Cavitation in brittle metallic glasses - Effects of stress state and distributed weak zones

Experimental studies and atomistic simulations have shown that brittle metallic glasses fail by a cavitation mechanism whose origin has been traced to the presence of intrinsic atomic density fluctuations which give rise to weak zones with reduced yield strength. It has been shown recently through continuum analysis that the presence of these zones can lower the cavitation stress considerably under equibiaxial loading. The objective of the present work is to study the effect of the applied stress state on the cavitation behavior of such a heterogeneous plastic solid with distributed weak zones. To this end, 2D plane strain finite element simulations are performed by subjecting a unit cell containing a weak zone to different (biaxiality) stress ratios. The volume fraction and yield strength of the weak zone are varied over a wide range. The results show that unlike in a homogeneous plastic solid, the cavitation stress of the heterogeneous aggregate does not reduce appreciably as the stress ratio decreases from unity when the yield strength of the weak zone is low. It is found that a non-dimensional parameter characterizing the stress state prevailing in the weak zone and its yield properties uniquely control the cavitation stress. The nature of cavitation bifurcation may change from unstable bifurcation to the left at sufficiently low stress ratio to one involving snap cavitation at high stress ratio. (C) 2014 Elsevier Ltd. All rights reserved.

Crystallographic studies of the extracytoplasmic function sigma factor sigma(J) from Mycobacterium tuberculosis

Mycobacterium tuberculosis has multiple sigma factors which enable the bacterium to reprogram its transcriptional machinery under diverse environmental conditions. sigma(J), an extracytoplasmic function sigma factor, is upregulated in late stationary phase cultures and during human macrophage infection. sigma(J) governs the cellular response to hydrogen peroxide-mediated oxidative stress. sigma(J) differs from other canonical sigma factors owing to the presence of a SnoaL_2 domain at the C-terminus. sigma(J) crystals belonged to the tetragonal space group I422, with unit-cell parameters a = b = 133.85, c = 75.08 angstrom. Diffraction data were collected to 2.16 angstrom resolution on the BM14 beamline at the European Synchrotron Radiation Facility (ESRF).

Dual Stress and Thermally Driven Mechanical Properties of the Same Organic Crystal: 2,6-Dichlorobenzylidene-4-fluoro-3-nitroaniline

An elastic organic crystal, 2,6-dichlorobenzylidine-4-fluoro-3-nitroaniline (DFNA), which also shows thermosalient behavior, is studied. The presence of these two distinct properties in the same crystal is unusual and unprecedented because they follow respectively from isotropy and anisotropy in the crystal packing. Therefore, while both properties lead from the crystal structure, the mechanisms for bending and thermosalience are quite independent of one another. Crystals of the low-temperature (a) form of the title compound are bent easily without any signs of fracture with the application of deforming stress, and this bending is within the elastic limit. The crystal structure of the a-form was determined (P2(1)/c, Z = 4, a = 3.927(7) angstrom, b = 21.98(4) angstrom, c = 15.32(3) angstrom). There is an irreversible phase transition at 138 degrees C of this form to the high-temperature beta-form followed by melting at 140 degrees C. Variable-temperature X-ray powder diffraction was used to investigate the structural changes across the phase transition and, along with an FTIR study, establishes the structure of the beta-form. A possible rationale for strain build-up is given. Thermosalient behavior arises from anisotropic changes in the three unit cell parameters across the phase transition, notably an increase in the b axis parameter from 21.98 to 22.30 angstrom. A rationale is provided for the existence of both elasticity and thermosalience in the same crystal. FTIR studies across the phase transition reveal important mechanistic insights: (i) increased pi...pi repulsions along 100] lead to expansion along the a axis; (ii) change in alignment of C-Cl and NO2 groups result from density changes; and (iii) competition between short-range repulsive (pi...pi) interactions and long-range attractive dipolar interactions (C-Cl and NO2) could lie at the origin of the existence of two distinctive properties.

The X-ray photoelectron spectroscopy and high-temperature structural studies of Zn1-xNixO/NiO two-phase composites

Detailed investigation of the chemical states and local atomic environment of Ni and Zn in the two-phase composites of Zn1-xNixO/NiO was reported. The X-ray photoelectron spectra of both Ni-2p and Zn-2p revealed the existence of a doublet with spin-orbit splitting approximate to 17.9 and 23.2eV, respectively confirming the divalent oxidation state of both Ni and Zn. However, the samples fabricated under oxygen-rich conditions exhibit significant difference in the binding energy approximate to 18.75eV between the 2p3/2 and 2p1/2 states of Ni. The shift in the satellite peaks of Ni-2p with increasing the Ni composition x within the Zn1-xNixO/NiO matrix signifies the attenuation of nonlocal screening because of reduced site occupancy of two adjacent Zn ions. The temperature dependence of X-ray diffraction analysis reveals a large distortion in the axial-rhombohedral angle for oxygen-rich NiO. Conversely, no significant distortion was noticed in the NiO system present as a secondary phase within Zn1-xNixO. Nevertheless, the unit-cell volume of both wurtzite h.c.p. Zn1-xNixO and f.c.c. NiO exhibits an anomalous behavior between 150 and 300 degrees C. The origin of such unusual change in the unit-cell volume was discussed in terms of oxygen stoichiometry.

Common effect of chemical and external pressures on the magnetic properties of RCoPO (R = La, Pr, Nd, Sm). II.

We investigate the direct correspondence between Co band ferromagnetism and structural parameters in the pnictide oxides RCoPO for different rare-earth ions (R = La, Pr, Nd, Sm) by means of muon-spin spectroscopy and ab initio calculations, complementing our results published previously G. Prando et al., Common effect of chemical and external pressures on the magnetic properties of RCoPO (R = La, Pr), Phys. Rev. B 87, 064401 (2013)]. We find that both the transition temperature to the ferromagnetic phase T-C and the volume of the crystallographic unit cell V are conveniently tuned by the R ionic radius and/or external pressure. We report a linear correlation between T-C and V and our ab initio calculations unambiguously demonstrate a full equivalence of chemical and external pressures. As such, we show that R ions influence the ferromagnetic phase only via the induced structural shrinkage without involving any active role from the electronic f degrees of freedom, which are only giving a sizable magnetic contribution at much lower temperatures.

Interrelationship between Interphase Boundaries and Phase Contents near the Critical Compositions of Lead-Free Ferroelectric (Na0.5Bi0.5)TiO3-BaTiO3

Heterophase structures in lead-free perovskite-type ferroelectric solid solutions of (1 - z)(Na0.5Bi0.5)TiO3 - zBaTiO(3) are analysed for a few critical compositions near the morphotropic phase boundary (z = 0.05-0.07). Examples of the phase coexistence and elastic matching of the phases from different symmetry groups are considered to find optimum volume fractions of specific domain types and coexisting phases at the complete stress relief in two-phase samples. Some interrelations between these volume fractions are described using variants of the domain arrangement at changes in the composition and unit-cell parameters. The evaluated room-temperature volume fractions of the ferroelectric monoclinic (Cm symmetry) and tetragonal (P4mm symmetry) phases near the morphotropic phase boundary are in agreement with experimental data.

Pressure-induced phase transition in Bi2Se3 at 3 GPa: electronic topological transition or not?

In recent years, a low pressure transition around P similar to 3 GPa exhibited by the A(2)B(3)-type 3D topological insulators is attributed to an electronic topological transition (ETT) for which there is no direct evidence either from theory or experiments. We address this phase transition and other transitions at higher pressure in bismuth selenide (Bi2Se3) using Raman spectroscopy at pressure up to 26.2 GPa. We see clear Raman signatures of an isostructural phase transition at P similar to 2.4 GPa followed by structural transitions at similar to 10 GPa and 16 GPa. First-principles calculations reveal anomalously sharp changes in the structural parameters like the internal angle of the rhombohedral unit cell with a minimum in the c/a ratio near P similar to 3 GPa. While our calculations reveal the associated anomalies in vibrational frequencies and electronic bandgap, the calculated Z(2) invariant and Dirac conical surface electronic structure remain unchanged, showing that there is no change in the electronic topology at the lowest pressure transition.

A New Deformation Theory with Strain Gradient Effects

A new phenomenological deformation theory with strain gradient effects is proposed. This theory, which belongs to nonlinear elasticity, fits within the framework of general couple stress theory and involves a single material length scale l. In the present theory three rotational degrees of freedom omega(i) are introduced in addition to the conventional three translational degrees of freedom u(i). omega(i) has no direct dependence upon ui and is called the micro-rotation, i.e. the material rotation theta(i) plus the particle relative rotation. The strain energy density is assumed to only be a function of the strain tensor and the overall curvature tensor, which results in symmetric Cauchy stresses. Minimum potential principle is developed for the strain gradient deformation theory version. In the limit of vanishing 1, it reduces to the conventional counterparts: J(2) deformation theory. Equilibrium equations, constitutive relations and boundary conditions are given in details. Comparisons between the present theory and the theory proposed by Shizawa and Zbib (Shizawa, K., Zbib, H.M., 1999. A thermodynamical theory gradient elastoplasticity with dislocation density Censor: fundamentals. Int. J. Plast. 15, 899) are given. With the same hardening law as Fleck et al. (Fleck, N.A., Muller, G.H., Ashby, M.F., Hutchinson, JW., 1994 Strain gradient plasticity: theory and experiment. Acta Metall. Mater 42, 475), the new strain gradient deformation theory is used to investigate two typical examples, i.e. thin metallic wire torsion and ultra-thin metallic beam bend. The results are compared with those given by Fleck et al, 1994 and Stolken and Evans (Stolken, J.S., Evans, A.G., 1998. A microbend test method for measuring the plasticity length scale. Acta Mater. 46, 5109). In addition, it is explained for a unit cell that the overall curvature tensor produced by the overall rotation vector is the work conjugate of the overall couple stress tensor. (C) 2002 Elsevier Science Ltd. All rights reserved.

On the mechanism of void growth and the effect of straining mode in ductile materials

Finite element analysis is employed to investigate void growth embedded in elastic-plastic matrix material. Axisymmetric and plane stress conditions are considered. The simulation of void growth in a unit cell model is carried out over a wide range of triaxial tensile stressing or large plastic straining for various strain hardening materials to study the mechanism of void growth in ductile materials. Triaxial tension and large plastic strain encircling around the void are found to be of most importance for driving void growth. The straining mode of incremental loading which favors the necessary strain concentration around void for its growth can be characterized by the vanishing condition of a parameter called "the third invariant of generalized strain rate". Under this condition, it accentuates the internal strain concentration and the strain energy stored/dissipated within the material layer surrounding the void. Experimental results are cited to justify the effect of this loading parameter. (C) 2000 Elsevier Science Ltd. All rights reserved.

Three-dimensional finite element analysis of composites with coated spherical inclusions

A three-dimensional finite element analysis has been used to determine the internal stresses in a three-phase composite. The stresses have been determined for a variety of interphase properties, the thicknesses of the interphase and the volume fractions of particles. Young's modulus has been calculated from a knowledge of these stresses and the applied deformation. The calculations show that stress distributions in the matrix and the mechanical properties are sensitive to the interphase property in the three-phase composites. The interfacial stresses in the three-dimensional analysis are in agreement with results obtained by an axisymmetric analysis. The predicted bulk modulus in three-dimensional analysis agrees well with the theoretical solution obtained by Qui and Weng, but it presents a great divergence from that in axisymmetric analyses. An investigation indicates that this divergence may be caused by the difference in the unit cell structure between two models. A comparison of the numerically predicted bulk and shear modulus for two-phase composites with the theoretical results indicates that the three-dimensional analysis gives quite satisfactory results.

Effect of phase-transformation on mechanical-behavior of dual-phase steel plate

The mechanical behavior of dual phase steel plates is affected by internal stresses created during martensite transformation. Analytical modelling of this effect is made by considering a unit cell made of martensite inclusion in a ferrite matrix. A large strain finite element analysis is then performed to obtain the plane stress deformation state. Displayed numerically are the development of the plastic zone and distribution of local state of stress and strain. Studied also are the shape configuration of the martensite (hard-phase) that influences the interfacial condition as related to stress transmission and damage. Internal stresses are found to enhance the global flow stress after yield initiation in the ferrite matrix. Good agreement is obtained between the analytical results and experimental observations.

Displacive To Order-Disorder Two-Step Phase Transition Model For Para-Ferroelectric Transition

Two-step phase transition model, displacive to order-disorder, is proposed. The driving forces for these two transitions are fundamentally different. The displacive phase transition is one type of the structural phase transitions. We clearly define the structural phase transition as the symmetry broking of the unit cell and the electric dipole starts to form in the unit cell. Then the dipole-dipole interaction takes place as soon as the dipoles in unit cells are formed. We believe that the dipole-dipole interaction may cause an order-disorder phase transition following the displacive phase transition. Both structural and order-disorder phase transition can be first-order or second-order or in between. We found that the structural transition temperatures can be lower or equal or higher than the order-disorder transition temperature. The para-ferroelectric phase transition is the combination of the displacive and order-disorder phase transitions. It generates a variety of transition configurations along with confusions. In this paper, we discuss all these configurations using our displacive to order-disorder two-step phase transition model and clarified all the confusions.

Thin metastructures with engineered thermal expansion

The geometry and constituent materials of metastructures can be used to engineer the thermal expansion coefficient. In this thesis, we design, fabricate, and test thin thermally stable metastructures consisting of bi-metallic unit cells and show how the coefficient of thermal expansion (CTE) of these metastructures can be finely and coarsely tuned by varying the CTE of the constituent materials and the unit cell geometry. Planar and three-dimensional finite element method modeling is used to drive the design and inform experiments, and predict the response of these metastructures. We demonstrate computationally the significance of out-of-plane effects in the metastructure response. We develop an experimental setup using digital image correlation and an infrared camera to experimentally measure full displacement and temperature fields during testing and accurately measure the metastructures’ CTE. We experimentally demonstrate high aspect ratio metastructures of Ti/Al and Kovar/Al which exhibit near-zero and negative CTE, respectively. We demonstrate robust fabrication procedures for thermally stable samples with high aspect ratios in thin foil and thin film scales. We investigate the lattice structure and mechanical properties of thin films comprising a near-zero CTE metastructure. The mechanics developed in this work can be used to engineer metastructures of arbitrary CTE and can be extended to three dimensions.

Phase behavior of complex superprotonic solid acids

Superprotonic phase transitions and thermal behaviors of three complex solid acid systems are presented, namely Rb3H(SO4)2-RbHSO4 system, Rb3H(SeO4)2-Cs3H(SeO4)2 solid solution system, and Cs6(H2SO4)3(H1.5PO4)4. These material systems present a rich set of phase transition characteristics that set them apart from other, simpler solid acids. A.C. impedance spectroscopy, high-temperature X-ray powder diffraction, and thermal analysis, as well as other characterization techniques, were employed to investigate the phase behavior of these systems.

Rb3H(SO4)2 is an atypical member of the M3H(XO4)2 class of compounds (M = alkali metal or NH4+ and X = S or Se) in that a transition to a high-conductivity state involves disproportionation into two phases rather than a simple polymorphic transition [1]. In the present work, investigations of the Rb3H(SO4)2-RbHSO4 system have revealed the disproportionation products to be Rb2SO4 and the previously unknown compound Rb5H3(SO4)4. The new compound becomes stable at a temperature between 25 and 140 °C and is isostructural to a recently reported trigonal phase with space group P3̅m of Cs5H3(SO4)4 [2]. At 185 °C the compound undergoes an apparently polymorphic transformation with a heat of transition of 23.8 kJ/mol and a slight additional increase in conductivity.

The compounds Rb3H(SeO4)2 and Cs3H(SeO4)2, though not isomorphous at ambient temperatures, are quintessential examples of superprotonic materials. Both adopt monoclinic structures at ambient temperatures and ultimately transform to a trigonal (R3̅m) superprotonic structure at slightly elevated temperatures, 178 and 183 °C, respectively. The compounds are completely miscible above the superprotonic transition and show extensive solubility below it. Beyond a careful determination of the phase boundaries, we find a remarkable 40-fold increase in the superprotonic conductivity in intermediate compositions rich in Rb as compared to either end-member.

The compound Cs6(H2SO4)3(H1.5PO4)4 is unusual amongst solid acid compounds in that it has a complex cubic structure at ambient temperature and apparently transforms to a simpler cubic structure of the CsCl-type (isostructural with CsH2PO4) at its transition temperature of 100-120 °C [3]. Here it is found that, depending on the level of humidification, the superprotonic transition of this material is superimposed with a decomposition reaction, which involves both exsolution of (liquid) acid and loss of H2O. This reaction can be suppressed by application of sufficiently high humidity, in which case Cs6(H2SO4)3(H1.5PO4)4 undergoes a true superprotonic transition. It is proposed that, under conditions of low humidity, the decomposition/dehydration reaction transforms the compound to Cs6(H2-0.5xSO4)3(H1.5PO4)4-x, also of the CsCl structure type at the temperatures of interest, but with a smaller unit cell. With increasing temperature, the decomposition/dehydration proceeds to greater and greater extent and unit cell of the solid phase decreases. This is identified to be the source of the apparent negative thermal expansion behavior.

References

[1] L.A. Cowan, R.M. Morcos, N. Hatada, A. Navrotsky, S.M. Haile, Solid State Ionics 179 (2008) (9-10) 305.

[2] M. Sakashita, H. Fujihisa, K.I. Suzuki, S. Hayashi, K. Honda, Solid State Ionics 178 (2007) (21-22) 1262.

[3] C.R.I. Chisholm, Superprotonic Phase Transitions in Solid Acids: Parameters affecting the presence and stability of superprotonic transitions in the MHnXO4 family of compounds (X=S, Se, P, As; M=Li, Na, K, NH4, Rb, Cs), Materials Science, California Institute of Technology, Pasadena, California (2003).

Crystal Coulomb energies: I. Organic donor-acceptor complexes--a review. II. Classical Ewald calculations of the Coulomb binding energy of four donor-acceptor crystals and Wurster's blue perchlorate. III. A rapid-convergence quantum-mechanical formalism for crystal electronic energies

Chapter I

Theories for organic donor-acceptor (DA) complexes in solution and in the solid state are reviewed, and compared with the available experimental data. As shown by McConnell et al. (Proc. Natl. Acad. Sci. U.S., 53, 46-50 (1965)), the DA crystals fall into two classes, the holoionic class with a fully or almost fully ionic ground state, and the nonionic class with little or no ionic character. If the total lattice binding energy 2ε₁ (per DA pair) gained in ionizing a DA lattice exceeds the cost 2ε_o of ionizing each DA pair, ε₁ + ε_o less than 0, then the lattice is holoionic. The charge-transfer (CT) band in crystals and in solution can be explained, following Mulliken, by a second-order mixing of states, or by any theory that makes the CT transition strongly allowed, and yet due to a small change in the ground state of the non-interacting components D and A (or D⁺ and A^-). The magnetic properties of the DA crystals are discussed.

Chapter II

A computer program, EWALD, was written to calculate by the Ewald fast-convergence method the crystal Coulomb binding energy E_C due to classical monopole-monopole interactions for crystals of any symmetry. The precision of E_C values obtained is high: the uncertainties, estimated by the effect on E_C of changing the Ewald convergence parameter η, ranged from ± 0.00002 eV to ± 0.01 eV in the worst case. The charge distribution for organic ions was idealized as fractional point charges localized at the crystallographic atomic positions: these charges were chosen from available theoretical and experimental estimates. The uncertainty in E_C due to different charge distribution models is typically ± 0.1 eV (± 3%): thus, even the simple Hückel model can give decent results.

E_C for Wurster's Blue Perchl orate is -4.1 eV/molecule: the crystal is stable under the binding provided by direct Coulomb interactions. E_C for N-Methylphenazinium Tetracyanoquino- dimethanide is 0.1 eV: exchange Coulomb interactions, which cannot be estimated classically, must provide the necessary binding.

EWALD was also used to test the McConnell classification of DA crystals. For the holoionic (1:1)-(N,N,N',N'-Tetramethyl-para- phenylenediamine: 7,7,8,8-Tetracyanoquinodimethan) E_C = -4.0 eV while 2ε_o = 4.6₅ eV: clearly, exchange forces must provide the balance. For the holoionic (1:1)-(N,N,N',N'-Tetramethyl-para- phenylenediamine:para-Chloranil) E_C = -4.4 eV, while 2ε_o = 5.0 eV: again EC falls short of 2ε₁. As a Gedankenexperiment, two nonionic crystals were assumed to be ionized: for (1:1)-(Hexamethyl- benzene:para-Chloranil) E_C = -4.5 eV, 2ε_o = 6.6 eV; for (1:1)- (Napthalene:Tetracyanoethylene) E_C = -4.3 eV, 2ε_o = 6.5 eV. Thus, exchange energies in these nonionic crystals must not exceed 1 eV.

Chapter III

A rapid-convergence quantum-mechanical formalism is derived to calculate the electronic energy of an arbitrary molecular (or molecular-ion) crystal: this provides estimates of crystal binding energies which include the exchange Coulomb inter- actions. Previously obtained LCAO-MO wavefunctions for the isolated molecule(s) ("unit cell spin-orbitals") provide the starting-point. Bloch's theorem is used to construct "crystal spin-orbitals". Overlap between the unit cell orbitals localized in different unit cells is neglected, or is eliminated by Löwdin orthogonalization. Then simple formulas for the total kinetic energy Q^(XT)_λ, nuclear attraction [λ/λ]^XT, direct Coulomb [λλ/λ'λ']^XT and exchange Coulomb [λλ'/λ'λ]^XT integrals are obtained, and direct-space brute-force expansions in atomic wavefunctions are given. Fourier series are obtained for [λ/λ]^XT, [λλ/λ'λ']^XT, and [λλ/λ'λ]^XT with the help of the convolution theorem; the Fourier coefficients require the evaluation of Silverstone's two-center Fourier transform integrals. If the short-range interactions are calculated by brute-force integrations in direct space, and the long-range effects are summed in Fourier space, then rapid convergence is possible for [λ/λ]^XT, [λλ/λ'λ']^XT and [λλ'/λ'λ]^XT. This is achieved, as in the Ewald method, by modifying each atomic wavefunction by a "Gaussian convergence acceleration factor", and evaluating separately in direct and in Fourier space appropriate portions of [λ/λ]^XT, etc., where some of the portions contain the Gaussian factor.