Bond-valence theory is used to explore the local arrangements involving vacancies at the Y and Z sites in the tourmaline structure. The local bond-valence requirements of all possible local arrangements around the O8, O7, O6, O3 and O1 anion-sites have been determined for Y- and Z-site vacancies locally associated with Li1+, Mg2+, Al3+, Fe2+, Fe3+, B3+ and Si4+. The results show that arrangements involving tetrahedrally coordinated TR3+-cations and octahedrally coordinated YR2+- and ZR2+-cations around O8, 07 and O6 can be ruled out, together with arrangements involving vacancies and YLi1+. As the occurrence of a Y-site vacancy (Y☐) is more in accord with the valence-sum rule than the occurrence of a Z-site vacancy (Z☐), Y☐ is more likely to occur than Z☐ in tourmaline. Local arrangements involving vacancies around O1- and O3-sites can be stable for OH−, but not for O2−. Of particular interest in this regard are the arrangements [YR3+YR3+Y☐]−O1(OH−) and [ZR3+ZR3+Y☐]−O3(OH−), which yield the smallest deviations from the valence-sum rule. Coupling these stable arrangements with 2 × [TSi4+ZR3+Y☐]−O6(O2−) forms larger vacancy clusters: [Y(R3+)2−O1(OH−)−y(☐)− O3(OH−)−O6(O2−)2−(ZR3+TSi4+)2]. In tourmaline, vacancies are more favoured to occur at Y rather than at Z, in tandem with OH− at O3 and O1, R3+ at Y and Z and Si4+ at T.

Although the United States (US) federal bureaucracy is plagued by high vacancy rates generally, quorum requirements and small board sizes make vacancies particularly problematic within major independent regulatory commissions. Not all vacancies, however, are created equal. By statute, some major boards allow members to continue serving beyond their original term in the absence of a confirmed replacement. The difference between an empty seat and a holdover official is important as it can determine whether a board is functional or inoperable. In this article, we examine how the presence of holdover provisions within such commissions alters confirmation dynamics and vacancy rates. Evidence suggests that holdover provisions lead to quicker confirmation on nominations as well as fewer complete vacancies. Such structures thus help mitigate the short-term problems stemming from staffing independent regulatory boards, especially given the tendency towards obstruction in the US Senate.

The modified embedded atom method (MEAM) with the universal form of embedding function and a modified energy term along with the pair potential has been employed to determine the potentials for alkali metals: Na, K, by fitting to the Cauchy pressure (C12 − C44)/2, shear constants Gν = (C11 − C12 + 3C44)/5 and C44, the cohesive energy and the vacancy formation energy. The obtained potentials are used to calculate the phonon dispersions of these metals. Using these calculated phonons we evaluate the local density of states of neighbours of vacancy using Green’s function method. The local density of states of neighbours of vacancy has been used to calculate mean square displacements of these atoms and formation entropy of vacancy. The calculated mean square displacements of both 1st and 2nd neighbours of vacancy are found to be lower than that of host atom. The calculated phonon dispersions agree well with the experimental phonon dispersion curves and the calculated results of vacancy formation entropy compare well with the other available results.

Surface pretreatment using Cl2 plasma was applied to n-type GaN and Ti/Al ohmic contacts with resistivity of ~ 10−6 Ω cm2, realized without annealing. Using synchrotron radiation photoemission spectroscopy, it was observed that the Fermi level moved by 0.5 eV toward the conduction band edge and the atomic ratio of Ga/N was increased by the treatment. This suggests that a number of N vacancies were produced at the treated surface and the Fermi level was pinned at the energy level of N vacancies near the conduction band. The N vacancies acting as donors for electrons produced a number of electrons, resulting in the near surface region to be in the degenerate state. Both the shift of Fermi level and the production of electrons at the treated surface lead to the reduction in contact resistivity through the decrease of the effective Schottky barrier for conduction of electrons.

The spacings have been widely applied to many situations, such as for example the coverage problem of the circle or the line, under the hypothesis of uniformity. The paper examines the asymptotic behaviour of the maximal spacings under non-uniformity, assuming that the existing density f has a minimum point m with f(m) = 0. The results are applied to the coverage of the circle by randomly placed arcs.

Point processes on the circle with circumference 1 are considered, which are related to the coverage problem of the circle by n randomly placed arcs of a fixed length. The anticlockwise endpoint of each arc is assumed to be uniformly distributed on the circle. We deal with a general limit result on the convergence of these point processes to a Poisson process on the circle. This result is then applied to several cases of the coverage problem, giving improved limit results in these cases. The proof uses a new convergence result of general point processes.

Place n arcs of equal lengths randomly on the circumference of a circle, and let C denote the proportion covered. The moments of C (moments of coverage) are found by solving a recursive integral equation, and a formula is derived for the cumulative distribution function. The asymptotic distribution of C for large n is explored, and is shown to be related to the exponential distribution.