Microanalysis In Electron Microscopy (EDS And WDS)
GG 711: Advanced Techniques in Geophysics and Materials ScienceNano-Microscopy. Lecture 3.Microanalysis in Electron Microscopy(EDS and WDS)Pavel ZininHIGP, University of Hawaii, Honolulu, USAwww.soest.hawaii.edu\ zinin
Electron Structure of Atoms and Quantum NumbersMax Planck in 1900 first began to analyze atomic structure in terms of the thendeveloping quantum theory of energy. Plank proposed that an oscillating (ionized)atom could not have any arbitrary energy, but rather only certain selected energyvalues (quanta) were possible. Plank reasoned that if only certain energy levels werepossible, there ought to be a relationship between the energy of an atom undergoingchange and both the energy and wavelength of the radiation emitted during theprocess. He suggested that the wavelength of electromagnetic radiation, , itsfrequency, , and its energy, E, are related:nhcE nhn lwhere n is a positive integer, h is Plank's constant (6.626 10-34Joule·sec), and c is thespeed of light (3.0 108m/s). In x-ray physics, E is measured in electron volts, eV, and isa unit of energy (1.6021 10–19 J/eV), such that E hc 12.397 (eV·Å).
Bohr‘s atom modelAt the beginning of the 20th century, scientists were perplexed by the failureof classical physics in explaining the characteristics of atomic spectra. Whydid hydrogen emit only certain lines in the visible part of the spectrum?Further- more, why did hydrogen absorb only those wavelengths that itemitted?In 1913, the Danish scientist Niels Bohr (1885- 1963) provided anexplanation of atomic spectra that included some features contained in thecurrently accepted theory. Bohr's theory contained a combination of ideasfrom classical physics, Planck's original quantum theory, Einstein's photontheory of light, and Rutherford's model of the atom. Bohr's model of thehydrogen atom contains some classical features as well as somerevolutionary postulates that could not be justified within the framework ofclassical physics. The Bohr model can be applied quite successfully to suchhydrogen-like ions as singly ionized helium and doubly ionized lithium.
Bohr ModelThe first application of the quantum theory ofatomic structure was made in 1913 by Niels Bohr.Bohr developed a model of the hydrogen atom,which allowed him to explain why the observedfrequencies (i.e., wavelengths) of energy emittedobeyed simple relationships. Although it was latershown to be too simplistic, Bohr's model allowedhim to calculate the energies of the allowed statesfor the hydrogen atom.Introduced by Niels Bohr in 1913, the model'skey success lay in explaining the Rydberg formulafor the spectral emission lines of atomichydrogen.Niels Henrik David Bohr1985-1962The Rutherford–Bohr model of the hydrogen atom(Z 1) or a hydrogen-like ion (Z 1), where thenegatively charged electron confined to an atomicshell encircles a small, positively charged atomicnucleus and where an electron jump between orbitsis accompanied by an emitted or absorbed amountof electromagnetic energy (Wikipedia 2009).
Quantum Numbers1. l. The electron moves in circular orbits about the nucleus (the planetary modelof the atom) under the influence of the Coulomb force of attraction between theelectron and the positively charged nucleus.2. The electron can exist only in very specific orbits; hence the states are quantized(Planck's quantum hypothesis). The allowed orbits are those for which the angularmomentum of the electron about the nucleus is an integral multiple of h/2π, whereh is Planck's constant. The angular momentum of the electron is mvr, where m isthe mass of electron, r is radius of the orbit, V is the linear velocity. Applying thecondition that the angular momentum is quantized, we havemVr nh/2πBohr could determine the energy spacing between levels using rule3 and come to an exactly correct quantum rule: the angularmomentum L is restricted to be an integer multiple of a fixed unit:hL n2 where n 1, 2, 3, . is called the principal quantum number. The lowest value of n is 1; thisgives a smallest possible orbital radius of 0.0529 nm known as the Bohr radius. Once anelectron is in this lowest orbit, it can get no closer to the proton.
Quantum Numbers3. The electrons do not continuously lose energy as they travel. They can only gain andlose energy by jumping from one allowed orbit to another, absorbing or emittingelectromagnetic radiation with a frequency determined by the energy difference ofthe levels according to the Planck relation E E2 E1 nhwhere n 1, 2, 3, . is called the principal quantumnumber. The lowest value of n is 1; this gives a smallestpossible orbital radius of 0.0529 nm known as the Bohrradius. Once an electron is in this lowest orbit, it can get nocloser to the proton.4. Thefrequency of the radiation emitted at an orbit of period T is as it wouldbe in classical mechanics; it is the reciprocal of the classical orbit period:1 T
De Broglie Waves and the Hydrogen Atom(a) Standing wave patternfor an electron wave in astable orbit of hydrogen.There are three fullwavelengths in this orbit.(b) Standing wave patternfor a vibrating stretchedstring fixed at its ends.This pattern has three fullwavelengthsIn general, the condition for a de Broglie standing wave in an electron orbit is that thecircumference must contain an integral multiple of electron wavelengths. We can expressthis condition asDe Broglie's equation for the wavelength of an electron in terms of its momentum isThis is precisely the quantization of angular momentum condition imposed by Bohr in hisoriginal theory of hydrogen. The electron orbit shown in Figure contains three completewavelengths and corresponds to the case where the principal quantum number n equals three.The orbit with one complete wavelength in its circumference
Quantum Numbers
Quantum NumbersThere are a set of quantum numbers associated with the energy states of the atom. The four quantumnumbers n, l, m, and s specify the complete and unique quantum state of a single electron in an atomcalled its wavefunction or orbital. No two electrons belonging to the same atom can have the same fourquantum numbers which is shown in the Pauli exclusion principle.n principal quantumnumberThe bound state energies of theelectron in the hydrogen atom aregiven by:- 13.6 eVn2n 1, 2,3, 4.En The principle quantum number (n): The principle quantum number (n) caninclude any positive integral value. It determines the major energy level ofan electron. It is designated K, L and M for n 1, 2 and 3 respectively. Themaximum number of electrons allowed is 2n2.
Number of ElectronsMaximum number of electrons in any electron shell 2n2n 1n 2n 32(1)22(2)22(3)2 2818Each principal energy level, which is known as a shell, has one or more subshellsNOTE: Electrons generally fill into shells with smallest n first; however, the fillingorder gets more complicated after Argon (element 18).For the first 20 electrons:Shell122e8e38e42e
Quantum Numbers The azimuthal momentum quantum number (l): The azimuthal or angular momentumnumber (or orbital angular momentum quantum number, second quantum number)symbolized as l, is a quantum number for an atomic orbital that determines its orbitalangular momentum and describes the shape of the orbital. Higher values of l correspondto greater angular momentum. L may assume integer values from 0 to n-1. The orbitalsare s, p, d and f for l 0, 1, 2 and 3 respectively. The orbitals have distinctive shapes. Themaximum number of electrons allowed is: s 2, p 6, d 10 and f 14.The s-orbitalsThe d-orbitalsThe magnetic quantum number (m): Anelectron with angular momentum generates amagnetic field. m can assume any integerfrom -l to l.
Quantum Numbers The spin quantum number: A small "particle", like an electron, spinning on its own axisalso behaves as a small magnet, hence the electron itself has an intrinsic magneticproperty. We say that the electron has a spin and describe it as being either 1/2 or -1/2.Electron Spin and the Pauli ExclusionPrincipleSince electron spin is quantized, we definems spin quantum number ½.Pauli‘s Exclusions Principle: noelectrons can have the same setquantum numbers. Therefore,electrons in the same orbital mustopposite spins.twoof 4twohaveThe specific quantum numbers assigned tothe electrons are determined bythermodynamic considerations that requirethe occupation of states having the lowestenergies first, and the Pauli ExclusionPrinciple.
Interaction of electrons with matter in an electron microscope Back scatter electrons – compositional Secondary electrons – topography X-rays – chemistry
History of X-rays and EDS 1912, von Laue, Friedrich and Knipping observe Xray diffraction. Laue demonstrated with the dispersionof x-rays that their wavelength must be on the order ofatomic dimensions. Subsequently, the wavelengths ofcharacteristic x-ray radiation were measured to be inthe range of 10 -8 to 10 -11 meters, and the dimensionalunit angstrom (Å 10 –10 m) was introduced. The theory of diffraction of x-rays, originallyproposed by Laue, was conclusively demonstrated byW.H. Bragg and W.L. Bragg in 1913 by obtaining thefirst x-ray diffraction pattern a sodium chloride crystal. 1913, Henry G.J. Moseley was researching thecharacteristics of x-ray emission from different targetmaterials. He noticed a systematic progression of x-raywavelengths with increasing atomic number of thematerial generating the radiation. Based on thisregularity, the previously unknown elements hafniumand rhodium were discovered with x-ray spectralanalysis.Photographic recording of Kαand Kβ x-ray emission lines fora range of elements
History of X-rays Moseleyfoundthatwavelength of characteristicX-rays varied systematically(inversely)withatomicnumberZf k1 Z k2 Henry G. J. Moseley(1887-1915)where: f is the frequency of the main or K xray emission line k1 and k2 are constants thatdepend on the type of line. For example, thevalues for k1 and k2 are the same for all K lines,so the formula can be rewritten thus:f (2.47 1015 (Z - 1)2 HzThe next year, he was killed in Turkey in WWI. ―In view of what he might still have accomplished(he was only 27 when he died), his death might well have been the most costly single death of thewar to mankind generally,‖ says Isaac Asimov (Biographical Encyclopedia of Science&Technology).
EM Spectrum Lines Produced by Electron Shell al(1, 2, 3, )Electron shell(1 K, 2 L, 3 M )lAzimuthal0 to n-1Electron cloudshapemMagnetic-l to lElectron shellorientation in amagnetic fieldsSpin ½Electron spindirectionjInner precessionl ½But j -½Total angularmomentum
Inner-shell ionization:Production of X-rayTimeK shell( photoelectron)123L shellBlue Lines indicatesubsequent times: 1to 2, then 3 wherethere are 2 alternateoutcomesIncident electron knocks innershell (K here) electron out of itsorbit (time 1). This is anunstable configuration, and anelectron from a higher energyorbital (L here) ‗falls in‘ to fillthe void (time 2). There is anexcess of energy present andthis is released internally as aphoton. The photon has 2 waysto exit the atom (time 3), eitherby ejecting another outer shellelectron as an Auger electron(L here, thus a KLL transition),or as X-ray (KL transition).(Goldstein et al, 1992, p 120)
History of the Electron Microprobe MicroscopyIn order to return the atom to itsnormal state, an electron froman outer atomic shell ―drops‖into the vacancy in the innershell. This drop results in theloss of a specific amount ofenergy, namely, the differencein energy between the vacantshell and the shell contributingthe electron. This energy isgiven up in the form ofelectromagnetic radiation xrays. Since energy levels in allelements are different, elementspecific, or characteristic, xrays are generated.
EM Spectrum Lines Produced by Electron Shell IonizationK X-ray is produced due to removal of K shell electron, with L shell electron taking its place.K occurs in the case where K shell electron is replaced by electron from the M shell.L X-ray is produced due to removal of L shell electron, replaced by M shell electron.M X-ray is produced due to removal of M shell electron, replaced by N shell electron.
Moseley‘s LawThe amount of energy needed to remove theelectron from the inner atomic shell, Eq,which is related to the minimum potential,Vq, required to eject the electron with anelectronic charge, e. Moseley's law is afunction of atomic number, Z.2Eq eVq µ (Zs )where the proportionality and the ―screeningconstant‖, s, differ depending on whichinner shell (K, L, etc.) is ionized
EM Spectrum Lines Produced by Electron Shell Ionization
X-ray spectroscopy in SEMX-ray spectrometers are of two kinds.(a) The energy-dispersive (ED) type records X-raysof all energies effectively simultaneously andproduces an output in the form of a plot ofintensity versus X-ray photon energy. Thedetector consists of one of several types ofdevice producing output pulses proportional inheight to the photon energy.(b) The wavelength-dispersive (WD) type makesuse of Bragg reflection by a crystal, and operatesin 'serial' mode, the spectrometer being 'tuned' toonly one wavelength at a time. Several crystalsof different interplanar spacings are needed inorder to cover the required wavelength range.Spectral resolution is better than for the ED type,but the latter is faster and more convenient touse. X-ray spectrometers attached to SEMs areusually of the ED type, though sometimes asingle multi-crystal WD spectrometer is fitted.
SEM with EDSEDS detectorSEM combined with Energydispersive spectrometer (EDS)andWavelengthDispersiveSpectrometer (WDS).WDSspectrometers
How the EDS Detector Works The central component of an EDS system is a solid-state detector, consisting of asemiconductor. As each X-ray photon hits the detector, a very small current is produced byknocking out electrons from the semi-conductor. How the EDS Detector Works: The EDS detector converts the energy of each individualX-ray into a voltage signal of proportional size. This is achieved through a three stageprocess. Firstly the X-ray is converted into a charge by the ionization of atoms in thesemiconductor crystal. Secondly this charge is converted into the voltage signal by the fieldeffect transistor (FET) preamplifier. Finally the voltage signal is input into the pulseprocessor for measurement. The output from the preamplifier is a voltage ‗ramp‘ whereeach X-ray appears as a voltage step on the ramp. How the crystal converts X-ray energy into charge: When an incident X-ray strikes thedetector crystal its energy is absorbed by a series of ionizations within the semiconductor tocreate a number of electron-hole pairs. The electrons are raised into the conduction band ofthe semiconductor and are free to move within the crystal lattice. When an electron is raisedinto the conduction band it leaves behind a ‗hole‘, which behaves like a free positive chargewithin the crystal. A high bias voltage, applied between electrical contacts on the front faceand back of the crystal, then sweeps the electrons and holes to these opposite electrodes,producing a charge signal, the size of which is directly proportional to the energy of theincident X-ray. The charge is converted to a voltage signal by the FET preamplifier.
EDS assemblageGoldstein et al fig 5.21There are several types of solid state EDSdetectors, the most common (cheapest) being theSi-Li detector. Components: thin window (Be, C,B); SiLi crystal, FET (field effect transistor: initialamp), vacuum, cold finger, preamp, amp and MDAelectronics (―multi channel analyzer‖).
EM Spectrum Lines Produced by Electron Shell Ionization
EM Spectrum Lines Produced by Electron Shell Ionization
Synthesis of BCx diamondsSEM image of thepost-heatedBC3sample recoveredfrom 50 GPa and2033 K and withthe NaCl layerbeingremoved.Marker is 10 m.C-K mapRaman Intensity/Counts35000(a)3000025000Raman spectrum ofthe BC3 sampleafter laser heating(50 GPa, 2033 241 K)200001500010000200 400 600 800 1000 1200 1400 1600 1800B-K mapWavenumber/cm-1
Synthesis of cubic C3N4 diamonds(a)(a) SEM image of the recovered C3N4sample after heating to 2000 K at 33GPa. Marker is 100 m. (b) map of thenitrogen distribution; (c) map of thecarbon distribution.
Generic EMPA/SEM WDSEach element produces a unique set of characteristic Xrays when bombarded with electrons. Each X-ray willhave a specific energy and wavelength. Energydispersive spectrometers (EDS) sort the X-rays basedon their energy; while wavelength dispersivespectrometers (WDS) sort the X-rays based on theirwavelengths. WDS systems use X-ray diffraction as themeans by which they separate X-rays of differentwavelengths. The spectrometer consists of an analyzingcrystal and a detector. Those X-rays that hit the crystaland diffract will enter the detector. Whether an X-rayphoton will diffract depends on its wavelength, theorientation of the crystal, and the crystal‘s latticespacing. Only X-rays of a given wavelength will enterthe detector at any one time. To measure X-rays ofanother wave length, the crystal and detector are movedto a new position. Since a specific WO spectrometercan measure only one X-ray wavelength at a time, it isimportant that a WDS system has an array ofspectrometers in order to work efficiently. Electronmicro- probes typically have up to five WOspectrometers, allowing them to measure five elementssimultaneously.
X-ray as a plane waveThe most convenient wave to write down introduce equation describing a plane wave isto use complex exponent ei expi cos i sin : Aei kx t A cos kx t iA sin kx t ;
Deriving Bragg‘s equation C DFEd The angle of incidence of the x-raysis The angle at which the x-rays arediffracted is equal to the angle of incidence, The angle of diffraction is the sumof these two angles, 2 The two x-ray beams travel at different distances. This difference is related to thedistance between parallel planes. We connect the two beams with perpendicular lines(CD and CF) and obtain two equivalent right triangles. CE d (interplanar distance)sin DEm ; d sin DE EF 2d sin EF DE difference in path length m dkReflection (signal) only occurs when conditions for constructive interference betweenthe beams are met. These conditions are met when the difference in path length equals anintegral number of wavelengths, m. The final equation is the BRAGG‘S LAW2d sin EF DE m m k
WDSThe fact that characteristic x-ray photons are described by either their energy or theirwavelength enables us to isolate and count x-rays for a desired element either bydiscrimination baseed on energy or by wavelength. This fact produces two principaltypes of x-ray detection systems:WDS: wavelength dispersive detection system in which x-rays from differentelements are recognized and separated from one another by their wavelength usingBragg diffraction. WDS systems use X-ray diffraction as the means by which theyseparate X-rays of different wavelengths. The spectrometer consists of an analyzingcrystal and a detector. Those X-rays that hit the crystal and diff ract will enter thedetector. Whether an X-ray photon will diffract depends on its wavelength, theorientation of the crystal, and the crystal‘s lattice spacing. Only X-rays of a givenwavelength will enter the detector at any one time. To measure X-rays of anotherwave length, the crystal and detector are moved to a new position. Since a specificWO spectrometer can measure only one X-ray wavelength at a time, it is importantthat a WDS system has an array of spec trometers in order to work efficiently.Electron micro- probes typically have up to five WO spectrometers, allowing them tomeasure five elements simultane ously. Each spectrometer typically has between twoand four analyzing crystals, each with a different lattice spacing, because each typeof crystal can diffract only a given range of wavelengths
EDS versus WDSThemost significant difference betweenWDS and EDS systems is their energyresolution. A Mn Kcx X-ray line on anEDS system will typically be between135-150 eV wide. On a WDS system,this same X-ray line will only be about10 eV wide. This means that theamount of overlap between peaks ofsimilar energies is much smaller on theWDS system. To the right is acomparison of spectra collected from aPt- Au-Nb alloy on a WDS comparedto an EDS system. On the WDS systemsix X-ray lines can be identified, withan overlap occurring only between theAu Mc and the Pt MJ3 lines. It wouldbe very straightforward to identify theelements present and to quantify theirabundance without resorting to anelaborate deconvolution procedure.On the EDS system. the broad nature of the X-ray linesmask each other and they appear to be a single peak. Itwould be impossible to reliably deconvolute this peakinto the individual X-ray lines.
EDS versus WDS The second major problem with EDSsystems is their low count rates and poorreproducibility. Typically a WDS systemwill have a count rate about l0x that of anEDS system. There are some EDSsystems that can collect at a higher countrate, but they sacrifice even more on theenergy resolution — their peaks are evenwider. To the left is a comparison of thereproducibility of an EDS system and aWDS system. The data were collectedsimultanlously, so the conditions underwhich they were collected were identical,The plots show that the EDS data hadalmost 8x the scatter of the WOS data.For serious quantitative analyses, theEDS data would not be acceptable. Thespread on the EDS data could be reducedby counting longer, but that would alsoimprove the WDS data.
EDS versus WDS Intensities of Kα line for pureelements (Z is atomic number)as recordered by an EDSspectrometer and a WDspectrometer with differentcrystals (S.J. B. Reed . ElectronMicroprobe Analysis).
Mapping Elements - WDSThe picture on the [LEFT] shows a large piece of the Murchison meteorite courtesy ofthe Natural History Museum, London. [RIGHT] This image is known as a 'combined Xray elemental map.' It was created by combining X-ray intensities due to magnesium(red), calcium (green) and aluminum (blue) from a thin slice of the Murchisonmeteorite, courtesy of Alexander Krot, a meteorite researcher at the University ofHawai‗i. The x-rays were made by bombarding the sample with a beam of electrons inan electron microprobe.
Mapping Elements - WDSCombined x-ray map composed of Mg K (red), Ca K (green), and Al K (blue) of apolished section of the Efremovka meteorite containing Ca, Al-rich inclusion E104, andamoeboid olivine aggregate E1. The calcium-aluminum-rich inclusion (CAI) consists ofspinel ( purple), Al-diopside (dark green), anorthite (light blue), and melilite (light green). Itis surrounded by a multilayered Wark-Lovering rim and a thick forsterite-rich rim (red).(Krot et al., Science 295 2002).
Home Work1. Derive Bagg‘s law (SO).2. Describe Moseley's law (KK).3. Describe principles EDS (KK).4. Describe principles WDS (SO).5. Provide definition of the atomic numbers (KK).
The Bohr model can be applied quite successfully to such hydrogen-like ions as singly ionized helium and doubly ionized lithium. Bohr Model The first application of the quantum theory of atomic structure was made in 1913 by Niels Bohr. Bohr developed a model of the hydrogen atom, which allowed him to explain why the observed .
Electron Microscopy and X-Ray Crystallography Tianyi Shi 2020-02-13 Contents 1 Introduction 1 2 X-Ray Crystallography 1 3 Cryo-Electron Microscopy 2 4 Comparison of Strengths and Limitations 3 5 Combining X-ray and Cryo-EM studies 3 6 Concluding Remarks 4 References 4 Compare the strengths and limitations of Electron Microscopy and X-ray .
Fundamentals of Scanning Electron Microscopy and Energy Dispersive X-ray Analysis in SEM and TEM Tamara RadetiÉ, University of Belgrade Faculty of Technology and Metallurgy, Beograd, Serbia NFMC Spring School on Electron Microscopy, April 2011 Outline SEM – Microscope features – BSE –SE † X-ray EDS – X-rays - origin & characteristics
Practical fluorescence microscopy 37 4.1 Bright-field versus fluorescence microscopy 37 4.2 Epi-illumination fluorescence microscopy 37 4.3 Basic equipment and supplies for epi-illumination fluorescence . microscopy. This manual provides basic information on fluorescence microscopy
MULTIPHOTON LASER SCANNING MICROSCOPY Introduction to Multiphoton Laser Scanning Microscopy Carl Zeiss LSM 510 NLO 8-6 B 40-055 e 09/02 8.2 Introduction to Multiphoton Laser Scanning Microscopy Multiphoton laser scanning microscopy (MPLSM) has become an important technique in vital and deep tissue fluorescence imaging.
1. Static atomic force microscopy 958 2. Dynamic atomic force microscopy 959 III. Challenges Faced by Atomic Force Microscopy with Respect to Scanning Tunneling Microscopy 960 A. Stability 960 B. Nonmonotonic imaging signal 960 C. Contribution of long-range forces 960 D. Noise in the imaging signal 961 IV. Early AFM Experiments 961 V. The Rush .
1. Static atomic force microscopy 958 2. Dynamic atomic force microscopy 959 III. Challenges Faced by Atomic Force Microscopy with Respect to Scanning Tunneling Microscopy 960 A. Stability 960 B. Nonmonotonic imaging signal 960 C. Contribution of long-range forces 960 D. Noise in the imaging signal 961 IV. Early AFM Experiments 961 V. The Rush .
3. MICROSCOPY 37 3.1 Historical Background 37 3.2 Nature of Light 39 3.3 Compound Microscope 41 3.4 Image Formation in a Light Microscope 43 3.5 Phase Contrast Microscopy 47 3.6 Fluorescence Microscopy 51 3.7 Electron Microscopy 54
the standard represented by the Associated Board of the Royal Schools of Music (ABRSM) Grade 5 Theory examination. The module will introduce you to time-based and pitch-based notation, basic principles of writing melody, harmony and counterpoint, varieties of rhythmic notation, simple phrasing, and descriptive terms in various languages.
