AP 5301/8301 Instrumental Methods of Analysis and Laboratory Zhengkui XU Office: G6760 Tel:

Course Objectives Basic understanding of materials characterization techniques Physical basis – basic components and their functions Common modes of analysis Range of information provided by the techniques Recent development of the techniques Emphasis on applications Typical examples and case studies How to use different techniques to solve different problems in manufacturing and research

Microscopy and Related Techniques Light (optical) microscopy (LM) or (OM) Scanning electron microscopy (SEM) Energy dispersive X-ray spectroscopy (EDS) & Wavelength dispersive X-ray spectroscopy (WDS) X-ray diffraction (XRD)/X-ray fluorescence (XRF) Transmission electron microscopy (TEM) Surface Characterization Techniques Scanning probe microscopy (AFM & STM) Auger electron spectroscopy (AES) X-ray photoelectron spectroscopy (XPS) Secondary ion mass spectroscopy (SIMS) Rutherford backscattering spectroscopy (RBS)

Processing-structure-property Chemical composition Microstructure Processingstructureproperty Properties Intrinsic Materials Selection Ceramic Fabrication Crystal Structure ( ) (Characterization)

Effect of Microstructure on Mechanical Property  f  d -1/2 d-grain size 50m10m abab Mechanical test:  fa >  fb Mechanical property Microscopic analysis: d a < d b Microstructure OM images of two polycrystalline samples.

Scale and Characterization Techniques Microstructure ranging from crystal structure to Engine components (SiC) XRD,TEM,STM SEMOM Grain I Grain II atomic Valve Turbo charge 1

SiC turbine blades TEM image Grain 1 Grain 2 2nm Intergranular amorphous phase crack

Identification of Fracture Mode 4m4m Intergranular fracture 20m Intragranular fracture Cracks Pores Grain boundary

OM and SEM 50m 5m5m Growth step OM - 2D SEM – 3D BaTiO 3

High Resolution Z-contrast Imaging Atomic Ordering in Ba(Mg 1/3 Nb 2/3 )O 3 (STEM) [110]  IZ2Z2

STM - Seeing Atoms STM image showing single-atom defect in iodine adsorbate lattice on platinum. 2.5nm scan Iron on copper (111)

Optical Microscopy Introduction Lens formula, Image formation and Magnification Resolution and lens defects Basic components and their functions Common modes of analysis Specialized Microscopy Techniques Typical examples of applications

How Fine can You See? Can you see a sugar cube? The thickness of a sewing needle? The thickness of a piece of paper? … The resolution of human eyes is of the order of 0.1 mm. However, something vital to human beings are of sizes smaller than 0.1mm, e.g. our cells, bacteria, microstructural details of materials, etc.

Microstructural Features which Concern Us Grain size: from <m to the cm regime Grain shapes Precipitate size: mostly in the m regime Volume fractions and distributions of various phases Defects such as cracks and voids: <m to the cm regime …

Introduction- Optical Microscopy Use visible light as illumination source Has a resolution of ~o.2m Range of samples characterized - almost unlimited for solids and liquid crystals Usually nondestructive; sample preparation may involve material removal Main use – direct visual observation; preliminary observation for final charac- terization with applications in geology, medicine, materials research and engineering, industries, and etc. Cost - $15,000-$390,000 or more

Old and Modern Light Microscopes

Simple Microscope Low-power magnifying glasses and hand lenses 2x 4x10x

Refraction of Light Incident angle  1 Refracted angle  2 Normal N - Refractive index of material - Speed of light in vacuum - Velocity of light in material Materials N Air Water 1.33 Lucite 1.47 Immersion oil Glass 1.52 Zircon 1.92 Diamond 2.42  Sin 1 V 1 N 2 = Sin 2 V 2 N 1 Snell’s Law N  1 Light path bends at interface between two transparent media of Different indices of refraction (densities) air

Focusing Property of A Curved Surface In entering an optically more dense medium (N 2 >N 1 ), rays are bent toward the normal to the interface at the point of incidence. normal Curved (converging) glass surface F f N2N2 N1N1 F - focal pointf – focal length Focal plane Air

Curvature of Lens and Focal Length N2N2 N1N1 Normal N1N1 N2N2 F F f f The larger curvature angle The shorter focal length 11 22 1 > 21 > 2 Centerline of the lens Optical axis

Converging (Convex) Lens f The simplest magnifying lens f  curvature angle and lens materials (N) the larger N, the shorter f luciteglassdiamond N: Focal plane F f

Magnifier – A Converging Lens nearest distance of distinct vision ( NDDV ) retina I’ If o’-o’ is ~0.07mm,  o =0.016 o Ray diagram to show the principle of a single lens NDDV-ability to distin- guish as separate points which are ~0.07mm apart.  o - visual angle subtended at the eye by two points o’-o’ at NDDV. Magnification m = = I-I o”-o” I’-I’ o’-o’ m =  /  o o” oo  o 25cm h o -object distance Virtual image Real inverted image A B

1 1 1 _ = _ + _ f O i Lens Formula f -focal length (distance) O-distance of object from lens i -distance of image from lens I1I1 O i i O = momo Magnification by objective Lens formula and magnification Objective lens -Inverted image ff hoho hihi hihi hoho

Maximum Magnification of a Lens Angular magnification is maximum when virtual image is at “near point” of the eye, i.e. 25 cm (i = -25 cm) Using the lens formula, o = 25f/(25+f )  0  h/25and   h/o 1/f = 1/O + 1/i f in cm

Magnification when the Eyes are Relaxed The eyes can focus at points from infinity to the “near point” but is most relaxed while focus at infinity. When o = f, i =  For this case,  0  h/25 and   h/f 1/f = 1/O + 1/i

Limitations of a Single Lens From the formula, larger magnification requires smaller focal length The focal length of a lens with magnification 10 is approximately 2.5cm while that of a 100 lens is 2.5mm. Lens with such a short focal length (~2.5mm) is very difficult to make Must combine lenses to achieve high magnifications

Image Formation in Compound Microscope Object (O) placed just outside focal point of objective lens A real inverted (intermediate) image (I 1 ) forms at or close to focal point of eyepiece. The eyepiece produces a further magnified virtual inverted image (I 2 ). L – Optical tube length 25cm Compound microscope consists of two converging lenses, the objective and the eyepiece (ocular).

Magnification of Compound Microscope Magnification by the objective m 0 = -s’ 1 /s 1 Since s’ 1  L and s 1  f 0, therefore magnification of objective m o  L/f o Magnification of eyepiece m e = 25/f e (assuming the final image forms at  ) Overall magnification M = m o m e =

How Fine can You See with an Optical Microscope?  Magnification M = 25L/f o f e If we can make lenses with extremely short focal length, can we design an optical microscope for seeing atoms?  Can you tell the difference between magnification and resolution?  Imagine printing a JPEG file of resolution 320240 to a A4 size print!!

Empty Magnification Higher resolution Lower resolution

Diffraction of Light Sin=/d film 1 st 2 nd 3 rd Light waves interfere constructively and destructively.

Resolution of an Optical Microscope – Physical Limit  Owing to diffraction, the image of a point is no longer a point but an airy disc after passing through a lens with finite aperture!  The disc images (diffraction patterns) of two adjacent points may overlap if the two points are close together.  The two points can no longer be distinguished if the discs overlap too much

Resolution of Microscope – Rayleigh Criteria Rayleigh Criteria: Angular separation  of the two points is such that the central maximum of one image falls on the first diffraction minimum of the other  = m  1.22/d

Resolution of Microscope – Rayleigh Criteria Image 1 Image 2

Resolution of Microscope – in terms of Linear separation  To express the resolution in terms of a linear separation r, have to consider the Abbe’s theory  Path difference between the two beams passing the two slits is  Assuming that the two beams are just collected by the objective, then i =  and d min = /2sin I II III

Resolution of Microscope – Numerical Aperture  If the space between the specimen and the objective is filled with a medium of refractive index n, then wavelength in medium n = /n  The d min = /2n sin = /2(N.A.)  For circular aperture d min = 1.22/2(N.A.)=0.61/(N.A.) where N.A. = n sin is called numerical aperture Immersion oil n=1.515

NA of an objective is a measure of its ability to gather light and resolve fine specimen detail at a fixed object distance. NA = n(sin  ) n: refractive index of the imaging medium between the front lens of objective and specimen cover glass Numerical Aperture (NA)  Angular aperture One half of A-A NA=1 - theoretical maximum numerical aperture of a lens operating with air as the imaging medium (72 degrees)

Factors Affecting Resolution  Resolution = d min = 0.61/(N.A.)  Resolution improves (smaller d min ) if  or n or   Assuming that sin = 0.95 ( = 71.8°)  (The eye is more sensitive to blue than violet)

The smallest distance between two specimen points that can still be distinguished as two separate entities d min = 0.61/NA NA=nsin – illumination wavelength (light) NA – numerical aperture - one half of the objective angular aperture n-imaging medium refractive index d min ~ 0.3m for a midspectrum of 0.55m Resolution of a Microscope (lateral)

Optical Aberrations Spherical (geometrical) aberration – related to the spherical nature of the lens Chromatic aberration – arise from variations in the refractive indices of the wide range of frequencies in visible light Two primary causes of non-ideal lens action: Astigmatism, field curvature and comatic aberrations are easily corrected with proper lens fabrication. Reduce the resolution of microscope

Defects in Lens  Spherical Aberration – Peripheral rays and axial rays have different focal points (caused by spherical shape of the lens surfaces.  causes the image to appear hazy or blurred and slightly out of focus.  very important in terms of the resolution of the lens because it affects the coincident imaging of points along the optical axis and degrade the performance of the lens.

 Chromatic Aberration  Axial - Blue light is refracted to the greatest extent followed by green and red light, a phenomenon commonly referred to as dispersion  Lateral - chromatic difference of magnification: the blue image of a detail was slightly larger than the green image or the red image in white light, thus causing color ringing of specimen details at the outer regions of the field of view Defects in Lens A converging lens can be combined with a weaker diverging lens, so that the chromatic aberrations cancel for certain wavelengths: The combination – achromatic doublet

 Astigmatism - The off-axis image of a specimen point appears as a disc or blurred lines instead of a point.  Depending on the angle of the off-axis rays entering the lens, the line image may be oriented either tangentially or radially Defects in Lens o A

 Curvature of Field - When visible light is focused through a curved lens, the image plane produced by the lens will be curved  The image appears sharp and crisp either in the center or on the edges of the viewfield but not both Defects in Lens

 Coma - Comatic aberrations are similar to spherical aberrations, but they are mainly encountered with off- axis objects and are most severe when the microscope is out of alignment. Defects in Lens Coma causes the image of a non-axial point to be reproduced as an elongated comet shape, lying in a direction perpendicular to the optical axis.

Depth of focus (f mm) The distance above and below geometric image plane within which the image is in focus The axial range through which an object can be focused without any appreciable change in image sharpness (F m) M NA f F Axial resolution – Depth of Field Depth of Field Ranges (F m) F is determined by NA. NA f F

/lens.htm Please visit the following site and have some fun Do review problems on OM Read “dispersion and refraction of light and lens”

Derivation of Snell’s Law Normal 11 11 22 22 Incident angle Refracted angle AB – Common wavefront of two parallel rays A’A and B’B interface t-time for the wavefront to travel from AB to CD BD=ct=ADsin 1 c-velocity of light in vacuum AC=vt=ADsin 2 v-velocity of light in medium sin 1 sin 2 = = N c v c/v 1 =N 1 c/v 2 =N 2 sin 1 sin 2 = v1v1 v2v2 = N1N1 N2N2