Having made several sets of intensity measurements we are now
in a position to comment on the performance of the curved crystal
spectrometers as instruments for measuring relative intensities of
X -rays and soft X-rays. It must be admitted that the difficulties
of making such measurements accurately have proved greater than
was anticipated.In Chapter 3 it was seen that sensitivity calibration was in
practice a different procedure, very liable to error on account
of the "step by step" nature of the method adopted. This method
was adopted because of the absence of suitable sources to provide
a more reliable method. The comparison, in Chapter 5, of the RaD
-ray with the RaE L X -rays showed that the curve obtained was,
in fact, unreliable for this energy difference.However, the difficulties are not merely practical ones. Though the calibration curve may be unreliable for large energy
differences it does show that the sensitivity of the spectrometers
in their present form is rapidly varying in a non -uniform way over
the energy region in which they are most useful. Thus good
sensitivity -energy calibration is inherently difficult, quite
apart from the practical difficulty of finding suitable
calibrating lines.The problem, then, is to make the sensitivity more uniform
over the range for which the present spectrometers are useful.We should like, in the first place, to see if this can be done
without making any drastic alteration in the way in which they
are used (i.e. with an extended source and photographic recording).The sensitivity has to be increased at both the low and high
energy ends of the curve. The steep fall -off at low energies is
to a certain extent due to decreasing sensitivity of the emulsion
but the main cause is rapidly increasing absorption in the path
between source and detector. This could be reduced in two ways.
Firstly, by placing the whole apparatus in vacuum to eliminate
ahsorption in air and, secondly, by using a thinner crystal.
The reduction in crystal thickness must not be carried too far,
however, since reflections from the whole crystal thickness
contribute to the image. While reduction in intensity due to
this may be less than the gain due to smaller absorption for low
energies, the reverse is likely to be true for higher energies
where absorption is unimportant. The crystals at present
employed are 0.25 mm. thick, in which distance a line of energy
10 Rev is reduced by a factor of 7 by absorption, whereas one of
100 Rev is reduced by a factor of 1.01. If the crystal thickness
is halved the absorption factors become 2.6 and 1.005. This
means that for the 10 Rev line the nett gain in intensity would be 7/2.6 x
1/2
= 1.35 whereas the 100 Key would be reduced by half.
One must, therefore, ensure that the thickness is not reduced by
so much that the sensitivity gained at low energies is lost two - or three -fold at high energies. From the rough figures quoted
it can be seen that the thickness should not be reduced by a
factor of more than 2 if the instrument is to be used over the whole range of 0 - 100 Kev or so. Of course if higher energies
are not required then a further reduction could be tolerated.Assuming the intensity of the image to be proportional to
de⁻μᵈ where d = crystal thickness, and μ = total linear
absorption coefficient of the crystal for a given energy, then
the optimum thickness for that energy is 1/μ. The thickness
must be chosen to give the most uniform response over the range
required.The fall -off in sensitivity at high energies is due to
decreasing reflecting power of the crystal planes and decreasing
sensitivity of the emulsion. The reflecting power of the crystal
cannot be increased except by using a different crystal but not
much improvement is possible here. In any case if it were increased it would be increased for all energies and would not,
therefore, produce more uniform sensitivity.The total reflection from the crystal could of course be
increased by using a thicker crystal but here all the remarks
about reducing thickness apply in reverse. This would however
be profitable if the spectrometer were to be used in the range
50 - 100 Kev, say. Notice, however, that the optimum thickness
for 100 Kev is about 1.8 cm. and, even supposing a good enough
crystal could be obtained of such a thickness, it would be very
difficult to bend it with the required precision.The sensitivity of the plate could be increased by using a
thicker emulsion but for high energies the gain in sensitivity is
approximately proportional to the increase in thickness, and as G5 emulsions several hundred microns thick are very difficult to
process, not much can conveniently be gained in this way. In
addition, background stain is increased so that contrast between
a line and the background is not much improved. A more
promising possibility is to increase the absorption of the
emulsion by soaking it in a solution of a lead compound before
exposing - or by using specially manufactured emulsion containing
lead.To sum up, therefore, we can say that if a spectrometer is
to be used for intensity measurements over its entire useful range
(up to 120 Kev) then a little improvement can be expected by
evacuating the apparatus and impregnating the emulsion with lead.
If, however, we do not wish to cover the whole range at once, but
could divide it into a few smaller ranges (even two, from 0 - 25
Key, and from 25 Kev upwards) and could use a different
spectrometer for each energy band, then considerable improvement
might be expected by a judicious choice of crystal thickness. Fo
instance, the optimum thickness for 100 Kev mentioned above would
give about 3C times the intensity of the crystal at present used.For energies above 120 Key the instruments would have to be
used like Dumond's (1947) - with a line source on the focussing
circle and a counter with suitable collimation on the other side
of the crystal. The performance of such a spectrometer as regards
precision intensity measurements is beyond the scope of the present
research but it is quite evident that here again the sensitivity
must vary rapidly - though presumably continuously decreasing for
energies above 100 Kev or so
