On the lattice dynamics of AgGaS2

Summary The vibrational spectrum and one-phonon density of states of a chalcopyrite crystal AgGaS₂ are calculated in an extended Keating’s model with two-bond-stretching and one-bond-bending force constants. Three charges of ions and three force constants are determined by a least-square fitting to experimental frequencies of long-wave phonons taken from Raman-scattering experiments. The calculated constant-volume specific heat, Debye temperature and elastic constants, of AgGaS₂ are in agreement with the experimental data of other authors.     

Crystal lattice dynamics of ZnGeP2 and AgGaS2 in hard ion model

A calculation is made of the long-wavelength phonon spectrum of ZnGeP₂ and AgGaS₂ in the hard ion model. The parameters of short-range forces and dynamic charges are found by comparing the theory with the experimental data on infrared absorption and Raman scattering of light. The elastic and piezoelectric constants are calculated. The available experimental data are discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 3–10, May, 1980.     

The theory of infrared dispersion of light in crystals with chalcopyrite lattice

The low-frequency dielectric tensor is calculated for A^IIB^IVC ₂ ^V and A^IB^IIIC ₂ ^VI crystals in terms of the long-wave frequencies of lattice vibrations, corresponding to various orientations of the wave vector. The qualitative shape of the spectrum of mechanical polaritons is obtained. The coefficient of light reflection is calculated as a function of the frequency and direction of propagation for a CdGeP₂ crystal.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 39–43, June, 1978.     

Absolute sense of piezoelectric coefficients in the chalcopyrites ZnGeP2 and AgGaS2

The absolute orientation of single crystals of ZnGeP₂ and AgGaS₂ on which the relative sense of the d₁₄ and d₃₆ piezoelectric coefficients had been measured, was determined by the X-ray absorption edge method. Both coefficients were thereby found to be positive, corresponding in the point charge model to positive charge associated with the metal and negative charge with the nonmetal atoms, in contrast with the negative d_33′ reported in GaP.     

Vibrational spectrum of Li2B4O7 crystals

Polarized IR reflection spectra of Li₂B₄O₇ crystals are studied in a spectral range of 80–1600 cm^?1 and compared with their Raman spectra. Based on the results of the dispersion analysis of the spectra, the frequencies, damping constants, and oscillator strengths of all vibrations are determined. The inversion of frequencies of the longitudinal and transverse vibrations of the A ₁ and E symmetry in a range of 900–1150 cm^?1 is found. Based on the data thus obtained, the effective charges are calculated and the types of chemical bonds are analyzed for structural groups of the Li₂B₄O₇ crystal.     

Chemical shift of the Ga and As Kα1,2 and Kβ1,3 X-ray emission lines

By means of a double crystal spectrometer and a computer the chemical shifts of the Ga Kα_1,2, As Kα_1,2 and Kβ_1,3 lines were determined with high accuracy. An interpretation of the results obtained with a free ion model and a calculation according to the Hartree method shows agreement of the values calculated for the effective atomic charges with those based on chemical experience, and also the presence of a charge transfer from the A atom to the B atom in A^IIIB^V compounds. The existence of binding charges is one of the reasons for the fact that |q_A| ≠ |q_B|. The interpretation of the Kβ_1,3 and Lα shifts shows the limitations of the free ion model.     

Vibrational spectrum of Li2B4O7 crystals

The polarized infrared reflection spectra of Li₂B₄O₇ were studied in the spectral range 80–1600 cm^?1 and compared with Raman spectra. From the spectrum dispersion analysis, the frequencies, damping, and dielectric oscillator strengths were determined for all vibrational modes observed. A calculation of the effective charges and an analysis of the chemical-bond types of the Li₂B₄O₇ crystal structural units were carried out on the basis of the obtained data.     

Photoluminescence of AgGaS2 and CuGaS2 doped with rare-earth impurities

Photoluminescence (PL) related to rare-earth (RE) impurities (Ho, Er and Eu) in AgGaS₂ and CuGaS₂ crystals has been studied. In Ho-doped AgGaS₂ and CuGaS₂, two series of PL lines are observed in 1.86–1.92 eV region and 2.24 eV region, and they are assigned to ⁵F₃–⁵I₇ and ⁵S₂–⁵I₈ transitions of the Ho³⁺ ion, respectively. Similarly, in Er-doped AgGaS₂ and CuGaS₂, Er³⁺-related two PL series are observed: 1.83–1.88 eV region (⁴F_9/2–⁴I_15/2) and 2.22–2.26 eV region (⁴S_3/2–⁴I_15/2). For both Ho and Er impurities, the profile of the PL spectrum in AgGaS₂ is complex, and PL exhibited large number of lines compared with that in CuGaS₂. The differences in PL spectra between this two compounds are related to the crystal field at the cation site and the local atomic arrangement of the RE impurities. This work also refers to the PL band at 2.28 eV observed for the Eu-doped AgGaS₂ crystal.     

AgGaS2- and Al-doped GaSe Crystals for IR Applications

We report a systematic study of AgGaS₂- and Al-doped GaSe crystals in comparison with pure GaSe and S-doped GaSe crystals. AgGaS₂-doped GaSe (GaSe:AgGaS₂) crystal was grown by Bridgman technique from the melt of GaSe:AgGaS₂ (10.6 wt.%). Its real composition was identified as GaSe:S (2 wt.%). Al-doped GaSe (GaSe:Al) crystals were grown from the melt of GaSe and 0.01, 0.05, 0.1, 0.5, 1, 2 mass % of aluminium. Al content in the grown crystals is too small to be measured. The hardness of GaSe:S (2 wt.%) crystal grown from the melt of GaSe:AgGaS₂ is 25% higher than that of GaSe:S (2 wt.%) crystal grown by a conventional S-doping technique and 1.5- to 1.9-times higher than that of pure GaSe. GaSe:Al crystals are characterized by 2.5- to 3-times higher hardness than that of pure GaSe and by extremely low conductivity of ≤ 10^− 7 Om^− 1 cm^− 1. A comparative experiment on SHG in AgGaS₂-, Al-, S-doped GaSe and pure GaSe is carried out under the pumps of 2.12-2.9 μm fs OPA and 9.2−10.8 μm ns CO₂ laser. It was found that GaSe:S crystals possess the best physical properties for mid-IR applications among these doped GaSe crystals. GaSe:Al crystals have relatively low conductivity which have strong potential for THz application.     

Quadratic crystal field tensors and spin Hamiltonian tensors of Fe3+ in Li2Ge7O15 above and below the phase transition temperature

Dopant Fe³⁺ ions in tetrahedral and octahedral positions of Ge⁴⁺ in the crystal Li₂Ge₇O₁₅ were studied using EPR. Fe³⁺ substitutes for Ge⁴⁺ with a local charge compensation. The octahedral site and the tetrahedral sites significantly differ by the value of the invariant sumS(B ₄) of theB ₄ tensor of the spin Hamiltonian of Fe³⁺. The irreducible tensor products {V ₄ ? V ₄}₄ and {V ₄?V ₄}₂ theV ₄ tensor of the crystal field calculated using the point-charge model for octahedral and tetrahedral complexes provide the predominant contribution of the crystal field to theB ₄ andB ₂ tensors of the spin Hamiltonian of Fe³⁺, respectively. A comparison of the fourth-rank tensorsB ₄ of the spin Hamiltonian and {V ₄?V ₄}₄ of the crystal field determined at 300 K with those determined at 77 K supports the conclusion that the phase transition is accompanied by combined rotation of the [GeO₄] tetrahedra with the [Ge(1)O₆] octahedron almost unaltered. The spectrum lines are narrow and the variety of point defects in the vicinity of the paramagnetic impurity ions Fe³⁺, Cr³⁺ and Cu²⁺ is not detected. These facts are inconsistent with the statistically distributed model for the Li(2) atom. In specific cases at 300 K, when the wings of the two spectrum lines of theM→M+1 and theM+2 →M+3 transitions of Fe³⁺ ions belonging to one system of translationally equivalent positions overlap an extra line appears in the center between these lines. It is suggested that this effect is due to the soft phonon mode above the phase transition temperature.     

Simulation of parametric oscillation in the submillimeter range at pumping of the ZnGeP2 crystal by a train of 100-ps high-power pulses

Analysis is given for a possibility of singly resonant parametric oscillation in the submillimeter range at synchronous pumping of the ZnGeP₂ crystal by a train of 100-ps second-harmonic pulses from the CO₂ laser with the radiation energy 1.0 J. The calculation shows that using the ZnGeP₂ crystal and the second harmonic of the CO₂ laser with the energy density 1.8 J cm⁻², one can get the peak submillimeter radiation power from 3.6 to 12 MW in the range from 95 to 300 μm (1.0–3.3 THz). The expected peak power values are larger than the experimental ones obtained by other nonlinear optics methods.     

Exact four-body calculation of the 4ΛHe-4ΛH binding energy difference

The coupled, two-variable integral equations that determine the ⁴_ΛHe and ⁴_ΛH bound states, when the NN and ΛN interactions are represented by separable potentials, are derived from the Schrödinger equation. The integral equations are solved numerically for simple s-wave potentials and for tensor potentials in the truncated t-matrix approximation without resort to separable expansion of the kernels. The Λ-separation energy difference ΔB_Λ resulting from the genuine four-body model is shown to be approximately twice as large as that coming from an “effective two-body” model calculation, when identical central potentials are used. The four-body model estimate of ΔB_Λ made with tensor forces is consistent with the experimental value, indicating that charge symmetry breaking implied by the low energy Λ N scattering parameters is compatible with that suggested by the known binding energy difference in the A = 4 hypernuclear isodoublet.     

Force field of A(I)B(III)−S2 chalcopyrite compounds at zero wave vector

Published experimental frequencies are used to calculate Urey-Bradley force fields and ionic charges of some ABS₂ chalcopyrite compounds. The values obtained for the A?S and B?S force constants as well as the ionic charges are discussed.     

Lattice vibrations in the orthorhombic commensurate charge density wave phase of 2H-TaSe2

Lattice vibrations in 2H-TaSe₂ have been reinvestigated by Raman scattering in view of the recent orthorhombic structure of the commensurate charge density wave (CCDW) phase. The renormalization of six charge density waves on two layers gives four A_g modes and two B_1g modes in the orthorhombic CCDW phase, in place of two A_1g modes and two E_2g modes in the hexagonal CCDW phase which had been believed. The splitting of the E_2g modes to the A_g and B_1g modes in the orthorhombic symmetry depends on the interlayer interaction. The observed small splitting less than 3 cm^-1 shows the weak interlayer interaction. The energies of the four A_g modes and the two B_1g modes are presented as a function of temperature.     

Behavior of impurity copper in ZnGeP2 single crystals with diffusion doping

Results from a study of electrophysical and luminescent properties of zinc-germanium diphosphide single crystals, diffusion doped with copper, are presented. The nature of the dominant defects formed upon copper diffusion in ZnGeP₂ is determined using a thermodynamic analysis of defect formation processes in ZnGeP₂ and a ZnGeP₂: Cu solid solution performed within the framework of the quasichemical analysis method. It is demonstrated that by choosing the copper diffusion method the hole concentration in the ZnGeP₂ can be varied over the range 10¹²–10¹⁶ cm^–3. A retrograde character was observed in copper solubility in ZnGeP₂ compounds. Defect formation processes in ZnGeP₂ upon copper diffusion depend on the degree of atomic ordering in the cation sublattice at the diffusion annealing temperature.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 64–69, February, 1985.     

Energy band structure and modulation spectra of A2B4C25 semiconductors

The results of the energy band structure calculations of A²B⁴C₂⁵ compounds are reviewed, and the differences in the energy spectra passing from A³B⁵ semiconductors to their closest ternary analogs are described. The origin of the lowest conduction band minima of A²B⁴C₂⁵ compounds was determined from the slopes of the fundamental absorption edge and the pressure coefficients of the energy gap. The investigations of the valence band structure from electroreflectance (ER), thermoreflectance (TR) and wavelength modulated absorption (WMA) spectra are reviewed. In the higher energy region the ER and TR spectra of A²B⁴C₂⁵ compounds were found to be more complicated in comparison with those of their binary analogs. A model of an assignment of the structures in optical spectra of A²B⁴C₂⁵ compounds is discussed.     

Cohesive energy of zincblende (A<Superscript>III</Superscript>B<Superscript>V</Superscript> and A<Superscript>II</Superscript>B<Superscript>VI</Superscript>) structured solids

In this paper we present an expression relating the cohesive energy (E _coh in kcal/mol) of A^IIIB^V and A^IIB^VI semiconductors with the product of ionic charges (Z ₁ Z ₂) and nearest-neighbour distance d (Å). The cohesive energy values of these solids exhibit a linear relationship when plotted on a log-log scale against the nearest-neighbour distance d (Å), but fall on different straight lines according to the ionic charge product of the solids. A good agreement has been found between the experimental and calculated values of the cohesive energy of A^IIIB^V and A^IIB^VI semiconductors.     

Broadband frequency conversion of laser radiation in ZnGeP2 crystal

The phase matching conditions in the ZnGeP₂ crystal are calculated and analyzed from the viewpoint of broadband frequency conversion of mid-IR radiation. The frequency conversion of Cr:ZnS laser radiation in the ZnGeP₂ crystal is calculated. The results show the possibility of developing a broadband laser source whose spectrum spans a wavelength range of 3.2–9.5 µm.     

Thermal property of binary tetrahedral semiconductors

In this paper we present an expression relating the lattice thermal expansion coefficient α_L (10⁻⁶ K⁻¹) for the A^IIIB^V and A^IIB^VI semiconductors with the product of ionic charges (Z₁Z₂), melting temperature (T_m) and nearest neighbor distance d (Å). The lattice thermal expansion coefficient of these compounds exhibit a linear relationship when plotted on a log–log scale against the melting temperature (T_m), but fall on different straight lines according to the ionic charge product of the compounds. A good agreement has been found between the experimental and calculated values of the lattice thermal expansion coefficient for A^IIIB^V and A^IIB^VI semiconductors.     

Effective charges in binary and ternary oxide compounds

Effective charges in non-cubic binary oxide crystals are evaluated on the basis of their transverse and longitudinal optical phonon frequencies. The temperature dependence of the effective charge is reported in quartz, rutile and corundum. Three procedures which allow the determination of effective charges in ternary compounds are presented and applied to halogenate, silicate, aluminate and ABO_n-type crystals, where A is an alkali or alkaline earth and B is a transition-metal element. Results are compared with Phillips's ionicities.