Energy versus Wavelength of Photons E = h. ergs per single photon E = h. c / ergs per single photon h = Planck's constant = 1.38 10 -16 erg sec Fundamental Equivalency For light, the minimum resolvable distance between 2 points: = / NA Limiting case for light 200m or nm The smaller wavelengths of X-Rays (0.1 – 10 nm) are similar to the size of atoms (0.1 – 0.2 nm), and have energies that correspond to the energy differences between the inner atomic orbitals.
Black Body Radiation: All matter emits continuous background electromagnetic radiation whose energy is a function of its temperature. Total emitted radiant energy: Etotal = . T 4 = ergs/sec/m 2 = Stefan-Boltzmann constant = 5.672 10 -16 erg/K Eλ = 2hc 2 /λ 5 ×1/(e(hc/ λ (T-1) ) Energy of most abundant photon: E = h m = hc/ m 3. . T = Boltzmann factor = 1.38 10 -16 erg/K T = hc/3 m T = (2897.8 / m) K = Wien’s Law, where m is the wavelength of the most abundant photons Our eyes are tuned to the Sun whose Photosphere is 5780 K
X-Ray Fluorescence Analysis The excitation is produced by X-rays. The advantage of XRF analysis is that it can analyze many elements down to levels of ppm. The disadvantage of XRF analysis is that X-rays are difficult to focus, and thus it is difficult to analyze small volumes. XRF is the method of choice for obtaining the chemical compositions of powdered or fused bulk rock samples.
Electron Microprobe Electrons can be focused with magnetic fields to spot sizes on the order of 1 micron or less. By using an electron beam as the excitation source, one can analyze very small spots on mineral grains, and thus investigate phenomena such as compositional zoning in crystals, partitioning of elements between coexisting phases, etc. The disadvantage of electron beam excitation is that a relatively high background radiation is created by the electrons, which makes the detection limits for most elements ~0.01 wt.%.
Secondary electrons are produced by inelastic collisions of electrons from beam with valence electrons. These secondary electrons typically have lower energies than backscattered electrons. Auger electrons are produced by the interaction between the characteristic X-rays produced by an element with electrons in higher energy orbitals. Auger electrons typically have energies that are the difference between the energy of the initial electronic transition that produced the characteristic radiation and the ionization energy of the element. Back-scattered electrons are those which interact with atomic nucleii electrostatically and are flung back out of the sample, in much the same way that a comet interacts gravitationally with the sun. Interaction between the Electron Beam and Sample Surface Bremsstrahlung X-rays are the radiation that is emitted when electrons are decelerated by a target. Accelerated charges give off electromagnetic radiation, and when the energy of the bombarding electrons is high enough, that radiation is in the X-ray region and is characterized by a continuous distribution of radiation which becomes more intense and shifts toward higher frequencies as the energy of the bombarding electrons is increased. This background radiation is the principle limitation in analyzing elements at very low concentrations with the electron microprobe.
Interaction between the Electron Beam and Sample Surface ~ 1 micron spot
WDS: Wavelength Dispersive Analysis Electron Microprobe AnalysisX-Ray Fluorescence Analysis
The counter is a chamber containing a gas that is ionized by x-ray photons. A central electrode is charged at ~ +1700 V with respect to the conducting chamber walls, and each photon triggers a pulse- like cascade of electrons across this field. The signal is amplified and transformed into an accumulating digital count. Gas-Flow Proportional Counter
In energy dispersive analysis, the dispersion and detection of X-rays is a single operation. The fluorescent X- rays emitted by the sample are directed into a solid-state detector which produces a continuous distribution of pulses, the voltages of which are proportional to the incoming photon energies. These detectors consist of a 3- 5 mm thick silicon junction type p-i-n diode with a bias of ~ -1000 Volts across it. The lithium-drifted centre part forms the non-conducting i-layer. When an x-ray photon passes through, it causes a swarm of electron-hole pairs to form, and this causes a voltage pulse. The detector must be maintained at low temperature with liquid-nitrogen for the best energy resolution. Energy Dispersive Analysis (EDS) The electrical pulses generated by the detector are processed by amplifiers and significant computer power is required to correct for pulse-pile up and for extraction of peaks from poorly-resolved spectra. P-type Si is doped with 3 + cation such as Al to provide electron holes. N-type Si is doped with 5 + cation such as P to provide excess electrons. I-type intrinsic semiconductor
Olivine (Mg,Fe) 2 SiO 4 Diopside Ca(MgFe)Si 2 O 6 Hornblende Energy Dispersive Analysis EDS
Wavelength dispersive analysis (WDS) is inherently more precise because of the better resolution of the spectral peaks. The disadvantage of WDS is that peaks must be occupied sequentially by the spectrometer, which slows the analytical process. With 4 spectrometers, a 10 element major analysis takes approximately ~ 4 minutes of data acquisition. WDS is the method of choice for high-quality quantitative analysis. Energy dispersive analysis (EDS) has less energy resolution, but has the advantage that all spectral lines are accumulated simultaneous, giving a complete analysis in ~ 20 seconds. EDS is the method of choice for qualitative “identification” analyses.
Matrix effects can affect the X-ray spectrum produced in an electron microprobe analysis and have to be corrected for an accurate analysis. These matrix corrections are called ZAF corrections, in reference to their three components: atomic number (Z), absorption (A), and fluorescence (F). Matrix Corrections Atomic Number Correction X-ray emission is dependent on atomic number because of the stopping power of the target and backscattering from the target. Stopping power is the ability of a material to reduce the energy of an electron by inelastic scattering. This property is a function of A/Z, in which A is the atomic mass and Z is the atomic number. A/Z increases with increasing Z, as a result, the X-ray intensity per unit concentration increases with Z. Some of the electrons hitting the sample will be ejected back out. This process is known as backscattering and it is strongly affected by atomic number. The effect of backscattering is to decrease the X-ray intensity with increasing Z, which is opposite to the effect of stopping power. However, the backscattering effect is greater and, therefore, the overall atomic number correction follows the same trend. Minerals with high mean atomic number appear brighter in back- scattered electron images because they backscatter more electrons. Fe-rich Mg-rich Back-scattered electron image of olivine phenocryst
Back Scattered Electron Image Showing Compositional Zoning in Tourmaline
Back-scattered electron image of zoned clinopyroxene phenocryst with superimposed chemical analysis of Al content and Mg # (Mg/(Mg+Fe))
Absorption Correction X-rays are generated throughout the analytical volume during a probe analysis. Those X-rays produced at depth must pass through a certain distance within the sample and risk being absorbed, reducing the X-ray signal of the element of interest. Fluorescence Correction The critical excitation energy (Ec) of an element is the energy threshold needed to dislodge inner electrons and generate characteristic X-rays. In addition to the incident electrons, however, X-rays from the ionization of elements with higher Ec will also ionize atoms of elements with lower Ec, whose own characteristic X-ray emission lines will then be enhanced. There is also fluorescence caused by the X-ray continuum or continuous X-ray background emission produced by electron deflections. As an electron passes near an atomic nucleus, it may be slowed by the electric field of the nucleus, causing a quantum jump to a lower energy state and the emission of more X-rays.