This is a review of Collected Works of John Tate. Parts I, II, edited by Barry Mazur and Jean-Pierre Serre. American Mathematical Society, Providence, Rhode Island, 2016. For several decades it has been clear to the friends and colleagues of John Tate that a “Collected Works” was merited. The award of the Abel Prize to Tate in 2010 added impetus, and finally, in Tate’s ninety-second year we have these two magnificent volumes, edited by Barry Mazur and Jean-Pierre Serre. Beyond Tate’s published articles, they include five unpublished articles and a selection of his letters, most accompanied by Tate’s comments, and a collection of photographs of Tate. For an overview of Tate’s work, the editors refer the reader to [4]. Before discussing the volumes, I describe some of Tate’s work. 1. Hecke L-series and Tate’s thesis Like many budding number theorists, Tate’s favorite theorem when young was Gauss’s law of quadratic reciprocity. When he arrived at Princeton as a graduate student in 1946, he was fortunate to find there the person, Emil Artin, who had discovered the most general reciprocity law, so solving Hilbert’s ninth problem. By 1920, the German school of algebraic number theorists (Hilbert, Weber, . . .) together with its brilliant student Takagi had succeeded in classifying the abelian extensions of a number field K: to each group I of ideal classes in K, there is attached an extension L of K (the class field of I); the group I determines the arithmetic of the extension L/K, and the Galois group of L/K is isomorphic to I. Artin’s contribution was to prove (in 1927) that there is a natural isomorphism from I to the Galois group of L/K. When the base field contains an appropriate root of 1, Artin’s isomorphism gives a reciprocity law, and all possible reciprocity laws arise this way. In the 1930s, Chevalley reworked abelian class field theory. In particular, he replaced “ideals” with his “idèles” which greatly clarified the relation between the local and global aspects of the theory. For his thesis, Artin suggested that Tate do the same for Hecke L-series. When Hecke proved that the abelian L-functions of number fields (generalizations of Dirichlet’s L-functions) have an analytic continuation throughout the plane with a functional equation of the expected type, he saw that his methods applied even to a new kind of L-function, now named after him. Once Tate had developed his harmonic analysis of local fields and of the idèle group, he was able prove analytic continuation and functional equations for all the relevant L-series without Hecke’s complicated theta-formulas. Received by the editors September 5, 2016. 2010 Mathematics Subject Classification. Primary 01A75, 11-06, 14-06. c ©2017 American Mathematical Society

The collected works

Materials research plays a vital role in transforming breakthrough scientific ideas into next-generation technology. Similar to the way silicon revolutionized the microelectronics industry, the proper materials can greatly impact the field of plasmonics and metamaterials. Currently, research in plasmonics and metamaterials lacks good material building blocks in order to realize useful devices. Such devices suffer from many drawbacks arising from the undesirable properties of their material building blocks, especially metals. There are many materials, other than conventional metallic components such as gold and silver, that exhibit metallic properties and provide advantages in device performance, design flexibility, fabrication, integration, and tunability. This review explores different material classes for plasmonic and metamaterial applications, such as conventional semiconductors, transparent conducting oxides, perovskite oxides, metal nitrides, silicides, germanides, and 2D materials such as graphene. This review provides a summary of the recent developments in the search for better plasmonic materials and an outlook of further research directions.

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Alternative Plasmonic Materials: Beyond Gold and Silver

This article presents an overview of the developments in stainless steels made since the 1990s. Some of the new applications that involve the use of stainless steel are also introduced. A brief introduction to the various classes of stainless steels, their precipitate phases and the status quo of their production around the globe is given first. The advances in a variety of subject areas that have been made recently will then be presented. These recent advances include (1) new findings on the various precipitate phases (the new J phase, new orientation relationships, new phase diagram for the Fe–Cr system, etc.); (2) new suggestions for the prevention/mitigation of the different problems and new methods for their detection/measurement and (3) new techniques for surface/bulk property enhancement (such as laser shot peening, grain boundary engineering and grain refinement). Recent developments in topics like phase prediction, stacking fault energy, superplasticity, metadynamic recrystallisation and the calculation of mechanical properties are introduced, too. In the end of this article, several new applications that involve the use of stainless steels are presented. Some of these are the use of austenitic stainless steels for signature authentication (magnetic recording), the utilisation of the cryogenic magnetic transition of the sigma phase for hot spot detection (the Sigmaplugs), the new Pt-enhanced radiopaque stainless steel (PERSS) coronary stents and stainless steel stents that may be used for magnetic drug targeting. Besides recent developments in conventional stainless steels, those in the high-nitrogen, low-Ni (or Ni-free) varieties are also introduced. These recent developments include new methods for attaining very high nitrogen contents, new guidelines for alloy design, the merits/demerits associated with high nitrogen contents, etc.

Recent developments in stainless steels

Elements Of X Ray Diffraction

Atomic-scale control and manipulation of the microstructure of polycrystalline thin films during kinetically limited low-temperature deposition, crucial for a broad range of industrial applications, has been a leading goal of materials science during the past decades. Here, we review the present understanding of film growth processes—nucleation, coalescence, competitive grain growth, and recrystallization—and their role in microstructural evolution as a function of deposition variables including temperature, the presence of reactive species, and the use of low-energy ion irradiation during growth.

Microstructural evolution during film growth

The mechanical properties and machining performance of Ti 1− x Al x N-coated cutting tools have been investigated. Processing by arc evaporation using cathodes with a range of compositions was performed to obtain coatings with compositions x =0, x =0.25, x =0.33, x =0.50, x =0.66 and x =0.74. As-deposited coatings with x ≤0.66 had metastable cubic structures, whereas x =0.74 yielded two-phase coatings consisting of cubic and hexagonal structures. The as-deposited and isothermally annealed coatings were characterised by nanoindentation, scanning electron microscopy (SEM) and X-ray diffraction (XRD). Cutting tests revealing tool wear mechanisms were also performed. Results show that the Al content, x , promotes a (200) preferred crystallographic orientation and has a large influence on the hardness of as-deposited coatings. The high hardness (∼37 GPa) and texture of the as-deposited Ti 1− x Al x N coatings are retained for annealing temperatures up to 950 °C, which indicates a superior stability of this system compared to TiN and Ti(C,N) coatings. We propose that competing mechanisms are responsible for the effectively constant hardness: softening by residual stress relaxation through lattice defect annihilation is balanced by hardening from formation of a coherent nanocomposite structure of c-TiN and c-AlN domains by spinodal decomposition. This example of secondary-phase transformation (age-) hardening is proposed as a new route for advanced surface engineering, and for the development of future generation hard coatings.

Mechanical properties and machining performance of Ti1−xAlxN-coated cutting tools

The thermal stability of Ti1−xAlxN films deposited by arc evaporation from Ti–Al cathodes with 67 and 75 at. % aluminum, respectively, has been investigated. The microstructure of as-deposited and ...

Thermal stability of arc evaporated high aluminum-content Ti1−xAlxN thin films

The mechanical properties of (001)‐, (011)‐, and (111)‐oriented MgO wafers and 1‐μm‐thick TiN overlayers, grown simultaneously by dc magnetron sputter deposition at 700 °C in a mixed N2 and Ar discharge, were investigated using nanoindentation. A combination of x‐ray‐diffraction (XRD) pole figures, high‐resolution XRD analyses, and Auger electron spectroscopy was used to show that all TiN films were single crystals with N/Ti ratios of 1.0±0.05. The nanoindentation measurements were carried out using a three‐sided pyramidal Berkovich diamond indentor tip operated at loads ranging from 0.4 to 40 mN. All three orientations of MgO substrates, as‐received, exhibited identical hardness values as determined using the Oliver and Pharr method. After a 1 h anneal at 800 °C, corresponding to the thermal treatment received prior to film growth, the measured hardness of MgO(001) was 9.0±0.3 GPa. All TiN films displayed a completely elastic response at low loads. Measured hardness values, which decreased with increasin...

Nanoindentation studies of single‐crystal (001)‐, (011)‐, and (111)‐oriented TiN layers on MgO

Evolution of the residual stress state in a duplex stainless steel during loading

Multilayer thin films consisting of titanium nitride (TiN) and silicon nitride (SiNx) layers with compositional modulation periodicities between 3.7 and 101.7 nm have been grown on silicon wafers u ...

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Magnus Odén

Papers

Mechanical properties and machining performance of Ti1−xAlxN-coated cutting tools

Thermal stability of arc evaporated high aluminum-content Ti1−xAlxN thin films

Nanoindentation studies of single‐crystal (001)‐, (011)‐, and (111)‐oriented TiN layers on MgO

Evolution of the residual stress state in a duplex stainless steel during loading

Nanostructure formation during deposition of TiN SiNx nanomultilayer films by reactive dual magnetron sputtering