ASSESSMENT OF UPGRADING WITH REGARD TO THE LIBERATION DISTRIBUTION AND THE SEPARATOR PERFORMANCE

Transcription

1 ASSESSMENT OF UPGADING WITH EGAD TO THE LIBEATION DISTIBUTION AND THE SEPAATO PEFOMANCE T. Leißner 1) ; K. Bachmann 2) ; J. Gutzmer 2, 3) and U. A. Peuker 1) 1) Technische Universität Bergakademie Freiberg, Institute of Mechanical Process Engineering and Mineral Processing, Agricolastraße 1, 9599 Freiberg, Germany 2) Helmholtz-Zentrum Dresden-ossendorf, Helmholtz-Institute Freiberg for esource Technology, Halsbrücker Straße 34, 9599 Freiberg, Germany 3) Technische Universität Bergakademie Freiberg, Department of Mineralogy, Brennhausgasse 14, 9596 Freiberg, Germany ABSTACT The article describes a method for the evaluation of the upgradeability of a material based on the mineralogical limiting curve (liberation) and the performance of the separator used for concentration (separation). The characteristic curves of both process steps are plotted together in a FUESTENAU upgrading diagram evaluating the recovery of valuables into concentrate versus the recovery of gangue into concentrate. Hereby, a comparable basis is obtained which allows the definition of new parameters describing the influence of liberation and separation on upgradeability. By case studies of lab based processing (comminution and magnetic separation) of two different types of ores, the applicability of this method is shown. Based on this, advantages as well as limits of the method and parameters are discussed.

2 1 Introduction The upgradeability of valuables is dependent on their liberation from gangue minerals and particle size (upstream grinding steps) as well as on the separation features of the minerals (e.g. density, magnetic susceptibility, wettability ). Besides, the features of the material upgradeability is also dependent on the parameters of the separating machines (Drzymala, 27b). An exact evaluation of upgrading processes has to consider all of these influences. A large variety on parameters describing liberation (Bérubé and Marchand, 1984; Dell, 1969; Gaudin, 1939; Hsih, 1994) or the result of separation processes (Drzymala, 26, 27a, 28; Schulz, 197; Steiner, 1964) can be found in literature. None of these curves and parameters were used to evaluate the result of separation processes with regard to the materials inherent liberation distribution. This is due to the lack of powerful methods to measure the liberation distribution in the past. The first approach to consider the mineral liberation taken from image analysis was published by Finch and Gomez (1989). They used a plot of the parameter η, which is the difference from valuables recovery ( 1,c ) and gangue recovery ( ) known as HANCOOK-index, versus 1,c. This allows to find the maximum technical efficiency based on the separation feature used to virtually sort the particles. Miller and coworkers (29) used grade-recovery-curves from computer tomography and added results from separation test work. Unfortunately no parameter can be calculated based on this approach. Therefore, evaluation is limited to verbal description. A way to overcome this lack of comparable parameters describing the success of liberation as well as the success of separation can be made by using equal basis upgrading curves (Drzymala, 27b), whereby the liberation distribution (mineralogical limiting curve) based on the separation criterion (Finch and Gomez, 1989) is plotted together with upgrading curves. One model which can be used was published as early as 1966 by Helfricht (1966). This model later was transferred by Tolke (197) to an equal basis upgrading curve suggested by Steiner (1964). The following article describes the use of SEM-based liberation analysis (Sutherland and Gottlieb, 1991) combined with lab based results from studies on mineral properties (magnetic susceptibility) and magnetic separation test work for the assessment of upgrading with regard on both liberation distribution and separator performance. This is done using case studies on the lab based processing (comminution, classification and magnetic separation) of two different ores. A detailed description of the model (Leißner et al., 213; Leißner et al., 214), the method used for stereological correction (Lin et al., 1995) and the mathematical equations used to fit upgrading curves (Drzymala and Ahmed, 25) is given together with a critical discussion of chances and limits of this approach. 2 Material and Methods 2.1 Material Two different types of materials were studied to evaluate the applicability of the model. Greisen-type ore The greisen-type ore origins from the polymetallic (Li-Sn) greisen deposit of Zinnwald/Cínovec located in the eastern Ore Mountains at the German-Czech border. Sample material used in this

3 valuables recovery, 1,c / % perfect separation study was obtained from a large bulk sample, about 2 t in weight, collected underground in the old mine workings of the Zinnwald/Cinovec deposit. This greisen-type ore comprises of around 67 % quartz, 2 % zinnwaldite, 8 % topaz, 3 % muscovite, and 2 % others (Leißner et al., 212). The valuable mineral is the lithium bearing mica zinnwaldite. Zinnwaldite is known to have the chemical composition: KLiFe 2+ Al(AlSi 3 )O 1 (F;OH) 2, with a corresponding lithium content of ca wt.% (Anthony et al., 211). Zinnwaldite has a considerable content of iron of wt.% (Platonov et al., 29; ieder et al., 197). This iron results in a magnetic susceptibility of zinnwaldite high enough to enable a separation in a magnetic field from both quartz and topaz. Nepheline-syenite The nepheline-syenite origins from the Norra Kärr deposit located in the south-eastern part of Sweden. A nepheline-syenite sample of around 4 kg ore was comminuted in the facilities of UV-FIA GmbH Freiberg and handed to the authors for further processing and studies. Nepheline-syenite is an igneous rock free of quartz (Le Bas and Streckeisen, 1991). The sample material mainly comprises of around 4 wt.-% feldspar, 22 wt.-% aegirine, 15 wt.-% zeolite, 9 wt.-% nepheline, 8 wt.-% eudialyte and 21 wt.-% others. The mineral of interest is the EE containing mineral eudialyte, which can be enriched by magnetic separation and flotation (Ferron and awling, 1993; udolph and Peuker, 214). The main paramagnetic minerals are pyroxenes, namely aegirine and augite and the EE containing mineral eudialyte. More detailed information about the deposit and the material can be found in (Bluemel et al., 213; Guillet, 1994; Sjöqvist et al., 213). 2.2 Model and remixing t( ) u( ) locking curve s( ) upgrading curve gangue recovery, / % Figure 1: Fuerstenau-II-diagram showing the theoretical limits together with a locking and an upgrading curve. The model used in this investigation is based on the comparison of areas enclosed by curves in a plot of valuables recovery versus gangue recovery (Figure 1) known as Fuerstenau-II-curve (Drzymala, 27b) which harks back to the work of Helfricht (1966), Steiner (1964) and Tolke (197). These curves are the upgrading curve s( ), which are created by separation tests with

4 parameter variation, and the two limiting curves perfect mixture r( ) and perfect separation with remixing t( ). Due to the lack of powerful methods for liberation analysis in the past, this model was limited to the comparison of the upgrading curve to the theoretical limit given by the perfect separation and remixing. As the feed of a separation is characterized by its liberation distribution, the theoretical limit for process upgrading valuables is defined by the locking curve u( ). Using modern SEM-based devices for liberation analysis the model can be refined by adding a locking curve (Leißner et al., 213). This enables the definition of two parameters describing the influence of the upstream grinding (ratio of liberation, B lib ) as well as the separator performance on the upgrading of valuables (ratio of separation, B sep ). and u( )d r( )d u( )d 5 B lib (1) 5 t( )d r( )d sep s( u( )d )d r( r( )d )d s( u( )d )d 5 B (2) 5 The combination of the liberation parameter and the separation parameter (Equation 3) leads to the overall upgrading parameter B which follows the postulation of Finch and Gomez (1989), that an efficiency should take regard to both processes. B (3) B lib B sep When these parameters are measured on size-classed materials their evolution with particle size can be studied. Furthermore, a combination of mineral liberation data with physical properties of the minerals enables the creation of mineralogical limiting curves with regard to the separation criterion, used in downstream concentrators. Similar models to the one of Helfricht (1966) and Tolke (197) using areas enclosed by limiting curves for the assessment of separation can be found in Govindarajan and ao (1994) and Mohanty et al. (1999). Beside the model introduced above, the approach of Finch and Gomez (1989) can be used in a similar way. The main difference to the model described above origins from the evaluation based on a single point of the liberation distribution compared to the HANCOOK-index of a single separation test using defined parameters. 2.3 Procedure The model, the experimental procedure and the steps for data processing used, can be visualized by the scheme in Figure 2. Common lab tests on the separation with varying parameters were performed to get the points of the upgrading curve. A smooth curve can be created out of these points by using a valid function taken from literature (Drzymala and Ahmed, 25).

5 1,c / % Mineralogical limiting curves related to the type of separation process can be created when the compositional data of each individual particle measured during liberation analysis is combined with the features separation is based on. In the case of magnetic separation this feature is the magnetic susceptibility ( g ) of the minerals (Bleil and Petersen, 1982; Carmichael, 199; Hunt et al., 1995) the particle is composed of. Such features can either be measured in laboratory (if possible) or taken from literature (if being tabulated). When two-dimensional methods for liberation analysis are used, the data inhibits the so called stereological bias. Therefore, a suitable stereological correction procedure should be used. Software lab tests with parameter variation + chemical analysis 8 6 literature, lab tests, analysis individual particle n g w i g, i1 mineral liberation analysis i 4 2 locking curve upgrading curve / % stereological correction fit function Figure 2: Experimental procedure for the generation of experimental data and data processing. 2.4 Experimental Sample preparation ore comminution sieving size class 1 size class 2 size class n magnetic separation mag. fraction 1 mag. fraction 2 mag. fraction n Figure 3: Schematic flow sheet of the lab-based processing.

6 The scheme showing the principle design of experiments of this study is given in Figure 3.The ores have been ground to a defined upper particle size and then sized into different classes (cf. Table 1). Each size class was analyzed on its particle composition distribution (MLA), its chemical composition (ICP-OES) and its magnetic susceptibility (MSB). Two different types of magnetic separators, a ring-type separator and an isodynamic separator similar to the Frantztype one (McAndrew, 1957), were used to study the upgrading of magnetic components. After magnetic concentration each fraction was given to chemical analysis and susceptibility measurement. Table 1: Overview of studied samples and the machine settings used for the experiments Greisen-type ore Pin mill, x o = 3.15 mm -.1 /.1-.2 / / /.5-.8 /.8-1. / Analysis: MLA, ICP-OES, MSB Nepheline-syenite Grinding Screen discharge ball mill, x o = 2. mm Size classes (mm) -.63 / / / /.5-1. / Analysis: MLA, ICP-OES, MSB Magnetic separation: ring-type separator (2. mm gap) -.1 /.1-.2 / / / / / /.5-.8 / Analysis: ICP-OES, MSB Analysis: ICP-OES, MSB Magnetic separation: isodynamic separator (side slope 14, longitudinal slope 25 ) -.1 /.1-.2 / / / /.5-.8 Analysis: ICP-OES, MSB Analysis: MLA, MSB Liberation measurement Particle composition data was generated at the Geometallurgy Laboratory at Technische Universität Bergakademie Freiberg using a Mineral Liberation Analyzer. The MLA comprises a FEI Quanta 65F SEM (FE-SEM) equipped with two Bruker Quantax X-Flash 53 EDX detectors and FEI s MLA suite for data acquisition. Identification of mineral grains by MLA is based on backscattered electron (BSE) image segmentation and collection of EDXspectra of the particles and grains distinguished in BSE-imaging mode. In this study GXMAP measurements were carried out on subsamples of around 3 g mounted in epoxy blocks of 3 mm in diameter. Detailed information on the measurement setup is provided in (Leißner et al., 216a; Leißner et al., 216b) information about the functionality of the MLA system can be found in Fandrich et al. (27) and Gu (23), a description of the exact analytical procedure is provided by Sandmann & Gutzmer (213) Stereological correction aw data from MLA does not comprise stereological correction. As true stereological correction is a complex problem, which needs to be adjusted to the material (Barbery, 1991; Fandrich et al., 1998; King and Schneider, 1998), a simple way to reduce the influence of the stereological bias was used. Stereological correction procedures have been tested by various authors (Lätti and Adair, 21; Lin et al., 1994, 1995; Lin et al., 1999; Spencer and Sutherland, 2). It can be taken from literature, that when size classed material is analyzed, an exclusion of particles sliced outside its center (evidently to small) can help to significantly reduce the

7 influence of the stereological bias on the liberation distribution (Lin et al., 1995; Lin et al., 1999). This procedure is known as large section correction (LS). The LS was applied to the data comparing the particle dimension length-mb (length of a minimum bordering rectangle) with the 9 percent mesh size of the sieves as a knock-out criterion Chemical analysis For chemical analysis the samples were digested and measured with a Thermo Fisher icap63 inductive coupled plasma optical emission spectrometer (ICP-OES). Therefore, around 1 g of material were split out of the bulk samples and ground to % passing 63 µm. Aliquots of around mg were then digested with a mixture of hydroflouric acid (HF) and nitric acid (HNO 3 ) 1:2, diluted and handed to ICP-OES. In the case of the greisen-type ore the elements Al, K, Fe and Li were measured. The concentration of Li was used to calculate the zinnwaldite grade of the greisen samples. In case of the nepheline-syenite the measurement was focused on the elements Al, Ca, Fe, K, Mg, Mn, Na and Zr. The grades of the main magnetic minerals were calculated using the elements Mn (Eudialyte), Fe (Aegirine) and Mg (Aegirine-Al) Magnetic susceptibility measurement For magnetic susceptibility measurements three subsamples of 35 to 4 mg were taken out of the bulk samples and analyzed using a Johnson Matthey MSB MK II auto. Each subsample was analyzed three times, whereby the whole measurement procedure was repeated. Overall, the magnetic susceptibility of a sample is thus based on 9 individual measurements. 3 esults and Discussion 3.1 Magnetic susceptibility In magnetic separation the magnetic susceptibility of the particles is the main feature defining weather a particle is recovered into concentrate or rejected into tailings. This particle susceptibility is made up of the mineral susceptibilities by mass and their weight fraction in this particle (equation 4) (McAndrew, 1957). n mi g g, i (4) m i1 total If the magnetic susceptibilities of all minerals of an ore are known, they can be combined with particle composition data provided by MLA. Unfortunately magnetic susceptibilities are rarely tabulated (Bleil and Petersen, 1982; Carmichael, 199; Hunt et al., 1995; osenblum and Brownfield, 1999) and furthermore vary with chemical composition of the minerals (Fraas, 1964; Vernon, 1961). Consequently, the magnetic susceptibility of the main minerals as well as of the minerals showing strong paramagnetic behavior should be studied on the ore trying to process. In Figure 4 the relation of zinnwaldite grade and magnetic susceptibility of samples from the greisen-type ore are put together. It can be seen that there is a difficult relation between the sample composition and its magnetic susceptibility. Once a particle comprises of more than two

8 Magnetic susceptibility, χ g / 1-9 m³/kg minerals, a particle susceptibility value can created by various particle compositions (cf. equation 4) Quartz, Topaz Muscovite Limonite Zinnwaldite ,1 (.1) mm mm,1,2 (.1.2) mm,2,315 (.2.315) mm,315,5 (.315.5) mm,5,8 (.5.8) mm Zinnwaldite grade, c zin / % Figure 4: Magnetic susceptibility as a function of zinnwaldite grade shown for the size classes of the greisen-type ore. From the point of magnetic separation, the mineralogy of the greisen-type ore is not to complex. A determination of the magnetic susceptibilities of the main minerals can therefore be achieved by chemical analysis and susceptibility measurements (Chehreh Chelgani et al., 215). It can be taken from Figure 4 that there seems to be a size dependent relation of composition and magnetic susceptibility. This is due to the anisotropy of magnetic susceptibility of zinnwaldite (Litovchenko et al., 1982) and muscovite (Martıń-Hernández and Hirt, 23) and the measurement procedure used in this study (Leißner et al., 216a). In case of the complex mineralogy of the nepheline-syenite this approach was not successful. An alternative way to investigate the mineral susceptibility therefore was developed. When a bulk sample is separated into classes of different magnetic susceptibility and composition, equation 4 can be rewritten in form of a system of equations (equation 5). w11, w1,i m,1 m,1 w j,1 w j, i m, i m, j (5) A x b (6) The lines of the matrix A describe the sample composition, the vector b describes the samples magnetic susceptibility. A can be obtained by mineralogical analysis, b can be measured directly using a magnetic susceptibility balance. The magnetic susceptibilities of the minerals inside a sample can be calculated by solving the system of equations. To obtain a unique solution as much equations are needed as unknown susceptibilities exist. Otherwise special statistical methods are needed for this purpose (Matos Camacho et al., 215). This was done for the nepheline-syenite (Matos Camacho et al., 215) using MLA and susceptibility measurements. In comparison with literature data, the calculated mineral susceptibilities were then combined with the MLA data of the separator feed.

9 Grade, c 1,c / % Valuables recovery, 1,c / % 3.2 Liberation distribution Mineralogical limiting curves are based on the liberation distribution of the components supposed to be upgraded in downstream separation. Commonly the limiting curves are created using the grade of the particles instead of using the particle feature separation is sensitive to. The effect of changing the criterion the limiting curves is generated by is shown in Figure 5. The theoretical limit no separation process can exceed, no matter what the separation feature is, is given by the limiting curve based on the grade of particles. The more suitable the feature used for separation is to upgrade the minerals of interest, the closer the curve created using the separation feature is to the curve created using the grade of the particles. Two helpful information can be taken out of this: 1. Calculation B lib based on limiting curves generated with different particle features can be used to assess, which feature will be the best to upgrade the minerals of interest with regard to the particle composition distribution. 2. When a specific separation process is used for upgrading, the separation feature should be taken to generate the limiting curve particle grade particle susceptibility particle density particle grade particle susceptibility particle density Valuables recovery, 1,c / % Gangue recovery, / % Figure 5: Zinnwaldite grade versus recovery (left) and Fuerstenau-II diagram (right) of the size fraction (.315.5) mm from the greisen-type ore showing curves generated using different particle features. 3.3 Stereological correction Figure 6 shows the liberation distribution of two selected size fractions from both materials. As expected, the LS correction mainly reduces the amount of high grade and liberated particles. That is why such sections are generated by particles not sliced centrically locking free but being locked (Barbery, 1991; Jones and Shaw, 1974). When these particles erroneously locking liberated are eliminated from the data, the liberation distribution will change in the direction of locked particles. Thus, the theoretical limit for upgrading will change slightly to less good upgradebility. With regard to the parameters defined above, B lib will decrease (equation 1) whereas B sep increases (equation 2) and their product B (equation 3) remains the same.

10 fraction, 1,i / % fraction, 1,i / (%) Zinwaldite locking (greisen-type ore) Eudialyte locking (nepheline-syenite) 12 (.2.315) mm ( ) mm Original Large-Section 1 8 Original Large-Section grade fractions grade fractions Figure 6: Liberation distributions of zinnwaldite in the greisen-type ore (size class ( ) mm), left hand side and of eudialyte in the nepheline-syenite (size class ( ) mm) right hand side. The LS correction can only be applied to samples having a defined lower particle size. The smallest size fractions of both ores lack of a lower size limit. Consequently, no LS correction was applied to these fractions. 3.4 Upgrading curves The parameters to assess upgrading are calculated using the integral of the curves between and percent. Therefore, a suitable mathematical function is needed to approximate the results from separation tests. A large number of approximation functions can be found in literature (Drzymala and Ahmed, 25). These functions are compiled for the Fuerstenau-I plot ( 1,c versus the recovery of gangue into tailings, 2,t ). By using the relation 2, c % 2, t the approximation functions have been transferred to the Fuerstenau-II plot and applied to the data. Based on a statistical evaluation of a large number of approximation functions the equation 6 was found to be most suitable. a a b 1,c (6) ab1 Figure 7 shows the approximation of equation 6 on the results from separation test work with the ring-type separator of two different size classes from the nepheline-syenite. Besides a good correlation (high ²) a physical meaningful shape of the function is needed. Some functions tested also showed high ² but crossed the locking curve ore exceeded values of percent 1,c. In the latter case a piecewise definition of the approximation function can help to get a physical meaningful shape. Anyway, the choice for one approximation function must not be done just on the basis of the ² value.

11 parameter / % parameter / % 1,c / % 1,c / % ( ) mm a = 11,2949 b =,5829 ²= ( ) mm a = 3,51861 b =,56115 ²= / % / % Experimental results Approximation function Locking curve Figure 7: Fuerstenau-II plot showing the locking curve, the points from separation tests with the ring-type separator and the approximation function (equation 6) as well as their parameters a and b for two different size classes of the nepheline-syenite. As far as transformations to other upgrading diagrams are needed, the approach of Duchnowska and Drzymala (211) can be used. Note that equal basis upgrading diagrams should be used if variations in feed grade are expected (Drzymala, 26, 27a, 28). 3.5 Process parameters The final results of the study are displayed in the diagrams of Figure 8 for the greisen-type ore and in Figure 9 for the nepheline-syenite. Upgrading of zinnwaldite from the greisen-type ore shows good results over a broad range of particle size. The minerals inside the ore are relatively coarse grained (mean grain sizes > 1 mm) which leads to high values in liberation below 1 mm ring-type separator particle size, x / mm isodynamic separator particle size, x / mm Aufschluss liberation, B lib Sortierung separation, B sep Anreicherung upgrading, B Figure 8: Process parameters of the greisen-type ore describing the upgrading of zinnwaldite using a ring-type separator (left) and an isodynamic magnetic separator (right). Separation of the magnetic components of the ore works very good even at coarse particle sizes. The decrease in the separation parameter at the coarse end is lower than for the liberation

12 parameter / % parameter / % parameter. At the fines end of the diagram the performance of separation is insufficient due to increasing influence of particle interactions. Agglomerates of valuables and gangue get recovered into concentrate as far as the agglomerate susceptibility is high enough. Otherwise valuables get lost into tailings. This causes a strong decrease in the separation parameter. Deagglomeration works better in the isodynamic separator, whereby the decrease in the separation is lower compared to the ring-type separator ring-type separator particle size, x / mm isodynamic separator particle size, x / mm Aufschluss liberation, B lib Trennung separation, B sep Anreicherung upgrading, B Figure 9: Process parameters of the nepheline-syenite describing the upgrading of eudialyte using a ring-type separator (left) and an isodynamic magnetic separator (right). The curves for the nepheline-syenite differ from the ones of the greisen-type ore, which is related to different mineral grain sizes in both materials. Anyway the principle insight is similar. As expected the parameters describing liberation and separation increase with decreasing particle size. A good upgrading of the valuables by magnetic separation can be achieved below.25 mm. Separation works good also at coarse particle sizes. This may help to design a preconcentration of magnetic components before an additional grinding to improve liberation and a final concentration (e.g. flotation). The upgrading of the fines fraction below.63 mm was not studied, therefore a decrease in the separation parameter caused by increasing particle interactions cannot be shown for this material. 2 4 Conclusions This article describes a method for the assessment of upgrading with regard to the liberation distribution and the performance of the separator used for upgrading. All steps required to generate the curves and parameters for the assessment using the model have been shown and discussed. On the grinding and magnetic separation of two different ores the applicability of the approach was proved. Using size classed material during the investigation, the evolution of the model parameters with particle size was shown. It has to be mentioned that the generation of all information required to use the approach is time consuming. Nevertheless the unique quality of information obtained is believed to be worth the effort. Besides this model a particular use of single parameters like the ratio of liberation B lib can be done. A first successful implementation of the newly introduced liberation parameter on the grinding of an iron ore was already been done by eichert (214).

13 Acknowledgements esearch for this study was mainly performed at the research groups of Mineral Processing at the Institute of Mechanical Process Engineering and Mineral Processing, TU Bergakademie Freiberg and Helmholtz-Zentrum Dresden-ossendorf, Helmholtz-Institute Freiberg for esource Technology. It was supported and benefited from numerous discussions and measurements by Petya Atanasova. The Authors also like to thank the Federal Ministry of Education and esearch for the funding of the project Hybride Lithiumgewinnung (3WKP18A). Furthermore, the authors are particularly indebted to Tasman Metals Ltd. for providing rock samples and useful information about the Norra Kärr deposit. eferences Anthony, J.W., Bideaux,.A., Bladh, K.W., Nichols, M.C., 211. Handbook of Mineralogy, Chantilly, VA , USA. Barbery, G., Mineral Liberation Measurement, Simulation and Practical Use in Mineral Processing, Québec, Canada. Bérubé, M.A., Marchand, J.C., Evolution in the mineral liberation characteristics of an iron ore undergoing grinding. International Journal of Mineral Processing 13, Bleil, U., Petersen, N., Magnetic properties of natural minerals, in: Angenheister, G. (Ed.), Landolt-Börnstein - Group V Geophysics, pp Bluemel, B., Leijd, M., Dunn, C., Hart, C.J.., Saxon, M., Sadeghi, M., 213. Biogeochemical expression of rare earth element and zirconium mineralization at Norra Kärr, Southern Sweden. Journal of Geochemical Exploration 133, Carmichael,.S., 199. Practical Handbook of Physical Properties of ocks and Minerals. CC Press, Inc. Chehreh Chelgani, S., Leißner, T., udolph, M., Peuker, U.A., 215. Study of the relationship between zinnwaldite chemical composition and magnetic susceptibility. Minerals Engineering 72, Dell, C.C., An expression for the degree of liberation of an ore. Transactions of the Institution of Mining and Metallurgy, Section C: Mineral Processing and Extractive Metallurgy 78, C89. Drzymala, J., 26. Atlas of upgrading curves used in separation and mineral science and technology. Physicochemical Problems of Mineral Processing 4, Drzymala, J., 27a. Atlas of upgrading curves used in separation and mineral science and technology (Part II). Physicochemical Problems of Mineral Processing 41, Drzymala, J., 27b. Mineral Processing, Foundations of theory and practice of minerallurgy. Oficyna Wydawnicza PWr. Drzymala, J., 28. Atlas of upgrading curves used in separation and in mineral science and technology: Part III. Physicochemical Problems of Mineral Processing 42, Drzymala, J., Ahmed, H., 25. Mathematical equations for approximation of separation results using the Fuerstenau upgrading curves. International Journal of Mineral Processing 76, Duchnowska, M., Drzymala, J., 211. Transformation of equation y=a(-x)/(a-x) for approximation of separation results plotted as Fuerstenau's upgrading curve for application in other upgrading curves. Physicochemical Problems of Mineral Processing 47, Fandrich,., Gu, Y., Burrows, D., Moeller, K., 27. Modern SEM-based mineral liberation analysis. International Journal of Mineral Processing 84, Fandrich,.G., Schneider, C.L., Gay, S.L., Two stereological correction methods: Allocation method and kernel transformation method. Minerals Engineering 11,

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