AP 5301/8301Instrumental Methods of Analysisand Laboratory Zhengkui XU Office: G6760 Tel: 27889143 Email:email@example.com
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 Processingstructureproperty Chemical composition ( Crystal Structure ) Ceramic Fabrication Intrinsic Materials Selection Microstructure Properties (Characterization)
Effect of Microstructure on Mechanical Property f d-1/2 d-grain size 10m 50m a b OM images of two polycrystalline samples. Mechanical test: fa>fb Mechanical property Microscopic analysis: da< db Microstructure
Scale and Characterization Techniques XRD,TEM,STMSEM OM Valve Turbo charge Grain I Grain II atomic 1 Microstructure ranging from crystal structure to Engine components (SiC)
SiC turbine blades crack Grain 1 Intergranular amorphous phase Grain 2 2nm TEM image
Identification of Fracture Mode Pores Cracks Cracks Grain boundary 4m 20m Intergranular fracture Intragranular fracture
OM and SEM BaTiO3 Growthstep 50m OM - 2D 5m SEM – 3D
High Resolution Z-contrast ImagingAtomic Ordering in Ba(Mg1/3Nb2/3)O3 a I Z2  (STEM)
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.2m • 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
Simple Microscope Low-power magnifying glasses and hand lenses 2x 4x 10x
Light path bends at interface between two transparent media of Different indices of refraction (densities) Refraction of Light Snell’s Law Incident angleq1 Normal Refracted angleq2 air Sinq1 V1 N2 = = Sinq2 V2 N1 Materials N Air 1.0003 Water 1.33 Lucite 1.47 Immersion oil 1.515 Glass 1.52 Zircon 1.92 Diamond 2.42 N - Refractive index of material - Speed of light in vacuum • Velocity of light • in material N 1
Focusing Property of A Curved Surface In entering an optically more dense medium (N2>N1), rays are bent toward the normal to the interface at the point of incidence. Curved (converging) glass surface normal N1 N2 Air F Focal plane f F - focal point f – focal length
Curvature of Lens and Focal Length Normal The larger curvature angle The shorter focal length 1 N1 N2 F Optical axis f 1>2 2 N1 N2 F f Centerline of the lens
Converging (Convex) Lens f f F Focal plane The simplest magnifying lens fcurvature angle andlens materials (N) the larger N, the shorter f lucite glass diamond N: 1.47 1.51 2.42
Magnifier – A Converging Lens If o’-o’ is ~0.07mm, o=0.016o 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. retina I’ I’ nearest distance of distinct vision (NDDV) o” o-object distance Magnification I-I o”-o” A m= = B o h I’-I’ o’-o’ o” Virtual image o m = /o 25cm Real inverted image Ray diagram to show the principle of a single lens
Lens formula and magnification Objective lens ho f f hi O i -Inverted image I1 1 1 1 _ = _ + _ Lens Formula f-focal length (distance) O-distance of object from lens i-distance of image from lens f Oi i Magnification by objective hi mo = = ho O
Maximum Magnification of a Lens 1/f = 1/O + 1/i • 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/25 and h/o f in cm
Magnification when the Eyes are Relaxed 1/f = 1/O + 1/i • 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
Limitations of a Single Lens • From the formula, larger magnificationrequires 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 Compound microscope consists of two converging lenses, the objective and the eyepiece (ocular). • Object (O) placed just outside focal point of objective lens • A real inverted (intermediate) image (I1) forms at or close to focal point of eyepiece. • The eyepiece produces a further magnified virtual inverted image (I2). • L – Optical tube length 25cm
Magnification of Compound Microscope • Magnification by the objective m0 = -s’1/s1 • Since s’1 L and s1 f0, therefore magnification of objective mo L/fo • Magnification of eyepiece me = 25/fe (assuming the final image forms at ) • Overall magnification M = mome =
How Fine can You See with an Optical Microscope? • Magnification M = 25L/fofeIf 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 320240 to a A4 size print!!
Empty Magnification Higher resolution Lower resolution
Diffraction of Light Light waves interfere constructively and destructively. Sin=/d 1st 2nd 3rd film
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 dmin = /2sin I II I II
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 dmin = /2n sin = /2(N.A.) • For circular aperture dmin= 1.22/2(N.A.)=0.61/(N.A.)where N.A. = n sin is called numerical aperture Immersion oil n=1.515
Numerical Aperture (NA) NA=1 - theoretical maximum numerical aperture of a lens operating with air as the imaging medium Angular aperture (72 degrees) One half of A-A 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
Factors Affecting Resolution • Resolution = dmin = 0.61/(N.A.) • Resolution improves (smaller dmin) if or n or • Assuming that sin = 0.95 ( = 71.8°) • (The eye is more sensitive to blue than violet)
Resolution of a Microscope (lateral) The smallest distance between two specimen points that can still be distinguished as two separate entities dmin = 0.61l/NA NA=nsin() l – illumination wavelength (light) NA – numerical aperture -one half of the objective angular aperture n-imaging medium refractive index dmin ~ 0.3m for a midspectrum l of 0.55m
Optical Aberrations Reduce the resolution of microscope Two primary causes of non-ideal lens action: • 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 Astigmatism, field curvature and comatic aberrations are easily corrected with proper lens fabrication.
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.
Defects in 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 A converging lens can be combined with a weaker diverging lens, so that the chromatic aberrations cancel for certain wavelengths: The combination – achromatic doublet
Defects in Lens • 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 A o
Defects in Lens • 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. 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.
Axial resolution – Depth of Field Depth of focus (f mm) Depth of Field Ranges (F m) (F mm) NA f F 0.1 0.13 15.5 0.4 3.8 5.8 .95 80.0 0.19 The distance above and below geometricimage planewithin which the image is in focus The axial range through which an object can be focused without any appreciable change in image sharpness M NA fF M NA fF F is determined by NA.
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Derivation of Snell’s Law AB – Common wavefront of two parallel rays A’A and B’B Normal Incident angle q1 q1 interface q2 Refracted angle q2 t-time for the wavefront to travel from AB to CD BD=ct=ADsinq1 c-velocity of light in vacuum AC=vt=ADsinq2 v-velocity of light in medium sinq1 c v1 N1 sinq1 c/v1=N1 c/v2=N2 = = N = = sinq2 sinq2 v2 N2 v