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\begin{document} 
\title{Calcium Fluoride}
\author{\\H. Romero\\
         Department of Physics\\ 
         University of Cincinnati \\
         Cincinnati, Ohio 45221\\[1em]}
 
\date{December 8,1995}
\maketitle
\begin{abstract}
A review is given on some of the physical and optical properties of calcium fluoride relevant to undestand the thermoluminescence properties of this material. The spectral-luminescence properties of these crystals doped with some rare-earth is described and several references on the status of study of colour centres in calcium fluoride are presented.\\[1em]

\end{abstract}
\pagebreak
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\indent
A significant advantage of CaF$_{2}$ is that it is naturally occurring in single crystal as mineral fluorite but contains about 500 parts of Al and Fe as well as rare-earth impurities. A standard natural fluorite used to be marketed by MBLE, Belgium, although this is now discontinued.

\section{The lattice structure}

\indent
The fluorite lattice is shown in Fig.~1\@. In this lattice each calcium ion is surrounded by eight equivalent nearest neighbor fluorine ions forming the corners of a cube of which calcium is the center\@. Each ion of fluorine is surrounded by a tetrahedron of four equivalent calcium ions\@. The lattice constant is $a$ = 5.4629 \AA\@. If the structure is interpreted in terms of this primitive cube of side $a$, as marked in Fig.~1, it comprises three interpenetrating face-centred-cubic lattices\@. The first is a lattice of calcium ions with its origin at the point ($0$,$0$,$0$) and with primitive translational vectors of ($0$,$\frac{1}{2}a$,$\frac{1}{2}a$); ($\frac{1}{2}a$,$0$,$\frac{1}{2}a$); and ($\frac{1}{2}a$,$\frac{1}{2}a$,$0$) in the cube side $a$\@. The fluorine ions are located on two further lattices with similar translational vectors but with origins at ($\frac{1}{4}a$,$\frac{1}{4}a$,$\frac{1}{4}a$) and at ($\frac{3}{4}a$,$\frac{3}{4}a$,$\frac{3}{4}a$)\@. The site of the calcium ion has $O_{h}$ symmetry and the site of the fluorine ion has $T_{d}$ symmetry\@. The interstitial site again has $O_{h}$ symmetry, being at the center of a cube of eight fluorine ions\@. The crystal is not piezoelectric.

\begin{figure}[htb]
\centerline{\psfig{figure=fig1.ps,height=2in}}

\caption[]{\em{The structure of the fluorite CaF$_{2}$ lattice\@. $a$ is the lattice parameter of the conventional cubic unit cell.$^{\cite{ref14}}$}}
\end{figure}

The fluorine structure has considerable thermal stability with a melting point of 1300$^{\circ}$C, which make available a vast range of temperature over which a particular phenomenon may be studied.

The strongest evidence that CaF$_{2}$ comprises an assembly of singly- and dobly-charged electrons ions, with little covalent bonding, comes from the comparison of the observed cohesive energy with that calculated on the assumption of an ionic lattice\@. 

\section{The eletronic energy-band structure}

\indent
The forbidden band gap for CaF$_{2}$ is large, being about 12~eV\@. The optical measurements are therefore difficult.

By forming the structure from the constituent ions, the outermost filled shell of the Ca$^{2+}$ ion, the $3p$ shell, is raised from $-51.2$ eV with respect to the vacuum level to $-31.25$ eV. The outermost fluorine-ion level initially at $-3.59$ eV drops to $-14.3$ eV and will form the basis of the highest filled valence band of the crystal\@. The Ca$^{2+}$ levels are well separated in energy from this F$^{-}$ ion level and little admixture is expected. We may therefore anticipate a valence band with maximum at the center of the Brillouin zone.

The basis of the lowest conduction bands is formed by a $4s$ level with ionization energy of 11.9 eV in the free Ca$^{2+}$ ion, followed by $3d$ and $4p$ levels higher in energy respectively by 1.7 and by 3.1 eV.

\section{The optical properties}

\indent
The wide band-gap of the CaF$_{2}$ has restricted the measurement of its optical properties. Calcium fluoride is commonly used as a window material able to transmit ultraviolet radiation with photon energies of up to 10 eV.

In Fig.~2 we see measurements of the optical reflectance spectra of calcium fluoride at near normal incidence. Superimposed are spectra measured at 90K, 300K, and 400K\@. At lower energies the specimens, when pure, are transparent until the onset at long wavelength of the absortion and dispersion associated with phonon generation.

\begin{figure}
\centerline{\psfig{figure=fig2.ps,height=2in}}

\caption[]{\em{The optical reflectance of CaF$_{2}$ near normal incidence\@. The spectral regions I, II and III correspond to the formation of different types of excitation.}}
\end{figure}

\section{Colour centres and Thermoluminescence}

\indent
Thermoluminescence relates to the property of certain substances that releases light upon heating after they have been exposed to ionizing radiation\@. These materials contain trace quantities of imputity atoms that capture electrons released by radiation\@. These captured electrons can later be released by heating the material (usually at a rate of about 22$^{\circ}$F/s or 10$^{\circ}$C/s) and either the peak intensity of the light emitted (the glow curve) or the integrated light can be measured\@. The thermoluminescence (TL) of calcium fluoride has been intensively studied as the presence of rare earth (RE) impurity ions provides a very bright phosphor for high TL sensitivity (useful range from 1 mrad to $10^{5}$ rad) and the possible applications in radiation dosimetry, geology$^{\cite{ref3}-\cite{ref5}}$ and in UV radiation dosimetry\@.$^{\cite{ref6}}$ CaF$_{2}$ proved to be a very interesting host for studying the RE ions because it was found that ionizing radiation could convert those trivalent RE ions into the divalent state\@.$^{\cite{ref7}}$ One major problem of using natural fluorite is the complexity of its glow curve\@.$^{\cite{ref1}}$ Most samples of CaF$_{2}$ after exposure to gamma radiation give glow curves as in Fig.~3\@. The temperatures of the glow peaks extend from 70$^{\circ}$C to 600$^{\circ}$C\@. Peaks III and III' are most useful for dosimetry purposes, as they are located between 250$^{\circ}$C and 300$^{\circ}$C\@. The very-high-temperature peaks are difficult to measure without permanently damaging the phosphor by the heat treatment\@. The integrated light emitted under peaks III and III' represent $\sim$~75\% of the total TL\@. Earlier TL studies of CaF$_{2}$ doped with Mn, Dy, Tb, Ce, etc. were reviewed by Sunta$^{\cite{ref2}}$ and, as a result of the high sensitivity to radiation dose, the material has been exploited in the form of a commercial CaF$_{2}$:Dy TL dosimeter\@. Additive colouration in CaF$_{2}$ usually produces two strong absorption bands at 375 and 525 nm {usually referred as $\alpha$ and $\beta$ band respectively), while irradiation produces four bands at 225, 335, 400 and 580 nm.$^{\cite{ref15}}$

\begin{figure}
\centerline{\psfig{figure=fig3.ps,height=2.5in}}

\caption[]{\em{Glow curves from several samples of CaF$_{2}$:natural}}
\end{figure}

CaF$_{2}$:natural, shows an enhancement of sensitivity after being irradiated to high gamma exposure\@. This increase in sensitivity is quite dependent on the temperature and on the duration of annealing after sensitizing irradiation\@. Natural CaF$_{2}$ is also sensitive to light, specially ultraviolet\@. The buildup of TL is very weak in the low temperature peaks but is much stronger in peak III', because of the direct light-induced TL and the transfer of charge carriers from deeper traps (mainly V and VI) to peak III'\@. In addition, these crystals are found to be photochromic\@.$^{\cite{ref8},\cite{ref9}}$ These photochromic colour-centres in CaF$_{2}$ crystals have important practical applications for information storage and display\@.$^{\cite{ref10},\cite{ref11}}$ CaF$_{2}$(Eu) scintillators are used for X-ray and charged particle measurements.$^{\cite{ref12},\cite{ref13}}$  


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\bibitem{ref2} C.M.\ Sunta, Radiat.\ Protect.\ Dosimetry. {\bf 8}, 25(1984).
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\bibitem{ref8} D.L.\ Staebler and S.E.\ Schnatterly, Phys.\ Rev.\ {\bf B3}, 516(1971).
\bibitem{ref9} D.L.\ Staebler and Z.J.\ Kiss, Appl.\ Phys.\ Lett.\ {\bf 14}, 93(1969).
\bibitem{ref10} Z.J.\ Kiss, Physics Today {\bf 23}, 42(1970).
\bibitem{ref11} B.W.\ Faughnan, D.L.\ Staebler and Z.J.\ Kiss, Applied Solid State Science Vol.\ 2, ed.\ R.\ Wolfe (Academic Press, New York, 1971).
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\bibitem{ref13} S.\ Murali Dhara Rao and L.H.\ Peshori, J Mysore University, Sec.\ B.\ {\bf 26}, 389(1977).


\end{thebibliography}


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