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CONTENTS [The Nature of Strain Markings in Alpha Brass (paper by J. E. BURKE and C. S. BARRETT, Met. Tech. Feb. 1948. TP 2327). ......................... 2 X Ray Studies of Twinning and Untwinning in Magnesium Alloys (paper by J. B. HESS and R. L. DIETRICH, Met. Tech. Feb. 1948. TP 2328) ................ 11 ]

Jan 1, 1948

By H. P. Croft

[ ] Professor Hibbard's paper presents a very interesting theory concerning the influence of texture on the tendency of brass tube to stress-corrosion crack. I should like to present the result of some work done in 1941 which may throw further light on the subject. In the first place, in regard to his review of the influences of grain boundaries, we not only confirmed the findings which he quoted, but also were unable to crack single crystals of beta brass in the standard mercurous nitrate test in 50 hr under loads up to 18,500 psi. Samples containing two or more crystals of beta brass always cracked at grain boundaries and generally followed the same pattern as for alpha brass, although cracking occurred sooner than in alpha brass under the same conditions. Such a specimen is shown in Fig 4. Second, at the possible risk of repetition, we should like to call attention to the reported role of grain size as influencing the tendency to stress-corrosion crack. This phenomenon, originally mentioned by Dr. Allan Morris in the Transactions, AIME, 1931, is illustrated in Fig 5, showing the effect of variations in grain size on the tendency of drawn brass wires to crack under load in the mercurous nitrate solution. This was taken from my work published in Proceedings A.S.T.M. 41, (1941), 905.

Jan 1, 1948

By B. R. Queneau

[ ] B. R. QUENEAU-One of the difficulties in metallurgy has always been a lack of precision in measurement, and I think the authors are to be congratulated on developing a method which will give us an accurate and dependable quantitative estimate of the amount of retained austenite. O. ZMESKAL*-As Chairman Queneau said, this is indeed an ingenious and needed determination. We have seen figures presented of 1/2 pct retained austenite determined, and I would like to ask the authors the lower limits of this method. How far down do they feel they can go in improving the technique still more?

Jan 1, 1948

[ ] DISCUSSION F A LORIA*-The method of testing gun steel for resistance to surface cracking described in this paper was restricted to the examination of small, rod-shaped specimens The writer would like to point out the importance of other factors in producing defects in forged and bored gun tubes which would not be apparent in this investigation because of the nature of )he test Actual section size would accentuate the possibility of internal wall (bore) defects arising from unequal expansion between the internal and external wall surfaces on firing, resulting in internal tearing Checks and tears on the inside walls arise from internal tensions and nonuniformity on cooling, but the internal tearing can be reduced by using alloys of low expansion and of good thermal conductivity so as to reduce the difference between the outer and inner wall surfaces Also, the possibility of the location of inclusion segregates within a machined gun tube becomes more likely than in a small test specimen The effect of these nonmetallics on gun life and performance is evident when one realizes that the inclusions are soft yet brittle They reduce the amount of plastic deformation which can take place before cohesive failure occurs Once localized fracture has occurred at the position of a chain of these inclusions, a sharp notch (crack) is formed which produces stress conditions more favorable to cohesive failure than to plastic deformation These cracks aid erosion by providing channelways for the explosive gases, eventually leading to the tearing out or spalling of blocks of metal Oxidation of the surface may be partly responsible for the change in the surface of gun steel during firing observed by the author The appearance of burn on the surface is an indication that high temperatures were reached on firing, resulting in a slight oxidation of the surface Since the color of the oxidized film depends on both temperature and time, a higher temperature is required for a given color to form when it is caused by explosive heat, which acts for only an extremely short time at a given spot, than when it is caused by ordinary tempering The cross section of the gun steel specimen, Fig 16, illustrates that the repeated firing temperatures were high enough to cause

Jan 1, 1948

By R. M. Schuster, F. M. Benavides

Samuel G. Bonasso The article by Benavides and Schuster provides an in-depth study of three transportation alternatives for a four-mine complex in western Kentucky. The examination of aerial tramways was not undertaken as an alternative solution. We feel this is an oversight since industrial ropeways are competitive with both belt conveyance and overland truck hauling. In fact, there are aerial tramway systems, operational today, which are 100 years old and operating with some original components. Maybe unfortunately, there are no fixed rules or guidelines whereby the most cost-effective means of transporting and handling material for a given situation may be selected. Each situation must be evaluated so the variables that influence the selection of the desired alternative can be clearly defined. However, there are in-place industrial ropeway systems that have proven economically feasible over a range of 1.6-50 km (1-31 miles). The more difficult the terrain, the greater the cost efficiency.

Jan 1, 1983

By A. G. Sciulli, G. P. Ballock, K. K. Wu

Waste disposal underground is the most effective method when viewed from an environmental aspect. As costs of other methods of disposal continue to escalate, the cost effectiveness of underground disposal during the mining cycle becomes increasingly attractive. The use of concrete for sealing abandoned mines has proved to be suspect when associated with a relatively incompetent adjacent strata due to its shrinkage characteristics. Complete failure of the plug has been known to occur in some instances. A more effective, cost competitive seal can be obtained using pneumatically stowed material and incorporating a polyurethane grout, which has greater adhesion characteristics than concrete. Injection of the surrounding strata and of the stowed material helps to ensure an impervious barrier and prevent the plug from moving when subject to high pressure heads. When properly placed, impervious seals cause the old workings to flood, raise the mine pool level, and thus eventually eliminate the potential for oxidation, which is the primary cause of acidity in the water.

Jan 11, 1986

By V. Miller

C. Hertzler The difference of means of milling characteristics by rock and ore type is tested in a statistical manner in the paper. The null hypothesis being tested is that the sample means of two different populations are equal. It is assumed that the null hypothesis is true when performing the test. Because of this, acceptance of this hypothesis leads to the conclusion that the sample means of the two different populations are equal (or there is no significant difference between the sample means), not that the samples come from the same population, as the author asserts. Rejection of the null hypothesis leads to the conclusion that the sample means of the two different populations are not equal. A P value for this test is reported in Table 2 and is incorrectly identified as the probability that the two samples came from different populations. Actually, what was recorded was 100(1 - p) where p is the usual p-value. The usual p-value measures, on a scale of zero to one, the extent to which the data agree with the null hypothesis. It is the probability of observing a value of the test statistic (Z score) that is at least as contradictory to the null hypothesis as the one computed from the sample data (McClave and Dietrich II, 1982). The author makes no mention of the fact that were these tests to be conducted together, the chances of determining that the null hypothesis is not true when it is really true are increased considerably (Snedecor and Cochran, 1980). This is a multiple comparisons problem and should be dealt with accordingly. The usual methods involve adjusting the level of the individual tests. Table 2 reports an incorrect 100(1 - p) value in the comparison of concentrate grades for other rock types with .30 to .69 % Cu vs other rock types with .70 + % Cu; 86 % should be 98.6 %. Although the article can be criticized for poor data presentation and discussion of that data, the point the author makes regarding the use of these statistics in the ore reserve estimation process is well taken. It does not appear that inaccuracies in the statistical interpretations have hindered that usefulness. References McClave, J.T., and Dietrich, II, F.H., 1982, "Statistics," Dellen Publishing Co., San Francisco and Santa Clara, CA, 766 p. Snedecor, G.W., and Cochran, W.G., 1980, "Statistical Methods," The Iowa State University Press, Ames, IA, 561 p. Reply by V. Miller After reading Ms. Hertzler's comments, it appears that the differences noted were basically semantics. If the paper is ever presented at a math symposium, some changes will be needed. When deciding the best way to present the data to mining engineers and geologists, I decided that presenting the probability that the two sample groupings came from different populations (reverse to the Null hypothesis) was easier and would require less verbage to explain. Hence, the 100(1 - p) difference which was noted. Ideally, I would have preferred to give the recovery and concentrate grades, then comment which ones had significant differences. Unfortunately, Kennecott Corp. did not grant permission to publish the ore body's actual recoveries and concentrate grades. The conclusion is that there was, as expected, a relationship between the ore's geologic properties and the metallurgical properties, and by determining this relationship, the overall mineral model was greatly improved.

Jan 8, 1984

A. G. Cockbain—The paper by Burlingame, Bitsianes and Joseph is of great interest in extending the work done on high grade sinters, particularly that of Hessle, and the development and application to them of the technique of McBriar, Johnson, Andrews and Davies on ironstone sinters. In this laboratory the work of McBriar et al. has also been continued and extended to cover high grade sinters, and a sectioning technique similar to that used by McBriar et al. was attempted on sinter cakes made in the laboratory sinter unit, using magnetite concentrates (containing 64 pct Fe). In these experiments no attempt was made to flush out the products of combustion with nitrogen before cooling. It was considered that free air penetration would occur on only a limited scale with the size of sinter cake made (14 in. sq x 12 in. deep). Chemical analyses of the zones showed generally similar features of those described by Burlingame et al. and especially the FeO rich region at and just behind the flame front, i.e. zones of ignition and combustion. This seems to indicate that the nitrogen atmosphere does not materially affect the states of oxidation in the sinter cake or at least that special care is not required unless the sinter cake is small. Burlingame et al. consider that FeO present has some significant part to play in the mechanism of sintering. This view does not find favor with the author. The reduction of iron oxides in the presence of red hot coke is a well known phenomenon, whether conducted in an atmosphere of nitrogen or in a crucible in air, and in view of the presence of some carbon in the hot sinter, especially just at the ignition zone, cessation of the progress of the flame front will in no way affect the reduction of iron oxides near hot coke. Even in a nitrogen atmosphere some CO and CO, will be generated by reduction and by continual oxidation and reduction of CO as the transfer agent, the oxidation state of the iron oxides can be lowered quite rupidly so long as free carbon exists with enough heat. Knowing the composition of the gas at the flame front (obtainable by probes), it would be possible to calculate the static oxidation state of Fe2O3/Fe3O2 in equilibrium with it and hence obtain a check on the chemical analyses to see if in fact direct reduction of the Fe2O3/Fe2O1 to FeO has taken place. Have the authors attempted this? It appears to this writer that what is required is some means of reducing rapidly the heat content of the ignition zone and immediately behind, and at the same time insuring no oxidation by the air. In ironstone sinters the difficulty of oxidation state of the iron did not arise on account of the very large slag bulk. However, in high grade sinters knowledge of this, and also the mechanism whereby high oxidation states can be obtained in the final sinter, is of great interest. R. D. Burlingame (author's reply)—The question has been raised as to whether the high FeO content found in high-fuel sinters is due to actual reduction at the advancing flame front or due to unavoidable direct reduction during the quenching period. For such direct reduction to have taken place in the freshly-formed sinter, a considerable amount of solid carbon would have had to escape combustion and be available throughout the hot sinter zone during the quenching period. A simple stoichiometric calculation with the limited data available indicates that a zone of freshly-formed sinter over 2 in. wide must have averaged roughly 2 pct C to accomplish the amount of reduction found. Furthermore, the presence of this amount of carbon would indicate that the fuel in the charge had not burned over a narrow front but over a zone at least 2 in. thick. In contrast to such a condition, the data of the present investigation indicate that the combustion of fuel is confined mainly to a narrow front in which high temperatures and reducing conditions favor. the formation of excess ferrous iron.

Jan 1, 1959

I have attended these meetings, every year, since 1926 and have served on both the Pittsburgh and the National Executive Committees, so that I am fully aware - of the ruling of this organization regarding, "No Papers by Vendors". Since I am now classified as a VENDOR, I wish to express my sincere appreciation for the invitation to formally discuss these very interesting papers --all of which herald the coming of an entirely new era in the manufacture of quality steels. I also appreciate the references by Mr. Mosser and Dr. Swinkels to my first paper on the oxygen probe which was presented at the meeting of this group, here in Chicago, in 1966 and was subsequently published in the NOH Proceedings of that year. (1)

Jan 1, 1972

By D. G. Krige

Discussion by D.G. Krige I read the paper "The jackknife approach" with interest. There appears to be a widespread misunderstanding of the kriging variance as a measure of the error variance of the kriged grade estimate of an ore block. Virtually all mineral deposits display skew frequency distributions and are subject to the well-known proportional effect. Thus, it is usual to find in an ore body, when subdivided a really into subpopulations, that the variances of the grades (or the total sills of the variograms) for the subpopulations will be correlated with the corresponding mean grades (usually linearly with the squares of the mean grades). Thus, the variogram will be station. When this feature is evident, the relative variograms for the subpopulations (i.e., with variogram values divided by the relevant mean squared) will be similar, or they could even be accepted at an averaged model for the whole ore body with stationarity. Using this approach, the kriging variance will reflect the relative error variance that is to be multiplied by the kriged block grade estimate squared to yield the usual kriging variance for purposes of confidential limits. The objection that the kriging variance does not take into account the local grades used for a block valuation then falls away. In the example given by the authors, the global mean grade is not recorded. But the global variance, taken at the value of the total sill, is 0.005, whereas the variance of the 11 values used in the example is 0.000152. The two variances differ by a factor of nearly six. If the relative variogram approach is applicable in this case, the need for a jackknife technique will fall away. Also note that, for skew distributions, the confidence limits for ore-block estimates will be skew as well, and symmetrical normal limits will not apply. RepIy by G.S. Adisoma and M.G. Hester There are a few interesting ways to utilize the block-by-block kriging variance that the authors have encountered. One of them is to classify a particular block into a proven-probable reserve or a possible-resource category, using a somewhat subjectively determined kriging variance value. Here, the kriging variance still represents the drilling density, i.e., data configuration more than the data values. Professor Krige mentions another ingenious approach through the use of relative variograms. This will yield a block kriging variance that takes into account local (block) grade, as he correctly points out, for purposes of confidence limits. However, we are more interested in quantifying the uncertainties associated with grade estimation in a much larger scale than a block. e.g., for a mining phase or the minable reserve. The jackknife, through the block kriging shortcut, provides a simple solution to obtain a single estimation variance for a general shape. The authors' main reference discusses different ways to handle skewed distributions typical in mineral resource estimation, e.g., the weighted jackknife approach or data transformation. Also, as with any technique, we can always improve our estimate by subdividing into smaller populations that are geologically and statistically separate domains. As we have mentioned; the jackknife is but a tool in our collection of tools to solve estimation problems. The jackknife's appeals are its simplicity and versatility. It is handy when no other solution is available, or when the available solution is not practical. It is used with other methods, not to replace them altogether. ?

Jan 1, 1997

By R. J. Sweigard, R. V. Ramani

G.F. Learning The paper by R.V. Ramani and R.J. Sweigard is a wonderful description of the labyrinthine web that has been spun about the mining industry by energetic bureaucrats and politicians over the past 50 years. The remedy for the problem, however, is not more of the same, but less. That may be difficult for the industry to achieve, for it is not a technical solution but a political one. And the current fervor for more detailed planning at all levels of government and private enterprise has become deeply ingrained. The authors recommend the provision of more information about mining and mineral resources to "macro" (i.e., government) land use planners. They apparently overlook, however, the already strong tendency on the part of most government land use planners to consider themselves omniscient. Thus, giving them more information about the technical problems of mining will only make them want to get more and more involved in the "micro" (private, site specific) mine development and production plans of the individual mining firm. In fact, this has already happened at all levels of jurisdiction from municipal to federal government. Examples are legion. The most effective way to ameliorate the adverse impacts of government land use planning on existing and potential mining operations is to: (1) introduce greater flexibility in the definition of land use zones by local and state governments; (2) adopt realistic and relevant ambient environmental performance standards in governing relationships between mineral land uses and concurrent or subsequent nonmining land uses; (3) allow greater leeway for economic considerations in land use decisions in contrast to the explicit legalistic approach now in vogue; (4) recognize that all minerals are not the same and that sand and gravel mining should not be treated the same as underground metal mining, coal stripping, oil field production, or in situ leaching; and (5) eliminate the notion that mining operators should be responsible for determining in detail the use of land by subsequent owners of mined land. This last bit of conventional ethic really makes no more sense than requiring the builders of every shopping center or government office complex to provide detailed plans for the use of that land when its use for shopping or government is ended. Did the builder of Ebbetts Field plan for Brooklyn after the Dodgers went to Los Angeles? Should the developer of the Bingham Pit plan for suburban Salt Lake City after the copper mining goes to Chile? The nation's mining industry must address these questions before further bankrupting itself to provide more data to planners and spending thousands of dollars per acre to create land that when reclaimed is worth only a few hundred dollars per acre. Reply by R.V. Ramani and R.J. Sweigard We thank Mr. Leaming for his valuable contribution. His views on the problems of land use planning and mineral resources are most welcome additions to our paper. As the title indicates, our paper was more concerned with the impacts of land use planning on mineral resource conservation than with the details of the planning process. On the whole, his five recommendations would be helpful for mineral resource conservation. However, we would suggest that the argument he presents for his final recommendation does not address the differences between mining as a land use and commercial or institutional uses. We believe that this difference is the crux of the issue. We share Mr. Leaming's desire to ameliorate the adverse impacts of land use planning. Possibly the most detrimental impact is the loss of mineral resources. Any development, whether mineral or community, that does not give proper consideration to other resources can result in permanent loss or sterilization of resources. With proper planning, some of these losses can be avoided. As our paper indicated, one factor that limits the consideration of mineral resources, and ultimately leads to their sterilization, is the generally inadequate levels of resource characterization and understanding of the unique nature of mineral resources and mining operations. The last point raised by Mr. Leaming is also important. In terms of reclamation and land use planning in mining districts, we certainly do not advocate spending more than what the results are worth. The main thrust of the paper was to explore the avenues for conserving the mineral resources so that, at some appropriate time, the issue of mining and reclamation can still be addressed.

Jan 4, 1985

By G. Chi, M. C. Fuerstenau, R. C. Bradt, A. Ghosh

Technical Papers, Mining Engineering Vol. 49, No. 12, pp. 70-75, Discussion by McIvor, R. and Fink, R. P. We must challenge what we consider to be dubious statements in the above-mentioned article. Much of what is reported was published elsewhere over a year ago (i.e., in their reference: Chi, G., Fuerstenau, M.C., Brandt, R.C. and Ghosh, A., 1996, "Improved comminution efficiency through controlled blasting during mining," International Journal of Min¬eral Processing, Vol. 47, p. 93). There is nothing unusual or significant about a 10% or more difference in grindability between two materials of apparently similar origin and other attributes (such as chemical assays, hardness and specific gravity). Consider also that: • the materials came from different locations in the pit; • only two sets of four blastholes were considered per blast: • spatial orientation with respect to the face and other blastholes was also altered; • only two pairs of data were collected; • the impact of sampling error and bias, • both of which could be significant in this case; and • normal experimental error in parameter measurement and calculation. It is clearly inappropriate to draw any conclusions with regard to cause-and-effect relationships without first presenting a thorough error analysis. A substantial number of randomly selected test and control areas might provide meaningful statistical evidence of the claimed effect of the variables being studied. Even that appears doubtful, however, because Figures 3 and 4 show about as much variation in crushing energy for the two "regular" conditions vs. regular and altered conditions. On a separate, but also important issue, broad experience with autogenous/semiautogenous milling has shown that smaller or weaker feed material results in reduced tonnage. ? Reply Thank you for the opportunity to respond to the comments of Messrs. Mclvor ant Fink. The points raised are addressed in the order of presentation. As the commenters noted, there are parallels between this article and a previous manuscript. The reason for these complementary articles is that the audiences for the two publications are different, although there is obviously some overlap. We believe that the different audiences each profit from the technical aspects of the two manuscripts. We are not in agreement that a grindability difference of 10% is insignificant. The laboratory work is corroborated by data obtained at plant scale, which confirms that an increase in throughput of the same magnitude (between 5% and 10%) is achieved when the blasting pattern is modified, i.e., reduced from 9 to 8 m (29.5 to 26.2 ft). This increase in throughput translates into substantial power savings for ore grinding. No differences in appearance in the rock were noted between the two adjacent areas. Rock in both areas belonged to the same rock mass/block, which was quite homogeneous and without geological features in between that could create drastic differences in comminution characteristics. Given the resources, we would have sampled from all of the holes. Additional data would certainly have been desirable, as would have been additional funding to expand the study. Their comment, "spatial orientation with respect to the face and other blastholes was also altered," is not clear. Figure 1 does not show the initiation sequence. Without the initiation sequence, we do not understand how the commenters concluded that spatial orientation with respect to the face and other blastholes was altered. The commenters may be trying to make the point that the four-hole configurations with respect to the original bench face are not exactly the same. In fragmenting the

Jan 1, 1999

H. H. Bleakney (Dept. of Mines and Technical Surveys, Ottawa, Canada)— The work of Dr. Machlin and his colleagues at Columbia University is so scholarly that one hesitates to take issue with them. Nevertheless the writer feels compelled to enter a demurrer to the mechanism of intercrystalline cracking proposed in this paper. The principal obstacle to its acceptance is found in its preoccupation with purely mechanical influences and its disregard for the chemical effect of impurities. The writer believes that the destruction of metallic cohesion by concentration of impurities at the grain boundaries is a necessary and sufficient condition for the development of intercrystalline cracking; and he believes that discussion of the numerous mechanical explanations proposed should wait until some valid objection to the chemical hypothesis has been advanced. It is nearly twenty years since Gillett" drew attention to the possibility that the chemical influence of precipitation might be the cause of intercrystalline cracking. As early as 1935, Greenwood'" remarked that grain-boundary precipitation of impurities in lead appeared to promote intercrystalline cracking. Again in 1939, Scott commented as follows on a paper by Thielemann and Parker:'" "There are at least two familiar phenomena that can influence grain-boundary cohesion: 1) intergranular oxidation; and 2) grain boundary precipitation. An important consideration in this work, therefore, is to determine which, if either, of these factors is responsible for the low values of cohesive strength observed." In 1952. the writer presented evidence," some original and some abstracted, which indicated that in copper, silver, aluminum, lead and iron, intergranular cohesion was a function of the purity of the metal. In 1954 Glen, discussing a paper by Ridley and Tapsell14 indicated his belief in a precipitation mechanism for the intercrystalline embrit-tlement of molybdenum steel and suggested that with an absolutely pure metal it would be almost impossible to obtain an intercrystalline crack. This suggestion has

Jan 1, 1959

K. T. Aust and J. W. Rutter (General Electric Research Laboratory)—We find it difficult to reconcile the activation energies determined by Gifkins with his general conclusion that "migration during both creep and grain growth can thus be treated on the basis of the same model" (that of Lucke and Detert). Gifkins finds the activation energy for grain boundary migration during creep to be 24.5 kcal per rnol and that for grain boundary migration during grain growth to be 7.5 kcal per mol. The calculation carried out by Gifkins of the activation energy for grain boundary migration during grain growth, using the Lucke and Detert model, gives a value of 20 to 24.5 kcal per mol, rather than his experimental value of 7.5 kcal per mol. The theory of Lucke and Detert was developed to account for the rates of migration of grain boundaries in the presence of impurities during grain growth. The theory does not take into account the effect on the boundary migration of another, simultaneous process such as creep deformation and would be expected, therefore, to be applicable only to migration during grain growth. The fact that Gifkins measured a different activation energy for boundary migration during grain growth (7.5 kcal per mol) from that during creep (24.5 kcal per mol), although the specimens were of the same composition, shows clearly that such an effect exists under his experimental conditions; the presence of a simultaneous creep deformation markedly affects the boundary migration process in comparison with what would be observed under the same conditions but without the creep deformation. The failure of McLean's equation (Eq. [4] of Gifkins' paper) to give a satisfactory dislocation density difference for boundary migration during creep is not surprising, since the activation energy which must be used in this equation refers only to the elementary atom transfer process of grain boundary migration. This activation energy value is approximately 6 kcal per mol for zone-refined lead, as determined in both the grain boundary migration experiments of Aust and Rutter31, 32 and the grain growth experiments of Bolling and Winegard.33 Using this activation energy value, McLean's equation gives reasonable agreement with observed migration rates for grain boundaries moving free of the influence of impurities.31, 32 The value of 24.5 kcal per mol is probably associated with the presence of impurity atoms, as Gifkins suggests. It should be noted, however, that this value was obtained using lead of only one composition and measurements at only two temperatures. The work of Aust and Rutter3"' on the effects of tin, silver, and gold on grain boundary migration in zone-refined lead in the temperature range from 320" to 200°C, as well as the work of Bolling and Winegard34 on the effect of silver and gold on grain growth in zone-refined lead, shows that the measured activation energy is markedly dependent upon the kind and amount of solute present. Gifkins' work does not permit evaluation of the effect of the 8 ppm of impurities other than oxygen present in his specimens. One incidental point: the symbols used to designate the experimental points of Fig. 6 appear to be in incorrect order in the figure caption. As the caption is printed, it would indicate that larger grain sizes were obtained after annealing at 47°C than at 100°C, which does not agree with the text (point M, p. 1019). Finally, it seems clear from Gifkins' results that any serious attempt to determine whether grain boundary migration and grain boundary sliding during creep occur with the same activation energy, as Gifkins suggests and McLean rejects, must take into account the effects of impurities on these two processes, Although the work of Weinberg35 indicated that adding small amounts of copper, iron and silicon to aluminum did not affect the grain boundary shear behavior, it should be noted that his starting material contained approximately 60 ppm of impurities. Gifkins' results indicate impurity effects at an impurity level of 8 ppm, suggesting strongly that the most significant impurity range to be investigated lies substantially below that value. R. C. Gifkins (author's reply) — As Drs. Aust and Rutter suggest, the results under discussion may have to be reinterpreted in the light of their own work on grain boundary migration, which was not available to me when the paper was written. Because of their work, Aust and Rutter attach more importance than I did to the activation energy for grain boundary migration during annealing (7.5 kcal per mol) obtained from a "direct" plot of log-rate against the reciprocal of absolute temperature. At the time it was obtained, this value seemed rather low, although it was similar to the value obtained by Bolling and Winegard.36 It was then, and still is, difficult to accept this value because of the low value of the index in the power law for grain growth, which seemed to indicate the influence of impurities. It was also concluded that the low value of the activation energy might have arisen from the manner of selecting rates of grain growth which were truly comparable at the two temperatures. There were many other indications in these experiments and those on recrystallization during creep3? that an impurity, probably oxygen, was of importance. The model for grain-boundary migration which Lucke and Detert had proposed was an obvious possibility and its use yielded an activation energy for boundary migration during annealing of 20 to 25 kcal per mol.

Jan 1, 1961

By C. H. Gerould

I would like to take a moment to consider our polystyrene-silica replica technique, which was developed at the Dow Chemical Co. and which was mentioned in the paper just given by Mr. Thielsch. He stated that he feared that our replica technique would cause difficulty due to deformation of the metal as a result of the application of pressure during the molding process. We at the Dow have never had any reason to suspect that any deformation of the metal was occurring during the molding process. Our procedure has been to heat the polystyrene to a temperature of 160°C. before applying any pressure, at which temperature the polystyrene is a viscous liquid. By so doing the pressure of the polystyrene against the metal is essentially hydraulic and is therefore applied equally in all directions, which we feel should not cause deformation. Our work using this replica technique has brought forth several indications that deformation of the specimen is negligible. These indications are: I. Direct comparisons have been made between the light and electron microscopes when studying a specific spot on a metal surface. These "same spot" studies were obtained by first taking micrographs at high magnification, with a light microscope, of a specific structure that could be readily recog-

Jan 1, 1947

M.S. Azun I have many objections to the content of the author's paper. Before discussing it, however, I would like to repeat the property of semivariogram function. Second order stationary properties of regionalized variables (ReV's) such as semivariogram function y(h) are perfectly known in geostatistics. Also, the kriging equations in the language of mathematical statistics using second order stationary properties are well understood. However, the way to use the sample (estimated) semivariogram function in any one of the kriging procedures is vague. The sample semivariogram function is given as follows: [ ] where N is the total number of samples, Xi is the sample value at the i - th location, Xi+h is the sample value at the i + h - th location, and h is the distance among the samples. An estimation variance of sample semivariogram function of first lag is smaller than that of higher order lag. The theoretical semivariogram function reaches the variance of samples asymptotically. But this is not easily observable because of the larger variation involved in the estimate of semivariogram function. In general, an estimation procedure is done for h = 0, 1, 2, up to the greatest integer less than N/2, even though sample semivariogram function can be computable through N-1. After estimating semivariogram function, the critical question of how to model sample semivariogram function arises. As seen in the above equation, sample semivariogram function is discrete and can be smoothed by the model being selected. Therefore, modeling of sample semivariogram function is the most important step in geostatistics. It not only smoothes a discrete function but also affects the results of the kriging procedure. When the only aim is to model the semivariogram function, which is the basic point of the author's paper, one can employ any fitting techniques, such as curve fitting, or any arbitrary functions, which are called submodels in the paper. The term "arbitrary function" is used rather than "submodel" because there is no basic understanding of developing them. The author suggests that the sum of those submodels can also be used for the modeling of sample semivariogram function. The combination of any arbitrary functions brings many problems instead of giving an insight of the domain structure considered. The author used two arbitrary functions and the nugget effect in response to sample semivariogram function (Fig. 10). For the same example, he stated that the parameters involved in the mixed arbitrary function model can be accepted when the discrepancy between sample semivariogram function and the model is small visually. For verifying the fitting behavior of any selected model, one should not be contented with the visual satisfactory. Some statistical measure such as goodness of fit has to be used. The author's practice is no more than an exercise in curve fitting without any fundamental understanding or conceptualization of the underlying physical mechanism. Furthermore, the selection of any model is not an easy task if the purpose is the search for the "best" response to the observed second order properties of ReV's. I suggest that the Markovian model (Azun, 1983), on the basis of a theoretical understanding of underlying mechanism, which gives more information about the occurrence of regionalized variables, is used to respond all properties of ReV's. There are a lot of problems for modeling of one-dimensional sample semivariogram function. Thus, it is not appropriate to go to higher order dimensional sample semivariogram function modeling. In the meantime, I would recommend that one can connect the values of standardized sample semivariogram function rather than simple values of semivariogram function in the two-dimensional estimation. The standardized values can be computed in dividing the semivariogram function value by the number of sample pairs involved in each lag regardless of the directions. In conclusion, geostatistics is an interdisciplinary area in mining that uses the principles of mathematical statistics. Thus, it should not violate any probabilistic and statistical rules. When Matheron was developing the theory of geostatistical study in the early years of geostatistics, many mining people had a reservation accepting the geostatistical tools. However, this does not mean that we, the geostatisticians, might try to convince those people using some "strange" tools or rules as some authors implied (Baafi and Kim, 1984). Instead, we have to develop and explain the geostatistical tools staying only in the framework of statistical concepts and properties. References Azun, M.S., 1983, "Stochastic Process Modeling of Spatially Distributed Geostatistical Data," Columbia University, Ph.D. Thesis. Baafi, E.Y., and Kim, Y.C., 1984, "Discussion - Comparison of Different Ore Reserve Estimation Methods Using Conditional Simulation," Mining Engineering, Vol. 36, No. 3, p. 280. Reply by J.M. Rendu The interactive method proposed by Rendu allows practitioners to develop semivariogram models that take into account not only the numerical information obtained by sampling, but also highly significant additional information that often cannot be quantified. The geology of the deposit - including hypotheses concerning its genesis, sampling methods, assaying methods, and mathematical methods used to calculate the semivariograms - all have an influence on the numerical results obtained and on how these results should be interpreted. If all the information concerning the spatial distribution of values in a mineral deposit was contained in the sample values, it could be argued that statistical techniques alone would produce optimum models. However, this is rarely, if ever, the case. Methods that allow the user to take into account his experience and his geologic understanding of the deposit should not be rejected for the sake of theoretical statistical purity.

Jan 11, 1985

By M. S. Azun

M.S. Azun I have many objections to the content of the author's paper. Before discussing it, however, I would like to repeat the property of semivariogram function. Second order stationary properties of regionalized variables (ReV's) such as semivariogram function ?(h) are perfectly known in geostatistics. Also, the kriging equations in the language of mathematical statistics using second order stationary properties are well understood. However, the way to use the sample (estimated) semivariogram function in any one of the kriging procedures is vague. The sample semivariogram function is given as follows: [1 N-hy*(h) = 2(N h) i21 {Xi-Xi+h}Z, h=0, 1, N-1] where N is the total number of samples, Xi is the sample value at the i - th location, X i+h is the sample value at the i +h - th location, and h is the distance among the samples. An estimation variance of sample semivariogram function of first lag is smaller than that of higher order lag. The theoretical semivariogram function reaches the variance of samples asymptotically. But this is not easily observable because of the larger variation involved in the estimate of semivariogram function. In general, an estimation procedure is done for h = 0, 1, 2,…., up to the greatest integer less than N/2, even though sample semivariogram function can be computable through N-1. After estimating semivariogram function, the critical question of how to model sample semivariogram function arises. As seen in the above equation, sample semivariogram function is discrete and can be smoothed by the model being selected. Therefore, modeling of sample semivariogram function is the most important step in geostatistics. It not only smoothes a discrete function but also affects the results of the kriging procedure. When the only aim is to model the semivariogram function, which is the basic point of the author's paper, one can employ any fitting techniques, such as curve fitting, or any ar¬bitrary functions, which are called submodels in the paper. The term "arbitrary function" is used rather than "submodel" because there is no basic understanding of developing them. The author suggests that the sum of those submodels can also be used for the modeling of sample semivariogram function. The combination of any arbitrary functions brings many problems instead of giving an insight of the domain structure considered. The author used two arbitrary functions and the nugget effect in response to sample semivariogram function (Fig. 10). For the same example, he stated that the parameters involved in the mixed arbitrary function model can be accepted when the discrepancy between sample semivariogram function and the model is small visually. For verifying the fitting behavior of any selected model, one should not be contented with the visual satisfactory. Some statistical measure such as goodness of fit has to be used. The author's practice is no more than an exercise in curve fitting without any fundamental understanding or conceptualization of the underlying physical mechanism. Furthermore, the selection of any model is not an easy task if the purpose is the search for the "best" response to the observed second order properties of ReV's. I suggest that the Markovian model (Azun, 1983), on the basis of a theoretical understanding of underlying mechanism, which gives more information about the occurrence of regionalized variables, is used to respond all properties of ReV's. There are a lot of problems for modeling of onedimensional sample semivariogram function. Thus, it is not appropriate to go to higher order dimensional sample semivariogram function modeling. In the meantime, I would recommend that one can connect the values of standardized sample semivariogram function rather than simple values of semivariogram function in the two-dimensional estimation. The standardized values can be computed in dividing the semivariogram function value by the number of sample pairs involved in each lag regardless of the directions. In conclusion, geostatistics is an interdisciplinary area in mining that uses the principles of mathematical statistics. Thus, it should not violate any probabilistic and statistical rules. When Matheron was developing the theory of geostatistical study in the early years of geostatistics, many mining people had a reservation accepting the geostatistical tools. However, this does not mean that we, the geostatisticians, might try to convince those people using some "strange" tools or rules as some authors implied (Baafi and Kim, 1984). Instead, we have to develop and explain the geostatistical tools staying only in the framework of statistical concepts and properties. ? References Azun, M.S., 1983, "Stochastic Process Modeling of Spatially Distributed Geostatistical Data," Columbia University, Ph.D. Thesis. Baafi, E.Y., and Kim, Y.C., 1984, "Discussion - Comparison of Different Ore Reserve Estimation Methods Using Conditional Simulation," Mining Engineering, Vol. 36, No. 3, p. 280. Reply by J.M. Rendu The interactive method proposed by Rendu allows practitioners to develop semivariogram models that take into account not only the numerical information obtained by sampling, but also highly significant additional information that often cannot be quantified. The geology of the deposit - including hypotheses concerning its genesis, sampling methods, assaying methods, and mathematical methods used to calculate the semivariograms - all have an influence on the numerical results obtained and on how these results should be interpreted. If all the information concerning the spatial distribution of values in a mineral deposit was contained in the sample values, it could be argued that statistical techniques alone would produce optimum models. However, this is rarely, if ever, the case. Methods that allow the user to take into account his experience and his geologic understanding of the deposit should not be rejected for the sake of theoretical statistical purity. ?

Jan 1, 1986

R. Schuhmann, Jr. (Purdue University)— Fulton and Chipman's results on rate of silica reduction from slags are analogous in many was to the results of Parlee, Seagle, and Schuhmann10 on rate of alumina reduction from alumina crucibles. Both investigations have given comparably low rates of reduction and slow approaches to equilibrium. Accordingly, we may hypothesize that the rate-determining step is the same in both kinds of experiments; that is, oxygen diffusion across the stagnant boundary layer on the liquid-metal side of the interface between the liquid metal and the oxide phase (slag or solid oxide). I suggest that silica reduction involves the following consecutive steps: I) At the slag-metal interface: SiO2(slag) Si+ 20 II) Transport of oxygen from slag-metal to gas-metal interface: a) diffusion across liquid-metal boundary layer at slag-metal interface. b) convection within the body of liquid metal. c) diffusion across boundary layer at metal-gas interface. 111) At the metal-gas interface: C +O- CO (gas) Iv) At the graphite-metal interface: C (graphite) -C At steelmaking temperatures it is reasonable to assume that equilibrium is attained in all three chemical reactions (I, 111, and IV) right at the respective interfaces. Convection within the stirred liquid metal (step IIb) is also rapid. Transport of Si and C should be orders of magnitude easier than transport of 0, because of the relatively high concentrations of Si and C. Accordingly, we might expect the overall reaction rate to be determined by boundary-layer diffusion of oxygen, either IIa or IIc. Fulton and Chipman's demonstration that bubbling CO through the system had no major effect on reaction rate indicates that IIc is not the slowest step. Therefore, it becomes logical to estimate the maximum rate for step IIa and to compare this theoretical estimate with Fulton and Chipman's experimental data. If oxygen diffusion across the liquid metal boundary layer at the slag metal interface (step IIa) is rate-determining, In this equation, dn sio, /dt is the rate of silica reduction in moles per sec,A is the area of slag-metal interface in sq cm, Do is the diffusivity of oxygen in sq cm per sec, 6, is the boundary layer thickness in cm, c,* is the oxygen concentration right at the slag-metal interface in moles per cubic cm, and co is the oxygen concentration in the body of the liquid metal, also in moles per cubic cm. Equilibrium data" on the silicon deoxidation reaction in liquid iron and steel at 1600°C indicate that the oxygen contents of the liquid metal in Fulton and Chipman's experiments at 1600°C probably fell in the range of 0.5 x10-3 x10-3wt pct. That is, the maximum conceivable value of co*-co for the system under consideration was on the order of 10"5 mole oxygen per cubic cm. On the basis of previously published data,1O,11 it is estimated that Do/0 will fall somewhere in the range from 10-3 to 10-1 cm per sec. The surface area A in Fulton and Chipman's experiments was approximately 20 sq cm, and the weight of metal involved was about 500 grams. Combination of all these figures with the above rate equation leads to an estimate that the rate of silica reduction should fall within the range from 0.002 to 0.2 wt pct Si per hr. This estimate is consistent with the experimental data. For example, Fulton and Chipman's Fig. 2 shows a change of about 0.3 pct Si in 10 hr, corresponding to an average rate of 0.03 pct per hr. According to the proposed hypothesis, increasing the temperature will increase the reaction rate ill two ways: 1) by increasing oxygen diffusivity and 2) by increasing the oxygen concentration (oxygen solubility) in the liquid metal. The combination of these two effects accounts for the high value of the observed activation energy. Summarizing, I propose that the rate of silica reduction, like that of the carbon-oxygen reaction, is diffusion controlled and that low oxygen concentration in the liquid metal is the major factor accounting for the very low observed rates of silica reduction. John Chipman (author's reply)—The authors thank Professor Schuhmann for his interesting contribution. His proposed explanation may well prove to be the correct one. There is clearly a need for much further experimental work on this problem, and further research is in progress.

Jan 1, 1961

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Jan 1, 1946

The apparent small effect of skimming on desulphurization is somewhat misleading because the data was collected during the first months of use on the skimmer. During this period of time, the operators were, of course, just learning to use the equipment and, consequently, in many cases a so-called skimmed heat may have only been partially skimmed. In addition, during this period, the percentage of sulphur in the blast furnace slag was gradually increasing because of the increasing oil injection rates being employed at the blast furnace. An additional factor that cannot be disregarded is the apparent slower slag formation rate obtained in the BOF when the blast furnace slag is removed. This is evidenced at our shop by a much stronger tendency toward sparking and related lance skulling problems with deslagging, in spite of satisfactory manganese levels in the hot metal. Naturally, slower slag formation could account for poor desulphurization which would partially offset the beneficial effect of a lower sulphur input.

Jan 1, 1972