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By D. F. DeSante, A. S. Tetelman

MICROCRACKS are often introduced into commercial metals during fabrication processes such as swaging, cold rolling, deep drawing, and welding. These microcracks act as strain concentrators and may be capable of causing premature catastrophic failure of a component or weld. The present investigation was undertaken to determine whether high-temperature annealing treatments may be capable of reducing or negating the detrimental effects of such existing microcracks. Internal microcracks, ranging from 0.1 to 0.85 mm in length and averaging 0.23 mm, were introduced into polycrystalline Fe-3 pct Si tensile specimens (0.155 mm grain size) by the cathodic charging of hydrogen.1'2 The typical appearance of such microcracks and their associated strain patterns (made visible by the technique of dislocation etch pitting3) is shown in Fig. 1. The stress fields of the dislocation loops formed during plastic relaxation stabilize the microcracks so that, when the internal hydrogen pressure is removed: the microcracks stay open, rather than disappear as perfectly elastic cracks would be expected to do.' As shown in Fig. 2, such stopped microcracks cause a 36 pct decrease in the macroscopic cleavage fracture strength at -196°C.

Jan 1, 1969

By M. H. Waxman, L. J. M. Smits

A simple physical model was used to develop an equation that relates the electrical conductivity of a water-saturatedshaly sand to the water conductivity and the cation-exchange capacity per unit pore volume of the rock. This equation fits both the experimental data of Hill and Milburn and data obtained recently on selected shaly sands with a wide range of cation-exchange capacities. This model was extended to cases where both oil and water are present in the shaly sand. This results in an additional expression, relating the resistivity ratio to water saturation, water conductivity and cation-exchange capacity per unit pore volume. The effect of shale content on the resistivity index - water saturation function is demonstrated by several numerical examples. INTRODUCTION A principal aim of well logging is to provide quantitative information concerning porosity and oil saturation of the permeable formations penetrated by the borehole. For clean sands, the relationships between measured physical quantities and porosity or saturation are well known. However, the presence of clay minerals greatly complicates log interpretation, particularly the electrical resistivity and SP logs, and considerably affects evaluation of hydrocarbon-bearing formations. The conductance and electrochemical behavior of shaly sands and their relation to log interpretation have been studied by many workers. wylliel and Lunch2 reviewed this work in some detail. Virtually all laboratory measurements of electrical resistivity and electrochemical potential of shaly sands published to date are the work of Hill and Milburn.3 Their measurements were made on about 300 cores covering a large variety of sedimentary rocks, and a wide range of equilibrating NaCl solution concentrations. Hill and Milburn described their conductivity data by an empirical equation in which the shaly sand conductivity Co was expressed as a function of the solution conductivity C and two parameters b and F01 . The quantity b was shown to be a measure of the effective clay content of the rock, being approximately proportional to the cation-exchange capacity of the rock divided by its pore volume. The latter ratio is designated as 9, in this paper and has the dimensions meq/ml or equiv/liter. Qv is identical with the term representing the concentration of fixed charges in the Meyer-Sieved and Teorel15 theory of permselective membrane behavior. F01 is a formation resistivity factor referred to a hypothetical equilibrating solution resistivity of 0.01 ohm m at 25C,* where clay effects presumably are minimized. F01 was correlated to porosity by an Archie-type equation.6 The Hill-Milburn equation describes their data with a standard deviation of approximately 1 percent and a maximum deviation of + 10 percent. Shaly sands behave as permselective cation-exchange membranes, their electrochemical efficiencies increasing with increasing clay content. The electrochemical potential data of Hill and Milburn were expressed graphically, and demonstrate that the membrane efficiency (or cation transport number) of these sands is a function only of the b value (i.e., Qv) and the respective salt concentrations of the two solutions forming the liquid junction in the sand. The diffusion potentials are not dependent on F01 or any parameter relating to the porosity or pore geometry of the rock. The Hill-Milburn resistivity equation correctly predicts a decreasing sand conductivity Co with decreasing solution conductivity C?. However, at some low value of C,, the calculated Co-C, function goes through a minimum; with further decrease in C?, the predicted sand conductivity increases sharply. As pointed out by Hill and Milburn, an increasing value of Co with decreasing C, is physically meaningless. Since this occurs below the range of practical values of C,, the usefulness of the empirical equation is not affected when

Jan 1, 1969

By Jon C. Jenkins

In order to plan the most efficient mine installation, a company should take advantage of all available information and tools. One of the first factors of a coal reserve that needs to be determined as accurately as possible is the quality of coal the mine will have access to during the life of the installation. With the aid of many types of well logs and computor analysis, we are investigating several methods of log correlation to determine such data as moisture, ash, sulphur, and BTU on an in place basis. It may be possible to determine this data more accurately in this manner than by using diamond drill cores for analysis and thus allow for a more profitable mine installation. The production of an underground mine is based on many factors, two of these being roof control and line water, where present either in the roof or coal seam. Using many of the same logs obtained from reserve and active mine areas, we have attempted to determine roof and floor characteristics such as strength, lithology, and moisture properties. Using data obtained from this program, we will make comments on possible length of bolt to be used, possible mining width, and pillar size as they would pertain to these reserves and active mine areas.

Jan 1, 1969

By J. C. White

This paper, after a brief introduction giving the history and geology of the area, deals with mining operations at the Copper Mountain mine of Gaspe Copper Mines, Limited. It discusses development operations, and then goes into the mining methods employed, covering drilling, grade control, blasting practice, loading and hauling, and the road and service machines used.

Jan 1, 1969

By J. J. Frawley, W. J. Childs

The dynamic nucleation of supercooled bismuth and Bi-Sn alloys has been studied over a frequency range of 15 to 20,000 cps. For low-frequency vibration, a minimum vibrational energy was required for enhancement of nucleation. Above this critical energy, the dynamic supercooling was less than static supercooling showing that vibration promoted nucleation. The amount of dynamic supercooling continued to decrease with increasing vibrational energy until a minimum or threshold value was reached. This minimum value of supercooling for nucleation remained constant joy all further increases in vibrational energy. For higher frequencies, similar results were observed. This behavior has been related to the necessity of cavitation for dynamic nucleation. When a liquid is cooled to a temperature below its equilibrium melting point, the solid phase is more thermodynamically stable. However, for solidification to occur, a two-step process, nucleation and subsequent growth of the solid phase, must occur. When a liquid is supercooled, that is cooled below the equilibrium melting point, the controlling process for solidification to begin is the rate of nucleation. Once nucleation has occurred, the solidification process is controlled by the rate of growth. Nucleation can be induced by two factors: either by a catalyst or by the use of mechanical shock. Numerous investigators1-4 have studied the effect of nucleation catalysis but much less systematic study has been made of nucleation by mechanical shock waves. The influence of vibrations on grain size in castings and ingots has been studied by many authors but no clear understanding of the mechanism or accurate prediction of the effect has been presented.5 It would be intuitively expected that the further the departure from equilibrium (i.e., the greater the supercooling), the easier it would be to induce nucleation. This has been quantitatively demonstrated both by walker6 and later by Stuhr,7 that the greater the degree of supercooling the easier it is to nucleate by a shock wave. Stuhr also attempted to obtain the mechanical energy required for nucleation of bismuth as a function of supercooling. He vibrated a crucible containing supercooled metal at low frequencies and various amplitudes and noted the corresponding dynamic supercooling obtained. The amount of supercooling was inversely proportional to the mechanical energy applied. Limitation of his experiment was the problem of the confinement of the liquid in the crucible without splashing and minimizing other unwanted modes of vibration. Tiller et al.8,9 did similar work on tin and Sn-Pb alloys using an electromagnetic stirring device. Their conclusions were that the magnitude of the magnetic field strength did not affect the amount of undercooling at which nucleation was initiated. While conclusive experimental results have been lacking to explain this effect of mechanical vibration on inducing nucleation, a number of theories have been proposed. Two of these theories are discussed below. 1) The Change in Melting:- Point Locally Due to the Change in Pressure (Clapeyron Equation). According to Vonnegut10 the most plausible explanation for the nucleation of a supercooled melt by cavitation is the effect of changing the melting point by a change in pressure. For materials where the volume decreases on solidification, an increase in pressure raises the melting point; for materials which expand on solidification, the melting point is raised for a decrease in pressure, i.e., rarefaction. Using the Clapeyron equation, the melting point of a metal can be calculated as a function of pressure. If it is assumed that the equation can also be used to calculate the temperature of nucleation of a supercooled melt as a function of pressure (i.e., the temperature of heterogeneous nucleation will increase with pressure at the same rate as the melting point), the amount of supercooling required for nucleation will be constant at all pressures as shown in Fig. 1. It is obvious that an isothermal change which results in an increase in melting point results in an equal increase in supercooling. This increase in supercooling may now be sufficient for nucleation. A pressure of 80,000 atm was calculated, using the Clapeyron equation, as the pressure required to increase the temperature of nucleation of nickel by 200°C. According to Lord Rayleigh,11 this very large pressure could be generated for a very brief period of time by the collapse of a cavity. This pressure wave is radiated in all directions from the collapsed cavity. If the temperature of the melt is slightly below its equilibrium melting temperature at atmospheric pressure, stable growth can follow; that is, once nucleation occurs, growth becomes the main driving force of the solidification process. This proposal has been extended to water which expands on freezing by assuming that nucleation occurs during rarefaction following the pressure pulse. This negative pressure pulse should follow immediately after the positive pressure pulse with its magnitude approaching the critical tensile strength of the liquid. The negative pressure developed during this period would raise the melting point of water and thus promote nucleation. Hunt and jackson12 have suggested this for water. Similarly, it could be postulated that bismuth which also expands on freezing could be nucleated during the negative pressure pulse. 2) Nucleation by a High-pressure Phase. An extension of the Clapeyron equation to systems where density decreased on freezing at atmosphere pressure has been proposed by Hickling.13 The phase diagram for water initially shows the well-known decrease in

Jan 1, 1969

By G. Knight

"Results of a program of dust research carried out at the Mines Branch Laboratory, Elliot Lake, indicate that dust-concentration estimates vary greatly, depending on the sampling instrument, the assessment technique and the properties of the dust cloud. The wide range of the ratio between the estimates by any pair of instruments shows that the correlation between the health hazard and dust-concentration estimates by most existing sampling instruments must be questionable. Important studies are being carried out to permit the definition of mine environments in more precise technical terms. The influence of size selection, the physical property measured, composition and sampling period on the assessment of the health hazard are discussed."

Jan 1, 1969

By D. M. Steelman

Digital systems have been employed in industry as an aid in process evaluation and control for about 20 years. The earlier systems were quite simple and did little more than periodically scan a multitude of process variables, perhaps comparing them to alarm limits, and print out the results. As time passed, the needs of industry and the imagination of process engineers became more demanding. Rather than perform only alarm checking and logging, operating guides were generated to help the operator gain optimum performance from the process. Eventually, systems were entrusted with the job of manipulating the set points of the local analog control loops in a (DDAC) digitally directed analog control mode. Today digital systems are used to gather all-the process information, including both analog and digital variables; to make the necessary data manipulations; and to control the process end elements in a (DDC) direct digital control mode. During these years of transition from the very simplest systems to the complex systems of today, the demands upon the system engineer have been every increasing. The process engineer has required, among other things, more computational ability at high speeds, faster input and output rates, greater flexibility, better communication facilities (man-machine interface), (process oriented software), and finally, greater reliability at lower cost.

Jan 1, 1969

By William E. Bruce

The Bureau of Mines performed drill calibration tests on two industrial percussive drills of 2-5/8- and 3-1/2-inch piston diameters to determine operating characteristics for their use in conjunction with penetration rate data in developing drillability equations and furthering the knowledge of percussive drills. The use of a linear velocity transducer for measuring piston velocities and application of its instrumentation are described. Data presented include relationships between maximum piston velocity and feed air pressure other results confirm the theory or data of previous investigators, and some comparisons are made with the performance prediction formulas of other investigators.

Jan 1, 1969

By R. L. Klueh, W. W. Mullins

During the course of a study on the periodic precipitation (Liesegang phenomenon) of water vapor bubbles in solid silver, some interesting observations were made concerning the formation and growth of these bubbles. Under certain conditions it was found that the bubbles which formed in the single crystals led to the formation of large blisters ad cracks, and when poly crystalline specimens were used grain boundary cracking was observed. These two phenomena were examined in some detail, and it was found that an important step in the formation of the blisters and grain boundary cracks was the impingement of neighboring bubbles. DURING the study of Liesegang precipitation in solid silver,' some interesting observations were made concerning the formation and growth of water vapor bubbles. The bubbles were formed by annealing oxygen-saturated silver in hydrogen. Because of the similarity of this phenomenon to the hydrogen embrittlement of tough pitch copper,' it is known in the literature" as the hydrogen embrittlement of silver. In some respects it appears that the hydrogen embrittlement of silver is similar to the processes of hydrogen attack of steel5 and blister formation.' Hydrogen attack results from the high-temperature reaction of hydrogen with dissolved carbon or carbides in the steel to form methane (usually at grain boundaries). Blister formation occurs in steel and other materials as a result of hydrogen produced by corrosion, pickling, and so forth. Because of these similarities, some speculations were made concerning these other processes. EXPERIMENTAL PROCEDURE Water vapor bubbles were formed in 99.999+, 99.99+, and 99.9 pct Ag by annealing in a partial pressure of oxygen (pq) until saturated and then in a partial pressure of hydrogen (pH,). The hydrogen diffuses into the silver and reacts with the dissolved oxygen to form water vapor which precipitates in the form of bubbles. The specimens were then sectioned, silver-plated, mounted in cold-setting plastic, ground and polished through a preliminary polishing, and finally chemically polished.' The bubbles were visible without etching.

Jan 1, 1969

By Robert M. Jimeson

The competitive market potential for solvent refined coal is estimated. Market advantages of solvent refined coal are enumerated. Markets are possible in combustion, railroad locomotion, and carbon electrodes. The combustion characteristics are consistent with expected air pollution restrictions on the emission of sulfur and particulate matter. A market potential of sufficient size exists to support the initiation of solvent refining in the United States. The market analysis should help fuel producers determine the advisability of their undertaking the solvent refining of coal.

Jan 1, 1969

By H. T. Kennedy, J. E. Little

An empirical equation for the prediction of the viscosity of several pure paraffin hydrocarbons and nitrogen is presented. It involves temperature, pressure and six constants of the material, and it applies reliably to both liquids and gases. The equation is similar in form to van der Waal's equation of state. For the paraffin hydrocarbons methane through r-hexane and nitrogen, an average absolute deviation of 1.9 percent was obtained on 1,006 data points described in the literature by 14 authors. When this equation is extended to complex, liquid hydrocarbon mixtures, a correlation was obtained with an average absolute deviation of 9.9 percent. INTRODUCTION Equations describing the flow of gas and liquid through porous media contain the viscosity coefficient of the fluid. If other pertinent variables remain constant, the volume rate of flow is inversely proportional to this coefficient. In dealing with condensate fluids and volatile oils, however, the compositional effects resulting from changing pressure materially affect the viscosity. The effect of compositional changes also may be significant in certain secondary recovery or pressure maintenance processes, notably miscible displacement or gas injection. Early attempts to describe the performance of reservoirs utilized a volumetric material balance method wherein gas and liquid in the reservoir were identified as produced gas and liquid at the surface. This method of analysis proved adequate for reservoirs at moderate temperature and pressure that contained gas with moderately low amounts of condensable materials. The volumetric material balance procedures for "black oil" reservoirs leave much to be desired when applied to condensate and volatile oil reservoirs because phase behavior and compositional changes are relatively more important in these cases. The alternative is a compositional material balance, which in turn, requires a correlation of properties of the reservoir fluid with composition. This paper supplies this correlation in regard to viscosity, for reservoir crude oils. REVIEW OF LITERATURE The literature contains many empirical equations describing the effects of composition, temperature and pressure on the viscosities of pure liquids and binary liquid mixtures. However, the applicability of a majority of these equations is limited to very low pressures and to a small number of systems. Most of them, when applied to complex hydrocarbon systems, are of little value. The lack of utility of the majority of equations results from the fact that they were developed to show the separate effect of temperature, pressure or composition on viscosity, but not to predict the viscosity as a function of all three variables. And with the few exceptions noted below, they were developed to apply to much simpler systems than hydrocarbon mixtures. Eakin1 developed an equation for the viscosity of pure light hydrocarbons applicable in the gas, liquid and dense fluid regions, and in its most general form is written as µ - µo =A(ebP - e-cpk) The pure component viscosity at atmospheric pressure and temperature T, µo, was calculated using the Sutherland equation: µo = BT3/2/T + S The constants in Eakin's equation permitted the term e-CPk to become quite small at high densities (above 0.215 gm/cc), and the general equation would simplify to

Jan 1, 1969

By J. D. Wright

This paper describes current milling practice at Endako Mines Ltd., a molybdenum producer in central British Columbia. The various steps in the crushing, grinding and flotation of the ore are outlined, with emphasis on the metallurgy of the latter operation. Tailings disposal and concentrate assaying methods are also described.

Jan 1, 1969

This list is part of the long-range conservation program of the Bureau of Mines and is intended for use by those interested in the Bureau's publications dealing with oil shale and shale oil. The items included represent 51 years of research by Bureau of Mines employees on oil shale and shale oil and are available at any U.S. depository library. DISTRIBUTION U.S. Bureau of Mines report series contain both free and sales publications. An asterisk (*) designates publications for sale. Such publications can be obtained from Superintendent of Documents U.S. Government Printing Office Washington, D.C. 20402

Jan 1, 1969

By A. J. Barry

This report presents observations made by Bureau engineers regarding hydraulic-powered roof supports that are currently being used or have been used on nearly all operating longwalls in the United States, A comparative summary of specifications for various types of powered supports with a brief description of the mine conditions has been compiled to enable mining engineers and mine operators to readily evaluate the differences in design data. Some of the support data furnished in the field may vary from those listed in manufacturers' brochures because of the trend to customize various support components to meet specific mine conditions. A method of estimating support requirements for different assumed operating conditions is presented. Similar computations for specific mine conditions may be used to make preliminary estimates of support requirements.

Jan 1, 1969

By C. A. Young

"The stabilization of tailings has been a matter of concern to the Mining Industry for many years. In earlier times, when mines were small and only high grade ore deposits were mined, the problem was not a great one. But, more recently - during the last 30 to 40 years - the increased world demand for various metals, combined with the vast strides that have been made in the improvement of metallurgical extraction processes, have resulted in the development of lower grade ore bodies.About 30 years ago The International Nickel Company started experiments to stabilize the surface of the tailings and prevent them from becoming a dust source under certain weather conditions. The use of chemicals to form seals, covering with crushed stone, mulching with straw and some early seedings were some of the stabilizing methods tried. Results were either unsuccessful or impractical economically.In 1954 a series of experiments to establish vegetation on the tailings began. Varying degrees of success were achieved but however unsuccessful a particular scheme turned out, the attempt to find a solution was never written off. As we look back, we realize that the first significant break-through came as the result of three test plots planted in the spring of 1957. Each plot covered an area of approximately one-third of an acre. One plot was successful and persisted until it was covered up by the expansion of the tailings area in 1961.In 1960 a review of all our test plots to that date was carried out to assess the factors which effect the chance of grass being established."

Jan 1, 1969

By D. Mills, G. B. Craig

The defortnaliotz of zirconicltt single crystals conlaining osygen in the range 740 to 6800 atom parts per nilllion was esanined oc7er the range 77" to 950°K. An anctlsis of the dqfarmaliotz parameters leads to the cotcllsiotr that the rale -cotzfrolling thermally activated dqivr,irrtion process oe-r /he range 77" to 560°K is oc.crco,ling osvgen alotns. A thermally actitaled defor,ilntion process is not found between 600" and 800", but does occur aboz%e 800°K. THE present investigation was undertaken to measure the effects of controlled amounts of oxygen on the deformation parameters of a zirconium single crystals over the temperature range 77" to 950°K and to determine the rate-controlling mechanisms. Although there is no doubt that the mechanical properties of the group IV metals, titanium, zirconium, and hafnium, are strongly influenced by the interstitial impurities oxygen, nitrogen, carbon, and hydrogen, there are many conflicting theories as to the role played by the interstitials during the deformation proess.'- There is general agreement that the mechanisms which control plastic flow in a metal impose characteristic values on such parameters as the flow stress and its temperature dependence, the activation volume, and the activation energies. These parameters will be used to analyze the deformation mechanisms. eltham,' Sargent,16 and ibbs' have shown that the stress relaxation technique allows the activation volume characteristic of the deformation process to be found during the course of a simple tension test. In many cases it is found that the relaxation of stress is logarithmic with time and obeys a relationship of the following form: T-T = AT =S logl0(qt + C) [I] where t, is the shear stress at the start of the relaxation test, t is the shear stress at time t, and S. q, and C are experimental constants, and S is the strain rate sensitivity of the stress t as shown in the appendix. The slope found from a semilogarithmic plot of At vs time is approximately equal to S. The activation volume u, association with the deformation process, is found from the following relationship: The theoretical treatment of thermally activated plastic flow due to schoeck18 shows that the activation volume when combined with the temperature dependence of the flow stress gives the activation energy for the process according to equations: seegerZ3 considers that the flow stress at lower temperatures ld is composed of two parts such that Tapplied = tinternal + Teffective , where Teffective 3 ff , is the stress necessary to overcome the local obstacles to deformation and Tinternal, ri, is the stress necessary to overcome the long-range elastic stress field of dislocations on other planes. ri is considered to be largely elastic in origin and can be estimated from the stress value at the temperature independent portion of the flow stress-temperature curve. EXPERIMENTAL The crystal bar zirconium used in this investigation was supplied by Wah Chang Corp. whose certified analysis gave the following impurity contents in parts per million by weight: oxygen, 150; nitrogen, 10; iron, 180. All others were less than 100 ppm. The oxygen and iron contents were confirmed by neutron activation and chemical analyses, respectively. Single crystals were grown in an electron beam furnace according to the method of Wilson and Pickle-simer'' and ills.'' The orientation of the crystals was such that the specimen axes were located in the lower third of the standard section of the basal plane stereographic projection for zirconium. This orienta-

Jan 1, 1969

By H. F. Feldmann

This Bureau of Mines report presents a method for the computer solution of the equilibrium compositions of any complex, multiphase, chemical system for which appropriate thermodynamic data are available. The method describes in detail the computation of systems in which solid or liquid species can form by heterogeneous chemical reactions where these species do not occur in any equilibrium equations. Also described are the calculation of phases formed by condensation (pure or solutions) and the inclusion of other system restrictions such as electroneutrality. The method is being used to compute the equilibrium composition of mixtures of an electrically conductive plasma and a liquid slag phase arising from the high-temperature combustion of coal for magnetohydrodynamic power generation. These mixtures can contain up to 65 species including gases, liquids, free electrons, and ions.

Jan 1, 1969

By Tuncel M. Yegulalp, Malcolm T. Wane

In general, many problems relating to the exploitation of mineral deposits are probabilistic in nature. This derives from the fact that the geologic universe is inherently random. Probability theory and statistics have been found useful for forecasting the behavior of natural events that occur in the geologic universe. The objective of this paper is to illustrate the application of the theory of extremes to this fore-casting problem. For example, it is customary for design purposes to determine the rupture strength of geologic materials. The theory of extremes is exceedingly useful in describing that portion of the frequency distribution of rupture strength which contains the least strengths. Parameters describing the distribution of the least strengths are more important to the designer of mining excavations than parameters describing the total distribution. The basic principles of the theory of extremes will be detailed and illustrated. Any person required to work in the laboratory of nature is aware that uncertainty is a salient feature of all mining enterprises. A mining engineer required to plan the most efficient, practicable, profitable, and safe mine finds himself face to face with numerous ill-understood and often unquantifiable states of nature. Basic information necessary for adequate planning is often lacking or derived from incomplete tests on samples or experience of doubtful validity. The planning procedure usually takes the form of determining a feasible layout with the intent of determining an optimal layout when and if the necessary details and information become available. The crux of the entire procedure is the choosing of numbers to put into the operational and structural models which encompass the plan. Many times these numbers must be assigned qualitatively from past experiences and are called the "most probable ones." At other times, load records, performance records and material tests provide a basis for extrapolation. In any event, the numbers are chosen from a distribution or set of all numbers. Since each number in the distribution represents a possible state, the choice of any particular value is based upon a decision rule. To illustrate, consider the design of an underground structure or the design of a rock slope. The initial step is the formulation of the various possible structural actions which result from the geometry of the layout. For a given structural model various intensities of behavior are possible depending upon the load, deformation, and material characteristic spec-trums, respectively. Of particular interest to mining people is the failure behavior or condition, i.e., when there is a complete collapse of structural resistance by either structural instability or fracture. A necessary feature of the analysis is the "rupture strength" of the material. Information on the rupture strength is derived from testing either in situ or in the laboratory and the usual outcome is a variation in the test results. The methodology used to overcome this variation is to construct a frequency distribution of rupture strengths, and then determine a measure of central tendency and variability. The main idea involved is that the central tendency number will be used in the failure calculations and the measure of dispersion will be used to estimate the probability of failure. In particular if the distribution of rupture strength is normal, the mean rupture strength is the central tendency number and the standard deviation of the rupture strength is the measure of variability. Suppose the mean value of rupture strength is 1000 psi and the standard deviation is 200 psi. Insertion of 1000 psi into the failure calculation produces results that are unsafe, hence a common decision rule is to reduce the mean value by a "factor of ignorance" so that the failure calculation will produce a "safe result." If two is chosen as a factor of ignorance, this means the value inserted in the calculation is 500 psi or 2.5 times the standard deviation. The next step is to determine the percentage chance that failure will occur from a design created on this basis. Tables on the normal distribution function show that this percentage chance is 0.621% or approximately 7 times out of 1000. In practice, however, the situation is more complicated than represented by the foregoing illustration. The laboratory or field testing program usually constitutes a pathetically small sample of the geologic universe of interest and not enough testing is carried out to determine the exact form of the distribution of the test results. The normal, Cauchy and Student's T distributions are strikingly similar, and it becomes a matter of mathematical convenience to assume the normal law for phenomena which follow other laws.

Jan 1, 1969

By John W. Cahn

The spinodal has long been regarded as a limit beyond which a homogeneous phase could no longer be metastable. But only recently has it become apparent that a phase beyond the spinodal would decompose by simple diffusional clustering mechanism quite different from the nucleation and growth mechanisms encountered for metastable phases. The theory of spinodal decomposition, which is based on the diffusion equation modified by thermodynamic requirements , is phenomenological, and each parameter can be measured by independent thermodynamic or diffusion experiments. The details of the theory have been carefully verified in a number of simple systems. It appears that the spinodal mechanism is commonly encountered in clustering reactions in solids and glasses. HISTORICAL INTRODUCTION The understanding of the earliest stages of precipitation in alloys has been the subject of three prior Institute of Metals Lectures. In 1932 Paul ~erica' reviewed the puzzling evidence that hardening of duralumin is completed before precipitation of CuAlz takes place and suggested that hardening occurs when the copper atoms "assemble in random groups on lattice positions of the duralumin, not of the CuAlz lattice". He called these random groups knots. This modification of his dispersion hardening theory seemed to fit all the facts, but Merica worried that the required diffusion "is just the reverse of what we deem normal; although quite spontaneous, it proceeds uphill, if you please". The reality of Merica's knots was quickly confirmed by Guinier's' and preston's3 X-ray work and these knots are today known as G.P. zones in their honor. Theoretical justification for uphill diffusion was also quickly provided by Becker and Dehlinger~ who noted that the diffusion coefficient could be negative in certain regions of phase diagrams. The boundaries of such regions could be described by a 90-year-old thermodynamic concept first described by ~ibbs' in 1877 as a limit of metastability for fluid phases, which by 1890 had received the name spinodal (see Appendix A). Spinodal in fluids is as old as nucleation theory. Both appear for the first time in the same paper by Gibbs who called the spinodal the limit of metastability. For the first 50 years, nucleation theory was forgotten and the spinodal was extensively treated in every good thermodynamics textbook.81Q The idea was simple and logical and it was accepted as part of a rigorous thermodynamic development of metastable phases, and for a while it was extensively investigated theoretically.

Jan 1, 1969

By J. M. Eldridge, P. Balk

Phosphosilicate glass films were formed, by reacting gaseous P2O5 with SiO2, over a large range of temperature (800° to 1200°C) and gas phase composition (nearly two orders of magnitude of effective P2Ospressure). The film compositions generally corresponded with the liquidus curve, delineating the maximum solubility of the tridymite Phase of SiO 2 in phosphosilicate liquid solution at the temperature of film formation. It is shown that the P2O5 concentration of the phosphosilicate liquid film tends to decrease by reaction with the underlying SiO 2 layer until the liquidus curve is reached. The validity of the thermodynamic argument used in this explanation is supported by the results of a determination of the composition of borosili-cute films, prepared by reacting gaseous B2O3 with SiO2 at different temperatures. The kinetics of phosphosilicate film formation were described by a model predicated on a steady-state diffusion of P2O5 through the film. UNDERSTANDING of the processes leading to formation of phosphosilicate and borosilicate glasses is of great importance for producing passivating layers on FET devices. Passivating films with optimum characteristics are preferably formed in a separate step, independent of the doping of the semiconductor.' The results of an investigation carried out to gain improved insight into the mechanism of glass formation are presented in this paper. It would be expected that application of the known Pz05-Si02 and B 2 O 3-SiO2 phase diagrams should be useful in extending understanding of the glass-forming processes. However, the question of the propriety of treating thermally grown SiO2 in these binary oxide systems by the methods of equilibrium thermodynamics must be considered when this application is attempted. Although Sah et a1.' and Allen et al. 3 investigated the kinetics of formation of phosphosilicate glass (PSG), they failed to adequately relate their diffusion models to the occurrence of experimentally observed phases in the PSG/SiO 2/Si system. Horuichi and yamaguchi4 investigated the diffusion of boron through an oxide layer and described their results in terms of a model similar to that of Sah and coworkers. More recently, Kooi 5 and Snow and Deal6 reported the compositions of PSG films formed by depositing P2 O 5 onto SiO2. These compositions apparently coincide with those at the liquidus curve delineating the maximum solubility of crystalline SiO2 in phosphosilicate liquid solutions. These authors did not discuss the thermodynamic implications of their results on the structure of thermally grown SiO2 films. The structure of thermally grown Sio2 films and that of vitreous silica are generally thought to be quite similar. Since the solubility of a substance depends on its structure, it is relevant that the solubility of vitreous silica in water7 is highly reproducible, like the solubility of thermally grown SiOz in phosphosilicate liquid. Furthermore, the vitreous silica-water system appears to be in true thermodynamic equilibrium (viz., the same solubility value can be approached from both supersaturated and under-saturated solutions). Sosman7 suggested that a type of two-dimensional lattice may form at the silica/solution interface, resulting in the observed solubility behavior that is characteristic of a crystalline solid. An alternative explanation may be that vitreous silica has a microcrystalline grain structure. Other investigators have suggested that vitreous silica has essentially the structure of B cristobalite,' or is composed of microcrystals of p tridymite or cristobalite, or a mixture of both. Presumably the grain size would be sufficiently large to minimize any appreciable contribution of the grain boundaries to the solubility of the crystalline matrix. The present investigation was carried out to clarify the significance of the boundaries in the Pa,-SiO, and B2O3-SiO2 Systems in determining PSG and BSG (borosilicate) film compositions. Furthermore, the kinetic data for PSG film formation were extended, using a wider range of formation parameters than were previously reported. One model describing the kinetics of film formation will be presented that is compatible with the thermodynamics of the Pa5-Si02 system. EXPERIMENTAL PROCEDURE Glass Film Preparation. SiO2 films (1000 to 8000A thick) were obtained by oxidation of silicon substrates in dry O2 at 1100°C. PSG and BSG films were prepared by exposing these layers to gaseous oxides obtained by reacting high-purity POC13 and BBr3, respectively, with O2. A double-columned saturator was used to ensure complete saturation of the N 2 carrier

Jan 1, 1969