Shear Elastic Constants Research Articles

Computational approach to identify structural and elastic relationship in metastable crystalline and amorphous alloy thin films: Mo1-xNix and Mo1-xSix case studies

Previously well-established experimental trends of ground-state properties of crystalline and amorphous Mo1-xSix and Mo1-xNix alloys with 0 ≤ x ≤ 1 are predicted by first-principles calculations and inter-relationship with sound velocities and elastic properties are identified. The free energy of mixing, calculated at 300 K provides accurate values of the critical Si and Ni concentrations leading to the crystalline-to-amorphous transition. Specifically, a transition from BCC to amorphous state is predicted for xSi ~ 0.14 and xNi ~ 0.32, while FCC to amorphous transition is observed for xNi ~ 0.77. These structural transitions are accompanied by modifications of the out-of-plane longitudinal and shear elastic constants. In the crystalline region, a pronounced softening of elastic moduli is predicted for both solid solution alloys. While for amorphous Mo-Ni, the elastic constants do not undergo significant changes, for amorphous Mo-Si, they exhibit two distinct behaviors depending on the electronic properties and bonding character. For 0.2 ≤ xSi ≤ 0.7, the metallic character of the amorphous alloys is maintained and the elastic properties are remarkably stable. For xSi > 0.7, a progressive increase in the atomic volume is observed and the amorphous alloys acquire a covalent character and a reduced coordination number. Surprisingly, during this transition, both the longitudinal and shear acoustic velocities continuously increase, despite a progressive softening of the elastic stiffness constants. These calculations provide deep insight at the atomic-scale and reproduce satisfactorily the earlier experimental works of magnetron co-sputtered Mo-Si films, while some disagreement on elastic properties remain for more energetic ion beam sputtered Mo-Ni films, likely partially attributed to point-defects.

Research progress on dynamic testing methods of wood shear modulus: A review

Wood is a non-homogeneous and orthotropic natural polymer material. It is important to test the wood shear modulus and elastic constants accurately and reliably using dynamic methods. Based on the introduction of the advantages of six common methods for dynamic testing of wood shear modulus, such as free plate torsional mode method, free bar torsional vibration method, and Timoshenko beam iterative method, issues associated with the applicability and accuracy of these methods are also pointed out. Recent methods, such as the free square plate torsional mode method and the square plate static torsional strain method, that were developed to dynamically test the shear modulus of wood and wood composite materials, are presented as effective ways to tackle these issues. These new approaches are expected to provide beneficial technical support for using small specimens, overcoming the size effect of specimens, simplifying the testing procedures, improving the test accuracy, and expanding the application range in the dynamic testing of wood shear modulus. These approaches have practical significance in promoting the industrialization and development of structural engineering, furniture and interior decoration, transportation, military, and musical instrument industries.

Alloying and magnetic disordering effects on the thermodynamic properties and phase stability of Co2Cr(Ga, Si) and Co2Cr(Al, Si) Heusler alloys

Using the first-principles exact muffin-tin orbital method in combination with the coherent potential approximation, the alloying and magnetic disordering effects on the thermodynamic properties and phase stability of the ferromagnetic L21- and D022-CoxCr78−xZ11Si11 (Z=Ga and Al, 46≤x≤62) alloys are systematically investigated. It is shown that at 0 K, with increasing x the D022 structure gets relatively more and more stable in the energy and stabilized instead in the two groups of alloys with x≥56 and 60, respectively. There, upon the martensitic transformation (MT) the bulk modulus gets a little larger than that of the austenite, and both significant magnetocaloric and magnetovolume effects could be also expected. The tetragonal shear elastic constant (C′=(C11−C12)/2) of the L21 phase decreases whereas that (Cs=C11+C12+2C33−4C13) of the D022 phase increases with the Co addition, mechanically favoring the relative stability of the more ductile D022 martensite as well. The magnetic excitations decrease the electronic total energy but increase the phonon vibrational free energy of the D022 phase relative to the L21 one. The two effects nevertheless almost offset each other at their Curie temperature. The reentrant MT (RMT) is then predicted without the magnetic excitations effect in the Z=Ga and Al alloys with 50≤x≤54 and 54≤x≤58, respectively, and their critical temperatures (TM) for the RMT decrease with increasing x, in line with the measured data of the Z=Ga alloys. With the Co addition, the increase of the relative stability of their D022 phase is finally confirmed maybe originating from the increase of the Co 3d minority DOS around the Fermi level in their L21 phase.

Elastic properties of porous silicon nitride fabricated via a low-temperature processing route

Porous silicon nitride is a promising material for many advanced applications due to its many outstanding properties. In this work, porous silicon nitride was fabricated at 1200 °C using a mixture of silicon nitride powder and phosphoric acid. The dual role of phosphoric acid as inorganic binder and pore former has been critically analyzed through a detailed structural characterization. Elastic constants of the porous silicon nitride samples were determined using non-destructive ultrasound phase spectroscopy, and the influence of the phosphoric acid content on the elastic properties was studied at depth. Both longitudinal and shear elastic constants were determined and Young's modulus and Poisson's ratio were calculated as a function of porosity considering the actual elastic symmetry of the fabricated samples. The experimentally determined elastic constants were compared with the predictions from different analytical models to understand the influence of porosity and pore morphology on the stiffness of the fabricated samples.

Modified extended Finnis Sinclair potential for cubic crystal metal

Unlike the modified embedded atom method (MEAM), which requires consideration of the bond angles, the embedded atom method (EAM) and Finnis Sinclair (FS) potential have achieved a wide range of applications in molecular dynamics simulations of amorphous alloys and disordered systems. In this paper, the potential functions of 10 cubic crystalline metals are reconstructed using the extended Finnis Sinclair (EFS) potential to improve the FS potential in terms of defects, surface energy and thermal properties. First of all, for the BCC crystal structure and FCC crystal structure, the fitted physical quantity expressions suitable for EAM potential and FS potential are deduced, including pressure, bulk modulus, shear elastic modulus elastic constant, vacancy formation energy and surface energy. Then, based on these physical quantities and the Rose equation of state, the least-squares method is used to fit the new potential parameters. Finally, using the current potential, the cohesive energy, elastic constants (C11, C12 and C44), vacancy formation energy, self-interstitial formation energy, surface energy, coefficient of thermal expansion, specific heat capacity and the melting point of 10 kinds of cubic crystals are calculated by molecular dynamics simulation. The reliability of the current potential is verified by comparing with other potential functions, experimental values and first-principles calculations. The results show that the current potential can well reproduce the characteristics of physical quantities such as lattice constant, cohesive energy and elastic constants (C11, C12 and C44). Compared with the previous EFS potential, the current potential is closer to the Rose equation of state. The calculated surface energy is more accurate, and the performance of defects and thermal properties shows the reliability of the current potential function, and these improvements are due to the improvement of the fitting method.

Anisotropic nematic fluctuations above the ferroquadrupolar transition in TmVO4

TmVO$_4$ exhibits ferroquadrupolar order below 2.15 K with a well-isolated non-Kramers ground state doublet, and is a model system to understand Ising nematic order. We present $^{51}$V nuclear magnetic resonance data as a function of field orientation in a single crystal. Although the spectra are well understood in terms of direct dipolar hyperfine couplings, the spin lattice relaxation rate exhibits strong anisotropy that cannot be understood in terms of magnetic fluctuations. We find that the spin lattice relaxation rate scales with the shear elastic constant associated with the ferroquadrupole phase transition, suggesting that quadrupole (nematic) fluctuations dominate the spin lattice relaxation for in-plane fields.

Determining elastic anisotropy of textured polycrystals using resonant ultrasound spectroscopy

Polycrystalline materials can have complex anisotropic properties depending on their crystallographic texture and crystal structure. In this study, we use resonant ultrasound spectroscopy (RUS) to nondestructively quantify the elastic anisotropy in extruded aluminum alloy 1100-O, an inherently low-anisotropy material. Further, we show that RUS can be used to indirectly provide a description of the material’s texture, which in the present case is found to be transversely isotropic. By determining the entire elastic tensor, we can identify the level and orientation of the anisotropy originated during extrusion. The relative anisotropy of the compressive (c11/c33) and shear (c44/c66) elastic constants is 1.5% ± 0.5% and 5.7% ± 0.5%, respectively, where the elastic constants (five independent elastic constants for transversely isotropic) are those associated with the extrusion axis that defines the symmetry of the texture. These results indicate that the texture is expected to have transversely isotropic symmetry. This finding is confirmed by two additional approaches. First, we confirm elastic constants and the degree of elastic anisotropy by direct sound velocity measurements using ultrasonic pulse echo. Second, neutron diffraction (ND) data confirm the symmetry of the bulk texture consistent with extrusion-induced anisotropy, and polycrystal elasticity simulations using the elastic self-consistent model with input from ND textures and aluminum single-crystal elastic constants render similar levels of polycrystal elastic anisotropy to those measured by RUS. We demonstrate the ability of RUS to detect texture-induced anisotropy in inherently low-anisotropy materials. Therefore, as many other common materials have intrinsically higher elastic anisotropy, this technique should be applicable for similar levels of texture, providing an efficient general diagnostic and characterization tool.

Laser-Ultrasonic Characterization of Strongly Anisotropic Materials by Transient Grating Spectroscopy

Transient grating spectroscopy (TGS) is a laser-ultrasonic method allowing measurement of the surface acoustic wave (SAW) velocity in an examined material for a given direction of the wave vector. We explore the capability of TGS for determination of shear elastic coefficients ( $$c^\prime$$ and $$c_{44}$$ ) of strongly anisotropic cubic materials. TGS is tested on a set of single crystals with an anisotropy factor up to $$A=25$$ . Using a numerical simulation based on a Ritz-Rayleigh approach, we show that strong anisotropy may lead to significant coupling of SAWs with bulk shear waves, which complicates TGS measurements in specific directions. Based on the obtained TGS data, we discuss the possibility of also using the TGS technique for assessing the longitudinal elastic coefficient ( $$c_L$$ ). Despite the energy focusing and other effects originating from the strong anisotropy, the TGS method can be used to reliably determine the directional dependence of the SAW velocity in these materials, and the resulting experimental datasets are sufficient for inverse determination of both the soft shear elastic constant ( $$c^\prime$$ ) and the hard shear elastic constant ( $$c_{44}$$ ). The longitudinal coefficient can be determined with lower accuracy. TGS is a suitable experimental tool for contactless characterization of strongly anisotropic materials.

First principles prediction of exceptional mechanical and electronic behaviour of Titanite (CaTiSiO5)

Titanite (CaTiSiO5) is a naturally occurring silicate phase, recently recognised as a potential material for immobilization of nuclear wastes, high-end ceramic lining and optical device development. The silicate undergoes a pressure-induced structural transition (P21/c to C2/c) at ~3.5 GPa, which we confirm from density function perturbation theory. Using first principles calculations pressure-dependent structural parameters of both the phases are presented. This article features the mechanical property of C2/c titanite characterized by a negative component (C36 = -16.41 GPa) of the elastic constant tensor (Cij), an enigmatic phenomenon seen not only in low symmetry (monoclinic), but also in the high symmetry system (cubic). We propose rotational kinematics of bonds, controlled by the valence charge distributions as a crucial atomic scale mechanism for structural collapse of the lattice under strain resulting in negative C36. This kinematic model allows us to predict the necessary and sufficient condition for the pressure dependent softening of their shear elastic constants (C44 and C55). The present study also sheds a new light upon the electronic properties of titanite, accounting for the intraband and interband transitions that influence the optical activity. Its anisotropic optical properties of titanite evaluated in the range 0–60 eV are marked by an attractive optical behaviour of this phase. It is transparent in the visible spectra, but showing excellent absorption and reflectivity in the UV region. We thus project titanite as an industrially potential UV shield material. Our theoretical estimate yields the highest value of anisotropic refractive index, 2.21 in [001].

Trends in elastic properties of Ti–Ta alloys from first-principles calculations

The martensitic start temperature (M s) is a technologically fundamental characteristic of high-temperature shape memory alloys. We have recently shown [Chakraborty et al 2016 Phys. Rev. B 94 224104] that the two key features in describing the composition dependence of M s are the T = 0 K phase stability and the difference in vibrational entropy which, within the Debye model, is directly linked to the elastic properties. Here, we use density functional theory together with special quasi-random structures to study the elastic properties of disordered martensite and austenite Ti–Ta alloys as a function of composition. We observe a softening in the tetragonal shear elastic constant of the austenite phase at low Ta content and a non-linear behavior in the shear elastic constant of the martensite. A minimum of 12.5% Ta is required to stabilize the austenite phase at T = 0 K. Further, the shear elastic constants and Young’s modulus of martensite exhibit a maximum for Ta concentrations close to 30%. Phenomenological, elastic-constant-based criteria suggest that the addition of Ta enhances the strength, but reduces the ductile character of the alloys. In addition, the directional elastic stiffness, calculated for both martensite and austenite, becomes more isotropic with increasing Ta content. The reported trends in elastic properties as a function of composition may serve as a guide in the design of alloys with optimized properties in this interesting class of materials.

Theoretical and Experimental Overview of Structural, Dielectric, Crystallographic, Electronic, Optical, and Physical Tensors of α-DIPAB and Iodine-Doped α-DIPAB Molecular Ferroelectric Crystals

Self-consistent ab initio calculations of the structural, crystallographic, electronic, optical, and physical properties as well as spontaneous polarization of P21 (α)-ferroelectric phase of diisopropylammonium bromide (α-DIPAB) molecular crystal are carried out. Examination of the total density of states as obtained using the generalized gradient approximation and hybrid exchange–correlation functional (HSE06) methods yields an optical bandgap of ∼ 5 eV and 6 eV, respectively. Furthermore, by using the Berry phase approach, we found that polar DIPAB exhibits a spontaneous polarization of 22.64 μC/cm2, indicating that this remarkable ferroelectric molecule could be used as an alternative to replace several known ferroelectrics for piezoelectric and optoelectronic applications such as capacitors, sensors, and data storage as well as microelectromechanical system (MEMS) devices. Using the vdW + DF2 approximation, we identify the majority of the vibrational modes in the Raman spectra and analyze the modes generated by the bromine (Br) deficiency. We find that the Br deficiency strongly affects the electric and elastic properties of α-DIPAB. Furthermore, the elastic, dielectric, and piezoelectric tensors of α-DIPAB are calculated and interpreted. α-DIPAB is found to exhibit a static dielectric tensor of ∼ 2.5, i.e., slightly smaller than that of typical perovskite-based ferroelectrics. In addition, the clamped-ion piezoelectric tensor is calculated. We found that the piezoelectric coefficient e21 corresponding to applying uniaxial strain in the direction perpendicular to the N–C bonds is smaller than the e22 principle coefficient. Moreover, the components e15 = 0.220 C/m2 and e35 = −0.2032 C/m2 correspond to applying shear strain η31, indicating a reasonable piezoelectric response of this polar crystal and making it a cheap attractive candidate for piezoelectric applications. The components of the elastic moduli tensor are calculated and interpreted. The α-DIPAB exhibits Young’s modulus of up to 50 GPa along specific crystalline directions despite its relatively low hardness. We attribute such a large value to the presence of a dense H–Br bond network between the Br and DIPAB molecule. The Poisson ratio is also strongly anisotropic, with values ranging from 0.5 to 0.2. The DIPAB systems are brittle based on the ratio between the bulk and shear elastic constants, suggesting that this material has potential for use in flexible electronic applications. A real-part dielectric anomaly at T = 140 K induced by iodine doping of α-DIPAB exhibits switchable behavior. This abnormality can be attributed to suppression of ferroelectricity induced by trapping of vortices at dislocation defects generated by iodine. Another dielectric anomaly found in the vicinity of the Curie temperature of α-DIPAB can be explained in terms of a structural phase-induced ferroelectric-to-paraelectric transition.

Structure, stress, and mechanical properties of Mo-Al-N thin films deposited by dc reactive magnetron cosputtering: Role of point defects

In this work, the structural and mechanical properties of ternary Mo-Al-N alloys are investigated by combining thin film growth experiments and density functional theory (DFT) calculations. Mo1−xAlxNy thin films (∼300 nm thick), with various Al fractions ranging from x = 0 to 0.5 and nitrogen-to-metal (Al + Mo) ratio ranging from y = 0.78 to 1.38, were deposited by direct-current reactive magnetron cosputtering technique from elemental Mo and Al targets under Ar + N2 plasma discharges. The Al content was varied by changing the respective Mo and Al target powers, at a fixed N2 (20 SCCM) and Ar (25 SCCM) flow rate, and using two different substrate temperatures Ts = 350 and 500 °C. The elemental composition, mass density, crystal structure, residual stress state, and intrinsic (growth) stress were examined by wavelength dispersive x-ray spectroscopy, x-ray reflectivity, x-ray diffraction, including pole figure and sin2ψ measurements, and real-time in situ wafer curvature. Nanoindentation tests were carried out to determine film hardness H and elastic modulus EIT, while the shear elastic constant C44 was measured selectively by surface Brillouin light spectroscopy. All deposited Mo1−xAlxNy films have a cubic rock-salt crystal structure and exhibit a fiber-texture with a [001] preferred orientation. The incorporation of Al is accompanied by a rise in nitrogen content from 44 to 58 at. %, resulting in a significant increase (2%) in the lattice parameter when x increases from 0 to 0.27. This trend is opposite to what DFT calculations predict for cubic defect-free stoichiometric Mo1−xAlxN compounds and is attributed to variation in point defect concentration (nitrogen and metal vacancies) when Al substitutes for Mo. Increasing Ts from 350 to 500 °C has a minimal effect on the structural properties and phase composition of the ternary alloys but concurs to an appreciable reduction of the compressive stress from −5 to −4 GPa. A continuous increase and decrease in transverse sound velocity and mass density, respectively, lead to a moderate stiffening of the shear elastic constant from 130 to 144 GPa with increasing Al fraction up to x = 0.50, and a complex and nonmonotonous variation of H and EIT is observed. The maximum hardness of ∼33 GPa is found for the Mo0.81Al0.19N1.13 film, with nitrogen content close to the stoichiometric composition. The experimental findings are explained based on structural and elastic constant values computed from DFT for defect-free and metal- or nitrogen-deficient rock-salt MoAlN compounds.

Ab Initio Calculations on Elastic Properties of IF Steel Matrix Phase at High Temperature Based on Lattice Expansion Theory

Elucidating the evolution law of the elastic properties of the matrix phase is of great significance for the control of steel properties and quality during continuous casting and subsequent heat treatment. In this paper, thermal expansion experiments and ab initio calculations are used to study the elastic properties of the interstitial free (IF) steel matrix phase in different magnetic states and crystal structures. The results show that the bulk modulus B and the tetragonal shear elastic constant C’ for the entire temperature range decrease with increasing temperature, but C44 is the opposite. While from paramagnetic (PM) to ferromagnetic (FM) state, C’(C44) have changed ~188% (~27%), B increases by ~55% during the crystal structure change (fcc→bcc). With the FM to PM state, the Zener anisotropy parameter increases sharply, and Young’s modulus decreases significantly in the [001] direction; the maximum difference is ~76 GPa. The evolution rate of average Young’s modulus in single bcc-phase FM (fcc-phase PM) range reaches ~5.5(~5.6) × 10−2 GPa K−1. The research provides an effective method for ab initio calculation of the elastic properties of interstitial free and ultra-low carbon steels at high temperature, also furnishing a basis for the application of ab initio calculations to the high temperature performance of steel materials.

First Principles Prediction of Exceptional Mechanical and Electronic Behaviour of Titanite (CaTiSiO5)

Titanite (CaTiSiO5) is a naturally occurring silicate, recently recognised as a potential material for immobilization of nuclear wastes, high-end ceramic lining and optical device development. However, a detailed analysis of its mechanical and electronic properties is still lacking. This article shows that the mechanical properties of titanite is characterized by negative elasticity, an enigmatic mechanical behaviour seen not only in low symmetry (monoclinic), but also in the high symmetry system (cubic). Using first principles calculations a new microscopic basis is developed to explain the negative elasticity of titanite. Rotational bond kinematics, controlled by the valence charge distributions is proposed as a crucial atomic scale mechanism for structural collapse of the lattice under strain, leading to the negative elastic constant. Our bond dynamic model provides a novel approach to characterise materials with unique strain–energy behaviour, which allows us to predict the necessary and sufficient condition for the pressure dependent softening of its shear elastic constants. This article also sheds a new light upon the electronic properties of titanite, accounting for the intraband and interband transition that influence the optical activity. We report the anisotropic optical properties of titanite in the 0–60 eV range for the first time, featuring an attractive optical behaviour of this phase. It is transparent in the visible spectra, but shows excellent absorption and reflectivity in the UV region. We thus project titanite as an industrially potential UV shield material. Our theoretical estimate yields the highest value of anisotropic refractive index, 2.21 in [001].

Ultralow shear modulus of incommensurate [SnSe]n[MoSe2]n layers synthesized by the method of modulated elemental reactants

We demonstrate that the shear elastic constant of misfit-layered dichalcogenide films ${[\mathrm{SnSe}]}_{n}{[{\mathrm{MoSe}}_{2}]}_{n}$ with $n=1,2,3$, synthesized by the modulated elemental reactants method, is ${c}_{44}\ensuremath{\approx}1$ GPa, an order of magnitude lower than ${c}_{44}$ of typical layered crystals that have weak interlayer van der Waals bonding. The films are synthesized by alternating deposition of the elements to a total thickness of $\ensuremath{\approx}60$ nm followed by thermal annealing. We determine ${c}_{44}$ through measurements of the velocities of 700 nm wavelength surface acoustic waves propagating along the surface of Al/${[\mathrm{SnSe}]}_{n}{[{\mathrm{MoSe}}_{2}]}_{n}$/Si structures in combination with picosecond acoustics measurements of ${c}_{33}$ and calculations of the ${c}_{11}$, ${c}_{12}$, and ${c}_{13}$ elastic constants by density functional theory. We attribute the low value of ${c}_{44}$ to incommensurate interfaces between SnSe and ${\mathrm{MoSe}}_{2}$ layers and turbostratic disorder within the ${\mathrm{MoSe}}_{2}$ layers. We conclude that the ultralow shear modulus of disordered layered materials contributes significantly to their exceptionally low thermal conductivity.

Engineering heat transport in nanoparticle-in-alloy composites: The role of Mie scattering

Previous work toward engineering lower thermal conductivity of nanoparticle-in-alloy semiconductor composites have indicated that optimal nanoparticle sizes should lie between the Rayleigh and geometric phonon scattering regimes (i.e. the Mie regime); yet, phonon scattering models that are accurate in the Mie regime have never been employed to investigate the thermal transport. Here, we exploit exact solutions from continuum mechanics that separately treat longitudinal and transverse phonon scattering from nanoparticles across a wide spectrum of wavelengths, including the Rayleigh, Mie, and geometric scattering regimes. The solutions intrinsically account for material contrast effects from density and both normal and shear elastic constants. We find that consideration of Mie scattering effects drastically alters the material selection and particle sizing process for optimal nanocomposites. In particular, a previously unreported inter-relationship between density and elastic contrast is reported: in the Mie regime, a suppression of the scattering cross section is found in cases where the sound speeds of the matrix and nanoparticle are closely matched. This suppression can extend the transition wavelength to geometric scattering by more than an order-of-magnitude, with severe effects to thermal transport. We explore how these considerations change the optimal sizing of nanoparticles for metal/semiconductor composites, with specific application to the experimentally significant case of InGaAs composites.

Dopant-Type and Concentration Dependence of Total-Ionizing-Dose Response in Piezoresistive Micromachined Cantilevers

Lighter doping, pretreatment (exposure to hydrogen in a steam bath), and lower dose rate are each found to exacerbate 10-keV X-ray-induced negative frequency shifts and increase in resistivity measured in T-shaped, asymmetric, piezoresistive, micromachined, and resonating cantilevers. All devices recover to levels close to preirradiation after several hours of postirradiation annealing. The effects are attributed to dose-rate-dependent efficiencies of the depassivation of dopants by hydrogen and surface charging effects, which alter the effective Young’s modulus and shear elastic constants. Increases in resistivity are attributed to increases in scattering causing decreases in mobility. Results indicate the need to consider dopant type and concentration when choosing microelectromechanical systems for use in radiation environments in addition to accounting for low-dose-rate effects.

Prediction of the phase stability and elastic property of ϵ-Pu at high temperature from theoretical study

The phase stability and elastic property of ϵ-Pu at 800 K are predicted through systematically theoretical calculations, by taking the temperature-dependent phonon smearing, spin fluctuation, phonon vibration, and volume expansion effects into account. Dominated by the phonon smearing at 800 K, ϵ-Pu is thermodynamically stabilized in the paramagnetic state with the absolute value of the local magnetic moment (μPu) about 3.8 μB, being smaller than the 0 K value (about 5.0 μB). The resulted thermal spin fluctuation, which prefers the δ−ϵ phase transition, greatly decreases the volume (V) and the shear elastic constants (C′ and C44) of the ϵ phase. However, the phonon smearing itself prefers the expansion of V and also the increase of C′ and C44. Besides the influence of the spin fluctuation and phonon smearing at 800 K, the equilibrium V of ϵ-Pu seems to be dominated by the phonon vibration, and the lattice thermal expansion also further increases C′ whereas decreases C44. The determined V as well as C′ and C44 of ϵ-Pu at 800 K is reasonable in comparison with the previous studies. This insight provides a good understanding of the physical mechanisms driving the thermodynamical stability of ϵ-Pu at high temperature.

Novel insight into the formation of α″-martensite and ω-phase with cluster structure in metastable Ti-Mo alloys

On the basis of the “-Mo-Ti-Mo-” linear unit along the specific <111>β, <110>β, and <100>β directions, the cluster structures of α″-martensite and ω-phase were constructed in metastable Ti-Mo alloys to examine phase stability, elastic property, and crystal structure evolution by first-principles calculations combined with experimental analyses. With the increase in Mo content, the orthorhombicity and shuffle magnitude of {110}β plane along <110>β direction decreased, leading to change in the crystal structure of martensite from hexagonal close-packed to orthorhombic structure; the displacive collapse degree of {112}β plane along <111>β direction decreased, indicating that the crystal structure of ω-phase transited from hexagonal to trigonal structure. The softening effect of tetragonal shear elastic constant (C′) and Young's modulus (E100) was favorable for the shuffle and shear components of α″-martensite, respectively, whereas that of shear modulus (G111) was beneficial to the collapse component of ω-phase. The competition among C′, E100, and G111 affected the phase transformation following the sequence of hexagonal close-packed α′-martensite, orthorhombic α″-martensite, hexagonal ω-phase, and trigonal ω-phase in metastable titanium alloys.

First-principles study of phase stability and elastic properties in metastable Ti-Mo alloys with cluster structure

ABSTRACTThis paper provided a novel approach for evaluating phase stability and elastic properties in metastable Ti–Mo alloys with low Mo content by first-principles combined with cluster structure. In 54-atom body-centered-cubic supercell by substituting Ti atoms with 2–7 Mo atoms (7.1–23.0 wt% Mo), individual cluster structure of β-phase was constructed by ‘-Mo-Ti-Mo-’ cluster unit having the lowest cohesive energy. The distorted supercell was more stable than undistorted one at a low Mo content. With increasing Mo content, the density of state at Fermi level decreased, and bonding electron number increased, indicating β-phase stability was gradually promoted. Tetragonal shear elastic constant (C′ = (C11 – C12)/2), shear modulus (G111) and anisotropy factor (A = C44/C′) exhibited a fluctuation with Mo addition, while the change trend of A was opposite to C′ and G111. Calculated Young’s modulus exhibited similar changing trend to the C′, implying that the softening of C′ resulted in low Young’s modulus of β-phase. Measured Young’s modulus exhibited significant difference from calculated one, which was mainly caused by formation of α″-martensite and ω-phase. The values of C′, G111 and A were considered to associate with not only elastic properties of β-phase itself but also transition from β-phase to α″-martensite and/or ω-phase.