SIST EN ISO 80000-12:2019

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.

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SIST EN ISO 80000-12:2019

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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.

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SIST EN ISO 80000-12:2019
EN ISO 80000-12:2019 (E)
Contents Page
European foreword . 3

2

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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.

3

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SIST EN ISO 80000-12:2019

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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

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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

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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

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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

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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

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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.

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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:
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
0
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
0
physics>
where R is particle position vector (item 12-
7.1) and R is position vector of an ion or atom
0
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
−1
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:
p
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
2π
   k=
λ
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.
B
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.
−1
12-9.2 Fermi angular k angular wavenumber (item 12-9.1) of electrons in m In condensed matter physics, angular wave-
F
wavenumber, states on the Fermi sphere number is often called wavenumber.
Fermi angular
repetency
−1
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.
D
wavenumber, model of the vibrational spectrum of a solid
In condensed matter physics, angular wave-
Debye angular number is often called wavenumber.
repetency
−1
12-10 Debye angular ω cut-off angular frequency (ISO 80000-3) in the Debye s The method of cut-off must be specified.
D
frequency model of the vibrational spectrum of a solid

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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
Θ
D
fitting a Debye model result to a certain quan-
ω
tity, for instance, the heat capacity at a certain
D
   Θ =
D
temperature.
k
where k is the Boltzmann constant, (ISO 80000-1), ħ is
the reduced Planck constant (ISO 80000-1), and ω is
D
Debye angular frequency (item 12-10)
−3
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 ==
()
ω
dω
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.

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oSIST prEN ISO 80000-12:2015

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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
ii

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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
ii

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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.
Å
−1
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.
3
�
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.
Å
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
1
12-5 order of reflexion
radiation, and n is an integer
OR
angle between the scattered ray and the lattice plane
© ISO 2015 – All rights reserved
v

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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
a
by the atom and E is the radiation amplitude
e
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
n
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
vi

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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
0
where R is particle position vector (item 12-
8.1) and R is position vector of an ion or atom
0
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
−1
12-10.1 angular wavenumber, k, (q) linear momentum divided by the reduced Planck
rad m
called the wave vector.
angular repetency
constant
−1

m
This can be expressed by:
Fermi angular p
12-10.2 k angular wavenumber (item 12-10.1) of electrons in

F
k =
wavenumber,

states on the Fermi sphere
Fermi angular
where p is the linear momentum (ISO 80000-
repetency
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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
D
wavenumber, electron gas and  is the Planck constant h
Debye model of the vibrational spectrum of a solid
−1
Debye angular (ISO 80000-10:2009, item 10-6.1), divided by
m
��
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

B
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
−1
12-11 ω cut-off angular wavenumber (item 12-10.1) in the The method of cut-off shall be specified.
rad s
D
frequency
Debye model of the vibrational spectrum of a solid
−1

s
Debye temperature
12-12 Θ in the Debye model K A Debye temperature may also be defined by
D
�
� fitting a Debye model result to a certain
Θ = ħ
D
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
D
angular frequency (item 12-11)
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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
ω
interval of angular frequency (ISO 80000-3:2006, item
dω
−3
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-
V
5:2007, item 5-3.2), � is isothermal compressibility
T
(ISO 80000-5:2007, item 5-5.1), c is specific heat
V
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
γ
�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
l
12-16.1 m
p
phonons phonons travel between two successive interactions

mean free path of average distance (ISO 80000-3, item 3-1.9) that
l
12-16.2
e
electrons electrons travel between two successive interactions
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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) =
E
states
dE V entities, e.g. phonons. It can, for e
...