luminescence of BaGa<Subscript>2</Subscript>Se<Subscript>4</Subscript> crystals activated by Eu<Superscript>2+</Superscript> and Ce<Superscript>3+</Superscript> ions

We have studied the effect of doping with Eu²⁺ and Ce³⁺ ions on the photoluminescence (PL) of BaGa₂Se₄ crystals in the temperature range 77–300 K. We have established that the broad bands with maxima at wavelengths 456 nm and 506 nm observed in the photoluminescence spectra of BaGa₂Se₄:Ce³⁺ crystals are due to intracenter transitions 5d → ²F_7/2 and 5d →²F_5/2 of the Ce³⁺ ions, while the broad photoluminescence band with maximum at 521 nm in the spectrum of BaGa₂Se₄:Eu²⁺ is associated with 4f⁶ 5d → 4f⁷ (⁸S_7/2) transitions of the Eu²⁺ ion. We show that in BaGa₂Se₄:Eu²⁺,Ce³⁺ crystals, excitation energy is transferred from the Ce³⁺ ions to the Eu²⁺ ions.     

Spectroscopic properties of Er<Superscript>3+</Superscript> ions in LiNbO<Subscript>3</Subscript> crystals codoped with HfO<Subscript>2</Subscript>

The results of the spectroscopic analysis of transition strengths for Er³⁺ ions in a series of Hf:Er:LiNbO₃ crystals with variable Hf content and fixed Er content are reported. Unpolarized UV-VIS-NIR absorption spectra, upconversion fluorescence spectra excited at 800 nm, and microsecond time-resolved spectra excited at 400 nm and 800 nm by 800 nm femtosecond laser were measured at room temperature. The HfO₂ incorporation has influence on Er³⁺ radiative lifetimes, and fluorescence branching ratios. For Hf(4 mol %):Er(1 mol %):LiNbO₃, Ω₂=2.63×10^-20 cm², Ω₄=2.86×10^-20 cm², and Ω₆=0.72×10^-20 cm². Ω₂<Ω₄ is contrary to the Er³⁺ general trend of Ω₂>Ω₄>Ω₆ when the Hf content is below its threshold concentration. In addition, the sum of Ω increases with the Hf content when the HfO₂ content below 6 mol % is unfamiliar. The upconversion mechanism is discussed in this work. PACS 71.20.Eh; 77.84.Dy; 42.62.Fi; 42.65.Ky     

Spectroscopic properties of Er<Superscript>3+</Superscript> in Sc:LiNbO<Subscript>3</Subscript> crystal

The results of Er³⁺ ion spectroscopic analysis in Sc:LiNbO₃ crystals were reported. The line strengths from the ground state to the excited state were evaluated from the measured unpolarized absorption spectrum and analyzed by using standard Judd–Ofelt theory. For Sc(3 mol. %):Er (1 mol. %):LiNbO₃ crystal, the obtained intensity parameters are: Ω₂=3.72×10^-20 cm², Ω₄=1.07×10^-20 cm², and Ω₆=0.98×10^-20 cm². The fluorescence spectra and microsecond time-resolved spectra were investigated in the visible region. The excited state absorption transition strengths at 800 nm excitation were evaluated based on Judd–Ofelt theory. The results obtained here were compared to results from other research on Er:LiNbO₃ crystals. PACS 71.20.Eh; 77.84.Dy; 42.70.Hj; 42.62.Fi; 42.65.Ky     

Luminescence and thermally stimulated recombination processes in Li<Subscript>6</Subscript>Gd(BO<Subscript>3</Subscript>)<Subscript>3</Subscript>:Ce<Superscript>3+</Superscript> crystals

The luminescence and thermally stimulated recombination processes in lithium borate crystals Li₆Gd(BO₃)₃ and Li₆Gd(BO₃)₃:Ce have been studied. The steady-state luminescence spectra under X-ray excitation (X-ray luminescence), temperature dependences of the intensity of steady-state X-ray luminescence (XL), and thermally stimulated luminescence (TSL) spectra of these compounds have been investigated in the temperature range of 90–500 K. The intrinsic-luminescence 312-nm band, which is due to the ⁶ P _J → ⁸ S _7/2 transitions in Gd³⁺ matrix ions, dominates in the X-ray luminescence spectra of these crystals; in addition, there is a wide complex band at 400–420 nm, which is due to the d → f transitions in Ce³⁺ impurity ions. It is found that the steady-state XL intensity in these bands increases several times upon heating from 100 to 400 K. The possible mechanisms of the observed temperature dependence of the steady-state XL intensity and their correlation with the features of electronic-excitation energy transfer in these crystals are discussed. The main complex TSL peak at 110–160 K and a number of minor peaks, whose composition and structure depend on the crystal type, have been found in all crystals studied. The nature of the shallow traps that are responsible for TSL at temperatures below room temperature and their relation with defects in the lithium cation sublattice are discussed.     

Up-conversion emissions of Er<Superscript>3+</Superscript>-Yb<Superscript>3+</Superscript> codoped Al<Subscript>2</Subscript>O<Subscript>3</Subscript> nanoparticles by the arc discharge synthesis method

The Er³⁺-Yb³⁺ codoped Al₂O₃ nanoparticles with an average particle size of about 50 nm have been synthesized by an arc discharge synthesis method. The green and red up-conversion emissions centered at about 526, 547 and 677 nm, corresponding respectively to the ²H_11/2→⁴I_15/2, ⁴S_3/2→⁴I_15/2 and ⁴F_9/2→⁴I_15/2 transitions of Er³⁺, were detected by a 978-nm semiconductor laser diode excitation. The Annealing has evident effect on the up-conversion emissions of the samples: The red up-conversion emission is noticeable before annealing; however, the green up-conversion emission becomes predominant after annealing. The mixture of (Er,Yb)₃Al₅O₁₂ and α-(Al,Er,Yb)₂O₃ phases is more favorable for green up-conversion emissions due to an enhancement of the ESA (I) of ⁴I_11/2+a photon→⁴F_7/2 and ET (III) of ²F_5/2(Yb³⁺)+⁴I_11/2(Er³⁺)→²F_7/2(Yb³⁺)+⁴F_7/2(Er³⁺) processes. The two-photon absorption up-conversion process is involved in the green and red up-conversion emissions. The results have proved that arc discharge synthesis is a new promising preparation technology for optical materials. Supported by National Natural Science Foundation of China (Grant No. 10804015), the Scientific Research Foundation for Doctor of Liaoning Province (Grant No. 20071095), and the Educational Committee Foundation of Liaoning Province (Grant No. 2008123)     

Optical spectra and excited state relaxation dynamics of Sm<Superscript>3+</Superscript> in Gd<Subscript>2</Subscript>SiO<Subscript>5</Subscript> single crystal

Single crystals of gadolinium orthosilicate Gd₂SiO₅ containing 0.5 at% and 5 at% of Sm³⁺ were grown by the Czochralski method. Optical absorption spectra, luminescence spectra and luminescence decay curves were recorded for these systems at 10 K and at room temperature. Comparison of optical spectra recorded in polarized light revealed that the anisotropy of this optically biaxial host affects the intensity distribution within absorption and emission bands related to transitions between multiplets rather than the overall band intensity. It has been found that among four bands of luminescence related to the ⁴G_5/2→⁶H_J (J=5/2–11/2) transitions of Sm³⁺ in the visible and near infrared region the ⁴G_5/2 →⁶H_7/2 one has the highest intensity with a peak emission cross section of 3.54×10⁻²¹ cm² at 601 nm for light polarized parallel to the crystallographic axis c of the crystal. The luminescence decay curve recorded for Gd₂SiO₅:0.5 at% Sm³⁺ follows a single exponential time dependence with a lifetime 1.74 ms, in good agreement with the ⁴G_5/2 radiative lifetime τ _rad=1.78 ms calculated in the framework of Judd-Ofelt theory. Considerably faster and non-exponential luminescence decay recorded for Gd₂SiO₅:5 at% Sm³⁺ sample was fitted to that predicted by the Inokuti-Hirayama theory yielding the microparameter of Sm³⁺–Sm³⁺ energy transfer C _da=1.264×10⁻⁵² cm⁶×s⁻¹.     

Luminescence and electronic excitations in Li<Subscript>6</Subscript>Gd(BO<Subscript>3</Subscript>)<Subscript>3</Subscript>: Ce<Superscript>3+</Superscript> crystals

This paper reports on a study of the luminescence emitted by Li₆Gd(BO₃)₃: Ce³⁺ crystals under selective photoexcitation to lower excited states of the host ion Gd³⁺ and impurity ion Ce³⁺ within the 100–500-K temperature interval, where the mechanisms of migration and relaxation of electronic excitation energy have been shown to undergo noticeable changes. The monotonic 10–15-fold increase in intensity of the luminescence band at 3.97 eV has been explained within a model describing two competing processes, namely, migration of electronic excitation energy over chains of Gd³⁺ ions and vibrational energy relaxation between the ⁶ I _j and ⁶ P _j levels. It has been shown that radiative transitions in Ce³⁺ ions from the lower excited state 5d ¹ to ² F _5/2 and ² F _7/2 levels of the ground state produce two photoluminescence bands, at 2.08 and 2.38 eV (Ce1 center) and 2.88 and 3.13 eV (Ce2 center). Possible models of the Ce1 and Ce2 luminescence centers have been discussed.     

Upconversion excitations in Pr<Superscript>3+</Superscript>-doped BaY<Subscript>2</Subscript>F<Subscript>8</Subscript> crystal

We report the orange-to-blue and infrared-(IR)-to-blue wavelengths upconversion luminescence in Pr³⁺:BaY₂F₈ crystals. Mechanism of the orange light upconversion into blue ³P₀ state emission was confirmed to be energy transfer between two Pr³⁺ ions in the ¹D₂ state. IR-to-blue upconversion has only been observed under two different color IR pumping. The first resonant step was the ³H₄→¹G₄ ground state absorption transition, and the second resonant transition was the excited state absorption from the ¹G₄ to ¹I₆ and ³P_J levels. A comparison of the efficiency of the IR-to-blue upconversion in several praseodymium activated host is presented and discussed. A model of the IR pumped upconversion praseodymium blue laser is presented and the population inversion conditions are calculated.     

The influence of the specific surface of grains on the luminescence properties of Nd<Superscript>3+</Superscript>-doped Y<Subscript>3</Subscript>Al<Subscript>5</Subscript>O<Subscript>12</Subscript> nanopowders

Nd³⁺:Y₃Al₅O₁₂ (Nd:YAG) powders were prepared by the Pechini method in the temperature range of 800 to 1400 °C. The pure garnet phase of the obtained materials was confirmed by XRD studies. The size of the grains was controlled by the annealing temperature of the samples. Their morphologies were investigated by TEM and porosity measurements (BET). The effect of annealing temperature on the morphology and luminescence properties of Nd:YAG nanocrystallites was studied, and the results were compared to the properties of a Nd:YAG single crystal. A significant enhancement of the ⁴F_3/2→⁴I_9/2/⁴F_3/2→⁴I_11/2 intensity ratio with decreasing grain size was observed. It was found that the decay times of the Nd³⁺ luminescence depends on the specific surface and is significantly longer for well crystallized nanocrystalline grains than for single crystals having the same concentration of Nd³⁺ ions. The role of crystallinity and specific surface on the radiative processes is analyzed. PACS 78.55.-m; 78.20.Ci; 78.67.Bf; 78.68.+m     

Defect Structure and Up-conversion Luminescence Properties of ZrO<Subscript>2</Subscript>:Yb<Superscript>3+</Superscript>,Er<Superscript>3+</Superscript> Nanomaterials

The up-converting ZrO₂:Yb³⁺,Er³⁺ nanomaterials were prepared with the combustion and sol–gel methods. FT-IR spectroscopy was used for analyzing the impurities. The crystal structures were characterized with X-ray powder diffraction and the mean crystallite sizes were estimated with the Scherrer formula. Up-conversion luminescence measurements were made at room temperature with IR-laser excitation at 977 nm. The IR spectra revealed the conventional and OH⁻ impurities for the combustion synthesis products. The structure of the ZrO₂:Yb³⁺, Er³⁺ nanomaterials was cubic except for the minor monoclinic and tetragonal impurities obtained with the sol–gel method. The materials showed red (650–700 nm) and green (520–560 nm) up-conversion luminescence due to the ⁴F_9/2→⁴I_15/2 and (²H_11/2, ⁴S_3/2)→⁴I_15/2 transitions of Er³⁺, respectively. The products obtained with the combustion synthesis exhibited the most intense luminescence intensity and showed considerable afterglow.     

Growth,spectroscopic and laser properties of Yb<Superscript>3<Emphasis Type="Bold">+</Emphasis></Superscript>-doped GdAl<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>4</Subscript> crystal: a candidate for infrared laser crystal

Yb³⁺:GdAl₃(BO₃)₄ (hereafter Yb³⁺:GAB) crystals with large sizes and good optical quality have been grown by the top-seed solution growth (TSSG) method. The polarized absorption and emission spectra have been investigated at room temperature. For the σ-polarization, the intensities of both absorption and emission spectra are stronger than those for the π-polarization, the σ-absorption cross section of Yb³⁺ in GAB being 3.43×10^-20 cm² at 977 nm, and the σ-emission cross section being 0.98×10^-20 cm² at 1045 nm. The fluorescence lifetime of the ² F _5/2→² F _7/2 transition was measured to be 800 μs in the 5% doped sample used for our laser experiments, 993 μs in a 10% doped sample and 569 μs in a 0.5% doped sample. The laser parameters were estimated as: β_min=0.022, I_sat=10.4 kW/cm² and I_min=0.23 kW/cm². About 0.4 W laseroutput at the wavelength of 1043 nm was achieved when the Yb³⁺:GAB crystal was pumped by a 974 nm laser diode, with 27.4% slope efficiency. PACS 42.55.-f; 42.70.Hj; 78.20.-e; 81.10.Dn     

Spectroscopic Properties and Energy Transfer Analysis of Tm<Superscript>3+</Superscript>-Doped BaF<Subscript>2</Subscript>-Ga<Subscript>2</Subscript>O<Subscript>3</Subscript>-GeO<Subscript>2</Subscript>-La<Subscript>2</Subscript>O<Subscript>3</Subscript> Glass

This paper reports on the spectroscopic properties and energy transfer analysis of Tm³⁺-doped BaF₂-Ga₂O₃-GeO₂-La₂O₃ glasses with different Tm₂O₃ doping concentrations (0.2, 0.5, 2.0, 2.5, 3.0, 3.5, 3.5, 4.0 wt%). Mid-IR fluorescence intensities in the range of 1,300 nm−2,200 nm have been measured when excited under an 808 nm LD for all the samples with the same pump power. Energy level structure and Judd-Ofelt parameters have been calculated based on the absorption spectra of Tm³⁺, cross-relaxation rates and multi-phonon relaxation rates have been estimated with different Tm₂O₃ doping concentrations. The maximum fluorescence intensity at around 1.8 μm has been obtained in Tm₂O₃-3 wt% sample and the maximum value of calculated stimulated emission cross-section of Tm³⁺ in this sample is about 0.48 × 10⁻²⁰ cm² at 1,793 nm, and there is not any crystallization peak in the DSC curve of this sample, which indicate the potential utility of Tm³⁺-doped BaF₂-Ga₂O₃-GeO₂- La₂O₃ glass for 2.0-μm optical fiber laser.     

On the Luminescence of Ce<Superscript>3+</Superscript>, Eu<Superscript>3+</Superscript>, and Tb<Superscript>3+</Superscript> in Novel Borate LiSr<Subscript>4</Subscript>(BO<Subscript>3</Subscript>)<Subscript>3</Subscript>

This paper reports on the photoluminescence (PL) and time-resolved properties of Ce³⁺, Eu³⁺, and Tb³⁺ in novel LiSr₄(BO₃)₃ powder phosphors. Ce³⁺ shows an emission band peaking at 420 nm under 350-nm UV excitation. Energy transfer from Ce³⁺ to Mn²⁺ takes place in the co-doped samples. Eu³⁺ shows red emission under near UV excitation. LiSr₄(BO₃)₃:Eu³⁺ phosphor could be a suitable candidate for phosphor-converted solid state lighting. The luminescence lifetime is 2.13 ms for Eu³⁺ in LiSr₄(BO₃)₃:0.001Eu³⁺. As Eu³⁺ concentration increasing, the decay curves deviate from exponential behavior. Tb³⁺ shows the strongest ⁵D₄→⁷ F₅ emission line at 540 nm. Decay curves of ⁵D₄→⁷ F₅ and ⁵D₃→⁷ F₅ emission with different Tb³⁺ concentrations were also measured. Cross-relaxation process is discussed based on the decay curves.     

Spectroscopic properties of Nd<Superscript>3+</Superscript>:CaNb<Subscript>2</Subscript>O<Subscript>6</Subscript> crystal

The absorption spectra, fluorescence spectrum and fluorescence decay curve of Nd³⁺ ions in CaNb₂O₆ crystal were measured at room temperature. The peak absorption cross section was calculated to be 6.202×10⁻²⁰ cm² with a broad FWHM of 7 nm at 808 nm for E//a light polarization. The spectroscopic parameters of Nd³⁺ ions in CaNb₂O₆ crystal have been investigated based on Judd-Ofelt theory. The parameters of the line strengths Ω _t are Ω ₂=5.321×10⁻²⁰ cm²,Ω ₄=1.734×10⁻²⁰ cm²,Ω ₆=2.889×10⁻²⁰ cm². The radiative lifetime, the fluorescence lifetime and the quantum efficiency are 167 μs, 152 μs and 91%, respectively. The fluorescence branch ratios are calculated to be β ₁=36.03%,β ₂=52.29%,β ₃=11.15%,β ₄=0.533%. The emission cross section at 1062 nm is 9.87×10⁻²⁰ cm².     

Study of spectroscopic characteristics of holmium-doped double sodium-yttrium fluoride crystals Na<Subscript>0.4</Subscript>Y<Subscript>0.6</Subscript>F<Subscript>2.2</Subscript>:Ho<Superscript>3+</Superscript>

We have grown crystals Na_0.4Y_0.6F_2.2:Ho³⁺ (NYF:Ho³⁺) by the Bridgman-Stockbarger method. The optical spectra and luminescence kinetics of NYF:Ho³⁺ crystals have been studied. Based on the analysis of low-temperature absorption spectra, we determine the structure of the Stark splitting of holmium levels in NYF:Ho³⁺ crystals. From absorption spectra examined at T = 300 K, we calculate absorption cross-section spectra and oscillator strengths of transitions from the ground state of holmium to excited multiplets. We show that the absorption spectra of NYF:Ho³⁺ crystals consist of broad bands that lie in the UV, visible, and near-IR ranges. The most intense bands are observed in the visible range, they correspond to transitions ⁵ I ₈ → (⁵ F ₁, ⁵ G ₆) and ⁵ I ₈ → (⁵ F ₄, ⁵ S ₂), and their maximal absorption cross sections are σ_abs^max (λ = 450.3 nm) = 1.16 × 10⁻²⁰ cm² and σ_abs^max (λ = 535.1 nm) = 0.9 × 10⁻²⁰ cm². The intensity parameters Ω _t have been calculated by the Judd-Ofelt method taking into account 10, 12, and 20 transitions from the ⁵ I ₈ ground state to excited multiplets. We show that, with an increasing number of transitions taken into account in the calculation, the parameters Ω _t somewhat increase. For 20 transitions, we have obtained the following intensity parameters: Ω₂ = 0.97 × 10⁻²⁰, Ω₄ = 1.74 × 10⁻²⁰, and Ω₆ = 1.15 × 10⁻²⁰ cm². With these parameters, we have calculated the probabilities of radiative transitions, the radiative lifetimes, and the branching ratios. The rates of multiphoton nonradiative transitions have been estimated. The luminescence decay kinetics from excited holmium levels ⁵ F ₃ (⁵ F ₄, ⁵ S ₂) and ⁵ F ₅ have been studied upon selective excitation in the range of 490 nm, and the lifetimes of these levels have been experimentally determined. We find that the calculated and experimental rates of radiative and nonradiative relaxation from excited holmium levels agree well with each other. We show that, upon pumping in the range of 490 nm, the multiplet (⁵ F ₄, ⁵ S ₂) is populated as a result of the radiative and nonradiative excitation relaxation from the ⁵ F ₃ level, while the lower-lying ⁵ F ₅ level is populated due to direct radiative transitions ⁵ F _{3, 2} → ⁵ F ₅, obviating the cascade scheme ⁵ F ₃ → (⁵ F ₄, ⁵ S ₂) ↝ ⁵ F ₅. We conclude that NYF:Ho³⁺ crystals are processable; admit doping by holmium in high concentrations (up to 100%); and, with respect to all their radiative characteristics, can be considered as potential active media for solid-state continuously tunable lasers in the IR and visible ranges.     

Leading-order 2πγ exchange NN interaction: Central potentials proportional to g<Subscript>A</Subscript><Superscript>0</Superscript> and g<Subscript>A</Subscript><Superscript>2</Superscript>

We calculate at two-loop order in chiral perturbation theory the electromagnetic corrections to the leading-order 2π exchange NN interaction proportional to g _A ⁰ and g _A ². The resulting 2πγ exchange potential contains isospin-breaking components which reach up to about -2% of the corresponding isovector 2π exchange potential. With a value of only -17keV at r = m _π ^-1 = 1.4fm the charge-independence breaking central potential obtained here is negligibly small in comparison to the one generated by the isoscalar c₃ contact vertex. Our calculation confirms that the largest long-range isospin-violating NN potentials arise from the 2πγ exchange diagrams involving the large low-energy constants c ₄ ≃ - c ₃ ≃ 3.3GeV^-1 representing the important Δ(1232) dynamics.     

Intense Upconversion Luminescence of Yb<Superscript>3+</Superscript>-Er<Superscript>3+</Superscript> in Li<Subscript>2</Subscript>O Content Tungsten-tellurite Glasses

The Er³⁺ -Yb³⁺ codoped in Li₂O content tungsten -tellurite (TWL) transparent glasses are synthesized and measured the absorption, Raman and upconversion luminescence (UPL) spectra. At room temperature intense green emission peak at 560 nm ( ⁴S_3/2→⁴I_15/2) and red emission peak at 670 nm ( ⁴F_9/2→⁴I_15/2) of Er³⁺ observed even at minimum 86 mW pumping power of infrared 980 nm excitation. For structure of the TWL glass, Raman spectrum result revealed that an important role of WO₃ in the formation of glass network linkage with Li₂O. Under this influence estimated lifetime of the ⁴I_11/2 of Er³⁺ was 1.89 μs and due to lower phonon energy of the glass produce strong upconversion signal. The effect of Er₂O₃ concentration on emission intensity result indicated that green emission intensity initially increase in compare to red emission. Under the 980 nm pump power variation measured the relatively increases the red emission to the green emission intensity and analyze the possible upconversion mechanism and process.     

Superhyperfine Structure of EPR Spectra in LiLuF<Subscript>4</Subscript>:U<Superscript>3+</Superscript> and LiYF<Subscript>4</Subscript>:Yb<Superscript>3+</Superscript> Single Crystals

Electron paramagnetic resonance (EPR) spectra of doped paramagnetic crystals LiLuF₄:U³⁺ and LiYF₄:Yb³⁺ have been investigated at a frequency of about 9.42 GHz in the temperature range of 10–20 K. The U³⁺ ion spectrum is characterized by g-factors g _∥ = 1.228 and g _⊥ = 2.516, and contains the hyperfine structure due to the ²³⁵U isotope with nuclear spin I = 7/2 and natural abundance of 0.71%. The observed hyperfine interaction constants are A _∥ = 81 G and A _⊥ = 83.8 G. Moreover, the spectrum reveals the well-resolved superhyperfine structure (SHFS) due to two groups of four fluorine ions forming the nearest surrounding of the U³⁺ ion. This SHFS contains up to nine components with the spacing between components being about 12.7 G. The SHFS is observed also in the EPR spectrum of the LiYF₄:Yb³⁺ crystal; up to 17 components with spacing of about 3.7 G may be traced. Some parameters of the effective Hamiltonian of the SHF interaction are estimated, the contribution of covalent bonding of f-electrons with ligands into these parameters is discussed. Authors' address: Igor N. Kurkin, Kazan State University, Kremlevskaya ulitsa 18, Kazan 420008, Russian Federation     

Electronic spectra and phase transitions in thin [N(CH<Subscript>3</Subscript>)<Subscript>4</Subscript>]<Subscript>2</Subscript>CuCl<Subscript>4</Subscript> microcrystals

Optical absorption spectra in thin [N(CH₃)₄]₂CuCl₄ crystals in the thickness range 10 μm ≤ d < 100 μm have been studied. Strengthening of the crystal field has been found with a decrease in the [N(CH₃)₄]₂CuCl₄ crystal size. The reasons for absorption band shifts in the visible region depending on the [N(CH₃)₄]₂CuCl₄ crystal thickness and the manifestation of a size effect in crystals with an incommensurate superstructure are discussed.     

Effect of Sr<Superscript>2+</Superscript> ion substitution with trivalent ions (Sc<Superscript>3+</Superscript>, In<Superscript>3+</Superscript>, La<Superscript>3+</Superscript>, Bi<Superscript>3+</Superscript>) on its ferroelectric instability in SrTiO<Subscript>3</Subscript>

The vibration frequencies of unstable ferroelectric and antiferrodistortion modes and the dependences of the energy on the ion displacement amplitude have been calculated within the generalized Gordon-Kim model for distortions along eigenvectors of these modes in the mixed compounds Sr_{1 − x} A _x Ti_{1 − x} /₄□ _x/4O₃ and Sr_{1 − y} A _2y /₃□ _y/3TiO₃ (A = Sc³⁺, In³⁺, La³⁺, Bi³⁺; □ is the vacancy). To compensate an excess positive charge, vacancies are introduced into the Ti⁴⁺ or Sr²⁺ site. Calculations have been performed in the “daverage” crystal approximation for impurity concentrations of 0.25 and 0.50. To this end, a set of 40 atomic superlattices with various orderings of heterovalent ions Sr²⁺ and impurity A ³⁺ has been considered. It has been found that each impurity type, independently of charge balance, induces ferroelectric instabilities in doped compounds. In the case of doping with In³⁺ and La³⁺ for concentration x = 0.25, the possibility of rotating the polarization vector has been shown.