Session D38: Metals: Defects and Elastic Properties

Atomic short-range order effects on magnetostriction in Fe-rich Fe-Ga

We have measured diffuse x-ray scattering from an Fe-rich Fe-Ga BCC single crystal. Measurements were made on beamline 33-ID at the Advanced Photon Source using a wavelength dispersive spectrometer to suppress Compton, Fluorescence and Resonant Raman backgrounds. Data was collected over a large volume in reciprocal space and measurements were made at two energies to maximize and minimize the x-ray scattering contrast between Fe and Ga. We recovered short-range order (SRO) parameters for the crystal. Using these SRO parameters we use KKR-CPA and locally self-consistent multiple scattering (LSMS) calculations to study the effects of local atomic environment on electronic and magnetic structure of the alloy Research sponsored by the Division of Materials Sciences and Engineering. Research in part performed on Beamline 33-ID at the Advanced Photon Source which is sponsored by the U.S. Department of Energy, Office of Basic Energy Sciences   

First-principles study of helium bubble formation at a palladium lattice vacancy

Helium ($^{3}$He) generated from the tritium decay is one of the main reasons for macroscopic radiation damage in the structural components of nuclear devices such as fission reactors and tritium storage media. In contrast to the hydrogen isotopes, helium with its closed electron shell is inert inside metals and tends to aggregate into bubbles which can cause deterioration of materials and influence the lifetime of reactor components. To examine this behavior, we have performed \textit{ab initio} calculations of helium atoms inside palladium (Pd) using density functional theory (DFT) and the projector augmented wave (PAW) method within the generalized gradient approximation (GGA). We find that He diffuses easily in a defect-free Pd lattice. However, it is energetically favorable for multiple He atoms to be trapped at an isolated Pd vacancy site, forming a cluster of up to 8 atoms. The atomistic mechanisms of He-vacancy interaction in Pd are investigated by studying the corresponding electronic structural properties.   

Embedded Atom Method Potential for Titanium-Vanadium Alloys

Titanium alloys are important materials for aerospace applications due to their large strength-to-weight ratio and their ability to resist corrosion. Vanadium is an important alloying element for titanium since it stabilizes the high temperature bcc phase of titanium at lower temperatures, and bcc-stabilized titanium alloys generally showed improved hardness and forgeability [1]. Titanium-vanadium is also a reasonable starting point in the study of more complex titanium alloys of commercial importance. The calculation of many alloy properties requires the use of large numbers of atoms simulated over long periods of time. These calculations are currently only feasible through the use of classical interatomic potentials. An embedded atom method (EAM) potential for titanium-vanadium is presented, and thermodynamic and mechanical properties of this alloy are calculated using the potential. The results are compared to density functional theory results and experimental results when available. \newline \newline [1] M. J. Donachie, Jr., \emph{Titanium: A Technical Guide}, 2nd ed. ASM International: Metals Park, OH (2000).   

Atomistic dislocation simulation of aluminum using a tight-binding method

Atomistic simulation of dislocation in aluminum has been performed using a tight-binding method where the parameters are based on the works of Mehl and Papaconstantapoulous at the Naval Research Laboratory. We study the dissociation of a perfect edge dislocation (the dislocation line is along the $[11{\overline 2}]$ direction) of Burgers vector of $\frac{a}{2}[1{\overline 1} 0]$ into two partials of $\frac{a}{6}[2 {\overline 1}{\overline 1}] $ and $\frac{a}{6}[1 {\overline 2}1] $ on the $(111)$ slip plane. By performing a large scale atomistic relaxation, we observe a separation of partials of about 14~\AA\ and a stacking fault region. We will comment on the estimate of partials separation predicted by the elasticity theory, which relates to certain quantities such as the stacking fault energy.   

First-principles calculation of dislocation properties of ductile rare-earth intermetallic compounds

We have used first-principles calculations to study the mechanical properpies of rare-earth intermetallic B2 compounds which exhibit significant ductility. According to Peierls-Nabarro model and slip plane observed in tensile experimens, we have calculated and compared the {110} gamma surface energy for both brittle NiAl and ductile YCu. We also compared unstable stacking fault and twinning energy for a series of B2 compounds with different ductilily. Correlation between these energetics and the ductilily are discussed.   

Effect of Chemistry on Dislocation Core Properties in $\alpha$-Fe: AN \emph{ab initio}-Based Approach

Screw dislocations in $\alpha$-Fe and its alloys play an important role on the low-temperature mechanical properties. The solute atom can cause a significant local reconstruction of the dislocation core and therefore affect the mobility. Since direct investigations of the solute-dislocation interaction by first principles calculation remains a difficult problem, we employ a hybrid coupling approach that includes atomistic dislocation modeling with ab initio parameterization of the inter-row interactions, proposed by Suzuki. Using this approach, we have investigated the change of core structure and the $a/2\langle111\rangle$ screw dislocation mobility induced by impurities of Cu and Cr. We find that Cu induces a change from a non-degenerate (P=0, where P is the core polarization) core structure in $\alpha$-Fe to a degenerate (P=1) one, while Cr impurity does not change the P at any concentration. We have also studied the behavior of these systems under stress, and found that Cr impurities lower the mobility of the screw dislocation, while Cu induces that the dislocation of Fe-Cu system under stress exhibits a peculiar \emph{stable} $\rightarrow$ \emph{metastable} $\rightarrow$ \emph{stable} transition, and strengthens $\alpha$-Fe. The above conclusions are supported by molecular dynamics calculation, which also show that Cu impurities, in addition to changing the core polarization, dramatically increase the edge components of screw dislocation in Fe.   

Dependence of the Strain Rate Sensitivity of Crystalline Materials on the Distribution of Obstacles to Dislocation Motion

The strength and strain rate sensitivity of metals is usually described in terms of the concentration of obstacles to dislocation motion, i.e. the mean of the obstacle spatial distribution function. In this study we investigate the role of higher moments of this distribution function on these parameters. It is shown that large local fluctuations of obstacle density influence to a large extent the strain rate sensitivity of the material, while the effect on the strength (critical resolved shear stress) is smaller. It is shown that a large reduction of the strain rate sensitivity is associated with a change in the dislocation motion mode from smooth to jerky. Populations composed from obstacles of same strength but different activation energy, as well as obstacles of same activation energy and different strength are also studied.   

Elastic properties of $\gamma $-Pu by Resonant Ultrasound Spectroscopy

Despite of intense experimental and theoretical work on Pu, there is still little understanding of the strange properties of this metal. We used resonant ultrasound spectroscopy method to investigate the elastic properties of pure polycrystalline Pu at high temperatures. Shear and longitudinal elastic moduli of the $\gamma $-phase of Pu were determined simultaneously and the bulk modulus was computed from them. A smooth linear and large decrease of all elastic moduli with increasing temperature was observed. We calculated the Poisson ratio and found that it increases from 0.242 at 519K to 0.252 at 571K. .   

The 50 K anomaly in the shear modulus of $\beta $-PdH$_{0.71}$

When palladium hydride, PdH$_{x}$, is rapidly cooled to liquid helium temperature and then slowly reheated, both the heat capacity and electrical resistivity show a peak in the range 50~$<$~$T$~$<$~80~K, depending on the composition $x$. This ``50~K anomaly'' has been previously explained in terms of formation of long-range ordered hydrogen superlattice structures. However, several aspects of the 50~K anomaly are inconsistent with an ordering phase transition, namely, the temperature of the anomaly depends on the rate of cooling, and the magnitude of the anomaly is larger for a fast cooling rate than for a slow cooling rate. We have studied the 50~K anomaly by measuring the elastic constants of single-crystal PdH$_{0.71}$ in the temperature range 1.4~$<$~$T$~$<$~300~K during both fast cooling and slow warming. During warming, we observed a peak in the shear modulus $C^{\prime }$~=~($C_{11}$~-~$C_{12}$/2) at 55~K, which we attribute to the 50~K anomaly. In contrast, we observed no peak in the temperature dependence of the shear modulus $C_{44}$ or of the bulk modulus $B$. We propose that the 50~K anomaly arises not from the formation of long-range ordered hydrogen superlattice structures, but from freezing of the hydrogen short-range order as the hydride is cooled.   

Field theoretical approach to deformation dynamics.

Based on a recent gauge theory called physical mesomechanics, an attempt is made to formulate the deformation dynamics of solid-state materials comprehensively. In this formalism, deformation is described as a linear transformation of the position vector connecting two nearby points of the material; the transformation is global in the elastic regime and local in the plastic regime. Request of local invariance leads to a Maxwell type field equation, in which a symmetry charge analogous to the electric charge is defined. Dynamics in the plastic regime is characterized by transverse force proportional to rotational displacement, as opposed to translational displacement in the elastic regime, and longitudinal force proportional to velocity. The transverse force is a restoring force, which can be interpreted as the recoverability mechanism that the material regains in the plastic regime. The longitudinal force can be interpreted as a field force acting on the above-mentioned charge, which is basically an energy dissipating force causing the irreversibility of plastic deformation. Fracture is considered to be the situation where the material completely loses recoverability. Supporting experimental data will be presented.   

Where is the Simple Hexagonal Structure in Tin?

The heavier elements of periodic table column IV exhibit number of structural phase transitions under pressure. Si and Ge transform from the ground-state diamond structure to, successively, the $\beta$-Sn structure, a body-centered orthorhombic structure, the simple hexagonal structure, etc., ending at a close-packed phase (fcc or hcp) near 200 GPa. Tin also transforms from diamond to $\beta$-Sn, but then to a body-centered tetragonal phase, ending with the body-centered cubic phase. The simple hexagonal phase is not seen, despite the fact that numerous tin-rich alloys exhibit a simple hexagonal structure. To understand this we performed DFT calculations on tin in various crystal structures, using both full-potential LAPW and VASP with a PAW potential. Surprisingly, we find that the simple hexagonal phase is degenerate with $\beta$-Sn over pressures at which the $\beta$-Sn phase is seen experimentally. This holds both for LAPW and VASP calculations, in both the LDA and the GGA. We explore reasons for the lack of a tin simple hexagonal phase, including zero point and spin-orbit effects.   

{\em Ab initio} study of Fe-rich Fe-Cu alloys

Cu precipitates are important for strengthening steel. Our {\em ab initio} study aims to model the thermodynamical stability of Cu precipitations in $\alpha$-Fe. As a first step, a density functional theory (DFT) supercell approach is applied to study $Fe_{1-x}Cu_x$ alloys at small concentrations $x$. From the DFT total energies a strongly nonbonding substitutional energy $E_{subs} \approx 0.7eV$ is derived, which is significantly larger than results of a previous DFT study [1]. Based on force constants derived by the same DFT approach the temperature dependent vibrational free energy is determined [2]. In particular at higher temperatures the vibrational entropy significantly reduces the formation energy. Finally, by using the entropy of mixing the dilute Fe-Cu alloy becomes stabilized. The derived phase diagram is in good agreement with experimental data [3]. According to our analysis, the vibrational free energy is very important for a correct modelling of the phase stability of Fe-rich Fe-Cu alloys. [1] C. Domain et al., PRB, 65, 024103 (2001) [2] D. Alf{\`e} et al, PRB, 65, 045123 (2001) [3] B. Predel, Landolt-B{\"o}rnstein - IV, Springer, Volume 5d (1994)   

Strain-induced interactions in size-mismatched alloys: A Kanzaki force approach

A perturbative approach to determining the strain-induced effective interactions in binary alloys with large atomic-size mismatch is presented. Using the chemical energy as the reference state, the strain-induced energy of the alloy is cast into a many-body (Kanzaki) force expansion that depends on both the configurational and displacive degrees of freedom. It is shown that the $k$-space energy expansion is valid for all wave-lengths. The theory is then applied to the Cu$_3$Au alloy where, due to the large difference between atomic sizes, considerable relaxations are observed from first-principles calculations. We found that the inhomogeneous contribution (\boldmath{$k$}$\neq$0) dominates the strain energy in Cu$_3$Au, whereas the homogeneous part ({\boldmath $k$}=0), notwithstanding its configurational dependence, contributes only a few percent.   

New candidates for the Pt$_8$Ti structures in intermetallics

The only known intermetallic structure with an 8:1 stoichiometry is that of Pt$_8$Ti. Because of its uniqueness, this structure has been studied in Pt, Pd, and Ni rich systems. However, these metals have only been paired with a handful of other elements. Are there more elements that when alloyed with Pt, Pd, or Ni order with the Pt$_8$Ti structure? We explored $\approx$40 different Pd- and Pt-based binary systems. We calculated their formation enthalpies for the Pt$_8$Ti structure, compared the value to the tie line between pure Pd/Pt and experimentally-observed ground states. We find that there are other (beyond those experimentally observed) possible alloys with this structure. These new Pt/Pd-rich alloys could fin application in the jewelry and catalysis industries.   

Properties of the type I Ge-based clathrates Ba$_{8}$Al$_{13}$Ge$_{33}$ and Ba$_{8}$Al$_{16}$Ge$_{30}$

The type I clathrate lattice is simple cubic with 46 atoms per unit cell. The cages in this lattice can host ``guests'' and the framework can have substituted atoms. Here, we focus on the ``alloy'' system Ba$_{8}$Al$_{x}$Ge$_{30-x}$ (x is an integer; 0$<$x$<$15). The Ba are guests and Al substitutes for some Ge framework atoms. Using the local density approximation (LDA), we have calculated some properties of the type I clathrates Ba$_{8}$Al$_{13}$Ge$_{33}$ and Ba$_{8}$Al$_{16}$Ge$_{30}$. Our calculations of the equilibrium structures predict that Ba$_{8}$Al$_{16}$Ge$_{30 }$and Ba$_{8}$Al$_{13}$Ge$_{33}$ have approximately the same lattice constant and that Ba$_{8}$Al$_{13}$Ge$_{33}$ is expected to be slightly more stable than Ba$_{8}$Al$_{16}$Ge$_{30}$. Our band structures and electronic density of states results predict that Ba$_{8}$Al$_{13}$Ge$_{33}$ is metallic and that Ba$_{8}$Al$_{16}$Ge$_{30}$ is a semiconductor with an indirect fundamental band gap of 0.3 eV. The vibrational spectrum predicts low frequency rattling modes caused by the Ba guests that are loosely bound in the Al-Ge framework cages. Such modes may scatter the heat-carrying acoustic vibrational framework modes, potentially reducing the thermal conductivity.