Search for improved-performance scintillator

Invited Paper

Search for improved-performance scintillator candidates among the electronic structures of mixed halides Qi Lia, Richard T. Williamsa, Arnold Burgerb, Rajendra Adhikaric, Koushik Biswas*c a

Department of Physics, Wake Forest University, Winston-Salem, NC 27109 b Department of Physics, Fisk University, Nashville, TN 37208 c Department of Chemistry & Physics, Arkansas State University, State University, AR 72467

ABSTRACT The application of advanced theory and modeling techniques has become an essential component to understand material properties and hasten the design and discovery of new ones. This is true for diverse applications. Therefore, current efforts aimed towards finding new scintillator materials are also aligned with this general predictive approach. The need for large scale deployment of efficient radiation detectors requires discovery and development of high-performance, yet low-cost, scintillators. While Tl-doped NaI and CsI are still some of the widely used scintillators, there are promising new developments, for example, Eu-doped SrI2 and Ce-doped LaBr3. The newer candidates have excellent light yield and good energy resolution, but challenges persist in the growth of large single crystals. We will discuss a theoretical basis for anticipating improved proportionality as well as light yield in solid solutions of certain systems, particularly alkali iodides, based on considerations of hot-electron group velocity and thermalization. Solid solutions based on NaI and similar alkali halides are attractive to consider in more detail because the end point compositions are inexpensive and easy to grow. If some of this quality can be preserved while reaping improved light yield and possibly improved proportionality of the mixture, the goal of better performance at the low price of NaI:Tl might be attainable by such a route. Within this context, we will discuss a density functional theory (DFT) based study of two prototype systems: mixed anion NaIxBr1-x and mixed cation NaxK1-xI. Results obtained from these two prototype candidates will lead to further targeted theoretical and experimental search and discovery of new scintillator hosts. Keywords: mixed crystal, solid solution, NaI, scintillator, electronic structure, nonproportionality, light yield, nonlinear quenching, hot electron

1. INTRODUCTION NaI:Tl and CsI:Tl have been the most widely deployed scintillator materials for a number of decades, because they perform reasonably well in many applications and large crystals can be produced in quantity at reasonable cost. Recently, research has focused on new materials with better light yield, timing, and energy resolution, which has led to the development of superior fast and/or high-resolution scintillators such as LaBr3:Ce1,2,3 and SrI2:Eu.4,5 Materials cost and expenses associated with crystal growth and device fabrication are important factors when it comes to large scale deployment such as for effective monitoring of nuclear materials. Solid solutions or mixed crystals of known scintillator materials where the parent compounds are readily available, proven at least moderately effective as scintillators, and are easy to grow constitute one avenue along which one can search for improved performance. If some of the desirable properties of the binary end point compounds can be preserved within the solid solutions, then the compositional degrees of freedom obtained via mixing may allow one to optimize and tune the processes that govern the scintillation response, including proportionality and light yield. This could lead to achieving the dual objective of better performance at low cost. There are several studies involving mixed alkaline earth halides of the type BaXY (X,Y = F, Cl, Br, I)6,7 doped with Eu. CsBa2I5 obtained by mixing CsI and BaI2 and activated by Eu have also been reported.8-12 Reported light yield of BaBrI:Eu range between 71,000-97,000 photons/MeV and energy resolution between 4.8-3.1% at 662 keV.8-12 CsBa2I5:Eu also shows impressive performance with light yield reports ranging 80,000-102,000 photons/MeV and 8,9

Hard X-Ray, Gamma-Ray, and Neutron Detector Physics XVI, edited by Arnold Burger, Larry Franks, Ralph B. James, Michael Fiederle, Proc. of SPIE Vol. 9213, 92130M © 2014 SPIE · CCC code: 0277-786X/14/$18 · doi: 10.1117/12.2063583 Proc. of SPIE Vol. 9213 92130M-1 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/09/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx

energy resolution about 3.9-2.55% at 662 keV.9-12 Gektin et al. recently directed attention to phenomenological evidence compiled from published studies over the last two decades of improved scintillation light yield achieved near the 50% composition point of mixed crystals relative to the two pure-crystal end points.13 This phenomenon has been noted in at least ten different solid solution systems. Gektin et al. have offered a reason based on limiting hot electron diffusion range so that electrons are more likely to stop within the Onsager radius of the hole, making a geminate pair. They suggested that modification of the phonon spectrum and electron scattering, inhomogeneity of the solid solution, and Anderson localization in the mixed crystal could be responsible factors. The mixed crystal appears to have higher light yield, possibly less hygroscopic, and improved mechanical properties relative to the end point compounds. Solid solutions based on NaI and similar alkali halides are attractive to consider in more detail because the end point compositions are inexpensive and easy to grow. We intend to thoroughly explore the fundamental trends in scintillator material properties within the chosen model system by theoretical and experimental means, and early results are presented in this paper. Here, we will discuss two representative systems, viz., NaI xBr1-x that has mixing in the anion sublattice and NaxK1-xI that has disorder in the cation sublattice. Using ab-initio density functional methods we investigate the miscibility, alloy phase diagram, and electronic properties of these two prototype systems and how they match with our model of hot electron transport and consequences on light yield and proportionality.

2. COMPUTATIONAL DETAILS Our calculations are based on density functional theory methods as implemented within the Vienna ab-initio simulation package (VASP).14,15 Exchange-correlation functionals as parametrized by Perdew-Burke-Ernzerhof within the generalized gradient approximation have been used.16 Electron-ion interactions are described using projector augmented wave potentials.15,17 The valence wavefunctions are expanded on a plane-wave basis with a cutoff energy of 260 eV. The alloys are simulated using special quasi-random structures (SQS’s).18 Alloy formation enthalpy (ΔH), band structure, and group velocity calculations are performed using 16-atom SQS. A Gamma-centered 6×6×6 k-mesh has been used for sampling the Brillouin zone and all structures are relaxed until the force components are less than 0.01 eV/Å. The lattice parameters for the binary hosts and the mixed crystals are allowed to relax while fixing the shape of the cells.

3. RESULTS AND DISCUSSION 3.1 Mixing Enthalpy and Phase Diagram We first consider the enthalpy of mixing as a function of concentration. The enthalpy of mixing for an alloy A1-xBxC is given by:

ΔH(A1x Bx C)  E(A1x Bx C)  xE(BC)  (1  x)E(AC)

(1)

where E(A1-xBxC) is the total energy of the ternary structure of composition x and E(AC) and E(BC) are the total energies of the two binary constituents. Figure 1 shows ΔH as a function of concentration x for NaIxBr1-x and NaxK1-xI. The data points representing the calculated values of ΔH at different x are connected by fitting with a polynomial function. We assume random mixing and the results are shown for SQS structures as discussed in Section 2. The ΔH values are moderate because the lattice mismatch between the constituent binaries is not large. A close look at the fitted curves in Fig. 1 reveals that the maximum values of ΔH occur above x = 0.5 in NaxK1-xI and below x = 0.5 in NaIxBr1-x, i.e., the two curves are marginally asymmetric with the former tilted to the right and the latter to the left.

Proc. of SPIE Vol. 9213 92130M-2 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/09/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx

FIGURE 1. Calculated mixing enthalpy (ΔH) in meV/cation as a function of concentration x of NaIxBr1-x and NaxK1-xI.

1000 800

,5°'

600

.65

a)

Q- 400 E

Ha)

200

FIGURE 2. Calculated temperature-concentration (T-x) phase diagram of NaIxBr1-x and NaxK1-xI. The critical temperature (Tc) above which the miscibility gap disappears and the corresponding concentration (xc) are also shown.

The phase stability of the mixed crystals is illustrated in Fig. 2, which shows the temperature versus concentration (T-x) phase diagram for the spinodal decomposition of the two systems. The phase diagrams were also calculated assuming random distribution within the regular solution model. 19,20 In Fig. 2, the miscibility gap (i.e., the immiscible region) shrinks considerably from T = 0 K to room temperature. It disappears at the critical temperature calculated to be Tc = 847 and 545 K for NaIxBr1-x and NaxK1-xI, respectively. The values of the corresponding concentrations are xc = 0.58 and 0.40, respectively. The calculated T c are below the melting temperatures of the original binary compounds (928±10K, 1014±10K, and 957±15K in NaI, NaBr, and KI, respectively21), which indicates a uniform mixing in the molten phase. As it is cooled, there may be kinetic barriers that prevent rapid nucleation and phase separation. It should be noted that we have not considered vibrational and short range ordering effects that may impact the phase diagram and further reduce the value of Tc. Non-equilibrium growth techniques may also increase solubility and further reduce the miscibility gap. The asymmetry of the phase diagrams are evident in Fig. 2 and also from the values of xc. This stems from the asymmetric nature of the ΔH versus concentration curve in Fig. 1 and is due to the difference in lattice parameters of the constituent binaries. It is easier to introduce smaller Na atoms in the larger KI lattice as seen from the rightward tilt of the NaxK1-xI phase diagram and vice versa for NaIxBr1-x.


3.2 Electronic Properties We have recently discussed that slow thermalization and a 3 rd order quenching model22,23,24 is favored for proportional response and high light yield among the halide compounds. Some of the best performing scintillators, e.g., LaBr3:Ce SrI2:Eu, have been shown to belong in this class. Note that these materials fall in the category of multivalent halides. On the other hand NaI:Tl, CsI:Tl are monovalent halides that are known for their moderate proportionality and moderate light yield25,26. This is, at least in part, due to their dispersive upper conduction bands that cause the hot electrons to diffuse rapidly to a much larger radius than the nearly immobile self-trapped holes (STH) in the track core. This creates charge separation and an electric field which, upon electron thermalization, draws the dispersed electrons back toward the approximate line charge of STH near the core. The current of electrons drawn to the positive charge of the core is at the same time subjected to capture on deep traps that represent a quenching channel for useful light within the detector gate interval. This competition favors exciton formation (hence light emission) toward the end of the track where the STH density in the core is higher, and it favors defect-trapping of electrons (light loss) nearer the beginning of a track where the STH density is lower. An important result of this competition and its variation along the length of the track is the nonproportionality feature of rising light yield with decreasing initial electron energy in monovalent halides, contributing to the so-called halide hump in Compton-coincidence and K-dip experiments.23 The deep trapping is also partly responsible for moderate light yield in the monovalent halides. As pointed out in Refs. 23, 24 and 27 the competition between defect trapping and successful radiative recombination in the track core gets tilted toward radiative recombination if the hot electron diffusion out from the core can be reduced, while the thermalized electron diffusion current back toward the core is maintained. For improved scintillation response, one wants poor hot electron mobility and good thermal electron mobility.28 The complex structure and large basis of the multivalent halides creates denser and flatter conduction bands so that the hot electrons are not flung as far out of the STH track core as in simpler binary halides with more dispersive upper conduction bands. Within this context, it becomes clear as to why in the case of the mixed crystals we anticipate reaping the advantages of cost-effective and easily growable crystals from the monovalent NaI:Tl family while attempting to invoke the superior properties of the multivalent halides. Figure 3 illustrates electronic band structure of NaI, NaBr, KI, NaI0.5Br0.5, and Na0.5K0.5I. To make direct comparison between the mixed crystals and the host, we generated a 16 atom SQS for NaI0.5Br0.5, and Na0.5K0.5I, and used the same size cell for the binary materials. Notice the denser tangle of bands, especially in the mixed cation Na0.5K0.5I compound compared to the pure binaries. In the mixed anion Na I0.5Br0.5, the hybridization of p-orbitals of Br and I dominates in the valence band. In comparison, in Na0.5K0.5I, mixing of cations introduces significant Na-3s and K3d hybridization in the conduction band. In addition, more compact K-3d orbitals dominate the conduction band of this ternary, resulting in an overall “flatter” conduction band.


J

X

-- Y

(As) A6aauA

o

J

X

FIGURE 3. Calculated electronic band structures of NaI, NaBr, KI, NaI0.5Br0.5, and Na0.5K0.5I. The top of the valence band is set as zero of energy.

Figure 4 shows the calculated group velocities of NaI, NaBr, KI, NaI0.5Br0.5, and Na0.5K0.5I as a function of energy. Group velocities vg, are calculated using:

v g2 ( E ) g ( E ) 

2 (2 ) 3

 v

2 n (k ) ( E

 En (k ))d 3k

(2)

n BZ

where g(E) is the density of states, n is the band index, v n (k )  (1 / )k En (k ) . The factor 2 accounts for the spin degeneracy. The k-point sampling used for group velocity calculations is 32×32×32.27,29 The vg distribution in the valence band corresponds to holes while that in the upper conduction bands corresponds to that of the hot electrons. The hot electron vg are lower for both mixed crystals compared to the binary hosts. The lowest values are found in Na0.5K0.5I which quantifies the qualitative picture in Fig. 3 showing less dispersive and flat conduction bands. Complexity introduced due to the non-equivalent cations makes desirable changes in the band structure, lowering vg. Indeed our calculated hot-electron vg spectrum in Na0.5K0.5I is similar to that in SrI2.23,27 Thus, unlike NaI, the hot electrons in Na0.5K0.5I have smaller thermalization range, remaining close to the STH track core and encountering fewer deep traps during the return in the collective electric field of the immobile STH line charge in the track core. This should lead to better light yield along with a proportional response. The change in group velocities is not so pronounced in NaI0.5Br0.5 because of the mixing in the anion sublattice that mostly alters the valence bands. Another highlight of these mixed compounds is that the conduction band edges retain their dispersive character. It is evident from the high vg at the band edge of the binaries as well as the mixed crystals, as seen in Fig. 4. Good mobility after thermalization ensures that the electrons respond effectively to the electric field after kinetic-energy-driven charge separation and subsequent thermalization. The effective masses for electrons (me*) in Table 1 are calculated from the 2nd derivative of energy with respect to k-vector at the conduction band minimum which is located at Γ-point for NaI0.5Br0.5 and Na0.5K0.5I and the binary hosts.


x1o«

- -mm -NaBr

of

- NalBr - NaKI

D

5

1O

Energy (eV) FIGURE 4. Calculated group velocities of holes in the valence band and electrons in the conduction band of NaI, NaBr, KI, NaI0.5Br0.5, and Na0.5K0.5I. The zero of energy is aligned with the conduction band minimum of the materials.

TABLE 1. Calculated electron effective mass me* in terms of electron mass m0. Experimental value for KI is shown in parenthesis.

me*

NaI

NaBr

KI

NaI0.5Br0.5

Na0.5K0.5I

0.27

0.25

0.34 (0.4)21

0.31

0.29

3. CONCLUSION We have studied NaIxBr1-x and NaxK1-xI as representative mixed crystals with disorder in the anion and cation sublattice, respectively. The idea is to retain the benefits of readily available and easily grown starting materials while attempting to invoke the advantages normally found in complex halides. The mixing enthalpy and T-x phase diagram of the two candidate systems suggest stable solid solutions are possible. The complexity introduced by the non-identical atoms cause the desirable changes in the mixed crystals of reduced hot-electron thermalization range. Among the two mixed crystals studied here, cation mixing in Na0.5K0.5I creates more profound changes in the conduction bands and low hot electron vg while retaining the dispersive nature of the band edge (small electron effective mass). These properties are also the hallmarks of the known high performance scintillators such as LaBr 3:Ce and SrI2:Eu. The mixed crystals are promising candidates that should be explored to attain the goal of superior performance at low cost.

ACKNOWLEDGMENTS Williams, Burger, and Biswas acknowledge research support from the US Department of Homeland Security, Domestic Nuclear Detection Office, under National Science Foundation competitively awarded grants ECCS-1348361, 1348139, 1348341 of the Academic Research Initiative (ARI) program. This support does not constitute an express or implied endorsement on the part of the Government. The use of high-performance computing resources at the National Energy Research Scientific Computing Center is gratefully acknowledged.


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