Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

The application of Laser Induced Breakdown Spectroscopy sensor system for real time ore classification Cordova Torres, Rodrigo Fernando 2017

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
24-ubc_2017_february_cordovatorres_rodrigofernando.pdf [ 5.88MB ]
Metadata
JSON: 24-1.0340689.json
JSON-LD: 24-1.0340689-ld.json
RDF/XML (Pretty): 24-1.0340689-rdf.xml
RDF/JSON: 24-1.0340689-rdf.json
Turtle: 24-1.0340689-turtle.txt
N-Triples: 24-1.0340689-rdf-ntriples.txt
Original Record: 24-1.0340689-source.json
Full Text
24-1.0340689-fulltext.txt
Citation
24-1.0340689.ris

Full Text

THE APPLICATION OF LASER INDUCED BREAKDOWN SPECTROSCOPY SENSOR SYSTEM FOR REAL TIME ORE CLASSIFICATION   by  Rodrigo Fernando Cordova Torres  B.Sc. (Mining Engineering) University of Utah, 2012  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Mining Engineering)  UNIVERSITY OF BRITISH COLUMBIA (Vancouver)   December 2016  © Rodrigo Fernando Cordova Torres 2016 ii  Abstract Laser Induced Breakdown Spectroscopy (LIBS) is a geoanalytical tool capable of identifying elements, and measuring element concentrations and the composition of rock samples. LIBS is a method based on a laser energy pulse that creates an ablation in the surface of a rock sample and the ionization of photons to produce a breakdown of the sample’s elemental composition. The ionization process can be captured to produce a spectrum that contains information about elemental composition. The wavelength is used to identify elements, and its intensity peaks are used to identify the concentrations of the element.  The mining production cycle involves such processes as rock support, drilling, blasting, loading, hauling, dumping, reclamation and ventilation, depending on the mining method. Although pre-sorting, pre-concentration and classification techniques have been applied to aspects of mineral processing after the mining cycle, this research proposes the use of LIBS in the mining cycle, and defines the basic capabilities of a sensor with potential applications in the drilling and loading cycle, particularly with respect to shovels, drills and belt conveyors.  The purpose of LIBS is not to provide an accurate measurement of the target mineral, which in this research is Copper ore, but responses from different elements that can be mineralogically and statistically related to obtain a predicted concentration of the target mineral. In this paper, the methodologies and the foundations of LIBS have been developed as a sensor and proxy to an ore sorting system for the real-time in situ classification of rock material.  The research is based on samples from the Escondida Mine located in the north of Chile. The samples are divided into groups of Oxides and Sulphides. The results reveal the ability to predict Oxides, Sulphides and the discrimination of Oxide and Sulphide ores. The prediction regarding the target ores is obtained by comparing the LIBS data to Certified Analysis with ICP iii  techniques. The results include models for the prediction of Cu content for Oxides and Sulphide ore types by LIBS analysis, as well as the discrimination of Oxide ores from Sulphide ores using this technology.  iv  Preface This dissertation is an original intellectual product of the author, Rodrigo Fernando Cordova Torres. The laboratory results reported in Chapter 3:, Chapter 4: and Chapter 5: were obtained at Minesense Ltd. facilities in Vancouver, Canada.    v  Table of Contents Abstract .......................................................................................................................................... ii Preface ........................................................................................................................................... iv Table of Contents ...........................................................................................................................v List of Tables ................................................................................................................................ ix List of Figures .............................................................................................................................. xii List of Abbreviations ...................................................................................................................xv Acknowledgements .................................................................................................................... xvi Dedication .................................................................................................................................. xvii Chapter 1: Introduction and Thesis Outline ...............................................................................1 1.1 Motivation ....................................................................................................................... 1 1.2 Former research work done with LIBS in the mining industry ...................................... 2 1.3 Significance of the research ............................................................................................ 3 1.4 Outline............................................................................................................................. 4 Chapter 2: Laser Induced Breakdown Spectroscopy Background ...........................................6 2.1 What is LIBS? ................................................................................................................. 6 2.2 Wavelengths .................................................................................................................... 8 2.3 Apparatus Fundamentals ................................................................................................. 9 2.4 Importance of the Diffraction Grating .......................................................................... 11 2.4.1 Young’s Double Slit example ................................................................................... 11 2.4.2 Diffraction grating calculation .................................................................................. 14 2.5 LIBS machine specifications ........................................................................................ 16 2.6 White colouring problem .............................................................................................. 17 vi  Chapter 3: Experimental Approach...........................................................................................18 3.1 Experimental design...................................................................................................... 19 3.1.1 Project Initiation: LIBS Identification and Calibration ............................................ 19 3.2 Geology and Geochemistry of Escondida Mine Rocks for Correlation ....................... 21 3.3 LIBS correlation............................................................................................................ 23 3.4 Main problems expected when using LIBS as an ore sorter ......................................... 24 3.4.1 White colouring problem solution approach............................................................. 24 3.4.2 Spectrum analysis ..................................................................................................... 25 3.5 Sulphide samples difficult to read with LIBS ............................................................... 26 3.6 Identification of Wavelength List ................................................................................. 29 3.7 The Python Script ......................................................................................................... 34 3.8 Technical potential ........................................................................................................ 35 3.9 The Pearson Correlation ............................................................................................... 36 3.10 Confidence level over technical potential ..................................................................... 36 Chapter 4: Analysis of Oxide Rock Samples with Laser Induced Breakdown Spectroscopy .................................................................................................................................39 4.1 Data integration and analysis ........................................................................................ 42 4.2 Regression Analysis for the Oxide Rocks .................................................................... 42 4.3 Correlation of LIBS Cu Oxides response to ICP analysis ............................................ 42 4.4 Element regression analysis for Oxide samples............................................................ 46 4.5 Interaction effect analysis using multilinear regression analysis for Oxide samples ... 53 4.6 First procedure run analysis for the regression for Oxide samples ............................... 57 4.7 Second procedure run analysis for the regression......................................................... 59 vii  4.8 Proposed Method A ...................................................................................................... 60 4.9 Proposed Method B....................................................................................................... 65 4.9.1 Quantification of the number of responses ............................................................... 66 4.9.2 Final correlation for the Oxide samples .................................................................... 70 Chapter 5: Analysis of Sulphides with Laser Induced Breakdown Spectroscopy .................75 5.1 Correlation of LIBS Cu Sulphide response to ICP analysis ......................................... 76 5.2 Element correlation for LIBS responses for Sulphide samples .................................... 78 5.3 Interaction effect analysis using multilinear regression analysis for Sulphide samples 80 5.4 First procedure run analysis for the regression of Sulphide samples ............................ 83 5.5 Second procedure run analysis for the regression of Sulphide samples ....................... 84 5.6 Proposed correlation of Sulphide samples .................................................................... 85 Chapter 6: Sulphide versus Oxide discrimination ....................................................................90 6.1 Spectroscopy ambiguity regarding S III and O III for our LIBS machine ................... 90 6.2 Spectroscopy and observation of multiple strong lines ................................................ 91 6.3 Definition of the spectrum for Oxides and Sulphides ................................................... 94 6.4 Proposed solution for Oxide/Sulphide recognition using LIBS ................................... 97 Chapter 7: Discussion and recommendations .........................................................................100 7.1 Data quality and confidence........................................................................................ 100 7.1.1 Identification of elements and concentration recommendations ............................ 101 7.2 LIBS data acquisition and architecture ....................................................................... 102 7.3 LIBS statistics and repeatability analysis ................................................................... 104 7.4 LIBS future developments .......................................................................................... 105 Chapter 8: Conclusion ...............................................................................................................109 viii  Bibliography ...............................................................................................................................111 Appendices ..................................................................................................................................113 Appendix A Compiled LIBS responses for Oxide rock samples from Escondida Mine ........ 114 Appendix B ICP certified assay results for the 41 Oxide Escondida samples........................ 119 Appendix C Python Script for the processing of LIBS responses .......................................... 125 Appendix D Python Script for the multiplication of the LIBS responses............................... 130 Appendix E Number of responses per sample for each ion for the Oxide samples ................ 131 Appendix F Compiled LIBS responses for Sulphide rock samples from Escondida Mine .... 136 Appendix G Number of responses per sample for each ion for the Sulphide samples ........... 141 Appendix H ICP certified assay results for the 41 Sulphide Escondida samples ................... 146 Appendix I Details regarding the Python Script ..................................................................... 152 Appendix J Details of methodology and data treatment or the Oxide samples ...................... 154  ix  List of Tables  Table 2-1: Specification of FiberLIBS for its spectrometer ......................................................... 10 Table 2-2: Specifications for average spectrometers used in the construction of LIBS sensors .. 14 Table 2-3: Harmonic calculation for the grating ........................................................................... 15 Table 2-4: Laser specification for FiberLIBS ............................................................................... 16 Table 2-5: Spectrometer specification for FiberLIBS .................................................................. 16 Table 3-1: Summary of Mineralogy of Escondida Mine by Mineralogical Groups and Elements....................................................................................................................................................... 21 Table 3-2: Accuracy for transition strength .................................................................................. 31 Table 3-3: Weighting factors ........................................................................................................ 31 Table 3-4: Example of the database and the classifications of the ratings ................................... 32 Table 3-5: ID Wavelength proposed for the LIBS machine used in this research ....................... 33 Table 3-6: Extraction of the spectrum data from LIBS ................................................................ 34 Table 3-7: Technical potential summary ...................................................................................... 35 Table 3-8: Technical potential summary skewed by Certified ICP Analysis ............................... 35 Table 3-9: Confidence levels for technical potential to detect elements ...................................... 37 Table 4-1: Output of Python Scripts for the Oxide samples from Escondida Mine (Wavelength are in nm). ........................................................................................................................................... 41 Table 4-2: Results of regression analysis over LIBS responses ................................................... 46 Table 4-3: Selected elements for regression analysis ................................................................... 48 Table 4-4: ICP Cu vs Predicted Cu values in ppm ....................................................................... 50 Table 4-5: Histogram data of the 41 Oxide samples..................................................................... 52 x  Table 4-6: Truth Table using AND logic ...................................................................................... 54 Table 4-7: Extract of binomial multiplication of the ion responses from LIBS ........................... 55 Table 4-8: Extract of the square root of the binomial multiplication of the ion responses........... 56 Table 4-9: Results of the first run using Stepwise Fit regression in MATLAB for Copper ......... 58 Table 4-10: Second run using Stepwise Fit regression in MATLAB ........................................... 59 Table 4-11: Results for correlation for Oxide rocks ..................................................................... 61 Table 4-12: Final prediction equation for Predicted Copper ........................................................ 62 Table 4-13: Extraction of the quantification process for the binomials........................................ 67 Table 4-14: Summary of number of responses for the 41 Oxide samples .................................... 68 Table 4-15: Number of occurrences for the binomials analyzed .................................................. 69 Table 4-16: Weighting of the binomials ....................................................................................... 69 Table 4-17: Final correlation for Copper Oxides .......................................................................... 71 Table 5-1: Extraction of the output of the Python Script for the Sulphide samples ..................... 75 Table 5-2: Predicted Copper correlation using ions for Sulphide samples ................................... 78 Table 5-3: Binomial correlation for Sulphide samples with maximum 0.05 p-value ................... 81 Table 5-4: Stepwiselm output using the Sulphide ion responses .................................................. 82 Table 5-5: Correlation output for variables computed with 0.07 p-value ..................................... 82 Table 5-6:   Results of the first run using Stepwise Fit regression in MATLAB for Sulphide samples....................................................................................................................................................... 83 Table 5-7: Results of the second run using Stepwise Fit regression in MATLAB for Sulphide samples .......................................................................................................................................... 84 Table 5-8:  Binomial correlation for Sulphide samples with maximum 0.08 p-value .................. 85 Table 5-9: ICP Cu vs Predicted Cu values for Sulphide samples in ppm..................................... 86 xi  Table 6-1: Spectroscopies for ambiguity between O III and S III ................................................ 92 Table 6-2: Extraction of Ionization Energies (eV) ....................................................................... 93 Table 6-3: Final results table for Oxide versus Sulphide recognition .......................................... 97 Table 7-1: Minimum number of readings using LIBS to calculate each of the interaction effects used for the prediction of Oxides ................................................................................................ 104 Table J-1: O V vs. As I key indicators for element selection ..................................................... 154 Table J-2: Arsenic ICP certified results for the 41 rock samples from Escondida Mine............ 155 Table J-3: Trace of Rhenium in Oxide sample in Escondida Mine ............................................ 156 Table J-4: Statistical analysis of the spectrum for sample 33B1, S3, 1 ...................................... 156 Table J-5: Statistical analysis of noise to recognize LIBS responses ......................................... 159  xii  List of Figures  Figure 2-1: LIBS machine used for this experiment: a FiberLIBS model (SECOPTA) ................ 6 Figure 2-2: Spectrochemical methods for the currently most used sample analysis methods in mining ............................................................................................................................................. 7 Figure 2-3: Diffraction grating schematic (Fleischer) .................................................................... 8 Figure 2-4: Electromagnetic spectrum for light sources (Cyberphysics group) ............................. 9 Figure 2-5: Basic schematic of a LIBS machine .......................................................................... 10 Figure 2-6: Schematic of LIBS spectrometer (Rehse) .................................................................. 11 Figure 2-7: How the spectrum is generated in LIBS (Cremers and Radziemski) ........................ 13 Figure 2-8: Incident light beam over a grating (Ryer) .................................................................. 14 Figure 3-1: Escondida Mine samples. Left: sample #26 Oxide sample, Right: sample #12 Sulphide sample ........................................................................................................................................... 19 Figure 3-2: Twenty readings of Silica/Oxide sample spectrum from Escondida mine ................ 25 Figure 3-3: LIBS reading Sulphide samples from the top ............................................................ 26 Figure 3-4: LIBS reading Sulphide samples from the side ........................................................... 27 Figure 3-5: LIBS computer screen for Sulphide samples ............................................................. 28 Figure 3-6: LIBS computer screen for Sulphide sample #14 ....................................................... 28 Figure 3-7: Spectrum of pure Copper layer sample showing the characteristic peaks at 324.75 and 327.39 for Cu I .............................................................................................................................. 30 Figure 4-1: Characteristic Oxide sample spectrum processed with the Python script .................. 40 Figure 4-2: LIBS responses for Copper at wavelengths 324.75 and 327.39 vs ICP Cu (ppm) .... 43 xiii  Figure 4-3: LIBS responses for Copper at wavelengths 324.75 and 327.39 vs ICP Cu (ppm) with secondary axis ............................................................................................................................... 43 Figure 4-4: Correlation of Cu I at 324.75 nm ............................................................................... 44 Figure 4-5: Correlation of Cu I at 327.39 ..................................................................................... 45 Figure 4-6: Predicted Copper vs Certified ICP Copper (ppm) ..................................................... 49 Figure 4-7: ICP Cu vs Predicted Cu trending line along the 41 rock samples ............................. 50 Figure 4-8: Histogram of the 41 Oxide samples ........................................................................... 52 Figure 4-9: Standard Deviation dispersion of the predicted Copper ............................................ 53 Figure 4-10: Correlation equation for LIBS Copper responses .................................................... 63 Figure 4-11: Histogram for the correlation equation for LIBS Copper responses ....................... 64 Figure 4-12: Final correlation for Copper Oxides ........................................................................ 73 Figure 4-13: Histogram for the final correlation of Oxide samples.............................................. 74 Figure 4-14: Standard deviation for the final correlation of Oxide samples ................................ 74 Figure 5-1: LIBS responses for Copper ions for Sulphide samples .............................................. 77 Figure 5-2: Basic correlation between ICP Cu vs LIBS Copper ions responses .......................... 77 Figure 5-3: Predicted Copper correlation using ions for Sulphide samples ................................. 79 Figure 5-4: Final correlation for Sulphide samples ...................................................................... 87 Figure 5-5: Histogram for the final correlation for Sulphide samples .......................................... 89 Figure 5-6: Standard Deviation for the final correlation for Sulphide samples ............................ 89 Figure 6-1: Spectrum for Sulphide 1 ............................................................................................ 94 Figure 6-2: Spectrum for Oxide 12 ............................................................................................... 95 Figure 6-3: Spectrum for Sulphide 1 ............................................................................................ 95 xiv  Figure 6-4: Spectrum for Oxide 17 with characteristic wavelengths for Oxide/Sulphide definition....................................................................................................................................................... 96 Figure 6-5: Steel pointed at 393.42 nm ......................................................................................... 96 Figure 6-6: Steel spectrum with 393.42 nm wavelength peak ...................................................... 97 Figure 6-7: Final results table for Oxide versus Sulphide recognition ......................................... 99 Figure 7-1: Technical specifications for LIBS machine performance (Noll) ............................. 103 Figure 7-2: Neural Network Scheme for the Oxide samples using 10 neurons.......................... 106 Figure 7-3: Neural Network Fitting for Oxide rocks .................................................................. 106 Figure 7-4: Neural Network Diagram for Sulphide samples ...................................................... 107 Figure 7-5: Neural Network Fitting for Sulphide rocks.............................................................. 107 Figure J-1: Zoomed spectrum of sample 33B1,S3,1................................................................... 156 Figure J-2: Spectrum for sample 33B1, S3,1 .............................................................................. 158   xv  List of Abbreviations  Acc. - Accuracy Aki - Transition probability or Einstein Coefficient ASS - Atomic Absorption Spectroscopy CCD - Charged Coupled Plasma HFEMS - High Frequency Electro Magnetic Spectroscopy Hz - Hertz ICP - Induced Coupled Plasma ICP-AES - Induced Coupled Plasma Atomic Emission Spectroscopy ICP-MS - Induced Coupled Plasma Mass Spectroscopy ID - Identification l/mm - Lines per millimeter LIBS - Laser Induced Breakdown Spectroscopy mJ - Millijoule MW - Mega Watts NaN - Not a number NIR - Near Infra-Red NIST - National Institute of Standards and Technology nm - Nanometer ppm - Parts per million R - Pearson Coefficient SME - Society of Mining, Metallurgy and Exploration XRF - X-ray fluorescence     xvi  Acknowledgements  I would like to acknowledge the contributions of Dr. Michael Nelson, my former professor and the director of the Mining Department at the University of Utah, for sharing his previous work with LIBS sensors. I would also like to thank Dr. David Munoz Paniagua, for his academic supervision and support as an expert on Physical Chemistry. I am grateful to Minesense Technologies Ltd. for giving me the opportunity to work on their new potential technology for sorting sensors. I would also like to thank Mitacs for funding in conjunction with Minesense. I offer much gratitude to Dr. Andrew Bamber, and Dr. Bern Klein, my supervisor.  Furthermore, I would like to acknowledge to Matthew Dirks, a current Ph.D. student from the Computer Sciences Department for his support, training and ideas regarding Python Script and computer applications applied to LIBS. Finally, I would like to thank Michael McClintock for his continued support throughout the research process.  xvii  Dedication  I would like to dedicate this dissertation to Edgar Cordova and Mariela Torres, my parents and also engineers, because they have inspired me since childhood with a love for science and a passion to provide excellent service.  Also, I would like to share this thought:   “Every single organization, society, community in the world is responsible for developing their own technologies to secure their survival, no matter what their conditions or heritage are. Otherwise, they will perish.” Rodrigo Fernando Córdova Torres, 2016   To my beloved country: Peru1  Chapter 1: Introduction and Thesis Outline 1.1 Motivation  Laser Induced Breakdown Spectroscopy (LIBS) is an optical spectrochemical method used for the identification of elements. It has a wide variety of applications. LIBS produces a stimulated emission spectroscopy that uses a light beam laser and releases 2 or more photons, resulting in an ionization stage. This spectrochemical method produces a spectrum that is read by a Czerny-Turner monochromator, and is ultimately sent to a photodiode array. This array produces a readable spectrum with data that has been converted into peaks of Intensity (counts-units) on the y-axis and Wavelength (nm-units) on the x-axis.  Minesense Ltd. (the sponsor company for this current research) focuses on the use of sensors for ore sorting. Currently, the main sensor techniques used at Minesense are X-Ray Fluorescence (XRF) and High Frequency Electro Magnetic Spectroscopy (HFEMS). LIBS has been identified as potentially being highly complementary to these modes on account of its use of the direct measurement principle, as well as the superior range of elements that it can detect when compared with, for example, XRF. The ultimate goal of defining LIBS’ capabilities is to eventually integrate this technique as a possible sensor for ore sorting at Minesense. In this research, we will review a set of proposed methodologies with the aim of gaining a better understanding of the applications of the LIBS machine in its use as a sensor for sorting ore.  Some of the main challenges currently faced by the mining industry involve creating more effective processes to decrease energy consumption, decrease the costs of extraction, and develop techniques for mining mineral deposits that were not economically feasible in the past due to either their low grade or metallurgical complexity. The majority of the mineral deposits located close to the surface, and with high metal concentrations, have already been mined. As such, mineral 2  deposits of high complexity have been left underground, waiting for such a time that technology and other developments are advanced enough to allow the deposits to be economically feasible to mine. Ore sorting is a potential solution for the pre-concentration and classification of ores for more cost effective metallurgical extraction.   1.2 Former research work done with LIBS in the mining industry Several applications of LIBS have been developed for the mining industry such as monitoring grade concentrations, inline volume flow grade analysis of minerals on a belt conveyor, laboratory analysis, and during exploration using fast scanning (SECOPTA). However, no evidence regarding any previous work on LIBS sensors with respect to an ore sorting system in the mining production cycle could be found.  Significant research regarding LIBS applications in mining was conducted by APTI (now British Aerospace) in conjunction with Idaho National Laboratories and the University of Utah (Idaho Nationl Engineering & Environmental Lab, Bechtel BWXT). However, the purpose of work done at APTI was to develop an ore grading device, while the purpose of this research is to develop an automated proxy between the primary target ore and related mineralogy, in order to provide a response for the ore sorting system.  Other academic work has been conducted by the Italian National Research Council (G. S. Senesi) in “Laser-Induced Breakdown Spectroscopy applied to terrestrial and extraterrestrial analogue geomaterials with emphasis to characterize minerals and rocks.” This work provides a chemometric approach to the identification and concentration of elements in rock samples, and discusses the quality and quantity of the data obtained from LIBS in comparison to concentrations determined by chemical analysis.  3  1.3 Significance of the research This research provides an initial approach regarding the capabilities of LIBS as a sensor for the sorting of Copper porphyry ores. Ore sorting has been mostly applied to the mineral processing system. This research involves one of the first attempts to include sorting as part of the mining production system. The mining production system is defined in the “SME Mining Engineering Handbook” (Darling) as 10 tasks for surface mining and 8 tasks for underground mining. Primarily, these tasks can be summarized as rock support, drilling, blasting, loading, hauling, dumping, reclamation of the land, and ventilation for underground mining methods. In the mining production cycle, the best location to assess ore quality such that material classified is during drilling and loading. Currently, ore quality is controlled by using reconciliation procedures between the grades of the drill holes and the grade estimated during the exploration cycle. Usually the reconciliation procedure creates a difference between the grades known as discrepancy. This analysis can monitor the expected ore grade, however it does not offer any possibility for control other than through setting the location boundaries of the ore, and estimating its dilution. An ore sorting system could improve grade control by providing an intelligent interface for a shovel operator in the loading cycle to help him/her make decisions regarding the quality of the material in the shovel so that a decision can be made regarding the correct destination for the loaded material.  The sorting would not only provide a reduction in the dilution and pre-concentration of the material, it could potentially be applied to decreasing the cut-off grade of the whole mine operation. This suggests an improvement in flotation capabilities and recovery efficiency during mineral processing.   4  If sorting systems could improve performance in mine operations, operating cost could be decreased. There is an opportunity to improve performance by increasing control of the grade processed in the concentrator.  Also, characterization of ore properties such as Oxide versus Sulphide would allow ore to be diverted to the appropriate process stream (eg heap leach versus flotation).  1.4 Outline The focus of this dissertation is the presentation of a methodology that could be used to incorporate LIBS as a new sensor for ore sorting systems, and to delineate the capabilities of LIBS in making correlations and yielding results. With respect to the intents of this dissertation, Chapter 2: explains the chemistry basics of LIBS, and highlights the important features of LIBS that need to be considered in order to achieve valid results in characterizing ore materials. Chapter 3: explains the experimental procedures, techniques and algorithms used to process the spectrum and data from LIBS. This chapter further describes some of the mathematical tools used to develop the scripts to acquire data, and also explains some of the challenges posed by laboratory testing, and the ways to address the existing challenges.  Chapter 4: presents a characterization of Oxide porphyry samples using LIBS, and a regression analysis of the results, ultimately providing a potential prediction equation for Cu content. This equation attempts to present a methodology rather than a criterion for sorting ore at the Escondida Mine. Furthermore, the methodology used for regression in Chapter 5:. Chapter 5: presents a characterization of Sulphide porphyry samples using LIBS, as well as regression analysis and prediction equations for Cu content.   5  Chapter 6: presents a potential methodology for differentiating between Oxide and Sulphide samples for ore sorting systems. Here, the chemistry background needed to understand this distinction is explained. Chapter 7: provides a discussion of the methodology and its potential for improving the results. Finally, Chapter 8: provides a set of conclusions that encompass the outcomes of the LIBS applications found in this research for sorting of Copper porphyry ores.  6  Chapter 2: Laser Induced Breakdown Spectroscopy Background 2.1 What is LIBS? LIBS (Laser Induced Breakdown Spectroscopy) is an optical spectrochemical method based on spontaneous emission (DAGDIGIAN) that utilizes an intense laser pulse to determine the elemental composition of a sample. LIBS uses high temperature micro-plasma read by a lens according to a determined time frame. The time frame consists of a 1.5 nanosecond pulse, followed by 10 microseconds of energy dissipation.     Figure 2-1: LIBS machine used for this experiment: a FiberLIBS model (SECOPTA) Figure 2-1 shows an image of the LIBS machine that was used for this research project. LIBS emits a laser beam through the measurement head.  This laser beam creates a plasmatic formation at the surface of a sample. Once an electrical breakdown is created by the laser in the plasma, LIBS detects the photon movement of the spontaneous emission through a spectrometer and a detector. A detector for LIBS consists of a Charge-Couple Device (CCD) that receives image information from the spectrometer and transforms it into a digital signal. The photon movement 7  describes the wavelength, which is unique for every ionization stage of an element. This wavelength allows LIBS and the computer to identify the elements in a sample, or elements in specific rock samples in an operation.   Figure 2-2: Spectrochemical methods for the currently most used sample analysis methods in mining The current techniques for sample analysis use similar optical spectrochemical methods to those used by LIBS. Figure 2-2 shows the more popular methods for spectrochemical analysis used in mining. This thesis research project bases its calibrations and comparison analysis on Inductively Coupled Plasma – Atomic Emission Spectroscopy (ICP-AES) and Inductively Couple Plasma – Mass Spectroscopy (ICP-MS) Certified Analysis.  The most common type of analysis of Fire Assay beads is either Atomic Absorption Spectroscopy (ASS) or ICP-MS.  The method used to determine the Cu content from the samples was by Aqua Regia digestion and ICP-AES.   8  2.2 Wavelengths LIBS photon excitation has a random direction that is captured by the lens in the measurement head.  LIBS produces a visible spectrum of light that can be seen in ambient conditions. The wavelength is separated by diffraction grating. The grating is used to diffract the light source generated by the photon excitation that is read by the lens. The grating diffracts the light source into different colours that are calibrated to provide a signal for a determined wavelength. This wavelength bandwidth is processed by a photodiode that calculates the intensity for the different wavelengths.    Figure 2-3: Diffraction grating schematic (Fleischer) LIBS provides factory specifications for wavelengths. The LIBS machine used in this research is a SECOPTA FiberLIBS unit with wavelengths from 2.29*10^-7 to 5*10^-7 m. Different commercial LIBS machines can observe and process wavelengths from approximately 50 nm up to 2000 nm. One characteristic aspect of LIBS wavelengths is that LIBS does not use ionizing radiation as do the XRF and Prompt Gamma methods. 9   Figure 2-4: Electromagnetic spectrum for light sources (Cyberphysics group) 2.3 Apparatus Fundamentals Figure 2-5 shows the basic schematic of a LIBS machine. The computer sends a signal to the laser to emit the light beam over the rock sample, resulting in the vaporization of the sample, which is also known as ablation. Once emitted, the optical spectrometer reads the intensity of light as a function of wavelength. A spectrometer consists of a combination of a monochromator and a detector (CCD). There are two types of monochromators: a) Bunsen prism, and b) Czerney-Turner. 10   Figure 2-5: Basic schematic of a LIBS machine LIBS uses the Czerney-Turner monochromator, which is capable of reading wavelengths from 190 to 1000 nm. Optical resolution ranges from a pixel size of 0.05 to 1 nm as part of the spectrometer features. However, the optical resolution, as defined for FiberLIBS, varies from 0.135 nm to 0.15 nm. The FiberLIBS machine used in this research has 2048 pixels with wavelengths from 229.21 to 499.58 nm.  Table 2-1: Specification of FiberLIBS for its spectrometer Spectrometer 1 or 2 thermal stabilized Czerny-Turner spectrometers Wavelength range:190-1000 nm Optical Resolution: 0.05 - 1 nm (depending on application)  The monochromator, or spectrometer, acts as a photodiode array that receives the light source diffracted by the grating. The lens works with a slit in the measurement head, allowing the lens to capture only one part of the plasmatic formation that occurs after the ablation of the surface of the rock sample. The laser beam created out of the ablation and radiative flux goes through the slit and reflects on concave mirrors to reflect over the grating, and then once again 11  over another concave mirror. This effect allows the light beam to be diffracted, as shown in Figure 2-6.   Figure 2-6: Schematic of LIBS spectrometer (Rehse) 2.4 Importance of the Diffraction Grating 2.4.1 Young’s Double Slit example In order to explain the importance of the grating in the LIBS apparatus, it is necessary to define how the spectrum is generated. A simple way to explain the functionality of LIBS from a physics perspective is through an understanding of Young’s Double Slit experiment. Young’s Double Slit experiment can be performed with a laser pen and 3 pencil leads. Three leads are held parallel so that two slits are created on either side of the center lead. The laser pen has to light through 2 slits created by the 3 pencil leads that are held parallel to each other, and reflected on a wall. The diffraction of the laser pen will result in the laser beam multiplying the reflected light on the wall with a high intensity in the center, and a lower intensity as it gets farther from the center.  12  The same principle is at play with the LIBS machine. The effect of the grating is similar to that which occurs in Young’s Double Slit experiment. As seen in Figure 2-7, the light sources pass through two slits. The interaction of the waves creates both constructive and destructive harmonics. The central Δx= 0 has a complete constructive harmonic and defines the higher intensity peak in the spectrum. The location of this point can be found by following the center of the two waves exactly in the middle of the 2 wavelets. When Δx= 0.5λ, the superposition of the waves is destructive. The next harmonic Δx= λ already has the destructive effect and the intensity is lower than Δx= 0. After the third harmonic, the signal to noise ratio is too high and is no longer considered efficient. This spectrum is the main indicator of efficiency in the Czerney-Turner monochromator. The spectroscope spectrum reflects the intensity of light that is read by the detector as intensity, and the intensity is calibrated in order to calculate the concentration of the photon excited by the light source.   13   Figure 2-7: How the spectrum is generated in LIBS (Cremers and Radziemski)   14  2.4.2 Diffraction grating calculation Even though the design of the LIBS machine is not part of the ore sorting analysis, it is important to have a full understanding of the internal specifications of the LIBS machine.  This is important in order to hold control over the quality of the responses and the concentrations measured as outputs of the spectrum. The equation for the incident angle of the light beam over the grating is shown in Figure 2-8. The incident light is reflected over the grating with “d” as the spacing between slits, “α” as the incident light beam and “β” as the diffracted light beam.   Figure 2-8: Incident light beam over a grating (Ryer) Table 2-2: Specifications for average spectrometers used in the construction of LIBS sensors Spectrometer Type Czerny-Turner Bandwidth 190 to 800 nm Grating 2400 l/mm & 600 l/mm Resolution 2 angstroms Coverage 65 nm 15  “m” in Figure 2-8 or “n” in the equation below is the harmonic.  For this example, the calculation uses data from the TRACER™ 2100 Laser Element Analyzer, a grating slit of 2000 lines per millimeter (l/mm), an incident angle of 48 degrees and a diffracted (or refractive “r”) angle of 20 degrees.   “d” is transformed to nm/l units and λ is calculated for the first harmonic. Table 2-3 shows the calculation for the harmonic with varying refracted angles.  Table 2-3: Harmonic calculation for the grating   n r 1 2 3 20 542.58 271.29 180.86 10 458.40 229.20 152.80 0 371.57 185.79 123.86 -10 284.75 142.37 94.92 -20 200.56 100.28 66.85  Table 2-3 shows that for a given wavelength of 500 nm of the laser beam and a spacing of 2000 l/nm, the harmonics has an effective bandwidth from 180 to 540 nm. Also, the table suggests that readings in the range of 180 to 270 nm will be less responsive or noisy in terms of the spectrum 16  because these wavelengths belong to the second or third harmonic. As explained through Young’s Double Slit experiment, these harmonics are less intense and slightly noisier. It is not recommended to work with harmonic values greater than 3 because the spectrum becomes too noisy to give a good reading.  2.5 LIBS machine specifications The LIBS machine used for this research work is the FiberLIBS from Secopta. The basic specifications for its laser are provided in Table 2-4. LIBS machines have ranges from 1 mJ to 10 mJ of pulse energy. This machine has a frequency of 100 Hz as a pulse rate, meaning that it is capable of taking 100 readings in 1 second.   Table 2-4: Laser specification for FiberLIBS   Table 2-5: Spectrometer specification for FiberLIBS   17  The spectrometer for FiberLIBS has a10 micron entry slit and a bandwidth of 229.21 to 499.58 nm. The resolution of a peak varies from 0.135 nm to 0.15 nm, which is described by the Resolution Full Width at Half Maximum (FWHM). This term shows the half power point resolution for the peak.  2.6 White colouring problem LIBS has difficulty reading white surfaces since white surfaces are more likely to reflect the laser beam rather than absorb the light energy and as a result a good spectrum is not generated by the LIBS machine. If the laser is reflected and not absorbed, then the plasma formation and ablation will not produce enough breakdown of the photon to reproduce the desired spectrum in order to identify elements and measure concentrations. The reason for the reflectance of the laser beam or any other light source is that molecules and atoms of white surfaces do not absorb any of the visible colours of light, while other colours do absorb the light.  Current industrial laser cutters use intense power to cut steel accurately. It is a common practice with this technology to paint the surface black prior to the cutting procedure as the black surface improves the effectiveness of the laser. At the very least, the surface must have a dark colouration in order to allow the molecules and atoms on the surface to absorb the energy so that the material could be cut successfully.   The Kirchhoff rules of spectroscopy indicate that a good reflective material is a poor absorber, while a good absorber is a good re-emitter. This means that if LIBS reads a material that reflects the light spectrum, then the amount of energy absorbed will be low. If not enough energy is captured by the surface of a rock material, then LIBS won’t be able to create the plasma formation and subsequently, readings will be noisy and of poor spectrum quality.  18  Chapter 3: Experimental Approach A key goal of this research project is to develop a sensor that is capable of collecting data from elements that are not traceable with XRF and HFEMS. The objectives of this program are to develop and demonstrate the effectiveness of the LIBS system in characterizing Copper porphyry ore, to test and analyze the repeatability of the bench scale LIBS system, and to demonstrate the efficiency of the LIBS system for Copper ore. In particular, there was a desire to explore the applications of LIBS in discriminating Oxides vs. Sulphides, where XRF has been shown to be ineffective. Although current XRF sensors at Minesense Ltd. (the sponsor company for this research) are similar to the LIBS sensor, the physical-chemical analysis conducted by both systems is significantly different. In XRF sensors, the X-ray process involves the electromagnetic radiation of a short wave produced by the deceleration of electrons (Skoog y Leary). In contrast, LIBS involves plasma formation as a result of an intense laser pulse of a high-temperature followed by the process of optical spectroscopy. LIBS is considered by many material manufacturers as the new option for sensing alloy properties that XRF is not capable of accomplishing. This relegates the XRF to the position of a proven technology that nevertheless is limited in certain areas. However, no real research has been conducted regarding the use of LIBS responses in correlations for ore sorting sensors. One of the improvements with respect to material recognition in which LIBS is superior to XRF is the lack of radiation passing over the work area. Current technology has improved significantly, and has evolved to the point where portable LIBS systems have been developed for use as hand tools. For this reason, the topic of radiation is an important one to consider.  19  This chapter highlights the details of the experiment that was performed for this research, as well as the challenges involved in developing a LIBS sensor for sorting ore.  3.1 Experimental design The experiment was divided in 2 parts: 1. Project initiation: LIBS identification and calibration 2. LIBS correlation 3.1.1 Project Initiation: LIBS Identification and Calibration The rock samples for this research were taken from ore deposits from the Escondida Mine, in Chile. Escondida is a Copper mine in the Atacama Desert.           This research used forty-one samples from the Oxide ores, 38 samples from the Sulphide ores, and 1 chipped sample of the Sulphide ore was not ultimately used in this research.  Figure 3-1: Escondida Mine samples. Left: sample #26 Oxide sample, Right: sample #12 Sulphide sample 20  One of the characteristics of LIBS is that it does not require any sample preparation. This research therefore took an “as-is” approach regarding the rock samples that were taken from the mine site and as such, they were not washed, polished, or cut.  The samples were weighed, and then scanned by the LIBS machine. The samples were read with the LIBS on 4 faces of the rock, and 10 readings were taken per face. In the initial phases of experimentation and trial, readings were taken randomly, usually at the default value of 100 readings per shot. One of the most time-consuming tasks during this stage was to solve the white colouring problem with respect to the Sulphide rock samples.  Upon the completion of this stage, the experiment was focused on the identification and characterization of the rock samples. To identify the rocks, it was important to have a valid reference regarding the wavelength and spectroscopy observed in the LIBS spectrums. In order to understand the behaviour of the LIBS system, it was necessary to shoot over the known surfaces, such as the pure Copper or steel layers, in order to start developing an understanding regarding how the literature and online references matched the reality of the LIBS spectrum.  Finally, the construction of a Python Script was initiated in order to transform the spectrum information into a readable format. The development of the initial script was attempted in MATLAB, but as a result of the amount of information processed, and the continuous data coming from LIBS, it was decided to migrate the data and algorithms to Python. Several techniques from the computer sciences, data analysis, and liner programming were applied into this construction in conjunction with the basics of physical chemistry.  21  3.2 Geology and Geochemistry of Escondida Mine Rocks for Correlation Escondida Mine is a Copper porphyry deposit that is located in the north of Chile, and is one of the largest mining operations in the world. It belongs to a big supergene Copper deposit morpho-techtonic with the intervention of shallow gravel-filled basins.  The mineralogy groups are as follows: 1. Hypogene Sulphides 2. Supergene sulfides 3. Copper Oxides In order to decide which Mineralogy group should be accepted into the equation, Table 3-1 was developed to provide detailed information about each mineral, or type of rock expected from every geological region (Ruben Padilla Garza). This table consolidates information from a variety of reference sources, but has a strong focus on “Geology of the Escondida Porphyry Copper Deposit, Antofagasta Region, Chile” (Ruben Padilla Garza). Mineralogical references are very important at this stage in order to create associations between the elements and minerals. Although no direct mineral association can be made here because LIBS is not able to identify minerals directly, we can create associations between the elements and the ion responses.  Table 3-1: Summary of Mineralogy of Escondida Mine by Mineralogical Groups and Elements  Mineralogical group Mineral/Rock Elements Advanced Argillic Alteration Pyrite Fe S                 Bornite Cu Fe S             Chalcopyrite Cu Fe S             Sulfides S                 Covellite Cu S               Enargite Cu As S             Chalcocite Cu S               22  Mineral/Rock Elements Galena Pb S               Sphalerite Zn Fe S             Alunite K Al S O H         Quartz-Sericite Quartz Si O                 Sericite Na Al Si O H         Chalcopyrite Cu Fe S             Pyrite Fe S               Molybdenite Mo S               Sericite-Chlorite Chalcopyrite Cu Fe S               Pyrite Fe S               Molybdenite Mo S               Biotitic Biotite K Mg Fe Al Si O H F     Chlorite Mg Fe Ni Mn Al Si O H Cl Potassic Alteration k-feldspar Biotite K Mg Fe Al Si O H F     Anhydrite Ca S O             Chalcopyrite Cu Fe S             Bornite Cu Fe S             Orthoclase K Al Si O           Potassic Alteration Biotitic Biotite K Mg Fe Al Si O H F     Magnetite Fe O               Bornite Cu Fe S             Chalcopyrite Cu Fe S             Propylitic Alteration Calcite Ca C O               Chalcopyrite Cu Fe S             Grossular Ca Al Si O           Chlorite Mg Fe Ni Mn Al Si O H Cl Epidote Ca Al Fe Si O H       Sulfide enrichment blanket Chalcocite Cu S               The best Copper grades of the supergene zone Andesite Si O               Atacamite Cu Cl O H           Covellite Cu S               Digenite Cu S               Idaite Cu Fe S             Pyrite Fe S               Leached capping zone Limonite Fe O H               Hematite Fe O               Covellite Cu S               Copper Oxides Brochantite Cu H S O             Antlerite Cu S O H           ElementsAlAsCCaClCuFFeHKMgMnMoNaNiOPbSSiZn23  Mineral/Rock Elements Atacamite Cu Cl O H           Chrysocolla Cu Al Si H O         Tenorite Cu O               Chlorite Mg Fe Ni Mn Al Si O H Cl Sericite Na Al Si O H         Andesite Si O                 3.3 LIBS correlation To use LIBS as a measuring device, the quality of the response relies on the limits of detection, the concentration calibration that is based on the analysis of pure samples (Cremers and Radziemski). At its core, this research investigates another method through which to develop correlations with respect to the LIBS spectrum. This in turn makes a difference with respect to other LIBS research projects. It was not the intention of this project, however, to develop LIBS’ capabilities in accurately calculating the grade of a rock because this is not the purpose of an ore sorting sensor.  The technical capabilities of LIBS can be seen with respect to LIBS’ ability to function as an ore sorting sensor. It is necessary to define which elements can be identified, and compare these to a certified analysis. The technical capabilities represent the basic resources through which to build correlations from the responses to the target element, Cu content, for this project.  From this perspective, this section of the research was focused on: 1. Completing the identification of wavelengths for the elements. 2. Comparing the readings of the elements obtained from LIBS with the readings of the elements obtained from the Certified ICP analysis. 3. Developing a logical thought process regarding to how the spectrums can be processed with the tools and resources available. 24  4. Application of several types of regression analysis in a trial and error scheme to develop correlations. 5. Validation of the data.  3.4 Main problems expected when using LIBS as an ore sorter  While attempting to record LIBS spectra, two measurement challenges were encountered.  Firstly, it was difficult to obtain good quality spectrum from white surfaces and secondly how to assess LIBS for sorting applications as compared to sample analysis.   3.4.1 White colouring problem solution approach Initially, LIBS was expected to be able to read any surface or rock sample. As explained in section 2.6, the white colour on a surface stops the absorption of the energy of a laser beam because white colours reflect the light. After the initiation of the project, several samples were used in experimentation, including white rocks that belonged to the categories of Escondida Sulphides and “mixto” ore (Spanish word for “mixed” that refers to the geological interaction zone between Oxide and Sulphide ores). The initial reading process using LIBS was to place the measurement head in a static position at the indicated distance provided by the manufacturer. The white samples could not be read for several weeks. The problem was solved by taking the measurement head and moving it along the surface. It was an unexpected solution that may be related to the Interaction of Light with Matter Theory and the low absorption capabilities of white minerals, as explained in section 2.6. 25  3.4.2 Spectrum analysis One of the key problems to solve involved how to train LIBS as an ore sorting sensor rather than a laboratory measurement device. In contrast to in the laboratory, in mining, bulk material handling systems using either in a shovel or a belt conveyor will not allow the operation to stop in order to read one rock several times at the exact same spot. As such, it was necessary to develop a reliable method that was capable of reading data instantly, and that did not involve repetitive readings. Even though a moving rock can be hit twice, or even several times, it is very unlikely that it will be hit in the exact same point in subsequent hits.    Figure 3-2: Twenty readings of Silica/Oxide sample spectrum from Escondida mine Figure 3-2 provides evidence that the spectrum can vary due to impurities or to the white colouration effect. The first three peaks differ from the fourth peak; and after the fifth reading, the spectrum develops stability. The peak in red is likely to be a bad reading, and LIBS has the option to average all peaks to avoid this variation in the spectrum. However, a LIBS sensor for ore sorting 26  cannot focus on the same point over several milliseconds which is required to average several peaks. For this reason, it was necessary to build an algorithm or computer script to reveal which peaks should, and should not, be used. The development of this script was based on statistics and basic methods in Artificial Intelligence. This script evolved according to the needs of the project’s changing parameters, as will be explained later.   3.5 Sulphide samples difficult to read with LIBS The Sulphide samples were difficult to be read with the LIBS sensor because of the white colouration of the rocks. As shown in Figure 3-3 and Figure 3-4, several attempts were made to obtain responses from the LIBS machine. The rocks were placed both horizontally and vertically, measuring the respective mirror’s effective focal lengths, as described in the machine’s manual.   Figure 3-3: LIBS reading Sulphide samples from the top  27   Figure 3-4: LIBS reading Sulphide samples from the side  Figures 3-3 and 3-4 shows the laser beam shooting the rock samples at different positions. The structure that holds the laser measurement head kept the laser beam perpendicular with respect to the rock surface. Even though several angles were attempted, problems came up while taking the readings. Figure 3-5 illustrates the LIBS computer screen as data is being collected while LIBS is working. “Mat.” stands for the type of material, and consists of input information that is not relevant for our correlation. “Sampl.” is the sample number for the current set of readings, e.g. 4 samples were taken with 10 readings per sample. For the last example, the number of readings requested by the LIBS operator is reflected in “spectra.” “Now” indicates the current number of readings obtained until that moment. Finally, “del” shows the number of samples deleted because they did not fit the LIBS machine default threshold. As seen, there are 7896 samples deleted, and only 1 that was accepted. When the machine ran for several minutes, if the number of readings requested were not obtained, it automatically stopped the reading.   28   Figure 3-5: LIBS computer screen for Sulphide samples    Figure 3-6: LIBS computer screen for Sulphide sample #14  29  This difficulty in reading the samples will prove to be a serious problem if the LIBS sensor reaches the stage of proof of concept. As such, it is likely that some of the data for the Sulphide samples is not as reliable as it is for the Oxide samples, which do not show the white colouring. Good data is obtained, but over longer periods of times, and this data does not depend on the length of exposure of the laser to the rock surface, as with the XRF sensors. Rather, obtaining reliable data depends on how much power the laser beam emits while not being interrupted by the light reflection. Figure 3-6 indicates that although good spectrums are being obtained, it takes relatively long to acquire the data. As seen within Table 3-6, 10 readings were obtained after deleting 50283. If the sensor has a frequency of 100 Hz, then the 10 readings took 60 seconds instead of 0.1 seconds.  3.6 Identification of Wavelength List The wavelength list identifies the characteristic wavelength of a particular ion of an element from the periodic table. In order to create this wavelength list, certain parameters, which will be discussed later, were taken into account. Figure 3-7 shows the spectrum of a pure Copper layer sample. The peaks can be recognized by matching the wavelength from the x-axis with the ID wavelength proposed in Table 3-5. This ID wavelength acts as a primary key for the identification of elements in the Python Script that is described in section 3.7, and attached in Appendix C  . To build a table for the identification of wavelengths, data was acquired from the National Institute of Standards and Technology (NIST) database (Laboratory). The selection regarding the ID wavelength is based on the likelihood and certainty of finding the ionization stage in that 30  particular wavelength. For this reason, the main parameter for quantifying this likelihood is the Aki, which is the transition probability, also known as the Einstein Coefficient.           Furthermore, Aki is the emission transition probability of the ion stage excited to move to another ionization stage, and which has been excited by the LIBS laser. Another element related to the likelihood of this transition is the Absorption Oscillator Strength (𝑓𝑖𝑘), also known as the f-value. However, the Aki is directly proportional to the f-value, and because of this, it is redundant to analyze the f-value as well. It was very important to have certainty with respect to the readings. The best indicator is the Accuracy (Acc.). Accuracy can be understood as a rating for the likelihood that a transition of the ionization stage takes place. David A. Cremers defines it as: “how close a measurement result is to the “true” value of the property measured” (Cremers and Radziemski). The likelihood is measured in the NIST database following the pattern shown in Table 3-2. Relevant information was retrieved from the NIST website (National Institute of Standards and Technology NIST). CuI 324.75 CuI 327.39 Figure 3-7: Spectrum of pure Copper layer sample showing the characteristic peaks at 324.75 and 327.39 for Cu I 31  Table 3-2: Accuracy for transition strength AAA ≤ 0.30% AA ≤ 1% A+ ≤ 2% A ≤ 3% B+ ≤ 7% B ≤ 10% C+ ≤ 18% C ≤ 25% D+ ≤ 40% D ≤ 50% E > 50%.  Table 3-3 shows a proposed set of values for each accuracy rating in order to quantify the accuracies, and include them with the Relative Intensity. The weighting factors were created for this project as a tool through which to provide significance to the values with higher Acc. ratings. The logic used was to provide a maximum of 400 for an Acc. of 400. Subsequently, decrease 50 units to the next lower levels of Acc. The sequence was intended to end at D+ where the accuracy is not significant for the selection of wavelengths.   Table 3-3: Weighting factors AAA 400 AA 350 A+ 300 A 250 B+ 200 B 150 C+ 100 C 50 D+ 1 D 1 E 1  1  32  This pattern was created in order to quantify the Acc. rating into numbers, and to highlight the elements that are likely to be seen in the spectrum. The relative Intensity number (14000) in Table 3-4 has been multiplied by the Acc. values from Table 3-3 (150). This value is shown in the column titled “Weighted Relative Intensity in Table 3-4. The final Weighted Relative Intensity is 2100000 is used to sort the higher values for Weighted Relative Intensity, and depends on likelihood and the intensity. The final proposed pattern for the ID wavelength is presented in Table 3-5 below. Table 3-4: Example of the database and the classifications of the ratings  Ion Observed Wavelength Air (nm) Ritz Wavelength Air (nm) Acc. Rel. Int. number Weighted Rel. Intensity Ca III 289.9785 289.9785 B 14000 2100000 Ca III 337.2671 337.2679 B 10000 1500000 Ca III 292.4326 292.4331 B 7000 1050000   Table 3-5 was included in the Ritz Wavelength. The main difference between the observed wavelength and the Ritz wavelength is that the Ritz is a calculated wavelength, while the Observed Wavelength refers to the results of experiments. Most of the Observed Wavelengths have been tracked and repeatedly found from different experiments. NIST provides detailed information about the wavelengths. A Python Script was developed for the purposes of this research. Observed wavelength is being used here unless only a Ritz Wavelength is available. Although it is suggested to use the Observed Wavelength, the Ritz wavelength provides critical information in Chapter 6: with respect to the discrimination of Oxides and Sulphides. For this reason, it is important to include this value as part of the input for the Python Script.   33                         IonObserved Wavelength Air (nm)Ritz Wavelength Air Acc.Rel . Int. number Aki IonObserved Wavelength Air (nm)Ritz Wavelength Air (nm) Acc.Rel . Int. number AkiAg II 232.02 232.02 B 730000 2.9E+08 Mn II 261.02 261.02 C 10000 3E+08Ag II 241.32 241.32 B+ 470000 2.1E+08 Mo VI 329.33 329.33 30000 7.2E+08Al  I I 281.62 281.62 A 4000 3.6E+08 Mo VI 338.70 338.70 50000 4.5E+08As  I 234.98 350 3.1E+08 N II 399.50 399.50 A 1000 1.2E+08Au I 267.60 267.59 3400 1.6E+08 N IV 347.87 347.87 B 570 1.1E+08Au I 242.80 242.79 2600 2E+08 Na II 298.42 298.42 B 1300 1.7E+07Ba I 350.11 350.11 B 860 3.5E+07 Na II 307.83 307.83 A 550 1.2E+08Ba II 455.40 455.40 B 9300 1.1E+08 Ni  I 349.30 349.30 C+ 5500 9.8E+07Be II 272.89 272.89 AA 310 3.2E+07 Ni  I 341.48 341.48 C 8200 5.5E+07Be II 482.82 482.81 A 710 7870000 O V 278.10 278.10 B 1000 1.4E+08Be II I 448.73 448.70 AAA 100 2.1E+08 O III 245.50 245.50 B 200 3.4E+08Bi  I 289.80 289.79 4000 1.5E+08 O III 393.48 393.48 C+ 9.93E+07Bi  I 306.77 306.77 9000 1.7E+08 P IV 334.77 334.77 C+ 650 2.1E+08Br I 447.77 20000 1300000 P I 253.56 253.56 C 950 9.5E+07C I 247.86 247.86 C+ 800 2.8E+07 Pb I 283.31 283.31 35000 5.8E+07C II 283.67 283.67 B+ 1000 3.3E+07 Pb I 280.20 280.19 25000 1.6E+08C III 229.69 229.69 A+ 800 1.4E+08 Pd I 340.46 340.46 24000 1.3E+08Ca I 422.67 422.67 B+ 50 2.2E+08 Rh I 369.24 369.24 9400 9.1E+07Ca II 317.93 317.93 C 180 3.6E+08 Ru I 372.80 372.80 11000 8.2E+07Ca II I 289.98 289.98 B 14000 2.5E+08 S VI 420.08 420.08 AA 50 4.8E+07Cd II 274.85 1000 2.8E+08 S VI 419.89 419.89 AA 120 2.9E+08Cl  I I 479.46 479.46 C 99000 1E+08 Sb I 231.15 231.15 2500 1.7E+08Cl  I I 481.01 481.01 C 29000 9.9E+07 Sc II I 273.40 273.40 D 230 3.3E+08Co I 347.40 347.40 B 8000 5.6E+07 Sc II I 269.91 269.91 C 350 3.4E+08Co II 258.03 258.03 B+ 210000 2.1E+08 Si  I 288.16 288.16 B 1000 2.2E+08Co II 237.86 237.86 B+ 140000 1.9E+08 Si  I I 413.09 413.09 B 500 1.7E+08Cr I 427.48 427.48 B 2500 3.1E+07 Sn II 328.31 328.31 B+ 15000 1.7E+08Cr I 425.44 425.43 B 2480 3.2E+07 Sn II 335.20 335.20 B+ 13000 1.8E+08Cu I 324.75 324.75 AA 10000 1.4E+08 Ta I 362.66 980 7100000Cu I 327.40 327.40 AA 10000 1.4E+08 Te I 238.58 238.58 1200000 8.1E+07Cu II 271.35 700 6.8E+07 Ti  I 399.86 399.86 A 10000 4.8E+07F II 350.56 350.56 C 220 2.9E+08 Ti  I I 376.13 376.13 A 11900 1.2E+08Fe I 374.95 374.95 A 1150000 7.6E+07 Ti  I I I 251.61 251.60 D 25 3.4E+08Fe II 234.35 234.35 A+ 1000000 1.7E+08 Tl  I 276.79 276.79 4400 1.3E+08Fe II 238.20 238.20 B+ 1800000 3.1E+08 Tl  I 351.92 351.92 20000 1.2E+08Ga I 294.36 294.36 1.3E+08 V I 411.18 411.18 B 8900 1E+08Ge I 265.12 265.12 2E+08 V II 292.40 292.40 B 2400 1.7E+08Hf I 368.22 368.22 2200 2.6E+07 W I 400.88 400.87 B 1000 1.6E+07Hg II 284.77 284.77 3500000 3E+08 W II 248.92 248.92 B 422 7E+07In II 294.10 294.10 B 9600 3.4E+08 Y I 410.24 1800 1.3E+08Ir I 269.42 269.42 3000 4.8E+07 Y II 371.03 13000 1.5E+08Mg I 285.21 285.21 A 50 4.9E+08 Zn I 334.50 800 1.7E+08Mg II 279.55 279.55 A+ 13 4.8E+08 Zn II 491.16 800 1.6E+08Mg III 239.51 239.52 A 20 1.7E+08 Zr II I 266.43 266.43 5000000 3.2E+08Mn I 279.83 279.83 C 5100 3.6E+08 Zr II I 262.06 262.06 10000000 3.9E+08Table 3-5: ID Wavelength proposed for the LIBS machine used in this research 34  3.7 The Python Script The Python Script is attached in Appendix C  . This script uses the ID Wavelength file and the spectrum data from LIBS as input. An extraction of this file is shown in Table 3-6. This table contains the wavelength from 229.21 to 499.58 nm in the columns, and shows each rock sample (Su1), the shot number (S1) and the reading number (1,2,3,…) in the rows.  The script starts with asking the sample wanted to be plotted, and the user has the option to select the spectrum to plot. The Python Script attempts to solve the problem of reading data that is not averaged because within the mining cycle, it is impossible to take several readings in 1 spot.  Table 3-6: Extraction of the spectrum data from LIBS wavelength Su1,S1,0 Su1,S1,1 Su1,S1,2 Su1,S1,3 Su1,S1,4 Su1,S1,5 Su1,S1,6 Su1,S1,7 Su1,S1,8 229.21 856 809 699 700 703 901 820 735 828 229.36 907 869 730 717 685 1011 854 766 909 229.5 856 815 705 694 721 943 826 763 844 229.65 756 733 691 723 690 795 745 694 738 229.79 806 749 685 699 731 810 743 725 775 229.94 786 770 737 692 701 822 770 729 766 230.08 759 722 677 674 668 745 719 701 730 230.22 784 785 708 723 704 797 767 721 762 230.37 776 778 685 725 725 795 748 741 763 230.51 763 756 710 711 699 745 751 720 765 230.66 753 751 682 704 712 759 733 714 739 230.8 689 737 710 669 692 732 735 688 723 230.95 766 734 712 675 682 756 731 678 739 231.09 750 747 710 736 724 753 732 690 695 231.24 759 742 713 703 707 726 741 714 732 231.38 736 745 705 698 720 713 700 713 725 231.53 744 726 725 704 698 762 723 724 727 231.67 703 753 696 697 715 744 731 715 729  Due to the heterogeneity of the geology and the constant movement of a belt conveyor or mining shovel, it was necessary to gather LIBS data that had previously been validated. In contrast to laboratory test work, samples in a production line cannot be taken apart for analysis because of the mining production cycle and the efficiency expected with respect to mining machinery. As 35  such, it was necessary to build data filters to simulate that which could be read in several readings in one static test, in only one reading, and in constant movement.  There are 3 filters proposed for validating the data without the need to average several readings over a static sample: 1. Minimum peak of 10 counts 2. Local maximum using the second derivate kernel smoother density at 1.0 3. A low pass filter analyzing the noise frequency using the Fast Fourier Transform (FFT)  3.8 Technical potential Table 3-7 provides a summary of the 43 elements obtained from the responses of LIBS over the porphyry Copper samples from Escondida Mine. Table 3-7  has been constructed based on data that was collected, and is attached in Appendix A   and Appendix F  . This table indicates which elements LIBS has been able to detect based on wavelength identification. In contrast, Table 3-8 shows only the 26 elements that have been identified through LIBS and the ICP Certified Analysis for both Oxide and Sulphide samples of Escondida Mine. Table 3-7: Technical potential summary Ag Cd Hg Ni Sn Zr Al Cl In O Ta Co Au Cr Ir P Ti Sc Ba Cu Mg Pb Tl  Be F Mn Pd V  Bi Fe Mo S W  C Ga N Sb Y  Ca Hf Na Si Zn   Table 3-8: Technical potential summary skewed by Certified ICP Analysis Ag Ca Mg Sb Co 36  Al Cd Mn Si Sc Au Cr Mo Sn   Ba Cu Na Ti   Be Fe Ni Zn   Bi Hg Pb Zr    3.9 The Pearson Correlation The Pearson Correlation is a ratio or percentage of the dependence between 2 variables. This value is calculated by dividing the covariance by the partial standard deviations.  𝒓 =𝝈𝒔𝒚𝑺𝒙𝑺𝒚 Equation 1 Pearson Correlation Coefficient This coefficient is used to measure the dependence of the Certified ICP Results and the LIBS responses.   3.10 Confidence level over technical potential The identification of elements through LIBS is based on the likelihood of the occurrence of the transition of ionization stage. Wavelengths with possible false identification are summarized in this section. The main reason for this problem is the lack of an Identification of Wavelength set provided by the manufacturer of FiberLIBS, for that reason the wavelengths are vulnerable to error. Even when identified precisely, wavelengths can have error with respect to overlap (Cremers and Radziemski). As such, the best approach to verifying the wavelengths is through comparing them with the results of the Certified ICP analysis of the Oxide and Sulphide samples.    37  Table 3-9: Confidence levels for technical potential to detect elements  ICP data    ICP data   unit Min Max Confidence   unit Min Max Confidence Ag II@232.02 ppm <2 <2 Good  N IV@347.87       Unknown Ag II@241.32 ppm <2 <2 Good  N II@399.5       Unknown Al II@281.62 % 0.41 1.94 Good  Na II@298.42 % 0.03 0.11 Very Good Au I@242.8       Unknown  Na II@307.83 % 0.03 0.11 Good Ba II@455.4 ppm <5 64 Good  Ni I@341.48 ppm <1 10 Good Be II@272.89 ppm <0.5 <0.5 Poor  Ni I@349.3 ppm <1 10 Poor Be III@448.73 ppm <0.5 <0.5 Poor  O III@393.48       Unknown Bi I@306.77 ppm <5 <5 Poor  O V@278.1       Unknown C I@247.86       Unknown  P I@253.56 % <0.01 0.05 Good C III@229.69       Unknown  P IV@334.77 % <0.01 0.05 Good Ca I@422.67 % <0.01 0.13 Good  Pb I@280.2 ppm <2 154 Very Good Ca II@317.93 % <0.01 0.13 Poor  Pb I@283.31 ppm <2 154 Good Cd II@274.85 ppm <11 <11 Poor  Pd I@340.46       Unknown Cl II@481.01       Unknown  S VI@419.89 % 0.08 4.48 Poor Co I@347.4 ppm <1 47 Good  S VI@420.08 % 0.08 4.48 Poor Cr I@427.48 ppm <1 3 Poor  Sb I@231.15 ppm <5 <5 Poor Cu I@324.75 ppm 393 25700 Very Good  Sc III@269.91 ppm <0.5 1.1 Good Cu I@327.4 ppm 393 25700 Very Good  Si I@288.16* % 45.9 70 Very Good Cu II@271.35 ppm 393 25700 Poor  Si II@413.09 % 45.9 70 Poor F II@350.56       Unknown  Sn II@335.2 ppm <10 <10 Poor Fe I@374.95 % 0.07 8.31 Very Good  Ta I@362.66       Unknown Fe II@234.35 % 0.07 8.31 Very Good  Ti I@399.86 % <0.01 0.07 Good Fe II@238.2 % 0.07 8.31 Very Good  Ti II@376.13 % <0.01 0.07 Good Ga I@294.36       Unknown  Ti III@251.61 % <0.01 0.07 Good Hf I@368.22       Unknown  Tl I@276.79       Unknown Hg II@284.77 ppm <1 1 Poor  Tl I@351.92       Unknown In II@294.1       Unknown  V I@411.18 ppm 3 38 Poor Ir I@269.42       Unknown  V II@292.4 ppm 3 38 Poor Mg I@285.21 % 0.01 0.51 Very Good  W I@400.88 ppm <10 <10 Good Mg II@279.55 % 0.01 0.51 Good  W II@248.92 ppm <10 <10 Good Mg III@239.51 % 0.01 0.51 Good  Y II@371.03 ppm <0.5 4.3 Unknown Mn I@279.83 ppm 6 296 Poor  Zn I@334.5 ppm <1 207 Good Mn II@261.02 ppm 6 296 Poor  Zn II@491.16 ppm <1 207 Good Mo VI@329.33 ppm 7 1830 Poor  Zr III@262.06 ppm <0.5 1.5 Good Mo VI@338.7 ppm 7 1830 Poor  Zr III@266.43 ppm <0.5 1.5 Very Good       * Si calculated based on SiO concentrations   Table 3-9 provides a summary of the confidence levels for the technical potential of the whole sample in providing a source of information with respect to choosing the ions for prediction equations. The confidence levels are classified as follows:  Very good: Wavelengths with obvious correlation to those identified in the ICP  Good: Wavelengths with some correlation to those identified in the ICP 38   Poor: Wavelengths that are present in the LIBS responses, but no real correlation can be identified  Unknown: Wavelengths seen in LIBS spectrum but not in the ICP The values in this table define the limits for the identification of elements, and classify the elements as either belonging to the area of chemical analysis or to that of mining technology, the latter of which is the focus of this thesis.  Based on the approach that was used for this study, elements corresponding to wavelengths that have very low concentrations, as indicated by ICP, are likely to be falsely identified and therefore the wavelengths are likely represent a different element. However, the regression analysis indicated that the magnitude of the peak at this wavelength is significant, and therefore the unknown elements associated with the wavelength are considered significant. For the purpose of this thesis and for ease of presentation, for the elements identified by the approaches used in this chapter, the element label is used to represent the wavelength.  39  Chapter 4: Analysis of Oxide Rock Samples with Laser Induced Breakdown Spectroscopy  The purpose of this research is to generate a response for a sensor using correlations between LIBS responses and Certified ICP assays, and not to measure the actual grades. One significant obstacle in developing a response from LIBS involves being able to generate repeatability with respect to the sensor.  This is because the spot area that LIBS targets on the rock surface is 1 mm, which represents a statistically small sample size for classifying a much larger particle and rock sample. Rock samples of this research were in the size range of 3 to 5 cm. Following an idealization of a perfect spherical rock sample, the typical rock used had a surface area of 11,309 mm2.  This signifies that there is a chance of 0.008% (1 mm2/ 11,309 mm2) that LIBS is able to hit the same point on a rock sample.  Previous research has demonstrated that LIBS capabilities are superior in terms of accuracy to those of other techniques such as ICP-AES, therefore, as a system, LIBS is favoured (G. S. Senesi). LIBS has shown a higher degree of accuracy in a variety of studies, and has reached accuracies from 1.82% to 6.25% based on ICP-AES Certified Analysis as compared with prepared and homogenized rock samples from Phosphate mines (INEEL). One of the significant problems encountered however, is the small amount of area covered by the laser beam that takes the reading. The analysis of the samples starts with the compilation of the data taken from all of the samples and put into one data file. The LIBS data was processed through the use of a Python Script, as explained in Chapter 3:. Output data is shown in Appendix A  .  A spectrum from the Oxide samples is shown in Figure 4-1. The spectrum was processed with the Python script proposed in Appendix C  . The blue line belongs to the spectrum representing a 40  potential peak in the area highlighted in grey. Some notable readings can be seen close to wavelengths 324 and 327 in the x-axis, leading to a correspondence of both wavelengths to Copper. Furthermore, another characteristic feature includes the 3 peaks from 394 to 396, which this thesis proposes as a ratio for Oxides versus Sulphides.             Figure 4-1: Characteristic Oxide sample spectrum processed with the Python script  The data shown in Table 4-1 includes the rock sample name, followed by the face-sample that it was taken from (S1 to S4), and then the reading taken (0 to 9). In order to obtain a significant measurement, 4 faces of the rock were sampled, with 10 readings for each sample, yielding a total of 40 readings per rock. In total there were 21,458 elements identified (including repetitions in the same rock) along with all of the readings.  41  “Peak Wavelength” refers to the wavelength read in the sample that might differ from the theoretical wavelength shown in the column “Observed Wavelength Air.” The difference between these columns occurs because LIBS needs a calibration of the wavelengths along its photodiode array.  Table 4-1: Output of Python Scripts for the Oxide samples from Escondida Mine (Wavelength are in nm).  Sample Rock Peak Wavelength Element Intensity Acc. Observed Wavelength Air 0 15B1,S1,0 350.55 F II 1119 C 350.563 1 15B1,S1,0 294.46 Ga I 957  294.3636 2 15B1,S1,0 279.56 Mg II 1332 A+ 279.5528 … …     … 21455 21B1,S4,9 288.15 Si I 1612 B 288.1579 21456 21B1,S4,9 251.54 Ti III 1588 D 251.6053 21457 21B1,S4,9 276.73 Tl I 955  276.787 21458 21B1,S4,9 266.53 Zr III 887  266.4286   “Element” shows the ionization state of the element. “Intensity” measures the relative concentration of the element, and has arbitrary units since different LIBS machines will have different Intensity scales. This intensity varies from experiment to experiment depending on the configuration and features of the LIBS machine in use. In the same way, the NIST database (Laboratory) provides a Relative Intensity that consists of a ratio of the Intensity to its real concentration, which is used to represent the strengths of the lines in the spectrum. This might vary depending on the machines used. “Acc” (Accuracy), as described in Table 3-2, is a rating for the likelihood that a transition of the ionization stage occurs. This rating represents a direct “quality” factor of confidence for the data read.   42  4.1 Data integration and analysis Once the data has been processed through the Python script, the data is grouped by element and ionization stage. This table groups data according to ion and element, as shown in Appendix A  . The units of the table are considered to be “counts” or “arbitrary units.” Each of the blank values in Appendix A   represent readings that cannot be detected using the filters in the Python script. One of the main challenges of grouping elements is determining the uncertainty of the ID wavelength chosen for the Python script.   4.2 Regression Analysis for the Oxide Rocks Once the samples had been reviewed with respect to any possibility for error, the data was taken into a regression analysis. A Stepwise regression was used to develop this correlation. The main purpose of this research was to elicit a response from the sensor to provide an indicator of the presence of ore, Sulfide or Oxide. It is possible to elicit such a response by conducting a multilinear regression analysis that will predict the target element, in this case Copper.   4.3 Correlation of LIBS Cu Oxides response to ICP analysis This section presents an analysis of the direct correlation between the LIBS responses with respect to Copper versus those of the ICP Copper assays. The direct response of Copper has been obtained through the LIBS response. The Copper wavelengths analyzed correspond to Cu I at 324.75 and Cu I at 327.39. The wavelengths provide readings only in the areas covered by the LIBS laser beam, and it is for this reason that the LIBS response might not represent an accurate measurement of the Copper. However, as shown below, useful results have been obtained.  43   Figure 4-2: LIBS responses for Copper at wavelengths 324.75 and 327.39 vs ICP Cu (ppm)   Figure 4-3: LIBS responses for Copper at wavelengths 324.75 and 327.39 vs ICP Cu (ppm) with secondary axis The intention behind showing two charts with the same information is to provide a perspective regarding the relationship of the correlation between the LIBS response and the ICP assays for Copper. Figure 4-2 provides the correlation using the same primary axis, and Figure 4-3 050001000015000200002500030000350001 2 3 4 5 6 7 8 9 1011121314151617181920212223242526272829303132333435363738394041ICP Cu (ppm), LIBS responses (counts)Oxide rock samplesCorrelation between ICP Cu vs LIBS CuICP Cu CuI@324.75 CuI@327.3995014501950245029503450050001000015000200002500030000350001 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41LIBS responses (counts)ICP Cu (ppm) Oxide rock samplesCorrelation between ICP Cu vs LIBS CuICP Cu CuI@324.75 CuI@327.3944  shows the correlation with different axes. The correlation shown in Figure 4-4 is a normalization (from 0 to 1) of the two variables, and the Pearson Correlation Coefficient is 0.48.   Figure 4-4: Correlation of Cu I at 324.75 nm The reason that these variables have been normalized is because they do not have a common unit, as it is ppm for ICP Cu, and counts for LIBS Cu.  The optimum number would be 1 on this regression, however obtaining a value of 0.48 means that the value is significant for the whole correlation developed in later sections of this chapter.  0.00.20.40.60.81.00 0.2 0.4 0.6 0.8 1Cu I@324.75 (counts)ICP Copper normalized (ppm)CuI@324.751:1Pearson Correlation = 0.48401142445   Figure 4-5: Correlation of Cu I at 327.39 In the same way, Figure 4-5 shows the correlation between the ion Cu I at 327.39 nm. The Pearson Correlation Coefficient is 0.45, and the interaction between these two variables is more clear in Figure 4-3. However, a coefficient in the range of 0.5 +-0.1 suggests a moderate uphill relationship.  Direct LIBS correlations is recommended depending on the geology type. For example, coal seams that have low heterogeneity and can produce a good response using this direct correlation. Copper 0.00.20.40.60.81.00 0.2 0.4 0.6 0.8 1CuI@327.39 (counts)ICP Copper normalized (ppm)CuI@327.391:1Pearson Correlation =0.44990404846  ore deposits do not match these characteristics, and as such, LIBS responses will not follow properly with this type of correlation.   4.4 Element regression analysis for Oxide samples The data, as shown in Appendix A  , is a compendium of the large database of responses from LIBS readings over Oxide rocks. Appendix B  shows the results of the Certified ICP results. The responses were taken into MATLAB to process the Stepwise Fit regression analysis. The input data is 0 and the second input to fit all of these elements is Cu concentration (ppm) from Appendix B  . As shown in Table 4-2, the results of this analysis provide a coefficient for the ion, a standard deviation and a p-value. The regression selection is based on the p-value, which represents the null-hypothesis where the coefficient is equal to zero.   It is important to mention that the software (MATLAB) does not accept empty data into the matrices to create this correlation. This is a source of non-measurable error because empty cells are being filled with zeros “0” in order to calculate the correlation prediction. There is no solution to this problem because the LIBS responses and the predictions may be contaminated as a result of garbage data even when the LIBS responses are compared with the ICP assays because ICP provides a geochemical analysis for the entire sample rather than a surface reading, as does LIBS. Although not directly the subject of this research, it is therefore recommended to develop a mathematical algorithm that does not fill empty spaces with zeros in the matrices when calculating the predictions using Stepwise regression.   Table 4-2: Results of regression analysis over LIBS responses 47  Element Coefficient Std. Error p value Ag II@232.02 3.665 2.203 0.105 Ag II@241.32 1.402 1.157 0.234 Al II@281.62 -1.719 1.039 0.107 Ba II@455.4 0.369 2.018 0.855 Be II@272.89 0.165 1.002 0.86 Be III@448.73 0 22.10 1 Bi I@306.77 -1.96 1.007 0.060 Ca I@422.67 -1.12 12.78 0.9302 Ca II@317.93 -0.7 1.059 0.465 Cd II@274.85 -2.38 2.635 0.371 Cl II@481.01 0.365 2.149 0.8661 Co I@347.4 -2.776 4.350 0.527 Cr I@427.48 4.0494 2.058 0.057 Cu I@324.75 50.50 18.02 0.0083 Cu I@327.4 -56.6 24.00 0.024 Cu II@271.35 -1.3188 0.95 0.174 F II@350.56 -1.261 1.413 0.378 Fe I@374.95 -1.013 1.493 0.502 Fe II@234.35 1.0135 2.75 0.714 Fe II@238.2 -3.157 3.531 0.3776 Ga I@294.36 -0.02 1.597 0.9851 Hf I@368.22 -2.6298 3.501 0.4579 In II@294.1 -0.822 1.369 0.552 Ir I@269.42 -1.38 1.1206 0.225 Mg I@285.21 -4.744 12.72 0.711 Mg II@279.55 -0.615 3.604 0.8654 Mg III@239.51 -4.3487 4.3426 0.323 Mn I@279.83 7.7559 1.713 7.01E-05 Mn II@261.02 -1.55 6.0825 0.799 N II@399.5 -0.5061 2.4213 0.835 N IV@347.87 -1.0638 1.615 0.514 Na II@298.42 0.5653 3.01 0.852 Na II@307.83 -2.2515 0.700 0.0028 Ni I@349.3 -0.162 1.3748 0.906 O III@393.48 9.80552 15.88 0.541 O V@278.1 1.52244 0.899 0.100 P I@253.56 0.3609 1.098 0.744 P IV@334.77 -0.7648 0.77 0.332 Pb I@280.2 -1.156 0.98 0.248 Pb I@283.31 0.67120 1.443 0.645 S VI@419.89 -0.612 1.407 0.66 S VI@420.08 -0.28 1.2408 0.821 Sc III@269.91 5.417 3.580 0.13 Si I@288.16 -26.35 5.374 2.29E-05 Si II@413.09 -0.042 1.241 0.9730 Sn II@335.2 4.7879 2.123 0.0305 Ta I@362.66 -0.63 3.34 0.849 Ti I@399.86 0.44 1.37 0.745 Ti II@376.13 0.453 1.66 0.787 Ti III@251.61 -15.76 12.8 0.229 Tl I@276.79 0.32 1.76 0.855 Tl I@351.92 1.07 1.899 0.575 V II@292.4 0.1568 1.285 0.903 48  Element Coefficient Std. Error p value W I@400.88 5.140 3.397 0.139 W II@248.92 -0.29 1.117 0.795 Y II@371.03 0.824 1.183 0.490 Zn I@334.5 1.712 1.266 0.185 Zn II@491.16 5.479 3.622 0.139 Zr III@266.43 0.124 1.233 0.920  The p-value represents how extreme the measure is with respect to its model. The p-value for this statistical analysis provides the significance of the term inside the regression analysis. For practical purposes, only p-values below 0.05 will be considered for the regression. In Table 4-2, p-values with values below 0.05 have been highlighted in red. A summary of the results, including the intercept for the equation, is shown in Table 4-3 below.  Table 4-3: Selected elements for regression analysis Element Coefficient Std. Error p value Occurrence Occurrence% Cu I@324.75 50.505 18.021 8.31E-03 1461 90% Cu I@327.39 -56.664 24.009 2.41E-02 1334 82% Mn I@279.82 7.756 1.714 7.01E-05 1 0% Na II@307.83 -2.252 0.701 2.88E-03 82 5% Si I@288.15 -26.351 5.375 2.29E-05 1247 77% Sn II@335.19 4.788 2.123 3.07E-02 4 0% Intercept         42,336            𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 𝐶𝑢(𝑝𝑝𝑚)= 42,336 + [50.50 ∗ 𝐶𝑢 𝐼@324.75] − [56.66 ∗ 𝐶𝑢 𝐼@327.39]+ [7.75 ∗ 𝑀𝑛 𝐼@279.82] − [2.25 ∗ 𝑁𝑎 𝐼𝐼@307.83] − [26.35 ∗ 𝑆𝑖 𝐼@288.15]+ [4.78 ∗ 𝑆𝑛 𝐼𝐼@335.19] This formula was used to plot the y-axis for Figure 4-6. For the purposes of this chart, the size ratio was adjusted to 1:1 to provide a realistic graphical plot of the predictive model.  49   Figure 4-6: Predicted Copper vs Certified ICP Copper (ppm)  The Pearson Correlation provides an idea of how disperse the 2 models are. It also resembles a moment of inertia, and can be considered to be a precision. In this case, the correlation does not appear to be a reliable model for sorting. Although there is no standard with respect to dispersion for sorting sensors, some logic standards can be used as a pattern. The average cut-off grade for an open pit mine operation ranges between 0.27% to 0.5% Cu, or 2700 to 5000 ppm. Ideally, the results would fall along the 1:1 line, however this is not the case. The prediction tells 050001000015000200002500030000350000 5000 10000 15000 20000 25000 30000 35000Predicted Copper (ppm)ICP Copper (ppm)Predicted Cu1:1Pearson Correlation = 0.770366492P50  us that 23% (1-0.7703) will be off the predicted value. This means that if we work with a cut-off of 0.27% Cu, we might attain readings of 0.2% Cu or vice versa, which could result in wrong sensor responses and indeed, loose ore.   Figure 4-7: ICP Cu vs Predicted Cu trending line along the 41 rock samples Figure 4-7 shows the predicted Copper levels versus those of the certified analysis for the sample. This figure provides an idea of the accuracy of the sensor prediction through a basic multivariable regression analysis.  The accuracy for this response has been calculated as the average of the individual accuracies, giving a final value of 77%. The individual accuracies have been calculated as: 𝑨𝒄𝒄𝒖𝒓𝒂𝒄𝒚 =  𝒂𝒃𝒔(𝑰𝑪𝑷 𝑪𝒖 − 𝑷𝒓𝒆𝒅𝒊𝒄𝒕𝒆𝒅 𝑪𝒖)𝑰𝑪𝑷 𝑪𝒖 Equation 2 Accuracy calculation for the correlation  Table 4-4: ICP Cu vs Predicted Cu values in ppm Accuracy ICP Cu Predicted Cu 89% 1540 172 42% 15900 9207 34% 7240 4772 -5000050001000015000200002500030000350001 2 3 4 5 6 7 8 9 1011121314151617181920212223242526272829303132333435363738394041Concentration of Cu (ppm)Samples numberPredictionICP Cu Predicted Cu51  Accuracy ICP Cu Predicted Cu 20% 12100 9721 10% 13700 12271 120% 3080 6770 49% 4750 7099 153% 3130 7905 13% 9320 8139 64% 2890 4735 16% 5600 4710 30% 7170 9291 64% 3600 5903 151% 2350 5901 21% 8440 6653 15% 9720 8303 73% 774 209 65% 1680 2773 11% 13800 12350 39% 12900 7865 44% 2990 4307 16% 3410 3956 26% 5680 7147 7% 2100 1947 138% 1110 2637 15% 9150 7779 14% 5230 4494 26% 7480 5562 16% 7310 8498 11% 1930 1718 30% 15300 10725 986% 370 -3280 406% 1940 9809 2% 8790 8626 23% 4710 5784 122% 1530 3390 92% 1410 2713 39% 7360 4470 83% 3450 6298 5% 7820 7425 79%    The accuracy of the response is 79%. In previous chapters it was explained that, as a result of the time frame and LIBS capabilities with respect to number of readings, accuracy is not as important as precision. Accuracy can be estimated and improved upon by taking more than one reading per sample once the sensor is working in a sorting system. However, 79% means that only 21% of the readings are aimed at the target. This might be critical, even if a high level of precision is expected.  52  In contrast, precision can be achieved if we understand the statistical behavior of the sample.  Table 4-5: Histogram data of the 41 Oxide samples Bin Frequency Cumulative % -3 0 0.00% -2 1 2.50% -1 4 12.50% 0 13 45.00% 1 17 87.50% 2 4 97.50% 3 1 100.00% More 0 100.00%   Figure 4-8: Histogram of the 41 Oxide samples Figure 4-8 and Table 4-5, shows the historic data of the regression analysis. This chart is a Pareto chart that has been calculated with the 3 standard deviations obtained from the correlation of ICP Cu and Predicted Cu. The histogram plays a significant role with respect to the correlation because we are taking responses from cut-off grades. The histogram suggests that the bias tends to the positive side (mean is greater than the predicted value) and is less likely to trend to the negative side (mean is lesser than the predicted value). This suggests that if there is a cut-off grade 0%10%20%30%40%50%60%70%80%90%100%024681012141618-3 -2 -1 0 1 2 3 MoreFrequencyStandard DeviationHistogramFrequencyCumulative %53  of 0.3% Cu, then 25% will be below the cut-off, and the other 75% will be around or greater than the target. In contrast, in Figure 4-9 the trend indicates that from 0 to 3% Cu, the prediction turns to be negative.    Figure 4-9: Standard Deviation dispersion of the predicted Copper  4.5 Interaction effect analysis using multilinear regression analysis for Oxide samples The analysis of the interaction effects begins with the development of another Python Script to multiply each element response by another element response. The input of this script is shown in the table in Appendix A  . In the script there are 59 elements, giving an output of 3481 interaction effects of elements, including repetitions such as “Ag II@232.02*Ag II@232.02”. The problem described in section 4.4 in terms of zeros in the matrices calculations is increased here. Every single space has been calculated as the multiplication of 2 responses, and if one or two of the responses are empty (or zero for the calculation), then the result will also be empty, or zero.    -4-3-2-101230 2000 4000 6000 8000 10000 12000 14000 16000 18000Standard DeviationConcentrations of Cu (ppm)Standard Deviation of the Predicted Cu 54  Table 4-6: Truth Table using AND logic AND A B AB 0 0 0 0 1 0 1 0 0 1 1 1 To gain an understanding of how this will effect the results of the calculations, Table 4-6 shows the results of a Truth Table with the operator AND. In this case, A represents one ion and B another ion in the multiplication script. A zero represents an empty space, and 1 represents a numeric response different than an empty space. As such, it is indicated that only 25% of the possibilities will provide a numeric response for the 3481 binomial elements. This increases the potential for error, and it is recommended that this situation be investigated in more detail.  The multiplication provides responses that are in the numerical range of squared power because they have been multiplied. Evidence of this is shown in the extract of the output of the script in  Table 4-7. This chart simply provides a random extraction from the whole table. This portion of the table, however, has been shown on purpose to provide at least some visible data because most of the tables have no interaction effect responses.  The interaction effects are developed with the purpose of creating links between the target ore (Copper) and the host minerals. The mineralogy of the bearing minerals of the target ore provides a good trace for the presence of the target element. However, this approach is appropriate for ores such as gold, in that direct gold readings are unlikely through LIBS or any other sensor, due to particle size. Massive ore bodies such as Copper porphyries do not allow for the creation of strong links to a specific mineralization because of the natural and complex geological formation of the ore body. Because of this, the current research focuses on the statistical analysis of the interaction of the elements and not on the mineral-bearing association of host minerals, also 55  referred to as ore genesis. For example, host minerals of gold provide a strong response to the presence of gold because the fine, or very fine grain size of gold might not be read by a sensor. As such, the gold associated to Tellurides, Sulphides, Arsenopyrites or Carbonaceous materials, and can be difficult to read as gold. However, the association to gold would be easier if the predictive equation searches for Arsenic, Antimony or Tellurium, depending on the local ore genesis. This would provide a good tool for searching over high grade veins where gold is occluded into the mentioned host minerals. However, if the ore body is a massive disseminated porphyry, then the interaction effect might limit the statistical capacity of predicting the element concentration by not accepting some of the elements. Indeed, the best approach to the interaction effect is to provide some logical acceptance or rejection of the variables under the geological perspective based on their mineralogical associations. Copper porphyry deposit genesis typically belongs to a hydrothermal magmatic fluid for which a better approach might be geo-spatial characterization via geostatistical analysis rather than heterogeneity and host mineralization.  Table 4-7: Extract of binomial multiplication of the ion responses from LIBS Rock Mg I@285.21*Be III@448.73 Mg I@285.21*Bi I@306.77 Mg I@285.21*Ca I@422.67 Mg I@285.21*Ca II@317.93 Mg I@285.21*Cd II@274.85 Mg I@285.21*Cl II@481.01 Mg I@285.21*Co I@347.4 1     1052956   1173146.9     2     1012570   1194120.2     3     1045180 1062383.85 1129281.0     4     1045832   1197269.8     5     1051358 996808.1515 1037441.6 823450.2   6     978493   1067929.7     7     1045516   1052351.5     8   1361130.225 1034371   1455831.0     9     1111389 1161952.0 1315768.1 957001.3   10   1260264.6 1045583   1420121.4     11     1117576 1508004.4 1268463.3     12   1269411.11 1014349 1078216.8 2131788.4     13     1040576   1190350.9     14     949752   1134324.3     15     867266   979689.1     16     1026289   1089395.4 936682   17 973928.7   959216 1093710.791 1170050.6     18   1095843.214 1070755 1127179.8 1792358.7     56  Rock Mg I@285.21*Be III@448.73 Mg I@285.21*Bi I@306.77 Mg I@285.21*Ca I@422.67 Mg I@285.21*Ca II@317.93 Mg I@285.21*Cd II@274.85 Mg I@285.21*Cl II@481.01 Mg I@285.21*Co I@347.4 19   1099832.767 1033135 1112472.288 1362796.2     20   1034505 1047562 1082070.9 1076614.5     21     971638 956096.7 1191059.4 895723.2   22   1444833.113 1032193   1732889.3     23   1254677.907 1002130   1184938.5     24   1131976.625 1054606 1237411.5 1486248.5   1032334.8 25     1014031 1057703.4 1150800.1     26   1242154.05 1048500 1004045.2 1410501.7     27     1084227 1168885.1 1198292.6     28     1028212 1084348.35 1398646.7     29     1058327   1140914.1     30     1021557 1130917.282 1368772.1     31     990900   1287859.9     32     991509   1266436.2     33     1044814   1116409.9     34     1040522 1008561.8 1128178.6 981586.075   35     1102378 1144697.88 1389501.3     36     1003450 1050617 1112683.3     37     1007754 1009750.3 1239945.7     38   1396766.7 1085700 1093554 1904927.6     39     997601   1494442.3     40     1087467 1109302.074 1031189.2     41     1088747   1314198.8 1003087.05    This numerical range will disable the sensitivity of the ion responses from LIBS because the numbers are higher in quantity than are the raw LIBS responses. As such, values in Table 4-7 were re-calculated as the square root for all of the values. As in Table 4-7, this part is shown on purpose for the reason of providing some visible data. Table 4-8: Extract of the square root of the binomial multiplication of the ion responses Rock Zr III@266.43*Ag II@232.02 Zr III@266.43*Ag II@241.32 Zr III@266.43*Al II@281.62 Zr III@266.43*Ba II@455.4 Zr III@266.43*Be II@272.89 Zr III@266.43*Be III@448.73 1 0 0 900 0 912 0 2 0 0 0 0 926 0 3 0 0 0 0 0 0 4 0 0 0 0 0 0 5 0 0 946 0 0 0 6 0 0 0 0 0 0 7 0 0 0 0 0 0 8 0 0 1153 0 1263 0 9 0 1060 1025 0 1321 0 10 0 0 0 0 1015 0 11 0 0 996 916 1207 0 57  Rock Zr III@266.43*Ag II@232.02 Zr III@266.43*Ag II@241.32 Zr III@266.43*Al II@281.62 Zr III@266.43*Ba II@455.4 Zr III@266.43*Be II@272.89 Zr III@266.43*Be III@448.73 12 0 1021 0 0 1244 0 13 0 0 0 994 1084 0 14 0 0 0 0 0 0 15 0 0 0 0 0 0 16 0 0 0 0 0 0 17 0 0 0 914 1059 929 18 0 0 966 0 1033 0 19 0 0 0 0 1046 0 20 0 0 920 0 957 0 21 0 0 0 856 924 0 22 0 0 1069 0 1245 0 23 0 1062 1081 0 1314 0 24 0 0 989 0 1089 0 25 0 0 0 0 951 0 26 0 0 0 0 1153 0 27 0 0 0 0 0 0 28 0 0 0 939 1100 0 29 0 0 0 0 0 0 30 0 0 0 842 940 0 31 0 0 0 0 1045 0 32 1084 1242 0 0 0 0 33 0 1084 1068 1079 1240 0 34 0 0 884 844 0 0 35 0 0 0 0 1028 0 36 0 0 0 0 0 0 37 0 0 0 0 1072 0 38 0 0 0 0 1161 0 39 0 0 0 0 978 0 40 0 0 0 0 0 0 41 0 0 0 0 1179 0  An extraction of the 3481 square rooted binomials is shown in Table 4-8. This numerical range is similar to that of the LIBS responses. The empty spaces were filled with zeros to make the computing of the responses possible. Table 4-8 will not be included into this thesis due to its size, but can be easily replicated through the use of the Python Script included in Appendix D  .  4.6 First procedure run analysis for the regression for Oxide samples The first run for the regression uses data from Table 4-8. The entire table was processed with the MATLAB Stepwise fit function, providing statistical results for the 3481 binomials. The 58  results indicate that 3443 values, or 98.9 % of all of the binomials provided a NaN result for the p-value. MATLAB (MathWorks) describes NaN returns as “Not-a-Number” values that result from operations with undefined numerical results. For all of these NaN results for p-value, the calculated coefficient was zero. Table 4-9 shows the calculated values of p-values and coefficients in MATLAB for the first run in the algorithm. It is expected that the calculated p-value of zero “0” is due to the large amount of variables processed by the software. The values were calculated for Copper in ppm from the ICP Certified Results (ICP certified assay results for the 41 Oxide Escondida samples), a target dependent variable. The maximum allowed p-value was set at 0.05.    Table 4-9: Results of the first run using Stepwise Fit regression in MATLAB for Copper Binomials p-value Coefficient Al II@281.62*Ba II@455.4 0 4.7660 Ba II@455.4*Ca II@317.93 0 -0.7830 Ba II@455.4*Fe I@374.95 0 -3.7101 Be II@272.89*Ca I@422.67 0 -13.306 Be II@272.89*Cu I@324.75 0 163.232 Be II@272.89*Cu I@327.4 0 -132.49 Be II@272.89*Na II@298.42 0 -19.509 Be II@272.89*Ti I@399.86 0 -13.512 Be III@448.73*Cr I@427.48 0 6.0267 Ca I@422.67*Mg III@239.51 0 7.2111 Ca II@317.93*Al II@281.62 0 0.2186 Ca II@317.93*Cl II@481.01 0 -2.3148 Ca II@317.93*Cr I@427.48 0 -4.6994 Cd II@274.85*Mn II@261.02 0 -0.0390 Cd II@274.85*Ti II@376.13 0 0.0333 Cl II@481.01*Ir I@269.42 0 1.0694 Cr I@427.48*P I@253.56 0 -0.078 F II@350.56*Si II@413.09 0 0.5143 Fe I@374.95*Fe I@374.95 0 -2.0133 Fe II@234.35*P I@253.56 0 -13.075 Ga I@294.36*Ni I@349.3 0 1.7984 Ga I@294.36*Pb I@280.2 0 0.0006 In II@294.1*W II@248.92 0 0.4223 In II@294.1*Y II@371.03 0 0.0001 Mg III@239.51*Si I@288.16 0 -31.205 N II@399.5*P I@253.56 0 -2.7507 O III@393.48*P I@253.56 0 15.6554 O III@393.48*P IV@334.77 0 -0.206 P I@253.56*F II@350.56 0 -6.006 P I@253.56*Zr III@266.43 0 0.0197 59  Binomials p-value Coefficient P IV@334.77*Sn II@335.2 0 -0.6383 P IV@334.77*Ti II@376.13 0 -1.0461 Pb I@280.2*Tl I@276.79 0 0.7423 Pb I@280.2*Tl I@351.92 0 0.8022 S VI@419.89*V II@292.4 0 0.2601 Ti I@399.86*V II@292.4 0 -0.6404 Ti I@399.86*Zr III@266.43 0 9.3700 Ti II@376.13*Tl I@276.79 0 2.1956  Table 4-9 represents a preselection of the set of variables from Table 4-8. All of these interaction effects have a higher statistical interdependence with respect to the target value, and were selected based on t-statistics assumptions in order to build an equation with respect to which variables provide a better fit to the target dependent variable (Cu ppm).   4.7 Second procedure run analysis for the regression Once the first set of variables was selected, the set of responses for each of these binomials was re-entered into MATLAB in order to process the data. The same process employed in the first run was used for this stage, but the dataset consisted of the binomials selected in Table 4-10. Table 4-10: Second run using Stepwise Fit regression in MATLAB Binomials p-value Coefficient Be II@272.89*Ti I@399.86 1.26E-16 -13.512 Ti I@399.86*Zr III@266.43 2.00E-16 9.370 Be II@272.89*Cu I@324.75 9.34E-16 163.23 P I@253.56*F II@350.56 1.50E-15 -6.006 Al II@281.62*Ba II@455.4 8.78E-15 4.765 Be II@272.89*Cu I@327.4 1.41E-14 -132.5 Mg III@239.51*Si I@288.16 1.43E-14 -31.21 Ca II@317.93*Cr I@427.48 5.45E-14 -4.699 Ca II@317.93*Cl II@481.01 5.92E-14 -2.314 Ba II@455.4*Fe I@374.95 1.15E-13 -3.709 O III@393.48*P I@253.56 1.21E-13 15.65 N II@399.5*P I@253.56 2.27E-13 -2.750 Fe I@374.95*Fe I@374.95 2.71E-13 -2.014 Ti II@376.13*Tl I@276.79 2.88E-13 2.196 Be II@272.89*Na II@298.42 2.99E-13 -19.50 Fe II@234.35*P I@253.56 4.06E-13 -13.07 Be III@448.73*Cr I@427.48 4.79E-13 6.026 Pb I@280.2*Tl I@276.79 1.02E-12 0.742 60  Binomials p-value Coefficient Ga I@294.36*Ni I@349.3 3.64E-12 1.798 Ba II@455.4*Ca II@317.93 6.56E-12 -0.783 Ca I@422.67*Mg III@239.51 9.90E-12 7.202 F II@350.56*Si II@413.09 1.66E-11 0.515 Be II@272.89*Ca I@422.67 1.87E-11 -13.30 Pb I@280.2*Tl I@351.92 2.19E-11 0.801 Ti I@399.86*V II@292.4 3.28E-11 -0.640 Cl II@481.01*Ir I@269.42 5.62E-11 1.0676 P IV@334.77*Ti II@376.13 8.94E-11 -1.046 Ca II@317.93*Al II@281.62 4.36E-10 0.2193 P IV@334.77*Sn II@335.2 6.11E-10 -0.638 S VI@419.89*V II@292.4 1.99E-09 0.260 In II@294.1*W II@248.92 2.57E-09 0.42 O III@393.48*P IV@334.77 4.64E-08 -0.205 Cr I@427.48*P I@253.56 1.08E-06 -0.076 Cd II@274.85*Ti II@376.13 5.44E-06 0.03 P I@253.56*Zr III@266.43 7.25E-05 0.018 Cd II@274.85*Mn II@261.02 0.0044785 -0.032 Ga I@294.36*Pb I@280.2 0.2195562 0.0003 In II@294.1*Y II@371.03 0.5953761 -0.0003 The calculations depend on the number of statistical variables because they are matrix multipliers, and as such, p-values might change for different runs. Values highlighted in red do not fit the minimum standard of 0.05 for p-value, and will be removed from the set of variables. The above table is sorted from smallest to largest p-value.   4.8 Proposed Method A The variables with the smaller p-values were taken from the set of values in Table 4-10 to continue with the algorithm. The reason for choosing this set of values is that a reasonable equation for predicting Copper values cannot hold “too many variables,” meaning that there should be no more than 10 or 12 variables in the equation. Smaller p-values show a higher interdependence between the dependent and interdependent variables, which is the key target in the sorting algorithm.  For this method, we used the first 20 interaction effects shown in Table 4-10. These effects have the smallest p-values in the correlation matrix, and are added to the 6 elements from Table 61  4-3. The reason that it is necessary to add elements to this binomial set is because the geological variable interaction corresponds directly to some presence of the elements. In this case, our target is Copper, and Copper alone must be added. Silicon, Magnesium and Sodium are found in abundance on the earth’s crust (Yaroshevsky), and they show a statistical correlation with the target variable (ICP Copper assays).  The final input for the computation of the correlation will include 26 variables, as shown in Table 4-11. This table indicates the p-values and the coefficients for each variable computed. Unexpectedly, the p-value for elements such as Cu, I, or Na II are high, and do not fit with the standards suggested for inclusion into a prediction equation.  Table 4-11: Results for correlation for Oxide rocks Variables p-value Coefficient Be II@272.89*Ti I@399.86 1.95E-12 -11.883 Ti I@399.86*Zr III@266.43 9.52E-11 8.623 Be II@272.89*Cu I@324.75 7.36E-10 142.45 P I@253.56*F II@350.56 2.98E-09 -4.478 Al II@281.62*Ba II@455.4 4.72E-04 2.99 Be II@272.89*Cu I@327.4 1.03E-06 -119.8 Mg III@239.51*Si I@288.16 6.70E-09 -25.62 Ca II@317.93*Cr I@427.48 0.0786 -1.492 Ca II@317.93*Cl II@481.01 0.056 -1.253 Ba II@455.4*Fe I@374.95 0.006 -2.585 O III@393.48*P I@253.56 4.63E-07 3.07 N II@399.5*P I@253.56 0.0012 -2.943 Fe I@374.95*Fe I@374.95 0.012 -1.805 Ti II@376.13*Tl I@276.79 0.0064 1.446 Be II@272.89*Na II@298.42 0.00019 -24.93 Fe II@234.35*P I@253.56 0.825 -0.678 Be III@448.73*Cr I@427.48 1 0 Pb I@280.2*Tl I@276.79 0.027 0.919 Ga I@294.36*Ni I@349.3 0.188 0.68 Ba II@455.4*Ca II@317.93 0.011 -2.6411 Cu I@324.75 0.601 -1.188 Cu I@327.4 0.560 -1.669 62  Variables p-value Coefficient Mn I@279.83 9.39E-06 3.2323 Na II@307.83 0.354 0.291 Si I@288.16 0.755 -0.999 Sn II@335.2 0.275 0.839  Appendix A  shows the responses for Mn I at 279.83 nm. For this particular ion, only one response was found. While the stepwise regression suggests that the Mn term is significant, it does not provide a significant amount of information and was therefore eliminated from the model. By comparing Table 4-11 and Table 3-1, some of the interaction effects proposed for building the predicted Copper formula can be confirmed. Magnesium and Silicon are likely to be found together, and to create a numerical correlation to Copper because the Biotitic and Quartz-Sericite mineral groups contain these two elements. The elements shown in the mineralogical group are not necessarily good predictors for copper. The 1st and 2nd Interaction Effect indicators show the confidence level of the identification of each. These indicators are based on Table 3-9.  Table 4-12: Final prediction equation for Predicted Copper 1st I. E. 2nd I. E. Variables Coefficient p-value Poor Good Be II@272.89*Ti I@399.86 -11.78 1.33E-08 Good Very Good Ti I@399.86*Zr III@266.43 8.71 1.14E-07 Poor Very Good Be II@272.89*Cu I@324.75 157.8 1.63E-08 Good Unknown P I@253.56*F II@350.56 -3.16 0.00041 Intercept: 37480.607 Poor Very Good Be II@272.89*Cu I@327.4 -160.5 3.16E-08 Good Very Good Mg III@239.51*Si I@288.16 -30.32 1.11E-07 Unknown Good O III@393.48*P I@253.56 1.968 0.01079 Poor  Mn I@279.83 4.11 0.0002  The values were computed with Stepwise Fit in MATLAB, the variables in this table are used to build the predictive equation for copper. This final equation with its intercept, is used to plot Figure 4-10. This chart shows a very good correlation of 0.9614 that has the highest Pearson 63  Coefficient found for the Oxide samples. However, this method is inconsistent, and needs to be subject to revision.  𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 𝐶𝑢(𝑝𝑝𝑚) = 37480.6 − 11.78 ∗ Be II@272.89 ∗ Ti I@399.86 + 8.71 ∗ Ti I@399.86 ∗ Zr III@266.43 + 157.87 ∗Be II@272.89 ∗ Cu I@324.75 − 3.16 ∗P I@253.56*F II@350.56-160.59* Be II@272.89*Cu I@327.4-30.32* Mg III@239.51*Si I@288.16+1.96* O III@393.48*P I@253.56+4.11* Mn I@279.83 Equation 3 Predicted Copper for Oxide samples - Method A  Figure 4-10: Correlation equation for LIBS Copper responses 050001000015000200002500030000350000 5000 10000 15000 20000 25000 30000 35000Predicted Copper (ppm)ICP Copper (ppm)Predicted Cu1:1Pearson Correlation = 0.96148952964  The negative coefficient indicates that there is an inverse correlation between the Copper grade and the response parameter or element. For example, the high concentration of an element associated with a gangue mineral would imply a low concentration of Copper.   A common mistake that is made while developing regression analysis is to follow the patterns that had been developed during former projects. In this case, LIBS has a different set of values. This set of values varies with regard of the amount of information present, such as for example, Mn I at 279.83 nm.  Figure 4-11: Histogram for the correlation equation for LIBS Copper responses The LIBS responses fit very well, and this histogram shows how the trend does not reach the limits of the third standard deviation which demonstrate an excellent fit to the prediction. Some of the data barely reaches the 1st or 2nd standard deviation for the whole set.  0%20%40%60%80%100%120%024681012141618-3 -2 -1 0 1 2 3FrequencyStandard DeviationsHistogramFrequency65  As mentioned, this information is quite good, and fits very well with respect to the intended target. However, this method is not reliable because it does not consider the number of responses available from the interaction effects. It is necessary to see how many responses can be counted in order to fill this regression.  Also, the number of responses available are not explicitly shown in Appendix A   because this is a pivot table that provides a lump sum of the total responses from LIBS. The real responses are shown in Table 4-1. The data fits very well in this prediction, but will not function well in the real world once the sensors are built-in to the belt conveyors, or the buckets of shovels or front end loaders.   4.9 Proposed Method B This method is similar in procedure to Method A but includes the amount of responses obtained from LIBS in its analysis. Appendix E  indicates the amount of LIBS responses attained for each of the 41 samples from Escondida Mine. It is important to know the number of responses in order to determine the mathematical error. Calculating mathematical error does not need to be considered because it will be assessed as part of the proof of concept but it is expected to be taken into account once the algorithm is applied to a sensor system either on a belt conveyor or a mining shovel, for ore sorting. The mathematical error refers to the availability of responses for the terms in the Predicted Formula. Some variables, such as Pb I@280.2 or Tl I@276.79 included in Table 4-11, have a positive statistical correlation with the target variable and are mathematically viable. However, once inserted into a correlation equation, they will not work as expected because there are not enough responses to feed the model in a sorter device.  66  As a result of the mathematical error, LIBS will loose its potential to produce the elements used for the interaction effects. If one of the elements needed for one interaction effect variable is not easily read in the first readings, then the predictive equation will be incomplete and the prediction inaccurate. The reading will not necessarily be taken several times on the same rock, and the likelihood of getting a response from a binomial with two ions will be low, and as such, will result in a high level of inaccuracy and low level of precision. A clear presentation of this problem will be done later in this chapter.   It is important to mention that a low amount of data for an independent variable provides higher correlation because there is less squared error to be taken into account. These variables can be computed successfully, but will not provide optimal results.    4.9.1 Quantification of the number of responses In order to quantify which independent variables should be chosen to create a prediction, one proposed method is to weigh the p-values times the occurrences of the response along the whole data set. Table 4-13 shows an extraction of the way in which these readings have been quantified. It is true that the average value for each ion can be processed to calculate the binomial value for the predictive equation. However, there is no guarantee that each single rock will be shot with LIBS enough times to elicit a valid response. A valid response is understood as a reading using LIBS capable to generate values for all of the elements in the predictive equation, particularly elements in the interaction effects. In order to fix this potential hazard, it is necessary to obtain an individual analysis for each LIBS reading. Table 4-13 below indicates the rock number and its 67  respective readings. As mentioned previously, every rock sample was shot 40 times, obtaining 4 samples (S1 to S4) of 10 readings per sample.  Table 4-13: Extraction of the quantification process for the binomials Rock Reading Be II 272.89 Ti I 399.86 5   Rock Reading Be II 272.89 Cu I 327.4 125 1           1           S1,2 1         S1,0   1     S1,9   1       S1,1   1     S4,3   1       S1,2 1 1 1   S4,4   1       S1,3   1     S4,5   1       S1,6   1     S4,6   1       S1,8   1     S4,7   1       S1,9   1     S4,8   1       S2,0   1     S4,9   1       S2,1   1   2             S2,2   1     S1,6   1       S2,3   1     S3,2   1       S2,4   1     S4,7 1         S2,5   1     S4,8 1 1 1     S2,6   1   3             S2,7   1     S1,2   1       S2,8   1     S1,8   1       S2,9   1     S3,8   1       S3,0   1   4             S3,1   1     S1,0   1       S3,2   1   5             S3,3   1     S2,2   1       S3,4   1   6             S4,1   1     S2,3   1       S4,2   1     S2,5   1       S4,3   1     S3,9   1       S4,4   1   7           2           S3,3   1       S1,0   1     S4,8   1       S1,3   1   8             S1,4   1     S1,2 1         S1,5   1     S1,3 1         S1,6   1     S1,4 1 1 1     S1,7   1     S1,5 1 1 1     S1,8   1     S1,7 1         S1,9   1     S1,8 1         S2,0   1     S1,9 1         S2,1   1     S2,3   1       S2,2   1   9             S2,3   1     S2,9 1 1 1     S2,4   1     S4,0 1 1 1     S2,5   1    68  An individual analysis of these readings provides a clear breakdown of what we can get from LIBS as a sorting sensor. The “1” in the third column means that there exists a reading for the ion Be II@272.89, and the same for Ti I@399.86. The next column can show either a “1” meaning a valid reading for each of the two components of the interaction effect; or “-“, meaning no valid interaction. For example, no valid value can be obtained for the interaction from rock 1. For rock 2 only one valid interaction value can be obtained. The lump sum of all possible valid binomial values is 5 for Be II@272.89*Ti I@399.86. For the next interaction effect, Be II@272.89*Cu I@327.4, a valid lump sum of 125 binomial values is obtained. In this way, the values were obtained for each pre-selected binomial. Table 4-14 provides a summary of the number of responses of LIBS for each ion, and for each of the 41 samples. The maximum possible value of number of responses is 40 readings x 41 numbers of readings/samples, resulting in 1640.    Table 4-14: Summary of number of responses for the 41 Oxide samples Maximum 264 Maximum possible 1640 Number of samples 40 Number of readings/sample 41  1640 is the maximum number of responses that could be obtained for any binomial or ion variable in this project for the 41 Oxide samples. Table 4-15 shows the 20 binomials that were pre-selected from Table 4-10 with higher p-values. It is curious to note that the computation of this set of interaction effects included Fe I@374.95*Fe I@374.95, but Fe I@374.95 alone was not included when computing the ions in Table 4-2, obtaining a p-value of 0.71 (the maximum ideal p-value allowed is 0.05).  69  The maximum number of responses that could be obtained from this pre-selection is 266. The number of occurrences per maximum number of occurrences from Table 4-15 is 32/264=12%, and for the number of occurrences per maximum possible occurrences, it is 32/1640=1.95%.  Table 4-15: Number of occurrences for the binomials analyzed Binomials Number of occurrences N occurrences / Max N occurrences N occurrences / Max possible Be II@272.89*Ti I@399.86 32 12% 1.95% Ti I@399.86*Zr III@266.43 46 17% 2.80% Be II@272.89*Cu I@324.75 126 47% 7.68% P I@253.56*F II@350.56 4 2% 0.24% Al II@281.62*Ba II@455.4 0 0% 0.00% Be II@272.89*Cu I@327.4 120 45% 7.32% Mg III@239.51*Si I@288.16 158 59% 9.63% Ca II@317.93*Cr I@427.48 0 0% 0.00% Ca II@317.93*Cl II@481.01 0 0% 0.00% Ba II@455.4*Fe I@374.95 1 0% 0.06% O III@393.48*P I@253.56 35 13% 2.13% N II@399.5*P I@253.56 0 0% 0.00% Fe I@374.95*Fe I@374.95 266 100% 16.22% Ti II@376.13*Tl I@276.79 26 10% 1.59% Be II@272.89*Na II@298.42 127 48% 7.74% Fe II@234.35*P I@253.56 32 12% 1.95% Be III@448.73*Cr I@427.48 1 0% 0.06% Pb I@280.2*Tl I@276.79 91 34% 5.55% Ga I@294.36*Ni I@349.3 16 6% 0.98% Ba II@455.4*Ca II@317.93 1 0% 0.06%  This method provides a mathematical quantification to allow a greater significance for the binomials that are more likely to be seen. Table 4-16 shows the full pre-selection of ions and binomials, and it is already sorted by p-value/occurrence. For each of these independent variables, their respective coefficient, p-value, occurrence ratio and p-value per occurrence are shown.  Table 4-16: Weighting of the binomials Binomials & Elements Coefficient p-value Occurrence % p-value / Occurrence Be II@272.89*Ti I@399.86 -11.883 1.95E-12 1.95% 9.98918E-11 Ti I@399.86*Zr III@266.43 8.6230 9.52E-11 2.80% 3.39557E-09 Be II@272.89*Cu I@324.75 142.45 7.36E-10 7.68% 9.5787E-09 Mg III@239.51*Si I@288.16 -25.625 6.70E-09 9.63% 6.95332E-08 P I@253.56*F II@350.56 -4.478 2.98E-09 0.24% 1.22368E-06 70  Binomials & Elements Coefficient p-value Occurrence % p-value / Occurrence Be II@272.89*Cu I@327.4 -119.80 1.03E-06 7.32% 1.41409E-05 O III@393.48*P I@253.56 3.0743 4.63E-07 2.13% 2.17127E-05 Be II@272.89*Na II@298.42 -24.9375 0.00019267 7.74% 0.00248 Mn I@279.83 3.2323 9.39E-06 0.06% 0.0154 Fe I@374.95*Fe I@374.95 -1.805 0.012 16.22% 0.0754 Ti II@376.13*Tl I@276.79 1.4465 0.0064 1.59% 0.4084 Pb I@280.2*Tl I@276.79 0.91964 0.0279 5.55% 0.5040 Cu I@324.75 -1.1882 0.6015 91.46% 0.6577 Cu I@327.4 -1.6698 0.5600 83.66% 0.6695 Si I@288.16 -0.999 0.7555 78.60% 0.9613 Na II@307.83 0.2915 0.3545 6.46% 5.485 Ba II@455.4*Fe I@374.95 -2.585 0.0060 0.06% 9.851 Ba II@455.4*Ca II@317.93 -2.641 0.0115 0.06% 19.006 Ga I@294.36*Ni I@349.3 0.6803 0.188 0.98% 19.353 Fe II@234.35*P I@253.56 -0.6785 0.8258 1.95% 42.32427175 Sn II@335.2 0.8393 0.2757 0.24% 113.04 Be III@448.73*Cr I@427.48 0 1 0.06% 1640 Al II@281.62*Ba II@455.4 2.990 0.0004 0.00% No occurrence Ca II@317.93*Cr I@427.48 -1.492 0.0786 0.00% No occurrence Ca II@317.93*Cl II@481.01 -1.253 0.056 0.00% No occurrence N II@399.5*P I@253.56 -2.9436 0.0012 0.00% No occurrence  The idea behind this statistical sort is to select the interaction effects or ions with the smaller p-values and the higher occurrences. The values with smaller p-value/occurrence ratios are located at the top of the table, while those with higher ratios are at the bottom.  𝑝 − 𝑣𝑎𝑙𝑢𝑒 ↓𝑂𝑐𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑒 % ↑ Some of these variables have no occurrence. However, while being computed, these values could have been selected for correlation. This provides clear evidence of the error and the importance of analyzing the variables independently.   4.9.2 Final correlation for the Oxide samples  The final selection of the variables consists of the top 8 binomials listed in Table 4-16. Furthermore, the two Copper ions available from LIBS responses were also added because they have a high occurrence, and provide a direct response for the predicted copper. Silicon was also 71  included as part of the variables because it has a high occurrence, and it is geologically related to Copper. The 1st Interaction Effect (I.E.) and 2nd Interaction Effect provide a reference for the confidence of the value with regard to the identification of the elements. Table 4-17: Final correlation for Copper Oxides 1st I. E. 2nd I. E. Elements/Binomials Coefficient p-value Poor Good Be II@272.89*Ti I@399.86 -11.867 2.63E-07 Good Very Good Ti I@399.86*Zr III@266.43 8.243 5.49E-06 Poor Very Good Be II@272.89*Cu I@324.75 158.5 1.10E-06 Good Very Good Mg III@239.51*Si I@288.16 -36.10 1.74E-08 Good Unknown P I@253.56*F II@350.56 -3.835 0.0002 Poor Very Good Be II@272.89*Cu I@327.4 -160.4 2.06E-06 Unknown Good O III@393.48*P I@253.56 2.317 0.009 Poor Very Good Be II@272.89*Na II@298.42 -10.13 0.343 Very Good Very Good Cu I@324.75 -1.43 0.946 Very Good Very Good Cu I@327.4 6.111 0.041 Very Good Very Good Si I@288.16 5.678 0.2876   Intercept 37480.6  The final proposed predictive equation for Oxide Copper given the 41 samples is: 𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 𝐶𝑢(𝑝𝑝𝑚) = 37480.6 −  11.86 ∗ 𝐵𝑒 𝐼𝐼@272.89 ∗ 𝑇𝑖 𝐼@399.86 +  8.24 ∗ 𝑇𝑖 𝐼@399.86 ∗ 𝑍𝑟 𝐼𝐼𝐼@266.43 +158.59 ∗ 𝐵𝑒 𝐼𝐼@272.89 ∗ 𝐶𝑢 𝐼@324.75 −  36.10 ∗ Mg III@239.51*Si I@288.16-3.83* P I@253.56*F II@350.56 - 160.45*Be II@272.89*Cu I@327.4 + 2.31 O III@393.48*P I@253.56-10.13* Be II@272.89*Na II@298.42-1.43* Cu I@324.75 + 6.11* Cu I@327.4 + 5.67* Si I@288.16 Equation 4 - Predicted Copper for Oxide Samples Method B   The prediction has a Pearson Correlation Coefficient of 0.949. Although it shows a slightly lower value than the coefficient in the last regression of 0.961, this value is more reliable. The standard deviation is 1779. The histogram below provides evidence that the Predicted Cu values tend to be lower values than the real values (assumed as the ICP Copper). Figure 4-14 shows a map of standard deviations for the 41 samples. The critical numbers for correlation prediction land on values near to those for the cut-off of the mine. 0 to 5000 ppm (0 to 0.5%) is a typical range for cut-off grades. Further research is suggested in order to group grade ranges for different mines so that error could be better controlled at grades close to the cut-off ranges.  72  It is notable that there is a negative correlation between the Copper concentration, as indicated by the coefficient for the wavelength 324.75. As shown in Table 4-4 there is a positive correlation between Copper grade and the magnitude of the Copper peak from LIBS at this wavelength. Therefore, the negative correlation is an artifact of the regression analysis that uses more than 1 wavelength to represent Copper.   73   Figure 4-12: Final correlation for Copper Oxides   050001000015000200002500030000350000 5000 10000 15000 20000 25000 30000 35000Predicted Copper (ppm)ICP Copper (ppm)Predicted Cu1:1Pearson Correlation = 0.94932009174   Figure 4-13: Histogram for the final correlation of Oxide samples    Figure 4-14: Standard deviation for the final correlation of Oxide samples 0%10%20%30%40%50%60%70%80%90%100%02468101214-3 -2 -1 0 1 2 MoreFrequencyStandard DeviationsHistogramFrequencyCumulative %-2.5-2-1.5-1-0.500.511.522.530 5000 10000 15000 20000 25000 30000 35000Standard DeviationConcentration of Cu (ppm)Standard deviation for final correlation of Oxides75  Chapter 5: Analysis of Sulphides with Laser Induced Breakdown Spectroscopy LIBS responses were obtained by shooting 38 Sulphide samples from Escondida Mine. Each sample was shot on 4 faces, had 10 readings per face, with a total of 40 readings per sample.  The methodology for the analysis of the Sulphide samples is similar to the methodology used for the Oxide samples. Thirty-eight Sulfuro (Sulphide) samples were analyzed with LIBS, and the responses are attached in Appendix F  . The ICP Sulfuro results shown in Appendix H  include Sulfuro-3, which is not included in the LIBS responses. Sulfuro-3 is a dust-type material that is difficult, if not impossible, to read it using LIBS. Because of this, it was not included in this analysis. An extraction of the output of the Python Script for the Sulphide sample analysis is shown in Table 5-1, and the compiled output is attached in Appendix F  .  Table 5-1 includes the rock sample, as well as each ion identified in the reading of that rock. Table 5-1: Extraction of the output of the Python Script for the Sulphide samples  Sample Rock Peak Wavelength Element Intensity Acc. Observed Wavelength Air 0 Su1,S1,0 274.89 Cd II 1211  274.854 1 Su1,S1,0 324.82 Cu I 2530 AA 324.754 2 Su1,S1,0 327.43 Cu I 2145 AA 327.3957 3 Su1,S1,0 374.88 Fe I 1002 A 374.9485 4 Su1,S1,0 234.42 Fe II 897 A+ 234.3495 5 Su1,S1,0 238.17 Fe II 1100 B+ 238.2037 6 Su1,S1,0 285.2 Mg I 860 A 285.2127 7 Su1,S1,0 279.56 Mg II 942 A+ 279.5528 8 Su1,S1,0 239.61 Mg III 1012 A 239.5149 9 Su1,S1,0 298.37 Na II 927 B 298.4186 10 Su1,S1,0 419.97 S VI 841 AA 420.083 11 Su1,S1,0 419.97 S VI 841 AA 419.89 12 Su1,S1,0 288.15 Si I 1220 B 288.1579   76    5.1 Correlation of LIBS Cu Sulphide response to ICP analysis  The initial LIBS correlations for the Sulphide samples using only the LIBS responses for Copper ions are shown in Figure 5-1. In comparison to the values shown in Figure 4-4 and Figure 4-5, these samples reveal a very low correlation coefficient of 0.077 for Cu I at 327.4, and -0.06 for Cu I at 324.75. The correlation coefficient is based on the standard deviations. The same value for the correlation coefficient was obtained using the raw data from LIBS, or through normalizing the data. The normalization of the data was initially done by taking the maximum peak of a spectrum and then setting that value as 1. The noise was calculated in a similar manner as it had been for Table J-4, with the noise value set at 0. However, the correlation coefficient is the same. It is important to note that the Sulphide samples have a white colouration, which makes it more difficult to read using LIBS, and increases the noise in the spectrum.  In order to improve this correlation coefficient, it is suggested to determine the Lower Limit of Detection and the range for the LIBS machine. The Lower Limit of Detection can be calculated by reading pure metal samples with known concentration to develop a calibration curve for each ion.  Such a calibration renders LIBS a powerful device for measuring concentration. However, this research does not aim to develop the measuring capabilities of LIBS, but rather its intention is to develop LIBS’ correlation capabilities in a geological environment.  77   Figure 5-1: LIBS responses for Copper ions for Sulphide samples   Figure 5-2: Basic correlation between ICP Cu vs LIBS Copper ions responses 01000200030004000500060000500010000150002000025000300001 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37LIBS responses (counts)Cu (ppm)LIBS responses to Copper ionsICP Cu Cu I@324.75 Cu I@327.40.00.10.20.30.40.50.60.70.80.91.00.0 0.2 0.4 0.6 0.8 1.0Cu I@324.75 & Cu I@327.4ICP Copper (ppm)Cu I@324.751:1Pearson Correlation = 0.077750254Cu I@327.478  5.2 Element correlation for LIBS responses for Sulphide samples The ion responses in Appendix F  were used to build a basic correlation based on “t-statistics” and p-values. The first interpretation of this correlation suggests a new unexpected component with respect to the list of ions for Sulphides - the presence of the Carbon element. The presence of C III at 229.69 was not expected to be present, and the ICP results in Appendix H  do not report the presence of Carbon. In addition, there are no readings of C III at 229 in the Oxide LIBS responses, making the presence of the element even more suspicious. However, even small responses in LIBS could be accepted as good responses because of the particle size of the elements. ICP is bulk testing while LIBS is a superficial test. Appendix G  shows the number of responses for the C III ion, and as expected, the responses are small in number in comparison to other ions in the same table.   A geological interpretation of this unexpected scenario may be that Sulphide oxidation takes place during the natural weathering process, thus generating acid that will dissolve carbonates. As such, Carbon responses are not present in the Oxide samples.  The predicted Copper correlation was conducted in MATLAB once the responses were processed in the Python Script. The results for the basic correlation are shown in Figure 5-2. They have a Pearson Correlation Coefficient of 0.824, which is high in comparison to the 0.77 coefficient for the Oxide samples that were seen in Figure 4-6. Table 5-2: Predicted Copper correlation using ions for Sulphide samples Elements Coefficient Std. Error p-value Occurrence Occurrence% C III@229.69 -6.036 2.0991 0.0075 29 2% Ag II@241.32 6.1057 2.0347 0.0055 79 6% Al II@281.62 -6.317 1.6232 0.0005 57 4% Ba II@455.4 -6.816 2.0373 0.0023 31 2% Ga I@294.36 -6.959 2.2109 0.0038 144 11% Mg III@239.51 -4.554 1.2981 0.0015 421 32% Ta I@362.66 -7.451 2.8549 0.0142 4 0% Zr III@262.06 -3.819 1.6705 0.0297 37 3% Intercept 23165     79   Figure 5-3: Predicted Copper correlation using ions for Sulphide samples  One issue not discussed in the chapter regarding the Oxide sample analysis was the relationship to the low p-value, which is the key element for the selection of the independent variables. A suspiciously high correlation coefficient was found in Table 5-2. There exists a relationship between the p-value, standard error, and the number of responses obtained from LIBS. As in  Table 4-3, Table 5-2 shows that the p-value is significantly small (good for correlation) when occurrence is low. Occurrence calculation involves the sum of responses for each ion, and the percentage is based on the maximum number of responses for all of the ions. The discrepancy 05,00010,00015,00020,00025,00030,0000 5,000 10,000 15,000 20,000 25,000 30,000Predicted Copper (ppm)ICP Copper (ppm)Predicted Cu1:1Pearson Correlation = 0.824380  between the two tables mentioned provides evidence to affirm that there is a relationship between the low number of responses and a possible low p-value.  Sections 4.8 and 4.9 explain in detail the reasons that a low occurrence of responses in a laboratory research project should be avoided.   5.3 Interaction effect analysis using multilinear regression analysis for Sulphide samples Binomial regression analysis is performed to find possible interaction effect variables that can generate a good response for the LIBS sensor correlation. Much like the methodology described for the Oxide samples, the Sulphide samples were processed using the Python Script that can be found attached in Appendix C  . The 65 samples from Appendix F  were processed, obtaining 4225 binomials. These binomials will generate numbers in different magnitudes than found in the ion responses. To solve this issue, the square root was applied to all the binomials obtained from the Python Script. Once the sheets were ready to be processed, the data was analysed with MATLAB in order to find potential interaction effect responses to meet the requirements for mathematical correlation.  The mathematical correlation defines the p-value at 0.05 as a standard, which means that 1 in 20 samples will exceed the 2 standard deviations. The Stepwise procedure will remove elements from the list that do not meet this criterion.  The LIBS responses were processed using the Python Script that is attached in Appendix D  . This multiplication was processed in MATLAB using the Stepwise Fit procedure. The correlation was not successful with respect to the small number of significant interaction effects and the geological interpretation of those effects. Table 5-3 shows the binomial correlation if a p-value of 0.05 is imposed.  81  Table 5-3: Binomial correlation for Sulphide samples with maximum 0.05 p-value Binomial Coefficient p-value Std. Error Al II@281.62*Cd II@274.85 -5.48 4.11E-04 1.394 Ba II@455.4*Ca II@317.93 -14.52 7.49E-04 3.908 C III@229.69*Ga I@294.36 -9.61 9.86E-06 1.844 Cu I@324.75*Cu I@324.75 -8.16 1.38E-02 3.139 Intercept 33084.15    In comparison to the Oxide samples that used a p-value of 0.05, using 0.05 for the Sulphide rocks does not provide a good output to use for correlation. Only 4 binomials passed the p-value requirement, and one of them is Cu I@324.75*Cu I@324.75, which has a bigger p-value when analyzed through the element analysis described in section 5.2.  This regression analysis was not successful because of the small number of significant variables.  Therefore, other types of linear correlation were attempted. One of the functions tested was Stepwiselm in MATLAB, which performs a linear regression analysis using forward and backward elimination for arriving at the final model, and provides a decision based on the Akaike Information Criterion (AIC). The AIC value for this correlation is 747.93. A lower number for the AIC represents a better correlation. The AIC value for the Oxide samples was 772.55. However, there was no need to use this tool because the correlation output was satisfactory.  The results of Stepwiselm used the data from Appendix F  and the final output is shown in Table 5-4.  82  Table 5-4: Stepwiselm output using the Sulphide ion responses        Where X# stands for: X Elements 2 C III@229.69 4 Ag II@241.32 5 Al II@281.62 7 Ba II@455.4 22 Ga I@294.36 29 Mg III@239.51 52 Ta I@362.66 64 Zr III@262.06  Stepwiselm will use the independent variables for computing either alone or multiplied by another independent variable. This means that for the Sulphide samples, there are no binomials that will show a good fit for the correlation using a p-value threshold of 0.05. Using this information, it was inferred that the p-value of 0.05 was too low to invalidate the correlation. It was necessary to increase the threshold p-value to 0.08. Testing was conducted several times for 0.06 and 0.07, however same results were obtained.  Table 5-5: Correlation output for variables computed with 0.07 p-value Binomial Coefficient p-value Std. Error Al II@281.62*Cd II@274.85 -5.47 0.00041 1.394 Ba II@455.4*Ca II@317.93 -14.5 0.00074 3.907 C III@229.69*Ga I@294.36 -9.61 9.86485E-06 1.844 Cu I@324.75*Cu I@324.75 -8.1 0.01381 3.138                    Estimate      SE       tStat       pValue                      ________    ______    _______    __________      (Intercept) 231     2351.2     9.852    9.2415e-11     x2             -6.03     2.091     -2.87       0.0074     x4              6.10      2.03       3.007       0.0054     x5             -6.31     1.62      -3.899      0.00053     x7             -6.81     2.03      -3.345       0.0022     x22            -6.95     2.21     -3.145      0.0037     x29            -4.55     1.29      -3.501      0.0014     x52            -7.45     2.85      -2.61        0.0141     x64            -3.81     1.67    -2.281       0.0297 83  5.4 First procedure run analysis for the regression of Sulphide samples The problem with increasing the p-value is that the procedure will accept more values with a higher error than for 2 standard deviations. In other words, the correlation will not be as good as expected. The correlation was computed using a 0.08 p-value for the interaction effect variables.  Table 5-6:   Results of the first run using Stepwise Fit regression in MATLAB for Sulphide samples Binomial Coefficient p-value Std. Error Ag II@232.02*Ag II@241.32 1.290 0 0 Al II@281.62*Ba II@455.4 -11.784 0 0 Al II@281.62*Cd II@274.85 -3.314 0 0 Al II@281.62*Cr I@427.48 -1.084 0 0 Ba II@455.4*Be II@272.89 -7.853 0 0 Ba II@455.4*Ca II@317.93 -3.278 0 0 Ba II@455.4*Si II@413.09 9.481 0 0 C III@229.69*Ga I@294.36 -6.833 0 0 Ca I@422.67*Zr III@262.06 -1.206 0 0 Ca II@317.93*W II@248.92 0.655 0 0 Cd II@274.85*Mn I@279.83 12.620 0 0 Cd II@274.85*Si I@288.16 -0.001 0 0 Cu I@324.75*Cu I@324.75 -16.317 0 0 Cu I@327.4*Si I@288.16 50.920 0 0 Fe I@374.95*O III@393.48 0.560 0 0 Fe II@234.35*O III@393.48 3.223 0 0 Fe II@238.2*Pb I@283.31 -7.528 0 0 In II@294.1*Zr III@262.06 6.014 0 0 Ir I@269.42*P I@253.56 -11.868 0 0 Mg I@285.21*Mn I@279.83 -6.416 0 0 Mg III@239.51*O III@393.48 -1.503 0 0 Mn I@279.83*N IV@347.87 -2.375 0 0 Na II@298.42*Zr III@262.06 -12.288 0 0 O III@393.48*Tl I@351.92 -0.486 0 0 P I@253.56*Pb I@283.31 8.475 0 0 P I@253.56*V II@292.4 0.006 0 0 P I@253.56*Zr III@262.06 -0.873 0 0 P IV@334.77*Sn II@335.2 5.993 0 0 Pb I@283.31*Zr III@262.06 1.547 0 0 Sn II@335.2*Tl I@276.79 -1.402 0 0  As mentioned before, a p-value of 0 and standard error of 0 reflects a computer error because of the large amount of data processed into matrices.   84  5.5 Second procedure run analysis for the regression of Sulphide samples The second run for the regression analysis was conducted using a p-value of 0.08. By using a different p-value, the coefficients, standard errors and p-values will change as a result of the mathematical procedure. P-values of less than 0.05 have been added in red. Table 5-7: Results of the second run using Stepwise Fit regression in MATLAB for Sulphide samples Binomial Coefficient p-value Std. Error Ag II@232.02*Ag II@241.32 0.417 0.936 5.201 Al II@281.62*Cd II@274.85 -5.201 0.000 1.157 Al II@281.62*Cr I@427.48 -0.536 0.796 2.058 Ba II@455.4*Be II@272.89 -3.630 0.233 2.983 Ba II@455.4*Ca II@317.93 -8.198 0.031 3.623 Ba II@455.4*Si II@413.09 1.841 0.509 2.756 C III@229.69*Ga I@294.36 -10.010 4.62E-07 1.550 Ca I@422.67*Zr III@262.06 -0.638 0.79 2.438 Ca II@317.93*W II@248.92 1.863 0.495 2.7006 Cd II@274.85*Mn I@279.83 -2.162 0.252 1.852 Cd II@274.85*Si I@288.16 0.486 0.75 1.544 Cu I@324.75*Cu I@324.75 -21.010 0.000 4.690 Cu I@327.4*Si I@288.16 34.875 0.002 10.71 Fe I@374.95*O III@393.48 -0.661 0.660 1.49 Fe II@234.35*O III@393.48 -0.789 0.593 1.462 Fe II@238.2*Pb I@283.31 -3.009 0.03 1.350 In II@294.1*Zr III@262.06 2.705 0.23 2.232 Ir I@269.42*P I@253.56 -5.502 0.014 2.119 Mg I@285.21*Mn I@279.83 -2.025 0.362 2.189 Mg III@239.51*O III@393.48 -0.157 0.913 1.440 Mn I@279.83*N IV@347.87 -1.316 0.651 2.88 Na II@298.42*Zr III@262.06 3.232 0.321 3.202 O III@393.48*Tl I@351.92 0.314 0.835 1.499 P I@253.56*Pb I@283.31 3.447 0.13 2.230 P I@253.56*V II@292.4 0.118 0.962 2.495 P I@253.56*Zr III@262.06 -2.158 0.4391 2.749 P IV@334.77*Sn II@335.2 3.392 0.218 2.696 Pb I@283.31*Zr III@262.06 0.150 0.964 3.380 Sn II@335.2*Tl I@276.79 -0.176 0.956 3.186  MATLAB calculates the matrices for correlation based on a p-value of 0.08. However, binomials with a value of less than 0.05 are selected. This is done to isolate the binomials with higher significance.  85  5.6 Proposed correlation of Sulphide samples Selected binomials from Table 5-7 were joined with the ions selected from Table 5-2. Due to the reduced amount of independent variables favourable for correlation, geological background information was not included for this correlation. However, elements such as Cu, Si and Ca are related to the Copper Sulfide ores. MATLAB computed the variables for the third time, as seen in Table 5-8. Table 5-8:  Binomial correlation for Sulphide samples with maximum 0.08 p-value 1st I. E. 2nd I. E. Variables Coefficient p-value Std. Error Good Poor Al II@281.62*Cd II@274.85 -5.170 0.000 1.219 Good Poor Ba II@455.4*Ca II@317.93 -9.736 0.014 3.736 Unknown Unknown C III@229.69*Ga I@294.36 -9.529 0.000 1.616 Very Good Very Good Cu I@324.75*Cu I@324.75 -21.521 0.000 4.935 Very Good Very Good Cu I@327.4*Si I@288.16 32.521 0.007 11.226 Very Good Good Fe II@238.2*Pb I@283.31 -2.801 0.058 1.419 Unknown Good Ir I@269.42*P I@253.56 -4.530 0.046 2.178 Unknown  C III@229.69 2.680 0.578 4.763 Good  Ag II@241.32 0.281 0.886 1.945 Good  Al II@281.62 -2.302 0.307 2.214 Good  Ba II@455.4 -0.398 0.854 2.144 Unknown  Ga I@294.36 -1.647 0.398 1.921 Good  Mg III@239.51 0.518 0.719 1.425 Unknown  Ta I@362.66 -2.665 0.347 2.789 Good  Zr III@262.06 -2.867 0.100 1.687   Intercept 16154.47    This time, variables with p-values of less than 0.08 were coloured in red, and this set of variables represents the variables proposed for a final correlation of the Sulphide ores at Escondida Mine. Negative coefficients express the mathematical shaping of the predictive equation. 𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 𝐶𝑢(𝑝𝑝𝑚) = 16154.4 + 𝐴𝑙 𝐼𝐼@281.62 ∗ 𝐶𝑑 𝐼𝐼@274.85 ∗ −5.170 + 𝐵𝑎 𝐼𝐼@455.4 ∗𝐶𝑎 𝐼𝐼@317.93 ∗ −9.736 + 𝐶 𝐼𝐼𝐼@229.69 ∗ 𝐺𝑎 𝐼@294.36 ∗ −9.529 + 𝐶𝑢 𝐼@324.75 ∗𝐶𝑢 𝐼@324.75 ∗ −21.521 + 𝐶𝑢 𝐼@327.4 ∗ 𝑆𝑖 𝐼@288.16 ∗ 32.521 + 𝐹𝑒 𝐼𝐼@238.2 ∗𝑃𝑏 𝐼@283.31 ∗ −2.801 + 𝐼𝑟 𝐼@269.42 ∗ 𝑃 𝐼@253.56 ∗ −4.530 Equation 5 - Predicted Copper for Sulphide samples 86   Table 5-9: ICP Cu vs Predicted Cu values for Sulphide samples in ppm Accuracy ICP Cu Predicted Cu 52%            6,560              3,157  11%            8,470              7,569  10%          11,400            10,249  55%            7,420            11,526  8%          12,200            13,232  33%            5,150              3,448  3%          15,000            14,483  120%            1,330               (266) 2%            9,620              9,398  86%            1,500              2,792  4%            2,510              2,408  8%          15,000            16,207  65%            6,160            10,139  368%            1,370              6,418  34%          25,700            17,017  302%            1,180            (2,381) 2%            5,490              5,576  91%            4,430              8,472  28%          13,700            17,519  11%            5,540              6,137  8%            1,060                 973  38%          19,100            11,822  30%            6,950              9,046  89%            4,190              7,900  25%            3,340              2,519  51%            4,610              6,941  144%            5,420            13,243  39%            2,300              3,187  10%            9,210              8,287  30%            6,130              7,950  418%               393              2,037  48%          20,100            10,438  8%               849                 784  0%          14,100            14,121  2%          10,400            10,192  8%          18,300            16,817  13%          19,200            16,793  16%            4,690              3,924  60%    87   Figure 5-4: Final correlation for Sulphide samples  Figure 5-4 shows the final correlation for the Sulphide ores. The Pearson Correlation Coefficient is 0.84, which is close to the 0.82 coefficient value for the correlation of elements only. It is interesting to note the similarities between the correlations in Table 5-2 and Table 5-4, 05,00010,00015,00020,00025,000 -  5,000  10,000  15,000  20,000  25,000Predicted Cu (ppm)ICP Copper (ppm)Predicted Cu1:1Pearson Correlation = 0.842 Std. Dev. +2 Std. Dev. -88  which look very similar in terms of the variables used. The Linear Stepwise or “Stepwiselm” did not suggest any binomial, as it had for the Oxide samples. This means that the best fits obtained in Figure 5-4 are not necessarily the best possible fits. We can confirm this information by analyzing the Pearson Correlation Coefficients that are lower than 0.9. The lines corresponding to the 2 standard deviations calculated from the correlation have been added to the chart. As mentioned previously, a p-value of 0.05 suggests that only 1 out of 20 samples will be out of the two standard deviations. In this case, a p-value of 0.08 was used to calculate this correlation. This means that 2 out of 25 values will be out of the range. As such, a projection of the number of samples that will be out of the range for 38 samples is 3.04, and in the graph, we see that 3 samples are outside of the lines for the two standard deviation.  If material is sorted on a daily basis, 8% of the material will result in blind sorting. Blind sorting could be defined as the material that sensors cannot read properly. A good way to control for and measure blind sorting is through the use of histograms of standard deviations, as shown in Figure 5-5. This histogram shows the trend of the prediction as being mostly slightly above the real value. The optimum situation would see the histogram inclined to the negative standard deviation so that the sensor could take the response as a low value instead of as processing waste. 89   Figure 5-5: Histogram for the final correlation for Sulphide samples    Figure 5-6: Standard Deviation for the final correlation for Sulphide samples 0%10%20%30%40%50%60%70%80%90%100%0246810121416-3 -2 -1 0 1 2 MoreFrequencyStandard DeviationSulphide HistogramFrequencyCumulative %-3-2-10123 -  5,000  10,000  15,000  20,000  25,000  30,000Standard DeviationConcentration of Cu (ppm)Standard Deviation of the Predicted Copper for Sulphides 90  Chapter 6: Sulphide versus Oxide discrimination The determination of an ore as an Oxide or a Sulphide is crucial for mine-mill reconciliation. The main purpose of the determination of Oxide or Sulphide ores during the mining process is to select the recovery method to be used for that ore. Sulphides are usually processed in the concentrator, while Oxides are usually leached. Although a discussion of the efficiency of each method is not the subject of this research, the economic impact of dilution in mining is an issue that has an effect on the efficiency of the recovery method, and can be solved through LIBS sorting.   6.1 Spectroscopy ambiguity regarding S III and O III for our LIBS machine The wavelengths taken for the ions were obtained from the NIST database. The use of S III and O III are based solely on the probabilities of transition shown in the NIST database, and represent the only options available for the bandwidth used by FiberLIBS. A detailed discussion of the selection of the wavelengths can be found in Chapter 3:. However, there is ambiguity in defining the most appropriate wavelengths for Oxygen and Sulphur. Wavelengths were identified according to following pattern:  1. Transition strength (Aki) 2. Accuracy (Acc.) 3. Relative Intensity  The rocks analyzed for this research belong either to Oxide or Sulphide ores. There is a characteristic triplet of spin around the wavelengths at 393.42, 394.45 and 396.15 nm. According to the theory of Nuclear Magnetic Resonance Spectroscopy, spins happen because ions have slightly different chemical shifts, represent slightly different spin flip energies, or have nucleii with slightly different magnetic environments.  91  The wavelength characteristics for these 3 wavelengths were verified using the NIST database as:  393.42 nm for O III  394.45 for O III  396.15 for S III and O III in overlap situation, favourable for S III  6.2 Spectroscopy and observation of multiple strong lines The main reason that it is necessary to analyze this ambiguity is because the LIBS machine used for this research has limitations with respect to bandwidth. The bandwidth of the machine can detect a range from 229 nm to 500 nm, creating smaller wavelength pixels possible to analyze in comparison to broader LIBS bandwidths. Stronger lines for Oxygen and Sulphur can be found beyond 500 nm with a higher definition, however this limitation does not limit LIBS’ capacity to recognize an Oxide or Sulphide sample.  In order to define the parameters to allow LIBS to recognize an Oxide or Sulphide, it is necessary to understand the wavelength characteristics for Oxygen and Sulphur. Table 6-1 shows the spectroscopies taken from the NIST database (National Institute of Standards and Technology NIST), providing a mining search criteria of C+ for accuracy.        92  Table 6-1: Spectroscopies for ambiguity between O III and S III Spectrum Observed Ritz Rel. Aki Acc. Ei Ek Ei Ek  Wavelength Wavelength Int. s^-1  (cm-1) (cm-1) eV eV  Air (nm) Air (nm) (?)       Nd II 393.482 393.4815+ 610 1.37E+07 B+ 2585.46 27992.425 0.32 3.46 O III  393.4823  9.93E+07 C+ 366802.62 392209.53 45.284274 48.42093 C IV  393.489  3.30E+07 A 445368.5 470775 54.98 58.12 W II 393.54325 393.54325 39 3.09E+06 B 13173.337 38576.313 1.63 4.76 Fe I 393.58122 393.58124 9300 1.14E+07 C+ 22838.323 48238.847 2.82 5.96           Fe I 394.33404 394.33404 3630 6.46E+05 C+ 17726.988 43079.023 2.19 5.32 Al I 394.40058 394.4006 24g 4.99E+07 B+ 0 25347.756 0.00 3.13 Ar II 394.42712 394.42712 49 4.10E+06 B 132327.36 157673.41 16.34 19.47 O III  394.4854  1.17E+08 C+ 366488.45 391830.76 45.25 48.37 Fe I 394.4889 394.4889 2820 1.40E+06 B 24118.819 49460.902 2.98 6.11           Fe I 396.02789 396.02786 1000 4.10E+06 C+ 29356.744 54600.35 3.62 6.74 F V  396.08  1.52E+06 B 784099 809339.5 96.80 99.92 W II 396.08582 396.08601 5 4.24E+05 B 19637.309 44877.209 2.42 5.54 S III 396.1516 396.1526 12 9.45E+06 B 147551.6 172787.26 18.22 21.33 Al I 396.152 396.15201 26g 9.85E+07 B+ 112.061 25347.756 0.01 3.13           O III 396.159 396.1573 200 1.25E+08 B 306586.08 331821.44 37.85 40.97 Nd II 396.221 396.2205+ 510 7.10E+06 B+ 2585.46 27816.795 0.32 3.43 Ti I 396.28508 396.28507 2500 4.71E+06 A 0 25227.222 0.00 3.11 Nd II 396.3114 396.3105+ 1400 3.98E+07 B+ 3801.93 29027.535 0.47 3.58 Nd II 396.39 396.3905+ 270 1.14E+07 B+ 5085.64 30306.15 0.63 3.74  An extraction from this chart, along with the surrounding ions that could be used to define and understand this ambiguity, can be found in Table 6-1. For 393.48 nm, the biggest transition strength is given to O III, with a total Aki of 9.93E+07. Similar conditions are set for the O III at 394.48, with an Aki of 1.17E+08. The biggest problem regarding the triplet definition is with respect to wavelength 396.15. The only surrounding ion with a higher Aki value is Al I, but it has a “g” comment which stands for “Transition involving a level of the ground term.” The best fits for its Aki and Accuracy are S III or O III. We conclude that this is a case of overlap, as discussed 93  in Chapter 5 of the “Handbook of Laser Induced Breakdown Spectroscopy” (Cremers and Radziemski). In order to define this ambiguity, it is possible to analyze the ionization energies with respect to the expected energy provided by the laser. As shown in Table 6-2, higher ionization levels require the provision of higher energy. For LIBS, the energy is limited, and it is likely to have greater certainty over smaller ionization energies than higher ones. The O III has a 54.93 eV in contrast to the S III 34.79 eV. This means that S III has a higher probability of being seen. However, the Relative Intensity of O III is 200 in comparison to S III with only 12 (Relative Intensity does not have units).  Table 6-2: Extraction of Ionization Energies (eV) Element   I II III IV V Hydrogen H 1 13.5984     Helium He 2 24.5874 54.41776    Lithium Li 3 5.3917 75.64 122.45429   Beryllium Be 4 9.3227 18.21114 153.89661 217.71865  Boron B 5 8.298 25.1548 37.93064 259.37521 340.2258 Carbon C 6 11.2603 24.3833 47.8878 64.4939 392.087 Nitrogen N 7 14.5341 29.6013 47.44924 77.4735 97.8902 Oxygen O 8 13.6181 35.1211 54.9355 77.41353 113.899 Fluorine F 9 17.4228 34.9708 62.7084 87.1398 114.2428 Neon Ne 10 21.5646 40.96296 63.45 97.12 126.21 Sodium Na 11 5.1391 47.2864 71.62 98.91 138.4 Magnesium Mg 12 7.6462 15.03527 80.1437 109.2655 141.27 Aluminum Al 13 5.9858 18.82855 28.44765 119.992 153.825 Silicon Si 14 8.1517 16.34584 33.49302 45.14181 166.767 Phosphorus P 15 10.4867 19.7695 30.2027 51.4439 65.0251 Sulfur S 16 10.36 23.33788 34.79 47.222 72.5945  In conclusion, we can say that both ions might be seen at 396.16 for this set of rock samples.  94  6.3 Definition of the spectrum for Oxides and Sulphides In contrast to the belief that Oxygen will be found present in any reading because it exists in the air or because is abundant in rock samples, LIBS has shown the ability to recognize an Oxide or a Sulphide. This recognition is based on the plasma formation created by LIBS during the reading. Once excited, the ion of Oxygen or Sulphur will create a wavelength that cannot be contaminated by the air, at least for the particular wavelength we are examining in this section.    Figure 6-1: Spectrum for Sulphide 1 This set of figures showing the spectrums of the Sulphide and Oxide samples, provides a typical characterization of the spectrum. Three wavelengths together define that we can be seeing either an Oxide or a Sulphide sample.  95   Figure 6-2: Spectrum for Oxide 12 Although Oxide samples will show as 3 wavelengths with peaks, the critical key for their identification will be a wavelength at 393.48 nm. For example, if we analyze another sample that is known to contain ions of Oxygen, then we should be able to see at least 2 of these mentioned wavelengths.   Figure 6-3: Spectrum for Sulphide 1 96  This turns out to be false as Figure 6-5 shows the spectrum for steel, which contains oxygen ions and it does not have the same 3 peak configuration as do the ore samples. Figure 6-6 shows another sample of a steel plate, and in this case, the spectrum reads the presence of an oxygen ion, possibly because of oxidation. The next peak for this spectrum is 396.8 nm, which does not correspond to the wavelengths mentioned. This particular ionization configuration and arrange of peaks can be seen in Oxide and Sulphide ores with this particular ore deposit.  Figure 6-4: Spectrum for Oxide 17 with characteristic wavelengths for Oxide/Sulphide definition   Figure 6-5: Steel pointed at 393.42 nm 97   Figure 6-6: Steel spectrum with 393.42 nm wavelength peak  6.4 Proposed solution for Oxide/Sulphide recognition using LIBS It is recommended that an automated script be developed with the following parameters. 1. Recognize the wavelength 396.15 as a peak 2. Recognize the wavelength 394.48 as a peak 3. Recognize the wavelength 393.42 as a peak 4. Normalize the spectrum from 0 to 1 a. Calculate the mode based on the noise, as shown in Table J-5 b. Subtract the mode from the whole spectrum and divide the rest by the maximum value of the current spectrum 5. Set a threshold of 0.15 and above for Oxides and 0.15 and below for Sulphides Table 6-3: Final results table for Oxide versus Sulphide recognition  Oxides Sulphides   O III@393.48 O III@394.46 S III@396.15 O III@393.48 O III@394.46 S III@396.15  OXIDE 0.261 0.255 0.369 0.084 0.224 0.330 SULPHIDE OXIDE 0.203 0.215 0.310 0.115 0.278 0.411 SULPHIDE OXIDE 0.204 0.219 0.317 0.054 0.129 0.198 SULPHIDE 050010001500200025003000229.21237.02244.79252.54260.26267.95275.6283.22290.81298.37305.89313.38320.84328.25335.63342.98350.28357.55364.78371.96379.11386.22393.29400.31407.29414.23421.12427.97434.77441.53448.24454.9461.51468.08474.6481.06487.48493.85Fe-2plate,S1,1498   Oxides Sulphides   O III@393.48 O III@394.46 S III@396.15 O III@393.48 O III@394.46 S III@396.15  OXIDE 0.184 0.174 0.252 0.092 0.226 0.337 SULPHIDE OXIDE 0.691 0.203 0.301 0.096 0.238 0.353 SULPHIDE SULPHIDE 0.117 0.279 0.398  0.238 0.351 SULPHIDE OXIDE 0.317 0.217 0.303 0.082 0.172 0.257 SULPHIDE OXIDE 0.211 0.240 0.347 0.164 0.154 0.223 OXIDE OXIDE 0.486 0.253 0.309 0.215 0.214 0.324 OXIDE SULPHIDE 0.128 0.222 0.323  0.318 0.461 SULPHIDE OXIDE 0.434 0.199 0.245 0.095 0.169 0.254 SULPHIDE OXIDE 0.187 0.135 0.248 0.073 0.280 0.411 SULPHIDE OXIDE 0.221 0.194 0.280 0.119 0.249 0.337 SULPHIDE SULPHIDE 0.101 0.183 0.271 0.068 0.243 0.361 SULPHIDE OXIDE 0.184 0.176 0.262 0.054 0.257 0.382 SULPHIDE OXIDE 0.292 0.218 0.321 0.070 0.229 0.333 SULPHIDE SULPHIDE 0.131 0.160 0.241 0.152 0.243 0.358 OXIDE OXIDE 0.495 0.360 0.544 0.067 0.279 0.407 SULPHIDE OXIDE 0.237 0.203 0.301 0.103 0.287 0.424 SULPHIDE OXIDE 0.574 0.258 0.225 0.087 0.251 0.373 SULPHIDE OXIDE 0.297 0.194 0.280 0.115 0.196 0.291 SULPHIDE SULPHIDE 0.111 0.207 0.306 0.107 0.195 0.288 SULPHIDE SULPHIDE 0.096 0.237 0.353 0.125 0.209 0.314 SULPHIDE OXIDE 0.156 0.302 0.438 0.088 0.290 0.420 SULPHIDE OXIDE 0.254 0.255 0.370  0.247 0.373 SULPHIDE OXIDE 0.188 0.257 0.373 0.093 0.225 0.340 SULPHIDE OXIDE 0.283 0.174 0.205 0.068 0.187 0.284 SULPHIDE OXIDE 0.278 0.200 0.288 0.104 0.275 0.418 SULPHIDE OXIDE 0.203 0.184 0.267 0.067 0.314 0.457 SULPHIDE OXIDE 0.407 0.196 0.266 0.113 0.247 0.361 SULPHIDE OXIDE 0.157 0.246 0.349 0.053 0.335 0.498 SULPHIDE OXIDE 0.179 0.175 0.261 0.109 0.211 0.324 SULPHIDE OXIDE 0.301 0.324 0.474  0.292 0.430 SULPHIDE OXIDE 0.420 0.247 0.361 0.137 0.246 0.363 SULPHIDE OXIDE 0.282 0.145 0.198 0.097 0.215 0.330 SULPHIDE OXIDE 0.285 0.181 0.258 0.065 0.266 0.389 SULPHIDE SULPHIDE 0.103 0.183 0.267 0.051 0.274 0.394 SULPHIDE OXIDE 0.167 0.191 0.279 0.105 0.154 0.235 SULPHIDE SULPHIDE 0.117 0.228 0.335     OXIDE 0.529 0.243 0.311     OXIDE 0.196 0.174 0.255     99   Table 6-3 shows the 41 Oxide rock samples and the 38 Sulphide samples in order of magnitude. Based on the criteria provided, the algorithm recognizes whether the rock is an Oxide or a Sulphide rock. It is interesting to mention that the algorithm can be used to classify the degree of oxide or sulphide. Some of the rocks can be seen to display either less or more Oxide, thus providing even more value to sorting.  Figure 6-7: Final results table for Oxide versus Sulphide recognition 00.10.20.30.40.50.60.70.81 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41Normalized Intensity Cu (ppm)Samples numberPlotted values for Oxide vs Suphide recognitionOxides Sulphides100  Chapter 7: Discussion and recommendations The main purpose of this research has been to develop a greater understanding of the capabilities of LIBS for ore sorting, and to provide the sensor system with a response. The responses of the sensors should be based on good quality readings, statistics, and machine learning processes through which it is possible to train the machine to achieve better predictions. Currently, ore sensors base their responses on the statistical correlations and geological information available for tuning the correlation parameters. LIBS cannot rely solely on the correlations made from field readings, and while a prototype for its sensor is developed, it must have a constant machine learning process available to it through which to gather data and tune itself. One of the purposes of this research was to train the machine to achieve good values for decision making. The main reason that this is not possible is because of the limited amount of data available to build an artificial neural network (ANN). Also, the architecture of the LIBS sensor would need to be examined for every single mine, depending on the characteristics of the mine, and the needs of the spectrometer. Finally, it would be necessary to define the needs of the LIBS features and capabilities (such as bandwidth, intensity of the laser, resolution, and frequency) to achieve total control over the LIBS sorting sensor. In this chapter, suggestions are offered with respect to useful information that was gathered throughout the progress of the research, and recommendations are made with regarding its potential impact on the performance of the LIBS sensor.   7.1 Data quality and confidence The data presented in this research is unreliable due to the limited number of rock samples analyzed through ICP. The results are considered unreliable to less 2 standard deviations of 101  confidence, or at a greater than 5% of error rate. Indeed, this was expected as of the beginning of the project, and does not signify a problem for the next stage of research and development. Empirical data simulated through Montecarlo Simulation suggests that for an expected R2 =0.05, the estimated error is 9% (approximately) for the 41 Oxide samples, or 10% used for the 38 samples (Austin and Steyerberg).  The minimum recommended number of Subjects Per Variable (SPV) is 100. In order to improve the quality of the data using this methodology, it is necessary to use between 100 to 400 samples, as is statistically recommended when using the Montecarlo Simulation. This concept, as well as the technology, is statistically scalable to the universe of samples subject to prediction while using a sorter in a mine.  The final Pearson Correlation factor for Oxide is 0.94, and for Sulphide it is 0.84. As such, it is possible that the data obtained could be improved upon if expecting correlations close to 3 standard deviations. Also, it is important to note that, within this research, calculations and predictions are not as important as the methodology described because the intention of this research is to provide solid foundations for prediction and correlation, and not final values.   7.1.1 Identification of elements and concentration recommendations It is recommended that the characteristic wavelength or ID Wavelength, as defined in this research, be acquired from the manufacturer in order to confront the ionization transition probabilities assumed. The reason is that the manufacturer has invested in a great deal of research to find the most probable transitions using its LIBS machine, and as such, spending time and effort towards developing potential ionization transition wavelengths for different LIBS machines is not recommended.  102  Also, it is necessary to recognize that in contrast to XRF, LIBS is capable of reading the concentration of a sample in nanoseconds. For this reason, at the Research and Development level, it would save time to acquire the software of the manufacturer for element recognition and concentration in order to make it possible to correlate percentages rather than peaks with varying magnitudes.   7.2 LIBS data acquisition and architecture The data acquisition of LIBS is based on the Nd:YAG, 3 mJ laser pulse at 100 Hz. For LIBS sensors, the data acquisition method is linked to the architecture of the LIBS machine. The main problem with respect to this topic is the reading of white surfaces, mostly for Sulphide rock material. The primary challenge held by the LIBS sorting sensors involves how to acquire reliable data for all types of rock material. As shown in Figure 3-5 and Figure 3-6, several LIBS readings show evidence of high amounts of invalid data obtained during this research. The main reasons of acquiring large numbers of invalid readings are: a. the low amount of energy absorbed by the surface  b. the capacity of the surface to reflect the energy Details regarding the white colouring problem were provided in section 2.6. However, the problem was avoided rather than solved. The use of such a strategy will not address the problem once the sensor is placed in operation in a mine.   Robert Noll, in his book “Laser-Induced Breakdown Spectroscopy, Fundamentals and Applications” (Noll), proposes the following chart shown in Figure 7-1.  103   Figure 7-1: Technical specifications for LIBS machine performance (Noll) This chart provides a location of LIBS applications given the frequency, or repetition rate (Hz) versus the laser pulse energy (mJ).  The red circle indicates the current location of the LIBS machine used for this research. This red location suggests that this machine works well for scanning microanalysis. However, LIBS sensors need high speed application capabilities with high pulse energy, and this is currently still limited with respect to commercial availability. (Noll). An increase in the laser pulse energy will increase the probability of achieving reliable instant readings over mining material. The capacity of energy absorption by the surface of the rock is increased if the laser energy is increased, and the temperature of the crater created by the laser is made larger within a short period of time.  As made evident in Figure 7-1, the use of a LIBS machine with a laser pulse energy in the range of 100 to 500 mJ is recommended.  104  7.3 LIBS statistics and repeatability analysis In terms of the repetition rate, the LIBS machine uses electro-optical Q-switching with rates of between 10 to 100 Hz or 0.1 to 0.01 seconds per reading. The ideal velocity of bulk material processed on a belt conveyor is 3 m/s. If a rock with an average size of 3 cm crosses the laser sensor, then the time frame for the LIBS sensors is 0.01 s.  Table 7-1 shows the values for the minimum number of readings needed to gather information from the two ions that conform the interaction effects. These ions were taken in the order in which LIBS acquired the data. The information provided is based purely on the geo-spatial characterizations that the LIBS sensor is sorting.  Table 7-1: Minimum number of readings using LIBS to calculate each of the interaction effects used for the prediction of Oxides Binomials #readings needed Be II@272.89*Ti I@399.86 2 Ti I@399.86*Zr III@266.43 2 Be II@272.89*Cu I@324.75 3 P I@253.56*F II@350.56 2 Al II@281.62*Ba II@455.4 15 Be II@272.89*Cu I@327.4 3 Mg III@239.51*Si I@288.16 1 Ca II@317.93*Cr I@427.48 9 Ca II@317.93*Cl II@481.01 2 Ba II@455.4*Fe I@374.95 60 O III@393.48*P I@253.56 71 N II@399.5*P I@253.56 38 Fe I@374.95*Fe I@374.95 1 Ti II@376.13*Tl I@276.79 2 Be II@272.89*Na II@298.42 1 Fe II@234.35*P I@253.56 7 Be III@448.73*Cr I@427.48 3 Pb I@280.2*Tl I@276.79 13 Ga I@294.36*Ni I@349.3 10 Ba II@455.4*Ca II@317.93 9 Average 12.7  For example, a rock might have a reading of Barium in one small spot of the analyzed rock sample, and LIBS will not provide a value to the interaction effects of Ba II@455.4*Fe I@374.95 105  until the laser takes a good reading over this small spot. This data was calculated in similar way as was done in Table 4-13. For example, in order to calculate the binomial Be II@272.89*Cu I@327.4, we need at least 3 good readings. The values highlighted belong to the group of binomials that are part of the final prediction equation for Copper Oxides. The binomial O III@393.48*P I@253.56 is a special case because it has a fairly large number of occurrences (refer to Table 4-15). However, LIBS needed to take up to 71 good readings in order to obtain 1 value for this binomial.  In addition, this calculation was based on the assumption that 100% of the readings are valid. This is not the case, as shown in Figure 3-5 and Figure 3-6.  If it is necessary to take 71 readings to complete the prediction equation, then addressing the introductory problem in this section about the frequency of the LIBS machine under a belt moving at 3 m/s, we can conclude that the needed frequency is 104 hertz.  𝑋 (𝑠𝑒𝑐𝑜𝑛𝑑𝑠𝑟𝑒𝑎𝑑𝑖𝑛𝑔) ∗ 71 (𝑟𝑒𝑎𝑑𝑖𝑛𝑔𝑠) = 0.01 (𝑠𝑒𝑐𝑜𝑛𝑑𝑠)  𝑥 = 1.4𝐸 − 4 (𝑠𝑒𝑐𝑜𝑛𝑑𝑠𝑟𝑒𝑎𝑑𝑖𝑛𝑔) ≈ 104𝐻𝑧   There are no current commercial LIBS machines available at this frequency. The use of the highest frequency possible with a tentative range of 103 hertz is recommended.   7.4 LIBS future developments This section discusses an optional method that have been attempted by the author, but not developed further due to lack of time and resources regarding the amount of ICP assays. One of the most important methods applicable to the LIBS ore sorting method is Artificial Neural Networks (ANN). Previous research on ANN (Alexander Koujelev) suggests that the Mean 106  Deviation is in the range of 5% to 20% for direct measurement concentration instead of through the use of correlation. An argument regarding the preference of ANN over that of LIBS is that most previous experiments have been based on homogenously prepared material. This research attempts to break the heterogeneity problem with respect to LIBS sorting and the reading of moving material.  The ANN algorithm attempts to acquire the target output by summing all of the input and adding the bias to obtain a transfer function, and finally, the output.  Figure 7-2: Neural Network Scheme for the Oxide samples using 10 neurons  Figure 7-3: Neural Network Fitting for Oxide rocks It is not the intention of this thesis to present an analysis regarding Artificial Neural Network, but rather to comment on the potential applicability of ANN to the Oxide and Sulphide 107  ore analysis conducted in this research. One particular aspect of ANN application is the final correlation coefficient obtained out of the 59 ions gotten from LIBS for the Oxide samples. It is possible to differentiate the only high grade sample at the x-axis value of 29000 ppm of Copper. For this set of samples, a better correlation coefficient was obtained in section 4.9.2. However, for the Sulphide rocks, ANN provides an unexpected correlation coefficient of 0.95. This correlation works better than the prediction equation proposed in section 5.6    Figure 7-4: Neural Network Diagram for Sulphide samples  Figure 7-5: Neural Network Fitting for Sulphide rocks It is important to note that there were problems in reading the Sulphide samples with the LIBS machine, and that most of the readings did not show any type of direct correlation between ICP Cu% and LIBS Cu concentration. In conclusion, it is suggested that further investigation be 108  conducted into the use of ANN for LIBS sorting systems when looking for a positive outcome for difficult readings such as those with white surfaces.      109  Chapter 8: Conclusion  Although some conclusions can be drawn based on the findings of this study, there remain questions that would require more research on the LIBS sorting system in order to develop a better understanding regarding its potential uses and applicability.   1. The first conceptual question regards LIBS’ capabilities for ore sorting. LIBS can sort rock samples very efficiently if proper statistical and mineralogical information is provided to the computer in charge of processing the spectrums.  2. LIBS can perform to a proven Pearson Correlation Coefficient of 0.94 for Oxides and 0.84 for Sulphides. 3. LIBS achieves a lower performance when sorting Sulphide ore. 4. LIBS has demonstrated proven capacities to act as an ore sorting sensor, and it is recommended that LIBS be brought to a level of Research and Development.  5. Approaches were used to identify elements associated with wavelengths, but in some cases, ICP results showed that the identified element was not probable. Despite this and for simplicity, the element symbol was used to represent the wavelength response.  6. It is necessary to work with specific LIBS machines for different mine projects, depending on the needs of the bandwidth spectrum with respect to acquiring data that is easy to correlate. 7. The Experimental Approach Design used here was correct, but inefficient in terms of theoretical workload. It is necessary to divide the development of LIBS into specialized groups to develop the Computational, Chemometrics and Mining parts separately.  110  8. The current LIBS laser should be upgraded to a higher pulse laser in order to acquire better readings and obtain better repeatability and data reliability.  9. Developments with respect to the Python Script’s ability to recognize peaks and wavelengths should be reviewed and tuned to the maximize LIBS capacity for data acquisition, and its ability to work with moving samples.  10. The purpose of this research was to develop correlation without measuring grades. However, it is a good proactive process for the Python Script to determine the limits of detection and the grades of the rock samples by using a calibrated homogenous scale for all of the available ions. 11. LIBS provides good and reliable readings for Oxide ores, but not for Sulphide ores.  12. Some of the wavelengths overlap for different elements. It is necessary to increase the bandwidth capabilities of the LIBS machine in order to more clearly distinguish between elements with overlapping wavelengths. 13. The Sulphide ores showed better correlation performance using Artificial Neural Networks than through using Stepwise correlations.  111  Bibliography Alberty, Robert A. and Robert J. Silbey. Physical Chemistry. New York: John Wiley & Sons, Inc, 1996. Alexander Koujelev, Vincent Motto-Ros, Daniel Gratton, and Alexander Dudelzak. "Laser-induced breakdown spectroscopy as a geological tool for field planetary analogue research." Can. Aeronaut. Space (2009): 97-106. Document. Anderson, Steven T. "2005 Minerals Yearbook." 2007. Document. Austin, Peter C and Ewout W Steyerberg. "The number of subjects per variable required in linear regression analyses." ELSEVIER (2015): 627-636. Cremers, Davi and Leon J. Radziemski. Handbook of Laser-Induced Breakdown Spectroscopy. Alburquerque, NM: Wiley, 2013. Cyberphysics group. Cyberphysics. Date retrieved: 2 Dec 2016. November 2016. <http://www.cyberphysics.co.uk/topics/light/emspect.htm>. DAGDIGIAN, P. J. Laser spectroscopy for sensing. Fundamentals, techniques and applications. Baltimore: The John Hopkins University, 2014. Publication. Darling, Peter. Mining Engineering Handbook. Society for Mining, Metallurgy, and Exploration, 2011. Document. Fleischer, Sharly. Physical Chemistry Laboratory. Date retrieved: 2 December 2016. October 2016. <http://www.tau.ac.il/~phchlab/experiments_new/SemB01_Hydrogen/02TheoreticalBackground.html>. Geological Association of Canada. Journal of the Geological Association of Canada. 2008. January 2016. <https://journals.lib.unb.ca/index.php/gc/article/view/11269/12010>. Idaho Nationl Engineering & Environmental Lab, Bechtel BWXT. Development of a Mine Compatible LIBS Instrument for Ore Grading. Confidential. Washington, DC, 2001. INEEL. Mine Compatible LIBS Instrument for Ore Grading. Idaho, March 2000. Document. John Tyson, George Asimellis, Stu Rosenwasser. Development of a Mine Compatible LIBS Instrument for Ore Grading Phase II –Final Report. Washington DC: Idaho National Engineering & Environmental Lab; Bechtel BWXT Idaho LLC (BBWI), 2001. Laboratory, Physical Measurement. NIST database. Date retrieved:  2011. June 2016. <http://physics.nist.gov/PhysRefData/ASD/lines_form.html>. Marsden, John and Iain House. "The Chemestry of Gold Extraction." The Chemestry of Gold Extraction. Colorado: SME, 2006. MathWorks. "Matlab Documentation." 2016. https://www.mathworks.com/help/matlab/ref/nan.html. Document. Date retrieved: 31 October 2016. 112  National Institute of Standards and Technology NIST. NIST lines help. July 2012. Date retrieved:  February 2016. <http://physics.nist.gov/PhysRefData/ASD/Html/lineshelp.html#OUTACC>. Noll, Reinhard. Laser Induced Breakdown Spectroscopy. Berlin: Springer, 2012. Reader, Joseph; Corliss, Charles. "Wavelengths and Transition Probabilities for Atoms and Atomic Ions." 1980 Date retrieved: September 2016.. National Institute of Standards and Technology. <https://www.google.ca/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwi23OP467nLAhUN1WMKHXjgDKMQFggbMAA&url=http%3A%2F%2Fwww.nist.gov%2Fdata%2Fnsrds%2FNSRDS-NBS-68.pdf&usg=AFQjCNEGlOc9cloW1NIVpdUH6Ar7c02QOA&sig2=OOTgWDeR0hX7JBuTUdcIkQ&b>. Rehse, Steven J. "Wayne State University." Date retrieved: 1 June 2010. <www1.uwindsor.ca/people/.../final%20draft%20Rehse%20May%2031%202010.pdf>. Ruben Padilla Garza, Specer Titley, Francisco Pimentel. "Geology of the Escondida Porphyry Copper Deposit, Anofagasta Region, Chile." Economic Geology (2001): 307-324. Document. Ryer, Alex. Manipulating Light. 26 September Date retrieved: 1997. March 2016. <http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/RYER/ch04.html>. Samuel M. Clegg, a,* Roger Wiens,a Anupam K. Misra,b Shiv K. Sharma,b James Lambert,Steven Bender,a Raymond Newell,a Kristy Nowak-Lovato,a Sue Smrekar,c M. Darby Dyar,dSylvestre Mauricee. "Spectroscopy, Planetary Geochemical Investigations Using Raman and Laser-Induced Breakdown." Applied Spectroscopy (2014): 935-936. Document. SECOPTA. Secopta Analytics GmbH. n.d. Product catalog. 27 November 2016. Senesi, Giorgio S. "Laser-Induced Breakdown Spectroscopy (LIBS) applied to terrestrial and extraterrestrial analogue geomaterials with emphasis to minerals and rocks." ELSEVIER (2014): 231-267. Document. Senesi, Giorgio S. "Laser-Induced Breakdown Spectroscopy (LIBS)applied to terrestrial and extraterrestrial analogue geomaterials with emphasis to minerals and rocks." ELSEVIER (2016): 231-267. Document. Skoog, Douglas and James Leary. Análisis Instrumental. Madrid: McGraw'Hill, 1994. Yaroshevsky, A. A. "Abundances of Chemical Elements in the Earth’s Crust." Geochemistry International (2006): 48-55.    113  Appendices                       114  Appendix A   Compiled LIBS responses for Oxide rock samples from Escondida Mine       Ag II Ag II Al II Ba II Be II Be III Bi I Ca I Ca II Cd II Cl II Co I Cr I Sample 232.02 241.32 281.62 455.40 272.89 448.73 306.77 422.67 317.93 274.85 481.01 347.40 427.48 1     912   937     904   1007       2         952     880   1038       3               877 891 947       4               888   1017       5     940         995 943 981 779     6     870         872   952       7     971         923   929       8     1092   1312   1167 887   1248       9   908 850   1411     984 1029 1165 848     10         1028   1044 866   1176       11     942 797 1383     999 1348 1134     830 12   874     1298   1108 886 941 1861     931 13       932 1109     893   1021       14   863 1006         842   1006       15   865           800   904       16     928 820       903   958 824     17       842 1130 870   857 977 1045     952 18     932   1064   1002 979 1031 1639       19         1088   943 886 954 1168       20     919   994   970 982 1015 1009       21       827 964     885 871 1085 816   822 22     945   1282   1220 871   1463       23   858 880   1379   1039 893   1116       24     945   1145   977 910 1068 1283   891   25         962     897 936 1018       26         1245   1059 894 856 1203       27               897 967 991       28       829 1136     930 981 1265     916 29               886   955       30       773 962     906 1003 1214       31         1063     882   1146       32 1374 1803           854   1091       33   985 975 1015       978   997     1135 34     881 803       945 916 1025 892     35         1098     918 953 1157       36               879 920 974       37         1096     869 871 1070       38         1249   1124 874 880 1533       39         1020     878   1316       40               989 1009 938       41         1270     927   1119 854     115      Cu I Cu I Cu II F II Fe I Fe II Fe II Ga I Hf I In II Ir I Mg I Sample 324.75 327.40 271.35 350.56 374.95 234.35 238.20 294.36 368.22 294.10 269.42 285.21 1 998 944   970 860 865 955         1165 2 1205 1051     945 905 974         1150 3 1118 1004   1013   869 916     1035   1192 4 1207 1058     986 903 965         1177 5 1269 1124     934 979 934       948 1057 6 985 910     913 879 928         1122 7 1083 980   1018   829 892     929   1132 8 1160 1061 1268 926 1098 1142 1133     959 1077 1166 9 1428 1230 1129 985 1043 1219 1086         1129 10 1070 966 1024 953 971 961 1095         1207 11 1446 1272   1090 1120 1046 1054         1119 12 1244 1090 1157   1052 1329 1596   897   1061 1145 13 1165 1051   1018 1115 897 969         1166 14 1059 953   1103 957 883 945 1002   978   1128 15 907 866   1122   799 876 965       1083 16 1271 1121       861 926         1137 17 1775 1532     914 966 988     988   1119 18 1166 1014 1041 1011 1019 1127 1441     981 931 1094 19 1052 971 1165 1078 978 1035 1082 1129     1000 1167 20 1186 1038     921 922 952         1067 21 1387 1224     889 923 1030         1098 22 1065 978 1026   1127 1156 1276         1185 23 1121 1018   1055 1185 1155 1000 1005     1089 1135 24 1257 1114 1127 979 1003 1011 1186         1159 25 1048 961 954   953 930 976         1130 26 1084 1002 925   981 1043 1121       1081 1173 27 1023 951     862 873 947         1209 28 1571 1404 1033 1125 1047 1148 1130 1031     1057 1105 29 1016 942   986 847 839 917         1195 30 1250 1084 1016 947 935 966 1124         1128 31 1022 958   1104 949 956 1069 1017       1124 32 1153 1029     890 900 1030         1161 33 1186 1106   1450     960 1347   1047   1104 34 1604 1372     906 900 985         1101 35 1013 928   902 948 969 1067         1201 36 1061 970   860   900 934         1142 37 982 945   1119 1022 1004 1002 1034       1159 38 1187 1059 1030   977 1123 1354       1097 1243 39 1106 1018 999   953 997 1205         1136 40 974 933     942   893         1099 41 1071 991 1245   1065 1139 1039         1175    116      Mg II Mg III Mn I Mn II N II N IV Na II Na II Ni I O III O V P I Sample 279.55 239.51 279.83 261.02 399.50 347.87 298.42 307.83 349.30 393.48 278.10 253.56 1 2195 901   928     871 1437 838 1135 969 1028 2 2182 921   956     866 1165   1048 972 1026 3 2311 883   915     836 1388   1091 962   4 2353 928   937     886     1071 958   5 1846 927   925     985     1832 975   6 2226 900   909     881   833 1000 924   7 2177 859   879     846 1285 822 1248 957   8 2177 1092   901   841 1156     1087 953   9 2154 1022   959     1090   927 1520 976 1084 10 2412 1018   1036   847 947 1376   1005 985 1135 11 1990 1035   984     1006 1481 1014 1396 989 1126 12 1842 1430   1343     1155 1158   1072 1023   13 2209 923   922     966 1001   1114 960 968 14 2229 896   930     905 1547 908 930 919 1061 15 2031 838   859   846 914 1503 930 981 900   16 2283 886   917     888     1209 949   17 1748 948 2207 975     1009 1031   978 985 1212 18 1987 1260   1130     1028 1496 863 1520 964 1166 19 2179 1015   988     996 1337   1127 961 1032 20 1956 926   932     906     1564 940   21 2128 979   979     886     1227 916 1084 22 2146 1184   1097     1103 1374   954 983 1295 23 2133 1040   900   892 1141 1488 827 940 946   24 2190 1081   1041     999 1457 933 1042 957 1244 25 2308 921   907     943     1164 929   26 2322 1028   982     1014     1091 963   27 2443 894   926     881     1202 1027 1031 28 1944 1078   967     1046 1571 925 1207 1001 1237 29 2353 874   897     901 1368 846 1061 984   30 2115 1042   1024   788 902 1300 836 1345 952 1123 31 2215 990   973     948 1536 891 1033 961   32 2233 966   986     877     1057 977 1080 33 2000 918   943   946 1082 1827 1084 1289 922 1443 34 2161 940   953     901     1409 929   35 2427 1019   1031     937 1081   1250 1024 1182 36 2262 894   914     858 1122   1194 960 1118 37 2206 949   960   904 978 1376   945 961   38 2381 1244   1095 882   1011 1206 943 1048 1028 1399 39 2178 1100   1113     954     970 973 1344 40 1982 889   883           1615 912   41 2285 990   908 938   1057     1087 989 990    117      P IV Pb I Pb I S VI S VI Sc III Si I Si II Sn II Ti I Ti II Sample 334.77 280.20 283.31 419.89 420.08 269.91 288.16 413.09 335.20 399.86 376.13 1             1360     892 1082 2 861           1207     852 927 3   1739         1291     852 953 4         818   1276     871 915 5 935 1234         1156     947 890 6 929           1281     887 903 7 925 1315         1196     855 1072 8 916 1568 1195   926   1250     917 909 9 916 1377 1084   1003   1391     938 881 10     967       1285     872 1141 11 892 1332 1215 875 884   1339     969 1003 12   1369 1062 903 879   1196 912     984 13   1727         1269     1020 898 14 925           1232     895 1357 15 915 1167         1101     863 1080 16 904 1147         1319       891 17   1340         1175       897 18   1611 958 869 861   1524 866   892   19   1639 1039 825 874   1315 959   900 1163 20 889 1168         1333   846   893 21   1311         1335 837     896 22   1731 1182 943 975   1264 906   923 957 23 996 1298 1110 918 915   1161 906   915 1105 24   1658 1189   1000   1399 918 964 928 1250 25   1685         1475     869   26 900 1825         1429 934   845 885 27 859           1227     827 870 28   1396 1083 959 914   1293 893   958 1406 29   1717 940       1201 916   926 1251 30 983 1303         1238     881 1074 31 921 1497     905   1471 954 886 897 1357 32 890 1060         1198     859 858 33 1006 1388       977 1454     1105 1807 34   1390         1359       842 35 896 1642         1133       968 36 869           1238       931 37 895 1563   907 871   1210 910   912 1154 38 917 1603 1112 874 890   1400 890   894   39       913 889   1368 945       40   1219         1228         41 899 1651 1052   929   1247       866    118     Ti III Tl I Tl I V II W I W II Y II Zn I Zn II Zr III Sample 251.61 276.79 351.92 292.40 400.88 248.92 371.03 334.50 491.16 266.43 1 1314 864       922   960   888 2 1177 927       849 848     901 3 1258 912                 4 1254 928       1009 837 931   892 5 1148 1017         845 978   953 6 1237 883                 7 1154           814       8 1321 1334   1096     920     1216 9 1398 1171   942     960 1000   1237 10 1292 977       860 858     1002 11 1301 1037       885 892     1053 12 1314 1308       900 903     1192 13 1228 1037       901       1060 14 1213 898 915     894         15 1067   890     880         16 1297 941       843   949     17 1186 986       917       992 18 1557 1067         882     1002 19 1294 1071       940 878     1006 20 1273 916       890   982   922 21 1315 896         829 980   886 22 1288 1271   1089   908 1009     1210 23 1193 1246         966 892   1252 24 1428 1032       958 932     1036 25 1428 991         881     941 26 1422 1079       926 940 944   1068 27 1199 947       876         28 1291 1100 911       916     1064 29 1177 817       914         30 1291 933       1067 866     918 31 1425 981       943 928     1027 32 1212 903   850           856 33 1451   1146   1132 960 922   966   34 1372 894       920   1198   887 35 1166 998   946     898     962 36 1201 863       930       838 37 1216 1044   873           1048 38 1441 1115         922     1079 39 1422 989         900 932   938 40 1171                   41 1248 1145   985   880 898 916   1095     119  Appendix B  ICP certified assay results for the 41 Oxide Escondida samples ANALYTE WtKg Ag Al As Ba Be Bi Ca Cd METHOD G_WGH79 GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B DETECTION 0.01 2 0.01 3 5 0.5 5 0.01 1 UNITS kg ppm % ppm ppm ppm ppm % ppm EscOx1B2 0.05 <2 1.91 <3 75 <0.5 <5 0.05 <1 EscOx2B2 0.114 <2 2.66 4 40 <0.5 <5 0.04 <1 EscOx3B2 0.068 <2 1.33 4 80 0.9 <5 0.22 <1 EscOx4B2 0.048 <2 4.94 4 49 0.6 <5 0.12 <1 EscOx5B2 0.035 <2 1.3 4 86 0.7 <5 0.26 <1 EscOx6B2 0.04 <2 1.73 9 47 <0.5 <5 0.22 <1 EscOx7B2 0.035 <2 1.66 4 116 0.9 <5 0.16 <1 EscOx8B2 0.219 <2 3.73 8 96 <0.5 <5 0.04 <1 EscOx9B2 0.125 <2 1.03 <3 68 <0.5 <5 0.37 <1 EscOx10B2 0.119 31 3.81 3 51 <0.5 <5 0.05 <1 EscOx11B2 0.044 <2 1.11 <3 61 <0.5 <5 0.3 <1 EscOx12B2 0.033 <2 2.63 19 91 0.5 <5 0.06 <1 EscOx13B2 0.227 <2 1.23 <3 41 <0.5 <5 0.13 <1 EscOx14B2 0.081 3 1.1 15 81 0.5 <5 0.05 <1 EscOx15B2 0.051 6 3.91 6 59 0.6 <5 0.04 <1 EscOx16B2 0.097 <2 1.28 4 128 <0.5 <5 0.14 <1 EscOx17B2 0.3 2 0.8 10 105 <0.5 <5 0.08 <1 EscOx18B2 0.035 <2 1.25 <3 26 <0.5 <5 0.75 <1 EscOx19B2 0.03 <2 1.51 3 50 <0.5 <5 0.04 <1 EscOx20B2 0.074 <2 2.08 4 64 <0.5 <5 0.14 <1 EscOx21B2 0.037 <2 1.08 3 66 0.8 <5 0.28 <1 EscOx22B2 0.056 12 3.07 7 62 <0.5 <5 0.05 <1 EscOx23B2 0.032 <2 2.43 14 73 0.5 <5 0.04 <1 EscOx24B2 0.044 <2 1.9 11 52 3.3 <5 0.05 <1 EscOx25B2 0.06 <2 1.16 3 44 0.8 <5 0.03 <1 EscOx26B2 0.083 <2 0.79 3 71 <0.5 <5 0.04 <1 EscOx27B2 0.091 <2 2 4 58 <0.5 <5 0.07 2 EscOx28B2 0.049 <2 0.93 <3 62 <0.5 <5 0.18 <1 EscOx29B2 0.052 <2 2.29 4 95 <0.5 <5 0.03 <1 EscOx30B2 0.05 <2 1.05 <3 45 0.8 <5 0.35 <1 EscOx31B2 0.269 <2 0.77 <3 90 0.6 <5 0.16 <1 EscOx32B2 0.167 <2 3.61 6 45 <0.5 <5 0.28 <1 EscOx33B2 0.205 <2 1.39 3 86 <0.5 <5 0.05 <1 EscOx34B2 0.177 2 1.09 3 86 <0.5 <5 0.53 <1 EscOx35B2 0.082 <2 2.91 4 64 <0.5 <5 0.53 1 EscOx36B2 0.159 <2 1.06 4 63 <0.5 <5 0.22 <1 EscOx37B2 0.084 <2 1.14 7 83 <0.5 <5 0.04 <1 EscOx38B2 0.087 <2 0.98 5 64 <0.5 <5 0.04 <1 EscOx39B2 0.119 <2 0.84 12 55 0.5 <5 0.14 <1 EscOx40B2 0.104 <2 0.94 3 59 <0.5 <5 0.11 <1 EscOx41B2 0.117 <2 1.06 4 72 0.6 <5 0.18 <1      120   Co Cr Cu Fe Hg K La Li Mg Mn GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B 1 1 0.5 0.01 1 0.01 0.5 1 0.01 2 ppm ppm ppm % ppm % ppm ppm % ppm 10 8 1540 2.57 <1 0.45 11.7 6 0.68 293 16 12 >10000 4.11 <1 0.35 14.4 14 1.43 237 3 6 7240 1.16 <1 0.39 24.7 5 0.35 160 24 17 >10000 5.19 <1 0.31 19 28 2.48 180 4 4 >10000 1.21 <1 0.42 14.6 4 0.28 114 5 3 3080 1.69 <1 0.58 20.9 7 0.58 355 4 5 4750 1.36 <1 0.49 24.3 7 0.48 188 12 25 3130 3.42 <1 0.39 16 18 1.87 572 4 8 9320 1.7 <1 0.22 17.9 4 0.37 138 19 25 2890 5.27 <1 0.38 14 15 1.24 344 4 8 5600 1.68 <1 0.22 14.1 5 0.41 127 9 15 7170 6.03 <1 0.46 13.3 21 1.33 1010 6 5 3600 2.05 <1 0.14 16.7 6 0.5 152 3 3 2350 1.38 <1 0.46 20.5 4 0.41 221 27 27 8440 5.14 <1 0.37 10.3 25 2.52 527 7 7 9720 1.28 <1 0.3 16.7 6 0.5 141 2 6 >10000 1.37 <1 0.38 18.5 2 0.21 95 1 4 774 1.79 <1 0.77 2.3 <1 0.07 74 4 5 1680 2.16 <1 0.2 11 6 0.51 234 14 20 >10000 4.39 <1 0.36 10.8 15 1.12 341 5 7 >10000 1.9 <1 0.19 19.8 6 0.49 125 16 20 2990 4.41 <1 0.38 18.9 14 1.23 1000 5 11 3410 3.09 <1 0.52 15.6 10 0.93 183 2 4 5680 2.02 <1 0.48 25.5 4 0.19 87 4 7 2100 1.6 <1 0.26 13 4 0.44 145 2 5 1110 0.99 <1 0.31 16.2 2 0.21 101 11 6 9150 2.67 <1 0.23 15.1 15 1.19 286 4 6 5230 1.58 <1 0.19 12.2 4 0.39 145 9 5 7480 2.27 <1 0.25 26.5 11 1.07 245 4 6 7310 1.78 <1 0.14 16.4 7 0.47 133 3 4 1930 1.42 <1 0.34 12.5 2 0.16 107 15 22 >10000 4.95 <1 0.27 11.3 16 1.42 398 <1 3 370 0.68 <1 0.42 22.5 2 0.15 35 3 3 1940 1.23 <1 0.36 14.2 4 0.35 122 18 21 8790 5.65 <1 0.39 8 17 1.51 478 6 5 4710 1.75 <1 0.21 17.7 8 0.48 129 5 5 1530 1.49 <1 0.31 30.9 5 0.42 139 4 5 1410 1.52 <1 0.26 23.7 4 0.41 132 7 2 7360 1.58 <1 0.25 9.1 3 0.27 242 4 7 3450 1.6 <1 0.09 16.2 7 0.47 116 5 6 7820 1.91 <1 0.2 14.4 7 0.52 144      121  Mo Na Ni P Pb S Sb Sc Sn Sr GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B 1 0.01 1 0.01 2 0.01 5 0.5 10 5 ppm % ppm % ppm % ppm ppm ppm ppm 15 0.16 10 0.03 22 <0.01 <5 5.2 <10 41 14 0.11 14 0.12 11 0.01 <5 10.7 <10 41 22 0.13 5 0.23 30 0.27 <5 1.4 <10 76 7 0.12 20 0.06 15 0.02 <5 13.7 <10 50 30 0.14 5 0.16 11 0.36 <5 1.7 <10 73 7 0.09 6 0.03 6 0.24 <5 1.2 <10 17 16 0.11 6 0.11 17 0.17 <5 1.8 <10 73 109 0.1 22 0.04 31 0.02 <5 14.8 <10 147 13 0.13 12 0.09 14 0.41 <5 2 <10 62 11 0.11 23 0.02 31 0.02 <5 12.7 <10 71 11 0.14 6 0.04 8 0.31 <5 2 <10 46 412 0.09 12 0.13 552 0.04 <5 8.4 <10 20 10 0.11 5 0.08 6 0.12 <5 1.7 <10 83 135 0.04 4 0.13 136 0.04 <5 2.1 <10 20 43 0.11 25 0.03 9 0.01 <5 10.3 <10 29 67 0.12 9 0.08 18 0.25 <5 1.6 <10 54 17 0.09 4 0.06 7 0.9 6 1.5 <10 33 16 0.05 3 <0.01 22 0.66 <5 <0.5 <10 13 6 0.16 5 0.07 13 0.02 <5 1.4 <10 42 34 0.11 16 0.14 5 0.02 <5 15 <10 38 10 0.14 7 0.05 8 0.48 <5 2.2 <10 80 22 0.11 20 0.05 98 0.02 <5 9.5 <10 120 96 0.05 9 0.2 83 0.05 <5 10.9 <10 65 37 0.08 4 0.87 159 0.04 <5 1.2 <10 18 33 0.11 5 0.2 19 0.02 <5 1.3 <10 32 46 0.07 4 0.03 25 0.02 <5 0.6 <10 14 77 0.1 12 0.08 7 <0.01 <5 8.2 <10 28 44 0.12 7 0.06 6 0.22 <5 1.3 <10 29 38 0.1 7 0.07 5 0.02 <5 4.3 <10 135 87 0.12 6 0.11 9 0.38 <5 3.1 <10 76 152 0.08 4 0.04 29 0.22 <5 <0.5 <10 36 21 0.1 18 0.13 4 0.02 <5 13.8 <10 38 11 0.14 2 0.02 48 0.23 <5 0.7 <10 74 32 0.1 5 0.08 17 0.48 <5 0.8 <10 32 15 0.17 18 0.1 3 <0.01 <5 15.8 <10 36 19 0.13 6 0.05 6 0.23 <5 3 <10 72 22 0.09 7 0.05 17 0.03 <5 0.7 <10 114 19 0.09 5 0.04 10 0.02 <5 0.8 <10 97 12 0.08 8 0.09 82 0.24 <5 0.8 <10 16 5 0.1 6 0.06 7 0.11 <5 3.2 <10 97 23 0.09 7 0.08 9 0.31 <5 2.1 <10 45       122  Ti V W Y Zn Zr Au Al2O3 Ba CaO GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_FAA313 GO_ICP95A GO_ICP95A GO_ICP95A 0.01 1 10 0.5 1 0.5 5 0.01 0.001 0.01 % ppm ppm ppm Ppm ppm ppb % % % 0.02 85 <10 4.2 465 0.7 54 18.1 0.079 0.66 0.09 149 <10 9.8 102 1.1 21 18.9 0.025 0.85 <0.01 22 <10 49.6 132 <0.5 18 17.2 0.056 0.67 0.11 164 <10 10.5 347 1.1 7 18.8 0.032 0.93 <0.01 20 <10 5.2 165 <0.5 28 17.2 0.068 0.85 <0.01 22 <10 4.4 281 <0.5 5 19.2 0.036 0.34 <0.01 22 <10 12.1 256 <0.5 21 17.6 0.05 0.76 0.05 167 <10 3.1 375 0.9 7 21.4 0.024 0.39 0.02 32 <10 8.2 169 0.5 53 16.2 0.078 1.32 0.04 203 <10 124 734 1.2 <5 19.7 0.018 0.47 0.03 31 <10 5 138 0.7 28 16.2 0.075 1.34 <0.01 114 <10 2.1 1030 1.2 8 18.4 0.041 0.1 0.03 34 <10 2.8 114 0.6 22 17.8 0.056 1.67 <0.01 23 <10 4.1 121 <0.5 30 19.1 0.065 0.09 <0.01 129 <10 9.4 282 1.3 9 19.2 0.026 0.54 <0.01 19 <10 1.1 164 <0.5 82 16.2 0.077 0.7 <0.01 20 <10 0.7 63 <0.5 135 13.7 0.057 0.21 <0.01 7 <10 0.6 23 0.5 17 18.6 0.007 1.09 0.01 34 <10 0.8 103 0.7 9 18.4 0.027 1.14 0.17 203 <10 14 909 1.3 107 17.8 0.028 2.71 0.04 34 <10 16.8 143 0.7 65 16.4 0.085 1.57 0.03 156 <10 27.7 714 1.2 <5 19.5 0.028 0.37 <0.01 101 <10 3.6 250 1 9 18.3 0.036 0.06 <0.01 13 <10 1.9 182 0.5 7 17.7 0.037 0.08 <0.01 23 <10 0.8 159 <0.5 5 16.6 0.081 0.35 <0.01 12 <10 3.3 223 <0.5 29 14.9 0.057 0.11 0.07 91 <10 9.2 814 1.1 128 18.9 0.041 1.38 <0.01 24 <10 1.3 160 0.6 25 15.5 0.063 0.99 0.01 64 <10 10.8 160 0.8 7 19.4 0.042 0.75 0.04 34 <10 5.7 166 0.7 40 16 0.065 1.63 <0.01 13 <10 2.8 116 <0.5 43 15.6 0.056 0.31 0.16 170 <10 13.9 307 1.7 <5 18.1 0.025 1.53 <0.01 16 <10 0.7 16 <0.5 93 18.8 0.047 0.14 <0.01 14 <10 0.7 125 <0.5 194 17.3 0.052 0.9 0.24 206 <10 12.3 558 1.8 17 17.8 0.021 3.56 0.08 37 <10 21.5 243 0.7 71 17.2 0.048 2.05 <0.01 16 <10 1.7 189 <0.5 5 15.7 0.077 0.26 <0.01 16 <10 1.1 121 <0.5 13 16.1 0.073 0.36 <0.01 16 <10 2.5 188 0.5 54 16.9 0.048 0.3 0.04 34 <10 118 118 0.6 53 16.8 0.073 1.85 0.02 27 <10 3 239 0.6 42 16 0.078 0.95       123  Cr2O3 Fe2O3 K2O MgO MnO Na2O Nb P2O5 SiO2 Sr GO_ICP95A GO_ICP95A GO_ICP95A GO_ICP95A GO_ICP95A GO_ICP95A GO_ICP95A GO_ICP95A GO_ICP95A GO_ICP95A 0.01 0.01 0.01 0.01 0.01 0.01 0.001 0.01 0.01 0.001 % % % % % % % % % % <0.01 4.39 3.05 1.42 0.04 4.28 0.002 0.08 65.1 0.039 <0.01 6.82 1.91 2.7 0.03 4.01 0.002 0.28 55.3 0.039 <0.01 2.05 2.52 0.86 0.02 5.1 0.001 0.45 66.6 0.045 <0.01 7.85 1.4 4.16 0.02 2.29 0.002 0.14 53.3 0.026 <0.01 2.18 3.24 0.75 0.02 4.38 0.001 0.36 68.3 0.054 <0.01 3.07 4.59 1.61 0.05 0.18 0.001 0.07 63.6 0.004 <0.01 2.45 3.08 1.16 0.03 3.11 0.001 0.21 65.1 0.038 <0.01 5.61 1.89 3.44 0.08 2.16 0.003 0.06 54.7 0.031 <0.01 2.69 2.64 0.72 0.02 5.06 0.001 0.22 65.3 0.055 <0.01 8.14 1.78 2.28 0.05 1.38 0.003 0.04 54.3 0.022 <0.01 2.63 2.71 0.79 0.02 5.01 0.001 0.11 66 0.063 <0.01 9.09 4.07 2.63 0.13 0.23 0.003 0.25 55.4 <0.001 <0.01 3.22 1.79 0.94 0.02 5.53 0.001 0.17 64.9 0.078 <0.01 2.77 5.63 1.66 0.05 0.12 0.002 0.24 61.2 0.004 <0.01 7.71 2.09 4.36 0.07 2.69 0.002 0.09 54.1 0.026 <0.01 2.17 2.76 1.03 0.02 4.61 0.001 0.26 67.4 0.047 <0.01 2.18 2.85 0.68 0.01 3.4 <0.001 0.18 65.1 0.02 <0.01 2.6 4.84 0.49 0.02 0.12 0.002 <0.01 65.3 0.004 <0.01 3.43 1.26 0.97 0.03 5.67 0.001 0.12 67.7 0.071 <0.01 6.56 1.23 1.89 0.05 4.34 0.003 0.3 54.4 0.059 <0.01 2.92 2.77 0.9 0.02 5.15 0.001 0.15 64.4 0.066 <0.01 7.21 2.74 2.43 0.14 1.5 0.003 0.11 55.2 0.027 <0.01 5.03 3.94 2.16 0.04 0.13 0.003 0.41 59.8 0.005 <0.01 3.41 4.05 1.02 0.03 0.14 0.001 1.81 62.1 0.003 <0.01 2.63 3.42 0.96 0.02 4.57 0.001 0.49 67.2 0.037 <0.01 2 3.47 0.85 0.02 1.51 0.001 0.08 68.8 0.005 <0.01 4.27 1.94 2.2 0.04 5.21 0.002 0.2 59.7 0.044 <0.01 2.61 1.92 0.77 0.02 5.25 0.001 0.13 68.1 0.054 <0.01 3.85 1.81 2.05 0.03 4.52 0.002 0.13 61.4 0.051 <0.01 2.79 2.23 0.9 0.02 5.45 0.001 0.29 63.8 0.067 <0.01 2.56 2.92 0.64 0.02 3.28 0.001 0.1 67.6 0.019 <0.01 7.64 1.66 2.53 0.06 2.99 0.002 0.27 55.3 0.035 <0.01 1.74 2.83 0.78 <0.01 2.53 0.002 0.06 65.2 0.022 <0.01 2.29 2.87 1.01 0.02 4.08 0.002 0.17 66.4 0.026 <0.01 8.04 1.29 2.51 0.07 3.41 0.002 0.22 54.2 0.049 <0.01 2.68 1.66 0.84 0.02 5.89 0.002 0.18 64.4 0.076 <0.01 2.52 3.31 0.99 0.02 3.57 0.001 0.14 66.3 0.039 <0.01 2.7 2.96 0.92 0.02 4.63 0.001 0.12 68.8 0.049 <0.01 2.7 2.43 0.8 0.04 4.62 0.001 0.18 65.9 0.021 <0.01 2.54 2.05 0.84 0.02 5.33 0.001 0.12 66.6 0.075 <0.01 3.07 2.98 1.03 0.02 4.42 0.001 0.2 65.7 0.052       124  TiO2 Y Zn Zr LOI Cu GO_ICP95A GO_ICP95A GO_ICP95A GO_ICP95A G_PHY01K GO_ICP13B 0.01 0.001 5 0.001 0.01 0.01 % % ppm % % % 0.77 0.001 487 0.015 3.22 N.A. 0.96 0.001 121 0.012 4.77 1.59 0.43 0.005 170 0.015 3.35 N.A. 0.91 0.001 375 0.012 7.1 1.21 0.45 <0.001 233 0.015 3.65 1.37 0.53 <0.001 449 0.017 6.07 N.A. 0.43 0.001 381 0.015 4.06 N.A. 1.26 0.001 378 0.013 7.28 N.A. 0.39 <0.001 211 0.014 3.36 N.A. 1.07 0.014 708 0.011 7.7 N.A. 0.38 <0.001 157 0.014 2.76 N.A. 1.05 0.001 1010 0.011 6.31 N.A. 0.46 <0.001 128 0.015 2.54 N.A. 0.68 0.001 151 0.016 4.08 N.A. 1.08 0.002 285 0.011 6.17 N.A. 0.38 <0.001 200 0.014 3.02 N.A. 0.33 <0.001 89 0.012 4.95 2.9 0.51 <0.001 26 0.017 5.94 N.A. 0.49 <0.001 119 0.016 3.09 N.A. 1 0.002 908 0.01 3.44 1.38 0.42 0.002 177 0.014 2.71 1.29 1.06 0.003 737 0.012 6.94 N.A. 0.89 0.001 250 0.01 5.66 N.A. 0.41 <0.001 341 0.015 6.5 N.A. 0.42 <0.001 190 0.015 2.58 N.A. 0.37 <0.001 365 0.012 3.27 N.A. 0.78 0.001 770 0.015 3.84 N.A. 0.36 <0.001 221 0.013 2.54 N.A. 0.64 0.002 176 0.016 4.36 N.A. 0.41 <0.001 207 0.015 3.53 N.A. 0.34 <0.001 216 0.014 3.07 N.A. 1.01 0.002 336 0.011 5.9 1.53 0.44 <0.001 22 0.015 6.76 N.A. 0.46 <0.001 194 0.014 4.39 N.A. 1 0.002 574 0.011 3.77 N.A. 0.49 0.002 297 0.015 2.53 N.A. 0.37 <0.001 222 0.014 3 N.A. 0.38 <0.001 154 0.015 2.27 N.A. 0.46 <0.001 263 0.014 3.61 N.A. 0.38 0.013 155 0.015 2.08 N.A. 0.4 <0.001 347 0.014 3.21 N.A.       125  Appendix C  Python Script for the processing of LIBS responses from __future__ import division from __future__ import division  import matplotlib.pylab as plt import pandas as pd import numpy as np from scipy.optimize import leastsq import os  import matplotlib.ticker as plticker  import mtl.processing.convolution2 as conv from mtl.misc import gaussianDerivKernel, gaussianKernel from mtl.sensors.xray import lorentz from scipy.ndimage.filters import convolve from scipy.optimize import leastsq # Levenberg-Marquadt Algorithm  saveplot=False readingsFilename = 'Oxido_Escondida_unified.csv' SIGMA = 2. outDir = readingsFilename+'_plots' if saveplot:  os.makedirs(outDir)   #****************** ''' columns = df.columns[1:] table = [] for name in columns:  table.append(name.split(',')) '''  ### Load database of wavelengths and elements, and clean it up badChar = u'\xa0'  def fixValue(x):  if (isinstance(x, unicode)):   return x.strip().replace(badChar,'')  else:   return x  def clean(col):  return col.apply(fixValue)    ### Load ID wavelengths 126  idWavelengths = pd.read_csv('ID wavelength.csv')   ### Load spectra TOL = 0.132  spectra = pd.read_csv(readingsFilename) wavelengths = spectra['wavelength'] for col in spectra.columns:  print col readingtoplot = raw_input('Enter the reading to plot from the list:')  matches = [] for whichReading in spectra.columns:  if whichReading != 'wavelength':   spectrum = spectra[whichReading]    #########################################   PEAK_THRESHOLD = 890      #######################################   ### NUMERICAL DERIVATIVE WRT X   kernel = gaussianDerivKernel.get(sigma=SIGMA, threshold=0.005)   deriv = -1 * convolve(spectrum, kernel)    ### FIND PEAKS   ### by looking for when derivative crosses 0 from positive to negative   min2ndDeriv = 1.0   peakIndices = []   prevSlope = False   for idx, slope in enumerate(deriv):    if (prevSlope > 0 and slope <= 0 and abs(slope-prevSlope) > min2ndDeriv):     #print abs(slope-prevSlope)     peakIndices.append(idx)     prevSlope = slope    peakIndices = np.array(peakIndices)    ############ 2nd deriv example   kernel2 = np.array([-1,0,1])   deriv2 = -1 * convolve(deriv, kernel2)   if saveplot or whichReading == readingtoplot:     # if whichReading==readingtoplot:    # plot example 127     fig, ax = plt.subplots(1,1, figsize=(30,20))    loc = plticker.MultipleLocator(base=10) # this locator puts ticks at regular intervals    yaxis_loc = plticker.MultipleLocator(base=0.1)    ax.xaxis.set_major_locator(loc)    ax.yaxis.set_major_locator(yaxis_loc)    ax.plot(wavelengths, spectrum, c='b')    ax.plot(wavelengths, deriv, c='r')    ax.plot(wavelengths, deriv2, c='g')    ax.set_xlim((wavelengths.min(), wavelengths.max()))    # for peakIdx in peakIndices:   #  ax.axvline(wavelengths[peakIdx], ls='--', c='#555555')    peakTable = []    BELOW = False   x0 = None   x1 = None   maxval = 10   for idx, value in enumerate(deriv2):    if (BELOW):     maxval = max(abs(value), maxval)     if (value < 0 and not BELOW):     BELOW = True     x0 = idx     if (value >= 0 and BELOW):     BELOW = F23alse     x1 = idx      if (maxval >= 10):      # accept as peak      peakIdx = spectrum[x0:x1+1].argmax()      peakTable.append([peakIdx, wavelengths[peakIdx], spectrum[peakIdx]])            if saveplot or whichReading == readingtoplot:        ax.fill_between([wavelengths[x0],wavelengths[x1]], -0.2, 1, alpha=0.3, colour='y')      maxval = 0   maxval = 0      if len(peakTable)==0: 128     print ("No peaks found")   if saveplot:    plt.savefig(os.path.join(outDir, 'Plot'+whichReading+'.jpg'))  #********   if whichReading==readingtoplot:    plt.show()   if saveplot or whichReading == readingtoplot:     plt.close()    peakTable_df = pd.DataFrame(peakTable, columns=['pixel', 'wavelength', 'peakIntensity'])    #######################################   ### FIND MATCHING ELEMENTS      TOL = 0.132      for pIdx, row in idWavelengths.iterrows():    w = row['Observed Wavelength Air (nm)']     # print '>>> w = ', w    idx = (peakTable_df['wavelength'] - float(w)).abs().argmin()    matchedRow = peakTable_df.iloc[idx]     if (abs(matchedRow['wavelength'] - w) < TOL):     # Found a match     concentration = (matchedRow['peakIntensity'] )     matches.append([whichReading, matchedRow['wavelength'], row['Ion'], concentration, row['Acc.'],w])                 matches_df = pd.DataFrame(matches, columns=['Sample Rock','Peak Wavelength', 'Element', 'Intensity','Acc.','Observed Wavelength Air']) matches_df.to_excel('Matches_'+readingsFilename+'.xlsx') ####################################### ### FIT LORENTZIAN if (False):  OFFSET = 800.0  lorKernel = lorentz.makeLorentzKernel_FWHM(4)   def residual(peakAmounts, peakLocations, observedSpectrum):   peakArray = np.zeros(len(observedSpectrum))   peakArray[peakLocations] = peakAmounts    # to generate spectrum: convole peak array with lorentzian kernel 129    reconstructedSpectrum = convolve(peakArray, lorKernel) + OFFSET    return np.abs(observedSpectrum - reconstructedSpectrum)   initAmounts = np.array([1000.0]*len(peakIndices))  results = leastsq(residual, initAmounts, args=(peakIndices, spectrum), full_output=1)   # get results  solnAmounts, cov_x, infodict, mesg, ier = results   peakArray = np.zeros(len(spectrum))  peakArray[peakIndices] = solnAmounts  reconstructedSpectrum = convolve(peakArray, lorKernel) + OFFSET   # plot example  fig, ax = plt.subplots(1,1)  ax.plot(wavelengths, spectrum, c='b', label='LIBS spectrum')  ax.plot(wavelengths, deriv, c='r', label='Derivative of spectrum')  ax.plot(wavelengths, reconstructedSpectrum, c='g', lw=2, alpha=0.7, label='Reconstruction')  ax.set_xlim((wavelengths.min(), wavelengths.max()))  ax.legend()   for peakIdx in peakIndices:   ax.axvline(wavelengths[peakIdx], ls='--', c='#555555')   plt.show()                     130  Appendix D   Python Script for the multiplication of the LIBS responses from __future__ import division from __future__ import division  import matplotlib.pylab as plt import pandas as pd from pandas import DataFrame import numpy as np from scipy.optimize import leastsq import os  import matplotlib.ticker as plticker import xlrd   def fixValue(x):  if (isinstance(x, unicode)):   return x.strip().replace(badChar,'')  else:   return x  def clean(col):  return col.apply(fixValue)    readingFilename='pythonbinomial2.csv' spectra=pd.read_csv(readingFilename) ##rocks=spectra['Rocks']  result_data = {}  for col1 in spectra:     for col2 in spectra:         result_data[col1+'*'+col2] = spectra[col1]*spectra[col2] pd.DataFrame(result_data).to_csv('result2.csv')          131  Appendix E  Number of responses per sample for each ion for the Oxide samples  Ag II Ag II Al II Ba II Be II Be III Bi I Ca I Ca II Cd II Cl II Co I Cr I Row 232.02 241.32 281.62 455.40 272.89 448.73 306.77 422.67 317.93 274.85 481.01 347.40 427.48 1   1  1   26  39    2     2   21  35    3        28 1 38    4        27  37    5   2     38 2 25 1   6   1     15  33    7   2     23  35    8   8  7  4 29  39    9  1 1  3   36 5 37 2   10     3  1 19  40    11   1 3 2   24 3 37   1 12  1   20  3 22 5 39   1 13    1 1   28  40    14  7 1     18  33    15  2      25  35    16   1 1    29  38 1   17    1 1 1  14 1 31   1 18   6  21  7 35 5 39    19     3  3 26 2 38    20   4  1  1 33 5 31    21    1 1   38 3 40 1  2 22   1  9  4 14  38    23  1 1  2  2 8  33    24   1  6  1 27 1 39  1  25     1   34 1 39    26     4  3 30 1 40    27        24 2 38    28    3 8   28 2 35   3 29        18  40    30    1 5   37 4 37    31     1   24  37    32 1 1      29  36    33  7 2 2    28  30   1 34   1 1    37 2 36 2   35     3   25 5 40    36        33 1 40    37     3   18 1 39    38     10  1 25 1 40    39     8   15  40    40        36 1 20    41     3   14  39 1       132    Cu I Cu I Cu II F II Fe I Fe II Fe II Ga I Hf I In II Ir I Mg I Row 324.75 327.40 271.35 350.56 374.95 234.35 238.20 294.36 368.22 294.10 269.42 285.21 1 26 24  5 4 10 40     40 2 38 37   1 8 39     40 3 39 36  1  3 39   1  40 4 39 39   1 8 38     40 5 40 40   1 2 27    1 33 6 33 25   1 6 36     40 7 31 29  1  1 35   1  39 8 30 24 3 1 8 15 39   1 1 40 9 40 40 1 1 8 7 38     39 10 37 26 2 5 5 22 40     40 11 36 33  2 4 13 38     39 12 39 38 4  27 30 40  1  3 39 13 39 34  1 1 9 40     40 14 34 35  6 1 7 38 2  2  40 15 30 22  3  1 37 3    39 16 40 39    4 40     40 17 38 37   2 8 35   1  24 18 40 39 3 4 27 33 39   1 3 40 19 30 25 1 2 7 14 38 1   1 40 20 40 40   2 7 33     40 21 40 39   13 18 40     40 22 28 17 2  17 25 40     40 23 26 22  6 4 8 37 2   1 40 24 40 39 2 2 17 26 39     40 25 40 39 2  5 8 40     40 26 40 37 1  11 17 40    1 40 27 40 35   1 11 39     40 28 32 29 1 7 11 13 38 1   1 40 29 28 26  2 1 2 39     40 30 39 39 1 3 9 23 36     38 31 38 37  2 7 16 39 2    40 32 40 37   2 20 36     38 33 24 23  11   30 6  3  38 34 40 40   2 10 39     40 35 40 35  1 8 21 40     40 36 39 32  1  2 40     40 37 36 26  2 3 8 40 1    40 38 39 39 1  29 31 40    3 40 39 39 35 2  19 33 40     40 40 15 11   1  26     27 41 39 35 2  4 7 40     40     133    Mg II Mg III Mn I Mn II N II N IV Na II Na II Ni I O III O V P I Row 279.55 239.51 279.83 261.02 399.50 347.87 298.42 307.83 349.30 393.48 278.10 253.56 1 40 34  32   9 3 3 38 24 1 2 40 34  21   11 7  37 26 2 3 40 24  17   1 1  30 25  4 40 29  20   3   37 27  5 39 15  10   1   37 11  6 40 18  16   4  1 19 25  7 40 26  24   2 3 2 31 20  8 40 31  17  1 9   39 21  9 40 33  14   8  1 40 14 1 10 40 37  24  1 16 2  31 28 2 11 40 27  21   11 4 2 32 14 1 12 40 40  11   28 1  31 10  13 40 31  27   3 3  34 21 1 14 40 33  22   12 4 3 37 22 1 15 40 23  19  1 3 3 1 33 25  16 40 28  16   2   39 17  17 35 28 1 19   2 1  26 10 1 18 40 39  9   33 6 3 38 5 1 19 40 35  23   13 3  33 28 1 20 40 24  21   8   38 14  21 40 32  23   14   38 15 2 22 40 38  21   21 1  31 16 5 23 40 21  14  2 7 8 1 18 17  24 40 39  22   19 2 1 37 19 3 25 40 33  25   6   40 19  26 40 40  25   11   36 15  27 40 31  22   3   37 27 1 28 40 32  20   16 6 5 36 12 1 29 40 28  24   1 2 1 26 32  30 39 33  18  1 25 3 2 39 20 1 31 40 38  23   9 2 1 35 14  32 40 34  16   12   38 25 6 33 40 21  15  4 9 8 7 32 13 1 34 40 29  24   7   40 10  35 40 33  25   17 2  37 28 3 36 40 31  17   2 3  37 23 1 37 40 33  22  1 5 2  33 26  38 40 38  18 1  30 2 1 39 25 1 39 40 40  18   23   29 18 1 40 31 10  12      38 19  41 40 33  16 1  6   35 26 1     134     P IV Pb I Pb I S VI S VI Sc III Si I Si II Sn II Ta I Ti I Ti II Row 334.77 280.20 283.31 419.89 420.08 269.91 288.16 413.09 335.20 362.66 399.86 376.13 1             35     8 7 40 2 1           26     3 4 40 3   3         36     3 7 40 4         1   24     1 4 39 5 2 13         34     1 1 36 6 3           34     3 7 40 7 1 4         33     2 4 40 8 1 3 2   4   26     3 8 39 9 1 10 3   2   32     3 3 39 10     1       26     5 6 40 11 1 13 2 1 2   28     3 3 39 12   21 9 2 9   26 3     3 19 13   2         24     1 9 40 14 1           28     10 10 40 15 3 3         30     2 8 40 16 3 1         30       1 40 17   2         29       2 33 18   30 3 5 9   39 5   10   40 19   5 2 1 2   30 1   5 7 37 20 2 13         36   1   6 40 21   9         38 1     3 40 22   2 5 3 8   27 2   10 2 32 23 1 3 2 1 3   26 1   9 18 39 24   5 1   2   28 3 2 6 3 39 25   2         35     2   40 26 2 4         31 1   1 1 40 27 1           32     1 9 40 28   18 3 1 3   36 2   8 4 39 29   1 1       33 1   3 3 40 30 1 5         33     3 8 36 31 2 5     1   32 1 1 3 2 40 32 2 2         28     2 5 40 33 1 7       1 24     12 16 40 34   5         35       1 40 35 1 1         31       4 39 36 1           26       9 40 37 1 3   1 2   29 1   4 7 39 38 2 4 3 3 7   28 1   4   37 39       1 2   25 1       39 40   3         37         40 41 1 3 1   1   27       2 40     135     Ti III Tl I Tl I V II W I W II Y II Zn I Zn II Zr III Row 251.61 276.79 351.92 292.40 400.88 248.92 371.03 334.50 491.16 266.43 1 4       2   1   1 1 2 7       1 1     3 3 3 2                   4 3       2 1 2   2 2 5 1         1 8   1 1 6 1                   7           1         8 8   2     4     8 8 9 7   1     4 5   4 4 10 13       1 3     4 4 11 11       1 7     5 5 12 26       1 19     25 25 13 2       2       1 1 14 3 2     1           15   1     1           16 1       1   7       17 5       2       2 2 18 30         18     29 29 19 8       3 5     8 8 20 6       2   3   2 2 21 13         3 1   3 3 22 16   7   1 9     13 13 23 6         4 1   4 4 24 18       1 6     10 10 25 3         1     3 3 26 11       3 2 2   8 8 27 4       2           28 14 1       7     10 10 29 1       1           30 19       1 2     11 11 31 7       1 2     3 3 32 11   1           2 2 33   6   2 2 2   1   1 34 6       1   17   1 1 35 14   1     2     8 8 36 3       3       1 1 37 5   1           3 3 38 26         7     18 18 39 27         2 1   22 22 40                     41 6   1   1 3 1   5 5     136  Appendix F  Compiled LIBS responses for Sulphide rock samples from Escondida Mine    C I C III Ag II Ag II Al II Au I Ba II Be II Bi I Ca I Ca II Cd II Cl II Cr I Row 247.86 229.69 232.02 241.32 281.62 242.80 455.40 272.89 306.77 422.67 317.93 274.85 481.01 427.48 1   727   798     881     922   1007   908 2   743 730 835 861         876         4             830             878 8         878   904     905       881 9               1295 1102 864   1455   927 10   715   900 916         875   957   858 11           984       855   1102   875 12         972     1132 974 875 913 1505 801 865 13 1065     928 935         992   1196   875 14   777           1174       1815     15         1048   806   983 856   1315   1006 16                   873       836 18         928         849   898   843 20       811 935   846     876   1255   1039 22       893               941   919 25   742   831 913         831   916   873 27   800         821 1319 1090 920 978 2149     30       847 885             893   869 31       851 935         835       1065 32       808 882         943   1076   827 33             843 1107   849 938 1213   849 35             826     840   961   834 37   884           1522 1245 951 1059 2596   828 39   718   846 883                   42   774   846 924       1340         941 44   771   828     835 1103   854   1181   906 45       890           846   1167   920 46   778   885 1030     1257 1020 848 928 1146   894 48   783   869 1390             921     49         849     1178 1079 944   2030   858 50   751   861 906   888 1012   847   1321   793 51       846 914         891   1165   971 54   752     906     1118 1122     1450     55               1179 1098     1580   862 57       827 957             969   952 58         890                 874 59   824   819       1568 1224 927 1052 1787   847 62   885   825       1640 1220 984 1086 2907 988       137      Cu I Cu I Cu II F II Fe I Fe II Fe II Ga I Hf I Hg II In II Ir I Mg I Row 324.75 327.40 271.35 350.56 374.95 234.35 238.20 294.36 368.22 284.77 294.10 269.42 285.21 1 2619 2175   1049 969 908 1043 928     986   856 2 2146 1596   1106       964     957   881 4 2520 2151   1017             920   884 8 2713 2261                     862 9 2368 1979 1269 1026 1048 1121 1300 928     925 1054 930 10 2350 1996   1165     897 1024     1028     11 2290 1986     891 955 1060           876 12 2360 1960 1059   1065 1043 1302 948       944 1044 13 2357 1853 1022 1203 956 1041 1021 1131     1110   1064 14 2136 1841 1135 1029 1079 1227 1435 942     988 994 934 15 3036 2562     1021 1049 1192     995     964 16 2290 1909   1027       958     927   899 18 2439 1993   1004     884 896         900 20 2530 1903   1024 958 1012 1064 916     931   881 22 2408 2015   1060     896 905     1005   897 25 2631 2037   1047     865 963     990   906 27 1760 1510 1114   1199 1324 1789   894     1018 1062 30 2176 1677   1036     844 972     948   955 31 2161 1746   1071       939     1029   862 32 2359 1952   1052 932 891 999 920     957   898 33 2369 1983 1047 998 948 993 1106 892         818 35 2258 1913     931 904 924           904 37 2160 1795 1170   1307 1556 2110         1042 1054 39 2068 1687   1051     822 965     978   872 42 2385 1637   1113       1009     1017   871 44 2373 1954   1033 940 974 1122 960     905   901 45 2532 2118   1129 929 973 1088 949     1018   936 46 2019 1635   1150 1355 1185 1000 1059 895   1015   941 48 1863 1440 1022 1137     866 946   1779 1067   968 49 2325 1939   976 1204 1244 1252 905     909   843 50 2141 1819 990 1041 1073 995 1164 990     935   913 51 2319 1882   1063 1072 961 1104 966     940   926 54 1741 1106 1125 1046 1123 1104 1258 922     990   949 55 2184 1822 1093 1134 1084 1212 1355           836 57 2249 1696   1111     918 959     1018   953 58 2245 1980   1008       904     911   813 59 2028 1713 1363 1143 1219 1306 1578   984   983   956 62 2391 1935 1208 938 1404 1659 2336 1024 1050     1077 1175     138      Mg II Mg III Mn I Mn II Mo VI Mo VI N IV Na II Na II Ni I Ni I O III O V P I Row 279.55 239.51 279.83 261.02 329.33 338.70 347.87 298.42 307.83 341.48 349.30 393.48 278.10 253.56 1 962 1012 879       867 908 1468   878 971     2 974     818     877 938 1585   869 964     4 953   794       844   1448     859     8 955         976           1005     9 1044 1208   1273     863 1021 1470   889 924     10 913 843   930     878 974 1582   914       11 1005 1041 912 1112       921       894   1163 12 1339 1183   1229       1022 1105   828 1008 962 1449 13 1040 1010   956     855 1026 1804   958 1156   1207 14 1038 1434   1388     871 1076 1507   892     1869 15 1142 1177   1259       1001   984   919     16 964             840 1462   830 882     18 1048           812 884 1421   846 1078     20 988 1092   1082     860 938 1501   819 936     22 976           913 988 1606   948       25 1006 880   857     831 897 1521   841 888     27 1197 1587   1509       1219 958     1035   1461 30 962           879 924 1539   863 881     31 1026     825     966 1091 1565   884 936     32 947 949   1033     815 888 1476   849 922     33 896 1064   1020     809 901 1398   825 956   995 35 950 926   944       863       908     37 1307 1867   2091       1354 1119   903 1018     39 922     830     880 934 1520   877       42 967     879     891 949 1621   901       44 1017 1062   1145     867 938 1526   853 948     45 981 1024 982 1134     856 963 1491   916 910   1035 46 1059 1151   968     909 1000 1696   881 942     48 1073     904 1436   876 983 1644   892 919     49 996 1488 852         1153 1566   816 921     50 1008 1084   1123     877 999 1538   872 929   1084 51 1104 1034   1084     892 950 1551   883 999   1283 54 1071 1176   1115     859 1026 1550   893     1048 55 952 1331   1360     860 1102 1671   869 964     57 1014 884   946     893 918 1580   876       58 915     807     829 852 1447   830 820     59 1087 1536   1206       1181 1684   931     1079 62 1295 2027   2030       1416 1570     1025         139      P IV Pb I Pb I Pd I S VI S VI Sb I Si I Si II Sn II Ta I Ti I Ti II Row 334.77 280.20 283.31 340.46 419.89 420.08 231.15 288.16 413.09 335.20 362.66 399.86 376.13 1   1004     841 841   1138       912 1319 2   970 990         1234   913   907 1452 4 1014 923           1026   882   888 1089 8 947 988           1209         869 9 906 1037 1118   852 885   1263 985     915 1167 10 999             1225       937 1534 11 847 1035     815 815   1079       907   12   1169 1036   871 869   1167 837     879 1000 13   1141           1247       955 1529 14   1042 958   915 906   1296 912     916 1347 15 1064 1138     903 897   1227 893     890   16 844 966           1206       883 1348 18   1043           1243       908 1329 20   968           1258       886 1284 22 879 1018           1303   911   941 1415 25   1034           1201   825   896 1387 27 922 1085 1041   948 972 905 1289 931     882   30   995 921         1204   868 795 917 1337 31   1002           1240       933 1334 32 845 993 889   863 863   1136       910 1409 33   899       834   942 821     875 1071 35 856 1052       826   968 827         37 1104 1239 1181   998 1003   1419 962     948 867 39   1046 962         1221     883 916 1406 42   984 974         1228   837 864 925 1498 44 973 1029       922   1212       894 1387 45 949 1088           1187       913 1353 46   1033 971   1026 1017 805 1305       958 1559 48   1015   1049       1407       939 1472 49 851 1003           1153       885 1094 50   1017 935   870 892 750 1236 885     931 1494 51   1076 906     930   1376       903 1461 54   1047 1021   870 887   1308 891     913 1468 55 857 930 922   876 902   1201 914 883   902 1284 57 995 1051           1253       925 1370 58   934           1146       868 1285 59 993 1080 1157   1016 1041   1275 987     929 1252 62   1234 1246   1006 1043   1376 945   829 962 1753     140      Ti III Tl I Tl I V I V II W I W II Y II Zn I Zr III Zr III Row 251.61 276.79 351.92 411.18 292.40 400.88 248.92 371.03 334.50 262.06 266.43 1 1094 968 920 973     840 849   986 843 2 1176   936                 4 1072 913         826     848   8 1156 924   961     903     1008   9 1332 1044         1139 916     1057 10 1186   993       866     859   11 1144 908         815 797     877 12 1278 1012         1195 885 944   981 13 1245 897 1017     869 862 874   858 1001 14 1336 1164     939     916     1088 15 1291 1022     1002   930 908   1076 993 16 1171           849     856   18 1178 846         872     845   20 1229 1064         1031       1016 22 1244           906         25 1145   861       875     839   27 1603 1268     925   1888 973     1183 30 1187   923       858     845   31 1197   962       908     843   32 1115 856 858       804     821 830 33 947 858         829 855   856 1012 35 992 845         909 819     873 37 1580 1459     1240   905 1051   910 1335 39 1164   1014                 42 1189   918       839 880       44 1232 961 868       946 934     969 45 1200 968 963       890 811   896 874 46 1258 1223 951   948     1009     1133 48 1319   984   1799             49 1085 1193 851       816 953     1076 50 1249 962 928       984 887     957 51 1342 955 886       991 857     926 54 1299 1090 948   937     916     1047 55 1191 1060 910       960 905     1093 57 1213 875 921                 58 1083 802 807       825     821   59 1263 1235 906   1127   885 1007     1288 62 1772 1556   969 1182     1080     1407     141  Appendix G  Number of responses per sample for each ion for the Sulphide samples     C I C III Ag II Ag II Al II Au I Ba II Be II Bi I Ca I Ca II Cd II Cl II Cr I Row 247.86 229.69 232.02 241.32 281.62 242.80 455.40 272.89 306.77 422.67 317.93 274.85 481.01 427.48 1   2   1     9     6   5   4 2   1 1 4 1         3         4             1             5 8         1   6     11       9 9               4 5 10   34   4 10   1   6 1         2   2   2 11           1       10   28   7 12         1     9 11 32 3 39 2 1 13 1     4 1         2   6   2 14   4           13       18     15         3   2   1 16   25   10 16                   5       4 18         2         1   2   10 20       1 2   1     6   5   3 22       2               1   2 25   2   5 4         2   8   5 27   1         2 22 24 18 8 40     30       4 3             1   1 31       2 5         2       1 32       3 2         3   4   6 33             4 1   7 1 5   7 35             3     9   20   4 37   5           27 18 19 6 37   1 39   1   3 5                   42   1   8 4       1         1 44   1   3     2 3   7   30   4 45       1           1   13   4 46   1   8 3     3 3 11 1 21   3 48   1   8 4             6     49         1     1 1 1   1   6 50   2   3 4   1 8   4   37   1 51       4 2         11   19   3 54   1     4     10 3     29     55               9 2     22   3 57       7 3             9   1 58         1                 2 59   2   1       8 7 3 3 26   1 62   3   1       27 28 22 13 39 1      142       Cu I Cu I Cu II F II Fe I Fe II Fe II Ga I Hf I Hg II In II Ir I Mg I Row 324.75 327.40 271.35 350.56 374.95 234.35 238.20 294.36 368.22 284.77 294.10 269.42 285.21 1 28 28   9 2 2 3 6     3   6 2 5 7   17       11     12   4 4 38 38   2             1   2 8 40 40                     6 9 36 36 2 2 22 21 33 1     1 1 13 10 20 21   19     3 7     10     11 38 39     14 11 27           8 12 40 40 3   33 35 40 1       1 32 13 25 30 1 16 1 2 8 6     1   7 14 4 4 9 8 13 16 21 2     3 5 7 15 40 40     20 16 27     1     12 16 33 32   11       2     8   7 18 34 36   5     3 2         15 20 25 31   10 3 4 8 2     7   9 22 34 34   6     2 2     6   7 25 15 18   15     9 12     5   12 27 40 39 2   38 40 40   3     4 10 30 17 18   22     1 9     9   3 31 32 33   13       4     5   13 32 29 31   6 2 2 5 5     3   4 33 38 39 1 1 6 3 5 1         1 35 40 40     9 3 19           2 37 40 40 2   36 36 37         1 18 39 7 7   25     1 12     7   1 42 11 19   23       16     8   4 44 38 36   10 11 19 29 3     4   10 45 36 36   6 5 5 15 3     4   4 46 13 13   22 3 4 26 7 1   9   18 48 11 13 1 17     5 3   1 7   7 49 36 36   5 1 1 2 3     1   16 50 1 1 2 24 14 29 37 2     3   3 51 33 31   18 3 12 16 7     3   19 54 4 8 5 25 12 20 29 5     3   10 55 40 40 8 2 13 14 23           5 57 20 25   18     9 6     10   6 58 23 20   15       3     5   5 59 38 38 1 2 18 19 23   4   2   11 62 39 39 5 1 38 39 39 1 3     2 8    143       Mg II Mg III Mn I Mn II Mo VI Mo VI N IV Na II Na II Ni I Ni I O III O V P I Row 279.55 239.51 279.83 261.02 329.33 338.70 347.87 298.42 307.83 341.48 349.30 393.48 278.10 253.56 1 31 2 1       7 6 11   2 14     2 33     1     8 8 31   16 4     4 20   1       1   2     3     8 32         1           9     9 39 28   11     1 25 4   1 18     10 8 2   3     5 11 13   6       11 25 19 1 16       14       18   3 12 39 39   13       38 2   2 26 6 3 13 36 5   8     5 9 13   8 2   1 14 26 16   9     4 19 14   4     2 15 20 19   13       18   1   15     16 35             3 3   7 9     18 30           1 1 3   2 2     20 40 5   5     5 5 14   4 7     22 35           2 1 10   3       25 30 2   10     11 12 21   11 3     27 26 40   10       37 1     11   2 30 21           7 5 27   10 1     31 37     1     3 1 12   5 7     32 36 4   2     2 5 6   5 4     33 13 4   1     1 5 1   1 10   1 35 17 10   9       7       20     37 38 37   10       36 3   2 15     39 19     2     12 5 30   7       42 31     1     10 11 25   12       44 35 24   14     7 17 8   1 14     45 24 6 1 4     2 6 8   3 1   1 46 36 8   16     11 20 26   11 11     48 26     6 1   5 10 19   10 1     49 30 1 1         1 2   1 3     50 36 33   21     4 34 26   10 2   3 51 40 14   15     3 17 19   6 14   3 54 35 25   20     6 25 28   9     1 55 25 17   7     2 14 2   1 1     57 34 3   3     2 11 16   8       58 26     1     6 1 16   5 3     59 32 19   9       20 2   3     1 62 25 39   5       40 3     11        144          P IV Pb I Pb I Pd I S VI S VI Sb I Si I Si II Sn II Ta I Ti I Ti II Row 334.77 280.20 283.31 340.46 419.89 420.08 231.15 288.16 413.09 335.20 362.66 399.86 376.13 1   10     1 1   30       17 17 2   11 1         22   1   36 33 4 1 2           30   1   3 5 8 2 7           36         8 9 2 12 3   6 12   35 3     12 3 10 1             28       22 22 11 1 8     1 1   34       1   12   20 2   5 20   40 5     6 1 13   12           31       20 22 14   3 6   1 9   20 2     19 13 15 1 9     2 5   38 1     5   16 2 10           36       16 16 18   15           37       7 7 20   12           25       15 15 22 2 3           30   1   11 12 25   14           29   1   24 21 27 1 10 14   10 23 1 37 7     13   30   3 1         23   1 1 31 31 31   14           30       19 22 32 1 8 1   1 1   35       11 14 33   2       3   34 1     3 6 35 3 3       2   32 3         37 1 25 17   13 30   37 9     25 1 39   2 1         29     1 33 32 42   8 1         22   1 1 32 31 44 1 10       1   30       13 12 45 2 3           35       11 10 46   20 4   2 3 1 18       31 24 48   13   2       16       26 21 49 2 12           38       7 14 50   16 5   4 8 1 31 2     37 25 51   23 1     1   38       26 20 54   22 6   1 7   31 4     40 21 55 4 4 1   5 10   37 1 2   9 4 57 1 10           32       24 27 58   4           35       17 25 59 2 10 8   2 11   37 5     13 6 62   14 23   13 34   33 10   1 24 2 145      Ti III Tl I Tl I V I V II W I W II Y II Zn I Zr III Zr III Row 251.61 276.79 351.92 411.18 292.40 400.88 248.92 371.03 334.50 262.06 266.43 1 40 3 1 1     2 2   3 2 2 40   3                 4 33 1         1     6   8 40 3   1     5     5   9 37 25         2 11     12 10 40   5       2     1   11 24 18         1 2     8 12 23 36         3 28 11   29 13 38 3 6     1 1 1   1 1 14 24 16     2     12     16 15 27 19     1   2 7   1 9 16 40           2     1   18 40 2         5     2   20 40 3         2       2 22 40           3         25 37   3       4     1   27 20 39     2   1 30     36 30 40   2       2     1   31 40   2       3     2   32 39 3 2       1     2 1 33 24 6         6 3   8 1 35 22 11         4 3     1 37 22 37     3   1 30   1 34 39 40   1                 42 40   6       1 1       44 38 17 1       2 1     7 45 39 9 2       4 1   1 1 46 37 3 3   1     3     3 48 30   3   1             49 40 1 1       5 1     1 50 37 26 3       1 16     17 51 40 8 4       1 3     4 54 37 16 1   1     11     13 55 34 19 1       3 12     12 57 40 1 4                 58 40 2 1       4     1   59 32 20 1   1   2 13     13 62 9 39   1 2     33     37     146  Appendix H  ICP certified assay results for the 41 Sulphide Escondida samples  ANALYTE WtKg Ag Al As Ba Be Bi Ca Cd METHOD G_WGH79 GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B DETECTION 0.01 2 0.01 3 5 0.5 5 0.01 1 UNITS kg ppm % ppm ppm ppm ppm % ppm Sulfuro-1 0.428 <2 0.85 4 61 <0.5 <5 0.01 <1 Sulfuro-2 0.157 <2 1.69 7 13 <0.5 <5 <0.01 <1 Sulfuro-3 0.181 <2 0.59 11 26 <0.5 <5 0.03 <1 Sulfuro-4 0.07 <2 0.92 11 43 <0.5 <5 0.02 <1 Sulfuro-8 0.101 <2 0.72 3 47 <0.5 <5 0.01 <1 Sulfuro-9 0.346 <2 0.42 5 11 <0.5 <5 0.03 <1 Sulfuro-10 0.402 <2 1.21 4 13 <0.5 <5 <0.01 <1 Sulfuro-11 0.267 <2 0.41 3 16 <0.5 <5 0.01 <1 Sulfuro-12 0.198 <2 0.61 3 31 <0.5 <5 0.13 <1 Sulfuro-13 0.141 <2 0.6 9 17 <0.5 <5 0.02 <1 Sulfuro-14 0.159 <2 0.9 7 7 <0.5 <5 <0.01 <1 Sulfuro-15 0.17 <2 0.43 <3 39 <0.5 <5 0.02 <1 Sulfuro-16 0.065 <2 0.88 6 10 <0.5 <5 0.04 <1 Sulfuro-18 0.06 <2 1.4 7 21 <0.5 <5 <0.01 <1 Sulfuro-20 0.045 <2 1.09 <3 <5 <0.5 <5 0.02 <1 Sulfuro-22 0.028 <2 1.16 4 30 <0.5 <5 0.02 <1 Sulfuro-25 0.026 <2 0.75 6 42 <0.5 <5 0.05 <1 Sulfuro-27 0.038 <2 0.55 5 31 <0.5 <5 0.02 <1 Sulfuro-30 0.014 <2 1.94 10 26 <0.5 <5 0.01 <1 Sulfuro-31 0.026 <2 1.51 5 48 <0.5 <5 0.02 <1 Sulfuro-32 0.018 <2 1.34 3 50 <0.5 <5 0.03 <1 Sulfuro-33 0.025 <2 0.86 <3 62 <0.5 <5 0.02 <1 Sulfuro-35 0.022 <2 0.68 5 50 <0.5 <5 0.03 <1 Sulfuro-37 0.028 <2 0.59 4 23 <0.5 <5 0.03 <1 Sulfuro-39 0.035 <2 1.33 8 12 <0.5 <5 <0.01 <1 Sulfuro-42 0.046 <2 1.01 4 12 <0.5 <5 0.01 <1 Sulfuro-44 0.018 <2 0.74 3 64 <0.5 <5 0.01 <1 Sulfuro-45 0.018 <2 0.82 3 24 <0.5 <5 0.02 <1 Sulfuro-46 0.018 <2 0.87 18 11 <0.5 <5 0.04 <1 Sulfuro-48 0.018 <2 1.1 6 18 <0.5 <5 0.02 <1 Sulfuro-49 0.019 <2 1.66 5 48 <0.5 <5 0.02 <1 Sulfuro-50 0.017 <2 1.32 5 22 <0.5 <5 0.01 <1 Sulfuro-51 0.022 <2 0.69 <3 15 <0.5 <5 0.03 <1 Sulfuro-54 0.03 <2 1.72 10 26 <0.5 <5 0.01 <1 Sulfuro-55 0.029 <2 1.31 7 14 <0.5 <5 0.02 <1 Sulfuro-57 0.019 <2 0.82 9 30 <0.5 <5 0.03 <1 Sulfuro-58 0.018 <2 1.23 5 16 <0.5 <5 0.02 <1 Sulfuro-59 0.015 <2 0.95 <3 40 <0.5 <5 0.02 <1 Sulfuro-62 0.016 <2 0.52 4 39 <0.5 <5 0.03 1    147    Co Cr Cu Fe Hg K La Li Mg Mn GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B 1 1 0.5 0.01 1 0.01 0.5 1 0.01 2 ppm ppm ppm % ppm % ppm ppm % ppm <1 <1 6560 0.12 <1 0.2 7.2 <1 0.03 11 <1 <1 8470 0.07 <1 0.07 4.4 3 0.01 12 5 1 6390 0.28 1 0.11 3.1 <1 0.02 17 <1 1 >10000 0.22 <1 0.2 7.6 1 0.03 30 <1 <1 7420 0.12 <1 0.19 6.6 <1 0.03 9 11 <1 >10000 3.26 <1 0.1 <0.5 <1 0.01 8 <1 <1 5150 0.15 <1 0.05 6.9 2 <0.01 7 10 2 >10000 0.71 <1 0.14 0.6 <1 0.01 18 5 3 1330 1.33 <1 0.1 18.7 4 0.51 296 1 1 9620 0.14 <1 0.12 5.1 <1 0.02 15 <1 <1 1500 0.74 <1 0.06 3.5 <1 0.01 19 6 2 2510 0.37 <1 0.16 1.2 <1 0.02 15 <1 <1 >10000 0.13 <1 0.13 0.8 <1 0.02 12 <1 <1 6160 0.28 <1 0.12 7.4 2 0.02 18 <1 <1 1370 0.09 <1 0.12 5.3 2 0.01 9 <1 <1 >10000 0.12 <1 0.11 4.5 <1 0.02 10 <1 1 1180 0.15 <1 0.09 1.2 <1 0.02 11 47 <1 5490 6.91 <1 0.11 <0.5 <1 0.01 14 <1 1 4430 0.18 <1 0.1 7.2 2 0.02 29 <1 <1 >10000 0.11 <1 0.15 6.5 1 0.02 10 1 1 5540 0.21 <1 0.25 4.3 1 0.03 15 4 3 1060 0.48 <1 0.33 1.2 <1 0.03 37 9 2 >10000 3.33 <1 0.32 0.8 <1 0.03 22 43 <1 6950 1.94 <1 0.14 1.4 <1 0.02 11 <1 <1 4190 0.11 <1 0.09 5.8 2 0.01 10 <1 <1 3340 0.09 <1 0.07 6.6 1 0.01 9 15 1 4610 0.65 <1 0.21 4.3 <1 0.03 12 7 1 5420 0.5 <1 0.1 4.7 <1 0.01 15 <1 <1 2300 0.18 <1 0.14 1 <1 0.02 10 4 1 9210 0.38 <1 0.12 6.4 1 0.02 19 <1 1 6130 0.19 <1 0.24 6.5 2 0.03 15 <1 2 393 1.54 <1 0.08 6 2 0.01 45 6 1 >10000 0.56 <1 0.22 <0.5 <1 0.02 19 <1 1 849 0.62 <1 0.13 8 2 0.02 35 1 <1 >10000 0.83 <1 0.07 2.3 2 0.01 6 3 1 >10000 0.25 <1 0.21 1.8 <1 0.03 16 <1 <1 >10000 0.13 <1 0.07 4.1 1 0.01 8 3 1 >10000 0.38 <1 0.29 1.4 <1 0.03 18 32 <1 4690 8.31 <1 0.12 <0.5 <1 <0.01 20    148    Mo Na Ni P Pb S Sb Sc Sn Sr GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B 1 0.01 1 0.01 2 0.01 5 0.5 10 5 ppm % ppm % ppm % ppm ppm ppm ppm 75 0.03 1 <0.01 3 0.21 <5 <0.5 <10 6 80 0.04 1 <0.01 3 0.3 <5 0.6 <10 10 66 0.03 2 <0.01 <2 0.33 <5 <0.5 <10 8 80 0.05 1 <0.01 5 0.32 <5 0.7 <10 5 77 0.03 <1 <0.01 <2 0.21 <5 <0.5 <10 6 20 0.05 4 <0.01 7 4.31 <5 <0.5 <10 8 15 0.03 <1 <0.01 <2 0.26 <5 <0.5 <10 <5 141 0.03 3 <0.01 7 1.16 <5 0.5 <10 16 7 0.05 5 0.05 154 0.73 <5 0.6 <10 7 106 0.05 1 <0.01 3 0.31 <5 <0.5 <10 7 18 0.03 1 <0.01 <2 0.14 <5 0.6 <10 <5 19 0.03 2 <0.01 <2 0.36 <5 <0.5 <10 14 107 0.1 2 <0.01 6 0.58 <5 1 <10 13 77 0.03 <1 <0.01 2 0.21 <5 0.5 <10 <5 30 0.08 1 <0.01 <2 0.17 <5 0.5 <10 <5 121 0.04 1 <0.01 10 0.69 <5 0.5 <10 15 15 0.07 2 <0.01 <2 0.14 <5 0.6 <10 38 52 0.06 10 <0.01 7 >5 <5 <0.5 <10 16 25 0.04 1 <0.01 <2 0.2 <5 0.8 <10 12 20 0.05 1 <0.01 4 0.43 <5 0.7 <10 21 13 0.08 2 <0.01 <2 0.23 <5 0.9 <10 16 10 0.06 2 <0.01 <2 0.2 <5 0.6 <10 20 1830 0.06 4 <0.01 10 4.48 <5 0.8 <10 18 25 0.05 4 <0.01 4 2.55 <5 <0.5 <10 7 51 0.04 <1 <0.01 <2 0.17 <5 <0.5 <10 <5 31 0.03 1 <0.01 <2 0.16 <5 <0.5 <10 7 13 0.04 3 <0.01 <2 0.8 <5 <0.5 <10 8 19 0.05 3 <0.01 <2 0.61 <5 0.5 <10 6 80 0.11 1 <0.01 <2 0.2 <5 1.1 <10 28 88 0.04 1 <0.01 2 0.55 <5 0.6 <10 6 45 0.04 1 <0.01 <2 0.22 <5 0.9 <10 5 20 0.04 <1 <0.01 <2 0.08 <5 1 <10 8 26 0.05 2 <0.01 6 1.07 <5 0.8 <10 8 31 0.04 <1 <0.01 <2 0.09 <5 0.8 <10 <5 40 0.03 1 <0.01 6 1.38 <5 0.6 <10 11 41 0.06 1 <0.01 <2 0.34 <5 0.6 <10 20 29 0.03 1 <0.01 6 0.55 <5 <0.5 <10 6 280 0.07 2 <0.01 8 0.9 <5 1 <10 27 156 0.06 6 <0.01 6 >5 <5 <0.5 <10 21    149    Ti V W Y Zn Zr Al2O3 Ba CaO Cr2O3 GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GE_ICP14B GO_ICP95A GO_ICP95A GO_ICP95A GO_ICP95A 0.01 1 10 0.5 1 0.5 0.01 0.001 0.01 0.01 % ppm ppm ppm ppm ppm % % % % <0.01 5 <10 0.6 9 <0.5 25.1 0.091 0.04 <0.01 <0.01 5 <10 0.6 5 0.6 28.7 0.029 0.04 <0.01 0.02 4 <10 <0.5 5 <0.5 20.5 0.045 0.08 <0.01 0.02 6 <10 0.6 5 <0.5 20.9 0.045 0.04 <0.01 <0.01 3 <10 <0.5 3 <0.5 21.4 0.079 0.04 <0.01 <0.01 5 <10 <0.5 2 0.6 19.1 0.03 0.24 <0.01 <0.01 3 <10 <0.5 2 <0.5 25.8 0.027 0.03 <0.01 <0.01 4 <10 <0.5 4 0.6 16.3 0.036 0.08 <0.01 <0.01 13 <10 4.3 207 <0.5 15.7 0.037 0.76 <0.01 0.01 3 <10 <0.5 4 <0.5 18.8 0.028 0.07 <0.01 0.03 20 <10 <0.5 4 <0.5 26.1 0.03 0.05 <0.01 <0.01 4 <10 <0.5 4 <0.5 18.4 0.061 0.1 <0.01 <0.01 7 <10 0.6 5 <0.5 19.1 0.016 0.14 <0.01 <0.01 8 <10 0.5 4 <0.5 27.7 0.039 0.03 <0.01 <0.01 5 <10 0.6 5 <0.5 22.9 0.016 0.08 <0.01 <0.01 5 <10 0.6 7 <0.5 24.9 0.04 0.05 <0.01 <0.01 4 <10 0.6 5 <0.5 21.4 0.037 0.15 <0.01 <0.01 5 <10 <0.5 <1 1.2 16.9 0.04 0.2 <0.01 <0.01 6 <10 0.7 8 <0.5 27.4 0.028 0.04 <0.01 <0.01 6 <10 0.6 3 <0.5 26.8 0.059 0.05 <0.01 <0.01 9 <10 0.7 4 <0.5 21.1 0.045 0.07 <0.01 <0.01 9 <10 0.6 6 <0.5 16.6 0.047 0.08 <0.01 <0.01 5 <10 <0.5 1 0.8 16.5 0.055 0.21 <0.01 <0.01 6 <10 <0.5 2 0.7 20.2 0.038 0.15 <0.01 <0.01 4 <10 <0.5 2 <0.5 30.2 0.026 0.04 <0.01 <0.01 3 <10 0.6 5 <0.5 26.4 0.023 0.04 <0.01 <0.01 4 <10 <0.5 3 <0.5 19.7 0.082 0.05 <0.01 <0.01 5 <10 0.6 4 <0.5 22.6 0.032 0.07 <0.01 0.03 6 <10 0.5 4 <0.5 24.5 0.02 0.17 <0.01 <0.01 5 <10 0.6 2 <0.5 25.1 0.03 0.06 <0.01 <0.01 7 <10 0.6 6 <0.5 23.3 0.04 0.04 <0.01 0.07 38 <10 0.6 2 0.5 26.5 0.032 0.05 <0.01 <0.01 9 <10 <0.5 2 <0.5 18.1 0.02 0.13 <0.01 0.03 18 <10 0.7 3 <0.5 28.3 0.028 0.03 <0.01 <0.01 5 <10 0.5 3 <0.5 26.1 0.021 0.06 <0.01 0.01 4 <10 <0.5 2 <0.5 20.3 0.036 0.09 <0.01 <0.01 4 <10 0.6 4 <0.5 26.5 0.026 0.05 <0.01 <0.01 10 <10 0.6 3 <0.5 20.4 0.05 0.09 <0.01 <0.01 5 <10 <0.5 <1 1.5 19.4 0.055 0.24 <0.01    150    Fe2O3 K2O MgO MnO Na2O Nb P2O5 SiO2 Sr GO_ICP95A GO_ICP95A GO_ICP95A GO_ICP95A GO_ICP95A GO_ICP95A GO_ICP95A GO_ICP95A GO_ICP95A 0.01 0.01 0.01 0.01 0.01 0.001 0.01 0.01 0.001 % % % % % % % % % 1.41 4.15 0.56 <0.01 0.49 0.002 0.04 56.5 0.014 0.43 1.23 0.14 <0.01 0.59 0.002 0.11 52.1 0.023 1.21 2.61 0.3 <0.01 0.69 0.001 0.08 64.5 0.027 1.14 2.71 0.36 <0.01 0.69 0.002 0.04 64.7 0.012 1.18 3.46 0.43 <0.01 0.48 0.002 0.04 63.9 0.01 5.13 2.38 0.17 <0.01 1.3 0.002 0.36 57.2 0.053 0.53 1.04 0.11 <0.01 0.49 0.002 0.03 57.7 0.011 1.77 3.32 0.29 <0.01 0.56 0.002 0.25 58.8 0.057 2.15 1.4 1.02 0.04 5.44 0.001 0.12 70.1 0.052 0.92 2.44 0.28 <0.01 0.89 0.001 0.08 61.3 0.026 2.27 1.75 0.15 <0.01 0.69 0.002 0.15 52.8 0.03 1.75 3.89 0.44 <0.01 0.61 0.002 0.18 66.7 0.044 0.58 1.75 0.14 <0.01 1.33 0.002 0.2 64.8 0.02 1.03 2.05 0.22 <0.01 0.47 0.002 0.06 55.1 0.012 0.51 1.65 0.16 <0.01 1.19 0.002 0.09 59.2 0.015 0.65 1.83 0.21 <0.01 0.59 0.002 0.06 57.3 0.023 0.62 1.46 0.17 <0.01 1.29 0.002 0.24 64.8 0.068 10.2 1.65 0.1 <0.01 1.11 0.002 0.36 56.9 0.074 0.62 1.33 0.16 <0.01 0.45 0.002 0.06 60.6 0.014 0.71 2.08 0.26 <0.01 0.63 0.002 0.08 56.5 0.026 0.98 2.71 0.3 <0.01 0.83 0.002 0.06 65.8 0.015 1.69 3.61 0.38 <0.01 0.56 0.002 0.15 65.4 0.031 5.1 3.69 0.32 <0.01 0.63 0.003 0.28 58.2 0.038 3.59 2.66 0.27 <0.01 0.99 0.002 0.18 58.5 0.028 0.61 1.63 0.17 <0.01 0.59 0.002 0.04 53.4 0.009 0.5 1.3 0.16 <0.01 0.57 0.002 0.06 58.7 0.015 2.02 3.49 0.36 <0.01 0.7 0.002 0.06 63.8 0.017 1.25 1.93 0.19 <0.01 0.99 0.002 0.04 65.4 0.015 0.81 2.22 0.19 <0.01 1.76 0.002 0.26 60.2 0.03 1.1 2.19 0.22 <0.01 0.69 0.002 0.07 55.4 0.019 0.97 2.51 0.34 <0.01 0.42 0.002 0.03 61 0.006 3.7 1.49 0.14 <0.01 0.63 0.002 0.09 54.3 0.02 1.65 3.17 0.38 <0.01 0.81 0.002 0.17 64 0.024 1.66 1.66 0.22 <0.01 0.51 0.002 0.04 58.1 0.008 1.65 1.06 0.14 <0.01 0.39 0.002 0.1 54.4 0.028 1.2 2.84 0.35 <0.01 0.97 0.001 0.12 62.2 0.026 0.55 1.34 0.13 <0.01 0.47 0.002 0.06 58.2 0.023 1.41 3.67 0.29 <0.01 0.97 0.002 0.22 60.8 0.055 14.1 2.4 0.12 <0.01 1.33 0.003 0.45 45.9 0.074    151    TiO2 Y Zn Zr LOI Cu GO_ICP95A GO_ICP95A GO_ICP95A GO_ICP95A G_PHY01K GO_ICP13B 0.01 0.001 5 0.001 -10 0.01 % % ppm % % % 0.66 <0.001 9 0.017 6.79 N.A. 0.92 0.001 9 0.021 12.5 N.A. 0.58 <0.001 5 0.015 5.8 N.A. 0.6 0.001 7 0.015 6.08 1.14 0.54 <0.001 16 0.014 5.79 N.A. 0.66 0.001 <5 0.015 8.86 1.22 0.64 <0.001 7 0.017 9.83 N.A. 0.49 <0.001 7 0.011 6.81 1.5 0.3 <0.001 210 0.013 1.88 N.A. 0.6 0.001 9 0.014 5.49 N.A. 0.76 0.001 8 0.017 12.6 N.A. 0.55 <0.001 5 0.013 4.71 N.A. 0.65 <0.001 11 0.014 8.79 1.5 0.83 0.001 8 0.019 10.6 N.A. 0.86 0.002 6 0.02 11.3 N.A. 0.7 0.001 6 0.016 8.92 2.57 0.63 0.001 10 0.016 6.94 N.A. 0.54 <0.001 <5 0.012 10 N.A. 0.85 0.001 9 0.018 10.2 N.A. 0.76 0.001 5 0.017 9.47 1.37 0.62 0.001 5 0.016 6.52 N.A. 0.43 <0.001 7 0.013 4.35 N.A. 0.61 <0.001 5 0.014 6.1 1.91 0.72 0.001 <5 0.016 9.09 N.A. 0.83 0.001 7 0.02 10.8 N.A. 0.79 0.001 6 0.018 9.98 N.A. 0.51 <0.001 11 0.015 5.57 N.A. 0.67 0.001 7 0.016 6.74 N.A. 0.86 <0.001 8 0.019 9.33 N.A. 0.78 0.001 5 0.017 9.1 N.A. 0.73 0.001 7 0.016 8.4 N.A. 0.79 0.001 <5 0.017 10.4 N.A. 0.59 <0.001 6 0.013 6.97 2.01 0.82 0.001 <5 0.018 10.1 N.A. 0.81 0.002 5 0.017 11.4 1.41 0.6 <0.001 7 0.014 5.78 1.04 0.78 0.001 <5 0.016 9.58 1.83 0.55 0.001 8 0.013 9.27 1.92 0.66 0.001 <5 0.014 12.8 N.A.    152   Appendix I  Details regarding the Python Script GAUSSIAN SMOOTH TECHNIQUE In order to develop a curve with a valid derivative, it was necessary to use the Gaussian Blur or Gaussian Smoothing Technique.  𝑮(𝒙) =  𝟏𝝈√𝟐𝝅𝒆−𝒙𝟐𝟐𝝈𝟐  Equation 6 Gaussian function used in the construction of the Python Script  𝑮′(𝒙) =  𝟏𝝈√𝟐𝝅𝒆−𝒙𝟐𝟐𝝈𝟐 (−𝒙𝝈𝟐) Equation 7 First derivative of the Gaussian Function  𝑮′′(𝒙) =  −𝟏𝟐𝝅𝝈𝟒𝒆−𝒙𝟐𝟐𝝈𝟐 (𝟐 −𝒙𝟐𝟐𝝈𝟐) Equation 8 Second derivative of the Gaussian Function This equation allows for the calculation of the derivative because it smoothens the peaks, converting them into a concave local maximum.  The value of sigma is calculated by the Fast Fourier Transform (FFT), which provides the best approach to measuring that which can be considered a noise and that which can be considered a peak. With respect to the examination of the FFT, it was suggested that a sigma value of 2.0 be used. The convolution also plays an important role in converting the peaks into a spectrum that is able to derivate.  The principal algorithm for recognizing a peak is the use of the first derivative of the smoothened spectrum, which has to be previously positive and currently 0 to be considered a local maximum 153  and, the second derivative has to show a negative value to confirm that this wavelength belongs to a peak.  POSSIBLE NUMBERS TO TUNE FROM THE PYTHON SCRIPT In this section, some detail that can be modified by the user, is provided for the use of the Python Script. The proposed Python Script provides the option to plot the whole spectrum with the variable “saveplot”. “SIGMA=2” can be changed depending on the reliability of the data obtained during the sorting process. It is important to notice that this sigma value smoothens the data and the increase of this value will filter more data that has low peaks, but also will remove potential noise from complicated surfaces such as samples of white rock. “idWavelengths” allows for the choice of which file can be used as the ID Wavelength. “maxval” can be changed to the minimum peak that is required in order be similar to a minimum spectrum threshold.              154  Appendix J  Details of methodology and data treatment or the Oxide samples Case Arsenic – Oxygen distortion ambiguity There is an ambiguity with regard to the readings for the quadruple ionization stage of Oxygen (or O V) and the neutral ion of Arsenic (As I). Both readings have a wavelength of around 278.1 nm. Arsenic can be heavily associated with Sulphurs, creating a positive expectancy regarding the presence of Copper, and an optimum material for froth flotation. Paxite can be found in hydrothermal calcite veins, and its composition is CuAs2. The overlapping responses act favourably toward the ion that has the biggest Aki, in this case for O V, which was not expected because ionization stages larger than III are less likely to happen since they are more stable and require higher energy for the transition.  Table J-1: O V vs. As I key indicators for element selection Ion Observed Wavelength Air (nm) Ritz Wavelength Air (nm) Acc. Rel. Int. number Aki O V 278.101 278.101 B 1000   140,000,000  As I 278.022     170  78,000,000   the distance in terms of Wavelength for As I (272.02 nm) and O V (278.10 nm) creates a confusion that can be easily resolved using LIBS machine. Further information about this feature is explained in Chapter 3:, the distance between each pixel varies between 0.135 nm to 0.15 nm. Distances between wavelengths lesser than 0.15 nm have been avoided for the selection of the ID wavelength.    155  Table J-2: Arsenic ICP certified results for the 41 rock samples from Escondida Mine SAMPLE  As (ppm)  SAMPLE  As (ppm)  SAMPLE  As (ppm) 1    15 6  29 4 2 4  16 4  30   3 4  17 10  31   4 4  18    32 6 5 4  19 3  33 3 6 9  20 4  34 3 7 4  21 3  35 4 8 8  22 7  36 4 9    23 14  37 7 10 3  24 11  38 5 11    25 3  39 12 12 19  26 3  40 3 13    27 4  41 4 14 15  28       To gain a better understanding of how the LIBS machine works, the LIBS responses and the ICP Certified Analysis have been contrasted.    Rhenium response found in Laser Induced Breakdown Spectroscopy It is unlikely to find Rhenium. Rhenium is the 70th most abundant element in the earth’s crust (Yaroshevsky) with 7x10-8 % (7x10-4 ppm). This is in contrast with Oxygen with 47%, Si with 29.5% or Al with 8.05%. Chile has the largest reserves of Rhenium in the world (Anderson). However, even in Chile, obtaining a trace of Rhenium from a sensor is difficult as the area sensed is relatively small (100 um for LIBS), and the occurrence Rhenium is limited.  Tests conducted on Oxide rocks only showed 1 reading out of 1640 readings that successfully detected Rhenium. LIBS was sensitive enough to provide a reading for such a small amount that was not even traceable using ICP.  156  Table J-3: Trace of Rhenium in Oxide sample in Escondida Mine Sample Rock Peak Wavelength Element Intensity Acc. Observed Wavelength Air 33B1,S3,1 346.09 Re I 1046  346.046   The reason that this trace can be accepted as a valid reading is because it has a valid Intensity that is statistically outside of the 3 standard deviations of the total noise.   Figure J-1: Zoomed spectrum of sample 33B1,S3,1  In Figure J-1 the spectrum has been zoomed between the wavelengths 340 nm to 350 nm. The full spectrum of the same rock sample is shown in Figure J-2. The chart shows the peak of interest of Re I at 346.09 nm. Table J-4 indicates the calculation of the standard deviation of the noise as 0500100015002000340 342 344 346 348 350Oxide Sample 33B1, S3, 1Table J-4: Statistical analysis of the spectrum for sample 33B1, S3, 1 u 884.4361  Stan Dev 50.39881  2*S D 985.2337 783.6384 3*S D 1035.632 733.2396 157  represented with red and green lines in Figure J-2. An algorithm was built to calculate this standard deviation of the noise.  The logic behind this algorithm is to find  𝐼𝑓 ‖𝑋𝑖 − 𝑎𝑣𝑔(𝑋𝑖)‖ <  2 ∗ 𝑆𝑇𝐷 (𝑋𝑖) 𝑡ℎ𝑒𝑛 𝑋𝑖 𝑒𝑙𝑠𝑒 ∅ Where:  𝑋𝑖 = 𝐼𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 𝑝𝑖𝑥𝑒𝑙 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑝𝑒𝑐𝑡𝑟𝑢𝑚 This pseudocode finds the 2 and 3 standard deviations of the whole noise in the spectrum by removing all the peaks, and leaving only that which the algorithm can recognize as noise. It is necessary to repeat the algorithm until the final output achieves the same value.  158   Figure J-2: Spectrum for sample 33B1, S3,1 159  Table J-5: Statistical analysis of noise to recognize LIBS responses     Avg 982.14 933.02 909.9 898.66 893.39 890.74 888.5 887.36 886.38 885.4 884.84 Wavelength 33B1,S3,1 Std. Dev 254.74 124.67 81.5 66.31 59.58 56.35 54.25 53.33 52.35 51.35 50.81 229.21 788  788 788 788 788 788 788 788 788 788 788 788 229.36 788  788 788 788 788 788 788 788 788 788 788 788 229.5 774  774 774 774 774               229.65 691  691 691                   229.79 752  752 752 752                 229.94 776  776 776 776 776 776             230.08 754  754 754 754                 230.22 785  785 785 785 785 785 785 785 785 785 785 785 230.37 793  793 793 793 793 793 793 793 793 793 793 793 230.51 758  758 758 758                 230.66 774  774 774 774 774               230.8 741  741 741                   230.95 762  762 762 762                 231.09 824  824 824 824 824 824 824 824 824 824 824 824 231.24 773  773 773 773 773               231.38 755  755 755 755                 231.53 756  756 756 756                 231.67 799  799 799 799 799 799 799 799 799 799 799 799 231.82 804  804 804 804 804 804 804 804 804 804 804 804 231.96 792  792 792 792 792 792 792 792 792 792 792 792 232.11 781  781 781 781 781 781 781 781 781       232.25 782  782 782 782 782 782 782 782 782 782     232.4 771  771 771 771 771               232.54 800  800 800 800 800 800 800 800 800 800 800 800 232.68 796  796 796 796 796 796 796 796 796 796 796 796 232.83 788  788 788 788 788 788 788 788 788 788 788 788 This back-calculated formula creates blank cells that represent the peaks of the spectrum, leaving just the values that do not correspond to a LIBS response. In the first row, Table J-5 shows the average value of the previous sample group. E.g. 928.14 is the average of all of the values in the second column, which are the LIBS responses for the sample 33B1,S3,1. Likewise, the standard deviation of 254.74 is calculated using all of the LIBS responses. In the next column, 933.02 is calculated from the values previously processed, removing the responses that do not fit with the logic, and 124.67 is the standard deviation for the value in the 4th column previously processed.  Once it has been tested that 2 contiguous columns do not change, the variation in the statistical analysis becomes insignificant, and then, it can be concluded that the standard deviation calculated 160  is the correct response for all of the noise responses. In this case it is 50.39, which is calculated from all of the values for the last column. The occurrence of Rhenium in geological deposits can be found as part of the Platinum Group Metals PGM (Pt, Re, Os, Ir) or Tarkianite (Cu0.85 Fe2+0.1Re2.8Mo1.2S8), which can be found in mineral grain sulfide concentrates.   We can conclude that the response for Rhenium is correct, providing evidence for the geological occurrence of the mineral, the statistical analysis of the response, and the 3 filters described in section 3.7 and used by the Python Script to analyze a correct signal.  The value of the Rhenium case analysis does not have to do with the need for getting the Re signal. Indeed, Re is not significant, and is very unlikely to be observed. However, the importance of this exercise is to provide an idea of the real capabilities of LIBS, which can read an element that in the earth’s crust is less than 7x10-8 %. This provides LIBS with a qualitative capability rate and a quantitative capability, leaving behind certified methods such as ICP.  The main reason that this same response has not been repeatable, despite the 40 readings in the rock, is because the laser beam is small (100 um), with a chance of 0.008% of shooting back in the same position. Rhenium, as mentioned, is a very scarce element in the environment. For practical purposes, Rhenium has been taken away from the ID wavelength input for the Python Script and for the analysis of the rock samples.   

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.24.1-0340689/manifest

Comment

Related Items