We prove that all p-adic period domains (and their non-minuscule analogues) are geometrically connected. This answers a question of Hartl and has consequences for the geometry of Shimura and local Shimura varieties.

Continuous-wave diamond Raman lasers (DRLs) operated at high pump power commonly suffer from power roll-off and output instability, even when high-thermal-conductivity gain media are employed. These degradations originate from thermally induced cavity-mode mismatch and cavity-length drift, which limit further power scaling. In this work, we establish a thermo–optical chain-linked model that quantitatively describes the coupled evolution of thermal deposition, equivalent thermal lensing, intracavity-mode matching and output power in high-power DRLs, providing a direct physical link between pump power and cavity-length compensation. Based on this model, a peak–valley co-location criterion is proposed to determine the optimal cavity-length compensation point. Both theoretical and experimental results show that the output power exhibits a single-peak dependence on cavity-length offset, while the power stability follows a U-shaped distribution, and their extrema coincide at an optimal compensation value ΔL*. By operating at ΔL*, the maximum Stokes output power increases from 27 to 32 W, and the root mean square power fluctuation decreases from 4.8% to 3.2%. These results demonstrate that thermal-lens-induced performance degradation can be effectively mitigated by cavity-length compensation using a single control parameter, providing a practical design rule for simultaneous enhancement of output power and stability in high-power Raman laser systems.

The extant literature on diamond industries in Africa has predominantly focused on men, with few attempts to examine the industry from a gendered lens. I trace women and highlight their gendered roles in the diamond-mining industry in colonial Ghana (Gold Coast). Relying on archival, oral, and visual sources, this article highlights women’s involvement in Ghana’s diamond industry in different capacities—as discoverers, washers, licensed prospectors, and dealers. Ultimately, I argue that the dominance men have enjoyed in studies about diamond mining in Ghana (and Africa generally) reproduces the colonial archive but can be overcome through creative and innovative research.

We present U–Pb dates from peridotitic pyrope-rich garnet from four mantle xenoliths entrained in a kimberlite from Bultfontein, South Africa. Garnet dates magmatic emplacement due to the high mantle residence temperatures of the source material prior to eruption, which were most likely above the closure temperature for the pyrope U–Pb system. We determine a U–Pb date of 84.0 ± 8.1 Ma for the emplacement of the Bultfontein kimberlite from garnet in our four xenolith samples. The date reproduces previous dates obtained from other mineral-isotope systems (chiefly Rb–Sr in phlogopite). Garnet can be dated despite extremely low concentrations of U (median ∼0.05 μg/g), because concentrations of common Pb are often low or non-detectable. This means that sub-concordant garnets can be dated with moderate precision using very large laser-ablation spots (130 μm) measured by quadrupole inductively coupled plasma – mass spectrometry (LA-Q-ICP-MS). Our strategy demonstrates successful U–Pb dating of a U-poor mineral due to high initial ratios of U to common Pb in some grains, and the wide spread of isotopic compositions of grains on a concordia diagram. In addition, the analytical protocol is not complex and uses widely available analytical methods and strategies. This new methodology has some advantages and disadvantages for dating kimberlite emplacement versus established methods (U-based decay systems in perovskite and zircon, or Rb- or K-based systems in phlogopite). However, this method has unique promise for its potential application to detrital diamond prospecting and, more speculatively, to the dating of pyrope inclusions in diamond.

This article argues for a renewal of the discipline of New Testament studies through a focus on the question of truth. To make the argument, the article first engages a recent essay that is highly critical of mainstream NT scholarship and subsequently works with the thought of Søren Kierkegaard, Stanley Cavell, Cora Diamond and Hans-Georg Gadamer to pursue the interpreter's implications in the NT's assertions of truth. The article also briefly exegetes five passages from the NT to illustrate the way the NT makes claims that require judgements about truth. Along the way, the article also engages contemporary NT scholars who argue vociferously against ‘theological’ readings of the NT and others who argue for their inherent necessity.

Stimulated Raman-scattering-based lasers provide an effective way to achieve wavelength conversion. However, thermally induced beam degradation is a notorious obstacle to power scaling and it also limits the applicable range where high output beam quality is needed. Considerable research efforts have been devoted to developing Raman materials, with diamond being a promising candidate to acquire wavelength-versatile, high-power, and high-quality output beam owing to its excellent thermal properties, high Raman gain coefficient, and wide transmission range. The diamond Raman resonator is usually designed as an external-cavity pumped structure, which can easily eliminate the negative thermal effects of intracavity laser crystals. Diamond Raman converters also provide an approach to improve the beam quality owing to the Raman cleanup effect. This review outlines the research status of diamond Raman lasers, including beam quality optimization, Raman conversion, thermal effects, and prospects for future development directions.

This article reports findings when using a molybdenum–tungsten (MoW) interlayer for diamond thin film deposition on steel substrates. The main focus was on the postdeposition stress within the diamond films and its impact on the coating's tribological properties. The effect of MoW interlayer thickness and the effect of chemical vapor deposition (CVD) process temperature have been investigated. Nanocrystalline diamond films were deposited on steel substrates with MoW interlayers (thickness of 1.1, 4.5, and 8.3 μm) at two different deposition temperatures (650 and 875 °C). It was found that when depositing good quality diamond films on steel substrates, increasing interlayer thickness and decreasing CVD process temperature have to be jointly considered to obtain the optimal result. The diamond-coated steel substrates with the 8.3 μm interlayer deposited at the lower CVD processing temperature exhibited the least residual stress combined with excellent mechanical properties.

To study the interface characteristics between substrates and homoepitaxially grown single crystalline diamond layers, the high-pressure/high-temperature Ib diamond seeds with homoepitaxial diamond layers were annealed by low-pressure/high-temperature treatment in a hydrogen environment. The stress evolution and related impurity transformation near the interface were characterized by Raman spectroscopy, photoluminescence, and micro-infrared spectroscopy before and after annealing. It is found that the stress is the smallest in a 100 μm wide zone near the interface, accompanying with the similar change in substitutional nitrogen (Ns) concentration. After annealing at 1050 °C, 1250 °C, and 1450 °C, the local compressive stress is released gradually with temperature change. It is decreased by 1.03 GPa in maximum after annealing at 1450 °C. The concentration of nitrogen–vacancy (NV) complexes in the chemical vapor deposition (CVD) layer is dramatically reduced at 1450 °C. The value of ${{I_{{\rm{NV}}^ \hbox- } } \mathord{\left/ {\vphantom {{I_{{\rm{NV}}^ - } } {I_{{\rm{diamond}}} }}} \right. \kern-\nulldelimiterspace} {I_{{\rm{diamond}}} }}$ decreases much more than ${{I_{{\rm{NV}}^0 } } \mathord{\left/ {\vphantom {{I_{{\rm{NV}}^0 } } {I_{{\rm{diamond}}} }}} \right. \kern-\nulldelimiterspace} {I_{{\rm{diamond}}} }}$ in the CVD layer, which is due to the lower stability of NV− compared with NV0 at high temperature.

The development of GaN-on-diamond devices offers bright prospects for the creation of high-power density electronics. This article presents a process of fabricating GaN-on-diamond structure by depositing diamond films on dual sides, including heat dissipation diamond film and sacrificial carrier diamond film. Prior to heat dissipation diamond film layer preparation, aluminum nitride (AlN) is chosen as a dielectric layer and pretreated by nanodiamond (ND) particles, to enhance the nucleation density. Zeta potential measurements and X-ray photoelectron spectroscopy are used to analyze the AlN surface after each treatment. The results show that oxygen-terminated ND particles tend to adhere to an AlN surface because the oxygen-terminated NDs have –COOH and –OH groups, and hold a negative potential. On the contrary, fluorine-terminated AlN prefers to attract the hydrogen-terminated ND seeds, which resulted in higher diamond nucleation density. Based on this preliminary study, a dense high-quality GaN-on-diamond wafer is successfully produced by using AlN as the dielectric layer and a diamond film as the sacrificial carrier.

We are proposing a novel fabrication method for single crystal diamond scanning probes for atomic force microscopy (AFM), exploiting Faraday cage angled etching (FCAE). Common, oxygen-based, inductively coupled plasma (ICP) dry etching processes for diamond are limited with respect to the achievable geometries. The fabrication of freestanding micro- and nanostructures is therefore challenging. This is a major disadvantage for several application fields e.g., for realizing scanning magnetometry probes based on nitrogen vacancy (NV) centres and capable of measuring magnetic fields at the nanoscale. Combining a planar design with FCAE and state-of-the-art electron beam lithography (EBL) yields a reduction of process complexity and cost compared to the established fabrication technology of micro-opto-mechanical diamond devices. Here, we report on the direct comparison of both approaches and present first proof-of-concept planar-FCAE-prototypes for scanning probe applications.

We have investigated a diamond crystal that consists of several misorientated subgrains. The main feature of the crystal is the dark areas in the cathodoluminescent core that has ‘estuary-like’ boundaries extending along the subgrain interfaces. The core has >3100 ppm of nitrogen, and the share of the B form is >95%; the absorbance of the centre N3VH at 3107 cm–1 reaches 75 cm–1. The N3 centre absorbance, as well as N3 luminescence, is absent in the core. In the outer part of the crystal, bright blue luminescence of the N3 centre is apparent, and the N3 absorbance reaches 5.3 cm–1. These observations could be explained by the conversion of N3 centres to N3VH after attaching a hydrogen atom. After the full conversion of the N3 centres, the diamond becomes darker under CL. We hypothesise the dark core has a specific shape due to the post-growth diffusion of the hydrogen.

This work demonstrates the in situ growth of carbon nanowalls (CNWs) on diamond semiconductors by microwave plasma-assisted chemical vapor deposition. The resulting CNW/diamond junctions behave as photomemristors having both photocontrollable multiple resistance states and nonvolatile memory functions. The resistance state (high or low resistance) can be selected by irradiation with blue or violet light in conjunction with the application of a bias voltage, giving a large resistance switching ratio of ∼106. The photoinduced resistance switching behaviors are rarely observed and has only been observed in a few materials and/or heterostructures. These junctions also exhibit a photoresponsivity of ∼12 A/W, which is much larger than that obtained from photodiodes composed of other materials. These results suggest that CNW/diamond (i.e., carbon sp2/sp3) junctions could have applications in novel photocontrollable devices, which have photosensing, memory, and switching functions.

We derive a forcing axiom from the conjunction of square and diamond, and present a few applications, primary among them being the existence of super-Souslin trees. It follows that for every uncountable cardinal $\unicode[STIX]{x1D706}$, if $\unicode[STIX]{x1D706}^{++}$ is not a Mahlo cardinal in Gödel’s constructible universe, then $2^{\unicode[STIX]{x1D706}}=\unicode[STIX]{x1D706}^{+}$ entails the existence of a $\unicode[STIX]{x1D706}^{+}$-complete $\unicode[STIX]{x1D706}^{++}$-Souslin tree.

We investigate which filters on ω can contain towers, that is, a modulo finite descending sequence without any pseudointersection (in ${[\omega ]^\omega }$). We prove the following results:

1. (1) Many classical examples of nice tall filters contain no towers (in ZFC).

2. (2) It is consistent that tall analytic P-filters contain towers of arbitrary regular height (simultaneously for many regular cardinals as well).

3. (3) It is consistent that all towers generate nonmeager filters (this answers a question of P. Borodulin-Nadzieja and D. Chodounský), in particular (consistently) Borel filters do not contain towers.

4. (4) The statement “Every ultrafilter contains towers.” is independent of ZFC (this improves an older result of K. Kunen, J. van Mill, and C. F. Mills).

Furthermore, we study many possible logical (non)implications between the existence of towers in filters, inequalities between cardinal invariants of filters (${\rm{ad}}{{\rm{d}}^{\rm{*}}}\left( {\cal F} \right)$, ${\rm{co}}{{\rm{f}}^{\rm{*}}}\left( {\cal F} \right)$, ${\rm{no}}{{\rm{n}}^{\rm{*}}}\left( {\cal F} \right)$, and ${\rm{co}}{{\rm{v}}^{\rm{*}}}\left( {\cal F} \right)$), and the existence of Luzin type families (of size $\ge {\omega _2}$), that is, if ${\cal F}$ is a filter then ${\cal X} \subseteq {[\omega ]^\omega }$ is an ${\cal F}$-Luzin family if $\left\{ {X \in {\cal X}:|X \setminus F| = \omega } \right\}$ is countable for every $F \in {\cal F}$.

A suite of ultramafic-mafic alkaline igneous rocks in the Damodar Valley, eastern India, contains carbonate, phosphate and titanate minerals that are not characteristic or common in minettes or lamproites, but are typical of orangeites (Group II kimberlite) from southern Africa. Phlogopite grains from the Damodar alkaline rocks yield mean 40Ar/39Ar ages of 116.6±0.8 Ma, 113.5±0.5 Ma and 109.1±0.7 Ma (1σ errors) using laser dating techniques. These ages are similar to the Rb-Sr ages of African orangeites, which lie mostly in the range 121 to 114 Ma. Prior to this study, only one possible occurrence of orangeite (the ∼820 m.y.-old Aries pipe, Western Australia) was known outside the Kaapvaal craton and its environs. If the Damodar alkaline rocks are bona fide orangeites, it is likely that they were generated at depths of >150 km, within the stability field of diamond.

Carbonado and yakutite are both porous aggregates of polycrystalline micrometre-size diamond, with very different characters from those of monocrystalline diamond. The genesis of carbonado is very controversial, whereas yakutite is thought to have been formed by meteorite impact. Neutron activation analyses of trace elements in carbonado and yakutite indicate that their rare earth element (REE) abundance patterns have common characteristics: heavy REEs are not much depleted and a negative Eu anomaly is observed. These patterns are quite different from those of kimberlite and monocrystalline diamond and are similar to those of crustal materials such as shale, supporting the hypothesis of a crustal origin for carbonado and yakutite.