ISO 20804:2022

Determination of the specific surface area of porous and particulate systems by small-angle X-ray scattering (SAXS)

This document specifies the application of small-angle X-ray scattering (SAXS) for the determination of specific surface area. Both the mass specific surface area in the order of 1 m2g-1 to 2 000 m2g-1 and the volume specific surface areas in the range from 0,01 m2cm-3 to 1 000 m2cm-3 can be obtained. The method described is applicable to dilute and concentrated systems. NOTE: In ISO 17867:2020, the determination of the particle size by SAXS is limited to dilute systems. The determination of surfaces with SAXS is straightforward for two-phase systems only. Surface determination in systems with more than two phases is beyond the scope of this document. The term ‘surface’ refers to any interface between domains of different density (more precisely: electron density) and is not restricted to the external surface of particles. As any interfaces between areas with different electron density, not only to air or vacuum, can be probed, the method can be applied to any heterogeneous system. SAXS measures not only the specific surface area of open pores but also of inaccessible, closed pores or inclusions. NOTE: This is in contrast to gas sorption methods which are described in ISO 9277:2010. In addition to porous systems, there can be contributions of internal interfaces to the measured specific surface area of any heterogeneous compact solid system, such as between crystalline and amorphous phases, provided there is an electron density contrast. Although materials comprising micropores (pore width

Détermination de la surface spécifique pour des systèmes poreux et particulaires par diffusion des rayons X aux petits angles (SAXS)

General Information

• Status: Published
• Publication Date: 26-May-2022
• ICS: 19.120 - Particle size analysis. Sieving
• Technical Committee: ISO/TC 24/SC 4 - Particle characterization
• Drafting Committee: ISO/TC 24/SC 4/WG 10 - Small angle X-ray scattering method
• Current Stage: 6060 - International Standard published
• Start Date: 27-May-2022
• Due Date: 22-Jan-2022
• Completion Date: 27-May-2022

Overview

ISO 20804:2022 specifies how to determine the specific surface area of porous and particulate systems using small-angle X‑ray scattering (SAXS). The standard covers both mass specific surface area (approx. 1 to 2 000 m2·g‑1) and volume specific surface area (0.01 to 1 000 m2·cm‑3). It applies to both dilute and concentrated systems and is focused on two‑phase systems where an electron‑density contrast exists between domains. SAXS as described in ISO 20804:2022 probes any interface between domains of different electron density - including internal interfaces and closed pores - unlike gas sorption methods.

Key topics and technical requirements

• Principle and models: small‑angle scattering theory for two‑phase systems; ideal two‑phase model and assumptions (isotropy, sharp density boundaries).
• Evaluation approaches:
  • K/Q (Invariant) method - suitable up to several hundred nanometres structural size.
  • Absolute‑scale method - enables extension to larger structures (µm range with USAXS).
• Porod law and Porod constant: used to relate high‑q scattering to specific surface area.
• Instrumentation and setup:
  • Optics, focusing, collimation and angular resolution requirements.
  • Options for laboratory SAXS and synchrotron beamlines; ultra‑small‑angle X‑ray scattering (USAXS) for larger features.
• Sample preparation and handling: recommendations include degassing, thickness/density considerations, and transmission measurement.
• Data quality and calibration: requirements for absolute scaling, background correction, and documentation of measurement conditions.
• Scope and limitations:
  • Applicable to hetero‑phase systems with electron density contrast; not for systems with more than two phases.
  • SAXS measures both open and closed pores/inclusions. Materials with micropores (< 2 nm) can be analyzed but are not covered by this document.

Practical applications and users

ISO 20804:2022 is relevant to laboratories and professionals performing surface characterization of:

• Nanoporous and nanoparticulate materials (catalysts, adsorbents, membranes)
• Mesoporous and partly macroporous ceramics, cements and construction materials
• Battery and electrode materials with internal interfaces (crystalline/amorphous)
• Quality control and R&D teams in materials science, chemical engineering and nanotechnology
• Synchrotron and instrument facility staff implementing SAXS/USAXS methods

Benefits include reproducible, inter‑laboratory comparable surface area measurements that capture interfaces inaccessible to gas sorption.

Related standards

• ISO 9277:2010 - determination of surface area by gas adsorption (BET)
• ISO 17867:2020 - particle size by SAXS (noting its dilute‑system limitation)
• ISO 15901 series - pore size classification and terminology

Keywords: ISO 20804:2022, SAXS, small‑angle X‑ray scattering, specific surface area, porous systems, particulate systems, Porod law, K/Q invariant, absolute‑scale method.

Standards Content (Sample)

INTERNATIONAL ISO
STANDARD 20804
First edition
2022-05
Determination of the specific surface
area of porous and particulate systems
by small-angle X-ray scattering (SAXS)
Détermination de la surface spécifique pour des systèmes poreux et
particulaires par diffusion des rayons X aux petits angles (SAXS)
Reference number
© ISO 2022
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
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or ISO’s member body in the country of the requester.
ISO copyright office
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Published in Switzerland
ii
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols . 3
5 Principle of the method . 4
5.1 General . 4
5.2 Ideal two-phase model . 5
5.3 Porod law - Specific surface area . 7
6 Apparatus . 8
6.1 Optics - Focusing - Collimation – Resolution . 8
6.2 Additional requirements for the absolute-scale method . 10
7 Preliminary procedures and instrument set-up .10
8 Sample preparation .11
8.1 General . 11
8.2 Degassing . 11
9 Determination of the specific surface area .11
9.1 K/Q (‘Invariant’) method . 11
9.2 Absolute-scale method . 13
10 Documentation and test report .15
10.1 Test report . 15
10.2 Technical records . 16
Annex A (informative) Example of a typical experimental protocol.17
Bibliography .22
iii
Foreword
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www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 24 Particle characterization including
sieving, Subcommittee SC 4, Particle characterization.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.
iv
Introduction
Small-angle X-ray scattering (SAXS) can be used to determine the specific surface area of nanoporous
(presence of nanopores) and nanoparticulate systems which include mesoporous and partly
macroporous materials. SAXS is a well-established method to obtain structural information on
inhomogeneities in materials at the nanoscale, typically between 1 nm and 100 nm, and is thus
perfectly suited for nanoporous, i.e. materials comprising nanopores and nanoparticulate systems
which include mesoporous (presence of mesopores) and partly macroporous (presence of macropores)
materials. With special instrumentation, and/or by using absolute-scale techniques, the limits can be
significantly extended. User-friendly commercial instruments are available worldwide from a number
of manufacturers for both routine and more sophisticated analyses, and state-of-the-art research
instruments are available at synchrotron radiation facilities.
As in all measurement techniques for surface area, care is required in all aspects of the use of
the instrument, collection of data, and further interpretation. Therefore, there is a need for an
International Standard that allows users to obtain good inter-laboratory agreement on the accuracy
and reproducibility of the technique.
SAXS can be applied to any hetero-phase system, in which the two or more phases have a different
electron density. A ‘phase’ is in this context understood as a homogeneous electron density domain in
the typical size range for SAXS between about 1 nm and 100 nm. State-of-the-art SAXS instruments
and synchrotron SAXS beamlines allow significantly extending the limit of 100 nm to several hundred
nanometres. Special instrumentation for ultra-small angle X-ray scattering (USAXS) pushes the upper
size limit even up to the µm range. This document describes two different evaluation approaches for
determining the specific surface area: The Invariant (K/Q) method has an upper size limit for the
structure of up to several hundred nanometres, whereas for the absolute-scale method the size of the
structure can even be in the µm range.
Because SAXS is sensitive to the squared electron density difference, it does not matter whether the
scattering system is composed of pores or particles within a matrix, respectively.
Small-angle neutron scattering is not described in this document but can be used without restriction
because the theory and application are similar.
v
INTERNATIONAL STANDARD ISO 20804:2022(E)
Determination of the specific surface area of porous and
particulate systems by small-angle X-ray scattering (SAXS)
1 Scope
This document specifies the application of small-angle X-ray scattering (SAXS) for the determination of
2 -1 2 -1
specific surface area. Both the mass specific surface area in the order of 1 m g to 2 000 m g and the
2 -3 2 -3
volume specific surface areas in the range from 0,01 m cm to 1 000 m cm can be obtained.
The method described is applicable to dilute and concentrated systems.
NOTE In ISO 17867:2020, the determination of the particle size by SAXS is limited to dilute systems.
The determination of surfaces with SAXS is straightforward for two-phase systems only. Surface
determination in systems with more than two phases is beyond the scope of this document.
The term ‘surface’ refers to any interface between domains of different density (more precisely: electron
density) and is not restricted to the external surface of particles. As any interfaces between areas with
different electron density, not only to air or vacuum, can be probed, the method can be applied to any
heterogeneous system.
SAXS measures not only the specific surface area of open pores but also of inaccessible, closed pores or
inclusions.
NOTE This is in contrast to gas sorption methods which are described in ISO 9277:2010.
In addition to porous systems, there can be contributions of internal interfaces to the measured specific
surface area of any heterogeneous compact solid system, such as between crystalline and amorphous
phases, provided there is an electron density contrast. Although materials comprising micropores
(pore width < 2 nm) can also be analysed with respect to their specific surface area with SAXS, this
document does not cover these materials.
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:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
3.1
nanopore
pore with width of 100 nm or less
[SOURCE: ISO 15901-2:2021, 3.10]
3.2
macropore
pore with width greater than 50 nm
[SOURCE: ISO 15901-1:2016, 3.7]
3.3
mesopore
pore of internal width between 2 nm and 50 nm
[SOURCE: ISO 15901-1:2016, 3.8]
3.4
micropore
pore of internal width less than 2 nm
[SOURCE: ISO 15901-1:2016, 3.9]
3.5
surface area
extent of accessible surface area as determined by a given method under stated conditions
[SOURCE: ISO 15901-1:2016, 3.30]
3.6
mass specific surface area
surface area of the sample divided by sample mass
3.7
volume specific surface area
surface area of the sample divided by sample volume
3.8
external (outer) surface
envelope surface of particles in the micrometre and sub-micrometre range
3.9
internal (inner) surface
surface of pores, cavities, or any other heterogeneity within particles or bulk materials
3.10
closed pore
pore totally enclosed by its walls and hence not interconnecting with other pores and not accessible to
fluids
[SOURCE: ISO 15901-1:2016, 3.10]
3.11
open pore
pore not totally enclosed by its walls and open to the surface either directly or by interconnecting with
other pores and therefore accessible to fluid
[SOURCE: ISO 15901-1:2016, 3.11]
3.12
powder
porous or nonporous solid composed of discrete particles with maximum dimension less than about
1 mm, powders with a particle size below about 1 µm are often referred to as fine powders
[SOURCE: ISO 15901-1:2016, 3.4]
3.13
granules
granules (granular material) is a conglomeration of discrete solid, macroscopic particles
3.14
monolith
monolith is a single discrete, solid object
4 Symbols
Table 1 — Symbols
Symbol Description Unit
S Total surface area m
2 −3
S Volume specific surface area (surface to volume ratio) m cm
v
2 −1
S Mass specific surface area (surface to mass ratio) m g
m
m Mass of the scattering sample g
s
V Volume of the scattering sample cm
−3
ρ Density of the sample g cm
s
−3
ρ Density of the matrix g cm
m
−3
ρ Density of the pore phase or particle g cm
p
-3
ρ Bulk density g cm
bulk
-3
ρ Grain density g cm
grain
-3
ρ Density of packed beds of nanoparticles g cm
packed-bed
-3
ρ Density of dispersion of nanoparticles g cm
dispersion
-3
ρ Density of phase 1 g cm
-3
ρ Density of phase 2 g cm
−3
ρ Electron density nm
e
−3
β Mass concentration g cm
−1
q Momentum transfer, (4π/λ)sinθ, with scattering angle 2θ nm
φ Volume fraction of phase 1
φ Volume fraction of phase 2
φ Volume fraction of the matrix
m
φ Volume fraction of the pore phase (or particle)
p
3 −1
V Mass specific pore volume cm g
p
λ Wavelength of the incident X-rays nm
Ω Solid angle sr
−1 −1
dΣ/dΩ Macroscopic differential scattering cross-section m sr
I(q), I(q) Scattered intensity of the sample
s
I(q) Scattered intensity of the reference (standard)
ref
Ĩ(q) Scattered intensity (line-smeared data)
−3
Q Invariant nm

Invariant (line-smeared data)
Q
K Porod constant

Porod constant (line-smeared data)
K
−5
K Absolute Porod constant m
abs
A Constant background term

Constant background term (line-smeared data)
A
Table 1 (continued)
Symbol Description Unit
−1
A Absolute constant background term m
abs
T Transmission of the sample
s
T Transmission of the reference (standard)
ref
t Thickness of the sample mm
s
t Optimum thickness of the sample mm
o
t Thickness of the reference (standard) mm
ref
−1
µ Linear attenuation coefficient (including coherent scattering) m
tot
r Classical electron radius m
e
Z Number of protons
−1
M Molar mass g mol
v
−1
N Avogadro constant mol
A
−1
C Conversion factors between mass densities and electron densities g
1,2
−1
C Conversion factors between mass densities and electron densities g
m,p
C Conversion factor (for SiO )
m 2
Table 2 — Overview of sample density ρ
s
Solid samples with Solid samples with Liquid-suspended

defined sample thickness unknown thickness particles
dis-
non-porous meso-po- non-porous
mesoporo- persed referred to referred
porous particles rous particles
Eq. us powder/ na- whole mass to particle
monolith (packed powder/ (packed
a
granules no-parti- of dispersion phase only
bed) granules bed)
cles
10 ρ β
dispersion
11 ρ ρ n.a. ρ ρ n.a. n.a. n.a.
bulk grain bulk grain
12 ρ β
dispersion
14 n.a. n.a.
15 ρ ρ ρ* ρ* ρ* ρ β
packed-bed packed-bed dispersion
ρ
bulk
18 n.a. n.a.
19 ρ n.a. n.a. n.a. n.a. ρ β
grain dispersion
a
Equivalent to dry powder.
*
Equivalent values for irregular particles, e.g. unknown thickness and/or sample density (see 9.2)
n.a. not applicable
5 Principle of the method
5.1 General
When electromagnetic radiation passes through matter, a small fraction of the radiation may be
scattered due to electron density differences in the matter. The scattered radiation intensity profile
(as a function of the scattering angle or momentum transfer, q), contains information that can be used
to deduce morphological characteristics of the material. In the small-angle regime (typically 2θ < 5°;
wavelength dependent), information on the particle or pore dimensions within a 2-phase material is
available from the elastic scattering arising from the electron density contrast between the particles
or pores and the medium or matrix in which they reside. This is analogous to static light scattering and
Absolute-scale K/Q
Method
method method
small-angle neutron scattering. The measured scattering profile is used for determining the specific
surface area of porous materials using two approaches described in this document.
5.2 Ideal two-phase model
For the purposes of this document, the term ‘phase’ shall refer to any domain, within the mentioned
limits of resolution within which the electron density is constant and which is confined by a sharp
boundary. It is also assumed that there is no long-range order or orientation, such that the system as a
whole is isotropic. A schematic density profile is shown in Figure 1.
Key
1 ρ
2 ρ (ρ = φ ·ρ + φ ·ρ )
s s 1 1 2 2
3 ρ
Figure 1 — Density profile in an ideal two-phase model
Such an idealized system is defined by two parameters, the volume fractions of the two phases φ
and φ (= 1 – φ ), and the volume specific surface area S of the interface between the phases. In
2 1 V
general, a combination of scattering by inner and outer surfaces is measured. However, for porous or
heterogeneous particles larger than 10 µm the contribution of outer surface is very small.
In practice, different sample types can be distinguished: porous monolithic samples, porous irregular
monolithic samples such as powders and fragments (see Figure 2), packed beds of nanoparticles or
nanoparticles in liquid suspension.
There are different terms for the density commonly used in the field of porous materials (see Table 2
and Figure 2). For reasons of simplification, this document uses mainly the density of the sample ρ and
s
the density of the matrix ρ for calculating the mass specific surface area. The density of the matrix ρ
m m
is the true solid-state density in case of porous materials, and the density of the suspending medium
in case of nanoparticles in liquid suspension. Depending on the studied sample material (e.g. monolith,
powder, particle) and the used evaluation method (K/Q method, absolute-scale method) the correct
density of the sample ρ shall be calculated or used in the relevant formulae (see Table 2).
s
a) Porous powder
b) Monolith
Key
1 ρ (density of the sample)
s
2 ρ (density of the matrix)
m
3 ρ (grain density)
grain
4 ρ (bulk density)
bulk
a
Outer surface – particle envelope
b
Inner surface – pores (microphase separation)
NOTE The outer surface area of particles usually is very small as compared to the inner surface area, if the
particle sizes are in the 10 μm range and above.
Figure 2 — Schematic view of outer and inner surfaces in a system of porous particles or grains
The situation within a bed of coarse grain powder (granules consisting of porous entities) or in a system
of liquid-suspended particles, with its equivalent volume fractions is schematically shown in Figure 3.
NOTE SAXS ‘sees’ the internal structure at the scale below several hundred nm within the porous powder
grains. The volume V of the scattering sample in a system of porous particles, with volume fractions φ , φ can be
1 2
imagined as one continuous block.
Figure 3 — Internal structure at within the powder grains
5.3 Porod law - Specific surface area
The general basis for surface area determination by SAXS is the Porod law which states that the
4π
scattering intensity I(q), where q = ⋅sinθ , with 2θ the scattering angle, decays towards large angles
λ
asymptotically with the inverse fourth power of the scattering vector q; hereby, the total surface area S
within the irradiated volume is a proportionality factor as given in Formula (1):
−4
lim Iq() ∝⋅ Sq (1)
q→∞
In practice, the following master formula is found to apply for the tail of the scattering curve towards
large q values:
−4
lim Iq()=+AK⋅q (2)
q→∞
where A denotes a constant background term for the short-range atomic structure and K contains
the surface area information. Using a double-log plot according to Formula (2) the q-range for the
Porod extrapolation can be determined. A and K are derived directly via a non-linear fit according to
Formula (2) in this plot.
As an alternate procedure, A and K can be determined from the ‘Porod plot’ (see Figure 4) according to
Formula (3), which is a linearization of Formula (2).
Iq ⋅=qK +⋅Aq (3)
()
This can be done by performing a linear least-squares fit according to this linearized equation. For the
search of the linear region in the Porod plot either the transition zone between the Porod slope and
flattening towards larger q values is used or the q-range is taken from the double-log plot as described
above.
In the case of infinite line-smearing, e.g. with Kratky optics (see Figure 6 - right), the Porod slope
−3 −4
becomes proportional to q instead of q . Line-collimation instruments confine the beam in one
dimension so that the beam profile is a long and narrow line.
−3
  
lim Iq()=+AK⋅q (4)
q→∞
Key
X q
Y l(q)· q
1 K
2 A (tanα = A)
3 α
Figure 4 — ‘Porod plot’, from which the parameters A and K can be determined.
The Porod law is found to hold in many cases. Therefore, the volume specific surface area can be
straightforwardly determined by SAXS. In practice however, in complex systems or fractal materials the
−4
scattering intensity frequently deviates from the Porod law, q , which could be caused by a transition
layer between the two phases, or a high degree of rugosity (surface roughness). These cases are not
described in this document.
To arrive at the mass specific or volume specific surface area (S or S ) the following two methods find
m V
widespread use in practice:
— K/Q (‘Invariant’) method
— Absolute-scale method
6 Apparatus
6.1 Optics - Focusing - Collimation – Resolution
The general design of a SAXS instrument is shown in Figure 5.
Key
X 2Ɵ or q
Y scattered intensity
1 X-ray source
2 optics
3 collimation system
4 sample
5 detector
a 2Ɵ
Figure 5 — Schematic design of a SAXS instrument, consisting of X-ray source, optics,
collimation system, sample holder, and X-ray detector
The above outlined principles strictly apply only for scattering patterns obtained with ideal point-
collimation optics, i.e. point-shaped X-ray beam cross-section and monochromatic radiation. However,
a widely used instrument design (e.g. Kratky camera) uses line collimation, i.e. the probing X-ray beam
is confined in one dimension so that the beam profile is a long and narrow line. This has the advantage
of producing higher intensities in the weak outer part of the scattering curve (towards large q), but
generally requires numerical corrections (desmearing). The two principles are shown in Figure 6.
Key
1 X-ray source
2 collimation system
3 sample
4 detector
Figure 6 — Schematic view of point- (left) and line-collimation (right) optics
6.2 Additional requirements for the absolute-scale method
The technical requirements for the absolute-
...