Deep Inorganic Fraction Characterization of PM 10 , PM 2.5 , and PM 1 in an Industrial Area Located in Central Italy by Means of Instrumental Neutron Activation Analysis

: Atmospheric pollution is an important task in life sciences and, in particular, inorganic fraction characterization is considered as an important issue in this ﬁeld. For many years, researchers have focused their attention on the particulate matter fraction below 10 µ m: in this case, our attention was also focused on PM 2.5 (i.e., particles with a size fraction smaller than 2.5 µ m) and PM 1 (below 1 µ m). This paper would like to investigate whether the element accumulation in di ﬀ erent granulometric fractions is similar, or whether there are behavior dissimilarities. Among the di ﬀ erent analytical techniques, the instrumental neutron activation analysis, an instrumental nuclear method, was used for its peculiarity of investigating the sample without performing any chemical-physical treatment. Forty-two daily samples using the reference method were collected, 15 ﬁlters for PM 10 , 18 for PM 2.5 , and 12 for PM 1 ; the ﬁlters, along with primary standards and appropriate standard reference materials, were irradiated at the National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA) R.C.-Casaccia’s Triga MARK II reactor. The irradiations carried out in the Rabbit and Lazy Susan channels allowed for the investigation of 36 elements and the relative Pearson’s correlations between elements and PM-fractions (PM 10 vs. PM 2.5 was good, whereas PM 10 vs. PM 1 was the worst). The Enrichment Factors were studied for the three fractions to show how anthropogenic sources have a ﬀ ected the element content. A comparison between these data and element levels determined worldwide showed that our concentrations were lower than those determined in similar scenarios. Furthermore, a statistical approach (source discrimination, hierarchical cluster analysis, principal component analysis) has allowed us to identify similarities between the samples: the airborne ﬁlters can be divided in two main groups (i.e., one made of PM 10 and PM 2.5 ﬁlters and one only of PM 1 ﬁlters), meaning a di ﬀ erent element contribution to this fraction coming from other sources present at the site.


Materials and Methods
The sampling, performed in an area around a large incinerator in Central Italy, was 24-h long for each filter by means of a dual channel sampler, mod. Swam Dual Channel sampler (FAI Instruments, Fonte Nuova, Italy) (flux 16.7 L min −1 , i.e., 1 m 3 h −1 ), equipped with PM 10 /PM 2.5 /PM 1 sampling heads, alternatively: 45 samples (15 filters PM 10 , 18 PM 2.5 , and 12 PM 1 ) were collected during the seasonal sampling campaign between the middle of May and the middle of October to also understand the element content and distribution. The sampling points were fixed and located in a radius of 20 m from the plant boarders, no residences were present in the area, few commercial activities were positioned over 50 m from the site. During all samplings, the incinerator operated. All the treatments of sample storage and handling were carried out at the National Institute for Insurance against Accidents at Work's (INAIL) laboratory according to European Union (EU) regulations [33].
Samples (i.e., filter samples), blank and standards were put in nuclear-grade polyethylene cylinders (Kartell, Milan, Italy). The irradiation was performed in the rotatory rack "Lazy Susan" of the TRIGA nuclear reactor at R.C.-Casaccia ENEA: the irradiation time was 25 h at 1 MW. The rotatory rack was held at constant rotation for having a uniform thermal flux, 2 × 10 12 n × cm −2 × s −1 (and relative fluency 2.34 × 10 17 n × cm −2 ): the flux stability (>99.8%) was tested irradiating the Au standard as a monitor.
For INAA analysis, primary and secondary standards were used. This procedure was followed to obtain good quality assurance and quality control (QA/QC): standard reference materials (SRMs) with high reproducibility and precision were used. These SRMs have been certified by several international proficiency tests, to which our laboratory routinely takes part. Primary standards (Carlo Erba, Milano, Italy) were Ag, As, Au, Ba, Ca, Cd, Co, Cr, Cs, Eu, Fe, Hg, Ir, K, Mo, Na, Ni, Rb, rare earth elements (REE, i.e., La, Sm, Yb, Nd, Gd, Dy, Er, Yb), Sb, Se, Sn, Sr, Tb, Th, U, W, and Zn whereas, as secondary standards, two SRMs such as GXR-3 from the U.S. Geochemical Survey (USGS), and coal fly ash (CFA 1633b) from the National Institute of Standards and Technology (NIST). It would be better to use a reference material with a matrix as similar as possible to the samples investigated: two SRMs (i.e., USGS-GXR-3 2709 and NIST 1633b), coal fly ash, along with 35 primary standards (at different concentrations, alone or in mixing standard solutions) were used for overcoming this issue.
After irradiation, γ-ray spectrometry measurements of different durations were carried out using a Ge(HP) Canberra detector (Meriden, CT, USA) (full width at half maximum 1.75 keV at 1332 keV, relative efficiency 35%; peak/Compton ratio 60.2:1) connected to a multichannel analyzer equipped with software packages (Canberra Genie 2k) for a γ-spectra analysis. For the energy and efficiency calibrations, two sources were used (i.e., a multi-peak source, BML 1517B ( 241 Am, 109 Cd, 57 Co, 51 Cr, 137 Cs, 88 Yr, 60 Co: 1 cc of this source was placed in the Kartell nuclear grade tube) and a 152 Eu source).
The BML 1517B source was produced and certified by the ENEA National Institute of Ionizing Radiation Metrology (INMRI-ENEA) whereas the 152 Eu source was by the Centre Nationale pour l'Energie Atomique (CNEA), respectively.
According to the half-life time of each radionuclide [34], two gamma measurements were performed. The first series occurred after 66-70 h from the end of irradiation and the measurement time ranged between 3600 s (1 h) and 18,000 s (5 h), each irradiated sample was placed at 4 cm from the detector; the second series after three weeks from the end of irradiation and the measurement time was 24-48 h long; each sample was placed in contact with the detector. Table 1 reports all the nuclear data and limits of detection (LODs) for the elements studied in this work.

Instrumental Neutron Activation Analysis (INAA) Validation
All of the analytical procedures are performed to obtain as much information as possible. For this aim, the use of a nuclear analytical technique such as INAA is strongly recommended because it allows for high sensitivity and quantification of elements to be achieved at very low (ultra-trace) concentrations. On the other hand, using nuclear analytical techniques, the problem could regard the reference material used for the analysis. This is considered a critical point: SRMs should show a composition quite similar to the investigated matrices. According to the experience of this laboratory, largely involved in round-robin comparisons with other international laboratories for both verifying the instrumental drift and quality control, the authors solved this problem by analyzing secondary reference materials [35][36][37] along with primary certified standards. In particular, over the mixture of primary standard solutions (obtained starting from 1 mg mL −1 of each one) above reported, USGS GRX-3 and NIST 1633b (coal fly ash) were used for the evaluation of the methodology. Furthermore, in the analysis of such matrices, high attention should be focused on the precision and accuracy, along with information about the area characterization on the anthropogenic sources present in the territory. Table 2 shows the comparison between our data and the relative certified values for the investigated SRMs. As reported in previous papers [38,39], the authors refer to the precision, calculated as the coefficient of variation (CV%), for defining a mean value as good, acceptable, or unsatisfactory (i.e., <20%, between 20-30% and >30%, respectively, for concentration levels <500 µg g −1 ; <10%, between 10-20% and >20%, respectively, for concentration levels >500 µg g −1 ). Furthermore, the table shows the accuracy, calculated as the difference between found and certified values and reported as ∆, and the z-scores, which represent the distance between the raw score and the population mean in units of the standard deviation and also includes the relative uncertainties of each certified value and the measurement performed (a positive z-score means a value above the mean, a negative z-score is a value below the mean). All overall means fit into the confidence intervals. In particular, the comparison was good/acceptable for most of the elements and all the data were good in terms of precision and accuracy. Only a few elements (i.e., Ba, Na, Sm for USGS GRX-3, and As, Fe, Zn for NIST 1633b) showed poor accuracy, even if the precision was high.
3.2. PM 10 , PM 2.5 , and PM 1 Analysis Table 3 shows the analytical data of each element investigated in this study. First, the concentrations of the three PM fractions should be noted: the mean levels of PM 10 and PM 2.5 were below the law limit values (PM 10 daily average 50 µg m −3 , PM 10 annual average 40 µg m −3 , and PM 2.5 annual average 25 µg m −3 ) [40] whereas no limits were reported for PM 1 . For this last fraction, very few data are present in the literature: Roemer and van Wijnen [41] reported PM 1 levels ranging between from 20 µg m −3 to 26 µg m −3 for the background, street, and motorway sites in the Netherlands; Perez et al. [42] confirmed the scarce presence of PM 1 data on levels and speciation and reported a mean level of 19 µg m −3 in Barcelona from October 2005 to October 2006; Vecchi et al. [43] showed levels of 29-34 µg m −3 in Milan; Pakkanen et al. [44] measured 11-12 µg m −3 in Helsinki; and the same levels were also found by Spindler et al. [45] in rural areas in Germany. The situation was quite different as determined by Bathmanabhan and Madanayak [46]: they found hourly average PM 1 concentrations ranging between 32 and 66 µg m −3 near an urban roadway in Chennai city (India), where the levels depend on the meteo-climatic conditions (post-monsoon period, winter and summer seasons). Therefore, the concentrations found in this paper could be considered as quite good, considering the environmental conditions present in the area.
First, among the 36 elements investigated, their distribution in the three different fractions was not regularly distributed: for instance, Au, Ca, Cd, Co, Eu, Fe, La, Mo, Na, Ni, Sm, Sn, Ta, and Tb showed decreasing levels passing from PM 10 to PM 1 , whereas Ce, Hg, Sc, and Zn did not show any significant difference in any of the three fractions. Other elements were instead distributed between PM 10 , PM 2.5 , and PM 1 in different ways (e.g., As was at 1.0 µg m −3 , 0.38 µg m −3 , and 1.1 µg m −3 in PM 10 , PM 2.5 and PM 1 , respectively).
With the exception of Cd and U (their levels were below the respective LODs), our attention only focused on some elements: As, Au, Br, Ce, Co, Cr, Cs, Fe, Hg, Ni, Sb, Sc, Se, Th, and Zn. Their importance is due to different reasons such as the toxicological point of view, the identification of the anthropogenic or natural sources, or the possible common origin between them. In this way, an important example is described by bromine: its level in the atmosphere is essentially due to natural, (i.e., marine aerosol) and anthropogenic (i.e., auto-vehicular traffic, sources) [1,47]: the levels of this element were 0.22 ng m −3 , 0.17 ng m −3 , and 0.52 ng m −3 , respectively in PM 10 , PM 2.5 and PM 1 with a coefficient of variation (CV%) varying between 43.5%, 55.8%, and 7.5%, respectively. It should be noted that the CV% for each element shows its concentration level variability across the whole sampling period. As can be seen, the minimum CV% is related to the PM 1 fraction, meaning a low data dispersion for this size.
The Br level in PM 10 (0.22 ng m −3 ) was really below the level found in downtown Rome (22.2 ng m −3 ) [2] and the level in PM 2.5 (0.17 ng m −3 ) was really below that found in the same city (17.1 ng m −3 ) [1], whereas the correlation (r) with another important element, Sb, was very good for PM 10 (0.9998), good for PM 1 (0.761), and less good for PM 2.5 (0.156). This occurrence (i.e., the high correlation between Br and Sn within PM 10 and low within PM 2.5 ) suggests a different contribution to Br levels. In particular, sources of Br within particles larger than 1 µm differ from the sources of Br in submicron particles.
Regarding the protection of human health, very few elements showed limit values. In European legislation, As, Cd, and Ni should be at levels below 6.0 ng m −3 , 5 ng m −3 , and 20 ng m −3 (actually, these target values will be entered into force on December 2020) whereas the World Health Organization (WHO) suggests [48] a guide value for Cd of 5 ng m −3 : in all cases, our data were much lower than those fixed; even the maximum values were significantly below these levels.
Particular attention should be given to the CV% whose meaning has just been reported above: it ranged between 9% and 164% in PM 10 , between 18% and 91% in PM 2.5 , and between 7% and 114% in PM 1 . In particular, except for a few cases in PM 10 (Au, CV% 164%; Co, 92.9%), PM 2.5 (K, 71,8%; Na, 90.9%; Ta, 81.5), and PM 1 (Fe, 88.1%; Sc, 114.7), the CV% in these three fractions were below 60%, which means that the elements in these fractions showed slight variations and that not many sources influenced the element levels. This last information was also confirmed by the good correlation reported in Figure 1 between the various fractions (PM 10 vs. PM 2.5 : equation curve y = 0.328x + 7.252, r 2 = 0.635; PM 2.5 vs. PM 1 : y = 0.521x + 2.817, r 2 = 0.551; PM 10 vs. PM 1 : y = 0.112x + 9.139, r 2 = 0.150). The last correlation (PM 10 /PM 1 ) was not so good, which is not surprising considering the large difference between these two sizes.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 1 of 20 In particular, sources of Br within particles larger than 1 µm differ from the sources of Br in submicron particles.
Regarding the protection of human health, very few elements showed limit values. In European legislation, As, Cd, and Ni should be at levels below 6.0 ng m −3 , 5 ng m −3 , and 20 ng m −3 (actually, these target values will be entered into force on December 2020) whereas the World Health Organization (WHO) suggests [48] a guide value for Cd of 5 ng m −3 : in all cases, our data were much lower than those fixed; even the maximum values were significantly below these levels.
Particular attention should be given to the CV% whose meaning has just been reported above: it ranged between 9% and 164% in PM10, between 18% and 91% in PM2.5, and between 7% and 114% in PM1. In particular, except for a few cases in PM10 (Au, CV% 164%; Co, 92.9%), PM2.5 (K, 71,8%; Na, 90.9%; Ta, 81.5), and PM1 (Fe, 88.1%; Sc, 114.7), the CV% in these three fractions were below 60%, which means that the elements in these fractions showed slight variations and that not many sources influenced the element levels. This last information was also confirmed by the good correlation reported in Figure 1 between the various fractions (PM10 vs. PM2.5: equation curve y = 0.328x + 7.252, r 2 = 0.635; PM2.5 vs. PM1: y = 0.521x + 2.817, r 2 = 0.551; PM10 vs. PM1: y = 0.112x + 9.139, r 2 = 0.150). The last correlation (PM10/PM1) was not so good, which is not surprising considering the large difference between these two sizes. On the other hand, the correlations between elements in each fraction (Table 4) confirmed the common sources for all elements, both natural (crustal origin) and anthropogenic (plant emissions and auto-vehicular traffic): the elements showing r-values above 0.6 were considered well correlated [1,2,49] such as Br, Sm, Au, Th, Ce, Ni, Eu, and Ag, (r > 0.8). Regarding the toxic elements, it should be underlined that the correlation between Ni and the other elements was not good, except with the rare earth elements (REEs), meaning a main component of natural sources for this element. For Cr and As, which are largely diffused in nature, the situation was slightly different: over the natural origin, their presence in the atmosphere could be due to auto-vehicular traffic and industrial emissions (e.g., metallurgical industries, coal-fired power plants, galvanic industries, waste incinerators). On the other hand, the correlations between elements in each fraction (Table 4) confirmed the common sources for all elements, both natural (crustal origin) and anthropogenic (plant emissions and auto-vehicular traffic): the elements showing r-values above 0.6 were considered well correlated [1,2,49] such as Br, Sm, Au, Th, Ce, Ni, Eu, and Ag, (r > 0.8). Regarding the toxic elements, it should be underlined that the correlation between Ni and the other elements was not good, except with the rare earth elements (REEs), meaning a main component of natural sources for this element. For Cr and As, which are largely diffused in nature, the situation was slightly different: over the natural origin, their presence in the atmosphere could be due to auto-vehicular traffic and industrial emissions (e.g., metallurgical industries, coal-fired power plants, galvanic industries, waste incinerators).

Studies performed in European Union (EU) countries have shown chromium values in ambient air ranging between 4 and 70 ng m −3 in urban areas, and between 5 and 200 ng m −3 in industrial areas.
Arsenic values in ambient air, on the other hand, vary between 1 and 3 ng m −3 in urban areas and between 20 and 30 ng m −3 in industrial areas [48,50,51].
In this study, these two elements (i.e., Cr and As) defined as carcinogenic compounds for human health (Group 1) by the International Agency for Research on Cancer (IARC) and the Environmental Protection Agency (EPA) [48,50], showed good correlations in all cases, meaning that they have common origins. This consideration was strengthened by their correlations with Fe, an element widely present in the crustal composition.
The correlation is really important when analyzing the correlation data for the REEs: their good values (most of them showed a r > 0.8) allow to take information about the evaluation of data quality, to understand the mass transport events because their presence affects the sample homogeneity, and the particulate matter composition and aging [52,53]. Table 5 shows a comparison among the element levels in the three fractions determined in this study and similar determinations in other locations. First, it should be underlined that in the literature, very few papers have dealt with such evaluations in different fractions: basically, the main fractions considered are PM 10 and PM 2.5 , whereas few authors have approached the PM 1 fraction. In the table, different scenarios are reported: PM 10 and PM 2.5 were determined around a waste-to-energy plant in the Central of Italy; PM 10 around a hazard waste landfill (HWL) in Spain; PM 2.5 sampled in different areas around Shanghai; and PM 10 , PM 2.5 , and PM 1 in downtown Algiers and Rome [1,2,26,[54][55][56]. Preliminarily, the levels determined in this study were lower than those reported by Buonanno et al. [26], where PM 10 and PM 2.5 were determined around a waste plant: in fact, the difference was not that great, but As, Hg, and Sb showed lower levels whereas Cd and Ni had similar values. No information on fraction PM 1 has been reported for that site. On the other hand, the comparison between similar fractions (PM 10 ) investigated at this site and around the HWL plant in Spain [54] reported almost 10-times lower levels at the Spanish site (e.g., Cr 3.6 vs. 0.4 ng m −3 ; Ni 3.8 vs. 0.58 ng m −3 ; Hg 0.12 ng m −3 vs. not detected). Furthermore, the comparisons with the data determined in downtown Rome [1,2] or in urban, residential, suburban, or industrial locations around Shanghai [55] showed significant differences between the three sites. Finally, in Algiers [56], where the three fractions were determined, the levels were very high (e.g., As at 59.8-178.5 ng m −3 for PM 10 , 48.5-137.9 ng m −3 for PM 2.5 , 38.4-70.9 ng m −3 for PM 1 ; Cr 57.3-100.2 ng m −3 , 30.7-60.2 ng m −3 , 7.3-32.3 ng m −3 , respectively). Among the different reasons for these very high levels found in Algiers, the authors reported "poor combustion of the car fleet, which is increasingly dieselized, aging and poorly maintained and where the use of unleaded gasoline is still very low", a scenario quite different with respect to that present in European countries. Some comments could be also withdrawn in relationship to the PM x amount: in this case, the global situation is quite different. First, no comparison was possible with the data collected around the waste-to-energy plant in Cassino, Italy [26] (data not available in the paper). Regarding the comparison with the data from Rome (site B in Table 5), some elements determined in this study showed a higher presence in relation to their respective PM 10 and PM 2.5 levels: among all elements, Ba, Cd, Co, Fe, La, Ni, Se, and Zn in PM 10 and Ba, Co, Cr, Fe, La, Mo, Ni, Se, and Zn in PM 2.5 should be considered for their environmental and human health roles. Similarly, the same comparison with the data collected at sites D and E ( Table 5) described a different situation. Each site showed minimum and maximum data for each element, so the comparison occurred with low and high values. Looking at the PM data, both sites evidenced data lower than those determined in this study, especially in Algiers. At this site, only Ca in the PM 10 and PM 2.5 fractions and Cr in PM 1 was displayed in proportion to the PM measures. The identification of natural and anthropogenic origins of the investigated elements was an important aspect of this research: in comparison with previous studies or speculation of the sources, the authors focused their attention on the study of the Enrichment Factors (EFs). This approach allows the element presence to be correlated with respect to the same element abundance in the upper continental crust [49,57]. The EFs were calculated according to the equations reported in Misaelides et al. [58] and Bergamaschi et al. [59] using La as the normalizing element: if the EF value is below 10, the element has a crustal origin and therefore is defined as "no enriched element"; in contrast, if the EF value is higher than 40-50, the elements are of anthropogenic origin and are called "elements enriched"; values between these two thresholds show a mixed origin of the element investigated (long-transport phenomena from other natural and/or anthropogenic sources). Figure 2 shows the EF profile for all of the elements investigated in the three fractions. As can be seen, most of the considerations above reported were confirmed: Ni, Cr, Fe, Rb, Ni, Br and As can be considered as no enriched elements (their EFs were below 10), in other words, having a crustal origin. Actually, the As in the PM 1 fraction showed an EF almost at the border (i.e., EF 44.5), meaning a contribution from anthropogenic sources. A similar condition was found for Hg, whose values were in the range 10-50. On the other hand, elements such as Zn, Sb, Ag, Sc, Cd, and Au showing EFs >50 (up to 3413 for Au in the PM 10 ) came from anthropogenic sources (e.g., the waste plant, the heavy traffic): among them, Sb and Cd involve problems related to human health, but their low levels, compared with their relevant limit/guideline values, should not raise an alarm in the population.

Comparison with Other Scenarios Worldwide
Appl. Sci. 2020, 10, x FOR PEER REVIEW 1 of 20 The identification of natural and anthropogenic origins of the investigated elements was an important aspect of this research: in comparison with previous studies or speculation of the sources, the authors focused their attention on the study of the Enrichment Factors (EFs). This approach allows the element presence to be correlated with respect to the same element abundance in the upper continental crust [49,57]. The EFs were calculated according to the equations reported in Misaelides et al. [58] and Bergamaschi et al. [59] using La as the normalizing element: if the EF value is below 10, the element has a crustal origin and therefore is defined as "no enriched element"; in contrast, if the EF value is higher than 40-50, the elements are of anthropogenic origin and are called "elements enriched"; values between these two thresholds show a mixed origin of the element investigated (long-transport phenomena from other natural and/or anthropogenic sources). Figure 2 shows the EF profile for all of the elements investigated in the three fractions. As can be seen, most of the considerations above reported were confirmed: Ni, Cr, Fe, Rb, Ni, Br and As can be considered as no enriched elements (their EFs were below 10), in other words, having a crustal origin. Actually, the As in the PM1 fraction showed an EF almost at the border (i.e., EF 44.5), meaning a contribution from anthropogenic sources. A similar condition was found for Hg, whose values were in the range 10-50. On the other hand, elements such as Zn, Sb, Ag, Sc, Cd, and Au showing EFs >50 (up to 3413 for Au in the PM10) came from anthropogenic sources (e.g., the waste plant, the heavy traffic): among them, Sb and Cd involve problems related to human health, but their low levels, compared with their relevant limit/guideline values, should not raise an alarm in the population.
. Figure 2. Enrichment Factors of all the elements investigated in this study in the three PM fractions. La was used as the normalized agent.

Statistical Analysis
For evidencing the relationship between the elements and possible similarities among the fractions, a statistical approach was performed, in particular, a source discrimination analysis followed by a chemometric methodology allowed us to gain some information on the fractions sampled.
The uncertainties due to variation in counting geometry is a typical error in the INAA methodology, depending on the equipment and sample-holder used. It can be minimized by means of the Aspinall protocol [60], in other words, the application of the source discrimination approach in relation to the Sc (considered as the internal standard due to its high accuracy in the determination), calculated according to the following formula: (1)

Statistical Analysis
For evidencing the relationship between the elements and possible similarities among the fractions, a statistical approach was performed, in particular, a source discrimination analysis followed by a chemometric methodology allowed us to gain some information on the fractions sampled.
The uncertainties due to variation in counting geometry is a typical error in the INAA methodology, depending on the equipment and sample-holder used. It can be minimized by means of the Aspinall protocol [60], in other words, the application of the source discrimination approach in relation to the Sc (considered as the internal standard due to its high accuracy in the determination), calculated according to the following formula: This procedure, also used when the sample numbers are few, allows for very close differences to be discriminated among the samples. Figure 3 shows the source discrimination equation applied to the samples investigated in this study: as can be seen, all the samples could be grouped in a single cluster. This means that the sampled aerosol, PM 10 , PM 2.5 , and PM 1 , come from a single common source. Although this analysis allows us to draw such information, the elements involved (i.e., Ce, Cs, La, Rb, Sc, Ta and Th) were not enough to discriminate the samples satisfactorily.
This procedure, also used when the sample numbers are few, allows for very close differences to be discriminated among the samples. Figure 3 shows the source discrimination equation applied to the samples investigated in this study: as can be seen, all the samples could be grouped in a single cluster. This means that the sampled aerosol, PM10, PM2.5, and PM1, come from a single common source. Although this analysis allows us to draw such information, the elements involved (i.e., Ce, Cs, La, Rb, Sc, Ta and Th) were not enough to discriminate the samples satisfactorily. These data should be considered preliminary: in fact, the results are subjected to large uncertainty. To overcome these doubts, advanced statistical methods, quite similar to those used in cultural heritage studies (e.g., provenance) or in the quality control of goods, were used. Cluster analysis (CA) and multivariate analysis [61,62] manage to describe a source apportionment character through a wide "chemical composition profile" [37].
Statistical analysis was carried out with Tanagra open-source software [63] using the centroid merge method and the Euclidean distance as a measure of proximity [64,65]. First, application of the hierarchical cluster analysis (HAC) gives a dendrogram showing that the three-fraction aerosol samples can be grouped in the following three clusters: Starting from this consideration, the chemometric investigation was addressed to validate the information about the samples with a high percentage of accuracy. Particularly, considering the three different size granulometric fractions as the main characteristics and the elements determined in the samples as variables, the discriminating factorial analysis was applied. The main purpose of the discriminant function analysis is to determine whether groups (i.e., the three aerosol fractions) differ with regard to the mean of a variable, and then to use that variable to predict group membership.
The application of the principal component analysis (PCA) to the entire dataset managed to obtain three principal components describing 99% of the total variance of the data matrix (only with two components was almost 81% of the data described). Afterward, using the discriminating factorial analysis, the composition linear models of the discriminant functions were found. The statistical test showed the separation of the samples in two groups (Figure 4): the principal one was formed by the PM10 and PM2.5 fractions whereas the second cluster was made of PM1 aerosol filters. These findings confirm the strict relationship between PM10 and PM2.5 about the sources, whereas similar evidence shows possible additional sources to the PM1 contribution. This occurrence can be explained considering previous studies on aerosol size distributions [8,66]. In fact, they have These data should be considered preliminary: in fact, the results are subjected to large uncertainty. To overcome these doubts, advanced statistical methods, quite similar to those used in cultural heritage studies (e.g., provenance) or in the quality control of goods, were used. Cluster analysis (CA) and multivariate analysis [61,62] manage to describe a source apportionment character through a wide "chemical composition profile" [37].
Statistical analysis was carried out with Tanagra open-source software [63] using the centroid merge method and the Euclidean distance as a measure of proximity [64,65]. First, application of the hierarchical cluster analysis (HAC) gives a dendrogram showing that the three-fraction aerosol samples can be grouped in the following three clusters: 1st Cluster (eleven members): W, Zn, Ba, Cr, Sc, Ag, Rb, Ce, Th, Sb, Ta. 2nd Cluster: (ten members): Br, Co, Eu, Sm, Mo, Se, Fe, Ni, Hf, Tb. 3rd Cluster (six members): As, Ca, Na, Cs, La, Au.
Starting from this consideration, the chemometric investigation was addressed to validate the information about the samples with a high percentage of accuracy. Particularly, considering the three different size granulometric fractions as the main characteristics and the elements determined in the samples as variables, the discriminating factorial analysis was applied. The main purpose of the discriminant function analysis is to determine whether groups (i.e., the three aerosol fractions) differ with regard to the mean of a variable, and then to use that variable to predict group membership.
The application of the principal component analysis (PCA) to the entire dataset managed to obtain three principal components describing 99% of the total variance of the data matrix (only with two components was almost 81% of the data described). Afterward, using the discriminating factorial analysis, the composition linear models of the discriminant functions were found. The statistical test showed the separation of the samples in two groups (Figure 4): the principal one was formed by the PM 10 and PM 2.5 fractions whereas the second cluster was made of PM 1 aerosol filters. These findings confirm the strict relationship between PM 10 and PM 2.5 about the sources, whereas similar evidence shows possible additional sources to the PM 1 contribution. This occurrence can be explained considering previous studies on aerosol size distributions [8,66]. In fact, they have highlighted that the PM 2.5 convention includes particles from both fine and coarse modes. The aerosol size spectra showed that there is a region where the tails of the PM 10 and PM 2.5 may overlap to some extent. In this region, PM is dominated neither by anthropogenic sources (essentially fine PM) nor by natural sources (essentially coarse PM). Thus, this means that the PM2.5 fraction "contains" PM 10 . For this reason, it could be stated that PM 10 and PM 2.5 have the same origin, whereas the presence of other sources (for instance, a highway close to site) is relevant for the PM 1 fraction.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 20 highlighted that the PM2.5 convention includes particles from both fine and coarse modes. The aerosol size spectra showed that there is a region where the tails of the PM10 and PM2.5 may overlap to some extent. In this region, PM is dominated neither by anthropogenic sources (essentially fine PM) nor by natural sources (essentially coarse PM). Thus, this means that the PM2.5 fraction "contains" PM10. For this reason, it could be stated that PM10 and PM2.5 have the same origin, whereas the presence of other sources (for instance, a highway close to site) is relevant for the PM1 fraction. Finally, the loadings and the percentage of the variance obtained for each of the components are reported in Table 6. Variable factor loadings were used to identify pollution sources and to evaluate the anthropogenic and natural contributions at the sampling site. Only variables with factor loadings greater than 0.5 (in italics in the table) were taken into account in order to characterize the source of pollution. Factor 1 is related to elevated local non-crustal contribution, as expressed by the factor loadings in Br and Cr, whereas F3 is related to both crustal and anthropogenic contributions, by the factor loadings in Na and Zn as well as F4 by the factor loadings in Th and As.  Finally, the loadings and the percentage of the variance obtained for each of the components are reported in Table 6. Variable factor loadings were used to identify pollution sources and to evaluate the anthropogenic and natural contributions at the sampling site. Only variables with factor loadings greater than 0.5 (in italics in the table) were taken into account in order to characterize the source of pollution. Factor 1 is related to elevated local non-crustal contribution, as expressed by the factor loadings in Br and Cr, whereas F3 is related to both crustal and anthropogenic contributions, by the factor loadings in Na and Zn as well as F4 by the factor loadings in Th and As.

Conclusions
The inorganic characterization of the three different PM-fractions is an important issue in environmental science to both identify the contamination sources and in attempting a risk assessment according to the element content. This paper focused attention on the inorganic fraction of PM 10 , PM 2.5 , and PM 1 airborne filters sampled in a site close to an incineration plant: the levels of about 40 elements were determined, and the correlations between the elements and PM-fractions showed good correlation of PM 10 vs. PM 2.5 and the worst between PM 10 vs. PM 1 . The EFs were studied for all the fractions: among the highly toxic metals, Sb and Cd showed a well-defined anthropogenic contribution whereas Hg and As only did partially. A statistical approach was performed to identify similarities among the filter samples. From the source discrimination test, similar behavior was evaluated overall for the samples; the HAC divided the elements in three main clusters whereas the PCA allowed the samples to be separated into two groups, in other words, one formed by PM 10 and PM 2.5 filters and one only by PM 1 filters (the two groups were well-separated between them), meaning a different element contribution to this fraction coming from other relevant sources present at the site (and not identified because this was not part of the study).