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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
NASA NTRS1998

The Role of Marangoni Convection for the FZ-Growth of Silicon

Fluctuations of the electrical resistivity due to inhomogeneous dopant distribution are still a serious problem for the industrial processing yield of doped silicon crystals. In the case of silicon floating-zone growth, the main sources of these inhomogeneities are time- dependent flows in the liquid phase during the growth process. Excluding radio frequency (RF) induced convection, buoyancy and thermocapillary (Marangoni) convection are the two natural reasons for fluid flow. Both originate from temperature/concentration gradients in the melt, buoyancy convection through thermal/concentrational volume expansion, and thermocapillary convection through the temperature/concentration dependence of the surface tension. To improve the properties of grown crystals, knowledge of the strength, the characteristic, and the relation of these two flow mechanisms is essential. By the use of microgravity, the effect and the strength of buoyancy (gravity dependent) and thermocapillary (gravity independent) convection can be separated and clarified. Applying magnetic fields, both convective modes can be influenced: fluid flow can either be damped (static magnetic fields) or overlaid by a regular flow regime (rotating magnetic fields). Two complementary approaches have been pursued: Silicon full zones (experiments on the German sounding rockets TEXUS 7, 12, 22, 29, and 36) with the maximum temperature at half of the zone height and silicon half zones (experiments on the Japanese sounding rockets TR-IA4 and 6) with the maximum temperature at the top of the melt. With the full zone arrangement, the intensity and the frequency of the dopant striations could be determined and the critical Marangoni number could be identified. The half zone configuration is suited to classify the flow pattern and to measure the amplitude and the frequency of temperature fluctuations in the melt by inserting thermocouples or temperature sensors into the melt. All experiments have been carried out in monoellipsoid mirror furnaces. Typical zone geometries are approx. 8 to 14 mm in diameter and height. The crystals grown under microgravity are compared to crystals grown in static axial magnetic fields (B<5 tesla) and in transversal rotating magnetic fields (B<7.5 mT / f=50 Hz). Experimental results are completed by 3D numerical simulations: the obtained temperature and concentration distribution in the melt confirm the damping effect of rotating magnetic fields and explain the change in the radial segregation under static magnetic fields.

Dold, P.↗
NASA NTRS1998

Magnetic Damping of Solid Solution Semiconductor Alloys

The objective of this study is to conduct the Earth-based research sufficient to successfully propose a flight experiment (1) to experimentally test the validity of the modeling predictions applicable to the magnetic damping of convective flows in conductive melts as this applies to the bulk growth of solid solution semiconducting materials in the reduced gravitational levels available in low Earth orbit and (2) to assess the effectiveness of steady magnetic fields in reducing the fluid flows occurring in these materials during space processing. To achieve the objectives of this investigation, we are carrying out a comprehensive program in the Bridgman and floating-zone configurations using the solid solution alloy system Ge-Si. This alloy system was chosen because it has been studied extensively in environments that have not simultaneously included both low gravity and an applied magnetic field. Also, all compositions have a high electrical conductivity, and the materials parameters permit high growth rates compared to many other commonly studied alloy semiconductors. An important supporting investigation is determining the role, if any, that thermoelectromagnetic convection (TEMC) plays during growth of these materials in a magnetic field. Some compositional anomalies observed by us in magnetic grown crystals can only be explained by TEMC; this has significant implications for the deployment of a Magnetic Damping Furnace in space. This effect will be especially important in solid solutions where the growth interface is, in general, neither isothermal nor isoconcentrational. It could be important in single melting point materials, also, if faceting takes place producing a non-isothermal interface.

Szofran, Frank R.↗
NASA NTRS1999

Control of Meridional Flow by a Non-Uniform Rotational Magnetic Field

The diffusive mass transfer of species during crystal growth in vertical ampoules is significantly affected by fluid flow in the liquid mother phase (melt). For electrically conductive melts, an elegant way of remotely inducing and controlling this flow is by utilizing a uniform rotational magnetic field (RMF) in the transverse direction. It induces an azimuthal flow which tends to homogenize the thermal and solutal fields. The rotating field also reduces the diffusion boundary layer, stabilizes temperature fluctuations, and promotes better overall crystal growth. For moderate strengths of the applied magnetic field (2-20 m Tesla) with frequencies of up to 400 Hz, the induced secondary meridional flow becomes significant. It typically consists of one roll at the bottom of the liquid column and a second roll (vortex) at the top. The flow along the centerline (ampoule axis) is directed from the growing solid (interface) towards the liquid (melt). In case of convex interfaces (e.g. in floating zone crystal growth) such flow behavior is beneficial since it suppresses diffusion at the center. However, for concave interfaces (e.g. vertical Bridgman crystal growth) such a flow tends to exacerbate the situation in making the interface shape more concave. It would be beneficial to have some control of this meridional flow- for example, a single recirculating cell with controllable direction and flow magnitude will make this technique even more attractive for crystal growth. Such flow control is a possibility if a non-uniform PNE field is utilized for this purpose. Although this idea has been proposed earlier, it has not been conclusively demonstrated so far. In this work, we derive the governing equations for the fluid dynamics for such a system and obtain solutions for a few important cases. Results from parallel experimental measurements of fluid flow in a mercury column subjected to non-uniform RMF will also be presented.

Mazuruk, Konstantin↗
NASA NTRS2000

Effects of End-Wall Vibration on Oscillatory Thermocapillary Flow

Our previous float zone experiments 1,2 with NaNO3 revealed that steady thermocapillary flow (TC flow) can be balanced/offset by the controlled surface streaming flow (CSS flow), induced by end-wall vibration. In the current experiments, we are examining the effects of surface streaming flow on steadying/stabilizing oscillatory thermocapillary flow. To this effect, we have set up a controlled NaNO3 half-zone experiment, where the processing parameters like zone dimensions and temperature gradients scan be easily varied to achieve oscillatory TC flow. In the present paper, we discuss the thermal signature of the TC flow, and how it is affected by imposition of CSS flow. The results will also include a comparison of the microstructure of a NaNO3- BaNO3 eutectic, processed under oscillatory TC conditions, with and without imposed CSS flow.

Bhowmick, J.↗
NASA NTRS2000

Crystallography of Alumina-YAG-Eutectic

Multiple descriptions of the alumina-YAG eutectic crystallography appear in the ceramic literature. The orientation between two phases in a eutectic system has direct impact on residual stress, morphology, microstructural stability, and high temperature mechanical properties. A study to demonstrate that the different crystallographic relationships can be correlated with different growth constraints was undertaken. Fibers produced by Laser-Heated Float Zone (LHFZ) and Edge-defined Film-fed Growth (EFG) were examined. A map of the orientation relationship between Al2O3 and Y3Al5O12 and their relationship to the fiber growth axis as a function of pull rate are presented. Regions in which a single orientation predominates are identified.

Farmer, Serene C.↗
NASA NTRS2000

Convection Induced by Traveling Magnetic Fields in Semiconductor Melts

Axisymmetric traveling magnetic fields (TMF) can be beneficial for crystal growth applications. such as the vertical Bridgman, float zone or traveling heater methods. TMF induces a basic flow in the form of a single roll. This type of flow can enhance mass and heat transfer to the growing crystal. More importantly, the TMF Lorentz body force induced in the system can counterbalance the buoyancy forces, so the resulting convection can be much smaller and even the direction of it can be changed. In this presentation, we display basic features of this novel technique. In particular, numerical calculations of the Lorentz force for arbitrary frequencies will be presented along with induced steady-state fluid flow profiles. Also, numerical modeling of the TMF counter-balancing natural convection in vertical Bridgman systems will be demonstrated.

Konstantin, Mazuruk↗
NASA NTRS1999

Stability of Shapes Held by Surface Tension and Subjected to Flow

Results of three problems are summarized in this contribution. Each involves the fundamental capillary instability of an interfacial bridge and is an extension of previous work. The first two problems concern equilibrium shapes of liquid bridges near the stability boundary corresponding to maximum length (Plateau-Rayleigh limit). For the first problem, a previously formulated nonlinear theory to account for imposed gravity and interfacial shear disturbances in an isothermal environment is quantitatively tested in experiment. For the second problem, the liquid bridge is subjected to a shear that models the effect of a thermocapillary flow generated by a ring heater in a liquid encapsulated float-zone configuration. In the absence of gravity, this symmetric perturbation can stabilize the bridge to lengths on the order of 30 percent beyond the Plateau-Rayleigh limit, which is on the order of heretofore unexplained Shuttle observations. The third problem considers the dynamics of collapse and pinchoff of a film bridge (no gravity), which happens in the absence of stabilization. Here, we summarize experimental efforts to measure the self-similar cone-and-crater structure predicted by a previous theory.

Chen, Yi-Ju↗
NASA NTRS2001

Some Novel Solidification Processing Techniques Being Investigated at MSFC: Their Extension for Study Aboard the ISS

The float-zone and the Bridgman techniques are two classical directional solidification processing methods that are used to improve materials properties. Unfortunately, buoyancy effects and gravity-driven convection due to unstable temperature and/or composition gradients still produce solidified products that exhibit segregation and, consequently, degraded properties. This presentation will briefly introduce how some novel processing applications can minimize detrimental gravitational effects and enhance microstructural uniformity. Discussion follows that to fully understand and model these procedures requires utilizing, in conjunction with a novel mixing technique, the facilities and quiescent microgravity environment available on the ISS.

Grugel, R. N.↗
NASA NTRS1997

Single Crystal Fibers of Yttria-Stabilized Cubic Zirconia with Ternary Oxide Additions

Single crystal fibers of yttria (Y2O3)-stabilized cubic zirconia, (ZrO2) with ternary oxide additions were grown using the laser float zone fiber processing technique. Ternary additions to the ZrO2-Y2O3 binary system were studied aimed at increasing strength while maintaining the high coefficient of thermal expansion of the binary system. Statistical methods aided in identifying the most promising ternary oxide candidate (Ta2O5, Sc2O3, and HfO2) and optimum composition. The yttria, range investigated was 14 to 24 mol % and the ternary oxide component ranged from 1 to 5 mol %. Hafnium oxide was the most promising ternary oxide component based on 816 C tensile strength results and ease of fabrication. The optimum composition for development was 81 ZrO2-14 Y203-5 HfO2 based upon the same elevated temperature strength tests. Preliminary results indicate process improvements could improve the fiber performance. We also investigated the effect of crystal orientation on strength.

Ritzert, F. J.↗
NASA NTRS2001

Contact Angles and Surface Tension of Germanium-Silicon Melts

Precise knowledge of material parameters is more and more important for improving crystal growth processes. Two important parameters are the contact (wetting) angle and the surface tension, determining meniscus shapes and surface-tension driven flows in a variety of methods (Czochralski, EFG, floating-zone, detached Bridgman growth). The sessile drop technique allows the measurement of both parameters simultaneously and has been used to measure the contact angles and the surface tension of Ge(1-x)Si(x) (0 less than or equal to x less than or equal to 1.3) alloys on various substrate materials. Fused quartz, Sapphire, glassy carbon, graphite, SiC, carbon-based aerogel, pyrolytic boron nitride (pBN), AIN, Si3N4, and polycrystalline CVD diamond were used as substrate materials. In addition, the effect of different cleaning procedures and surface treatments on the wetting behavior were investigated. Measurements were performed both under dynamic vacuum and gas atmospheres (argon or forming gas), with temperatures up to 1100 C. In some experiments, the sample was processed for longer times, up to a week, to investigate any changes of the contact angle and/or surface tension due to slow reactions with the substrate. For pure Ge, stable contact angles were found for carbon-based substrates and for pBN, for Ge(1-x)Si(x) only for pBN. The highest wetting angles were found for pBN substrates with angles around 170deg. For the surface tension of Ge, the most reliable values resulted in gamma(T) = (591- 0.077 (T-T(sub m)) 10(exp -3)N/m. The temperature dependence of the surface tension showed similar values for Ge(1-x)Si(x), around -0.08 x 10(exp -3)N/m K, and a compositional dependence of 2.2 x 10(exp -3)N/m at%Si.

Croell, A.↗
NASA NTRS2001

Dynamic Magnetic Field Applications for Materials Processing

Magnetic fields, variable in time and space, can be used to control convection in electrically conducting melts. Flow induced by these fields has been found to be beneficial for crystal growth applications. It allows increased crystal growth rates, and improves homogeneity and quality. Particularly beneficial is the natural convection damping capability of alternating magnetic fields. One well-known example is the rotating magnetic field (RMF) configuration. RMF induces liquid motion consisting of a swirling basic flow and a meridional secondary flow. In addition to crystal growth applications, RMF can also be used for mixing non-homogeneous melts in continuous metal castings. These applied aspects have stimulated increasing research on RMF-induced fluid dynamics. A novel type of magnetic field configuration consisting of an axisymmetric magnetostatic wave, designated the traveling magnetic field (TMF), has been recently proposed. It induces a basic flow in the form of a single vortex. TMF may find use in crystal growth techniques such as the vertical Bridgman (VB), float zone (FZ), and the traveling heater method. In this review, both methods, RMF and TMF are presented. Our recent theoretical and experimental results include such topics as localized TMF, natural convection dumping using TMF in a vertical Bridgman configuration, the traveling heater method, and the Lorentz force induced by TMF as a function of frequency. Experimentally, alloy mixing results, with and without applied TMF, will be presented. Finally, advantages of the traveling magnetic field, in comparison to the more mature rotating magnetic field method, will be discussed.

Mazuruk, K.↗
NASA NTRS2001

Crystallographic Texture and Orientation Variants in Al2O3-Y3Al5O12 Directionally Solidified Eutectic Crystals

Eutectic rods of Al2O3 and Y3Al5O12 were grown by a laser-heated float zone method, and their microstructure and crystallographic texture were studied by scanning electron microscopy, electron backscattered diffraction and x-ray diffraction. The composites were found to be highly textured with two twin-related crystallographic orientation relationships between the phases. Electron backscattered diffraction was employed to determine the spatial distribution of the orientational variants within the samples and to define the crystallographic orientation of various microstructural features.

Frazer, Colleen S.↗
NASA NTRS2001

Passive and Active Stabilization of Liquid Bridges in Low Gravity

Tests are planned in the low gravity environment of the International Space Station (ISS) of new methods for the suppression of the capillary instability of liquid bridges. Our suppression methods are unusual in that they are not limited to liquid bridges having very special properties and may impact a variety of low-gravity and earth-based technologies. There are two main approaches to be investigated: (1) Passive Acoustic Stabilization (PAS); and (2) Active Electrostatic Stabilization (AES). In PAS, the suppression of the mode growth is accomplished by placing the bridge in an acoustic field having the appropriate properties such that the acoustic radiation pressure automatically pulls outward on the thinnest portion of the bridge. In AES, the bridge deformation is sensed optically and counteracted by actively adjusting the electrostatic Maxwell stresses via two ring electrodes concentric with the slightly conducting bridge to offset the growth of the unstable mode. While the present work emphasizes cylindrical bridges, the methods need not be restricted to that case. The methods to be explored are relevant to the suppression of capillary instabilities in floating zone crystal growth, breakup of liquid jets and columns, bubbles, and annular films as well as the management of coolants or propellants in low-gravity.

Marston, Philip L.↗
NASA NTRS2003

Control of Thermal Convection in Layered Fluids Using Magnetic fields

Immiscible fluid layers are found in a host of applications ranging from materials processing, for example the use of encapsulants in float zone crystal growth technique and a buffer layer in industrial Czochralski growth of crystals to prevent Marangoni convection, to heat transfer phenomena in day-to-day processes like the presence of air pockets in heat exchangers. In the microgravity and space processing realm, the exploration of other planets requires the development of enabling technologies in several fronts. The reduction in the gravity level poses unique challenges for fluid handling and heat transfer applications. The present work investigates the efficacy of controlling thermal convective flow using magnetic fluids and magnetic fields. The setup is a two-layer immiscible liquids system with one of the fluids being a diluted ferrofluid (super paramagnetic nano particles dispersed in carrier fluid). Using an external magnetic field one can essentially dial in a volumetric force - gravity level, on the magnetic fluid and thereby affect the system thermo-fluid behavior. The paper will describe the experimental and numerical modeling approach to the problem and discuss results obtained to date.

Ramachandran, N.↗
NASA NTRS2003

Basic and Applied Materials Science Research Efforts at MSFC Germane to NASA Goals

Presently, a number of investigations are ongoing that blend basic research with engineering applications in support of NASA goals. These include (1) "Pore Formation and Mobility (PFMI) " An ISS Glovebox Investigation" NASA Selected Project - 400-34-3D; (2) "Interactions Between Rotating Bodies" Center Director's Discretionary Fund (CDDF) Project - 279-62-00-16; (3) "Molybdenum - Rhenium (Mo-Re) Alloys for Nuclear Fuel Containment" TD Collaboration - 800-11-02; (4) "Fabrication of Alumina - Metal Composites for Propulsion Components" ED Collaboration - 090-50-10; (5) "Radiation Shielding for Deep-Space Missions" SD Effort; (6) "Other Research". In brief, "Pore Formation and Mobility" is an experiment to be conducted in the ISS Microgravity Science Glovebox that will systematically investigate the development, movement, and interactions of bubbles (porosity) during the controlled directional solidification of a transparent material. In addition to promoting our general knowledge of porosity physics, this work will serve as a guide to future ISS experiments utilizing metal alloys. "Interactions Between Rotating Bodies" is a CDDF sponsored project that is critically examining, through theory and experiment, claims of "new" physics relating to gravity modification and electric field effects. "Molybdenum - Rhenium Alloys for Nuclear Fuel Containment" is a TD collaboration in support of nuclear propulsion. Mo-Re alloys are being evaluated and developed for nuclear fuel containment. "Fabrication of Alumina - Metal Composites for Propulsion Components" is an ED collaboration with the intent of increasing strength and decreasing weight of metal engine components through the incorporation of nanometer-sized alumina fibers. "Radiation Shielding for Deep-Space Missions" is an SD effort aimed at minimizing the health risk from radiation to human space voyagers; work to date has been primarily programmatic but experiments to develop hydrogen-rich materials for shielding are planned. "Other Research" includes: BUNDLE (Bridgman Unidirectional Dendrite in a Liquid Experiment) activities (primarily crucible development), vibrational float-zone processing (with Vanderbilt University), use of ultrasonics in materials processing (with UAH), rotational effects on microstructural development, and application of magnetic fields for mixing.

Source record↗
NASA NTRS2000

Directionally Solidified Ceramics Produced

Produced Multiphase, interpenetrating structures are an alternative route to obtaining structural ceramic materials with adequate strength, toughness, and stability for high-temperature aerospace applications. The eutectic architecture, a continuous-reinforcing phase within a higher volume phase or matrix, can be described as a naturally occurring, in situ composite. The phases of a eutectic are thermodynamically compatible at high homologous temperatures. Strong and stable materials have been produced. Toughness, however, remains a technical obstacle. The potential for producing materials with enhanced toughness along with adequate strength and stability was demonstrated using the laser-heated float zone (LHFZ) growth method at the NASA Glenn Research Center at Lewis Field. LHFZ growth at Glenn provides a means to efficiently produce and record the underlying growth phenomena associated with two-phase structures. To initiate directional solidification, a seed of single-crystal sapphire (<0001> direction) was lowered onto the molten liquid until wetting occurred and then withdrawn at a constant rate. Neither the crystal nor the source rod was rotated. The materials produced were tested mechanically in tension, and the resulting microstructure was examined with a scanning electron microscope. Both the inherent properties of the constituent phases and the properties of the interface between them affect the mechanical behavior and the fracture surfaces. The following scanning electron micrographs show the microstructures of two different materials that were tested to failure in tension. In the left micrograph, the flat fracture surface is typical of a material that is strong but has low toughness. In the right micrograph, the crack is effectively deflected at the interface between the two phases, achieving higher toughness at moderately lower strength levels. Conducting mechanical tests to determine the high temperature properties of these materials is the next step in determining their eventual suitability.

Farmer, Serene C.↗
NASA NTRS2004

New Effective Material Couple--Oxide Ceramic and Carbon Nanotube-- Developed for Aerospace Microsystem and Micromachine Technologies

The prime driving force for using microsystem and micromachine technologies in transport vehicles, such as spacecraft, aircraft, and automobiles, is to reduce the weight, power consumption, and volume of components and systems to lower costs and increase affordability and reliability. However, a number of specific issues need to be addressed with respect to using microsystems and micromachines in aerospace applications--such as the lack of understanding of material characteristics; methods for producing and testing the materials in small batches; the limited proven durability and lifetime of current microcomponents, packaging, and interconnections; a cultural change with respect to system designs; and the use of embedded software, which will require new product assurance guidelines. In regards to material characteristics, there are significant adhesion, friction, and wear issues in using microdevices. Because these issues are directly related to surface phenomena, they cannot be scaled down linearly and they become increasingly important as the devices become smaller. When microsystems have contacting surfaces in relative motion, the adhesion and friction affect performance, energy consumption, wear damage, maintenance, lifetime and catastrophic failure, and reliability. Ceramics, for the most part, do not have inherently good friction and wear properties. For example, coefficients of friction in excess of 0.7 have been reported for ceramics and ceramic composite materials. Under Alternate Fuels Foundation Technologies funding, two-phase oxide ceramics developed for superior high-temperature wear resistance in NASA's High Operating Temperature Propulsion Components (HOTPC) project and new two-layered carbon nanotube (CNT) coatings (CNT topcoat/iron bondcoat/quartz substrate) developed in NASA's Revolutionary Aeropropulsion Concepts (RAC) project have been chosen as a materials couple for aerospace applications, including micromachines, in the nanotechnology lubrication task because of their potential for superior friction and wearf properties in air and in an ultrahigh vacuum, spacelike environment. At the NASA Glenn Research Center, two-phase oxide ceramic eutectics, Al2O3/ZrO2(Y2O3), were directionally solidified using the laser-float-zone process, and carbon nanotubes were synthesized within a high-temperature tube furnace at 800 C. Physical vapor deposition was used to coat all quartz substrates with 5-nm-thick iron as catalyst and bondcoat, which formed iron islands resembling droplets and serving as catalyst particles on the quartz. A series of scanning electron micrographs showing multiwalled carbon nanotubes directionally grown as aligned "nanograss" on quartz is presented. Unidirectional sliding friction eperiments were conducted at Glenn with the two-layered CNT coatings in contact with the two-phase Al2O3/ZrO2(Y2O3) eutectics in air and in ultrachigh vacuum. The main criteria for judging the performance of the materials couple for solid lubrication and antistick applications in a space environment were the coefficient of friction and the wear resistance (reciprocal of wear rate), which had to be less than 0.2 and greater than 10(exp 5) N(raised dot)/cubic millimetes, respectively, in ultrahigh vacuum. In air, the coefficient of friction for the CNT coatings in contact with Al2O3/ZrO2 (Y2O3) eutectics was 0.04, one-fourth of that for quartz. In an ultrahigh vacuum, the coefficient of friction for CNT coatings in contact with Al2O3/ZrO2 (Y2O3) was one-third of that for quartz. The two-phase Al2O3/ZrO2 (Y2O3) eutectic coupled with the two-layered CNT coating met the coefficient of friction and wear resistance criteria both in air and in an ultrahigh vacuum, spacelike environment. This material's couple can dramatically improve the stiction (or adhesion), friction, and wear resistance of the contacting surfaces, which are major issues for microdevices and micromachines.

Miyoshi, Kazuhisa↗
NASA NTRS2001

Single-Crystal Elastic Constants of Yttria (Y2O3) Measured to High Temperatures

Yttria, or yttrium sesquioxide (Y2O3), has been considered for use in nuclear applications and has gained interest relatively recently for use in infrared optics. Single crystals of yttria have been grown successfully at the NASA Glenn Research Center using a laser-heated float zone technique in a fiber and rod. Such samples allow measurement of the single-crystal elastic properties, and these measurements provide useful property data for the design of components using single crystals. They also yield information as to what degree the elastic properties of yttria ceramics are a result of the intrinsic properties of the yttria crystal in comparison to characteristics that may depend on processing, such as microstructure and intergranular phases, which are common in sintered yttria. The single-crystal elastic moduli are valuable for designing such optical components. In particular, the temperature derivatives of elastic moduli allow the dimensional changes due to heating under physical constraints, as well as acoustic excitation, to be determined. The single-crystal elastic moduli of yttria were measured by Brillouin spectroscopy up to 1200 C. The room-temperature values obtained were C(sub 11) = 223.6 + 0.6 GPa, C(sub 44) = 74.6 + 0.5 GPa, and C(sub 12) = 112.4 + 1.0 GPa. The resulting bulk and (Voigt-Reuss-Hill) shear moduli were K = 149.5 + 1.0 GPa and G(sub VRH) = 66.3 + 0.8 GPa, respectively. Linear least-squares regressions to the variation of bulk and shear moduli with temperature resulted in derivatives of dK/dT = -17 + 2 MPa/C and dG(sub VRH)/dT = -8 + 2 MPa/ C. Elastic anisotropy was found to remain essentially constant over the temperature range studied.

Sayir, Ali↗