Integrating Dosimeters III

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Integrating Dosimeters III

• Calorimetric Dosimetry

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Calorimetric Dosimetry

• The measurement of the temperature rise in
  calorimetric dosimeters comes closest of any
  method to providing a direct measurement of the
  full energy imparted to matter by radiation
• Only relatively small corrections for thermal
  leakage and for chemical reactions are necessary

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Temperature Measurement

• In principle any kind of thermometer can be
  applied in a calorimeter if the temperature
  change is large enough to measure with sufficient
  accuracy and precision
• In practice only thermocouples and thermistors
  are sufficiently sensitive and small thermistors
  are usually preferable because of their greater
  sensitivity

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Temperature Measurement (cont.)

• The temperature increase per unit of absorbed
  dose to the material in the calorimeters
  sensitive volume depends on its thermal capacity,
  which is usually expressed in cal/g C or J/kg C
• The exact value of the calorie (i.e, the energy
  required to raise 1 g of water 1 C) depends upon
  the temperature of the water to which it refers
• Usually thermal-capacity (or specific-heat)
  tables assume the value of the calorie for water
  at 15 C hence 1 cal 4.185 J, and 1 cal/g C
  4185 J/kg C

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Temperature Measurement (cont.)

• For a sensitive volume containing a material of
  thermal capacity h (J/kg ?C), mass m (kg), and
  thermal defect ?, and that absorbs E joules of
  energy, the temperature increase is given by
• where D is the average absorbed dose (Gy) in
  the sensitive volume

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Temperature Measurement (cont.)

• Thus a measurement of D does not require
  explicit knowledge of m if h is known
• The thermal defect ? is the fraction of E that
  does not appear as heat, due to competing
  chemical reactions, if any
• ? is negative for exothermic reactions
• A few typical values of h are given in the
  following table

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Thermal capacity of several calorimetric materials
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Temperature Measurement (cont.)

• For example, in Al a dose of 1 Gy causes a
  temperature increase of 1.12 ? 10-3 ?C
• To measure this temperature rise with 1
  precision would require a thermometer capable of
  detecting temperature changes of the order of 10
  ??C

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Temperature Measurement Thermocouples

• Thermocouples typically have temperature
  coefficients of 40 70 ?V/?C
• A temperature change of 10 ??C would then give a
  potential change of (4 7) ? 10-10 V
• This is too small to detect with available
  instruments, such as a nanovoltmeter
• Increasing the dose to 100 Gy would cause a
  temperature rise of 0.112 ?C, requiring detection
  of (4 7) ? 10-8 V for 1 precision, which can
  be accomplished with a nanovoltmeter

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Thermocouples (cont.)

• Thermocouples are generally found to be most
  useful in calorimeters where large doses (gt 10
  Gy) are given, usually in a short enough time
  period for thermal leakage to be negligible
  (i.e., under adiabatic conditions)
• Thermocouple sensitivity can be multiplied by
  constructing a thermopile, consisting of a number
  of thermocouples in series, but this is usually
  not practical for calorimetric dosimetry because
  of the increase in perturbation of the medium and
  the number of thermal leakage paths

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Temperature Measurement Thermistors

• Thermistors can be obtained in sized comparable
  to thermocouples
• They are semiconductors made of metallic oxides
  and other constituents that are usually not
  specified by the manufacturer
• They exhibit negative temperature coefficients of
  the order of several percent per C at room
  temperatures, increasing in negative coefficient
  with decreasing temperature, as shown in the
  following diagram

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A typical resistance-vs.-temperature curve for a
thermistor. The slope is the temperature
coefficient of resistance at any temperature.
For example, the slope dR/dT at 20 C, shown by
the dashed line, is ?-120 ?/?C or 3.7/?C.
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Thermistors (cont.)

• The resistance of a thermistor at room
  temperature is typically 103 105 ?, which can
  be conveniently measured with great precision and
  accuracy by a Wheatstone bridge as shown in the
  following diagram
• The bridge null detector must be sensitive enough
  so that the power dissipated in the thermistor is
  negligible compared to the radiation heating

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A Wheatstone bridge circuit for measuring the
resistance of a thermistor in the sensitive
volume (or core) of a calorimetric dosimeter.
When Rx is set to produce a null current
reading,Rc/Rx R1/RJ, from which Rc can be
determined.
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Calorimeter Design

• We will consider three general types of
  radiometric calorimeter designs, depending on
  whether absorbed dose in a reference medium,
  energy fluence in a radiation beam, or power
  output of a radioactive source is to be measured

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Calorimeter Design Absorbed-Dose Calorimeters

• An absorbed-dose calorimeter must have a
  sensitive volume that is small compared to the
  penetrating ability of the radiation and is
  thermally insulated from its surroundings to the
  extent necessary to attain acceptably small
  levels of thermal leakage
• The sensitive volume (often called the core) is
  made of a thermally conductive material identical
  to, or simulating, a medium of dosimetric
  interest (e.g., graphite, tissue-equivalent
  plastic, or silicon), and contains a temperature
  sensor of negligible mass, usually a thermistor

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Absorbed-Dose Calorimeters (cont.)

• The core is surrounded by a shell (jacket or
  mantle) of the same material to provide
  charged-particle as well as thermal equilibrium
• If the thermal capacity and thermal defect of the
  core material are known, if the temperature
  sensor is correct, and if the thermal leakage is
  negligible, then the calorimeter can be operated
  adiabatically, without any energy calibration, to
  measure the average absorbed dose in the core by
  application of
• The mass of the core need not be known in that
  case

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Absorbed-Dose Calorimeters (cont.)

• An example of such a calorimetric dosimeter that
  does not require calibration is shown in the
  following diagram
• This was designed to measure the dose deposited
  in silicon by intense single pulses of
  penetrating x rays
• The core was a pea-sized sphere of high-purity
  silicon of known thermal capacity, enclosed in an
  equilibrium-thickness shell of the same material,
  which was insulated from the surrounding air by a
  shell of styrofoam

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An absolute adiabatic silicon calorimetric
dosimeter of simple spherical design for
measuring the absorbed dose to silicon from
intense single pulses of penetrating x-rays
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Photograph of the complete dosimeter, with scale
in inches
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Absorbed-Dose Calorimeters (cont.)

• The core, containing a very small calibrated
  thermistor, was centered in a spherical void by
  four conical points of silicon projecting from
  the inside of the shell
• Since the radiation pulse raises the temperature
  of the shell almost instantaneously ( 10-7 s) by
  the same amount as the core, the heat-loss rate
  from the core was found to be initially
  negligible even with evacuating the surrounding
  gap, thus permitting the very simple design shown

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Absorbed-Dose Calorimeters (cont.)

• Arguably, to avoid the complication of including
  an ohmic heater in the core and the need to know
  the mass of the core, one should build the core
  and surrounding shell from a material that has an
  accurately known thermal capacity
• Classical methods are available for measuring the
  thermal capacity of any given sample of material
  before it is incorporated into a calorimetric
  dosimeter

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Absorbed-Dose Calorimeters (cont.)

• The conventional practice has been to design an
  ohmic heater into the core, which can then be
  made of a material (or materials) for which the
  thermal capacity is only approximately known in
  advance
• Electrical energy E results in a temperature rise
  ?T in the core, thus allowing the average value
  of h for the materials making up the core to be
  determined if its total mass is known

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Absorbed-Dose Calorimeters (cont.)

• The following diagram is a schematic
  representation of this kind of absorbed dose
  calorimeter
• The core is surrounded by two or more thermally
  insulated layers of the same material as the
  core, and the entire assembly is usually
  surrounded by a constant-temperature environment
• Each layer may contain a thermistor and/or an
  ohmic heater, thus allowing measurement and
  control of the temperature environment of the core

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Schematic arrangement of a typical absorbed-dose
calorimeter containing several concentric thermal
bodies. Each may include thermistors and/or
ohmic heaters for temperature measurement and
control
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Absorbed-Dose Calorimeters (cont.)

• Dosimetry by means of such an apparatus is
  generally complicated and time-consuming
• Some simplifications have been devised to shorten
  the time necessary to reach thermal equilibrium
  before an exposure run and automatically correct
  for heat leakage from the core to the jacket
• A modification in the Wheatstone bridge results
  in the measurement of the ?T that would have
  occurred in the core due to electrical heating if
  none of the heat had leaked into the jacket

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Modified Wheatstone bridge for measuring the core
jacket temperature rise, assuming that the two
thermistors are identical in characteristics, and
that the jacket has the same mass and is made of
the same material as the core
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Absorbed-Dose Calorimeters (cont.)

• This requires that the jacket have the same mass
  and be made of the same material as the core, and
  that their two thermistors must be virtually
  identical with respect to dR/dT as well as
  resistance
• When the bridge is initially balanced,
• where RJ is the resistance of the thermistor
  in the jacket, and the other resistances are
  identified as in the earlier Wheatstone bridge
  schematic

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Absorbed-Dose Calorimeters (cont.)

• After electrical heating of the core and
  readjusting Rx by the small amount ?Rx necessary
  to balance the bridge again
• Assuming that R1 Rx RJ Rc, we have
• in which for small changes ?RJ and ?Rc, the
  last term is vanishingly small

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Absorbed-Dose Calorimeters (cont.)

• This equation means that ?Rx has the same value
  whether all the electrical energy stays in the
  core or some leaks to the surrounding jacket
• Thus heat leakage out of the core during the
  electrical calibration is automatically corrected
  for, provided that thermal leakage from the
  jacket into the shield is negligible
• This can be assured by feedback control of the
  shield to maintain it at the same temperature as
  the jacket

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Absorbed-Dose Calibration (cont.)

• Before exposing the calorimeter to radiation, the
  Wheatstone bridge circuit is to be switched back
  to the original circuit, with RJ RJ
• If the radiation is sufficiently penetrating, the
  core, jacket, and shield will be heated equally
  by the uniform dose
• Supplementary electrical energy can be supplied
  to the shield to compensate for its thermal
  losses
• Heat losses from the core can again be made
  negligible, so that the ?T measured in the core
  can be correctly interpreted in terms of the core
  jacket ?T that was observed during the
  electrical calibration

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Calorimeter Design Energy-Fluence Calorimeters

• An energy-fluence calorimeter contains a core,
  usually consisting of a cylindrical piece of
  dense material such as lead or gold, large enough
  to stop an incident beam of radiation
• The geometry is shown schematically in the
  following diagram

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Schematic arrangement of an energy-fluence
calorimeter
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Energy-Fluence Calorimeters (cont.)

• The core is suspended by nylon strings in an
  insulated vacuum chamber, sometimes adjacent to a
  twin core that serves as a control to determine
  thermal leakage
• Because of the size of the core, more than one
  thermistor may be necessary to sample the
  temperature adequately, and the heater should be
  designed to distribute the heat uniformly
• The high-Z core may require a significant
  backscattering correction

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Energy-Fluence Calorimeters (cont.)

• h can be determined through electrical
  calibration as discussed before
• The energy fluence of the radiation beam passing
  through the aperture of area A is given
  (neglecting ?) by

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Calorimeter Design Power Output of a Radioactive
Source

• A power-output calorimeter has a cup-shaped core
  into which a radioactive source can be inserted
  for measurement
• The walls of the core are made thick enough to
  stop all the radiation to be measured from
  escaping
• The usual method for electrical calibration can
  be used to determine h

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Power Output (cont.)

• Then the power output (W) is given by
• where temperature rise ?T (?C) occurs in the
  core of mass m (kg) during the time interval ?t
  (s), and ? has been neglected

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Advantages of Calorimeters

• They can be made absolute, either intrinsically
  or by means of electrical-heating calibration.
• The measurement of temperature rise comes closest
  of any dosimetric technique to being a direct
  measurement of the energy involved in the
  absorbed dose. Only relatively small exothermic
  or endothermic chemical reactions, and thermal
  leakage, must be corrected for, and these are
  often negligible.

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Advantages (cont.)

• Almost any absorbing material, solid or liquid,
  can be employed in the calorimeter sensitive
  volume, so long as it is reasonably conductive
  thermally and has a known thermal defect
• Calorimeters are inherently dose-rate-independent
  under adiabatic conditions, and become more
  convenient to use as the dose-rate increases
  because thermal leakage during dose delivery
  becomes negligible. At high dose rates, where
  other dosimeters show saturation effects,
  calorimeters are at their best.

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Advantages (cont.)

• Calorimeters add up the energy contributions in
  the sensitive volume from different types of
  radiations (e.g., neutrons and ? rays) with
  weighting factors of unity, neglecting
  differences in thermal defect.
• Calorimeters have no LET dependence (neglecting
  minor differences in thermal defect, if any),
  since ionic recombination is irrelevant to the
  temperature rise.

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Advantages (cont.)

• Calorimeters are relatively stable against
  radiation damage at high doses the thermistor
  (if used as the temperature sensor) is usually
  the limiting factor in this respect.

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Disadvantages of Calorimeters

• Temperature rises to be measured are typically
  very small, usually only a minute fraction of a
  degree, which limits calorimetry to relatively
  large doses.
• Thermal insulation, and instrumentation for
  thermal control and measurement, often make the
  calorimeter apparatus bulky and difficult to
  transport and set up. This limits the kinds of
  situations to which calorimetry is usually
  applied to calibration of other dosimeters.

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Disadvantages (cont.)

• For low dose rates, thermal leakage in and out of
  the calorimetric sensitive volume limits the
  accuracy and precision available.
• Some materials undergo radiation-induced
  endothermic or exothermic reactions which cause a
  difference between the integral dose and the
  energy available to heat the sensitive volume.
  In A150-type TE plastic about 4 of the absorbed
  dose goes to an endothermic reaction instead of
  heat.

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Conclusions

• The present brief introduction to calorimetric
  dosimetry deliberately errs on the side of
  simplicity, for two reasons
• In the simplest applications at high dose or
  fluence rates, especially for intense single
  pulses, adiabatic operation is well approximated,
  ?T is large, and calorimetry becomes the method
  of choice
• In the difficult applications of calorimetry
  (i.e., at low dose rates), the problems of heat
  leakage and temperature drift are too complicated
  to be dealt with adequately in an introductory
  course