Fourier transform infrared spectroscopy (FT-IR) is an established technique for the qualitative determination of organic structure. Absorption infrared spectroscopy can be employed quantitatively using Beer’s law. However, reliable quantitative analysis requires that the pathlength is known within 1%. Calculations based on nominal spacer thickness are not sufficient for accurate work, due to variances in cell assembly and thermal expansion. The “interference pattern” method provides an accurate determination of cell pathlength, but requires plotting of empty cell spectra and counting of the fringes. This work provides a MATLAB application with a graphical user interface implementing an interactive plot where the user selects the spectral region for the calculation. Then, the program automatically computes the cell pathlength, providing a rapid determination of pathlength for practitioners.

Absorption infrared (IR) spectroscopy is an established instrumental method for qualitative determination of molecular functionality via characteristic bond resonance frequencies and absorbance intensities. Modern IR spectrophotometers utilizing Fourier transforms allow for fast and efficient data collection. This technological advance has enhanced the utility of IR spectroscopy, making it an expedient method for qualitative as well as quantitative measurements.

Vibrational excitation occurs when chemical bonds absorb photons whose frequency matches that of the bond. For this excitation to be IR-active, the magnitude of the dipole moment vector must change with oscillation. In absorption spectroscopy, the fraction of incident light absorbed by the sample at a specific wavelength is proportional to the concentration of absorbing molecules in the optical path, as described by the Beer-Lambert law

where ϵ is the molar attenuation coefficient (known as the molar extinction coefficient in older literature), 

 is the concentration of the chromophore, and 

 is the pathlength. Provided that the molar attenuation coefficient and pathlength are known, the formula can be rearranged, allowing for concentration to be calculated from an absorbance peak height or area. Harris (1) provides in-depth discussion of the interplay of concentration, pathlength, and intensity.

Cell pathlength is typically set using lead or Teflon spacers sandwiched between two salt plate windows. According to Meloan (2), quantitative reliability of IR measurements necessitates that the pathlength must be known within 1%. Because cells are often disassembled for cleaning and polishing of windows, the pathlength can vary upon reassembly relative to calibrations and the nominal spacer dimensions provided by the manufacturers are not adequate for quantification. Since cell pathlength may change due to thermal expansion (3), in-situ measurements provide the most reliable pathlength (4). The pathlength should be calculated during calibration, followed by determination of the attenuation coefficient based on the known concentration and absorbance measurement:

If the cell is reassembled, the pathlength

 should be measured before the sample is loaded, and then the concentration is determined using:

Pathlength Measurement Using the Interference Pattern

When the cell is empty, the refractive indices are significantly different for the salt plate windows and the inert gas (such as nitrogen) in the sample cell. Thus, a measurable amount of the irradiating light is internally twice reflected at the gas-salt interfaces within the cell before exiting on the detector side. Constructive and destructive interference occurs between the irradiating light and internally reflected light at all wavelengths. Maximum intensities are observed when the wavelength of light exiting the cell is an integer multiple of twice the cell pathlength. Likewise, minima in intensity occur when the wavelengths of exiting light are half integer multiples of twice the cell pathlength. Wavelengths lying between half and full integer multiples give rise to intermediate absorbance intensities. The resulting spectrum is comprised of successive oscillations known as an 

, which allows for the pathlength to be calculated from the span of several adjacent minima using Equation 4:

 is the number of cycles (fringes), and ν̃

 are the high and low wavenumbers selected for the calculation (4).

The application can be run on any operating system where MATLAB is installed. No additional MATLAB toolboxes are required. The code is developed for absorption spectroscopy. Before scanning the empty cell, a background scan should be collected to remove environmental effects. The cell should be clean, and the windows free of surface imperfections or clouding. Next, the empty cell should be scanned, ideally with a dry inert gas in the sample space, and the instrument output should be saved in a .csv format, with the first column containing wavenumbers and the second column containing absorbance or percent transmittance. The app will disregard any lines in the file containing text.An example .csv file is provided at the link that appears in the Appendix section of this article.

A screenshot of the application graphical user interface is shown in Figure 1. The empty cell spectrum is loaded by clicking the 

 button, which opens a standard file browser allowing the practitioner to select the empty cell .csv file. After the file has loaded, the file name will be displayed as the title of the plot; in Figure 1, the file is Path.csv. The entire empty cell spectrum is displayed as a blue line (obscured by the smoothed red line in Figure 1), enabling the user to visually inspect the spectra before selecting the region to be used for the pathlength calculation. The user can vary the region of the spectrum used for the calculation by adjusting the maximum and minimum values in the Wavenumber Window box. Data resolution is calculated and displayed.

A smoothing filter is provided since noise in the spectra can interfere with determination of the intensity minima used for counting cycles. The smoothing filter applies a quadratic spline fitted to a specified wavenumber span. Setting the smoothing span to the width of the top third of the cycle typically works well. The plot is interactive, thus clicking on the curve displays coordinates, permitting rapid determination of a reliable span to use
for smoothing.

Once the desired region has been established, and the span specified, depressing the 

 button performs the calculation, and generates a value for the cell pathlength in centimeters. The smoothed spectrum is displayed as a red line. The number of fringes used in the calculation are determined automatically, eliminating tedious counting where user errors may occur. Circles appearing on the plot of Figure 1 denote the fringe minima detected by the program and the 

) relative to the first minimum. The first and last circle observed on the plot coincide with the actual wavenumber values used to perform the calculation. The calculation should be performed two to three times, using different wavenumber ranges to confirm the pathlength. Values should vary by less than 0.2% (4). The app is configured so that smoothing can be changed without resetting the selected wavenumber range. Noise in the spectra can cause incorrect identification of the cycle minima if the smoothing span is too small. The user can identify this behavior when viewing the circles on the calculated plot, reset the smoothing filter, and recalculate the pathlength. The complete cycles within the active plot window are used in the calculation, not the nominal wave numbers used in the GUI to select the window.

The pathlength application provides a convenient method to accurately and quickly calculate the pathlength of IR cells. The app is easy to use, and the visualization of the fringe pattern provides an opportunity for the user to interactively change the selected wavenumber window and smoothing to use for the pathlength calculation. The app eliminates tedious counting where user error may occur. Code is provided in the Appendix, and the pathlength app is distributed via the MATLAB Central File Exchange repository at 

https://www.mathworks.com/matlabcentral/fileexchange/77353-pathlength

. Documentation is provided with the app download for users who may need to edit the data .csv file as well as an example data file and step-by-step instructions.

A text file containing a description of the Excel data file, and the actual MATLAB code, is published online at 

https://www.egr.msu.edu/thermoprops/pathlength

. An example Excel data file (InstrumentFile.csv) is also provided at the link.

This work was supported by the National Science Foundation under Grant No. 1603705 and USDA National Institute of Food and Agriculture, Hatch/Multi-State project MICL04192. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funding agencies.

 (W. H. Freeman: New York, New York, 7th Edition, 2006).

K.E. Amunson, B.A. Anderson, and J. Kubelka, 

Chemical Infrared Spectroscopy, Vol. 1: Techniques

 (John Wiley & Sons, Inc, New York, New York, 1963).

William G. Killian, Jr., Jackson A. Storer, and Carl T. Lira 

are with the Department of Chemical Engineering and Materials Science at Michigan State University, in East Lansing, Michigan. 

is with the Department of Physical Sciences at Ferris State University, in Big Rapids, Michigan. Direct correspondence to 

Articles

Tutorial

Reliable quantitative FT-IR measurements require that the pathlength be known to within 1%. Pathlength estimations based on nominal spacer thickness are not reliable and require that the actual pathlength be measured for accurate data. We demonstrate how.

A MATLAB Application for Calculation of Cell Pathlength in Absorption Transmission Infrared Spectroscopy

It is fairly easy to generate a surface enhanced Raman scattering (SERS) signal. However, there are severalissues to be aware of when trying to use these signals in analytical applications. The SERS signal arises from the combination of the number of molecules (

), the polarizability or cross section of the molecule (σ), and the electric field (

) experienced by the molecules. Understanding how these different variables interact to generate the enhanced SERS response is the key to applying SERS accurately. Here, we try to share experiences and some helpful references to assist people interested in applications using SERS.

It has been more than40 years since the realization that Raman signals are enhanced on nanostructured metal surfaces (1). Figure 1 illustrates the advantages of surface enhanced Raman scattering (SERS), which provides a larger signal from fewer molecules. Over those past 40 years, significant progress has been made toward understanding the origin of the signal enhancement, enabling SERS to become a promising technique for chemical-specific analytical analysis. It is now understood how the electric fields originating from localized surface plasmon resonances on nanoparticles can concentrate the incident laser and generate significant enhancements in Raman scattering from molecules at the surface (2). In particular, nanoparticle dimers and larger aggregates with nanometer-scale gaps and crevices produce some of the largest electromagnetic field enhancements (3). In fact, it is fairly easy to generate a SERS signal; however, as many SERS practitioners will testify, there are a few things to be aware of when trying to use these signals in analytical applications (Table I). The SERS signal arises from the combination of the number of molecules (

) experienced by the molecules. Understanding how these different variables combine to generate the SERS response is the key to applying SERS. Here, I share my experiences and try to provide some helpful references to help people interested in applications using SERS. The following sections highlight some key concepts that people should be aware of when using SERS.

Much of the pioneering work in SERS has been performed using a molecule such as rhodamine or other molecules that have electronic resonance in the visible region (2). These experiments are often called 

surface enhanced resonance Raman scattering

 (SERRS). Just as resonance Raman increases the cross-section (σ) of spontaneous Raman scattering, it also enables the lowest limits of detection in SERS experiments. Most people studying single molecules use this additional enhancement (4). It turns out that many of these molecules are fluorescent dyes, and even with excitation away from the peak absorption, some level of pre-resonance is accessed boosting the SERS response.

The other class of molecules that is commonly detected in SERS is aromatic thiols and pyridines. Although these molecules do not have an intrinsic resonance, they are reported to form charge transfer complexes on the plasmonic surfaces that also increase the relevant cross-section of the analyte and boost the enhancement. These charge-transfer mechanisms are commonly associated with “chemical enhancement” (which has become a default category for enhancement that is not from the enhanced electric field).

Some molecules are just difficult. Glucose is one example. Although glucose has been detected by SERS, this often involves some form of surface functionalization or capture, such as reacting with boronic acid on the surface (5,6). It is often worth measuring the spontaneous Raman limit of detection for a molecule; with SERS one should be able to detect the molecule at a lower concentration. This is one way to distinguish SERS from weak spontaneous Raman scattering. However, if molar concentrations are needed to see the spontaneous Raman signal, the SERS signal may be difficult to measure.

SERS Enhances the Signal from the Molecules at the Surface

The SERS effect is a very short-range enhancement. Studies done on the distance dependence of SERS show the signal enhancement goes away within a few nanometers (7,8). Other studies indicate the molecule is physisorbed to the surface (9). There was even discussion of a “first layer effect,” where the molecules adsorbed to the surface showed a larger enhancement (10).The number (

) of molecules at the surface can often be modeled with a Langmuir isotherm, which correlates the surface coverage to the affinity of the molecule to the surface. At concentrations where your molecule is unlikely to have significant coverage, it is unlikely that one will detect SERS. Both electromagnetic and chemical enhancement mechanisms increase the signal of molecules at the surface. For nanoparticles dropped onto a substrate and dried, the molecules that stick to the nanoparticles are easier to detect.

The idea of a SERS tag is to put a molecule on the surface that gives a strong signal (see above) and then incorporate some form of chemical recognition agent (such as DNA, an antibody, or an aptamer) that binds the target molecule (11,12). Although these approaches have been very successful, it is worth remembering that your limit of detection and sensitivity will now be controlled by the chemical recognition agent on your tag.

Intensities Depend on the Nanostructures, Too

It has been shown that the large majority of the SERS signal originates from “hotspots,” (13) generally regarded as the high electric-field (

) regions associated with gaps and crevices. This means that one molecule in an electric field enhanced region of 106 will be as bright as either 106 molecules in solution, or 105 molecules in a region with an electric field enhancement of 10. This tells us that small changes in the number of molecules in “hotspots” can create large intensity variations. This is particularly problematic when using colloidal nanoparticles, where it can be very challenging to aggregate nanoparticles in a reproducible manner.

A lot of effort has gone into making patterned nanostructures as SERS substrates (14). Many of these substrate approaches still have some variation in the electric field enhancements, and it is common to observe intensity variation on the scale of 10% in these systems. One approach to averaging out this heterogeneity is to measure multiple spots. One study suggested that more than 100 spots are needed to properly capture this variance (15).

This is not to say that SERS cannot be quantitative (16). The use of internal standards, assumed to have the same intensity distribution as an analyte, can correct for this variance. This correction can be a co-adsorbed molecule (17), or, perhaps preferably, a stable isotope variant of the target molecule (18).

The metric used to compare the enhancement observed from a SERS active material is the enhancement factor (

) (19). In theory, this number represents the increase in the Raman signal expected from a molecule. In practice, this is really difficult to determine. It requires that you measure a SERS signal (

SERS), and you have the spontaneous Raman signal (

Raman) from a known number of molecules (

Raman) under similar experimental conditions. With these four numbers, the EF can be calculated as follows:

In perhaps the simplest case, a monolayer of thiol on a patterned nanostructured surface, approximations are still required. Because of the influence of hotspots, the number of molecules detected by SERS (

SERS) is difficult to know. Further, the free molecule may have a different cross-section than the adsorbed molecule, making 

Raman also uncertain. Given these uncertainties, the 

 is at best a relative number for the conditions under which it was determined. When reporting 

s, it is important to provide as much information as possible about how the 

 was determined. As noted above, just because one molecule enhances well, another type of molecule may have a very different 

The Molecule You Put in Your Sample May Not Be What You Detect

One frustrating aspect of SERS is the vibrational frequencies observed may vary from those of the molecules in solution or powder forms, such as is observed in Figure 1. In SERS, there is a strong polarization dependence that selectively enhances those modes aligned with the enhanced electric field. In the past 10 years, experiments show that the electrons in the metals, which generate the plasmon resonance and enhance the Raman signal, can also do chemistry on the analytes. One classic example is para-aminothiophenol, where theories on changes in selection rules to activate Raman-inactive B2 modes were developed, only to find out the new frequencies arose from the formation of dimercaptoazobenzene on the surface (20). Understanding these effects is an active area of SERS research today. To avoid these effects, it is important to use low laser powers, generally less than 1 mW of power, in a diffraction-limited focus of a microscope objective focus. These low powers can minimize these photoreactions as well as heating that can cause problems in your measurement. For those seeking to use SERS, the best practice is to generate a calibration curve with known concentrations of your analyte at low laser powers, and use a strong band (or multivariate model) that provides the most accurate concentration determination.

P.L. Stiles, J.A. Dieringer, N.C. Shah, and R.R. Van Duyne, 

K.L. Wustholz, A.-I. Henry, J.M. McMahon, R.G. Freeman, N. Valley, M.E. Piotti, M.J. Natan, G.C. Schatz,and R.P. Van Duyne, 

B. Sharma, P. Bugga, L.R. Madison, A.I. Henry, M.G. Blaber, N.G. Greeneltch, N.H. Chiang, M. Mrksich, G.C. Schatz, and R.P. Van Duyne,

X. Gu, H. Wang, Z.D. Schultz, and J.P. Camden, 

J.A. Dieringer, A.D.McFarland, N.C. Shah, D.A. Stuart, A.V. Whitney, C.R. Yonzon, M.A. Young, X. Zhang, and R.P. Van Duyne, 

S. Lal, N.K. Grady, G.P. Goodrich, and N.J. Halas, 

D. Graham, B.J. Mallinder, and W.E. Smith, 

N.R. Isola, D.L. Stokes, and T. Vo-Dinh, 

B. Sharma, M.F. Cardinal, S.L. Kleinman, N.G. Greeneltch, R.R. Frontiera, M.G. Blaber, G.C. Schatz, and R.P. Van Duyne, 

A. Subaihi, Y. Xu, H. Muhamadali, S.T. Mutter, E.W. Blanch, D.I. Ellis, and R. Goodacre, 

P.L. Stiles, J.A. Dieringer, N.C. Shah, and R.P. Van Duyne, 

Y.-F. Huang, H.-P. Zhu, G.-K.Liu, D.-Y. Wu, B. Ren, and Z.-Q. Tian, 

is with the Department of Chemistry and Biochemistry at The Ohio State University, in Columbus, Ohio. Direct correspondence to:


SERS offers many advantages. However, there are several issues to be aware of when trying to use SERS signals in analytical applications.

Demystifying SERS: A Newcomer’s Guide to Using Surface Enhanced Raman Scattering

In writing this column over the years, we have covered many topics related to the use of statistics and chemometrics in spectroscopy. At this point, we are taking a break (so to speak) to build a scorecard of chemometric techniqu es consisting of topics we have either previously discussed or plan to discuss going forward. Although it is quite difficult to define these complex topics in short sentences, without the use of graphical or mathematical representations, we have attempted to do so here. In this column, we show method comparison tables of chemometric methods, and include the method name, a brief text description, key tutorial references, whether the method was previously discussed in detail within previous “Chemometrics in Spectroscopy” articles, and the primary analytical purpose of the method. In past articles, we have addressed many details associated with quantitative and qualitative spectroscopy, particularly the fine points of calibration methods, and we plan to continue to do so into the future. We note that we have already covered some aspects of signal preprocessing in the context of other topics, but have not addressed these in great detail. As we progress with this series, we intend to cover the essential chemometric methods in greater detail and expand into new frontiers.

 (2nd edition, Elsevier) recommended that the subjects of neural networks (NNs)and multivariate curve resolution (MCR) be covered, as well as other advanced chemometrics techniques that have not been described to date in our column series of the same name (1,2). Although we have addressed many topics in the column, there are still more to cover. Some of the techniques we have not addressed will receive attention in future columns. And to expand on that, at some point we hope to provide more information on available open source code and programming languages for chemometric methods, as well as commercial software options. We may not get to write detailed articles on all of the topics listed in the following tables, but, at some future time, we plan to discuss many more of them. We note that, for the tables below, we restricted ourselves to one tutorial or descriptive reference for each of the topics (rows), resulting in 29 additional references (3–31). These summary tables are an imperfect approach, because there are several (or many) very good references for each topic, but, given space limitations, we selected a single reference for each topic that we considered most applicable to 

 readers, and also tried to select those references that might be considered “classic,” or tutorial papers. As we delve into each subject or topic, we will include additional references that will be helpful to the reader in understanding and using the various chemometric methods.

Table I represents signal preprocessing techniques; these data processing methods are often used prior to the application of explorative, qualitative, or quantitative methods. Table II lists component analysis techniques used mostly for data exploration and discovery. Table III shows the variety of quantitative (calibration) methods used to take raw or preprocessed data, and compute predictive calibration models for quantitative determination of physical or chemical parameters in a dataset. Table IV provides a summary of the qualitative (calibration) methods used to take raw or preprocessed data and compute predictive calibration models for qualitative (classification) of different groups or types of samples or of physical or chemical parameters in a dataset. As noted, because of space limitations, a single primary reference is included for each method.

(Elsevier, Academic Press, London, United Kingdom, 2nd Ed., 2018).

A. Jirasek, G. Schulze, M.M.L. Yu, M.W. Blades, and R.F.B. Turner, 

B.K. Alsberg, W.G. Wade, and R. Goodacre, 

A. Kohler, J. Sulé-Suso, G.D. Sockalingum, M. Tobin, F. Bahrami, Y. Yang, J. Pijanka, P. Dumas, M. Cotte, D.G. Van Pittius, and G. Parkes, 

N.B. Zorov, A.A. Gorbatenko, T.A. Labutin, and A.M. Popov, 

R.J. Barnes, M.S. Dhanoa, and S.J. Lister, 

M.C.U.Araújo, T.C.B. Saldanha, R.K.H. Galvao, T. Yoneyama, H.C. Chame, and V. Visani, 

S. Prahl, “Everything I Think You Should Know About Inverse Adding-Doubling” (Oregon Medical Laser Center, St. Vincent Hospital, 2011), pp. 1–74.

D. Svozil, V. Kvasnicka, and J. Pospichal, 



Partial Least Squares (PLS) Regression (Inverse Least Squares)

A.J. Myles, R.N. Feudale, Y. Liu, N.A. Woody, and S.D. Brown, 



Linear Classifiers: Logistic Regression, Naive Bayes Classifier

I. Rish, “An Empirical Study of the Naive Bayes classifier,” In 

IJCAI 2001 
Workshop on Empirical Methods in Artificial Intelligence 

M.G. Sowa, L. Leonardi, J.R. Payette, K.M. Cross, M. Gomez, and J. Fish, 

W. Wu, B. Walczak, D.L. Massart, S. Heuerding, F. Erni, I.R. Last, and K.A. Prebble, 

N.L. Afanador, A. Smolinska, T.N. Tran, and L. Blanchet, 



Soft Independent Modeling By Class Analogy (SIMCA)

O.G. Meza-Márquez, T. Gallardo-Velázquez, and G. Osorio-Revilla,


 J. Luts, F. Ojeda, R. Van de Plas, B. De Moor, S. Van Huffel, and J.A. Suykens, 

 serves on the Editorial Advisory Board of 

. He is also a Certified Core Adjunct Professor at U.S. National University in La Jolla, California. He was formerly the Executive Vice President of Research and Engineering for Unity Scientific and Process Sensors Corporation.

serves on the Editorial Advisory Board of 

, and runs a consulting service, Mark Electronics, in Suffern, New York. Direct correspondence to: 

Chemometrics in Spectroscopy

We provide a scorecard of chemometric techniques used in spectroscopy. The tables and lists of reference sources given here provide an indispensable resource for anyone seeking guidance on understanding chemometric methods or choosing the most suitable approach for a given analysis problem.

A Survey of Chemometric Methods Used in Spectroscopy

Total reflection X-ray fluorescence (TXRF)spectroscopy is one of the most impressive analytical techniques, and provides spectral signatures of materials that can be used to unravel their elemental composition. Within a few seconds, and with minute sample amounts and limited sample preparation, a first characterization of qualitative character can be obtained, where previouslythorough and quantitative information would require a full experimental design approach. TXRF extends the capabilities of XRF down to the ultratrace elemental range, with detection limits reaching the femtogram levels. However, given that TXRF is a highly sensitive technique, variations between the samples or the analysis conditions may cause very slight spectral differences that may be difficult to distinguish or identify. Therefore, and despite its apparent versatility and ease of use, many issues remain in TXRF analysis, and its application requires knowledge and care. A network (1) was set up for training and expanding the user community, as well as tackling the challenges of the technique. Here, we provide a tutorial on the techniques and key steps that any user, and particularly new users, should follow.


TXRF is a surface sensitive multielement microanalysis technique, based on the principle that a collimated X-ray beam is totally reflected when striking a flat, highly polished, and reflective surface material at an incident angle below the critical angle of the substrate (2–5). The fundamentals of TXRF are based on Fresnel formalism and on the complex index of refraction for X-rays (

 the decrement of the refractive index, and 

the absorption term). Considering absorption negligible, the critical angle 

 refers to incoming photon energy (keV), 

 is the atomic weight (g/mol), and ƿ is the substrate density (g/cm3) of the substrate.

A complex triangular volume of X-ray interferences dominated by waves is created by the superposition of the incoming and refracted beam, the intensity of which varies according to the distance above the surface (Figure 1). This standing-wave field is composed of an alternated node and antinode pattern whose period is a function of the incident angle and photon energy. The period (∝

) is typically only several tens of nanometers, while the height of the standing-wave triangular volume can reach several micrometers. For an ideal 100% reflective surface, and angles below the critical angle, the intensity of the standing-wave lies alternatively between zero (nodes) and four times (antinodes) the intensity of the incident photon energy. But, even for highly reflective materials, some photons penetrate the substrate, the intensity of which varies radically with the angle of incidence. The 

 is defined as the depth at which the intensity of the primary radiation is reduced to 

 (about 37%), and its value remains low (almost constant) below the critical angle. Working below 

 thus favors low scattered contributions to the background from the substrate, which, in turn, directly improves the low detection limits and high sensitivity and detection power of TXRF.

Any thin sample placed on the substrate within the standing-wave field will be irradiated by both the incident and the reflected beam as the incident radiation experiences total reflection at the substrate interface. A thin solid residue (from a droplet, or powder, a few 100 nm thick) will be subjected to a great number of standing waves, and its fluorescence emission intensity on average will be doubled, whereas a thin monolayer or layered structure (<100 nm thick) will experience standing waves arising above and within its structure, and the fluorescence intensity will vary, according to the layer position within nodes and antinodes. Indeed, the intensity of the fluorescence radiation emitted by the elements present on or at the substrate surface is directly proportional to the intensity of the standing-wave field, and, thus, of the primary photon energy intensity.

Calculate your critical angle, and check the penetration depth for your experimental conditions.

Know Your Instrument, and Check its Performance

A number of instruments are available to the TXRF community, ranging from different types of commercial TXRF spectrometers (such as benchtop or portable), to custom-made instruments in laboratories or synchrotron facilities (4,8). The main components are the X-ray source, the beam guidance (for example, monochromator, apertures, filters), the reflector sample stage (with or without angle scan option), and the energy dispersive X-ray fluorescence detector (for example, silicon drift diode and germanium). All these parts can be carefully selected to optimize the instrumental conditions of analysis, according to the nature of the sample and
characterization needs.

The X-ray source choice is crucial to ensure successful excitation of the elements of interest. Indeed, the efficiency of the excitation decreases for elements whose absorption edges are away from the primary photon energy. Laboratory X-ray sources like molybdenum (17.4 keV) are favored, but if lower Z elements are to be assessed, chromium (5.4 keV) or a plasma source should be considered. To ensure low background, a high level of monochromaticity, spectral purity, low divergence, and flux are required. Additionally, the beam needs to be shaped in size, ideally to illuminate a 1 mm2 area (for example, 1 mm by 40 μm) on the sample. Using a synchrotron as the X-ray source presents flux, a tunable energy range (0.078–90 keV), spectral purity, collimation, and linear polarization, thus providing excitation and detection advantages (Table I). Lastly, the detector, placed at 90 o above the sample surface, must have its solid angle maximized for effective collection of the emitted radiation, by getting close to the sample (a few mm or less) or using a large sensor area (30 to 100 mm2). The type or size of detector and detector windows will determine the spectral resolution obtained from the data, and the sensitivity to the light elements.

Check the stability of your X-ray source flux, size, position, and
spectral characteristics.

Check the repeatability of the substrate positioning for the critical
angle considered.

If adjustable, properly select your critical angle with respect to the angular scan shape obtained. This also ensures that your sample complies with TXRF conditions. If not adjustable, use a reflector substrate that best matches your beam incoming angle.

Check the response function of your detector for the energy employed, and your detector stability.

If not fixed, check the rotation axis for your source–substrate–detector system.

Use blank and certified reference materials to perform quality control of your setup.

Establish or follow standard operating procedures.

A key aspect for reliable elemental analysis is knowing the sample under investigation. A plethora of samples can be investigated with TXRF, coming from many different fields of research (Table II). As a consequence, the sample can present itself under various physical and chemical states, most of them allowing for elemental content determination either directly (such as liquids or fine powders) or after some sample preparation steps (4–7,8) to transfer or optimize them into liquid form. Many procedures, including grinding, suspension, dilution, digestion, and preconcentration,
have been proposed.

Carefully select your reflector substrate. Use a flat (<ʎ/20), smooth (<1 nm roughness), pure, and surface-clean material. Quartz reflectors allow for the best results.

Use only reagents of ultrahigh purity grade and that will not modify the elemental composition of your sample.

Carefully select your internal calibration standard. It should not present any spectral interference at any position of the emission spectra, its emission lines should frame the elemental range of analysis, and its concentration should lie within the average sample concentration range. Also, add it prior to any preparation steps.

Evaluate the total sample mass deposition placed onto the reflector. It should not exceed the microgram level, and is highly matrix-dependent.

Ensure that the final deposit of sample or residue is homogeneous, thin (a few 100 nm thick), and entirely contained in the surface so as to be illuminated by the incoming beam.

Thoroughly check the recovery rates obtained for the elements
of interest.

For each type of sample, optimize and revise the sample preparation procedures.

Building a consistent system via standard operating procedures (9) and experimental design ensures the quality and reliability of the results obtained.

Run blank or certified reference materials (Figure 2) to check your instrument, and eventually derive the instrumental parameters, if not determined.

Optimize the counting time to improve the signal-to-noise ratio (100 s to 1 h, depending on the elemental concentrations targeted), and maintain a low detector dead time.

< 20), work under vacuum (this is also efficient to improve the background and the detection in general), with low excitation photon energy, and use a germanium detector, or an silicon drift detector (SDD) without windows, or with thin polymer windows.

Calculate your total budget uncertainty (comprising sample preparation, and instrumental and data analysis).

Critically assess your data, and compare them with other techniques, taking into account the analytics’ inherent strengths and drawbacks.


Calibration of the spectrometer is a prerequisite to any quantitative analysis, and provides relative sensitivity values (

) of all the elements targeted versus a reference element for specific measurement conditions. It uses multi-element reference materials of various concentrations to build a linear relationship of 

, by measuring the net intensity or area (

) of an elemental peak and its concentration (

). These sensitivities can be retrieved by calculations using fundamental data tables, if all instrumental parameters are perfectly known.

The quantification procedure can be undertaken in one of three ways. The first is the use of an internal calibration standard of known concentration (

The second is the use of external calibration with reference materials close to the sample itself, and with graduated concentrations of the unknown elements. The third is reference-free quantification, which requires perfect knowledge of the instrumental set up parameters (such as source and detectors), and the use of the fundamental
parameters approach.

Build your quantification strategy carefully.

Supervise your peak deconvolution and fitting algorithms procedure.

Assess the various elemental detection limits of your setup with respect to minimum mass deposition, which is background dependent. According to IUPAC rules:

back is the net background intensity or area below the element’s net area of interest.


Total-Reflection X-ray Fluorescence Analysis and Related Methods

 (Wiley and Sons, Hoboken, New Jersey, 2nd Edition, 2015).

I. De La Calle, N. Cabaleiro, V. Romero, I. Lavilla, and C. Bendicho, 

E. Margui, I. Queralt, R. Van Grieken, in 

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J. Lubeck, B. Beckhoff, R. Fliegauf, I. Holfelder, P. Hoenicke, M. Mueller, B. Pollakowski, F. Reinhardt, and J. Weser, 

L. Borgese, R. Dalipi, A. Riboldi, f. Bilo, A. Zacco, S. Federici, M. Bettinelli, E. Bontempi, and L.E. Depero, 

is with Elettra–Sincrotrone Trieste in Trieste, Italy. Direct correspondence to 

Total reflection X-ray fluorescence (TXRF) spectroscopy offers impressive performance, providing ultratrace elemental analysis with detection limits reaching the femtogram levels. Here, we provide a tutorial on the technique and the key steps that users should follow.

Spectroscopy-08-01-2020

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