Isotopic Mixed Crystals Research Articles

Isotope effects on the lattice dynamics of crystals

Abstract It seems likely that isotope effects are most clearly manifested in crystal lattice dynamics, which is evidenced by works in this field that have been published for more than half a century. A great number of stable isotopes and well-developed methods of their separation has made it possible to date to grow crystals of C, LiH, ZnO, ZnSe, CuCl, GaN, GaAs, CdS, Cu2O, Si, Ge and α-Sn with a controllable isotopic composition. The accumulated voluminous theoretical and experimental data suggest that the isotopic composition of a crystal lattice exerts some influence on the thermal, elastic, and vibrational properties of crystals. These effects are quite large and can be readily measured by modern experimental techniques (ultrasound, Brillouin and Raman scattering, and neutron scattering). For example, the change in the lattice constant is Δa/a=10−3 to 10−4, while the change δcik in the elastic constants amounts to several percent. The maximum km (where km is the maximum of thermal conductivity) measured for the most highly enriched 70 Ge (99.99%) sample is 10.5 kW/mK, one order of magnitude higher than for the natural Ge (analogous for C and Si). In addition, crystals of different isotopic compositions possess different Debye temperatures. This difference between a LiH crystal and its deuteride exceeds hundred degrees. Of the same order of magnitude is the difference between Debye temperatures for diamond crystals. Very pronounced and general effects of isotopic substitution are observed in phonon spectra. The scattering lines in isotopically mixed crystals are not only shifted (the shift of LO lines exceeds 100 cm−1) but are also broadened. This broadening is related to the isotopic disorder of a crystal lattice. It is shown in this review that the degree of change in the scattering potential is different for different isotopic mixed crystals. In the case of germanium and diamond crystals, phonon scattering is weak, which allows one to successfully apply the coherent potential approximation (CPA) for describing shift and broadening of scattering lines. In the case of lithium hydride, the change in the scattering potential is so strong that it results in phonon localization, which is directly observed in experiments. Capture the thermal neutrons by isotope nuclei followed by nuclei decay produces new elements in a very large number of possibilities for isotope selective doping of different materials. The review closes with a section describing future developments and applications of isotope technology and engineering.

Isotope and disorder effects in the Raman spectra of LiHxD1−x crystals

AbstractMost of the physical properties of a solid depend on its isotopic composition in some way or another. Scientific interest, technological promise and increased availability of highly enriched isotopes have led to a sharp rise in the number of experimental and theoretical studies with isotopically controlled crystals. A great number of stable isotopes and well‐developed methods for their separation have made it possible to grow crystals of C, LiH, ZnO, ZnSe, CuCl, GaN, GaAs, CdS, Cu2O, Si, Ge and α‐Sn with a controllable isotopic composition. Among these compounds, LiH possesses the largest value of the isotope effect. The great number of theoretical and experimental data suggest that the isotopic composition of a crystal lattice exerts some influence on the vibrational properties of crystals. These effects are fairly large and can be readily measured by modern experimental techniques (ultrasound, Brillouin and Raman scattering and neutron scattering). In addition, crystals of different isotopic compositions possess different Debye temperatures. This difference between an LiH crystal and its deuterated analogue exceeds a 100 K. Very pronounced and general effects of isotopic substitution are observed in phonon spectra. The scattering lines in isotopically mixed crystals are not only shifted (the shift of LO lines exceeds 100 cm−1) but are also broadened. This broadening is related to the isotopic disorder of the crystal lattice. It is shown that the degree of a change in the scattering potential is different for different isotopic mixed crystals. In the case of germanium and diamond crystals, phonon scattering is weak, which allows one to apply successfully the coherent potential approximation (CPA) for describing the shift and broadening of scattering lines. In the case of lithium hydride, the change in the scattering potential is so strong that it results in phonon localization, which is directly observed in experiments. The common nature of the isotopic and disorder effects in a wide range of crystals is emphasized. Copyright © 2001 John Wiley & Sons, Ltd.

Scaling behavior of diffusion limited annihilation reactions on random media

We investigate numerically the kinetics of diffusion limited annihilation reactions in disordered binary square lattices where the reacting particles are constrained to diffuse on a concentration p of the lattice sites. We find that the asymptotic decay of the particle concentration in the percolative regime is of the form c(t,p)−cr(p)∝t−ds/2, where cr(p) is the concentration of residual particles. We recover well known results such as ds(p≳pc)=d=2 with logarithmic corrections, and ds(pc)=1.34±0.02. For p<pc we employ a scaling theory and collapse the data onto a universal form dc/dt=τ−(ds(pc)/2+1)f(t/τ), with τ being a characteristic diffusion time and f(t/τ) representing the crossover from a power law decay to a stretched exponential one. We relate the present results with the kinetics of the excitation reaction (triplet + triplet → singlet) on isotopic mixed crystals of naphthalene.

Steady-state vs. pulsed excitation recombination kinetics: Simulations and experiments on pores, powders and random media

Abstract The non-classical kinetics of exciton recombination in restricted geometries provides the foundation for a new experimental technique of probing the exciton dynamics and the sample topology. The phosphorescence and delayed flourescence decays exhibit a dramatic dependence on the duration of the excitation. The comparison of pulsed and steady-state excitation provides information on the local topology of the sample and on the average hopping time of the exciton and the exciton diffusion length. This is possible because the distribution of the exciton population is non-Poissonian under steady-state excitation conditions. In addition, the pulse-created distribution also loses its Poissonian character with time. The experimental systems are: 1) isotopic mixed naphthalene crystals above and below percolation; 2) naphthalene crystalline powder; 3) naphthalene embedded into porous glass. Except for the mixed crystals above the percolation concentration, all samples exhibit non-classical effects. The interpretation is aided by Monte Carlo simulations.

Steady-State vs. Pulsed Excitation Recombination Kinetics: Simulations and Experiments on Pores, Powders and Random Media

Abstract The non-classical kinetics of exciton recombination in restricted geometries provides the foundation for a new experimental technique of probing the exciton dynamics and the sample topology. The phosphorescence and delayed fluorescence decays exhibit a dramatic dependence on the duration of the excitation. The comparison of pulsed and steady-state excitation provides information on the local topology of the sample and on the average hopping time of the exciton and the exciton diffusion length. This is possible because the distribution of the exciton population is non-Poissonian under steady-state excitation conditions. In addition, the pulse-created distribution also loses its Poissonian character with time. The experimental systems are: 1) Isotopic mixed naphthalene crystals above and below percolation; 2) Naphthalene crystalline powder; 3) Naphthalene embedded into porous glass. Except for the mixed crystals above the percolation concentration, all samples exhibit the non-classical effects. The...

Quasi‐Resonance in Hydrostatically Compressed Isotopic Mixed Crystals of Deuteronaphthalene

AbstractSpectra of absorption and luminescence of two isotopic mixed crystals (IMC) of deuteronaphthalene for the 0.1% C10H8 guest in C10D8 host and for the 0.1% C10H8 guest in C10H2D6 host are measured in the range of the lowest singlet exciton transition at T = 4.2 under hydrostatic pressure up to 2 GPa. The dependence of the binding energy E and of the localization amplitude |a0|2 of the exciton on the impurity is determined in a wide range of values, involving the cross region. The dependences are verified quantitatively by the Rashba theory of quasiresonance.

Exciton cluster states of isotopic impurities in molecular crystals

Infrared spectra of isotopic mixed crystals of chloroform have been recorded over a wide concentration range. We have studied the fine structure of the chloroform ν 4 (E) band, near 1216 cm −1, in isotopic mixed crystals. Absorption lines of monomer, dimers are observed and identified from their characteristic concentration dependance. The exciton coupling constants of guest pairs are determined.

Rate processes on fractals: Theory, simulations, and experiments

Heterogeneous kinetics are shown to differ drastically from homogeneous kinetics. For the elementary reaction A + A → products we show that the diffusion-limited reaction rate is proportional tot − h[A]2 or to [A]x, whereh=1- d s/2, X=1+2/d s =(h-2)(h-1), andd s is the effective spectral dimension. We note that ford = d s =1, h =1/2 andX = 3, for percolating clustersd s = 4/3,h = 1/3 andX = 5/2, while for “dust” ds h > 1/2 and ∞ >X > 3. Scaling arguments, supercomputer simulations and experiments give a consistent picture. The interplay of energetic and geometric heterogeneity results in fractal-like kinetics and is relevant to excitation fusion experiments in porous membranes, films, and polymeric glasses. However, in isotopic mixed crystals, the geometric fractal nature (percolation clusters) dominates.

Luminescent fractal reactions: Exciton fusion on percolation clusters

Experimental measurements of exciton annihilation in isotopic mixed crystals of naphthalene-h 8 in naphthalene-d 8 exhibit fractal reaction kinetics on samples well below and slightly above the percolation threshold. The effective spectral dimensions are in very good agreement with the superuniversality conjecture and 2-dim. random walk simulations. Crystals well above the percolation threshold exhibit the expected classical behavior.

Triplet exciton transport in isotopic mixed naphthalene crystals. II. Master equation analysis

The experimental data on triplet exciton transport in isotopically mixed crystals of naphthalene/perdeuteronaphthalene (paper I) are contrasted with singlet exciton transport in the same samples (20%–100%) and analyzed in terms of incoherent hopping models. The master equation approach is emphasized and extended. We modify the conventional continuum master equations via a physically plausible cutoff of the high-frequency transfer rates. This results in an experimentally acceptable functional form (transport linear with high power of concentration) and nearest-neighbor transfer time (100 ps). We also developed a lattice master equation (numerically soluble), using an experimentally tested exciton superexchange formula. The somewhat surprising result is that the lattice master equations do not fit the experimental functional form. The success of the continuum models and the failure of the lattice models are attributed to the latter’s neglect of the spread in transfer rates for a given intersite distance. We claim that clusterization as well as diagonal homogeneous and/or inhomogeneous disorder cause the above spread. On the other hand, these energy mismatches are small with respect to the thermal energy, in contrast to the singlet exciton transport case, where, due to larger energy mismatches, a percolation-like critical concentration is observed. Thus for the given concentration and temperature regimes, the triplet exciton transport is diffusive while the singlet exciton transport is percolative. Lower temperatures and/or concentrations are required for percolative triplet energy transport in these systems.

Triplet exciton transport in isotopic mixed naphthalene crystals. I. Kinetic analysis of trapping and fusion

Time-resolved triplet exciton transport in binary mixed crystals has been studied for C10H8 in C10D8 (20%–100%) at liquid helium temperatures. The delayed fluorescence decays are exponential and range from milliseconds to nanoseconds as Cg goes from 0.2 to 1.0. The analysis is based on the presence of a BMN supertrap in large amounts (10−3) and on the fact that supertrapping of the guest excitons dominates the kinetics while heterofusion (triplet guest-triplet supertrap annihilation) dominates over the homofusion (guest–guest annihilation) and was used to monitor the kinetics. We also investigated in detail photodetrapping and the relative efficiencies of the various fusion channels. An analysis of the transport data is given in paper II.

Reaction kinetics on fractals: Random-walker simulations and excition experiments

Both computer simulations and laboratory experiments on binary reactions of random walkers on fractal spaces bear out a recent conjecture: The time development of the reaction is dominated by the intrinsic fractal (fracton, spectral) dimension. For the Sierpinski gasket the effective spectral dimension for reactions is ${d}_{s}^{\ensuremath{'}}=1.38$ (actual spectral dimension ${d}_{s}=1.365$). For the percolating cluster (60%, square lattice) ${d}_{s}^{\ensuremath{'}}=1.34$ (${d}_{s}=1.333$). From the exciton percolation laboratory experiments ${d}_{s}^{\ensuremath{'}}=1.5$, based on triplet-triplet annihilation in naphthalene isotopic mixed crystals at 2 K.

Self Consistent Diagram Determination of the Monomer State in Isotopic Mixed Molecular Crystals

Abstract The diagram approach is used to determine the locations of the singularities of the monomer self energy in isotopic mixed molecular crystals. The cumulant functions, which are the relative weights of the diagrams in the series, are evaluated in a self consistent manner. The resulting self energy expression is seen to contain singularities which are dependent on the concentration of guest molecules in the system. The formalism is used to obtain the locations of the singularities as a function of the reciprocal trap depth for different concentrations of naphthalene-h 8 in a host naphthalene-d 8 crystal.

Quasiresonant excitation transfer in molecular aggregates

Excitation transfer in finite molecular aggregates is analyzed in the context of the Haken–Strobl model. Explicit solutions are presented for a trimer and a rectangular tetramer. Special emphasis is placed upon population transfer among subunits (monomers, dimers) and its relationship to energy transfer, and upon the problems associated with coherence of this transfer process. These aggregates serve as models for the problem of excitation transfer in disordered media, where partial coherence resulting from short-range interactions has been largely ignored. Our most intriguing result is the greatly diminished effectiveness of the longer-ranged transfer in the presence of short-range clusters. Under some conditions the ensuing energetic mismatches may well dominate the overall energy transport and render invalid the usual description in terms of hopping among individual sites. An application to triplet energy transport in isotopic mixed naphthalene crystals is given; it is seen that the reduced efficiency of non-nearest-neighbor transfer processes reinforces the two-dimensional characteristics of the energy transport.

Resonance energy transfer, motional narrowing, and vibrational dephasing in molecular crystals: 390 cm−1 internal vibration of naphthalene

For the naphthalene-h8 crystal, the vibrational dephasing of the 390 cm−1 Raman active vibration is investigated by the temperature dependence of the linewidth and the line shape in the Raman spectra. This mode shows a relatively large resonance transfer interaction with a consequent factor group splitting of ∼5.5 cm−1. The corresponding transition in the isotopic mixed crystal, composed of 10% naphthalene-h8 and 90% naphthalene-d8, is, predominantly, due to the monomer. This monomer transition exhibits a Gaussian line shape at 4 K and has a width of ∼1.5 cm−1. In the neat naphthalene-h8 crystal at 4 K, the line shape of the higher energy Davydov component is found to be a motionally narrowed Lorentzian with a width much smaller than that of the monomer transition in the isotopic mixed crystal. In contrast to this, the line shape of the lower energy Davydov component is asymmetric. The low energy side of the lower Davydov component is found to obey the Urbach rule, while its high energy side is a Lorentzian. Furthermore, the width of the lower Davydov component is larger than that of the upper Davydov component but still smaller than what is observed for the corresponding monomer transition in the isotopic mixed crystal. This result suggests that the vibrational exciton band k-scattering mechanism, which involves the exciton–phonon scattering, does not contribute significantly to the vibrational dephasing. It is because such a mechanism predicts that at 4 K the upper Davydov component would be broader than the lower Davydov component as observed for the electronic excitons in molecular crystals. A detailed study of temperature dependence of the linewidth of the upper Davydov component also supports the assumption that the k scattering within the vibrational exciton band is not the main contributor to the dephasing of the 390 cm−1 vibration. This observed temperature dependence of the linewidth is found to be consistent with the mechanism of pure dephasing which involves an off-diagonal quartic anharmonic interaction with the high-frequency in-plane librational phonon motions.

Percolative versus homogenous energy transport kinetics: time-resolved donor and acceptor fluoresence of isotopic mixed naphthalene crystals

Tune-resolved spectral studies of the singlet exciton transport threshold in doped naphthalene-perdeuteronaphthalene mixed crystals are presented. While a homogeneous kinetic model adequately explains many of the results, some strong deviations from its predictions are found. These are attributed to clusterization effects.

Spectra of direct excitation of phosphorescence in an isotopic mixed naphthalene crystal. High resolution excitation of the two Davydov components of the N- d8 host crystal

Direct excitation spectra of the triplet exciton band of deuterated naphthalene are presented. The high resolution spectra (0.1 cm −1) of the two Davydov components show a substructure that we attribute to the presence in the crystal of natural traps and local strains. A model based on the calculation of the eigenstates of a finite plane of molecules is provided for lineshape simulations. In this work the artificial edge effects introduced by the finite size of the model crystal are eliminated by appropriate boundary conditions. Our method allows us to introduce a random distribution of traps, with variable energies, located inside and outside the exciton band, thus featuring a real crystal. Comparison between calculations and experimental results accounts for the salient effects of the traps on the spectroscopic properties of a mixed crystal.

Isotopic mixed crystal exciton spectra in the far infrared: Naphthalene

The far infrared vibrational exciton spectra of isotopic mixed crystals of naphthalene- h 8 and d 8 were studied. The two observed translational phonon modes were determined to fall into the amalgamated band limit while the lowest energy B 3u, A u and B 1u vibrational exciton bands were found to be in the separated band limit. The lowest energy B 3u “butterfly” mode with its large (15 cm −1) exciton splitting was found to agree well with CPA calculations of mixed crystal spectra. A peak at 185 cm −1 was also assigned as a peak in the vibrational exciton density-of-states of the B 3u mode.

Exciton spectra of isotopic mixed crystals of anthracene: C 14H 10-C 14D 10

The amalgamation type 0-0 excitons in the isotopic mixed anthracene crystals are investigated by simultaneous measurements of the reflection and emission spectra. The observed features of the bulk and surface excitons in the mixed crystals are analyzed by the coherent potential approximation model.

Vibrational exciton cluster states, percolation and pairwise interactions: Benzene A 2u band

Infrared spectra of isotopic mixed benzene crystals (C 6H 6/C 6D 6) were obtained at about boiling nitrogen temperature, with, emphasis on the umbrella mode (at about 700 cm −1). These are interpreted in terms of guest cluster spectra (monomers, pairs, etc.) up to about 55% mole. Static percolation sets in at about 50%, resulting in an extended exciton band. The line positions, line intensities and the percolation concentration all agree quantitatively with an effective 2-dimensional square lattice exciton interaction topology. This means that very short range, nearest neighbor interchange equivalent, excitation exchange interactions dominate over the long range transition-dipole type terms even in this most intense, dipole allowed IR band. These results fully support our recent picture of the umbrella mode exciton band, in both solid and liquid benzene. Similarities between these solid and liquid exciton bands are pointed out. The existence of pseudolocalized states, in the middle of the energy band of the extended states, is illustrated.