US 3764805 A Abstract The use of multiple linear regression analysis in correlating the data obtained by the X-ray fluorescence analysis of propellant compositions. Ingredient concentrations and particle sizes are predicted by means of multiple regression equations which relate characteristic emission line intensities with particle sizes and ingredient concentrations. These equations give more accurate predictions than simple regression equations which are commonly used.
Claims available in Description (OCR text may contain errors) United States Patent [191 Alley [451 Oct. 9, 1973 1 CONTROL or PROPELLANT COMPOSITIONS BY X-RAY FLUORESCENCE ANALYSIS [21] Appl. No.: 652,654 Related US. Application Data [63] Continuation-in-part of Ser. No. 306,393, Sept. 3, 1963, abandoned. [56] I References Cited UNITED STATES PATENTS 1591303 7/1971 7 SPi lPEl ".1 6 c: Q |.O7[' as E Q|.o5- 3 SULFUR Ka 5 8 LOB-- d5 0 a l.Ol x z CHLORINE Ka [Z O 3 F. .99-- EL: 0 52% Primary Examiner-Carl D. Quarforth Assistant Examiner-J. M. Potenza Attorney-Harry M. Saragovitz, Edward J. Kelly, Herbert Berl and Elihu L. Turetsky [5 7] ABSTRACT The use of multiple linear regression analysis in correlating the data obtained by the X-ray fluorescence analysis of propellant compositions. Ingredient concentrations and particle sizes are predicted by means of multiple regression equations which relate characteristic emission line intensities with particle sizes and ingredient concentrations. These equations give more accurate predictions than simple regression equations which are commonly used. 17 Claims, 2 Drawing Figures ALUMINUM Ka CORRECTION FACTOR,C ' l CONTROL OF PROPELLANT COMPOSITIONS BY X-RAY FLUORESCENCE ANALYSIS CrossReference to Related Applications: This application is a continuation-in-part of application Ser. No. 306,393, filed Sept. 3, 1963, now abandoned. BACKGROUND OF THE INVENTION dures used must be precise and accurate enough to allow, with a high degree of confidence, the acceptance, rejection, or correction of batches. Also, the decision to accept or reject a batch must be made rapidly to prevent costly production delays. Chemical procedures currently being used are sufficiently precise and accurate for routine quality control. Their speed of analyses for some propellant compositions, however, is slow and faster procedures are needed. Further analysis is necessary after the propellant composition is cured to insure that the ingredients fall within the required concentration and size ranges. This analysis insures that the rocket motor propellant will perform as intended. Moreover, additional analysis is made at periodic intervals to determine if moisture, gassing or other conditions are altering the composition to the extent ,that it no longer meets acceptable standards. X-ray fluorescence techniques for analyzing composite propellants have been developed and tested. This has demonstrated that the X-ray fluorescence method can be advantageously used as a tool to control and improve the quality of production propellants. The X-ray fluorescence method described in applicants above referred to application was developed to replace existing chemical procedures for controlling propellant compositions. The method was specifically applied to polybutadiene-acrylic acid (PB AA) propellants. It can readily be applied, with little or no modification, to other types of composite propellants. X-ray fluorescence analysis, like other physical methods, is not absolute. That is, the concentrations and sizes of ingredients in unknown samples are determined with the aidof calibration curves or equations which relate elemental emission line intensities with sizes and concentrations. The calibration equations for propellants are established by analyzing carefully prepared batches whose ingredient concentrations and sizes are accurately known and cover the required ranges. The most widely used calibration method for X-ray fluorescence analysis consists of establishing a simple linear regression relationship among the concentrations or sizes of an ingredient and the intensities of one of its elemental emission lines: R b, bx where R the corrected analytical intensity ratio X the concentration of an ingredient (or its size), b, a constant, and b, another constant. Ingredient concentrations (or sizes) in unknown samples are estimated either from calibration curves or the inverse of equation I: X id/( 1) The accuracy of prediction using equation 2' is inadequate for the direct control analysis of propellants and many other types of materials. The true intensityconcentration or intensity-size relationship for multicomponent materials is generally much more complex than that shown by equation 1'. Theintensity of characteristic radiation from an element in a material depends not only on the concentration or size of that element but also on the concentrations or sizes of all other elements in the material. These interactions among elements are commonly called interelement effects. Interelement effects are inherentin X-ray fluorescence analysis, but the magnitudes of the effects vary markedly, depending on the types and relative quantities of elements in the material. Because of these interelement effect variations, special analysis techniques are ,usually developed for each type of material analyzed. Equation 2 may give concentration and particle size predictions of suitable accuracy if interelement effects are minimized experimentally. Three main experimental techniques have been used to minimize or correct for interelement effects: a. Introduction of internal standards b. Dilution of the material with an inert component c. Restriction of ingredient calibration concentrations and sizes to narrow ranges. The first two are impractical for rapid propellant analysis and were not attempted. The last technique was attempted; however, the analytical error was greater than could be tolerated for propellant control analysis. Accordingly, it is an object of this invention to provide an improved method of X-ray fluorescence analy- SIS proved method of X-ray fluorescence analysis which can be used in PBAA propellant compositions. A particular object of this-invention is to provide an improved method of X-ray fluorescence analysis which can be used'for'the simultaneous determination of particle sizes and ingredient concentrations in propellant compositions. Another object of this invention is to provide an improved method of X-ray fluorescence analysis which can be used in PBAA propellant compositions and also which can be applied, with little or no modification, to Another object of this invention is to provide an imelement to be analyzed are evaluated simultaneously. The general techniques of multiple linear regression analysis are described, for example, by Ostle, Statistics in Research, 2nd ed., p. 159, Iowa State University Press, Ames, 1963. Alley and Myers, Anal. Chem. 37, 1685 (1965) have reported the special application of multiple,regression methods to the analysis of ingredient concentrations and particular sizes in propellants. BRIEF DESCRIPTION OF THE DRAWING This invention will become more clearly understood by reference to the following detailed description of which the accompanying drawing forms an integral part thereof, and in which: FIG. 1 is a graph of the Mylar film correction curves for sulfur Ka and chlorine Ka radiations plotted against the aluminum Ka correction factor; and FIG. 2 is a graph showing the effect of ferrocence sublimation in the analysis of ferrocene. Description of the Preferred Embodiments Since propellant formulations using the copolymers of polybutadiene and acrylic acid as a binder, aluminum as a fuel ingredient, ammonium perchlorate as an oxidizer and ferrocene or ferric oxide as a burning rate modifier are of current interest, the analytical method of this invention has been developed using such formulations. However, applying the procedures explained herein, it will be obvious to those skilled in the art that the method of this invention can be utilized in analyzing other propellant formulations. The polybutadieneacrylic acid copolymers referred to herein are the type wherein elemental sulfur in a fixed amount is present in the molecules due to a sulfur compound being utilized as a chain-stopper in the preparation of the polymer. Therefore, the amount of sulfur in a composition can be directly related to the polybutadiene-acrylic acid copolymer present. With other binders, it may be necessary to analyze for some other element having a known fixed ratio to the polymer to determine the amount of polymer present. The equipment required by this invention is of the standard commercial type. A Philips Universal Vacuum X-Ray Spectograph was used in the development of this invention. Specific instrumentation and operating conditions are set forth in Table I below: TABLE I X-ray tube Philips FA-60 with tungsten target X-ray tube setting 50 Kilovolts (peak); 45 milliamperes Entrance collimator Parallel plates with 20 mil spacings Detector Detector flow gas Gas flow proportional counter P-lO (90% argon, l% methane); 0.5 cu. ft./hr. flow rate (air calibration) Flat crystal inverted Helium; l.0 liters/min. flow rate (air calibration) Sodium chloride and ethylene diamine D-tartrate (EDDT) X-ray optics Xray optical path Analyzing crystals type of composition which is to be analyzed. That is, the K0: intensity of a particular element in the standard should be as similar as possible to the K11 intensity of that same element in the unknown formulations to be analyzed. Where possible, the same compounds or elements used in the preparation of the unknown formulations should be used in the standards. However, this is not always possible since the constituents of the unknown may deteriorate on standing, undergo slow reaction, decompose upon exposure to X-rays, or otherwise be unstable. It is also desirable that the valence of the particular element in the standard be the same as, or very close to, that of the element in the unknown compositions. It has been determined that an excellent standard for use in analyzing unknown formulations for aluminum, chlorine, sulfur, and iron can be made from aluminum, inorganic chlorides, stable sulfides other than hydrogen sulfide, ferric oxide, and a binder. Among inorganic chlorides the light metal chlorides, particularly the alkali metal chlorides such as sodium chloride and potassium chloride are especially preferred. The inorganic sulfides, especially metallic sulfides such as zinc sulfide and cadmium sulfide are illustrative of stable sulfides. Ferric oxide is the logical source of iron since it is stable to X-rays and is itself employed in some of the propellant mixes. As aluminum is sued in the formulation to be analyzed and as it meets the criteria necessary for incorporation into a standard as previously explained, aluminum etal powder is used in the standards. Any conventional binder can be used for holding the various constituents of the standard together as long as it does not interfere with the analysis. Methyl cellulose, nylons, various methyl methacrylate resins such as those sold under the trademark Plexiglass, starch, and the like are examples of suitable binders. Standards comprising 20 to percent of the inorganic chloride, 10 percent to 30 percent aluminum metal powder, 25 percent to 45 percent binder, 0.5 to 5 percent ferric oxide and 0.5 percent to 5 percent sulfide are completely satisfactory for use in this invention. The percentages refer to the composition in terms of per cent by weight. The standards, one for use with cured propellant and one for use with uncured propellant, are used in the present discussion. The ingredients of the two standards are given in Table II below: TABLE II Compositions of Standards Ingredient Uncured Propellant Cured Propellant percent by weight percent by weight Sodium Chloride 35.00 54.00 Aluminum powder 22.00 14.00 Methyl Cellulose 4l.00 30.60 Ferric Oxide 0.80 0.70 Zinc Sulfide 1.20 0.70 Sodium chloride is used in lieu of ammonium perchlorate since the latter decomposes after approximately 30 minutes of continuous exposure to X-rays at 50 kilovolts (peak) and 45 milliamperes. However, al- lowance has to be made for the fact that chlorine The actual reference standards are prepared by thoroughly mixing the ingredients and then pelletizing the mixture according to established techniques. The standard pellets referred to hereinafter were prepared by mixing the ingredients in Pica blender for 30 minutes and then forming 5 gram pellets under a pressure of 30,000 psi. The pellets withstand continuous X-ray exposure of 50 kilovolts (peak) and 45 milliamperes for six hours with no detectable decomposition. Even after use for analyzing several hundred propellant samples, no change is detected. in addition to being stable when exposed to X-rays, the pellets provide almost complete correction for large changes in power output of the X-ray tube, the latter characteristic being a critical test of the corrective ability of a standard. Two standards are used since the Ka intensity of the element in the compositions being analyzed varies in the cured and uncured states. The compositions are varied as shown in Table II so that the Ka intensities approximate those of the elements in the uncured and cured propellant states. However, this is an extreme step to reduce all experimental error to a minimum. When either of the two standards are used for analyzing propellant formulations, both cured and uncured, the results of the analysis show that no appreciable practical variation is found when compared to the results obtained if the standard for cured propellant is used only in cured propellant analysis or when the standard for uncured propellant is used only in uncured propellant analysis. Nevertheless, for the very optimum in accuracy, it is best to have the Ka intensity of the element in the standard approximate the Ka intensity of the element in the particular unknown samples being analyzed. This is not a problem since the desired composition of the product is known in quality control operations. I The standards, as described, permit accurate analysis of many conventional propellant formulations. In addition to the propellant compositions using the copolymers of polybutadiene and acrylic acid, accurate analyses have been made of propellant compositions using liquid polysulfide binders such as LP-33. However, as should be apparent to those of ordinary skill in the art, many modifications to those exemplary standards are possible without adversely affecting their use. The incorporation of additional ingredients may be necessary if the analysis is to include additional elements. An ingredient can be deleted if there is no requirement in analyzing for the particular elements of which it is com posed. The use of transparent film, such as Mylar film, in the analysis of heavy elements in liquids and slurries is known in the prior art. Mylar is the trademark for a commercially available transparent polyester film (polyethylene terephthalate resin) manufactured by E. l. Dupont de Nemours and Company, Inc., Film Department, Wilmington, Dela. The thickness of the Mylar film generally used in X-ray analysis is on the order of.0.00025 inch. Other film can be used, however, All that is required of a film is that it be (1) relatively thin, that is, on the order of 0.00010 to 0.00050 inch in thickness; (2) of sufficient strength to hold a sample; and (3) transparent to X-ray radiation. Thin polyethylene films are available which can be used in the same manner as the Mylar films although they do not exhibit as great a strength as the Mylar films. Obviously, the thinner the film employed, the less effect the film has on the analytical results. It has been found that these films have serious disadvantages in the analysis of light elements since the films absorb the characteristic X-rays of these elements. In Table III below, the approximate percentage transmission through nominal 0.00025 inch Mylar film of characteristic Ka radiations from four light elemnts is shown. As is apparent from the Table, percentage transmission varies markedly with wavelength variation. TABLE [ll Transmission of X-rays by nominal 0.00025 inch Mylar Element Emission Wavelength Percent Line Angstroms Transmission lron Kn L94 98.0 Chlorine Ka 4.73 76.1 Sulfur Ka 5.37 68.0 Aluminum Ka 8.34 24.2 As used herein, the terminology light element or lighter element refers to those elements having an atomic number up to and including atomic number 2 l The term light metal designates those metals which are included in the range of atomic numbers up to and including number twenty-two. However, the method of this invention can be used when X-ray absorption by a transparent film is a problem in the X-ray analysis of any element. Another serious objection to using films in the analysis of light elements such as aluminum is that the actual thickness of the films varies about the nominal value. Since the percentage transmission of the characteristic radiation is greatly influenced by the film, as shown in Table III, the variations in actual film thickness lead to serious errors in the analysis of light elements. A practical, effective method has been determined whereby correction factors and curves can be established for thickness variations in transparent films used in the analysis of light elements. The method is illustrated with Mylar film and the light elements chlorine, aluminum, and sulfur. Analytical parameters for determining the correction curves are shown in Table [V below. The peak Ka angle for each element is determined experimentally according to well established procedures in the art. It will be apparent to those skilled in the art that the method is applicable to establishing cor- 1 rection-curves for other elements. TABLE IV Parameters for Determining Mylar Correction Curves Ana- Peak Total Ana- Pulse Element lytical angle counts lyzing height line degrees collected crystal analyzer 20 Chlorine Ka ll3.96 1,024,000 NaCl Integral Sulfur Ka 144.78 64,000 NaCl Differential Aluminum Ka l42.74 128,000 EDDT' Difierential Ethylene Diamine D-Tartrate The method for determining correction factors is based on utilizing interchangeable aluminum standards. An aluminum standard is prepared for each position of the spectrograph to be used. In the case of the equipment used herein this amounted to four standards. The standards were cut from a single aluminum bar and machined to 1% inches in diameter to one inch in length to fit the standard, circular sample holder. level. Care should be exercised in storage of the standards so that moisture and other agents do not alter the aluminum Ka intensities. In determining the film correction factors, a fixed count technique is used and all intensity measurements are recorded as the number of seconds required to collect the preselected total counts listed in Table IV, thus eliminating conversion to counts per second. The fixed count selected is not critical although, generally, the higher the fixed count, the less error. However, the number selected should be one that can be reached in about 60 seconds or less. Sulfur Ka and chlorine Ka intensities are measured from standard pellets described hereinafter while aluminum Ka intensities are measured from the aluminum standards. Peak-tobackground ratios from sulfur and aluminum are increased with pulse height analysis and only peak intensities are measured. Since, in every instance herein, the peak-to-background ratio exceeded 100 to 1, errors resulting from the uncorrected background are small. The method of preparing Mylar film correction curves is illustrated by Table V where a portion of the data obtained for the chlorine Ka film correction is shown. Similar data were obtained for the sulfur Ka film correction factor. The following technique was used to obtain the data: a. Load aluminum standards into sample holders containing nominal 0.00025-inch Mylar film of different thickness. The difference in thickness should be established by prior measurement of aluminum Ka intensities transmitted by a large number of film samples using the standards. Differences in thickness are reflected by different aluminum Ka intensities transmitted by various film samples. Divide the sample holders into groups of two or pairs. b. Place each member of a pair of loaded sample holders into one of two reproducible spectrograph positions. Measure in rapid succession the peak aluminum Ka intensities transmitted through each film by the aluminum standards. Determine the ratio of the number of seconds for the transmitted Ka radiation of one standard to reach the established number of counts to the number of seconds for the second standard sample to reach the number of counts. Then determine the ratio of the number of seconds required by the second sample to reach the required number of counts to the number of seconds required by the first or, in other words, determine the reciprocal of the first ratio. c. Remove the aluminum standards and replace each in turn with a standard pellet containing a light element such as chlorine, using the same Mylar films for the sample holders. Measure the peak chlorine Ka intensi ties transmitted through each film by the standard pellets. Determine the ratio of the number of seconds for the transmitted Karadiation of one standard to reach the number of counts. Then determine the ratio of the number of seconds required by the second sample to reach the required number of counts to the number of seconds required by the first, that is, the reciprocal of the first ratio. d. Repeat steps (a) through (c) using different pairs of Mylar film until the range of Mylar film thickness differences encountered are covered. e. Plot on a graph the aluminum ratios for each pair of film samples against the chlorine ratios for the same pair of film samples and fit a straight line to this data by the method of least squares as shown in FIG. 1. TABLE V DATA FOR CHLORINE CORRECTION CURVE ALUMINUM Ka CHLORINE Ka Mylar Seconds for Ratio Seconds for Ratio Sample 128,000 1,024,000 Counts Counts 1 47.55 1.051 54.65 1.009 2 45.25 0.9516 54.15 0.9908 3 45.80 1.084 53.05 1.016 4 42.25 0.9255 52.20 0.9840 5 48.95 1.112 48.95 1.019 6 44.00 0.8989 48.05 0.9816 7 46.25 1.073 49.45 1.013 8 43.10 0.9319 48.80 0.9869 9 45.40 1.006 52.10 1.001 10 45.15 0.9945 52.05 0.999 The equations for the chlorine Ka and sulfur Ka curves shown in FIG. 1 are: log C 0.2078 log C log C 0.3189 log C, In equations l and (2), C C and C represented the correction factors shown in Flg. l for chlorine, sulfur and aluminum respectively. The plots in FIG. 1 show the magnitude of error encountered when no correction for Mylar thickness is made. From this data, it is apparent that the accurate analysis of many light elements with Mylar film is impossible without the use of correction factors for the variations in film thickness. On the other hand, 0.00025-inch Mylar thickness variations have little effect on the precision of iron determinations as shown by the data in Table 111. The maximum error that would occur because of thickness variations in 0.00025-inch Mylar film in iron determinations would be about 0.5 percent relative, and rarely would this maximum occur. Because of this small error, no correction factors were determined for iron Ka radiation. However, the correction factors for other elements can be determined in the same way. The method of correcting raw analytical data to obtain a valid analytical ratio of the intensity of the unknown to the intensity of the standard (l /1, by the process of this invention is illustrated below wherein a single slurry batch and a standard pellet are analyzed for chlorine, sulfur, and aluminum. The step-by-step procedure is as follows: a. A 0.00025-inch Mylar film is attached to the reference standard holder of the analyzing device and to one or more unknown sample holders depending on the number of unknown samples to be analyzed, in this case, three unknown holders. The Mylar film for the reference standard holder can be repeatedly used until it is no longer serviceable. b. The unknown sample holders are numbered to facilitate data recording. Next, the aluminum Ka intensities form an aluminum standard transmitted by the film in each sample holder including the reference sample holder is measured with a fixed goniometer setting. Each measurement is recorded as the number of seconds taken to reach a predetermined count. The reference standard holder should be placed in a reproducible spectrograph position. The results for-two sets of sample holders, four sample holders including the reference standard holder to the set, are given in Table VI. In the interest of better accuracy, two runs are made on each holder (columns 2 and 3) and the results averaged (column 4). However, the value of the average compared with the value of each run clearly illustrates that it is not essential that two runs be made to get reliable results. c. The standard pellet for uncured propellant is placed in the reference standard holder and a sample of the unknown slurry is placed in each of the unknown sample holders. Two sets of three unknown samples each are used. Each unknown sample, as well as the standard pellet, is analyzed for chlorine, sulfur, and aluminum by recording the number of seconds required for the transmitted Ka radiation to reach the predetermined count. The results are set forth in column 2 of Tables VII through IX. d. The aluminum correction factor for the film in each unknown holder for aluminum Ka radiation is determined by dividing the average number of seconds for the aluminum standard to reach the predetermined count in the reference standard holder by the seconds for the aluminum standard to reach the predetermined count in each unknown sample holder. These factors are shown in column 3 of Table IX. e. The film correction factor for chlorine and sulfur for each sample holder is determined by substituting the corresponding aluminum correction factor from Table IX in equations (1) and (2) set forth hereinbefore or by referring to the curves of FIG. 1. These correction factors are shown in column 3 of Tables VII and VIII. f. The number of seconds in the initial analysis of each unknown sample for chlorine, sulfur, and aluminum is then multiplied by the appropriate correction factor as determined in step (e) above. The results are recorded in column 4 of Tables VII, VIII, and IX. g. Steps (a) through (f) correct for film thickness variations within the group and analyzed in relation to the thickness of the film in the reference standard holder. By dividing the number of seconds for the reference standard to reach the predetennined total count of K: radiation for a given element by the number of corrected seconds for the unknown samples an analytical ratio of the given element is obtained. Since more than one unknown sample was analyzed in the above procedure, the average of the individual analytical ratios was taken. These ratios are recorded in the lower portions of Tables VII IX. TABLE VI ALUMINUM STANDARD ANALYSIS SAMPLE Seconds for aluminum standards to reach 128,000 counts TABLE VII CHLORINE Ka ANALYSIS Seconds SAMPLE for sample to Correction Seconds reach 512,000 counts Factor Corrected (Column 1) (column (Column (Column 2) 3) 4) Standard Pellet 23.7 23.7 '1 40.5 0.9858 39.92 2 39.6 .9908 39.24 3 40.0 .9939 39.76 Standard Pellet 23.7 23.7 4 40.0 0.9851 39.40 5 40.5 0.9816 39.75 40.4 0.9788 39.54 Analytical Ratio 0.598 TABLE VIII SULFUR Ka ANALYSIS Seconds SAMPLE for sample to CORRECTION Seconds reach 16,000 counts FACTOR Corrected (Column 1) (Column (Column (Column 2) 3) 4) Standard Pellet 38.8 38.8 1 46.7 0.9743 45.50 2 47.3 0.9829 46.49 3 46.3 0.9883 45.76 Standard Pellet 39.2 39.2 4 48.0 0.9732 46.71 5 48.5 0.9672 46.91 47.6 0.9622 45.80 Analytical R tio 0.844 TABLE IX ALUMINUM Ka ANALYSIS Seconds SAMPLE for sample to Correction Seconds reach 16,000 counts Factor Corrected (Column 1) (Column (Column (Column 2) 3) Standard Pellets 60.9 60.9 1 37.3 0.9172 34.21 2 36.0 0.9454 34.03 3 34.4 0.9629 33.12 Standard Pellet 61.1 61.1 4 37.8 0.9136 34.53 5 38.0 0.8940 33.97 0.8780 33.89 38.6 Analytical Ratio 1.80 If the K0: intensities are measured in counts per second, the aluminum correction factor for each unknown sample holder is detennined by dividing the aluminum Ka intensity from an aluminum standard in the reference standard holder into the Km intensity for each unknown standard holder. This ratio is the Al correction factor (abscissa of FIG. 1) with which one may enter into the graph of FIG. 1 to obtain the ordinate. The chlorine Ka and sulfur Ka correction factors are then determined from the curve in FIG. 1 or equations (1) and (2). Then, the uncorrected analytical ratio (I,,/I,), that is the Ka intensity of a given element in an unknown sample (I,,) divided by the Ku intensity of the same element from the standard pellet (I,), is corrected for film thickness variation by dividing it by the appropriate film correction factor for the particular sample holder. This latter method will be used in preference to that set forth in steps (*d) through (g) above when quality control instrumentation, such as the Autrometer, is used since these instruments automatically analyze each sample and print out the intensity ratios of the unknown to the standard, that is I./l,. The reference standard as used above compensates for film thickness variations among groups of unknowns and for short-term and long-term instrumental changes in the analytical device itself, thus permitting the determination of accurate analytical ratios. The analytical ratio is the proper standard of measure to use for checking batch-to-batch reproducibility of a product in quality control such as propellant formulations. The use of the reference standard permits the analysis of light elements in liquid slurries and mixtures which could not previously be achieved by normal X-ray fluorescence methods. The application of the method of this invention to the actual analysis of propellant formulations is described hereinafter. As previously mentioned, a propellant formulation utilizing the copolymer of a polybutadiene and acrylic acid (PBAA polymer) as a binder and aluminum as a fuel is used to demonstrate the process. On this basis, and assuming the functional relationship between the dependent and independent variables to be linear over the percentage ranges of the calibration ingredients, the statistical model for the analyses of four ingredients in a mixture when particle size is held constant is: where R, is the intensity ratio for ingredient i; X X X and X are the concentrations of the individual ingredients, the Bs are regression coefficients, and E is the random error associated with R Equations (3) can be used to develop a set of working expressions for estimating the ingredient concentrations; that is, where R represents the vector of intensity ratios, and l the vector of intercept terms. The b element of l is the coefficient of X in the i"' regression equation. X is the vector of unknown concentrations determined by the analysis. inverting equation (4), then gives it 8- (a Equation (5) represents a set of working equations for estimating ingredient concentrations at constant particle sizes or for estimating particle sizes at constant concentrations by replacing the Xs in equation (3) with the particle size values. Equation (5) gives more accurate analyses than equation (2'), because it contains terms which correct for matrix effects. in fact, most propellants can only be analyzed with sufficient accuracy by means of equation (5). The X-ray fluorescence method can also be used to determine ingredient concentrations and particle sizes when both are varied simultaneously. The analysis is restricted, however, to the determination of a number of parameters equal to the number of intensity mea-. surements made. The particle sizes of two ingredients (designated W and W are considered in this illustration. Consider a set of multiple regression equations of the following type, Equation (6) contains both particle size and concentration terms and can be written as The intensity ratio vector can now be corrected for either particle size or concentration to give a combined parameter determination equal to the number of intensity measurements. Solving for concentration, 1 gives, 3 B, (a Bay) and solving for particle size, 1!, gives The particle size, W is expressed as the weight fraction of fine component i in a bimodal particle size mixture. In this description, the four ingredients are ferric oxide, ammonium perchlorate, polymer and aluminum in PBAA propellants. Analyses apply to cured and uncured samples, and the same methods can be applied to other types of propellants. The analysis of a typical set of uncured PBAA propellant calibration standards is given in Table X. TABLE X X-Ray Intensity Ratios from Analyses of Calibration Standards Mixture Fe,0, Nl-LClO. Polymer Al, R4 Particle size was held constant for this analysis. In the analysis of the uncured mixes, a sample from each was placed in an unknown sample holder whose aluminum Ka Mylar filmcorrection factor had previously been determined according to the procedure set forth hereinbefore. The goniometer is positioned at the peak K01 angle for each element to be analyzed and the intensities of the appropriate emission lines from the standard pellet (1,) and the unknown sample (1,) are measured in rapid succession. The samples for analysis of the cured propellant were discs cut from a larger body of cured propellant. The discs were cut to conform to the size of the sample holder, three-eights inch in thickness by 1% inch in diameter. No Mylar film is necessary for the analysis of the cured propellant other than for the ferrocene analysis. Since ferrocene sublimes from the propellant at room temperature, the sample is placed in contact with Mylar films. The influence of ferrocene sublimation on measured iron Ka intensity, and the effectiveness of 0.00025-inch Mylar in preventing ferrocene sublimation are shown in FIG. 2. Repetitive measurements of iron Ka intensity were made on two freshly cut samples, one placed against 0.00025-inch Mylar, and the other exposed to the helium environment of the spectrograph. Because of the rapid decrease in iron Ka intensity, analysis for ferrocene requires the use of the Mylar film immediately after cutting the sample. After analyzing the ferrocene, the Mylar film is removed and the open sample surface is analyzed for the remaining constituents. The same procedure as described above for analyzing the uncured propellant is used. The parameters for the analysis of the cured and uncured propellants are set forth in Table XI. W, and W, are particle sizes of ammonium perchlorate and aluminum powders, respectively. The values of X (s are determined by analysis to obtain R through R folls lowed by R through R, and the known values of W, and W in equations (1 1). The errors of estimating the ingredient concentrations in the nine calibration standards are given in Table XIII. TABLE XI.PARAMETERS FOR PROIELLANT ANALYSIS Analyt- Punk Annlyz- 'lotnl counts lcul tingle lug Pulse-height Element llno 20 crystal Cured Uncurecl analyzer 113. 95 NnCl 1, 024, 000 512, 000 Integral. 142. 77 EDDT 000 16, 000 Diflerential. 144. 57 NBC] 16, 000 16, 000 Do. 40. 22 NnCl 512, 000 512, 000 Integral. The errors of estimating the ingredient percentages in the nine calibration standards by means of equation 40 (10) are given in Table XII. wt.% ferric oxide 0.9779 0.5615R, 30 TABLE XIII Residual Errors in Estimating Concentrations Using Equations (1 l) MIXTURE 2.x, 2.x, 2.x, 2.x, 1 0.0063 0.22 -0.| -0.02 2 0.0038 0.33 -0.15 -0.04 a 0.0l36 0.54 0.26 -0.o1 4 0.0036 -0.07 0.04 0.05 5 0.0084 -0.27 0.14 -0.03 6 0.00l6 0.02 -0.01 0.01 7 0.0040 -0.10 0.05 -0.05 8 0.0019 0.26 0.12 0.03 9 0.0078 -0.s7 0.31 Likewise, equations (ll) can be used to determine TABLE XII.-ERRORS OF ESTIMATING INGREDIENT PEROENTAGES IN WEIGHT PERCENT A A Mixture X1 X1-X X3 Xg-Xz X3 Xg-X; X4 XrX Xi is the known percentage of ingredient i and Xi is the estimated percentage. The results in Table XII are considerably more accurate than the results obtained by simple linear regression analysis in the above referred to patent application. The determination of ingredient concentrations in PBAA propellants when both concentrations and particle sizes are varied simultaneously is given in the following example. Nine calibration standards were prepared according to a one-eighth fraction of a 2 factorial design, and the following working equations were derived: the particle sizes of ammonium perchlorate and aluminum when the concentrations of any two ingredients are known beforehand. The ability to directly determine ingredient particle sizes in finished propellants is unique to the X-ray fluorscence method described here, but is not restricted to ammonium perchlorate and aluminum. The method of this invention gives a more rapid and extensive propellant analysis than any other method, and the precision and accuracy are sufficient for routine quality control. Thus, multiple regression equations for concentrations and particle size as a function of intensities are used for the precise calculation of propellant compositions from the measured X-ray fluorescent intensities of sample ingredients, eliminating the need for calibration curves. The multiple regression equations them- 5 selves may be programmed for computer calculation. Calibration equations developed from empirical data are valid only on the equipment on which the intensity measurements are made, and only for the ranges of concentrations and particle sizes included by the stanl dards. If other laboratories are to use the same calculations, they must calibrate their own X-ray spectrographs on the same standards, reading at the same intensity levels. However, other equations may be established by the technique of multiple linear regression l analysis on the basis of sets of intensity measurements from the particular X-ray spectrograph used. The technique of multiple linear regression analysis is not limited to the propellant composition disclosed herein. The X-ray emission spectrograph disclosed in the above referred to patent application may be used to determine the concentration of any element having an atomic number greater than ten. However, if resort is had to other commercially available spectrographs, the concentration of any element having anatomic number greater than four may be determined. The particle size is not so limited, as the particle size of almost any solid ingredient may be determined. It is therefore to be understood that within the spirit and scope of this invention, it may be practiced otherwise than as specifically described. I claim l. The method of analyzing propellant compositions containing light elements by means of X-ray emission spectrography wherein Ka emission lines are transmitted through a thin film sample having a thickness lying in a range of film thickness variations, said method comprising the steps of: I a. measuring with an X-ray spectrograph the K0: emission line intensity of an aluminum standard 40 transmitted separately through each sample of a plurality of pairs of samples of said film, said plurality covering the range of film thickness variations in said film, recording the number of seconds for the aluminum Ka radiation for each sample of said plurality of pairs of samples of film to reach a predetermined fixed count, subsequently determining the ratio of the number of seconds of one sample of each pair of said plurality of pairs of samples of film to the number of seconds of the other sample of said pair, and determining the value of the reciprocal of said ratio; b. measuring with said spectrograph the Ku emission line intensity of a light element from a standard containing said light element, said Ka emission line from said light element being transmitted separately through each sample of said plurality of pairs of samples of film, recording the number of seconds required by each member of said plurality of pairs of samples of film to transmit sufficient Ka radiation from said light element to reach a prede-' termined fixed count, subsequently determining the ratio of the number of seconds of one sample member of each pair of said plurality of pairs of samples of film to the number of seconds of the other sample of said pair, and determining the value of the reciprocal of said ratio; c. plotting on a graph all of the ratios derived from film against the value of said reciprocal of the ratio derived from measuring the K0: radiation from said light element from said one sample of each of said plurality of pairs of samples of film; d. measuring with said spectrograph the Ka emission line intensity in counts per second for the Ka radiation transmitted from said aluminum standard through each of the members of a pair of samples of said thin film to reach a predetermined fixed count, determining the aluminum Ka intensity ratio of the aluminum Ka intensity transmitted through one of said members to the aluminum Ka intensity transmitted through the other of said members, and selecting from said graph as a correction factor thefitioof said light element on said graph corresponding to said aluminum Ka intensity ratio; e. measuring with said spectrograph the Ka emission line intensity of said light element from said standard containing said light element in counts per second for the K01 radiation transmitted through said other member of said pair of samples of thin film to reach a predetermined fixed count, measuring the Ka emission line intensity of said light element in a sample of said composition in counts per second for the Km radiation transmitted through said one of said other member of said pair of samples to reach a predetermined fixed count, and determining the ratio of said Ka intensity from said light element in said composition to said Ka intensity from said light element in said standard; f. dividing said ratio of said Ka intensity from said light element in said composition to said Ka intensity from said light element in said standard by said correction factor to determine the corrected analytical intensity ratio of the Ku intensity of said light element in said composition to the K0: intensity of said light element in said standard containing said light element; and g. applying said corrected analytical intensity ratios to multiple regression means to determine the concentrations of ingredients, each containing a said light element, and the particle sizes of solid ingredients, each containing a said light element. 2. The method of claim 1 wherein said concentrations of said ingredients are held constant. 3. The method of claim 1 wherein said particle sizes of said solid ingredients are held constant. 4. The method of claim 1 wherein said particle sizes of said solid ingredients and said concentrations of said ingredients are held constant. 5. The method of claim 1 wherein said corrected analytical intensity ratios are determined from the same composition and are used to derive any combination of said ingredients concentrations and said particle sizes in the same composition. 6. The method of analyzing compositions containing a light element to determine the corrected analytical ratio of said element in said composition by means of X-ray emission spectrography wherein the K: lines are transmitted through a thin film sample having a thickness lying in a range of film thickness variations, said method comprising the steps of: a. Measuring with an X-ray spectrograph the Ka emission line intensity of an aluminum standard transmitted separately through each sample of a plurality of pairs of samples of said film, said plurality covering the range of film thickness variations in said film, recording the number of seconds for the aluminum Ka radiation for each sample of said plurality of pairs of samples of film to reach a predetermined fixed count, subsequently determining the ratio of the number of seconds of one sample of each pair of said plurality of pairs of sample of film to the number of seconds of the other sample of said pair, and determining the value of the reciprocal of said ratio; b. Measuring with said spectrograph the Ka emission line intensity of a light element from a standard containing said light element, said Ka emission line from said light element being transmitted separately through each sample of said plurality of pairs of samples of film, recording the number of seconds required by each member of said plurality of pairs of samples of film to transmit sufficient Ka radiation from said element to reach a predetermined fixed count, subsequently determining the ratio of the number of seconds of one sample member of each pair of said plurality of pairs of samples of film to the number of seconds of the other sample of said pair, and determining the value 'of the reciprocal of said ratio; c. Plotting on a graph all of the ratios derived from measuring the aluminum Ka radiation from one sample of each of said plurality of pairs of samples offilm against the ratio derived from measuring the Km radiation of said element from said one sample of each of said plurality of pairs of samples of film and plotting on said graph the value of said reciprocal of all of the ratios derived from measuring the aluminum Ka radiation from said one sample of each of said plurality of pairs of samples of film against the value of said reciprocal of the ratio derived from measuring the Ku radiation from said element from said one sample of each of said plurality of pairs of samples of film. d. Measuring with said spectrograph the Ka emission line intensity in counts per second for the Ka radiation transmitted from said aluminum standard through each of the members of a pair of samples of said thin film to reach a predetennined fixed count, determining the aluminum Ka intensity ratio of the aluminum Ka intensity transmitted through one of said members to the aluminum Ka intensity transmitted through the other of said members, and selecting from said graph as a correction factor the ratio of said element on said graph corresponding to said aluminum Ka ratio; e. Measuring with said spectrograph the Ka emission line intensity of said element from said standard containing said element in counts per second for the Ka radiation transmitted through said other member of said pair of samples of thin film to reach a predetermined fixed count, measuring the K0: emission line intensity of said element in a sample of said composition in counts per second for the Ka radiation transmitted through said one of said other member of said pair of samples to reach a predetermined fixed count, and determining the ratio of said [(01 intensity from said element in said compo sition to said Ka intensity from said element in said standard; f. dividing said ratio of said Ka intensity from said element in said composition to said [(01 intensity from said element in said standard by said correction factor to determine the corrected analytical ratio of the Ku intensity of said light element in said standard containing said light element. 7. The method of claim 6 wherein said composition comprises an uncured mixture of polybutadiene-acrylic acid copolymer, powdered aluminum, ammonium perchlorate, and a member selected from the group consisting of ferric oxide and ferrocene. 8. The method of claim 6 wherein said light element is chlorine. 9. The method of claim 8 wherein said thin film is polyethylene terephthalate resin. 10. The method of of claim 9 wherein said standard containing said light element is a pellatized mixture comprising about 35 percent by weight sodium chloride, about 22 percent by weight aluminum powder, 41 percent by weight methyl cellulose, 0.8 percent by weight ferric oxide, and 1.2 percent by weight zinc sulfide. 11. The method of claim 6 wherein said light element is aluminum. 12. The method of claim 6 wherein said light element is sulfur. 13. In the process of analyzing compositions containing a light element by X-ray spectrography wherein the Ka emission lines are transmitted through a thin, transparent film sample having a thickness lying in a range of film thickness variations, the improvement which consists of a method for determining a correction factor for said film, said method comprising the steps of: a. Measuring with an X-ray spectrograph the Ku emission line intensity of an aluminum standard transmitted separately through each sample of a plurality of pairs of samples of said film, said plurality covering the range of film thickness variations in said film, recording the number of seconds for the aluminum Ka radiation for each sample of said plurality of pairs of samples of film to reach a predetennined fixed count, subsequently determining the ratio of the number of seconds of one sample of each pair of said plurality of pairs of samples of film to the number of seconds of the other sample of said pair, and determining the value of the reciprocal of said ration; b. Measuring with said spectrograph the Ka emission line intensity of a light element from a standard containing said light element, said Ka emission line from said light element being transmitted separately through each sample of said plurality of pairs of samples of film, recording the number of seconds required by each member of said plurality of pairs of samples of film to transmit sufficient Ka radiation from said element to reach a predetermined fixed count, subsequently determining the ratio of the number of seconds of one sample member of each pair of said plurality of pairs of samples of film to the number of seconds of the other sample of said pair, and determining the value of the reciprocal of said ratio; c. Plotting on a graph all of the ratios derived from said standard containing said light element is a compomeasuring the aluminum Ka radiation from one sition comprising 20 percent to 60 percent by weight sample of each of said plurality of pairs of samples alkali metal chloride, 0.5 percent to percent by weight of film against the ratio derived from measuring the zinc sulfide, 6.5 percent to 5 percent b'ffiimfiic Ka radiation of said element from said one sample 5 oxide, percent to 30 percent by weight powdered of each of said plurality of pairs of samples of film aluminum, and 25 percent to 45 percent by weight and plotting on said graph the value of said recipromethyl cellulose. cal of all of the ratios derived from measuring the 15. The improvement according to claim 14 wherein aluminum Ka radiation from said one sample of said light element is chlorine. each of said plurality of pairs of samples of film 0 16. The improvement according to claim 14 wherein against the value of said reciprocal of the ratio deaid light l m nt i aluminumrived from measuring the radiation from said 17. The improvement according to claim 14 wherein element from said one sample of each of said plurality of pairs of samples of film. 14. The improvement according to claim 13 wherein l5 0: a a s t said light element is sulfur. Patent Citations
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