self-trapping, providing actually the related coupling between an electron (hole) and a localized soft motion mode in the surrounding atomic configuration. In this sense, unlike the well-known polaronic self-trapping, the self-trapping under discussion is entirely of quantum mechanical origin.

Pre-Transitional Behavior in Cubic Potassium Niobate

ABSTRACTPre-transitional behavior prior to the onset of the cubic-to-tetragonal phase transformation in KnbO3 has been studied with synchrotron x-ray scattering at NSLS, Brookhaven National Lab. Measurements of the Thermal Diffuse Scattering (TDS), Grazing Incidence X-ray Scattering (GIXS), and precursor Bragg scattering have been performed at a series of temperatures on a single crystal sample in the cubic phase (Tc = 405 °C). The TDS was measured in the (001), (011) and (111) cubic planes. The GIXS was measured above, at and below the critical scattering angle of the sample. Based on localized soft mode theory, dynamic tetragonal fluctuations may be expected prior to the onset of the phase transition initiated by defects or surfaces. The GIXS data indicate that the tetragonal phase is apparent prior to the phase transition of the bulk - - consistent with the notion that nucleation originates from potent defect sites during a martensitic-like displacive transformation. The TDS intensity distribution is disk-shaped; arising from a localized, low energy transverse optic mode in the [100] directions extending out to the Brillouin zone boundary (reduced wave vector, q =0.5). Scans made in the (011) planes show TDS intensity extending out to a reduced wave vector of q ˜ 0.2. Preliminary analysis indicates that a low energy transverse optic mode extends in the [011] direction as well. The TDS intensity decreases as the transition temperature is approached from above. Comparison of the TDS results with inelastic neutron scattering data will be made.

Coherent Nucleation and Growth of Marte1Nite in B2 Nial Oberved in Computer Simulations

AbstractIn atomistic simulations of B2 NiAl usirn Molecular Dynamics and Emxbedded Atom Method Ni-Al potentials, both thermally induoed and stress induced crent martensitic nucleation and growth processes of a tetragonal Llo phase have been observed, including the formation of self-accommodating martensite variants. Nucleation is found to occur only at special heterogeneous sites that can be well characterised. Prior to nucleation, clear evidence of the buildup of large amplitude localized soft modes can be seen. A discussion of the kinetics of these processes is presented.

Martensitic toughening of ceramics

Current knowledge of displacive phase transformations in non-metals (in particular, in ceramics) is reviewed. Using the tetragonal-to-monoclinic transformation in zirconia ( ΔV = 4.9% at room temperature) as a model system, the factors controlling the metastability of confined particles are discussed, i.e. matrix constraint, chemical composition position and nucleation barrier to the transformation. The model for martensitic nucleation in ceramics is based on a localized soft mode mechanism at strain singularities or concentrations in faceted particles. Other potential transformation togerther alternative to zirconia have been identified. For the first time, preliminary mechanical toughness data using the new tougheners is briefly presented. Composites of 20wt.% BTb 2O 3 in 80 vol.% MgO causes a thresfold increase at 1400°C. Monoclinic (β) dicalcium silicate dispersed in calcium zirconate exhibits a fivefold increase in toughness. Other new materials including refractory sulfides are examined from the point of view of transformation toughening. The application of high pressures during processing makes it feasible to alter thermodynamic phase fields and to develop yet other new transformation-toughened composites.

Inelastic flow processes in nanometre volumes of solids

The authors consider the types of inelastic process that may occur in very small volumes of material, using the model system of a sharp tip coming into contact with a flat. Both molecular dynamics simulations and experimental results are presented. Theoretical lattice strength is observed, adhesion between clean surfaces is strong and involves inelastic flow, and the adhesion is considerably reduced by differing atomic species at the interface. The MD simulations, using long-range potentials, show that the processes likely to be occurring include local sintering or diffusion-like flow, enhanced by local soft modes, and net material transfer upon adhesive unloading.

Simple extension of the Frenkel-Kontorova model: a different world

Incommensurate configurations of Torus and Cantorus type, respectively, in a 3-harmonics variant of the Frenkel-Kontorova model are investigated. Novel phenomena that further relativize and generalize the conventional scenario based on the “standard map” are observed. In particular various competing types of Cantorus configurations can be detected. Besides cascades of secondorder Torus-Cantorus transitions the groundstate phase diagram contains an extremely complicated pattern of second-order and quasi-first order Cantorus-Cantorus transition lines. The system also supports metastable Cantorus configurations, especially unsymmetrical ones coming in degenerate pairs. The annihilation of hysteretic configurations is shown to be driven by exponentially localized soft modes.

Oxygen K-edge EXAFS of the high-TC superconductor Y-Ba-Cu-O

EXAFS spectra above the oxygen K absorption edge of the high-TC superconductor Y-Ba-Cu-O have been studied by measuring the total electron yield (TEY) as a function of x-ray energy. Temperature variation of the TEY spectra was examined between 77K and 300K. These data provide evidence for the existence of local soft modes in the material.

The precursor effect of the athermal βaihω transformation in Ti-9.62Fe alloy

Ti-9.62Fe alloy was quenched from 1000°C into ice water. The athermal ω phase has been observed at room temperature. In the as-quenched alloy the resistivity, Mössbauer recoil-free fraction, and X-ray diffraction all show anomalous variations with temperature. The anomalous variations existing in a wide range of temperatures below RT are found to be reversible. The explanation of the anomalous phenomena is based on the instability of the β phase, which shows the localized soft modes. The instability can be referred to as a precursor effect of ω transformation. One of the reasons that the precursor effect can be observed in a wide range of temperatures below RT is due to the slightly higher oxygen concentration and as a result the oxygen atoms suppress the formation of the ω phase. The partially filled 3d-band of this alloy may have some influence on the precursor effect of the ω transformation.

Quasi-one-dimensional model of pretransitional soft mode behavior

Pretransitional effects at displacive phase transitions are temperature dependent responses to fluctuations of the order parameter; these give rise to 1-D correlations in martensitic transformations when lattice dynamical constraints divide the “hard mode” 3-D correlation of the Bain distortion in order to maintain the mean field on a macroscopic scale. The quasi-one-dimensional (QOD) soft mode model of the latttice-variant-shear-theory (LVST) is described and its relevance to pretransitional nucleation and soft mode behavior, discussed. The 1-D correlations give rise to localized soft modes aboveT m , which nucleate microdomains of an intermediate phase at dissociated dislocations; these grow with second order kinetics and maintain the mean field when microdomains of opposite displacement vector cancel each other. Pretransitional behavior, predicted by LVST, are compared with experimental data in a wide range of materials and show why materials with different order parameters show similar transformation behavior.

Low energy dislocation structures caused by martensitic transformations

The low energy dislocation structures in microdomains, twin domains and self-accommodating interfaces, causes by martensitic transformations, are evaluated for several B2 alloys with 18R, 9R and 3R martensite structures by the modern theory of martensitic transformations. The transformations are accomplished by two lattice-variant shears and a volume change relaxation and are one dimensional in origin when the order parameter couples linearly with the spontaneous strain. The primary shear, on a system with degenerate stress sense, periodically alternates its direction to minimize long-range stress fields, while the habit plane shear minimizes long-range stress fields by “self-accomodation” between variants. The habit planes and shape strains, computed by this theory, are the same as those for the phenomenological theory; this is discussed. The lattice-variant transformation dislocations originate from the three-dimensional network, where screw dislocation segments dissociate to form fluctuating microdomains (localized soft modes), and these thicken when the transformation dislocations multiply by a cross-slip dissociation mechanism. The computed Schmid factors for variants in self-accommodating groups show opposite signs, indicative of a minimum long-range stress field. The resulting low energy dislocation structure is an interface of primary shear dislocations of alternating signs and habit plane shear dislocations in self-accomodating variants with almost opposite shear strains. The results indicate criteria for high pseudoelasticity and shape memory behavior with a mobile low energy dislocation structure which is highly susceptible to an applied stress.

Overview no. 45: On the nucleation of the martensitic transformation in zirconia (ZrO 2)

The kinetics of the martensitic tetragonal ( t)→monoclinic ( m) transformation in ZrO 2 are nucleation-controlled, as they are in metals and alloys, and classical and non-clasical models for martensitic nucleation are considered in this paper. Transmission electron microscopy studies of the several types of transformation-toughened ZrO 2-containing ceramics now available do not reveal any obvious defects that could act as classical heterogeneous nuclei. This is true for t-ZrO 2 as a coherent precipitate phase, as an incoherent dispersed phase, as a fine-grain matrix phase, or as an incoherent precipitate phase in internally-oxidized alloys. On the other hand, nucleation via a Clapp-type localized soft mode mechanism at strain concentrations is consistent with all observations. Nucleation is always stress-assisted, even when the transformation occurs spontaneously. In these latter cases, the stresses arise from thermal expansion mismatch or thermal expansion anisotropy and are enhanced by the stress concentrations provided by particle or grain facets and corners.

Pre-transition phenomena in an iron-nickel alloy

X-ray diffraction from an Fe-30.5Ni single crystal has been examined to obtain information on the vibrational state of the sample prior to the martensite transformation. The measurements included integrated intensities of Bragg peaks as well as diffuse scattering along several directions in reciprocal space. Data were obtained from room temperature to within approximately 1°K of the transformation temperature. Previous reports of an increase in the mean-square atomic displacements on approaching M s (determined with Mössbauer techniques) were not confirmed by measurements of the integrated X-ray diffraction peaks. The results of this study reveal a decrease in the mean-squared amplitude of vibration with temperature which is in close agreement with that predicted by harmonic theory. Diffuse X-ray scattering, examined to sample the temperature dependence of particular vibrational modes, gave no indication of softening of short wavelength modes. However, these measurements did reveal a softening of long wavelength (100) [100] modes as the sample approached the M s temperature. The softening of this mode provides a Bain distortion which can lead to a lattice instability near defects as predicted by localized soft mode theories. Such an instability can be viewed as one mechanism by which a martensite nucleus is formed.

Domain wall instability in biaxial ferromagnets

The energetic and dynamic stability of domain walls (DW's) in a 1D Heisenberg ferromagnet with orthorhombic anisotropy is examined in the framework of classical continuum theory. It is shown that in the undamped chain the critical slowing-down accompanying the energetic instability of the static DW's at a critical ratioac of the anisotropy fields is not marked (as one might expect) by a localized soft dynamic mode of the DW's, but it is realized by a mechanism which may be termed “softening of the velocity change”. The role of the soft eigenmode is taken over by the perturbation which carries the static DW into a moving one with infinitesimal velocity, and the role of the soft-mode frequency is taken over by the velocity change induced by the perturbation. When spin damping is included, one does find a soft relaxation mode: Attenuation of the velocity of moving DW's gives rise to a perturbation which may be described as a superposition of the Goldstone mode and a relaxation mode. This behaviour is not a special feature of the system under consideration, but a similar situation arises in general, when a static DW becomes unstable with respect to a perturbation connecting it with a family of other static DW's. For moving DW's the “softening of the velocity change” also occurs, but here no energetic stability criterion is available and inclusion of spin damping makes the DW motion nonstationary. Thus, in the case of moving DW's no possibility seems to exist to define stability and instability in the usual terms of linear analysis.

Planar ferromagnets: Low-velocity kink dynamics near to the easy plane and static solitary spin structures bifurcating from the azimuthal kink

Ferromagnetic spin chains with planar single ion anisotropy, exchange anisotropy and with an external fieldb applied in the easy plane are considered in classical continuum approximation. It is pointed out that in the static case the sine-Gordon approximation is only accidentally exact: it breaks down in the neighborhood of the easy plane already for infinitesimal kink velocities, unlessb→0. It is also shown that at certain valuesb n ,n=0, 1, 2, 3, ... of the applied field there bifurcate from the static in-plane kink (“azimuthal kink”) other static out-of-plane kink solutions. The azimuthal kink is linearly stable below the critical strengthb 0 of the applied field. For increasingb, there occurs at each of the bifurcation fieldsb 1<b 2<b 3... an instability with respect to an additional mode. In the undamped system the instabilities atb 2k ,k=0, 1, 2, ... are associated with the recently discovered “soft-velocity change” mechanism of the critical slowing-down, whereas atb 2k+1 , soft localized dynamic modes occur. If phenomenological spin damping is included, soft relaxation modes occur in the neighborhood of all the bifurcation fields.

A localized soft mode model for the nucleation of thermoelastic martensitic transformation: Application to the β → 9r transformation

A nucleation model for bcc → 9R martensitic transformation has been developed based on the experimental data from a Cu-Zn-Al alloy. It has been shown through the third order elastic constants values that the C′ = 1/2(C11 - C12) elastic constant in the bcc phase is very sensitive to the homogeneous {011} (011) shear strains. Consequently it has been demonstrated that, around defects like dislocations, mechanically unstable zones are present where C softens dramatically. The C′ constant is related to the {011} (011) type shear which is precisely the homogeneous lattice strain involved in the bcc → 9R transformation. Nuclei can, therefore, develop in such zones without generating any resistive strain energy. Nucleation is postulated to occur in the zones when the reduced critical nucleus size becomes equal to the unstable zone size.

Pretransformation effects of localized soft modes on neutron scattering, acoustic attenuation, and Mössbauer resonance measurements

The localized soft mode model of martensitic nucleation is used to predict pretransformation effects of such regions on inelastic neutron scattering, ultrasonic acoustic attenuation and Mossbauer resonance absorption. The theoretical predictions are compared with the available experimental data.

Localized soft modes and ultrasonic effects in first order displacive transformations

Based on a previously published theory of localized soft modes as precursors of first order displacive transformations, explicit formulae for the ultrasonic attenuation and velocity change near the transition are derived and compared satisfactorily with experiments in TiNi, InTl and FeNi.