LOD and Other Error Sources

8/3/2019 LOD and Other Error Sources

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Sample Preparation

Page 1 2009 Bruker Biosciences Commercial in Confidence

,Powders and Solids

Sources of Error

02/11/2009Bruker Confidential1

n

X-ray Fluorescence

Overview

General introduction in sample preparation for XRF

Sample Preparation for Liquids, Powders and Solids Introduction

Penetration- and Information Depth

Grain- or Particle Size Effect (Powders)

Crystallographic- or Mineralogical Effect (Powders)

Sample Preparation Techniques

Sources of Error Introduction

Sample Preparation Errors

Instrument Errors


Definitions

Sample PreparationIntroduction

Parameters of interest in Sample Preparation:

Physical form (liquid, powder, rock, bulk, ...)

Sample size (does it fit in the sample cup)

Ease of sampling: representative

Quantity of sample

Time per sample

Cost per sample

Reproducibility of preparation



XRF is an analysis by comparison

Accuracy of the analysis will be dependent on:

Quality of standards: primary or secondary standards

Quality of calibration: use of the right correction model

Calibration maintenance: re-calibration against drift

Instrument reproducibility: stable spectrometer?

Sample taking: representative for the bulk?

Sample preparation: is the method reproducible?

no sample preparation reproducibility... no measurement reproducibility



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Sample Preparation



Sample preparation is the largest source of error

Many forms of samples exist, 3 broad categories of specimen

preparation can be distinguished:

directly measurable after one simple treatment

significant pre-treatment, e.g. heterogeneous samples

special treatment, e.g. radioactive samples

Types of samples:

Bulk solids

Powders

Li uids


Gases


Methods of specimen preparation:

Form TreatmentBulk SolidsHomogeneousHeterogeneous

PowdersHomogeneousHeterogeneous

L i u ids

Grind to give flat surfaceDissolve or react to give a solution or ahomogeneous melt

Grind and press into a pelletGrind and fuse with a flux (e.g. borax)


Homogeneous (concentrated)Homogeneous (diluted)Heterogeneous

GasesAirborne Dusts

Analyse directly or dilutePreconcentrationFilter to remove solids

Aspirate through a filter to remove thesolids

Sample PreparationPenetration- and Information Depth

Penetration Depth

Information or Critical Depth


high energy photons

Surface treatment is moreimportant for heavy matrices !

Light matrices are more criticalwhen it comes to informationdepths

Sample PreparationPenetration- and Information Depth

Line Energy Graphite Glass Iron Lead

Cd KA1 23,17 keV 14,46 cm 8,20 mm 0,70 mm 77,30 m

Mo KA1 17,48 6,06 3,60 0,31 36,70

Cu KA1 8,05 5,51 mm 0,38 36,40 m 20,00

Ni KA1 7,48 4,39 0,31 29,80 16,60Fe KA1 6,40 2,72 0,20 * 164,00 11,10

Cr KA1 5,41 1,62 0,12 104,00 7,23

S KA1 2,31 116,00 m 14,80 m 10,10 4,83

Mg KA1 1,25 20,00 7,08 1,92 1,13

F KA1 0,68 3,70 1,71 0,36 0,26

N KA1 0,39 0,83 1,11 0,08 0,07


0,001 m = 1 nm = 10

Atomradius: 0,5 - 3

C KA1 0,28 * 13,60 0,42 0,03 0,03

B KA1 0,18 4,19 0,13 0,01 0,01


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Sample Preparation


Sample PreparationSample taking

Bulk10x kg

10 - 1000 g

Sampling

Pulverising,Pelletising orFusing


1 - 10 g

Specimen

X- ray Spectrometer Precise and accurate result

Sample Preparation

Definition of Accuracy and Precision

High AccuracyHigh Precision

High AccuracyLow Precision


Low AccuracyLow Precision

Low AccuracyHigh Precision

Sample Preparation for

Liquids, Powders and Solids


Sample PreparationPowders

Sampling

Grinding or pulverizing reducing the grain size and homogenising grinding vessel: WC, ZrO2, Stainless Steel

o hardness and application (contamination possibility)o cross contamination after cleaning, pre-grinding

grinding time grinding or binding aid

sieve diameter

Direct measurement in a liquid cup or...


binding aid pressure and pressure time


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Sample Preparation


Sample preparation simple recipes, not rocket science

Pressed PelletsUseweighedamount of

Addgrindingtablets

Mill ingrindingvessel

sample

Finishedpowder

Pour intoSample

GetPressed


material Press Pellet

Effect of binder on analyte line intensity



minimum quantity is generally 5g

little quantities: small spot analysis,

r r

pressure as pure pellet, on a support

layer of boric acid, in steel rings or in

aluminum cups

binder if necessary

(contamination with binder elements!)

Mowiol (components: C, H and O)

boric acid (components: B, H and O)

wax (components: C and H)

r ind in a ids


Sample PreparationPowdersGrain- or particle size effect

analysed layerSiO2

Al2O3


ISi= f (NpSiO2)Volume

IAl = f (NpAl2O3)Volume

Analysed layer = homogeneous distribution


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Sample Preparation



Crystallographic- or mineralogical effect

SiO2

AlxSiyOz

pressed powdersloose powders

analysed layer


ISi= f ((NpSiO2)+(NpAlAlxSiyOz ))Volume

IAl= f (NpAlxSiyOz)Volume

SSiO2(kcps/%)SAlxSiyOz

Sample PreparationPowders as Pressed pellets


Quelle: Socachim 2006

Influence of particle size and pressure on analyte intensity


Sample Preparation

Fusion technique


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Sample Preparation


Sample preparation simple recipes, not rocket scienceFusions

Pour flux meltingagent into mortar

Weigh sampleand flux

Add sample toflux

Mix sample andflux material


Pour materialinto crucible

Heat crucible inmelting furnace

Casting mold withfinished glass bead

Sample PreparationFused beads

better reproducibility, accuracy

matrix and particle size effects areeliminated

Hom eneity is im roved

Flat surface;

Relatively fast (depends on)


What is fusion?

Chemical reaction based on kovalent binding betweenboron groups and oxides. The result is a glass bead.

Quelle: Socachim2006




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Sample Preparation







What is fusion?



Sample PreparationXRF-analysis offused beads

minimum quantity in general: 1g

modern fluxes

lithiumtetraborate Li2B4O7

lithiummetaborate LiBO2 fusion in electrical, induction or gas


mixtures of Li2B4O7 and LiBO2

o eventually some LiBr can be added as

a non-wetting agent

platinum ware necessary

(crucibles and moulds)

, -automated


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Sample Preparation





What is fusion?



Important parameters


Particle size (< 100m)

Sample to flux ratio (Dilution varies to 1/30)

Type of flux (LiT,LiM, both)

Temperature ( 975C 1275C)

Time (3-10, 20 Minutes) depends on.

Furnace or fusion device

Oxidizing agent (Nitrates, Iodates)

Additives like Halides (NaI, LiBr, LiI)

Crucible and dish material (preheating is important)

Cooling and solidification

Additives


Efficiency of fusion and casting

o LiF, B2O3, Li 2CO3

Non wetting

o Iodides, Bromine's,Perjodides, (Chlorides) of Li, NH4,

Heavy absorbers

o La, Ce, Ba oxides

Internal standards


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Sample Preparation


Cooling and Solidification


0C

Complete crystallization

LiMBNaTB

Crystallization Curve

Time

White Opaque Bead

Bead will crack as a result of stress

Cooling OK

Sample PreparationSolution for sample effects in Powders

Elimination of grain size- and mineralogical effects:

Grain SizeEffect

MineralogicalEffect

Grain sizereduction

YES NO

Pressed Pellet YES NO


Fusion YES YES

Sample Preparation

Preparation in Liquid cups

Sample preparation simple recipes, not rocket scienceLiquids

Cover bottom of liquidcup with transparentfilm

Check for holesPipette sampleamount to definedweight



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Sample Preparation


Sample PreparationLiquids

Water, oil, fuel, solvents, slurries

He-device necessary

In principle liquids are homogeneous

Depending on sampling, measurement in liquid cups

or on filters (liquids with particles: filtering and

measuring filter and filtrate)

filters with hydrofobic ring

Dilution leads to intensit loss


Sample PreparationLiquids

element range: from Na to U

minimum quantity in general: 5g

selection of foil

resistance

(chemical attack by sample

material, embrittlement by X-

ray exposure)

"as thick/stable as necessary"


transm ttance absorption

LLD for light elements

"as thin/transparent as

possible"

Sample Preparation: LiquidsDegradation Resistance of Thin-Film Substances

Chemical Classification Mylar Polycarbonate Polypropylene Polyimide(Kapton)

Prolene Ultra-Polyester

Acids, dilute or weak G G E N G G

Acids, concentrated G G E N E G

Alcohols, aliphatic N G E G E NAldehydes U F E E E U

Alkalies, concentrated N N E E E N

Esters N N G G G N

Ethers F N N U N F

Hydrocarbans, aliphatic G N G G G G

Hydrocarbons, aromatic F N F F F F


Hydrocarbons, halogenated F N N F N F

Ketones N N G G G N

Oxidizing agents F N F N F F

E = Excellent, G = Good, F = Fair, N = Not Recommended, U = Unknown

Sample Preparation: LiquidsTransmittance Curves for Various Thin-FilmSubstances



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Sample Preparation


Sample PreparationSolids

Types of solid samples:

Metals & Alloys: Steel, Aluminum, Zinc,

Plastics: PE, PP,

Rocks/Large pieces of metals (Fe-alloys)

Odd shaped Solids

The aim is obtaining a surface that can easily be measuredwith XRF



Metals & Alloys

. . Resurfacing: depends on the type of material

Grinding: refer to powders

Turning: for soft materials: e.g. Pb and Al

Polishing: for hard materials: e.g. steel Important parameters:

Hardness of material

Grit size


Cross contamination

Sample preparation simple recipes, not rocket scienceMetals

Clamp metal cut Check sample heightat molding cutter

Mill Check surface



Plastics as hot pressed tablet or as grains in a liquid cup

Rocks/Large pieces of metals (Fe-alloys) Reduce size and treat as powder

Odd shaped solids Dissolve in acid or make as a glass bead

Small s ot calibration: direct anal sis


Standardless Analysis


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Sample Preparation


Sample PreparationInfluence of bad sample surface

R( k c ps) = f ( 1 / d 2)

Non flat samples

Concave (Distance, Shadow effect)

Convex (Distance, Shadow effect)

Surface finish (Shadow effect)

= part of spectrum not

being irradiated,

especially for lighter

elements

Sample PreparationConclusions

Sampling and sample preparation depend on many

parameters

Important physical effects have to be taken into account for

the specimen preparation

Powder- and liquid samples can be prepared in a relatively

simple way

Different preparation techniques exist to prepare specimens

46

Sample preparation is always compromise: costs, time tospend, analytical tasks and available lab stuff

Sample PreparationThe one commandment

Whatever sample preparation method you

choose, verify its reproducibility before you

start preparing the calibration standardsSources of Error


S l P i


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Sample Preparation


Sources of ErrorIntroduction

Possible sources of error:

Sample taking

Samp e preparation

Instrument precision

Counting Statistical Error (CSE)

Chemical data of standards

Inaccuracies during calibration

===> Total error in the end result of the analysis of the unknownsamples


Sources of ErrorTypes of error

Random Errors: non-systematic fluctuations Equipment errors

o Generator and/or X-ray tube instability

Operator errorso Bad sample preparation

o Count ing s ta t i s t i cs (time dependant)

Systematic Errors: a consistent deviation Equipment errors

o Errors in calibration (model, corrections)


o Dead time losses Sample errors: Absorption, enhancement , particle effects, chemical state

Sources of ErrorTypes of error

i

(Rp)i = Si C(%)i + (Rb)i

p i

X

Si Random Error

Systematic Error


(Rb)i

Concentration (%)i

Sources of ErrorSensitivity

The Sensitivity Si of the spectrometer for an element i

= the number of detected X-ray photons N (counts)

divided by the measurement time t

divided by the concentration Ci of the element i

( kcps / % or kcps / ppm )


i

i

Ct

NS

=

S l P ti


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Sample Preparation


Sources of ErrorThe Counting Statistical Error (CSE)

r = counts per second (cps)

CSE

N

NCSE

=

=

%100(%)

%100(%)

r =S . C


trCSE

=

%100(%)

Longer counting time,better relative CSE

Sources of ErrorThe Counting Statistical Error

For N = 100

N +/- 1 * SQRT (N) 1 68.3 % 90 - 110

N +/- 2 * SQRT (N) 2 95.5 % 80 - 120

N +/- 3 * SQRT (N) 3 99.7 % 70 - 130


Sources of ErrorThe Counting Statistical Error

The precision is limited by the CSE, mostly expressed as %CSE(relative value)

This means for 3-sigma:

= 100 SQRT (N) = 10 %CSE = 30 %

= 1000 SQRT (N) = 30 %CSE = 10 %

= 10 000 SQRT (N) = 100 %CSE = 3 %

NCSE

%100(%) =

For 1-sigma


= 100 000 SQRT (N) = 300 %CSE = 1 %

= 1000 000 SQRT (N) = 1000 %CSE = 0.3 %

= 10 000 000 SQRT (N) = 3000 %CSE = 0.1 %

Sources of ErrorThe Counting Statistical Error Sensitivity

N = S . t . C A high precision measurement

Counting statistical error (%)

u

a low statistical error

a high number of counts

therefore you need

an instrument with high sensitivity

or

long measurement times

3

%1003 =N

N


%1003

=

=

CtS

N

Sample Preparation


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Sample Preparation


Sources of ErrorMaximum Count Rate

The maximum count rate is limited by the detection system:

--

20 - 50 kcps

for the whole spectrum



Example 1:

major element

e.g. Cu in brass

0.1% counting statistical error

10 000 000 counts

Minimum measurement time given by maximum of detector countrate:

ED-XRF: 200 - 500 s



Example 2:

1 % Ni in steel

1 % counting statistical error

100 000 counts

the concentration of Fe is close to 100%

the intensity of Fe is about 100 times higher than the intensity of Ni



ED-XRF with Si(Li)-detector

maximum total signal 20 - 50 kcps

maximum Ni signal 200 - 500 cps

minimum measurement time 200 to 500 s


Sample Preparation


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Sample Preparation


Sources of ErrorThe Lower Limit of Detection (LLD)

e ana y ca per ormance ortrace elements is determined bythe peak-to-background ratio

typically the background in XRFis primary radiation scattered bythe sample


Sources of ErrorThe Lower Limit of Detection

the peak-to-background ratio is

equal in both diagrams

the measurement shown bottom left

is clearly better because the nett

signal is better separated from the

background signal

What parameter can

describe this difference ?



Lower Limit of Detection (LLD)e ne as:

the concentration giving

a net signal equal to

3 times the background noise

background noise

= CSE of the background signal


tcpsBKG = )(


Lower Limit of Detection in ppm

The LLD is typically defined for t = 100 s (S in cps/ppm)

tcpsBKG = )(3

tLLDCSsignalNett = )(_


tSppmLLD )( =

Sample Preparation


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Sample Preparation


Sources of ErrorConclusions

Two main types of error: random and systematic

Equipment, sample and operator are the largest sources of error

Sensitivity and measurement time are very important parameters in

the counting statistic

Good counting statistics means reaching low limits of detection

Many parameters have to be taken into account in order to obtain a

good analytical result


Documents

LOD and Other Error Sources