Slip energy barriers in aluminum and implications for ductile versus brittle behavior

We conisder the brittle versus ductile behavior of aluminum in the framework of the Peierls-model analysis of dislocation emission from a crack tip. To this end, we perform first-principles quantum mechanical calculations for the unstable stacking energy $\gamma_{us}$ of aluminum along the Shockley partial slip route. Our calculations are based on density functional theory and the local density approximation and include full atomic and volume relaxation. We find that in aluminum $\gamma_{us} = 0.224$ J/m$^2$. Within the Peierls-model analysis, this value would predict a brittle solid which poses an interesting problem since aluminum is typically considered ductile. The resolution may be given by one of three possibilites: (a) Aluminum is indeed brittle at zero temperature, and becomes ductile at a finite temperature due to motion of pre-existing dislocations which relax the stress concentration at the crack tip. (b) Dislocation emission at the crack tip is itself a thermally activated process. (c) Aluminum is actually ductile at all temperatures and the theoretical model employed needs to be significantly improved in order to resolve the apparent contradiction.Comment: 4 figures (not included; send requests to [email protected]

The Megamaser Cosmology Project: IV. A Direct Measurement of the Hubble Constant from UGC 3789

In Papers I and II from the Megamaser Cosmology Project (MCP), we reported initial observations of water masers in an accretion disk of a supermassive black hole at the center of the galaxy UGC 3789, which gave an angular-diameter distance to the galaxy and an estimate of Ho with 16% uncertainty. We have since conducted more VLBI observations of the spatial-velocity structure of these water masers, as well as continued monitoring of its spectrum to better measure maser accelerations. These more extensive observations, combined with improved modeling of the masers in the accretion disk of the central supermassive black hole, confirm our previous results, but with signifcantly improved accuracy. We find Ho = 68.9 +/- 7.1 km/s/Mpc; this estimate of Ho is independent of other methods and is accurate to +/-10%, including sources of systematic error. This places UGC 3789 at a distance of 49.6 +/- 5.1 Mpc, with a central supermassive black hole of (1.16 +/- 0.12) x 10^7 Msun.Comment: to appear in Ap

The Megamaser Cosmology Project. V. An Angular Diameter Distance to NGC 6264 at 140 Mpc

We present the direct measurement of the Hubble constant, yielding the direct measurement of the angular-diameter distance to NGC 6264 using the H$_{2}$O megamaser technique. Our measurement is based on sensitive observations of the circumnuclear megamaser disk from four observations with the Very Long Baseline Array, the Green Bank Telescope and the Effelsberg Telescope. We also monitored the maser spectral profile for 2.3 years using the Green Bank Telescope to measure accelerations of maser lines by tracking their line-of-sight velocities as they change with time. The measured accelerations suggest that the systemic maser spots have a significantly wider radial distribution than in the archetypal megamaser in NGC 4258. We model the maser emission as arising from a circumnuclear disk with orbits dominated by the central black hole. The best fit of the data gives a Hubble constant of $H_{0} =$ 68$\pm$9 km s$^{-1}$ Mpc$^{-1}$, which corresponds to an angular-diameter distance of 144$\pm$19 Mpc. In addition, the fit also gives a mass of the central black hole of (3.09$\pm$0.42)$\times10^{7}$ $M_{\odot}$. The result demonstrates the feasibility of measuring distances to galaxies located well into the Hubble flow by using circumnuclear megamaser disks.Comment: 29 pages, 8 figures, Accepted by Ap

The Megamaser Cosmology Project: I. VLBI observations of UGC 3789

The Megamaser Cosmology Project (MCP) seeks to measure the Hubble Constant (Ho) in order to improve the extragalactic distance scale and constrain the nature of dark energy. We are searching for sources of water maser emission from AGN with sub-pc accretion disks, as in NGC 4258, and following up these discoveries with Very Long Baseline Interferometric (VLBI) imaging and spectral monitoring. Here we present a VLBI map of the water masers toward UGC 3789, a galaxy well into the Hubble Flow. We have observed masers moving at rotational speeds up to 800 km/s at radii as small as 0.08 pc. Our map reveals masers in a nearly edge-on disk in Keplerian rotation about a 10^7 Msun supermassive black hole. When combined with centripetal accelerations, obtained by observing spectral drifts of maser features (to be presented in Paper II), the UGC 3789 masers may provide an accurate determination of Ho, independent of luminosities and metallicity and extinction corrections.Comment: 18 pages, 3 figures, 4 table

Nonlinear Stress Fluctuation Dynamics of Sheared Disordered Wet Foam

Sheared wet foam, which stores elastic energy in bubble deformations, relaxes stress through bubble rearrangements. The intermittency of bubble rearrangements in foam leads to effectively stochastic drops in stress that are followed by periods of elastic increase. We investigate global characteristics of highly disordered foams over three decades of strain rate and almost two decades of system size. We characterize the behavior using a range of measures: average stress, distribution of stress drops, rate of stress drops, and a normalized fluctuation intensity. There is essentially no dependence on system size. As a function of strain rate, there is a change in behavior around shear rates of $0.07 {\rm s^{-1}}$.Comment: accepted to Physical Review

Sheared Solid Materials

We present a time-dependent Ginzburg-Landau model of nonlinear elasticity in solid materials. We assume that the elastic energy density is a periodic function of the shear and tetragonal strains owing to the underlying lattice structure. With this new ingredient, solving the equations yields formation of dislocation dipoles or slips. In plastic flow high-density dislocations emerge at large strains to accumulate and grow into shear bands where the strains are localized. In addition to the elastic displacement, we also introduce the local free volume {\it m}. For very small $m$ the defect structures are metastable and long-lived where the dislocations are pinned by the Peierls potential barrier. However, if the shear modulus decreases with increasing {\it m}, accumulation of {\it m} around dislocation cores eventually breaks the Peierls potential leading to slow relaxations in the stress and the free energy (aging). As another application of our scheme, we also study dislocation formation in two-phase alloys (coherency loss) under shear strains, where dislocations glide preferentially in the softer regions and are trapped at the interfaces.Comment: 16pages, 11figure

The Megamaser Cosmology Project. III. Accurate Masses of Seven Supermassive Black Holes in Active Galaxies with Circumnuclear Megamaser Disks

Observations of H$_2$O masers from circumnuclear disks in active galaxies for the Megamaser Cosmology Project allow accurate measurement of the mass of supermassive black holes (BH) in these galaxies. We present the Very Long Baseline Interferometry (VLBI) images and kinematics of water maser emission in six active galaxies: NGC~1194, NGC~2273, NGC~2960 (Mrk~1419), NGC~4388, NGC~6264 and NGC~6323. We use the Keplerian rotation curves of these six megamaser galaxies, plus a seventh previously published, to determine accurate enclosed masses within the central $\sim0.3$ pc of these galaxies, smaller than the radius of the sphere of influence of the central mass in all cases. We also set lower limits to the central mass densities of between 0.12 and 60 $\times 10^{10} M_{\odot}$~pc$^{-3}$. For six of the seven disks, the high central densities rule out clusters of stars or stellar remnants as the central objects, and this result further supports our assumption that the enclosed mass can be attributed predominantly to a supermassive black hole. The seven BHs have masses ranging between 0.76 and 6.5$\times$10$^7 M_{\odot}$. The BH mass errors are $\approx11$\%, dominated by the uncertainty of the Hubble constant. We compare the megamaser BH mass determination with other BH mass measurement techniques. The BH mass based on virial estimation in four galaxies is consistent with the megamaser BH mass given the latest empirical value of $\langle f \rangle$, but the virial mass uncertainty is much greater. MCP observations continue and we expect to obtain more maser BH masses in the future.Comment: 18 pages, 4 figures. This paper has been submitted to ApJ. An updated version of this paper will be posted when it gets accepte