ISO 20804:2022
(Main)Determination of the specific surface area of porous and particulate systems by small-angle X-ray scattering (SAXS)
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)
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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 20804:2022(E)
© ISO 2022
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ISO 20804:2022(E)
COPYRIGHT PROTECTED DOCUMENT
© 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
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii
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ISO 20804:2022(E)
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
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ISO 20804:2022(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to
the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see
www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 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.
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ISO 20804:2022(E)
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.
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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]
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ISO 20804:2022(E)
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]
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ISO 20804:2022(E)
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
2
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
3
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
1
-3
ρ Density of phase 2 g cm
2
−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
1
φ Volume fraction of phase 2
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
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ISO 20804:2022(E)
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
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Absolute-scale K/Q
Method
method method
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ISO 20804:2022(E)
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
1
2 ρ (ρ = φ ·ρ + φ ·ρ )
s s 1 1 2 2
3 ρ
2
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
1
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
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ISO 20804:2022(E)
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.
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ISO 20804:2022(E)
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).
44
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.
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ISO 20804:2022(E)
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
4
X q
4
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.
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ISO 20804:2022(E)
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.
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ISO 20804:2022(E)
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-scale method with respect to the SAXS-instrument are:
a) A stable X-ray source, i.e. a constant photon rate over time. After switching on the SAXS-instrument
(X-ray source and detector), it takes some time until a stable photon/time rate is reached (usually
several hours). The stability of X-ray source and detector also depend on the temperature of the
instrument’s environment; therefore, an actively temperature-controlled room is favourable. All
samples as well as the primary/secondary standard shall be measured in one “run” as a change
of the instrument’s set-up or switching off devices of the SAXS-instrument usually changes the
photon/time rate.
b) The transmission T of a sample shall be determined. It can, e.g. be derived by recording the
s
intensity of the primary beam with and without sample by a photodiode or the detector itself. If the
detector is used, the detector-response shall be linear in the appropriate range.
c) The sample, standard (if used), and empty beam scattering measurements shall be made under
identical conditions. If this is not the case, then this will invalidate the transmission and calibration
measurements.
With certain solid-state pixel detectors that have a large linear dynamic range, it has become possible to
measure the intensity of the direct, un-attenuated (or attenuated by calibrated filter, if monochromatic
X-rays are used) beam, which then makes the procedure of absolute-scale method very simple.
7 Preliminary procedures and instrument set-up
Generally, it is of greatest importance to ensure that the instrument background (from optics, detector,
and sample windows, air) be strictly minimized, since the validity of Porod’s law extends into the low-
intensity outer (large-q) parts of the scattering curve. On the other hand, however, the typical samples
for specific surface area determination are solids (powders, pastes, bulk materials) with strong SAXS
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ISO 20804:2022(E)
intensity, so that the background may become uncritical. In any case, this shall be verified by control
measurements. Apart from this, there are no particular requirements for the instrument set-up, except
of choosing a sufficiently large q-range for the measurement of K and/or Q according to Formula (2) and
(4). For all measurements requiring background subtraction, the stability of the X-ray source, optics,
and detector is of paramount importance.
8 Sample preparation
8.1 General
Sample preparation is simple and fast for SAXS measurements. The required sample quantity is
generally small: for powder samples less than 1 g is required, in the case of solid sample slices an area of
2 2
(1 × 1) mm to (1 × 20) mm is sufficient. The sample thickness is typically smaller than 1 mm and can
be tuned to optimize the scattering and limit the X-ray absorption, depending on the composition of the
sample.
NOTE According to ISO 17867:2020, the ideal specimen transmits about 37 % of the incident radiation. The
specimen thickness can be adjusted accordingly to optimize transmission.
The samples are usually filled in sample holders (cuvettes/capillaries, sandwich-type holders
comprising windows) which shall be transparent to X-rays and exhibit little scattering themselves.
Frequently used window materials include polyimide films, mica or silicon nitride. Care should be
taken that the scat
...
FINAL
INTERNATIONAL ISO/FDIS
DRAFT
STANDARD 20804
ISO/TC 24/SC 4
Determination of the specific surface
Secretariat: BSI
area of porous and particulate systems
Voting begins on:
2021-12-13 by small-angle X-ray scattering (SAXS)
Voting terminates on:
Détermination de la surface spécifique pour des systèmes poreux et
2022-02-07
particulaires par diffusion des rayons X aux petits angles (SAXS)
RECIPIENTS OF THIS DRAFT ARE INVITED TO
SUBMIT, WITH THEIR COMMENTS, NOTIFICATION
OF ANY RELEVANT PATENT RIGHTS OF WHICH
THEY ARE AWARE AND TO PROVIDE SUPPOR TING
DOCUMENTATION.
IN ADDITION TO THEIR EVALUATION AS
Reference number
BEING ACCEPTABLE FOR INDUSTRIAL, TECHNO-
ISO/FDIS 20804:2021(E)
LOGICAL, COMMERCIAL AND USER PURPOSES,
DRAFT INTERNATIONAL STANDARDS MAY ON
OCCASION HAVE TO BE CONSIDERED IN THE
LIGHT OF THEIR POTENTIAL TO BECOME STAN-
DARDS TO WHICH REFERENCE MAY BE MADE IN
NATIONAL REGULATIONS. © ISO 2021
---------------------- Page: 1 ----------------------
ISO/FDIS 20804:2021(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2021
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii
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ISO/FDIS 20804:2021(E)
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
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ISO/FDIS 20804:2021(E)
Foreword
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This document was prepared by Technical Committee ISO/TC 24 Particle characterization including
sieving, Subcommittee SC 4, Particle characterization.
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ISO/FDIS 20804:2021(E)
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.
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FINAL DRAFT INTERNATIONAL STANDARD ISO/FDIS 20804:2021(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]
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ISO/FDIS 20804:2021(E)
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]
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ISO/FDIS 20804:2021(E)
3.13
granules
granules (granular material) is a conglomeration of discrete solid, macroscopic particles
3.14
monolith
monolith is a single discrete, solid object
Table 2 — Overview of sample density ρ
s
Solid samples with Solid samples with Liquid-suspended parti-
defined sample thickness unknown thickness cles
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
4 Symbols
Table 1 — Symbols
Symbol Description Unit
2
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
3
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
1
-3
ρ Density of phase 2 g cm
2
−3
ρ Electron density nm
e
−3
β Mass concentration g cm
3
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Absolute-scale K/Q
Method
method method
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Table 1 (continued)
Symbol Description Unit
−1
Q Momentum transfer, (4π/λ)sinθ, with scattering angle 2θ nm
φ Volume fraction of phase 1
1
φ Volume fraction of phase 2
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
−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
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
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.
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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
1
2 ρ (ρ = φ ·ρ + φ ·ρ )
s s 1 1 2 2
3 ρ
2
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
1
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
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ISO/FDIS 20804:2021(E)
a)
b)
Key
a porous powder
b monolith
1 ρ (density of the sample)
s
2 ρ (density of the matrix)
m
3 ρ (grain density)
grain
4 ρ (bulk density)
bulk
Left hand side Outer surface – particle envelope
Right hand side 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.
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ISO/FDIS 20804:2021(E)
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).
44
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.
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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
4
X q
4
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.
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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.
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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-scale method with respect to the SAXS-instrument are:
a) A stable X-ray source, i.e. a constant photon rate over time. After switching on the SAXS-instrument
(X-ray source and detector), it takes some time until a stable photon/time rate is reached (usually
several hours). The stability of X-ray source and detector also depend on the temperature of the
instrument’s environment; therefore, an actively temperature-controlled room is favourable. All
samples as well as the primary/secondary standard shall be measured in one “run” as a change
of the instrument’s set-up or switching off devices of the SAXS-instrument usually changes the
photon/time rate.
b) The transmission T of a sample shall be determined. It can, e.g. be derived by recording the
s
intensity of the primary beam with and without sample by a photodiode or the detector itself. If the
detector is used, the detector-response shall be linear in the appropriate range.
c) The sample, standard (if used), and empty beam scattering measurements shall be made under
identical conditions. If this is not the case, then this will invalidate the transmission and calibration
measurements.
With certain solid-state pixel detectors that have a large linear dynamic range, it has become possible to
measure the intensity of the direct, un-attenuated (or attenuated by calibrated filter, if monochromatic
X-rays are used) beam, which then makes the procedure of absolute-scale method very simple.
7 Preliminary procedures and instrument set-up
Generally, it is of greatest importance to ensure that the instrument background (from optics, detector,
and sample windows, air) be strictly minimized, since the validity of Porod’s law extends into the low-
intensity outer (large-q) parts of the scattering curve. On the other hand, however, the typical samples
for specific surface area determination are solids (powders, pastes, bulk materials) with strong SAXS
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intensity, so that the background may become uncritical. In any case, this shall be verified by control
measurements. Apart from this, there are no particular requirements for the instrument set-up, except
of choosing a sufficiently large q-range for the measurement of K and/or Q according to Formula (2) and
(4). For all measurements requiring background subtraction, the stability of the X-ray source, optics,
and detector is of paramount importance.
8 Sample preparation
8.1 General
Sample preparation is simple and fast for SAXS measurements. The required sample quantity is
generally small: for powder samples less than 1 g is required, in the case of solid sample slices an area of
2 2
(1 × 1) mm to (1 × 20) mm is sufficient. The
...
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