Diamagnetyzm

1. Diamagnetyzm Bolesław AUGUSTYNIAK

2. Spis zagadnień • Opis ogólny • Rys historyczny • Dodatek o strukturze powłok elektronowych • Kilka modeli diamagnetyzmu • Przykłady diamagnetyków • Lewitacja... Bolesław AUGUSTYNIAK

3. Bo applied Istota ‘diamagnetyzmu’ The applied field induces circulation of the valence electrons - this generates a magnetic field that opposes the applied field. valence electrons shield the nucleus from the full effect of the applied field magnetic field lines Bolesław AUGUSTYNIAK [4]

4. Diamagnetyzm – opis ogólny 1 Diamagnetism is a very general phenomenon, because all paired electrons, including the electrons of an atom, will always make a weak contribution to the material's response. However, for materials that show some other form of magnetism (such as ferromagnetism or paramagnetism), the diamagnetism is completely overpowered. Substances that mostly display diamagnetic behaviour are termed diamagnetic materials, or diamagnets. Materials that are said to be diamagnetic are those that are usually considered by non-physicists to be "non-magnetic", and include water, wood, most organic compounds such as petroleum and some plastics, and many metals including copper, particularly the heavy ones with many core electrons, such as mercury, gold and bismuth. The diamagnetism of various molecular fragments are called Pascal's constants. [11] Bolesław AUGUSTYNIAK

5. Diamagnetyzm – opis ogólny 2 Diamagnetic materials have a relative magnetic permeability that is less than 1, thus a magnetic susceptibility which is less than 0, and are therefore repelled by magnetic fields. However, since diamagnetism is such a weak property its effects are not observable in every-day life. For example, the magnetic susceptibility of diamagnets such as water is = −9.05×10−6. The most strongly diamagnetic material is bismuth, = −1.66×10−4 , although pyrolytic graphite may have a susceptibility of = −4.00×10−4 in one plane. Nevertheless, these values are orders of magnitudes smaller than the magnetism exhibited by paramagnets and ferromagnets. [11] Bolesław AUGUSTYNIAK

6. Diamagnetyzm – opis ogólny 3 Superconductors may be considered to be perfect diamagnets ( = −1), since they expel all fields from their interior due to the Meissner effect. However this effect is not due to eddy currents, as in ordinary diamagnetic materials. Additionally, all conductors exhibit an effective diamagnetism when they experience a changing magnetic field. The Lorentz force on electrons causes them to circulate around forming eddy currents. The eddy currents then produce an induced magnetic field which opposes the applied field, resisting the conductor's motion. Bolesław AUGUSTYNIAK

7. Materiał   χm=x 10-5 Bismuth -16.6 Carbon (diamond) -2.1 Carbon (graphite) -1.6 Copper -1.0 Lead -1.8 Mercury -2.9 Silver -2.6 Water -0.91 Superconductor -105 Przykłady diamagnetyków Bolesław AUGUSTYNIAK

8. Diamagnetyzm - historia In 1778 s. J. Bergman was the first individual to observe that bismuth and antymony were repelled by magnetic fields. However, the term "diamagnetism" was coined by Michael Faraday in September 1845, when he realized that all materials in nature possessed some form of diamagnetic response to an applied magnetic field. Bolesław AUGUSTYNIAK

9. Diamagnetyzm – doświadczenie Farady’a In 1845, Faraday discovered that many materials exhibit a weak repulsion from a magnetic field, a phenomenon he named diamagnetism. Image of Faraday holding a glass bar of the type he used to show that magnetism affects light http://en.wikipedia.org/wiki/Michael_Faraday#Diamagnetism Bolesław AUGUSTYNIAK

10. Dodatek o strukturze powłok elektronowych Bolesław AUGUSTYNIAK

11. Periodic Table • In 1870 Mendeleev arranged the known elements in what now is known the periodic table. • He arranged them in depending on both physical and chemical properties • He predicted both the discoveries of elements and their properties. • Example Bolesław AUGUSTYNIAK [6]

12. Quantum Numbers • n= Principal QN =period(energy level) • l= Angular moment QN=sublevel(PT block) • ml= magnetic moment QN=orbital • ms= electron spin QN= electron spin Bolesław AUGUSTYNIAK [6]

13. The Pauli Exclusion Principle Bolesław AUGUSTYNIAK [6]

14. Electrons can be identified with an address (n,l,ml,ms) and like us not two electrons can occupy the same space. • The Pauli exclusion principle, which summarizes experimental observations, states that no two electrons can have the same four quantum numbers. • In other words, an orbital can hold at most two electrons, and then only if the electrons have opposite spins. Bolesław AUGUSTYNIAK

15. Electron Configuration • An “electron configuration” of an atom is a particular distribution of electrons among available sub shells. • The notation for a configuration lists the sub-shell symbols sequentially with a superscript indicating the number of electrons occupying that sub shell. • For example, lithium (atomic number 3) has two electrons in the “1s” sub shell and one electron in the “2s” sub shell 1s2 2s1. Bolesław AUGUSTYNIAK [6]

16. Electron Configuration Bolesław AUGUSTYNIAK [6]

17. Each orbital is represented by a circle. • Each group of orbitals is labeled by its sub shell notation. 1s 2s 2p • Electrons are represented by arrows: up for ms = +1/2 and down for ms = -1/2 Electron Configuration • An orbital diagram is used to show how the orbitals of a sub shell are occupied by electrons. Bolesław AUGUSTYNIAK [6]

18. The Pauli Exclusion Principle • The maximum number of electrons and their orbital diagrams are: Bolesław AUGUSTYNIAK [6]

19. Aufbau Principle(zasada ‘budowania’) • Every atom has an infinite number of possible electron configurations. • The configuration associated with the lowest energy level of the atom is called the “ground state.” • Other configurations correspond to “excited states.” • Table 8.1 lists the ground state configurations of atoms up to krypton. Bolesław AUGUSTYNIAK [6]

20. Aufbau Principle • To obtain the “ground state” electron configuration: • make a ladder like arrangements of the energy sublevels (lowest at bottom). • Place one electron on your ladder at the lowest available sublevel for each element before your element and plus one for the element in question. (atomic # = electrons on ladder). • This is the Aufbau Principle (Build-up Principle) Bolesław AUGUSTYNIAK [6]

21. Order for Filling Atomic Subshells 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 6f Bolesław AUGUSTYNIAK [6]

22. Building Up: fill orbitals starting with the lowest energy (aufbau principle), pairing electrons as determined by the Pauli principle. Bolesław AUGUSTYNIAK [9]

23. Orbital Energy Levels in Multi-electron Systems Bolesław AUGUSTYNIAK [6]

24. Orbital Energy Levels in Multi-electron Systems 2 Bolesław AUGUSTYNIAK [7]

25. Aufbau Principle • Using the abbreviation [He] for 1s2, the configurations are • Here are a few examples. Bolesław AUGUSTYNIAK [6]

26. Aufbau Principle • With boron (Z=5), the electrons begin filling the 2p subshell. Bolesław AUGUSTYNIAK [6]

27. Z=18 Argon 1s22s22p63s23p6 or [Ne]3s23p6 Aufbau Principle • With sodium (Z = 11), the 3s sub shell begins to fill. • Then the 3p sub shell begins to fill. Bolesław AUGUSTYNIAK [6]

28. Configurations and the Periodic Table • Note that elements within a given family have similar configurations. • For instance, look at the noble gases. Bolesław AUGUSTYNIAK [6]

29. Configurations and the Periodic Table • Note that elements within a given family have similar configurations. • The Group IIA elements are sometimes called the alkaline earth metals. Bolesław AUGUSTYNIAK [6]

30. Configurations and the Periodic Table • Electrons that reside in the outermost shell of an atom - or in other words, those electrons outside the “noble gas core”- are called valence electrons. • These electrons are primarily involved in chemical reactions. • Elements within a given group have the same “valence shell configuration.” • This accounts for the similarity of the chemical properties among groups of elements. Bolesław AUGUSTYNIAK [6]

31. Configurations and the Periodic Table • The following slide illustrates how the periodic table provides a sound way to remember the Aufbau sequence. • In many cases you need only the configuration of the outer elements. • You can determine this from their position on the periodic table. • The total number of valence electrons for an atom equals its group number. Bolesław AUGUSTYNIAK [6]

32. Configurations and the Periodic Table Bolesław AUGUSTYNIAK [6]

33. Use the position of element in the periodic table to determine electron configuration [9] Bolesław AUGUSTYNIAK

34. [9] Bolesław AUGUSTYNIAK

35. Three possible arrangements are given in the following orbital diagrams. 1s 2s 2p • Diagram 1: • Diagram 2: • Diagram 3: Orbital Diagrams • Consider carbon (Z = 6) with the ground state configuration 1s22s22p2. • Each state has a different energy and different magnetic characteristics. Bolesław AUGUSTYNIAK [6]

36. 1s 2s 2p Orbital Diagrams • Hund’s rule states that the lowest energy arrangement (the “ground state”) of electrons in a sub-shell is obtained by putting electrons into separate orbitals of the sub shell with the same spin before pairing electrons. • Looking at carbon again, we see that the ground state configuration corresponds to diagram 1 when following Hund’s rule. Bolesław AUGUSTYNIAK [6]

37. 1s 2s 2p 1s 2s 2p • The last electron is paired with one of the 2p electrons to give a doubly occupied orbital. Orbital Diagrams • To apply Hund’s rule to oxygen, whose ground state configuration is 1s22s22p4, we place the first seven electrons as follows. • Table 8.2 lists more orbital diagrams. Bolesław AUGUSTYNIAK [6]

38. Electron Configurations Bolesław AUGUSTYNIAK [6]

39. Closed shell unpaired electrons - paramagnetic All electrons paired: diamagnetic Bolesław AUGUSTYNIAK [9]

40. Magnetic Properties • Although an electron behaves like a tiny magnet, two electrons that are opposite in spin cancel each other. Only atoms with unpaired electrons exhibit magnetic susceptibility. • A paramagnetic substance is one that is weakly attracted by a magnetic field, usually the result of at least oneunpaired electrons. • A diamagnetic substance is not attracted by a magnetic field generally because it has only paired electrons. Bolesław AUGUSTYNIAK [6]

41. Para... i dia .... Up Singly occupied Doubly occupied Down « Paramagnetic » S = ± 1/2 « Diamagnetic » S = 0 Bolesław AUGUSTYNIAK [5]

42. Uproszczony model diamagnetyzmu ... Bolesław AUGUSTYNIAK

43. Zmiana prędkości kątowej elektronu w polu B Dwa elektrony maja przeciwne momenty pędu Siła dośrodkowa Pole magnetyczne Siła Lorentza: Ma pozostać stała wartość promienia r -> zmienia się prędkość kątowa [2] Bolesław AUGUSTYNIAK

44. Zmiana momentu magnetycznego dla sparowanych elektronów [2] Bolesław AUGUSTYNIAK

45. Oszacowanie zmiany momentu magnetycznego [2] Bolesław AUGUSTYNIAK

46. Model Langevin’a diamagnetyzmu Bolesław AUGUSTYNIAK

47. Paul Langevin Langevin is noted for his work on paramagnetism and diamagnetism, and devised the modern interpretation of this phenomenon in terms of spins of electrons within atoms. His most famous work was in the use of ultrasounds using Pierre Curie's piezoelectric effect. During world war I, he began working on the use of these sounds to detect submarines through echo location. However the war was over by the time he had it operational. During his career, Paul Langevin also did much to spread the theory of relativity in France and created what is now called the twin paradox. In 1910 he reportedly had an affair with the then widowed Marie Curie Paul Langevin (1872-1946) http://en.wikipedia.org/wiki/Paul_Langevin Bolesław AUGUSTYNIAK

48. Założenia modelu dla orbitalnych momentów magnetycznych: 1. Elektron krąży po orbicie kołowej o promieniu r z prędkością liniową v 2. Pole magnetyczne o natężeniu H prostopadłe do powierzchni orbity zmienia prędkość kątowąa tym samym i moment magnetyczny elektronu 3. Można wyznaczyć średnią wartość zmiany momentu dla zbioru momentów dowolnie skierowanych względem pola H 4. Można oszacować podatność magnetyczną znając gęstość atomów [1] Bolesław AUGUSTYNIAK

49. Zmiana momentu po włączeniu pola magnetycznego 1. Moment magnetyczny orbitalny mo bez pola: 2. Zmienne pole magnetyczne –> zmiana strumienia indukcji -> wirowe pole E wzdłuż orbity -> siła od E zmienia prędkość elektronu 1. Zmiana prędkości i momentu magnetycznego po ustaleniu pola H UWAGA: H jest prostopadłe do A Bolesław AUGUSTYNIAK

50. Uśrednienie przestrzenne zmiany momentu • Rzut R orbity o promieniu r na płaszczyznę prostopadłą do kierunku pola H. • R = r sin(q) 2. Uśrednienie R po wszystkich możliwych kątach q Zastąpienie r przez R Zastąpienie r2 przez <R2> Wzór Langevin’a [1] Bolesław AUGUSTYNIAK