P. J. Potts (auth.) - A Handbook of Silicate Rock Analysis (1992, Spring...

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To Barbara, Edmund, Esther, Samuel, Tessa and Roland

P . J . POTTS Senior Research Fellow in Earth Sciences The Open University Milton Keynes, UK

Springer Science+Business Media, LLC

© 1992 Springer Science+Business Media New York Originally published by Blackie & Son Ltd in 1992

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, recording or otherwise, without prior permission of the Publishers.

British Library Cataloguing in Publication Data Potts, P.J. A handbook of silicate rock analysis. 1. Title 549.028 ISBN 978-0-216-93209-8 ISBN 978-1-4615-3270-5 (eBook) DOI 10.1007/978-1-4615-3270-5

Contents 1 Concepts in analytical chemistry 1.1 1.2

Introduction Terms and definitions in analytical chemistry

1.3

Units of measurement: the international system (SI) of units Statistics

1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11

Detection limits Sampling strategies: inhomogeneity effects Contamination effects Reporting analytical data Standard additions calibrations Rock reference materials Which technique for which element?

4 7 15 18 20 27 28 28 42

4.7

Schemes of analysis using flame atomic

4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16

absorption Interference suppression Detection limits Routine performance Electrothermal atomization Atomization in the hollow graphite furnace Background correction Geological applications of furnace AAS Cold vapour and hydride generators Solid sampling and novel atomization devices

122 123 127 128 128 130 138 144 146 150

5 Inductively coupled plasma-atomic emission spectrometry

5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9

Historic development and analytical capabilities The inductively coupled argon plasma Nebulizers and spray chambers Physical structure of the plasma Temperature distribution in the plasma Atomization and excitation processes Interferences in the argon plasma Measurement and analysis of emission spectra Some instrument considerations-simultaneous v. sequential monochromators

5.10 5.11 5.12 5.13

Optimizing operating parameters Calibrations for ICP-AES Silicate rock analysis

173 175 179 183

Direct current plasma-optical emission spectrometry

192

6 Arc and spark source optical emission spectrometry 6.1 Historical perspective 6.2 Instrumentation Sample preparation 6.3 6.4 Behaviour of elements in an arc discharge 6.5 Simultaneous multi-element analysis 6.6 Conclusions

198 198 200 201 205 212

2 Classical and rapid methods of analysis 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11

Rock dissolution techniques: acid attack Rock dissolution procedures: fusion with alkali salts Classical methods of rock analysis Evolution of rapid methods of analysis Photometry Flame photometry Titrations involving ethylenediaminetetraacetic acid (EDTA) A rapid scheme of analysis Determination of ferrous iron The determination of water and carbon dioxide The auto-analyser

47 52 55 58 58 62 64

66 67 70 75

3 Optical spectrometry: principles and instrumentation 3.1 3.2 3.3 3.4 3.5

3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15

Principles The nature of light Atomic spectroscopy The electronic structure of atoms: quantum theory Spectroscopic notation for electron orbital configurations: the Russell-Saunders coupling scheme The absorption oflight The emission of light Instrumentation for optical spectroscopy Monochromator Optical filters Slits Photon detectors Classical monochromator designs Stray light effects Errors in spectrometric measurements

4 Atomic absorption spectrometry Introduction 4.1 Instrumentation 4.2 Properties of flames 4.3 Flame chemistry and atomization interferences 4.4 4.5 4.6

in the flame: atomization processes in the flame Instrumental and spectral interferences Instrument optimization for routine analysis

71 78 80 80

82 86 88 90 91 97 98 99 100 103 103

7 Ion-selective electrodes 7.1 Analytical perspective 7.2 Instrumentation The Nernst equation 7.3 7.4 Interference effects: non-ideal Nernst behaviour 7.5 Schemes for the analysis of geological samples 7.6 7.7

8 106 107 114 117

120 121

for fluorine Determination of chlorine by ion-selective electrodes Other techniques for the determination of chlorine and fluorine

153 153 156 163 165 165 167 169

213 213 216 217 218 219 222

X-ray fluorescence analysis: principles and practice of wavelength dispersive spectrometry Analytical characteristics 8.1 226 8.2 Energy and wavelength of x-rays 226 8.3 The origin of x-ray spectra 227 Competing de-excitation routes 8.4 233 8.5 Excitation of x-ray spectra 236 Interaction of x-rays with matter 8.6 239

v

CONTENTS

8.7 8.8 8.9 8.10 8.11 8.12 8.13

Matrix effects in geological samples Mathematical procedures for the correction of absorption-enhancement effects Instrumentation for wavelength dispersive XRF analysis Experimental considerations Routine operating conditions and statistical considerations Performance in routine analysis Concluding remarks

242

9.8 9.9 9.10 9.11 9.12 9.13 9.14

The development of energy dispersive XRF The Si(Li) detector Detector configuration and characteristics Pulse processing electronics Interaction of x-rays with the silicon detector Comparison of ED and WD spectrometers Silicate rock analysis by ED-XRF using direct tube excitation Spectrum analysis procedures Routine analysis using direct tube excitation Indirect excitation methods Monochromatic polarized excitation using Bragg diffraction at 2IJ = 90°C Radioisotope excitation Total reflection of primary beam Concluding remarks

10.4 10.5 10.6 10.7 10.8 10.9 10.10 10.11 10.12 10.13 10.14 10.15 10.16 10.17 10.18 10.19

The development of microprobe techniques Microbeam techniques Instrumentation for the electron probe microanalyser Electron column design Vacuum requirements Interactions between the electron beam and sample: the excited volume Phenomena within the excited volume X-ray production Matrix correction procedures X-ray spectrometers Calibration and routine operation Energy dispersive spectrometers Sample preparation requirements Microprobe mineral standards Routine analytical performance Analysis of non-silicate minerals: uranium, thorium and rare-earth elements Bulk rock analysis by electron microprobe The SEM as a microprobe Concluding remarks

396

12 Neutron activation analysis 253 271 278 282 285

286 286 289 293 297 299 300 307 308 315 321 322 323 325

10 Electron probe microanalysis 10.1 10.2 1003

Transmission electron microscopy: the chemical analysis of thin foils

249

9 Energy dispersive X-ray spectrometry 9.1 9.2 9.3 9.4 9.5 9.6 9.7

11.6

326 326 327 331 335 336 337 343 348 353 358 360 364 364 366 371 378 380 381

12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 12.10 12.11 12.12 12.13 12.14 12.15 12.16 12.17 12.18 12.19

Introduction The growth and decay of radioactivity Radioactive decay schemes Instrumentation Pulse-processing electronics Interaction of gamma radiation with germanium detectors Typical spectrum Detector characteristics Practical considerations-instrumental neutron activation Determination of photo peak areas Other analytical considerations Interferences and systematic errors Routine schemes of analysis Chondrite normalized abundances Epithermal v. thermal irradiations Short -lived isotopes Radiochemical separation procedures Prompt gamma neutron activation analysis Concluding remarks

399 399 402 405 409 411 413 414 416 419 422 424 429 430 432 435 435 438 439

13 Nuclear techniques for the determination of uranium and thorium and their decay products 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8

13.9

Techniques for uranium/thorium determination The uranium-thorium decay chain Delayed neutron fission activation analysis Fission track analysis Other autoradiography techniques for locating and analysing specific elements in thin section Gamma spectrometry Alpha spectrometry Secular equilibrium with particular reference to uranium/thorium disequilibrium measurements Uranium and thorium series disequilibrium

440 441 441 445 448 452 459

461 462

14 Ion exchange preconcentration procedures 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8

Introduction Ion exchange techniques Characteristics of ion exchange resins Some theoretical aspects of ion exchange Optimizing column separations Applications of ion exchange chromatography to rare-earth element separations Chelating ion exchange resins Other preconcentration procedures

472 472 474 477 480 480 484 485

15 Gold and platinum group element analysis 11 Other microbeam and surface analysis techniques 11.1 1I.2 11.3 11.4 1I.5

VI

Introduction The ion probe The laser microprobe Particle-induced x-ray emission (PIXE) Electron spectroscopy for chemical analysis (ESCA)

383 383 391

392 395

15.1 15.2 15.3 15.4 15.5 15.6 15.7

Introduction Fire assay procedures Acid extraction of noble metals Other methods of noble metal analysis Noble metal analysis-{;omparisons of data A note on the distribution of noble metals Graphical presentation ofPGE data

486 487 492 492 493 494 496

CONTENTS

16 Mass spectrometry: principles and instrumentation 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 16.10 16.11 16.12 16.13 16.14 16.15 16.16

Introduction Mass spectrometric techniques in geology The ion source The mass analyser Resolution Double-focusing mass spectrometer Quadrupole mass spectrometer Ion detectors Vacuum requirements Abundance sensitivity Beam switching v. multiple collection Isotopes and mass spectra: the structure of atoms and nuclear stability Mass defect phenomena Radioactive isotopes in nature Geochronology Geochronometers of geological importance

497 497 498 498 500 502 503 505 508 508 509 510 512 512 514 516

Introduction Ion production Rubidium-strontium isotope analysis Neodymium-samarium isotope analysis Lead, uranium and thorium isotope analysis Isotope dilution

523 523 525 528 531 536

Hydrogen isotope analysis Carbon isotope analysis Nitrogen isotope analysis Oxygen isotope analysis Sulphur isotope analysis Noble gas analysis Potassium-argon geochronometry

552 554 555 556 558 559 560

19 Spark source mass spectrometry 19.1 19.2 19.3 19.4 19.5 19.6 19.7

Introduction Instrumentation and ion production Internal standardization Routine data acquisition Photoplate calibration and element sensitivities Applications and results Future developments

566 566 568 568 569 571 573

20 Inductively coupled plasma-mass spectrometry 20.1 20.2

] 7 Thermal ionization mass spectrometry 17.1 17.2 17.3 17.4 17.5 17.6

18.4 18.5 18.6 18.7 18.8 18.9 18.10

20.3 20.4 20.5 20.6 20.7

Introduction Development of ICP-MS instrumentation: the plasma-mass spectrometer interface The inductively coupled plasma as ion source ICP-mass spectrometry instrumentation Performance and applications Internal standardization Isotope dilution

575 575 578 582 583 583 584

]8 Gas source mass spectrometry 18.1 18.2 18.3

Geological applications Instrumentation The delta convention for reporting isotope data

546 546 552

References

587

Index

611

VII

Preface The techniques available for the chemical analysis of silicate rocks have undergone a revolution over the last 30 years. No longer is the analytical balance the only instrument used for quantitative measurement, as it was in the days of classical gravimetric procedures. A wide variety of instrumental techniques is now commonly used for silicate rock analysis, including some that incorporate excitation sources and detection systems that have been developed only in the last few years. These instrumental developments now permit a wide range of trace elements to be determined on a routine basis. In parallel with these exciting advances, users have tended to become more remote from the data production process. This is, in part, an inevitable result of the widespread introduction of microcomputers for instrument control, and in part a consequence of the logistics of organizing a modern laboratory for rapid and efficient routine analysis. The resultant lack of interaction between user and machine leads to the danger of a 'black-box' attitude towards analytical chemistry-samples in at one end, result out at the other-

without an appreciation of what happens in between. However, to use an analytical technique most effectively, it is essential to understand its analytical characteristics, in particular the excitation mechanism and the response of the signal detection system. In this book, these characteristics have been described within a framework of practical analytical aplications, especially for the routine multi-element analysis of silicate rocks. All analytical techniques available for routine silicate rock analysis are discussed, including some more specialized procedures. Sufficient detail is included to provide practitioners of geochemistry with a firm base from which to assess current performance, and in some cases, future developments. This manuscript could not have been completed without the constant help of my wife Barbara, the assistance of many friends and colleagues at the Open University and the patient encouragement of the publishers.

PJ.P.

ix

1 Concepts in analytical chemistry 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.1 0 1.11

Introduction Terms and definitions in analytical chemistry Units of measurement: the international system (SI) of units Statistics Detection limits Sampling strategies: inhomogeneity effects Contamination effects Reporting analytical data Standard additions calibrations Rock reference materials Which technique for which element?

1.1

Introduction

The analytical chemistry of silicate rocks and minerals takes in a diverse range of techniques employing a wide variety of physical phenomena. Although the concepts on which many of these techniques are based appear to have little in common, a degree of uniformity does embrace each in terms of the underlying analytical principles. Thus the desired goal is to measure a signal related to the concentration of an elemental constituent of a sample. This analyte signal invariably possesses a background component, the magnitude of which usually limits the lowest concentration that can be satisfactorily analysed (the detection limit). The precision with which the signal can be measured depends on a variety of factors, both fundamental and instrumental in origin. These could include counting statistical errors, signal to background ratios, instrumental noise, drift and sensitivity. All techniques suffer interference effects and, in some, account must be taken of blank and contamination levels. It is generally necessary to prove the accuracy of measurements by the comparative analysis of international rock reference materials. The purpose of this introductory chapter is to discuss some of these basic concepts so that it will then be possible to examine in more detail the characteristics of individual techniques in subsequent sections.

arises from two sources. The first is a natural background component (such as the x-ray continuum on which a characteristic x-ray line sits). The second is an instrumental background component characteristic of the measuring device. In the example outlined above, this could arise from fluorescence of the diffracting crystal or Compton scatter with an Si(Li) detector used for x-ray spectrum measurements. detection limit: This refers to the limit down to which an analytical signal can be measured and distinguished at a specified confidence level from the background signal. This concept is considered in more detail in section 1.5. Unfortunately, the term 'detection limit' is one of the most abused in analytical chemistry, since without precise specification this term can be applied to a variety of signal levels. sensitivity: This term is often qualitatively used to refer to the detection limit of a technique, although strictly this connection is secondary. The sensitivity of a technique refers to the gradient of a signal v. concentration calibration line and is measured as the signal strength per unit concentration. As a means of referring to the detection limit capability, account must be taken of the background intensity. However, for constant background, an element that shows high sensitivity must also possess a lower detection limit and vice versa (see Figure 1.1). bias: In an analytical context, bias is the phenomenon whereby the average tendency of analysed results is either high or low compared with the expected composition. In electronic terminology, bias refers to an electrical potential applied to an electrode (for example, a bias of 1 kV). drift: Drift arises when an instrument response changes with time, and is often associated with the effect of changes in ambient temperature on the stability of electronic circuits. gain: Gain is the amplification factor applied to an electronic circuit. noise: Short-term instability, which is often associated with

1.2 Terms and definitions in analytical chemistry Several terms are in widespread use to describe phenomena affecting all analytical techniques. Some have specialized usage in analytical chemistry. The more important of these terms are as follows. signal, background: The signal is the physical response containing analytical information related to the concentration of an elemental component of a sample. It is therefore the object of measurement. The magnitude of the signal is not, however, always linearly related to concentration (in some schemes of x-ray fluorescence analysis, for example, it is necessary to apply a non-linear iterative correction to raw count data to account for the influence of matrix composition on fluorescence x-ray emission). A variety of signals, including weight changes, voltage differences and special measurements, is used in analytical techniques applied to rock analysis: some of these are listed in Table 1.1. All signals have a background component, this being the unwanted part of the signal which usually contains no analytically useful information. In general, the background

detection limit signal

---------------

c2

concentration

Figure 1.1 Relationship between sensitivity and detection limits. The diagram shows the signal v. concentration calibration plot for two elements, one having high sensitivity and the other having low sensitivity. Providing the magnitude of the detection signal limit for both is the same, the detection limit, converted to concentration, of the high-sensitivity element will be the lower.

1.2

CONCEPTS IN ANALYTICAL CHEMISTRY

Table 1.1 Analytical signals and instrumentation used in geochemical analysis. Analytical signal

Method of excitation

Instrumentation for detecting signal

Gravimetry

Weight loss or gain

Analytical balance

Titrimetry

Volume of titrant

Colorimetry

Colour intensity as measured by optical absorption

Precipitation of element as insoluble compound or ignition of sample to release volatile phase (e.g. H 20 or CO2) Stoichiometric reaction of elemental species with specific reagent in solution Reaction of elemental species in solution with a chromophore (a reagent that forms a coloured complex with the element in question) Excitation of sample with x-ray spectrum from an x-ray tube

Technique

Acronym

X-ray fluorescence analysis

WD--XRF or ED--XRF

Count rate of secondary fluorescence x-ray line

Electron probe micro-analysis

EPMA

As above

Flame photometry

Intensity of emission of characteristic optical radiation from an atomized sample Intensity of emission of characteristic optical radiation from atoms and ions

Spark/arc discharge optical emission spectrometry

Bombardment of sample with a focused beam of electrons accelerated to 15 to 30kV Atomization and excitation of a sample solution in a flame (e.g. air/propane) Atomization (ionization), and excitation of a sample in an electrical discharge

Inductively coupled plasma optical emission spectrometry

ICP-OES or ICP-AES

As above

Atomization (ionization), and excitation of a sample solution in an argon plasma

Atomic absorption spectrometry

AAS

Degree of absorption of characteristic optical radiation by atoms

Neutron activation analysis

INAA or RNAA

Intensity of gamma-ray emission from radioactive isotopes

Atomization of sample solution in a flame (e.g. air/acetylene) Absorption of monochromatic radiation from a hollow cathode lamp by atomic species in the flame Neutron capture by element nuclei to form radioactive daughter nuclei during irradiation by neutrons in a nuclear reactor Neutron-induced fission of 235U during irradiation by neutrons in a nuclear reactor Diffusion of ions through an ion-selective membrane causing a change in the potential generated in an electro-chemical cell Atomization and ionization of sample in a radiofrequency electrical discharge Atomization and ionization of a chemically purified sample on an incandescent metal filament

Delayed neutron fission

Intensity of neutron emission following fission of 235U

Ion-selective electrodes

ISE

Voltage change across an ion-specific electrode

Spark source mass spectrometry

SSMS

Intensity of mass/ charge signal

Thermal ionization mass spectrometry

TIMS

As above

2

Burette

Optical monochromator or optical filters plus photomultiplier tube

Bragg diffraction from a crystal spectrometer fitted with gas proportional or scintillation counter detectors or solid state Si (Li) detector coupled to a multichannel analyser As above

Optical monochromator or simple optical filters plus photomultiplier tube Optical monochromator often with a large number (20 to 40) of fixed exit slits each with its own photomultiplier detector. Older instruments used a photographic plate for detection Optical monochromator (scanning or fixed channel) plus photomultiplier tube Scanning optical monochromator plus photomultiplier tube

Solid state germanium gamma-ray detector coupled to a multichannel analyser Boron trifluoride neutron counter

Voltmeter

Ions dispersed using both electrostatic and electromagnetic sectors. Photographic plate detection Ions dispersed by a single magnetic sector and detected using Faraday cup, electron multiplier or Daly detectors

CONCEPTS IN ANALYTICAL CHEMISTRY

1.2

Table 1.1 (Continued) Technique

Acronym

Analytical signal

Method of excitation

Instrumentation for detecting signal

Gas source mass GSMS spectrometry

As above

Inductively coupled plasma mass spectrometry

As above

Stepped combustion of sample to release gas (e.g. H2 , CO2, S02 or noble gases) that are chemically purified and ionized by electron bombardment in the ion gun of mass spectrometer Atomization and ionization of a sample solution by aspirating into an inductively coupled argon plasma

Ions dispersed by a single electromagnetic sector and detected using Faraday cup or electron multiplier. Detectors often designed to operate in tandem or triplicate to permit simultaneous detection of the ion beams of interest Plasma gases sampled into a quadrupole mass analyser and detected using an electron channel multiplier coupled to a multichannel analyser

ICP-MS

WD-XRF = wavelength-dispersive XRF. ED-XRF = energy-dispersive XRF. INAA = instrumental neutron activation analysis. RNAA = radiochemical neutron activation analysis. ICP-AES = ICP atomic emission analysis. Acronyms generally follow those given by Delaey and Arkens (1981).

the random movement of electrons in individual electronic components, causes a random variation in the analytical signal called noise. figure of merit: In the optimization of an analytical technique, measurements are normally made at a variety of instrumental settings. It is then desirable to plot some parameter as a function of those instrument settings in order to identify optimum operating conditions. The parameter selected is the figure of merit. The simplest form is the signal to background ratio, although this is not universally applicable. precision and accuracy: Precision is a measure of the analytical reproducibility of a measurement. Accuracy is a measure of the closeness of this measurement to the 'true' value. In geochemical analysis precision is easy to measure: accuracy is occasionally impossible. In most cases values quoted for the precision of a technique are a grossly optimistic measure of accuracy. These concepts are discussed further in section 1.4.2. reference material: Reference materials are the means by which the accuracy of analytical results can be assessed. They comprise silicate rock powders of proven homogeneity that have been distributed for analysis by a variety of techniques to as many laboratories as possible worldwide, usually on a voluntary co-operative basis. The assessment of resultant analytical data to estimate 'true' compositions is not trivial since data are usually affected by discrepancies arising from interlaboratory bias, particularly in trace elements analysis. For this reason rock reference materials never aspire to the name 'standards'. The reliability and status of rock reference materials are considered further in section

1.10. standards: Standards are the samples selected by the analyst to calibrate an instrument. They may consist of rock reference materials or samples prepared from high-purity reagents. The use of this term when applied to reference materials in this context is not meant to imply that these samples can be used as an international basis for 'standard' measurements. standard additions: A method of calibration in which differ-

ent aliquots of a sample are 'spiked' with increasing amounts of an element. The graph of analysed signal v. concentration of element added, gives a calibration line, the intercept of which with the concentration axis gives the amount of that element present in the unspiked sample. This technique is sometimes used when analyses are subject to interferences that cannot be compensated easily in any other way. More details are given in section 1.9. aliquot: this refers to that fraction of the sample taken for analysis C5g sample aliquots'). analyse, determine: Samples are 'analysed' for elements but elements are 'determined' in a sample. analyte: The species for which a determination is sought. Interference: A non-linearity introduced into the analytical signal, the magnitude of which depends on the concentration of some other components in the sample. matrix effect: An interference caused by the composition (or mineralogical structure) of the matrix in which the element to be analysed resides. stoichiometry: A mineral or a chemical compound is said to be stoichiometric if the elemental constituents exist in the exact atomic proportions predicted by the chemical formula (for example, EU203 is stoichiometric, Eu 2_ x0 3 is not). blank: The analytical blank is the concentration of an element in a sample that has been chemically prepared and analysed without the addition of a silicate rock sample. Blank concentrations of an element arise from impurities in chemical reagents used for preparative chemistry and from contamination from the laboratory environment. Measures to overcome these contamination effects are considered in section 1.7. homogeneity: Homogeneity relates to the property that different aliquots of the same sample are identical in chemical composition. Since almost all silicate rocks are composed of discrete minerals, and therefore have bulk compositions that are intrinsically inhomogeneous at the mineral level, it is necessary to specify the mass at which the rock sample is expected to be homogeneous Chomogeneous at the 19 sampling level'). Sample homogeneity is discussed further in section 1.6.

3

1.3

CONCEPTS IN ANALYTICAL CHEMISTRY

Table 1.2 SI base units Physical quantity length mass time electric current thermodynamic temperature amount of substance luminous intensity Supplementary units: plane angle solid angle

Table 1.4 SI defined prefixes for multiples and fractions of 10 Name ofSI unit metre kilogram second ampere

Symbol m kg s

A

kelvin mole candela

K mol cd

radian steradian

rad sr

Fraction or multiple 10- 18

10-"

10- 12 10- 9 10- 6 10- 3 10-2 10- 1 10 102 103 106 109 10 12

SI prefix

Symbol

atto femto pico nano micro milli centi deci deca hecto kilo mega giga tera

a f p n u m c d da h k M

G T

1.3 Units of measurement: the international system (81) of units

1.3.1

The Sf system

The present generation of scientists has seen some major changes in the units internationally adopted for scientific measurements. In the tussle between the proponents of the cgs system (based on the centimetre, gram and secpnd) and the MKS system (based on the metre, kilogram and second), the latter prevailed. The ruling body on these matters is the General Conference on Weights and Measures (CIPM). In general, as far as analytical chemistry is concerned, these decisions are enacted through the influential International Union of Pure and Applied Chemistry (lUPAC). The convention internationally adopted for the reporting of all scientific measurements is the SI system (the International System of units). This convention defines not only base units but also a range of compatible derived units together with rules for abbreviations and terminology. The system recognises seven base units and two additional supplementary units. These units form a unique and coherent system.

1.3.2 Sf base units The base units used in the SI system are all dimensionally independent. They are listed in Table 1.2, together with the two supplementary units. Each of these units is precisely defined as shown in Table 1.3. Particular emphasis must be placed on distinguishing between the meaning of mass and mole. The mass of a substance is related to the amount of that substance present as normally measured in the laboratory by its weight. The number of moles present is related to the quantity of discrete entities present. In 0.012 kg (i.e. 12 g) of carbon-12, the number of carbon atoms present is given by the Avogadro constant, that is 6.022 x 10 23. This constitutes one mole of carbon-12 atoms. Similarly one mole of the reagent ferric chloride (FeCI3) is equivalent to 162.206 g of reagent (Fe = 55.847+3CI = 3 x 35.453), one mole of Fe has a mass of 55.847 g and one mole of electrons e- has a mass of 5.4859 x 10- 10 g. Each of these masses contains the same number of specified entities (6.022 x 10 23).

Table 1.3 SI base units Metre: the length equal to I 650763.73 wavelengths in vacuum of the radiation corresponding to the transition between the levels 2PlO and 5ds of the krypton-86 atom. Kilogram: the mass equal to the mass of the international prototype of the kilogram; that is a certain piece of platinum-iridium kept at the International Bureau of Weights and Measures, Sevres, France. Second: the duration of 9 192 631 770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the caesium-l33 atom. Ampere: that constant current which if maintained in two straight parallel conductors of infinite length of negligible circular cross-section, and placed one metre apart in vacuum, would produce between these conductors a force equal to 2 x 10- 7 newton per metre oflength. Kelvin: unit of thermodynamic temperature being the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. The triple point of~ater is the temperature at which ice, water and water vapour can coexist in equilibrium. Mole: the amount"1}f a substance of a system which contains as many elementary entities as there are atoms in 0.012 kilograms of carbon12. When the mole is used, the elementary entities must be specified (e.g. atoms, molecules, ions, electrons etc). Candela: the luminous intensity, in the perpendicular direction, of a surface of 1/600 000 square metre of a black body at the temperature of freezing platinum under a pressure of 101325 newtons per square metre. Supplementary SI units Radian: the plane angle between two radii of a circle which cuts off on the circumference an arc of length equal to the radius. Steradian: solid angle which, having its vertex at the centre of a sphere, cuts off an area of the surface of the sphere equal to that of a square with sides of length equal to the radius of the sphere.

4

CONCEPTS IN ANALYTICAL CHEMISTRY

1.3

Table '1.5 SI derived units Physical quantity

Name of SI unit

area concentration

square metre mole per cubic metre kilogram per cubic metre metre per second cubic metre I per metre hertz joule newton watt pascal coulomb

density velocity volume wavenumber frequency energy force power pressure electric charge electrical potential difference electrical resistance electrical conductance electrical capacitance magnetic flux inductance magnetic flux density (magnetic induction) radioactivity radiation absorbed dose radiation absorbed dose equivalent

1.3.3

Symbol

m' molm- J kgm- 3

volt ohm siemens farad weber henry tesla

Wb H T

kgm's-J A-I =1 A -I S-I kg m' s - J A -, = VA - I = S - I kg-I m-'sJ A' = g-I A's4 kg- I m-' = AsV- 1 kgm's- 2A- I =Vs kgm's-'A- 2 = VA-IS kgs- 2 A- I = Vsm-'

becquerel gray sievert

Bq Gy Sv

S-I Jkg- I J kg-I in tissue

V g S F

Fractions and multiples of ten

Derived units

Having established a set of base units, the SI system then defines a set of dimensionally compatible derived units. These units are listed in Table 1.5. Thus the SI unit of pressure is the pascal. Note that the unit itself is written with a lowercase p (even though it might otherwise be assumed to represent a proper name) whereas the symbol is written in uppercase: Pa.

1.3.5

ms I m3 m- I S-I kgm's-' kgms-' = Jm- I kgm's-J = J S-I kgm- I S-2 = N m-' = Jm- J As

Hz J N W Pa C

The SI convention defines prefixes for specifying fractions and multiples of ten of the base units. These prefixes and symbols are listed in Table 1A. When applied to the kilogram, these prefixes are used as if the base unit were the gram (that is 10- 6 kg = milligram, not microkilogram).

1.3 A

Definition in SI units

litre (instead of the cubic decimetre) and the tonne (instead of the megagram). Their use has been continued under the SI system due to their widespread adoption in science and commerce. In Table 1.7, some non-SI units, which nevertheless continue to be used under the SI system, are listed. These units include the hour and day and geometric degree, minute and second. It is interesting to note from the point of view of measuring the half-life of long-lived radioactive elements or the age of rocks, neither the month nor the year appear to be exactly defined under the SI system. Both the atomic mass unit and the electron volt continue to be used in scientific circles due to the lack of a suitable alternative. Neither is exactly defined under the S1 system, since both arc physical quantities, the measurement of which involves finite error. All the units defined above are suitable for modern scientific usage and, with the exceptions mentioned, are fully coherent. The Sf symbol is internationally accepted for all

Other Sf units

Due to popular usage or the lack of a suitable SI alternative a few 'rogue' units are tolerated under the SI system. These are listed in Tables 1.6 and 1.7. Table 1.6 lists two units that effectively represent 'nicknames' of legitimate SI units, the

Table 1.7 Non-Sl units accepted for use Physical quantity time

Table 1.6 Common names for SI units accepted for use under the SI system Physical quantity

Symbol Common name of unit

SI name of unit

volume mass

litre tonne

cubic decimetre megagram

L

SI symbol dm' Mg

Name of unit

minute hour day geometric degree angle minute second mass atomic mass unit energy electron volt

Symbol

SI definition of unit

mm h d

I min = 60s I h = 3600s 1 d = 86400s 1 = (n/180) rad l' = (n/l0 800) rad I" = (n/648 000) rad 1/12 mass of a 12C atom 1 amu ;::; 1.6605 x 10- 27 kg 1 eV;::; 1.6022 x 1O- 1Q J 0

amu eV

5

1.3

CONCEPTS IN ANALYTICAL CHEMISTRY

scientific publications although some language variations exist in the spelling of the corresponding SI name. SI units may be used flexibly and usage is not strictly limited to dimensions specified in terms of base units. Thus density measurements quoted in traditional units of g cm- 3 are acceptable under the SI system as an alternative to the more formal kg m- 3 . 1.3.6

Units not compatible with the Sf system

Several traditional units are still in widespread scientific use. All are unnecessary, since perfectly acceptable SI alternatives exist: the continued use of these units is therefore discouraged and is likely to be eventually outlawed in scientific publications. Units in this category are listed in Table 1.8. They can be divided into two categories: units which are exact multiples of 10 of equivalent units under the SI system, and secondly, units where conversion involves multiplication by some other factor. For the more important

units in the latter category, the exact conversion factor has been agreed under the SI system and is listed in Table 1.8. It can be seen that one or two of these non-compatible units have very persistent scientific traditions, for example, the use of the barn to quote nuclear reaction cross-sections, the torr to measure vacuum pressure and the degree Celsius (or even worse, the degree Centigrade) to measure temperature. All are, however, doomed: use of the femtometre 2, pascal and kelvin will eventually prevail! Although discomaged, their use is perpetuated in this text where it reflects CUffent scientific practice. 1.3.7

Physical constants

Many physical phenomena are used to make analytical measurements. In the mathematical treatment of these phenomena, various physical constants are used. The more important of these, expressed in SI units, are listed in Table 1.9.

Table 1.8 Non-SI units, use of which is discouraged Non-SI units exactly defined

Decimal fractions of SI units Physical quantity

Name of unit

length

angstrom micron

mass area

/l

barn

b

force pressure

dyne bar

dyn bar

energy kinematic viscosity dynamic viscosity magnetic flux magnetic flux density (magnetic induction) activity radioactive exposure

Symbol

Definition

Name of unit

Symbol

Definition

A

1O-lOm 1O- 6m = l/lm

inch

in

2.54 x IO-'m

pound

lb

0.453 592 37 kg

atmosphere millimetre of mercury torr

atm mmHg

kilowatt hour thermochemical calorie

kWh

101 325Pa 13.5951 x 9.80665Pa (101325/ 760)Pa 3.6 x 106J

cal'h

4.184J

curie

Ci

3.7 x 101Os- 1

rontgen

R

2.58 x 1O- 4 Ckg- 1 (in air)

10- 28 m' = 100fm' 1O- 5N 105Pa

erg

erg

1O- 7J

stokes

St

1O- m's-1

poise maxwell

P Mx

1O- 1Pas 1O- 8Wb

gauss

G,Gs

1O- 4T

Torr

4

radiation absorbed dose

rad

rad

10- 2 Jkg- 1 = IO-'Gy

radiation absorbed dose equivalent

rem

rem

10- 2 J kg-I = IO-'Sv

thermodynamic temperature interval

Celsius

0C

T -273.15K .~-------

By international agreement, conversion factors given in this table are exact. Data from McGlashan (1971).

6

CONCEPTS IN ANALYTICAL CHEMISTRY

Table 1.9 Recommended values of selected physical constants. Name of physical constant

Symbol

Value

speed of light in vacuum unified atomic mass constant mass of a proton mass of a neutron mass of an electron charge on an electron electron radius Boltzmann constant Planck constant Bohr magneton Avogadro constant gas constant Faraday constant

c

2.9979250 x 10'ms- '

mu

= m/'C)j 12

1.660531 x 10

27

kg

m, e

1.672614 x 1O- 27 kg 1.674920 x 10- 27 kg 9.109558 x 10- 31 kg 1.6021917 x 1O- '9 C

r, = e'/4rreom,c' k h m B = eh/4rrm, Lor NA R = Lk F = Le

2.817939 x 1O- lS m 1.380622 x 10- 23 JK- ' 6.626 196 x 10- 34 Js 9.274096 x 10- 24 Am' 6.022 x 1023 mol-I 8.314 34JK -Imol-I 9.648670 x 104 Cmol- '

mp mn

Data from McGlashan (1971).

1.3.8

Molarity, normality and concentrations

When specifying the concentration of reagent in solution for use in a chemical reaction, strict SI conventions are not followed, and we enter an area where the tradition of the chemical literature is not supported by SI ratification. The formal unit of concentration under the SI system is the mole per cubic metre (or the mole per kg for solid solutions). However, this convention is not followed in the chemical literature. Concentration of reagents is normally expressed as molarity or molar concentration. This is the moles of reagent dissolved in one litre of solution (concentrations in grams per litre are also sometimes used). Thus a one molar (1M) solution of HCI contains a concentration equivalent to 36.461g of anhydrous HCI (i.e. one mole) dissolved in one litre of solution. By the same reasoning, a 0.5M solution of H 2 S04 contains the equivalent of 0.5 x 98.074 = 49.04g of anhydrous H 2S04 in one litre of solution. In some circumstances it is desirable to specify the concentration of a reagent that is equivalent to that of another reagent participating in a specified chemical reaction. The unit selected to describe this phenomenon is the normality. This unit has meaning only if the participating reaction is specified. Such reactions could include acid-base neutralization, oxidation-reduction, complex formation or precipitation reactions. In a simple example of an acid-base neutralization, (1.1)

for this reaction to go to completion one equivalent of hydrochloric acid solution must be mixed with one equivalent of sodium hydroxide solution. The equivalent weight in the context of this acid-base reaction is the weight of reagent (in grams) that reacts with, or contributes one mole of hydrogen ions to, the reaction. A one normal solution of the reagent contains one equivalent weight of the reagent dissolved in one litre of solution. Thus, in the above example, a one normal (IN) solution of HCI represents a concentration equal to one equivalent

1.4

weight ofHCI (i.e. 36.46Ig) in one litre of solution. For both these reagents (HCI and NaOH) the concentration of a 1M solution is exactly equivalent to that of a IN solution. However this is not the case for the acid-base reaction H 2S0 4+2NaOH

-->

Na2S04+2H20

(1.2)

Sulphuric acid, although not fully ionized in solution, can nevertheless contribute two hydrogen ions to this reaction. A IN solution is therefore now identical to a 0.5 M solution of H 2S04 and contains 0.5 x 98.074 = 49.04g of anhydrous sulphuric acid per litre of solution. Similar definitions of equivalent weight and normality exist for solutions used in oxidation-reduction and complexformation reactions. In each case, the molarity of a reagent refers to its concentration expressed as the proportion of formula weight (in grams) per litre of solution and the normality refers to the equivalent weight per litre identified in terms of a specific reaction. In trace element solution chemistry it is frequently necessary to prepare or specify solutions at low concentrations where mg, {lm or ng of element per mL of solution are the appropriate units. In this context the unit 'part per million' (ppm) is both unnecessary and ambiguous as an alternative to the {lg mL - I, since it is often misinterpreted as representing one part by weight of analyte per 106 parts by volume (not weight) of solution. This would only be the case on the unlikely asumption that the solution density was exactly I kg m - 3 Use of the ppm is equally unnecessary, though still widely used, in reporting trace element concentrations as a fraction of sample weight. The SI equivalent {lg/g is more correct. Major elements are normally reported as % by weight calculated as the oxide.

1.4 Statistics Two views are taken of statistics. One is a political condemnation as lies, damned lies and statistics, and the other is a more positive definition in terms of the art of determining the probable from the possible. Whatever the point of view, there is no doubt that statistics have an essential, though sometimes abused, role to play in analytical chemistry. 1.4.1

Errors in analytical data

All analytical measurements are subject to error and these can be classified into three groups. (a) Indeterminate or random errors. Such errors arc an inherent part of the operation of all analytical instrumentation and cannot be eliminated, though it is sometimes possible to reduce their magnitude. Indeterminate errors arise from electronic noise, the random emission of x-ray or gamma-ray photons, flame flicker effects, etc. The magnitude of these errors can be determined by repetitive measurement on the same sample. The principal use of statistical procedures is to predict the 'true' value from a group of individual measurements each containing random errors. (b) Determinate errors or systematic bias. One of the more pragmatic laws of analytical chemistry is that all analytical techniques are subject to determinate error and that all analysts are subject to systematic bias. Often such bias 7

1.4

CONCEPTS IN ANALYTICAL CHEMISTRY

remains unsuspected and undetected and is the major cause of interlaboratory discrepancies. Systematic bias can arise from instrumental drift effects, uncertainties in matrix correction procedures, or instrument misalignment. Questionable personal judgments, such as an inappropriate choice of reference materials to set up a calibration, or doubtful choice of operating conditions, also result in systematic bias. Personal bias also has the effect of influencing results so that they come closer to a preconceived notion of the true value for a measurement. The only guard against bias is a careful and systematic study of the performance of a technique in the analysis of as many reference materials as are available. Given the uncertainties in 'recommended' compositions of such materials (see section 1.10.7), this remains the ultimate challenge facing the analyst. Systematic bias does have one prominent feature-it normally affects results in one direction so that all data are either too high or too low. (c) Gross errors. A third class of error affects analytical results. These are much less insidious than systematic bias, are usually readily detected, and lead to the abandonment of the analysis. Such errors arise from serious malfunction of equipment, mislabelling of samples or failure of the operator to press the correct buttons in the right order (i.e. finger trouble). Usually such errors are temporary and have a readily identifiable source. Errors in this category can be avoided by self-discipline, a systematic scheme of work with cross-checking, and sometimes by automation so that repetitive operations are carried out under computer control. In these categories, statistics can only be used to predict the true value from sets of data subject to random error. Statistics can be used to test for the presence of, but not to correct for, the effects of systematic bias. 1.4.2

Accuracy and precision

The distinction between accuracy and preClSlon often causes some confusion to new users of analytical techniques. The difference can be seen from data in Figure 1.2. Precision is a measure of the analytical repeatability. A precise analysis is one where a set of replicate analyses forms a tight cluster about the average. The degree of precision is normally measured by the standard deviation of the analyses (see below), a measure of width of the data distribution peak. Accuracy is a measure of how close the analysed data lie to the 'true' composition of the sample. One of the difficulties in silicate rock analysis is that the true composition even in reference material is sometimes poorly known. To charaterize the difference between accuracy and precision, data in Figure 1.2 show the hypothetical determination of cobalt by two techniques. The neutron activation data in Figure 1.2a are of high precision, cobalt being efficiently excited by INAA. Conversely, the x-ray fluorescence data are of rather poor precision (this particular element is usually inefficiently excited by XRF and suffers some spectrum interferences). However, neither set of data in Figure 1.2a can be considered to be accurate since each set clusters about an average which does not centre on the 'true' value. Data obtained by INAA in Figure 1.2b can be considered to be both precise and accurate. The equivalent XRF data could not be considered to be accurate since the precision is

8

(a)

(b)

----'