CEN/TS 18094:2024

SLOVENSKI STANDARD
01-april-2025
Neporušitvene preiskave - Preskusne metode za ugotavljanje preostalih napetosti
s sinhrotronskim uklonom rentgenskih žarkov
Non-destructive testing - Test method for determining residual stresses by synchrotron x-
ray diffraction
Zerstörungsfreie Prüfung - Prüfverfahren zur Bestimmung von Eigenspannungen mittels
Synchrotron-Röntgendiffraktometrie
Essais non-destructifs - Méthode d'essai pour l'analyse des contraintes résiduelles par
diffraction des rayons X au synchrotron
Ta slovenski standard je istoveten z: CEN/TS 18094:2024
ICS:
19.100 Neporušitveno preskušanje Non-destructive testing
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

CEN/TS 18094
TECHNICAL SPECIFICATION
SPÉCIFICATION TECHNIQUE
December 2024
TECHNISCHE SPEZIFIKATION
ICS 19.100
English Version
Non-destructive testing - Test method for determining
residual stresses by synchrotron x-ray diffraction
Essais non-destructifs - Méthode d'essai pour l'analyse Zerstörungsfreie Prüfung - Prüfverfahren zur
des contraintes résiduelles par diffraction des rayons X Bestimmung von Eigenspannungen mittels
au synchrotron Synchrotron-Röntgendiffraktometrie
This Technical Specification (CEN/TS) was approved by CEN on 20 October 2024 for provisional application.

The period of validity of this CEN/TS is limited initially to three years. After two years the members of CEN will be requested to
submit their comments, particularly on the question whether the CEN/TS can be converted into a European Standard.

CEN members are required to announce the existence of this CEN/TS in the same way as for an EN and to make the CEN/TS
available promptly at national level in an appropriate form. It is permissible to keep conflicting national standards in force (in
parallel to the CEN/TS) until the final decision about the possible conversion of the CEN/TS into an EN is reached.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Türkiye and
United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION

EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2024 CEN All rights of exploitation in any form and by any means reserved Ref. No. CEN/TS 18094:2024 E
worldwide for CEN national Members.

Contents Page
European foreword . 4
Introduction . 5
1 Scope . 6
2 Normative references . 6
3 Terms and definitions . 6
4 Symbols and abbreviated terms . 11
4.1 Symbols and units . 11
4.2 Subscripts . 12
4.3 Abbreviations . 12
5 Summary of the synchrotron XRD measurement method . 12
5.1 General. 12
5.2 Diffraction techniques. 14
5.2.1 General information . 14
5.2.2 Effects due to the material structure . 15
5.3 Synchrotron high energy X-ray diffraction . 16
5.3.1 General. 16
5.3.2 Monochromatic beam for angle-dispersive X-ray diffraction (ADXRD) . 16
5.3.3 Polychromatic beam for energy-dispersive X-ray diffraction (EDXRD) . 17
5.4 Residual stress calculation . 17
5.4.1 Strain . 17
5.4.2 Stress . 19
5.5 Sources of error and uncertainty . 21
5.5.1 Errors and misapplications . 21
5.5.2 Uncertainties . 22
6 Preparation of measurement and calibration . 23
6.1 Sample preparation . 23
6.1.1 General. 23
6.1.2 Geometry . 23
6.1.3 Composition . 23
6.1.4 Thermal/mechanical history. 24
6.1.5 Phases and crystals . 24
6.1.6 Homogeneity, microstructure and texture . 24
6.1.7 Grain size . 24
6.2 Instrumentation preparation . 24
6.2.1 Instrumentation calibration . 24
6.2.2 Verification of the instrumentation . 24
6.3 Experimental setup . 25
6.3.1 Choosing the measurement method and beam type . 25
6.3.2 Reflection geometry . 25
6.3.3 Transmission geometry . 25
6.3.4 Energy-dispersive (EDXRD) mode . 25
6.3.5 Angle dispersive (ADXRD) mode . 25
6.3.6 Determination of the gauge volume (GV). 26
6.3.7 Peak selection . 26
6.3.8 Temperature . 27
6.4 Measurement procedure: EDXRD – transmission. 27
6.4.1 General considerations . 27
6.4.2 Calibration of the detector . 27
6.4.3 Instrument alignment . 27
6.4.4 Calibration of scattering angle . 27
6.5 Measurement procedure: EDXRD – reflection . 28
6.5.1 General considerations . 28
6.5.2 Calibration of detector . 28
6.5.3 Instrument alignment . 28
6.5.4 Calibration of scattering angle . 28
6.5.5 Determination of gauge volume (GV) . 28
6.5.6 Sample positioning . 29
6.5.7 Slit positioning . 29
6.6 Measurement procedure: ADXRD – transmission and reflection . 29
6.6.1 General considerations . 29
6.6.2 Calibration of detector . 29
6.6.3 Instrument alignment . 30
6.6.4 Calibration of scattering angle . 30
6.6.5 Detector distance . 30
6.6.6 Defining beam parameters. 30
6.6.7 Performing the measurement . 31
6.7 Measurement procedure: ADXRD – CSC . 31
6.7.1 General considerations . 31
6.7.2 Calibration of detector . 31
6.7.3 Instrument alignment . 31
7 Measurement and recording requirements . 31
7.1 General . 31
7.2 Measurements . 31
7.3 Recording requirements . 32
7.4 Reduction of measurement data and data fitting . 32
8 Data analysis and stress calculation . 33
8.1 Specific equations for synchrotron radiation-based diffraction techniques . 33
8.1.1 General . 33
8.1.2 Data input . 33
8.1.3 Stress-free reference input . 34
8.1.4 Strain calculation . 34
8.1.5 Elastic constant input . 34
8.1.6 Stress calculation . 34
8.2 Evaluation of uncertainty in the measurement . 35
8.2.1 Random and systematic uncertainties . 35
8.2.2 Interlaboratory comparison . 36
8.3 Description of the final residual stress data output format . 36
9 Reporting . 37
Annex A (informative) Reference samples . 38
Annex B (informative) Harmonization of data structures . 41
Bibliography . 47

European foreword
This document (CEN/TS 18094:2024) has been prepared by Technical Committee CEN/TC 138 “Non-
destructive testing”, the secretariat of which is held by AFNOR.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
Any feedback and questions on this document should be directed to the users’ national standards body.
A complete listing of these bodies can be found on the CEN website.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the
following countries are bound to announce this Technical Specification: Austria, Belgium, Bulgaria,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland,
Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of
North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Türkiye and the
United Kingdom.
Introduction
This document has been developed with support from the EASI-STRESS project which has received
funding from the European Union’s Horizon 2020 research and innovation programme under grant
agreement No 953219.
Much of the content of this document has been supplied by the partners from EASI-STRESS either by
converting information from EASI-STRESS deliverables or through direct engagement with individuals
to draft and review different parts of this document.
The engagement of experts in CEN/TC 138/WG 10 not affiliated with EASI-STRESS who also made
essential contributions to this document has been equally important. A heartfelt gratitude is extended to
these individuals whose exceptional dedication and voluntary contributions have significantly enriched
the work.
The EASI-STRESS project (active from January 2021 until June 2024) aimed to increase industrial trust
in synchrotron X-ray and neutron diffraction-based residual stress characterization techniques by
validation and benchmarking, developing standard operating procedures and creating this document.
The industrial aim was to revolutionize industrial residual stress management in metals, potentially
enabling up to 15 % material savings from reducing over-dimensioning of components due to lack of
knowledge of residual stress levels.
In order to improve industrial accessibility, the project also focused on professionalising the
measurement service by harmonizing data formats and developing software tools for data analysis and
establishing an industrial service function for residual stress measurement.
EASI-STRESS has also been used as practical case study on adopting advanced characterization principles
according to the CHADA (CHAracterization Data).
Another source of inspiration comes from the VAMAS initiative (Versailles Project on Advanced Materials
and Standards), which ultimately led to the establishment of the standard for neutron residual stress
measurement, EN ISO 21432:2020.
The following EASI-STRESS deliverables are available online at the European Commission CORDIS
website for EASI-STRESS and have been used for the drafting of this document:
— D2.1 Benchmark samples and relevant information for their manufacture
— D2.2 Development of best practice in correlation of modelled and measured stress data. This includes
details to consider during modelling and experiments and reporting formats.
— D2.3 Round-robin results from laboratory techniques and synchrotron and neutron facilities.
— D3.1 Report on technical specifications as identified in collaboration with the industrial users and at
the interface with WP2, WP4 and WP5.
— D3.2 Report on SOPs (Standard Operating Procedures) for instruments dedicated to bulk analysis
and to near-surface analysis.
— D4.2 Technical report with mathematical formalisms (equations), dedicated technical drawings and
diagrams that describes coordinate systems, variables, workflows for data processing, and that
includes the description of the experimental parameters to be included in FE-modelling software.

: https://cordis.europa.eu/project/id/953219/results
1 Scope
This document describes the test method for determining residual stresses in polycrystalline materials
by the synchrotron X-ray diffraction method. The method can be applied to both homogeneous and
inhomogeneous materials including those containing distinct phases.
Information on how to carry out residual stress measurements by the synchrotron X-ray diffraction
technique is provided as:
— the selection of appropriate diffracting lattice planes on which measurements should be made for
different categories of materials,
— the specimen directions in which the measurements should be performed,
— the volume of material examined in relation to the material grain size and the envisaged stress state,
— the selection of the stress-free reference (sample) facilitating the residual strain calculation, and
— the methods available for deriving residual stresses from the measured strain data.
Procedures are presented for calibrating synchrotron X-ray diffraction instruments, enabling:
— accurately positioning and aligning test pieces;
— precisely defining the volume of material sampled for the individual measurements;
and also for:
— making measurements;
— carrying out procedures for analysing the results;
— determining their uncertainties.
The principles of the synchrotron X-ray diffraction technique are described and put into perspective with
EN 15305:2008 and EN ISO 21432:2020, which are used to measure stresses in the bulk of a specimen.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— IEC Electropedia: available at https://www.electropedia.org/
— ISO Online browsing platform: available at https://www.iso.org/obp/
3.1
absorption
reduction in the intensity of radiation in a medium resulting from energy conversion within the medium
Note 1 to entry: In this document, the term attenuation is also used to describe absorption when the focus is on the
beam.
[SOURCE: EN 1330-11:2007, 3.1, modified - Note 1 to entry modified.]
3.2
alignment
adjustment of the specimen position and orientation and also of all the components of the instrument
such that measurements can be performed precisely at the desired location in the specimen
3.3
angle-dispersive diffraction
beam scattering using constructive interference based on a monochromatic photon beam
Note 1 to entry: The diffraction pattern is collected by scanning the scattering angle.
3.4
anisotropy
dependence of material properties of a sample on the spatial direction
3.5
attenuation
reduction of the X-ray beam intensity
3.6
background
intensity considered not belonging to the diffraction (3.12) signal
Note 1 to entry: Background dependence on the scattering angle (3.34) is not uncommon and can have an influence
on the peak position (3.30) resulting from data analysis.
[SOURCE: EN ISO 21432:2020, 3.5, modified - Note 1 to entry modified by deletion of ‘or time-of-flight ‘.]
3.7
beam alignment
intensity scan procedure to determine the position of the gauge volume in the system of the instrument
to set the reference point using a special sample (e.g. thin foil, plate, wire)
3.8
beam-defining optics
arrangement of devices used to define the properties of an X-ray beam such as the wavelength and
intensity distributions, divergence and shape
Note 1 to entry: These include devices such as apertures, slits, monochromators and mirrors.
3.9
Bragg peak
intensity distribution of the beam diffracted by a specific (hkl) lattice plane
3.10
data analysis
process to derive the desired information from the measured data
Note 1 to entry: In general, this applies to the fitting of analytical functions to the reduced data in order to derive,
e.g. peak positions, FWHM, peak intensity, etc.
3.11
data reduction
conversion of detector signal to angle/energy by integration and peak fit
3.12
diffraction
scattering arising from coherent interference phenomena
3.13
diffraction elastic constants
E
hkl
ν
hkl
elastic constants associated with diffraction (3.12) from individual (hkl) lattice planes for a
polycrystalline material
3.14
diffraction pattern
intensity distribution of X-rays diffracted from a crystalline material over the available wavelength,
energy-dispersive diffraction (3.15) and/or diffraction (3.12) angle ranges
3.15
energy-dispersive diffraction
beam scattering using constructive interference based on a polychromatic (or white) photon beam
covering a broad energy spectrum
Note 1 to entry: The diffraction pattern is collected at a fixed scattering angle using an energy-resolving detector.
3.16
entry scan
procedure to determine the position of a specimen surface or interface with respect to the reference point
(3.33)
Note 1 to entry: The result is often called an entering curve.
3.17
full pattern analysis
determination of the crystallographic structure and/or strain from a measured (multi-peak) diffraction
pattern (3.14) of a crystalline material
Note 1 to entry: In general, the full pattern analysis is termed after the method used (e.g. Rietveld refinement). See
also single peak analysis (3.35).
3.18
full width at half maximum
FWHM
width of the Bragg peak (3.9) at half the peak height (3.28) above the background (3.6)
3.19
gauge volume
intersection between the incident beam and the projection of the aperture slits, i.e. the volume from
which information is obtained
3.20
incoherent scatterer
material scattering of X-rays in an uncorrelated way thus giving rise to a strong background (3.6) signal
and no Bragg peaks (3.9) or only some with low amplitude
3.21
lattice parameters
linear and angular dimensions of the crystallographic unit cell
3.22
lattice spacing
d-spacing
lattice plane spacing
distance between adjacent parallel crystallographic lattice planes
3.23
metadata
information necessary to interpret the set-up and conditions of the experiment related to the acquisition
of the raw data in order to ensure reproducibility
3.24
monochromatic beam
X-ray beam with narrow band of energies (wavelengths)
3.25
monochromatic instrument
instrument employing a narrow band of X-ray energies (wavelengths)
3.26
orientation distribution function
quantitative description of the crystallographic texture (3.36)
Note 1 to entry: The orientation distribution function is necessary to calculate the elastic constants of textured
materials.
3.27
peak function
analytical expression to describe the shape of the Bragg peak (3.9)
3.28
peak height
maximum number of signal counts of the Bragg peak (3.9) above the background (3.6)
3.29
peak intensity
integrated intensity
area under the diffraction (3.12) peak above the background (3.6), normally calculated from the
associated fitted parameters of a selected peak function (3.27) and a background function
3.30
peak position
single value describing the angular, energy, or lattice spacing position of a Bragg peak (3.9) in the
measured spectrum
Note 1 to entry: The peak position is normally derived from fitting an analytical function to the measured data.
Note 2 to entry: The peak position is the determining quantity to calculate the strain based on this method (see
Figure 3).
3.31
polychromatic beam
X-ray beam containing a broad band of energies (wavelengths)
3.32
raw data
measurement data as recorded by the instrument together with the metadata of a measurement prior to
any processing for evaluation
3.33
reference point
centroid of the instrumental gauge volume (3.19)
3.34
scattering angle
diffraction angle
angle at which diffraction from an incoming X-ray beam in the specimen material creates a Bragg peak
Note 1 to entry: Diffraction angle is defined as θ and scattering angle as 2θ.
3.35
single peak analysis
mathematical procedure to determine the characteristics of a peak and the background (3.6) from the
measured diffraction (3.12) data
3.36
texture
crystallographic texture
preferred orientation
deviation of the crystallite orientation distribution from randomness in a polycrystalline specimen
[SOURCE: EN 1330-11:2007, 3.130]
3.37
Type I stress
macrostress
stress that self-equilibrates over a length scale comparable to the structure or component, thereby
spanning multiple grains and/or phases
3.38
Type II stress
stress that self-equilibrates over a length scale comparable to the grain size
Note 1 to entry: Stresses of Type II and Type III are collectively known as microstresses.
3.39
Type III stress
stress that self-equilibrates over a length scale smaller than the grain size
Note 1 to entry: Stresses of Type II and Type III are collectively known as microstresses
4 Symbols and abbreviated terms
4.1 Symbols and units
For the purposes of this document, the following symbols and units apply.
a,b,c Lengths of the edges of a unit cell, here referred to as nm
lattice parameters
B Background at the peak position —
−1
c Speed of light in vacuum ms
ph
d Lattice plane spacing nm
E Macroscopic elastic modulus (Young’s modulus) GPa
E Elastic modulus associated with the (hkl) diffracting GPa
hkl
lattice planes
E Photon energy J
γ
E Initial photon energy J
0y
h Planck’s constant Js
hkl Indices of a crystallographic lattice plane
NOTE In the remainder of the document (hkl) will be
used bearing in mind that each plane of the family
{hkl} will diffract under the same conditions.
hkil Alternative Miller index notations of a
crystallographic lattice plane for hexagonal structures
H Peak height above the background —
−1
q Absolute value of scattering vector nm
u Standard uncertainty —
x,y,z Axes of the specimen coordinate system
−1
α Coefficient of thermal expansion K
λ Wavelength nm
Δ Variation of, or change in, the parameter that follows
ε Elastic strain —
Strain tensor —
εˆ
ε Components of the elastic strain tensor —
ij
Normal elastic strain associated with the (hkl) —
εhkl
diffracting lattice plane
ν Poisson’s ratio
v Poisson’s ratio associated with the (hkl) diffracting
hkl
lattice plane
𝜎𝜎� Stress tensor MPa
σ Components of the stress tensor MPa
ij
σ Yield stress MPa
Y
Θ diffraction angle Degree
2θ scattering angle Degree
𝜏𝜏 Shear stress value in a direction defined by the angle MPa
ϕ
ϕ
𝜏𝜏 Attenuation depth m
ϕ, ψ Orientation angles Degree
4.2 Subscripts
For the purposes of this document, the following subscripts apply.
hkl, hkil Indicate relevance to crystallographic (hkl) or (hkil) lattice planes
x, y, z Indicate components of the quantity concerned along the x-, y-, z-axes
ϕ ψ Indicate the normal component, in the (ϕ ψ) − direction of the quantity concerned
0 (zero) Indicates stress-free value of the quantity concerned
Ref Indicates reference value of the quantity concerned
4.3 Abbreviations
For the purposes of this document, the following abbreviations apply.
ADXRD Angle Dispersive X-Ray Diffraction
CSC Conical Slit Cell
DEC Diffraction elastic constants
EBSD Electron backscatter diffraction
EDXRD Energy-Dispersive X-Ray Diffraction
FEA Finite element analysis
FWHM Full Width at Half Maximum
GV Gauge Volume
MCA Multi-Channel Analyser
PSD Position-Sensitive Detector
SGV Sampled gauge volume
SXRD Synchrotron X-ray Diffraction
XRD X-ray Diffraction
5 Summary of the synchrotron XRD measurement method
5.1 General
This document deals with the determination of residual stresses that are needed in engineering analyses.
The stresses are determined from X-ray synchrotron diffraction measurements of lattice spacings within
engineering components. From changes in these spacings, elastic strains can be derived from which
stresses can be calculated. The stress at any point in an engineering body has 9 components, 6 of which
are independent (see Figure 1).
Key
σx, σy, σz normal components of the stress tensor
σzx shear components of the stress tensor
σ shear components of the stress tensor
yz
σxy shear components of the stress tensor
x, y, z axes of the specimen co-ordinate system
Figure 1 — The six independent stress components that describe a complete stress state at a
given location inside a body
The outcome of any residual stress measurement is normally reported as scalar values of these stresses
together with the location and the measurement direction(s) corresponding to these particular stress
values, as well as the volume over which the measurement had been taken.
Synchrotron facilities offer the possibility to study residual stresses away from the surface in the bulk of
specimens. The high intensity, flux, collimation, and wavelength tunability of the radiation allow
instruments to provide performance and flexibility, which surpass the possibilities of conventional
laboratory apparatus. Instruments operating with a monochromatic beam (i.e. using an angle dispersive
set-up) or a polychromatic beam (i.e. using an energy-dispersive set-up), can be used. The general
properties of synchrotron radiation include:
— high brilliance, i.e. a highly collimated, intense X-ray beam, which cannot be achieved by conventional
laboratory X-ray instruments;
— high flux of photons delivered at the sample;
— a range of available wavelengths extending from low to high X-ray energies depending on the facility
and beamlines.
More information about synchrotron radiation can be found in the literature, see References [10, 11 and
12].
5.2 Diffraction techniques
5.2.1 General information
The synchrotron X-ray diffraction (SXRD) technique enables the measurement of residual stress within
the bulk of crystalline specimens or components. The measurements represent an average over the
sampled gauge volume (SGV). The basic physical principles are the same for all diffraction methods, as
they rely on the crystal structure of the material under investigation to determine relative changes in the
distance between parallel atomic planes oriented with their normal parallel to the scattering vector. The
interplanar distances are calculated using Bragg’s law (Formula (1)) using the beam wavelength λ and
the diffraction angle θ (see Figure 2).
𝜆𝜆 = 2𝑑𝑑 sin𝜃𝜃 (1)
Key
d lattice plane spacing
λ beam wavelength
θ diffraction angle
Figure 2 — Bragg’s law connects the wavelength of the incident beam with the lattice plane
spacing d and the diffraction angle θ
Bragg’s law states that the lattice plane spacing d between parallel crystallographic planes in a crystalline
material can be precisely determined by knowing the wavelength λ of the radiation used, and the
diffraction angle θ.
Figure 3 illustrates the most important parameters to describe a diffraction peak which include the peak
height and intensity, position (scattering angle 2θ) and full width at half maximum (FWHM).
Key
B background
I max maximum intensity
I peak area
int
X angle
Y intensity
2θ peak position (scattering angle)
Figure 3 — Most important features of a schematic diffraction peak
From a practical standpoint, Type I stresses are calculated from the shift of the diffraction peak of a
certain lattice plane with respect to the peak obtained from a stress-free sample from the same material.
5.2.2 Effects due to the material structure
Problems arise when strains and stresses of different types (i.e. Type I and II strains and stresses) have
to be interrelated. When there are multiple phases present, or when a single reflection is employed, then
the measurement may be biased towards either an elastically stiffer or more compliant phase. The end
result is that the Type II stresses do not average out for that particular phase or reflection. In such
instances, Type II stresses shall be taken into account if a reliable measure of the Type I stresses is to be
obtained. The effect of Type II strains on Type I arises in cases when the gauge volume (GV) is comparable
with the grain size in one of the phases. The measurement of several peaks can help to understand the
situation.
Further, the study of textured materials and the lack of knowledge of the single crystal elastic constants
in some cases can lead to large differences between residual stresses measured with diffraction
techniques and those obtained from strain-relief methods and those estimated by finite element analysis
(FEA). In addition to the above elastic anisotropy, plastic anisotropy can also mean that the peak shift
recorded for a specific reflection may not be representative of the macrostress. It is therefore desirable
to choose lattice planes weakly affected by plastic anisotropy.
Finally, a correct determination of stress-free reference values is critical for reliable residual stress
measurements by diffraction. Different methodologies to accomplish this have been devised, see
Reference [13]. If possible, elastic constants should be determined experimentally i.e. pulling or pressing
or bending a suitable sample. For further information on the determination of elastic constants, see
Reference [9].
5.3 Synchrotron high energy X-ray diffraction
5.3.1 General
SXRD employs high X-ray energies resulting in mean scattering angles 2θ in the range 5-20° which can
be divided into two main types: energy dispersion and angular dispersion. The following describes their
key facets as well as their best practices.
5.3.2 Monochromatic beam for angle-dispersive X-ray diffraction (ADXRD)
A monochromatic beam illuminates the area of interest in the specimen. The diffracted beam cones are
collected, usually, by a 2D detector which allows to obtain simultaneous information of the strains in a
plane orthogonal to the incident beam (see Figure 4).

Key
d lattice spacing for plane 1
d2 lattice spacing for plane 2
2θ1 scattering angle 1
2θ scattering angle 2
X incident beam
Y Debye-Scherrer rings
Figure 4 — Cones and diffracting planes
A depth-resolved strain analysis can be performed with a conical slit cell (CSC), which allows the GV to
be spatially defined, see Reference [14]. A CSC comprises several concentric slits that are focused on a
spot within the sample by their conical shape, while the focal distance is always constant. Depending on
the phase to be analysed, the beam wavelength shall be tuned such that the diffraction cones pass the
slits. The GV is elongated in the beam direction because of the low diffraction angles mostly observed in
SXRD. The incident beam size typically varies between 50 µm - 200 µm in lateral dimensions. For thin
samples, the beam can penetrate the entire thickness, with the incoming beam slits defining the area of
interest. CSCs are not used in such cases as the GV stretches across the entire thickness of the sample.
X-ray attenuation along the beam path and non-homogeneous illumination of the GV should be taken into
account, e.g. by a proper correction factor, in particular for measurements in reflection geometry.
5.3.3 Polychromatic beam for energy-dispersive X-ray diffraction (EDXRD)
When the observed scattering angle is fixed by using an energy-sensitive point detector, a diffraction
pattern with several diffraction peaks can be recorded with a polychromatic incident beam. Two-point
detectors can be used simultaneously to acquire strain information from two orthogonal directions at the
same time, see Reference [15]. The GV can be defined by simple slits in the incident and the diffracted
beam. Experiments can be performed either in transmission mode (bulk average strains) or in reflection
mode (near surface strains), see Figure 5. In common with the case of the CSC, the GV is elongated in the
beam direction.
Key
a vertical detector
b diffracted beam slits in front of the horizontal and vertical detectors
c horizontal detector
d beam stop
e diffraction cone
f Eulerian cradle
ω sample rotation about the vertical axis
h sample
i beam slit
Figure 5 — Energy-dispersive X-ray diffraction setup
5.4 Residual stress calculation
5.4.1 Strain
When employing diffraction methods for determining residual stresses in (poly)crystalline materials,
Bragg’s law (Formula 1) is used.
The lattice spacing for a specific crystallographic plane (hkl) can be used as a strain gauge in a stressed
material (externally and/or internally), where the strain ε in the direction of the scattering vector can be
calculated as:
dd−
hkl 0,hkl
ε = (2)
hkl
d
0,hkl
where 𝑑𝑑 is the lattice spacing corresponding to the stress-free state of the material, the so-called
0,ℎ𝑘𝑘𝑘𝑘
stress-free reference value. This value should be obtained from the same material but with the stresses
minimized as much as possible. This can be achieved by cutting a single or a series of small coupons, e.g.
in the shape of a comb, and/or applying stress relief heat treatments provided this can be done without
changing the microstructure. The reference measurement could also be taken in a location far away from
the stressed region of the sample where a very similar microstructure is expected. Based on reference
samples like these, this method allows absolute stress values determination.
For the angle-dispersive diffraction method (ADXRD), the change of the lattice spacing is reflected in the
shift of the position of the scattering angle 2θ relative to the one of the reference samples. Inserting
Bragg’s-law (Formula (1)) in (Formula (2), hkl specific strains can be determined directly from the
measured diffraction angles as follows:
sinθ
0,hkl
ε − 1 (3)
hkl
sinθ
hkl
Energy dispersive X-ray diffraction techniques (EDXRD) are typically applied with polychromatic
incoming X-ray beams in accordance with 5.3.3 and Figure 5. Depending on the material investigated and
the range of photon energies probed by the detector, such measurements render diffraction spectra with
multiple diffraction peaks emanating from various lattice planes.
The energy of a photon is linked to its wavelength through:
c
ph
Eh⋅ (4)
γ
λ
...