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1.
Sci Justice ; 55(2): 131-8, 2015 Mar.
Article in English | MEDLINE | ID: mdl-25753999

ABSTRACT

Forensic anthropologists are generally able to identify skeletal materials (bone and tooth) using gross anatomical features; however, highly fragmented or taphonomically altered materials may be problematic to identify. Several chemical analysis techniques have been shown to be reliable laboratory methods that can be used to determine if questionable fragments are osseous, dental, or non-skeletal in nature. The purpose of this review is to provide a detailed background of chemical analysis techniques focusing on elemental compositions that have been assessed for use in differentiating osseous, dental, and non-skeletal materials. More recently, chemical analysis studies have also focused on using the elemental composition of osseous/dental materials to evaluate species and provide individual discrimination, but have generally been successful only in small, closed groups, limiting their use forensically. Despite significant advances incorporating a variety of instruments, including handheld devices, further research is necessary to address issues in standardization, error rates, and sample size/diversity.


Subject(s)
Bone and Bones/chemistry , Dental Enamel/chemistry , Trace Elements/analysis , Animals , Cremation , Forensic Anthropology , Humans , Microscopy , Species Specificity , Spectrometry, X-Ray Emission , Spectroscopy, Near-Infrared , Spectrum Analysis, Raman
2.
Article in English | MEDLINE | ID: mdl-33946547

ABSTRACT

Firefighters are exposed to burning materials that may release toxic partial combustion and pyrolysis products into the environment, including compounds listed as priority pollutants by the United States Environmental Protection Agency (EPA). A novel passive sampling dosimeter device containing firefighter turnout gear as a diffusion membrane and an activated charcoal strip (ACS) for volatile analyte collection was designed and used to monitor potential exposures of firefighters to volatile organic compounds. Solvent extracts from the ACS and turnout gear diffusion layer were analyzed using Gas Chromatography-Mass Spectrometry (GC-MS) to determine the diffusion of compounds from burned substrates through firefighter turnout gear and compound adsorption to the turnout gear. The compounds in these samples were identified using target factor analysis (TFA). An activated carbon layer (ACL) was added to the dosimeter between the turnout gear and the ACS. The presence of combustion and pyrolysis compounds identified on the ACS in the dosimeter was reduced.


Subject(s)
Firefighters , Occupational Exposure , Volatile Organic Compounds , Gas Chromatography-Mass Spectrometry , Gases , Humans , Occupational Exposure/analysis , Volatile Organic Compounds/analysis
3.
Appl Spectrosc ; 60(10): 1181-7, 2006 Oct.
Article in English | MEDLINE | ID: mdl-17059671

ABSTRACT

A comparative analysis of the discriminating power of laser-induced breakdown spectroscopy (LIBS) and laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS), each coupled with refractive index (RI) measurements, is presented for a study of 23 samples of automobile float glass. Elemental emission intensity ratios (LIBS) and elemental concentration ratios (LA-ICP-MS) and their associated confidence intervals were calculated for each float glass sample. The ratios and confidence intervals were used to determine the discrimination power of each analytical method. It was possible to discriminate 83% of the glass samples with 99% confidence based on LIBS spectra alone, and 96-99% of the samples could be discriminated based on LIBS spectra taken in conjunction with RI data at the same confidence level. LA-ICP-MS data allowed for 100% discrimination of the samples without the need for RI data. The results provide evidence to support the use of LIBS combined with RI for forensic analysis of float glass in laboratories that do not have access to LA-ICP-MS.

4.
Forensic Sci Int ; 264: 113-21, 2016 07.
Article in English | MEDLINE | ID: mdl-27081767

ABSTRACT

Results are presented from support vector machine (SVM), linear and quadratic discriminant analysis (LDA and QDA) and k-nearest neighbors (kNN) methods of binary classification of fire debris samples as positive or negative for ignitable liquid residue. Training samples were prepared by computationally mixing data from ignitable liquid and substrate pyrolysis databases. Validation was performed on an unseen set of computationally mixed (in silico) data and on fire debris from large-scale research burns. The probabilities of class membership were calculated using an uninformative (equal) prior and a likelihood ratio was calculated from the resulting class membership probabilities. The SVM method demonstrated a high discrimination, low error rate and good calibration for the in silico validation data; however, the performance decreased significantly for the fire debris validation data, as indicated by a significant increase in the error rate and decrease in the calibration. The QDA and kNN methods showed similar performance trends. The LDA method gave poorer discrimination, higher error rates and slightly poorer calibration for the in silico validation data; however the performance did not deteriorate for the fire debris validation data.

5.
Forensic Sci Int ; 259: 179-87, 2016 Feb.
Article in English | MEDLINE | ID: mdl-26774249

ABSTRACT

Gas chromatography-electron ionization-mass spectrometry (GC-EI-MS) and physical characteristics data for 726 smokeless reloading powders were analyzed by pairwise comparisons of samples comprising the same product and different products. Pairwise comparisons were restricted to samples having matching kernel shape, color, presence or absence of a perforation and measurements. Discrete results were analyzed for same and different products having matching chemical composition determined from a list of 13 organic components. A continuous score-based likelihood ratio was determined for same and different product comparisons using the Fisher transform of the Pearson correlation between the total ion spectra of the compared samples. Probability distributions for same product and different product comparisons appeared bimodal and were modeled with kernel density distributions. In the discrete and continuous data comparisons, the likelihood ratios for probabilities conditioned on same shape, color, presence/absence of perforation and size were found to provide relatively limited support for either the proposition of same product or different product. Further restricting the pairwise comparisons to samples belonging to the same cluster, as determined by agglomerative hierarchical cluster analysis, provided probability distributions for same product and different product comparisons that were more normal, but did not improve the resulting likelihood ratios. These results inform the forensic analyst regarding the evidentiary value of database search results and direct comparisons of recovered and control samples of smokeless powders.


Subject(s)
Explosive Agents/analysis , Bombs , Collodion/analysis , Gas Chromatography-Mass Spectrometry , Nitroglycerin/analysis , Powders , Sensitivity and Specificity
6.
J Forensic Sci ; 60(2): 382-90, 2015 Mar.
Article in English | MEDLINE | ID: mdl-25620077

ABSTRACT

One of the tasks of a forensic anthropologist is to sort human bone fragments from other materials, which can be difficult when dealing with highly fragmented and taphonomically modified material. The purpose of this research is to develop a method using handheld X-ray fluorescence (HHXRF) spectrometry to distinguish human and nonhuman bone/teeth from nonbone materials of similar chemical composition using multivariate statistical analyses. The sample materials were derived primarily from previous studies: human bone and teeth, nonhuman bone, nonbiological materials, nonbone biological materials, and taphonomically modified materials. The testing included two phases, testing both the reliability of the instrument and the accuracy of the technique. The results indicate that osseous and dental tissue can be distinguished from nonbone material of similar chemical composition with a high degree of accuracy (94%). While it was not possible to discriminate rock apatite and synthetic hydroxyapatite from bone/teeth, this technique successfully discriminated ivory and octocoral.


Subject(s)
Bone and Bones , Spectrometry, X-Ray Emission , Tooth , Animals , Calcium/analysis , Forensic Anthropology/methods , Humans , Phosphorus/analysis , Principal Component Analysis , Species Specificity
7.
J Forensic Sci ; 60(6): 1534-41, 2015 11.
Article in English | MEDLINE | ID: mdl-26234321

ABSTRACT

Identification of osseous materials is generally established on gross anatomical features. However, highly fragmented or taphonomically altered materials may be problematic and may require chemical analysis. This research was designed to assess the use of scanning electron microscopy-energy-dispersive X-ray spectrometry (SEM/EDX), elemental analysis, and multivariate statistical analysis (principal component analysis) for discrimination of osseous and nonosseous materials of similar chemical composition. Sixty samples consisting of osseous (human and nonhuman bone and dental) and non-osseous samples were assessed. After outliers were removed a high overall correct classification of 97.97% was achieved, with 99.86% correct classification for osseous materials. In addition, a blind study was conducted using 20 samples to assess the applicability for using this method to classify unknown materials. All of the blind study samples were correctly classified resulting in 100% correct classification, further demonstrating the efficiency of SEM/EDX and statistical analysis for differentiation of osseous and nonosseous materials.


Subject(s)
Microscopy, Electron, Scanning , Multivariate Analysis , Principal Component Analysis , Spectrometry, X-Ray Emission , Animal Shells/chemistry , Animals , Apatites/chemistry , Bone and Bones/chemistry , Calcium Carbonate/chemistry , Dental Enamel/chemistry , Dentin/chemistry , Forensic Sciences/methods , Glass/chemistry , Humans , Plastics/chemistry , Sea Urchins/chemistry , Starfish/chemistry , Wood/chemistry
8.
Forensic Sci Int ; 252: 177-86, 2015 Jul.
Article in English | MEDLINE | ID: mdl-26005858

ABSTRACT

Forensic chemical analysis of fire debris addresses the question of whether ignitable liquid residue is present in a sample and, if so, what type. Evidence evaluation regarding this question is complicated by interference from pyrolysis products of the substrate materials present in a fire. A method is developed to derive a set of class-conditional features for the evaluation of such complex samples. The use of a forensic reference collection allows characterization of the variation in complex mixtures of substrate materials and ignitable liquids even when the dominant feature is not specific to an ignitable liquid. Making use of a novel method for data imputation under complex mixing conditions, a distribution is modeled for the variation between pairs of samples containing similar ignitable liquid residues. Examining the covariance of variables within the different classes allows different weights to be placed on features more important in discerning the presence of a particular ignitable liquid residue. Performance of the method is evaluated using a database of total ion spectrum (TIS) measurements of ignitable liquid and fire debris samples. These measurements include 119 nominal masses measured by GC-MS and averaged across a chromatographic profile. Ignitable liquids are labeled using the American Society for Testing and Materials (ASTM) E1618 standard class definitions. Statistical analysis is performed in the class-conditional feature space wherein new forensic traces are represented based on their likeness to known samples contained in a forensic reference collection. The demonstrated method uses forensic reference data as the basis of probabilistic statements concerning the likelihood of the obtained analytical results given the presence of ignitable liquid residue of each of the ASTM classes (including a substrate only class). When prior probabilities of these classes can be assumed, these likelihoods can be connected to class probabilities. In order to compare the performance of this method to previous work, a uniform prior was assumed, resulting in an 81% accuracy for an independent test of 129 real burn samples.

9.
J Forensic Sci ; 49(2): 238-49, 2004 Mar.
Article in English | MEDLINE | ID: mdl-15027537

ABSTRACT

LC-MS is used for the identification of dyes extracted from textile fibers and the utility of the method for forensic trace analysis is demonstrated. The technique is shown to provide a high degree of chemical structural information, making dye identification highly specific in comparison to optical and/or chromatographic methods of dye analysis. A UV-visible absorbance detector, placed in series before the MS detector, facilitates monitoring the elution of dyes in the presence of other non-dye components extracted from colored textile fibers. In this way, dye identification becomes practical, even when a dye standard is not available for comparison. A set of 22 reference dyestuffs and 10 dyes extracted from textile fibers were analyzed to demonstrate the utility of the method. Six of the extracted dyes corresponded to dyes also contained in the set of 22 reference dyestuffs. Reference dyestuffs were not available for four of the extracted dyes. Triethylamine (TEA) was shown to increase the electrospray ionization-mass spectrometry (ESI-MS) response of dyes containing multiple sulfonated groups.

10.
J Forensic Sci ; 59(4): 927-35, 2014 Jul.
Article in English | MEDLINE | ID: mdl-24502629

ABSTRACT

A multistep classification scheme was used to detect and classify ignitable liquid residues in fire debris into the classes defined by the ASTM E1618-10 standard method. The total ion spectra (TIS) of the samples were classified by soft independent modeling of class analogy (SIMCA) with cross-validation and tested on fire debris. For detection of ignitable liquid residue, the true-positive rate was 94.2% for cross-validation and 79.1% for fire debris, with false-positive rates of 5.1% and 8.9%, respectively. Evaluation of SIMCA classifications for fire debris relative to a reviewer's examination led to an increase in the true-positive rate to 95.1%; however, the false-positive rate also increased to 15.0%. The correct classification rates for assigning ignitable liquid residues into ASTM E1618-10 classes were generally in the range of 80-90%, with the exception of gasoline samples, which were incorrectly classified as aromatic solvents following evaporative weathering in fire debris.

11.
J Forensic Sci ; 59(5): 1198-204, 2014 Sep.
Article in English | MEDLINE | ID: mdl-24962674

ABSTRACT

Gas chromatography-mass spectrometry (GC-MS) data of ignitable liquids in the Ignitable Liquids Reference Collection (ILRC) database were processed to obtain 445 total ion spectra (TIS), that is, average mass spectra across the chromatographic profile. Hierarchical cluster analysis, an unsupervised learning technique, was applied to find features useful for classification of ignitable liquids. A combination of the correlation distance and average linkage was utilized for grouping ignitable liquids with similar chemical composition. This study evaluated whether hierarchical cluster analysis of the TIS would cluster together ignitable liquids of the same ASTM class assignment, as designated in the ILRC database. The ignitable liquids clustered based on their chemical composition, and the ignitable liquids within each cluster were predominantly from one ASTM E1618-11 class. These results reinforce use of the TIS as a tool to aid in forensic fire debris analysis.

12.
Forensic Sci Int ; 236: 84-9, 2014 Mar.
Article in English | MEDLINE | ID: mdl-24529778

ABSTRACT

The unsupervised artificial neural networks method of self-organizing feature maps (SOFMs) is applied to spectral data of ignitable liquids to visualize the grouping of similar ignitable liquids with respect to their American Society for Testing and Materials (ASTM) class designations and to determine the ions associated with each group. The spectral data consists of extracted ion spectra (EIS), defined as the time-averaged mass spectrum across the chromatographic profile for select ions, where the selected ions are a subset of ions from Table 2 of the ASTM standard E1618-11. Utilization of the EIS allows for inter-laboratory comparisons without the concern of retention time shifts. The trained SOFM demonstrates clustering of the ignitable liquid samples according to designated ASTM classes. The EIS of select samples designated as miscellaneous or oxygenated as well as ignitable liquid residues from fire debris samples are projected onto the SOFM. The results indicate the similarities and differences between the variables of the newly projected data compared to those of the data used to train the SOFM.

13.
J Forensic Sci ; 58(4): 887-96, 2013 Jul.
Article in English | MEDLINE | ID: mdl-23551258

ABSTRACT

Principal components analysis (PCA), linear discriminant analysis (LDA), and quadratic discriminant analysis (QDA) were used to develop a multistep classification procedure for determining the presence of ignitable liquid residue in fire debris and assigning any ignitable liquid residue present into the classes defined under the American Society for Testing and Materials (ASTM) E 1618-10 standard method. A multistep classification procedure was tested by cross-validation based on model data sets comprised of the time-averaged mass spectra (also referred to as total ion spectra) of commercial ignitable liquids and pyrolysis products from common building materials and household furnishings (referred to simply as substrates). Fire debris samples from laboratory-scale and field test burns were also used to test the model. The optimal model's true-positive rate was 81.3% for cross-validation samples and 70.9% for fire debris samples. The false-positive rate was 9.9% for cross-validation samples and 8.9% for fire debris samples.

14.
Forensic Sci Int ; 222(1-3): 373-86, 2012 Oct 10.
Article in English | MEDLINE | ID: mdl-22920087

ABSTRACT

A bayesian soft classification method combined with target factor analysis (TFA) is described and tested for the analysis of fire debris data. The method relies on analysis of the average mass spectrum across the chromatographic profile (i.e., the total ion spectrum, TIS) from multiple samples taken from a single fire scene. A library of TIS from reference ignitable liquids with assigned ASTM classification is used as the target factors in TFA. The class-conditional distributions of correlations between the target and predicted factors for each ASTM class are represented by kernel functions and analyzed by bayesian decision theory. The soft classification approach assists in assessing the probability that ignitable liquid residue from a specific ASTM E1618 class, is present in a set of samples from a single fire scene, even in the presence of unspecified background contributions from pyrolysis products. The method is demonstrated with sample data sets and then tested on laboratory-scale burn data and large-scale field test burns. The overall performance achieved in laboratory and field test of the method is approximately 80% correct classification of fire debris samples.

15.
Anal Chim Acta ; 753: 19-26, 2012 Nov 13.
Article in English | MEDLINE | ID: mdl-23107132

ABSTRACT

A method is described for performing discriminant analysis in the presence of interfering background signal. The method is based on performing target factor analysis on a data set comprised of contributions from analyte(s) and interfering components. A library of data from representative analyte classes is tested for possible contributing factors by performing oblique rotations of the principal factors to obtain the best match, in a least-squares sense, between test and predicted vectors. The degree of match between the test and predicted vectors is measured by the Pearson correlation coefficient, r, and the distribution of r for each class is determined. A Bayesian soft classifier is used to calculate the posterior probability based on the distributions of r for each class, which assist the analyst in assessing the presence of one or more analytes. The method is demonstrated by analyses performed on spectra obtained by laser induced breakdown spectroscopy (LIBS). Single and multiple bullet jacketing transfers to steel and porcelain substrates were analyzed to identify the jacketing materials. Additionally, the metal surrounding bullet holes was analyzed to identify the class of bullet jacketing that passed through a stainless steel plate. Of 36 single sample transfers, the copper jacketed (CJ) and non-jacketed (NJ) class on porcelain had an average posterior probability of the metal deposited on the substrate of 1.0. Metal jacketed (MJ) bullet transfers to steel and porcelain were not detected as successfully. Multiple transfers of CJ/NJ and CJ/MJ on the two substrates resulted in posterior probabilities that reflected the presence of both jacketing materials. The MJ/NJ transfers gave posterior probabilities that reflected the presence of the NJ material, but the MJ component was mistaken for CJ on steel, while non-zero probabilities were obtained for both CJ and MJ on porcelain. Jacketing transfer from a bullet to steel as the projectile passed through the steel also proved difficult to analyze. Over 50% of the samples left insufficient transfer to be identified. Transfer from NJ and CJ jacketing was successfully identified by posterior probabilities greater than 0.8.

16.
Forensic Sci Int ; 191(1-3): 97-103, 2009 Oct 30.
Article in English | MEDLINE | ID: mdl-19647961

ABSTRACT

A method for the analysis of dyes and vehicles within writing inks was developed. The method was tested on a set of 18 black ink pens comprised of 6 ballpoint, 6 gel, and 6 rollerball pens. The sampling procedure utilized a small number of ink-coated paper fibers collected surreptitiously from the document, causing minimal damage and providing a sufficient quantity of ink for analysis. Methanol proved suitable for the extraction of ink components from ballpoint, gel and rollerball pens. Three separate electrospray ionisation-mass spectrometry (ESI-MS) methods were required to detect the dyes and vehicles from the inks. The ions present in the ESI-MS spectra at a signal-to-noise ratio of greater than 3:1 provided sufficient information to allow differentiation between the inks of each type. A tentative identification of the ink components was made based on a comparison of the ions present in the ink extract ESI-MS spectra with the ions present in a series of standards. The limits of detection for the standards were generally in the 2.5-10 ppm range. The method reported here extends the ESI-MS method of ink analysis to include gel and rollerball pens, includes the analysis of vehicles as well as dyes in the inks and demonstrates a minimally destructive sampling method that does not require a "biopsy" of the document.

17.
Rapid Commun Mass Spectrom ; 23(3): 349-56, 2009 Feb.
Article in English | MEDLINE | ID: mdl-19125413

ABSTRACT

Oligomeric peroxides formed in the synthesis of triacetone triperoxide (TATP) have been analyzed by mass spectrometry utilizing both electrospray ionization (ESI) and chemical ionization (CI) to form sodiated adducts (by ESI) and ammonium adducts (by CI and ESI). Tandem mass spectrometry and deuterium isotopic labeling experiments have been used to elucidate the collision-induced dissociation (CID) mechanisms for the adducts. The CID mechanisms differ for the sodium and ammonium adducts and vary with the size of the oligoperoxide. The sodium adducts of the oligoperoxides, H[OOC(CH(3))(2)](n)OOH, do not cyclize under CID, whereas the ammonium adducts of the smaller oligoperoides (n < 6) do form the cyclic peroxides under CID. Larger oligoperoxide adducts with both sodium and ammonium undergo dissociation through cleavage of the backbone under CID to form acyl- and hydroperoxy-terminated oligomers of the general form CH(3)C(O)[OOC(CH(3))(2)](x)OOH, where x is an integer less than the original oligoperoxide degree of oligomerization. The oligoperoxide distribution is shown to vary batch-to-batch in the synthesis of TATP and the post-blast distribution differs slightly from the distribution in the uninitiated material. The oligoperoxides are shown to be decomposed under gentle heating.

18.
Rapid Commun Mass Spectrom ; 22(2): 84-90, 2008.
Article in English | MEDLINE | ID: mdl-18058960

ABSTRACT

The explosive triacetone triperoxide (TATP) has been analyzed by electrospray ionization mass spectrometry (ESI-MS) on a linear quadrupole instrument, giving a 62.5 ng limit of detection in full scan positive ion mode. In the ESI interface with no applied fragmentor voltage the m/z 245 [TATP + Na](+) ion was observed along with m/z 215 [TATP + Na - C(2)H(6)](+) and 81 [(CH(3))(2)CO + Na](+). When TATP was ionized by ESI with an applied fragmentor voltage of 75 V, ions at m/z 141 [C(4)H(6)O(4) + Na](+) and 172 [C(5)H(9)O(5) + Na](+) were also observed. When the precipitates formed in the synthesis of TATP were analyzed before the reaction was complete, a new series of ions was observed in which the ions were separated by 74 m/z units, with ions occurring at m/z 205, 279, 353, 427, 501, 575, 649 and 723. The series of evenly spaced ions is accounted for as oligomeric acetone carbonyl oxides terminated as hydroperoxides, [HOOC(CH(3))(2){OOC(CH(3))(2)}(n)OOH + Na](+) (n = 1, 2 ... 8). The ESI-MS spectra for this homologous series of oligoperoxides have previously been observed from the ozonolysis of tetramethylethylene at low temperatures. Precipitates from the incomplete reaction mixture, under an applied fragmentor voltage of 100 V in ESI, produced an additional ion observed at m/z 99 [C(2)H(4)O(3) + Na](+), and a set of ions separated by 74 m/z units occurring at m/z 173, 247, 321, 395, 469 and 543, proposed to correspond to [CH(3)CO{OOC(CH(3))(2)}(n)OOH + Na](+) (n = 1,2 ... 5). Support for the assigned structures was obtained through the analysis of both protiated and perdeuterated TATP samples.

19.
Anal Chem ; 79(9): 3462-8, 2007 May 01.
Article in English | MEDLINE | ID: mdl-17388567

ABSTRACT

A set of 10 fresh (unevaporated) gasoline samples from a single metropolitan area were differentiated based on a covariance mapping method combined with a t-test statistic. The covariance matrix for each sample was calculated from the retention time-ion abundance data set obtained by gas chromatography/mass spectrometry analysis. Distance metrics were calculated between the covariance matrices from replicate analyses of the same sample and between the replicate analyses of different samples. The distance metric for the same-sample comparisons were shown to constitute a population significantly different from the distance metric for the different-sample comparisons. A power analysis was performed to estimate the number of analyses needed to discriminate between two samples while maintaining a probability of type II error, beta, below 1%, e.g., a test power greater than 99%. Triplicate analyses of two gasoline samples was shown to be sufficient to discriminate between the two using a t-test, while keeping beta<0.01 at a significance level, alpha, of 0.05. Analysis of the 45 possible pairwise comparisons between samples found that 100% of the samples were statistically distinguishable, and no type II errors occurred. Blind tests were conducted wherein 2 of the 10 gasoline samples where presented as unknowns. One of the unknowns was found to be indistinguishable from the original source, and one unknown was determined to be statistically different from the original source, constituting a type I error. The effects of evaporation on sample comparison are not addressed in this paper. The results from this study demonstrate a statistically acceptable method of physical evidence comparison in forensic casework.


Subject(s)
Gas Chromatography-Mass Spectrometry/methods , Gasoline/analysis , Analysis of Variance , Sensitivity and Specificity
20.
Rapid Commun Mass Spectrom ; 20(3): 427-32, 2006.
Article in English | MEDLINE | ID: mdl-16397843

ABSTRACT

Binary aqueous mixtures of NaNO3, KNO3 and NaClO4 oxidizers were analyzed using electrospray ionization mass spectrometry. Sodium nitrate solutions were observed to form doubly charged clusters of the type [(NaNO3)n2Na]2+ and [(NaNO3)n2NO3]2-, where n = 11, 13, 15, etc., in addition to singly charged cluster ions that have been reported previously. The identity of the doubly charged clusters was determined by tandem mass spectrometry. Two-component NaNO3-KNO3 salt solutions were observed to form cluster ions of the type [(NaNO3)i(KNO3)jNO3]- in the negative ion mode and [(NaNO3)i(KNO3)jNa]+ and [(NaNO3)i(KNO3)jK]+ in the positive ion mode, where i + j = 1, 2, 3 ... 10. Two-component solutions of KNO3-NaClO4 formed ions of the type [(KNO3)i(NaClO4)j(KClO4)k(NaNO3)lK](+) and [(KNO3)i(NaClO4)j(KClO4)k(NaNO3)lNa]+ in the positive ion mode, where i + j + k + l = 1, 2, 3 ... 10. Similar clusters containing excess nitrate and perchlorate to provide the charge are formed in the negative ion mode. In each case, the maximum number of spectral lines for a cluster of size n can be calculated as the number of combinations of n(th) order (where n = i + j) of N different cation-anion pairs taken with replication and without regard for the ordering of the N cation-anion pairs. The actual number of lines observed may be reduced due to degeneracy of nominal m/z values for some ions.

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