Probing crystalline phases in cubic boron nitride as a function of boron content by massive nanoindentation and microsample testing

Polycrystalline cubic boron nitride (cBN) is a super-hard multiphase composite is extensively used in highly demanding applications, where improved and consistent performances together with high reliability are required. The remarkable mechanical properties of these materials result from a two-fold effectiveness associated with its composite character. On the one hand in terms of composite nature: combination of a brittle cBN particles and a ceramic TiN binder with optimal interface properties, as given by a very low interfacial energy and very good adhesion between cBN and TiN. Information on the small-scale mechanical response mainly for superhard materials is rather scarce in the literature This is particularly true regarding experimental data and analysis on the influence of phase and/or chemical nature and interfacial adhesion on hardness. It is clear that knowledge of these issues is crucial not only to improve the performance of this superhard materials but also to designer of new PCBN systems, which will lead to highly desirable improvements in the cost and time on the materials development cycle. The present work aims to evaluate the boron effect on the cBN particles by doing a systematic micro- and nanomechanical study of the mechanical integrity for different superhard systems, with different binder and reinforcement content. In doing so, different micromechanical approaches are followed: i) Assessment of the micromechanical properties by using the statistical approach, ii) evaluation of the fracture toughness by microcantilever deflection, strength by micropillar compression, and iii) finite element modelling based on 3D FIB tomography is performed by using the acquired micromechanical data in order to correlate micromechanical behavior with macroscopic response of the material. From the obtained results by the statistical method it is found that the boron content strongly modifies the cBN hardness; which produces a modification of this superhard particles being this tetragonal or octhoedrical depending the amount of the boron content dissolved inside the parti

The Paley-Wiener Theorem and the Local Huygens' Principle for Compact Symmetric Spaces

We prove a Paley-Wiener Theorem for a class of symmetric spaces of the compact type, in which all root multiplicities are even. This theorem characterizes functions of small support in terms of holomorphic extendability and exponential type of their (discrete) Fourier transforms. We also provide three independent new proofs of the strong Huygens' principle for a suitable constant shift of the wave equation on odd-dimensional spaces from our class.Comment: 26 pages, 1 figur

Transmutation operators as a solvability concept of abstract singular equations

One of the methods of studying differential equations is the transmutation operators method. Detailed study of the theory of transmutation operators with applications may be found in the literature. Application of transmutation operators establishes many important results for different classes of differential equations including singular equations with Bessel operato