ISO 16666:2025

International
Standard
ISO 16666
First edition
Surface chemical analysis — Total
2025-11
reflection X-ray fluorescence
— Principles and general
requirements
Reference number
© ISO 2025
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms, definitions and abbreviations . 1
3.1 Abbreviated terms .1
4 Physical background of TXRF . 2
4.1 General .2
4.2 Definition of angle and X-ray path in TXRF geometry .3
4.3 Beam projection .4
4.4 X-ray standing waves (XSW) .4
4.5 Fluorescence intensity .6
5 Instrumental requirements . . 6
5.1 Description of various possible TXRF measurement setups .6
5.2 Beam conditioning .8
5.2.1 Requirement .8
5.2.2 Beam guidance .8
5.2.3 Beam modulation (tuning) .8
5.2.4 Measurement angles in TXRF .8
5.3 Reflector (sample carrier) .9
5.3.1 General requirements .9
5.3.2 Reflectors for chemical analysis.9
5.4 Reflector alignment.9
5.5 Detector .10
5.6 Sample station . .10
5.7 Control unit .10
6 Calibration and quality control .10
6.1 Angle inspection .10
6.2 Energy calibration .10
6.3 Calibration of the element sensitivities .11
6.4 Inspection of the sample excitation . 12
6.5 Inspection of the element detection . 12
7 Spectra analysis and Reporting .12
7.1 Spectra Processing . . 12
7.2 Reporting Spectra . 13
8 Samples .13
9 Qualitative and quantitative analysis . 14
9.1 Qualitative analysis .14
9.2 Quantitative analysis .14
9.2.1 Methods of quantitative analysis .14
9.3 Preparation of a measurement for quantitative analysis . 15
9.4 Procedure of a quantitative analysis by the element-specific sensitivity method
(internal standard addition) .16
9.5 Verification of quantitative TXRF measurements .17
9.6 Traceability in TXRF .17
Annex A (informative) Measurement angles in TXRF, background correction, peak correction,
spectrum deconvolution .18
Annex B (informative) Round-robin test for verification of the precision and accuracy of TXRF
spectroscopy .21
Bibliography .22

iii
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out through
ISO technical committees. Each member body interested in a subject for which a technical committee
has been established has the right to be represented on that committee. International organizations,
governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely
with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are described
in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the different types
of ISO document should be noted. This document was drafted in accordance with the editorial rules of the
ISO/IEC Directives, Part 2 (see www.iso.org/directives).
ISO draws attention to the possibility that the implementation of this document may involve the use of (a)
patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed patent
rights in respect thereof. As of the date of publication of this document, ISO had not received notice of (a)
patent(s) which may be required to implement this document. However, implementers are cautioned that
this may not represent the latest information, which may be obtained from the patent database available at
www.iso.org/patents. ISO shall not be held responsible for identifying any or all such patent rights.
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and expressions
related to conformity assessment, as well as information about ISO's adherence to the World Trade
Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 201, Surface chemical analysis, Subcommittee
SC 10, X-ray Reflectometry (XRR) and X-ray Fluorescence (XRF) Analysis.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.

iv
Introduction
Through general technical developments, total reflection X-ray fluorescence analysis (TXRF) has been
developed into a robust independent physical method of instrumental analytical chemistry. TXRF is
a distinct multi-element micro-method and a method of surface analysis. It is used for the simultaneous
qualitative detection of the elements and quantification of the element masses. Notably, only small
quantities of material are used for the analysis to benefit from all the advantages inherent to the procedure
and thus to achieve correct analysis values. TXRF is used alongside other atomic spectroscopic methods,
such as atomic absorption spectrometry (AAS) or inductively coupled plasma-based techniques (ICP-AES
and ICP-MS) that are also established in the field of element analysis. In addition, TXRF is used in surface
analysis and complements techniques such as Auger electron spectroscopy (AES), Rutherford backscattering
spectrometry (RBS) or secondary ion mass spectrometry (SIMS). The rapid and in part non-destructive
measurement process of a TXRF configuration allows screening or qualitative analysis of unknown flat,
film-like and particulate samples and is therefore a valuable addition to other analytical techniques.
The main difference between TXRF and conventional X-ray fluorescence spectrometry (XRF) is the efficient
way to excite the material to be examined to fluoresce which is achieved by a special geometrical arrangement
in the spectrometer. The spectral background is drastically reduced, the fluorescence intensity increased
resulting in a significant enhancement of the signal to noise ratio. Special sample treatment and sample
presentation are required for this purpose. If these boundary conditions are met, TXRF achieves a high
degree of accuracy and repeatability of the analyses, although a simplified calibration and quantification is
−12 10 2
used. The detection limits currently achievable with TXRF are approximately 10 g or 10 atoms/cm and
are thus orders of magnitude lower than for XRF. The relative element concentrations are, depending on the
matrix or the main components of the sample and for the elements to be examined, between 0,1 % and up to
−9
10 for the low concentrations.
This document describes the physical principles and instrumentation required for TXRF analysis
assuming that the conditions for total reflection are met, without referring to the samples’ specificity. As a
demonstration of the good reproducibility of the TXRF instruments, data from a round-robin test performed
using centrally prepared and optimized samples are presented (see Annex B).
Other standards focussing on specific case studies and procedures are available for silicon wafers (see
ISO 14706 and ISO 17331), environmental and biological samples (see ISO/TS 18507), and water (ISO 20289).

v
International Standard ISO 16666:2025(en)
Surface chemical analysis — Total reflection X-ray
fluorescence — Principles and general requirements
1 Scope
The document provides the physical principles and specifies instrumental requirements for total reflection
X-ray fluorescence analysis (TXRF) spectrometers. This document specifies general procedures for
calibration, method development and verification of TXRF measurements and quality control.
The document describes measurements with TXRF conditions having a fixed glancing angle below the
critical angle of total reflection and considerably enhanced excitation radiation intensity. Although certain
definitions of grazing incidence geometry are shown for clarification, this document is not applicable to
measurement setups working under such conditions.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content constitutes
requirements of this document. For dated references, only the edition cited applies. For undated references,
the latest edition of the referenced document (including any amendments) applies.
ISO 18115-1, Surface chemical analysis — Vocabulary — Part 1: General terms and terms used in spectroscopy
ISO 20289, Surface chemical analysis — Total reflection X-ray fluorescence analysis of water
JCGM 100, 2008, Joint Committee for Guides in Metrology, Evaluation of measurement data - Guide to the
expression of uncertainty in measurement
3 Terms, definitions and abbreviations
For the purposes of this document, the terms and definitions given in ISO 18115-1 apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1 Abbreviated terms
AAS Atomic Absorption Spectroscopy
FWHM Full Width at Half Maximum
GIXRF Gracing Incidence X-ray Fluorescence
ICP-MS Inductively Coupled Plasma-Mass Spectroscopy
ICP-AES Inductively Coupled Plasma –Atomic Emission Spectroscopy
SDD Silicon Drift Detector
XRF X-ray fluorescence
XRR X-ray reflectometry
XSW X-ray Standing Wave
TXRF Total Reflection X-ray Fluorescence
4 Physical background of TXRF
4.1 General
TXRF is based on the excitation (and detection) of element-specific X-ray fluorescence radiation at a very
small glancing angle (smaller than the critical angle of the total reflection of the sample carrier, see Figure 3
[1]
and 4.2) of the incident radiation .
Total reflection has two beneficial effects on the measurement.
a) Since the primary beam penetrates only a few nanometres into the sample carrier,
the proportion of radiation generated and detected by scattering and fluorescence
excitation of the carrier material is significantly lower than, e.g. in classic XRF,
which enables a lower background signal and thus better detection limits (Figure 1).
Key
X photon energy/keV
Y recorded counts
MES ICP-IV 1 mg/kg
blank
Figure 1 — Illustration of typical TXRF spectra. TXRF spectrum of a clean quartz carrier generated
by excitation with a Mo X-ray tube (dashed line); TXRF spectrum of a reference material with
23 elements of the same concentration (solid line)
b) With a well collimated beam (for details refer to [2]) and a sufficiently good substrate surface as well
as a suitable structure of the analyte, X-ray standing waves (XSW) with a location-dependent intensity
distribution (typically between 0 and 4 I ) are formed above the sample carrier surface, which on average
lead to an excitation of X-ray fluorescence which is about twice as strong (see detailed discussion in 4.4).
If no standing wave field occurs, the radiation passes through the analyte twice as an incident and a
reflected beam, which also leads to doubled fluorescence intensity.
The attenuation length is defined as perpendicular distance from the sample surface within the reflecting
medium at which the amplitude of the electric field associated with the propagating wave field is reduced

to 1/e of its original value at the surface. The value of the attenuation length depends on the primary X-ray
energy and the material properties of the reflector (Figure 2).
Key
X θ/°
Y attenuation length/µm
1 Si
2 Ni
3 Pt
Figure 2 — Attenuation length of X-radiation with an energy of 17,4 keV (Mo-Kα fluorescence line
[3]
energy) in various materials as a function of the grazing incidence angle θ
4.2 Definition of angle and X-ray path in TXRF geometry
An X-ray beam striking a surface at the grazing incidence angle (glancing angle) θ is partially reflected on
the surface (angle of the reflected beam to the surface also θ ) and partially penetrates the material
(Figure 3, beams C1/C2 and B1/B2). The angle of the refracted beam to the surface, θ , is calculated using
cos()θ n
1 2
Snell's law = with the energy-dependent refractive indices n for the material from which the
cos θ n
()
2 1
incident beam originates (typically air or vacuum) and n for the material on which the beam is refracted.
Since n is typically ≈ 1 and n is almost always less than 1 for X-rays, there is an angle θ for which θ
1 2 1 2
becomes zero and below this angle total external reflection occurs on the surface (Figure 3, beam A1). This
n
 
critical angle of total external reflection θ is calculated approximately according to θ =arccos .
c c  
n
 
Since very small angles in TXRF occur relative to the reflective surface, this document consistently uses
the so-called grazing incidence angle or glancing angle between the beam propagation direction and the
reflective surface as the measurement angle. In contrast to the so-called incidence angle, as it is usually
denoted by α, e.g. in Snell's law, the glancing angle is denoted by θ in this document.
With a larger grazing incidence angle (θ . θ . θ ), a larger part of the radiation penetrates the material
A1 B1 C1
and stimulates fluorescence radiation at greater sample depths which can be measured with a detector
above the sample (XRF measurement). Simultaneously, the intensity of the reflected radiation which is
detected along the X-ray path (XRR measurement) decreases with a larger angle.

With divergent primary excitation or a different grazing incidence angle θ, both the illuminated surface
or the photon density per area and the attenuation length of the primary beam change depending on the
position which can have a significant influence on the intensity of the measured fluorescence radiation.
Key
1 X-ray source
2 sample
3 XRF detector
Figure 3 — Definition of angle and X-ray path in TXRF and GIXRF geometries
4.3 Beam projection
Since very small glancing angles occur with TXRF, this has a large influence on the size of the primary beam
on the sample, the beam projection (surface) or, in the more common expression, the beam footprint. For a
uniform rectangular beam of height h and width w at a glancing angle θ the beam footprint will be
rectangular with an area of:
Fh= /sin()θ ×w (1)
With a beam height h = 0,1 mm and a typical glancing angle of 0,07° (70 % of the critical angle of the total
reflection of Mo-Kα radiation on Si), the footprint length is, for example, approximately 8 cm, which is
significantly larger than typical sample carriers and in particular than the entrance window size of the
detector. As a result, the majority of the photons are not available to excite detectable fluorescence radiation,
or they can excite parts of the measurement equipment (which should be prevented by further reducing the
beam size by means of slits or beam-shaping optics).
Furthermore, the beam projection surface can be very susceptible to adjustment errors and deviations in
the sample position and surface orientation due to the small glancing angle.
4.4 X-ray standing waves (XSW)
With monochromatic, parallel incident X-rays and a flat, smooth surface of the substrate, interference of the
electric fields of the incident and the reflected beam creates a location-dependent intensity distribution of
the radiation (Figure 4). It has usually a periodic structure with alternating intensity maxima and minima
depending on the distance to the substrate surface, the wavelength and the glancing angle of the incident
radiation.
When a standing wave is formed over a flat surface (e.g. an uncoated silicon or glass substrate), the
so-called period of the standing wave field is calculated, i.e. the constant distance between adjacent minima
perpendicular to the surface of the medium, according to
λ
d = (2)
XSW
2sinθ
For typical measurement parameters, e.g. Mo-Kα radiation (17,4 keV, λ = 0,071 nm) and glancing angle
θ = 0,057° (1 mrad) the resulting period is d = 35 nm.
XSW
If the sample quantity is small enough not to disturb the formation of the wave field, the local strength of
the electric field (and thus the intensity) is between 0 I and 4 I with I as intensity of the incident beam
0 0 0
radiation. If the analyte is in this case evenly distributed over a larger area of the wave field, there is an
average excitation of 2 I , just like without a wave field. In the case of an uneven distribution or size of the
analyte element over areas which are in the order of magnitude of the period of the XSW (typically a few nm),
it can be the case, however, that more of it is in the area of intensity maxima (or minima) and the excitation
of the fluorescence radiation is significantly higher (or lower). If an internal standard (IS) is used, it shall be
ensured in this case that the IS is locally distributed exactly like the element to be analysed, since the higher
(or lower) excitation intensity then applies to both and is compensated during quantification.
A more detailed description of the standing wave field including calculation examples and references can be
found in Reference [4].
Figure 4 — Illustration of the standing X-ray waves (XSW) above a reflective surface. Intensity
maxima are shown brightly. The grayscale illustrates the variation between 0 and 4 I with I being
0 0
the intensity of the incident beam (see 4.4). As the glancing angle θ increases, the distance d
XSW
[3]
between the maxima decreases (see Formula 2)
Figure 4 shows a simulation for the standing wave field above a flat, reflective surface. At 17,4 keV and a
grazing incidence angle θ = 0,07° intensity minima and maxima at approximately 30 nm distance are formed
above the substrate, while the amplitude of the electric field within the substrate decreases exponentially
with depth.
4.5 Fluorescence intensity
As a result of the standing waves generated, the intensity of the fluorescence radiation can vary depending
on both the measurement angle and the spatial extension (geometry) of the analysis sample. It is not the
sample type (see Clause 8) that is decisive here, but rather the material distribution on the surface and
the formation or disturbance of the standing wave field which depends on it. Thin layers but also very
evenly distributed small residues lead to an angle dependence of the fluorescence intensity with a clearly
pronounced intensity maximum (peak) in the area of the critical angle of total external reflection. In
contrast, the signal for inhomogeneous and large sample quantities is characterized by increased excitation
below this angle (since the beam penetrates the sample material twice) and lower intensity above.
In the area of total reflection, the fluorescence intensity of the sample radiation is doubled compared to the
intensity above the critical angle, corresponding to the mean intensity in the area of the standing wave (zero
in the minima, four times in the maxima). In the angular range below the critical angle, the fluorescence
intensity of residue or particle samples is therefore essentially independent of the angle. There is an
exception if the size of the sample or the particles perpendicular to the substrate is less than or in the same
order of magnitude as the period of the standing waves. Then, the assumption of an average intensity is no
longer correct, and an angle dependence appears again.
Furthermore, note that with increasing sample quantity, the formation of the standing wave field is
increasingly disturbed or completely prevented. This means, amongst others, that even with the same
measurement setup, the fluorescence signal does not mandatorily change analogously with the sample
quantity.
Depending on the structure of the layer system, a more complex angle-dependent fluorescence signal
can also occur, which is examined, e.g., with Grazing Incidence X-ray Fluorescence Analysis (GIXRF). By
modelling the sample and the standing wave field, conclusions can be drawn about the examined system.
In TXRF, the measurement usually takes place at a small angle below the prominent maximum, whereby
the exact angular position has a very strong influence on the intensity, which is in contrast to the less
angle-dependent intensity for particle-shaped samples below the critical angle of total reflection.
5 Instrumental requirements
5.1 Description of various possible TXRF measurement setups
a) d)
b) e)
c) f)
Key
1 X-ray source
2 detector
3 sample carrier, reflector
4 beam stop
5 primary beam
6 reflected beam
7 detector aperture
8 filter
9 beam-limiting (aperture)
10 crystal monochromator, Bragg or simple reflector
11 double crystal monochromator
12 Bragg reflector, double multilayer monochromator
13 focusing or parallel beam shaping, focusing or collimating multilayer
[3]
Figure 5 — Schematic representations of various possible TXRF measurement setups
Various TXRF measurement setups are possible and presented schematically in Figure 5.
a) Simple structure, radiation from an X-ray source is directed onto a sample carrier at a very small angle
and reflected there. If a small sample quantity is arranged on the sample carrier, it is efficiently excited
to X-ray fluorescence.
b) With effective beam guidance using filters and apertures, a significantly improved signal to background
ratio is achieved.
c) If a reflector, Bragg reflector or filters and apertures are used, an almost monochromatic primary beam
is generated. The effect of the components is that of a band-pass filter.
d) Like c), but with two reflectors or Bragg reflectors.
NOTE A setup at synchrotron facilities can apply more complex and configurable beam defining optics.
e) The use of a pair of reflectors or a pair of Bragg reflectors allows a parallel, tunable monochromatic
primary beam.
f) With a focusing reflector or focusing Bragg reflector, the photon density and thus the intensity of the
primary beam on the sample carrier can be increased.
For each configuration a different degree of photon density, monochromaticity, residual divergence/
convergence, and coherence of the incident beam and thus the XSW field is provided.

5.2 Beam conditioning
5.2.1 Requirement
In laboratory-based systems, the X-ray tube should be a line focus or micro focus tube; X-ray tubes to be used
are air-cooled low power or water-cooled high-power tubes. The primary X-ray energy shall be sufficiently
high to excite detectable fluorescence lines of the relevant elements. The irradiation of the sample along
beam direction at the angle of incidence should not be larger than 2/3 of diameter of the reflector. The
divergence shall be limited to guarantee total reflection conditions for the energy bandwidth of the exciting
beam spectrum. For details of setups at synchrotron facilities refer to [1].
Depending on the excitation energy or excitation mode and carrier material, the beam angle shall be below
the critical angle of total reflection and should be fixed to about 70 % of the critical angle. For certain
applications lower angles are permitted. The divergence of the primary beam should be restricted to ±0,02°.
Since the divergence of the beam is not under control by the user the excitation angle shall be checked
frequently as described in 6.1.
5.2.2 Beam guidance
A beam guidance, which is designed to be as clear, simple and for the shortest possible routes has advantages.
In addition to the photon density of the primary beam, which usually decreases with distance, parallel
radiation causes the sample in the spectrometer to be illuminated as homogeneously as possible. The
illuminated area on the sample carrier shall be selected to be significantly larger than the field of view of the
detector, while the size of the sample on the sample carrier should only fill an area of up to 70 % of the field
of view of the area of the detector to avoid partial shadowing effects. In the case of sample inhomogeneities,
they can lead to an incorrect quantitative analysis.
5.2.3 Beam modulation (tuning)
The primary beam can be modulated and shaped by a monochromator, a high- and low-pass filter, absorption
foils (primary beam filters), edge filters and beam-limiting apertures. Primary beam filters serve both for
coarse intensity control of the primary beam and for optimization of the excitation conditions via absorption
of the low-energy components of the radiation not removed by the monochromator or low-pass filter.
Typical monochromators are crystal reflectors, gratings or multilayer mirrors. A band-pass filter is used to
limit the range of the emitted X-ray spectrum. A band-pass filter can be designed as a combination of a high-
and low-pass filter, or as a monochromator. A beam-limiting aperture is a device for restricting the spatial
extension of the primary beam that cuts out undesirable components of the primary beam.
The low-pass filter generally consists of two beam-limiting apertures and a mirror for total reflection
located in-between. The inclination of the mirror can be chosen so that total reflection occurs only for low
energies (long wavelengths), whereas the critical angle is exceeded for high energies (short wavelengths)
and these are therefore only reflected to a very small extent.
In contrast, absorption foils (primary beam filters) can also be used to reduce the proportion of low-energy
radiation, since it is typically more strongly absorbed than high-energy photons.
Each beam modification has advantageous and disadvantageous effects. For example, a perfectly collimated
beam leads to the most effective XSW formation. However, a certain convergence provides a higher photon
flux at the sample position and thus more fluorescence radiation. An optimized trade-off has to be found for
different set-ups.
5.2.4 Measurement angles in TXRF
In this document, the measurement angle always means the glancing angle or the grazing incidence angle.
Regarding TXRF, the measurement angle is usually smaller than the critical angle, since total reflection only
occurs in this case. This angle depends on the photon energy and the material used for the reflector. For
details refer to Annex A.1.
If a curved monochromator is used, which is a common method to achieve higher flux density at the sample
location in laboratory instruments, it shall be ensured, that the beam convergence is significantly lower
than the total reflection angle. Otherwise, the total reflection condition may not be fulfilled over the entire
sample carrier and strong location-dependent differences in the measurement signal can occur.
When selecting the grazing angle of incidence, the following shall be taken into account: the critical angle for
the reflector material and the selected excitation radiation E, its energy bandwidth and the beam divergence.
The grazing incidence angle for the energy E must be smaller than the critical angle and selected so that the
contribution of the divergence at the reflector enables the conditions for total reflection at the upper end of
the energy bandwidth.
If an increased background signal occurs in the measurement spectrum, this can indicate that the glancing
angle is too large, i.e., that the measurement is no longer carried out in total reflection condition and there is
no TXRF.
5.3 Reflector (sample carrier)
5.3.1 General requirements
TXRF samples are generally applied to a reflector or sample carrier. Suitable sample carriers shall meet
certain physical and chemical requirements:
— no or only weak own fluorescence lines in the relevant photon energy range;
— good surface properties (flatness, roughness);
— chemical inertness;
[2]
— for reusable carriers, insensitivity of mechanical and chemical properties to cleaning protocols .
Frequently used materials for sample carriers are: quartz glass, acrylic glass, borosilicate glass (with
limitations), pure silicon, silicon carbide, boron nitride, glassy carbon, synthetic sapphire.
5.3.2 Reflectors for chemical analysis
Typical minimum requirement is to hold a reflector of a size of 30 mm in diameter and 2 mm to 3 mm in height.
Other types of reflectors are possible according to the manufacturer’s recommendation. The reflectors shall
be flat (λ/4; reference wavelength λ 632,8 nm) with a roughness of <5 nm and shall be free of impurities,
scratches and damages, with fluorescence peaks outside the region of interest and chemically inert.
For semiconductor applications, other reflector materials are used as described in ISO 14706.
5.4 Reflector alignment
Samples shall be loaded towards a reference plane which is defined as plane of reflection, either against
3 or 4 ball points or two cutting edges. Alternatively, a high precision goniometer can be used if an angle
deviation of lower than ±0,01° can be achieved. Although the angle of incidence is fixed an angle adjustment
(manually or automatically) shall be enabled (see 6.1).
The incident beam, the reflector surface and the detector shall be centred on the centre of rotation of the
reflector, by suitable means, capable of guaranteeing that, at the fixed angle of incidence, a 4 mm circular
dry residue at the centre of the reflector is within 80 % of the footprint of the beam and inside the field of
view of the detector.
NOTE With a beam height h = 0,1 mm, a typical glancing angle of 0,07° (70 % of the critical angle of the total
reflection of Mo Kα radiation on Si) and a 20 mm detector active area close to the surface, a sphere of confusion/
tolerance up to 0,04 mm is acceptable for beam centring.
If the instrument (e.g., at synchrotron facilities) is provided with a sample positioning device, the reference
line can also be defined by the direct beam itself. The sample is correctly aligned with respect to the beam

and set at the desired angle of incidence. In this case, sample positioning devices with a minimum step size
of 1 µm and 0,005°, respectively are recommended.
5.5 Detector
The energy dispersive X-ray detector shall provide a stable signal during long-term measurements of several
replicates of a sample. The XRF detector can be positioned at an angle of 90° to the excitation beam and
therefore very close to the reflector, which increases the solid angle of detection.
An energy-dispersive Silicon Drift Detector (SDD) should be used with an active area of ≥20 mm and an
energy resolution of ≤160 eV at Mn Kα (5,9 keV). Energy calibration shall be performed on a regular basis
(see 6.2). Depending on the active area of the SDD, the sample size shall be taken in consideration (see 5.2.2
and 9.4).
If TXRF conditions are met, current detector technologies should not have significant dead time losses
(<30 %). Otherwise, the effect on quantification must be carefully examined.
5.6 Sample station
The sample station consists of a single sample changer or automatic sample changer. The measurement
environment is in air, He or N flux (elements Z ≥ 11) or in vacuum.
5.7 Control unit
A commercial computer system with control software for spectra acquisition and data evaluation.
6 Calibration and quality control
6.1 Angle inspection
The inspection of the glancing angle of the primary beam (alternatively the glancing angle of the reflected
beam) shall be carried out frequently following the standard operation procedures or software routines
provided by the manufacturer of the spectrometer (for details refer to A.1).
Commercial devices often do not incorporate automatic functions for the inspection of the angle setting.
In this case, a simple angle inspection can be carried out manually (e.g., by a slight mechanical movement
of the X-ray tube or by adjusting the reference plane) and with a sample made from droplet depositions
(homogeneous single-element droplet sample with a defined area density of e.g., Ga or As on a quartz carrier,
see 6.3) or laterally homogeneous thin layers or specific layer stacks, which are well reproducible, stable for
many years and available from numerous elements.
a) During a first step, the grazing incidence angle is changed during the measurement of the sample until
the ratio of the peak areas of the silicon of the quartz carrier and the argon from the air is in the range
from 1 to 3.
b) During the second step, the peak area of the element with a defined mass is considered in relation to the
Compton peak and the incidence angle is finely adjusted until the quotient reaches a maximum.
6.2 Energy calibration
Energy calibrations shall be carried out frequently enough such that uncertainties in the identification
of analytes in a spectrum are not impacted by neglected recalibrations. In the case of commercial
spectrometers or detection systems, specifications from the manufacturer shall be considered; in all other
cases, an interval for the calibration shall be specified in operating procedures.
For the energy calibration, residue samples prepared from single element solutions as well as sample
carriers coated with pure metals can be used.

6.3 Calibration of the element sensitivities
The relationship between the X-ray fluorescence intensity of an analyte and its concentration is linear if
the conditions for the total reflection quantification method are met. The slope of the linear relationship is
referred to as the absolute sensitivity.
The calibration factor is a proportionality factor B which in the ideal case of a linear relationship between
x
the net intensity N from a peak of the analyte x and the concentration by volume of the analyte C for the
x x
same volume dosage is expressed by the relationship:
NB=⋅C (3)
xx x
The various analytes generally have different absolute sensitivities that depend strongly on the measurement
conditions.
Different elements have different slopes or sensitivities. The ratios of these absolute sensitivities in relation
to a specific element are referred to as the relative sensitivity. The relative sensitivity can be calculated by
the absolute sensitivity of an analyte (index x) and the absolute sensitivity of a reference element (index b),
whereby both absolute sensitivities are determined under identical measurement conditions:
N 
x
 
 
B c
 
x x
 
Sb()== (4)
x
B  N 
 
b b
 
 
c
 
b
The relative sensitivity S of the analyte j can also be calculated from theoretical values according to
j
Formula (5):
SK=⋅gf⋅⋅ωτ⋅ /ρ (5)
()
jj jj
jE,
where
K is the calibration factor;
g is the relative emission rate of
...