Io 
Al 
Ha 
Ta 
Ip 
Hb 
Za 
Zp 
166 
Zs 
SYMBOLS 
= ionization current with 
material of thickness z, 
amperes 
= thickness in units of mass 
per unit area, mg/cm? 
= ionization current with 
material of thickness 0 (in 
thickness measurements) 
or ionization current back- 
scattered by the solvent 
when it contains no solute 
(in concentration meas- 
urements), amperes 
= change in ionization cur- 
rent caused by material, 
amperes 
= absorption coefficient, 
(mg/cm?)—! = 0.693m/R,, 
empirically determined; 
due to scattering effects, 
it will show some depend- 
ence on the atomic num- 
ber of the material being 
measured 
K 
Z. 
Jm 
= maximum range of beta 
particles, mg/cm? 
412 #1.265—0.220 log, (when 
E < 3 Mev) 
= 542EF — 133 (when E> 
0.8 Mev) 
= maximum energy beta 
emitted, Mev 
=a number from 6 to 13, 
depends on the geometry 
of the setup and on the 
beta particle energy spec- 
trum characteristic of the 
source isotope 
= ionization current obtained 
for a saturation thickness 
of A 
= ionization current from B 
with zero thickness of A 
= reflection coefficient, (mg/ 
cm?)—! = fu, (empirically) 
= empirical factor 
= 2.5 to 3 
= effective atomic number 
of A 
= effective atomic number 
of B 
= empirical exponent 
= 0.7 to 0.8 
= saturation thickness, mg/ 
em? 
Sz 
dave 
or 
(9?) ave” 
a constant dependent on 
setup (K ~4 X10 in 
author’s experiments) 
effective atomic number 
of solute 
effective atomic number 
of solvent 
concentration of solute 
dissolved in a low-atomic- 
number solvent (water or 
organic), weight per cent 
empirical exponent (j ~ 
0.95; in author’s experi- 
ments) 
empirical exponent (k ~ 
0.99 in author’s experi- 
ments) 
meter reading, ya 
load resistance from ioni- 
zation chamber anode to 
ground, ohms 
amplification = effective 
transconductance of elec- 
trometer tube amplifier 
system, ya/volt 
sensitivity of thickness 
gage, na /mg/cm? 
sensitivity of concentra- 
tion gage, pa/wt % 
uncertainty in thickness z 
uncertainty in concentra- 
tion c 
uncertainty in meter read- 
ing 
number of betas entering 
ionization chamber per 
second 
capacity of ionization cir- 
cuit, farads 
average charge produced 
by a beta particle in ioni- 
zation chamber, coulombs/ 
beta particle 
standard deviation of ioni- 
zation current, 7, through 
R 
= root-mean-square devia- 
tion of g 
om = Standard deviation of 
meter reading due to sta- 
tistical fluctuations 
7 = equilibrium time, sec 
Thickness-by-reflection. When a 
thin material, A, is laid over a thick 
material, B (usually thick enough to 
cause saturation backscattering from 
B), and beta particles backscatter into 
the ion chamber 
AI = I — Ig = (Ia — Ip)(1 — e7*s?) 
For saturation backscattering 
ly _ (ZV 
Ip Zp 
and 
AI =I —TIs, 
= I5[(Za/Zs)” — 1](1 — e*) 
Saturation thickness is 
a, ~ 116 E87 
Concentration-by-reflection. 
When the beta particles received in 
the ionization chamber have been 
backscattered from a solution (liquid 
or solid) of at least saturation thickness 
AI =I —In = InK(Z — Z,)ick 
where Z<Z 
Accuracy 
The usefulness of the gage is deter- 
mined by the over-all accuracy with 
which measurements can be made. 
As an example, assume that meas- 
urements are being made using a d-c 
electrometer bridge amplifier circuit 
with a d-c microammeter as the indi- 
cating meter. If the meter is zeroed 
for AJ = 0 and the polarity is such 
that a positive reading is obtained, then 
M = |AIRg,,| 
Sensitivity. For each of the three 
types of gages, the sensitivity is 
Thickness-by-transmission 
dM 
Sz = aR = ToRQ mae #27 
Thickness-by-reflection 
dM 
oe Ta 
= |IsRgnl(Za/Zs)" — 1] use| 
Concentration-by-reflection 
SS a = I[)RgmkK(Z — Z,)ic& 
dc 
Precision. Two factors influence 
the precision of measurement: (1) The 
uncertainty in the meter reading 
associated with its inherent accuracy; 
and, (2) The fluctuation in the meter 
due to statistical fluctuations in the 
number of beta particles and the 
