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\begin{document} 
\title{Characterizing Superheated Halocarbons for use as a Radiation Detectors}
\author{ Dagnachew W. Workie \\
	 \\
         Department of Physics\\ 
         University of Cincinnati \\
         Cincinnati, Ohio 45221\\[1em]}
 
\date{March 05, 2002 }
\maketitle
\begin{abstract}

	A variety of superheated halocarbons of different chemical compositions and boiling points have been studied in the past two decades. Halocarbons have been characterized in terms of their sensitization to radiation energy  and temperature. The vaporization curves obtained allows us to predict the radiation responses threshold of different halocarbons emulsions using a single parameter called reduced superheat. That is, by appropriate choice of the degree of superheat and chemical composition of the emulsions, a selective detection can be achieved of different directly and indirectly ionizing radiations.  In particular, halocarbons with moderate degree of superheat can be used for neutron detection since they are only nucleated by energetic heavy ions such as produced by fast neutrons, Halocarbons with an elevated degree of superheat have proven useful in the detection of sparsely ionizing radiations, such as photons and electrons. This papers reviews the basic selection of halocarbons by studding their sensitization and response curves.\
\\[1em]
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\section{Introduction}

 The ``superheated emulsions'' system or superheated drop detectors (SSD) was originally proposed in 1979 by R. E. Apfel, at Yale University. These detectors consists of uniform dispersions of over-expanded halocarbons and/or hydrocarbon droplets suspended in a complaint material such as a polymeric or an aqueous gel\cite{refA}. Superheated emulsions operate like the bubble chamber, long used in high energy particle physics\cite{refB}. Charged particles liberated by radiation interactions nucleate the phase transition of superheated liquid and generate detectable bubbles.  Superheated emulsions are continuously sensitive since the liquid is kept in steady-state superheated conditions, i.e,  above their boiling point. 

	A variety of superheated  emulsions  containing halocarbons of  different chemical compositions and boiling points have been characterized in terms of their sensitivity to ionization radiations\cite{refC, refD}. These studies  confirmed some recent theoretical models\cite{refE, refF, refG}. It was shown that bubble nucleation only occurs when sufficient energy is deposited within an extremely localized region of a  superheated drops in order to nucleate their vaporization. Charged particles (i.e, primary ions from charged beams, recoils from neutron beams and electrons from photon/electron beams) generate trails of microscopic vapor cavities inside the droplets, but those exceeding a minimum critical size can overcome the surface tension in the drops and develop in to babbles. When this size is reached, the expansion becomes irreversible and the whole droplet suddenly evaporates. The amount of energy and the critical bubble size which are necessary for bubble nucleation depend on the composition of the emulsions (halocarbons) and on its degree of superheat. Halocarbons with a moderate degree of operating temperature and boiling point , can be used in neutron dosimetery and spectroscopy since they are only nucleated by energetic heavy ions such as those produced by fast neutrons. More recently, halocarbons with an elevated degree of supearheat have been utilized to produce superheated drop detectors which nucleate with much smaller energy deposition. These detectors have proven useful in the detection of low energy transfer (LET) radiations, such as photons and electrons \cite{refH}. In this paper  basic review of selection of halocarbons by studding their sensitization and response curves of different halocarbons is presented.
\section{ Superheated Halocarbons and Mechanism of Bubble Formation}
	A fluid is superheated ( or over expanded ) when it is in liquid form at a temperature and pressure values corresponding to the vapor region in the phase diagram (Fig.1a). Due to the presence of high number of microparticles  and /or gas pockets which are normally present at the interface with the container surfaces these metastable state is fragile and short-lived. The microparticles and gas pocket acts as seeds for the phase transition and are called ``heterogeneous nucleation'' sites. However, a liquid may be kept in steady state superheated condition by a process called emulsification\cite{refI,refJ}. In this process the liquid is fractionated  in to droplets and dispersed in an emmiscible host fluid. These procedure creates perfectly smooth spherical interfaces, free of of nucleating impurities or irregularities. In order to achieve a steady-state, the drops must be moderately superheated , i.e, present a relatively small difference between their operating temperature and boiling point. And of course the  emulsifier material must be clean and de-gassed, i.e, free of heterogeneous nucleation sites. Vials containing homogeneous  and stable suspensions of $ 10^{4}-10^{5}$ droplets of 10-100 $\mu m $ diameter are currently manufactured\cite{refK,refL}. Numbers, size and composition of the droplets can be varied in the formation of the detectors, and this permits a wide range of application.
\begin{figure}[htb]

\centerline{\includegraphics*[height=2in]{Figure1.ps}}

\caption[]{\em{ (a) Phase diagram of a material\cite{refM}. (b) Bubble formation steps in superheated emulsion\cite{refN} }}
\end{figure}
	
	The passage of charged particles in the supperheated emulsion generate trails of microscopic vapor cavities inside the droplets. When these cavities exceed a critical size they keep growing  until the whole droplet evaporates (Fig.1b). On the contrary, sub-critical cavities collapse back to the liquid phase under the action of external pressure and surface tension. The energy and the critical size that are necessary for bubble nucleation depend on the compositon and the degree of supearheat of an emulsion (halocarbon). The metastable droplets vaporize, creating detectable bubbles when they are nucleated by the energy deposited through radiation interaction. 

	Currently there is no universally accepted quantitative theory but there is a general agreement on this qualitative description of the nucleation process. Semi-empirical models of the detection process have been developed\cite{refE, refF, refG} based on the thermodynamics of the isothermal spontaneous nucleation modified according to the ``thermal spike'' theory\cite{refO}. The latter suggests that when a charged particles slow down crossing a liquid its kinetic energy is transferred as heat, creating trails of vapor cavities. In this theory, it is further assumed that embryonic bubbles can grow indefinitely if they exceed a critical radius, $ R_{c}$. This critical radius is derived from the condition of mechanical equilibrium between surface tension and pressure difference through the walls of the cavity:\
\begin{equation}
R_{c}=\frac{2\sigma}{(P^{''}-P^{'})}\sim \frac{2\sigma}{[(P_{s}-P^{'})(1-\frac{\upsilon ^{'}}{\upsilon^{''}})]} ,
\end{equation}
where $\sigma $ is the surface tension, P is the pressure $(P_{s}$ is saturation value), $ \upsilon $ is the specific volume , while $^{ '}$ and $^{''}$  denote the liquid and vapor phases. For bubble chambers the energy, $W_{o}$,   required in the radiation-induced nucleation in the supperheated  liquids is give by the semi-empirical formula\cite{refP}:\
\begin{equation}
W_{o}=\frac{16\pi\sigma^{3}}{3(P_{s}-P^{'})^{2}(1-\frac{\upsilon ^{'}}{\upsilon ^{''}})^{2}}[1 + \frac{2\Delta H}{(P_{s}-P^{'})(1-\frac{\upsilon ^{'}}{\upsilon ^{''}})}-3\frac{T}{\sigma}\frac{d\sigma}{dT}] ,
\end{equation}
where $\Delta H$ is the latent vaporization heat of the fluid and other symbols are as defined in the previous equation. The first factor represents the energy required for the isothermal spontaneous nucleation of a critical size bubble in equilibrium with the surrounding ( a process called homogeneous nucleation)\cite{refM}. The second factor in the square bracket  expresses  the additional work required when the liquid is not superheated enough to homogeneous nucleation, and vaporization is hetrogeneously initiated by ionizing particles. The  assumptions underlying this factor are that the energy is available in the form of heat and that the evaporation process is initially adiabatic, which is reflected by the last term.\

 Irreversible energy loss, $W_{irr}$, occurs during the formation of the bubble. This is generated by the contrasting action of the viscous forces, and the transfer of the kinetic energy to the liquid by the motion of the vapor wall, to the emission of sound waves. The proposed expression for the kinetic energy and viscous-force loss is \cite{refQ}:\
\begin{equation}
W_{irr}=2\pi{\rho^{'}} R^{3}_{c}\dot{R}^{2},
\end{equation}
where $\dot{R}=\frac{4D}{R_{c}}(\frac{\rho ^{'}}{\rho ^{''}})^{1/3}$  the vapour-wall velocity with  $D=\frac{k}{\rho ^{'}c_{p}}$  is the thermal diffusivity of the liquid, $k$ thermal conductivity and $c_{p}$ specific heat. The total vaporization energy is therefore $ W_{tot}=W_{o}+W_{irr}$.\

A unified parameterization of the properties of supearheated emulsions based on the light halocarbons called 'reduced supreheat'' has been proposed\cite{refR}. the reduced superheat represents the normalized operating point of an emulsion within the temperature range corresponding to the methastable superheated state and is defined:
\begin{equation}
s = \frac{(T-T_{b})}{(T_{c}-T_{b})}
\end{equation}
At a given pressure, the boiling temperature $T_{b}$ is the temperature above which a fluid becomes either a vapor or a superheated liquid. Therefore, this temperature represents the lower limit of supearheat emulsion. The critical temperature, $T_{c}$, is the value above  which the liquid phase can no longer exist. 
\section{Response of Halocarbon Emulsions to Neutrons}

Superheated emulsions can detect both charged particles and neutrons. In the latter case bubble formation is induced by highly  ionizing charged particles generated through neutron interactions inside  or next to the superheated droplets. The response of a variety of emulsions to neutrons of different energies has been investigated as a function of operating temperature ( i.e. , degree of superheat)\cite{refS}.
\subsection{Response to Fast Neutrons}
Experiments with a standard monoenergetic neutron beams in the 25 keV to 19 MeV energy range has been done to study the fluence response of different halocarbons emulsions. The fluence response of dichlorotetrafluoroethane (R-12), octafluorocyclobutane (C-318), monochlodifluoroethane (R-142B) and dichlorotetrafluoroethane (R-114) emulsions are shown in Fig.2. We can observe that the higher the degree of the superhet of the liquid (see Table I),  the lower the minimum energy the neutrons ( or rather the secondary charged particles) must impart to the drops in order to nucleate their vaporization. This means the emulsions present thresholds at a particular energies followed by a fairly flat response at the higher energies. This observation is valid for a variety of pure halocarbons, such as fluorocarbons, chlorfluorocarbons, and halogenated hydrocarbons. Sealed bubble detectors present a similar behavior with temperature\cite{refT}
\begin{figure}[htb]

\centerline{\includegraphics*[height=2.5in]{Figure2.ps}}

\caption[]{\em{Fluence responses of superheated emulsions of dichlorotetrafluoroethane (R-12), octafluorocyclobutane (C-318), monochlodifluoroethane (R-142B) and dichlorotetrafluoroethane (R-114), measured as a function of neutron energy at $ 25^{o}C(\bigcirc), 30^{o}C() , 35^{o}C(\diamondsuit) and 40^{o}C(\triangle)$ \cite{refM}}}
\end{figure}
\begin{table}[htb]

\centerline{\includegraphics*[height=2in]{TableI.ps}}

\caption[]{\em{Selection of halocarbons employed in superheated emulsions\cite{refB}}}
\end{table}

\subsection{Response to Slow Neutrons}
	Sufficiently superheated halocarbon droplets containing chlorine may be nucleated by the products of  $ ^{35}Cl(n,p)^{35}S$ capture reaction. Dichlorofluoromethane (R-12) emulsions at room temperature are found to be sensitive to thermal and intermediate neutrons. A question of great relevance to bubble nucleation thermodynamics was whether all chlorocarbons become sensitive to thermal neutrons at a particular temperatures, and whether these temperatures correspond to a single value of the reduced superheat. Experiments with slow thermal neutrons have been done with emulsions of dichlorotetrafluoroethane (R-12), monochodifluoroethane (R-142B) and dichlorotetrafluoroethane (R-114). The experiments confirmed that all chlorocarbons become sensitive to thermal neutrons when they are raised to sufficiently high temperature (Fig.3a). And the sensitization of all chlorocarbons corresponds to a reduced superheat $ s\geq 0.33$, above which the response increases with a sigmoid trend and approaching saturation for $s\geq 0.45$ (Fig.3b).
\begin{figure}[htb]

\centerline{\includegraphics*[height=2in]{Figure3.ps}}

\caption[]{\em{Thermal neutron sensitization of superheated emulsion of dichlorotetrafluoroethane (R-12), monochodifluoroethane (R-142B) and dichlorotetrafluoroethane (R-114) , versus (a) operating temperature (b) reduced temperature\cite{refM}}}
\end{figure}

\section{ Photon sensitization of Halocarbon emulsions}
	When they are sufficiently superheated, halocarbon emulsions are able to detect low LET radiations, namely photons via their secondary electrons. Photon sensitization curves have been determined for different superheated halocarbon emulsions. The photon sensitization curves measured for the different superheated emulsions irradiated with a $ ^{137}Cs\qquad {\gamma} $ ray sources are shown in Fig. 4a.
\begin{figure}[htb]

\centerline{\includegraphics*[height=2in]{Figure4.ps}}

\caption[]{\em{Photon sensitization of superheated emulsions based on various halocarbons as a function of (a) temperature, and (b) reduced superheat. The vertical line represent the temperature limits of the halocarbons \cite{refF}}}
\end{figure}

For each emulsions, the response arises at a sensitization temperature termed $T_{\gamma} $ above which the count rates increase rapidly as a function of temperature. The halocarbons with a lower degree of superheat (see Table I) present higher sensitization temperatures. For each material, the measured homogeneous nucleation point or temperature limit , $ T_{l}$, is also indicated in Fig.4 as a vertical line which is gradually approached by the count rates. The homogeneous nucleation temperature is determined for each superheatd emulsion by increasing their temperature until bubble vaporization occurred in a low radiation-background environment.\
	When the photon sensitization data are plotted against reduced superheat (Fig.4b), results for all emulsions follow a single curve indicating the photon sensitization arises for $ S_{\gamma}={(T_{\gamma}-T_{b})/(T_{c}-T_{b})}\geq 0.51 $, i.e, immediately above the mid point between boiling and critical temperatures of the halocarbons. This finding appears to have general validity for all light halocarbons since it spans fluorocarbons, chlorofluorocarbons, and halogenated hydocarbons\cite{refH}. Fig. 4b shows also that the homogeneous nucleation temperatures correspond to a singe limit value of the reduced supearheat $ S_{l}={(T_{l}-T_{b})/(T_{c}-T_{b})}\geq 0.65 $. It is not surprising that that all data approach a single limit, since the light halocarbons employed  in the superheat emulsions are a class of fairly similar fluids.
\section{Conclusions}
Total vaporization energies, $W_{tot}$, and the critical radii, $R_{c}$, have been computed for different halocarbons for which a constant set of thermodynamic parameters is available \cite{refU}. When results are plotted versus reduced superheat, all data fall on a single curve. On the contrary, data are scattered if plotted against conventional thermodynamic parameters such as reduced temperature $ t	=T/T_{c}$. The vaporization curve allows us to predict the radiation response threshold of the different emulsions using a single parameter,(i. e.,  reduced superheat). The reduced superheat concept allows us to predict fast neutrons  detection threshold sensitizations to thermal neutrons, and also sensitization to photons. Superheated emulsions are best know for their ability to detect neutrons and discriminate sparsely ionization radiations, such as photons and electrons. That is, by appropriate choice of the degree of superheat and composition of the emulsions, a selective detection can be achieved of different directly and indirectly ionizing radiation. Halocarbons with a moderate degree of superheat , i.e., a relatively small difference between their operating temperature and boiling point can be used in neutron dosimetery and spectrometr. For example,  dichloroterafluoroethane (R-114) and octaflurocyclobutane (C-318) require the deposition of hundreds of keV per $\mu m$ and are nucleated by high-energy heavy ions, e.g. the recoils generated by fast neutrons inside or next to the superheated drops. They are completely insensitive to photons and are ideal for fast neutron spectrometry as well as for the detection of charged particles  above specific energy and linear energy transfer (LET) values.  Emulsions of dichlorofluoromethane (R-12) are sensitive to thermal and intermediate neutrons.  On the other hand, halocarbons with an elevated degree of superheat have been utilized to produce superheated drop detectors which nucleate with much smaller energy deposition. These detectors have proven useful in the detection of low linear energy  transfer (LET) radiations, for example,  monochloropentafluorothane (R-115) are sensitive to  electrons (or, photons through their secondary electrons).
\pagebreak
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\begin{thebibliography}{99}
\bibitem{refA} R.E. Apfel, ``The superheated detector,'' Nucl. Instrum. Methods 162, 603-608 (1979).
\bibitem{refB} D. A. Glasser, Phys. Rev. 87 (1952)665.
\bibitem{refC} F. d'Errico and W. G. Alberts, and M. Mtzke, `` Advances in superheated drop (bubble) detectors,'' Radiat. Prot. Dosim. 70(1-4)103-108 (1997).
\bibitem{refD} F. d'Errico and W. G. Alberts, ``Superheated drop (bubble) detectors and their compliance with ICRP 60.'' Radiat. Proct. Dosim. 54(3-4) 357-360 (1994). 

\bibitem{refE}R. E. Apfel, Y. Y. Sun and R. Nath, ``Transient thermal and mechanical response of water subject to ionizating radiation.'' Radiat. Res. 131, 124-132 (1992).
\bibitem{refF} F. d'Errico, R. Nath, and R. Nolte, ``A model for photon detection and dosimetry with superheated emulsions,'' Med. Phys. 27(2), 402-409(2000).
\bibitem{refG}C. D. West, ``Cavitation buuble nucleation by energetic particles,'' Report ORNL/TM -13683, ORNL, Oak Ridge, TN, 1998.
\bibitem{refH} F. d'Errico, ``fundamental properties of superheated drop (bubble) detectors,'' Radiat.Prot. Dosim. 83, 55-62 (1999).
\bibitem{refI}R. E. Apfel, Nucl. Instr. and Meth. 162(1979) 603.
\bibitem{refJ}H. Ing, H. C. Birnboim, Nucl. Tracks Radiat. Meas. 8(1-4)(1984)285.
\bibitem{refK}F. d'Errico and W. G. Alberts, M. Matzke, Radiat. Prot. Dosim. 70(1-40(1997)103.
\bibitem{refL}H. Ing, R. A. Noulty, T. D. Mclean, Radiat. Meas. 27(1)(1997)1.
\bibitem{refM}F. d'Errico, ``Radiation dosimetry and spectrometry with superheated emulsions,'' Nucl. Inst. Meth B 184(2001) 229-254.
\bibitem{refN}E. d'Errico, R. Nath, M. Lamba, and S. K. Holland, ``A position sensitive superheated chamber for three-dimensional photon dosimetry,'' Phys. Med. Biol. 43 (199) 1147-1158.
\bibitem{refO}F. Seitz, Phys. Fluids 1(1) (1958)2.
\bibitem{refP}V. P. skripov, ``Metastable Liquids,'' Wiley, New York, 1974.
\bibitem{refQ}A. Norman, P. Spiegler, Nucl. Sci. Eng. 16 (1963)213.
\bibitem{refR}F. d'Errico, Radiat. Prot. Dosim. 83(1-4)(1999)55.
\bibitem{refS}S. Guldbakke, E. Doetz, H. Kluge, D. Schlegel, ``in: W. Kolzer, R. Masushart (Eds.), Strahlenschutz: Physik und Messtechnik, Verlag TUV, rheinland, Koln, 1994, p. 240.
\bibitem{refT}M. A. Buckner, R. A. Noulty, T. Cousins, Radit. Prot. Dosim. 55 (1) (1994) 23.
\bibitem{refU}M. O McLinden, S. A., Klein, E. W. Lemmon, A. P. Peskin, in: NIST standard Reference Database, Vol. 23, NIST, Gaithersburg, MD, 1998.

\end{thebibliography}
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