Structural relaxation and crystallisation of bulk metallic glasses Zr41Ti14Cu12.5Ni10−xBe22.5Fex (x = 0 or 2) studied by mechanical spectroscopy

The measurements of the internal friction and dynamic shear modulus as well as differential scanning calorimetry have been performed in order to investigate the structural relaxation and crystallization of Zr₄₁Ti₁₄Cu_12.5Ni_10−xBe_22.5Fe_x (x=0 or 2) bulk metallic glasses. It is found that the glass transition is retarded and the thermal stability of supercooled liquid is increased by the Fe addition. The experimental results are well analyzed using a physical model, which can characterize atomic mobility and mechanical response of disordered condensed materials.     

Mechanical relaxation in glasses

The basic properties of glasses and the characteristics of mechanical relaxation in glasses were briefly reviewed, and then our studies concerned were presented. Experimental methods adopted were viscosity, internal friction, ultrasonic attenuation, and Brillouin scattering measurements. The specimens used were several kinds of inorganic, organic, and metallic glasses. The measurements were mainly carried out from the room temperature up to the glass transition temperature, and the relaxation time was determined as a function of temperature. The “double relaxation” composed of two Arrhenius-type relaxations was observed in many materials. In both relaxations, the “compensation effect” showing a correlation of the pre-exponential factor and the activation energy was observed. These results were explained by considering the “complex relaxation” due to cooperative motions of atoms or group of atoms. Values of activation energy near the glass transition determined by the various experimental methods were compared with each other.     

Dynamics and mechanics below the glass transition: The non-equilibrium state

There is much interest in the dynamics of glass-forming systems above the glass transition temperature. However, in many applications the behavior of the systems needs to be understood in the glass-transition T_g range and particularly in the non-equilibrium state. We present a set of empirical observations for the dynamics of material behaviors near to, but below the glass transition for polymer glass formers and outline a “minimal” set of requirements that might be expected of computer simulations in the non-equilibrium glass near to T_g. The survey includes the kinetics and nonlinearity of the structural (volume or enthalpy) recovery of the glass and its impact on the mechanical response (physical aging). These are presented with the thought that computer simulations may well be able to provide insights to the origins of an extremely complicated set of experimental observations.

Additionally, we present some results of glass formation of simple liquids constrained to nanometer size pores with the expectation that such experiments may be readily simulated because of the small number of molecules in such pores.     

A modified effective crack-length formulation in elastic-plastic fracture mechanics

In examining the performance of standard effective crack-length formulations, the authors noted quantitative accuracy up to “high” fractions of limit load under loading conditions for which the elastic T-stress was non-negative, while a pronounced deviation from the corresponding continuum elastic-plastic plane-strain finite-element solutions was seen in shallow-cracked geometries having negative T-stress. This trend can be rationalized by noting that, under modified boundary layer (K_I and T) loading, the maximum plastic zone radius strongly increases as the T-stress decreases from zero (J.R. Rice (1974), J. Mech. Phys. Solids 22, 17–26; S.G. Larsson and A.J. Carlsson (1973), J. Mech. Phys. Solids 21, 263–277; N.P. O'Dowd and C.F. Shih (1991), J. Mech. Phys. Solids 39(8), 989–1015.) Accordingly, we formulate a modified effective crack length to account for the effects of the elastic T-stress.

The new formulation consistently extends the load range for which accurate predictions of compliance, J-integral, and crack-tip constraint are obtained in several plane strain specimen geometries. The magnitude of influence of the T-stress varies with specimen type and relative crack depth. The greatest “improvement” to standard effective crack length approximations occurs in specimens of “moderately” negative T-stress.     

On the combined influences of Young''s modulus and stress ratio on the LEFM fatigue crack growth process: A new mechanistic approach

A new mechanistic approach (NMA) was used recently to examine the physical aspects of LEFM (long) fatigue crack growth (FCG) process in crack-ductile materials in stages I and II. In this paper, NMA is extended to examine both the physical and analytical aspects of the combined effects of Young's modulus, E and stress ratio, R, in the same stages of the same materials. It is shown that, (i) with submicroscopic cleavage or reversed shear mechanism operating in the pure form, E is the most influential intrinsic “material” property controlling FCG, (ii) E-dependence of da/dN is a natural consequence of near-crack-tip displacement control proposed previously, and (iii) the demonstrated similarity of FCG curves and the existence of characteristic “pivot points” on these curves for a “class of materials” results from E-influence which continues even at a higher R. A simple analytical model based on “strain intensity factor,” K₀, which contains E-influence implicitly and controls da/dN in all materials irrespective of class, is proposed. Model-predicted K₀-based theoretical values of threshold, “Idealised Master Growth Curves (IMGCs)” and mechanism transition point, all agreed excellently with experimental data for at least three classes of materials, i.e. steels, Al-alloys and Ti-alloys at extreme R-values of 0 and ≥ 0.6. The K₀-parameter concept is used here to raise the status of the analysis of the E-effect from a simple “normalisation” to that of direct data “representation”. Using NMA existing empirical relations are given some sound theoretical base. In addition to aiding in a clearer physical understanding of the FCG process, the unique IMGCs developed for different R-values are considered useful in quick, accurate and conservative life estimations, and performing failure analyses usually required in selection and design of materials.     

Mechanical relaxation in simple molecular liquids from the liquid to the supercooled state

Attenuation and velocity of acoustic waves have been revealed at ultrasonic frequencies (2, 5 and 10 MHz) in some glass-forming liquids. The mechanical response has been studied following continuously the materials from the liquid to the supercooled state, using an experimental set-up developed to this purpose. A peak in the attenuation of longitudinal acoustic waves has been observed in a temperature region in which the liquids are supercooled. Correspondingly, the sound velocity shows a dispersion, increasing from liquid-like to solid-like values for decreasing temperatures. Both features develop above the calorimetric glass transition temperature (T_g). In the deeply supercooled liquids, nearly 10 K above their calorimetric T_g, also the propagation of transverse wave sound (which is a characteristic behaviour of solid-like materials) has been experimentally detected. Shear and longitudinal relaxation times are not decoupled in the time–temperature region investigated. Compared to the mechanical one, the dielectric relaxation studied as a function of temperature at the same frequency of the ultrasonic experiments shows a loss peak centred at the same temperature. Depending on the liquid investigated, the mechanical relaxation spectrum can be broader than the dielectric one, specially in the low temperature flank, suggesting that some dissipative processes at lower energies can contribute to the mechanical loss, even though they do not couple to the electric probe field.     

Computer simulations of structure and transport in glasses and supercooled liquids

In terms of development in the study of glasses and glass-forming liquids via computer simulation, during 1997 and early 1998, notable advances have been made in the quantification of dynamical heterogeneities in supercooled liquids; in particular several studies have identified a growing dynamical length scale as the glass transition is approached. New insights into the origins of ‘polyamorphism’ have been obtained from simulations of water and silica. Most significantly, a connection between equilibrium relaxation and inherent structures of liquids has been identified that suggests an underlying static origin for the glass transition.     

The resistance of silicon carbide to static and impact local loading

The physical nature of the resistance of SiC crystals to static and local impact loading has been examined. Investigation of the temperature dependence of hardness for SiC crystals allows the determination of the characteristic deformation temperature (T* ≈ 1600 K), the parameter that characterizes the degree of covalence in interatomic bonds ( ≈ 6) and the temperature range in which a phase transition under pressure during indentation is possible (T < 800 K). Indentation technique gives possibility to construct stress-strain curves for brittle materials and to determine Hugoniot Elastic Limit. During dynamic penetration of a kinetic projectile into a SiC target the phase transition takes place.     

An equivalent domain integral method for computing crack-tip integral parameters in non-elastic, thermo-mechanical fracture

The crack-tip parameters, such asJ; T^*, ΔT^* etc, which quantify the severity of the stress/strain fields near the crack-tip in elastic-plastic materials subject to thermo-mechanical loading, are often expressed as integrals over a path that is infinitesimally close to the crack-tip (front). The integrand in such integrals involves the stress-working density, stress, strain and displacement fields arbitrarily close to the crack-tip. In a numerical analysis, such data near the crack-tip are not expected to be very accurate. This paper describes simple approaches and attendant computational algorithms, wherein, the “crack-tip integral” parameters may be evaluated through “equivalent domain integrals” (EDI) alone. It is also seen that the present (EDI) approaches form the generic basis for the popular “virtual crack extension” (VCE) methods. Several examples of thermo-mechanical fracture, including: (i) thermal loading of an elastic material, (ii) arbitrary loading/unloading/reloading of an elastic-plastic material, containing a single dominant crack, are presented to illustrate the present approach and its accuracy.     

Icosahedra from liquid droplets?

Quenching of a liquid Pb droplet containing 8217 atoms to T 0.65 T_m is studied on the nanosecond time scale using molecular dynamics and a “glue” force model. Crystallization takes place, and analysis of the final structure reveals an icosahedral-like shape, even if cuboctahedral single crystal structures are energetically favoured by our potential for all sizes. This result appears to be a consequence of the rapid formation of {111} crystallization fronts at the liquid surface and moving inward, and provides an explanation for the rapid structural fluctuations observed in electron microscopy experiments.     

DSC study of some Ge-Sb-S glasses

Differential scanning calorimetric analysis was made on three glasses of the Ge-Sb-S system in order to obtain insight into the kinetics of glass transition and of the inherent relaxation processes occurring in the glass transition region. The heat capacity of the supercooled liquid referred to as the glass was measured. The value of the heat capacity jump at the glass transition, C_p, has been obtained for each glass. These values are in good agreement with those found for similar chalcogenide glasses. The relaxation process in the glassy alloy Ge₃₀Sb₁₀S₆₀ was investigated by measuring the excess heat capacity of the annealed glass in the glass transition region. A relaxation enthalpy of 2.7 meV for annealing at 595 K for 17 h was determined. A kinetic study of the glass transition in the Ge₂₀Sb₁₀S₇₀ glass was done. From the change in the glass transition temperature with scanning rate, an apparent activation energy of 3.9 eV was obtained. This value agrees with those measured for the apparent activation energy of the shear viscosity in similar glasses.     

Preparation and crystallization of Ti53Cu27Ni12Zr3Al7Si3B1 bulk metallic glass with wide supercooled liquid region

Ti-based bulk metallic glass (BMG) alloy with the composition of Ti₅₃Cu₂₇Ni₁₂Zr₃Al₇Si₃B₁ was prepared by copper molder casting method and ribbon sample was prepared by melt spinning to compare. The thermal instability of this glass phase was examined by using differential scanning calorimetry (DSC) and differential thermal analysis (DTA). The results revealed that the supercooled liquid region (ΔT_x), glass transition temperature (T_g) and reduced glass transition temperature (T_g/T_m) of the glassy alloy are detected to be 69, 685 and 0.62 K, respectively. The crystallization behavior of the Ti-based glass phase was also investigated by annealing the glass phase at series temperatures above T_g. The annealed microstructures were examined by means of X-ray diffraction experiments. The crystallization process of the BMG can be characterized by metastable crystalline phases at the first crystallization step and further transition to stable crystalline phases at high temperature through metastable crystalline phase.     

Chemical-bonding and high-pressure studies on hydrogen-storage materials

From gradient-corrected, all-electron, full-potential, density-functional calculations, including structural relaxation, it is shown that the metal-hydride series RTInH_1.333 (R=La, Ce, Pr, or Nd; T=Ni, Pd, or Pt) violate the “2-Å” rule as well as the hole-size requirement. These hydrides possess unusually short H–H separations which in the most extreme case for LaPtInH_1.333 is as short as 1.454 Å. These findings have been analyzed in terms of charge density, charge transfer, electron-localization function, crystal-orbital Hamilton population, and density of states analyses. From high-pressure studies it is predicted several successive pressure-induced structural transitions in MgH₂ within the 20 GPa range. Calculations have also shown several pressure-induced structural transitions in alkali aluminum tetrahydrides with large volume reductions at the phase-transition points and small energy differences between the ambient-pressure and subsequent high-pressure phases.     

HPGe detectors for low-temperature nuclear orientation

Using the Low-Temperature Nuclear Orientation (LTNO) technique one can study various interesting properties of atomic nuclei and nuclear decay which can be deduced from the measurements of the angular distributions of charged particles emitted during the decay. However, the use of particle detectors working in conditions of LTNO devices (which are generally not available commercially) is a necessary precondition for the realization of these experiments.

Planar HPGe detectors for detection of charged particles at “liquid helium” temperatures were developed and produced at NPI e . Relatively simple technology using vacuum evaporation and diffusion was employed. The performance of detectors at low temperatures was tested and their characteristics measured in a testing cryostat before using them in real experiments.

The HPGe detectors were extensively used in a whole range of LTNO experiments with various physical objectives — in offline (IKS Leuven) as well as online (CERN-ISOLDE, Louvain-la-Neuve — LISOL) experiments. In frame of the project “Meson-Exchange Enhancement of First-Forbidden Beta Transitions in the Lead Region”, the measurements of angular distribution of emitted β-particles allowed to determine experimentally the “meson-exchange currents” contribution to the β-decay. In the project “Isospin Mixing in NZ nuclei”, the isospin-forbidden β-transitions of the nuclei in region (A=50–100) were studied in order to obtain information on the isospin structure of the nuclear states. A new project looking for the possible presence of the tensor currents contribution to the β-decay is being prepared for the CERN-ISOLDE facility.     

Effect of ferroic domain pattern changes on the Raman spectra of some ferroic crystals

The influence of changes in the pattern of ferroic domain structure on the Raman spectra of β-LiNH₄SO₄ and (NH₄)₃H(SO₄)₂ single crystals were studied. It was shown that the Raman spectra of β-LiNH₄SO₄ passed from the ferroelastic phase differ from those of “as-grown” crystal and those of the crystal, which was in the paraelectric phase. Significant changes could be observed in the Raman bands related to triply degenerated ν₃ and ν₄ vibrations of the SO₄ tetrahedron. Detailed temperature studies of the Raman spectra of β-LiNH₄SO₄ close to the paraelectric–ferroelectric phase transition, exhibit anomaly of some internal vibrations of SO₄ in the temperature range where a regular large-scale structure is observed. Different types of evolution of the ferroelastic domain structure and temperature behaviour of the donor and acceptor vibrations were shown while heating and cooling the (NH₄)₃H(SO₄)₂ crystal. Different values of temperature hysteresis were found in temperature studies of the ferroelastic domain structure (ΔT_S  3–5 K) and in Raman spectra studies (ΔT_S  12 K). No changes were observed in the pattern of ferroelastic domain structure at the temperature T_II–III  265 K, at which C2/c → P2/n structural phase transition takes place. On the other hand, at T_III–IV  135 K additional domains with W′-type of domain wall orientation were found.     

Modifying the buckyball

Structural and electronic properties of carbon clusters, in particular the C₆₀ “buckyball” molecule as well as structurally and chemically modified fullerenes, are calculated using a combination of predictive ab initio techniques and parametrized total energy schemes. These calculations indicate that single- and multi-shell fullerenes are the most stable C_n isomers at T = 0 for n < 20. More open structures are favored by entropy at higher temperatures. Upon interaction with donor elements, C₆₀ molecules form stable M@C₆₀ endohedral complexes; analogous acceptor-based complexes are unstable. Solid C₆₀ reacts with alkali metals and forms a stable intercalation compound which shows superconducting behavior. The relatively high value of the critical temperature for superconductivity can be explained quantitatively within the Bardeen-Cooper-Schrieffer formalism.     

Internal friction and elastic modulus of bulk metallic glasses

The mechanical relaxation in binary, ternary, quaternary, and quitary bulk metallic glasses with widely different glass-forming ability, or the critical cooling rate, has been studied. A single-roller melt-spinning apparatus was used for preparing thin specimens. The internal friction Q⁻¹ and the oscillation frequency f of the specimens were measured using an inverted torsion pendulum with the free decay method. The measurements were performed from room temperature, through the glass transition temperature T_g, up to the crystallization temperature T_x. As the temperature is increased, the background Q⁻¹ increases, and peaks can usually be seen near T_g and T_x. The shear modulus, which is proportional to f², is changed near the Q⁻¹ peak. The experimental data are presented and overall features of the results are discussed.     

A mechanistic model for the effect of stress ratio on the LEFM fatigue crack growth behavior of metals and alloys—II. Crack-brittle materials

A recently proposed mechanistic model for the effect of stress ratio, R, on the LEFM (long) fatigue crack growth behavior of “crack-ductile” materials is extended here to explain and predict similar behavior under similar conditions of “crack-brittle” materials characterised by the presence of “static” modes of fatigue fracture in stages II and III. It is shown that in these materials the stage I behavior is similar, but the stages II and III behave differently from crack-ductile materials. Mechanism-based existence of two types of stage II curves characterised respectively by “ pure shear mode ” (SM-II) and “mixed-mode” (MM-II), both plotting linear but having different slopes, is introduced. It is shown that while stage SM-II is insensitive, stage MM-II is significantly sensitive to R, in the same material. Similar to stage I, another “ moving pivot-point ” exists at the transition from SM-II to MM-II, which slides down the “ master shear-curve ” with increasing R. Assuming a critical K_max for the initiation of static modes, a critical R for saturation of these modes, and Paris-type growth relations, a quantitative predictive model containing growth equations for stages SM-II and MM-II, has been developed. Stage III is discussed only qualitatively. Reasonably good agreement was found between predicted curves at selected R-values and a relatively large volume of experimental data for steels, Al-alloys and Ti-alloys. This simple, alternative model may be used for obtaining quick, fairly accurate and conservative estimates of R-influenced crack growth rates for design applications in preference to crack-closure which frequently requires elaborate and tedious experimental procedures.     

Frequency dependent electrical conductivity and dielectric relaxation behavior in amorphous (90V2O5–10Bi2O3) oxide semiconductors doped with SrTiO3

We report on the experimental results of frequency dependent a.c. conductivity and dielectric constant of SrTiO₃ doped 90V₂O₅–10Bi₂O₃ semiconducting oxide glasses for wide ranges of frequency (500–10⁴ Hz) and temperature (80–400 K). These glasses show very large dielectric constants (10²–10⁴) compared with that of the pure base glass (≈10²) without SrTiO₃ and exhibit Debye-type dielectric relaxation behavior. The increase in dielectric constant is considered to be due to the formation of microcrystals of SrTiO₃ and TiO₂ in the glass matrix. These glasses are n-type semiconductors as observed from the measurements of the thermoelectric power. Unlike many vanadate glasses, Long's overlapping large polaron tunnelling (OLPT) model is found to be most appropriate for fitting the experimental conductivity data, while for the undoped V₂O₅–Bi₂O₃ glasses, correlated barrier hopping conduction mechanism is valid. This is due to the change of glass network structure caused by doping base glass with SrTiO₃. The power law behavior (σ_ac=A(ω^s) with s<1) is, however, followed by both the doped and undoped glassy systems. The model parameters calculated are reasonable and consistent with the change of concentrations (x).