U.S. patent number 3,764,805 [Application Number 04/652,654] was granted by the patent office on 1973-10-09 for control of propellant compositions by x-ray fluorescence analysis.
This patent grant is currently assigned to The United States of America as represented by the Secretary of the Army. Invention is credited to Bernard J. Alley.
United States Patent |
3,764,805 |
Alley |
October 9, 1973 |
CONTROL OF PROPELLANT COMPOSITIONS BY X-RAY FLUORESCENCE
ANALYSIS
Abstract
The use of multiple linear regression analysis in correlating
the data obned 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.
Inventors: |
Alley; Bernard J. (Huntsville,
AL) |
Assignee: |
The United States of America as
represented by the Secretary of the Army (Washington,
DC)
|
Family
ID: |
24617634 |
Appl.
No.: |
04/652,654 |
Filed: |
July 6, 1967 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
|
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306393 |
Sep 3, 1963 |
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Current U.S.
Class: |
378/48;
378/44 |
Current CPC
Class: |
G01N
23/223 (20130101); G01N 2223/076 (20130101) |
Current International
Class: |
G01N
23/223 (20060101); G01N 23/22 (20060101); G01n
021/00 () |
Field of
Search: |
;250/51.5,71.5,71.5S,71.5R |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Quarforth; Carl D.
Assistant Examiner: Potenza; J. M.
Parent Case Text
Cross Reference to Related Applications: This application is a
continuation-in-part of application Ser. No. 306,393, filed Sept.
3, 1963, now abandoned.
Claims
I claim
1. The method of analyzing propellant compositions containing light
elements by means of X-ray emission spectrography wherein K.alpha.
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:
a. measuring with an X-ray spectrograph the K.alpha. 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 K.alpha.
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 K.alpha. emission line
intensity of a light element from a standard containing said light
element, said K.alpha. 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 K.alpha. radiation from said light 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 K.alpha. radiation from one sample of each of said
plurality of pairs of samples of film against the ratio derived
from measuring the K.alpha. radiation of said light 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 K.alpha.
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 K.alpha. 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 K.alpha. emission line
intensity in counts per second for the K.alpha. 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 K.alpha. intensity ratio of
the aluminum K.alpha. intensity transmitted through one of said
members to the aluminum K.alpha. intensity transmitted through the
other of said members, and selecting from said graph as a
correction factor the ratio of said light element on said graph
corresponding to said aluminum K.alpha. intensity ratio;
e. measuring with said spectrograph the K.alpha. emission line
intensity of said light element from said standard containing said
light element in counts per second for the K.alpha. radiation
transmitted through said other member of said pair of samples of
thin film to reach a predetermined fixed count, measuring the
K.alpha. emission line intensity of said light element in a sample
of said composition in counts per second for the K.alpha. 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 K.alpha. intensity from said light element in said
composition to said K.alpha. intensity from said light element in
said standard;
f. dividing said ratio of said K.alpha. intensity from said light
element in said composition to said K.alpha. intensity from said
light element in said standard by said correction factor to
determine the corrected analytical intensity ratio of the K.alpha.
intensity of said light element in said composition to the K.alpha.
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.alpha. 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 K.alpha. 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 K.alpha.
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 K.alpha. emission line
intensity of a light element from a standard containing said light
element, said K.alpha. 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 K.alpha. 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 K.alpha. radiation from one sample of each of said
plurality of pairs of samples of film against the ratio derived
from measuring the K.alpha. 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 K.alpha. 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 K.alpha. 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 K.alpha. emission line
intensity in counts per second for the K.alpha. 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 K.alpha. intensity ratio of
the aluminum K.alpha. intensity transmitted through one of said
members to the aluminum K.alpha. 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 K.alpha. ratio;
e. Measuring with said spectrograph the K.alpha. emission line
intensity of said element from said standard containing said
element in counts per second for the K.alpha. radiation transmitted
through said other member of said pair of samples of thin film to
reach a predetermined fixed count, measuring the K.alpha. emission
line intensity of said element in a sample of said composition in
counts per second for the K.alpha. 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
K.alpha. intensity from said element in said composition to said
K.alpha. intensity from said element in said standard;
f. dividing said ratio of said K.alpha. intensity from said element
in said composition to said K.alpha. intensity from said element in
said standard by said correction factor to determine the corrected
analytical ratio of the K.alpha. 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 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 K.alpha. 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 K.alpha. 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 K.alpha.
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 ration;
b. Measuring with said spectrograph the K.alpha. emission line
intensity of a light element from a standard containing said light
element, said K.alpha. 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 K.alpha. 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 K.alpha. radiation from one sample of each of said
plurality of pairs of samples of film against the ratio derived
from measuring the K.alpha. 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 K.alpha. 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 K.alpha. radiation from said element from said one
sample of each of said plurality of pairs of samples of film.
14. The improvement according to claim 13 wherein said standard
containing said light element is a composition comprising 20
percent to 60 percent by weight alkali metal chloride, 0.5 percent
to 5 percent by weight zinc sulfide, 0.5 percent to 5 percent by
weight ferric oxide, 10 percent to 30 percent by weight powdered
aluminum, and 25 percent to 45 percent by weight methyl
cellulose.
15. The improvement according to claim 14 wherein said light
element is chlorine.
16. The improvement according to claim 14 wherein said light
element is aluminum.
17. The improvement according to claim 14 wherein said light
element is sulfur.
Description
BACKGROUND OF THE INVENTION
This invention relates to an improvement in X-ray fluorescence
analysis of propellant compositions and particularly to the
quantitative determinations of concentration and particle size in
such propellant compositions.
Uncured propellants must be analyzed before being cast into motors
to insure that they are homogeneous, are of the correct particle
size, and have the correct concentrations of ingredients. The
analytical procedures 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 applicant's above
referred to application was developed to replace existing chemical
procedures for controlling propellant compositions. The method was
specifically applied to polybutadiene-acrylic acid (PBAA)
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 aid of 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.sub.o + b.sub. X ( 1'),
where
R = the corrected analytical intensity ratio
X = the concentration of an ingredient (or its size),
b.sub.o = a constant, and
b.sub.1 = another constant.
Ingredient concentrations (or sizes) in unknown samples are
estimated either from calibration curves or the inverse of equation
1':
X = (R - b.sub.o)/(b.sub.1) (2')
The accuracy of prediction using equation 2' is inadequate for the
direct control analysis of propellants and many other types of
materials. The true intensity-concentration or intensity-size
relationship for multicomponent materials is generally much more
complex than that shown by equation 1'. The intensity 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 inherent in 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 analysis.
Another object of this invention is to provide an improved 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 other types of composite propellants.
Still another object of this invention is to provide an improved
method of X-ray fluorescence analysis for use in composite
propellants, which method is both fast and accurate.
Summary of the Invention: The method of this invention used to
correct for elemental interactions in X-ray fluorescence analysis
is multiple linear regression analysis.
Multiple linear regression analysis is a logical extension of
simple linear regression analysis; the influences of all analyzed
elements on the X-ray intensity from the element 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
K.alpha. and chlorine K.alpha. radiations plotted against the
aluminum K.alpha. 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 polybutadiene-acrylic 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 Gas flow proportional counter
Detector flow gas P-10 (90% argon, 10% methane); 0.5 cu. ft./hr.
flow rate (air calibration) X-ray optics Flat crystal inverted
X-ray optical path Helium; 1.0 liters/min. flow rate (air
calibration) Analyzing crystals Sodium chloride and ethylene
diamine D-tartrate (EDDT)
there are two critical aspects of this invention which make it
possible to analyze propellant mixtures through X-ray emission
spectography. These are the development of a suitable standard and
a method of film corrections.
The development of a stable reference standard is essential to the
analysis of propellants. A standard should be stable to long-term
storage and X-ray exposure while at the same time being reasonably
similar to the type of composition which is to be analyzed. That
is, the K.alpha. intensity of a particular element in the standard
should be as similar as possible to the K.alpha. 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 60 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 41.00 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, allowance has to be made for the fact that chlorine
K.alpha.radiations from sodium chloride and from ammonium
perchlorate occur at different angles. Using the equipment
identified in the manner described hereinafter, the chlorine
K.alpha.radiation from sodium chloride occurred at
114.05.degree.2.theta., and that from ammonium perchlorate at
113.95.degree.2.theta..
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 K.alpha. 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 K.alpha. 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 K.alpha. intensity of the element in the standard approximate
the K.alpha. 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.
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
composed.
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. I. 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 K.alpha. radiations from four light
elemnts is shown. As is apparent from the Table, percentage
transmission varies markedly with wavelength variation.
TABLE III
Transmission of X-rays by nominal 0.00025 inch Mylar
Element Emission Wavelength Percent Line Angstroms Transmission
Iron K.alpha. 1.94 98.0 Chlorine K.alpha. 4.73 76.1 Sulfur K.alpha.
5.37 68.0 Aluminum K.alpha. 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 21. 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 IV below. The
peak K.alpha. 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 correction 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 2.theta. Chlorine
K.alpha. 113.96 1,024,000 NaCl Integral Sulfur K.alpha. 144.78
64,000 NaCl Differen- tial Aluminum K.alpha. 142.74 128,000 EDDT*
Differen- tial *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
11/4 inches in diameter to one inch in length to fit the standard,
circular sample holder. The aluminum obviously should be free from
impurities, particularly those that would interfere with the
measurement of aluminum K.alpha. intensities. The aluminum K.alpha.
intensities of the four samples differed less than 0.3 percent
relative at the 95 percent confidence level. Care should be
exercised in storage of the standards so that moisture and other
agents do not alter the aluminum K.alpha. 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 K.alpha. and chlorine K.alpha. intensities are
measured from standard pellets described hereinafter while aluminum
K.alpha. intensities are measured from the aluminum standards.
Peak-to-background 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
K.alpha. film correction is shown. Similar data were obtained for
the sulfur K.alpha. 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
K.alpha. intensities transmitted by a large number of film samples
using the standards. Differences in thickness are reflected by
different aluminum K.alpha. 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 K.alpha. intensities transmitted
through each film by the aluminum standards. Determine the ratio of
the number of seconds for the transmitted K.alpha. 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 K.alpha. intensities transmitted through each film by the
standard pellets. Determine the ratio of the number of seconds for
the transmitted K.alpha.radiation 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 K.alpha. CHLORINE K.alpha. 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 K.alpha. and sulfur K.alpha. curves
shown in FIG. 1 are:
log C.sub.Cl = 0.2078 log C.sub.Al (1)
log C.sub.S = 0.3189 log C.sub.Al (2)
In equations (1) and (2), C.sub.Cl, C.sub.S, and C.sub.Al
represented the correction factors shown in FIg. 1 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 III.
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
K.alpha. 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 (I.sub.u /I.sub.s ) 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 K.alpha. 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
K.alpha. 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 K.alpha. 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 predetermined total
count of K.alpha. 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
(Column (Column (Column (Column 1) 2) 3) 4) First Second Average
count count count Reference Standard 41.7 41.4 41.5 1 45.2 45.4
45.3 2 44.1 43.8 43.9 3 43.3 43.0 43.1 Reference Standard 41.8 41.7
41.7 4 45.7 45.7 45.7 5 46.7 46.7 46.7 6 47.6 47.5 47.5
TABLE VII
CHLORINE K.alpha. 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 6 40.4 0.9788 39.54 Analytical Ratio =
0.598
TABLE VIII
SULFUR K.alpha. 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 6 47.6 0.9622 45.80 Analytical
Ratio = 0.844
TABLE IX
ALUMINUM K.alpha. ANALYSIS
Seconds SAMPLE for sample to Correction Seconds reach 16,000 counts
Factor Corrected (Column 1) (Column (Column (Column 2) 3) 4)
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 6 38.6 0.8780 33.89 Analytical
Ratio = 1.80
If the K.alpha. intensities are measured in counts per second, the
aluminum correction factor for each unknown sample holder is
determined by dividing the aluminum K.alpha. intensity from an
aluminum standard in the reference standard holder into the
K.alpha. intensity for each unknown standard holder. This ratio is
the A1 correction factor (abscissa of FIG. 1) with which one may
enter into the graph of FIG. 1 to obtain the ordinate. The chlorine
K.alpha. and sulfur K.alpha. correction factors are then determined
from the curve in FIG. 1 or equations (1) and (2). Then, the
uncorrected analytical ratio (I.sub.u /I.sub.s), that is the
K.alpha. intensity of a given element in an unknown sample
(I.sub.u) divided by the K.alpha. intensity of the same element
from the standard pellet (I.sub.s), 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.sub.u /I.sub.s.
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:
R.sub.ij = B.sub.i,o + B.sub.i,l X .sub.lj + B.sub.i,2 X .sub.2j +
B.sub.i,3 X .sub.3j + B.sub.i,4 X .sub.4j + E.sub.ij (3)
i = 1, 2, 3, 4
where R.sub.i is the intensity ratio for ingredient i; X.sub.1,
X.sub.2, X.sub.3, and X.sub.4 are the concentrations of the
individual ingredients, the B's are regression coefficients, and
E.sub.ij is the random error associated with R.sub.ij. Equations
(3) can be used to develop a set of working expressions for
estimating the ingredient concentrations; that is,
R = b + BX (4)
where R represents the vector of intensity ratios, and b the vector
of intercept terms. The b.sub.ik element of B is the coefficient of
X.sub.k in the i.sup.th regression equation. X is the vector of
unknown concentrations determined by the analysis.
Inverting equation (4), then gives
X = B.sup.-.sup.1 (R - b) (5)
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 X's 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 measurements made. The particle sizes of two ingredients
(designated W.sub.2 and W.sub.4) are considered in this
illustration. Consider a set of multiple regression equations of
the following type, ##SPC1##
Equation (6) contains both particle size and concentration terms
and can be written as
R = B.sub.1 X + B.sub.2 W (7)
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, X gives,
X = B.sub.1 .sup.-.sup.1 (R - B.sub.2 W) (8)
and solving for particle size, W, gives
W = B.sub.2.sup.-.sup.1 (R - B.sub.1 X) (9)
the particle size, W.sub.i, 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.sub.3 O.sub.2 NH.sub.4 ClO.sub.4 Polymer Al, R.sub.4
R.sub.1 R.sub.2 R.sub.3 1 1.1240 0.8980 0.8219 0.9906 2 0.9285
0.8872 0.9308 0.9944 3 1.1214 0.8030 0.7668 1.1221 4 1.1635 0.8706
0.9272 0.9832 5 0.9415 0.8064 0.9026 1.1127 6 0.9039 0.8314 0.7596
1.0994 7 1.0712 0.8404 0.8662 1.0836 8 0.9561 0.8731 0.8206 1.0290
9 1.0186 0.8431 0.8346 1.0591
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 K.alpha. Mylar film correction factor
had previously been determined according to the procedure set forth
hereinbefore. The goniometer is positioned at the peak K.alpha.
angle for each element to be analyzed and the intensities of the
appropriate emission lines from the standard pellet (I.sub.s) and
the unknown sample (I.sub.u) 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 11/4 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 K.alpha.
intensity, and the effectiveness of 0.00025-inch Mylar in
preventing ferrocene sublimation are shown in FIG. 2. Repetitive
measurements of iron K.alpha. 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 K.alpha. 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. ##SPC2##
The working equations from equation (5) are:
X.sub.1 = wt.% ferric oxide = -0.9779 + 0.5615R.sub.1 +
0.5543R.sub.2 - 0.01339R.sub.3 + 0.4213R.sub.4
x.sub.2 = wt. % ammonium perchlorate = 113.37 - 3.687R.sub.1 +
0.3575R.sub.2 - 17.87R.sub.3 - 25.25R.sub.4
x.sub.3 = wt. % polymer = -4.028 +1.285R.sub.1 - 2.932R.sub.2 +
16.31 l R.sub.3 + 4.663R.sub.4
x.sub.4 = 58.08 = 0.3090 r.sub.1 - 35.34r.sub.2 - 4.413r.sub.3 -
7.537r.sub.4 (10)
the errors of estimating the ingredient percentages in the nine
calibration standards by means of equation (10) are given in Table
XII. ##SPC3##
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.sup.6 factorial design, and the following working equations were
derived:
X.sub.1 = wt.% ferric oxide = -9.887.7 + 12.00 R.sub.1 +
5.98.5R.sub.2 + 82.08R.sub.3 + 395.8 R.sub.4 - 13.59W.sub.2 -
2.280W.sub.4
x.sub.2 = wt. % ammonium perchlorate = -5226 + 8.843R.sub.1 +
3207R.sub.2 + 439.3R.sub.3 + 2109R.sub.4 - 74.76W.sub.2 -
11.49W.sub.4
x.sub.3 = wt. % polymer = -1437 + 1.654R.sub.1 + 867.3R.sub.2 +
137.4R.sub.3 + 578.0R.sub.4 -19.38W.sub.2 - 3.022W.sub.4
x.sub.4 = wt.% aluminum = -2073 + 3.044 R.sub.1 + 1258R.sub.2 +
175.7R.sub.3 + 847.6R.sub.4 - 28.46W.sub.2 - 5.325W.sub.4 (11)
w.sub.2 and W.sub.4 are particle sizes of ammonium perchlorate and
aluminum powders, respectively. The values of X.sub.i 's are
determined by analysis to obtain R.sub.1 through R.sub.4, followed
by R.sub.1 through R.sub.4 and the known values of W.sub.2 and
W.sub.4 in equations (11). The errors of estimating the ingredient
concentrations in the nine calibration standards are given in Table
XIII.
TABLE XIII
Residual Errors in Estimating Concentrations Using Equations
(11)
MIXTURE X.sub.1 -X.sub.1 X.sub.2 -X.sub.2 X.sub.3 -X.sub.3 X.sub. 4
-X.sub.4 1 -0.0063 0.22 -0.10 -0.02 2 -0.0088 0.33 -0.15 -0.04 3
-0.0136 0.54 -0.26 -0.07 4 0.0036 -0.07 0.04 -0.05 5 0.0084 -0.27
0.14 -0.03 6 -0.0016 0.02 -0.01 0.01 7 0.0040 -0.10 0.05 -0.05 8
0.0079 -0.26 0.12 -0.03 9 0.0078 -0.87 0.34 0.37
likewise, equations (11) can be used to determine 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
themselves 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 standards. 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 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 an atomic 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.
* * * * *