EN ISO 80000-12:2019
(Main)Quantities and units - Part 12: Condensed matter physics (ISO 80000-12:2019, Corrected version 2021-11)
Quantities and units - Part 12: Condensed matter physics (ISO 80000-12:2019, Corrected version 2021-11)
This document gives names, symbols, definitions and units for quantities of condensed matter physics. Where appropriate, conversion factors are also given.
Größen und Einheiten - Teil 12: Physik der kondensierten Materie (ISO 80000-12:2019, korrigierte Fassung 2021-11)
Dieses Dokument enthält Benennungen, Formelzeichen, Definitionen und Einheiten für Größen der Physik der kondensierten Materie. Wo benötigt, sind auch Umrechnungsfaktoren aufgeführt.
Grandeurs et unités - Partie 12: Physique de la matière condensée (ISO 80000-12:2019, Version corrigée 2021-11)
Le présent document donne les noms, les symboles, les définitions et les unités des grandeurs de la physique de la matière condensée. Des facteurs de conversion sont également indiqués, s'il y a lieu.
Veličine in enote - 12. del: Fizika kondenzirane snovi (ISO 80000-12:2019, popravljena verzija 2021-11)
Ta dokument podaja imena, simbole, definicije in enote za veličine s področja fizike kondenzirane snovi. Kadar je primerno, so navedeni tudi pretvorniki (pretvorni dejavniki).
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
01-december-2019
Nadomešča:
SIST EN ISO 80000-12:2013
Veličine in enote - 12. del: Fizika kondenzirane snovi (ISO 80000-12:2019)
Quantities and units - Part 12: Condensed matter physics (ISO 80000-12:2019)
Größen und Einheiten - Teil 12: Physik der kondensierten Materie (ISO 80000-12:2019)
Grandeurs et unités - Partie 12: Physique de la matière condensée (ISO 80000-12:2019)
Ta slovenski standard je istoveten z: EN ISO 80000-12:2019
ICS:
01.060 Veličine in enote Quantities and units
07.030 Fizika. Kemija Physics. Chemistry
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
EN ISO 80000-12
EUROPEAN STANDARD
NORME EUROPÉENNE
October 2019
EUROPÄISCHE NORM
ICS 01.060 Supersedes EN ISO 80000-12:2013
English Version
Quantities and units - Part 12: Condensed matter physics
(ISO 80000-12:2019)
Grandeurs et unités - Partie 12: Physique de la matière Größen und Einheiten - Teil 12: Physik der
condensée (ISO 80000-12:2019) kondensierten Materie (ISO 80000-12:2019)
This European Standard was approved by CEN on 5 May 2019.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this
European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references
concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN
member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by
translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management
Centre has the same status as the official versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and
United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2019 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 80000-12:2019 E
worldwide for CEN national Members.
Contents Page
European foreword . 3
European foreword
This document (EN ISO 80000-12:2019) has been prepared by Technical Committee ISO/TC 12
"Quantities and units" in collaboration with Technical Committee CEN/SS F02 “Units and symbols” the
secretariat of which is held by CCMC.
This European Standard shall be given the status of a national standard, either by publication of an
identical text or by endorsement, at the latest by April 2020, and conflicting national standards shall be
withdrawn at the latest by April 2020.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
This document supersedes EN ISO 80000-12:2013.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland,
Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of
North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the
United Kingdom.
Endorsement notice
The text of ISO 80000-12:2019 has been approved by CEN as EN ISO 80000-12:2019 without any
modification.
INTERNATIONAL ISO
STANDARD 80000-12
Second edition
2019-08
Quantities and units —
Part 12:
Condensed matter physics
Grandeurs et unités —
Partie 12: Physique de la matière condensée
Reference number
ISO 80000-12:2019(E)
©
ISO 2019
ISO 80000-12:2019(E)
© ISO 2019
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
Fax: +41 22 749 09 47
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii © ISO 2019 – All rights reserved
ISO 80000-12:2019(E)
Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
Annex A (normative) Symbols for planes and directions in crystals .12
Bibliography .13
Index .14
ISO 80000-12:2019(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.o rg/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 12, Quantities and units, in collaboration
with Technical Committee IEC/TC 25, Quantities and units.
This second edition cancels and replaces the first edition (ISO 80000-12:2009), which has been
technically revised.
The main changes compared to the previous edition are as follows:
— the table giving the quantities and units has been simplified;
— some definitions and the remarks have been stated physically more precisely.
A list of all parts in the ISO 80000 and IEC 80000 series can be found on the ISO and IEC websites.
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 © ISO 2019 – All rights reserved
INTERNATIONAL STANDARD ISO 80000-12:2019(E)
Quantities and units —
Part 12:
Condensed matter physics
1 Scope
This document gives names, symbols, definitions and units for quantities of condensed matter physics.
Where appropriate, conversion factors are also given.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
Names, symbols, definitions and units for quantities used in condensed matter physics are given in
Table 1.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https: //www .iso .org/obp
— IEC Electropedia: available at http: //www .electropedia .org/
ISO 80000-12:2019(E)
2 © ISO 2019 – All rights reserved
Table 1 — Quantities and units used in condensed matter physics
Item No. Quantity Unit Remarks
Name Symbol Definition
12-1.1 lattice vector R translation vector that maps the crystal lattice on itself m The non-SI unit ångström (Å) is widely used
by x-ray crystallographers and structural
chemists.
12-1.2 fundamental lattice a , a , a fundamental translation vectors for the crystal lattice m The lattice vector (item 12-1.1) can be given as
1 2 3
vectors
a, b, c R = n a + n a + n a
1 1 2 2 3 3
where n , n and n are integers.
1 2 3
−1
12-2.1 angular reciprocal vector whose scalar products with all fundamental m
G
G
lattice vector
lattice vectors are integral multiples of 2π In crystallography, however, the quantity
2π
is sometimes used.
−1
12-2.2 fundamental b , b , b fundamental translation vectors for the reciprocal m
1 2 3
a · b = 2πδ
i i ij
reciprocal lattice lattice
vectors
In crystallography, however, the quantities
b
j
are also often used.
2π
12-3 lattice plane spacing d distance (ISO 80000-3) between successive lattice m The non-SI unit ångström (Å) is widely used
planes by x-ray crystallographers and structural
chemists.
12-4 Bragg angle ϑ angle between the scattered ray and the lattice plane 1 Bragg angle ϑ is given by
° 2d sin ϑ = nλ
where d is the lattice plane spacing (item 12-
3), λ is the wavelength (ISO 80000-7) of the
radiation, and n is the order of reflexion which
is an integer.
12-5.1 short-range order r, σ fraction of nearest-neighbour atom pairs in an Ising 1 Similar definitions apply to other order-disor-
parameter ferromagnet having magnetic moments in one direc- der phenomena.
tion, minus the fraction having magnetic moments in
Other symbols are frequently used.
the opposite direction
12-5.2 long-range order R, s fraction of atoms in an Ising ferromagnet having 1 Similar definitions apply to other order-disor-
parameter magnetic moments in one direction, minus the fraction der phenomena.
having magnetic moments in the opposite direction
Other symbols are frequently used.
ISO 80000-12:2019(E)
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
12-5.3 atomic scattering f quotient of radiation amplitude scattered by the atom 1 The atomic scattering factor can be ex-
factor and radiation amplitude scattered by a single electron pressed by:
E
a
f =
E
e
where E is the radiation amplitude scattered
a
by the atom and E is the radiation amplitude
e
scattered by a single electron.
12-5.4 structure factor quantity given by: 1 For the Miller indices h, k, l, see Annex A.
Fh,,kl
()
N
Fh(),,kl =+fhexpi2π xkyl+ z
[]()
∑ nn nn
n=1
where f is the atomic scattering factor (item 12-5.3)
n
for atom n, x , y , z are fractional coordinates of its
n n n
position, N is the total number of atoms in the unit cell
and h, k, l are the Miller indices
12-6 Burgers vector b closing vector in a sequence of vectors encircling a m
dislocation
12-7.1 particle position r, R position vector (ISO 80000-3) of a particle m Often, r is used for electrons and R is used for
vector atoms and other heavier particles.
12-7.2 equilibrium position R position vector (ISO 80000-3) of an ion or atom in m
vector equilibrium
physics>
12-7.3 displacement vector u difference between the position vector (ISO 80000-3) m The displacement vector can be expressed by:
u = R − R
physics>
where R is particle position vector (item 12-
7.1) and R is position vector of an ion or atom
in equilibrium (item 12-7.2).
12-8 Debye-Waller factor D,
...
SLOVENSKI STANDARD
01-december-2019
Nadomešča:
SIST EN ISO 80000-12:2013
SIST ISO 80000-12:2013
Veličine in enote - 12. del: Fizika kondenzirane snovi (ISO 80000-12:2019,
popravljena verzija 2021-11)
Quantities and units - Part 12: Condensed matter physics (ISO 80000-12:2019,
Corrected version 2021-11)
Größen und Einheiten - Teil 12: Physik der kondensierten Materie (ISO 80000-12:2019)
Grandeurs et unités - Partie 12: Physique de la matière condensée (ISO 80000-12:2019)
Ta slovenski standard je istoveten z: EN ISO 80000-12:2019
ICS:
01.060 Veličine in enote Quantities and units
07.030 Fizika. Kemija Physics. Chemistry
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
EN ISO 80000-12
EUROPEAN STANDARD
NORME EUROPÉENNE
October 2019
EUROPÄISCHE NORM
ICS 01.060 Supersedes EN ISO 80000-12:2013
English Version
Quantities and units - Part 12: Condensed matter physics
(ISO 80000-12:2019, Corrected version 2021-11)
Grandeurs et unités - Partie 12: Physique de la matière Größen und Einheiten - Teil 12: Physik der
condensée (ISO 80000-12:2019, Version corrigée kondensierten Materie (ISO 80000-12:2019,
2021-11) korrigierte Fassung 2021-11)
This European Standard was approved by CEN on 5 May 2019.
This European Standard was corrected and reissued by the CEN-CENELEC Management Centre on 8 December 2021.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this
European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references
concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN
member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by
translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management
Centre has the same status as the official versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,
Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and
United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATIO N
EUROPÄISCHES KOMITEE FÜR NORMUN G
CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2019 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 80000-12:2019 E
worldwide for CEN national Members.
Contents Page
European foreword . 3
European foreword
This document (EN ISO 80000-12:2019) has been prepared by Technical Committee ISO/TC 12
"Quantities and units" in collaboration with Technical Committee CEN/SS F02 “Units and symbols” the
secretariat of which is held by CCMC.
This European Standard shall be given the status of a national standard, either by publication of an
identical text or by endorsement, at the latest by April 2020, and conflicting national standards shall be
withdrawn at the latest by April 2020.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
This document supersedes EN ISO 80000-12:2013.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland,
Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of
North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the
United Kingdom.
Endorsement notice
The text of ISO 80000-12:2019, Corrected version 2021-11 has been approved by CEN as
INTERNATIONAL ISO
STANDARD 80000-12
Second edition
2019-08
Corrected version
2021-11
Quantities and units —
Part 12:
Condensed matter physics
Grandeurs et unités —
Partie 12: Physique de la matière condensée
Reference number
ISO 80000-12:2019(E)
ISO 80000-12:2019(E)
© ISO 2019
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
ISO 80000-12:2019(E)
Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
Annex A (normative) Symbols for planes and directions in crystals.12
Bibliography .13
Index .14
iii
ISO 80000-12:2019(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 12, Quantities and units, in collaboration
with Technical Committee IEC/TC 25, Quantities and units.
This second edition cancels and replaces the first edition (ISO 80000-12:2009), which has been
technically revised.
The main changes compared to the previous edition are as follows:
— the table giving the quantities and units has been simplified;
— some definitions and the remarks have been stated physically more precisely.
A list of all parts in the ISO 80000 and IEC 80000 series can be found on the ISO and IEC websites.
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.
This corrected version of ISO 80000-12:2019 incorporates the following corrections:
— the formula in 12.26 has been corrected (minus sign inserted).
iv
INTERNATIONAL STANDARD ISO 80000-12:2019(E)
Quantities and units —
Part 12:
Condensed matter physics
1 Scope
This document gives names, symbols, definitions and units for quantities of condensed matter physics.
Where appropriate, conversion factors are also given.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
Names, symbols, definitions and units for quantities used in condensed matter physics are given in
Table 1.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
ISO 80000-12:2019(E)
Table 1 — Quantities and units used in condensed matter physics
Item No. Quantity Unit Remarks
Name Symbol Definition
12-1.1 lattice vector R translation vector that maps the crystal lattice on itself m The non-SI unit ångström (Å) is widely used
by x-ray crystallographers and structural
chemists.
12-1.2 fundamental lattice a , a , a fundamental translation vectors for the crystal lattice m The lattice vector (item 12-1.1) can be given
1 2 3
vectors as
a, b, c
R = n a + n a + n a
1 1 2 2 3 3
where n , n and n are integers.
1 2 3
−1
12-2.1 angular reciprocal G vector whose scalar products with all fundamental m
G
In crystallography, however, the quantity
lattice vector lattice vectors are integral multiples of 2π
2π
is sometimes used.
−1
12-2.2 fundamental b , b , b fundamental translation vectors for the reciprocal m a · b = 2πδ
1 2 3
i i
ij
reciprocal lattice lattice
In crystallography, however, the quantities
vectors
b
j
are also often used.
2π
12-3 lattice plane spacing d distance (ISO 80000-3) between successive lattice m The non-SI unit ångström (Å) is widely used
planes by x-ray crystallographers and structural
chemists.
12-4 Bragg angle ϑ angle between the scattered ray and the lattice plane 1 Bragg angle ϑ is given by
° 2d sin ϑ = nλ
where d is the lattice plane spacing (item 12-
3), λ is the wavelength (ISO 80000-7) of the
radiation, and n is the order of reflexion which
is an integer.
12-5.1 short-range order r, σ fraction of nearest-neighbour atom pairs in an Ising 1 Similar definitions apply to other order-disor-
parameter ferromagnet having magnetic moments in one direc- der phenomena.
tion, minus the fraction having magnetic moments in
Other symbols are frequently used.
the opposite direction
12-5.2 long-range order R, s fraction of atoms in an Ising ferromagnet having 1 Similar definitions apply to other order-disor-
parameter magnetic moments in one direction, minus the fraction der phenomena.
having magnetic moments in the opposite direction
Other symbols are frequently used.
ISO 80000-12:2019(E)
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
12-5.3 atomic scattering f quotient of radiation amplitude scattered by the atom 1 The atomic scattering factor can be expressed
factor and radiation amplitude scattered by a single electron by:
E
a
f =
E
e
where E is the radiation amplitude scattered
a
by the atom and E is the radiation amplitude
e
scattered by a single electron.
12-5.4 structure factor quantity given by: 1 For the Miller indices h, k, l, see Annex A.
Fh(),,kl
N
Fh(),,kl =+fhexpi2π xkyl+ z
[]()
∑ nn nn
n=1
where f is the atomic scattering factor (item 12-5.3)
n
for atom n, x , y , z are fractional coordinates of its
n n n
position, N is the total number of atoms in the unit cell
and h, k, l are the Miller indices
12-6 Burgers vector b closing vector in a sequence of vectors encircling a m
dislocation
12-7.1 particle position r, R position vector (ISO 80000-3) of a particle m Often, r is used for electrons and R is used for
vector atoms and other heavier particles.
12-7.2 equilibrium position R position vector (ISO 80000-
...
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