2.1.  The LNHB determination of absorbed dose to graphite

The LNHB may realize absorbed dose using its primary standard in form of an originally designed graphite calorimeter [1], [2], [3]. The LNHB graphite calorimeter is associated with a homogeneous graphite phantom, consisting of set of well-caracterized discs. The LNHB graphite disc containing the ionization chamber in this work is of diameter $160\mathrm{mm}$ and $32\mathrm{mm}$ thick (“32a”). The disc contains a $10\mathrm{mm}$ diameter cavity in the radial direction into which a thimble-type ionization chamber is inserted. Note that measurements using this disc in its ‘normal’ orientation are corrected by the factor $k_{\text{asym}}$ for any change in ionization current measured with the disc (but not the transfer chamber) reversed. A photograph of the LNHB graphite phantom is shown in Figure 1.

Before the comparison, measurements were carried out at the LNHB, using the LNHB graphite phantom, in which an ionization chamber (NE 2571, serial number 642)² was calibrated in terms of absorbed dose to graphite at the reference depth of $5\mathrm{g}{\mathrm{cm}}^{-2}$. This chamber served as a transfer chamber in the comparison. The calibration factor and associated correction factors are listed in Table 1. The absorbed dose to graphite can hence be determined as

Figure 1 — Photograph of the LNHB graphite phantom placed in the LNHB Co-60 beam.

Table 1.  Calibration coefficient for the NE 2571 transfer chamber (serial number 642) of the LNHB, corrected for the asymmetry of the disc containing the chamber ($k_{\text{asym}}$), the polarity effect ($k_{\text{pol}}$) and ion recombination ($k_{\text{s}}$). The calibration coefficient is given for the reference conditions $p=101.325\mathrm{kPa}$, $T=20.0\mathrm{°C}$ and $\text{RH}=0\%$.

2.2.  The BIPM method to determine the absorbed dose to graphite

2.2.1.  Measurement principle

The BIPM absorbed-dose graphite calorimeter is described in [4], [5]. No electrical heating is employed, but rather the specific heat capacity of the graphite core $c_{p,\text{c}}$ has been determined previously in a separate experiment [6]. Quasi-adiabatic conditions are achieved by irradiating the core in a graphite jacket that is smaller than the radiation field, resulting in a relatively uniform dose distribution in the jacket. This arrangement is mounted in a PMMA³ support and vacuum container with graphite build-up plates to centre the core at the reference depth of $5\mathrm{g}{\mathrm{cm}}^{-2}$. The mean absorbed dose $D_{\text{c}}$ in the graphite core is determined using

${\mathrm{D}}_{\text{c}}=c_{p,\text{c}}\left(T\right)\cdot \Delta T\cdot k_{\text{imp}},$  (3)

where $\Delta T$ is the temperature rise in the core and $k_{\text{imp}}$ corrects for non-graphite materials in the core.

Two nominally identical parallel-plate ionization chambers with graphite walls and collector, similar in design to the existing BIPM standards for air kerma and absorbed dose to water, were fabricated for the determination of the absorbed dose to graphite from the measured absorbed dose to the graphite core. The first chamber (calo 3) is housed in a graphite jacket, nominally identical to the calorimeter jacket, and is irradiated in the same PMMA support and phantom arrangement. The second chamber (calo 5) is mounted in a large graphite phantom and irradiated with its centre at $5\mathrm{g}{\mathrm{cm}}^{-2}$. These measurement arrangements are represented schematically in Figure 2.

Figure 2 — Schematic representation of the three measurement situations giving rise to Monte Carlo calculations; the yellow arrow indicates the incoming beam. Two of the measurements are made in a common cubic PMMA phantom. a) The calorimeter is used in vacuum and $D_{\text{c}}$ is both measured and calculated. b) The graphite core is replaced by the transfer ionization chamber at atmospheric pressure. The ionization charge in graphite $Q_{\text{c}}$ is measured and the corresponding cavity dose $D_{\text{cav,c}}$ calculated. c) The ionization chamber is placed in a large graphite phantom. The ionization charge in graphite $Q_{\text{G}}$ is measured and the corresponding cavity dose $D_{\text{cav,G}}$ calculated. The mean absorbed dose to graphite $D_{\text{G}}$ in the absence of the chamber is also calculated for a graphite detector with the same dimensions as the cavity. It follows that a correction factor $k_{\text{rn}}$ is required for the radial non-uniformity of the radiation field over this dimension, measured for a homogeneous graphite phantom.

The method adopted by the BIPM combining calorimetric and ionometric measurements with Monte Carlo simulations to determine the absorbed dose to water is described in detail in [7] and has previously been applied for the determination of absorbed dose to water in [8], [9], [10]. In analogy, the absorbed dose to graphite $D_{\text{G}}$ can be evaluated as

$D_{\text{G}}=D_{\text{c}}\frac{Q_{\text{G}}}{Q_{\text{C}}}{\left(\frac{D_{\text{G}}}{D_{\text{C}}}\right)}^{\text{MC}}{\left(\frac{D_{\text{cav,c}}}{D_{\text{cav,G}}}\right)}^{\text{MC}}{k}_{\text{m}},$  (4)

where

$D_{\text{c}}$

measured absorbed dose to the graphite core;

$Q_{\text{c}}$

ionization charge measured when the transfer chamber is positioned in the graphite jacket, replacing the core;

$Q_{\text{G}}$

ionization charge measured when the transfer chamber is positioned in the graphite phantom;

${\left(\frac{D_{\text{G}}}{D_{\text{c}}}\right)}^{\text{MC}}$

calculated ratio of absorbed dose to the graphite phantom and to the graphite core using Monte Carlo simulations;

${\left(\frac{D_{\text{cav,c}}}{D_{\text{cav,G}}}\right)}^{\text{MC}}$

calculated ratio of cavity doses in the two graphite arrangements using Monte Carlo simulations;

$k_{\text{rn}}$

measured correction for radial non-uniformity in graphite.

In abbreviated form, $D_{\text{G}}$ can be expressed as

$D_{\text{G}}=D_{\text{c}}\frac{Q_{\text{G}}}{Q_{\text{c}}}{C}_{\text{G,c}}{k}_{\text{m}},$  (5)

where $C_{\text{G,c}}$ represents the total Monte Carlo conversion factor.

2.2.3.  BIPM Graphite Phantom

The BIPM graphite phantom was constructed in 1973 and consists of seven stacked graphite discs $300\mathrm{mm}$ in diameter. The density of the discs fabricated at that time varied within 1.2 % [14] but local density variations within one single disc were sometimes larger than 2 % [15]. For this reason, the centre of each disc was compared to a sample of known density to decrease the associated uncertainty contribution [16]. A cylindrical hole allowed the front graphite disc to house a primary standard parallel-plate ionization chamber. cf. Figure 3-1 and Figure 3-2.

Figure 3-1 — Photographs of the BIPM graphite phantom in 1973 where the first disc, facing the beam, has been removed (Fig. 11 in the photograph) to show the rear of the disc housing the parallel-plate ionization chamber (Fig. 12 in the photograph) [14].

Figure 3-2 — Photograph of the BIPM graphite phantom placed in the BIPM CisBIO Co-60 beam in 2011.

However, for the present comparison, a specially-adapted graphite disc was fabricated to house a newly-constructed parallel-plate ionization chamber {f} (calo5) with well-known cavity volume⁴. The dimensions of this “inner” disc {c} ($160\mathrm{mm}$ diameter, $32\mathrm{mm}$ thick) were chosen to be similar to the LNHB phantom centre plate with the aim of using it with both the BIPM and LNHB phantoms. To centre this disc in the BIPM phantom, a pre-existing graphite ring $30\mathrm{mm}$ in diameter {d}, and a $2\mathrm{mm}$ thick PMMA ‘spacer’ ring {e} were placed around the inner disc. The front face of the ionization chamber is recessed from the front face of the disc. To fill this space, a graphite cylinder {b} of well-known bulk density is placed so that it is coplanar with the front face of the disc.

2.3.  Configuration for the LNHB-BIPM Comparison.

To compare the determination of absorbed dose to graphite by the LNHB and the BIPM, two graphite phantom configurations were used. Firstly, the LNHB $160\mathrm{mm}$ diameter, $32\mathrm{mm}$ thick disc (“32a”) {g} was incorporated into the BIPM graphite phantom as described in 2.2.3, cf. Figure 4. Measurements were made in this configuration using the LNHB ionization chamber (NE 2571, serial number 642). Secondly, the BIPM $160\mathrm{mm}$ diameter, $32\mathrm{mm}$ thick disc was housed in the BIPM graphite phantom, cf. Figure 5. Measurements were made in this configuration using the BIPM ionization chamber (calo5). The bulk density and mass-thickness of the components are listed in Table 2.

Figure 4 — BIPM graphite phantom housing the LNHB graphite disc. The checked area corresponds to an outer graphite ring.

Figure 5 — BIPM graphite phantom housing the parallel plate ionization chamber ‘calo5’. The checked area corresponds to an outer graphite ring.

Table 2.  Components of the phantom assembly upstream the measurement plane. The density $\rho$ and mass thickness $d_{\text{m}}$ of graphite phantom components used in the comparison are given for the components in the centre of the beam.

component	symbol	$\rho$ / $\mathrm{g}{\mathrm{cm}}^{-3}$	$d_{\text{m}}$ / $\mathrm{g}{\mathrm{cm}}^{-2}$
{a} front disc in graphite		1.741	2.006
{b} BIPM small graphite cylinder		1.814	2.359
{c} BIPM inner graphite cylinder		1.814	1.438
{d} graphite ring		–	–
{e} PMMA ring		–	–
{f} BIPM ionization chamber, cf. Figure 5		1.834	1.015
{g} LNHB inner graphite cylinder, cf. Figure 4		1.837	2.939

The BIPM ionization chamber was placed in a so called ‘compensated’ configuration, i.e. the total mass thickness of graphite on the central beam axis from the front face to the centre of the chamber collector constitutes $4.998\mathrm{g}{\mathrm{cm}}^{-2}$ (nominal value: $5\mathrm{g}{\mathrm{cm}}^{-2}$). The mass thickness upstream of the LNHB ionization chamber was $4.945\mathrm{g}{\mathrm{cm}}^{-2}$, numerically close to the BIPM mass thickness, but in a so called ‘non-compensated’ configuration for which the chamber air cavity is considered to be graphite⁵. This results in slightly different SSDs⁶, as schematized in Figure 6.

Figure 6 — Illustration of the relative positioning of the BIPM (upper) and LNHB (lower) configurations. The red dashed line indicates the detector plane. The front faces are ‘misaligned’ by around $2\mathrm{mm}$.

3.1.  Measurement Results

The results obtained using the BIPM calorimeter and calo5 ionization chamber are listed in Table 3. The parameters ${\stackrel{.}{D}}_{\text{c}}$ and $I_{\text{c}}$ are the result of many repeat measurements in the small calorimeter phantom (Figure 2(a) and Figure 2(b), respectively) between 2009 to 2012 (including measurements made after the present comparison). The parameter $I_{\text{G}}$ represents the current measured for this comparison in the large phantom (Figure 5) at a mass thickness of $4.998\mathrm{g}{\mathrm{cm}}^{-2}$ in compensated mode. The difference between these conditions for $I_{\text{G}}$ and the non-compensated conditions used for the LNHB ionization chamber (Figure 4) is accounted for by the Monte Carlo factor $C_{\text{G,c}}$ in the table. Using Equation (5), the absorbed dose rate to graphite ${\stackrel{.}{D}}_{\text{c,BIPM}}$ in the CisBIO Co-60 beam at 2011-01-01 00:00:00 UTC and at the reference depth of $4.945\mathrm{g}{\mathrm{cm}}^{-2}$ (non-compensated) is determined as

with an associated relative standard uncertainty of 3.6 parts in 10³.

Table 3.  Measured or calculated parameters used to determine the absorbed dose to graphite in the BIPM Co-60 reference beam using the BIPM calorimeter.

The LNHB disc housing the transfer ionization chamber (serial number 642) was placed in the BIPM graphite phantom, replacing the corresponding BIPM disc (Figure 5). The results obtained for the LNHB transfer chamber at the BIPM are given in Table 4. A decay correction has been included to compare the data on 2008-01-01 (using the same Co-60 half-life for the LNHB and BIPM determinations). Further, the BIPM measurement system gives currents normalized to $0\mathrm{°C}$ and for a relative humidity of 50 %, giving rise to two supplementary corrections.

Table 4.  Measured or calculated parameters used to determine the absorbed dose to graphite in the BIPM Co-60 reference beam using the LNHB transfer chamber. The calibration coefficient $N_{\text{Dc}}$ for the transfer chamber is given for the reference conditions $p=101.325\mathrm{kPa}$, $T=20.0\mathrm{°C}$ and $\text{RH}=0\%$, and consequently the ionization current Ic measured at the BIPM is normalized to these conditions. Correction factors are applied for the asymmetry of the LNHB disc ($k_{\text{asym}}$), polarity ($k_{\text{pol}}$), recombination ($k_{\text{s}}$), radial non-uniformity ($k_{\text{rn}}$) and source decay ($k_{\text{decay}}$).

Using Equation (2), the LNHB determination of absorbed dose rate to graphite ${\stackrel{.}{D}}_{\text{c,LNHB}}$ in the CisBIO Co-60 beam at 2011-01-01 00:00:00 UTC and at the reference depth of $4.945\mathrm{g}{\mathrm{cm}}^{-2}$ (non-compensated) is determined as

with an associated relative standard uncertainty of 2.6 parts in 10³.

3.2.  Comparison Result and Discussion

From Equation (6) and Equation (7) the comparison result is derived as

with a combined relative standard uncertainty $u_{\text{c}}$ of 5 parts in 10³.

While the LNHB and BIPM standards agree at around 1.5 times the standard uncertainty of the comparison, there are several factors that complicate the comparison and might result in small differences between the determinations of absorbed dose to graphite.

The use of composite graphite phantoms containing a chamber holder, outer supporting rings and build-up plates with different bulk densities presents a particular difficulty for comparisons in terms of absorbed dose to graphite in the sense that, for a phantom and field size of given dimensions, the absorbed dose is not uniquely specified by the reference depth expressed in $\mathrm{g}{\mathrm{cm}}^{-2}$. One can see this qualitatively by recognizing that increasing the bulk density effectively increases the amount of material irradiated laterally and might therefore produce an effect similar to increasing the field size. The effect for a composite phantom is less easy to predict. Monte Carlo calculations were made at $5\mathrm{g}{\mathrm{cm}}^{-2}$ for a homogeneous phantom with bulk density $1.78\mathrm{g}{\mathrm{cm}}^{-2}$ and for a composite phantom where the first $2\mathrm{g}{\mathrm{cm}}^{-2}$ of build-up is a plate with density $1.74\mathrm{g}{\mathrm{cm}}^{-2}$ (similar to disc {a} in Figure 4 and Figure 5) and the chamber holder (making up the next $3\mathrm{g}{\mathrm{cm}}^{-2}$ and beyond) has density $1.84\mathrm{g}{\mathrm{cm}}^{-2}$ (similar to disc {g} in Figure 4). These show the absorbed dose for the composite phantom to be higher by 0.3 %, a surprisingly large effect for the realistic variations in bulk density simulated.

Furthermore, the mean bulk density measured (and simulated) for a given graphite component might not be a sufficiently good representation, especially if local inhomogeneities exist and in particular for the upstream graphite components close to the beam axis. The fact that the LNHB and BIPM transfer chambers are very different in cross section might also be relevant (aside from the first-order effect correct by $k_{\text{rn}}$). The magnitude of these effects and the associated uncertainty are difficult to estimate but might be possible to evaluate using a similar technique to that of Boutillon [16]. These effects represent a significant limitation when measuring absorbed dose to graphite.

To best take account of this in the present comparison, the BIPM absorbed-dose conversion from $D_{\text{c}}$ (the measured dose to the calorimeter core in its small phantom, i.e. jacket) to $D_{\text{G}}$ (the dose estimate used for the comparison), was calculated for the precise conditions of irradiation of the BIPM and LNHB chambers. In other words, the cavity dose $D_{\text{cav,G}}$ was calculated for the composite phantom used for the BIPM chamber, while $D_{\text{G}}$ was calculated for the phantom used for the LNHB transfer chamber (replacing the chamber itself by graphite of the same density as the chamber holder). By adopting this method, any remaining errors are expected to be below 0.1 % and an additional uncertainty of this value is included. Note that by using this method, slight deviations of the chamber depths from $5\mathrm{g}{\mathrm{cm}}^{-2}$ are taken into account and no depth corrections need be applied.

A BIPM.RI(I)-K6 comparison of calorimetric determinations of absorbed dose to water in accelerator photon beams was carried out between the LNHB and the BIPM in March 2012 [18]. For these beams, the BIPM standard is the same graphite calorimeter; however, for the LNHB the high-energy standard is a combination of results based on graphite and water calorimeters. The present result is in consistency with the results of the comparison between the two laboratories at $6\mathrm{MV}$ and $20\mathrm{MV}$, determined at 0.995 and 0.994, respectively, with a combined standard uncertainty of 5 parts in 10³. Meanwhile, the absorbed dose to water determined using the BIPM ionometric standard has been compared in the BIPM Co-60 reference beam with that determined using the BIPM graphite calorimeter system. The ratio of these determinations has been evaluated as 0.9995(25) [19]. As a consequence, the result presented in this report is also consistent with the result of the BIPM.RI(I)-K4 [20].