DOCSLIB.ORG

Units and Unity in Magnetism: a Call for Consistency

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Units and Unity in Magnetism: a Call for Consistency Units and unity in magnetism: a call for consistency What's the difference between a tesla and a gauss, the B-field and the H-field, or one joule per tesla squared per metre cubed and 10-7 emu per cubic centimetre? .John Crangle and Mike Gibbs report on a magnetic Tower of Babel . (.. WHEN wc measure any quantity it is discussions and makes recommendations important ta define the units that wc use. for usage in the simplest possjhle'I.~.uÇ If other worken are ta use the resuIts of rigorousJ temlS. ..~i::·;:~> our measurements it is essential rhat they SI unill have been adopted .complet;iy know how ta convert. our units inta their and are used unambiguou:sIYLin,ja1pl~st preferred unia. Ir is conve.nient ifthey use evay ares of science and ~~,;m co~~ ~ the lame unita, especia11y if everyone uses magnetismJ howeverJ a the same set 'of uniOi, universal1y defined of SI (in various versions) a.tt~,~~q11s and agreed. This· is not the case in still used. To illustrate· wa\.çonfuJÎ01;1,. magnetism as, for example, the two Hmagnetic field" can meaI}-:t'B-ti~d:·.>or feature articles in this issue of Physics "H-field". The SI unill for.th..e.are teila World illustrate. The article on giant .cT) or amperes pa m~tt:e:{4.lIl.-~);:in magne!Xlresisœnce (P34) Us.. oenreds 1 cgs they are gauss (G) and oena!â for the ma.gnetic field, whilst the i - (Oe). Al! four,unill are<in ~t.p.e·. sumor writing about nanocrystalline î .A related source of CO~OI\'san.pc magnell prefen tesla (P40). g . ttaoed back !Xl the differef!~-.essions The Système International d'Unités "propose<! by Arthur'. Klonne,!1y' fl936) (SI) was ==ende<! as the modem and Arnold So=erfel\l,(lH(l)4'or,the version of the metrie sysœm by the magnetic induction, B J iD. a.p'olarizalile Ilth Conférence Génénle d.. Poids et medium. There is no fundamèntal MesUtts in 1960. It replaoed the old ment in cither - bath 'are eqUiVaIent­ cgs - ceDrimetI'e, gram and second ­ in SI - and there is no reason why bath system with seven fundamental, or should not be used in parallel. 1 ;, 1 "base"J unit!: me mette, kilograrn, In the Sommerfeld conve.nponj second, ampere, kelvin, mole and . which was adopted by ..the Intel'­ candela, an definêd in an agreëd way. national Union of Pure and Applied ~uderived" unit! can he con­ Physics (IUPAPl. strueted from the base units. Sorne B = Jlo(H + M) = Bo+ l'oM have special names - the joule for where Jlo is the permeability of free energyJ the ohm for resistance etc ­ space, H is the H-fieldJ M is the whilst othersJ such as those for velocity magnetization per unit volumeJ and and momentum, do not. Ba is the free-space induction that In magnetism three derived units would remain if the !Jled!u.m. were have special names: the henry for taken away (the B-fie1d). inductance, the weber for magnetic 10 the Kennelly sY'tqn,. which la flux and the tesla for magnetic induc­ traditionaUy favoured ..by .electrical tion (also known as the magnetic flux engineersJ B is given by density). HowCV'er, the derived units B=JloH+J=Bo+J . for other magnetic quanrities, such as where J is the magnetic polarization. permeability and magnetization, do These [wo equations'dci~not confliet not have special names. SI does it - the Teslatron supercônd4cüng magnet from if we accept that magnetization and In sr there are also two "supple­ Oxford Instruments pro.duces a field pf'2Q T at 2.2 K. The polarizarion are indeed diffc:reI;l.t quan­ mentaryJJ units - for plane angle and tesla is the SI unit for magnl}!ic J.,~~ction {B-fJeld} tities and use different' symbols for for solid angle - that are dimensionless ·.;ii:... ~l • them as shawn here. The SI units for ~s (i.e. have no units). FinaUy, decimal tute of Ph)".iics Magnetism Group ttied B J M and J are given in the œblej Jlo 1 multiples of sr units can be constructed again and set up a unies 'oforking party. units of henrys per mette CH m- ) and H 1 by using one of the 20 SI prefixesJ which As a resuIt, and be.cause of worldwide has units of amperes per mette CA m- ). tang<: trom yocro- (10-"') te yottll- (10"). interestJ a discussion on magnetic unies But it is important ta note that there is was held at the joint Magnetism and Which rnagnetic field? only one SI unit for each physical quantity. Magnetic Materials-Intermag Conference in Albuquerque, New Mexico J in June. When dcaling with the magnetic field we The trouble with rnagnetisrn One of the authon (MG) was a member of can use either the B-field or the H-field. the international panel of magnetism These are distinguished by their behaviour sr unit! are almost universally accepted specialists that presided over the evening at a boundary between media having and l!l"C always used in schools and to train discussionJ which was attended by sorne different relative permeabilities (J.1). The young scientists. In the early days of 150 participants. The rest of this article nonnal camponent of the B-field and the magnerismJ howeverJ there was room for has been distilled from these various rangential componem of the H-field are !4JjI~!lIIJ!R!!!!!- :as::ae;:.'''..,~. '.UE a;::wt2a ••b !Il!.§1I33l12I!!11iJJl!!I3&l!!IYJI!!l.!.._t_5_lIlblllt3l1l;l!I!!.. !l!I.5l1l.Jl!I!!.ll.!!l!.1II331!lX;,;!-AAIll'•.'''''''''''''''''........;.".__:o---------..... 32 Physlc, World Novcmber 1~ continuous across thc bound­ SI units for important magnetic quantities and their equivalent in cgs quamity which is not defined ary. In &ce space B = J.loH in in the SI system. both the Sommerfeld and Quantity being Symbol SI unit cgs unit Kcnnelly s1'stcms. In SI measured I-Iystcrcsis loops J.lo =4r. x 10 1-1 m l, so thc Magnetic field D, T 10· Oe ll- and J·/-ficlds have diffcr- Magnetic induction D T 10· Oe 1[ysleresis loops 2:oe an im­ 1 1 1 em numerical values. In cgsJ Magnetization per CT JT- kg- 1 erg Oe- g' portant characteristic of ferro­ howeverJ J.lo = Il so thc B- and unit mass 1 emu g-' magnelie malerials. The H-ficlds have the same num­ magnerizarion, and hence the Magnetization per M JT-'m-3 lr erg Oe-1 cm-3 erical valuej this has always unit volume lr emucm-1 induction and polarization, in caused gauss (for the B-field) relatively weak applied fields J~-.2kg-1 and oerned (for the H-field) Z depend on the recent history ta become confused. (Note of the specimen with respect that the relative penneabilityJ ta the field. flit \>roperties Ji = B/BoJ is dimensionless displayed by t:h"t loops are and has the same value in often very important in tech­ both the sr and the cgs nical and applied tna.gnetism. systems.) It is possible to draw hysœr• So how do the B-field and esis loops in several, equally the H-field differ? Fonnulae validJ ways. dealing -,with forceJ energyJ magnetic the magnetic moment ofone eleetron spin: (i) The induction B (in tesla) is plotted on 24 1 moment and so on always use the B-field ~B = 9.2732 X 10- JT- • Ali other mag­ the ~s against the field B o (in tesla) on (for exampleJ the Lorentz force on a netic moments are derived from thîs. The the »-axis. particle with charge e moving with vela­ energy (in joules) ofone Bohr magneton in (ü) The mass magnetization a (measured l city v in a magneric field B is ev x B). The a magnetic field of Bo is J.ln.Bo. In cgs in JT- kg-I) or the volume magnetization 21 l l 3 H-field is rarely used alone. It oruy arises JJ.B =9.2732 X 10- ergOe- (the erg is the M (in JT- m- ) is plotted on the y-axis when calculating the magnetic effect of an cgs unit for energy: 1 J is equivalent ta against the field B o (in tesla) on the x-axis. electric currcnt or in similar cases. 107 erg). Altematively) M can he plotted against l The main attraction of quoring fields as When the temperature (and hence the BoIJ.lo with both axes given in A m- . B-fields is that the comparison ofnew data densiry) of a sampIe varies, its mass is (iii) The polarization J (in tesla) is plotted (in SI) and old data (in cgs) is precise and almost always better known than ilS on the y-axis agamst the field B o (in tesla) simple. Thus solid-state physicists working volume. 1berefore the magnetization per on the X'-axis. in fundamental magnetism tend to use unit massJ a, is frequently usedj thîs has The magnetic remanence and coercivity B-fields. For instance, a 10 T supercon­ units of J T 1kg-l. The cgs unit for a­ are often derived from hysteresis loops. ducting magner (100 kOe or 100 kG in erg Oe-l g-I (often loosely and ambigu­ The remanence is the quantity remaining cgs) would never be described as being a ously referred to as emu g-J) - is numeri­ on they-axis when the field (i.e. the x-axis) 1 7.958 MAm- Magnet. caUy equal tO the SI unit. is reduced te zeroJ frequently from satura­ HoweverJ electrical engineers often use In SI the unit for mapetization per unit tion.
Load more

Recommended publications
  • Magnetism, Magnetic Properties, Magnetochemistry
    Magnetism, Magnetic Properties, Magnetochemistry 1 Magnetism All matter is electronic Positive/negative charges - bound by Coulombic forces Result of electric field E between charges, electric dipole Electric and magnetic fields = the electromagnetic interaction (Oersted, Maxwell) Electric field = electric +/ charges, electric dipole Magnetic field ??No source?? No magnetic charges, N-S No magnetic monopole Magnetic field = motion of electric charges (electric current, atomic motions) Magnetic dipole – magnetic moment = i A [A m2] 2 Electromagnetic Fields 3 Magnetism Magnetic field = motion of electric charges • Macro - electric current • Micro - spin + orbital momentum Ampère 1822 Poisson model Magnetic dipole – magnetic (dipole) moment [A m2] i A 4 Ampere model Magnetism Microscopic explanation of source of magnetism = Fundamental quantum magnets Unpaired electrons = spins (Bohr 1913) Atomic building blocks (protons, neutrons and electrons = fermions) possess an intrinsic magnetic moment Relativistic quantum theory (P. Dirac 1928) SPIN (quantum property ~ rotation of charged particles) Spin (½ for all fermions) gives rise to a magnetic moment 5 Atomic Motions of Electric Charges The origins for the magnetic moment of a free atom Motions of Electric Charges: 1) The spins of the electrons S. Unpaired spins give a paramagnetic contribution. Paired spins give a diamagnetic contribution. 2) The orbital angular momentum L of the electrons about the nucleus, degenerate orbitals, paramagnetic contribution. The change in the orbital moment
    [Show full text]
  • Lecture #4, Matter/Energy Interactions, Emissions Spectra, Quantum Numbers
    Welcome to 3.091 Lecture 4 September 16, 2009 Matter/Energy Interactions: Atomic Spectra 3.091 Periodic Table Quiz 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 Name Grade /10 Image by MIT OpenCourseWare. Rutherford-Geiger-Marsden experiment Image by MIT OpenCourseWare. Bohr Postulates for the Hydrogen Atom 1. Rutherford atom is correct 2. Classical EM theory not applicable to orbiting e- 3. Newtonian mechanics applicable to orbiting e- 4. Eelectron = Ekinetic + Epotential 5. e- energy quantized through its angular momentum: L = mvr = nh/2π, n = 1, 2, 3,… 6. Planck-Einstein relation applies to e- transitions: ΔE = Ef - Ei = hν = hc/λ c = νλ _ _ 24 1 18 Bohr magneton µΒ = eh/2me 9.274 015 4(31) X 10 J T 0.34 _ _ 27 1 19 Nuclear magneton µΝ = eh/2mp 5.050 786 6(17) X 10 J T 0.34 _ 2 3 20 Fine structure constant α = µ0ce /2h 7.297 353 08(33) X 10 0.045 21 Inverse fine structure constant 1/α 137.035 989 5(61) 0.045 _ 2 1 22 Rydberg constant R¥ = mecα /2h 10 973 731.534(13) m 0.0012 23 Rydberg constant in eV R¥ hc/{e} 13.605 698 1(40) eV 0.30 _ 10 24 Bohr radius a0 = a/4πR¥ 0.529 177 249(24) X 10 m 0.045 _ _ 4 2 1 25 Quantum of circulation h/2me 3.636 948 07(33) X 10 m s 0.089 _ 11 1 26 Electron specific charge -e/me -1.758 819 62(53) X 10 C kg 0.30 _ 12 27 Electron Compton wavelength λC = h/mec 2.426 310 58(22) X 10 m 0.089 _ 2 15 28 Electron classical radius re = α a0 2.817 940 92(38) X 10 m 0.13 _ _ 26 1 29 Electron magnetic moment` µe 928.477 01(31) X 10 J T 0.34 _ _ 3 30 Electron mag.
    [Show full text]
  • 1. Physical Constants 1 1
    1. Physical constants 1 1. PHYSICAL CONSTANTS Table 1.1. Reviewed 1998 by B.N. Taylor (NIST). Based mainly on the “1986 Adjustment of the Fundamental Physical Constants” by E.R. Cohen and B.N. Taylor, Rev. Mod. Phys. 59, 1121 (1987). The last group of constants (beginning with the Fermi coupling constant) comes from the Particle Data Group. The figures in parentheses after the values give the 1-standard- deviation uncertainties in the last digits; the corresponding uncertainties in parts per million (ppm) are given in the last column. This set of constants (aside from the last group) is recommended for international use by CODATA (the Committee on Data for Science and Technology). Since the 1986 adjustment, new experiments have yielded improved values for a number of constants, including the Rydberg constant R∞, the Planck constant h, the fine- structure constant α, and the molar gas constant R,and hence also for constants directly derived from these, such as the Boltzmann constant k and Stefan-Boltzmann constant σ. The new results and their impact on the 1986 recommended values are discussed extensively in “Recommended Values of the Fundamental Physical Constants: A Status Report,” B.N. Taylor and E.R. Cohen, J. Res. Natl. Inst. Stand. Technol. 95, 497 (1990); see also E.R. Cohen and B.N. Taylor, “The Fundamental Physical Constants,” Phys. Today, August 1997 Part 2, BG7. In general, the new results give uncertainties for the affected constants that are 5 to 7 times smaller than the 1986 uncertainties, but the changes in the values themselves are smaller than twice the 1986 uncertainties.
    [Show full text]
  • Magnetism in Transition Metal Complexes
    Magnetism for Chemists I. Introduction to Magnetism II. Survey of Magnetic Behavior III. Van Vleck’s Equation III. Applications A. Complexed ions and SOC B. Inter-Atomic Magnetic “Exchange” Interactions © 2012, K.S. Suslick Magnetism Intro 1. Magnetic properties depend on # of unpaired e- and how they interact with one another. 2. Magnetic susceptibility measures ease of alignment of electron spins in an external magnetic field . 3. Magnetic response of e- to an external magnetic field ~ 1000 times that of even the most magnetic nuclei. 4. Best definition of a magnet: a solid in which more electrons point in one direction than in any other direction © 2012, K.S. Suslick 1 Uses of Magnetic Susceptibility 1. Determine # of unpaired e- 2. Magnitude of Spin-Orbit Coupling. 3. Thermal populations of low lying excited states (e.g., spin-crossover complexes). 4. Intra- and Inter- Molecular magnetic exchange interactions. © 2012, K.S. Suslick Response to a Magnetic Field • For a given Hexternal, the magnetic field in the material is B B = Magnetic Induction (tesla) inside the material current I • Magnetic susceptibility, (dimensionless) B > 0 measures the vacuum = 0 material response < 0 relative to a vacuum. H © 2012, K.S. Suslick 2 Magnetic field definitions B – magnetic induction Two quantities H – magnetic intensity describing a magnetic field (Système Internationale, SI) In vacuum: B = µ0H -7 -2 µ0 = 4π · 10 N A - the permeability of free space (the permeability constant) B = H (cgs: centimeter, gram, second) © 2012, K.S. Suslick Magnetism: Definitions The magnetic field inside a substance differs from the free- space value of the applied field: → → → H = H0 + ∆H inside sample applied field shielding/deshielding due to induced internal field Usually, this equation is rewritten as (physicists use B for H): → → → B = H0 + 4 π M magnetic induction magnetization (mag.
    [Show full text]
  • 31295015501306.Pdf (1.378Mb)
    A STUDY OF TK3 MGN3TIC PROPERTIES OF FERROCYAKTDij^S AND FERRICYANIDES by JACK ED7ARD RANDORFF, B. S. A THESIS IN PHYSICS Submitted to the Graduate Faculty of Texas Technological College in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCISIICE Approved Accented June, 1967 f^(A^fjin Cop. a ACKNO/JLEDGS-IENTS I am deeply appreciative of Dr. Billy J. I4arshall for his direction of this thesis; to the Robert A. Welch Foundation of Texas for financial support given to this project; to Dr. V/, 0, Milligan, research director of the forementioned Foundatior^ for the helpful and stimulating discussion with regard to this work and to his research group at Baylor University for the preparation of samples; and to the U. S. Department of Health, Education and V'elfrro for tho presentation of an N,D,E,A. Title IV Fellowship as financial support to pursue this study. ii TABLE OF COirrSxNTS ACKNO'WLEDG&IEOTS ii TABLE OF CONTENTS iii LIST OF TABLES iv LIST OF FIGURES v I, INTRODUCnON 1 II. EXPERIMEOTAL TECHMIQUE 3 Sample Preparation 3 Apparatus 3 Temperature Control and Detection 5 Calibrations and Corrections 6 Set-up Procedure 8 III, RESULTS Aim Discussion l6 IV. FUTURE WORK 33 LIST OF REFERENCES 34 APPENDIX I 35 APPENDIX II 42 APPENDIX III 43 iii LIST OF TABLES Table 1, The values of susceptibility and temperature.,, 19 Table 2, Effective number of Bohr Diagnetons per atom or per molecule, 20 iv LIST OF FIGURES Figure 1, Apparatus Assembly. 9 Figure lA. Internal view of Cahn RM Automatic Electrobalance, 10 Figure 2.
    [Show full text]
  • Lecture 41 (Spatial Quantization & Electron Spin)
    Lecture 41 (Spatial Quantization & Electron Spin) Physics 2310-01 Spring 2020 Douglas Fields Quantum States • Breaking Symmetry • Remember that degeneracies were the reflection of symmetries. What if we break some of the symmetry by introducing something that distinguishes one direction from another? • One way to do that is to introduce a magnetic field. • To investigate what happens when we do this, we will briefly use the Bohr model in order to calculate the effect of a magnetic field on an orbiting electron. • In the Bohr model, we can think of an electron causing a current loop. • This current loop causes a magnetic moment: • We can calculate the current and the area from a classical picture of the electron in a circular orbit: • Where the minus sign just reflects the fact that it is negatively charged, so that the current is in the opposite direction of the electron’s motion. Bohr Magneton • Now, we use the classical definition of angular momentum to put the magnetic moment in terms of the orbital angular momentum: • And now use the Bohr quantization for orbital angular momentum: • Which is called the Bohr magneton, the magnetic moment of a n=1 electron in Bohr’s model. Back to Breaking Symmetry • It turns out that the magnetic moment of an electron in the Schrödinger model has the same form as Bohr’s model: • Now, what happens again when we break a symmetry, say by adding an external magnetic field? Back to Breaking Symmetry • Thanks, yes, we should lose degeneracies. • But how and why? • Well, a magnetic moment in a magnetic field feels a torque: • And thus, it can have a potential energy: • Or, in our case: Zeeman Effect • This potential energy breaks the degeneracy and splits the degenerate energy levels into distinct energies.
    [Show full text]
  • Chapter 1 MAGNETIC NEUTRON SCATTERING
    Chapter 1 MAGNETIC NEUTRON SCATTERING. And Recent Developments in the Triple Axis Spectroscopy Igor A . Zaliznyak'" and Seung-Hun Lee(2) (')Department of Physics. Brookhaven National Laboratory. Upton. New York 11973-5000 (')National Institute of Standards and Technology. Gaithersburg. Maryland 20899 1. Introduction..................................................................................... 2 2 . Neutron interaction with matter and scattering cross-section ......... 6 2.1 Basic scattering theory and differential cross-section................. 7 2.2 Neutron interactions and scattering lengths ................................ 9 2.2.1 Nuclear scattering length .................................................. 10 2.2.2 Magnetic scattering length ................................................ 11 2.3 Factorization of the magnetic scattering length and the magnetic form factors ............................................................................................... 16 2.3.1 Magnetic form factors for Hund's ions: vector formalism19 2.3.2 Evaluating the form factors and dipole approximation..... 22 2.3.3 One-electron spin form factor beyond dipole approximation; anisotropic form factors for 3d electrons..................... 27 3 . Magnetic scattering by a crystal ................................................... 31 3.1 Elastic and quasi-elastic magnetic scattering............................ 34 3.2 Dynamical correlation function and dynamical magnetic susceptibility ............................................................................................
    [Show full text]
  • I Magnetism in Nature
    We begin by answering the first question: the I magnetic moment creates magnetic field lines (to which B is parallel) which resemble in shape of an Magnetism in apple’s core: Nature Lecture notes by Assaf Tal 1. Basic Spin Physics 1.1 Magnetism Before talking about magnetic resonance, we need to recount a few basic facts about magnetism. Mathematically, if we have a point magnetic Electromagnetism (EM) is the field of study moment m at the origin, and if r is a vector that deals with magnetic (B) and electric (E) fields, pointing from the origin to the point of and their interactions with matter. The basic entity observation, then: that creates electric fields is the electric charge. For example, the electron has a charge, q, and it creates 0 3m rˆ rˆ m q 1 B r 3 an electric field about it, E 2 rˆ , where r 40 r 4 r is a vector extending from the electron to the point of observation. The electric field, in turn, can act The magnitude of the generated magnetic field B on another electron or charged particle by applying is proportional to the size of the magnetic charge. a force F=qE. The direction of the magnetic moment determines the direction of the field lines. For example, if we tilt the moment, we tilt the lines with it: E E q q F Left: a (stationary) electric charge q will create a radial electric field about it. Right: a charge q in a constant electric field will experience a force F=qE.
    [Show full text]
  • Magnetic Susceptibility Measurements of Transition Metal Containing Compounds
    Magnetic susceptibility measurements of transition metal containing compounds Introduction: Measurements of magnetic properties have been used to characterize a wide range of systems from oxygen, metallic alloys, solid state materials, and coordination complexes containing metals. Most organic and main group element compounds have all the electrons paired and these are diamagnetic molecules with very small magnetic moments. All of the transition metals have at least one oxidation state with an incomplete d subshell. Magnetic measurements, particularly for the first row transition elements, give information about the number of unpaired electrons. The number of unpaired electrons provides information about the oxidation state and electron configuration. The determination of the magnetic properties of the second and third row transition elements is more complex. The magnetic moment is calculated from the magnetic susceptibility, since the magnetic moment is not measured directly. There are several ways to express the degree to which a material acquires a magnetic moment in a field. The magnetic susceptibility per unit volume is defined by: I H where I is the intensity of the magnetization induced in the sample by the external magnetic field, H. The extent of the magnetic induction (I) depends on the sample. The induction may be visualized as an alignment of dipoles and/or by the formation of charge polarization in the sample. H is the strength of the external magnetic field in units of oersteds (Oe). The κ is unitless. Generally, it is more convenient to use mass units, therefore the mass or gram susceptibility is defined as: g d where d is the density of the solid.
    [Show full text]
  • Magnetochemistry
    Magnetochemistry (12.7.06) H.J. Deiseroth, SS 2006 Magnetochemistry The magnetic moment of a single atom (µ) (µ is a vector !) μ µ μ = i F [Am2], circular current i, aerea F F -27 2 μB = eh/4πme = 0,9274 10 Am (h: Planck constant, me: electron mass) μB: „Bohr magneton“ (smallest quantity of a magnetic moment) → for one unpaired electron in an atom („spin only“): s μ = 1,73 μB Magnetochemistry → The magnetic moment of an atom has two components a spin component („spin moment“) and an orbital component („orbital moment“). →Frequently the orbital moment is supressed („spin-only- magnetism“, e.g. coordination compounds of 3d elements) Magnetisation M and susceptibility χ M = (∑ μ)/V ∑ μ: sum of all magnetic moments μ in a given volume V, dimension: [Am2/m3 = A/m] The actual magnetization of a given sample is composed of the „intrinsic“ magnetization (susceptibility χ) and an external field H: M = H χ (χ: suszeptibility) Magnetochemistry There are three types of susceptibilities: χV: dimensionless (volume susceptibility) 3 χg:[cm/g] (gramm susceptibility) 3 χm: [cm /mol] (molar susceptibility) !!!!! χm is used normally in chemistry !!!! Frequently: χ = f(H) → complications !! Magnetochemistry Diamagnetism - external field is weakened - atoms/ions/molecules with closed shells -4 -2 3 -10 < χm < -10 cm /mol (negative sign) Paramagnetism (van Vleck) - external field is strengthened - atoms/ions/molecules with open shells/unpaired electrons -4 -1 3 +10 < χm < 10 cm /mol → diamagnetism (core electrons) + paramagnetism (valence electrons) Magnetism
    [Show full text]
  • The Orbital Magnetic Moment in Terms of Bohr Magneton in the Vector Form Is
    Lecture 20 Title: Effect of Static Magnetic field on the spectral lines. Page-0 In this lecture we will discuss the effect of static magnetic field on the spectral lines. The effect is known as Zeeman effect and the pattern seen after applying the magnetic field is known as Zeeman pattern. We will also discuss the Normal and Anomalous Zeeman effect. We will see also the change of the Zeeman pattern when the magnetic field is increased. Page-1 When a source of light emitting line spectra is placed under a static magnetic field, it is observed that the spectral lines split into several components. Zeeman in 1896 first observed the phenomenon. Applying the magnetic field his observations were made in two directions with respect to the magnetic field directions. 1. Observations perpendicular to the magnetic field: (a) Spectral lines split into three components (b) Central line has the same frequency as the original line before applying the magnetic field. (c) Central line is linearly polarized and parallel to the magnetic field. (d) The two other components are equally separated on both sides of the central frequency. (e) Both of them are also linearly polarized and polarization is perpendicular to the magnetic field. 2. Observations along the magnetic field direction: (a) Central line is absent (b) The other two components are circularly polarized This effect is known as Normal Zeeman effect. It was also later observed that in some cases there were more than three lines. To differentiate, it was named as Anomalous Zeemen effect. In the following, we will discuss this in details.
    [Show full text]
  • A Supplementary Discussion on Bohr Magneton Magnetic Fields Arise from Moving Electric Charges. a Charge Q with Velocity V Gives
    A Supplementary Discussion on Bohr Magneton Magnetic fields arise from moving electric charges. A charge q with velocity v gives rise to a magnetic field B, following SI convention in units of Tesla, µ qv × r B = 0 , 4π r3 −7 −2 2 where µ0 is the vacuum permeability and is defined as 4π × 10 NC s . Now consider a magnetic dipole moment as a charge q moving in a circle with radius r with speed v. The current is the charge flow per unit time. Since the circumference of the circle is 2πr, and the time for one revolution is 2πr/v, one has the current as I = qv/2πr. The magnitude of the dipole moment is |µ| = I · (area) = (qv/2πr)πr2 = qrp/2m, where p is the linear momentum. Since the radial vector r is perpendicular to p, we have qr × p q µ = = L, 2m 2m where L is the angular momentum. The magnitude of the orbital magnetic momentum of an electron with orbital-angular- momentum quantum l is e¯h 1/2 1/2 µ = [l(l + 1)] = µB[l(l + 1)] . 2me Here, µB is a constant called Bohr magneton, and is equal to −19 −34 e¯h (1.6 × 10 C) × (6.626 × 10 J · s/2π) −24 µB = = −31 = 9.274 × 10 J/T, 2me 2 × 9.11 × 10 kg where T is magnetic field, Tesla. Now consider applying an external magnetic field B along the z-axis. The energy of interaction between this magnetic field and the magnetic dipole moment is e µB EB = −µ · B = Lz · B = BLz.
    [Show full text]