We completely classify the possible extensions between semistable vector bundles on the Fargues–Fontaine curve (over an algebraically closed perfectoid field), in terms of a simple condition on Harder–Narasimhan (HN) polygons. Our arguments rely on a careful study of various moduli spaces of bundle maps, which we define and analyze using Scholze’s language of diamonds. This analysis reduces our main results to a somewhat involved combinatorial problem, which we then solve via a reinterpretation in terms of the Euclidean geometry of HN polygons.

High-pressure-temperature (P-T) experiments were conducted in an attempt to determine the diffusion rates of C atoms in diamond, and the possibility of changes in the isotope compositions of diamond at high P-T in the Earth’s mantle. The starting material consisted of a polished plate of natural diamond (very largely 12C), which had been coated with 13C diamond by chemical-vapourdeposition to form a sharp interface between 12C and 13C diamond. Three experiments were performed at 1800, 2000 and 2300ºC, all at 7.7 GPa, for0.5 –20 h. Isotopic profiles obtained by ion microprobe before and after each experiment showed no evidence of relaxation of the sharp interface between 12C and 13C, and so diffusion must have been on a scale less than the ~32 nm depth resolution for this technique. Using 32 nm as the maximum length scale of diffusion across the interface, the maximum ln D (diffusion coefficient) values for the experiments were calculated to be in the range –38 to –42. Unlike previous experimental data, these results show that changes in the isotopic compositions of diamond on long time scales in the Earth’s upper mantle are unlikely. Furthermore, the results support empirical evidence from mapping of C isotope distributions in natural diamonds that C isotope compositions reflect diamond growth compositions.

Micro-inclusions (1 –10 μm) in 55 diamonds of cubic habit from the Udachnaya kimberlite pipe have been studied using vibrational spectroscopy. This has revealed a multiphase assemblage in cuboid diamonds from the Udachnaya kimberlite pipe. This assemblage includes carbonates, olivine, apatite, graphite, water and silicate glasses. The micro-inclusions preserve the high internal pressure and give confidence that the original materials were trapped during growth of the host diamond. The internal pressures, extrapolated to mantle temperatures, lie within the stability field of diamond and the relatively low temperatures are typical for the formation of cuboid diamonds. In contrast to previously reported data for African diamonds, the micro-inclusions in the cuboids from Udachnaya are extremely carbonatitic in composition (H2O/(H2O+CO2) ≈5 –20%) with the observed assemblage of microinclusions similar to some types of carbonatites. The low water and silica content testify that the material in the micro-inclusions of the Udachnaya diamonds was near-solidus carbonatitic melt. Vibrational spectroscopy has provided the evidence of carbonatitic melts in cuboid diamonds.

Nanodiamonds can be synthesized hydrothermally in the laboratory by using a C-O-H fluid in the graphite stability field, in which the graphite/nanodiamond transition depends on the crystal size as a function of temperature. In nature, the hydrothermal circulation of seawater in serpentinites plays an important role in the carbon speciation in the oceanic crust and exposed mantle, in which hydrocarbons (mainly CH4) of abiogenic origin (via Fischer-Tropsch-type reaction) and occasionally graphite particles are detected. Can nanodiamonds nucleate and grow in serpentinite-hosted hydrothermal systems? To answer this question, a theoretical modelling study which compares the physico-chemical conditions in hydrothermal synthesis with those observed in modern and fossil serpentinite-hosted hydrothermal systems is proposed. Nanodiamonds are predicted to precipitate from a C-O-H fluid, consisting of CH4-CO2-H2O at 350 – 400°C and P<0.2 GPa near the FMQ buffer (Fayalite-Magnetite-Quartz), which are conditions compatible with those existing in serpentinite-hosted hydrothermal systems. In these environments, carbon-supersaturated fluids can be derived from water consumption (serpentine formation) under low water/rock ratios, which may promote the growth of nanodiamonds. This theoretical approach sheds light on the intriguing problem of carbon speciation in abyssal-type hydrothermal systems, suggesting that serpentinites may host nanodiamond deposits, even though none have been found yet.

Secondary ion mass spectrometry (SIMS) techniques have been used to study the variation of C isotope ratio and N abundance within selected diamonds in relation to their crystal growth zones. The growth zones are seen in cathodoluminescence (CL), and include both octahedral and cuboid zones within typical diamonds of external octahedral morphology. Compositions were determined by use of a primary 133Cs+ ion beam and measurement of 12C−, 13C, and 12C14N− secondary ions at high mass resolution on a Cameca ims-4f ion microprobe at Edinburgh University.

In each of the diamonds, different growth zones have marked differences in N abundance, which are as great as 0–1400 ppm within one diamond. Changes of several hundred ppm N are common across both octahedral and cuboid growth zones, and appear sharp and abrupt at the boundaries of the growth zones. In general for the common blue CL, luminescence increases with N abundance. The changes in N abundance across fine scale (∼100 µm) growth zones show that the total N contents determined by IR spectroscopy may show great variations of abundance. In contrast, within detection limits, δ13C appears constant across many growth zone boundaries. Thus the factors controlling uptake of N from the fluid/melt reservoir in which natural diamonds grow often do not influence δ13C. No evidence of progressive variation or fractionation of C isotopes during growth was found.

Some original variation in C isotope composition may have been eliminated by diffusion of C atoms subsequent to growth, because of the storage of natural diamonds over millions of years in the Earth's mantle at temperatures of 950–1250°C. Such atomic mobility does not homogenize N distribution because of the proven tendency of N to form aggregates of atoms. A survey of experimental estimates of single atom (C) diffusion parameters, suggests that diffusion distances of ∼100 µm are likely at high temperatures (∼1100°C) over long time periods (∼1.0 Ga). Therefore, with refinement of the diffusion parameters and measurements, the extent of C isotope homogenization in natural diamonds, as well as N aggregation state, might provide quantitative evidence of their time-temperature history under mantle conditions.

The Companhia de Diamantes de Angola, or Diamang, mined for diamonds in colonial Angola from 1917 until independence in 1975. The enterprise’s Health Services Division (SSD) was responsible for supplying mine managers with an African labour force comprised of healthy, and therefore productive, employees. In practice, though, this otherwise ‘healthy’ system did not always work. While SSD personnel attempted to fulfil their charge by implementing a series of screening measures, production targets and a scarcely-populated regional labour pool regularly prompted senior officials to compel the SSD to clear recruits who were otherwise unfit for mine service. Drawing upon interviews with former SSD staff and African labourers, as well as company and colonial archival sources, this article focuses on the interplay over time between the SSD, the company’s production demands and these labourers.

Diamonds have a long global history in which India plays a pivotal though little-known role. Indeed, it was in India that diamonds were first mined, finished, and worn. Diamonds and their finishing techniques reached Europe in the fifteenth century. Subsequently, part of the industry moved from India to Europe, where manufacturing shifted from one city to another, before returning to India in the twentieth century. These shifts, I argue, are determined by changes in one or more segments of the global commodity chain and they reveal the global interconnections between mining, trading, polishing, and consuming. Furthermore, these shifting centres are themselves a sign of the globalized character of diamond production, exchange, and consumption.