Study of the physical properties of metals and oxides at extreme pressure and temperature conditions

The high-pressure and temperature investigations on transition metals, metal doped-oxide system, nanocrystalline materials are presented in this dissertation. The metal-doped oxide systems are technologically important because of their applications, e.g. LSC, opto electronic applications, luminescence from lasers, etc., and from the earth sciences point of view, e.g. the study of trace elements in the MgO-SiO2 system, which accounts for 50% of the Earth's chondritic model. We have carried out thorough investigations on Cr2O3 and on chromium bearing oxides at high PT-conditions using in situ X-ray diffractometry and florescence spectroscopy techniques. Having obtained exciting results, an attempt to focus on the mechanism of the coordination of transition metals in oxides has been made. Additionally, the florescence from the metals in host oxides was found to be helpful to obtain information on structural variations like changes in the coordination of the doped element, formation of new phases, the diffusion processes. The possible reactions taking place at extreme conditions in the MgO-SiO2 system has been observed using florescence as markers. A new heating assemblage has been designed and fabricated for a precise determination of temperature at high pressures. An equation combining pressure shifts of ruby wavelength and temperature has been proposed. We observed that the compressibility of nanocrystalline material (MgO and Ni) is independent of crystallite size. A reduction in the transition pressure of nanocrystalline ceria at high-pressure has been observed as compare to the corresponding bulk material. ^

The study of silicates and refractory materials at high pressures and temperatures

To better understand high pressure behavior of solids, both silicates and oxides have been investigated to clarify the high pressure melting, phase transformations and thermal parameters as well as their size dependences, both theoretically and experimentally. ^ To judge the precision of data determined experimentally, the reliabilities of different high pressure techniques have been discussed. A thermodynamic model has been developed and demonstrated to be able to closely reproduce the melting of solids by comparison between results calculated and data obtained experimentally, including metals (Al, Ni and Pt), Silicates (Mg3Al 2Si3O12 and CaMgSi2O6), Halides (NaCl, CsCl and LiF) and Oxides (MgO, FeO and Al2O3). The melting data obtained have been discussed to address the dynamics of the Earth's interior. ^ Results obtained with Raman spectroscopy and x-ray diffraction show that solids including silicates (andradite and pyrope) and oxides (CeO2 and TiO2) undergo a series of pressure-induced phase transformations. The effects of particle size under high pressures have been investigated. The results obtained indicate that the reduction of particle size leads to the enhancement of the bulk modulus and a significant decrease of transition pressure in TiO2 (rutile) and CeO2. The pressure-induced amorphization in anatase also results from the size effects. ^ Combining the data obtained with global seismic tomography, the physics and chemistry of the Earth's mantle and the dynamics of the core-mantle interaction have been discussed. The high pressure phases of Al3+- and Fe3+-bearing minerals play important roles in the dynamics of the lower mantle. ^

Exploring thermal and mechanical properties of selected transition elements under extreme conditions: Experiments at high pressures and high temperatures

Transition metals (Ti, Zr, Hf, Mo, W, V, Nb, Ta, Pd, Pt, Cu, Ag, and Au) are essential building units of many materials and have important industrial applications. Therefore, it is important to understand their thermal and physical behavior when they are subjected to extreme conditions of pressure and temperature. This dissertation presents: • An improved experimental technique to use lasers for the measurement of thermal conductivity of materials under conditions of very high pressure (P, up to 50 GPa) and temperature (T up to 2500 K). • An experimental study of the phase relationship and physical properties of selected transition metals, which revealed new and unexpected physical effects of thermal conductivity in Zr, and Hf under high P-T. • New phase diagrams created for Hf, Ti and Zr from experimental data. • P-T dependence of the lattice parameters in α-hafnium. Contrary to prior reports, the α-ω phase transition in hafnium has a negative dT/dP slope. • New data on thermodynamic and physical properties of several transition metals and their respective high P-T phase diagrams. • First complete thermodynamic database for solid phases of 13 common transition metals was created. This database has: All the thermochemical data on these elements in their standard state (mostly available and compiled); All the equations of state (EoS) formulated from pressure-volume-temperature data (measured as a part of this study and from literature); Complete thermodynamic data for selected elements from standard to extreme conditions. The thermodynamic database provided by this study can be used with available thermodynamic software to calculate all thermophysical properties and phase diagrams at high P-T conditions. For readers who do not have access to this software, tabulated values of all thermodynamic and volume data for the 13 metals at high P-T are included in the APPENDIX. In the APPENDIX, a description of several other high-pressure studies of selected oxide systems is also included. Thermophysical properties (Cp, H, S, G) of the high P-T ω-phase of Ti, Zr and Hf were determined during the optimization of the EoS parameters and are presented in this study for the first time. These results should have important implications in understanding hexagonal-close-packed to simple-hexagonal phase transitions in transition metals and other materials.

Obesity and Serum High Sensitivity C-Reactive Protein Levels Among Elderly Turkish Immigrants in the Netherlands with Type 2 Diabetes

The study examined the associations of anthropometric measures of obesity with high sensitivity C-reactive protein (hs-CRP) levels in Turkish immigrants with type 2 diabetes (T2D) living in the Netherlands. A total of 110 participants, physician-diagnosed with T2D, aged 30 years and older were recruited from multiple sources from The Hague, Netherlands. Serum hs-CRP levels were measured with immunoturbidimetric assay. Glycated hemoglobin (A1C) was determined by high-pressure liquid chromatography. Measures of obesity: body weight, body mass index (BMI), waist circumference (WC), hip circumference (HC), waist-to-hip ratio (WHR), and waist-to-height ratio (WHtR) were determined. Statistical analysis included descriptive statistics, Pearson’s correlations and multiple linear regressions (MLR) stratified by gender. Hs-CRP was log transformed to achieve normality. Subjects with hs-CRP levels >10 mg/L (n = 17) were excluded from the analysis. Females had a higher BMI (p = 0.007), HC (p < 0.001), and WHtR (p = 0.011) as compared to males. Conversely, males had a higher weight (p = 0.007), and WHR (p < 0.001) than females. MLR showed that after controlling for covariates, log hs-CRP was positively associated with BMI (B = 0.039, SE = 0.019, β = 0.287, p < 0.05), WC (B = 0.025, SE = 0.011, β = 0.332, p < 0.05) and WHtR (B = 4.015, SE = 1.464, β = 0.376, p < 0.01) in females only. Gender-specific associations between obesity measures and hs-CRP level need to be further investigated in the Turkish immigrant population. Hs-CRP assessment may be added as a standard of care for T2D treatment within this population.

The potential of solid phase microextraction (spme) for the recovery of explosives followed by gas and liquid chromatographic analysis

The potential of solid phase microextraction (SPME) in the analysis of explosives is demonstrated. A sensitive, rapid, solventless and inexpensive method for the analysis of explosives and explosive odors from solid and liquid samples has been optimized using SPME followed by HPLC and GC/ECD. SPME involves the extraction of the organic components in debris samples into sorbent-coated silica fibers, which can be transferred directly to the injector of a gas chromatograph. SPME/HPLC requires a special desorption apparatus to elute the extracted analyte onto the column at high pressure. Re suits for use of GC[ECD is presented and compared to the results gathered by using HPLC analysis. The relative effects of controllable variables including fiber chemistry, adsorption and desorption temperature, extraction time, and desorption time have been optimized for various high explosives.

Composition of noble gases in sediments and metasediments

Solar-type helium (He) and neon (Ne) in the Earth's mantle were suggested to be the result of solarwind loaded extraterrestrial dust that accumulated in deep-sea sediments and was subducted into the Earth's mantle. To obtain additional constraints on this hypothesis, we analysed He, Ne and argon (Ar) in high pressure-low temperature metamorphic rocks representing equivalents of former pelagic clays and cherts from Andros (Cyclades, Greece) and Laytonville (California, USA). While the metasediments contain significant amounts of 4He, 21Ne and 40Ar due to U, Th and K decay, no solar-type primordial noble gases were observed. Most of these were obviously lost during metamorphism preceding 30 km subduction depth. We also analysed magnetic fines from two Pacific ODP drillcore samples, which contain solar-type He and Ne dominated by solar energetic particles (SEP). The existing noble gas isotope data of deep-sea floor magnetic fines and interplanetary dust particles demonstrate that a considerable fraction of the extraterrestrial dust reaching the Earth has lost solar wind (SW) ions implanted at low energies, leading to a preferential occurrence of deeply implanted SEP He and Ne, fractionated He/Ne ratios and measurable traces of spallogenic isotopes. This effect is most probably caused by larger particles, as these suffer more severe atmospheric entry heating and surface ablation. Only sufficiently fine-grained dust may retain the original unfractionated solar composition that is characteristic for the Earth's mantle He and Ne. Hence, in addition to the problem of metamorphic loss of solar noble gases during subduction, the isotopic and elemental fractionation during atmospheric entry heating is a further restriction for possible subduction hypotheses.

Chemical characterization and evaluation of biological activity of Cynara cardunculus extractable compounds

The Mediterranean species Cynara cardunculus L. is recognized in the traditional medicine, for their hepatoprotective and choleretic effects. Biomass of C. cardunculus L. var. altilis (DC), or cultivated cardoon, may be explored not only for the production of energy and pulp fibers, but also for the extraction of bioactive compounds. The chemical characterization of extractable components, namely terpenic and phenolic compounds, may valorize the cultivated cardoon plantation, due to their antioxidant, antitumoral and antimicrobial activities. In this study, the chemical composition of lipophilic and phenolic fractions of C. cardunculus L. var. altilis (DC), cultivated in the south of Portugal (Baixo Alentejo region) was characterized in detail, intending the integral valorization of its biomass. The biological activity of cultivated cardoon extracts was evaluated in terms of antioxidant, human tumor cell antiproliferative and antibacterial effects. Gas chromatography-mass spectrometry (GC-MS) was used for the chemical analysis of lipophilic compounds. Sixty-five lipophilic compounds were identified, from which 1 sesquiterpene lactone and 4 pentacyclic triterpenes were described, for the first time, as cultivated cardoon components, such as: deacylcynaropicrin, acetates of β- and α-amyrin, lupenyl acetate and ψ-taraxasteryl acetate. Sesquiterpene lactones were the major family of lipophilic components of leaves (≈94.5 g/kg), mostly represented by cynaropicrin (≈87.4 g/kg). Pentacyclic triterpenes were also detected, in considerably high contents, in the remaining parts of cultivated cardoon, especially in the florets (≈27.5 g/kg). Taraxasteryl acetate was the main pentacyclic triterpene (≈8.9 g/kg in florets). High pressure liquid chromatography-mass spectrometry (HPLC-MS) was utilized for the chemical analysis of phenolic compounds. Among the identified 28 phenolic compounds, eriodictyol hexoside was reported for the first time as C. cardunculus L. component, and 6 as cultivated cardoon components, namely 1,4-di-O-caffeoylquinic acid, naringenin 7-O-glucoside, naringenin rutinoside, naringenin, luteolin acetylhexoside and apigenin acetylhexoside. The highest content of the identified phenolic compounds was observed in the florets (≈12.6 g/kg). Stalks outer part contained the highest hydroxycinnamic acids abundance (≈10.3 g/kg), and florets presented the highest flavonoids content (≈10.3 g/kg). The antioxidant activity of phenolic fraction was examined through 2,2-diphenyl-1-picrylhydrazyl (DPPH) free radical scavenging assay. Stalks outer part, and receptacles and bracts extracts demonstrated the highest antioxidant effect on DPPH (IC50 of 34.35 μg/mL and 35.25 μg/mL, respectively). (cont.) abstract (cont.) The DPPH scavenging effect was linearly correlated with the total contents of hydroxycinnamic acids (r = -0.990). The in vitro antiproliferative activity of cultivated cardoon lipophilic and phenolic extracts was evaluated on a human tumor cells line of triple-negative breast cancer (MDA-MB-231), one of the most refractory human cancers to conventional therapeutics. After 48 h of exposition, leaves lipophilic extract showed higher inhibitory effect (IC50 = 10.39 μg/mL) than florets lipophilic extract (IC50 = 315.22 μg/mL), upon MDA-MB-231 cellular viability. Pure compound of cynaropicrin, representative of the main compound identified in leaves lipophilic extract, also prevented the cell proliferation of MDA-MB-231 (IC50 = 17.86 μM). MDA-MB-231 cells were much more resistant to the 48 h- treatment with phenolic extracts of stalks outer part (IC50 = 3341.20 μg/mL) and florets (IC50 > 4500 μg/mL), and also with the pure compound of 1,5-di-O-caffeoylquinic acid (IC50 = 1741.69 μM). MDA-MB-231 cells were exposed, for 48 h, to the respective IC50 concentrations of leaves lipophilic extract and pure compound of cynaropicrin, in order to understand their ability in modelling cellular responses, and consequently important potentially signaling pathways for the cellular viability decrease. Leaves lipophilic extract increased the caspase-3 enzymatic activity, contrarily to pure compound of cynaropicrin. Additionally, leaves lipophilic extract and pure compound of cynaropicrin caused G2 cell cycle arrest, possibly by upregulating the p21Waf1/Cip1 and the accumulation of phospho-Tyr15-CDK1 and cyclin B1. The inhibitory effects of leaves lipophilic extract and cynaropicrin pure compound, against the MDA-MB-231 cell proliferation, may also be related to the downregulation of phospho-Ser473-Akt. The antibacterial activity of cultivated cardoon lipophilic and phenolic extracts was assessed, for the first time, on two multidrug-resistant bacteria, such as the Gram-negative Pseudomonas aeruginosa PAO1 and the Gram-positive methicillin-resistant Staphylococcus aureus (MRSA), two of the main bacteria responsible for health care-associated infections. Accordingly, the minimum inhibitory concentrations (MIC) were determined. Lipophilic and phenolic extracts of florets did not have antibacterial activity on P. aeruginosa PAO1 and MRSA (MIC > 2048 μg/mL). Leaves lipophilic extract did not prevent the P. aeruginosa PAO1 growth, but pure compound of cynaropicrin was slightly active (MIC = 2048 μg/mL). Leaves lipophilic extract and pure compound of cynaropicrin blocked MRSA growth (MIC of 1024 and 256 μg/mL, respectively). The scientific knowledge revealed in this thesis, either by the chemical viewpoint, or by the biological viewpoint, contributes for the valorization of C. cardunculus L. var. altilis (DC) biomass. Cultivated cardoon has potential to be exploited as source of bioactive compounds, in conciliation with other valorization pathways, and Portuguese traditional cheeses manufacturing.

Tris(2-ethylhexyl) trimellitate (TOTM) as a potential industrial reference fluid for viscosity at high temperatures and high pressures: New viscosity, density and surface tension measurements

Tris(2-ethylhexyl) trimellitate (TOTM) was recently suggested as a reference fluid for industrial use associated with high viscosity at elevated temperature and pressure. Viscosity and density data have already been published on one sample covering the temperature range (303-373) K and at pressures up to about 65 MPa. The viscosity covered a range from about (9 to 460) mPa s. In the present article we study several other characteristics of TOTM that must be available if it were to be adopted as a standard. First, we present values for the viscosity and density obtained with a different sample of TOTM to examine the important feature of consistency among different samples. Vibrating-wire viscosity measurements were performed at pressures from (5 to 100) MPa, along 6 isotherms between (303 and 373) K. Density measurements were carried out from (293 to 373) K up to 68 MPa, along 4 isotherms, using an Anton Paar DMA HP vibrating U-tube densimeter. Secondly, we report a study of the effect of water contamination on the viscosity of TOTM, performed using an Ubbelhode viscometer under atmospheric pressure. Finally, in order to support the use of TOTM as a reference liquid for the calibration of capillary viscometers, values of its surface tension, obtained by the pendant drop method, are provided. (C) 2016 Elsevier B.V. All rights reserved.

Computational modelling of non-equilibrium condensing steam flows in low-pressure steam turbines

The steam turbines play a significant role in global power generation. Especially, research on low pressure (LP) steam turbine stages is of special importance for steam turbine man- ufactures, vendors, power plant owners and the scientific community due to their lower efficiency than the high pressure steam turbine stages. Because of condensation, the last stages of LP turbine experience irreversible thermodynamic losses, aerodynamic losses and erosion in turbine blades. Additionally, an LP steam turbine requires maintenance due to moisture generation, and therefore, it is also affecting on the turbine reliability. Therefore, the design of energy efficient LP steam turbines requires a comprehensive analysis of condensation phenomena and corresponding losses occurring in the steam tur- bine either by experiments or with numerical simulations. The aim of the present work is to apply computational fluid dynamics (CFD) to enhance the existing knowledge and understanding of condensing steam flows and loss mechanisms that occur due to the irre- versible heat and mass transfer during the condensation process in an LP steam turbine. Throughout this work, two commercial CFD codes were used to model non-equilibrium condensing steam flows. The Eulerian-Eulerian approach was utilised in which the mix- ture of vapour and liquid phases was solved by Reynolds-averaged Navier-Stokes equa- tions. The nucleation process was modelled with the classical nucleation theory, and two different droplet growth models were used to predict the droplet growth rate. The flow turbulence was solved by employing the standard k-ε and the shear stress transport k-ω turbulence models. Further, both models were modified and implemented in the CFD codes. The thermodynamic properties of vapour and liquid phases were evaluated with real gas models. In this thesis, various topics, namely the influence of real gas properties, turbulence mod- elling, unsteadiness and the blade trailing edge shape on wet-steam flows, are studied with different convergent-divergent nozzles, turbine stator cascade and 3D turbine stator-rotor stage. The simulated results of this study were evaluated and discussed together with the available experimental data in the literature. The grid independence study revealed that an adequate grid size is required to capture correct trends of condensation phenomena in LP turbine flows. The study shows that accurate real gas properties are important for the precise modelling of non-equilibrium condensing steam flows. The turbulence modelling revealed that the flow expansion and subsequently the rate of formation of liquid droplet nuclei and its growth process were affected by the turbulence modelling. The losses were rather sensitive to turbulence modelling as well. Based on the presented results, it could be observed that the correct computational prediction of wet-steam flows in the LP turbine requires the turbulence to be modelled accurately. The trailing edge shape of the LP turbine blades influenced the liquid droplet formulation, distribution and sizes, and loss generation. The study shows that the semicircular trailing edge shape predicted the smallest droplet sizes. The square trailing edge shape estimated greater losses. The analysis of steady and unsteady calculations of wet-steam flow exhibited that in unsteady simulations, the interaction of wakes in the rotor blade row affected the flow field. The flow unsteadiness influenced the nucleation and droplet growth processes due to the fluctuation in the Wilson point.

Development of Advanced Combustions using Cylinder Pressure Signal

Zero-carbon powertrains development has become one of the main challenges for automotive industries around the world. Following this guideline, several approaches such as powertrain electrification, advanced combustions, and hydrogen internal combustion engines have been aimed to achieve the goal. Low Temperature Combustions, characterized by a simultaneous reduction of fuel consumption and emissions, represent one of the most studied solutions moving towards a sustainable mobility. Previous research demonstrate that Gasoline partially premixed Compression Ignition combustion is one of the most promising LTC. Mainly characterized by the high-pressure direct-injection of gasoline and the spontaneous ignition of the premixed air-fuel mixture, GCI combustion has shown a good potential to achieve the high thermal efficiency and low pollutants in compression ignited engines required by future emission regulations. Despite its potential, GCI combustion might suffer from low combustion controllability and stability, because gasoline spontaneous ignition is significantly affected by slight variations of the local in-cylinder thermal conditions. Therefore, to properly control GCI combustion assuring the maximum performance, a deep knowledge of the combustion process, i.e., gasoline auto-ignition and the effect of the control parameters on the combustion and pollutants, is mandatory. This PhD dissertation focuses on the study of GCI combustion in a light-duty compression ignited engine. Starting from a standard 1.3L diesel engine, this work describes the activities made moving toward the full conversion of the engine. A preliminary study of the GCI combustion was conducted in a “Single-Cylinder” engine configuration highlighting combustion characteristics and dependencies on the control parameters. Then, the full engine conversion was performed, and a wide experimental campaign allowed to confirm the benefits of this advanced combustion methodologies in terms of pollutants and thermal efficiency. The analysis of the in-cylinder pressure signal allowed to study in depth the GCI combustion and develop control-oriented models aimed to improve the combustion stability.

Predicting Outcomes Of Balloon Laryngoplasty In Children With Subglottic Stenosis.

The treatment of subglottic stenosis in children remains a challenge for the otolaryngologist and may involve procedures such as endoscopy, open surgery, and often both. In the recent past, high-pressure balloons have been used in endoscopic treatment due to their relative facility and high success rates. To report success rates in the treatment of acquired subglottic stenosis with balloon laryngoplasty in children and identify predictive factors for the success of the technique and its complications. Descriptive, prospective study of children who were diagnosed with acquired subglottic stenosis and underwent balloon laryngoplasty as the primary treatment. Balloon laryngoplasty was performed in 48 children with an average age of 20.7 months: 31 presented with chronic subglottic stenosis and 17 with acute stenosis. Success rate was 100% for acute and 39% for chronic subglottic stenosis. Success was significantly associated with several factors, including recently acquired stenosis, initial grade of stenosis, younger patient age, and the absence of tracheotomy. Complications were transitory dysphagia observed in three children and a submucosal cyst in one of the patients. Balloon laryngoplasty may be considered as a first line of treatment for acquired subglottic stenosis. In acute cases, the success rate was 100%, and even though results are less promising in chronic cases, complications were not significant and the patients can undergo open surgery without contraindications. Predictive factors of success were acute stenosis, less severe grades of stenosis, younger patient age, and the absence of tracheotomy.

Tecnologia de nanocristais em fármacos

The use of poorly water soluble molecules in pharmaceutical area has grown. Since these molecules exhibit low oral bioavailability, they are not used in intravenous administrations. Therefore, it is necessary to develop their new formulations with the aim to increase their oral bioavailabilities as to enable intravenous applications. One of the few possibilities in achieving this is a nanonization process that can produce crystals smaller than 1 μm by high pressure homogenization and without use of organic solvents. This mini-review describes technical aspects of the nanocrystal production, morphological aspects (polymorphisms), the market relevance of the nanocrystals products that are already in clinical phase or at the market, as well as, perspectives for the near future.

Desenvolvimento, produção e caracterização de nanocristais de fármacos pouco solúveis

Poorly soluble drugs have low bioavailability, representing a major challenge for the pharmaceutical industry. Processing drugs into the nanosized range changes their physical properties, and these are being used in pharmaceutics to develop innovative formulations known as Nanocrystals. Use of nanocrystals to overcome the problem of low bioavailability, and their production using different techniques such as microfluidization or high pressure homogenization, was reviewed in this paper. Examples of drugs, cosmetics and nutraceutical ingredients were also discussed. These technologies are well established in the pharmaceutical industry and are approved by the Food and Drug Administration.

Phase transformation and residual stress probed by Raman spectroscopy in diamond-turned single crystal silicon

Single-point diamond turning of monocrystalline semiconductors is an important field of research within brittle materials machining. Monocrystalline silicon samples with a (100) orientation have been diamond turned under different cutting conditions (feed rate and depth of cut). Micro-Raman spectroscopy and atomic force microscopy have been used to assess structural alterations and surface finish of the samples diamond turned under ductile and brittle modes. It was found that silicon undergoes a phase transformation when machined in the ductile mode. This phase transformation is evidenced by the creation of an amorphous surface layer after machining which has been probed by Raman scattering. Compressive residual stresses are estimated for the machined surface and it is observed that they decrease with an increase in the feed rate and depth of cut. This behaviour has been attributed to the formation of subsurface cracks when the feed rate is higher than or equal to 2.5 mu m/rev. The surface roughness was observed to vary with the feed rate and the depth of cut. An increase in the surface roughness was influenced by microcrack formation when the feed rate reached 5.0 mu m/rev. Furthermore, a high-pressure phase transformation induced by the tool/material interaction and responsible for the ductile response of this typical brittle material is discussed based upon the presented Raman spectra. The application of this machining technology finds use for a wide range of high quality components, for example the creation of a micrometre-range channel for microfluidic devices as well as microlenses used in the infrared spectrum range.

Quasiharmonic elastic constants corrected for deviatoric thermal stresses

The quasiharmonic approximation (QHA), in its simplest form also called the statically constrained (SC) QHA, has been shown to be a straightforward method to compute thermoelastic properties of crystals. Recently we showed that for noncubic solids SC-QHA calculations develop deviatoric thermal stresses at high temperatures. Relaxation of these stresses leads to a series of corrections to the free energy that may be taken to any desired order, up to self-consistency. Here we show how to correct the elastic constants obtained using the SC-QHA. We exemplify the procedure by correcting to first order the elastic constants of MgSiO(3) perovskite and MgSiO(3) postperovskite, the major phases of the Earth's lower mantle. We show that this first-order correction is quite satisfactory for obtaining the aggregated elastic averages of these minerals and their velocities in the lower mantle. This type of correction is also shown to be applicable to experimental measurements of elastic constants in situations where deviatoric stresses can develop, such as in diamond-anvil cells.