Temperature Gradient In Liquid Research Articles

On the morphology of <100>‐textured Germanium Crystallites in Zn—Ge Eutectic Alloy

AbstractDifferent geometry parameters for the cross‐like germanium crystallites (eutectic dendrites) of the Zn‐Ge eutectic alloys unidirectionally solidified have been related to the growth rate R and liquid temperature gradient G using linear regression analysis. It has been found that for eutectic dendrite spacing λ, balk length d and balk thickness b follow the relationship of the type w = CwR−rwG−gw; Cw is a constant. The spacing relationship of eutectic dendrites (rλ = 0.21; gλ = 0.48) shows a similarity with published experimental and theoretical results on primary dendrite arm spacing (rλ = 0.25; gλ = 0.5). It has been shown in terms of a profile ration λ/d that for geometrical similar morphologies the relationship λ2R = const. is valid.

A theoretical investigation of the development of interfacial cells during the solidification of a dilute binary alloy: Comparison with the experiments of Morris and Winegard

An investigation is made of the development of hexagonal cells on an initially planar interface of solid growing uniformly into the liquid phase during the unidirectional solidification of a dilute binary alloy. The model employed postulates three-dimensional diffusion of solute and heat under the simplifying assumptions that there is no convection in the liquid phase, no solute diffusion in the solid phase, both these phases are infinite in extent, latent heat is negligible, and the thermal fields satisfy Laplace's equation in each phase. A nonlinear stability analysis is performed analogous to that originally developed for the study of Bénard convection cells. The main results of this analysis are that, for a fixed value of the liquid temperature gradient, the structure of the planar interface evolves from nodes (circular depressions) to bands (elongated cells) to dome-shaped hexagonal cells as the solidification speed is increased. These results, which can only be obtained provided the variation of interfacial surface free energy with solute concentration is taken into account, are in excellent agreement with the experimental observations of Morris and Winegard [J. Inst. Metals 97 (1969) 220; J. Crystal Growth 5 (1969) 361] in regard to interface morphologies and solute segregation under their solidification conditions.

Flow transitions in Czochralski oxide melts

The interface inversion observed in Gd3Ga5O12 and other oxide systems with the resulting wave formation in the molten oxide has been found to represent a form of baroclinic instability. With suitable modifications, the correlations developed for baroclinic instabilities in simulated meteorological systems can be applied to the Czochralski geometry. Furthermore, it has been found that the radial liquid temperature gradient in a RF Czochralski growth system is most strongly influeced by the crucible radius with the furnace insulation playing a secondary role.

デンドライトの1次枝間隔に及ぼす凝固条件の影響

To examine the relationship between the primary dendrite arm spacing and solidification conditions, experiments were performed with Al-2.0%Cu, Al-4.0%Cu, Al-6.0%Cu, and Al-2.0%Si alloys which were unidirectionally solidified in three ways, i.e., by rapid cooling, by slow cooling, and by alternating rapid and slow cooling. The results are summarized as follows:(1) When the average cooling rate V ranged between 1.6 K/s and 12.6 K/s, the primary dendrite arm spacing Z1 (10−3 m) was proportional to (G2R)−1⁄4 which was expected from Hunt’s theory, G (103 K/m) is the temperature gradient in liquid and R (10−3 m/s) is the growth rate.(2) When the average cooling rate V for most of the slowly cooled specimens was lower than 1.6 K/s, the value n in the equation Z1∝(G2R)−n became smaller than 1⁄4.(3) When the temperature gradient in the solid-liquid coexisting region was expressed as Gs (103 K/m), the primary dendrite arm spacing Z1 was proportional to Gs−0.70R−0.35 for all the specimens.(4) For the specimens solidified by rapid cooling and slow cooling, the relationship between Z1 and the cooling rate V was expressed as Z1∝V−1⁄2. But for the ones solidified by alternating rapid and slow cooling, Z1 was not proportional to V−1⁄2.(5) For all the specimens, Z1 was proportional to (GsR)−1⁄2.

TEMPERATURE GRADIENT LIQUID PHASE EPITAXY UNDER A STEADY NATURAL CONVECTION FLOW

The temperature gradient liquid phase epitaxy under a steady natural convection flow was introduced. The steady natural convection flow was caused by applying a horizontal temperature difference to the growth solution. The growth rate in this process was calculated using a simple model. It was found that the growth rate is directly proportional to the square root of the horizontal temperature difference and for Ga0.85Al0.15 As growth under the condition employed in the present work the growth rate is 1124 times as great as that predicted by the steady state diffusion theory and the deviation of epitaxial layer thickness is not more than 10% over the most part of area of growth layer. The experimental growth system designed for the temperature gradient liquid phase epitaxy under a steady natural convection flow was described. This system was used to grow thick Ga0.85Al0.15 As layers. The experimental result shows that the observed growth rate is directly proportional to the power 0.45 of the horizontal temperature difference and for Ga0.85Al0.15 As growth the observed growth rate is 156 times as great as that predicted by the steady state diffusion theory and is one-eighth as great as that predicted by the convection theory and at a relatively small horizontal temperature difference the deviation of epitaxial layer thickness is in agreement with the calculated value by the convection theory. The calculated growth rate is higher than the observed growth rate. That is attributed to some approximations made and some indefinite parameters used. Owing to an increase in growth rate the present work was able to grew thick Ga1-xAlx As layers at the temperature which is 135-210℃ lower than that used for the similar work.

Measurements of cell and primary dendrite arm spacings in directionally solidified aluminium alloys

Cell and primary dendrite arm spacings have been measured in AlCu and AlMgSi alloys directionally solidified at steady state over a very large range of growth conditions. The AlMgSi alloys have been chosen so as to minimize gravitational fluid flow in the liquid. A spacing parameter, λ, has been correlated with the liquid temperature gradient G L , the growth velocity, V and the bulk alloy composition, C ∞. It has been found that for dendrites in the AlMgSi system λ = 272 G −0.55 L V −0.28 C +0.32 ∞ Si where C ∞ Si is the atom fraction of Si in the alloy. It has also been observed that there is a discontinuous change in the spacing relationship, as measured by λ, when the growth morphology changes from cellular to dendritic. Cells were found to form a roughly hexagonal array whereas dendrites adopted a much less regular pattern. This discontinuous change in λ is explained by considering how the nature of an array affects its average nearest neighbour spacing λ ∗.

Energy Extraction From a Laboratory Model Fractured Geothermal Reservoir

Energy recovery by sweep and steam-drive processes is demonstrated in a laboratory model of a fractured-rock geothermal reservoir that can be heated to a reservoir temperature of 500 deg. F at a pressure of 800 psig. Results show that energy up to 75 Btu/lbm of rock was extracted by the sweep process and about 9 Btu/lbm was extracted by the steam-drive process. Introduction Economic development of geothermal resources on a large scale will require advanced technologies to enhance energy recovery from hydrothermal and hot igneous-rock systems that presently are unproductive. Several fracture-stimulation techniques and energy-extraction methods have been proposed to improve total productivity and energy recovery from these geothermal resources. productivity and energy recovery from these geothermal resources. Stimulation techniques include hydraulic fracturing, explosive fracturing, and thermal stress cracking. These techniques are intended to increase the vertical and horizontal formation permeabilities, providing adequate fluid circulation and exposing new rock-surface area to allow heat transfer from hot rock to fluid. Nonisothermal production of the reservoir and energy recovery from hot rock may be achieved by such methods aspressure reduction and in-place boiling,artificial circulation of water, andfluid production using steam-drive. Nonisothermal processes may be achieved in the first method by lowering the system pressure until in-place boiling of the natural or recharged water present in the reservoir occurs. Steam is produced from the top of the reservoir at pressures determined by the saturation curve. The nonisothermal process in the second method may be achieved by injecting cold water at a low point in the hot rock formation under high pressure. The water is heated as it flows upward in the artificially fracture rock media to a higher point, where it is produced as hot water We call this the sweep process. The third method is similar to the first, except that hot water is produced from a point below the water/steam interface. Steam formed by evaporation from hot rock surfaces and noncondensable gases accumulates in a steam cap in the top portions of the reservoir and provides the drive for production. We refer to this as the steam-drive process. Energy extraction from hot rock by the in-place boiling process was studied in a laboratory model using two rock process was studied in a laboratory model using two rock systems with several characteristics resembling those of explosively fracture-stimulated, hydrothermal reservoirs. Results of these experiments reported in Refs. 7 through 9 show that up to 47 Btu/lbm (109 kJ/kg) of rock was extracted by the in-place boiling process for a broad range of experimental conditions. Heat transfer from the rock resulted in an increase in total energy extraction from the hydrothermal (liquid and rock) system ranging from 1.25 to 2.57 times the energy obtained by flashing the liquid. Fluid production and rock heat-transfer analyses were developed that closely predicted the behavior of the physical model as long as the axial liquid-temperature physical model as long as the axial liquid-temperature gradients were small. The rock heat-transfer analysis was applied to hypothetical, large-scale systems having a 30-year production time and similar fluid circulation characteristics and temperature conditions. Results showed that a mean rock size of about 200 ft (60 m) would result in about the same amount of specific energy extraction from the rock as was obtained experimentally. The physical model of the second rock system used for the in place boiling experiments subsequently was used for sweep experiments. JPT P. 712

Oscillatory Combustion of Monopropellant Droplets

A theoretical study of combustion response to imposed pressure oscillations was conducted for monopropellant droplets and sprays. A first-order perturbation analysis was used, yielding the linear response. Transient gas-phase phenomena were considered in some cases, but the bulk of the calculations assume a quasisteady gas phase. The calculations employed properties representative of hydrazine decomposition. Calculated steady combustion results and response predictions for large hydrazine droplets agreed favorably with earlier measurements. Droplet and spray response factors in excess of unity were found. High response was associated with high pressures (1000-10,000 kN/m2), large droplets, large mean liquid temperature gradients, and frequencies near the characteristic frequency of the liquid-phase thermal wave. Spray response factors are lower than the response factor of the largest injected drop; however, a small percentage of large drops can still provide substantial response for the combustion process.

Czochralski growth of large diameter LiTaO 3 crystals

The conditions necessary for the growth of large crystals of LiTaO 3 (3.8 cm diameter × 21 cm long) by the Czochralski technique have been determined. The effect of growth direction and the liquid temperature gradient as related to the density and distribution of dislocations and therefore the cracking probability has also been examined.

Computer model studies of dendritic growth

A computer model (simulation) approach to the study of the dendritic growth phenomenon is reviewed, and related to prior analytic work. Results are presented for the simulation of idealised tin crystals in the form of single fibers and in the form of arrays. The quantities generated by a long-term simulation are fitted within a theoretical framework. Tip shape is related to the temperature gradient in liquid near the tip using a stability argument. An independent relationship between tip radius and the adjacent gradient (a measure of growth velocity) is proposed as a replacement for the “maximum velocity criterion” used in prior studies to define a unique crystal. The possibility of oscillatory growth is discussed.

A Device for the Removal of Temperature Gradients in NMR Spinning Tubes

A simple paddle device is described for the removal of temperature gradients in liquids contained in high resolution NMR spinning tubes. Experiments show that this accessory reduces temperature gradients to less than 0.10°C along the length of the liquid without any impairment in spectrometer resolution or sensitivity. The device is readily adaptable to most conventional high resolution NMR spectrometers.

Formation of crystal structures in pure aluminum

This is the first progressive report on the crystallization of metals and alloys from liquid and describes the formation of macrostructures in pure aluminum. The controlling variables on forming macrostructures have been determined on the basis of the distance-time curves of the waves of freezing start and end taken from various sets of cooling curves.High purity, commercial purity and grain refined aluminum have particular types of macrostructures. Movement of the wave of freezing start is rather important than that of freezing end. The starting wave progresses parabolically at the early stage of directional freezing and linearly at the final stage. The transformation of structure from columnar to equiaxial occurs near this transitional point. The substantial location of the structural transformation is dependent on the purity of aluminum or existing stable nuclei. Although most of the thermal variables during freezing are not so important in forming the structure, only the thermal gradient in the liquid just ahead of growing solid is critical for each purity of aluminum. The ratio(linear freezing rate)1/2/(temperature gradient in liquid) first proposed by Tiller and Rutter probably depends on the temperature gradient to a great degree. The critical temperature gradient for structural transformation also depends on the stability and numbers of existing heterogeneous nuclei. Unfortunately, the substance, numbers, size and distribution of the heterogeneous nuclei have not yet determined particularly on the quantitative basis.