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).

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SLOVENSKI STANDARD
SIST EN ISO 80000-12:2019
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
SIST EN ISO 80000-12:2019 en,fr,de

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

---------------------- Page: 1 ----------------------
SIST EN ISO 80000-12:2019
---------------------- Page: 2 ----------------------
SIST EN ISO 80000-12:2019
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.
---------------------- Page: 3 ----------------------
SIST EN ISO 80000-12:2019
EN ISO 80000-12:2019 (E)
Contents Page

European foreword ....................................................................................................................................................... 3

---------------------- Page: 4 ----------------------
SIST EN ISO 80000-12:2019
EN ISO 80000-12:2019 (E)
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

EN ISO 80000-12:2019 without any modification.
---------------------- Page: 5 ----------------------
SIST EN ISO 80000-12:2019
---------------------- Page: 6 ----------------------
SIST EN ISO 80000-12:2019
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 2019
---------------------- Page: 7 ----------------------
SIST EN ISO 80000-12:2019
ISO 80000-12:2019(E)
COPYRIGHT PROTECTED DOCUMENT
© 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
© ISO 2019 – All rights reserved
---------------------- Page: 8 ----------------------
SIST EN ISO 80000-12:2019
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 2019 – All rights reserved
---------------------- Page: 9 ----------------------
SIST EN ISO 80000-12:2019
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).
© ISO 2019 – All rights reserved
---------------------- Page: 10 ----------------------
SIST EN ISO 80000-12:2019
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 2019 – All rights reserved
---------------------- Page: 11 ----------------------
SIST EN ISO 80000-12:2019
ISO 80000-12:2019(E)
© 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

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
12-2.1 angular reciprocal G vector whose scalar products with all fundamental m
In crystallography, however, the quantity
lattice vector lattice vectors are integral multiples of 2π
is sometimes used.

12-2.2 fundamental b , b , b fundamental translation vectors for the reciprocal m a · b = 2πδ

1 2 3
i i
reciprocal lattice lattice
In crystallography, however, the quantities
vectors
are also often used.

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.
---------------------- Page: 12 ----------------------
SIST EN ISO 80000-12:2019
ISO 80000-12:2019(E)
© ISO 2019 – All rights reserved
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:
f =
where E is the radiation amplitude scattered
by the atom and E is the radiation amplitude
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
Fh(),,kl =+fhexpi2π xkyl+ z
[]()
∑ nn nn
n=1
where f is the atomic scattering factor (item 12-5.3)
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, B factor by which the intensity of a diffraction line is 1 D is sometimes expressed as D = exp(−2W); in

reduced because of the lattice vibrations Mössbauer spectroscopy, it is also called the f

factor and denoted by f.
---------------------- Page: 13 ----------------------
SIST EN ISO 80000-12:2019
ISO 80000-12:2019(E)
© ISO 2019 – All rights reserved
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition

12-9.1 angular wavenum- k, (q) quotient of momentum (ISO 80000-4) and the reduced m The corresponding vector (ISO 80000-2)

ber, Planck constant (ISO 80000-1) quantity is called wave vector (ISO 80000-3),
angular repetency expressed by:
physics>
k=
where p is the momentum (ISO 80000-4) of
quasi free electrons in an electron gas, and ħ
is the reduced Planck constant (ISO 80000-1);
for phonons, its magnitude is
k=
where λ is the wavelength (ISO 80000-3) of
the lattice vibrations.
When a distinction is needed between k
and the symbol for the Boltzmann constant
(ISO 80000-1), k can be used for the latter.
When a distinction is needed, q should be
used for phonons, and k for particles such as
electrons and neutrons.
The method of cut-off must be specified.
In condensed matter physics, angular wave-
number is often called wavenumber.

12-9.2 Fermi angular k angular wavenumber (item 12-9.1) of electrons in m In condensed matter physics, angular wave-

wavenumber, states on the Fermi sphere number is often called wavenumber.
Fermi angular
repetency

12-9.3 Debye angular q cut-off angular wavenumber (item 12-9.1) in the Debye m The method of cut-off must be specified.

wavenumber, model of the vibrational spectrum of a solid
In condensed matter physics, angular wave-
Debye angular number is often called wavenumber.
repetency

12-10 Debye angular ω cut-off angular frequency (ISO 80000-3) in the Debye s The method of cut-off must be specified.

frequency model of the vibrational spectrum of a solid
---------------------- Page: 14 ----------------------
SIST EN ISO 80000-12:2019
ISO 80000-12:2019(E)
© ISO 2019 – All rights reserved
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition

12-11 Debye temperature in the Debye model, quantity given by: K A Debye temperature can also be defined by

fitting a Debye model result to a certain quan-
tity, for instance, the heat capacity at a certain
Θ =
k temperature.
where k is the Boltzmann constant, (ISO 80000-1), ħ is
the reduced Planck constant (ISO 80000-1), and ω is
Debye angular frequency (item 12-10)

12-12 density of vibration- g quotient of the number of vibrational modes in an in- m s

dn ω
gn()ω ==
al states finitesimal interval of angular frequency (ISO 80000-
3), and the product of the width of
...

SLOVENSKI STANDARD
SIST EN ISO 80000-12:2019
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
SIST EN ISO 80000-12:2019 en,fr,de

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

---------------------- Page: 1 ----------------------
SIST EN ISO 80000-12:2019
---------------------- Page: 2 ----------------------
SIST EN ISO 80000-12:2019
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.
---------------------- Page: 3 ----------------------
SIST EN ISO 80000-12:2019
EN ISO 80000-12:2019 (E)
Contents Page

European foreword ....................................................................................................................................................... 3

---------------------- Page: 4 ----------------------
SIST EN ISO 80000-12:2019
EN ISO 80000-12:2019 (E)
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.
---------------------- Page: 5 ----------------------
SIST EN ISO 80000-12:2019
---------------------- Page: 6 ----------------------
SIST EN ISO 80000-12:2019
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
---------------------- Page: 7 ----------------------
SIST EN ISO 80000-12:2019
ISO 80000-12:2019(E)
COPYRIGHT PROTECTED DOCUMENT
© 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
---------------------- Page: 8 ----------------------
SIST EN ISO 80000-12:2019
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 2019 – All rights reserved iii
---------------------- Page: 9 ----------------------
SIST EN ISO 80000-12:2019
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
---------------------- Page: 10 ----------------------
SIST EN ISO 80000-12:2019
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 2019 – All rights reserved 1
---------------------- Page: 11 ----------------------
SIST EN ISO 80000-12:2019
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
12-2.1 angular reciprocal vector whose scalar products with all fundamental m
lattice vector

lattice vectors are integral multiples of 2π In crystallography, however, the quantity

is sometimes used.

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
are also often used.

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.
---------------------- Page: 12 ----------------------
SIST EN ISO 80000-12:2019
ISO 80000-12:2019(E)
© ISO 2019 – All rights reserved 3
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:
f =
where E is the radiation amplitude scattered
by the atom and E is the radiation amplitude
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
Fh(),,kl =+fhexpi2π xkyl+ z
[]()
∑ nn nn
n=1
where f is the atomic scattering factor (item 12-5.3)
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, B factor by which the intensity of a diffraction line is 1 D is sometimes expressed as D = exp(−2W); in

reduced because of the lattice vibrations Mössbauer spectroscopy, it is also called the f

factor and denoted by f.
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SIST EN ISO 80000-12:2019
ISO 80000-12:2019(E)
4 © ISO 2019 – All rights reserved
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition

12-9.1 angular wavenum- k, (q) quotient of momentum (ISO 80000-4) and the reduced m The corresponding vector (ISO 80000-2)

ber, Planck constant (ISO 80000-1) quantity is called wave vector (ISO 80000-3),
angular repetency expressed by:
physics>
k=
where p is the momentum (ISO 80000-4) of
quasi free electrons in an electron gas, and ħ
is the reduced Planck constant (ISO 80000-1);
for phonons, its magnitude is
k=
where λ is the wavelength (ISO 80000-3) of
the lattice vibrations.
When a distinction is needed between k
and the symbol for the Boltzmann constant
(ISO 80000-1), k can be used for the latter.
When a distinction is needed, q should be
used for phonons, and k for particles such as
electrons and neutrons.
The method of cut-off must be specified.
In condensed matter physics, angular wave-
number is often called wavenumber.

12-9.2 Fermi angular k angular wavenumber (item 12-9.1) of electrons in m In condensed matter physics, angular wave-

wavenumber, states on the Fermi sphere number is often called wavenumber.
Fermi angular
repetency

12-9.3 Debye angular q cut-off angular wavenumber (item 12-9.1) in the Debye m The method of cut-off must be specified.

wavenumber, model of the vibrational spectrum of a solid
In condensed matter physics, angular wave-
Debye angular number is often called wavenumber.
repetency

12-10 Debye angular ω cut-off angular frequency (ISO 80000-3) in the Debye s The method of cut-off must be specified.

frequency model of the vibrational spectrum of a solid
---------------------- Page: 14 ----------------------
SIST EN ISO 80000-12:2019
ISO 80000-12:2019(E)
© ISO 2019 – All rights reserved 5
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition

12-11 Debye temperature in the Debye model, quantity given by: K A Debye temperature can also be defined by

fitting a Debye model result to a certain quan-
tity, for instance, the heat capacity at a certain
Θ =
temperature.
where k is the Boltzmann constant, (ISO 80000-1), ħ is
the reduced Planck constant (ISO 80000-1), and ω is
Debye angular frequency (item 12-10)

12-12 density of vibration- g quotient of the number of vibrational modes in an in- m s

dn()ω
al states finitesimal interval of angular frequency (ISO 80000-
gnω ==
3), and the product of the width of that interval and
volume (ISO 80000-3)
where n(ω) is the total number of vibrational
modes per volume with angular frequency
less than ω.
The density of states may also be normalized in
other ways instead of with respect
...

SLOVENSKI STANDARD
oSIST prEN ISO 80000-12:2015
01-december-2015
9HOLþLQHLQHQRWHGHO)L]LNDNRQGHQ]LUDQHVQRYL ,62',6
Quantities and units - Part 12: Condensed matter physics (ISO/DIS 80000-12:2015)
Größen und Einheiten - Teil 12: Physik der kondensierten Materie (ISO/DIS 80000-
12:2015)

Grandeurs et unités - Partie 12: Physique de la matière condensée (ISO/DIS 80000-

12:2015)
Ta slovenski standard je istoveten z: prEN ISO 80000-12 rev
ICS:
01.060 9HOLþLQHLQHQRWH Quantities and units
07.030 Fizika. Kemija Physics. Chemistry
oSIST prEN ISO 80000-12:2015 en,fr,de

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

---------------------- Page: 1 ----------------------
oSIST prEN ISO 80000-12:2015
---------------------- Page: 2 ----------------------
oSIST prEN ISO 80000-12:2015
DRAFT INTERNATIONAL STANDARD ISO/DIS 80000-12
ISO/TC 12 Secretariat: SIS
Voting begins on Voting terminates on
2015-10-01 2016-01-01

INTERNATIONAL ORGANIZATION FOR STANDARDIZATION  МЕЖДУНАРОДНАЯ ОРГАНИЗАЦИЯ ПО СТАНДАРТИЗАЦИИ  ORGANISATION INTERNATIONALE DE NORMALISATION

INTERNATIONAL ELECTROTECHNICAL COMMISSION  МЕЖДУНАРОДНАЯ ЭЛЕКТРОТЕХНИЧЕСКАЯ КОММИСИЯ  COMMISSION ÉLECTROTECHNIQUE INTERNATIONALE

Quantities and units —
Part 12:
Condensed matter physics
Grandeurs et unités —
Partie 12: Physique de la matière condensée
ICS 01.060
ISO/CEN PARALLEL PROCESSING

This final draft has been developed within the International Organization for Standardization (ISO), and

processed under the ISO-lead mode of collaboration as defined in the Vienna Agreement. The final draft

was established on the basis of comments received during a parallel enquiry on the draft.

This final draft is hereby submitted to the ISO member bodies and to the CEN member bodies for a parallel

two-month approval vote in ISO and formal vote in CEN.
Positive votes shall not be accompanied by comments.
Negative votes shall be accompanied by the relevant technical reasons.
This draft is submitted to a parallel enquiry in ISO and a CDV vote in the IEC.

THIS DOCUMENT IS A DRAFT CIRCULATED FOR COMMENT AND APPROVAL. IT IS THEREFORE SUBJECT TO CHANGE AND MAY NOT BE

REFERRED TO AS AN INTERNATIONAL STANDARD UNTIL PUBLISHED AS SUCH.

IN ADDITION TO THEIR EVALUATION AS BEING ACCEPTABLE FOR INDUSTRIAL, TECHNOLOGICAL, COMMERCIAL AND USER PURPOSES,

DRAFT INTERNATIONAL STANDARDS MAY ON OCCASION HAVE TO BE CONSIDERED IN THE LIGHT OF THEIR POTENTIAL TO BECOME

STANDARDS TO WHICH REFERENCE MAY BE MADE IN NATIONAL REGULATIONS.

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 SUPPORTING DOCUMENTATION.
© International Electrotechnical Commission, 2015
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oSIST prEN ISO 80000-12:2015
ISO/DIS 80000-12
© International Electrotechnical Commission, 2015
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oSIST prEN ISO 80000-12:2015
Contents Page

Foreword .........................................................................................................................................................................iii

1 Scope .................................................................................................................................................................... 4

2 Normative references .................................................................................................................................... 4

3 Quantities, units and definitions ............................................................................................................... 5

Annex A (normative) Symbols for planes and directions in crystals ..................................................... 14

Alphabetical index ..................................................................................................................................................... 15

© ISO 2015 – All rights reserved
---------------------- Page: 5 ----------------------
oSIST prEN ISO 80000-12:2015
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.

International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.

The main task of technical committees is to prepare International Standards. Draft International

Standards adopted by the technical committees are circulated to the member bodies for voting.

Publication as an International Standard requires approval by at least 75 % of the member bodies

casting a vote.

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.

ISO 80000-12 was prepared by Technical Committee ISO/TC 12, Quantities and units, Subcommittee SC ,

This second/third/... edition cancels and replaces the first/second/... edition (ISO 80000-12:2009),

[clause(s) / subclause(s) / table(s) / figure(s) / annex(es)] of which [has / have] been technically

revised.

ISO 80000 consists of the following parts, under the general title Quantities and units — Condensed

matter physics:
⎯ Part 1: General
⎯ Part 2: Mathematics
⎯ Part 3: Space and time
⎯ Part 4: Mechanics
⎯ Part 5: Thermodynamics
⎯ Part 7: Light and radiation
⎯ Part 8: Acoustics
⎯ Part 9: Physical chemistry and molecular physics
⎯ Part 10: Atomic and nuclear physics
⎯ Part 11: Characteristic numbers
⎯ Part 12: Condensed matter physics

IEC 80000 consists of the following parts, under the general title Quantities and units:

⎯ Part 6: Electromagnetism
⎯ Part 13: Information science and technology
⎯ Part 14: Telebiometrics related to human physiology
© ISO 2015 – All rights reserved
iii
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oSIST prEN ISO 80000-12:2015
DRAFT INTERNATIONAL STANDARD ISO/DIS 80000-12
Quantities and units — Condensed matter physics
1 Scope

This part of ISO 80000 gives names, symbols and definitions for quantities and units of condensed matter physics. Whe

given.
2 Normative references

The following referenced documents are indispensable for the application of this document. For dated references, o

references, the latest edition of the referenced document (including any amendments) applies.

⎯ ISO 80000-3:2006, Quantities and units — Part 3: Space and time
⎯ ISO 80000-4:2006, Quantities and units — Part 4: Mechanics
⎯ ISO 80000-5:2007, Quantities and units — Part 5: Thermodynamics
⎯ IEC 80000-6:2008, Quantities and units — Part 6: Electromagnetism
⎯ ISO 80000-8:2007, Quantities and units — Part 8: Acoustics

⎯ ISO 80000-9:2009, Quantities and units — Part 9: Physical chemistry and molecular physics

⎯ ISO 80000-10:2009, Quantities and units — Part 10: Atomic and nuclear physics

CODATA values: The indicated values are the last known before publication. The user is advised to refer to th

http://physics.nist.gov/cuu/Constants/index.html
© ISO 2015 – All rights reserved
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oSIST prEN ISO 80000-12:2015
3 Quantities, units and definitions
Item Quantity Unit
No.
Name Symbol Definition Symbol Remarks
12-1.1 lattice vector R For ångström (Å), see ISO 80000-3:2006, item
translation vector that maps the crystal lattice on itself m
3-1.a.
12-1.2 fundamental lattice a , a , a , R = n a + n a n a n a where n , n and
m + +

1 2 3 fundamental translation vectors for the crystal lattice 1 1 1 1 2 2 3 3 1 2

vectors
a, b, c n are integers.
12-2.1 angular reciprocal G m
vector whose scalar products with all fundamental
In crystallography, however, the quantity is
lattice vector
lattice vectors are integral multiples of 2π
sometimes used.
12-2.2 fundamental b , b , b a · b = 2πδ
1 2 3 fundamental translation vectors for the reciprocal i i ij
reciprocal lattice
lattice
vectors In crystallography, however, the quantities
are also often used.
12-3 lattice plane spacing

distance between successive lattice planes m For ångström (Å), see ISO 80000-3:2006, item

3-1.a.

12-4 Bragg angle angle defined by the equation rad For degree (°), see ISO 80000-3:2006, item 3-

5.b.
2d sin ϑ = nλ
where d is the lattice plane spacing (item 12-3), λ is the
wavelength (ISO 80000-7:2008, item 7-3) of the
12-5 order of reflexion
radiation, and n is an integer
angle between the scattered ray and the lattice plane
© ISO 2015 – All rights reserved
---------------------- Page: 8 ----------------------
oSIST prEN ISO 80000-12:2015
Item Quantity Unit
No.
Name Symbol Definition Symbol Remarks

12-6.1 short-range order r, σ fraction of nearest-neighbour atom pairs in an Ising 1 Similar definitions apply to other order-

parameter ferromagnet having magnetic moments in one disorder phenomena.
direction, minus the fraction having magnetic moments
Other symbols are frequently used.
in the opposite direction

12-6.2 long-range order R, s fraction of atoms in an Ising ferromagnet having Similar definitions apply to other order-

parameter magnetic moments in one direction, minus the fraction disorder phenomena.

having magnetic moments in the opposite direction
Other symbols are frequently used.

12-6.3 atomic scattering f quotient of radiation amplitude scattered by the atom This can be expressed by:

factor and radiation amplitude scattered by a single electron
where E is the radiation amplitude scattered
by the atom and E is the radiation amplitude
scattered by a single electron.
12-6.4 structure factor F(h, k, l)
� � � � ��
�ℎ, �, �=� �exp 2πi ℎ�+��+��
� � � �
���
where f is the atomic scattering factor (item 12.6.3) for
atom n, and x , y , z are fractional coordinates in the
n n n
unit cell; for h, k, l, see Annex A

12-7 Burgers vector b vector characterizing a dislocation m The closing vector in a Burgers circuit

encircling a dislocation line.
© ISO 2015 – All rights reserved
---------------------- Page: 9 ----------------------
oSIST prEN ISO 80000-12:2015
Item Quantity Unit
No.
Name Symbol Definition Symbol Remarks
particle position r, R

12-8.1 position vector (ISO 80000-3:2006, item 3-1.11) of a m Often, r is used for electrons and R is used for

vector
particle atoms and other heavier particles.
equilibrium position R
12-8.2 0 position vector (ISO 80000-3:2006, item 3-1.11) of an
vector (of an ion or an
ion or atom in equilibrium
atom)
displacement vector u

12-8.3 the difference between the position vector of an ion or This can be expressed by:

(of an ion or atom)
atom and its position vector in equilibrium
u = R − R
where R is particle position vector (item 12-
8.1) and R is position vector of an ion or atom
in equilibrium (item 12-8.2).
D, B
Debye-Waller factor

12-9 factor by which the intensity of a diffraction line is 1 D is sometimes expressed as D = exp(−2W); in

reduced because of the lattice vibrations Mössbauer spectroscopy, it is also called the f

factor and denoted by f.
The corresponding vector quantity k or q is
12-10.1 angular wavenumber, k, (q) linear momentum divided by the reduced Planck
rad m
called the wave vector.
angular repetency
constant
This can be expressed by:
Fermi angular p
12-10.2 k angular wavenumber (item 12-10.1) of electrons in
k =
wavenumber,
states on the Fermi sphere
Fermi angular
where p is the linear momentum (ISO 80000-
repetency
© ISO 2015 – All rights reserved
vii
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oSIST prEN ISO 80000-12:2015
Item Quantity Unit
No.
Name Symbol Definition Symbol Remarks
Debye angular −1 4:2006, item 4-8) of quasi free electrons in an
12-10.3 q cut-off angular wavenumber (item 12-10.1) in the rad m
wavenumber, electron gas and  is the Planck constant h
Debye model of the vibrational spectrum of a solid
Debye angular (ISO 80000-10:2009, item 10-6.1), divided by
repetency
2π; for phonons, its magnitude is k = where
λ is the wavelength (ISO 80000-3:2006, item
3-17) of the lattice vibrations.
When a distinction is needed between and the
symbol for the Boltzmann constant, k can be
used for the latter.
When a distinction is needed, q should be used
for phonons, and k for particles such as
electrons and neutrons.
The method of cut-off shall be specified.
In condensed matter physics, angular
wavenumber is often called wavenumber.
Debye angular

12-11 ω cut-off angular wavenumber (item 12-10.1) in the The method of cut-off shall be specified.

rad s
frequency
Debye model of the vibrational spectrum of a solid
Debye temperature
12-12 Θ in the Debye model K A Debye temperature may also be defined by
� fitting a Debye model result to a certain
Θ = ħ
quantity, for instance, the heat capacity at a
certain temperature.
where k is the Boltzmann constant, (ISO 80000-8:2009,
item 8.-37), ħ is the Planck constant (ISO 80000-
10:2009, item 9-7), divided by 2π, and ω is Debye
angular frequency (item 12-11)
© ISO 2015 – All rights reserved
viii
---------------------- Page: 11 ----------------------
oSIST prEN ISO 80000-12:2015
Item Quantity Unit
No.
Name Symbol Definition Symbol Remarks
density of states (in −1 −3
12-13 g number of vibrational modes in an infinitesimal s rad m
dN(ω)
g(ω)= N =
terms of angular
interval of angular frequency (ISO 80000-3:2006, item
frequency)
m s
3-16), divided by the range of that interval and by
where N(ω) is the total number of vibrational
volume (ISO 80000-3:2006, item 3-4)
modes with angular frequency less than ω,
divided by volume.
See also item 12-17.
thermodynamic
γ (Γ ) �
12-14 � 1
G G
� =
Grüneisen parameter �
��
� �
where α is cubic expansion coefficient (ISO 80000-
5:2007, item 5-3.2), � is isothermal compressibility
(ISO 80000-5:2007, item 5-5.1), c is specific heat
capacity at constant volume (ISO 80000-5:2007, item
5-16.3), and ρ is mass density (ISO 80000-4:2006, item
4-2)
Grüneisen parameter
�ln�
12-15 1 ω may also refer to an average of the
�= −
vibrational spectrum, for instance as
�ln�
represented by a Debye angular frequency
where ω is a lattice vibration frequency and V is volume
(item 12-11).
mean free path of average distance (ISO 80000-3, item 3-1.9) that
12-16.1 m
phonons phonons travel between two successive interactions
mean free path of average distance (ISO 80000-3, item 3-1.9) that
12-16.2
electrons electrons travel between two successive interactions
© ISO 2015 – All rights reserved
---------------------- Page: 12 ----------------------
oSIST prEN ISO 80000-12:2015
Item Quantity Unit
No.
Name Symbol Definition Symbol Remarks
energy density of N (E), −1 −3
dN (E) 1
12-17 E J m Density of states refers to electrons or other
N (E) =
states
dE V entities, e.g. phonons. It can, for e
...

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