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Units and Important Definitions
Appendix 1
Units and Important Definitions
Fundamental physical constants Constant Avogadro constant Boltzmann constant elementary charge rest mass of electron rest mass of proton absolute velocity permittivity of vacuum permeability of vacuum Planck constant reduced Planck constant Bohr magneton nuclear magneton fine structure constant electronic g-factor (Zeeman) —(spin-orbital) reduced Curie constant
Symbol
SI units
NK
6.022045 X lO^^moP^ 1.380662 X 10"^^ J K"^ 1.6021892 X 10"^^ C 9.109534 X 10"^^ kg 1.6726485 X 10"^^ kg 2.99792458 X 10^ ms"^ 8.854187818 x lO'^^C^N"^ m"^ 47rx lO-'^JA-^m"^ 6.626176 X lO-^'^Js 1.0545887 X 10"^^ J s 9.274078 X 10"^^ J T"^ 5.050824 X lO-^'^JT"^ 7.29735 X 10"^ 2.00231929 2.00463858 4.7141997 X lO-^Km^mol"'
kB,k e nig
nip
c £o Mo h
n = h/2n ptB = efi/2nig Atp = efi/2nip a — e^/(4ne()Pic) g g' Q = A^AMOMBA
Conversion factors {E/k), K temperature (E/k) wavenumber (E/hc)
(E/hc), cm 0.69503877
1.43876866
840
Appendices
Selected magnetic quantities Quantity
Relationship^
Unit
magnetic induction (physical vector)
B = IIQH
T = JA-^m-^
(volume)
M
Am"'
mass molar
Mp = M/p
magnetisation (physical vector)
Magnetic susceptibility (second-rank tensor)
volume, —differential
M^oi = M,Mp = Xab = Xab =
=
Am^kg-' Am^moP^
M,M/p
dimensionless
(dMJdHh)
fioi^MJdB,)
= (flo/V)Kab
—mean mass molar reduced
X = M/H =
fioM/B
m^kg-^ m^moP^
Xp = X/P Xmol = ^rXp = M,X/P Kab = -[^E/dBadBb)
Mr—^molar mass [kg mol ], p—density [kg m ], V—^volume
Spin-only values^ S
Curie constant. C (10-^ Km^ mol'-')
Product factor (Xmol r/Co), dimensionless
Effective magnetic moment,
1/2 1 3/2 2 5/2 3 7/2
4.71 12.6 23.6 37.7 55.0 75.4 99.0
1 8/3 5 8 35/3 16 21
1.73 2.83 3.87 4.90 5.91 6.93 7.94
Meff/MB
^ Curie constant: C = CQg^S{S-\-1)/3; product factor: P = C / Q ; effective magnetic moment: Meff/MB=2[S(5+1)]^/^
Sign conventions: (a) Condon-Shortley phase convention for spherical harmonics; ^ (b) constant factor in front of exchange coupUng constants: —J(S^ • 5^).
Units and Important Definitions
Fundamental physical constants Constant Avogadro constant Boltzmann constant elementary charge rest mass of electron rest mass of proton absolute velocity permittivity of vacuum permeability of vacuum Planck constant reduced Planck constant Bohr magneton nuclear magneton fine structure constant electronic g-factor (Zeeman) —(spin-orbital) reduced Curie constant
Symbol
SI units
NK
6.022045 X lO^^moP^ 1.380662 X 10"^^ J K"^ 1.6021892 X 10"^^ C 9.109534 X 10"^^ kg 1.6726485 X 10"^^ kg 2.99792458 X 10^ ms"^ 8.854187818 x lO'^^C^N"^ m"^ 47rx lO-'^JA-^m"^ 6.626176 X lO-^'^Js 1.0545887 X 10"^^ J s 9.274078 X 10"^^ J T"^ 5.050824 X lO-^'^JT"^ 7.29735 X 10"^ 2.00231929 2.00463858 4.7141997 X lO-^Km^mol"'
kB,k e nig
nip
c £o Mo h
n = h/2n ptB = efi/2nig Atp = efi/2nip a — e^/(4ne()Pic) g g' Q = A^AMOMBA
Conversion factors {E/k), K temperature (E/k) wavenumber (E/hc)
(E/hc), cm 0.69503877
1.43876866
840
Appendices
Selected magnetic quantities Quantity
Relationship^
Unit
magnetic induction (physical vector)
B = IIQH
T = JA-^m-^
(volume)
M
Am"'
mass molar
Mp = M/p
magnetisation (physical vector)
Magnetic susceptibility (second-rank tensor)
volume, —differential
M^oi = M,Mp = Xab = Xab =
=
Am^kg-' Am^moP^
M,M/p
dimensionless
(dMJdHh)
fioi^MJdB,)
= (flo/V)Kab
—mean mass molar reduced
X = M/H =
fioM/B
m^kg-^ m^moP^
Xp = X/P Xmol = ^rXp = M,X/P Kab = -[^E/dBadBb)
Mr—^molar mass [kg mol ], p—density [kg m ], V—^volume
Spin-only values^ S
Curie constant. C (10-^ Km^ mol'-')
Product factor (Xmol r/Co), dimensionless
Effective magnetic moment,
1/2 1 3/2 2 5/2 3 7/2
4.71 12.6 23.6 37.7 55.0 75.4 99.0
1 8/3 5 8 35/3 16 21
1.73 2.83 3.87 4.90 5.91 6.93 7.94
Meff/MB
^ Curie constant: C = CQg^S{S-\-1)/3; product factor: P = C / Q ; effective magnetic moment: Meff/MB=2[S(5+1)]^/^
Sign conventions: (a) Condon-Shortley phase convention for spherical harmonics; ^ (b) constant factor in front of exchange coupUng constants: —J(S^ • 5^).