untitled BRITISH STANDARD BS EN 13925 3 2005 Non destructive testing — X ray diffraction from polycrystalline and amorphous materials — Part 3 Instruments The European Standard EN 13925 3 2005 has the[.]
General
This description is particularly intended for instruments dedicated to the fields of application described in
EN 13925-1 For other applications, additional considerations may be required
− incident beam optics which may include monochromatisation or filtering, collimation and/or focusing or parallelism of the beam;
− diffracted beam optics which may include monochromatisation or filtering, collimation and/or focusing or parallelism of the beam;
The instrument's components are examined in greater detail below A data processing system is essential for generating measurements from the instrument Both manual and computerized data processing systems must adhere to the data processing procedures outlined in EN 13925-2.
A well-controlled environment (temperature and pressure) is strongly recommended for analysis where reproducible measurement of line profile position, width and shape is required
Humidity is may be important because compounds in the specimen may react with water or absorb it with a consequent change in their lattice constants, e.g clay minerals.
The X-ray beam experiences partial scattering and attenuation due to the air in its path, which impacts the background and intensity of the detected diffraction pattern To mitigate this effect, an evacuated or helium-filled beam path is often employed.
For all the items described in this clause the corresponding main characteristics to be controlled are given in Clause 5.
X-ray sources
General
X-ray sources for XRPD measurements vary from conventional laboratory sources to intense, well-collimated synchrotron sources, each with unique characteristics that enhance their suitability for specific analyses The primary types of these sources are outlined below.
Conventional X-ray sources (sealed tubes and rotating anode sources)
X-rays are obtained by bombarding a metal anode with electrons emitted by the thermoionic effect and accelerated in a strong electric field produced by a high-voltage generator Most of the kinetic energy of the electrons is converted to heat, which limits the power of the tubes and requires efficient anode cooling An increase of about two orders of magnitude in brilliance can be obtained using rotating anodes instead of sealed tubes Microfocus sources operate at relatively low power settings but maintain brightness by electrostatically or magnetically steering the beam inside the X-ray tube onto the target The spectrum emitted by a conventional X-ray source operating at sufficiently high voltage consists firstly of a continuous background of polychromatic radiation with a sharp cut off at short wavelengths determined by the maximum voltage applied Upon this is superimposed a limited number of narrow characteristic lines whose wavelengths are characteristic of the anode material The emitted radiation is not polarised
The type of X-ray source, along with the electron emission current and accelerating voltage from the high voltage generator, significantly influences X-ray intensity and energy distribution In conventional X-ray tubes, the emission current and accelerating voltage typically allow for consistent adjustments of the X-ray beam intensity and energy spectrum over several days However, it has been observed that absolute X-ray intensity can vary considerably among sources that are nominally equal, and it tends to decrease as the source ages.
Synchrotron radiation sources
A beam of charged particles, when strongly accelerated in an electric field and deflected in a magnetic field, produces a continuous spectrum of X-rays that can be up to \$10^{13}\$ times more brilliant than that emitted by sealed X-ray tubes This phenomenon is known as
Synchrotron radiation offers enhanced brilliance due to its broad energy spectrum, and the monochromatisation of the beam significantly boosts diffraction intensities, achieving levels one to two orders of magnitude higher than those from conventional sources.
The main advantages of using synchrotron radiation for XRPD measurements are:
- nearly parallel-beam diffraction geometry;
- highly monochromatised and tunable radiation;
- very small and almost symmetric contribution of the instrument to the observed line shape that leads to simpler characterisation of line profiles and very good angular resolution
This X-ray radiation source necessitates continuous monitoring of beam flux over time, as it can significantly decrease during experiments, along with the need for wavelength calibration Additionally, the emitted radiation is highly polarized within the plane of deflection of the charged particles.
Incident and diffracted X-ray beam optics
General
The incident and diffracted beams are defined by their wavelength spectrum, propagation direction, cross-sectional area and shape at the specimen, as well as their collimation and focusing characteristics The equipment responsible for these attributes is known as "beam optics," and the resulting effects are collectively termed "beam conditioning."
The items of equipment described below are used to obtain different degrees of radiation purity and different geometries, i.e a so-called "focused" beam, "monochromatised" beam, "collimated" beam, or "parallel" beam.
Monochromators
The wavelengths conventionally used with laboratory sources correspond to the characteristic spectral lines from specific anode materials
In various XRPD applications, it is beneficial to eliminate all spectral components emitted from the X-ray source or specimen Utilizing the K α1,2 doublet can be advantageous, and further suppression of the K α2-line allows for the use of highly monochromatic K α1-radiation.
Monochromatisation devices can be used singly or in combination
Partial monochromatisation can be obtained using Kβ filters, i.e foils made of a metal selected as having an absorption edge between the wavelengths of the Kα and Kβ radiation emitted by the source
Standard Kβ filters are designed to reduce the Kβ intensity to about two orders of magnitude less than the
A filter designed for Kα intensity not only reduces the Kα doublet intensity by approximately half but also diminishes the polychromatic radiation emitted from the source Often, two filters are combined to create what are known as "balanced filters."
When using spectral filters, caution is essential due to the absorption edges of the filter material, which create significant background steps near the observed diffraction lines These steps can hinder precise analysis, particularly in line-broadening studies that rely on complete line profiles.
To effectively attenuate the incident or diffracted beam, a foil made of a metal, typically aluminum, is employed This metal is chosen for its lack of an absorption edge near the radiation wavelength being utilized.
Monochromatisation of radiation is primarily achieved through diffraction from crystals, which can be categorized into two types: mosaic crystals and single crystals Mosaic crystals, typically made of graphite, offer a relative energy or wavelength resolution of a few parts per hundred, effectively eliminating most Kβ radiation and continuous polychromatic radiation while retaining over 50% of the incident intensity of the Kα1,2 doublet These monochromators are usually placed in the diffracted beam, allowing them to eliminate specimen fluorescence from all elements except the anode material In contrast, single crystal monochromators, often composed of nearly perfect quartz, silicon, or germanium, provide a superior energy resolution of better than two parts per thousand, enabling the separation of the Kα1,2 doublet and the elimination of Kα2 radiation However, they typically retain only about 15% of the incident intensity, as they are generally used in the primary beam in a focusing arrangement This intensity loss is compensated by a significant reduction in axial divergence, which negates the need for a set of Soller slits.
Combining two or more crystals can significantly enhance resolution compared to using a single crystal; however, this approach may result in inadequate intensity for standard powder diffraction It is crucial to eliminate harmonics of the selected wavelength by strategically positioning appropriate apertures (slits) within the monochromator or employing alternative methods.
These devices can be used in the incident and/or diffracted beams (see Figures 1 and 2)
3 Apparent source (on the goniometer circle)
Figure 1 - Positioning the monochromator on the incident beam
Figure 2 - Positioning the monochromator on the diffraction beam 4.3.2.4 Electronic filters
Electronic filtering, commonly known as pulse height discrimination or energy discrimination, utilizes photon-counting detectors to selectively process pulses generated by specific radiation in experiments.
A solid-state detector, such as a Peltier-cooled device, can achieve an effect similar to partial monochromatisation, offering a relative energy resolution comparable to that of a mosaic crystal monochromator (approximately one part per 100) This resolution is adequate for eliminating the K β component and most continuous background, although it cannot separate the K α1,2 doublet While these detectors typically exhibit high counting efficiencies, they are prone to dead time effects, leading to a non-linear response at count rates exceeding about 10,000 counts per second It is crucial to manage the maximum count rate to ensure proper detector functionality, and if necessary, apply an appropriate dead time correction.
Multilayer mirrors are composed of alternating thin layers of two materials, such as tungsten (W) and carbon (C), which are applied to a suitably curved substrate These layers typically have a thickness several times that of the X-radiation wavelength utilized.
Multilayer mirrors for X-radiation are essential for converting divergent beams into intense parallel or convergent beams, while also functioning as monochromators to eliminate Kβ and polychromatic radiation The layer thickness on the mirror's surface is designed to satisfy Bragg’s law across various beam divergence and incidence angles, achieving reflectivity near 100% for high-intensity output Typically, parabolic graded mirrors are employed to create nearly parallel beams from divergent radiation, whereas elliptic graded mirrors focus the radiation into convergent beams In specialized applications, multiple mirrors can be utilized in both the incident and diffracted beams.
Beam dimensions and geometry
The geometric dimensions of incident and diffracted X-ray beams can be effectively controlled through the use of collimators and slits Additionally, crystal monochromators and graded multilayer mirrors can significantly alter these dimensions.
The items described below define the beam dimensions and geometry and are illustrated schematically in Figure 3
1, 2 Possible position of divergence anti-scatter slit
3, 4 Possible position of receiving anti-scatter slit
A, B, D Possible position of Soller slit
C Centre of specimen surface and of the goniometer circle
Figure 3 — Schematic arrangement of the devices for control of beam dimension and geometry with respect to the centre of the goniometer circle (C) 4.3.3.2 Slits
Slits are essential components in beam paths, utilized to limit equatorial and axial divergence, reduce parasitic scattering, define the radius of the focusing circle, and control angular resolution Typically constructed from metals with high X-ray attenuation, orthogonal slit pairs are particularly useful for specific measurements, such as crystallographic texture analysis, to manage beam divergence effectively In the context of X-ray powder diffraction (XRPD), slits are predominantly favored over other types of apertures, as discussed in sections 4.3.3.2.2 to 4.3.3.2.7.
A useful quantitative geometric treatment of slits for Bragg-Brentano diffractometers is described in [4]
Mechanically or computer controlled slits can be applied as variable divergence, antiscatter and receiving slits
A variable aperture slit is commonly utilized in diffractometers featuring Bragg-Brentano geometry to ensure a consistent irradiated surface area of the specimen, even as the angle between the incident beam and the specimen surface changes This results in a variation of the irradiated specimen volume throughout the 2θ scan.
A matched variable anti-scatter slit may be used in conjunction with a variable divergence slit This can be particularly effective in minimising parasitic scattering at low 2θ angles
Divergence slits between the X-ray tube and the specimen They limit the equatorial divergence of the incident beam
Antiscatter slits are essential for minimizing parasitic scattering that occurs when incident and diffracted X-ray beams interact with air, the specimen stage, and optical system components Positioned strategically before or after the specimen or the receiving slit, these slits can be utilized individually or in combination When correctly aligned, they maintain the integrity of the incident and diffracted beams without altering the diffraction geometry.
The "knife edge" is a flat blade or wedge designed for use with flat specimens, positioned parallel to the specimen surface and the goniometer axis By limiting the irradiated area of the specimen, the knife edge effectively reduces parasitic scattering, serving a similar purpose as divergence and antiscatter slits Its position can be either stationary or variable, and it can be controlled mechanically or via computer.
A receiving slit is essential for selecting the radiation detected at a specific angular position It is positioned within the diffracted beam, either directly in front of the detector or before the monochromator, if one is utilized.
In Bragg-Brentano geometry, the receiving slit is positioned on the focusing circle, which is crucial for achieving optimal angular resolution This slit, often referred to as a "focusing slit" or "resolution slit," plays a significant role in determining the system's overall performance.
A detector slit is crucial for selecting the radiation diffracted by the specimen, ensuring that only relevant signals enter the detector It effectively blocks parasitic radiation, such as scattered radiation from instrument components or K β radiation when the monochromator is set to Κα radiation Often, the receiving slit functions as the detector slit.
In a monochromator setup, a detector slit can be positioned in the diffracted beam between the monochromator and the detector, often integrated within the monochromator housing For (para)focusing monochromators, this slit is typically located at the focusing point of the radiation that has been diffracted.
A collimator is a device that narrows the X-ray beam to make it more parallel by limiting its dimensions and divergence It is designed to minimize stray radiation from slits or diaphragms, ensuring that such radiation does not interfere with the diffraction pattern captured by the detector The design of collimators varies significantly based on the configuration of the diffractometer and the diffraction geometry employed Typically constructed from materials with high X-ray attenuation, collimators differ from simple slits, crystal monochromators, and graded multi-layer mirrors, which, while serving similar functions, are not classified as collimators.
4.3.3.3.2 Parallel plate collimators (Soller slits)
A parallel plate collimator, also known as a set of Soller slits, consists of an array of thin, parallel plates that restrict beam divergence perpendicular to the foils These collimators can be applied to both incident and diffracted beams, effectively limiting divergence in both axial and equatorial directions.
A tube collimator is a tube with diaphragms or sets of slits at each end to control the dimensions and the divergence of the beam
Capillary optics utilize hollow optical fibers to guide radiation through total internal reflection on their inner surfaces These fibers, when positioned in the incident beam, effectively limit divergence to approximately 0.3 degrees, suppress short-wavelength radiation, and enhance intensity at the specimen A single capillary generates a beam with a minimal cross-section, while a collection of numerous parallel fibers bundled together creates a larger cross-section beam with low divergence and diminished short-wavelength radiation.
Micromirrors are specialized monocapillaries featuring a parabolic, gold-coated inner surface Their curvature varies along the length of the mirror, enabling the formation of a focused X-ray beam through single bounce total reflection.
Detectors
Types of detector
Detectors utilized in X-ray Powder Diffraction (XRPD) vary significantly in type, size, shape, and operational principles They encompass a range of technologies, including photographic films, gas ionization counters (such as Geiger-Müller and proportional counters), solid-state detectors (like scintillators and semiconductors), fluorescent screens, and image plates These detectors can be classified based on the physical principles underlying their radiation detection mechanisms.
Integrating detectors, such as photographic films, image plates, and charge coupled devices (CCD), accumulate X-rays over a specific time interval while providing intrinsic spatial resolution However, these detectors have a limited dynamic range, which refers to the total number of X-rays per angular interval, and exhibit low energy resolution To ensure reproducible measurements, electronic readout of data from these detectors is essential.
Photon counting detectors, including Geiger-Müller counters, proportional counters, scintillation counters, and semiconductor detectors, offer an unlimited dynamic range when counts are stored in computer memory However, these detectors exhibit a limited linear response range for count rates, which affects their position sensitivity.
⎯ "spot" counters such as Geiger-Müller counters, proportional counters, scintillation counters and semi- conductor detectors, that only register the number of the detected X-ray photon;
Linear position sensitive detectors (1D PSDs), like proportional counters, allow for the detection of X-ray photons not only by their quantity but also by the specific position where they impact the device.
Area detectors, also known as two-dimensional position sensitive detectors (PSDs), include various technologies such as two-dimensional position sensitive proportional counters, photographic films, image plates, photo-luminescence tubes (commonly used in TV cameras), and charge-coupled devices (CCDs).
The physical principle of radiation detection plays a crucial role in X-ray Powder Diffraction (XRPD), as it impacts both the statistical counting error in observations and the detection efficiency In photon counting detectors, the variance in detected photons over a specific time interval corresponds directly to the number of photons detected, following Poisson statistics However, this straightforward relationship does not apply to integrating detectors.
A position sensitive detector (PSD) enhances data collection efficiency by enabling simultaneous count rate observations across various positions In diffraction geometries such as Bragg-Brentano and Seeman-Bohlin, the focusing conditions may degrade, leading to shifts and broadening of diffraction-line profiles that are significantly influenced by the diffraction angle The use of a PSD allows for contributions to the diffracted intensity from crystallites with orientations spanning half the range of diffraction angles, which increases the perceived randomness of orientation.
∆ω Maximum difference of the orientation of lattice planes (with identical spacing) that contribute simultaneously to the radiation detected by linear position sensitive detector
NOTE Technical characteristics of various types of detector can be found in references such as [6]
Figure 4 — Simultaneous registration of crystallite orientations when using a linear Position Sensitive
Spatial resolution of detectors
The spatial resolution of a "spot" counter and area-integrating detector is primarily influenced by the size of the receiving slit in front of it For both linear and two-dimensional detectors, this resolution is also affected by their technical specifications and electronic settings.
Energy resolution of detectors
The energy resolution of a detector depends on its technical characteristics and the electronic adjustment, including the upper and lower acceptance limits for energy discrimination.
Goniometers
General
The goniometer is the mechanical and electrical assembly in a diffractometer responsible for controlling the positioning of its components in relation to the specimen.
The plane of diffraction is defined as the plane that includes the centers of the source (or apparent source when utilizing an incident beam monochromator), the specimen, and the detector.
The equatorial plane, also referred to as the plane of diffraction, is crucial in powder diffraction measurements The axial direction, which is perpendicular to this plane and aligned with the goniometer axis, plays a significant role in the setup For accurate results, the surface of a flat specimen must be positioned perpendicular to the equatorial plane and aligned with the goniometer axis.
The measurement of the angle between the incident and diffracted beams is distinguished from the movement of the specimen itself
In diffractometers utilizing focusing or parafocusing diffraction geometry, the (apparent) X-ray source is located on the goniometer circle, where the diffracted intensities are also gathered When employing a linear or flat position-sensitive detector, the diffracted intensity is recorded in a plane that is tangent to the goniometer circle.
In Bragg-Brentano geometry, the apparent source, specimen, and receiving slit are positioned on a focusing circle with radius \( R_f \), which is related to the diffraction angle \( 2\theta \) and the goniometer circle radius \( R \) by the equation \( R_f = \frac{R}{2\sin \theta} \) In contrast, Seeman-Bohlin geometry features a goniometer circle that is superimposed on the focusing circle, resulting in \( R_f = R \).
The equatorial plane is established by the radiation source point (S) and the intersecting θ and 2θ axes Point (C) marks the intersection of these axes with the equatorial plane Additionally, the detector point (D) is located within the equatorial plane, equidistant from the coinciding θ and 2θ axes as point S A line drawn through point C runs parallel to the axes.
The specimen surface is denoted as SD, and the focusing circle is defined by points S, C, and D with radius R f In powder diffractometers, the diffraction plane aligns with the equatorial plane In a Bragg-Brentano parafocusing diffractometer, the goniometer axis aligns with the θ and 2θ axes, where S represents the center of the line-shaped radiation source perpendicular to the equatorial plane, and D is the center of the radiation detection area, which matches the size and shape of the radiation source The goniometer circle intersects at the center of the specimen.
A line-shaped radiation source is positioned at the center of the area designated for radiation detection, with the goniometer axis aligned through the center of the goniometer circle.
Figure 5 — Arrangement of the focusing circle and the goniometer circle in the parafocusing configuration
The diffraction pattern is typically captured by rotating around the goniometer circle using a "spot" detector or a position-sensitive detector positioned tangentially Additionally, segments of the diffraction pattern can be obtained by positioning a stationary one- or two-dimensional detector at a fixed diffraction angle along the goniometer circle.
Many diffractometers (e.g Bragg-Brentano and Seeman-Bohlin) can be distinguished with respect to the orientation of their goniometer axis as:
A horizontal goniometer features a circle with its axis positioned vertically, allowing the specimen surface to align with the goniometer axis and tilt around it In this setup, the equatorial plane remains horizontal while the axial direction is oriented vertically.
A vertical goniometer features a horizontal axis, allowing the specimen surface to tilt around this axis In this setup, the equatorial plane is oriented vertically while the axial direction remains horizontal Typically, if the specimen surface is flat, it is positioned to face upwards.
Such diffractometers can also be distinguished with respect to the functioning of their goniometer axis as:
When the flat specimen surface is tilted, it maintains an angle that is half the distance between the source and the receiving slit (or detector) during data collection Typically, the source remains stationary while the detector rotates at twice the speed of the specimen.
During data collection, the flat specimen surface remains static, typically positioned horizontally and secured in place The X-ray source and detector rotate simultaneously at the same speed but in opposite directions.
Specimen positioning
The specimen is positioned using a specimen stage (see 4.6)
Diffractometer geometries are primarily designed for flat or rod-shaped specimens, making it essential for the specimen shape to align closely with these design criteria The necessary positional precision varies based on the instrument and its configuration, generally ranging from a few microns for flat specimens to tens of microns for rod-shaped specimens.
4.5.2.2 Rod-shaped specimens (capillary, fibre)
A rod-shaped specimen, such as a capillary or fiber, must align its axis with the goniometer axis While the specimen does not move in sync with the 2θ-scan, it is typically rotated around its rod axis to enhance the statistical randomness of crystallite orientation In step-counting diffractometers, this rotation should be carefully timed to prevent periodic anomalies in the collected data, which can occur due to variations in diffracted intensities during a rotation cycle This can be achieved by using an integer number of rotations for each data point collected.
For accurate measurements of a flat specimen, it is essential to mount it so that its surface aligns with the goniometer axis Beyond the fundamental θ and 2θ movements in Bragg-Brentano geometry, certain analyses, such as texture and stress evaluations, necessitate additional rotational adjustments, as depicted in Figure 6.
⎯ Omega (ω), the angle between incident beam and the specimen surface, often coinciding with Theta (θ), half the diffraction angle (2θ):
• ω = θ when the goniometer is used in a Bragg-Brentano parafocusing system, i.e with incident and diffracted beams symmetrically at angle θ to the specimen surface;
The angle \$\omega\$ can differ from \$\theta\$, particularly when it is necessary to maintain a constant specimen depth across varying diffraction angles This is especially relevant in surface-sensitive techniques or when utilizing one- or two-dimensional position-sensitive detectors.
Phi (φ) is utilized to orient a flat specimen by rotating it within its plane This rotation, typically at a rate of one or more revolutions per data collection step, enhances the crystallite statistics.
⎯ Chi (χ) is used to orientate the specimen surface around the axis lying in the equatorial plane and normal to the goniometer axis
The angles omega (ω) and chi (χ), sometimes referred to as psi (ψ), are crucial in the context of texture and residual stress measurements Their movements are typically managed through specialized attachments or advanced diffractometers, such as the Eulerian cradle and Kappa goniometer.
2 In plane of specimen surface
4 θ axis, 2θ axis, ω axis psi (ψ), chi (χ): axes are perpendicular to the goniometer axis θ, 2θ, omega (ω): axes coincide with the goniometer axis phi (φφφφ) axis is perpendicular to the specimen surface
NOTE The sense of rotation around the θ, 2θ and ω axes is equivalent and related to the mounting of the flat specimen in the Bragg-Brentano diffractometer
Figure 6 — Identification of the θθθθ, 2θθθθ,φ,χχχχ,ψψψψ and, ωωω axes independent of diffraction geometry ω
For very large immobile specimens, specialised diffractometers have been made that allow all the required movements of the diffractometer components around a stationary specimen
For specimens featuring rough or curved surfaces, parallel beam geometry in diffractometer configurations offers significant benefits This setup allows for a less critical positioning of the specimen surface in relation to the goniometer axis, ensuring accurate registration of diffraction angles compared to other diffraction geometries.
Specimen stage
The specimen stage is a crucial device designed to securely hold and position specimens, which can either be exposed to the environment or enclosed to maintain specific atmospheric conditions, such as controlled humidity It may also include features for applying heating, cooling, or high pressure to the specimen If the specimen is not self-supporting and lacks an appropriate shape, it must be placed in a specimen holder and positioned on the stage for accurate transmission or reflection measurements Additionally, specimen holders are typically designed to enable rotation around a designated axis for optimal analysis.
Data collection system
The data collection system gathers X-ray data from the detector, along with the relevant information regarding the position and orientation of the specimen, X-ray source, and detector It then converts this data into the necessary format for the data processing and evaluation system.
The following Tables list the values of instrument characteristics that shall be traceable and made available as required
Manufacturers must provide nominal or measured values for new equipment and components, which should be documented by the user For existing equipment, users are encouraged to record as much relevant information as possible.
Table 1 — Instrument characteristics to be provided by the manufacturer Component type Component Nominal or measured values
High voltage generator ⎯ accuracy of voltage and current,
⎯ long and short time stability of voltage and current,
⎯ ripple, specified for 50 Hz, 100 Hz and frequency of switched power supply (if applicable),
⎯ Voltage and current range or settings
Sealed tubes, microfocus tubes and continuously pumped sources
⎯ material of anode, (Ag, Co, Cr, Cu, Fe, Mo, W, etc.) and its characteristic spectral purity when manufactured,
⎯ maximum electron emission current (mA) and recommended value for normal XRPD use,
⎯ maximum electron acceleration voltage (kV) and recommended value for normal XRPD use,
⎯ for microfocus tube: static or dynamic electron beam conditioning
⎯ the shape and dimensions, usually the length and width, of the anode area emitting X-rays,
⎯ material and thickness of tube window or window transmission,
Recommended operational characteristics for normal use of XRD
⎯ take-off angle of the X-rays from the anode,
⎯ anode coolant temperature range and stability,
⎯ apparent shape ("point focus" or "line focus") of the X-ray source at the recommended take-off angle,
⎯ electron current and electron acceleration voltage
Filters ⎯ material and thickness of filter(s),
⎯ material and thickness of attenuation filter(s) and attenuation for the wavelength(s) specified
⎯ material of monochromator crystal and lattice spacing used,
⎯ type of focusing and focal lengths,
⎯ any means of suppressing harmonics of the wavelength transmitted,
Electronic filters ⎯ type of electronic filter (counter)
Multilayer mirrors ⎯ type of multilayer mirror(s) (layer materials used, grading applied when available),
⎯ type of curvature of the mirror(s) and the values of the characteristic parameters of curvature.
Pre-configured combination of monochromating devices
⎯ types and arrangement of devices
Table 2 (continued) Component type Component Nominal or measured values
Slits for all divergence slits, variable aperture slits, antiscatter slits, knife edges and receiving slits used:
Parallel plate collimators (Soller slits)
⎯ number, thickness, material of foils, length and mutual distance of foils or the resulting divergence,
⎯ position(s) in the incident and/or diffracted beams,
⎯ maximum divergence in the direction parallel to the foils,
⎯ position(s) in the incident and/or diffracted beams,
⎯ divergence accepted and divergence/convergence produced,
⎯ type of detection systems and electronic discrimination,
⎯ spatial resolution of the detector (for position-sensitive detectors),
⎯ dark current of background count rate, or noise (depending on type of detector),
⎯ counting efficiency at specified energies or wavelengths,
⎯ recommended gas composition and recommended pressure
Table 3 (concluded) Component type Component Nominal or measured values
⎯ the type of goniometer the number and orientation of goniometer axes,
⎯ the range of available radii of the goniometer circle,
⎯ the minimum step size, repeatability and reproducibility of detector positioning
⎯ the minimum step size, repeatability and reproducibility of source positioning (θ-θ geometry),
⎯ the minimum step size, repeatability and reproducibility of specimen orientation (θ-2θ geometry),
⎯ the minimum angular displacement step possible,
⎯ minimum and maximum accessible 2θ angles (positive and negative).
⎯ the type of specimen stage, and its suitability for reflection or transmission measurements,
⎯ the method for mounting and/or exchanging the specimen,
⎯ the method for positioning the specimen surface,
⎯ the ability to rotate or oscillate the specimen in its plane or around an axis in its plane,
⎯ the ability to control the atmosphere composition, temperature and pressure that surrounds the specimen.
The table below outlines the essential equipment configuration characteristics that must be traceable and accessible to the user as needed It is crucial to document or reference the specific configuration for each experiment conducted.
Table 4 — Instrument characteristics to be provided by the user
Geometry type e.g Bragg-Brentano, Seemann-Bohlin, Guinier, etc
X-ray source ⎯ source type e.g sealed tube, rotating anodes, synchrotron (*) etc
⎯ material of anode (Ag, Co, Cr, Cu, Fe, Mo, W , etc.),
⎯ the shape and dimensions, usually the length and width, of the anode area emitting X-rays,
⎯ apparent shape ("point focus" or "line focus") of the X-ray source,
⎯ take-off angle of the X-rays from the anode.
⎯ the number and orientation of goniometer axes,
⎯ the radius of the goniometer circle,
⎯ the distance from the “apparent” source to the centre of the goniometer,
⎯ the distance from the centre of the goniometer to the detector or the receiving slits. Monochromator(s) ⎯ position(s) with respect to the beam(s) concerned,
⎯ type of focusing and focal lengths (if focusing is applied),
⎯ filter(s) used, position(s), materials and thicknesses,
⎯ type of electronic filter(s) (see detection systems),
⎯ nominal wavelength or range of wavelengths. Multilayer mirrors ⎯ type of multilayer mirror(s), position(s), curvature(s), focal length(s) (where relevant),
⎯ types and arrangement of optical monochromating devices.
Slits and collimators ⎯ type(s), position(s), size(s), shape(s) and orientation(s) if different from standard values
Capillary optics ⎯ position(s) when different from standard
Detection systems ⎯ type(s) of detector,
⎯ type of electronic filter, dead time correction, energy or wavelength window (where relevant). Specimen stage ⎯ type, position and movement,
⎯ specimen environment where applicable (e.g temperature, gas, pressure
The characteristics of the synchrotron source are influenced by its configuration and usage time, necessitating specific details in each analysis report It is essential to include the synchrotron source name, beam line name and configuration, operating energy, wavelength, spectral purity (∆λ/λ), the method for determining the wavelength, the monochromator used, beam intensity monitoring methods, any intensity normalization applied, and the measurement's time, date, and duration.
General
The powder diffraction technique is designed to accurately measure line positions (2θ), intensities (including line profile maximum and integrated intensities), and diffraction line shape parameters such as full width at half-maximum (FWHM) This method ensures that the accuracy and uncertainty of the measurements align perfectly with the specific application requirements.
To achieve optimal performance, it is essential to ensure that the equipment is accurately aligned and calibrated as needed for the specific application Additionally, careful consideration must be given to environmental factors, especially temperature and pressure.
Alignment
Proper alignment of goniometers and X-ray beam optics is crucial for accurate and reproducible XRPD results Each component of the diffractometer must be meticulously adjusted—through optical, mechanical, or other methods—to minimize systematic errors and enhance detector intensity Even a slight misalignment of 5 micrometers in commercial Bragg-Brentano diffractometers can significantly impact the quality of the collected data.
Various diffractometer configurations exist, each necessitating unique alignment procedures specific to the manufacturer Tools are often supplied to verify the accurate positioning of the goniometer relative to the X-ray source, specimen, holder, and detector While this document does not provide detailed alignment procedures, key parameters for alignment are outlined in Annex B for Bragg-Brentano diffractometers, as referenced in [7].
The alignment shall be verified by collecting (part of) the diffraction pattern of an appropriate calibrant (see WI
138070) The procedures described in Annex C are recommended C.2 is the simplest procedure and does not require additional information Other procedures such as C.3, C.7, C.8 and C.9 can be adopted when necessary.
Calibration
Calibration is crucial for quantifying non-removable systematic effects on measurements in experiments While not always mandatory, calibrating an XRPD instrument is advisable as it helps assess the instrumental contribution to the diffraction signal, which can influence the position, broadening, and shape of the line profile.
The calibration shall be performed using an appropriate and preferably certified calibrant for determining each of the above mentioned effects
Appropriate working standards can also be used as internal standards and for application-specific calibrations and instrument qualification
Calibration must be conducted following a documented procedure, with the recommendations outlined in Annex C Specifically, procedures C.3 to C.9 can be utilized to generate "instrument parameter curves," which are essential for estimating non-removable systematic deviations in experimental data interpretation, as well as for performance testing and monitoring.
Different instrument configurations and performance levels are essential based on the specific type of analysis being conducted It is crucial to define the required performance for each analysis type and to monitor this performance consistently Equipment performance monitoring should involve one or more appropriate test procedures carried out according to a predetermined schedule.
The frequency of monitoring instrument performance is influenced by the stability of the instrument configuration, the application field, and laboratory conditions, aiming to ensure accurate measurements under defined equipment and environmental conditions Initially, high-frequency monitoring can help establish a suitable, less frequent interval, while recognizing that any performance failure necessitates a re-evaluation of previously produced data Many laboratories typically find that weekly monitoring suffices Test procedures for overall diffractometer performance can vary in sophistication, and results may prompt further testing of individual equipment components.
Annex C gives several approaches to instrument performance testing at increasing levels of sophistication
The proposed parameters for monitoring each procedure outlined in Annex C include: a) mean absolute positioning error, intensity, and FWHM of specific diffraction peaks (procedure C.2); b) positioning error as a function of 2θ (procedure C.3); c) FWHM as a function of 2θ (procedure C.4); d) normalized intensity as a function of 2θ (procedure C.5); e) analytical profile function parameters as a function of 2θ (procedure C.6); f) refined lattice parameters or Smith and Snyder Figures of Merit (FOMs) or refined zero point correction (procedure C.7); g) fundamental parameters and derived parameters such as ∆2θ, FWHM, intensity, and shape (procedure C.8); h) during complete profile refinement (procedure C.9), one or more of the specified elements can be monitored.
The scale factor S is essential for relating measured and calculated intensities on an absolute scale It serves as a tool to monitor the aging of X-ray tubes and to ensure the proper alignment of the optical system following adjustments to the diffractometer.
⎯ the ratio I Kα2 /I Kα1 (to verify the stability of monochromator optics and absence of time–dependent tube window contamination, e.g by tungsten);
⎯ specimen offset ∆h (for monitoring the reproducibility of specimen positioning, e.g when an automatic specimen changer is used);
⎯ the lattice parameters (to verify the accuracy and precision of line positions measurements), parameters describing the 2θ-dependence of line profiles;
⎯ the figures of merit for Rietveld refinement (Rwp, χ 2 , etc.) (as a measure of the internal consistency of diffraction data)
Although the procedure C.9 is more complicated to apply than the other methods, it extracts more information from the diffraction pattern
Relationship between the XRPD standards
(Linking of the topics within the standards)
Type of Analysis Outlines of diffraction physics
Equipment parts of diffractometers and accessories characterisation
Nature and format of specimens
Alignment of Bragg-Brentano diffractometers
For typical diffractometers working in Bragg-Brentano geometry, the following list gives the minimum set of actions that are recommended in order to achieve reproducible results from standard samples:
⎯ assess radius of the goniometer circle and adjust the position of the receiving slit;
⎯ centre the incident beam on the goniometer axis;
⎯ centre the specimen surface reference plane on the goniometer axis;
⎯ adjust the parallelism of the line source, slit system and specimen surface to the goniometer axis;
⎯ align the Soller slits (incident and diffracted beam);
⎯ adjust the zero points for ω or θ and 2θ circles
Procedures for instrument performance characterisation
General
This annex describes procedures to characterise and assess the performance of a diffractometer as it is used in an
XRPD experiment for a particular analysis
All procedures can be used as calibration procedures if a certified calibrant is used These procedures have different levels of sophistication and can be used for testing the instrument performance.
Position, intensity and breadth of a limited number of diffraction lines
The accuracy and consistency of line position, intensity, and breadth can be effectively measured for specific diffraction lines Discrepancies between observed and reference line positions reveal errors in the 2θ scale Line intensity measurements help evaluate the performance and consistency of the X-ray source, the alignment of optical components, and detector efficiency Additionally, breadth values reflect the instrument's angular resolution and alignment status.
Angular Deviation Curve
It is recommended that this procedure is used in combination with C.4 and C.5
The angular deviation curve, or "angular calibration curve," is generated from the diffraction pattern of a calibrant (WI 00138070) across a defined angular range by assessing the residual line shifts post-alignment To achieve precise alignment, it is essential to reduce the residual misalignment—defined as the discrepancies between the observed and theoretical diffraction angle, \$2\theta_{theo}\$—to within 0.02° throughout the entire pattern.
The line shift in older instruments may be more pronounced, with significant causes and their dependence on 2θ theoretical values outlined in Table C.1 Each individual cause, also referred to as aberrations, contributes to the overall line shift.
The coefficient \( A_i \) represents the contribution of an instrument or specimen to line shift, which varies with the theoretical angle \( 2\theta_{\text{theo}} \) [9] The accuracy of this coefficient, denoted by the number "I," can range from 0 to 5 or more, as detailed in Table C.1 [10] These values are influenced by the configuration, optics used, and the specimen itself Wilson has provided expressions for \( A_i \) based on geometrical and physical parameters [7] The relationship between the observed line shift \( \Delta 2\theta \) and the theoretical angle \( 2\theta_{\text{theo}} \) of the calibrant is illustrated in the "Angular Deviation Curve."
Table C.1 — Most significant contributions of instrument and specimen to line shift i Sources of contributions Magnitude of contributions (deviations from the expected Bragg angle)
1 Error of the angle 2θ = 0 (zero shift) A0
3 Specimen transparency A2 sin 2θ (thick specimen, no X-rays transmitted) or A3cos θ (thin specimen, most X- rays transmitted through specimen)
5 Axial divergence A5cot 2θ (two sets of narrow Soller slits) a aFor arrangement with none or one set of Soller slit refer to [7], [11].
NOTE The magnitude of contributions included in this Table are intrinsically related to residual, not removable errors
If the calibration process reveals the presence of unexpected contributions of misalignment, the alignment shall be performed again according to Clause 6
To effectively monitor diffractometer performance, it is advisable to create Angular Calibration Curves for different aberrations As illustrated in Figure C.1, the practical Angular Calibration Curve for an α-quartz specimen considers only the parameters A2, A4, and A5.
The line "theoretical 2θ" describes the ideal situation
The "practical 2θ" curve is a predicted curve obtained by summing the contributions of the instrument and specimen, as calculated from the Wilson formulae [7], to line shift
The experimental points for a quartz specimen are marked ().
The “range of experimental 2θ” shows the acceptable experimental 2θ based on a tolerance of about ± 0,04° [12]
Figure C.1 — Practical Angular Calibration Curve
C.3.2 Example of the application of the angular deviation curve
AI coefficients can be estimated through an optimization process, allowing for the evaluation of results against theoretical benchmarks This method is particularly effective for comparing a large number of patterns, such as in round robin tests or when analyzing data from different laboratories or the same laboratory over time.
This process gives the “effective values of Ai coefficient of Equation C.1” The optimised ∆2θ shall not differ by more than ± 0,02° from zero (see Figure C.2)
The dashed line is the "theoretical ∆2θ" being 0
The point dashed line is the optimisation of model accounting for the Wilson formulae [7]
The experimental points are derived from the diffraction pattern of a quartz specimen, following the procedures outlined in section 6.3 of EN 13925-2:2003 The difference between the theoretical and experimental points is calculated as \(2\theta_{\text{theo}} - 2\theta_{\text{exp}}\), where \(2\theta_{\text{exp}}\) represents the line position obtained from the fitting process of the diffraction pattern.
2θ theo is the expected diffraction line position
The optimised points (Ƒ) still have residual shifts from the expected values These shifts have arisen from random errors The range shown of experimental 2θ is based on a tolerance of about ± 0,02°
Figure C.2 — Optimised Angular Calibration Curve
To effectively monitor a diffractometer's performance, it is essential to collect multiple angular deviation curves at different times and compile them into a single diagram Additionally, upon request, the angular deviation curve along with monitoring diagrams for the individual aberrations specified in Table C.1 should be provided to showcase the instrument's performance.
Line breadth
It is recommended that this procedure be used in combination with C.3 and C.5
The breadth curve is obtained from the diffraction pattern of a calibrant (WI 00138070) within a defined angular range, specifically by assessing the Full Width Half Maximum (FWHM) of selected diffraction lines The analysis type and required sophistication dictate the various plots illustrating this variation.
FWHM can be used: a) “tan θ diagram” When a calibrant material is used, which has negligible strain and size broadening effects, the
The full width at half maximum (FWHM) of all lines in the diffraction pattern is plotted against tan θ In the higher angular range, this relationship typically exhibits a nearly linear dependence when a fixed divergence slit is used.
A and B depend on the configuration, slits and other beam conditioning devices
To monitor the performance of a diffractometer, the parameters A and B shall be monitored with time b) "IRF diagram" The plot of FWHM 2 (2θ) is called the Instrument Resolution Function (IRF) [13]: θ θ θ 2 2
The parameters A, B, and C are influenced by the geometry and dimensions of the instrument, the spot size, the type of radiation employed, and the slit systems The parameter D is contingent upon the transparency of the specimen, and in cases where a highly absorbing calibrant is utilized, the value of D in formula (C.3) can be zero.
To monitor the performance of a diffractometer the parameters A, B, and C shall be monitored with time or different
Line Breadth Curves may be monitored with time.
Intensity diagrams
It is recommended that this procedure be used in combination with C.3 and C.4
The intensity calibration is performed by comparing the experimental relative peak heights with those expected
Diffraction pattern databases, such as the widely used PDF of ICDD, provide calculated or reported values Experimental data can be directly observed or derived from methods outlined in section 6.3 of EN 13925-2:2003 "Procedures." Intensities are normalized to the strongest reflection, with the strongest line set at 100% Corundum is commonly utilized to create an Intensity Calibration Curve, but its anisotropy may cause preferred orientation, which can affect accuracy.
The observed intensity shall be monitored against 2θ and with time in a diagram reporting the intensity (either normalised or not) to check the overall performance of the diffractometer
The integrated intensities (not normalised) of the strongest lines are often used to monitor the performance of the source and detection system (see C.2).
Shape Analysis Curve
It is recommended that this procedure be used in addition to other procedure in this Annex
For accurate determination of lattice parameters, line profile analysis, crystallographic texture, macrostress, or crystal structure, it is essential to consider the instrumental contribution to the line profile Currently, LaB6 is recommended as the reference material for calibration in these analyses.
The instrumental contribution is determined from the diffraction pattern of the calibrant (WI 138070) within a specified angular range This pattern is modeled using analytical functions such as Gaussian, Lorentzian, Voigt, pseudo-Voigt, and Pearson, as outlined in Annex D of EN 13925-2:2003 These functions serve as approximations for the instrument contribution When employing Pearson VII, Voigt, or pseudo-Voigt functions, the mixing parameter, or shape parameter, modifies the balance between the Lorentzian and Gaussian components It is essential to monitor and potentially report the value of the mixing parameter η in relation to 2θ theo, which often exhibits a linear dependence, especially for the pseudo-Voigt mixing parameter in fixed-slit Bragg Brentano geometry, expressed as η = k0 2θ + k1.
Non-linear deviations may indicate improper usage of beam conditioning devices, such as divergence and Soller slits, in both the axial and equatorial planes Therefore, it is essential to verify the alignment in these situations.
Multiple shape analysis curves can be plotted in a single diagram to monitor the performance of a diffractometer with time.
Lattice parameters
This procedure is only intended to give an overall indication of the angular performance It should be used in conjunction with other procedures in this annex
This involves monitoring changes in calculated lattice parameters refined on the basis of a wide angular range of the diffraction pattern of a reference material
The FOMs M20 and F30, as outlined in Annex E of EN 13925-2:2003, along with the angular position indicator and the 2θ-calibration curve defined by ⏐(2θobserved)i - (2θcalculated)i⏐ = f (2θ), serve as essential metrics for assessing diffractometer alignment These indicators are also valuable for monitoring stability over time.
Special attention should be paid to the temperature dependence of lattice parameters.
The use of the Fundamental Parameter Approach
The Fundamental Parameters Approach to X-ray diffraction-line profile fitting combines a:
⎯ function that describes the diffraction-line shape inherent to the material of the specimen;
⎯ function that describes the instrumental line shape in terms of the geometric parameters of the instrument;
⎯ mathematical function describing the spectral distribution of the X-ray beam [15], [16], [17], [18]
The observed profile results from the convolution of the instrument's contribution and that of the structural specimen Since the contribution of an ideal specimen is minimal, using a standard specimen yields a diffraction pattern that reliably approximates the instrument's contribution.
The Fundamental Parameter Approach evaluates instrument performance by considering various parameters such as the spectral distribution of the X-ray beam, diffractometer dimensions, receiving slit width and length, X-ray source size, and the divergence of the incident beam Additionally, it incorporates physical properties of the specimen, including the attenuation coefficient and surface roughness.
When the optical components of a diffractometer are accurately calibrated and aligned, the resulting profile can be effectively synthesized and matched using instrumental parameters that closely resemble the values obtained through direct measurement.
A significant difference between the calculated and measured diffraction patterns from a defect-free specimen suggests alterations in the diffractometer settings Further details on this approach can be found in reference [16].
Whole pattern fitting
A thorough analysis of diffraction patterns involves minimizing the differences between calculated and observed results while tracking changes in key refined parameters In practice, the complete diffraction pattern of a suitable specimen, such as a fine-grained quartz plate or corundum powder, is recorded periodically The Rietveld method is employed to refine the data, yielding optimized parameters and their standard deviations By monitoring the variations in these parameters, it is possible to detect instrument deviations over time.
Sample report forms for characterisation of instruments
Instruments and accessories utilized in the experiment will be defined based on the specifications outlined in Table 1 and Table 2 of Clause 5 These sample tables are divided into Parts A and B to distinctly present the information required from both the manufacturer and the user.
(normally to be provided by the manufacturer on instrument delivery)
Nominal (N)or measured (M) values Specify which
Component accuracy of voltage and current long and short time stability of voltage and current Voltage range or settings
Current range or settings ripple, specified for 50 Hz, 100 Hz
The H V Generator's frequency of the switched power supply, along with the anode material options such as Ag, Co, Cr, Cu, Fe, Mo, and W, plays a crucial role in determining its performance Additionally, the characteristic spectral purity, when available, and the maximum electron emission current measured in milliamperes (mA) are essential factors Finally, the maximum electron acceleration voltage, expressed in kilovolts (kV), is a key specification that influences the generator's efficiency and output.
The shape and dimensions of the anode area in a microfocus tube, including its length and width, play a crucial role in static or dynamic electron beam conditioning Additionally, the material and thickness of the tube window significantly affect window transmission and the take-off angle of the emitted X-rays from the anode.
Sealed tubes and rotating anode sources are essential for X-ray production, with recommended anode coolant temperatures ensuring stability The apparent shape of the X-ray source, whether "point focus" or "line focus," is influenced by the recommended take-off angle and the electron emission current.
Recommended operational characteristics for normal XRPD use electron acceleration voltage
Nominal (N) or measured (M) values Specify which
Monochromators Component material and thickness
The article discusses the attenuation of filters for specified wavelengths, detailing the type and reflection plane of the monochromator crystal, the type of focusing employed, and the focal lengths used It also addresses methods for suppressing harmonics of the transmitted wavelength.
Crystal monochromators and analysers energy resolution or wavelength resolution maximum acceptable count rate
The dead time of electronic filters is influenced by the type of multilayer mirrors utilized, including the specific layer materials employed Additionally, the grading applied to these mirrors, when available, plays a crucial role The curvature type of the mirrors and the values of their characteristic curvature parameters are also significant factors that affect performance.
Multilayer mirrors types and arrangement of optical monochromating devices
Nominal (N)or measured (M) values Specify which
For all the divergence slit mention the types: variable (or fixed) aperture slits antiscatter slits knife edges receiving slits
For each type specify: their positions in the diffractometer (p=…) the divergences accepted (Da = ….) the divergence produced (Dp =…) the geometric width and length (W =…, L=…)
The positioning of slits in both the incident and diffracted beams, along with the number, thickness, and material of the foils, significantly influences the overall setup Additionally, the length and spacing of the foils affect the resulting divergence, particularly the maximum divergence in the direction parallel to the foils Furthermore, these factors contribute to the intensity attenuation observed in the beams.
Parallel plate collimators (Soller slits) positions in the incident and/or diffracted beams divergences accepted or produced geometric dimensions
Tube collimators position in the diffractometer divergence accepted and divergence/convergence produced geometric dimensions number of capillaries
Detection systems and electronic discriminators vary in their component types, impacting key performance metrics such as spatial resolution, particularly for position-sensitive detectors Important factors include dead time, dark current or noise levels, and dynamic range, which collectively influence the energy resolution achievable Additionally, the maximum acceptable count rate and counting efficiency at specified energies or wavelengths are critical for optimal performance, alongside the energy detection limit.
Detection systems' life expectancy is influenced by several factors, including the type and orientation of goniometer axes, the range of available radii of the goniometer circle, and the dimensions of the minimum sphere enclosing the closest points of approach of the goniometer axes Additionally, it is essential to test the repeatability and reproducibility of detector positioning, assess the linearity of movement, determine the smallest angular displacement step for each goniometer axis, and evaluate the maximum scan speed.
Goniometers vary in their accessibility and the range of 2θ angles they can measure, depending on the type of specimen stage used They can be designed for either reflection or transmission measurements, influencing how specimens are mounted or exchanged Additionally, the positioning of the specimen surface and the ability to rotate or oscillate the specimen are crucial features that enhance measurement accuracy and versatility.
Specimen stage the possibilities to control the atmosphere, temperature and pressure that the surrounds the specimen
(to be provided by the instrument user)
Nominal (N)or measured (M) values Specify which
Geometry type e.g Bragg-Brentano, Seemann-Bohlin, Guinier, etc
− Source type e.g sealed tube, rotating anodes, synchrotron etc
− material of anode (Ag, Co, Cr, Cu, Fe, Mo, W, etc.)
− the shape and dimensions, usually the length and width, of the anode area emitting X-rays
− apparent shape ("point focus" or "line focus") of the X-ray source X-ray source
− take-off angle of the X-rays from the anode
− number and orientation of the goniometer axis,
− the radius of the goniometer circle
− “apparent” source to centre of goniometer distance Goniometer
− centre of goniometer to detector or receiving slits
− position(s) with respect to the beam(s) concerned
− type of focusing and focal lengths
− filter(s) used, position(s), material and thickness
− type of electronic filter(s) (see detection system)
[one block for each monochromator]
− nominal wavelength on the range of wavelengths
(*) Effective values as they are obtained from the calibration process C.2 to C.9 of Annex C when and if used.
Nominal (N)or measured (M) values Specify which
− type of multilayer mirror(s), position(s), curvature(s), focal length(s) Multilayer mirrors
[one block for each monochromator] − types and arrangement of optical monochromating devices
[one block for each slit and collimator]
Capillary optics − position(s) when different from standard
[one block for each detector]
− type of electronic filter(s), dead time correction or wavelength windows (when relevant)
Specimen stage − type, position and movement
(*) Effective values as they are obtained from the calibration process C.2 to C.9 of Annex C when and if used.
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Program BGMN”, Material Scienze Forum, Vols 378-381, 30-35
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[20] ISO 5725-1, Accuracy (trueness and precision) of measurement methods and results – Part 1: General principle and definitions