Diamond Cell Research Articles

High‐pressure experiments and the phase diagram of lower mantle and core materials

The interpretation of seismic data and computer modeling requires increased accuracy in relevant material properties in order to improve our knowledge of the structure and dynamics of the Earth's deep interior. To obtain such properties, a complementary method to classic shock compression experiments and theoretical calculations is the use of laser‐heated diamond cells, which are now producing accurate data on phase diagrams, equations of state, and melting. Data on one of the most important measurements, the melting temperatures of iron at very high pressure, are now converging. Two other issues linking core properties to those of iron are investigated in the diamond cell: One is the melting point depression of iron in the presence of light elements, and the other is the structure of iron at the conditions of the inner core. First measurements on eutectic systems indicate a significant decrease in the melting point depression with increasing pressure, which is in contrast to previous predictions. X‐ray diffraction measurements at simultaneously high pressure and high temperature have improved significantly with the installation of high‐pressure “beam lines” at synchrotron facilities, and structural measurements on iron are in progress. Considerable efforts have been made to develop new techniques to heat minerals at the conditions of the deep mantle in the diamond cell and to measure their phase relations reliably. Even measurements of the melting behavior of realistic rock compositions at high pressure, previously considered to be impossible in the diamond cell, have been reported. The extrapolated solidus of the lower mantle intersects the geotherm at the core‐mantle boundary, which may explain the seismically observed ultra low velocity zone. The diamond cell has great potential for future development and broad application, as new measurements on high‐pressure geochemistry at deep mantle and core conditions have opened a new field of research. There are, however, strict experimental requirements for obtaining reliable data, which are summarized in the present paper. Results from recent measurements of melting temperatures and phase diagrams of lower mantle and core materials at very high pressure are reviewed.

Pressure-induced phase transitions in gypsum

We report high-pressure Raman scattering spectroscopy and energy dispersive X-ray diffraction investigations on gypsum, CaSO4 · 2H2O, at room temperature in a diamond cell. With increasing pressure, measurements indicate that CaSO4 · 2H2O undergoes two stages of crystalline-state phase transitions at 5 and 9 GPa, and then converts to a disordered phase above 11 GPa. The structures of the three high-pressure phases of gypsum have not been determined yet. These phases are tentatively named as “post-gypsum-I” (PG-I), “post-gypsum-II” (PG-II) and “disordered” according to the sequence of their appearance with pressure. Gypsum shows anisotropic compressibility along three crystallographic axes with b > c > a below 5 GPa. The difference in the behavior of the two OH stretching modes in gypsum is attributed to the different reduction rate in the hydrogen bonding distances by the anisotropic axial compressibility.

In-situ Raman spectra of dissolved silica species in aqueous fluids to 900 °C and 14 kbar

The Raman spectra of fluids in equilibrium with solid quartz in the system H2O-SiO2 were measured to 900 °C and 14 kbar using an externally heated diamond cell. Dissolved silica species were identified by comparing the measured spectra with calculated normal mode frequencies and Raman intensities. At crustal pressures and temperatures, H4SiO4 is the dominant silica species in aqueous fluids, with a strong Raman band at 760-785 cm-1. At the P-T conditions of the upper mantle, however, H6Si2O7 dimers and possibly higher polymers coexist with H4SiO4 in the fluid. The most intense Raman bands of H6Si2O7 occur at about 630, 920, and 230 cm-1. The presence of high concentrations of ionized silica species in the solution can be ruled out. The observed speciation changes explain the drastic increase of silica solubility in water at lower crustal and upper mantle PT conditions.

Reversible coordination changes in crystalline silicates at high pressure and ambient temperature

In silicates, generally the less dense open structures of lower pressure polymorphs have four-coordinated silicon whereas the denser more close-packed structures have six-coordinated silicon. Transformation from the fourfold coordinated crystals to the denser sixfold coordinated structures upon compression usually requires an accompanying high temperature that is much greater than ambient. We report here a first-order, reversible SiO4-SiO6 coordination change in a crystalline silicate (MgSiO3) orthoenstatite at ambient temperature and quasi-hydrostatic conditions using Raman spectroscopic measurements in a diamond cell to 70 GPa. Annealing experiments using a CO2 laser, which controlled defect concentration, indicate that the four- to sixfold coordination change is facilitated by defects in the structure which may serve as nucleation sites for the formation of the octahedrally coordinated silicon phase.

Laser heating in the diamond cell: techniques and applications

Very high temperatures (>2000 K) at megabar presures (∼100 GPa) can be achieved by classic shock compression experiments and in laser-heated diamond cells, which have evolved to a formidable tool for accurately characterizing material properties at controlled pressure and temperature conditions of the Earth's lower mantle and core. The diamond cell has great potential for future development and broad application but due to the small sample dimensions there are strict experimental requirements for obtaining reliable data, some of which are described in the present paper. Results for measuring melting temperatures of iron at very high pressure, which constrain the temperature in the Earth's centre, are reviewed.

GLOBAL GRIDS FROM RECURSIVE DIAMOND SUBDIVISIONS OF THE SURFACE OF AN OCTAHEDRON OR ICOSAHEDRON

In recent years a number of methods have been developed for subdividing the surface of the earth to meet the needs of applications in dynamic modeling, survey sampling, and information storage and display. One set of methods uses the surfaces of Platonic solids, or regular polyhedra, as approximations to the surface of the earth. Diamond partitions are similar to recursive subdivisions of the triangular faces of either the octahedron or icosahedron. This method views the surface as either four (octahedron) or ten (icosahedron) tessellated diamonds, where each diamond is composed of two adjacent triangular faces of the figure. The method allows for a recursive partition on each diamond, creating nested sub-dimaonds, that is implementable as a quadtree, including the provision for a Peano or Morton type coding system for addressing the hierarchical pattern of diamonds and their neighborhoods, and for linearizing storage. Furthermore, diamond partitions, in an aperture-4 hierarchy, provide direct access through the addressing system to the aperture-4 hierarchy of hexagons developed on the figure. Diamond partitions provide a nested hierarchy of grid cells for applications that require nesting and diamond cells have radial symmetry for those that require this property. Finally, diamond partitions can be cross-referenced with hierarchical triangle partitions used in other methods.

Magnetic neutron diffraction under pressures up to 43 GPa. Study of the EuX and GdX compounds

We present some recent results on magnetic neutron studies at pressures above 40 GPa. We used diamond and sapphire anvil pressure cells for low temperature neutron studies and a powder diffractometer specialized for high pressure studies. Focusing systems and low-background conditions allowed us to study samples with volumes as small as 0.001 mm3 in a diamond anvil cell at a pressure of 50 GPa. This technical progress allowed us to obtain new results in studies of “textbook” magnetic insulators EuX (X = S, Se, Te) and GdX (X = As, Sb, Bi). We found new magnetic phases. In the Eu-chalcogenides we observed a strong anion-dependent increase of the ferromagnetic exchange with decreasing lattice constant. In contrast, in the GdX compounds the antiferromagnetic order remains stable up to a pressure of 43 GPa. We show the importance of our results to understand the origin of indirect exchange interactions in magnetic semiconductors with well localized magnetic shells.

Water speciation in rhyolitic melt determined by in-situ infrared spectroscopy

Near-IR spectra obtained from hydrous silicate melts, close to natural rhyolite, were acquired at both high temperature using a heating stage and simultaneously at high pressure and temperature using a hydrothermal diamond cell. The temperature dependence of the extinction coefficients for the peaks due to OH and H 2 O is negligible. In both sets of experiments, the speciation reaction H 2 O + O = 2OH is shifted to the right with increasing temperature above the glass transition but changes below this are negligible, within experimental uncertainty. For a sample containing 3.93 wt% total water, the temperature dependence of the speciation equilibrium can be described by two equations with temperature in K: ln k = -36.74/T - 4.02 for the glass phase (giving enthalpy and entropy of reaction values of ΔH = 0.31 kJ/mol and ΔS = -33.45 J/mol-K), and ln k = -3821.83/T + 1.61 for the melt phase (where ΔH = 31.77 kJ/mol and ΔS = 13.41 J/mol-K) respectively). The glass transition temperature of 670 K is defined by the intersection of these curves. Our values are in good agreement with previously published glass transition temperatures for similar compositions. Similar values for the enthalpy and entropy of reaction were obtained from all the other experiments including those at pressures up to 4.5, 5, and 10 kbars, suggesting that the speciation depends negligibly on pressure for this pressure range.

The MgTiO3-FeTiO3join at high pressure and temperature

The phase relations at high pressure and high temperature for the FeTiO 3 -MgTiO 3 join were de­termined using several different experimental methods. Through a series of multi-anvil experiments, a phase boundary with a negative slope was observed between MgTiO 3 I (ilmenite structure) and a high pressure phase with the MgTiO 3 II (lithium niobate structure) after quenching. The enthalpy of transformation of MgTiO 3 I to MgTiO 3 II was determined through transposed-temperature-drop calo­rimetry to be 28.78 ± 1.45 kJ/mol. The enthalpy of transformation from ilmenite to lithium niobate structure was also determined for three intermediate compositions on the FeTiO 3 -MgTiO 3 join, Fe 0.2 Mg 0.8 TiO 3 , Fe 0.5 Mg 0.5 TiO 3 and Fe 0.8 Mg 0.2 TiO 3 , and confirmed for FeTiO 3 , and was found to be a linear function of composition. These experiments represent one of the first successful calorimetric measurements on small samples (1 to 3 mg) synthesized at high pressures (15 to 21 GPa). X-ray analysis during compression of Fe 0.5 Mg 0.5 TiO 3 II in a diamond cell confirmed a room temperature transition at 28 GPa to Fe 0.5 Mg 0.5 TiO 3 III (a GdFeO 3 -type perovskite structure), similar to the transi­tions previously observed in FeTiO 3 and MnTiO 3 . The Fe 0.5 Mg 0.5 TiO 3 sample was heated to 802 ℃ at 21 GPa, and it was observed that the stable high temperature, high pressure phase is perovskite, Fe 0.5 Mg 0.5 TiO 3 III. The above data combined confirm the stability of a continuous perovskite solid solution at high pressure and temperature for the FeTiO 3 -MgTiO 3 join.

Compression studies of gibbsite and its high-pressure polymorph

Various X-ray diffraction methods have been applied to study the compression behavior of gibbsite, Al(OH)3, in diamond cells at room temperature. A phase transformation was found to take place above 3 GPa where gibbsite started to convert to its high-pressure polymorph. The high-pressure (HP) phase is quenchable and coexists with gibbsite at the ambient conditions after being unloaded. This HP phase was identified as nordstrandite based on the diffraction patterns obtained at room pressure by angle dispersive and energy dispersive methods. On the basis of this structural interpretation, the bulk modulus of the two polymorphs, i.e., gibbsite and nordstrandite, could be determined as 85 ± 5 and 70 ± 5 GPa, respectively, by fitting a Birch-Murnaghan equation to the compression data, assuming their Ko ′ as 4. Molar volume cross-over occurs at 2 GPa, above which the molar volume of nordstrandite is smaller than that of gibbsite. The differences in the molar volume and structure between the two polymorphs are not significant, which accounts for the irreversibility of the phase transition. In gibbsite, the axial compressibility behaves as c/c o > a/a o > b/b o. This is due to the fact that the dioctahedral sheets along the c-axis are held by the relatively weak hydrogen bonding, which results in the greater compressibility along this direction. In nord- strandite, the axial compressibility is b/b o > c/c o > a/a o, which can also be interpreted as resulting from the the existence of hydrogen bonds along the b-axis.

Spectrochemical characterization by micro-FTIR spectroscopy of blue pigments in different polychrome works of art

Analytical examination of blue paint samples, taken from different artworks dating from the second century AD until 1960, was carried out using FTIR microspectroscopy (both in reflection and transmission mode, the latter with the aid of a diamond cell) supported by micro-Raman spectroscopy and SEM observations as well as EDX spectrometry. Pigments examined included azurite, Egyptian blue and ultramarine blue, either natural or artificial. Characteristic spectra for each pigment are presented and an account for the principal differences observed is given. In particular, the FTIR's capability of probing single pigment grains on the surface of paint cross-sections, when integrated with a microscope, brought to light frequency differences and orientation behaviour of the bands of the various minerals used as painting materials. Indeed, a striking effect of shifting and variation of intensity of some of the bands of azurite and Egyptian blue was noted and related to polarization phenomena occurring when the incident light stroke differently oriented faces of the single pigment crystals. The effects of different mineralogical composition of the semi-precious stone lapis-lazuli (from which ultramarine blue is derived) on the appearance of the spectrum of the pigment are also discussed. Finally, a means of distinguishing the natural from the artificial ultramarine blue pigment, on the basis of their FTIR spectra, is proposed.

Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem

In this paper, a class of cell centered nite volume schemes, on general unstructured meshes, for a linear convection-diusion problem, is studied. The convection and the diusion are respectively approximated by means of an upwind scheme and the so called diamond cell method (4). Our main result is an error estimate of order h, assuming only the W 2;p (for p> 2) regularity of the continuous solution, on a mesh of quadrangles. The proof is based on an extension of the ideas developed in (12). Some new diculties arise here, due to the weak regularity of the solution, and the necessity to approximate the entire gradient, and not only its normal component, as in (12).

High‐pressure transformations in MgAl2O4

X ray diffraction and transmission electron microscopy on laser‐heated diamond cell samples show that with increasing pressure MgAl2O4 spinel transforms first to Al2O3 corundum + MgO periclase, then to the CaFe2O4‐structured phase, and finally to a new phase having the CaTi2O4 structure above ∼40 GPa. The CaFe2O4 and the CaTi2O4 structures are closely related and have almost the same densities and bulk moduli. Transformation from the CaFe2O4 to the CaTi2O4 phase would be expected to take place in oceanic crust that is subducted deep into the lower mantle.

High-pressure melting curve of platinum

The melting curve of platinum, determined to 70 GPa by spectroradiometry and visual observation through the laser-heated diamond cell, is described by Tm(P)=2057+27.2×P−0.1497×P2 K, where Tm is the melting temperature in K and P is pressure in GPa. This expression is valid to a precision of ±97 K in the pressure range 10 to 70 GPa.

A theory of the origin of the Earth's internal heat

A gravitational source of heat is added to secular cooling and the heat from the decay of radioactive elements to close the gap between heat loss and heat production for whole mantle convection. This unrecognized source of heat comes from viscous friction in sheet-like mantle plumes rising from the core-mantle boundary to create oceanic plates, cause earthquakes and raise mountains and volcanoes. The frictional heat generated in the plumes is equal to the gravitational potential energy lost because their heavy fraction, FeO, was absorbed by the molten iron at the top of the core. When mantle material is subjected to the temperature and pressure prevailing at the 670 km seismic discontinuity in the laser-heated diamond cell, it is transformed into a magnesium iron silicate perovskite and magnesiowuestite that remain stable to the temperature and pressure of the core-mantle boundary, where they lose their FeO to the core. The energy that had been expended by this process during the life of the Earth, has come from the composition Fe 2O of the outer core, as required by the seismic speeds and the moment of inertia of the Earth. This energy is 7.07 × 10 30 J, 2.3 times what would have been expended by plate creation at the present rate. Secular cooling does not originate from the primordial high temperature, but from the decay of the radioactivity and the decrease of the amount of FeO in the mantle (Schubert et al., 1980). At present plate creation by mantle plumes provides 47.5% of the heat of 44.2 TW. The larger part of this heat comes from viscous friction in the plumes, the remainder coming from the cooling of the core. Radioactivity gives 41%, and 11% comes from secular cooling that takes no part in plate creation. In apportioning the heat from these sources between land and sea, it is assumed that in very old oceans only 15% of the heat comes from plate creation and that the remaining 85% comes from radioactive elements uniformly disseminated in the mantle and secular cooling. The last two sources being world-wide, we extend this heat of 32.0 mW/m 2 over the 510 × 10 6 km 2 of the Earth's surface, 16.3 TW in all. At sea, where the heat flow is greater than 32.0 mW/m 2, the additional heat comes from plate creation, while on land the extra amount is from radionuclides concentrated in the crust. The measured losses on land and sea are 30% and 70% of 44.2 TW, respectively. On land, the total measured loss is 13.26 TW, 86% of it is radiogenic, and 14% is from cooling. At sea, the heat loss is 30.9 TW, 22% of it is radiogenic, 10% from cooling and 68% from plate creation. Table 2 lists the measured and computed quantities.

Single crystal hydrostatic compression of (Mg,Mn,Fe,Co) 2 SiO 4 olivines

Four synthetic endmember olivines (Mg,Mn, Fe,Co)2SiO4 with space group Pbnm were loaded together in one diamond cell mount. Their unit-cell parameters were determined by single crystal X-ray diffraction to 10 GPa. The linear compressibilities βa, βb, βc were 1.53, 2.90, 2.32; 1.45, 3.48, 1.98; 1.35, 3.29, 1.76; and 1.25, 2.82, 2.01×10−3 GPa−1 for Mg2SiO4, Mn2SiO4, Fe2SiO4 and Co2SiO4, respectively. The b axis is the most compressible direction in all crystals studied. Bulk modulus KT0 and its first pressure derivative were simultaneously determined for Mg2SiO4, Fe2SiO4 and Co2SiO4 crystals respectively by fitting volume data to a third order Birch-Murnaghan equation of state. They are 127(4) and 4.2(8), 136(3) and 4.1(7), and 144(2) and 4.1(5). The KT0 and could not simultaneously be determined unambiguously for Mn2SiO4. Direct comparisons of unit-cell volumes at high pressure among pairs of olivines reveal anomalous compression behavior of the Mg2SiO4 crystal regarding the bulk modulus-volume relationship. This behavior, however, could not be observed in the transition metal olivines (Mn,Fe,Co)2SiO4. The distinct electronic configurations of Mg2+ and the transition metal cations Mn2+, Fe2+, and Co2+ result in the different compression behaviors of Mg2SiO4 and (Mn,Fe,Co)2SiO4.

The transition of pyrope to perovskite

The stability field of Mg3Al2Si3O12-pyrope was examined for the first time under hydrostatic pressure conditions in a CO2-laser heated diamond cell in the pressure range 21–30 GPa between 2300 and 3200 K. The phases were characterized using Raman and fluorescence spectroscopy. With increasing pressure pyrope transforms to an ilmenite phase above ∼21.5 GPa, to perovskite plus ilmenite above ∼24 GPa, and to perovskite above 29 GPa. The pressures of the first occurrence of perovskite in this study are about 2 GPa above the corresponding phase boundary between end-member MgSiO3-ilmenite and perovskite. A small amount of Al2O3 coexists with perovskite up to 43 GPa, as evident from fluorescence spectra resembling those of ruby, but above 43 GPa the entire Al2O3 content of the pyrope starting material is accommodated in the perovskite structure.

Rapid determination of trans-fatty acids in human adipose tissue : Comparison of attenuated total reflection infrared spectroscopy and gas chromatography

A rapid attenuated total reflection (ATR) infrared (IR) spectroscopy procedure was used for quantitating the levels of total trans-fatty acid methyl ester (FAME) derivatives in neat (without solvent) test samples isolated from human adipose tissue. This procedure requires no weighing of the laboratory sample. The single-beam spectrum of the trans-containing FAMEs was `ratioed' against that of a reference material having only cis double bonds in order to obtain a symmetric absorption band at 966 cm −1 on a horizontal background. A single-reflection ATR diamond cell that requires only about 1 μl of neat FAMEs was used. The average level of trans-fatty acids in human adipose tissue found by ATR (3.07±0.27%) was generally higher than that obtained by gas chromatography (2.59±0.20%). Reasons for such a difference are discussed.

New Pressure Domain in Single Crystal X-ray Diffraction Using a Sealed Source.

The pressure range of single crystal structure determination using a sealed source was extended to over 30 GPa with the improved techniques in this study. Rare gas solid helium was found to be the only pressure medium that can secure hydrostatic environment to very high pressure. The solid argon or neon induces significant divitoric stresses in crystals at relatively low pressure. The crystal volume was doubled at certain targeting pressure by using a new gasket material. The intrinsic background of a pressure cell was significantly reduced by a special collimator. These procedures improved the signal/noise ratio to 3 - 4 times. The quality of the structure refinement and the accuracy of atomic coordinates at 33 GPa are comparable with measurements at ambient conditions in a diamond cell.

New Developments in Diamond-Cell Research.

Melting of the compressible alkali halides (KBr, KCl, CsI, NaCl, LiF) have been measured up to 1 Mbar. Their melting slopes approach values between 1 and 2 K/kbar at high pressures, a trend similar to almost all other materials measured thus far. Based on this trend and the close agreement in the melting temperatures between the diamond cell and shock wave experiments for the alkali halides and aluminum, and based on systematics in the magnitude of the change in sound velocity upon melting, we reinterpret the shock sound velocity measurements on iron as indicating onset of melting at 2 Mbar instead of 2. 4 Mbar as previously reported. This may reconcile the assumed discrepancies between static and shock experiments for iron. A new method for analyzing samples from laser heated diamond cells using an ion probe is presented. Chemical diffusion profiles were measured on samples with dimensions of order 10 μm by depth profiling with a radial resolution of about 2μm and a depth resolution of about 100 nm. We present first results on the partitioning and diffusion of nickel and cobalt in Mg-Si-perovskite at pressures up to 800 kbar and temperatures up to 2500 K.