FROM DETECTION TO QUANTIFICATION WITH LIBS: OVERVIEW AND MODERN PHYSICO‑CHEMICAL CONSIDERATIONS

ABSTRACT.

Laser-Induced Breakdown Spectroscopy (LIBS) offers rapid, multi-elemental analysis with minimal sample preparation, yet its routine application for high-precision quantitative analysis remains constrained by strong and samplespecific matrix effects. This review synthesizes recent advances in understanding how moisture content, electrical conductivity, mechanical properties, and other matrix variables alter ablated mass, plasma formation, and the key plasma parameters – electron temperature and electron density that determine spectral emission. Emphasis is placed on the need for integrated physico-chemical models that couple target-material properties to plasma dynamics and spectral output, enabling predictive correction of stoichiometric deviations. By introducing mechanistic insight, LIBS can transition from a predominantly qualitative tool to a reliable method for demanding industrial and scientific quantitative applications.

KEYWORDS: laser-induced breakdown spectroscopy, LIBS, matrix effects, physico‑chemical modeling, plasma parameters, quantitative analysis, elemental analysis.

For citation: Lapin I.I. From detection to quantification with LIBS: overview and modern physico‑chemical considerations. Trace elemets in medicine. 2026;27(3):31−42. DOI: 10.19112/2413-6174-2026-27-3-31-42 

ВВЕДЕНИЕ

Laser-induced breakdown spectroscopy (LIBS) is a relatively new atomic emission spectrometric method (Brech, 1962). This method can be used for qualitative, semi-quantitative, and, in some cases, quantitative elemental analysis of a wide range of samples (Rusak et al., 1998; Devia et al., 2015). It provides faster analysis, requires minimal sample preparation and consumables (primarily inert gases), is relatively simple to operate, and is applicable for the analysis of solid materials as well as, but to a lesser extent, for the analysis of liquids, gases, and aerosols (Lenk et al., 1996; Sneddon, Lee, 1998; Angel et al., 2001; Lee et al., 2000, 2004; Radziemski, 2002; Song et al., 2002; Le Drogoff et al., 2004a, 2004b; Gunaratne et al., 2006; Latkoczy, Ghislain, 2006; Lei et al., 2009, 2011; Wilsch, Strangfeld, 2022). Using LIBS, elemental analysis can be performed in both laboratory and field conditions. LIBS is a spectrochemical analytical method that uses light emitted by laser-induced plasma to obtain emission spectra of the sample for subsequent analysis of material composition (Hahn, Omenetto, 2010, 2012). In LIBS, a short, high-energy laser pulse is used to generate plasma (Kearton, Mattley, 2008). Most commonly, Nd:YAG lasers (using neodymium-doped yttrium aluminum garnet as the active medium) are used for plasma generation. The light emitted by the plasma during its radiative relaxation is used to obtain the sample’s spectra using a spectrometer (Radziemski, Cremers, 2013). The process begins with focusing the laser beam onto the surface of the sample being analyzed, which locally ablates and heats a small amount of the sample material to a high temperature, thereby generating plasma. The light emitted by the plasma during its relaxation is collected and directed into the spectrometer using focusing optics to obtain the emission spectrum. The emission spectrum of the laserinduced plasma contains emission lines corresponding to electronic transitions characteristic of the excited atoms and ions of the detected chemical elements. To identify emission lines, the corresponding database from the U.S. National Institute of Standards and Technology (NIST) is used.

For the quantitative determination of each element, either calibration curves are developed (for each element, and measurements are performed under identical conditions), or the calibration-free LIBS method is used (Bulajic et al., 2002; Anzano et al., 2006; Miziolek et al., 2006).

LIBS has been in use since the early 1960s, when the first ruby laser was developed (Maiman, 1961). In 1963, with the development of Q-switched lasers, LIBS methods became more widely used in practice (Moenke, Moenke-Blankenburg, 1973).

In the early 1970s, another major work devoted to LIBS was published (Yamamoto et al., 1996). In the 1980s, Nd:YAG lasers gained popularity and became the most common laser system. Since the 1980s, significant progress has been made in laser and detector technology. Over time, reliable components were developed that further improved LIBS as a method for the qualitative and quantitative study of various materials (Jurado-López, De Castro, 2003), including metal alloys for metallurgy and jewelry (Gruber et al., 2001).

Samples of gemstones and sedimentary rocks (Asgill, Hahn, 2009; Segnini et al., 2014), gas mixtures, and aerosols have also been analyzed using LIBS (Lawrence-Snyder et al., 2007; Zimmer, Tachibana, 2007). Solutions have also been studied using this method. This analytical method makes it possible to analyze samples of vegetables (Latkoczy, Ghislain, 2006), soils, plant parts (Khumaeni et al., 2011), a range of food products (Judge et al., 2013), fossils, and nuclear fuel (Abdulmadjid et al., 2006).

LASER-INDUCED EMISSION SPECTROSCOPY (LIBS)

LIBS offers numerous advantages over other spectroscopic analytical methods. In LIBS, a highenergy laser beam is focused onto the sample, which ablates and subsequently heats a small amount of sample material, resulting in the formation of a glowing plasma.

The light emitted during the radiative relaxation of the laser-induced plasma is collected and directed by focusing optics into a spectrometer, which records the emission spectrum. The wavelengths of the emission peaks detected in the spectrum are characteristic of the atoms and ions of the elements present in the sample material (Meissner et al., 2004; Wiens et al., 2005; Yueh et al., 2006).

Advantages of LIBS

LIBS has the following advantages over other methods (Meissner et al., 2004; Wiens et al., 2005; Yueh et al., 2006; Rakovský et al., 2014): 

• minimal sample preparation is required; in some cases, none is required at all;
• the method is insensitive to surface contamination of the analyzed sample, due to the possibility of preliminary irradiation with an additional laser pulse preceding the one used to “select” the analyzed portion of the sample;
• an extremely small amount (5–100 ng) of sample material is used, which allows LIBS to be classified as a semi- or non-destructive testing method;
• direct recording of the emission spectra of the ablated portion of the sample material is performed within a few seconds;
• it allows for the direct analysis of solid samples, liquids, and aerosols;
• the method demonstrates fairly high sensitivity in the determination of alkali metals (detection limits ranging from hundredths of a ppm);
• localized analysis (including “layer-bylayer” analysis), which can be useful in a number of applications.

The potential for miniaturization of measuring instruments.

Disadvantages of LIBS

Although LIBS is one of the best modern analytical methods, it is not without a number of limitations and disadvantages, listed below.

Detection limit. The detection limit for LIBS ranges from hundredths of a ppm, whereas such of other known methods is on the order of parts per billion (ppb) or parts per trillion (ppt) (Tripathi et al., 2015). 

Self-absorption and self-inversion. Radiation from hotter regions is absorbed by cooler atoms surrounding the plasma, which leads to a decrease in the spectral line intensity increment as the element concentration in the sample increases, which, in extreme cases, is accompanied by self-inversion (a decrease in intensity as the concentration of the element in the sample increases) of the spectral line. 

Matrix effect. The physical and chemical properties of the sample can influence ablation, plasma composition, plasma temperature, and the intensity of the emission signal; the combination of these phenomena is commonly referred to in the literature as the matrix effect(s). These include (yet, probably, are not limited to) the following:

• inhomogeneity; 
• moisture;
• proportion of pyrolyzable organic compounds;
• electrical conductivity;
• mechanical properties. 

TECHNICAL SPECIFICATIONS OF LIBS ANALYZERS
Excitation Source Q-switched mode allows for the generation of laser pulses with a duration of approximately 1 ns — nanosecond Q-switched lasers are the most commonly used in the manufacture of LIBS analyzers, offering a good compromise between laser pulse duration and laser cost. Pico- and femtosecond lasers are also currently available; however, the high cost of such devices and the complexity of their manufacture significantly hinder their widespread adoption and integration into commercially available LIBS analyzers.  

In most studies, the pulse energy ranges from 1 to 500 mJ.

 A set of focused quartz convex lenses is typically used to concentrate the laser beam onto the sample.

Light-collecting optics and spectrometer

Lighrs (Galbács, 2015). The spectrometer consists of a spectrograph and a det collection is usually performed using lenses and mirrotector. The spectrograph forms the spectrum, and the detector is used to measure the intensity of various lines. The performance of the spectrometer is determined by its spectral range, resolution, and response time (Day et al., 2015). Spectrometers with a wide spectral range are used for the simultaneous detection of multiple elements. An Echelle spectrometer is typically used in conjunction with a CCD array, providing maximum resolution and sensitivity in the 200–780 nm range. Optical CCD detectors used in LIBS systems consist of many pixels and, on top of that, may be constructed from multiple CCD subunits. Photoelectrons are generated when photons emitted by the relaxing plasma interact with the pixels of the CCD detector. Thus, the number of photoelectrons produced is a measure of spectral intensity (Stoian et al., 2000; Lorazo et al., 2003). 

For field and portable applications, optical fiber is used instead of a focusing lens system to collect and transport emitted photons to the detector (Singh, Thakur, 2020). 

LIBS OPERATIONAL PRINCIPLE 

As noted earlier, LIBS analyzers most commonly use a nanosecond Nd:YAG laser pulse with Q-switch modulation as the excitation source. The surface of the material being analyzed is exposed to pulsed laser radiation at one or multiple points, causing a small mass of the sample to vaporize and forming a plasma-vapor plume near the surface, which, upon further absorption of energy from the incident pulse (and/or an additional subsequent pulse), forms a laser-induced plasma. Photons emitted by the plasma are detected using a spectrometer, resulting in an emission spectrum, which is then used to identify elements and quantify the atoms present in the sample.

In general, the processes occurring in nanosecond LIBS proceed as follows:

• a short laser pulse is focused on the sample;
• the beam energy is absorbed by the atoms and molecules of the sample, causing a small amount of sample material to evaporate. A plume (cloud) of atomic vapor forms near the material’s surface. Subsequent laser pulses interact with the cloud, forming plasma;
• light resulting from the spontaneous emission of atoms and ions is directed and collected by a system of optical fibers and prisms and subsequently recorded by a spectrometer;
• the resulting spectral signature is analyzed and interpreted to identify elements and perform quantitative analysis.

The overall schematic representation of LIBS analytical routine is given in fig. 2 (see the attached pdf-file).

The Ablation Process
Initially, the sample is irradiated with a highenergy laser pulse (with the smallest possible spot size). The interval between successive pulses (if the analyzer design allows for this) is typically on the order of nanoseconds. The heat generated by the absorption of the beam’s energy vaporizes a small amount of the sample, resulting in the formation of a vapor plume above its surface. This process is called ablation (Pasquini et al., 2007; Batani et al., 2012). The ablated mass forms a plume on the sample surface. The incident laser light interacts with this plume. The absorption of energy by the plume from the incident laser beam leads to the formation of plasma. This plasma will prevent the beam from penetrating the sample. This effect is known as “plasma shielding.” Such disconnection of the laser beam from the sample stops further ablation, causing intense heating and ionization of the plasma. As a result, a plasma with high luminous intensity is formed. Depending on the density and temperature of the plasma, the excited levels become more populated. In response to the laser radiation, the plasma expands first isothermally and then adiabatically due to its internal energy. By the end of these processes, plasma condensation begins, and the temperature of the ions in the plasma drops. During condensation, excited atoms and ions emit electromagnetic radiation. The fiber-optic system directs this electromagnetic radiation to a spectrometer that records the emission spectrum of the relaxing plasma. The spectrum carries information about the atoms of the chemical elements comprising the sample.

Plasma Decay  
Two processes are responsible for plasma decay (Chen et al., 2021): 

• the presence of free electrons in the laser’s focal volume; 
• electron cascade in the focal region. 

The typical laser power density required to generate the cascade is on the order of 10⁸–1010 W·cm⁻² (Gondal et al., 2014). An atom becomes ionized by absorbing laser photons (Gondal et al., 2014). This is possible only if the laser intensity is very high. There is another possibility: an atom can absorb a large number of photons and stimulate a “bound-to-free” transition. Consequently, a free electron will be released, but the maximum “production” of free electrons occurs via an electron cascade. After the formation of the electron cascade, the plasma expands at supersonic speeds, and shock waves arise in the surrounding medium. The plasma becomes optically opaque when the “plasma frequency” equals the laser frequency, until the stage is reached where the “plasma frequency” exceeds the laser frequency. After that, the emitted photons will be absorbed by the plasma (Zhao et al., 2016). 

Light Emission and Spectrum Formation
As the plasma cools, the photons emitted from it are collected and directed into a spectrometer, which is connected to a computer for visualizing the resulting spectrum.  

The characteristics of the emission line are determined by the broadening mechanism. Typically, two broadening mechanisms are observed:

Doppler broadening. Occurs due to the thermal motion of electrons, and after broadening, the emission line is well approximated by a Gaussian. The contribution of Doppler broadening to the structure of the emission terms depends on the plasma temperature but does not depend on its electron density.

Stark broadening. This occurs due to the splitting of spectral terms in a strong electron field, and after broadening, the emission line is well approximated by a Lorentzian. 

The contribution of Stark broadening to the structure of the emission terms increases with increasing electron density of the plasma.

In practice, spectral lines in laser-induced emission spectra are extremely rarely described by a Gaussian. In the vast majority of cases, the emission lines of elements are adequately approximated by a Lorentzian; in some cases, by a Voigt curve, which is a linear combination of equal contributions from a Lorentzian and a Gaussian. Therefore, the Stark broadening makes the largest contribution to the broadening of emission lines in the spectra of laserinduced plasma (Bilge et al., 2016a).

DETERMINATION OF PLASMA TEMPERATURE AND ELECTRON DENSITY

The light emitted by the plasma is used for elemental analysis and the quantitative study of the properties of the sample and the plasma. The fundamental parameters of the plasma are plasma temperature and electron density. The determination of these plasma parameters is critical for quantitative LIBS analysis (da Silva Gomes et al., 2013).

 If the plasma does not satisfy the criteria for local thermodynamic equilibrium, self-absorption will occur and the concentration measurement will be in accurate. Temperature measurement is also important for understanding the processes occurring in the plasma.

The description of plasma begins with attempts to characterize the properties of the aggregate of atoms, molecules, electrons, and ions, rather than individual species. If local thermodynamic equilibrium exists, then plasma properties such as the relative population of energy levels and the particle velocity distribution can be described in terms of temperature (Rusak et al., 1998). Under conditions of local thermodynamic equilibrium, the kinetic temperature and the excitation temperature are identical and can be determined using the Saha–Boltzmann plot. The population of excited states follows a Boltzmann distribution, and their relative intensity of spectral lines Imn is defined as (Bilge et al., 2016b) - see the attached pdf-file.

QUANTITATIVE ANALYSIS

For quantitative analysis, one of three approaches can be used: calibration curve construction, calibration-free approach or one-point calibration: 

Calibration Approach
Regression methods are typically used to construct calibration curves. With this approach, calibration curves must be constructed for the quantitative determination of each element. A calibration curve is a graph showing the relationship between the intensity of an emission line (in practice, the ratio of the intensities of the emission lines of the element being analyzed and a reference element present in the analyzed “matrix” in a quantity that is sufficiently stable from sample to sample and detectable) on concentration (Hanif et al., 2011; da Silva Gomes et al., 2013). It has been established that this requires a set of standardized samples with a matrix possessing physicochemical properties and chemical composition similar to those of the samples being analyzed; however, obtaining such standard samples (reference materials) in the necessary quantities and assortment is quite difficult (Hanif, 2012; Galbács, 2015).

The most common method is the use of a standard reference material with a reliably and accurately measured concentration of the element of interest. In this case, the error of the analytical method (procedure) used to certify the reference materials must be negligible compared to the error of the LIBS analysis procedure. Such reference methods include inductively coupled plasma atomic emission spectrometry ICP-AES, inductively coupled plasma mass spectrometry (ICP-MS), and AAS with electrothermal atomization (AAS-ETA).

Calibration-free LIBS ( CF-LIBS)
The calibration-free LIBS method allows for quantitative studies without a set of reference materials (Hanif et al., 2012).

The principal CF-LIBS equation is as follows: see the attached file

The introduction of departure coefficients, or bifactors, offers a robust and physically rigorous alternative to conventional LTE-based approximations. The bi-factor explicitly quantifies the ratio between the actual population of a specific excited atomic level and its theoretical population derived under the assumption of Saha-Boltzmann equilibrium. Although the direct algebraic or deterministic extraction of these individual coefficients introduces a higher layer of computational complexity — demanding accurate atomic transition data, and reliable reference anchors such as atmospheric purge gas lines – the analytical advantages are profound. By embedding bi-factors into the CF-LIBS framework, the model effectively isolates individual quantumstate fluctuations.

One-point calibration (OPC-LIBS)
However, estimating or calculating F() λ with sufficient accuracy is itself quite an onerous task, requring a highly sophisticated LIBS setup. This problem is avoided by utilizing the framework of OPC-LIBS, requiring only one homogenous (or virtually homogenous) reference material sample with known elemental composition (Cavalcanti et al., 2013) – not to mention its relative acqusition and/or preparation easiness. 

THE EFFECT OF LASER PARAMETERS AND MATRIX EFFECTS ON THE PARAMETERS OF THE GENERATED PLASMA
Effect of laser parameters

Hanif et al. (Hanif et al., 2011, 2012; Hanif, 2012) studied the effect of laser energy on plasma parameters using lasers with operating wavelengths of 1064 nm and 532 nm. The electron temperature has also been determined by varying the energy of the laser from 90 to 116 mJ, for the fundamental (1064 nm) harmonic and from 58 to 79 mJ for the second (532 nm) harmonics of the laser. They report that «the [plasma] temperature increases from 14192 to 15765 K in the first case and from 13170 to 14800 K for the second case». Their results also indicate non-linear plateau-like relationship between laser pulse energy and resulting plasma temperature – as well as plasma electron density. In addition, the emission intensity of the laserinduced plasma is also influenced by the operating wavelength of the laser used. As the laser wavelength decreases, the mass of the ablated material increases; this relationship is well described in formal terms by the following equation (Fridman, 2008): see the attached file.

The shift in emitted photon energy of utilized laser (assuming both pulse energy and pulse duration remaining equal) from 1.16 eV (1064 nm) to 4.64 eV (266 nm), according to this equation will yield 6.35-fold mass ablated from sample. Furthermore, in the case of biological substrates, this transition facilitates a shift from purely thermal evaporation to direct photo-induced sublimation. Since, at 266nm wavelength, the 4.64 eV photon energy exceeds the binding energy of C-C and C-N bonds (approx. 3.6– 3.8 eV), UV radiation triggers efficient dissociative processes, significantly reducing the impact of stochastic "melt mixing" and thermal splashing inherent to IR irradiation-induced ablation. This suppression of the liquid phase ensures more stoichiometric ablation and a substantial reduction in matrix-dependent spectral fluctuations.

 Accounting for low efficiency of nonlinear optical crystals used for generation of 4th harmonic (approx. 12.5%) – such transition will still yield more than 3-fold greater ablated mass, contributing to a dramatic increase in emission intensity of generated plasma, therefore allowing for a similar improvement in terms of sensitivity of LIBS analyzer.

Influence of matrix effects
Moisture content. In the study conducted by Moon et al. (Moon et al., 2015), an attempt was made to analyze samples of cell pellets formed from aqueous suspensions of immortalized human keratocytes containing 10% to 40% moisture. As can be seen in fig. 4 and 5, as the moisture content increases from 10% to 40%, the intensity of the emission lines decreases by more than a factor of 2.

Electrical Conductivity of the Sample. In study by Li et al. (Li et al., 2024), the effect of electrically conductive additives on the analytical characteristics of soil samples was investigated. Thus, the addition of NaCl to a final concentration of 10 wt.% or graphite to 20 wt.% resulted in a significant improvement in the signal-to-noise ratio for the Pb I 283.31 and Pb I 405.78 lines. At the same time, the morphology of the ablation craters also changed significantly — in the presence of electrically conductive additives, the profile of the ablation craters acquired a more regular “conical” shape (fig. 6).

Mechanical Properties. In the work by Labutin et al. (Labutin et al., 2009), the authors investigated how the mechanical properties (in particular, microhardness) and microstructure of solid samples affect the characteristics of laser-induced plasma (LIP). Aluminum-lithium (Al-Li) alloys and lithium ferrites (ceramics) were used as test samples. 

In addition to the shape of the craters, changes were also observed in their dimensions (table 1).

Correlation between hardness and ablated mass. For Al-Li alloys, the authors found a negative correlation between the microhardness of the sample and the amount of material removed. 

Result: harder samples produced smaller craters and weaker optoacoustic signals.

Mechanism: mechanically harder materials are more resistant to physical deformation and evaporation caused by the laser shock wave, resulting in, probably, less mass being removed per pulse.

Correlation between hardness and plasma temperature. In contrast, they found a positive correlation between microhardness and plasma temperature. 

The excitation temperature (calculated using Li I transitions) was proportional to the microhardness of the solid sample.

Since harder materials produce a cloud with lower particle density upon laser irradiation, the fraction of ablated material thrown out of laser beam lightpath decreases as, arguably, does the the amount (mass) of ablated material. This results in higher energy per particle, leading to a hotter plasma (fig. 7).

Temporal “incubation” of correlations. The study notes that these correlations are not instantaneous but depend on surface modification:

Initial pulses: during the very first laser pulses, the mechanical properties did not correlate strongly with the ablated mass.

This indicates that the surface must be “prepared” (formation of a crater/roughness) before the mechanical properties of the material begin to dominate over other aspects of the physics and chemistry of ablation.

Steady state: the correlation coefficient (R2 ) is shown to increase upon incrementation of a number of consecutive laser pulses (fig. 8).

CONCLUSION
Laser-Induced Breakdown Spectroscopy (LIBS) has established itself as a versatile and powerful analytical tool, offering rapid, multi-elemental analysis with minimal sample preparation. However, qualitative detection to high-precision quantitative analysis remains a significant challenge. The primary obstacle lies in the complex nature of matrix effects − including variations in moisture content, electrical conductivity, and mechanical properties − which induce substantial fluctuations in the ablated mass and the fundamental plasma parameters, namely electron temperature and electron density of LIP. This review underscores that these sample-specific properties do not merely act as passive variables; they actively dictate the stoichiometry of the ablation process and the subsequent radiative relaxation of the plasma. Consequently, there is an evident and urgent necessity for the development of comprehensive mathematical models capable of accounting for the influence of the sample matrix on plasma generation.
Such models must bridge the gap between the physical state of the target material and the resulting spectral signature by quantifying the variations in plasma paramaters.

 Achieving this level of mathematical rigor is the key to ensuring the reproducibility and accuracy required for LIBS to achieve its full potential in demanding industrial and scientific quantitative applications.

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Information about the author:

Ilya I. Lapin – Laboratory Assistant at the Laboratory of Molecular Dietology Laboratory of the Center for Bioelementology and Human Ecology at the Institute of Preventive Medicine, Clinical Center ;
Assistant Professor of Department of Medical Elementology
E-mail: lpipowered@gmail.com; https://orcid.org/0009-0005-5176-9770; SPIN: 5281-1047