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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 2019
© ISO 2019
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ii © ISO 2019 – All rights reserved
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
Foreword
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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
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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/
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.
, a , a fundamental translation vectors for the crystal lattice m The lattice vector (item 12-1.1) can be given as
12-1.2 fundamental lattice a
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.
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, 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.
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
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 to volume.
See also item 12-16.
12-13 thermodynamic quantity given by: 1
γ , Γ
()
Grüneisen parameter G G
α
V
γ =
G
c ρ
TV
where α is cubic expansion coefficient (ISO 80000-5),
V
is isothermal compressibility (ISO 80000-5), c is
V
T
specific heat capacity at constant volume (ISO 80000-
5), and ρ is mass density (ISO 80000-4)
12-14 Grüneisen parameter quantity given by minus the partial differential 1 ω can also refer to an average of the vibration-
γ
quotient: al spectrum, for instance as represented by a
Debye angular frequency (item 12-10).
∂lnω
γ=−
∂lnV
where ω is a lattice vibration frequency (ISO 80000-3),
and V is volume (ISO 80000-3)
12-15.1 mean free path l average distance (ISO 80000-3) that phonons travel m
p
of phonons between two successive interactions
6 © ISO 2019 – All rights reserved
Table 1 (continued)
Item No. Quantity Unit Remarks
Name Symbol Definition
12-15.2 mean free path l average distance (ISO 80000-3) that electrons travel m
e
of electrons between two successive interactions
−1 −3
12-16 energy density quantity given by the differential quotient with respect J m Density of states refers to electrons or other
nE(),
E
of states to energy: entities, e.g. phonons. It may be normalized in
−1 −3
eV m
other ways instead of with respect to volume,
ρ()E
dnE −1 −5 2
()
e.g. with respect to amount of substance.
kg m s
nE =
()
E
dE
See also item 12-12.
where n (E) is the total number of one-electron states
E
per volume (ISO 80000-3) with energy less than E
(ISO 80000-5)
12-17 residual resistivity ρ for metals, the resistivity (IEC 80000-6) extrapolated Ω m
to zero thermodynamic temperature (ISO 80000-5)
3 −3
kg m s
−2
A
2 2
12-18 Lorenz coefficient L quotient of thermal conductivity (ISO 80000-5), and V /K The Lore
...