On the Effects of Resolution on APXS-GUAPX Analytical Results: from Spectrum to Peak Areas to Concentration Estimates

Home , Sample Analysis at Mars

On the Eﬀects of Resolution on APXS-GUAPX Analytical Results: From Spectrum to Peak Areas to Concentration Estimates

Renato Pardo

A Thesis Presented to The University of Guelph

In partial fulﬁlment of requirements for the degree of Master of Science in Physics

Guelph, Ontario, Canada

c Renato Pardo, July, 2015 ABSTRACT

On the Eﬀects of Resolution on APXS-GUAPX Analytical Results: From

Spectrum to Peak Areas to Concentration Estimates

Renato Pardo Advisers: University of Guelph, 2015 Dr. J.L Campbell Dr. R. Gellert

The thesis presents an in-depth investigation into the eﬀects of spectral resolution on

Alpha Particle X-ray Spectrometer (APXS) measurements processed using the GUAPX ﬁt- ting code. The APXS analytical results contribute to understanding rock and soil types on

Mars and the processes by which they formed. However, mission constraints, including instrumental degradation due to neutron damage and limited temperature control, mean that instrumental resolution cannot always be optimized. A methodology was developed using ratios of relevant analytical results to characterize the relationship between estimated peak areas, concentration estimates, and resolution. A differential effect favouring the heavier element concentration estimates with worsening resolution was observed and the underlying causes identified. The link between relative change in FWHM and concentration estimates was quantified for ten geochemical elements. Lastly, it was found that variations in estimated concentrations can fall outside precision error over resolution and concentration ranges similar to those seen on Mars. Dedicated to Carmenza de Lara (1927 - 2015)

iii Acknowledgements

It has been an honour to work alongside some of the brightest minds in the ﬁeld, and consider them my colleagues and superiors. Sitting alongside them, analyzing, and seeing how they work through various challenges has truly been an enriching and invaluable experience. To further ﬁnd that these people are some of the kindest souls I have met in my life is truly humbling. Thank you all!

To Dr. Campbell and Dr. Gellert I extend my eternal gratitude, for giving me the opportunity to pursue my passion for physics and its application as both an undergraduate and graduate student. This work was done with Dr. Campbell as my direct supervisor. Thus, I can attest the words written by his previous students are not embellished. Dr. Campbell is a man of eternal patience who is personally invested in the success of his students and shows the utmost respect for his colleagues and subordinates. The world of academia would be a better place were we all to follow his example.

Special thanks go out to Dustin, my right hand man and a great motivator for developing my passion for physics, and Dr. Perrett for her unwavering desire to help everyone in the research group reach their potential. It has truly been a wonderful 7 and 2 years, respectively.

I would not have made it to university or through the past 7 years of academic training were it not for my family. My father’s entrepreneurial and maverick spirit is responsible not only for him being the first member of the Pardo family to attend university, but also for setting the standard for all 6 of his siblings and myself to expand our horizons. Papa, “hasta la victoria siempre.” Equally as important is my mother and her kind, loving, and supportive spirit. The first Master’s graduate in the family and the embodiment of altruism. She has been my rock, my interlocutor, my inspiration, mimimi. Together they have made myriad sacrifices to pave the way for me, and above all they would never accept my gratitude as they felt this was their responsibility.

Last but certainly not least; this work was accomplished in great part thanks to Beth, my love and my wife. I would not have made it through the all-nighters that got me here. Whether it was diﬀerential equations, formal labs, or reports, she was always there to lend a kind ear, to give the most uplifting hugs, and to surround me with the animals we so love: Sancho, Bernie, Wally, Walter, Gustav, Faith, and whatever else comes into our lives. I am excited for our life together and incredibly thankful we found each other.

I am truly blessed for having had crossed paths with all of you. Thank you for believing in me.

iv Contents

List of Acronyms xi

1 Introduction1

2 Background4 2.1 APXS History...... 4 2.2 The MSL-APXS...... 7 2.2.1 Spectrum Acquisition...... 8 2.3 Resolution & Noise...... 9 2.3.1 Temperature, Radiation, and APXS Resolution...... 12 2.4 GUAPX...... 14 2.4.1 Top Hat Filter...... 16 2.4.2 Characterizing the System...... 18 2.4.3 The Yield Equation...... 20 2.5 Calibration...... 24

3 Precursory Work 26 3.1 Accuracy of AGV-2 Concentration Estimates...... 27

4 Laboratory 33 4.1 FEU-APXS Configurations...... 33 4.1.1 Sample Spectra Acquired Under Different Configurations...... 34 4.2 Dataset...... 36 4.2.1 Data Selection...... 37

5 Photopeak Areas (Background Removal and Deconvolution) 39 5.1 Count Rates & Source Decay Correction...... 39 5.2 Count Rate Ratio (RCPS) ...... 40 5.3 Results...... 40 5.3.1 Predominantly PIXE...... 41 5.3.2 Predominantly XRF...... 47 5.4 Discussion...... 50

6 From Peak Area to Concentration (Matrix Eﬀects & The Closure Rule) 56 6.1 GUAPX Concentration Ratio R[C] ...... 56 6.2 Results...... 56 6.2.1 Predominantly PIXE...... 58 6.2.2 PIXE & XRF...... 62

v 6.2.3 Predominantly XRF...... 66 6.3 Discussion...... 70 6.3.1 Mapping Count Rates to Concentrations...... 72 6.3.2 Matrix Corrections and the Closure Rule...... 72 6.3.3 Mg Correction...... 73

7 Concentration and Resolution 76 7.1 FWHM Ratio (RFWHM) ...... 76 7.2 Results...... 77 7.2.1 Primarily PIXE...... 78 7.2.2 PIXE & XRF...... 81 7.2.3 Predominantly XRF...... 83 7.3 Discussion...... 85 7.3.1 Negative Correlation...... 87 7.3.2 Positive Correlation...... 88 7.3.3 Precision Error & Estimate Variation...... 88 7.4 Conclusion...... 90

8 Conclusions 92 8.1 Future Work...... 94

A Campaign GRMs 99

vi List of Tables

3.1 Number of spectra summed for tranches A - F with average temperature and summed spectrum FWHM...... 27 3.2 GUAPX settings used for AGV-2 spectrum ﬁtting...... 28

4.1 Summary of different APXS configurations from May 2009 - August 2014... 34 4.2 GUAPX settings used for spectrum fitting in each configuration...... 36

5.1 Percent mean elemental composition for the diﬀerent igneous GRMs utilized for instrumental calibration [51]...... 51

7.1 Summary of results for the entire GRM suite and the subset that falls within the Martian concentration range (denoted MR)...... 85

A.1 Distribution of certiﬁed geochemical reference materials among sample groups in the 2012 campaign...... 99 A.2 Distribution of certiﬁed geochemical reference materials among sample groups in the 2013 campaign...... 100

vii List of Figures

2.1 X-ray spectra acquired from Allende meteorite using the ALPHA-X [14]....6 2.2 X-ray spectra acquired from Allende meteorite using the Pathﬁnder APXS [10].6 2.3 X-ray spectra acquired from basalt reference materials BCR-1 and BCR-2 using MER and MSL APXS instruments respectively [5]...... 7 2.4 Schematic cross-section of the MSL-APXS [5]...... 8 2.5 Schematic of the MSL-APXS Sensor Head [15]...... 9 2.6 Convolution of a top-hat digital ﬁlter function with a experimental spectrum. Adapted from [36]...... 17

3.1 GUAPX estimated Na concentration at various resolutions for AGV-2..... 28 3.2 GUAPX estimated Mg concentration at various resolutions for AGV-2..... 29 3.3 GUAPX estimated Al concentration at various resolutions for AGV-2..... 29 3.4 GUAPX estimated Si concentration at various resolutions for AGV-2..... 29 3.5 GUAPX estimated K concentration at various resolutions for AGV-2...... 30 3.6 GUAPX estimated Ca concentration at various resolutions for AGV-2..... 30 3.7 GUAPX estimated Ti concentration at various resolutions for AGV-2..... 30 3.8 GUAPX estimated Mn concentration at various resolutions for AGV-2..... 31 3.9 GUAPX estimated Fe concentration at various resolutions for AGV-2..... 31 3.10 GUAPX estimated Zn concentration at various resolutions for AGV-2..... 31

4.1 GSP-2 Spectrum taken in 2010 for the instrumental calibration (FWHM at 5.9 keV = 168 eV)...... 35 4.2 GSP-2 Spectrum taken in 2012 (FWHM at 5.9 keV = 198 eV)...... 35 4.3 GSP-2 Spectrum taken in 2013 (FWHM at 5.9 keV = 164 eV)...... 35

5.1 Na count rate ratios vs. [Na] as a fraction of [Mg+Al+Si]...... 42 5.2 Mg count rate ratios vs. [Mg] as a fraction of [Na+Al+Si], over the entire Mg concentration range...... 43 5.3 Zoom in on Mg count rate ratios vs. [Mg] as a fraction of [Na+Al+Si], over approximately half the Mg concentration range...... 43 5.4 Further zoom in on Mg count rate ratios vs. [Mg] as a fraction of [Na+Al+Si], at extreme low Mg concentrations...... 44 5.5 Al count rate ratios vs. [Al] as a fraction of [Na+Mg+Si]...... 45 5.6 Zoom in on Al count rate ratios vs. [Al] as a fraction of [Na+Mg+Si], at low Al concentrations...... 45 5.7 Si count rate ratios as a function of certificate [Si]...... 46 5.8 Mn count rate ratios as a function of certificate [Mn]...... 47 5.9 Fe count rate ratios as a function of certificate [Fe]...... 48

viii 5.10 Zn count rate ratios as a function of certiﬁcate [Zn]...... 49 5.11 Zoom in on Zn count rate ratios as a function of certiﬁcate [Zn] at low concentrations...... 49 5.12 Na, Mg, Al, and Si mean count rate ratios as a function of energy...... 50 5.13 Mn, Fe, and Zn mean count rate ratios as a function of energy...... 52 5.14 Mean count rate ratios as a function of energy for Na, Mg, Al, Si, K, Ca, Ti, Mn, Fe, and Zn...... 55

6.1 Na count rates (left) and concentration ratios (right) as a function of certificate [Na]...... 58 6.2 Mg count rates (left) and concentration ratios (right) as a function of certificate [Mg]...... 59 6.3 Zoom in on Mg count rates (left) and concentration ratios (right) as a function of certificate [Mg]...... 60 6.4 Al count rates (left) and concentration ratios (right) as a function of certificate [Al]...... 61 6.5 Zoom of Al count rates (left) and concentration ratios (right) as a function of certificate [Al]...... 61 6.6 Al count rates (left) and concentration ratios (right) as a function of certificate [Al]...... 62 6.7 K count rates (left) and concentration ratios (right) as a function of certificate [K]...... 63 6.8 Zoom of K count rates (left) and concentration ratios (right) as a function of certificate [K]...... 64 6.9 Ca count rates (left) and concentration ratios (right) as a function of certificate [Ca]...... 65 6.10 Ti count rates (left) and concentration ratios (right) as a function of certificate [Ti]...... 66 6.11 Mn count rates (left) and concentration ratios (right) as a function of certificate [Mn]...... 67 6.12 Fe count rates (left) and concentration ratios (right) as a function of certificate [Fe]...... 68 6.13 Zn count rates (left) and concentration ratios (right) as a function of certificate [Zn]...... 69 6.14 Zoom in on Zn count rates (left) and concentration ratios (right) as a function of certificate [Zn]...... 69 6.15 Percent difference from average 2013 campaign ratios to average 2012 campaign ratios.(2012−2013)/Mean...... 71 6.16 Mg concentration estimates as a function of certified abundance [51]...... 74

7.1 Na concentration ratios as a function of FWHM ratio for the full GRM suite (left) and for the Martian concentration range (right)...... 78 7.2 Mg concentration ratios as a function of FWHM ratio for the full GRM suite (left) and for the Martian concentration range (right)...... 79 7.3 Al concentration ratios as a function of FWHM ratio for the full GRM suite (left) and for the Martian concentration range (right)...... 80 7.4 Si concentration ratios as a function of FWHM ratio for the full GRM suite (left) and for the Martian concentration range (right)...... 80

ix 7.5 K concentration ratios as a function of FWHM ratio for the full GRM suite (left) and for the Martian concentration range (right)...... 81 7.6 Ca concentration ratios as a function of FWHM ratio for the full GRM suite (left) and for the Martian concentration range (right)...... 82 7.7 Ti concentration ratios as a function of FWHM ratio for the full GRM suite (left) and for the Martian concentration range (right)...... 82 7.8 Mn concentration ratios as a function of FWHM ratio for the full GRM suite (left) and for the Martian concentration range (right)...... 83 7.9 Fe concentration ratios as a function of FWHM ratio for the full GRM suite (left) and for the Martian concentration range (right)...... 84 7.10 Zn concentration ratios as a function of FWHM ratio for the full GRM suite (left) and for the Martian concentration range (right)...... 84 7.11 Mg count-rate ratios (left) and concentration ratios (right), within the Mar- tian concentration range, as a function of certiﬁcate [Mg]...... 86 7.12 Mean precision error for all GRMs across 2012 and 2013 campaigns compared to variation in concentration estimates for entire GRM suite and those within the Martian ranges...... 89 7.13 Mean precision error for 2013 campaign GRM suite compared to variation in concentration estimates for entire GRM suite and those within the Martian ranges...... 89

x List of Acronyms

The following is a list of common acronyms that are used throughout this thesis:

APXS: Alpha Particle X-ray Spectrometer

ED: Energy Dispersive

FEU: Flight Equivalent Unit

FWHM: Full Width at Half the Maximum

GRM: Geochemical Reference Material

IM: Iterative Matrix

LOD: Limit of Detection

LOQ: Limit of Quantitation

MCA: Multichannel pulse-height Analyzer

MEP: Mars Exploration Program

MER: Mars Exploration Rover

MSL: Mars Science Laboratory

NASA: National Aeronautics and Space Administration

PFM: Proto Flight Model

PIXE: Particle Induced X-ray Emission

SAM: Sample Analysis at Mars

SDD: Silicon Drift Detector

TEC: Thermoelectric Cooler/Peltier Cooler

XRF: X-Ray Fluorescence

xi Chapter 1

Introduction

The APXS is one of the competitively selected instruments carried on board the MSL rover,

Curiosity. Its primary objective is to determine the chemical composition of rocks and soils in order to characterize the materials in the vicinity of the rover and thus contribute to understanding the processes by which they formed. The results from the APXS play a role in rock type determination, salt content analysis, and sample selection triage by helping constrain mineralogy and elemental concentrations. It also aids complementary instruments on the rover, such as CheMin (Chemistry and Mineralogy) and SAM (Sample Analysis at

Mars), in characterizing materials [1,2].

MSL is a surface focused, field laboratory mission designed to address several of the high-priority scientific investigations recommended to NASA by the scientific community

[3,4]. It is part of the long-term systematic program for the scientiﬁc exploration of Mars, known as Mars Exploration Program (MEP). The overarching goal of the MEP is to answer the question, “Did life ever exist on Mars?” The scientiﬁc objectives established to address this goal are to search for evidence of past or present life, characterize the climate and volatile history of Mars, understand the surface and subsurface geology, and characterize the Martian environment quantitatively in preparation for human exploration [1].

The purpose of the MSL mission is to explore and quantitatively assess the habitability and environmental history of Gale crater and demonstrate technological advancements in the exploration of Mars [1,2]. The overall scientiﬁc goal of the mission can be divided into

1 four areas: (i) assessing the biological potential of the selected site on Mars, (ii) characterizing the geology and geochemistry of the landing region at all appropriate spatial scales, (iii) investigating planetary processes of relevance to past habitability, and (iv) characterizing the broad spectrum of the Martian surface radiation environment [1]. To be clear, MSL is not a life detection mission and does not possess the capability to detect extant vital processes [2].

The APXS has a deep legacy in the ﬁeld of extraterrestrial exploration, given its versa- tility as a low-power, low-mass, highly robust instrument. The MSL-APXS is an Energy-

Dispersive (ED) semiconductor X-ray spectrometer using radioactive 244Cm excitation sources to induce atomic inner-shell ionization and subsequent X-ray emission in analytes using both

Particle Induced X-ray Emission (PIXE) and X-ray Fluorescence (XRF) mechanisms. The detection and processing of the induced characteristic X-rays provides an estimate of the abundance of geologically relevant elements, ranging from Na to Y. Relative to the previous

APXS iteration (MER-APXS), the MSL-APXS features a threefold increase in sensitivity

[5], allowing it to take a full chemical analysis within 3 hours. Optimal performance is achieved at night with colder temperatures leading to the most advantageous resolution. At higher temperatures, the ability to activate the detector’s internal Thermoelectric Cooler

(TEC or Peltier) results in improved resolution.

On any particular sol, or Martian day, MSL science activities, including APXS deploy- ments, are governed by a number of constraints such as the Earth-Mars geometry and local time phasing, timing of telecommunication windows, down-link data volume capability, the time proﬁle of energy available for science, and any thermally driven operational constraints or energy needs of the payload, rover subsystems necessary for payload operations, or the rover [6]. Each sol is planned to exploit trades among resources to increase the science return. Thus, APXS measurements are not always planned around the achieving optimal instrumental performance and may be taken during daylight hours on Mars. Although, the TEC allows for instrument operation during the Martian day, the diurnal temperature swings make it such that resolution cannot always be optimized.

2 The eﬀects of varying energy resolution on the accuracy and precision of analytical results are not always clear [7]. It is necessary to investigate the relationship between the precision of the results given by the ﬁtting program and the spread of results due to variations in

FWHM. The ﬁrst step of this study is to provide background on the instrument: its history, physical processes, and the methodology behind the data products derived from it.

3 Chapter 2

Background

This chapter introduces the origins of the APXS and its various iterations with a focus on the MSL-APXS and its spectrum acquisition process. The theory behind resolution and noise is explored and presented in the context of the instrument. The spectrum evaluation code used for the present work, GUAPX, is introduced, including the different modalities for dealing with sample matrix effects. A brief description of relevant issues behind GUAPX is given. Lastly, the instrumental calibration using this software is briefly described.

2.1 APXS History

The instrument’s theoretical origins can be traced back to Ernest Rutherford’s laboratory.

It was there that Hans Geiger’s and Ernest Marsden’s experiments showed alpha-particles scattering oﬀ gold-foil at angles close to 180◦, a process commonly called backscatter [8].

This result led to Rutherford’s breakthrough interpretation of the nuclear structure of atoms.

Fifty years later, Dr. A. Turkevich and his team at the University of Chicago developed a technique, harnessing Rutherford α-backscattering, to perform the ﬁrst in-situ chemical composition analysis of an extraterrestrial body [9] for NASA’s Surveyor missions to the moon in 1967-1968. To accomplish this, samples were bombarded with alpha particles from a radioactive 242Cm source and the energy distribution of the backscattered particles was quantiﬁed using solid-state detectors. In addition to the measurement of backscattered

α-particles, these instruments contained detectors to determine the energy distribution of protons generated by (α,p) reactions on certain medium-heavy elements (F, Na, Mg, Al, Si,

4 S, and Cl) [10].

In the subsequent decade, Dr. T. Economou and Dr. Turkevich unsuccessfully proposed the Mini-Alpha for the Viking missions [10]; a reﬁned and miniaturized instrument including an X-ray detector, for analysis of the Martian surface [11]. Upon seeing the Mini-Alpha prototype, the Soviet Academy of Science’s Space Research Institute requested the instrument become part of the instrument suite taken to Mars’ satellite Phobos on the eponymous

Soviet missions [10]. Due to geopolitical tensions at the time, NASA did not consent to such an endeavour.

This development led to the design of a similar instrument, the Phobos bound ALPHA-

X, as a joint eﬀort between the Max-Planck Institute for Chemistry in Mainz (calibration and data interpretation) the Max-Planck-Institute for Extraterrestrial Physics in Garching

(hardware), and the Research Institute for Atomic Reactors in Dimitrovgrad (244Cm source production) [10]. Unfortunately, both Phobos probes failed to reach their destination. Af- terward, the instrument was selected for the eventually unsuccessful follow-up missions to

Mars, Marsokhod and Mars-96, on the contingency of further reduction in size, mass, and power consumption [10]. These requirements meant a complete redesign of the instrument.

In 1993, the team was invited to provide an instrument for the NASA Pathﬁnder mission rover, known as Sojourner. The Alpha Proton X-ray Spectrometer on Sojourner analyzed

12 rock and soil samples [12]. Signiﬁcant improvements were made for the succeeding APXS iteration that was selected as part of the instrument suite for the Mars Exploration Rover

(MER) mission. Among these improvements are the following: the X-ray emission analysis capabilities were enhanced, the Si-PIN detector was replaced with a Silicon Drift Detector

(SDD), a calibration target was employed, and titanium foil coverage was applied to the

α-sources to prevent contamination of samples with source material as a result of “recoil- sputtering” [13]. As of 2008, over 400 Martian rocks and soils had been analyzed by the

APXS instruments on board the MER Spirit and Opportunity rovers [12].

5 The MSL-APXS is an improved version of the APXS that ﬂew successfully on Pathﬁnder and the MER rovers, Spirit and Opportunity. It provides a threefold improvement in the rate of data accumulation, and hence lower element detection limits in a given time, as compared to the MER devices [5]. Furthermore, the temperature range for good resolution

X-ray spectra was extended upwards to approximately - 5◦C, whereas the MER APXS is only capable of providing acceptable resolution below -40◦C[5]. The evolution of the in-

strument’s sensitivity and resolution can be seen in Figures 2.1- 2.3.

Figure 2.1: X-ray spectra acquired from Allende meteorite using the ALPHA-X [14].

Figure 2.2: X-ray spectra acquired from Allende meteorite using the Pathﬁnder APXS [10].

6 Figure 2.3: X-ray spectra acquired from basalt reference materials BCR-1 and BCR-2 using MER and MSL APXS instruments respectively [5].

2.2 The MSL-APXS

The MSL-APXS is shown schematically in Figures 2.4 and 2.5. It carries six 244Cm radionu- clide sources arranged in an annulus that surrounds a collimated SDD. The device employs two diﬀerent inner-shell ionization modes for X-ray spectroscopy: PIXE, which uses the energetic α-particles emitted by the 244Cm decay; and XRF, which uses the Pu L X-rays emitted by the daughter product [12]. Henceforth, the term APXS will apply speciﬁcally to the iteration of the instrument used for the MSL mission, this includes both the FEU

(Flight Equivalent Model) and PFM (Proto-Flight Model) models in the laboratory and on the Martian surface, respectively.

The APXS was primarily calibrated using the FEU in the laboratory. A well characterized basaltic rock slab on board MSL is periodically used to check the performance and calibration of the instrument.

7 Figure 2.4: Schematic cross-section of the MSL-APXS [5].

2.2.1 Spectrum Acquisition

In the APXS, the SDD signal is fed through a preamplifier that outputs, for each X-ray detected, a pulse on the order of 200 mV, decaying over a few hundred microseconds. The height of the pulse is directly proportional to the energy of the incident X-ray. This signal is then fed through a shaping amplifier that produces an amplified, delayed, and broadened

Gaussian-shaped pulse with height on the order of 2 V. The Gaussian pulse is suitable for analysis by a peak hold circuit [16]. The peak hold circuit monitors a voltage of interest and retains its peak value as its output which is then fed into the analog-to-digital converter for digitization.

The digitized value is calibrated based on platinum resistance thermometer temperature sensors in the sensor head and main electronics to compensate for drifting in gain and oﬀset of the signal ampliﬁer circuit. Finally, the count is binned by energy into a spectrum in the typical spectroscopic fashion [16]. The spectra acquired are inherently digital and of relatively low resolution when compared to wavelength dispersive methods [17].

8 Open Source

Closed Source

Detector

Figure 2.5: Schematic of the MSL-APXS Sensor Head [15].

2.3 Resolution & Noise

The energy resolution of the semiconductor spectrometer system determines the ability of a given system to resolve characteristic X-rays from multi-element samples. In general, resolution is the single most accepted measurement of detector quality [18]. The resolution is quantiﬁed using the full-width at half the maximum (FWHM) of the acquired X-ray lines.

The weighted mean Mn Kα line at 5.895 keV is a convenient choice of X-ray energy to quantify resolution since it is readily available from 55Fe radioisotope sources and since the contribution of the unresolved Kα1 (5.898 keV) and Kα2 (5.887 keV) doublet to the FWHM can be neglected [17]. The SDD employed in the APXS can achieve a resolution of 153 eV at a temperature of 0◦C with a shaping time of 0.50µs [19].

The natural line-width of characteristic X-ray lines is ∼5-10 eV, an order of magni- tude smaller than what can be seen in acquired ED spectra [17]. Neglecting this natural line-width, the instrumental energy resolution of a semiconductor detector is a function of two independent factors: the properties of the detector itself and the nature of the electronic pulse processing employed. Thus, the measured FWHM of an X-ray line (∆ET otal)

is the sum, in quadrature, of the contribution due to detector processes (∆EDet) and that associated with the electronic pulse processing system (∆EElec):

9 q 2 2 ∆ET otal = ∆EDet + ∆EElec (2.1)

The ∆EDet component is determined by the statistics of the free-charge production pro-

cess occurring in the depleted volume of the semiconductor diode. The average number of

electron-hole pairs produced by an incident photon can be calculated as the total photon

energy, E, divided by the mean energy required to produce a single electron-hole pair ε.

However, the standard deviation in free electron-hole pair production observed is less than √ q E the expected σ = n = ε , implying the process is not governed by counting (Poisson) statistics. This explanation is that the events are not strictly independent, resulting in under-dispersion from the expected Poisson distribution.

The under-dispersion is quantiﬁed by the Fano factor, F , which is analogous to a coef-

ﬁcient of variation in statistics. A complete understanding of all the factors that lead to a non-unity value for F does not yet exist [20]. The eﬀect has been attributed to energy of the incident photon going into heating the lattice crystal structure via phonon production as well as the formation of ion pairs. Thus, an accurate calculation of the Fano factor requires a detailed accounting of the energy dependent cross sections and the density of states of the phonon modes [21]. Another proposed cause for this under-dispersion is that the number of ways an atom may be ionized is limited by the discrete electron shells [22]. As the initial photo-electron energy is dissipated in the diode, the pathways for energy absorption available are reduced; thus, this is not a purely stochastic process. Taking the Fano factor into account, the detector resolution can be mathematically described as follows:

√ ∆EDet = 2.35 F εE (2.2)

The 2.35 comes from the relationship between FWHM and the standard deviation of a nor-

mal distribution. The approximation to a Gaussian distribution is reasonable given the high

statistics collected [20].

The electronic pulse processing can be divided between the charge integration, which

10 takes place in the preamplifier, and the voltage amplification and pulse shaping, which occur in the main amplifier [18]. The function of the charge-sensitive preamplifier and subsequent amplification stages is to convert the integrated charge pulse, produced by collection of the photoelectrically induced ionization, to a voltage pulse that can be measured and stored in the multichannel pulse-height analyzer (MCA). However, the pulse processing must also amplify the weak charge signal to a measurable level while suppressing random fluctuations in the signal amplitude produced by noise.

By deﬁnition, noise is any undesired ﬂuctuation that appears superimposed on a signal source [20]. The contribution to resolution associated with electronic noise ∆EElec can

be traced to two mechanisms: number ﬂuctuations (“shot noise”) and velocity ﬂuctuations

(thermal noise). Both thermal and shot noise are purely random.

Quantum eﬀects cause spontaneous ﬂuctuations in both the number and velocity of the

ionized charge carriers, causing intrinsic noise. All semiconductor detectors have a leakage

current from the bias current applied to the sensor. In the absence of a radiation signal,

a small number of carriers continuously pass through the diode junction. This number is

subject to statistical ﬂuctuations, called “shot noise”, which are indistinguishable from ﬂuc-

tuations in the signal current. Even if the charge carriers have a mean velocity of zero, they

still undergo Brownian thermal motion. By the equipartition theorem of thermodynamics,

every mode of oscillation contributes approximately 1/2kbT average energy to the oscillation.

The root mean-square of the thermal velocity is not zero, giving rise to a ﬂuctuating instan- taneous current called thermal or Johnson-Nyquist noise [20].

Shot and Johnson-Nyquist noise can occur within the detector itself as well as the gate- source current of the field effect transistor in the input stage of the preamplifier [20]. These are important sources of noise as they occur near the beginning of the signal chain where the signal level is at a minimum. Noise generated at this point undergoes the same amplification as the signal, whereas noise generated further along the signal chain is usually much smaller than the signal.

11 The frequency spectrum of both series and parallel noise is very broad; by contrast, the frequency spectrum of the signal is confined to a much narrower band. The pulse-shaping role, traditionally carried out by the linear amplifier, is analogous to selective filtering that removes as much broad spectrum noise as possible without severely attenuating the useful signal components [20]. The pulse shaping is normally carried out through a combination of differentiating and integrating circuits. These operations can be regarded as high-pass and low-pass filtering, respectively.

2.3.1 Temperature, Radiation, and APXS Resolution

APXS resolution is susceptible to both the thermal and radiation environments of the sensor head. On Mars, the PFM-APXS is exposed to the planet’s temperature extremes and the radiation environment found at the sensor head. On Earth, the FEU-APXS is exposed to: buildng heating, ventilation, and air conditioning issues resulting in continuous temperature variations of several degrees that vary by season; internal and external Peltier cooler adjustments; as well as the radiation environment found at the sensor head.

Thermal Environment

Thermal generation of electron-hole pairs contributes to the random fluctuations of the leakage current in the semiconductor. This process will tend to obscure the small signal current that momentarily flows during an ionizing event and can be a significant source of noise. The electron-hole production rate can be reduced only by cooling the material.

Energy that goes into the creation of electron-hole pairs leads to fully reversible processes that leave no damage. On the other hand, non-ionizing energy losses to the atoms of the crystal lead to irreversible changes [23].

Radiation Environment

Proper operation of the semiconductor detector depends on the near perfection of the crystal lattice. The most fundamental type of bulk radiation damage is the Frenkel defect,

12 produced by the displacement of an atom in the semiconductor material from its normal lattice site. The vacancy left behind, together with the original atom now at an interstitial site, forms a trapping site for normal charge carriers. This creates additional energy levels in the semiconductor’s band gap [24] and may lead to incomplete charge collection for the event [20]. The displacement radiation induced damage in Si is mainly in the form of deep level single defects and defect clusters (extended defect regions). The first and most obvious radiation damage effect on the Si sensor is the increase of sensor leakage current with the radiation fluence [25]. The cause for the leakage current increase is the thermal generation of carriers from radiation-induced deep-level defects and defect clusters. This measurable increase in the leakage current can lead to a significant loss in the energy resolution of the detector [20]. The APXS sensor head produces its own radiation environment due to the approximately 60 mCi 244Cm excitation sources.

Each source is backed by lead shielding and a stainless steel holder. This shielding re- duces the 244Cm induced X-rays and alpha particles in the sensor head eﬀectively to zero.

However, the spontaneous ﬁssion branch of the source decay is non-trivial and emits a fast neutron continuum. Shielding the sensor head electronics from these neutrons is not feasible

[16]. The sensor head radiation environment is therefore characterized by fast neutrons with energies between 0 and 12 MeV [16]. For the MSL-APXS there are roughly 3000 neutrons

(n) emitted per second in 4π. This number translates into a neutron ﬂux rate of approximately 60 n/s/cm2 for a device 2 cm away from the sources[16]. Contrary to low-energy particles that produce point defects, more energetic particles, especially hadrons, may lead to a cascade of many successive displacements, resulting in the formation of a large diversity of extended defects as densely packed conglomerates (clusters) of vacancies and interstitials

[23]. The present knowledge on defect clustering is, however, very limited. Only until re- cently has some clear evidence for the formation of electrically active extended defects been reported [23].

An energy transfer of roughly 35 eV is required to displace a Si atom from its normal lattice site. A neutron with a minimum kinetic energy of 180 eV neutrons can meet this

13 transfer threshold; nearly all ﬁssion-produced neutrons exceed this minimum. Neutron radiation causes mostly displacement damage in the detector bulk. Fast neutrons usually transfer enough energy to induce clusters of crystalline damage. Neutron damage is generally distributed throughout the detector and the direction of incidence has little eﬀect. In the case of neutron radiation at the maximum level, the resolution starts to degrade based on non-linearities caused by displacement damage [25].

Holding temperature constant, the instrument’s resolution (FWHM) will continue to degrade over time[26]. Thus, it is advantageous to operate the APXS SDD at low temperatures; to mitigate the instrument’s resolutional deterioration due to the interplay of radiation damage and thermal generation of electron-hole pairs. However, in the case of the PFM-APXS, measurements are not always planned around the achieving optimal instrumental performance and may be taken during daylight hours on Mars. On the other hand, the cooling for the FEU-APXS in the laboratory is very limited due to the Canadian

Nuclear Safety Commission’s safety regulations regarding the laboratory set-up. As a result the resolution (FWHM) is not always the same and cannot always be optimized.

2.4 GUAPX

Given their digital nature and the availability of inexpensive and fast personal computers,

ED spectra lend themselves well to computational processing. Extraction of concentration data from spectra generally begins with determining the peak area for the principal line of each element present. Then, through various standardization techniques, the peak areas are converted to elemental concentrations. The first step is usually accomplished through a least-squares fit of a model to the measured spectrum; this process demands knowledge of the background spectrum shape, the detector response or line-shape, and the calibration of the detector/electronic system. It also requires accounting for relative X-ray line intensities and their modification, relative to their intrinsic values, by matrix effects [27].

GUPIX [27–30] provides a mature and sophisticated spectrum evaluation software based

14 on a Fundamental Parameters with Standards (FPS) approach for the analysis of ED-PIXE spectra. The Principal Investigator of the MER APXS team proposed to augment the

GUPIX spectrum treatment software with an analogous XRF treatment, and then merge these codes to cope with spectra that arise from two diﬀerent X-ray excitation mechanisms that are deployed simultaneously upon a single sample. In 2010 such a spectrum evaluation code was developed on the basis of GUPIX’s FPS approach, called GUAPX[31, 32]. It is used to interpret the PIXE-plus-XRF spectra acquired by α-particle X-ray spectrometers.

Fundamental parameters (FP) models attempt to describe the physics for all phenom- ena aﬀecting the detected intensity of the characteristic radiation emitted by the sample, deducing sample composition by combining spectral information with fundamental equations of X-ray physics. The emissions intensity from an element in a material is primarily dependent on the corresponding concentration of that element in the sample and is also susceptible to other parameters that can be divided into three groups: (i) spectrometer- dependent parameters, such as excitation source intensity, beam size, detector eﬃciency;

(ii) element-dependent parameters, such as the photo-ionization cross section and ﬂuores- cence yield; and lastly (iii) sample-dependent parameters, such as the sample thickness, attenuation coeﬃcients for primary and secondary radiation, and the sample geometry.

A FP equation allows for the calculation of the intensity of emitted radiation as a function of the specimen’s composition, the incident spectrum, and the configuration of the spectrometer used. All other variables used are fundamental parameters, such as the mass- attenuation coefficients for a given element at a given energy or its fluorescence yield. The intensities predicted are (almost always) net intensities, void of background, line overlap, and so on. Hence, the measured intensities must be corrected for such spectral artifacts. These theoretically predicted intensities are then linked to the measured ones. In the GUAPX code, the continuous background is dealt with by applying a top-hat filter to remove slowly varying components of the spectrum. The fundamental parameter equation used is the yield equation.

15 2.4.1 Top Hat Filter

There are, in principle, three ways to deal with the background continuum: (i) suppression by a suitable filter; (ii) estimation and subtraction from the spectrum prior to the estimation of the net peak areas; and (iii) modelling and simultaneous fitting with the other features in the spectrum [17]. Based on long experience with the top-hat digital filter in GUPIX

[28], GUAPX takes this approach to suppress the slowly varying continuous background in the data spectrum so that it need not be modelled [33]. This avoids any assumptions regarding the functional form of the background. The main grounds for its adoption are its widespread use and general success in Electron Probe Micro-Analysis (EPMA), and subsequently in PIXE [27].

The method chosen is a correlation technique, which convolves the original spectrum with a ﬁlter that approximates the shape of the peak and, therefore, emphasizes the peak.

Since a zero-area ﬁlter is used, the continuum is at the same time eﬀectively suppressed.

The top-hat is one of the simplest and most effective correlators, belonging to the group of zero-area rectangular filters. The top-hat filter has a central window with an odd number of channels, w, and two side lobes, each n channels wide; this configuration is characteristic of zero-area rectangular filters [17].

Originally formulated by Schamber [34], and independently developed by Statham [35], the top-hat ﬁlter has a central positive lobe. Its width is set at the FWHM at the centre of the spectrum. The lobe is ﬂanked by symmetric, negative outer lobes, each of half the central lobe width.

Mathematically, this symmetric, zero-weight ﬁlter has a central upper lobe consisting of

UW positive coeﬃcients fs = 1/UW and two negative outer lobes each having LW negative coeﬃcients fs = −1/(2LW ). The convolution replaces the contents Y (x) of every channel of the spectrum by

16 t X F ILT (Y (x)) = fsY (x + s) (2.3) s=−t

Where t = UW/2 + LW . As shown via the idealized spectrum of Figure 2.6, this convolution eliminates linear background entirely and doubly diﬀerentiates a Gaussian peak.

In introducing this technique for use in EPMA, Schamber showed that the optimum ﬁlter dimensions were UW = 1FWHM and LW = 0.5FWHM [34].

Figure 2.6: Convolution of a top-hat digital ﬁlter function with a experimental spectrum. Adapted from [36].

Maxwell et al. modified this filter by allowing it to vary the filter dimensions to match every channel of the spectrum. This modification improved the accuracy of peak fitting in the lower energy range of the PIXE spectra [37].

The top-hat filter is most reliable when the background curvature is low enough to pre- clude significant departure from linearity over several peak widths. Caution is required when the continuum has significant curvature [37]. The principal drawback of the methods may well be that the intensity errors and the ensuing concentration errors are larger when background is treated by a top-hat filter than when it is represented by a mathematical model

[37].

17 Despite the simplicity of the top-hat ﬁlter for background removal, many tests of GUPIX on standard reference materials have demonstrated accuracy in determining concentrations.

In one inter-comparison study, the least-squares fitting codes developed independently at five different laboratories were used to analyze PIXE spectra of a set of biological, environmental, and geological specimens [38]. Of the five methods used, GUPIX was the only one using a top-hat filter for background removal. At the time, the principal objection levelled at PIXE analyses concerned the accuracy of extraction of areas of overlapping peaks superposed on a rapidly varying background. A detailed comparison of the resulting five sets of X-ray intensity data revealed remarkably good agreement among the five techniques, despite major differences in their methodologies. The differences among the five codes were not alleviated by comparing peak areas with the corresponding standard peak areas. They arose from the background treatment and its interplay with the peak model [38]. Almost all standards analyzed fell within ±2% of the relevant mean [38].

2.4.2 Characterizing the System

The GUAPX fitting procedure is the slightly modified Marquardt non-linear least-squares method taken directly from GUPIX [27]. The height of the principal diagram line of each element is a variable of the fit [39]. This is the height of that element’s most intense X- ray line in the spectrum (usually Kα1 or Lα1). If N elements are present, the number of variables fit to describe the X-ray peak region of the spectrum is N + 4. The four additional parameters are variables of the least-squares fit used to characterize the system’s response and are referred to as ’A’ values. Two variables A1 and A2 are introduced to define the linear relationship between channel number, C, and X-ray energy, E (in keV):

C = A1 + A2E (2.4)

Once the energy calibration has been deﬁned, two additional variables, A3 and A4, similarly deﬁne the relationship between the peak width (standard deviation in channel units), σ, and X-ray energy:

18 2 σ = A3 + A4E (2.5)

It follows from eqn. 2.2 that

2 A4 = F εA2 (2.6)

Where F is the Fano factor mentioned earlier. The approach assumes a linear response

and takes advantage of the high accuracy for which characteristic X-ray energies are known.

This is important as regards achieving accurate separation of overlapping peaks [31]. The

characteristic X-ray peaks are modelled by Gaussian or Voigtian distributions, depending

on the number of counts measured [40]. For a given element, all other diagram and satellite

lines have their intensities coupled to the principal line’s intensity. These relative intensities

are modiﬁed by the absorber/eﬃciency term and by the matrix term in the well established

XRF and PIXE yield equations.

Although the calibration parameters are known with high accuracy from spectra of single-

element standards, they are varied and determined by the ﬁtting procedure, along with the

peak heights of the principal X-ray peak of each element present. The reasoning for this is

that small electronic drifts and the counting-rate dependence of these parameters can cause

slight variation in their values from run to run. It is preferable to allow the ﬁt to determine

them. Their inclusion as variables necessitates a nonlinear ﬁtting approach [27].

It should be noted that instead of varying the parameters of the model to achieve a good

ﬁt of the model spectrum with the measured spectrum, the parameters of the model are var-

ied to achieve a good fit between the filtered model and the filtered measured spectrum [27].

Thus, the reduced χ2 is altered by the smoothing effect of the filter, and the normal interpre- tations of the χ2 value and the parameter errors no longer hold; the “optimum” value of χ2 is no longer unity. Therefore, the best way to assess the spectrum fit is to look at the residuals.

19 It is worthwhile to point out that no spectral processing procedure, no matter how sophisticated, can produce more information than present originally. It is, therefore, much more eﬃcient to employ optimal experimental conditions when acquiring data rather than rely on mathematical techniques in an attempt to obtain information that is not present in the ﬁrst place [17].

2.4.3 The Yield Equation

In both PIXE and XRF methods, the yield of characteristic X-rays, Y (Z), of element, Z, produced by a number of mono-energetic ions or mono-energetic photons, N, incident on the inﬁnitely thick sample, is given by the following relationship:

Y (Z) = Y1 (Z,M) NCzΩtZ εZ (2.7)

The symbol M indicates that the X-ray yield depends not only upon the concentration,

CZ , of the element of interest, but also upon those of all the other elements that deﬁne the sample matrix. Y1(Z,M) is the theoretical X-ray yield from element Z per unit concentration within a deﬁned matrix, M, per steradian of solid angle, Ω, per ion or photon.

Here, N is the number of incident mono-energetic ions or mono-energetic photons, tZ is the transmission through any material between the detector and the sample, and εZ is the intrinsic efficiency of the detector; including the attenuating effects of the beryllium window, the nitrogen filling, and the aluminum contact.

Equation 2.7 cannot be used directly to deduce CZ from the measured value of Y (Z), because the term Y1(Z,M) contains the CZ values for all elements present. This “matrix term” describes the attenuation in the sample matrix of incoming or outgoing photons and the slowing down of incoming ions. In GUAPX, these eﬀects are computed from an exten- sive database of ionization cross sections, photoelectric cross sections, helium ion stopping powers, and X-ray attenuation coeﬃcients. In PIXE, the X-ray production decreases with

20 penetration depth as the ions slow down resulting in a decrease in the ionization cross section. In XRF there is also a decrease in X-ray production with depth, but in this case the number of exciting mono-energetic photons diminishes exponentially with depth in the sample. To compute Y1(Z,M), the code assumes that the elements are homogeneously distributed within the sample material. Notably, this assumption does not hold for the APXS, since it is used to analyze rocks and soils that are, in general, fundamentally heterogeneous.

The consequences of this discrepancy were investigated in depth by Dr. G.M. Perrett [19].

Ultimately, the instrument’s accuracy is limited by the microscopic heterogeneity of samples, and the results can be found in the journal article on the MSL-APXS calibration [40].

The number N is proportional to the measurement duration T , i.e., N = aT where a is a constant. Drawing the quantities a and Ω together into a single instrumental factor, H, equation 2.7 for either X-ray excitation method can be rewritten as follows:

Y (Z) = Y1 (Z,M) TCzHtZ εZ (2.8)

Summing over excitation produced by ﬁfteen of the approximately twenty mono-energetic

Pu L X-ray lines, we can now write the overall yield equation as employed in GUAPX for the APXS as follows:

h X i Y (Z) = HCzT Y1,P IXE (Z,M) + Y1,XRF (Z,M) tZ εZ (2.9)

GUAPX demands an accurate value for the intensity ratio between L X-rays and α-

particles emitted by 244Cm to properly establish the relative contributions from the two

excitation modes. Furthermore, in FP methods, the incidence and takeoﬀ angles are impor-

tant parameters. Since individual PIXE and XRF systems are customarily constructed with

geometrically well-deﬁned beams of exciting radiation, equation 2.7 is usually evaluated at

unique values for these angles. For the APXS, the geometry is very diﬀerent, as discussed

by Omand et al.[41]. There is a wide range of directions for the incident ions and photons,

and, as a consequence of that, there is also a wide range of directions for the excited char-

acteristic X-rays. Omand et al. showed via Monte Carlo calculations of X-ray yields that a

21 pair of “effective angles” could be defined such that equation 2.7, evaluated with these two angle values, provides essentially the same X-ray yields as the Monte Carlo approach which properly treats the full ranges of angles. This work was further refined by D. Thomson [42].

Matrix Eﬀects & GUAPX Modalities

Matrix effects, in the context of the APXS, refer to the influence of the atomic arrangement in the sample in (i) decreasing the energy of the incoming alpha particles and determining their range, (ii) attenuating the intensity of the incoming X-ray photons, (iii) attenuating the intensity of the outgoing characteristic X-ray photons, and (iv) secondary X-ray fluorescence between elements [40].

GUAPX offers two modalities for the treatment of matrix effects in the measured spectrum. In the “fixed-matrix” (FM) mode, the element concentrations from the GRM certificate are used for computation of the matrix effects. This is the more appropriate approach for treating standards within a calibration exercise. For the treatment of unknown samples

“iterative matrix” (IM) should be employed.

Iterative Matrix Mode & the Closure Rule

In a ﬁeld application of the instrument, such as its use on Mars, the analytical challenge is much more diﬃcult than the rather straightforward case of a terrestrial analysis of known reference materials. There is no a priori knowledge of the samples, and the exact distance to the detector is not known. The FM approach is obviously inapplicable. The only possibility is an iterative solution.

GUAPX commences with a preliminary ﬁt of the spectrum. The resulting peak areas are converted into element concentration estimates via equation 2.9 using the H-value (known from prior calibration on Earth) and subsequently into oxide concentrations via assumed stoichiometry. This ensures that the large O concentration plays its role in the matrix com- putations although, O does not contribute X-rays to the measured spectrum. The total concentration is then normalized to 100%; this step provides a ﬁrst estimate of the sample

22 matrix. Up to this point, no matrix corrections have been performed, for the obvious reason that no concentrations were known a priori. The ﬁrst estimate of the matrix composition is plugged into the yield equation which outputs a new set of concentrations. The process is iterated until the matrix concentrations are consistent.

The 100% closure condition renders the absolute value of H redundant; the program

determines a new, eﬀective, H-value consistent with the normalization. If these two values

diﬀer by more than 1%, their ratio (Hcorr) is provided in the GUAPX output as a diag-

nostic that the geometry, or some other factor, has changed relative to expectations. For

the purpose of this investigation, IM mode was employed since the eﬀects of resolutional

variation on concentration estimates for unknown samples is of interest for the MSL-APXS

at Gale crater, on Mars.

Samples that contain “X-ray invisible” components beyond the oxygen that is bound

via stoichiometry to the cations, increases the complexity of sample compositional analysis.

Such components include carbon, carbon dioxide, boron and lithium oxides, and mineralog-

ically bound water (H2O+). If signiﬁcant invisible components are present in an unknown

sample, one must expect the generated matrix to be incorrect. Furthermore, when the in-

strument is deployed on a planetary surface, the sample distance varies from one sample to

the next and is unknown. This necessitates invocation of the closure rule [43]. However, re-

sults are skewed by the imposition of the 100% closure rule. The problem has been described

under diﬀerent headings: the constant-sum problem, the closure problem, the negative bias

problem, and the null correlation diﬃculty [44].

As pointed out by Rollinson [45], expressing elemental abundance in rocks and minerals

as percentages is problematic, yet universally accepted. It seems to be the only way of

presenting a chemical analysis in a form that can be compared with other analyses. The

results, usually presented as percentages, are highly complex ratios containing variables in

their denominators that represent all constituents being examined. Geochemical concen-

tration percentages are of compositional nature and are prone to pitfalls when a closure

23 operation is performed. These pitfalls can be traced back to the fact that the sample space for compositional data is radically diﬀerent from the more common unrestricted real

Euclidean space. In short, the principal consequence of closure for geochemistry is that correlation theory, frequently used to examine major and trace element interrelationships, can produce misleading results. For example, if a strong inverse correlation between silica and other constituents is found, the cause and meaning of the association is not clear since silica usually makes up roughly half of the sample. This problem applies generally to major and trace element data since forced correlations are a property of compositional data [45].

2.5 Calibration

The APXS calibration combines the fundamental parameters approach, described above, with the use of standards. A subset of appropriate standards or elements is chosen to de-

α termine the value of the /LX ratio and instrument constant, H. The full suite of standards

is then ﬁt by GUAPX to provide concentrations of all detected elements. If the database

is appropriate, the knowledge of the detector is complete, and the methodology of matrix

corrections is correct, then these concentration values should be equal to the certiﬁcate val-

ues. Standard specimens for calibration of the APXS must cover the concentration range

of interest, be stable over time, have a certiﬁed composition, and be prepared for analysis

using a reproducible, quality assured technique [40].

As with the MER mission, the PFM-APXS calibration was performed after launch using

the FEU-APXS. On Earth special precautions are taken in sample preparation to obtain

homogeneous samples. For example, in routine XRF laboratory analyses, powdered samples

are homogenized and diluted by melting into a borated glass pellet. These procedures are

not beneﬁcial for the APXS calibration since powdered samples are more similar to sam-

ples expected on Mars, where sample preparation is limited. Most laboratory samples were

ground to grain sizes of less than 75 µm and ﬁlled into a shallow depression of a sample holder and pressed to provide a smooth surface [46].

24 To calibrate the FEU APXS instrument for MSL, the Geochemical Reference Material

(GRM) suite was more than doubled, relative to that used for calibration of the MER-

APXS. This doubling ensured that almost all elements observed in the MER mission were well represented over the reported concentration ranges. A database was compiled from 471 certiﬁed and validated samples by Dr. P. L. King from 29 sources [47]. It included igneous rocks (109), sediments and sedimentary rocks (233), and minerals (129). Most of the MSL calibration samples have siliceous matrices because they are expected to be the most common type of sample on Mars. This selection places a limitation on the variety of matrix eﬀects that may be encountered. However, other pure minerals and chemical compounds

(e.g. phosphates, sulfates, chlorides) were also measured to cover a large range of diﬀerent matrices [40].

A lower limit of abundance was empirically determined for some elements; abundances below this limit were not used for the calibration. Some samples that were used for the initial calibration were discarded from the ﬁnal calibration as they produced data that de- viated largely from the derived mean response [48].

In this chapter, the FEU-APXS spectrum acquisition process was described. The theory behind noise and resolution was presented and placed in the context of the thermal and radiation environments of the instrument. The spectrum evaluation code used for the present work, GUAPX, and the mathematical models behind it were introduced. This included discussion of the ﬁltering procedure, system characterization, the yield equation, matrix correction modalities, and closure operations. Lastly the FPS approach to the calibration of the instrument-software system was brieﬂy described. An understanding of the machinery behind the APXS-GUAPX system is essential for the investigation presented by this thesis.

25 Chapter 3

Precursory Work

In general, the accuracy and precision of ED X-ray spectroscopy is enhanced with improved detector energy resolution. Thus, energy resolution is commonly used to differentiate systems. However, the benefits of improved energy resolution, in terms of accuracy and precision of the analytical results, are not always clear [7]. Accuracy quantifies the correctness of a result; it is observed as the difference between the value of measurements and the true value.

Precision, on the other hand, quantiﬁes the reproducibility of a result, which is the variation arising from random errors. It is observed in repeated measurements under identical conditions including identical FWHM. Accuracy is associated with systematic errors and precision with random errors. As discussed in Section 2.4.3 the APXS accuracy is limited by the microscopic heterogeneity of the samples analyzed.

In the summer of 2013, Dr. I. Pradler and Dr. R. Gellert investigated the eﬀects of resolutional variations on APXS acquired measurements of the USGS andesite, AGV-2. By controlling the cooling of the sensor head the resolution was systematically altered, holding all other parameters constant. Various APXS measurements were taken of the same sample at various temperatures, achieved by adjusting the TEC duty cycle and/or power supply to six diﬀerent settings. Preliminary analyses by Dr. Pradler [49] showed that although the measurements acquired at similar resolutions displayed a high level of precision, there was a clear correlation between GUAPX estimated concentrations for Ca, Ti, Mn, and Fe with FWHM. In addition, Na and Si showed anomalous behaviour at the worst resolution achieved.

26 Dr. Pradler’s results raised interesting questions regarding the precision of analytical results taken at various resolutions. What was the underlying cause for these spurious concentration estimates? How did the variations in estimated elemental concentration compare with the precision error quoted for APXS-GUAPX analytical results?

3.1 Accuracy of AGV-2 Concentration Estimates

A total of 61 hour-long AGV-2 spectra were collected. The spectra were summed in tranches, or groups, deﬁned by the TEC and/or power supply settings employed and re-processed using

GUAPX. This was done to improve statistics. The number of spectra that comprise each tranche can be seen in Table 3.1, along with the average sensor head temperature and the

FWHM of the summed spectra at the Mn Kα line.

Summed Constituent Average Number of Spectrum Spectra Tranche Temperature Spectra FWHM FWHM (◦C) (eV) (eV) A 12 -12.3±0.3 166 163 - 166 B 5 -11.2±0.1 169 168 - 171 C 16 -7.7±0.3 181 180 - 184 D 4 -5.1±0.4 192 191 - 194 E 20 -1.8±0.5 210 203 - 217 F 4 2.5±0.2 241 241 - 243

Table 3.1: Number of spectra summed for tranches A - F with average temperature and summed spectrum FWHM.

The summed spectra were processed using GUAPX’s IM mode. The ﬁt options can be seen in Table 3.2. The results are presented below and brieﬂy analyzed in the context of accuracy with respect to resolutional variations.

27 GUAPX Set-Up Excitation Info MSL_FEU2012 Detector MSL_FEU_2012 Oﬀsets Zero H-value 0.1669 ECF ECF_Startup

A1 -22 A2 44 A3 (ﬁxed) 0 A4 8 A5 1

Table 3.2: GUAPX settings used for AGV-2 spectrum ﬁtting.

The estimated concentrations were plotted against the FWHM at the Mn Kα line for ten elements of geochemical interest. The plots, arranged by atomic number, can be seen in

Figures 3.1- 3.10. The certiﬁed concentrations, including the 2 σ bounds, are provided. The error bars attached to the estimated concentrations are two times the uncertainty provided by GUAPX.

3.4

3.2

2.8

2.6

GUAPX Estimated Concentration

Na Concentration (%) ! Na Concentration 2.4 USGS Recommended Value

2.2 2σ

2 160 170 180 190 200 210 220 230 240 250 Mn FWHM (eV)! Figure 3.1: GUAPX estimated Na concentration at various resolutions for AGV-2.

28 1.4

1.2

0.8

0.6

0.4 Mg Concentration (%) ! Mg Concentration GUAPX Estimated Concentration

USGS Recommended Value 0.2 2σ

0 160 170 180 190 200 210 220 230 240 250 Mn FWHM (eV)! Figure 3.2: GUAPX estimated Mg concentration at various resolutions for AGV-2.

9.4

9.2

8.8

8.6

Al Concentration (%) ! Al Concentration 8.4 GUAPX Estimated Concentration

USGS Recommended Value 8.2 2σ

8 160 170 180 190 200 210 220 230 240 250 Mn FWHM (eV)! Figure 3.3: GUAPX estimated Al concentration at various resolutions for AGV-2.

30.5 GUAPX Estimated Concentration

30.0 USGS Recommended Value

2σ 29.5

29.0

28.5

28.0 Si Concentration (%) ! Si Concentration 27.5

27.0

26.5 160 170 180 190 200 210 220 230 240 250 Mn FWHM (eV)! Figure 3.4: GUAPX estimated Si concentration at various resolutions for AGV-2.

29 2.9 GUAPX Estimated Concentration 2.8 USGS Recommended Value

2.7 2σ

2.6

2.5

2.4

2.3 K Concentration (%) ! K Concentration

2.2

2.1

2 160 170 180 190 200 210 220 230 240 250 Mn FWHM (eV)! Figure 3.5: GUAPX estimated K concentration at various resolutions for AGV-2.

4.2 GUAPX Estimated Concentration

4.1 USGS Recommended Value 2σ

3.9

3.8

Ca Concentration (%) ! Ca Concentration 3.7

3.6

3.5 160 170 180 190 200 210 220 230 240 250 Mn FWHM (eV)! Figure 3.6: GUAPX estimated Ca concentration at various resolutions for AGV-2.

0.95

0.85

0.75

0.65

0.55 GUAPX Estimated Concentration Ti Concentration (%) ! Ti Concentration

USGS Recommended Value 0.45 2σ

0.35 160 170 180 190 200 210 220 230 240 250 Mn FWHM (eV)! Figure 3.7: GUAPX estimated Ti concentration at various resolutions for AGV-2.

30 0.14 GUAPX Estimated Concentration 0.12 USGS Recommended Value 2σ 0.1

0.08

0.06

0.04

0.02 Mn Concentration (%) ! Mn Concentration 0 160 170 180 190 200 210 220 230 240 250 -0.02

-0.04 Mn FWHM (eV)!

Figure 3.8: GUAPX estimated Mn concentration at various resolutions for AGV-2.

5.5 GUAPX Estimated Concentration 5.4 USGS Recommended Value 5.3 2σ 5.2

5.1

4.9

4.8

Fe Concentration (%) ! Concentration Fe 4.7

4.6

4.5

4.4 160 170 180 190 200 210 220 230 240 250 Mn FWHM (eV)! Figure 3.9: GUAPX estimated Fe concentration at various resolutions for AGV-2.

0.018 GUAPX Estimated Concentration

0.016 USGS Recommended Value

2σ 0.014

0.012

0.010

0.008

0.006 Zn Concentration (%) ! Zn Concentration 0.004

0.002

0.000 160 170 180 190 200 210 220 230 240 250 Mn FWHM (eV)! Figure 3.10: GUAPX estimated Zn concentration at various resolutions for AGV-2.

31 The results above are similar to those produced by Dr. Pradler; they are indicative of a correlation between the GUAPX estimated concentrations and the instrument’s resolution.

As resolution worsens, systematic changes in concentration estimates were observed for some elements.

The results show a decrease in estimated concentration as FWHM increases for Na,

Mg, Al, and Mn. Si, K, Ca, and Fe show increased concentration estimates as FWHM increases. The concentration estimate response to FWHM variation is non-linear, showing slight variations at resolutions below 200 eV, at the Mn Kα line, and big deviations once resolutions higher than 200 eV, were reached. The exceptions to this are: Ti concentration estimates, which appear to be independent of resolution in the range analyzed; Zn concentration estimates, which do not show signiﬁcant changes, even at the worst resolution; and

Na concentration estimates, which could be described as varying linearly with FWHM.

Although it is clear from the results above that resolution affects the concentration estimates from APXS measurements of AGV-2, this is just the first step in understanding the overall effects of resolution on concentration estimates and answering the following questions: How does the variation in concentration estimates compare with the quoted precision errors for APXS analytical results? Are the variations in concentration estimates sample dependent? Are these variations a consequence of the filtering or fitting procedures? Are they caused by the closure rule? Do matrix corrections have anything to do with these variations? To tackle these questions a larger sample size and more in depth analysis of the spectrum processing using the APXS-GUAPX system was undertaken.

32 Chapter 4

Laboratory

The continuous degradation of FWHM due to neutron damage in conjunction with the limited temperature control capabilities of the FEU-APXS led to the development of a stepwise optimization of the cooling conﬁguration in the laboratory by Dr. Gellert and N. Boyd.

Consequently, the diﬀerent FEU-APXS instrumental conﬁgurations cover a broad resolution range. Thus, the GUAPX analytical results computed from spectra collected under various

APXS configurations serve as a laboratory to investigate the effects of resolution on concentration estimates. This chapter describes the three different APXS configurations employed to collect the spectra used for this investigation. Sample spectra collected from the GSP-2

GRM, under the diﬀerent conﬁgurations, are provided. The experimental setup options used to analyze the available spectra are also listed. The process of culling the compiled data of irrelevant and unreliable data from the database is described. The end product is a database comprised of analytical results that can be used to investigate the relationship between resolution, estimated photopeak areas, and estimated concentrations.

4.1 FEU-APXS Conﬁgurations

The FEU-APXS has featured 3 conﬁgurations from the start of the GUAPX calibration in

May 29, 2009 to August 2014. These are described in Table 4.1.

33 Activity Activity Energy Number of Resolution Time Open Closed α Conﬁguration Range Excitation Range H /LX Frame Sources Source(s) (keV) Sources (eV) (mCi) (mCi) Calibration May 2009 - Dec 2011 0.8 - 21.0 6 3x10 3x10 175 - 190 0.2246 0.54 × 107 2012 Jan 2012 - Mar 2013 1.0 - 23.5 4 3x10 1x30 185 - 208 0.1670 0.63 × 107 2013 Apr 2013 - Aug 2014 1.0 - 23.5 4 3x10 1x30 162 - 183 0.1670 0.63 × 107

Table 4.1: Summary of diﬀerent APXS conﬁgurations from May 2009 - August 2014.

The “open” sources let both α-particles and Pu L X-rays through and the “closed” sources only let Pu L X-rays through. Since the closed sources were replaced, the intensity ratio

α 244 between α-particles and Pu L X-rays ( /LX) emitted by the Cm sources diﬀers starting

α on January 1, 2012. Therefore, the /LX-value, required for the APXS yield equation, can-

not be assumed equal to the accurately known literature value and had to be determined

experimentally. The trial and error method outlined in [40] was employed by G. Perrett to

α empirically determine the FEU-APXS H and /LX values found in Table 4.1.

4.1.1 Sample Spectra Acquired Under Diﬀerent Conﬁgurations

The APXS spectra acquired for the Silver Plume Granodiorite (GSP-2) GRM, provided

by the USGS, under the three conﬁgurations outlined in Table 4.1, can be seen in Figures

4.1- 4.3. The second peak from the left, corresponding to Mg, is indicative of the issues

associated with a broader FWHM. In the 2010 calibration spectrum, a peak is discernible.

In the 2012 spectrum the peak is no longer visible, completely overshadowed by the Na, Al,

and Si peaks. In the 2013 spectrum the resolution was improved and the Mg peak is best

deﬁned. The eﬀects of the changes in resolution can also be seen in the separation between

the Al and Si peaks, as well as the K and Ca peaks.

34 Si

Fe Kα T

Na K Mg

Ca Fe Kβ

Figure 4.1: GSP-2 Spectrum taken in 2010 for the instrumental calibration (FWHM at 5.9 keV = 168 eV).

Fe Kα Na K

Ca Fe Kβ

Figure 4.2: GSP-2 Spectrum taken in 2012 (FWHM at 5.9 keV = 198 eV).

Fe Kα Na K Mg

Ca Fe Kβ

Figure 4.3: GSP-2 Spectrum taken in 2013 (FWHM at 5.9 keV = 164 eV).

35 4.2 Dataset

After the instrument changes in 2012, Dr. R. Gellert measured 25 GRMs with the FEU-

APXS. The spectra collected from this GRM suite is henceforth referred to as the 2012 campaign. After the optimization of the cooling conﬁguration in 2013, Dr. R. Gellert measured 46 GRMs with the FEU-APXS. The spectra collected from this GRM suite is henceforth referred to as the 2013 campaign. The list of GRMs measured in the 2012 and

2013 campaigns can be found in Appendix A (Tables A.1 and A.2 respectively). These spectra, in conjunction with the corresponding spectra collected for the instrument’s calibration and their analytical results as output by GUAPX, provide the testing ground for extracting

α the eﬀects of resolution on the estimated peak areas and concentrations, as well as the /LX correction factor.

The measured spectra fall into one of three groups: the 2013 campaign, the 2012 campaign, or the calibration (2009 - 2011). The latter serves as the reference point for the other two campaigns. The spectra for each group were processed using the IM-Batch Mode in

GUAPX. IM mode was chosen since it is used on Mars to deal with unknown samples [40], thus its performance is of interest for the mission. The ﬁt options for the three campaigns can be seen in Table 4.2.

GUAPX Set-Up Campaign 2009-2011 2012 2013

Excitation Info MSL_FEU MSL_FEU2012 MSL_FEU2012 Detector MSL_FEU MSL_FEU_2012 MSL_FEU_2012 Oﬀsets Zero Zero Zero H-value 0.2246 0.1669 0.1669 ECF ECF_Pre-calibration ECF_Pre-calibration ECF_Pre-calibration

A1 -24 -23 -22 A2 48 44 44 A3 (ﬁxed) 0 0 0 A4 8 8 8 A5 4 1 1

Table 4.2: GUAPX settings used for spectrum ﬁtting in each conﬁguration.

36 4.2.1 Data Selection

The empirical results for the ﬁtted elements were stored in a database, along with their uncertainties and certiﬁed elemental concentrations. Ten geochemically relevant elements were chosen for evaluation: Na, Mg, Al, Si, K, Ca, Ti, Mn, Fe, and Zn. The important task of culling irrelevant and unreliable data from the database was undertaken to ensure that only high-quality data-points were used for additional analyses.

The first step in the culling process was to eliminate data-points corresponding to elements absent from the certificate concentrations. In other words, if a GRM’s certificate did not provide the concentration for a particular element, the GUAPX output corresponding to that element for that GRM was eliminated. For example, the NIST certificate of analysis for

Standard Reference Material 70a (Potassium-Feldspar) does not provide a certiﬁed percent by weight value for the MgO constituent. Thus, the analytical results for Mg in SRM70a were not considered.

The obvious extension to the culling process was to eliminate unreliable data points.

GUAPX’s output provides a summary for its decisions regarding the presence of ﬁtted elements in the sample. The decision depends on the limit of detection (LOD) and the limit of quantitation (LOQ) for that particular element in the sample. The LOD is dependent on the surrounding photopeaks and the matrix. The LOQ is three times the LOD. The possible decision outcomes are as follows:

• Not Present (N): The measured signal is below the LOD

• Not Sure (?): The signal is above the LOD but below the LOQ

• Present (Y): The signal is above the LOQ

Only data points for which the signal was above the LOQ in both the calibration and campaign measurements were selected for further analyses. For example, Na from the biotite

Mica-Fe, provided by SARM, was between the LOD and LOQ during the calibration run.

However, in the 2012 campaign the signal was below the LOD and in the 2013 campaign

37 the signal was above the LOQ. Since the ﬁtting code’s output was not congruent between campaigns, the data for Na in Mica-Fe were eliminated from the database.

The ﬁnal step in the data culling was to ensure that only the data from GRMs used for the GUAPX-APXS calibration were kept. The reasoning for this is that specimens analyzed should be a subset of those used for the calibration [17]. For example, the K content in the

SARM provided kyanite GRM (DT-N) has a certiﬁed concentration value of 0.10±0.02 % and was above the LOQ in both the 2013 campaign and calibration measurements. How- ever, it was omitted from the GUAPX calibration due to its low concentration, thus it was omitted from further analyses here as well.

The following GRMs were found to behave poorly with markedly low count-rate ratios for most, if not all, elements. They were completely removed for the following reasons:

• DTS-2B: Persistent outlier for both 2012 and 2013 count-rate ratios. In the calibration

it is noted as being "likely bad since not made by Dr. G. Perrett and recycled dish

used"

• JMS-2: Consistent outlier, sample was noted as having had a colour change indicative

of a chemical change within the sample.

• SARM-5: Consistent outlier.

• SRM694: Consistent outlier. It is noted as having incomplete NIST and ActLabs

analyses. It was only used for P in the APXS-GUAPX calibration.

The 2012 and 2013 campaign spectra, collected using the FEU-APXS under diﬀerent resolutional environments, were ﬁt using GUAPX. The data acquired were methodically selected using the culling procedure described above. The compiled database was used for the ensuing investigation into the relationship between spectral resolution, estimated peak areas, and estimated concentrations.

38 Chapter 5

Photopeak Areas (Background Removal and Deconvolution)

Extraction of concentration estimates from measured spectra begins with the determination of the peak area for the principal line of each element present. It follows that the investigation into the eﬀects of resolutional variation on APXS-GUAPX analytical results begins with the analysis of the relationship between change in resolution and estimated peak areas.

5.1 Count Rates & Source Decay Correction

Total characteristic X-ray counts (peak areas) are dependent on measurement time. By normalizing the peak areas by the measurement time, the counts per second (CPS) can be extracted. These count rates are, however, dependent on the excitation source activity which is decaying over time.

The “open” sources were held constant through the three conﬁgurations used. Those sources have α-decayed at a constant rate with a half-life of 18.11 years. Their fraction of non-decayed nuclei on January 1, 2012, relative to May 29, 2009, is 0.906. Therefore, a decrease in the counts per second from predominantly PIXE-excited elements by a factor of 0.906 is expected. There is also a commensurate decrease in Pu L X-ray emission from these sources.

The replacement of the “closed” sources on January 1, 2012 led to a change in the Pu L

39 X-ray induced XRF emission rate associated with these sources, in addition to the decrease associated with source decay. However, the expected change in closed source activity value is not known since the replacement source’s activity is unknown. Thus, the changes in PIXE and XRF induced count rates from May 2009 to January 2012 need not be commensurate, and in fact they are not. Therefore, count rate measurements taken before January 1, 2012 must be corrected for source decay relative to May 29, 2009. Measurements taken after

January 1, 2012 can only be decay-corrected relative to that date. Ideally they would also be corrected for the change in activity associated with the “closed” source replacement.

5.2 Count Rate Ratio (RCPS)

Decay corrected count rate changes relative to the calibration measurements were quantiﬁed by calculating the ratio between the elemental CPS obtained from campaign spectra and those obtained from calibration spectra. This is called the count rate ratio, RCPS. The only

requirement is that the specimens have concentrations that are varied enough to cover the

calibration range [17]. The elements chosen for analysis were the most abundant elements

on Earth’s crust that are predominantly excited by PIXE interactions (Na, Mg, Al, Si) or

XRF interactions (Mn, Fe, Zn) in the APXS.

5.3 Results

The element count rate ratios were plotted against the GRM certiﬁcate concentrations, no

other numerical use was made here of these concentrations. The inverse-variance weighted

average count rate ratio, denoted as RCPS, was computed for each campaign. This was

done to give more weight to the more accurately determined peak areas. However, the

uncertainty quoted is the (unweighted) standard deviation (1σ) for each campaign. This

unweighted statistic was chosen because the average count rate ratio is determined from

various diﬀerent samples; had the average been calculated from repeated measurements of

the same sample it would be sensible to use the weighted standard deviation. The error bars

shown are the 2σ values from the GUAPX output.

40 The lightest visible elements (Na, Mg, Al, Si) are predominantly excited via PIXE interactions and have overlapping peaks superposed on a rapidly varying background [38].

They are crowded together in the spectrum and their size, relative to their neighbours, is of importance, especially as instrumental resolution decreases. Na, Mg, and Al were plotted against the ratio of that element’s certified concentration to the sum of the concentration of the neighbouring elements. For example, Na count rate ratios were plotted against the ratio [Na]/[Mg+Al+Si] to probe the effect of the Na peak size. This allows for the identification of outliers, as well as trends in count rate ratios with respect to relative abundance.

The heaviest elements analyzed, predominantly excited via XRF interactions, do not exhibit as much overlap as the lightest elements. Since both “open” and “closed” sources emit the Pu L X-rays used for XRF analysis, these elements are excited by both source types.

The count rate ratios were plotted against the corresponding certiﬁcate concentrations. This allowed for the identiﬁcation of outliers as well as trends in count rate ratios with respect to concentration. The count-rate ratios for the 2012 campaign are shown in red and those for the 2013 campaign are shown in blue. The inverse-variance weighted means for each campaign are provided in the corresponding colour. The decay correction value, expected for the predominantly PIXE excited elements, is provided as a dashed black line.

5.3.1 Predominantly PIXE

Figure 5.1 shows a dichotomy between the Na peak areas estimated from the 2012 and 2013 campaigns. The count rates of the latter campaign are consistently higher in value than those of the former. The 2013 campaign Na RCPS is 0.89 ± 0.06. For the 2012 campaign,

Na RCPS = 0.80 ± 0.06. Despite the 11% diﬀerence in these numbers, the results agree within the error estimates. Some samples with a [Na]/[Mg+Al+Si] value between 0.04 and

41 2013/Calibration! 1.15! 2012/Calibration! WS-E! Mean = 0.89 ± 0.06! PM-S! BE-N! 1.05! Mean = 0.80 ± 0.06! Decay Correction! BHVO-2 !

! 0.95!

CPS

0.85! Na R

0.75!

MAG-1! PM-S! 0.65! BHVO-2 & Jsd-2! SRM688!

0.55! 0.00! 0.02! 0.04! 0.06! 0.08! 0.10! 0.12! 0.14! 0.16! 0.18! 0.20! [Na]/[Mg+Al+Si]!

Figure 5.1: Na count rate ratios vs. [Na] as a fraction of [Mg+Al+Si].

0.09 show more pronounced contrast between campaigns. BE-N, BHVO-2, PM-S, and WS-

E measured in 2013 show an increase in Na count rates, relative to the campaign mean.

BHVO-2, JSd-2, MAG-1, PM-S, and SRM688 of the 2012 campaign show a decrease in count rate, relative to the campaign mean.

Figures 5.2- 5.4 show the entire domain of the dependent variable and zoomed-in sections of it. A dichotomy can be seen between the higher-valued ratios from the 2013 campaign and those from the 2012 campaign. Some outliers are identiﬁed on the plots.

For the 2013 campaign, Mg RCPS = 0.82 ± 0.05. For the 2012 campaign, Mg RCPS =

0.79 ± 0.08. Despite the 3.7% diﬀerence in these numbers, the results agree within the error estimates. As the Mg peak becomes less prominent there is more uncertainty in the peak area measurements, concomitant with a broader scatter in the count rate ratios, as would be expected.

42 1.2!

1.1!

WS-E 1! BE-N 0.9! UBN Mica-Mg (2012 & 2013) ! SARM-6 0.8! CPS BE-N

0.7! Mg R

0.6! 2013/Calibration!

0.5! 2012/Calibration! Mean = 0.82 ± 0.05!

0.4! Mean = 0.79 ± 0.07! Decay Correction! 0.3! 0.0! 0.2! 0.4! 0.6! 0.8! 1.0! 1.2! 1.4! [Mg]/[Na+Al+Si]!

Figure 5.2: Mg count rate ratios vs. [Mg] as a fraction of [Na+Al+Si], over the entire Mg concentration range.

1.2! 2013/Calibration! 2012/Calibration! 1.1! Mean = 0.82 ± 0.05! WS-E Mean = 0.79 ± 0.07! 1! Decay Correction! BE-N 0.9! ! CPS 0.8! BE-N Mica-Mg (2012 & 2013) Mg R

0.7!

0.6!

0.5!

0.4! 0.0! 0.1! 0.2! 0.3! 0.4! 0.5! 0.6! [Mg]/[Na+Al+Si]!

Figure 5.3: Zoom in on Mg count rate ratios vs. [Mg] as a fraction of [Na+Al+Si], over approximately half the Mg concentration range.

43 1.2! 2013/Calibration! 2012/Calibration! 1.1! Mean = 0.82 ± 0.05! Mean = 0.79 ± 0.07! 1! AN-G AGV-2 Decay Correction!

0.9! ! CPS 0.8! Mg R

0.7!

0.6!

0.5!

0.4! 0.00! 0.01! 0.02! 0.03! 0.04! 0.05! 0.06! 0.07! 0.08! [Mg]/[Na+Al+Si]!

Figure 5.4: Further zoom in on Mg count rate ratios vs. [Mg] as a fraction of [Na+Al+Si], at extreme low Mg concentrations.

Figures 5.5 and 5.6 show the complete data set and a zoom in on the domain spanning 0.15 to 0.5. The campaign-based dichotomy seen in the previous analytes is much less prominent for Al, but still discernible.

For the 2013 campaign, Al RCPS = 0.87 ± 0.04. For the 2012 campaign, Al RCPS =

0.85 ± 0.04. Despite the 2.3% diﬀerence in these numbers, the results agree within the error estimates. There are a few outliers visible by inspection including BE-N, WS-E, AL-I,

BHVO-2, Mica-Fe, JSd-2, and BCR-2.

44 1.05! 2013/Calibration! 2012/Calibration! Mean = 0.87 ± 0.04! 1! BE-N Mean = 0.85 ± 0.04! Decay Correction! WS-E 0.95! BHVO2

! AL-I Mica-Fe CPS 0.9! Al R

Mica-Fe 0.85!

DT-N

0.8!

Jsd-2 BCR-2

0.75! 0.10! 0.30! 0.50! 0.70! 0.90! 1.10! 1.30! 1.50! 1.70! 1.90! [Al]/[Na+Mg+Si]!

Figure 5.5: Al count rate ratios vs. [Al] as a fraction of [Na+Mg+Si].

1.05!

2013/Calibration!

BE-N 2012/Calibration! 1! Mean = 0.87 ± 0.04! Mean = 0.85 ± 0.04!

AL-I Decay Correction! 0.95! WS-E

! BHVO2 CPS 0.9! Al R

0.85!

BCR-2

0.8!

Jsd-2 BCR-2

0.75! 0.15! 0.20! 0.25! 0.30! 0.35! 0.40! [Al]/[Na+Mg+Si]!

Figure 5.6: Zoom in on Al count rate ratios vs. [Al] as a fraction of [Na+Mg+Si], at low Al concentrations.

In general, Si is the most abundant element in rocks that can be directly measured in the

APXS spectrum. Moreover, Si is particularly relevant, since it serves as a linchpin for the

APXS calibration (see [50] and [12]). It is the only predominantly PIXE excited analyte for

45 which the count rate ratios were plotted against the certiﬁcate concentrations.

Figure 5.7 shows that the count rate ratios for both campaigns lack the dichotomy seen in the other analytes and appear to have constant variance. For the 2013 campaign, Si

RCPS = 0.885 ± 0.025. For the 2012 campaign, Si RCPS = 0.879 ± 0.019. These values are well within error, showing a 0.7% diﬀerence between them.

0.95! 2013/Calibration! BHVO-2 2012/Calibration! 0.93! Mean = 0.885 ± 0.025! Mean = 0.879 ± 0.019! Decay Correction! 0.91! ! CPS 0.89! Si R

0.87!

0.85! GS-N DT-N GS-N

0.83! 14.5! 19.5! 24.5! 29.5! 34.5! [Si] (%)!

Figure 5.7: Si count rate ratios as a function of certiﬁcate [Si].

46 5.3.2 Predominantly XRF

Mn is a trace element found in nearly all rock samples. Given its scarcity and relatively low signal, high uncertainty and scatter were expected and observed in the count rate measurements. This can be seen in seen in Figure 5.8.

1.2! 2013/Calibration!

1.1! 2012/Calibration!

Mean = 0.75 ± 0.09! 1! AN-G Mean = 0.74 ± 0.04!

0.9! ! CPS 0.8! Mn R

0.7!

BCR-2 0.6!

Jsl-2 0.5!

0.4! 0.00! 0.05! 0.10! 0.15! 0.20! 0.25! 0.30! [Mn] (%) !

Figure 5.8: Mn count rate ratios as a function of certiﬁcate [Mn].

Although, Mn count rates were, on average, slightly greater at improved resolution, they were largely unaﬀected by resolution. For the 2013 campaign, Mn RCPS = 0.75 ± 0.09. For the 2012 campaign, Mn RCPS = 0.74 ± 0.05. These values are within error of each other and there is a 1.3% diﬀerence between them. It is worthwhile to note there is no visible campaign-based dichotomy in count rates. Although the 2013 campaign measurements have a better resolution than those taken in 2012, they exhibit a broader scatter. The Mn RCPS standard deviation for the 2013 campaign was 0.09; for 2012 it was 0.04.

In general, Fe is the most abundant element in rocks that is predominantly excited via

XRF interactions. The plots of Fe count rate ratios over certiﬁed Fe concentration can be

47 seen in Figure 5.9. The data are generally well behaved, except for a few notable samples.

UB-N is the GRM with the highest valued count rate change factor in the 2013 campaign.

BCR-2 shows depressed count rates relative to the calibration measurement across both campaigns. DR-N and SARM-39 also have depressed campaign count rates relative to the calibration. The trend of lower average count rates at poor resolutions, seen hitherto, was reversed. However, the dichotomy previously seen between campaigns is not observed for this element. The 2013 campaign Fe RCPS is 0.741 ± 0.019. For the 2012 campaign, Fe

RCPS = 0.750 ± 0.016. These values are within error of each other and there is a 1.2% diﬀerence between them.

0.81!

UB-N

0.79!

0.77! GXR-1 ! Mica-Fe CPS 0.75! Mica-Fe Fe R Fe

0.73! 2013/Calibration!

2012/Calibration!

0.71! Mean = 0.741 ± 0.019! Mean = 0.750 ± 0.016! SARM-39 DR-N BCR-2 BCR-2 0.69! 0! 5! 10! 15! 20! 25! [Fe] (%) !

Figure 5.9: Fe count rate ratios as a function of certiﬁcate [Fe].

Zn, the heaviest element chosen for analysis, is a trace element in rocks. Only eight samples have more than 0.02% Zn by weight. Of these, two are repeats (Mica-Fe and Mica-Mg were run in both the 2012 and 2013 campaigns). The ratios for the Zn count rates are found in

Figure 5.10. Given the low abundance of Zn in the samples and the consequent weak signal, relatively high scatter and uncertainty were expected and observed.

As was the case for Fe, Zn count rates are, on average, greater for measurements taken

48 at poorer resolutions. However, no campaign-based dichotomy is observed for this element either. For the 2013 campaign Zn RCPS = 0.70 ± 0.04. For the 2012 campaign Zn RCPS =

0.72 ± 0.03. Despite the 2.8% diﬀerence in these numbers, the results agree within the error estimates. It is worthwhile to note the decrease in these ratios compared to the other predominantly XRF excited elements.

0.9!

0.8! ! CPS 0.7! Zn R

0.6! 2013/Calibration!

2012/Calibration! 0.5! Mean = 0.70 ± 0.04!

Mean = 0.72 ± 0.03! 0.4! 0.00! 0.05! 0.10! 0.15! 0.20! [Zn] (%) !

Figure 5.10: Zn count rate ratios as a function of certiﬁcate [Zn].

0.9!

0.8! ! CPS 0.7! Zn R

0.6! 2013/Calibration!

2012/Calibration! 0.5! Mean = 0.70 ± 0.04!

Mean = 0.72 ± 0.03! 0.4! 0.000! 0.002! 0.004! 0.006! 0.008! 0.010! 0.012! 0.014! 0.016! [Zn] (%) !

Figure 5.11: Zoom in on Zn count rate ratios as a function of certiﬁcate [Zn] at low concentrations.

49 5.4 Discussion

Figure 5.12 shows the inverse-variance weighted averages for the light element count rate ratios (RCPS) as a function of characteristic Kα X-ray energy for both the 2012 and 2013 campaigns.

1.00!

0.95!

0.90! ! CPS 0.85!

0.80!

0.75! Weighted Mean R Weighted

0.70! 2013! 2012! 0.65! Si Mean = 0.882 ± 0.018! Decay Correction! 0.60! 1.0! 1.1! 1.2! 1.3! 1.4! 1.5! 1.6! 1.7! 1.8! Energy (keV)!

Figure 5.12: Na, Mg, Al, and Si mean count rate ratios as a function of energy.

The Na peak is aﬀected by its proximity to the low-energy cut-oﬀ of the spectrum [32].

The compounding of this cut-off with the peak broadening effect due to worsened resolution in the 2012 campaign results in the dichotomy seen in Figure 5.1, and partially explains the much lower Na RCPS in 2012 compared to Na RCPS in 2013. The identified outliers

are all basaltic rocks, except for BE-N, which is an altered basalt [51], and JSd-2, which

is a young basaltic sediment [46]. Looking at the mean light element composition of the

diﬀerent igneous GRMs utilized, found in Table 5.1, it can be seen that basaltic rocks have

the lowest Na content yielding relatively weak Na peaks. Notably, basaltic rocks have the

highest Mg abundance. As FWHM increases, resolution worsens, and the Na and Mg peak

overlap increases, the Na peak loses counts. Conversely, as FWHM decreases, resolution

improves, and the Na and Mg peaks are further separated, the Na peak gains counts.

50 Basalts Andesites Dacites [Na] 1.6±0.8 2.6±0.4 3.0±0.9 [Mg] 6±3 2.3±1.1 0.6±0.4 [Al] 8.0±2.2 8.4±0.8 7.7±0.6 [Si] 22.6±1.1 26.8±1.7 32.6±1.7

Table 5.1: Percent mean elemental composition for the diﬀerent igneous GRMs utilized for instrumental calibration [51].

The Mg peak is inﬂuenced by the size of its neighbouring peaks. Mg abundance in the

GRM suite used for this work spans a concentration range from 0.006% to 26.2%. The spectra from samples with relatively low Mg abundances may show a small Mg peak surrounded by Na, Al, or Si “mountains.” If this is the case, the uncertainty in the Mg peak area increases and the estimates may be altered. The 2013 campaign measurements for

Mg show an increase in count-rate in this situation. On the other hand, Mg measurements taken in 2012, with a wider FWHM, exhibit a decrease in the count rates. As the resolution worsens in the 2012 campaign, the ﬁtting code assigns Mg counts elsewhere resulting in

Mg RCPS = 0.79 ± 0.07, which is much lower than the expected 0.906. Although the Mg

RCPS = 0.82 ± 0.05 in 2013, which is higher than the 2012 value, it is not within error of the expected value.

As was the case for Na and Mg, Al count rates were lower, on average, for measurements taken at poor resolutions and a campaign-based dichotomy was observed. For the light elements, this dichotomy decreases as atomic number increases, becoming negligible at Si. This is believed to be a direct consequence of the worsened detector resolution. When resolution is worsened, peaks are widened and the peak tails change. In the case of overlapping peaks, such as this one, the local background for each peak is affected by changes in the tails of the neighbouring peaks. Of course, the situation only worsens for the peaks in the middle, which are affected by two neighbours. As FWHM increases, the peaks ‘blur’ into each other, and it is increasingly difficult for the filter to suppress the background. In short, the effect of worsened resolution on FEU-APXS acquired spectra, with overlapping peaks on a rapidly varying background, appears to be a systemic depression of estimated count rates.

51 Due to its abundance and accompanying high statistics, the most accurate peak area measurements are, in general, extracted from Si. Consequently, for both campaigns, the most accurate count rate ratio averages were acquired from this element. These were therefore chosen to determine the change in α-particle intensity from the “open” Cm sources between

May 29, 2009 and January 1, 2012, by taking their average. The result is Rα-particles =

0.882 ± 0.018. On January 1, 2012 the “open” sources in the FEU-APXS eﬀectively had

0.882 times the activity they did in May 29, 2009. This value is within 2σ of the expected decrease by a factor of 0.906.

For elements predominantly excited via XRF interactions, the mean count rate ratios, as a function of emission X-ray energy, can be seen in Figure 5.13. Although Mn and Fe are predominantly XRF excited elements, there is still a PIXE contribution to the total count rates. On average, for the samples analyzed, the percent X-rays emitted due to α-particles were 13%, 6%, and 1% for Mn, Fe, and Zn respectively [52]. However, this does not explain either the average increase in Fe count rates in 2012 or the low average Zn count rate ratios for both campaigns.

0.84! 2013! 2012! Mn & Fe Mean = 0.745 ± 0.025! 0.79! ! CPS 0.74!

0.69! Weighted Mean R Weighted

0.64!

0.59! 5.5! 6.0! 6.5! 7.0! 7.5! 8.0! 8.5! 9.0! Energy (keV)!

Figure 5.13: Mn, Fe, and Zn mean count rate ratios as a function of energy.

52 The count rate ratios for the predominantly XRF-excited analytes were used to compute the change-factor for the Pu L X-ray emission intensity between May 29, 2009 and Jan- uary 1, 2012, by taking their average. The Zn results were omitted from the average since their lower count rates relative to the calibration measurements are not fully understood.

These values were not corrected for PIXE contributions so that they are congruent with the methodology employed in the calibration, outlined in [40] and [50]. The resulting mean count rate ratio using Mn and Fe was determined as RPu L X-rays = 0.745 ± 0.025. This values is over 6σ away from the expected value of 0.906 and reﬂects that the closed sources were changed and the activity of the replacement sources is not accurately known.

The GUAPX calibration procedure for both the FEU and PFM APXS models is outlined in [40]. During this exercise, the total activity of each of the two source subsets

(“open” and “closed”) was approximately, but not precisely, the same. Consequently, the

α value of the parameter /LX was not equal to the accurately known value from available literature and had to be determined empirically. A trial-and-error method adjusting the H

α and /LX values until the mean ratios between the GUAPX concentrations and the certiﬁ- cate concentrations for both Fe and Si were within 1% of unity, across the GRM suite, was

α adopted [40]. This method, led to the /LX given in Table 4.1. The results above were used

α to independently determine the change in the /LX value between the calibration conﬁgura- tion (May, 29, 2009) and that used for both the 2012 and 2013 campaigns (January 1, 2012).

From the most abundant and reliable PIXE excited element, Si, the average count rate ratio from both campaigns was used as a proxy to Rα-particles = 0.882 ± 0.018. The predominantly XRF excited elements, Fe and Mn, had provided a mean Pu L X-ray intensity

α ratio of RPu L X-rays = 0.745 ± 0.025. The /LX change factor between the calibration and

campaign conﬁgurations can be determined by dividing Rα-particles by RPu L X-rays. This

α yields a correction factor of 1.18±0.04. Taking the same ratio from the /LX values given in Table 4.1 yields a value of 1.2, which is within error of the correction factor determined using the mean RCPS-values. This further proves the validity of the method used for the

α APXS calibration and strengthens the analyses by Dr. G. Perrett in determining the /LX

53 ratio for the various APXS conﬁgurations [50].

The change in peak area estimates for the two resolutional campaigns (2012 and 2013), relative to the calibration, was quantiﬁed by dividing the count rate acquired from the former by that of the latter. The elemental count rate ratios were weighted by the inverse of the square of the uncertainty output by GUAPX and averaged. Na, Mg, and Al showed a decrease in average count rate estimates with worsening resolution. Si and Mn were largely unaﬀected by resolution. Fe and Zn, at abundances higher than 0.05%, showed a slight increase in average count rate estimates with worsening resolution. Using the average

α change in count rates relative to the calibration, the /LX correction factor was computed as

1.18±0.04. This is within error of the independently deduced value of 1.2. It is concluded that varying FWHM in the instrument can, at least, partially aﬀect the spectral line count rates estimated by GUAPX in this rapidly varying, closely spaced, part of the spectrum.

The plot in Figure 5.14 summarizes the results discussed above, and includes the mean count rate ratios for the “intermediate” elements (K, Ca, Ti). These intermediate elements are further discussed in Section 6.2.2. The change in activity due to the replacement of the closed sources by a single closed source and its impact on the count rates is visible by inspection.

54 1.05! 2013/Calibration!

1.00! 2012/Calibration!

0.95!

! 0.90! CPS 0.85!

0.80!

0.75!

Weighted Mean R Weighted 0.70!

0.65!

0.60!

0.55! 1.0! 2.0! 3.0! 4.0! 5.0! 6.0! 7.0! 8.0! 9.0! Energy (keV)!

Figure 5.14: Mean count rate ratios as a function of energy for Na, Mg, Al, Si, K, Ca, Ti, Mn, Fe, and Zn.

The next step in extracting concentration data from spectra involves converting the acquired peak areas to elemental concentrations through use of the yield equation. Given the close relationship between estimated concentration and peak area, understanding the behaviour of peak area estimates, with respect to changes in resolution, is crucial in our goal of understanding the eﬀects of resolution on APXS analytical results.

55 Chapter 6

From Peak Area to Concentration (Matrix Eﬀects & The Closure Rule)

The next step in the processing of spectra is the conversion from peak areas to concentration estimates through the use of a standardization process. GUAPX’s IM mode, which employs the yield equation calibrated using the FPS approach, was used to achieve this. Since IM mode was used to treat the spectra, it is at this point in the process that matrix eﬀects are taken into account.

6.1 GUAPX Concentration Ratio R[C]

The methodology developed for the count-rate analyses was extended to investigate the

GUAPX concentration estimates. The changes in GUAPX concentration estimates from the 2012 and 2013 campaigns, relative to those from the calibration measurements, were quantiﬁed by dividing the former by the latter. This value is called the concentration ratio,

R[C].

6.2 Results

The elemental concentration ratios, R[C], for each GRM were plotted against the corresponding certiﬁed concentration. No numerical use was made here of these certiﬁed concentrations.

56 The inverse-variance weighted mean and 2σ bounds are provided for each campaign. This

allowed for the identiﬁcation of outliers and trends in the concentration ratios, with respect

to the certiﬁed concentration. The ten analytes were divided into three groups: those pre-

dominantly excited by PIXE interactions (Na, Mg, Al, Si), those excited by both PIXE and

XRF interactions (K, Ca, Ti), and lastly, those predominantly excited by XRF interactions

(Mn, Fe, Zn).

Given the dependence of concentration estimates on the peak area estimates, it is of

interest to see how the changes seen in count rate (and thus peak area) estimates compare

with changes seen in concentration estimates. To aid this comparison, plots of both count

rate and concentration ratios against certiﬁed concentration are provided. The range of

elemental concentrations seen on Mars is also provided by a black arrow on the upper portion

of the plots. The concentration estimates’ behaviour within this range is of particular

interest. All GRMs shown in the plots, including the labeled outliers, were utilized for

computing the mean and standard deviation for each campaign.

57 6.2.1 Predominantly PIXE

1.1 Martian Range 1.1 Martian Range WS-E PM-S WS-E PM-S BE-N (AB) BE-N

1 1

0.9 0.9

0.8 0.8 2012 2012 2013 2013 Na Count Rate Ratio SRM688 0.7 Mean=0.80 Na Concentration Ratio 0.7 BHVO-2 Mean=0.86 2σ=0.13 2σ=0.11 BHVO-2 JSd-2 Mean=0.89 Mean=0.95 SRM688 2σ=0.13 2σ=0.10 0.6 0.6 0 2 4 6 8 0 2 4 6 8 Na Certiﬁcate Concentration (%) Na Certiﬁcate Concentration (%)

Figure 6.1: Na count rates (left) and concentration ratios (right) as a function of certiﬁcate [Na].

Figure 6.1 shows that the campaign-based dichotomy observed in the count rates is carried

through to the concentration estimates. The ratios from the 2013 campaign are consis-

tently higher in value than those of the 2012 campaign. The concentration ratios exhibit

less scatter than the count-rate ratios across all campaigns. For the 2012 campaign, Na

R[C] = 0.86 ± 0.11. For the 2013 campaign, R[Na] = 0.95 ± 0.10. Despite the 9.9% diﬀerence in these values, the results agree within the error estimates. Some of the samples fall outside

the 2σ bounds in the 1.5% - 2.5% Na concentration range. These outliers are identiﬁed on

the plot. Except for the JSd-2, a young Japanese basaltic sediment [46], and BE-N, an al-

tered basaltic rock [51], all outliers are basaltic rocks; this is further discussed in Section 5.4.

Figures 6.2 and 6.3 show the campaign-based dichotomy seen in the count-rate ratios is

mirrored in the concentration ratios. In the concentration range from 9 - 30% Mg, the ratios

58 are equal to unity, or close to it. As the Mg abundance falls and the Mg peak weakens, the

concentration estimates increase for the 2013 campaign. Conversely for the 2012 campaign,

as the Mg abundance falls, so do the count-rate and concentration estimates. Outliers are

identiﬁed on the plots. Note, as the Mg peak becomes less prominent, there is more uncer-

tainty in the peak area measurements, as is expected.

1.2 1.3

Martian Range Martian Range 1.1 1.2 AN-G WS-E WS-E AGV-2 BCR-2 1 AN-G 1.1 AGV-2 BE-N BHVO-2 0.9 Mica-Fe 1

0.8 0.9

GXR-1 0.7 2012 0.8 BCR-2 2012 2013 2013

Mg Count Rate Ratio QLO-1 & GSP-2

JSd-2 Mean=0.79 Mg Concentration Ratio Mean=0.96 QLO-1 & GSP-2 0.6 BCR-2 2σ=0.14 0.7 2σ=0.15 Mean=0.82 Mean=1.01 2σ=0.10 2σ=0.10 0.5 0.6 0 5 10 15 20 25 0 5 10 15 20 25 Mg Certiﬁcate Concentration (%) Mg Certiﬁcate Concentration (%)

Figure 6.2: Mg count rates (left) and concentration ratios (right) as a function of certiﬁcate [Mg].

59 1.2 1.3

Martian Range Martian Range 1.1 1.2 AN-G

AGV-2 WS-E WS-E BCR-2 1 AN-G 1.1 AGV-2 BE-N (AB) Mica-Fe BHVO-2 0.9 1

0.8 0.9

2012 2012 GXR-1 0.7 0.8 BCR-2 2013 2013 Mg Count Rate Ratio QLO-1 Mean=0.96

JSd-2 Mean=0.79 Mg Concentration Ratio GSP-2 QLO-1 BCR-2 2σ=0.15 GSP-2 2σ=0.14 0.6 0.7 Mean=1.01 Mean=0.82 2σ=0.10 2σ=0.10 0.5 0.6 0 2 4 6 8 0 2 4 6 8 Mg Certiﬁcate Concentration (%) Mg Certiﬁcate Concentration (%)

Figure 6.3: Zoom in on Mg count rates (left) and concentration ratios (right) as a function of certiﬁcate [Mg].

For the 2013 campaign, Mg R[C] = 1.01 ± 0.10. For the 2012 campaign, Mg R[C] = 0.96 ± 0.15. Despite the 5.1% diﬀerence in these values, the results agree within the error

estimates.

Figures 6.4 and 6.5 show that the subtle campaign-based dichotomy observed in the Al

count rates is carried through to the concentration estimates. For the 2013 campaign, Al

R[C] = 1.01 ± 0.04. For the 2012 campaign, Al R[C] = 0.98 ± 0.04. Despite the 3.0% diﬀer- ence in these values, the results agree within the error estimates. BE-N and WS-E are the

two biggest outliers visible by inspection.

60 1.1 Martian Range 2012 Martian Range 2012 1 WS-E 2013 2013 Mean=0.85 WS-E Mean=0.98 2σ=0.07 2σ=0.04 BE-N (AB) Mean=0.87 BE-N (AB) Mean=1.01 0.95 BHVO-2 1.05 2σ=0.07 2σ=0.04

0.9 1

0.85

Al Count Rate Ratio 0.95 0.8 Al Concentration Ratio

0.75 0.9 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Al Certiﬁcate Concentration (%) Al Certiﬁcate Concentration (%)

Figure 6.4: Al count rates (left) and concentration ratios (right) as a function of certiﬁcate [Al].

For Al, as for Mg, the concentration range seen on Mars is much narrower than that of

the selected terrestrial GRMs. Limiting the analysis to samples within the Martian range, a

subtle dichotomy between higher valued 2013 campaign ratios and the smaller valued 2012

campaign ratio is observed.

1.1

1 WS-E Martian Range Martian Range WS-E

BE-N (AB) BE-N (AB) 0.95 BHVO-2 1.05

0.9 1

0.85 2012 2012

Al Count Rate Ratio 2013 0.95 2013 0.8 Mean=0.85 Al Concentration Ratio Mean=0.98 2σ=0.07 2σ=0.04 Mean=0.87 Mean=1.01 2σ=0.07 2σ=0.04 0.75 0.9 2 4 6 8 10 12 2 4 6 8 10 12 Al Certiﬁcate Concentration (%) Al Certiﬁcate Concentration (%)

Figure 6.5: Zoom of Al count rates (left) and concentration ratios (right) as a function of certiﬁcate [Al].

61 Si

1.05 BHVO-2 0.94 Martian Range Martian Range 1.04

0.92 UB-N BCR-2 1.03 0.9 1.02 0.88

1.01 0.86

2012 2012 0.84 1 Si Count Rate Ratio 2013 2013 Mean=0.879 Si Concentration Ratio Mean=1.010 2σ=0.038 0.99 2σ=0.017 0.82 BCR-2 Mean=0.885 Mean=1.004 AN-G 2σ=0.049 2σ=0.018 0.8 0.98 10 15 20 25 30 35 40 10 15 20 25 30 35 40 Si Certiﬁcate Concentration (%) Si Certiﬁcate Concentration (%)

Figure 6.6: Al count rates (left) and concentration ratios (right) as a function of certiﬁcate [Al].

Figure 6.6 shows Si R[C] = 1.004 ± 0.018 for the 2013 campaign, and 1.010 ± 0.017 for the 2012 campaign. These values are well within error of each other, with a 0.6% diﬀerence

between them. There are three samples outside the 2σ bounds: UB-N, AN-G, and BCR-2.

A campaign-based dichotomy can be observed between the concentration ratios that is not

visible in the count-rate. The 2012 campaign exhibits ratios that, on average, have a higher

value than those from the 2013 campaign.

6.2.2 PIXE & XRF

It is noted that the count-rate behaviour for these intermediate elements (K, Ca, Ti) was not

discussed in Chapter5. Their count-rate plots are discussed here in the context of mapping

from peak areas to concentrations.

Figure 6.7 shows a strong correlation between estimated peak areas and estimated concen-

trations. However, there is a separation of concentration ratio values between campaigns

62 that is not reﬂected in the count rate ratios. A dichotomy can be seen between the concen-

tration ratios. The 2012 campaign exhibits ratios that have a higher value than those from

the 2013 campaign. For the 2013 campaign, K R[C] = 0.99 ± 0.11. For the 2012 campaign,

K R[C] = 1.02 ± 0.12. Despite the 3.0% diﬀerence in these values, the results agree within error estimates.

Martian Range 1.1 Martian Range

0.9 1

0.8 0.9

2012 0.8 2012 PM-S K Count Rate0 Ratio .7 SARM39 (UM) 2013 2013

K Concentration Ratio AN-G & PM-S PM-S Mean=0.87 Mean=1.02 PM-S 2σ=0.11 2σ=0.12 AN-G Mean=0.86 0.7 Mean=0.99 2σ=0.11 2σ=0.11 0.6 0 2 4 6 8 10 0 2 4 6 8 10 K Certiﬁcate Concentration (%) K Certiﬁcate Concentration (%)

Figure 6.7: K count rates (left) and concentration ratios (right) as a function of certiﬁcate [K].

Figure 6.8 zooms in on the domain below 4% K certiﬁcate concentration. Here, the

biasing of concentration estimates from lower resolution observations toward higher values

can be observed.

63 1 1.15

Martian Range Martian Range 0.95 1.1

0.9 1.05

1 0.85

2012 0.95 2012

K Count Rate Ratio 2013 2013

0.8 K Concentration Ratio Mean=0.87 Mean=1.02 2σ=0.11 2σ=0.12 Mean=0.86 0.9 Mean=0.99 0.75 2σ=0.11 2σ=0.11 0 0.5 1 1.5 2 2.5 3 3.5 0 0.5 1 1.5 2 2.5 3 3.5

K CertiﬁcateSARM39 (UM) Concentration (%) K Certiﬁcate Concentration (%)

PM-S FigurePM-S 6.8: Zoom of K count rates (left) and concentration ratios (right) as a function of PM-S certiﬁcateAN-G [K]. AN-GPM-S

PM-S and AN-G are outside the 2σ bounds of the concentration ratio mean and are

primarily responsible for the large variation quantiﬁed by the standard deviation. The PM-S

certiﬁcate indicates working values of 0.14±0.02 wt% and 12.48±0.26 wt% for K2O and CaO

respectively. The AN-G certiﬁcate indicates working values of 0.13±0.04 wt% and 15.9±0.5

wt% for K2O and CaO respectively. It seems when there is a great abundance of Ca and

a relatively low amount of K, the widened Ca peak “steals” counts from K. Omitting these

two GRMs from the mean and standard deviation calculations yields K R[C] = 0.99 ± 0.05 for the 2013 campaign and 1.02±0.06 for the 2012 campaign.

For the 2013 campaign, Ca R[C] = 0.989 ± 0.028. For the 2012 campaign, Ca R[C] = 1.00 ± 0.06. Despite the 4.0% diﬀerence in these numbers, the results agree within the error

estimates. The GXR-1 GRM lies outside the 2σ bounds. Again, there is a separation of

concentration ratio values between campaigns that is not reﬂected in the count rate ratios.

The 2012 campaign exhibits ratios that have a slightly higher value than those from the

2013 campaign.

64 1

Martian Range 1.1 Martian Range

0.95 GXR-1

GXR-1

0.9 1.05

0.85 1 2012 2012 2013 2013 Ca Count Rate Ratio

0.8 Mean=0.86 Ca Concentration Ratio Mean=1.03 BCR-2 2σ=0.06 2σ=0.06 BCR-2 Mean=0.85 Mean=0.989 SARM39 (UM) 2σ=0.05 0.95 2σ=0.028 0.75 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16 Ca Certiﬁcate Concentration (%) Ca Certiﬁcate Concentration (%)

Figure 6.9: Ca count rates (left) and concentration ratios (right) as a function of certiﬁcate [Ca].

Figure 6.10 shows a systematic separation of the 2013 concentration ratios relative to the

2012 ratios. This separation is not reﬂected in the count rate ratios. The 2012 campaign

exhibits ratios that have a higher value than those from the 2013 campaign. For the 2013

campaign, Ti R[C] = 0.96 ± 0.07. For the 2012 campaign, Ti R[C] = 1.00 ± 0.05. Despite the 4.1% diﬀerence in these numbers, the results agree within the error estimates. The BCR-2

and SARM-39 GRMs lie outside the 2σ bounds.

65 0.9 1.1 Martian Range

Martian Range SARM39 (UM)

0.85 1.05

0.8 1

0.75 0.95 BCR-2 2012 2012

Ti Count Rate Ratio 2013 2013

0.7 Mean=0.80 Ti Concentration Ratio 0.9 Mean=1.00 2σ=0.04 2σ=0.05 Mean=0.79 BCR-2 Mean=0.96 BCR-2 2σ=0.06 2σ=0.07 0.65 0.85 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Ti Certiﬁcate Concentration (%) Ti Certiﬁcate Concentration (%)

Figure 6.10: Ti count rates (left) and concentration ratios (right) as a function of certiﬁcate [Ti].

6.2.3 Predominantly XRF

Mn is a trace element; due to its relatively low signal, high uncertainty and scatter were

expected and observed. Figure 6.11 shows no major alterations in the mapping from count

rates (peak areas) to concentration estimates for Mn. For the 2013 campaign, Mn R[C] =

1.00 ± 0.23. For the 2012 campaign, R[Mn] = 1.00 ± 0.10. These values are identical. It is interesting that although the 2013 campaign measurements have a better resolution than

those taken in 2012, they exhibit a broader scatter. This is described by the diﬀerence in

the standard deviations of both campaign averages.

66 1.2

Martian Range 1.4 Martian Range

1 AN-G AN-G 1.2

0.8 1

2012 2012 0.6 2013 2013 Mn Count Rate Ratio 0.8

Mean=0.74 Mn Concentration Ratio Mean=1.00 JSl-2 2σ=0.08 2σ=0.10 Mean=0.75 JSl-2 Mean=1.00 2σ=0.17 2σ=0.23 0.4 0.6 0 0.2 0.4 0.6 0 0.2 0.4 0.6 Mn Certiﬁcate Concentration (%) Mn Certiﬁcate Concentration (%)

Figure 6.11: Mn count rates (left) and concentration ratios (right) as a function of certiﬁcate [Mn].

Figure 6.12 shows a systematic separation of the 2013 campaign concentration ratios relative

to those from the 2012 campaign. This separation is reﬂected in the count-rate ratios. There

is a dichotomy between the higher valued 2012 campaign concentration ratios and the lower

valued 2013 concentration ratios. For the 2013 campaign, Fe R[C] = 0.98 ± 0.05, for the

2012 campaign, Fe R[C] = 1.02 ± 0.04. Despite the 4.0% diﬀerence in these numbers, the results agree within the error estimates.

67 SARM39 (UM) UB-N 0.8 Martian Range 1.1 Martian Range

UB-N GS-N 0.78 1.05

0.76

1 0.74

2012 2012

Fe Count Rate0 Ratio .72 2013 0.95 2013 Mean=0.75 Fe Concentration Ratio Mean=1.02 2σ=0.03 2σ=0.04 0.7 SARM39 (UM) Mean=0.74 Mean=0.98 DR-N BCR-2 BCR-2 2σ=0.04 2σ=0.07 0.9 0 5 10 15 20 25 0 5 10 15 20 25 Fe Certiﬁcate Concentration (%) Fe Certiﬁcate Concentration (%)

Figure 6.12: Fe count rates (left) and concentration ratios (right) as a function of certiﬁcate [Fe].

Zn is a trace element in rocks. Given the low abundance of Zn in the samples and con-

sequent weak signal, high scatter and uncertainty were expected and observed in Figures

6.13 and 6.14. For the 2013 campaign, Zn R[C] = 0.95 ± 0.15. For the 2012 campaign,

Zn R[C] = 1.02 ± 0.10. Despite the 7.0% diﬀerence in these numbers, the results agree within the error estimates. The concentration ratios corresponding to samples with high Zn

abundance diverge between campaigns; this behaviour is less pronounced in the count rate

ratios. Looking at samples with low Zn abundance a campaign-based separation of ratios is

not discernible. It is worthwhile to note that the decrease in the inverse-variance weighted

mean from the 2013 campaign relative to that from 2012 campaign is heavily inﬂuenced by

the high Zn abundance samples.

68 1 1.3

Martian Range SARM39 (UM) Martian Range 1.2 0.9

1.1 0.8

0.7 0.9 2012 2012 2013 2013 Zn Count Rate Ratio

0.6 Mean=0.71 Zn Concentration Ratio Mean=1.02 2σ=0.07 0.8 2σ=0.10 Mean=0.70 Mean=0.95 2σ=0.08 2σ=0.15 0.5 0.7 0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2 Zn Certiﬁcate Concentration (%) Zn Certiﬁcate Concentration (%)

Figure 6.13: Zn count rates (left) and concentration ratios (right) as a function of certiﬁcate [Zn].

1 1.3

Martian Range SARM39 (UM) Martian Range 1.2 0.9

1.1 0.8

0.7 0.9 2012 2012 2013 2013 Zn Count Rate Ratio

0.6 Mean=0.71 Zn Concentration Ratio Mean=1.02 2=0.07 0.8 2=0.10 Mean=0.70 Mean=0.95 2=0.08 2=0.15 0.5 0.7 0 0.005 0.01 0.015 0.02 0.025 0.03 0 0.005 0.01 0.015 0.02 0.025 0.03 Zn Certiﬁcate Concentration (%) Zn Certiﬁcate Concentration (%)

Figure 6.14: Zoom in on Zn count rates (left) and concentration ratios (right) as a function of certiﬁcate [Zn].

69 6.3 Discussion

As discussed in Section 2.4.3, in IM mode, GUAPX commences with a preliminary fit of the spectrum in which no matrix corrections are done. The resulting peak areas are converted via the yield equation (Equation 2.9) into element concentrations, and then into oxide concentrations via assumed stoichiometry. The closure rule is invoked and the total concentration is normalized to 100% to provide a first estimate of the sample composition. This estimate is used to generate the matrix corrections during the second iteration, which yields a new set of concentrations. The process is iterated, with the goodness-of-fit re-optimized within each iteration, until the matrix concentrations are consistent.

Given the dependence of concentration estimates on the peak area estimates, the compiled GUAPX analytical results are well suited to investigate the effects of the closure rule and iteratively deduced matrix corrections on the conversion from peak areas to concentration estimates at various resolutions. Figure 6.15 shows how the percent differences in count rate (peak area) estimates, seen in Chapter5, compare with the percent differences in concentration estimates, presented here. The plot shows the percent differences between the

2012 campaign ratios relative to those from the 2013 campaign, for each element analyzed.

In the previous chapter, it was concluded that varying FWHM can aﬀect the spectral- line peak areas determined by GUAPX. As shown in Figure 6.15, Na, Mg, Al, and to a lesser extent Si and Mn, show a decrease in average count rate estimates with worsening resolution. Conversely, K, Ca, Ti, Fe, and Zn show a more moderate increase in average count rate estimates with worsening resolution.

In general, the changes in concentration estimates for all elements except Si and Mn were very closely linked to the changes seen for count-rate estimates. The pattern of decreasing/increasing count rate concentration estimates with worsening resolution was carried over to decreasing/increasing concentration estimates for Na, Mg, Al, K, Ca, Ti, Fe, and

Zn. Paradoxically, Si showed a decrease in count-rates and an increase in concentration

70 Na! Concentration Ratio!

Mg! Count Rate Ratio!

Al!

Si!

Ca!

Ti! Atomic Number (Z) Atomic

Mn!

Fe!

Zn!

-12! -10! -8! -6! -4! -2! 0! 2! 4! 6! 8! Percent Diﬀerence

Figure 6.15: Percent diﬀerence from average 2013 campaign ratios to average 2012 campaign ratios.(2012−2013)/Mean. estimates with worsening resolution. Mn exhibited a large enough uncertainty that no conclusions were drawn.

The percent diﬀerences seen for Na, Mg, and Al mean concentration ratios closely match the percent diﬀerences seen for their peak area ratios. Except for Mn, the remaining elements showed a systematic increase in mean concentration ratios with worsening resolution.

For K, Ca, and Ti, the small percent difference in the average count-rate ratios between campaigns was amplified to a larger percent difference in the average of the estimated concentrations. As seen in Figures 6.6 and 6.12, a campaign-based dichotomy was induced in the concentration estimates for Si and Fe by processing the peak areas, which showed no such campaign-based difference.

There are three underlying causes for the patterns seen in the concentration ratios: the correlation between estimated count rates and estimated concentrations; the matrix corrections; and the closure rule.

71 6.3.1 Mapping Count Rates to Concentrations

As discussed earlier, the concentration estimates output by GUAPX are primarily dependent on the estimated peak area. In effect the measured peak area provides a first order estimate of the constituent concentration. This estimate is then refined by taking matrix effects into consideration. Na, Mg, Al, and Mn exemplify the mapping from count-rate to concentration, showing no major deviations from the former to the latter.

As seen in Chapter5, at poor resolutions the light elements (Na, Mg, Al) lose counts; conversely, with improved resolution those same elements gain counts. It would be expected that this gain or loss in counts is mapped directly to the concentration estimates. Looking at the concentration ratios for Na, Mg, and Al, this is indeed the observed behaviour; higher count-rate ratios map to higher concentration ratios. This correlation is not observed for the Si and Fe concentration ratios.

6.3.2 Matrix Corrections and the Closure Rule

Si and Mn concentration ratios exhibit a behaviour that diverges from that seen in the count-rate ratios. The count-rate ratios for both of these elements were well behaved. They lacked the dichotomy seen in other elements like Na, Mg, and Al, showing constant variance about means close in value across both campaigns. However, a campaign-based dichotomy emerged in their concentration ratios opposite to the one seen for the lightest elements.

Whereas Na, Mg, and Al showed lower concentration estimates at poor resolution, Si showed higher concentration estimates at poorer resolutions. Mn showed no change. Conversely, with improved resolution Na, Mg, and Al, showed higher concentration ratios, while Si and

Fe exhibited lower concentration ratios. This is an eﬀect of the “closure” rule and matrix corrections applied by GUAPX.

In the previous chapter, it was concluded that varying FWHM in the instrument can aﬀect the spectral-line peak areas estimated by GUAPX. When using IM mode, the underestimation of light element abundances results in an erroneous matrix correction. The

72 average atomic number of the estimated matrix is higher than that of the actual matrix.

The attenuation increases more for the light element X-rays and less for the heavier element

X-rays. This explains the diﬀerential eﬀect favouring the heavier element concentrations relative to the light element concentrations that was observed for Si, K, Ca, Ti, Fe, and Zn in the results presented here, as well as in Chapter3.

6.3.3 Mg Correction

Assuming that measurements taken with improved resolution, as part of the 2013 campaign, are closer to reality than those taken at poor resolution, it is worthwhile to consider corrections to the calibration based on the results presented here. As discussed in Section 5.4, the Mg peak is inﬂuenced by the size of its neighbouring peaks. When there are relatively low amounts of Mg in the sample, a small Mg peak may be surrounded by Na, Al, or Si

“mountains.” As the resolution worsens, the ﬁtting code assigns Mg counts elsewhere, resulting in much lower Mg peak areas, and much lower Mg concentration estimates. Thus, if measurements were taken at an improved resolution, then higher count rates would be expected.

Mg concentration ratios from the 2013 campaign relative to the calibration data set have been plotted against the certiﬁcate Mg concentration in Figure 6.16, provided by Dr. J. L.

Campbell. The plot stops at 8% Mg because samples with higher Mg concentration have a ratio very near 1.00. The result shows that as the Mg abundance falls, the 2013/Cali- bration concentration ratio increases, as expected. Moreover, the relationship appears to be linear. Thus, the ﬁt results computed by Dr. Campbell provide a gross correction to deal with the systematic depression of Mg concentration estimates taken at lower resolutions.

73 Figure 6.16: Mg concentration estimates as a function of certiﬁed abundance [51].

The correction derived from the figure successfully resolves some discrepancies in data used by the Dr. Perrett in her efforts to quantitatively determine the mineral phase effects observed in APXS analyses of GRMs [53, 54].

The mapping from estimated peak areas to estimated concentrations by GUAPX was probed with regards to variations in resolution. The change in concentration estimates between the two 2012 and 2013 campaigns was quantified by way of a ratio relative to the concentration estimates from the corresponding calibration spectra. A differential effect favouring the heavier element concentrations with worsening resolution, similar to that described in Section 3.1, was observed. The concentration estimates for Na, Mg, and Al were very closely linked to their corresponding count-rate estimates. The remaining elements (Si,

K, Ca, Ti, Mn, Fe, and Zn) showed a systematic oﬀset between campaigns when mapping from count-rates to concentration ratios.

In Chapter5 it was concluded that poor resolution can lead to an underestimation of light-element peak areas by GUAPX. When using IM mode, this underestimation results

74 in an erroneous matrix correction. The average atomic number of the estimated matrix is higher than that of the actual matrix. The attenuation increases more for the light element

X-rays and less for the heavier element X-rays. This would help explain the differential effect favouring the heavier element concentrations that was observed for Si, K, Ca, Ti, Fe, and Zn in the results above, as well as in Section 3.1. A gross correction for the systematic depression of Mg concentration estimates at lower instrumental resolution, based on the present data, was determined. This proved helpful in the quantitative determination of mineral phase effects observed in APXS analyses of GRMs [53].

75 Chapter 7

Concentration and Resolution

In the previous two chapters, APXS-GUAPX derived data products were used to investigate the effects of resolution on concentration estimates by analyzing the different steps of the spectrum evaluation process. A differential effect favouring the heavier element concentrations with worsening resolution was observed. The observed variations in concentration were found to be related to changes in the peak area estimates for the light elements. The focus of this chapter is on quantifying the relationship between resolution and concentration estimates.

The methodology developed to quantify changes in count-rate and concentration estimates was extended to analyze changes in resolution. The relationship between change in resolution and change in estimated concentration was investigated by use of regression analysis, for ten elements of interest, over the entire GRM suite, and the subset within the

Martian concentration range. The slope estimated from the regression was used to quantify this relationship. The variability in concentration estimates was compared with the mean precision error, output by GUAPX, on an elemental basis.

7.1 FWHM Ratio (RFWHM)

The methodology developed for the count-rate and concentration analyses was extended to investigate changes in resolution on a ﬁner basis than hitherto. The changes in the FWHM at the Mn Kα line from the 2012 and 2013 campaign spectra, relative to the calibration measurements, were quantiﬁed by dividing the former by the latter. The resulting quantity

76 is called the FWHM ratio, RFWHM.

The previously calculated concentration ratios were plotted against their corresponding

FWHM ratios. A routine was employed to identify linear trends at the 95% confidence level by way of an inverse-variance weighted least-squares (WLS) regression. An inverse-variance weighted linear regression was chosen to give more weight to more accurately determined concentration estimates. The slope from the regression fit and the coefficient of determination were provided for the elements analyzed. It is noted that the size for each GRM marker on the plot varies with respect to the certificate concentration of the chosen analyte.

The WLS regression minimizes the sum of squared residuals with respect to the linearly transformed variables. Assuming the appropriate weighting scheme was chosen, a better ﬁt will be achieved by WLS in the transformed coordinates. Drawbacks of employing WLS regression include some loss in interpretability and a coeﬃcient of determination that is frequently much larger than the value obtained from an Ordinary Least Squares (OLS) regression [55]. For this reason, both the WLS and OLS adjusted R2 are provided below.

7.2 Results

The estimated concentration ratios are plotted with respect to their corresponding FWHM ratios. For each element, plots are provided for all GRMs analyzed, as well as those within the concentration ranges seen on Mars. Statistically signiﬁcant linear trends found at the

95% confidence level are plotted along with the confidence interval for the slope. The variable adjusted coefficient of determination (R2) for the fit is provided as well. All data points on the plots were used in the mean computation. In other words, the red and blue data are all within the fit shown.

77 7.2.1 Primarily PIXE

The Na concentration ratios in Figure 7.1 show a negative correlation with respect to the

FWHM ratio. As the resolution worsens, the estimated concentration decreases.

Martian Range 1.1 1.1 WS-EPM-S WS-EPM-S BE-N BE-N

1 1

0.9 0.9

0.8 2012 0.8 2012 2013 2013

Na Concentration Ratio y=-0.47x + 1.340 Na Concentration Ratio y=-0.55x + 1.48 SRM688 SRM688 0.7 95% C.I. BHVO-2 0.7 95% C.I. BHVO-2 Adj R2 = 0.60 Adj R2 = 0.68 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 Mn FWHM Ratio Mn FWHM Ratio

Figure 7.1: Na concentration ratios as a function of FWHM ratio for the full GRM suite (left) and for the Martian concentration range (right).

Individually, the Na 2013 R[C] show a linear correlation over the entire GRM suite and the Martian range. Those from the 2012 campaign do not show a statistically signiﬁcant

linear trend.

78 Mg

1.4 1.2 2012 Martian Range 2013 WS-E Mean=1.00 2σ=0.20 1.1 1.2 AN-G

1 1

0.9 2012 0.8 BCR-2 2013 GSP-2 Mg Concentration Ratio QLO-1 Mg Concentration Ratio y=-0.87x + 1.88 0.8 95% C.I. Adj R2 = 0.78 0.6 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 0.9 0.95 1 1.05 1.1 1.15 1.2 Mn FWHM Ratio Mn FWHM Ratio

Figure 7.2: Mg concentration ratios as a function of FWHM ratio for the full GRM suite (left) and for the Martian concentration range (right).

In general, the Mg concentration ratios in Figure 7.2 show a negative correlation with re-

spect to the FWHM ratio. As the resolution worsens, the estimated concentrations decrease.

Samples with a high abundance of Mg have concentration estimates that are unaﬀected by

changes in FWHM and have a strong inﬂuence on the linear ﬁt.

Individually, the Mg 2012 R[C] show a linear correlation over the entire GRM suite and the Martian range. The ratios from the 2013 campaign over the Martian range do as well,

but not over the entire range.

The Al concentration ratios in Figure 7.3 show a negative correlation with respect to the

FWHM ratio. As the resolution worsens, the estimated concentrations decrease. Individu-

ally, the Al 2013 R[C] values show a linear correlation over the entire GRM suite and the Martian range. Those from the 2012 campaign do not show a statistically signiﬁcant linear

trend.

79 2012 WS-E WS-E Martian Range 2013 1.05 BE-N (AB) y=-0.26x + 1.26 1.05 95% C.I. Adj R2 = 0.50

1 1

0.95 2012 2013

Al Concentration Ratio y=-0.17x + 1.17 Al Concentration Ratio 0.95 0.9 95% C.I. Adj R2 = 0.29 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 0.9 0.95 1 1.05 1.1 1.15 1.2 Mn FWHM Ratio Mn FWHM Ratio

Figure 7.3: Al concentration ratios as a function of FWHM ratio for the full GRM suite (left) and for the Martian concentration range (right).

1.04 1.04 Martian Range UB-N BCR-2 UB-N

BHVO-2

1.02 1.02

1 1 2012 2012 2013 2013 Si Concentration Ratio y=0.045x + 0.960 Si Concentration Ratio y=0.058x + 0.948 95% C.I. 95% C.I. AN-G Adj R2 = 0.25 Adj R2 = 0.21 0.98 0.98 0.8 0.9 1 1.1 1.2 0.8 0.9 1 1.1 1.2 Mn FWHM Ratio Mn FWHM Ratio

Figure 7.4: Si concentration ratios as a function of FWHM ratio for the full GRM suite (left) and for the Martian concentration range (right).

The Si concentration ratios in Figure 7.4 show a positive correlation with respect to the

FWHM ratio. As the resolution worsens, the estimated Si concentrations increase. Sep-

arately, the Si concentration ratios from the 2013 campaign show a linear trend over the

entire GRM suite and the Martian range. Those from the 2012 campaign do not show a

80 statistically signiﬁcant linear trend. Notably, UB-N is estimated as having 11% additional

light invisible elements and is a clear outlier.

7.2.2 PIXE & XRF

The K concentration ratios show a positive correlation with respect to the FWHM ratio. As

the resolution worsens, the estimated concentration increases.

Martian Range

1 1.05

0.9 1

0.8 PM-S 2012 0.95 2012 AN-G PM-S 2013 SARM5 2013 K Concentration Ratio K Concentration Ratio y=0.23x + 0.76 y=0.25x + 0.74 0.7 95% C.I. 95% C.I. BE-N (AB) Adj R2 = 0.64 0.9 Adj R2 = 0.29 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 0.9 0.95 1 1.05 1.1 1.15 1.2 Mn FWHM Ratio Mn FWHM Ratio

Figure 7.5: K concentration ratios as a function of FWHM ratio for the full GRM suite (left) and for the Martian concentration range (right).

Separately, the K concentration ratios from the 2013 campaign show a linear correlation

over the entire GRM suite and the Martian range. The ratios from the 2012 campaign do

as well over the entire range, but not over the Martian range.

The Ca concentration ratios show a positive correlation with respect to the FWHM ratio.

As the resolution worsens, the estimated concentrations increase. Separately, the Ca con-

centration ratios do not show linear trends for the 2012 campaign over the entire GRM suite,

or the Martian range. Neither do the ratios from the 2013 campaign over the Martian range.

The 2013 ratios over the entire GRM set are the only ones to show linear trends.

81 1.1 2012 2013 1.06 Martian Range y=0.22x + 0.78 GXR-1 95% C.I. 1.04 Adj R2 = 0.45 1.05 1.02

1 0.98 2012 2013 Ca Concentration Ratio Ca Concentration Ratio 0.96 y=0.24x + 0.76 95% C.I. 0.95 Adj R2 = 0.48 0.94 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 Mn FWHM Ratio Mn FWHM Ratio

Figure 7.6: Ca concentration ratios as a function of FWHM ratio for the full GRM suite (left) and for the Martian concentration range (right).

The Ti concentration ratios show a positive correlation with respect to the FWHM ratio.

As the resolution worsens, the estimated concentrations increase. Individually, neither the

2013, nor the 2012 concentration ratios, show a linear correlation over the entire GRM suite

or the Martian range.

1.1 Martian Range SARM39 (UM) 1.05 1.05

1 1

0.95

2012 2012 2013 2013

Ti Concentration Ratio 0.9 Ti Concentration Ratio 0.95 y=0.18x + 0.80 y=0.23x + 0.76

BCR-2 95% C.I. 95% C.I. Adj R2 = 0.14 Adj R2 = 0.39 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 0.9 0.95 1 1.05 1.1 1.15 1.2 Mn FWHM Ratio Mn FWHM Ratio

Figure 7.7: Ti concentration ratios as a function of FWHM ratio for the full GRM suite (left) and for the Martian concentration range (right).

82 7.2.3 Predominantly XRF

The Mn concentration ratios show a negative correlation with respect to the FWHM ratio.

As the resolution worsens, the estimated concentrations decrease. Individually, the Mn 2013

R[C] values show a linear correlation over the entire GRM suite and the Martian range. Those from the 2012 campaign do not show a statistically signiﬁcant linear trend.

1.4 2012 Martian Range 2012 1.4 2013 2013 y=-0.36x + 1.34 y=-0.42x + 1.40

AN-G 95% C.I. 95% C.I. Adj R2 = 0.09 1.2 Adj R2 = 0.12 1.2

1 1

0.8 0.8 Mn Concentration Ratio Mn Concentration Ratio JSl-2 JSl-2

0.6 0.6 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 0.9 0.95 1 1.05 1.1 1.15 1.2 Mn FWHM Ratio Mn FWHM Ratio

Figure 7.8: Mn concentration ratios as a function of FWHM ratio for the full GRM suite (left) and for the Martian concentration range (right).

The Fe concentration ratios show a positive correlation with respect to the FWHM ratio. As

the resolution worsens, the estimated concentrations increase. Separately, the Fe concentra-

tion ratios do not show linear trends for the 2012 campaign over the entire GRM suite or the

Martian range. Neither do the ratios from the 2013 campaign over the entire GRM suite.

The 2013 ratios over the Martian range are the only ones showing linear trends. Notably,

both UB-N and SARM39 are estimated as having 11% additional light invisible elements,

and are outliers.

83 1.06 Martian Range SARM39 (UM) 1.1 1.04

UB-N GS-N 1.02 1.05 1

0.98 1 2012 2012 2013 0.96 2013 Fe Concentration Ratio Fe Concentration Ratio y=0.20x + 0.81 y=0.30x + 0.72 95% C.I. 95% C.I. 0.95 0.94 Adj R2 = 0.24 Adj R2 = 0.56 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 0.9 0.95 1 1.05 1.1 1.15 1.2 Mn FWHM Ratio Mn FWHM Ratio

Figure 7.9: Fe concentration ratios as a function of FWHM ratio for the full GRM suite (left) and for the Martian concentration range (right).

The Zn concentration ratios show a positive correlation with respect to the FWHM ratio.

As the resolution worsens, the estimated concentrations increase. Separately, neither the

2013, nor the 2012 concentration ranges, show a linear correlation over the entire GRM suite

or the Martian range.

1.4 2012 Martian Range 2012 2013 2013 y=0.36x + 0.60 y=0.31x + 0.65 SARM39 (UM) 95% C.I. 1.1 95% C.I. 1.2 Adj R2 = 0.53 Adj R2 = 0.30

1 1

0.9 Zn Concentration Ratio Zn Concentration Ratio 0.8

0.8 0.9 0.95 1 1.05 1.1 1.15 1.2 0.9 0.95 1 1.05 1.1 1.15 1.2 Mn FWHM Ratio Mn FWHM Ratio

Figure 7.10: Zn concentration ratios as a function of FWHM ratio for the full GRM suite (left) and for the Martian concentration range (right).

84 7.3 Discussion

The inverse-variance weighted means were computed for the elemental concentration ratios of each campaign. These means along with the slope coefficients and coefficients of determination from the results above are summarized in Table 7.1. The uncertainty provided for the weighted mean is two times the standard deviation of the data. The uncertainty attached to the R[C] values is equal to two times the standard deviation observed. The uncertainty provided for the regression slope is half the width of the 95% confidence interval.

This value is approximately equal to two times the standard deviation. The relative error is provided for both the mean R[C] and the regression slope. Relative errors greater than 50% are in bold. Pearson’s r was added as a measure of correlation between the concentration ratios and the FWHM. Pearson’s r, also known as Pearson’s product-moment correlation coeﬃcient, is the square root of the coeﬃcient of determination (R2).

Average R WLS Number of Mean [C] Precision Relative Error Adj Pearson’s Element Variation Regression GRMs used R Error (%) R2 r [C] (%) Slope (%) Na 54 0.91±0.18 20 3.2±2.4 -0.47±0.10 21 0.60 -0.78 50 0.91±0.18MR 20 -0.55±0.11MR 19 0.68 -0.83 50 0.91±0.18MR 20 -0.55±0.11MR 19 0.68 -0.83 Mg 54 1.00±0.20 20 5±7 - - - - 21 1.02±0.18MR 18 -0.87±0.20MR 23 0.78 -0.89 Al 61 1.00±0.05 5 6±8 -0.17±0.07 38 0.29 -0.55 43 1.01±0.05MR 5 -0.26±0.08MR 31 0.50 -0.72 Si 63 1.005±0.019 2 0.26±0.09 0.044±0.020 44 0.23 0.50 30 1.006±0.022MR 2 0.06±0.04MR 68 0.21 0.48 K 54 1.00±0.06 6 3±4 0.23±0.05 20 0.64 0.80 21 0.98±0.07MR 7 0.25±0.17MR 66 0.29 0.57 Ca 49 1.01±0.05 5 1.4±1.0 0.22±0.07 32 0.45 0.68 29 1.00±0.05MR 5 0.24±0.09MR 38 0.48 0.71 Ti 44 1.00±0.05 5 2.7±0.9 0.18±0.13 69 0.14 0.39 25 0.99±0.06MR 6 0.23±0.11MR 48 0.39 0.64 Mn 56 1.00±0.20 20 11±6 -0.36±0.28 78 0.09 -0.33 46 1.00±0.19MR 19 -0.42±0.31MR 73 0.12 -0.38 Fe 59 0.99±0.07 7 0.51±0.23 0.20±0.09 43 0.24 0.50 22 0.99±0.06MR 6 0.30±0.11MR 37 0.56 0.76 Zn 51 0.98±0.14 14 14±6 0.36±0.10 28 0.53 0.73 26 0.97±0.11MR 11 0.31±0.18MR 58 0.30 0.58

Table 7.1: Summary of results for the entire GRM suite and the subset that falls within the Martian concentration range (denoted MR).

Fit parameters were not provided for Mg over the entire GRM suite because the trend

85 was not significant at the 95% confidence level. The fit was heavily influenced by one ob-

servation with low uncertainty. More spectra from GRMs with high Mg abundance, taken

at low resolution, are required to determine if the above observation is spurious.

For the 2013 campaign, Mg R[C] = 1.01 ± 0.10. For the 2012 campaign, Mg R[C] =

0.96 ± 0.15. Despite the 5.1% diﬀerence between them, these values are within error. The

Martian Range for Mg is much narrower than that seen in terrestrial samples. The mean

count-rate ratios change signiﬁcantly if only samples within the Martian Mg concentration

range are analyzed. The count-rate and concentration ratios for this subset of the GRMs

are shown in Figure 7.11.

1.2 WS-E 1 WS-E

1.1 0.9

0.8 1

0.7 2012 0.9 2012 2013 2013

Mg Count Rate Ratio Mean=0.74 Mean=0.91

0.6 2σ=0.14 Mg Concentration Ratio 2σ=0.13 Mean=0.88 0.8 Mean=1.04 2σ=0.10 2σ=0.08 0.5 1 2 3 4 5 6 7 1 2 3 4 5 6 7 Mg Certiﬁcate Concentration (%) Mg Certiﬁcate Concentration (%)

Figure 7.11: Mg count-rate ratios (left) and concentration ratios (right), within the Martian concentration range, as a function of certiﬁcate [Mg].

Constraining the analysis to the Martian range, the 2013 campaign Mg R[C] = 1.04±0.08,

and for the 2012 campaign, Mg R[C] = 0.91 ± 0.13. These values are within error of each other; however, there is a 13.3% diﬀerence between them. The count-rate estimates show

a diﬀerence of 17.3%. In other words, concentration estimates, from sample spectra taken

with poor instrumental resolution that fall within the Martian Mg concentration range, are

expected to be approximately 13% lower than those taken with improved instrumental res-

olution.

86 The slope extracted from the WLS regression serves as an estimate of the link between changing resolution and the associated change in concentration estimates. The value is interpreted as the mean percent change in variance-weighted elemental concentration for a

1% relative increase in the variance-weighted spectral resolution. For example, within the

Martian concentration range, a 1% relative increase in weighted FWHM yields an average relative decrease in the weighted mean Na concentration of 0.55±0.11%.

The variable adjusted coeﬃcient of determination (adjusted R2) quantiﬁes how well the

regression line approximates the real data points. It is interpreted as the fraction of varia-

tion in weighted concentration ratios that can be accounted for by the change in weighted

FWHM. Going back to the Na example above, 68% of the variation in weighted Na concen-

tration ratios can be accounted for by weighted FWHM change.

Several guidelines exist for the interpretation of a correlation coeﬃcient. However, these

criteria are arbitrary and should not be observed too strictly. In this context, correlation

coeﬃcients below 0.5 are considered to show a weak correlation and are in bold. Adjusted

R2 values below 0.25 are in bold as well.

7.3.1 Negative Correlation

Four of the ten elements analyzed showed a negative correlation with respect to FWHM.

In other words, as the resolution worsened and the FWHM increased, the concentration

estimates decreased for Na, Mg, Al, and Mn. These elements also had the most intense re-

sponse to changes in FWHM, as quantiﬁed by the WLS regression slope. Of these, the three

lightest elements displayed the strongest correlation coeﬃcients and highest coeﬃcients of

determination, indicating that they are strongly inﬂuenced by variations in resolution. These

three analytes are predominantly PIXE excited and sit on a rapidly varying background.

Their susceptibility to changes in resolution is not surprising and is in agreement with the

count-rate ratio behaviour seen previously.

87 Mn shows the fourth most intense response to changes in resolution as quantiﬁed by the regression slope. However, it has the widest conﬁdence interval of all analytes, indicating the slope estimate is crude, at best. The broad scatter and high uncertainty seen in the

Mn concentration ratios is ascribed to low energy-tailing issues with the Fe peak having an adverse eﬀect on the ﬁtting of the Mn peak. The results for Mn, with respect to resolution, may be obfuscated by these issues.

7.3.2 Positive Correlation

The six remaining elements analyzed (Si, K, Ca, Ti, Fe, and Zn) showed a positive correlation with FWHM. Of special interest is Si, the only predominantly PIXE excited element showing a positive correlation with respect to FWHM. Although it does not show a very strong correlation (with a Pearson’s r of 0.51) it has a narrow 95% conﬁdence interval.

This indicates a well estimated slope for a linear trend that does not fully encompass the variability seen in the concentration ratios. This could mean that a different fit may yield improved results. Considering the nature of the data, a sigmoidal fit may be a better approach and looks reasonable by inspection; however this comes with a loss of interpretability.

The Fe, Ca, and Ti concentration estimates show strong correlations with changes in

FWHM. Weaker correlations were found for Zn and K. Although Zn shows an intense response to changes in resolution with a regression slope of 0.31, the slope is crudely estimated as evidenced by its relatively wide 95% confidence interval. Moreover, the correlation coefficient for Zn with FWHM is below 0.6 and there is a big discrepancy between the WLS and OLS coefficients of determination. Similarly, K shows a regression slope with a long confidence interval and a Pearson’s coefficient below 0.6.

7.3.3 Precision Error & Estimate Variation

The 2σ values attached to the R[C] above can be used to compare the variations in estimated

2σ elemental concentration ( /R[C] · 100%) to the average precision error for each element, computed from the GUAPX output.

88 Na!

Mg!

Al!

Si! Mean Precision Error! K! Entire GRM Suite Variation! Martian Range Variation! Ca! ! Element

Ti!

Mn!

Fe!

Zn!

0! 5! 10! 15! 20! Percentage Error or Variation (%)!

Figure 7.12: Mean precision error for all GRMs across 2012 and 2013 campaigns compared to variation in concentration estimates for entire GRM suite and those within the Martian ranges.

The histogram in Figure 7.12 oﬀers a visual comparison of the mean precision errors and the variation in concentration estimates for all GRMs across both the 2012 and 2013 campaigns. The resolution range for these measurements is 162 - 208 eV at the Mn Kα line.

The variation in concentration estimates is outside uncertainty of the mean precision error

for Na, Mg, Al, Mn, Si, Ca, and Fe over both the entire GRM suite and the Martian range.

In the case of K, only the Martian range falls outside the uncertainty of the precision error.

Na! 2013/Calibration Mean Precision Error!

2013/Calibration GRM Suite Variation! Mg! 2013/Calibration Martian Range Variation! Al!

Si!

Ca! ! Element

Ti!

Mn!

Fe!

Zn!

0! 5! 10! 15! 20! Percentage Error or Variation(%)!

Figure 7.13: Mean precision error for 2013 campaign GRM suite compared to variation in concentration estimates for entire GRM suite and those within the Martian ranges.

89 Figure 7.13, oﬀers a visual comparison of the mean precision errors and the variation in concentration estimates for the GRMs suite analyzed in the 2013 campaign. The resolution range for spectra collected under the 2013 campaign conﬁguration spans 162 - 183 eV at

5.9 keV. As expected, with improved resolution, the mean precision errors and variations in concentration estimates are smaller. The variation in concentration estimates seen in the

2013 campaign falls within uncertainty of the mean precision error for all elements over both the entire GRM suite and the Martian range, except for Fe.

The results presented here ﬂag the possibility that systematic errors associated with changes in resolution, could cause the data to be interpreted as exhibiting element correlations. Particuarly, as seen in Figure 7.12, Na, Mg, Al, Mn, Si, Ca, and Fe concentration estimate variations fall outside uncertainty for the corresponding precision error over resolution and concentration ranges similar to those seen on Mars [56]. Although the instrument’s accuracy is limited by microscopic heterogeneity [26, 40], precision is often more important for samples that are similar overall. Thus, APXS raster analyses are able to pick up deviations outside the smaller precision errors. These changes are used as mineral indicators by way of elemental correlations [26] and for chemostratigraphic analyses of sulfates and other salts [57]. APXS raster analyses are regularly performed on Mars [58], usually starting in the evening when the temperature is not optimal but gets better over time [26]. It has been shown that deviations in FWHM can be incorrectly interpreted as concentration changes outside the precision errors.

7.4 Conclusion

The relationship between changes in resolution and variations in estimated concentration was probed by use of concentration ratios and their corresponding FWHM ratios. WLS regression methods were used to quantify the change in estimated concentration with respect to change in FWHM, weighting observations by their uncertainty. This was done for the entire GRM suite and the subset with an analyte abundance within the Martian concentration range. The results can be found in Table 7.1. Statistically signiﬁcant trends

90 at the 95% conﬁdence level were found for all elements except Mg over the entire GRM suite.

Strong negative correlations between estimated concentrations and FWHM were found for Na, Mg, and Al. Si, K, Ca, Ti, Fe, and Zn concentrations showed positive, albeit, weaker correlations with FWHM. This is in agreement with the results in the previous three chapters. The 2σ values attached to the R[C] values above were used to compare the variations in estimated elemental concentrations with the mean precision errors, computed from the

GUAPX output. It was found that Na, Mg, Al, Mn, Si, Ca, and Fe concentration estimate variations fall outside uncertainty for the corresponding precision error over resolution and concentration ranges similar to those seen on Mars [56]. It is concluded that deviations in

FWHM can be incorrectly interpreted as concentration changes outside the precision errors, possibly obfuscating or fabricating elemental correlations.

91 Chapter 8

Conclusions

In X-ray spectroscopy, the drawbacks of degradation in energy resolution, in terms of accuracy and precision of the analytical results, are not always clear [7]. Previous work by Dr.

Gellert and Dr. Pradler showed a correlation between concentration estimates and spectral resolution for geochemically interesting elements. Further analyses into Dr. Pradler’s data showed a differential effect favouring the heavier element concentrations with worsening resolution. This motivated an in depth investigation into effects of varying resolution on APXS spectra processed using the GUAPX fitting code’s IM mode. On Mars, APXS measurements are not always planned around achieving optimal instrumental performance and may be taken during daylight hours. Although, the TEC allows for instrument operation during the Martian day, the diurnal temperature swings make it such that resolution cannot always be optimized.

APXS resolution is susceptible to both the thermal and radiation environments of the sensor head. The continuous degradation of FWHM due to neutron damage in conjunction with the limited temperature control capabilities of the FEU-APXS led to the development of a stepwise optimization of the cooling configuration in the laboratory. Consequently, the different FEU-APXS instrumental configurations cover a broad resolution range. Thus, the GUAPX analytical results acquired from spectra collected under various configurations serve as a laboratory to probe the relationship between resolution, estimated photopeak areas, and estimated concentrations.

92 The first step in the extraction of concentration data from spectra is to determine the peak area for the principal line of each element present. This requires the subtraction of the background and overlapping photopeaks. In GUAPX, the background is removed by use of the top-hat filter. By analyzing the time normalized peak areas (count rate) it was found that Na, Mg, Al, Mn, and to a lesser extent Si, showed a decrease in average count-rate estimates with worsening resolution. A campaign-based, and thus resolution-based, dichotomy was seen in the count-rate ratios for Na, Mg, and Al. These elements are predominantly excited via PIXE interactions and have overlapping peaks superposed on a rapidly varying background [38]. In a situation like this, the fitting code is more susceptible to weaknesses in the background filtering procedure. It is concluded that varying FWHM in the instrument can affect the spectral line count rates estimated by GUAPX in this rapidly varying, closely spaced, part of the spectrum. Using the average change in count-rates relative to the

α calibration, the /LX correction factor was computed as 1.18±0.04. This conﬁrms the value

of 1.2 deduced by G. Perrett from a subset of standards.

The next step in the processing of spectra is the conversion from peak areas to concen-

tration estimates through the use of the yield equation calibrated using the FPS approach.

At this point in the process, matrix eﬀects are taken into account; this requires application

of the closure rule. A diﬀerential eﬀect favouring the heavier element concentrations with

worsening resolution, similar to that seen in Section 3.1, was observed. The concentration

estimates for Na, Mg, and Al were very closely linked to their corresponding count-rate

estimates. The remaining elements (Si, K, Ca, Ti, Mn, Fe, and Zn) showed a systematic

diﬀerence between campaigns when mapping from count-rates to concentration ratios, as

seen in Figure 6.15.

An underlying cause for the variation in estimated concentrations was proposed. It was

concluded above that poor resolution can lead to an underestimation of light element peak

areas by GUAPX. When using IM mode, this underestimation results in an erroneous matrix

correction. The average atomic number of the estimated matrix is higher than that of the

actual matrix. The attenuation increases more for the light element X-rays and less for the

93 heavier element X-rays. This helps explain the diﬀerential eﬀect that favours the heavier element concentrations that was observed for Si, K, Ca, Ti, Fe, and Zn in Chapters3 and

6. A gross correction for the systematic depression of Mg concentration estimates at lower instrumental resolution based on the present data was quantiﬁed. This proved helpful in the quantitative determination of mineral phase eﬀects observed in APXS analyses of GRMs [53].

The relationship between resolution and variations in estimated concentrations was probed using WLS regression methods to quantify the average relative change in estimated concentration, with respect to changes in FWHM, weighting observations by their uncertainty. This was done for the entire GRM suite and the subset with analyte abundances within the concentration ranges seen in Mars. The results can be found in Table 7.1. The slope estimated from the regression was used to quantify the intensity of this relationship.

Strong negative correlations between estimated concentrations and FWHM were found for

Na, Mg, and Al. Si, K, Ca, Ti, Fe, and Zn concentrations showed positive, albeit, weaker correlations with FWHM. This is in agreement with the conclusions above.

Lastly, the 2σ values attached to the R[C] values above were used to compare the variations in estimated elemental concentration with the mean precision errors, computed from the GUAPX output. It was found that Na, Mg, Al, Mn, Si, Ca, and Fe concentration estimate variations fall outside uncertainty for the corresponding precision error, over resolution and concentration ranges similar to those seen on Mars [56]. It was concluded that deviations in FWHM can be incorrectly interpreted as concentration changes outside the precision errors.

8.1 Future Work

The results presented, ﬂag the possibility that systematic errors, associated with changes in resolution, can possibly obfuscate or fabricate elemental correlations. This ﬁnding is of particular relevance since APXS raster analyses, regularly performed on Mars [58], are usually started in the evening when the temperature, and thus instrumental resolution, is not

94 optimal but gets better over time [26]. Elemental correlations from these measurements are used as mineral indicators [26] and for chemostratigraphic analyses of sulfates and other salts [57] on Mars. Therefore, it is recommended that the effects of resolution on analytical results acquired from the PFM-APXS instrument’s BT-2 calibration target undergo an investigation similar to that performed here. Thereby, continuing to provide scientific support for researchers’ efforts to characterize the habitability and environmental history of the Gale crater field site.

95 Bibliography

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98 Appendix A

Campaign GRMs

Sample Group GRM suppliers and identification Minerals SARM: AL-I, Mica-Fe, Mica-Mg Basalts SARM: PM-S, WS-E NIST: SRM688 USGS: BHVO-2 Andesites USGS: AGV-2, BCR-2 Dacietes & Rhyolites SARM: GA, GH, GS-N Igneous rocks USGS: GSP-2, QLO-1 Trachytes SARM: ISH-G, MDO-G Ultramafic SARM: BE-N USGS: DTS-2B SACCRM: SARM-5, SARM-39 High alkali CCRMP: SY4 CNACIS: GBW07109 Sediments/ USGS: MAG-1, GXR-1 Sedimentary Materials Sedimentary rocks Phosphate NIST: SRM694 Total 25 Suppliers: SARM: Service d’Analyse des Roches et des Mineraux, CRPG-CNRS, Nancy, France; USGS: United States Geological Survey, Denver, Colorado; NIST: National Institute of Standards and Technology, Gaithersburg, Maryland; GSJ: Geological Survey of Japan; SACCRM: South African Bureau of Standards, Pretoria, South Africa; CCRMP: Canadian Certified Reference Materials Project, CANMET, Ottawa, Canada; CNACIS: China National Analysis Center for Iron and Steel, Beijing, China; AS-IGEM: Academy of Sciences: Institute for Geology of Ore Deposits, Petrography, Mineralogy and Geochemistry, Moscow, Russia.

Table A.1: Distribution of certiﬁed geochemical reference materials among sample groups in the 2012 campaign.

99 Sample Group GRM suppliers and identiﬁcation AL-I, DT-N, FK-N, Mica-Fe, Minerals SARM: Mica-Mg, UB-N, ZW-C Basalts SARM: PM-S, WS-E NIST: SRM688 GSJ: JGB1 USGS: BHVO-2, BIR-1a, DNC-1 AS-IGEM: 1045-94 (MO14), 1017-94 (MO15) Andesites SARM: DR-N USGS: AGV-2, BCR-2 GSJ: JA-2, JA-3 AS-IGEM: 2118-81 (MO4) CNACIS: GBW07104 Igneous rocks Dacietes & Rhyolites SARM: AC-E, GH, GS-N USGS: GSP-2 GSJ: JG1a Trachytes SARM: ISH-G, MDO-G Ultramaﬁc SARM: BE-N USGS: DTS-2B SACCRM: SARM6, SARM39 AS-IGEM: VS211381 (MU3) High alkali CCRMP: SY4 CNACIS: GBW07109 Anorthosite SARM: AN-G Sediments/ GSJ: JSd-2, JSl-1, JSl-2, JLk-1, JMS-2 Sedimentary Sedimentary rocks USGS: MAG-1 Materials CNACIS: GBW07316 Total 46 Suppliers as in Table A.1

Table A.2: Distribution of certiﬁed geochemical reference materials among sample groups in the 2013 campaign.

100