Importancia del proceso gradual de aprendizaje táctil, auditivo y visual.

I w 3.0 2.5 2.0 1.5 1 0.5 Ne P Ca Mn Zn Br Zr Rh Sn Cs I I I I 0 5 10 15 20 25 30 35 40 45 50 55 60 Atomic Number

Figure 3.31. Moseley plot of the and characteristic X-ray frequencies versus the atomic number Z. (From C. P. Poole, Jr, H. A. Farach, and R. J. Creswick, Superconductivity, Academic Press, Boston, 1995, p. 515.) 20 c 0 10 0 A

.

Kr

. . .

Xe

.

Rn

.

_U

_.

0 10 20 30 40 50 60 70 80 90 100

Figure 3.32. Experimentally determined ionization energy of the outer electron in various elements. (From R. Eisberg and R. Quantum Physics, New York, 1994, p. 364.)

Figure 3.33. Energy-level diagram of molybdenum showing the transitions of the K and series of X-ray lines.

monoenergetic electrons that have energies of, perhaps, 170 As the electrons traverse the film, they exchange momentum with the lattice and lose energy by exciting or ionizing atoms, and an electron energy analyzer is employed to measure the amount of energy that is absorbed. This energy corresponds to a transition of the type indicated in Fig. 3.33, and is equal to the difference between the kinetic energy of the incident electrons and that of the scattered electrons

(3.14) A plot of the measured electron intensity as a of the absorbed energy contains peaks at the binding energies of the various electrons in the sample. The analog of optical and X-ray polarization experiments can be obtained with electron energy-loss spectroscopy by varying the direction of the momentum transfer Ap

between the incoming electron and the lattice relative to the crystallographic axis. This vector Ap plays the role of the electric polarization vector E in photon spectroscopy. This procedure can increase the resolution of the absorption peaks. 3.4.3. Magnetic Resonance

Another branch of spectroscopy that has provided information on nanostructures is magnetic resonance that involves the study of microwave (radar frequency) and transitions. Most magnetic resonance measurements are made in fairly strong magnetic fields, typically B 0.33 T (3300 Gs) for electron spin resonance (ESR), and B for nuclear magnetic resonance (NMR). Several types of magnetic resonance are mentioned below.

3.4. SPECTROSCOPY 69

NMR involves the interaction of a nucleus possessing a nonzero nuclear spin I with an applied magnetic field to give the energy-level splitting into

+

1 lines with the energies

E, = (3.15)

where is the gyromagnetic ratio, sometimes called the mugnetogyric ratio,

characteristic of the nucleus, and assumes integer or half-integer values in the range -I m +I depending on whether I is an integer or a half-integer. The value of is sensitive to the local chemical environment of the nucleus, and it is customary to report the chemical shift of relative to a reference value that is,

= (y - Chemical shifts are very small, and are usually reported in parts

per million ( ppm). The most favorable nuclei for study are those with I = such as

H, and the latter isotope is only 1.1% abundant.

Fullerene molecules such as and are discussed in Chapter 5. The well- known buckyball has the shape of a soccer ball with 12 regular pentagons and

20 hexagons. The fact that all of its carbon atoms are equivalent was determined unequivocally by the NMR spectrum that contains only a single narrow line. In contrast to this, the rugby-ball-shaped C,, fullerene molecule, which contains 12

pentagons (2 regular) and 25 hexagons, has five types of carbons, and this is confirmed by the NMR spectrum presented at the top of Fig. 3.34. The five NMR lines from the a , b, d, and e carbons, indicated in the upper figure, have the intensity ratios 10 : 10 : 20 : 20 : 10 corresponding to the number of each carbon type in the molecule. Thus NMR provided a of the structures of these two fullerene molecules.

Electron paramagnetic resonance (EPR), sometimes called electron spin reso- nance (ESR), detects unpaired electrons in transition ions, especially those with odd numbers of electrons such as and Free radicals such as those associated with defects or radiation damage can also be detected. The energies or

resonant frequencies are three orders of magnitude higher than NMR for the same magnetic field. A different notation is employed for the energy E, =

where is the Bohr magneton and g is the dimensionless g factor, which has the value 2.0023 for a free electron. For the unpaired electron with spin = on a radical EPR measures the energy difference AE = - between-the levels

rn = to give a single-line spectrum at the energy level

(3.16)

Equations (3.15) and (3.16) are related through the expression = A y . If the unpaired electron interacts with a nuclear spin of magnitude I , then

+

1 hyperfine structure lines appear at the energies

d b, c

Hz

5000

6000

Figure 3.34. NMR spectrum from fullerene molecules. The five NMR lines from the a, c, and e carbons, indicated in the molecule on the lower right, have the intensity ratios 10 : 10 : 20 : 20 : 10 in the upper spectrum corresponding to the number of each carbon type in the molecule. The so-called two-dimensional NMR spectrum at the lower left, which is a plot of the coupling constant frequencies versus the chemical shift in parts per million (pprn), shows doublets corresponding to the indicated carbon bond pairs. The ppm chemical shift scale at the bottom applies to both the lower two-dimensional spectrum, and the upper conventional NMR spectrum. One of the NMR lines arises from the fullerene species which is present as an impurity. [From K. Kikuchi, S. Suzuki, Y. Nakao, N. Nakahara, T. Wakabayashi, H. Shiromaru, I. Ikemoto, and Y. Achiba, 216, 67

where A is the hyperfine coupling constant, and takes on the 21

+

1 values in the range

-I

m,

I.

Figure 3.35 shows an example of such a spectrum arising from the endohedral fullerene compound which was detected in the mass spectrum shown in Fig. 3.9. The lanthanum atom inside the cage has the nuclear spin line

I

= and the unpaired electron delocalized throughout the fullerene cage interacts with this nuclear spin to produce the eight-line hyperfine multiplet shown in the figure.

EPR has been utilized to study conduction electrons in metal nanoparticles, and to detect the presence of conduction electrons in nanotubes to determine whether the tubes are metals or very narrowband semiconductors. This technique has been employed to identify trapped oxygen holes in colloidal semiconductor nanoclusters. It has also been helpful in clarifying spin-flip resonance transitions and Landau bands in quantum dots.

The construction of new nanostructured biomaterials is being investigated by seeking to understand the structure and organization of supermolecular assemblies by studying the interaction of proteins with phospholipid bilayers. This can be

FURTHER READING 71

2 G H

Figure 3.35. Electron paramagnetic resonance spectrum of the endohedral fullerene molecule dissolved in toluene at The unpaired electron delocalized on t h e carbon cage interacts with the = nuclear spin of the lanthanum atom inside the cage to produce the observed eight-line hyperfine multiplet. [From R. D. Johnson, D. S. Bethune, C. S. Yannoni, Chem. Res. 25, 169

conveniently studied by attaching spin labels paramagnetic nitroxides) to the lipids and using EPR to probe the restriction of the spin-label motions arising from phospholipids associated with membrane-inserted domains of proteins.

Microwaves or radar waves can also provide useful information about materials when employed under nonresonant conditions in the absence of an applied magnetic field. For example, energy gaps that occur in the microwave region can be estimated by the frequency dependence of the microwave absorption signal. Microwaves have been used to study photon-assisted single-electron tunneling and Coulomb block- ades in quantum dots.

FURTHER READING

J. M. and C. H. Spence, in Nalwa Vol. 2, Chapter 1,2000. T. Hahn, ed., Tables Crystallography, 4th ed., Kluwer, Dordrecht, 1996.

M. and J. A. “Electron Microscopy Study of and

C. E. Krill, R. Haberkom, and R. “Specification of Microstructure and Character- G. E. Moore, IEEE ZEDM Tech. Digest. 1 3 (1975).

H. S . Nalwa, ed., Handbook Nanostructured Materials and Vols. 1-5, R. E. Whan, Materials Characterization, 10 of Metals Handbook, American Society for

Ancient Materials,” in Nalwa Vol. 2, Chapter 8, 2000.

ization by Scattering Techniques,” Nalwa Vol. 2, Chapter 3, 2000.

Academic Press, Boston, 2000. Metals, Metals Park OH, 1986.

4

PROPERTIES OF

IN

DUAL

In document Metodologías y recursos didácticos para el desarrollo del aprendizaje de los niños y niñas con discapacidad visual, del centro educativo integral Melvin Jones del cantón La Libertad, provincia de Santa Elena, año 2013 (página 60-64)