notas de metalurgia fisica - unidad 1 - 2012

UNIVERSIDAD AUTÓNOMA DE ZACATECAS

Programa de Ingeniería Mecánica

Av. López Velarde No. 801

Col. Centro

Zacatecas, Zacatecas, C.P. 98000

Tel. 01 (492) 923 94 07 ext. 1615

Notas del Programa

Metalurgia Física

Material Preparado por:

Dr. Víctor Hugo Baltazar Hernández

Notas de la materia Metalurgia Física

Dr. Víctor Hugo Baltazar Hernández 2012 2

CONTENIDO

1 LAS HERRAMIENTAS DEL METALURGISTA .............................................................................. 3

1.1 MÉTODOS PARA LA CARACTERIZACIÓN DE LOS METALES Y SUS ALEACIONES ................................. 3

1.1.1 La metalografía .................................................................................................... 3

1.2 MICROSCOPÍA ÓPTICA, ELECTRÓNICA (SEM) Y DE TRANSMISIÓN (TEM) ....................................... 8

1.2.1 Microscopía óptica (light microscopy) .............................................................. 8

1.2.2 Microscopía Electrónica de Barrido (Scanning Electron Microscopy) ....... 14

1.2.3 Microscopía Electrónica de Transmisión (Transmission Electron Microscopy)

............................................................................................................................ 24

1.3 ANALISIS DE XRD (X-RAY DIFFRACTION) ...................................................................................... 29

1.3.1 Electromagnetic radiation ................................................................................. 29

1.3.2 Production of X-Rays ........................................................................................ 30

1.3.3 X-Ray Diffraction ................................................................................................ 32

1.3.4 Diffractometers ................................................................................................... 34

1.3.5 Applications of X-Ray Diffraction ..................................................................... 35

1.4 ENSAYOS O PRUEBAS NO DESTRUCTIVAS (NON-DESTRUCTIVE TESTING) ...................................... 35

1.4.1 Líquidos Penetrantes ........................................................................................ 35

1.5 ENSAYOS MECÁNICOS ..................................................................................................................... 44

1.6 REFERENCIAS .................................................................................................................................. 45



1 Técnicas de Caracterización del Metalurgista

1.1 Métodos para la caracterización de los metales y sus aleaciones

1.1.1 La metalografía

La metalografía o microscopía estudia microscópicamente las características estructurales

de un metal o de una aleación. Sin duda, el microscopio es la herramienta más importante del

metalurgista tanto desde el punto de vista científica como desde el técnico.

Es posible determinar el tamaño de grano, y el tamaño, forma y distribución de varias fases

e inclusiones que tienen gran efecto sobre las propiedades mecánicas del metal. La microestructura

revelara el tratamiento mecánico y térmico del metal y, bajo un conjunto de condiciones dadas,

podrá predecirse su comportamiento esperado.

La experiencia ha demostrado que el éxito en el estudio microscopico depende en mucho

del cuidado que se tenga para preparar la muestra. El microscopio mas costoso no revelara la

estructura de una muestra que haya sido preparada en forma deficiente. El procedimiento que se

sigue en la preparación de una muestra es comparativamente sencillo y requiere de una técnica

desarrollada solo después de práctica constante. El último objetivo es obtener una superficie plana,

sin ralladuras, semejante a un espejo. Las etapas necesarias para preparar adecuadamente una

muestra metalográfica se explican en lo siguientes subíndices [1

1.1.1.1 Muestreo

].

La selección de una muestra para estudio micrasc6pico puede ser muy importante. Si lo que

se va a investigar es una falla, se debe escoger la muestra más próxima al área de la falla y

comparársele con una tomada de la sección normal o sana.

Si el material es suave, como metales o aleaciones no ferrosas y aceros no tratados

térmicamente, la sección puede obtenerse por corte manual con una segueta. Si el material es duro,

la sección puede obtenerse mediante un disco cortador abrasivo, el cual es un plato delgado

fabricado de un abrasivo de tipo adecuado, que gira a alta velocidad. La muestra debe mantenerse

fría durante la operación de corte [1].

1.1.1.2 Esmerilado burdo o tosco

Siempre que sea posible, la muestra debe ser de un tamaño fácil de manipular. Una muestra

blanda se puede aplanar si se mueve lentamente hacia arriba y hacia abajo a través de la superficie



de una lima plana poco áspera. La muestra blanda o dura puede esmerilarse burdamente sobre una

lija de banda (rotatoria), manteniendo la muestra fría sumergiéndola frecuentemente en agua

durante la operación de esmerilado. En todas las operaciones de esmerilado y pulido, la muestra

debe moverse en sentido perpendicular a las ralladuras existentes. Esto facilitara darse cuenta del

momento en que las ralladuras mas profundas hayan sido sustituidas por las menos profundas,

características del abrasivo más fino. El esmerilado continúa hasta que la superficie quede plana y

libre de mellas, rebabas, etc., y todas las ralladuras debidas al corte manual o al disco cortador no

son visibles. La Figura 1.1 muestra la superficie después del esmerilado [1].

a) b)

c)

Figura 1.1 a) Superficie de la muestra después del esmerilado burdo, amplificación 100x. b) Superficie de la muestra después del pulido intermedio en papel 400, amplificaci6n 100x. c) Superficie de la muestra sin ralladuras después del pulido final, amplificación 50x. Los puntos negros son impurezas de óxido.

1.1.1.3 Montaje

Las muestras pequeñas o de forma incomoda deben montarse de alguna manera para

facilitar el pulido intermedio y final. Alambres, varillas pequeñas, muestras de hoja metálica,

secciones delgadas, etc., deben montarse en un material adecuado o sujetarse rígidamente en una

monta mecánica.



Los materiales plásticos sintéticos que se acoplan a la muestra en una prensa para montar

especial proporcionan las bases de un tamaño uniforme conveniente (generalmente de 2,5, 3, ó 4 cm.

de diámetro) para manipular las muestras en ulteriores operaciones de pulido. Estas bases, cuando

se han hecho en forma adecuada, son muy resistentes a la acción de los reactivos de ataque que se

emplean comúnmente. La resina termofijadora que mas se emplea para montar muestras es la

baquelita. Los polvos para moldear baquelita se fabrican en colores de este material, lo cual

simplifica la identificaci6n de las muestras montadas. La muestra y la cantidad correcta de polvo de

baquelita, o una preforma de baquelita, se colocan en el cilindro de la prensa de montar. La

temperatura aumenta gradualmente hasta 150°C y se aplica una presión de moldeo de unas 4 000

lbs/pulg2 simultáneamente. Una vez que la baquelita esta adherida y curada cuando se alcanza esta

temperatura, la base con la muestra puede extraerse del dado de moldeo mientras esta caliente.

La lucita es la resina termoplástica mas común; es completamente transparente cuando se

moldea en forma adecuada, como se ve en la Figura 1.2. Esta transparencia resulta útil cuando es

necesario observar la sección exacta que se pule o cuando por cualquier otra razón se desea ver por

completo la muestra en la base. Al contrario de los plásticos termofijados, las resinas termoplásticas

no sufren cura a la temperatura de moldeo, sino que adquieren estabilidad al enfriarse. La muestra y

la cantidad de polvo de lucita adecuadas se colocan en la prensa para montar y se someten a la

misma temperatura y presión que para la baquelita (150°C y 4 000 Ibs,/pulg2

) . Una vez alcanzada

esta temperatura, se quita la bobina de calentamiento y las aletas de enfriamiento se colocan

alrededor del cilindro para enfriar la base hasta 75 °C en unos 7 min. al tiempo que se mantiene la

presión de moldeo. Si se saca la base todavía caliente o si se deja enfriar lentamente en el cilindro

de moldeo a la temperatura ambiente sin sacarla, se opacara.

Figura 1.2 a) Muestra montada en baquelita, aumentada 2x, b) muestra montada en lucita, aumentada 2x, c) muestra sostenida en un dispositivo de sujeción de metal, aumentada 2x

Las muestras pequeñas pueden montarse en forma conveniente para prepararlas

métalográficamente en un dispositivo de sujeción hecho en el laboratorio, como el de la Figura 1.2c.

Las muestras laminares delgadas, cuando se montan en tal dispositivo de sujeción, suelen alternarse



con hojas metálicas "rellenadoras" de metal que tienen aproximadamente la misma dureza que las

muestras. Si se usan hojas rellenadoras, se conservara la superficie libre de las irregularidades de la

muestra y se evitara, de alguna manera, que los bordes de la muestra se redondeen durante el pulido

[1].

1.1.1.4 Pulido intermedio

Después de montada, la muestra se pule sobre una serie de hojas de esmeril o lija con

abrasivos más finos, sucesivamente. El primer papel es generalmente No. 300, luego 400, 600, 800,

y finalmente 1200.

La Figura 1.1b muestra la superficie después del pulido intermedio con lija de 400. Por lo

general, las operaciones de pulido intermedio con lijas de esmeril se hacen en seco; sin embargo, en

ciertos casos, como el de preparación de materiales suaves, se puede usar un abrasivo de carburo de

silicio. Comparado con el papel esmeril, el carburo de silicio tiene mayor rapidez de remoción y,

como su acabado es a base de resina, se puede utilizar con un lubricante, el cual impide el sobre-

calentamiento de la muestra, minimiza el daño cuando los metales son blandos y también

proporciona una acción de enjuague para limpiar los productos removidos de la superficie de la

muestra, de modo que el papel no se ensucie [1].

1.1.1.5 Pulido fino

El tiempo utilizado y el éxito del pulido fino dependen en mucho del cuidado puesto

durante los pasos de pulido previo. La última aproximación a una superficie plana libre de

ralladuras se obtiene mediante una rueda giratoria húmeda cubierta con un paño especial cargado

con partículas abrasivas cuidadosamente seleccionadas en su tamaño. Existe gran disponibilidad de

abrasivos para efectuar el último pulido. En tanto que muchos harán un trabajo satisfactorio, parece

haber preferencia por la forma gamma del oxido de aluminio para pulir materiales ferrosos y de los

basados en cobre, y oxido de cerio para pulir aluminio, magnesio y sus aleaciones. Otros abrasivos

para pulido final que se emplean a menudo son la pasta de diamante, oxido de cromo y oxido de

magnesio.

La selección de un paño para pulir depende del material que vaya a pulirse y el propósito

del estudio metalográfico. Se pueden encontrar paños de lanilla o pelillo variable, desde aquellos

que no tienen pelillo (como la seda) hasta aquellos de pelillo intermedio (como paño ancho, paño de

billar y lonilla) además de aquellos de pelillo profundo (como el terciopelo). También se pueden

encontrar paños sintéticos para pulir con fines de pulido general, de los cuales el Gamal y el

Micropaño son los que se utilizan más ampliamente. Una muestra pulida en forma adecuada



mostrara únicamente las inclusiones no metálicas; además, estará libre de ralladuras (Figura 1.1c)

[1].

1.1.1.6 Ataque

El propósito del ataque químico es hacer visibles las características estructurales del metal o

aleación. El proceso debe ser tal que queden claramente diferenciadas las partes de la

microestructura. Esto se logra mediante un reactivo apropiado que somete a la superficie pulida a

una acción química.

a)

b) c)

Figura 1.3 a) Fotomicrografía de la diferencia en composición química de las fases. B) Fotomicrografía de hierro puro, c) Ilustración del aspecto microscópico de las fronteras de grano que aparecen como líneas obscuras.

En las aleaciones compuestas de dos o más fases, las componentes se revelan durante la

acción química, al atacar preferencialmente, el reactivo, a una o más de estas constituyentes debido

a la diferencia en composición química de las fases (Figura 1.3a). En las aleaciones uniformes de

una sola fase o metales puros, se obtiene contraste y las fronteras de grano se hacen visibles debido

a las diferencias en la rapidez a que los diversos granos son atacados por el reactivo (Figura 1.3b).

Esta diferencia en la rapidez de ataque esta asociada principalmente con el ángulo que guardan las

diferentes secciones de grano con el plano de la superficie pulida. Debido al ataque químico por el



reactivo de ataque, las fronteras de grano aparecerían como valles en la superficie pulida. Al chocar

con la orilla de estos valles, la luz del microscopio se reflejara fuera del microscopio, haciendo que

las fronteras de grano aparezcan como líneas oscuras. Esto se muestra en la Figura 1.3c. La

selección del reactivo de ataque esta determinada por el metal o aleación y la estructura especifica

que se desea ver. Ver tabla 1.3 en [] en el cual se enumeran algunos de los reactivos de ataque

comunes [1].

1.2 Microscopía óptica, electrónica (SEM) y de transmisión (TEM)

1.2.1 Microscopía óptica (light microscopy)

1.2.1.1 Basic Principles

The light microscope provides two-dimensional representation of structure over a total

magnification range of roughly ×40 to ×1250. Interpretation of such images is a matter of skill and

experience and needs to allow for the three-dimensional nature of features observed. The main

components of a benchtype microscope are (1) an illumination system comprising a light source and

variable apertures, (2) an objective lens and an ocular lens (eyepiece) mounted at the ends of a

cylindrical body tube, and (3) a specimen stage (fixed or rotatable). Metallic specimens that are to

be examined at high magnifications are successively polished with 6, 1 and sometimes 0.25 μm

diamond grit. Examination in the as-polished condition, which is generally advisable, will reveal

structural features such as shrinkage or gas porosity, cracks and inclusions of foreign matter.

Etching with an appropriate chemical reagent is used to reveal the arrangement and size of grains,

phase morphology, compositional gradients (coring), orientation-related etch pits and the effects of

plastic deformation. Although actually only a few atomic diameters wide, grain boundaries are

preferentially and grossly attacked by many etchants. In bright-field illumination, light is reflected

back towards the objective from reflective surfaces, causing them to appear bright. Dark-field

illumination reverses this effect, causing grain boundaries to appear bright. The degree of chemical

attack is sensitive to crystal orientation and an etched polycrystalline aggregate will often display its

grain structure clearly (Figura 1.4a). Preparation techniques for ceramics are essentially similar to

those for metals and alloys. However, their porosity can cause two problems. First, there is a risk of

entrapping diamond particles during polishing, making ultrasonic cleaning advisable. Second, it

may be necessary to strengthen the structure by impregnating with liquid resin in vacuo, provided

that pores are interconnected. The objective, the most important and critical component in the



optical train of the light microscope, is made up of a number of glass lenses and, sometimes, fluorite

(CaF2) lenses also. Lenses are subject to spherical and chromatic aberrations. Minimization and

correction of these undesirable physical effects, greatly aided by modern computational techniques,

is possible and objectives are classified according to the degree of correction, i.e. achromats,

fluorites (semi-apochromats), apochromats. Lenses are usually coated in order to increase light

transmission. As magnification is increased, the depth of field of the objective becomes smaller,

typically falling from 250μm at ×15 to 0.08μm at ×1200, so that specimen flatness becomes more

critical. The focal length and the working distance (separating its front lens from the specimen) of

an objective differ. For instance, an f 2mm objective may have a working distance of 0.15 mm. [2

]

Figura 1.4 (a) Reflection of light from etched specimen. (b) Use of oil to improve numerical aperture of objective.

Resolution, rather than magnification, is usually the prime concern of the skilled

microscopist. It is the smallest separating distance (δ) that can be discerned between two lines in the

image. The unaided eye, at the least distance of comfortable vision (about 250 mm), can resolve 0.1

mm. Confusingly, the resolution value for a lens with a so-called high resolving power is small.

Resolution is determined by (1) the wavelength (λ) of the radiation and (2) the numerical aperture

(NA) of the objective, and is expressed by the Abbe formula

δ=λ/2NA.

The numerical aperture value, which is engraved upon the side of the objective, indicates

the light-gathering power of the compound lens system and is obtained from the relation NA=n sin

α, where n is the refractive index of the medium between the front lens face of the objective and the

specimen and α is the semi-apex angle of the light cone defined by the most oblique rays collected

by the lens. Numerical apertures range in typical value from 0.08 to 1.25. Despite focusing

difficulties and the need for costly lenses, efforts have been made to use short-wavelength



ultraviolet radiation: developments in electron microscopy have undermined the feasibility of this

approach. Oil-immersion objectives enable the refractive index termto be increased (Figura 1.4b).

Thus, by replacing air (n=1) with a layer of cedar wood oil (n=1.5) or monobromonaphthalene

(n=1.66), the number of rays of reflected light accepted by the front lens of the objective is

increased, and resolution and contrast are improved. The range of wavelengths for visible light is

approximately 400–700 nm; consequently, using the Abbe formula, it can readily be shown that the

resolution limit of the light microscope is of the order of 200 nm. The ‘useful’ range of

magnification is approximately 500–1000NA. The lower end of the range can be tiring to the eyes;

at the top end, oil-immersion objectives are useful [2].

Magnification is a subjective term; for instance, it varies with the distance of an image or

object from the eye. Hence, microscopists sometimes indicate this difficulty by using the more

readily defined term ‘scale of reproduction’, which is the lineal size ratio of an image (on a viewing

screen or photomicrograph) to the original object. Thus, strictly speaking, a statement such as ×500

beneath a photomicrograph gives the scale of reproduction, not the magnification [2].

The ocular magnifies the image formed by the objective: the finally observed image is

virtual. It can also correct for certain objective faults and, in photomicrography, be used to project a

real image. The ocular cannot improve the resolution of the system but, if inferior in quality, can

worsen it. The most widely used magnifications for oculars are ×8 and ×12.5 [2].

Two-dimensional features of a standard bench microscope, the mechanical tube length tm

and optical tube length to, are of special significance. The former is the fixed distance between the

top of the body tube, on which the ocular rests, and the shoulder of the rotatable nosepiece into

which several objectives are screwed. Objectives are designed for a certain tm value. A value of 160

mm is commonly used. (In Victorian times, it was 250 mm, giving a rather unwieldy instrument.)

The optical tube length to is the distance between the front focal point of the ocular and the rear

focal plane of the objective. Parfocalization, using matched parfocal objectives and oculars, enables

the specimen to remain in focus when objectives are step-changed by rotating the nosepiece. With

each change, to changes but the image produced by the objective always forms in the fixed focal

phase of the ocular. Thus, the distance between the specimen and the aerial image is kept constant.

Some manufacturers base their sequences of objective and ocular magnifications upon preferred

numbers1 rather than upon a decimal series. This device facilitates the selection of a basic set of

lenses that is comprehensive and ‘useful’ (exempt from ‘empty’ magnification). For example, the

Michel series of ×6.3, ×8, ×10, ×12.5, ×16, ×20, ×25, etc., a geometrical progression with a

common ratio of approximately 1.25, provides a basis for magnification values for objectives and



oculars. This rational approach is illustrated in Figura 1.5. Dashed lines represent oculars and thin

solid lines represent objectives. The bold lines outline a box within which objective/ocular

combinations give ‘useful’ magnifications. Thus, pairing of a ×12.5 ocular with a ×40 objective

(NA=0.65) gives a ‘useful’ magnification of ×500 [2].

Figura 1.5 Range of ‘useful’ magnification in light microscope (from Optical Systems for the Microscope, 1967, p. 15; by courtesy of Carl Zeiss, Germany).

1.2.1.2 Selected microscopical techniques

Phase-contrast microscopy Phase-contrast microscopy is a technique that enables special surface features to be studied

even when there is no color or reflectivity contrast. The light reflected from a small depression in a

metallographic specimen will be retarded in phase by a fraction of a light wavelength relative to that

reflected from the surrounding matrix and, whereas in ordinary microscopy a phase difference in the

light collected by the objective will not contribute to contrast in the final image, in phase-contrast

microscopy small differences in phases are transformed into differences in brightness which the eye

can detect [2].

General uses of the technique include the examination of multi-phased alloys after light

etching, the detection of the early stages of precipitation, and the study of cleavage faces, twins and

other deformation characteristics. The optimum range of differences in surface level is about 20–50

nm, although under favorable conditions these limits may be extended. A schematic diagram of the

basic arrangement for phase contrast in the metallurgical microscope is shown in Figura 1.6a. A

hollow cone of light produced by an annulus A is reflected by the specimen and brought to an

image in the back focal plane of the objective. A phase plate of suitable size should, strictly, be



positioned in this plane but, for the ease of interchangeability of phase plates, the position Q in front

of the eyepiece E is often preferred. This phase plate has an annulus, formed either by etching or

deposition, such that the light it transmits is either advanced or retarded by a quarter of a

wavelength relative to the light transmitted by the rest of the plate and, because the light reflected

from a surface feature is also advanced or retarded by approximately λ/4, the beam is either in phase

or approximately λ/2 or π out of phase with that diffracted by the surface features of the specimen.

Consequently, reinforcement or cancellation occurs, and the image intensity at any point depends

on the phase difference produced at the corresponding point on the specimen surface, and this in

turn depends upon the height of this point relative to the adjacent parts of the surface. When the

light passing through the annulus is advanced in phase, positive phase contrast results and areas of

the specimen which are proud of the matrix appear bright and depressions dark; when the phase is

retarded, negative contrast is produced and ‘pits’ appear bright and ‘hills’ dark [2].

Figura 1.6 Schematic arrangement of microscope system for phase-contrast (a) and polarized light (b) microscopy.

Polarized-light microscopy

The basic arrangement for the use of polarized light is shown in Figura 1.6b. The only

requirements of this technique are that the incident light on the specimen be plane polarized and that

the reflected light be analyzed by a polarizing unit in a crossed relation with respect to the polarizer,

i.e. the plane of polarization of the analyzer is perpendicular to that of the polarizer [2].

The application of the technique depends upon the fact that plane-polarized light striking

the surface of an optically isotropic metal is reflected unchanged if it strikes at normal incidence. If

the light is not at normal incidence the reflected beam may still be unchanged, but only if the angle



of incidence is in, or at right angles to, the plane of polarization, otherwise it will be elliptically

polarized. It follows that the unchanged reflected beam will be extinguished by an analyzer in the

crossed position, whereas an elliptically polarized one cannot be fully extinguished by an analyzer

in any position. When the specimen being examined is optically anisotropic, the light incident

normally is reflected with a rotation of the plane of polarization and as elliptically polarized light;

the amount of rotation and of elliptical polarization is a property of the metal and of the crystal

orientation. If correctly prepared, as-polished specimens of anisotropic metals will ‘respond’ to

polarized light and a grain-contrast effect is observed under crossed polars as a variation of

brightness with crystal orientation. Metals which have cubic structure, on the other hand, will

appear uniformly dark under crossed polars, unless etched to invoke artificial anisotropy, by

producing anisotropic surface films or well-defined pits. An etch pit will reflect the light at oblique

incidence and elliptically polarized light will be produced. However, because such a beam cannot

be fully extinguished by the analyzer in any position, it will produce a background illumination in

the image which tends to mask the grain-contrast effect [2].

Clearly, one of the main uses of polarized light is to distinguish between areas of varying

orientation, since these are revealed as differences of intensity under crossed polars. The technique

is therefore very useful for studying the effects of deformation, particularly the production of

preferred orientation, but information on cleavage faces, twin bands and sub-grain boundaries can

also be obtained. If a ‘sensitive tint’ plate is inserted between the vertical illuminator and the

analyzer, each grain of a sample may be identified by a characteristic color which changes as the

specimen is rotated on the stage. This application is useful in the assessment of the degree of

preferred orientation and in recrystallization studies. Other uses of polarized light include

distinguishing and identifying phases in multi-phase alloys [2].

Near-perfect extinction occurs when the polars of a transmission microscope are crossed. If

a thin section or slice of ceramic, mineral or rock is introduced and the stage slowly rotated,

optically anisotropic crystals will produce polarization colors, developing maximum brilliance at

45◦ to any of the four symmetrical positions of extinction. The color of a crystal depends upon its

birefringence, or capacity for double-refraction, and thickness. By standardizing the thickness of the

section at 30–50μm and using a Michel–Lévy color chart, it is possible to identify crystalline

species. In refractory materials, it is relatively easy to identify periclase (MgO), chromite (FeCrO4),

tridymite (SiO2) and zircon (ZrSiO4) by their characteristic form and color [2].

As birefringence occurs within the crystal, each incident ray forms ordinary and

extraordinary rays which are polarized in different planes and travel through the crystal at different

velocities. On leaving the analyzer, these out-of-phase ‘fast’ and ‘slow’ rays combine to produce the



polarization color. This color is complementary to color cancelled by interference and follows

Newton’s sequence: yellow, orange, red, violet, blue, green. More delicate, higher-order colors are

produced as the phase difference between the emergent rays increases. Anisotropic crystals are

either uniaxial or biaxial, having one or two optic axes, respectively, along which birefringence

does not occur. (Optic axes do not necessarily correspond with crystallographic axes.) It is therefore

possible for quartz (uniaxial) and mica (biaxial) crystals to appear black because of their orientation

in the slice. Uniaxial (tetragonal and hexagonal systems) can be distinguished from biaxial crystals

(orthorhombic, triclinic and monoclinic systems) by introducing a Bertrand lens into the light train

of the microscope to give a convergent beam, rotating the stage and comparing their interference

figures: uniaxial crystals give a moving ‘ring and brush’ pattern, biaxial crystals give two static

‘eyes’. Cubic crystals are isotropic, being highly symmetrical. Glassy phases are isotropic and also

appear black between crossed polars; however, glass containing residual stresses from rapid cooling

produces fringe patterns and polarization colors. The stress-anisotropic properties of plastics are

utilized in photoelastic analyses of transparent models of engineering structures or components

made from standard sheets of constant thickness and stressoptic coefficient (e.g. clear Bakelite,

epoxy resin). The fringe patterns produced by monochromatic light and crossed polars in a

polariscope reveal the magnitude and direction of the principal stresses that are developed when

typical working loads are applied [2].

1.2.2 Microscopía Electrónica de Barrido (Scanning Electron Microscopy)

1.2.2.1 Introduction

In 1993, Charles Smithart was convicted of the murder of an 11-year-old girl in the town of

Glennallen, Alaska. Prosecutors suspected Smithart after he was spotted at the scene of the crime,

but they had no evidence directly linking him to the murder. That's where a scanning electron

microscope (SEM) came in.

Using the X-ray spectroscopy detector of an SEM, a forensic scientist analyzed bits of iron

found at the scene of the crime. He found that they had a globular shape that only welding or

grinding produces. As it turned out, Smithart had a welding rig in his shop and would sometimes

repair bicycles for the local children. Thanks to the tremendous capabilities of scanning electron

microscopes, prosecutors had the evidence they needed to link Smithart to the crime.

Why was an SEM, rather than a regular light, or optical, microscope from the local high

school, necessary to examine the evidence for Smithart's trial? For one thing, SEMs can magnify

objects at upward of 300,000 times the size of the object studied. Scientists refer to this number as

the magnification power and denote it, for example, as 300,000x. In contrast, run-of-the-mill

http://health.howstuffworks.com/x-ray.htm�

http://science.howstuffworks.com/welding.htm�



optical microscopes tend to have a magnification power of a few hundred times. SEMs also have

tremendous depth of field compared to traditional microscopes, providing an almost 3-D image for

researchers to analyze, as compared to the flatter image an optical microscope produces. Lastly,

these advanced microscopes can look past the surface of an object, telling researchers information

about its composition. All of these attributes proved essential in examining evidence from the

Smithart case.

Of course, SEMs have their share of drawbacks as well, like cost. Even the cheapest among

them cost tens of thousands of dollars. They're also bulky and complex instruments, requiring

considerable expertise to operate. As a result, their use is typically limited to research and

industrial applications, though recent breakthroughs have made SEMS more accessible in other

applications.

In this article, we'll learn how SEMs are able to produce such detailed and striking images.

In the process, we'll explore what goes into operating one, as well as some of the most recent

breakthroughs in SEM technology. But before we learn about where the technology is headed, let's

look at where it all began [3

1.2.2.2 How scanning electron microscope works

].

Figura 1.7 How scanning electron microscopes work



We've begun to get an idea of what SEMs are capable of. Now we're ready to take a look at

the various components of one and how they work together to form an image. While the variations

from one model to the next are seemingly endless, all SEMs share the same basic parts.

Electron gun: Electron guns aren't some futuristic weapon used in the newest Vin Diesel

movie. Instead, they produce the steady stream of electrons necessary for SEMs to operate. Electron

guns are typically one of two types. Thermionic guns, which are the most common type, apply

thermal energy to a filament (usually made of tungsten, which has a high melting point) to coax

electrons away from the gun and toward the specimen under examination. Field emission guns, on

the other hand, create a strong electrical field to pull electrons away from the atoms they're

associated with. Electron guns are located either at the very top or at the very bottom of an SEM

and fire a beam of electrons at the object under examination. These electrons don't naturally go

where they need to, however, which gets us to the next component of SEMs.

Lenses: Just like optical microscopes, SEMs use lenses to produce clear and detailed

images. The lenses in these devices, however, work differently. For one thing, they aren't made of

glass. Instead, the lenses are made of magnets capable of bending the path of electrons. By doing

so, the lenses focus and control the electron beam, ensuring that the electrons end up precisely

where they need to go.

Sample chamber: The sample chamber of an SEM is where researchers place the specimen

that they are examining. Because the specimen must be kept extremely still for the microscope to

produce clear images, the sample chamber must be very sturdy and insulated from vibration. In fact,

SEMs are so sensitive to vibrations that they're often installed on the ground floor of a building. The

sample chambers of an SEM do more than keep a specimen still. They also manipulate the

specimen, placing it at different angles and moving it so that researchers don't have to constantly

remount the object to take different images.

Detectors: You might think of an SEM's various types of detectors as the eyes of the

microscope. These devices detect the various ways that the electron beam interacts with the sample

object. For instance, Everhart-Thornley detectors register secondary electrons, which are electrons

dislodged from the outer surface of a specimen. These detectors are capable of producing the most

detailed images of an object's surface. Other detectors, such as backscattered electron detectors

and X-ray detectors, can tell researchers about the composition of a substance.

Vacuum chamber: SEMs require a vacuum to operate. Without a vacuum, the electron

beam generated by the electron gun would encounter constant interference from air particles in the

atmosphere. Not only would these particles block the path of the electron beam, they would also be

knocked out of the air and onto the specimen, which would distort the surface of the specimen.

http://science.howstuffworks.com/atom.htm�

http://science.howstuffworks.com/magnet.htm�

http://health.howstuffworks.com/x-ray.htm�



As with many things, an SEM is more than the sum of its parts. Read on to see how all of

these components work together to create astounding images of very, very tiny things [4

1.2.2.3 Effects of Electron Bombardment

].

Electron bombardment of a sample is unique to microprobe analysis and produces a large

number of effects from the target material (Figura 1.8). The incident electrons interact with

specimen atoms and are significantly scattered by them (rather than penetrating the sample in a

linear fashion). Most of the energy of an electron beam will eventually end up heating the sample

(phonon excitation of the atomic lattice); however, before the electrons come to rest, they undergo

two types of scattering: elastic and inelastic.

In elastic scattering, the electron trajectory changes, but its kinetic energy and velocity

remain essentially constant (due to large differences between the mass of the electron and nucleus).

This process is known as electron backscattering (although later we will confine the term

"backscattered electrons" to those scatter out of the sample).

Figura 1.8 Effects produced by electron bombardment of a material.

In inelastic scattering, the trajectory of the incident electron is only slightly perturbed, but

energy is lost through interactions with the orbital electrons of the atoms in the specimen. Inelastic

interactions produce diverse effect including:

phonon excitation (heating)

cathodoluminescence (visible light fluorescence)

continuum radiation (bremsstrahlung or “braking” radiation)



characteristic x-ray radiation

plasmon production (secondary electrons)

Auger electron production (ejection of outer shell electrons)

Two major factors control which effects can be detected from the interaction volume. First,

some effects are not produced from certain parts of the interaction volume (Figura 1.9). Beam

electrons lose energy as they traverse the sample due to interactions with it and if too much energy

is required to produce an effect, it will not be possible to produce it from deeper portions of the

volume. Second, the degree to which an effect, once produced, can be observed is controlled by

how strongly it is diminished by absorption and scattering in the sample.

For example, although secondary and Auger electrons are produced throughout the

interaction volume, they have very low energies and can only escape from a thin layer near the

sample's surface. Similarly, soft X-rays, which are absorbed more easily than hard X-rays, will

escape more readily from the upper portions of the interaction volume. Absorption is an important

phenomenon and is discussed in more detail below.

Figura 1.9 Generalized illustration of interaction volumes for various electron-specimen interactions. Auger electrons (not shown) emerge from a very thin region of the sample surface (maximum depth about 50 Å) than do secondary electrons (50-500 Å).

1.2.2.4 SEM imaging

Secondary Electrons

Figure 1.10 shows the microstructure of the specimen by means of secondary electrons

(SE) signal at a voltage level of 20kV and a spot size of 40 µm. Some features can be identified

from this SE signal based on the surface topography (due to prior etching). These features have

been labelled as “a” and “b” that possibly correspond to different phases (Figure 1.10), however the



information obtained from this SE signal is merely qualitatively and cannot provide further

information other than imaging. As secondary electrons are generated through inelastic interactions

and their interaction volume is in the order of a few hundreds of nanometers (50 to 500 Ǻ) into the

surface; only basic information of the topography is to be collected from this type of signal.

The interaction or excitation volume of electrons is hemispherical jug-shaped with neck of

jug at the specimens surface and is directly proportional on the accelerating voltage and inversely

proportional to material’s density. Electron penetration generally ranges from 1-5 µm with the

beam incident perpendicular to the sample. Thus for phases having high density the interaction

volume is lower. As the accelerating voltage increases, then the interaction volume (given by x and

y) increases according to the relations given by equations 1 and 2 [5

ρµ

5.11.0)( oEmx =

].

Equation 1

ρµ

5.1077.0)( oEmy = Equation 2

Where Eo is the accelerating voltage (keV) and ρ is the material’s density. Of course, the

interaction volume for SE signal has to be extracted from the total volume of interaction. For

example, bombarding a material with density of 2.7 g/cm3

(assuming an aluminium alloy) and

accelerating voltage of 20 kV (this experiment) the total penetration of electrons (in other words

volume of interaction) gives:

x = 3.3125 µm and y = 2.55 µm

The depth of electron penetration of an electron beam is also a function of its angle of

incidence, the magnitude of its current and the average atomic number.

Moreover, the main reason for coating a non-conductive specimen (such a conductive

sample mounted in bakelite) with a conductive material (such as gold) is to increase the number of

secondary electrons that will be emitted from the sample.



Figure 1.10 Secondary electrons (SE) image sampling

Backscattered Electrons

Figura 1.11 shows a SEM micrograph obtained by means of backscattered electrons (BS)

signal. Careful observations on this image clearly revealed three distinct regions (well contrasted)

identified as: dark, grey and white colored. Therefore, this metal resulted in three distinct phases as

identified by the difference on image contrast. The identified phases were labeled as “a”, “b” and “c”

as indicated in Figura 1.11. Black areas (indicated by the arrows) correspond apparently to gaps

within the material possibly due to the etching, in this work EDS analysis was not conducted in

those areas.

Backscattered electrons are produced by elastic interactions of beam electrons with nuclei

of atoms in the specimen. Many incident electrons undergo a series of such elastic event that cause

them to scattered back out the specimen. The fraction of the beam electrons backscattered in this

way varies strongly with the atomic number Z of the scattering atoms, but does not change much



with changes in Eo. The backscattered coefficient, which is the number of produced backscattered

electrons, is given by equation 3 [6

pe

bs

ηηη =

]:

Equation 3

where ηpe is the number of incident electrons and ηbs

3724 103.81086.1016.00254.0 ZxZxZ −− +−+−=η

is the number of backscattered

electrons. For a pure element, the backscattered coefficient, depend on Z, can be calculated by:

Equation 4

For homogeneous mixtures ηmix

∑=i

iimix Cηη

is calculated from the weight fractions of elemental

components by:

In summary, dark phase correspond to the lowest atomic number (Z) phase in this alloy.

Grey and lighter regions correspond to higher Z numbers. Basically as all phases (elements) have

different size nuclei, as the size of the atom nuclei increases, the number of BSE increases.

Figura 1.11 Backscattered electrons (BS) image sampling

1.2.2.5 Volume of Excitation

Two factors limit the size and shape of the interaction volume: (1) energy loss through

inelastic interactions and (2) electron loss or backscattering through elastic interactions. The

resulting excitation volume is a hemispherical to jug-shaped region with the neck of jug at the



specimen surface. The analyst must remember that the interaction volume penetrates a significant

depth into the sample and avoid edges where it may penetrate overlapping materials. The depth of

electron penetration of an electron beam and the volume of sample with which it interacts are a

function of its angle of incidence, the magnitude of its current, the accelerating voltage, and the

average atomic number (Z) of the sample. Of these, accelerating voltage and density play the largest

roles in determining the depth of electron interaction (Figura 1.12).

Figura 1.12 Schematic depiction of the variation of interaction volume shape with average sample atomic number (Z) and electron beam accelerating voltage (Eo

). The actual shape of the interaction volume is not as long-necked since the electron beam in microprobe analysis has a diameter of about 1 µm (see Figure 2.1b).

Electron penetration generally ranges from 1-5 µm with the beam incident perpendicular to

the sample. The depth of electron penetration is approximately (Potts, 1987, p. 336):

For example, bombarding a material with a density of 2.5 g/cm3, about the minimum

density for silicate minerals, with Eo = 15 keV, gives x = 2.3 µm. The width of the excited volume

can be approximated by (Potts, 1987, p. 337):



Both of these are empirical expressions. A theoretical expression for the "range" of an

electron, the straight line distance between where an electron enters and its final resting place, for a

given Eo

is (Kanaya & Okayama, 1972):

The volume of interaction can be modeled by Monte Carlo simulation. In such models, the

likelihood of incident electrons interacting with the sample and scattering and the angle of

deflection are determined probabilistically. X-ray generation depths depend strongly on density and

accelerating voltage (Figure 2.2b.). The results derived from Monte Carlo modeling yield a volume

of interaction that is very similar to that determined by etching experiments. The excited volume is

roughly spherical and truncated by the specimen surface. The depth of the center of the sphere

decreases with increasing atomic number of the target [7

].



Figura 1.13 Comparison of electron paths (top) and sites of X-ray excitation (bottom) in targets of aluminum, copper, and gold at 20 keV, simulated in a Monte Carlo procedure.

1.2.3 Microscopía Electrónica de Transmisión (Transmission Electron Microscopy)

1.2.3.1 Introduction

A typical commercial transmission electron microscope (TEM) costs about $2 for each

electron volt of energy in the beam, and if you add on all the options, it can cost about $4-5 per eV.

As you'll see, we use beam energies in the range from 100,000-400,000 eV, so a TEM becomes an

extremely expensive piece of equipment. Consequently, there have to be very sound scientific

reasons for investing such a large amount of money in one microscope [8

Transmission electron microscopy (TEM) is the pre-eminent method for determining

dislocations and other crystallographic defects character and for performing chemical and

crystallographic analysis of micrometer and smaller precipitates and other microstructures. Use of

TEM in materials science/engineering can be introduced here in only a few additional pages and is

well worth the small increment of effort. Since most defect characterization requires an

understanding of diffraction contrast, this is an important constituent of this chapter. A TEM

equipment is shown in

].

Figura 1.14.

Figura 1.14 A transmission electron microscope Philips CM-12



1.2.3.2 Depth of field

The depth of field of a microscope is a measure of how much of the object we are looking at

remains "in focus" at the same time. Like the resolution, this property is governed by the lenses in

the microscope. The best electron lens is not a very good one, as we've already mentioned, and has

been compared to using the bottom of a Coca-Cola bottle as a lens for light microscopy. To

minimize this problem we have to use very small limiting apertures in the lenses, narrowing the

beam down to a thin "pencil" of electrons which at most is a few micrometers across. These

apertures cut down the intensity of the electron beam, but also act to increase the depth of focus of

the images that we produce. Remember that "depth of field" refers to the specimen while "depth of

focus" refers to the image.

While this large depth of field is chiefly used in the SEM to produce 3D-like images of the

surfaces of specimens with large changes in topography, it is also critical in the TEM. It turns out

that in the TEM, all of the specimen is usually in focus at the same time, independent of the

specimen topography, as long as it's electron transparent!

Figura 1.15 shows a TEM image of some dislocations in a crystal. The dislocations appear

to start and finish in the specimen, but in fact they are threading their way through the specimen

from the top to the bottom, and they remain in sharp focus at all times. Furthermore, we can record

the final image at different positions below the final lens of the instrument and it will still be in

focus.

Figura 1.15 TEM image of dislocations in GaAs (Gallium arsenide). A band of dislocations threads through the thin specimen from the top to the bottom but remains in focus through the foil thickness.



1.2.3.3 Diffraction

Thompson and Reid showed that electrons could be diffracted when passing through thin

crystals of nickel, and the possibility of combining electron diffraction into TEMs was realized by

Kossel and Móllenstedt (1939). Today, electron diffraction is an indispensable part of TEM and is

arguably the most useful aspect of TEM for materials scientists. Figura 1.16 shows a TEM

diffraction pattern which contains information on the crystal structure, lattice repeat distance, and

specimen shape, as well as being a most striking pattern. We'll see that the pattern can always be

related to the image of the area of the specimen from which it came, in this case shown in the inset.

You will also see in Part II that, in addition to the things we just listed, you can conduct a complete

crystallographic symmetry analysis of minuscule crystals, including such esoteric aspects as point-

group and space-group determination, and at all times the crystallography can be related to the

image of your specimen. There is no similar capability on a light microscope because of the

relatively large wavelength of visible light.

So an electron microscope can produce atomic level images, can generate a variety of

signals telling you about your sample chemistry and crystallography, and you can always produce

images that are in focus. There are many other good reasons why you should use electron

microscopes. We hope they will become evident as you read through this book. At the same time

there are many reasons why you should not always seek to solve your problems with the TEM, and

it is most important that you realize what the instrument cannot do, as well as knowing its

capabilities [8].



Figura 1.16 TEM diffraction pattern from a thin foil of Al-Li-Cu containing various precipitate phases, shown in the inset image. The central spot (X) contains electrons that come directly through the foil and the other spots and lines are diffracted electrons which are scattered from different crystal planes.

1.2.3.4 Interpreting TEM images

Another problem is that the TEM presents us with 2D images of 3D specimens, viewed in

transmission. Our eyes and brain routinely understand reflected light images but are ill-equipped to

interpret TEM images, and so we must be cautious. Hayes (1980) illustrates this problem well by

showing a picture of two rhinos, side by side such that the head of one appears attached to the rear

of the other (see Figure 1.17). As Hayes puts it: "when we see this image we laugh" (because we

understand its true nature in 3D) "but when we see equivalent (but more misleading) images in the

TEM, we publish!" So beware of artifacts, which abound in TEM images.

Figure 1.17 Photograph of two rhinos taken so that, in projection, they appear as one two-headed beast. Such projection artifacts in reflected light images are easily discernible to the human eye but similar artifacts in TEM images are easily mistaken for "real" features.



One aspect of this particular drawback is that, generally, all the TEM information that we

talk about in this book (images, diffraction patterns, spectra) is averaged through the thickness of

the specimen. In other words, a single TEM image has no depth sensitivity, as is apparent.

1.2.3.5 Specimen Preparation

All the above advantages of the TEM bring accompanying drawbacks. First of all, the price

to pay for any high-resolution imaging technique is that you only look at a small part of your

specimen at any one time. The higher the resolution, therefore, the worse the sampling abilities of

the instrument. We have an instrument that is a terrible sampling tool! This only serves to

emphasize that before you put your specimen in the TEM you must have examined it with

techniques that offer poorer resolution but better sampling, such as your eyes, the visible-light

microscope, and the scanning electron microscope. In other words, know the forest before you start

looking at the leaves on the trees.

Your specimens have to be thin if you're going to get any information using transmitted

electrons in the TEM. "Thin" is a relative term, but in this context it means "electron transparent."

For a specimen to be transparent to electrons it must be thin enough to transmit sufficient electrons

such that enough intensity falls on the screen or photographic film to give us an interpretable image

in a reasonable time. Generally this requirement is a function of the electron energy and the average

atomic number of the specimen. Typically for 100-keV electrons, specimens of aluminum alloys

almost up to 1 pm would be thin, while steel would be thin up to about several hundred nm.

However, it is an axiom in TEM that thinner is better, and specimens below 100 nm should be used

wherever possible, and in extreme cases, such as when doing HRTEM or electron spectrometry,

specimen thicknesses <50 nm are essential. These demands become less strict as the beam voltage

increases, but this is offset by the danger of beam damage.

So it should be obvious to you by now that while TEM and associated techniques are

tremendously powerful characterization tools when used properly, they should never be used in

isolation to solve a materials problem. You must understand your material at low magnification

with your eyes and with visible-light microscopy and scanning electron microscopy (SEM) before

venturing into TEM studies. Otherwise you may fall foul of some of the limitations we have just

listed [8].



1.3 Análisis de XRD (X-Ray Diffraction)

1.3.1 Electromagnetic radiation

Discovered in 1885, these rays are invisible and travel in straight lines and more penetrating

than visible light.

What are x-rays?

X-rays are electromagnetic radiation which is exactly the same nature of visible light but of

very much shorter wavelength.

Wavelengths: X-rays – 0.5 to 2.5 Ǻ, visible light (V.L.) - 6000 Ǻ

X-rays are associated with and electric field E in the “y” direction and a magnetic field H in

the “z” direction.

Figure 1.18 Electric and magnetic fields associated with a wave moving in the x-direction

A – amplitude, ν – frequency

The variation of E is not sinusoidal but it matters little, the important issue is its periodicity.

Figura 1.19 shows the variation of E graphically



Figura 1.19 The variation of E, (a) with t at a fixed value of x and (b) with x at a fixed value of t

the wavelength and the frequency are connected by the relation

where c is the velocity of light of 3x108

m/s

What is the intensity?

Intensity is a flow of energy through unit area perpendicular to the direction of motion of

the wave.

The average value of the intensity is proportional to the square of the amplitude on the wave.

In absolute units intensity is measured in joules/m2

/sec but this measurement is difficult one. Most

x-rays intensity measurements are made by counting the number of photons incident on a detector.

Classical theory: electromagnetic radiation has been considered wave motion.

Quantum theory: electromagnetic radiation is considered can also been considered as a

stream of particles called quanta or photons.

Each photon is associated with it an amount of energy of hν where h is Planks constant

(6.63x10-34

joule*sec)

Radiation has thus a dual wave-particle character.

1.3.2 Production of X-Rays

How are x-rays produced?



X-rays are produced when an electrical charged particle (electron) of sufficient kinetic

energy decelerates. Electrons are being produced in an x-rays tube by maintaining a high voltage

across the electrodes drawing the electrons to the anode or target.

The kinetic energy of electrons on impact is given by

where e is the charge on the electron (1.6x10-19 coulombs) and V is the voltage across the

electrodes; m (9.11x10-31 kg) is the mass of the electron and υ2

is the velocity in m/sec just before

impact.

X-rays coming from the target are found to consist of a mixture of different wavelengths

and the variation of intensity with wavelength depends on the tube voltage (i.e.30,000V).

Since x-rays are produced whenever high-speed electrons collide with a metal target. Any

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 alwavs watercooled to prevent its melting.

A1l x-ray tubes contain two electrodes, an anode (the metal target) maintained, with few

exceptions, at ground potential, and 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 (obsolete), in which electrons

are produced by the ionization of a small quantity of gas (residual air in a partly evacuated tube),

and filament tubes, in which the source of electrons is a hot filament.

Filament tubes 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. Figure 1.20 is a photograph of such a tube, and Figure 1.21 shows its

internal construction.



Figure 1.20 Sealed x-ray tube.

Figure 1.21 Cross section of sealed x-ray tube (schematic)

1.3.3 X-Ray Diffraction

Differences in the path length of various rays arise quite naturally when considering how a

crystal diffracts x-rays. Figura 1.22 shows a section of a crystal, its atoms arranged on a set of

parallel planes A, B, C, D, ... , normal to the plane of the drawing and spaced a distance d' apart.

Assume that a beam of perfectly parallel, perfectly monochromatic x-rays of wavelength λ is

incident on this crystal at an angle θ, called the Bragg angle, where θ is measured between the

incident beam and the particular crystal planes under consideration.



Figura 1.22 Diffraction of x-rays by a crystal.

Whether this incident beam of x-rays will be diffracted by the crystal and, if so, under what

conditions, are the questions central to this chapter. A diffracted beam may be defined as a beam

composed of a large number of scattered rays mutually reinforcing one another. Diffraction is,

therefore, essentially a scattering phenomenon.

Atoms scatter incident x-rays in all directions and the following paragraphs demonstrate

that in some of these directions the scattered beams will be completely in phase and so reinforce

each other to form diffracted beams.

For the particular conditions described by Figura 1.22, the only diffracted beam formed is

that shown, namely one making an exit angle θ with respect to the diffraction planes equal to the

angle θ of incidence. This will be shown, first, for one plane of atoms and, second, for all the atoms

making up the crystal. Consider rays 1 and la in the incident beam; they strike atoms K and P in the

first plane of atoms and are scattered in all directions. Only in the directions 1 and 1a, however, are

these scattered beams completely in phase and so capable of reinforcing one another; they do so

because the difference in their length of path between the wave fronts XX' and YY' is equal to:

Similarly, the rays scattered by all the atoms in the first plane in a direction parallel to 1' are

in phase and add their contributions to the diffracted beam. This will be true of al1 the planes

separately, and it remains to find the condition for reinforcement of rays scattered by atoms in

different planes. Rays 1 and 2, for example, are scattered by atoms K and L, and the path difference

for rays 1K1' and 2L2' is:



This is also the path difference for the overlapping rays scattered by S and P in the direction

shown, since in this direction there is no path difference between rays scattered by S and L or P and

K. Scattered rays 1' and 2' will be completely in phase if this path difference is equal to a whole

number n of wavelengths, or if:

This relation was first formulated by W. L. Bragg and is known as Bragg's law. It states the

essential condition which must be met if diffraction is to occur, n is called the order of diffraction; it

may take on any integral value consistent with sinθ not exceeding unity and is equal to the number

of wavelengths in the path difference between rays scattered by adjacent planes.

The rays scattered by all the atoms in all the planes are therefore completely in phase and

reinforce one another (constructive interference) to form a diffracted beam in the direction shown.

In all other directions of space the scattered beams are out of phase and annul one another

(destructive interference). The diffracted beam is rather strong compared to the sum of all the rays

scattered in the same direction, simply because of the reinforcement which occurs, but is extremely

weak compared to the incident beam since the atoms of a crystal scatter only a small fraction of the

energy incident on them [9

1.3.4 Diffractometers

].

Depending solely on the way it is used, the basic x-ray diffractometer/spectrometer is really

two instruments:

1. An instrument for measuring x-ray spectra by means of a crystal of known structure.

2. An instrument for studying crystalline (and noncrystalline) materials by measurements of

the way in which they diffract (scatter) x-rays of known wavelength.

The term spectrometer was originally used to describe both instruments, but, properly, it

should be applied only to the first. The second instrument is aptly called a diffractometer: this name

serves well to emphasize the particular use to which the instrument is being put, namely, diffraction

analysis rather than spectrometry. An example of a diffractometer is shown in Figure 1.23.



Figure 1.23 Diffractometer

1.3.5 Applications of X-Ray Diffraction

In general the following applications can be found in a diffraction technique:

Phase identification

Determination of crystal structure

Phase diagram determination

Quantitative phase analysis

Precise parameter measurements

Structure of polycrystalline aggregates

Stress measurement

Orientation of single crystals

Crystal quality

Polymers

Small Angle scattering

1.4 Ensayos o pruebas no destructivas (non-destructive testing)

1.4.1 Líquidos Penetrantes

1.4.1.1 Introducción a los Líquidos Penetrantes

Discontinuidades que detecta, defectos superficiales como: poros, grietas, rechupes,

traslapes, costuras, laminaciones, etc. Materiales: Sólidos metálicos y no metálicos



VENTAJAS

Muy económico

Inspección a simple vista

No se destruye la pieza

Se obtiene resultados inmediatos.

DESVENTAJAS

Solo detecta fallas superficiales

Difícil establecimiento de patrones

La superficie a inspeccionar debe estar limpia y sin recubrimientos

No se puede inspeccionar materiales demasiado porosos

PRINCIPIOS FÍSICOS

Capilaridad: Es la acción que origina que un liquido ascienda o descienda a través de los

llamados tubos capilares.

Cohesión: Es la fuerza que mantiene a las moléculas de un cuerpo a distancias cercanas

unas de las otras.

Adherencia: Es la fuerza de atracción entre moléculas de sustancias diferentes.

Viscosidad: Es la resistencia al deslizamiento de una capa de un fluido sobre otra capa.

Tensión superficial: Es la fuerza no compensada que ejerce la superficie del líquido debido

a la tensión no compensada de las moléculas subsuperficiales sobre la membrana superior.

1.4.1.2 Características de los líquidos penetrantes

El líquido penetrante tiene la propiedad de penetrar en cualquier abertura u orificio en la

superficie del material. El penetrante ideal debe reunir lo siguiente:

Habilidad para penetrar orificios y aberturas muy pequeñas y estrechas.

Habilidad de permanecer en aberturas amplias.

Habilidad de mantener color o la fluorescencia.

Habilidad de extenderse en capas muy finas.

Resistencia a la evaporación.

De fácil remoción de la superficie.

http://ads.us.e-planning.net/ei/3/29e9/cfa010f10016a577?rnd=0.31005266569164846&pb=4872c43102fb1b28&fi=5f00699999ad0063�

http://ads.us.e-planning.net/ei/3/29e9/cfa010f10016a577?rnd=0.31005266569164846&pb=03bbcdf5e897b9ef&fi=5f00699999ad0063�

http://ads.us.e-planning.net/ei/3/29e9/cfa010f10016a577?rnd=0.31005266569164846&pb=c13e0006711eed2c&fi=5f00699999ad0063�

http://www.monografias.com/trabajos14/propiedadmateriales/propiedadmateriales.shtml�

http://www.monografias.com/trabajos35/categoria-accion/categoria-accion.shtml�

http://ads.us.e-planning.net/ei/3/29e9/cfa010f10016a577?rnd=0.31005266569164846&pb=fd8dd6218a8d0466&fi=5f00699999ad0063�

http://www.monografias.com/trabajos12/eleynewt/eleynewt.shtml�

http://ads.us.e-planning.net/ei/3/29e9/cfa010f10016a577?rnd=0.31005266569164846&pb=90e928f172004cc7&fi=5f00699999ad0063�

http://www.monografias.com/trabajos10/restat/restat.shtml�

http://ads.us.e-planning.net/ei/3/29e9/cfa010f10016a577?rnd=0.31005266569164846&pb=b1d4639afce2c182&fi=5f00699999ad0063�

http://www.monografias.com/trabajos16/romano-limitaciones/romano-limitaciones.shtml�

http://www.monografias.com/trabajos5/colarq/colarq.shtml�



De difícil eliminación una vez dentro de la discontinuidad.

De fácil absorción de la discontinuidad.

Atoxico.

Inoloro.

No corrosivo.

Antiinflamable.

Estable bajo condiciones de almacenamiento.

Costo razonable.

Propiedad

física

Penetrante Revelador

Capilarida

d

Alta Baja

Tensión

superficial

Baja Alta

Adherenci

a

Baja Alta

Cohesión Baja Alta

Viscosidad Baja Alta

Partículas Pequeñas Grandes

Tensión superficial: Es una de las propiedades más importantes. Se requiere una tensión

superficial baja para obtener buenas propiedades de penetración y mojado

Poder humectante: El penetrador debe ser capaz de mojar completamente la superficie del

material y es una de las propiedades más importantes. Esto se refiere al ángulo de contacto del

líquido con la superficie, el cual debe ser lo mas bajo posible.

Viscosidad: Esta propiedad no produce efecto alguno en la habilidad del líquido para

penetrar, aunque afecta la velocidad de penetración. Los penetrantes de alta viscosidad penetran

lentamente, en tanto que los de baja viscosidades escurren muy rápido y tiene la tendencia a no ser

retenidos en los defectos de poca profundidad; por lo tanto se recomienda una viscosidad media.

http://www.monografias.com/trabajos12/dispalm/dispalm.shtml�

http://www.monografias.com/trabajos13/cinemat/cinemat2.shtml#TEORICO�

http://www.monografias.com/trabajos13/visco/visco.shtml�



Volatilidad: Los líquidos penetrantes no deben ser volátiles. Si existe una evaporación

excesiva se los productos del penetrante, se verá afectada la sensibilidad de todo el proceso, debido

tanto al desequilibrio de la formula, como a la perdida del poder humectante.

Gravedad especifica o densidad relativa: No juega un papel directo sobre

el comportamiento de un penetrante dado; sin embargo, con densidades bajas se facilita

el transporte de materiales extraños que tenderán a sedimentar en el fondo cuando se usan tanques

abiertos. La mayoría de los líquidos penetrantes tienen densidades relativas que varían entre 0.86 y

1.06 a 16°C, por lo general la densidad es menor a 1.

Punto de inflamación: Como medida de seguridad practica los líquidos penetrantes deberán

poseer un punto de inflamación elevado con el fin de reducir los peligros de incendio. Generalmente

el punto de inflamación es mayor de 95 °C y en recipientes abiertos no debe ser menor de 65 °C.

Inactividad química: Los productos usados en la formulación de los líquidos penetrantes

deben se inertes y no corrosivos con respecto a los materiales a ser ensayados y a los recipientes que

los contienen.

Capacidad de disolución: El penetrante debe tener una elevada capacidad para contener

grandes concentraciones de pigmentos coloreados o fluorescentes usados y mantenerlos en solución.

1.4.1.3 Método de aplicación de los líquidos penetrantes en Pruebas No Destructivas

Se aplica el líquido penetrante a la superficie de la pieza a ser examinada, permitiendo que

penetre en las aberturas del material, después de lo cual el exceso del líquido es removido. Se aplica

entonces el revelador, el cual es humedecido o afectado por el penetrante atrapado en las

discontinuidades de esta manera se incrementa la evidencia de las discontinuidades, tal que puedan

ser vistas ya sea directamente o por medio de una lámpara o luz negra.

Tipo I = Penetrante fluorescente

Tipo II = Tintas permanentes o visibles

Proceso A = Penetrante lavable en agua

Proceso B = Penetrante postemulsificado

Proceso C = Penetrante removido con solvente

Revelador seco: Grano fino se aplica por espolvoreado, rociado o sumergido.

Revelador no acuoso: Es una suspensión absorbente, aplicado por rocío

Revelador húmedo: Es una suspensión absorbente de polvo en agua, se aplica por inmersión.

Portátil ( atomizador )

Estacionario ( inmersión )

http://www.monografias.com/trabajos12/elproduc/elproduc.shtml�

http://www.monografias.com/trabajos14/administ-procesos/administ-procesos.shtml#PROCE�

http://www.monografias.com/trabajos35/el-poder/el-poder.shtml�

http://www.monografias.com/trabajos5/estat/estat.shtml�

http://www.monografias.com/trabajos16/comportamiento-humano/comportamiento-humano.shtml�

http://www.monografias.com/trabajos/transporte/transporte.shtml�

http://www.monografias.com/trabajos36/inflamacion/inflamacion.shtml�

http://www.monografias.com/trabajos/seguinfo/seguinfo.shtml�

http://www.monografias.com/Quimica/index.shtml�

http://www.monografias.com/trabajos12/romandos/romandos.shtml#PRUEBAS�

http://www.monografias.com/trabajos5/natlu/natlu.shtml�

http://www.monografias.com/trabajos14/problemadelagua/problemadelagua.shtml�



Simple vista Spoteheck (portátil)

Luz negra Syglo (estacionario)

Portátil Estacionario

Liquido

penetrante

Rojo Verde

(fluorescente)

Removedor Incoloro Incoloro

Revelador Blanco Blanco

PREPARACIÓN Y LIMPIEZA DE LA PIEZA:

Limpiar cuidadosamente la superficie a inspeccionar de pintura, aceite, grasa y otros

contaminantes. Será necesario eliminar los restos de óxidos, pinturas, grasas, aceites, taladrillas,

carbonillas, etc. Y esto se hace por métodos químicos, ya que los mecánicos, están prohibidos por la

posibilidad que tiene su aplicación de tapar defectos existentes.

Se pueden usar todos aquellos procesos que dejen a la superficie limpia y seca; que no

dañen al espécimen y que no empleen productos que sean incompatibles con los componentes.

Soluciones detergentes en caliente por inmersión, desengrase en fase de vapor o desengrase

mediante disolvente, son los principales métodos para eliminar grasas y aceites. Los óxidos y las

carbonillas térmicas se eliminaran con desoxidantes alcalinos o ácidos y a veces, principalmente en

superficies rectificadas se hace un ataque ácido a fondo que abre las grietas durante la operación.

Las pinturas se eliminan con productos cáusticos en caliente o basados en ellos.

APLICACIÓN DEL PENETRANTE.

Los penetrantes se aplican por inmersión, rociado con un cepillo o brocha, vertiendo el

liquido sobre la pieza o cualquier otro método, vertiendo el liquido sobre la pieza o cualquier otro

método que cubra la zona que se inspecciona.

Será necesario obtener una película fina uniforme en toda la superficie y se deberá esperar

un tiempo llamado tiempo de penetración para que el liquido penetre en grietas. Este tiempo oscila

entre los 5 y 15 minutos dependiendo del material y la clase de grietas.

ELIMINACIÓN DEL EXCESO DE PENETRANTE.

Se debe retirar la capa superficial del penetrante de forma que lo único que permanezca sea

el que se hubiera alojado en las discontinuidades.

Se entiende por exceso de penetrante todo liquido que no se ha introducido en los defectos y

que permanece sobrante sobre la superficie de la pieza a inspeccionar.

http://www.monografias.com/trabajos13/histarte/histarte.shtml�

http://www.monografias.com/trabajos35/obtencion-aceite/obtencion-aceite.shtml�

http://www.monografias.com/trabajos28/grasas-en-la-alimentaciom/grasas-en-la-alimentaciom.shtml�

http://www.monografias.com/trabajos11/metods/metods.shtml�

http://www.monografias.com/trabajos14/administ-procesos/administ-procesos.shtml#PROCE�

http://www.monografias.com/trabajos5/aciba/aciba.shtml�

http://www.monografias.com/trabajos11/metods/metods.shtml�

http://www.monografias.com/trabajos901/evolucion-historica-concepciones-tiempo/evolucion-historica-concepciones-tiempo.shtml�

http://www.monografias.com/trabajos901/debate-multicultural-etnia-clase-nacion/debate-multicultural-etnia-clase-nacion.shtml�



Esta etapa es critica y de su correcta realización dependerá el resultado final de la

inspección, ya que es necesario eliminar y limpiar el exceso de penetrante de tal modo que no

extraigamos el penetrante introducido en los defectos. Si no se ha eliminado perfectamente el

liquido penetrante, en la inspección final aparecerán manchas de penetrante produciendo

indicaciones falsas e incluso, el enmascaramiento de las grietas. Para saber si hemos eliminado bien

el exceso de penetrante es necesario hacer una inspección visual. Es aconsejable quitar en primer

lugar la mayor parte del penetrante con trapos o papel absorbente y después eliminar el resto

utilizando trapos o papel ligeramente impregnados en disolvente.

APLICACIÓN DEL REVELADOR.

Aplicar el revelador y dejarlo actuar.

El revelado es la operación que hace visible al ojo humano la posición del defecto. El

revelador es básicamente un producto en polvo de compuestos químicos blancos, inertes y con una

granulometría tal que dispone de un gran poder de absorción. Una vez aplicado el revelador, hay

que esperar un tiempo para que absorba el penetrante, este tiempo oscila entre 5 y 15 minutos.

Durante la preparación de las piezas para la inspección es necesario secarlas después de la

aplicación del revelador húmedo o eliminar el remanente antes del uso del polvo revelador seco.

INSPECCIÓN FINAL DE LA PIEZA.

Una vez transcurrido el tiempo de revelado, se procede a la inspección de los posibles

defectos de las piezas procesadas.

El tiempo de revelado depende del tipo de penetración, del revelador y del defecto, pero

deberá permitirse tiempo suficiente para que se formen las indicaciones. La inspección se realiza

antes de que el penetrante comience a exudar sobre el revelador hasta el punto de ocasionar la

perdida de definición.

El proceso de inspección se compone de tres etapas.

Inspección.

Interpretación.

Una regla práctica es que el tiempo de revelado nunca debe ser menor a siete minutos.

Indicaciones relevantes. Son las causadas por discontinuidades que están generalmente

presentes en el diseño.

Indicaciones falsas. Son el resultado de alguna forma de contaminación con penetrantes,

estas indicaciones no pueden referirse a ningún tipo de discontinuidad.

http://www.monografias.com/trabajos12/elproduc/elproduc.shtml�

http://www.monografias.com/trabajos37/interpretacion/interpretacion.shtml�

http://www.monografias.com/trabajos13/diseprod/diseprod.shtml�

http://www.monografias.com/trabajos10/contam/contam.shtml�



LIMPIEZA FINAL.

Se debe llevar a cabo en razón de los productos usados en el ensayo.

Tiempo de Penetración

Material Proceso Tipo de

discontinuidad

Tipo I Y II

Proceso A

Tipo I Y II

Proceso B

Tipo I Y II

Proceso C

Aluminio

Fundición

Extrusión y forja

Soldadura

Todos

Todos

Porosidades

Traslapes

Falta de fusión

Porosidades

Grietas

Grietas de fatiga

5 a 10 min

NR

30

30

30

NR

5 min

10

5

5

10

30

3 min

7

3

3

5

5

Magnesio

Fundición

Extrusión y forja

Soldadura

Todos

Porosidades

Traslapes

Falta de fusión

Porosidades

Grietas

Grietas de fatiga

15

NR

30

30

30

NR

5

10

10

10

10

30

3

7

5

5

5

7

Acero

Fundición

Extrusión y forja

Soldadura

Todos

Todos

Porosidades

Traslapes

Falta de fusión

Porosidades

Grietas

Grietas de fatiga

30

NR

60

60

30

NR

10

10

10

10

10

30

5

7

7

7

7

10

Latón y bronce

Fundición

Extrusión y forja

Recubrimientos

Porosidades

Traslapes

Falta de fusión

10

NR

15

5

10

10

3

7

3

http://www.monografias.com/trabajos14/nociones-basicas/nociones-basicas.shtml�



Todos Porosidades

Grietas

15

30

10

10

3

3

Plásticos Todos Grietas 5 a 30 5 5

Vidrio Todos Grietas 5 a 30 5 5

Herramienta con

punta de carburo

Falta de fusión

Porosidades

Grietas

30

30

30

5

5

20

3

3

5

Titanio y

aleacionesa altas

temperaturas

Todos NR 20 a 30 15

Todos

metales

Todos Esfuerzos o

Granulación

Interna

NR 240 240

NR = no recomendable

Guía de Selección del proceso

PROBLEMA PROCESO

TIPO I Y II

OBSERVACIONES

Alta producción de artículos

pequeños

A Pequeñas cantidades mojadas en

canastas

Alta producción de artículos

grandes

B Grandes forjas, extrusiones, etc.

Alta sensibilidad para

discontinuidades finas

B Indicaciones mas claras y mas

brillantes

Discontinuidades superficiales,

rayones, etc. Deben detectarse

B Puede controlarse la profundidad

de emulsificación.

Artículos con rugosidad

superficial

A

Artículos con cuerdas y cuñeros. A El penetrante podría fijarse en las

esquinas.

http://www.monografias.com/trabajos15/biocorrosion/biocorrosion.shtml�

http://www.monografias.com/trabajos5/selpe/selpe.shtml�

http://www.monografias.com/trabajos54/produccion-sistema-economico/produccion-sistema-economico.shtml�



Artículos con rugosidad

superficial media

A – B La elección depende de los

requerimientos de producción y

sensibilidad.

Prueba por puntos. C

Se necesita equipo portátil. C

No se dispone de agua y

electricidad

C

Artículos anodizados, agrietados

después del anodizado

C – B – A De preferencia el orden indicado

Repetir el proceso C Cinco a seis repeticiones podrían

ser el limite.

Detección de fugas A – B

CARACTERÍSTICAS DEL PENETRANTE FLUORESENTE

TIPO VENTAJAS DESVENTAJAS

LAVADO CON

AGUA

La fluorescencia asegura

visibilidad

Fácilmente lavable con agua.

Grandes cantidades de

especimenes pequeños.

Superficies rugosas.

Cuñeros y cuerdas.

Amplio rango de

discontinuidades.

Rápido.

Proceso sencillo.

Requiere luz negra y áreas

obscuras.

No es seguro en la detección de

rayones y fallas superficiales.

No es seguro volver a probar.

No es seguro en superficies

anodizadas.

Ácidos y cromatos afectan la

sensibilidad.

Fácilmente sobre lavado.

El penetrante esta expuesto a

la contaminación del agua.


visibilidad.


obscuras.

http://www.monografias.com/trabajos5/segu/segu.shtml�

http://www.monografias.com/trabajos/contamagua/contamagua.shtml�



POST

EMULSIFICADO

Alta sensibilidad para

discontinuidades muy finas.

Bueno para discontinuidades

superficiales.

Fácilmente lavable con agua

después de la emulsificación.

Tiempo de penetración corto.

No puede ser fácilmente sobre

lavado

Requiere mas paso.

Requiere equipo para la

aplicación de emulsivo.

Difícil remoción del penetrante

en cuerdas, cuñeros, agujeros

ciegos y superficies rugosas

REMOVIDO

CON

SOLVENTE


visibilidad

Portátil.

No requiere agua.

Bueno sobre piezas anodizadas.

Para verificación por puntos.

Las piezas pueden ser re

probadas


obscuras.

Material inflamable.

No puede usarse en tanques

abiertos.

Difícil su empleo sobre

superficies rugosas tales como

fundición de magnesio.

1.5 Ensayos mecánicos

Se propone asignar los siguientes porcentajes a los diferentes rubros para la

http://www.monografias.com/trabajos36/teoria-empleo/teoria-empleo.shtml�



1.6 Referencias

[1] Avner, Sydney H., Introducción a la Metalurgia Física, McGraw Hill. (1988).

[2] R. E. Smallman, A.H.W. Ngan, Physical Metallurgy and Advanced Materials, seventh edition, Ed. Butterworth-Heinemann (2007).

[3] http://science.howstuffworks.com/scanning-electron-microscope.htm

[4] http://science.howstuffworks.com/scanning-electron-microscope2.htm

[5] http://www4.nau.edu/microanalysis/microprobe/interact-volume.html

[6] http://www.concrete.cv.ic.ac.uk/durability/research%20techniques%20sem.htm

[7] http://www4.nau.edu/microanalysis/Microprobe/Interact-Volume.html

[8] David B. Williams, C. Barry Carter, Transmission Electron Microscopy – Basics I, Springer Science+Business Media Inc., 1996

[9] B.D. Cullity, S.R. Stock, Elements of X-Ray Diffraction, Third Edition, Prentice Hall, 2001

http://science.howstuffworks.com/scanning-electron-microscope2.htm�

notas de metalurgia fisica - unidad 1 - 2012

Documents