*>EPA
United States
Environmental Protection
Agency
Environmental Sciences Research
Laboratory
Research Triangle Park NC 27711
EPA-600/7-80-081
May 1980
Research and Development
Beta Gauge
Instrumentation for the
Measurement of
Aerosol Mass
Interagency
Energy/Environment
R&D Program
Report
-------
RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
6. Scientific and Technical Assessment Reports (STAR)
7. Interagency Energy-Environment Research and Development
8. "Special" Reports
9. Miscellaneous Reports
This report has been assigned to the INTERAGENCY ENERGY-ENVIRONMENT
RESEARCH AND DEVELOPMENT series. Reports in this series result from the
effort funded under the 17-agency Federal Energy/Environment Research and
Development Program. These studies relate to EPA's mission to protect the public
health and welfare from adverse effects of pollutants associated with energy sys-
tems. The goal of the Program is to assure the rapid development of domestic;,
energy supplies in an environmentally-compatible manner by providing the nec-
essary environmental data and control technology. Investigations include analy-
ses of the transport of energy-related pollutants and their health and ecological
effects; assessments of, and development of, control technologies for energy
systems; and integrated assessments of a wide'range of energy-related environ-
mental issues.
EPA REVIEW NOTICE
This report has been reviewed by the participating Federal Agencies, and approved
for publication. Approval does not signify that the contents necessarily reflect
the views and policies of the Government, nor does mention of trade names or
commercial products constitute endorsement or recommendation for use.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
-------
EPA-600/7-80-081
May 1980
BETA GAUGE INSTRUMENTATION FOR THE
MEASUREMENT OF AEROSOL MASS
J. M. Jaklevic, R. C. Gatti,
F. S. Goulding, and B. W. Loo
Lawrence Berkeley Laboratory
University of California
Berkeley, California 94720 U.S.A.
Interagency Agreements No. EPA-IAG-79-D-X0712
EPA-IAG-D8-E681-CG, 80BCG
Project Officers
Thomas G. Dzubay
Atmospheric Chemistry and Physics Division
Environmental Sciences Research Laboratory
Research Triangle Park, N. C. 27711
and
Greg J. D'Alessio
U. S. Environmental Protection Agency
401 M Street, S. W.
Washington, D. C. 20460
ENVIRONMENTAL SCIENCES RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, N. C. 27711
-------
DISCLAIMER
This report has been reviewed by the Environmental Sciences Research
Laboratory, U. S. Environmental Protection Agency, and approved for publi-
cation. Approval does not signify that the contents necessarily reflect
the views and policies of the U. S. Environmental Protection Agency, nor
does mention of trade names or commercial products constitute endorsement
or recommendation for use.
This report was prepared as an account of work sponsored by the United
States Government. Neither the United States nor the Department of Energy
or the Environmental Protection Agency, nor any of their employees, nor any
of their contractors, subcontractors, or their employees, makes any war-
ranty express or implied, or assumes any legal liability or responsibility
for the accuracy, completeness or usefulness of any information, appar-
atus, product or process disclosed, or represents that its use would not
infringe privately owned rights.
This report was done with support under the interagency agreement with
the Department of Energy and Environmental Protecton Agency. Any conclus-
ions or opinions expressed in this report represent solely those of the
author(s) and not necessarily those of The Regents of the University of
California, the Lawrence Berkeley Laboratory or the Department of Energy,
nor does mention of trade names or commerical products constitute
endorsement or recommendation for use.
n
-------
ABSTRACT
An instrument developed at the Lawrence Berkeley Laboratory for the
routine measurement of aerosol mass using the beta-particle attenuation
method is described and evaluated. Factors affecting the precision and
accuracy of the measurement are discussed in detail. Results of inter-
comparison studies between the beta gauge method and conventional gravi-
metric are presented. The design of the present instrument is particularly
well suited for the automatic analysis of membrane filters used in modern
dichotomous samplers.
This report was submitted in fulfillment of Contract No. EPA-IA6-D8-
E681-CG, 80 BCG by the Lawrence Berkeley Laboratory under the sponsorship of
the U. S. Environmental Protection Agency. This report covers the period
August 28, 1978 to August 28, 1979.
-------
CONTENTS
Abstract iii
Figures vi
Tables vii
Acknowledgements viii
1. Introduction 1
2. Description of Method 2
3. Description of Instrument 10
4. Precision and Accuracy 13
Precision 14
Accuracy 15
Particle size and filter inhomogeneity 16
Atomic number dependence 19
5. Results And Summary 24
References 28
v
-------
FIGURES
Number Page
1. Schematic of a beta-gauge suitable for measuring
thin aerosol samples 3
2. Idealized beta-particle spectrum emitted from a
radioisotope source 5
3. Range-energy curves for monoenergetic electrons with energies
in the region appropriate for beta-thickness gauges. Curves
are shown for a) lead, b) copper, and c) carbon 6
4. Attenuation curves for thin polycarbonate films using two
radioisotopes a) ^C, and b) ^'Pm 8
5. Automatic sample handling and data acquisition system used
in conjunction with the beta-gauge 11
6. The discrepancy in beta-gauge mass measurements as a
function of particle size for the case of two commonly
used isotopes 18
7. Measured values for the mass absorption coefficients as a
function of atomic number and atomic mass 21
8. Comparison of beta-gauge results with those obtained by
gravimetric methods. These data were obtained by comparing
side-by-side samples of the same atmospheric aerosol collected
by different samplers. Case A represents high volume samples vs.
dichotomous. Case B was obtained with manual dichotomous vs.
automatic dichotomous samplers 25
9. Comparison of beta-gauge results with those obtained by
gravimetric methods. These data represent duplicate mass
measurements on the same sample. Samples for curve A were
obtained in our laboratory. The data shown in curve B were
obtained from workers at EPA13 26
-------
TABLES
Number Page
1 Commonly Available Sources Suitable for Beta Attenuation
Measurements 2
2 Stability Tests for Room Temperature Beta-Gauge Measure-
ments Represent Precision in the Calibration Parameters
and Calculated Masses Which Were Observed in the Repeated
Measurement of Fine Thin-Film Standards . 16
3 Measured Mass Absorption Coefficients for Substances with
Varying Effective Atomic Number and Mass 20
4 Effect of Atomic Number Dependence on the Measured Mass of
Several Compounds. Column Four Gives the Discrepancy with
Respect to the Polycarbonate Standards 23
vii
-------
ACKNOWLEDGEMENTS
The authors would like to acknowledge the support of several other
members of the Department of Instrument Techniques including D. Landis,
D. Adachi and N. Madden who assisted in the detector and electronic develop-
ment, and W. Searles who did much of the mechanical design. We have profited
from discussions with T. Dzubay of the United States Environmental Protection
Agency and W. Courtney of Northrup Services, Inc.
vi
-------
SECTION 1
INTRODUCTION
The beta-gauge method of mass measurement is based on the attenuation
which a beta-particle spectrum undergoes when traversing a thin film of
matter. If one measures the total number of electrons in a continuous
beta-particle spectrum emanating from a radioisotope source, the number of
electrons transmitted through a thin, uniform foil would be !>2
I = I0 e-^ (1)
where I0 is the incident flux, y is the mass absorption coefficient in
cm^/g and x is the thickness of the film expressed in g/cm^. If y and
I0 are accurately known, then a measurement of I can be directly related
to the mass of a given sample. The values of y and I0 are normally
determined by measuring I as a function of x for several known standards.
Beta thickness gauges based on the above model have been used for
several years in applications where continuous, non-destructive monitoring
of thin films is required, for example, in certain industrial processes.3>4
Several authors have recently applied the method to the measurement of par-
ticulate deposits collected from the atmospheric aerosol .556,7 jne use Of
the beta-gauge method has several potential advantages over direct weighings
for the measurements of aerosol samples. Handling of the fragile filter
samples is minimized, the risk of contamination is reduced, and the automated
analysis of many samples can be facilitated. Insofar as a beta-gauge can be
made to operate with a precision and accuracy comparable to current micro-
balance technology, it represents a preferred approach in modern, large-scale
monitoring programs.
The measurement of the aerosol particulate deposits collected on filter
substrates represents a particularly demanding mass measurement problem.
Modern air sampling techniques result in typical particulate deposits of 50
to 200 yg/cm^ on filter subtrates weighing 1 to 5 mg/cm^. Variations in
substrate mass from sample to sample require that each filter be weighed
before and after exposure. A precision of ± 5 yg/cm^ in the measurement
of the aerosol deposit requires a maximum error of ± 3 yg/cm? in each
individual weighing. A direct measurement on a 5 mg/cm^ substrate there-
fore requires a precision of ± 0.06%. The calibration accuracy must be
assured in the presence of potential particle size, filter non-uniformity
effects and additional artifacts unique to the beta particle attentuation
method. In order to achieve the desired performance, it is important that a
thorough understanding of the technique and its implications be achieved.
-------
SECTION 2
DESCRIPTION OF METHOD
A schematic of a simple beta-gauge is shown in Figure 1. It consists
of a radioactive source, detector and sample. The source is chosen such
that beta-particle emission is the predominant mode of decay. The half-life
should be sufficiently long that decay corrections over the duration of a
measurement cycle are avoided and frequent replacement of the source is not
required. Table 1 is a partial list of beta-decay sources which are of use
in beta-gauge measurements. Many of these sources are better suited for
measurement of thicker samples than those involved in aerosol analysis. The
most appropriate choices for thin specimens are ^C, l^'Pm, an
-------
total ionization produced by an incident particle within the sensitive volume
of a semiconductor crystal, typically silicon. The output pulses are amplif-
ied and a discriminator circuit used to register the detection of electrons
with energies above a certain lower limit. Other possible detectors include
Geiger tubes and proportional counters.
DETECTOR
HOUSING
SILICON SURFACE
BARRIER DETECTOR
3cm2 AREA
300pm DEPTH
147Pm SOURCE SAMPLE MOUNTED ON
1.0 mC, 3 cm2 AREA 5-1 x 5-J cm FRAME
5cm
Figure 1. Schematic of a beta-gauge suitable for measuring thin
aerosol samples.
-------
The sample is inserted between source and detector and the counts
accumulated in the sealer are recorded over some fixed counting interval.
The fact that the measurement depends only on the transmission of the
particles through the sample itself allows one to mount the filter sample
in relatively massive frames without affecting the sensitivity or accuracy.
A mechanical system for manipulating these frames can then be used. The
automated sample handling represents one of the most important advantages
of the beta-gauge method of measurement.
In order to choose a radioactive source for a-particular application,
the physical processes involved in the measurement should be considered.
Figure 2 shows an idealized beta-particle spectrum as emitted from the
source. It consists of a continuous energy distribution with an endpoint
Emax which is characteristic of the isotope used. The maximum number of
electrons in the distribution occurs at E ~ 0.4 Emax. We have indicated
a discrimination level ^^c below which the detector and electronics are
not sensitive to events; the shaded area represents the measured intensity
I.
When traversing the sample material between source and detector, the
individual electrons lose energy in a continuous manner via collisions with
the electrons in the sample. Their energy and direction are both affected
by repeated small energy losses. As the sample thickness is increased, the
spectrum of Figure 2 is not uniformly attenuated in terms of the number of
particles per unit energy but, instead, undergoes a shift to lower energies
accompanied by complete stopping of the lowest energy particles. The
measurement then consists of counting the number of electrons with energies
remaining above the value E
-------
o
DC
I-
u
UJ
_j
UJ
K
UJ
ffl
SWAX
ELECTRON ENERGY
Figure 2. Idealized beta-particle spectrum emitted from a radioisotope
source.
Figure 3 shows a curve of the maximum range of electrons in carbon,
copper, and lead as a function of energy.8 Of most importance for the
present discussion are the range curves for carbon since most filter sub-
strates consist of hydrocarbon materials. Curves for the other elements are
presented in order to show the atomic number dependence and alert us to pos-
sible effects which this might have on the mass measurement. Indicated on
the plots are the average and endpoint energies for the electron distribu-
tions from the commonly employed isotopes ^C and ^'Pm. Either of these
isotopes is seen to be a practical source for measurement in the 1 mg/cm^
to 10 mg/cm^ ranges.
-------
100.0
10.0-
(M
o
00
a) LEAD
b) COPPER
c) CARBON
100 200
ENERGY (keV)
300
Figure 3. Range-energy curves for monoenergetic electrons with energies in
the region appropriate for beta-thickness gauges. Curves are
shown for a) lead, b) copper, and c) carbon.
-------
Of more direct concern in the design of a beta-gauge is the relative
intensity versus mass thickness described in Equation 1. Figure 4 shows
plots of experimental curves for 14C and 147Pm. These were obtained by
measuring the variation in counting rates as a function of mass for a series
of thin uniform films whose masses were gravimetrical ly determined. The
dashed straight lines represent semi-empirical values calculated from a
relationship derived by Gleason et al2
w (cm2/mg) = 0.017 EmaJ'43 (2)
where Emax is the endpoint energy in MeV. This expression was deduced by
measuring the mass absorption coefficient for a number of isotopes with
Emax ranging from 0.15 to 3.5 MeV and is valid for mass ranges which are
small compared to the average electron range. This is consistent with the
results shown in Figure 4 where the theoretical slopes are tangent to the
experimental result at low mass values.
Based on the results shown one would conclude that C is the best
choice for the range of 5 mg/cm2 or less since the change of countin
rates with mass is greater resulting in a higher sensitivity. The
source has a lower rate of attenuation and is thus better suited to cover a
larger mass range. However, since the difference in sensitivity between the
two sources is small, the use of 147Pm is often preferred because of the
broader range of masses over which it is sensitive. This allows the use of
additional protective windows on source and detector. Furthermore, the
measurements are less susceptible to artifacts arising from particle size
and filter non-uniformity affects.
A close examination of the experimental curves shows that they are not
purely exponential over the wide range of masses shown. However, over a
relatively narrow range, a reasonable approximation can be maintained. For
these reasons, the calibration curve is normally derived from a very limited
range which overlaps the range of mass measurement to be made. Assuming a
typical deposit to be 200 yg/cm2 and a root mean square deviation in tare
weight of ± 500 yg/cm2, a calibration range of ± 1 mg/cm2 is adequate.
In normal operation, the system can be frequently calibrated in order
to minimize the effect of long term drift. Our current procedure employs
five uniform thin polycarbonate standards which span the mass range of
interest. The masses of these standards are first determined by weighing.
They are then processed through the beta-gauge and a least squares fit to
Equation 1 is performed to obtain I0 and y. In general, deviations from a
straight line can be observed due to slight inaccuracies (± 10 yg/cm2) in
the gravimetric mass measurement. After repeated measurement in the beta-
gauge, the mass values for the thin film standards are corrected to fit a
straight line within a typical precision of ± 2 yg/cm2. The procedure
whereby the gravimetric masses are adjusted to conform to the result
obtained in the beta-gauge has little effect on the accuracy of the measure-
ment since it involves only a slight correction to the observed slope. In
effect, the accuracy of the calibration standards is determined by the
average gravimetric mass. Slight systematic variations of the individual
-------
14
a) 1HC, EMAX = 156keV
b) 147Pm, EMAX= 225keV
5 10 15 20 25
SAMPLE THICKNESS (mg/cm2)
30
Figure 4. Attenuation curves for thin polycarbonate films using two radio-
isotopes a) 14C, and b) 147Pm. Solid curves are experimental
measurements. Dashed curves are derived from Eq. 2.
-------
samples are adjusted according to the higher precision afforded by repeated
beta-gauge measurements.
Subsequent mass determinations are made by using the y and I0 values
obtained from the least squares fit in order to calculate the mass from the
observed counting rate. The expression is:
x = lnVlnI (3)
-------
SECTION 3
DESCRIPTION OF INSTRUMENT
The present approach to mass measurement differs from other beta-gauge
procedures''^ in that the tare weights are directly calculated relative to
calibration standards and stored in that fashion. Although in principle it
is possible to store the counts only and compare the counts before and after
exposure, the stability of a calibration over a long period of time cannot
be guaranteed at the necessary level of precision. Consequently, we require
that individual calibration measurements be performed with each measurement.
The present beta-gauge design employs a source, sample, and detector geometry
similar to that shown in Figure 1, The source is a commercially obtained
147pm source in a 2.54 cm diameter cylindrical aluminum source holder.
The active area is 2.2 cm in diameter and is specified to be uniform to
better than ± 10%. The source is protected by a 600 pg/cm2 foil supplied
by the manufacturer; an additional 7 mg/cm2 Al foil is used to protect the
surface of the source from mechanical damage during normal handling and
operation.
The detector is an Ortec, Model CA-018-300-300 silicon surface barrier
detector operated at room temperature. The active area is 3 cm2 with a
300 ym (70 mg/cm2) sensitive depth. The electronic resolution is approxi-
mately 12 keV at the operating temperature. The front surface of the detec-
tor is also protected by a 7 mg/cm2 Al foil which reduces the sensitivity
of the device to ambient light. The source to detector distance is 0.7 cm
representing an air path of approximately 0.9 mg/cm2 equivalent mass.
Since the present instrument is designed for automatic operation, it is
interesting to consider the associated mechanical and electronic hardware.
These are illustrated schematically in Figure 5. The sample carrier is
designed to accomodate two standard trays with 36 samples each plus an
additional five standards at top and bottom. The two trays would typically
represent the coarse and fine particle fractions obtained from a dichotomous
sampler.10 The five standards at the bottom are normally used to calcu-
late the thin film calibration constants. The top standards are blank
filters of the type used in the study and are employed as cross checks on
system stability and calibration accuracy.
The detector preamplifier, amplifier, and discrimination circuitry were
designed and built in our laboratory and have been extensively tested for
stability. Repeated measurement of the same counting rate over extended
periods of time indicate a long term stability in the entire system of one
part in 3 x 10~4.
10
-------
i KEYBOARD INPUT
I SAMPLE I.D.,J)ATE, TIME, STANpARD_MAS£ES
HP 9815 |"cASSETTE~i7o
CALCULATOR
I PRINTER OUTPUT
| CALIBRATION DATA, RESULTS
CONTROLLER
SCALER/TIMER
AMPLIFIER/
DISCRIMINATOR
t^ BLANK-
SAMPLES::
DETECTOR
SOURCE
Figure 5. Automatic sample handling and data acquisition system used in
conjunction with the beta-gauge.
11
-------
The control of the system is incorporated into a Hewlett-Packard 9815
Calculator. An interface module is used to execute the instructions from
the calculator. The unit also includes a sealer and clock which are used to
count the pulses from the discriminator and communicate the result to the
calculator.
Additional analysis data such as sample numbers, calibration masses,
date and time are entered via the calculator keyboard. This information is
used to control the analysis procedure, calculate the calibration curve, and
file the results in the proper location. The cassette facility included
with the calculator is capable of storing the necessary program files and
the data for 10,000 samples in each cassette. Since the tare weight must be
individually stored and subsequently matched to the final weight for each
slide, the large storage capability allows one considerable flexibility in
the handling of samples. -For a typical study which might require less than
10,000 total samples, the programs would accommodate the analysis of these
samples in more or less random order. Final output of the data can be
either performed by the printer or the calculator or it can be transferred
from the calculator to a larger facility using a standard interface.
In the normal sample running procedure, an entire sequence of standards
and samples is run for a given counting period and the counts stored in a
buffer. Following completion of the entire stack, the stored standard
masses are fitted to the observed data using a least squares method and the
results printed. The deviations of the calculated masses from the stored
masses are also printed for both the thin film standards and the filter
blanks. Additional statistical tests can then be printed as an indicator of
system performance. The masses of the samples are then calculated and stored
either as tare weights, or as tare weight together with the added mass in the
case of exposed filters.
12
-------
SECTION 4
PRECISION AND ACCURACY
The precision of the beta-gauge instrument can be defined as the repro-
ducibility with which a given value can be obtained from the measurement of
an unknown mass. It will include the effects of counting statistics and
electronic stability on both the measurement of the calibration standards
and the unknown samples. It can also be affected by possible variations in
absorption characteristics as a result of misalignment of the standards and
unknowns in the instrument.
The accuracy of the measurements is defined in terms of the comparison
of the beta-gauge results with totally independent but equivalent methods of
measurement. In the case of a single mass measurement of a given sample,
the accuracy of the results depend upon the quality of the standards and
validity of the calibration procedure together with any artifacts which
might affect the application of a given calibration curve to the assignment
of unknown masses. Included in the category of artifacts would be particle
size effects, filter substrate inhomogeneity and possible atomic number
dependence of the mass absorption coefficient.
In the case of a difference measurement such as employed when determin-
ing the deposited mass on a substrate, the question of precision and accur-
acy must be carefully interpreted. If we can associate a root mean square
variation with both precision and accuracy (ap and a/^, respectively),
then the total uncertainty in the measurement is obtained by combining these
results in normal quadrature addition. Two different cases are possible.
If we perform both the tare weight and final weight measurement on the same
instrument using the same calibration standards and assuming negligible
particle size or filter homogenity effects, then the contribution to the
combined error due to the calibration uncertainty is correlated between the
two measurements and the error is:
o2 = 2 a2 + a2 (4)
P A
If the two measurements are performed on different systems or using com-
pletely different calibration procedures, then the errors are uncorrelated
and the combined uncertainty is:
o2 = 2 a2 + 2 a2 (5)
-------
Since the uncertainty in the calibration factors is typically a few percent
compared to a precision of a fraction of a percent, the effect of Equation 5
is to increase the error in the case of independent tare and final weight
measurements.
A far worse condition can exist if there is a systematic bias of the
calibration curve employed in one beta-gauge measurement relative to the
other. If we wish to detect a deposit of 10 pgm/cm2 on a 1 mg/cm2 sub-
strate, a shift of 1% in calibration slope between the two weighings can
completely eliminate any observed deposit. Since it is extremely difficult
to maintain accuracies below this level, such errors can easily occur. For
these reasons, it is important that the beta-gauge system be maintained in
as stable a configuration as possible so that measurement before and after
exposure can be performed under identical conditions. In cases where un-
avoidable modifications in detector-source geometry occur, repeated measure-
ment of standard samples should be used to determine if any systematic cali-
bration shifts have occurred.
PRECISION
The precision of the beta-gauge measurement depends both on statistical
fluctuations associated with normal counting experiments and on uncontroll-
ed, random fluctuations in counting rate or sample position. Ideally the
contributions due to the latter effects can be minimized with the result
that the precision is determined principally by counting rate and analysis
time.
Beginning with Equation 3 we can derive an expression
associated with the calculated mass as follows:
for the error
a2(x) =
3X
3y
3X
3lnl
Covar
Inl )
3_X
31
(I)
(6)
a2(x)
(Inl -Ini
9
a2(lnl
(Inl -Inl)
Covar (,
lnIQ)
2T2
u I
(7)
The first three terms in Equation 7 are associated with the errors
incurred in the linear least squares fitting procedure. The Covar (M,lnI0)
term is the usual error term arising from the interdependence of the slope
and intercept when fitting a straight line to the Inl vs. x calibration
14
-------
curve. The final term in the equation represents the statistical variation
associated with the counting measurement on the unknown mass.
The dependence of the error on terms involving inverse powers of y indi-
cates the importance of choosing a source which experiences maximum attenua-
tion. It can also be shown that the errors obtained from the least squares
fitting procedure are proportional to the relative errors associated with the
measurement of the individual I values. If we can assume that the standards
and unknowns are measured at approximately the same counting rate and for
the same interval, then
2 2
a (X) a S-LLL = _i_ (8)
r IT
This gives the expected result that the total precision of the measurement
scales as "[-*' 2 where T is the counting interval.
Table 2 gives a summary of results testing the precision of the current
beta-gauge design. These represent repeated measurements on a series of ten
filters using the same calibration standards for each measurement. The nom-
inal counting rate was 1.2 x 105 sec"1 and a 100 second interval was
used. If we calculate the root mean square deviation under these conditions
assuming statistical fluctuations only, we obtain a value of ± 2.56 yg/cm^.
This is consistent with the experimentally measured value. The temperature
range is included in the table since it is known to be the external param-
eter which will most seriously affect the system stability presumably
through variations in detector capacitance, amplifier gain and stability.
ACCURACY
Primary gravimetric mass standards in the form of thin, uniform films
can normally be prepared to an accuracy of ± I yg/cm^ using conventional
microbalance methods. These are usually hydrocarbon films (polycarbonate,
for example) which are weighed and mounted in standard sample holders. Mass
values range from 600 to 6000 yg/cm^ depending upon the average filter
mass to be measured. A series of measurements of Inl vs. mass are then
fitted to a straight line and the average value of y and I0 are computed.
The value of the standard masses are then adjusted slightly to conform to
the straight line fit. These adjustments compensate for small variations in
the measured mass due to possible non-uniformities in the thin films and any
non-linearities in the mass absorption curve in the vicinity of the least
squares fit. Following these adjustments, subsequent fits to the standard
typically exhibit root mean square deviations of ± 3 y
Of more serious concern to measurement accuracy are possible systematic
biases which arise from the application of the thin-film calibration curve
to aerosol particles collected on non-uniform filter media. Effects which
must be considered include particle size, filter inhomogenity, and atomic
number dependence.
15
-------
TABLE 2 STABILITY TESTS FOR ROOM TEMPERATURE BETA-GAUGE. MEASUREMENTS
REPRESENT PRECISION IN THE CALIBRATION PARAMETERS AND CALCULATED
MASSES WHICH WERE OBSERVED IN THE REPEATED MEASUREMENT OF NINE
THIN-FILM STANDARDS.
Parameter
I (blank counts)
In I (fitted intercept)
U (fitted slope)
Mass (yg/cm2)
Average deviation
Temperature range
Average Deviation
12145622 ± 19540
14.0794 ± 0.0018
1.5468 x 10-" ± 2.9 x 10'7
cm2/yg
686.1 ± 2.9
1093.8 ± 2.3
697.8 ± 2.2
729.1 ± 1.9
773.5 ± 1.8
341.4 ± 2.0
301.8 ± 2.7
357.9 ± 3.3
302.1 ± 2.6
+ 2.5 yg/cm2
24.6° ± 1.7° C
Particle Size And Filter Inhomogeneity
Particle size and filter inhomogenity effects are closely related. Both
arise because the measured mass per unit area represents the average over a
non-uniform mass distribution arising either from a finite number of discrete
particles or from a variable thickness substrate. In gravimetric mass deter-
minations, these non-uniformities present no problem since the average mass
per unit area can be computed directly from the total mass and area. However,
in the beta-gauge measurement, the mass is related to the measured quantity
via an exponential function. Insofar as the averaging is no longer performed
linearly, possible errors can be introduced.
16
-------
A simple method for estimating the effect assumes that the particles are
in the form of cubes lying on a uniform substrate. Assuming N cubes per
square centimeter with linear dimensions d and density P, then the mass per
unit area which one would measure by direct gravimetric means would be:
x (g/cm2) = Nd3P + t (9)
where t is the substrate thickness (the use of cubes instead of other par-
ticle shapes is done to simplify the calculations. In general, more compli-
cated shapes result in a smaller particle size effect than is experienced by
cubes). If the measurements are performed using a beta-gauge with char-
acteristic calibration constants of y and I0, then the mass must be deriv-
ed from the following attenuation data.
I = IQ {(1-Nd2) + Nd2 e-Mpd}e~ypt (10)
This equation describes a model in which beta particles incident on a frac-
tion of the filter area (Nd2) undergo an attenuation e~v^ e~v<*. The
remainder of the beam undergoes an attenuation e~^. The application of
the standard thin-film calibration curve requires that the mass x" be
obtained by interpreting the observed intensity I in Equation 10 according
to Equation 3.
The ratio of x'/x is a measure of the error introduced as a result of
finite particle size. Figure 6 is a plot of this ratio as a function of d
for the case of ^C and l^7Pm sources assuming a 100 yg/cm2 deposit of
unit density particles. In the small particle range, the number density of
particles approaches that of a thin film and the discrepancy vanishes. For
very-large particles, one can see that in the limit of a few very-large
cubes, the attenuation is proportional to the area of the particle compared
to the total filter. The mass of the particle is then practically undetect-
ed. The higher attenuation experienced by the 14C source causes it to be
more susceptible to particle size effect according to the model. If we allow
ourselves to interpret the linear dimension d in terms of aerosol particle
size, then we see that below 15 ym particle diameter, the discrepancy will
be less than 5% for a 147Pm beta-gauge source. Although the model used is
relatively simple, it is useful in that it gives an upper limit to the
observed effect. In the data processing normally employed, no correction
for particle size effects are made.
17
-------
(A
O
UJ
UJ
UJ
o
8-
_ a.
o
(O
o
CM
00 UJ
_j
O
to I
CE
<
O.
CM
O
in
d
OilVd
Figure 6. The discrepancy in beta-gauge mass measurements as a function of
particle size for the case of two commonly used isotopes.
18
-------
Inaccuracies due to filter inhomogeneities can be estimated using a
similar calculation. We assume that the small-scale inhomogenities in the
filter can be approximated by a model in which the filter thickness varies
by a factor of two. If we furthermore assume that the total area of the
thicker portion is one-half the total area, then calculations similar to
Equation 10 can be performed to estimate the discrepancies which arise from
the application of the uniform thin film calibration curve. The result is
expressed in Equation 11.
3dyp
- In2 (11
where d is the thickness of one-half the filter area and 2d is the thickness
of the remainder. Note that in this model it does not matter whether the
inhomogeneities are small-scale or large-scale as long as the area of each
portion is one-half the total. If we assume a 1 mg/cm2 average thickness,
then the discrepancies would be 0.976 and 0.987 for i4C and l^'Pm
respectively. For a 5 mg/cm2 substrate, the corresponding numbers are
0.891 and 0.939. Although the errors are small in a relative sense, the
magnitude of the absolute error ranges from 13 yg/cm2 to 109 yg/cm2 in
the least favorable case. The discrepancy vanishes when the difference
between initial and final masses are calculated, although, once again, the
importance of using identical systems for both mass measurements is empha-
sized. Discrepancies are minimized for the case of thinner substrates and
higher energy beta-particles.
The presence of large-scale inhomogeneities in the filter substrate
coupled with a slight non-uniformity in the spacial distribution of the
radioactivity emitted from the source can produce similar discrepencies.
These can be observed either when non-identical beta-gauge measurement are
performed or, in a much more likely case, if the filter is not placed in a
reproduciable geometry in the instrument. This applies both to rotations
and translations of the sample relative to the axis of the source-detector
system. Again the effect can be eliminated by the use of identical measure-
ment produces for both tare weight and final weight determinations.
ATOMIC NUMBER DEPENDENCE
The process by which the beta-particles interact within the sample
depends upon the number of electrons in the sample which scatter the
incident beam. The validity of the beta-gauge method depends upon the
proportionality between the number of electrons in the sample and the total
mass and also upon the equivalence of all electrons in terms of their scat-
tering properties. The fact that the range of electrons expressed in
nig/cm^ depends somewhat upon the atomic number of the absorber (see Figure
3), indicates that some departure from this simple behavior is expected.
19
-------
We have performed measurements of the mass absorption coefficient as a
function of atomic number for several substrates. The procedures were the
same as employed in normal calibration runs except different thin film
materials were used. Table 3 is a summary of the results. The measured mass
absorption coefficients are also presented graphically in Figure 7 as a
function of Z/A.
TABLE 3 MEASURED MASS ABSORPTION COEFFICIENTS FOR SUBSTANCES
WITH VARYING EFFECTIVE ATOMIC NUMBER AND MASS.
MATERIAL
Gold
Beryllium
Copper
Nickel
Aluminum
Polyvinyl dichloride
Polyimide
Polycarbonate
Polyethylene
Polypropylene
ATOMIC NUMBER/
ATOMIC MASS
Z/A
0.401
0.444
0.456
0.477
0.482
0.495
0.517
0.537
0.570
0.570
MASS ABSORPTION
COEFFICIENT
(cm2/mg)
0.217
0.116
0.173
0.178
0.156
0.165
0.141
0.154
0.167
0.165
From the plot shown in Figure 7, it is apparent that no simple relation-
ship between v and Z/A can be easily derived. For pure elemental samples we
have Z/A < 0.5 and the data seem to follow a straight line dependence. The
values for hydrocarbon films vary only slightly for Z/A values 0.48 < Z/A
< 0.57. A smooth curve can be drawn through the experimental points with the
exception of the measurement for Be. Be represents a somewhat unique case in
that it is an elemental sample with Z/A = 0.44, but is also the lightest ele-
ment standard with Z = 4.
20
-------
^ -^
UD
E
°-3
CM
UJ
O 0.2
Ul
O
O
0.1
O
CO
CO
0.4
METAL FOILS
o HYDROCARBON FILMS
3.
*
0.5
Z/A
0.6
Figure 7. Measured values for the mass absorption coefficients as a
function of atomic number and atomic mass.
21
-------
The atomic number dependence of the absorption coefficient can be
partially understood by considering in greater detail the energy loss
processes for electrons. As evident in Figure 2, the total range of elec-
trons expressed in mg/cm^ increases as a function of atomic number. This
would imply a lower mass absorption coefficient for the heavier elements
which is opposite to the behavior observed. However, as noted earlier, in
addition to the discrete energy loss processes which occur during collis-
ions, there is also a change in the direction of the scattered particle.
This average angular deflection is a function of atomic number and increases
for the heavier elements. A typical trajectory for an electron in Be is
relatively straight compared to the case of Au where a sizeable fraction of
the electrons can actually be backscattered from the foil-H It is this
strong angular dependence and its relationship to atomic number which results
in the observed behavior of mass absorption coefficient with Z/A. The
anomalously low absorption coefficient for Be can also be explained by this
simple interpretation.
Although a detailed model for the Z/A dependence cannot be easily cal-
culated, the effect of such variations upon realistic aerosols can be
estimated. If we neglect the anomaly of Be and assume a dependence describ-
ed by the curve shown in Figure 7, then the errors resulting from applying a
hydrocarbon thin-film calibration to variable Z particles can be estimated.
Table 4 gives the percent error in the mass measurement for various commonly
encountered aerosol compounds when the mass measurement is interpreted in
terms of the the normal calibration procedure.
As can be seen from the data, significant problems do not occur until
one reaches the Pb compounds where errors of 30% can be expected. However,
insofar as typical urban aerosol composition normally contains much less
than 10% of such Pb compounds, the error introduced in the total mass
measurement is minimal. In special cases where large Pb or other heavy
element concentrations are observed, it should be possible to apply a
correction to the calibration produced to reduce any discrepancy due to
atomic number dependence.
The fact that there is some variation in y with Z/A again emphasizes the
importance of maintaining a stable configuration in the beta-gauge calibra-
tion and measurement system. A slight variation in effective atomic number
brought about by using different standards or changes in the material used
for detection windows, absorbers, etc., can cause apparent shifts in the
measured masses.
22
-------
TABLE 4 EFFECT OF ATOMIC NUMBER DEPENDENCE ON THE MEASURED MASS OF
SEVERAL COMPOUNDS. COLUMN FOUR GIVES THE DISCREPANCY WITH
RESPECT TO THE POLYCARBONATE STANDARDS.
Compound
(NH,)2S04
NH4H S04
CaSO^-HzO
Si02
CaC03
Carbon
Fe203
NaCI
PbS04
PbCl2
PbBrCl
Cal ibration value
Z/A
0.530
0.521
0.511
0.499
0.500
0.500
0.476
0.478
0.429
0.417
0.415
y (cm2/mg)
0.153
0.152
0.152
0.154
0.154
0.154
0.163
0.172
0.193
0.204
0.206
Ratio to
Standard
0.99
0.99
0.99
1.00
1.00
1.00
1.06
1.12
1.25
1.32
1.34
0.154
23
-------
SECTION 5
RESULTS AND SUMMARY
The ultimate test of the beta-gauge method for aerosol mass measurement
consists in comparison of results with those obtained by more conventional
methods. The commonly accepted method for mass measurement is gravimetric
measurement using microbalance techniques. The results from several inde-
pendent studies which involved intercomparison of beta-gauge and gravimetric
mass determinations are now available. Data have been selected from these
studies in which the beta-gauge instrumentation was equivalent to the system
described in this paper.
Figure 8 shows scatter plots of data obtained in a side by side sampling
intercomparison performed in Charleston, W. Virginia in May, 1977.12 The
data quoted herein and the description of the sampling and analysis protocol
are taken from Reference 12. The mass concentrations are quoted in terms of
yg/m^ referred to the original atmospheric aerosol. Figure 8A compares
the results of Rodes obtained using a high-volume sampler and gravimetric
weighing with those from a dichotomous sampler and beta-gauge mass deter-
minations. The results for the latter case were calculated as the sum of
the coarse and fine fractions. The average slope of the data in the scatter
plots was calculated to be 1.23. The higher average mass obtained with the
high volume sampler probably reflects the larger effective particle size
cutoff obtained with this sampler relative to the dichotomous samples.
The plot of Figure 8B shows the results obtained from a gravimetric
analysis of samples acquired with separate dichotomous samplers relative to
the earlier beta-gauge results. The gravimetric measurements are those
quoted by Dzubay in Reference 12. The data shown are for the fine particle
fractions only since the upper cutoff for each of the dichotomous samplers
was unknown. The excellent agreement between the two data sets reflects the
relative precision of the two sampling methods. The calculated slope of the
line shown is 0.954.
24
-------
(A)
o
5
200
oo
100
100
DO
50
ro
en
(B)
x
X
X
X
X
x
XI
X
x«
100
(Mg/m3) 200
(Mg/m3)
BETA GAUGE RESULTS
Figure 8. Comparison of beta-gauge results with those obtained by gravimetric
methods. These data were obtained by comparing side-by-side samples
of the same atmospheric aerosol collected by different samplers.
Case A represents high volume samples vs. dichotomous. Case B was
obtained with manual dichotomous vs. automatic dichotomous samplers.
-------
IX)
en
300
200
o N
££ C
^ \
UJ t*
SSI
,^5
< 100
QJ
o
(A) '/ 300
/
/" C^"^
xx E
y u
v dfi
.r 3,
^ ^
x
- x" " 200
x
X
x
x
X
yS
4
- /* ' 100
x
^y
X
X
x
X
X
S
X
.' 1 1
(B)
x
x
X
X
X
X
X
X
X
*
x
X
X
X *
. X
xV>
xx.
^ »
x
v^
. r. '
'.
x
* . .
/ \ 1 1
0 100 200 2 300 0 100 , 200 300
-------
A more direct comparison which eliminates uncertainties due to non-
equivalent sampling methods can be obtained by sampling with membrane
filters mounted on thin frames which can be removed from the normal
5.1 cm x 5.1 cm carrying frame. The same sample can then be analyzed by
both beta-gauge and direct weighing. Figure 9 shows the results of two such
independent studies. The plot of Figure 9A was generated from data obtained
in our laboratory using aerosol samples collected locally. The fine and
coarse particle fractions were analyzed separately and are included in the
plot a separate points. The data are quoted directly in terms of pg/cm^
as deposited on the thin Teflon membrane filter. The observed slope of the
data was calculated to be 0.973. There were some slight systematic differ-
ences observed between the coarse and fine particle fraction which are not
obvious in the combined data set. This is probably due to non-uniformity of
the particle deposition together with possible particle size effect as
discussed earlier.
Figure 98 shows the results of a study performed at the EPA Environ-
mental Sciences Research Laboratory.-^ Fine particle samples were
acquired from an indoor aerosol and subjected to the same analysis as
discussed above. Again the agreement was excellent with a calculated slope
of 0.963.
SUMMARY
The beta-gauge method for the determination of the mass of atmosphere
aerosol samples has been demonstrated to be equivalent in accuracy to gravi-
metric methods when proper attention is paid to instrumental design and
calibration procedures. The advantages of automation and reduced sample
handling would make beta attenuation the method of choice for larger sized
monitoring programs. The present instrument design has been implemented
with the capability for the automatic storage and retrieval of large data
sets consistent with the large-scale approach to mass measurement.
27
-------
REFERENCES
1. R. D. Evans, The Atomic Nucleus, McGraw-Hill, New York, 1955.
2. G. I. Gleason, J. D. Taylor and P. L. Tabern, "Absolute Beta Counting at
Defined Geometries", Nucleonics 8_ (1951) 12.
3. "Symposium on Applied Radiation and Radioisotope Test Methods", ASTM
Special Technical Publication No. 268, (1959).
4. C. E. Compton, "The Versatility of Radiation Applications Involving
Penetration or Reflection", Proc. Intern. Conf. Peaceful Uses of Atomic
Energy, Genoa (1955) 15_, 124.
5. P- Lilienfeld, "Beta-Absorption-Impactor Aerosol Mass Monitor", Am. Ind.
Hygiene. Assoc. J. _31 (1970) 722.
6. P. Lilienfeld, "Design and Operation of Dust Measuring Instrumentation
Based on the Beta-Radiation Method". Staub-Reinhalt Luft 35_ (1975) 458.
7. E. S. Macias and R. B. Husar, "High Resolution On-Line Aerosol Mass
Measurement by the Beta Attenuation Technique". Proceedings of the
Second International Conference on Nuclear Methods in Environmental
Research. Edited by J. R. Vogt and W. Meyer. CONF-740701, p. 413
(1970).
8. M. J. Berger and S. M. Seltzer, "Tables of Energy Losses and Ranges of
Electrons and Positrons", in Studies in Penetration of Charged Particles
in Matter, Nat. Acad. Sci. NRC Publ. 1133, (1964) 2057
9. D. W. Cooper, "Statistical Errors in Beta Absorption Measurements of
Particulate Mass Concentration", Journal Air Poll. Conf. Assoc. 25
(1975) 1154. ~~
10. B. W. Loo, J. M. Jaklevic and F. S. Goulding, "Dichotomous Virtual
Impactors for Large-Scale Monitoring of Airborne Particulate Matter", in
Fine Particles: Aerosol Generation, Measurement, Sampling and Analysis,
B. Y. H. Liu Ed. (New York, Academic Press, 1976). 311.
11. G. D. Archard, "Back Scattering of Electrons", Jour, of App. Phys. 32
(1961) 1505. ~~
28
-------
12. D. C. Camp, A. L.VanLehn and B. W. Loo, "Intel-comparison of Samples Used
in the Determination of Aerosol Composition", Interagency Energy-
Environment Research and Development Series, Report No. EPA-600/7-78-118
13. W. J. Courtney, Northrup Services, Inc., Research Triangle Park, NC,
private communication.
29
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
REPORT NO.
EPA-600/7-80-081
I. RECIPIENT'S ACCESSIOf*NO.
4. TITLE AND SUBTITLE
BETA GAUGE INSTRUMENTATION FOR THE
MEASUREMENT OF AEROSOL MASS
6. PERFORMING ORGANIZATION CODE
AUTHOR(S)
J.M. Jaklevic, R.C. Gatti, F.S. Goulding, and
B.W. Loo
8. PERFORMING ORGANIZATION REF
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Lawrence Berkeley Laboratory
University of California
Berkeley, CA 94720
10. PROGRAM ELEMENT NO.
1NE833 EB-13 FY-79
11. CONTRACT/GRANT NO.
EPA-IAG-79-DX0712
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Sciences Research Laboratory RTF NC
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, N.C. 27711
13. TYPE OF REPORT AND PERIOD COVERED
Final
14. SPONSORING AGENCY CODE
EPA/600/09
15. SUPPLEMENTARY NOTES
16. ABSTRACT
An instrument developed by LBL for the routine measurement of aerosol mass
using the beta-gauge particle attenuation method is described and evaluated.
Factors affecting the precision and accuracy of the measurement are discussed in
detail. Results of intercomparison studies between the beta-gauge method and
conventional gravimetric are presented. The design of the present instrument
is particularly well suited for the automatic analysis of membrane filters
obtained from modern dichotomous samplers.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDEDTERMS
COSATI Field/Group
*Air pollution
*Aerosols
*Weight (mass)
^Measurement
Beta particles
Atenuation
Fluid filters
Membranes
Beta-gauge
13B
07D
2 OH
14K
11G
13. DISTRIBUTION STATEMEN1
RELEASE TO PUBLIC
19. SECURITY CLASS (This Report)'
UNCLASSIFIED
21. NO. OF PAGES
38
20. SECURITY CLASS (This page)
UNCLASSIFIED
22. PRICE
EPA Form 2220-t (3-73)
30
------- |