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Rentgeno spindulių fluorescencija (RSF) yra charakteringųjų "antrinių" (arba fluorescencinių)
Reiškinio fizikiniai pagrindai
Medžiagas apšvitinus trumpo bangos ilgio rentgeno ar gama spinduliais, įvyksta atomų jonizacija. Jonizacijos procesas susideda iš atomo vieno ar daugiau elektronų išlaisvinimo, kai atomas apšvitinamas spinduliuote, kurios energija viršija atomo jonizacijos energiją. Rentgeno ar gama spindulių energijos gali pakakti išlaisvinti elektronus iš vidinių atomo orbitalių. Toks elektrono pašalinimas sukelia atomo elektroninės struktūros nestabilumą ir elektronai iš aukštesnių orbitalių "nukrenta" į atsilaisvinusias žemesnes orbitales, taip jas vėl užpildydami. Perėjimo metu elektrono perteklinė energija yra atiduodama kaip fotonas, kurio energija lygi procese dalyvaujančių orbitalių energijų skirtumui. Tokiu būdu medžiaga spinduliuoja antrinę spinduliuotę, kurios energija yra charakteringa konkretiems medžiagos atomams. Terminas fluorescencija yra taikomas reškiniui, kuriame pirminės energijos sugerties rezultatas lemia antrinių spindulių emisiją, kurių energija yra skirtinga (dažniausiai žemesnė).
Charakteringoji spinduliuotė
Kiekvienas cheminis elementas turi jam būdingos energijos elektronų orbitales. Sekdamas vidinį elektroną, pašalintą didelės energijos fotono iš pirminio spinduliuotės šaltinio, elektronas iš išorinio sluoksnio pereina į atsilaisvinusią vietą. Yra ribotas kiekis būdų kaip tai gali nutikti, kaip kad yra parodyta paveiksle 1. Pagrindiniams perėjimams yra suteikti tokie vardai: L→K sluoksnių perėjimai yra tradiciškai vadinami Kα, M→K sluoksnių perėjimai yra vadinami Kβ, M→L sluoksnių perėjimai yra vadinami Lα ir t.t. Kiekvieną iš tokių perėjimų lydi fluorescencijos fotonas, kurio charakteringoji energija yra lygi energijų skirtumui tarp pirminės ir galinės orbitalės. Šios fluorescencinės spinduliuotės bangos ilgis gali būti apskaičiuotas naudojant Planko dėsnį:
Fluorescencinė spinduliuotė gali būti analizuojama arba išrūšiuojant spektro fotonų energijas (energijos dispersijos analizė), arba suskirstant spinduliuotę pagal bangos ilgį (banginės dispersijos analizė). Taip suskirsčius, charakteringosios spinduliuotės linijų intensyvumas yra tiesiogiai proporcingas medžiagą sudarančių cheminių elementų kiekiams. Toks principas yra pagrindas efektyviam pritaikymui analizinėje chemijoje. Paveiksle 2 parodytas tipiškas aštrių formų fluorescencinių linijų smailės, gautos banginės dispersijos metodu (žr. Mozlio dėsnį).
Pirminė spinduliuotė
In order to excite the atoms, a source of radiation is required, with sufficient energy to expel tightly held inner electrons. Conventional
Dispersija
In energy dispersive analysis, the fluorescent X-rays emitted by the material 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. This signal is processed by a multichannel analyser (MCA) which produces an accumulating digital spectrum that can be processed to obtain analytical data. In wavelength dispersive analysis, the fluorescent X-rays emitted by the material sample are directed into a diffraction grating monochromator. The diffraction grating used is usually a single crystal. By varying the angle of incidence and take-off on the crystal, a single X-ray wavelength can be selected. The wavelength obtained is given by the
where d is the spacing of atomic layers parallel to the crystal surface.
Detekcija
In energy dispersive analysis, dispersion and detection are a single operation, as already mentioned above.
In wavelength dispersive analysis, the single-wavelength radiation produced by the monochromator is passed into a photomultiplier, a detector similar to a Geiger counter, which counts individual photons as they pass through. The counter is a chamber containing a gas that is ionised by X-ray photons. A central electrode is charged at (typically) +1700 V with respect to the conducting chamber walls, and each photon triggers a pulse-like cascade of current across this field. The signal is amplified and transformed into an accumulating digital count. These counts are then processed to obtain analytical data.
Rentgeno spindulių intensyvumas
The fluorescence process is inefficient, and the secondary radiation is much weaker than the primary beam. Furthermore, the secondary radiation from lighter elements is of relatively low energy (long wavelength) and has low penetrating power, and is severely attenuated if the beam passes through air for any distance. Because of this, for high-performance analysis, the path from tube to sample to detector is maintained under vacuum (around 10 Pa residual pressure). This means in practice that most of the working parts of the instrument have to be located in a large vacuum chamber. The problems of maintaining moving parts in vacuum, and of rapidly introducing and withdrawing the sample without losing vacuum, pose major challenges for the design of the instrument. For less demanding applications, or when the sample is damaged by a vacuum (e.g. a volatile sample), a helium-swept X-ray chamber can be substituted, with some loss of low-Z (Z = atomic number) intensities.
Cheminė analizė
The use of a primary X-ray beam to excite fluorescent radiation from the sample was first proposed by Glocker and Schreiber in 1928.[1] Today, the method is used as a non-destructive analytical technique, and as a process control tool in many extractive and processing industries. In principle, the lightest element that can be analysed is beryllium (Z = 4), but due to instrumental limitations and low X-ray yields for the light elements, it is often difficult to quantify elements lighter than sodium (Z = 11), unless background corrections and very comprehensive inter-element corrections are made.
Energijos dispersijos spektrometrija
In
Si(Li) detektoriai
These consist essentially of a 3–5 mm thick silicon junction type p-i-n diode (same as PIN diode) with a bias of −1000 V across it. The lithium-drifted centre part forms the non-conducting i-layer, where Li compensates the residual acceptors which would otherwise make the layer p-type. When an X-ray photon passes through, it causes a swarm of electron-hole pairs to form, and this causes a voltage pulse. To obtain sufficiently low conductivity, the detector must be maintained at low temperature, and liquid-nitrogen cooling must be used for the best resolution. With some loss of resolution, the much more convenient Peltier cooling can be employed.[2]
Wafer detectors
More recently, high-purity silicon wafers with low conductivity have become routinely available. Cooled by the Peltier effect, this provides a cheap and convenient detector, although the liquid nitrogen cooled Si(Li) detector still has the best resolution (i.e. ability to distinguish different photon energies).
Stiprintuvai
The pulses generated by the detector are processed by
Apdorojimas
Considerable computer power is dedicated to correcting for pulse-pile up and for extraction of data from poorly resolved spectra. These elaborate correction processes tend to be based on empirical relationships that may change with time, so that continuous vigilance is required in order to obtain chemical data of adequate precision.
Panaudojimas
Banginės dispersijos spektrometrija
In
- "Simultaneous" spectrometers have a number of "channels" dedicated to analysis of a single element, each consisting of a fixed-geometry crystal monochromator, a detector, and processing electronics. This allows a number of elements to be measured simultaneously, and in the case of high-powered instruments, complete high-precision analyses can be obtained in under 30 s. Another advantage of this arrangement is that the fixed-geometry monochromators have no continuously moving parts, and so are very reliable. Reliability is important in production environments where instruments are expected to work without interruption for months at a time. Disadvantages of simultaneous spectrometers include relatively high cost for complex analyses, since each channel used is expensive. The number of elements that can be measured is limited to 15–20, because of space limitations on the number of monochromators that can be crowded around the fluorescing sample. The need to accommodate multiple monochromators means that a rather open arrangement around the sample is required, leading to relatively long tube-sample-crystal distances, which leads to lower detected intensities and more scattering. The instrument is inflexible, because if a new element is to be measured, a new measurement channel has to be bought and installed.
- "Sequential" spectrometers have a single variable-geometry monochromator (but usually with an arrangement for selecting from a choice of crystals), a single detector assembly (but usually with more than one detector arranged in tandem), and a single electronic pack. The instrument is programmed to move through a sequence of wavelengths, in each case selecting the appropriate X-ray tube power, the appropriate crystal, and the appropriate detector arrangement. The length of the measurement program is essentially unlimited, so this arrangement is very flexible. Because there is only one monochromator, the tube-sample-crystal distances can be kept very short, resulting in minimal loss of detected intensity. The obvious disadvantage is relatively long analysis time, particularly when many elements are being analysed, not only because the elements are measured in sequence, but also because a certain amount of time is taken in readjusting the monochromator geometry between measurements. Furthermore, the frenzied activity of the monochromator during an analysis program is a challenge for mechanical reliability. However, modern sequential instruments can achieve reliability almost as good as that of simultaneous instruments, even in continuous-usage applications.
Bandinio padavimas
In order to keep the geometry of the tube-sample-detector assembly constant, the sample is normally prepared as a flat disc, typically of diameter 20–50 mm. This is located at a standardized, small distance from the tube window. Because the X-ray intensity follows an inverse-square law, the tolerances for this placement and for the flatness of the surface must be very tight in order to maintain a repeatable X-ray flux. Ways of obtaining sample discs vary: metals may be machined to shape, minerals may be finely ground and pressed into a tablet, and glasses may be cast to the required shape. A further reason for obtaining a flat and representative sample surface is that the secondary X-rays from lighter elements often only emit from the top few micrometres of the sample. In order to further reduce the effect of surface irregularities, the sample is usually spun at 5–20 rpm. It is necessary to ensure that the sample is sufficiently thick to absorb the entire primary beam. For higher-Z materials, a few millimetres thickness is adequate, but for a light-element matrix such as coal, a thickness of 30–40 mm is needed.
Monochromatoriai
The common feature of monochromators is the maintenance of a symmetrical geometry between the sample, the crystal and the detector. In this geometry the Bragg diffraction condition is obtained.
The X-ray emission lines are very narrow (see figure 2), so the angles must be defined with considerable precision. This is achieved in two ways:
- Flat crystal with Soller collimators
The Soller collimator is a stack of parallel metal plates, spaced a few tenths of a millimetre apart. To improve angle resolution, one must lengthen the collimator, and/or reduce the plate spacing. This arrangement has the advantage of simplicity and relatively low cost, but the collimators reduce intensity and increase scattering, and reduce the area of sample and crystal that can be "seen". The simplicity of the geometry is especially useful for variable-geometry monochromators.
- Curved crystal with slits
The Rowland circle geometry ensures that the slits are both in focus, but in order for the Bragg condition to be met at all points, the crystal must first be bent to a radius of 2R (where R is the radius of the Rowland circle), then ground to a radius of R. This arrangement allows higher intensities (typically 8-fold) with higher resolution (typically 4-fold) and lower background. However, the mechanics of keeping Rowland circle geometry in a variable-angle monochromator is extremely difficult. In the case of fixed-angle monochromators (for use in simultaneous spectrometers), crystals bent to a logarithmic spiral shape give the best focusing performance. The manufacture of curved crystals to acceptable tolerances increases their price considerably.
Analitinės linijos
The spectral lines used for chemical analysis are selected on the basis of intensity, accessibility by the instrument, and lack of line overlaps. Typical lines used, and their wavelengths, are as follows:
element | line |
wavelength (nm) | element | line | wavelength (nm) | element | line | wavelength (nm) | element | line | wavelength (nm) | |||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Li | Kα | 22.8 | Ni | Kα1 | 0.1658 | I | Lα1 | 0.3149 | Pt | Lα1 | 0.1313 | |||
Be | Kα | 11.4 | Cu | Kα1 | 0.1541 | Xe | Lα1 | 0.3016 | Au | Lα1 | 0.1276 | |||
B | Kα | 6.76 | Zn | Kα1 | 0.1435 | Cs | Lα1 | 0.2892 | Hg | Lα1 | 0.1241 | |||
C | Kα | 4.47 | Ga | Kα1 | 0.1340 | Ba | Lα1 | 0.2776 | Tl | Lα1 | 0.1207 | |||
N | Kα | 3.16 | Ge | Kα1 | 0.1254 | La | Lα1 | 0.2666 | Pb | Lα1 | 0.1175 | |||
O | Kα | 2.362 | As | Kα1 | 0.1176 | Ce | Lα1 | 0.2562 | Bi | Lα1 | 0.1144 | |||
F | Kα1,2 | 1.832 | Se | Kα1 | 0.1105 | Pr | Lα1 | 0.2463 | Po | Lα1 | 0.1114 | |||
Ne | Kα1,2 | 1.461 | Br | Kα1 | 0.1040 | Nd | Lα1 | 0.2370 | At | Lα1 | 0.1085 | |||
Na | Kα1,2 | 1.191 | Kr | Kα1 | 0.09801 | Pm | Lα1 | 0.2282 | Rn | Lα1 | 0.1057 | |||
Mg | Kα1,2 | 0.989 | Rb | Kα1 | 0.09256 | Sm | Lα1 | 0.2200 | Fr | Lα1 | 0.1031 | |||
Al | Kα1,2 | 0.834 | Sr | Kα1 | 0.08753 | Eu | Lα1 | 0.2121 | Ra | Lα1 | 0.1005 | |||
Si | Kα1,2 | 0.7126 | Y | Kα1 | 0.08288 | Gd | Lα1 | 0.2047 | Ac | Lα1 | 0.0980 | |||
P | Kα1,2 | 0.6158 | Zr | Kα1 | 0.07859 | Tb | Lα1 | 0.1977 | Th | Lα1 | 0.0956 | |||
S | Kα1,2 | 0.5373 | Nb | Kα1 | 0.07462 | Dy | Lα1 | 0.1909 | Pa | Lα1 | 0.0933 | |||
Cl | Kα1,2 | 0.4729 | Mo | Kα1 | 0.07094 | Ho | Lα1 | 0.1845 | U | Lα1 | 0.0911 | |||
Ar | Kα1,2 | 0.4193 | Tc | Kα1 | 0.06751 | Er | Lα1 | 0.1784 | Np | Lα1 | 0.0888 | |||
K | Kα1,2 | 0.3742 | Ru | Kα1 | 0.06433 | Tm | Lα1 | 0.1727 | Pu | Lα1 | 0.0868 | |||
Ca | Kα1,2 | 0.3359 | Rh | Kα1 | 0.06136 | Yb | Lα1 | 0.1672 | Am | Lα1 | 0.0847 | |||
Sc | Kα1,2 | 0.3032 | Pd | Kα1 | 0.05859 | Lu | Lα1 | 0.1620 | Cm | Lα1 | 0.0828 | |||
Ti | Kα1,2 | 0.2749 | Ag | Kα1 | 0.05599 | Hf | Lα1 | 0.1570 | Bk | Lα1 | 0.0809 | |||
V | Kα1 | 0.2504 | Cd | Kα1 | 0.05357 | Ta | Lα1 | 0.1522 | Cf | Lα1 | 0.0791 | |||
Cr | Kα1 | 0.2290 | In | Lα1 | 0.3772 | W | Lα1 | 0.1476 | Es | Lα1 | 0.0773 | |||
Mn | Kα1 | 0.2102 | Sn | Lα1 | 0.3600 | Re | Lα1 | 0.1433 | Fm | Lα1 | 0.0756 | |||
Fe | Kα1 | 0.1936 | Sb | Lα1 | 0.3439 | Os | Lα1 | 0.1391 | Md | Lα1 | 0.0740 | |||
Co | Kα1 | 0.1789 | Te | Lα1 | 0.3289 | Ir | Lα1 | 0.1351 | No | Lα1 | 0.0724 |
Other lines are often used, depending on the type of sample and equipment available.
Kristalai
The desirable characteristics of a diffraction crystal are:
- High diffraction intensity
- High dispersion
- Narrow diffracted peak width
- High peak-to-background
- Absence of interfering elements
- Low thermal coefficient of expansion
- Stability in air and on exposure to X-rays
- Ready availability
- Low cost
Crystals with simple structure tend to give the best diffraction performance. Crystals containing heavy atoms can diffract well, but also fluoresce themselves, causing interference. Crystals that are water-soluble, volatile or organic tend to give poor stability.
Commonly used crystal materials include LiF (lithium fluoride), ADP (ammonium dihydrogen phosphate), Ge (germanium), graphite, InSb (indium antimonide), PE (tetrakis-(hydroxymethyl)-methane: penta-erythritol), KAP (potassium hydrogen phthalate), RbAP (rubidium hydrogen phthalate) and TlAP (thallium(I) hydrogen phthalate). In addition, there is an increasing use of "layered synthetic microstructures", which are "sandwich" structured materials comprising successive thick layers of low atomic number matrix, and monatomic layers of a heavy element. These can in principle be custom-manufactured to diffract any desired long wavelength, and are used extensively for elements in the range Li to Mg.
Properties of commonly used crystals
material | plane | d (nm) | min λ (nm) | max λ (nm) | intensity | thermal expansion | durability |
---|---|---|---|---|---|---|---|
LiF | 200 | 0.2014 | 0.053 | 0.379 | +++++ | +++ | +++ |
LiF | 220 | 0.1424 | 0.037 | 0.268 | +++ | ++ | +++ |
LiF | 420 | 0.0901 | 0.024 | 0.169 | ++ | ++ | +++ |
ADP | 101 | 0.5320 | 0.139 | 1.000 | + | ++ | ++ |
Ge | 111 | 0.3266 | 0.085 | 0.614 | +++ | + | +++ |
graphite | 001 | 0.3354 | 0.088 | 0.630 | ++++ | + | +++ |
InSb | 111 | 0.3740 | 0.098 | 0.703 | ++++ | + | +++ |
PE | 002 | 0.4371 | 0.114 | 0.821 | +++ | +++++ | + |
KAP | 1010 | 1.325 | 0.346 | 2.490 | ++ | ++ | ++ |
RbAP | 1010 | 1.305 | 0.341 | 2.453 | ++ | ++ | ++ |
Si | 111 | 0.3135 | 0.082 | 0.589 | ++ | + | +++ |
TlAP | 1010 | 1.295 | 0.338 | 2.434 | +++ | ++ | ++ |
YB66 | 400 | 0.586 | |||||
6 nm LSM | - | 6.00 | 1.566 | 11.276 | +++ | + | ++ |
Detectors
Detectors used for wavelength dispersive spectrometry need to have high pulse processing speeds in order to cope with the very high photon count rates that can be obtained. In addition, they need sufficient energy resolution to allow filtering-out of background noise and spurious photons from the primary beam or from crystal fluorescence. There are four common types of detector:
- gas flow proportional counters
- sealed gas detectors
- scintillation counters
- semiconductor detectors
Gas flow proportional counters are used mainly for detection of longer wavelengths. Gas flows through it continuously. Where there are multiple detectors, the gas is passed through them in series, then led to waste. The gas is usually 90% argon, 10% methane ("P10"), although the argon may be replaced with neon or helium where very long wavelengths (over 5 nm) are to be detected. The argon is ionised by incoming X-ray photons, and the electric field multiplies this charge into a measurable pulse. The methane suppresses the formation of fluorescent photons caused by recombination of the argon ions with stray electrons. The anode wire is typically tungsten or nichrome of 20–60 μm diameter. Since the pulse strength obtained is essentially proportional to the ratio of the detector chamber diameter to the wire diameter, a fine wire is needed, but it must also be strong enough to be maintained under tension so that it remains precisely straight and concentric with the detector. The window needs to be conductive, thin enough to transmit the X-rays effectively, but thick and strong enough to minimize diffusion of the detector gas into the high vacuum of the monochromator chamber. Materials often used are beryllium metal,
Sealed gas detectors are similar to the gas flow proportional counter, except that the gas does not flow through it. The gas is usually krypton or xenon at a few atmospheres pressure. They are applied usually to wavelengths in the 0.15–0.6 nm range. They are applicable in principle to longer wavelengths, but are limited by the problem of manufacturing a thin window capable of withstanding the high pressure difference.
Scintillation counters consist of a scintillating crystal (typically of sodium iodide doped with thallium) attached to a photomultiplier. The crystal produces a group of scintillations for each photon absorbed, the number being proportional to the photon energy. This translates into a pulse from the photomultiplier of voltage proportional to the photon energy. The crystal must be protected with a relatively thick aluminium/beryllium foil window, which limits the use of the detector to wavelengths below 0.25 nm. Scintillation counters are often connected in series with a gas flow proportional counter: the latter is provided with an outlet window opposite the inlet, to which the scintillation counter is attached. This arrangement is particularly used in sequential spectrometers.
Semiconductor detectors can be used in theory, and their applications are increasing as their technology improves, but historically their use for WDX has been restricted by their slow response (see EDX).
Extracting analytical results
At first sight, the translation of X-ray photon count-rates into elemental concentrations would appear to be straightforward: WDX separates the X-ray lines efficiently, and the rate of generation of secondary photons is proportional to the element concentration. However, the number of photons leaving the sample is also affected by the physical properties of the sample: so-called "
- X-ray absorption
- X-ray enhancement
- sample macroscopic effects
All elements absorb X-rays to some extent. Each element has a characteristic absorption spectrum which consists of a "saw-tooth" succession of fringes, each step-change of which has wavelength close to an emission line of the element. Absorption attenuates the secondary X-rays leaving the sample. For example, the mass absorption coefficient of silicon at the wavelength of the aluminium Kα line is 50 m²/kg, whereas that of iron is 377 m²/kg. This means that a given concentration of aluminium in a matrix of iron gives only one seventh of the count rate compared with the same concentration of aluminium in a silicon matrix. Fortunately, mass absorption coefficients are well known and can be calculated. However, to calculate the absorption for a multi-element sample, the composition must be known. For analysis of an unknown sample, an iterative procedure is therefore used. It will be noted that, to derive the mass absorption accurately, data for the concentration of elements not measured by XRF may be needed, and various strategies are employed to estimate these. As an example, in cement analysis, the concentration of oxygen (which is not measured) is calculated by assuming that all other elements are present as standard oxides.
Enhancement occurs where the secondary X-rays emitted by a heavier element are sufficiently energetic to stimulate additional secondary emission from a lighter element. This phenomenon can also be modelled, and corrections can be made provided that the full matrix composition can be deduced.
Sample macroscopic effects consist of effects of inhomogeneities of the sample, and unrepresentative conditions at its surface. Samples are ideally homogeneous and isotropic, but they often deviate from this ideal. Mixtures of multiple crystalline components in mineral powders can result in absorption effects that deviate from those calculable from theory. When a powder is pressed into a tablet, the finer minerals concentrate at the surface. Spherical grains tend to migrate to the surface more than do angular grains. In machined metals, the softer components of an alloy tend to smear across the surface. Considerable care and ingenuity are required to minimize these effects. Because they are artifacts of the method of sample preparation, these effects can not be compensated by theoretical corrections, and must be "calibrated in". This means that the calibration materials and the unknowns must be compositionally and mechanically similar, and a given calibration is applicable only to a limited range of materials. Glasses most closely approach the ideal of homogeneity and isotropy, and for accurate work, minerals are usually prepared by dissolving them in a borate glass, and casting them into a flat disc or "bead". Prepared in this form, a virtually universal calibration is applicable.
Further corrections that are often employed include background correction and line overlap correction. The background signal in an XRF spectrum derives primarily from scattering of primary beam photons by the sample surface. Scattering varies with the sample mass absorption, being greatest when mean atomic number is low. When measuring trace amounts of an element, or when measuring on a variable light matrix, background correction becomes necessary. This is really only feasible on a sequential spectrometer. Line overlap is a common problem, bearing in mind that the spectrum of a complex mineral can contain several hundred measurable lines. Sometimes it can be overcome by measuring a less-intense, but overlap-free line, but in certain instances a correction is inevitable. For instance, the Kα is the only usable line for measuring sodium, and it overlaps the zinc Lβ (L2-M4) line. Thus zinc, if present, must be analysed in order to properly correct the sodium value.
Other spectroscopic methods using the same principle
It is also possible to create a characteristic secondary X-ray emission using other incident radiation to excite the sample:
- electron beam: electron microprobe;
- particle induced X-ray emission(PIXE).
When radiated by an X-ray beam, the sample also emits other radiations that can be used for analysis:
- electrons ejected by the photoelectric effect: X-ray photoelectron spectroscopy (XPS), also called electron spectroscopy for chemical analysis (ESCA)
The de-excitation also ejects
Confocal microscopy X-ray fluorescence imaging is a newer technique that allows control over depth, in addition to horizontal and vertical aiming, for example, when analysing buried layers in a painting.[3]
Instrument qualification
A 2001 review,
See also
- Emission spectroscopy
- List of materials analysis methods
- Micro-X-ray fluorescence
- Mössbauer effect, resonant fluorescence of gamma rays
- X-ray fluorescence holography
Notes
- ^ Glocker, R., and Schreiber, H., Ann. Physik., 85, (1928), p. 1089
- ISBN 0-306-45324-X.
- .
- PMID 11267748.
References
- Beckhoff, B., Kanngießer, B., Langhoff, N., Wedell, R., Wolff, H., Handbook of Practical X-Ray Fluorescence Analysis, Springer, 2006, ISBN 3-540-28603-9
- Bertin, E. P., Principles and Practice of X-ray Spectrometric Analysis, Kluwer Academic / Plenum Publishers, ISBN 0-306-30809-6
- Buhrke, V. E., Jenkins, R., Smith, D. K., A Practical Guide for the Preparation of Specimens for XRF and XRD Analysis, Wiley, 1998, ISBN 0-471-19458-1
- Jenkins, R., X-ray Fluorescence Spectrometry, Wiley, ISBN 0-471-29942-1
- Jenkins, R., De Vries, J. L., Practical X-ray Spectrometry, Springer-Verlag, 1973, ISBN 0-387-91029-8
- Jenkins, R., R.W. Gould, R. W., Gedcke, D., Quantitative X-ray Spectrometry, Marcel Dekker, ISBN 0-8247-9554-7
- Penner-Hahn, James E. (2013). "Chapter 2. Technologies for Detecting Metals in Single Cells. Section 4, Intrinsic X-Ray Fluorescence". In Banci, Lucia (Ed.) (ed.). Metallomics and the Cell. Metal Ions in Life Sciences. Vol. 12. Springer. ISSN 1868-0402
- Van Grieken, R. E., Markowicz, A. A., Handbook of X-Ray Spectrometry 2nd ed.; Marcel Dekker Inc: New York, 2002; Vol. 29; ISBN 0-8247-0600-5
External links
- Spectroscopy at Curlie
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