19 research outputs found

    Kinetics and Mechanism of Hydroxyapatite Crystal Dissolution in Weak Acid Buffers Using the Rotating Disk Method

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    The dissolution rates of synthetic hydroxyapatite pellets under sink conditions were measured using the rotating disk method. The experimental data were analyzed by means of a physical model that yielded an ionic activity product of KHAP = a10Ca2+ a6 PO4 3- a2OH- = 1 × 10-124.5±1.0 that was found to govern the dissolution reaction. Also, a surface resistance factor of k' equal to about 174 sec/cm was deduced from the data.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/67157/2/10.1177_00220345760550033201.pd

    Creation of the CMB spectrum: precise analytic solutions for the blackbody photosphere

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    The blackbody spectrum of CMB was created in the blackbody photosphere at redshifts z>2x10^6. At these early times, the Universe was dense and hot enough that complete thermal equilibrium between baryonic matter (electrons and ions) and photons could be established. Any perturbation away from the blackbody spectrum was suppressed exponentially. New physics, for example annihilation and decay of dark matter, can add energy and photons to CMB at redshifts z>10^5 and result in a Bose-Einstein spectrum with a non-zero chemical potential (ÎĽ\mu). Precise evolution of the CMB spectrum around the critical redshift of z~2x10^6 is required in order to calculate the ÎĽ\mu-type spectral distortion and constrain the underlying new physics. Although numerical calculation of important processes involved (double Compton process, comptonization and bremsstrahlung) is not difficult, analytic solutions are much faster and easier to calculate and provide valuable physical insights. We provide precise (better than 1%) analytic solutions for the decay of ÎĽ\mu, created at an earlier epoch, including all three processes, double Compton, Compton scattering on thermal electrons and bremsstrahlung in the limit of small distortions. This is a significant improvement over the existing solutions with accuracy ~10% or worse. We also give a census of important sources of energy injection into CMB in standard cosmology. In particular, calculations of distortions from electron-positron annihilation and primordial nucleosynthesis illustrate in a dramatic way the strength of the equilibrium restoring processes in the early Universe. Finally, we point out the triple degeneracy in standard cosmology, i.e., the ÎĽ\mu and yy distortions from adiabatic cooling of baryons and electrons, Silk damping and annihilation of thermally produced WIMP dark matter are of similar order of magnitude (~ 10^{-8}-10^{-10})

    The critical role of the transition-state cusp diameter in understanding adiabatic and non-adiabatic electron transfer

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