Aula Raios - X02, Notas de aula de Engenharia de Materiais
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Aula Raios - X02, Notas de aula de Engenharia de Materiais

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Microsoft PowerPoint - DifraçãoRaios-X02.PPT

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- Para avaliar uma estrutura cristalina, é necessário usar as figuras de difração produzidas por ondas que interagem com os átomos e que possuem comprimentos de onda ( ) comparáveis (da ordem ou menores) com a ordem de grandeza das distâncias interatômicas.

- A estrutura cristalina pode ser estudada através da difração de fótons, elétrons de alta energia e neutrons.

- A difração depende da estrutura cristalina e do comprimento de onda da radiação.

- Because X-rays have wavelengths similar to the size of atoms, they are useful to explore within crystals.

Difração dos raios-X

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- Os raios-X podem afetar um filme fotográfico assim como a luz visível. - Raio-X é uma radiação eletromagnética exatamente com a mesma natureza da luz visível mas de comprimento de onda muito pequeno. - Os raios-X são mais penetrantes que a luz visível e podem facilmente atravessar o corpo humano, madeira, metal e outros objetos opacos.

Aplicação dos raios-X

Resolução da técnica: 10-3 mm

Resolução da técnica: 10-7 mm

Espectro de raios-X

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- Os raios-X se encontram na região entre os raios-gama e raios ultravioleta no espectro eletromagnético.

- A difração pode indiretamente mostrar detalhes de estrutura interna dos materiais da ordem de 10-7 mm de tamanho.

Características dos raios-X

1 Å = 10-10 m 1 nm = 10-9 m = 10 Å

Luz visível = 6000 Å Raios-X usado em difração - = 0.5 - 2.5 Å

X-rays are electromagnetic waves of very short wavelength (of the order of 0.1 nm). It would be impossible to construct a grating having such a small spacing by the cutting process. However, the atomic spacing in a solid is known to be about 0.1 nm.

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Espectro de ondas eletromagnéticas

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Energia dos raios-X

Comprimento de onda versus energia da partícula, para fótons, elétrons e neutrons.

A energia ( ) de um fóton de raio X é relacionada com o seu comprimento de onda segundo a equação de Einstein:

= h = hc/ onde: = energia

h = constante de Planck = 6,63 x 10-34 Joule.s = frequência

c = velocidade da luz = 3,0 x 108 m/s = comprimento de onda

1 eV = 1,602 x 10-19 joule

Em unidades mais usadas no laboratório:

(Å) = 12,4 / (keV)

Para o estudo dos cristais, os fótons devem possuir energias no intervalo entre 10 e 50 keV.

Logo, como os raios-X possuem menor comprimento de onda do que a luz visível, eles possuem energia mais elevada. Devido a sua elevada energia, os raios-X podem penetrar mais facilmente no material do que a luz visível. Esta capacidade depende também da densidade do material.

Para os elétrons: (Å) = 12 / [ (eV)]1/2

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Difração dos raios-X

Comprimento de onda versus energia da partícula, para fótons, elétrons e neutrons.

Raios atômicos e estrutura cristalina para diversos metais. FCC – face-centered cubic HCP – hexagonal close-packed BCC = body-centerd cubic

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From diffraction patterns we can: • measure the average spacings between layers or rows of atoms; • determine the orientation of a single crystal or grain; • find the crystal structure of an unknown material; and • measure the size, shape and internal stress of small crystalline regions.

There are various diffraction techniques currently employed which result in diffraction patterns. These patterns are records of the diffracted beams produced.

Difração dos raios-X

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X-ray tube – consist of: - On evacuated chamber with a tungsten filament at one

end of the tube, called the cathode, and a metal target at the other end, called an anode. - Electrical current is run through the tungsten filament, causing it to glow and emit electrons. A large voltage difference (measured in kilovolts) is placed between the cathode and the anode, causing the electrons to move at high velocity from the filament to the anode target. - Upon striking the atoms in the target, the electrons dislodge inner shell electrons resulting in outer shell electrons having to jump to a lower energy shell to replace the dislodged electrons. These electronic transitions results in the generation of X-rays. The X-rays then move through a window in the X-ray tube and can be used to provide information on the internal arrangement of atoms in crystals or the structure of internal body parts.

Produção dos raios-X Os raios-X são produzidos quando uma partícula carregada com suficiente energia é desacelerada rapidamente. Raios X podem ser produzidos quando elétrons são acelerados em direção a um alvo metálico.

Tubo para produção dos raios-X

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Na figura está representada esquematicamente a estrutura de um tubo eletrônico de Röntgen. O cátodo C é uma espiral de volfrâmio, que emite elétrons graças à emissão termoeletrônica. O cilindro Cl foca o feixe de elétrons que depois colidem com o eletrodo metálico (ânodo) A. Durante este processo, formam-se os raios X. A diferença de potencial entre o cátodo e o ânodo atinge várias dezenas de quilovolts. No tubo forma-se um alto vácuo; a pressão do gás neste tubo é de 10-5 - 10-7 mm Hg.

A estrutura do tubo de Röntgen

Produção dos raios-X

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Continuous and Characteristic X-ray Spectra

When the target material of the X-ray tube is bombarded with electrons accelerated from the cathode filament, two types of X-ray spectra are produced. The first is called the continuous spectra.

O choque do feixe de elétrons (que saem do catodo com energia de dezenas de KeV) com o anodo (alvo) produz dois tipos de raios X. Um deles constitui o espectro contínuo, e resulta da desaceleração do elétron durante a penetração no anodo. O outro tipo é o raio X característico do material do anodo. Assim, cada espectro de raios X é a superposição de um espectro contínuo e de uma série de linhas espectrais características do anodo.

11 Espectro de raios-X do Molibdenio em função da voltagem aplicada.

Espectro Contínuo

The continuous spectra consists of a range of wavelengths of X-rays with minimum wavelength and intensity (measured in counts per second) dependent on the target material and the voltage across the X-ray tube. The minimum wavelength decreases and the intensity increases as voltage increases.

SWL – short-wave-length limit

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The second type of spectra, called the characteristic spectra, is produced at high voltage as a result of specific electronic transitions that take place within individual atoms of the target material.

This is easiest to see using the simple Bohr model of the atom. In such a model, the nucleus of the atom containing the protons and neutrons is surrounded by shells of electrons. The innermost shell, called the K- shell, is surrounded by the L- and M - shells. When the energy of the electrons accelerated toward the target becomes high enough to dislodge K- shell electrons, electrons from the L - and M - shells move in to take the place of those dislodged.

Espectro Característico

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Each of these electronic transitions produces an X-ray with a wavelength that depends on the exact structure of the atom being bombarded. A transition from the L - shell to the K- shell produces a K X-ray, while the transition from an M - shell to the K- shell produces a K X-ray.

Espectro Característico

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Each of these electronic transitions produces an X-ray with a wavelength that depends on the exact structure of the atom being bombarded. A transition from the L - shell to the K- shell produces a K X-ray, while the transition from an M - shell to the K- shell produces a K X-ray.

These characteristic X-rays have a much higher intensity than those produced by the continuous sprectra, with K X-rays having higher intensity than K X-rays. Very important point - the wavelength of these characteristic x-rays is different for each atom in the periodic table (of course only those elements with higher atomic number have L- and M - shell electrons that can undergo transitions to produce X- rays). A filter is generally used to filter out the lower intensity K X-rays.

Espectro Característico

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Espectro Característico

Modelo de Bohr

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2.2909Cr

1.9373Fe

1.7902Co

1.5418Cu

0.7107Mo

K Wavelength

( ) Å Element

Espectro de raios-X do Mo para voltagem aplicada de 35 kV.

Espectro Característico

X-rays wavelengths for commonly used target materials in X-ray tubes.

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Produção dos raios-X

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FILTERS Many x-ray diffraction experiments require radiation which is as closely monochromatic as possible. However, the beam from an x-ray tube operated at a voltage above V, contains not only the strong K line but also the weaker K line and the continuous spectrum.

Produção dos raios-X

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Tubo de raios-X

The x-ray tube must contain: (a) a source of electrons, (b) a high accelerating voltage, and (c) a metal target. Furthermore, since most of the kinetic energy of the electrons is converted into heat in the target, the latter is almost always water-cooled to prevent its melting.

The x-ray tubes contain two electrodes: - an anode (the metal target) maintained, with few exceptions, at ground potential, - a cathode, maintained at a high negative potential, normally of the order of 30,000 to 50,000 volts for diffraction work.

X-ray tubes may be divided into two basic types, according to the way in which electrons are provided: -gas tubes - in which electrons are produced by the ionization of a small quantity of gas (residual air in a partly evacuated tube), - filament tubes - in which the source of electrons is a hot filament.

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Gas Tubes These resemble the original x-ray tube used by Roentgen. They are now obsolete.

Filament Tubes These were invented by Coolidge in 1913. They consist of an evacuated glass envelope which insulates the anode at one end from the cathode at the other, the cathode being a tungsten filament and the anode a water-cooled block of copper containing the desired target metal as a small insert at one end.

Tubos de raios-X

Esquema da secção transversal de um tubo vedado de raios-X

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Conceitos de Max von Laue - 1912

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Difração de luz em uma fenda Difração em duas fendas

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DIFRAÇÃO - Espalhamento coerente + Interferência

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Interferência e Espalhamento

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X-ray Diffraction

Since a beam of X-rays consists of a bundle of separate waves, the waves can interact with one another. Such interaction is termed interference. If all the waves in the bundle are in phase, that is their crests and troughs occur at exactly the same position (the same as being an integer number of wavelengths out of phase, nl, n = 1, 2, 3, 4, etc.), the waves will interfere with one another and their amplitudes will add together to produce a resultant wave that is has a higher amplitude (the sum of all the waves that are in phase.

If the waves are out of phase, being off by a non-integer number of wavelengths, then destructive interference will occur and the amplitude of the waves will be reduced. In an extreme case, if the waves are out of phase by a multiple of 1/2l (n/2l ), the resultant wave will have no amplitude and thus be completely destroyed.

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William Henry Bragg

William Henry Bragg was born at Westward, Cumberland, on July 2, 1862. He was educated at Market Harborough Grammar School and afterwards at King William's College, Isle of Man. Elected a minor scholar of Trinity College, Cambridge, in 1881, he studied mathematics under the well-known teacher, Dr. E. J. Routh. He was Third Wrangler in the Mathematical Tripos, Part I, in June 1884, and was placed in the first class in Part II in the following January. He studied physics in the Cavendish Laboratory during part of 1885, and at the end of that year was elected to the Professorship of Mathematics and Physics in the University of Adelaide, South Australia. Subsequently he became successively Cavendish Professor of Physics at Leeds (1909-1915), Quain Professor of Physics at University College London (1915-1925), and Fullerian Professor of Chemistry in the Royal Institution.

His research interests embraced a great many topics and he was an adept at picking up a subject, almost casually, making an important contribution, then dropping it again. However, the work of Bragg and his son Lawrence in 1913-1914 founded a new branch of science of the greatest importance and significance, the analysis of crystal structure by means of X-rays. If the fundamental discovery of the wave aspect of X-rays, as evidenced by their diffraction in crystals, was due to von Laue and his collaborators, it is equally true that the use of X-rays as an instrument for the systematic revelation of the way in which crystals are built was entirely due to the Braggs. This was recognized by the award of the Nobel Prize jointly to father and son in 1915.

July 2, 1862 - March 10, 1942

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William Lawrence Bragg, son of William Henry Bragg, was born in Adelaide, South Australia, on March 31, 1890. He received his early education at St. Peter's College in his birthplace, proceeding to Adelaide University to take his degree in mathematics with first-class honours in 1908. He came to England with his father in 1909 and entered Trinity College, Cambridge, as an Allen Scholar, taking first- class honours in the Natural Science Tripos in 1912. In the autumn of this year he commenced his examination of the von Laue phenomenon and published his first paper on the subject in the Proceedings of the Cambridge Philosophical Society in November.

In 1914 he was appointed as Fellow and Lecturer in Natural Sciences at Trinity College and the same year he was awarded the Barnard Medal. From 1912 to 1914 he had been working with his father, and the results of their work were published in an abridged form in X-rays and Crystal Structure (1915). It was this work which earned them jointly the Nobel Prize for Physics in 1915, and from this year to 1919, W. L. Bragg served as Technical Advisor on Sound Ranging to the Map Section, G.H.Q., France, receiving the O.B.E. and the M.C. in 1918. He was appointed Langworthy Professor of Physics at Manchester University in 1919, and held this post till 1937.

William Lawrence Bragg, March 31, 1890 / July 1, 1971

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