Introduction

Micronutrient deficiencies, especially those associated with malnutrition in iron (Fe), phosphorus (p), potassium (K), sulfur(S), magnesium (Mg), and aluminum affect billions of people around the world [1]. Undernutrition is a pervasive issue that impacts both wealthy and less-developed nations. Technologies such as X-ray Fluorescence (XRF) and laser-induced breakdown spectroscopy (LIBS) are viable options for exploration because they allow rapid detection of different elements in plants. Combining these techniques with botany can enhance the characterization of mineral ratios in plants more efficiently [2, 3]. In order to create a database, researchers typically have difficulty and need a significant amount of time to collect several leaf samples as raw datasets. It is vital to identify and categorize plants according to their respective roles through available technologies [4, 5].

There are many techniques to analyze the plant’s materials. One of the powerful analytical techniques is XRF. It is high-energy electromagnetic radiation that lies between gamma rays and ultraviolet rays [6]. There are two types of measurement of photon energy: Wavelength Dispersive X-ray fluorescence Analysis (WD-XRF) and Energy Dispersion X-ray fluorescence (ED-XRF) [7].

Among the previous studies in which laser-induced plasma met the necessary condition for local dynamic equilibrium (LTI) in its experiments can be summarized as: Andrade et al. (2018) used LIBS to study sugarcane leaves to determine the concentrations of microelements such as calcium, potassium, magnesium, phosphorus, boron, copper, iron, manganese, and zinc. The output of this work was to understand the effect of these minerals on leaf formation and plant health [8].

Rehan et al. (2021) used the LIBS technique to verify the essential elements found in dry fruits quantitatively. Pistachios, cashews, white walnuts, black walnuts, and almonds were examined using LIBS technique. It showed that the experimentally measured electron density is greater than the expected critical electron density [9].

Iman et al. (2023) studied the potential of LIBS technique to identify kidney failure in patients with iron deficiency. They observed statistically significant differences in the initial composition of blood samples among kidney failure patients, unlike healthy individual patients. This study focused on the benefit of LIBS in the Department of Kidney Health [10]. In (2024), Zainab et al. presented a survey on the principles of LIBS technique and its efficiency to detect the proportions and concentrations of plant minerals and elemental compositions within plant tissues by comparing the LIBS tool with other analytical tools [8].

This work aims to find the percentages of metal concentrations in dried flaxseed plants using the LIBS technique and compare it with XRF technique. It highlights the need for an accurate and reliable analytical tool in determining element profiles and distinguishing between micro- and macronutrients. There is a new equation used to calculate the concentration of metals. This equation depends on measure the concentration of metals using two lines in the spectral lines instead of one line.Keyword: Laser-induced breakdown, X-ray fluorescence, macronutrient, plants

Methodology

There is an analytical technique to measure the plant’s elements in a short time compared with other methods. The fastest and most accurate technique is LIBS, which depends on a high-pulsed laser with different wavelengths. The high energy generates the atomic emission of the tested material [11]. This emission is related to the ionized plasma that is generated at the sample surface, which is formed by projecting a laser pulse on the surface of the target. This reaction produces a cloud of plasma on the surface of the sample [12, 13]. Through the process of ionization of photons, the electronic seeds are formed to form a careful plasma so that these electronic seeds allow the laser energy to be absorbed [14]. Ionization is increased through the reverse bremsstrahlung process, so the increase in the rate of ionization causes the increase in the absorption of the laser beam and thus leads to the ionization of the skin collapse until it reaches the plasma [15, 16]. Then, the plasma reaches a critical density, and a large part of the laser is reversed; therefore, electron density (Ne) decreases due to the expansion of the plasma. The laser penetrates the plasma, which causes the surface of the target to heat. The composition of the plasma and ionization processes affect the transfer of energy to the form of plasma [17, 18]. The ionized gas is made up of positively and negatively charged particles with about equal charge densities [19,20,21]. The spectra lines of these emissions show the sample components precisely [22, 23].

Sample preparation

The sample of flax seeds plants was brought from orchards located in Baghdad-Iraq. The sample weight was 20 mg before putting them in the oven as shown in Fig. 1 (a). It is necessary to wipe the floor of the oven with ground detergents (Ethanol C2H6O, Acetone C₃H₆O). The temperature adjusted between 45 and 55 Cº. The sample is left inside the oven for about one hour and the nozzle opens so that we get rid of liquid materials. The sample is let to be dried and cooled by closing the oven nozzle. The sample is grinded by a 2 ml ceramic hand grinder to remove the crustacean material, then grind it with an electric grinder. The resulted grind sample sieved with a 2mL with 38 micros sieve to get rid of cellulose and large molecules. The tested sample is weighted as 5 mg because the pellet holder with this size under a 5-ton piston mold. The resulting coherent sample with diameter 1.5 cm according to the mold used as shown in Fig. 1 (b).

Fig. 1
figure 1

Sample (a) dried flax seeds preparation and (b) before measure by LIBS technique

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LIBS setup

Experimental setup chosen to be at room temperature, about 25 ºC. The laser system in LIBS used a single-pulse laser (Q-Switched Nd: YAG) with wavelength 1064 nm and energy 10 mJ. The laser pulse duration is 10 nanoseconds for one pulse. The setup consists of lenses and optical fibers to collect and transmit light. A Convex lens (quartz-silica) was used to focus the laser beam at a focal length (10 cm) on the surface of the sample placed on a moving platform of variable height.

The spectroscopy device is used to determine the elements and their relative concentrations. This is done by collecting light emissions from plasma and directing them to the spectrometer. Spectrum analyzer model (BIM_6002) used to determine the resulting spectral lines. The spectrometer transmits the digital signal to an operating system (OOIBase32- Spectrometer) from Ocean Optical Corporation (Ocean Optic, Inc.), which is then analyzed by computer software. The emission wavelengths from the sample are recorded in the range (187–915 nm). Figure 2 shows the experimental setup for the tested samples.

Fig. 2
figure 2

Schematic of the LIBS setup: LIBS System (1) Nd: YAG laser system, (2) Laser handle, (3) target holder, (4) Lens, (5) Fiber optics cable, (6) Spectrometer (spectrum analyzer), and (7) Computer

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EDXRF analysis

EDXRF depends on transition of electron from the inner shell by X-ray source. Thus, the detector generates a single package of X-rays focusing on the target material for irritating energy levels and, thus, the movement between higher energy levels. Hence, the occurrence of decay and the emission of different spectrums, the detector contains the number of silicone reagents that are described by the location of a different irritation energy, which results in high-energy rays falling in distant beginnings on the detector surface. Figure 3 shows the device that was used for experimental setup.

Fig. 3
figure 3

XRF system used for experiment

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Method and material

It is assumed that laser-induced plasma is present in the state of LTE, and the plasma must have enough humidity to ensure a high collision rate LTE. To achieve this condition, the temperature of the plasma and the number of electron densities must be determined. The temperature is determined by describing the energy levels in the thermal equilibrium through one spectral line as [24, 25]:

$$\:T\left(e\text{v}\right)=-\frac{Ek}{K*Ln\left(I*\lambda\:/Ak*gk\right)}$$
(1)

where Ek is the energy level excited, Ak is the transition probability, gk the statistical weight for the higher level, K Boltzmann constant, and I is intensity.

Electron density (Ne) is determined by the McWhirter criterion and is given by the following relationship [8]:

$$Ne\, \geqslant \,1.6\,*\,{10^{12}}\,*\,{T^{1/2}}\,*\,{\left( {\Delta E} \right)^3}$$
(2)

where T is the plasma temperature, ∆E is the highest energy transition.

The highest and lowest intensity of each element was taken to calculate the average of Ne and the temperature rate of each component in the sample to find the concentration ratios of the six metals. It is also shown that electron density affects the atomic interaction and the arrangement of electrons in atomic orbitals. These variables affect the concentrations measured in the sample.

The reason for finding the metal concentration (C) is that it is a necessary and vital factor to find the amount of element present in the sample and it is high or not, and the concentration equation is used in this work through the electron density of each element as:

$$\:C=\frac{ne1}{ne2}$$
(3)

where ne1 is the electron density of the first line of the element, and ne2 is the electron density of the second line of the element.

Results and discussions

The wavelength values recorded in the sample ranged from 187.786 nm to 915.914 nm. There is a matching between the values measured by the LIBS technique and the values approved by NIST. NIST has important parameters to measure the electron temperature like gk and Ek. gk is the change in quantum momentum and its value between 1 and 10 in the elements. Ek represents the energy of the highest level, which changes in terms of the lines of elements and from element to element, and this interpretation indicates a difference in the structure and order of the energies of the electronic levels in the atoms of the element. Table 1 represents the comparison between the Fe data of NIST and experimental data of LIBS technique. The data of Mg, P, Al, K, and S are represented in Tables 2, 3, 4 and 5, and 6, respectively. Figure 4 shows the spectrum of LIBS technique for the tested sample.

Table 1 Fe data of NIST and LIBS technique for the tested sample
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Table 2 Mg data of NIST and LIBS technique for the tested sample
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Table 3 P Data of NIST and LIBS technique for the tested sample
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Table 4 AL data of NIST and LIBS technique for the tested sample
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Table 5 K data of NIST and LIBS technique for the tested sample
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Table 6 S data of NIST and LIBS technique for the tested sample
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Fig. 4
figure 4

Spectra of the studied samples using LIBS technique

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The electron temperature of the sample elements is shown in Table 7, which relates to calculating the electron density for each line of the sample’s wavelengths.

Table 7 Plasma temperature with element
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The temperature of the elements for the tested sample is shown in Fig. 5. The behaviour is as expected according to the percentage for each element.

Fig. 5
figure 5

Elements and temperature of the sample

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Aluminum has the highest temperature among the elements, followed by phosphorus, iron, sulfur, magnesium, then potassium. Electron density (Ne) is related to the element temperature (T). So, there is a proportional relationship between T and Ne. The amount of concentration also depends on the temperature of the component.

Table 8 shows the concentration of each element depending on the new equation that we presented in this work. This equation depends on low and high intensity of λ for the selected element. This equation gives high accuracy in concentration compared with XRF. There is a small difference in presenting the elements in Tables 8 and 9 regarding the micronutrient. In Table 8, we presented only the elements that are involved with micronutrients, while Table 9 shows all the elements even with low concentrations.

It is important to point out that the McWhirter equation is satisfied with the resulted data. The laser-induced plasma is located in LTE equilibrium, the expected critical electron density was 2.715E + 16 cm− 3. This is less than the experimentally calculated electron density. This means laser-induced plasma does met the requirement for LTE in our experiments [17].

Table 8 First-line electron density (ne1), second-line electron density (ne2) and concentration of the sample
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The high concentration in Table 8 is about 3% for Al element. This is because of the sample origin and the environment that affected the element percentage. The other findings of flaxseed concentrations are different with ours data which are Fe (5.73 mg), Mg (392 mg), P (642 mg), and K (813 mg) in each 100 mg [26].

Figure 6 shows the spectrum of the XRF for the tested sample, and it shows the elements wavelength between 187 and 915 nm. And Table 9 shows the concentrations of elements in the laboratory sample with the percentage of error of the XRF device. The table shows that the highest concentration among the element concentrations is aluminum.

Fig. 6
figure 6

XRF spectrum of the sample

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Table 9 XRF analysis sample
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The comparison between LIBS technique and XRF data for element concentration is shown in Table 10. There is a small difference between the two methods which gives good indication for the resulting data. There is a strong agreement between the results of the XRF and LIBS tests using the weight ratios that were employed, indicating that the electron density essentially determines the presence of microscopic difference element characteristics like reactivity and bonding behavior.

Table 10 Comparison between LIBS and XRF
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Conclusion

XRF and LIBS technique used to analyze essential minerals in dried flax seeds. The local thermodynamic equilibrium of the laser-polluted plasma was established and verified using the McWhirter criterion based on the electron number density in the plasma.

There is a direct relationship between temperature, electron density, and concentration. The high concentration component of the dried flax seeds sample is the aluminum (Al) element at a concentration of (3.03%), followed by P (2.56%), S (1.60%), Mg (1.17%), Fe (0.65%), and K (0.64%).

There is a good agreement between XRF and LIBS technique data. Laser-induced plasma does meet the requirement for LTE in our experiment.