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By Li. Jiarong, Zuojian Liang, Qingyan Xu, Baicheng Liu, Shizhong Liu, Hailong Yuan

Single crystal solidification of turbine blades is a key technology for the production of reliable and high efficiency gas turbines. The solidification process of single crystal investment castings causes a number of problems that have to be solved such as the increase of casting defects and complexity of production process. Computer modeling and simulation is helpful to predict the defects and improve the process design. In the paper, a mathematical model for three dimensional simulation of solidification and single crystal growth of investment castings was developed based on CA, mechanism of crystal growth and basic transfer equations such as heat, mass transfer equations. Many factors including constitutional undercooling, curvature undercooling and anisotropy, which had vital influences on microstructure evolution, were considered in the model. Temperature, crystal growth interface and structure defects of investment castings of single crystal superalloy were investigated at withdrawal rates of 4.5mm/min and 7mm/min. Simulated results showed that microstructure evolution and structure defects were predicted reasonably and calculated results were coincident with experimental ones. The study indicated that three dimensional solidification simulation technique is a powerful tool for understanding the fundamental of solidification and the formation of structure defects in single crystal investment castings and finally for optimizing process design.

Jan 1, 2004

By Xiao-hui Fan, Xu-ling Chen, Xiao-xian Huang, Gui-ming Yang

Grate-kiln-cooler is a predominant process of producing iron ore pellets in China. Since this process is of multi-variant, strong coupling and large hysteresis characteristics, a reliable performance monitoring is thus essential to ensure product quality and economic benefits. Aiming to efficiently monitor the pellet induration within this process, this study proposed an approach that combines statistical analysis and quality soft-measurement. Soft-measurement of pellet quality was accomplished based on the predicted time-temperature profile, and the soft-measured indices were on-line monitored using statistical control charts. Based on the proposed approach, a monitoring system for grate-kiln-cooler thermal process was developed for a domestic pelletizing plant. Running results demonstrate that our system can assist in the detection or diagnosis of abnormal thermal state and finally helps to stabilize the pellet production.

Jan 1, 2016

By G. A. Irons, D. Guo

"The average spout height and width produced by bottom gas injection in a water model of a steel ladle were measured with an image processing technique. It was revealed that the spout height could be described by a Gaussian curve. A combined SIMPLE -VOF model was developed to simulate the liquid surface and flow. The results showed that, though the model produced reasonable velocity distributions and free surface positions, the spout height due to the dynamic head of the rising liquid was substantially lower than observed, indicating that the bubble dynamics at the bath surface play an important role in spout height.IntroductionDue to the enormous importance of gas injection and stirring in metallurgical processes, there have been numerous publications on water and numerical modeling of such vessels. The free surface of the bath has received considerably less attention, despite its importance. At the free surface there are often important chemical phenomena occurring that require a good understanding of the fluid flow; these would include reoxidation of steel, metal splash and fume formation. Furthermore, to understand the details of slag-metal interactions such as slag entrainment, metal losses to slag and the transport phenomena associated with refining reactions, it is necessary to understand the plume and spout interactions first.There have been few experimental studies of the free surface of liquid in gas-injected ladles [1- 3], and even fewer on numerical modeling. Brimacombe and co-workers [1] studied the gas void fraction in the spout region, using a double-tip electrical resistance probe. This sensor cannot distinguish between gas in bubbles about to break and gas in the freeboard. Thus, it is a matter of judgement as to the position of the free surface. Schwerdtfeger and co-workers [2] used a single probe configuration with a wire and a counter electrode in the liquid, so that the height of the continuous liquid phase was unambiguously determined. Irons and co-workers [3] measured the spout height by ultrasonic and electrical capacitance techniques. These techniques were as reliable as the resistance techniques, but were restricted to low flow rates."

Jan 1, 2001

By Jorge A. S. Tenorio, Chuanwei Zhuo, Joner O. Alves, Yiannis A. Levendis

"The disposal of wastes is a serious environmental problem, since available landfill space is dwindling. Their treatment by pyrolysis or combustion has merit, and the corresponding fuel or power production is of technological interest. However, such processes need a rigid control of emissions. This work addresses the gaseous light hydrocarbons (LHCs) generated during sequential pyrolysis and partial oxidation of unserviceable tires, PET bottles, com wastes (DDGS) and sugarcane bagasse in a two-stage laminar-flow horizontal furnace, kept at 1000 °C. Gas chromatography was used to identify and quantify the components of the emitted gaseous light hydrocarbons. The results showed that the biomass residues generated the highest emissions of aliphatic hydrocarbons, whereas PET generated the most aromatic hydrocarbons. When stainless steel meshes were inserted in the exhaust flow, it was found that hydrocarbon emissions were curtailed; as such meshes catalyzed partial conversion of these carbon-bearing gases to carbonaceous nanomaterials.IntroductionLight hydrocarbons (LHCs) are volatile organic compounds, consisting of hydrogen and carbon with low molecular weight; the most common species are methane, ethane, propane, butane, etc. LHCs are valuable since they are a very important energy resource. However, uncontrolled release of light hydrocarbon gases to the atmosphere should be avoided [l, 2]. In this work, a development is presented for the evaluation of LHCs generated during the controlled pyrolysis/combustion of several wastes in a two-stage laminar-flow horizontal furnace. Samples of unserviceable tires, post-consumer PET bottles and waste residues from the bioethanol industry (DDGS and sugarcane bagasse) were burned. A catalyst system, consisting of stainless steel screens, was tested for its effects on the gaseous emissions."

Jan 1, 2011

Several processes are now available for the recovery of free and WAD cyanide from gold plant solutions and pulps. In the past, the incentive for evaluating cyanide recovery in gold plant flowsheets has been economic. In many cases, it has been possible to demonstrate (at least in the laboratory and on paper), an improvement in process economics by; (i) reducing the costs of tailings detoxification, (ii) recycling cyanide at lower cost than the purchase/delivery price of new cyanide, and (iii) generating additional revenue via by¬product sales. Despite these convincing arguments, few cyanide recovery plants have been built at operating gold mines. Also, there is arguably an even more compelling reason for mining companies to consider cyanide recycling. With the growing storm of negative public opinion that the use of cyanide in the mining industry is attracting - following several highly publicized spills over the last couple of years - the time has come for the gold industry to demonstrate environmental diligence and stewardship in the use of this commodity that is so vital for their industry. There is no doubt that the widespread implementation of cyanide recycling will reduce the impact of the cyanidation process on the environment, both by reducing the risk of spills (with less cyanide being transported from manufacturing plants to gold mines), and by reducing the loading of toxic and non-toxic metals and ions in the tailings. In this paper, the various processes that are available for cyanide recovery are discussed, along with the process chemistry. Results of several laboratory and pilot plant trials that have been conducted over the last few years are also presented.

Jan 1, 1998

By Zeng Zheng, Liu Chen, Yu Xing-Fu, Tian Su-Gui, Zhang Chao

"Single crystal nickel-base superalloy is prepared by using the various withdrawing rates. By measuring creep properties and microstructure observation, the influence of the element segregation on creep properties of the superalloys is investigated. Results show that the dendrite spacing and the segregation extent of the elements decrease with the enhancing withdrawing rate. The superalloy with smaller dendrite spacing has lower segregation of the elements and better creep resistance. The dislocations climbing over the rafted y’ phase is thought to be the deformation mechanism of the alloy during steady state creep. In the later stage of creep, the fact that some dislocations shear into the rafted y’ phase may twist the rafted y’ phase. As the creep goes on, the initiation and propagation of the cracks occur up to occurring creep fracture, which is thought to be the fracture mechanism of the superalloy during creep.1. IntroductionSingle crystal nickel-based superalloys consist of high volume fraction of ?? strengthening phase and ? matrix, and possess the excellent high-temperature mechanical and creep properties, therefore, they have become the main material to make the blades of the advanced aeroengines[1-3]. Some literatures report that the temperature-bearing and creep-resistance properties of the single crystal nickel-based superalloys can be remarkably improved as the increases content of the refractory elements, such as W and Re[4-6]."

Jan 1, 2012

By Stephen K. Pave1

Over 1,100 tons per day of Fluid Catalytic Cracking Unit (FCCU) catalyst is used worldwide. During the cracking reaction, catalyst is contaminated by deposited metals including nickel, vanadium, potassium, copper, iron, sodium, etc. To compensate for contaminants, a portion of the circulating catalyst inventory is withdrawn for disposal and fresh catalyst is added. The DEMETR process takes spent FCCU catalyst and removes a portion of the metal contaminants, enabling the refiner to recycle demetallized catalyst, thus reducing the solid waste from the refinery. Through August, 1993, the operation of one unit for one refiner has resulted in the recycling of over 7,500 tons of spent catalyst.

Jan 1, 1994

By E. vanHuyssteen

A method of establishing the relationship between the mineralogy of a sinter and its subsequent processing behaviour in a lead blast furnace is demonstrated. It involves: 1) analyzing the Zn-spinels, hardystonite, larsenite, Pb-silicates, Pb-arsenates, Pb-(Ca)-sulphates and other femtes with an electron microprobe; 2) determining the extent of elemental substitutions in various mineral structures; 3) establishing a sequence in which the various phases formed during sintering. In this manner the relationship between the bulk chemistry of a sinter formulation and the speciation of elements into various phases in the sinter can be established. Specifically, the-substitution of Mg for Zn in hardystonite significantly influences sinter production. Mg substitution releases Zn into the surrounding matrix. This Zn reacts with the Pb-silicate to form larsenite thereby reducing the amount of Pb-silicate available for anhydrite digestion. Excessive amounts of residual anhydrite thus result if the sinter formulation is based solely on the CaO/Si& ratio.

Jan 1, 1993

By T. S. Montgomery

The performance of carbon-magnesia brick in electric arc furnaces (EAF) is interpreted in light of their observed optical microstructures. Features at the bricks' hot faces were protruding periclase grains, metal globules, graphite-metal contacts and linear void patterns. These features were com-pared to similar features previously seen from microstructures of basic oxygen furnace (BOF) refractories. Modes of formation were sought; an attempt was made to interpret their influence related to wear mechanisms.

Jan 1, 1982

By Hong Yong Sohn, Miguel Olivas-Martinez

"Different approaches are used for calculating the ‘energy requirement’ of a process. The determination of energy requirement becomes confusing for a process in which a fuel is also a reactant. The key issue is which heat of chemical reaction should be included in the ‘energy requirement’ value. We will use the example of ironmaking processes to illustrate the problem. The different approaches essentially boil down to the question: does one include the combustion heat of the reductant used in the reduction reaction or just the heat of the reduction reaction? Depending on the viewpoint, either approach can be accepted; it is a matter of convention. There is a need, however, to select a standard approach because the absolute value of ‘energy requirement’ of a process depends on the choice. The energy requirement of a novel flash ironmaking process will be compared with that of an average blast furnace operation.IntroductionDifferent approaches are used for performing energy balance calculations and perhaps more significantly in presenting the ‘energy requirement’ of a process. The question becomes more involved for a process in which one or more reactants are also used to generate the process heat by combustion. Often the key issue is which heat of chemical reaction to include in presenting the ‘energy requirement’ of the process.It is worthwhile to note at the outset that the difference in energy requirements between different processes for converting similar raw materials to the same desired product is largely unaffected by the choice of chemical reactions to be included. However, the absolute value presented as the ‘energy requirement’ of a process can be different by a large amount depending on the approach. We use the example of ironmaking processes to illustrate the problem. In these processes, as currently practiced or under development, carbon and/or hydrocarbons (including hydrogen) are used as the fuel as well as the reactant for reducing the iron oxide mineral.The different approaches in this case essentially boil down to the following question: does one include the combustion heat of the reductant used in the reduction reaction or treat the reductant portion as just a reactant? Depending on the viewpoint, either approach can be considered acceptable. It is a matter of convention. There is a need, however, to select a standard approach because the absolute value of ‘energy requirement’ of an ironmaking process (e.g., the currently dominant blast furnace process) depends on such a choice. It is particularly important to clearly state the specific approach used when the energy requirement of ironmaking is compared with those of other industrial processes such as petrochemicals production."

Jan 1, 2014

By B. G. Thomas

"Mathematical process models can be applied in several different ways to serve industry by inducing beneficial changes to process operation. This paper attempts to summarize the different uses, types, and attributes of these models, and to offer some ideas to consider when developing, using, and reporting on them. Process models range from empirical to mechanistic in nature and vary in complexity from simple analytical solutions to coupled, 3-D transient numerical simulations. They are classified here according to the way in which they are implemented in practice, viz. fully-online models, semi-online models, off-line models, and literature models. The purpose of the model should dictate how choices are made during its development. Ways to validate and compare the model with experiments are suggested. Examples are taken in the context of the author's experience in modeling the continuous casting of steel.IntroductionThe objective of this paper is to provide a partial introduction for this symposium by discussing some basic aspects of the application of mathematical process models in industry. Essentially, the aim is to explore how process models are used to benefit industry, and to offer some general comments and suggestions, based on the experience of the author, on how models can best meet this goal.This work is concerned with process models, which consist of systems of mathematical equations and constants that are solved on a computer to make quantitative predictions about some aspect(s) of the process. The specific variables required as input data and generated as output data are important features of the model. The equations often derive from a numerical solution to one or more differential equations and their boundary conditions. The model also includes the constants, which represent material properties, empirical relationships, and other knowledge about the process, and usually require considerable effort to obtain. Thus, general purpose commercial software packages, (ie. finite-element or finite-difference based codes), are not models in this context. They are useful tools, however, serving as frameworks for the development of process models."

Jan 1, 1994

By Phillip A. Armstrong, Charles A. Lewinsohn, John H. Gordon

"This paper describes the opportunity offered by employing systems based on mixed conductive ceramics, in particular, ceramics conductive to oxygen ions and electrons, in reducing CO2 emissions from metallurgical production. Membranes based on these mixed conducting properties enable commercial viability of several attractive metallurgical processes. One of these processes utilizes modular, ceramic-membrane structures for the generation of pure oxygen, in tonnage quantity. The membrane-based systems offer significant capital savings and operating efficiencies in various metallurgical processes. The current status of this technology is summarized below.IntroductionCryogenic oxygen supply technology is currently the state-of-the-art for applications that require large quantities of oxygen (hundreds to thousands of tons per day). Cryogenic technology, however, requires substantial energy inputs and, hence, adds significant costs and emissions to processes. Furthermore, cryogenic oxygen supply technology is mature and there is relatively little potential for substantial capital cost reduction or efficiency improvement in coming decades. Non-cryogenic technologies offer a means to reduce the environmental footprint and cost of the oxygen supply facility in various applications.Ion Transport membranesCommercially available non-cryogenic air separation technologies, such as adsorption-based and polymeric membrane-based methods, do not afford the economies of scale that the cryogenic distillation enjoys. Therefore, industrial gas industry researchers began searching for alternatives to the relatively inactive and unselective polymeric membrane materials available. In the late 1980’s, Air Products began developing a new class of highly selective membrane materials with exceptionally high activity for oxygen transport. The materials constitute a class of oxide ceramics, and conduct both oxygen (as oxygen ions) and electrons in the same membrane, separating oxygen from air electrochemically. Numerous detailed process economics studies have shown that, based on these ion-transport membranes (ITM’s), the cost of oxygen can be reduced by approximately one-third relative to that obtained from state-of-the-art cryogenic oxygen supply technology, through a combination of capital cost savings and efficiency improvements. [1,2,3]"

Jan 1, 2008

By James R. Myers

A source of clean gas containing sulfur dioxide and sufficient oxygen for convers.ion to sulfur trioxide ?is essential to the production of sulfuric acid. S02 containing gases obtained from roasting sulfide ores are heavily contaminated with inorganic dust and volatile impurities. If not removed, these contaminants will reduce product acid quality, foul the catalyst beds and mist eliminators, and accelerate equipment corrosion. This paper reviews conventional gas cleaning systems for metallurgical acid plants, followed by a discussion of modern systems utilizing DynaWave Scrubber technology. This technology is based on a unique approach to? gas scrubbing that can concurrently accomplish several gas cleaning/processing tasks scrubbing liquid is injected into the gas stream to create. a "Froth Zone". This is a region of extreme turbulence, with a very high rate of liquid .surface renewal. It efficiently removes both particulate matter and gas contaminants, and is also a cost effective quenching device for gases as hot as 1250º C. Smelter

Jan 1, 1992

By Chikabumi Yamauchi

The comprehensive scientific development of conventional industrial technologies stimulates the creation of new ones in the next generation. Prof. Akira Yazawa has just accomplished such an important work in the non-ferrous pyrometallurgical field. The results of his successful research are immortal. The research group of the author has conducted since 1985 fundamental studies on the application of sodium carbonate slag to copper fire refining. In the present paper, a calculation method for the distribution ratios of impurity elements between sodium carbonate slag and molten copper will be shown. The specific treatment by sodium carbonate slag will also be presented as an effective way for reducing each impurity content in the molten copper to 0.1 mass ppm, which is the level required for the production of high purity copper. The thinking-out of this evaluation method gets a hint from the Equation (2) in the text which was proposed by Prof. Akira Yazawa.

Jan 1, 2003

By James C. Foley, David K. Rehbein

"In-situ characterizations of green state part density and sintering state have long been desired in the powder metal community. Recent ·advances in non-contact electromagnetic acoustic transducer (EMAT) technology have enabled in-situ evaluations of the acoustic attenuation and velocity as sintering proceeds. Pure aluminum (99.999%) and aluminum alloy powders were prepared with high-pressure gas atomization (HPGA). The powders were pressed in a uniaxial die and examined with acoustic waves for changes in velocity and attenuation during sintering. The changes in acoustic properties were correlated with sample microstructures and mechanical properties. Evolution of the acoustic echo train during sintering is shown to provide information on the state of sintering as well as having the potential for detection of interior flaws.IntroductionThe versatility of powder metalallurgy (PIM) technology in the manufacture of complex shapes has enabled an increasing amount of wrought and casting production capacity to be converted to PIM technology. However, ultrasonic inspection of green components produced using PIM techniques remains a challenge and is not generally practiced [1]. Inspection of PIM components in the green state is highly desirable, because the green part can be reclaimed with only accepted components being subjected to further costly processing. Another potential benefit is characterization and greater understanding of the sintering process itself. An increased scientific understanding of the sintering process enables intelligent process control, greater reliability of the production process and a lower rate of rejection of the finished product. In order to realize these potential benefits, it is necessary therefore that accept/reject criterion be based on real time nondestructive evaluation of the green-state components and the sintering process.Most current nondestructive inspection techniques suffer from their inability to perform inspections below the near-surface region with the exception of X-ray and to some extent pulsed eddy current [2]. X-ray inspection requires extensive shielding of production personnel and expensive film and film processing. While development of pulsed eddy current techniques have lessened the impact of the well-known skin effect, the depth of penetration of the induced eddy currents remains somewhat of an issue [2]."

Jan 1, 2000

By Esther Carrera Martinez

Caraiba Metals is the sole brazilian copper custom smelter. The sulfur present in the various concentrates processed is recovered as sulfuric acid and oleum ,which are sold in the local market For quality assurance purposes, a study was carried out in order to determine how to control the arsenic content in the acid, allowing the continuous processing of concentrates with high levels impurity, The study was based on the process parameters of the washing towers and mist precipitators, Others process variables were investigated and their effects were used in support to confirm the results, After many analyses performed some interventions to improve the quality of the acid were implemented in the plant, which proved to be successful even by using a conventional purification system,

Jan 1, 1996

By George Oprea, Tom Troczynski, Joe A. Rigby, Waiman Lo

The refractory lining of the tuyere line in Peirce Smith converters have usually much shorter life in service than the rest of the lining, above or below it. There are already recognized chemical, thermal and mechanical factors which contribute to the wear of the lining. Our study presents the experimental results on microstructural changes occurring on these tuyere line bricks in a nickelcopper converter. The experimental bricks, after use at the tuyere line, were investigated using SEM/EDS and XRD techniques, to identify the mineralogical changes due to interactions with the nickel-copper matte or fayalite type slag at the process temperatures. The microstructural changes were correlated with physical and mechanical properties of the brick before and after use and a wear mechanism was suggested. Although the matte does not theoretically react with the mineralogical components of the brick, a partial oxidation of the Ni-Cu sulphides was identified using a line analysis by SEM/EDS in the densified layer at the hot face, which allows for mineralogical changes at the matte-refractory interfaces, with a high probability of microcrack formation due to the thermal cycling during use. These microcracks were also identified to open through inter-granular fractures parallel to the hot face, which appeared to be the main cause of lost lining during use. The reactions between the fayalite slag and refractory brick could eventually play a role in chemical dissolution of the brick only in the superficial layer at the hot face, as no slag components were identified deep into the brick.

Jan 1, 2009

By P. N. Anyalebechi

"The as-cast microstructure of two commercial-size ingots of aluminum alloy 3004 produced by the electromagnetic casting process was quantitatively characterized. This involved the quantitative determination of through-thickness and across-width variations in dendrite cell size, grain size, macrosegregation of alloying elements, interparticle spacing, and the types, volume fractions, and sizes of the constituent or second phase particles. More than ninety-five percent of the constituent phases in the ingots consisted of the A16(Mn,Fe) phase; the desirable a-Al 12(Fe,Mn)3Si phase was not detected in any of the ingots by Guinier X-ray diffraction analyses or electron probe X-ray microanalyses. A significant microstructural heterogeneity through the thickness and across the width of both ingots was observed. For example, macrosegregation, and the sizes of the constituent phase particles, dendrite cells, and grains increased concomitantly from edge to mid-width and from surface to center of the ingots. There was a -20% depletion (negative macrosegregation) of Mg and a +54-87% enrichment (positive macrosegregation) of Ti in the center of the ingots. With the exception of grain size, there was no significant microstructural difference between the two ingots examined. The causes and practical implications of the observed microstructural heterogeneity in the ingots are discussed.IntroductionThe first step in the fabrication of majority of wrought products of aluminum and its alloys is the casting of large ingots or billets of simple shapes (round or rectangular). The sizes of the ingots vary from 10 mm to 450 mm diameter or 25 mm to 780 mm thick. The quality of the finished products is established at the ingot casting stage. This is because the microstructural characteristics, such as secondary dendrite cell size or arm spacing, amount of alloying elements retained in solid solution, macrosegregation, and the characteristics of second phases, produced during casting cannot be reversed by subsequent processing. Up until twenty-five years ago, the effect of as-cast microstructure of large ingots on the structure and behavior of thin sheets (0.34 mm thick) during drawing and ironing processes was incorrectly assumed to be minimal or nonexistent. This was based on the erroneous notion that the thermal treatments and large reduction (>99.94%) and strain that the ingot undergoes during production of the sheets completely destroys the original ingot structure and its inherent heterogeneity. However, the effects of ingot structure can, a priori, be deduced from the observed effects of constituent phase particle size, type and volume fraction on recrystallization, development of texture during annealing and deformation, and earing. In fact, careful examination of the behavior of products produced from different size ingots or castings have shown that the original microstructure of the ingot has a direct impact on the properties and performance of the end products."

Jan 1, 2011

By G. A. Brooks

Reactive ball milling has been proposed as a new route for producing carbides from oxides through carbothcrmic reduction. It is claimed that through milling oxide and graphite powders to the nanoscale, amorphous materials with very high reactivity are formed, that allows for easy transformation of the starting material to another in a subsequent thermal process. Thermodynamic analysis of this proposed process suggests that unless particle sizes are reduced to below 10nm, then reduction in size alone cannot explain a change in the stability of oxides. Even with nanometer scale powders, the products formed need to have a lower total surface energy than the reactants before a chemical change will occur. A model developed by Bhattacharya and Arzt for predicting localized temperature changes based on milling conditions suggest that temperarure rises less than 400 K will be achieved in laboratory conditions. The present calculations suggest that nanometer scale powders formed through high speed ball milling (>10 mls) may have undergone a process analogous to melting and quenching. Further work is required to fully distinguish these features.

Jan 1, 2003

By Robert C. Laudon

Spectral reflectance data for 335 minerals, including 228 minimum-maximum combinations for anisotropic minerals giving a total of 563 data sets, have been collected from the literature and combined into a single database. Quantitative color values for x, y, Y, Ad , and Pe referred to ICI standard i11uminant C have been calculated from the spectral reflectance data and are included in the database. The programs plot spectral reflectance curves together with all quantitative color data for each mineral in the database. The plots and data can be directed to a dot-matrix printer such that a databook of quantitative color and spectral reflectance having one mineral per page can be generated for the ore microscopy laboratory. In addition, by sorting the database and grouping the minerals, groups or individual minerals can be plotted on the chromaticity diagram, and this plot can also be sent to a dot-matrix printer. The programs are written in compiled BASICA for an IBM-PC with graphics capabilities and at least 128KB random access memory (RAM). The databases are accessible either through the BASIC programs or through any commercial database system capable of loading and writing to an ASCII format sequential file. The programs and database are available by sending a blank diskette and self addressed, stamped envelope to the authors.

Jan 1, 1987