Eu‐, Tb‐, and Dy‐Doped Oxyfluoride Silicate Glasses for LED Applications

Luminescence glass is a potential candidate for the light‐emitting diodes (LEDs) applications. Here, we study the structural and optical properties of the Eu‐, Tb‐, and Dy‐doped oxyfluoride silicate glasses for LEDs by means of X‐ray diffraction, photoluminescence spectra, Commission Internationale de L'Eclairage (CIE) chromaticity coordinates, and correlated color temperatures (CCTs). The results show that the white light emission can be achieved in Eu/Tb/Dy codoped oxyfluoride silicate glasses under excitation by near‐ultraviolet light due to the simultaneous generation of blue, green, yellow, and red‐light wavelengths from Tb, Dy, and Eu ions. The optical performances can be tuned by varying the glass composition and excitation wavelength. Furthermore, we observed a remarkable emission spectral change for the Tb³⁺ single‐doped oxyfluoride silicate glasses. The ⁵D₃ emission of Tb³⁺ can be suppressed by introducing B₂O₃ into the glass. The conversion of Eu³⁺ to Eu²⁺ takes place in Eu single‐doped oxyfluoride aluminosilicate glasses. The creation of CaF₂ crystals enhances the conversion efficiency. In addition, energy transfers from Dy³⁺ to Tb³⁺ and Tb³⁺ to Eu³⁺ ions occurred in Eu/Tb/Dy codoped glasses, which can be confirmed by analyzing fluorescence spectra and energy level diagrams.     

Enhanced up-conversion luminescence of Tb3+-Yb3+ doped glass ceramics by doping Li+

Tb³⁺-Yb³⁺ co-doped transparent glass ceramics (GCs) containing Y₂Ti₂O₇ crystal phases were synthesized by the melt crystallization. The light transmittance of GCs in the visible region reached 78%, and the average grain size was 278 nm under the optimal heat treatment conditions (720 °C/2 h). The GCs exhibited greater up-conversion luminescence intensity than precursor glass, and the reason for this result was explained in accordance with the Judd-Ofelt theory. Moreover, the introduction of Li⁺ did not change the crystalline phase of GCs. The emission intensity of the green light of the 8% Li ⁺ doped GCs was significantly enhanced by nearly 4.48 times under 980 nm excitation. The XRD refinement results suggest that the enhanced luminescence intensity is correlated with the change of the Y₂Ti₂O₇ crystal lattice caused by Li⁺ doping. The relevant luminescence mechanism was elucidated. The results suggest that Li⁺ doped transparent GCs open novel avenues for green UC applications.     

稀土离子(Gd~(3+),Ce~(3+)/Ce~(4+),Eu~(3+))对Tb~(3+)掺杂硅酸盐玻璃发光性能的影响

研究了(Gd3+,Ce3+/Ce4+,Eu3+)对Tb3+掺杂硅酸盐玻璃发光性能的影响.结果表明:Tb3+掺杂硅酸盐玻璃可以发出弱蓝光(400～460 mm)和较强的绿光(480～600mm).Gd3+对Tb3+的发光起敏化作用,可提高TB3+掺杂硅酸盐玻璃的发光强度.在空气中熔制的玻璃中Ce3+和Ce4+同时存在,Ce3+对Tb3+发光起敏化作用;而Ce4+对Tb3+发光起淬灭作用.由于Ce4+比例比较高,CeO2加入导致TB3+发光强度降低,同时也缩短了Tb3+发光余辉.加入Eu2O3时,Eu3+自身发光分散了激发Tb3+发光的能量,使Tb3+的特征发射强度降低.     

Up-conversion luminescence and temperature-sensing properties of Li+, K+ doped Na2Zn3Si2O8: Er3+ phosphors

In this work we detail the preparation of new luminescent Li⁺ and K⁺ doped Na₂Zn₃Si₂O₈: Er³⁺ up-conversion phosphors using the high-temperature solid-phase method. We investigate the phosphors phase structure, elemental distribution, up-conversion luminescence characteristics and temperature sensing properties. Our fabricated samples were found to be homogeneous and when excited using 980 nm light, they emitted wavelengths in the green and red visible wavelength bands, which correspond to two major emission bands of Er³⁺. Doping with Li⁺ and K⁺ increased the luminescence intensity of the Na₂Zn₃Si₂O₈: Er³⁺ phosphor at 661 nm by 36 and 21 times respectively. The highest relative temperature sensitivity (Sa) of the fabricated phosphor reached a value of 19.69% K^?1 and the highest absolute temperature sensitivity (Sr) reached 1.20% K^?1. These values are superior to other materials which utilize up-conversion by Er³⁺ ions as a tool for temperature sensing. We anticipate that these new phosphors will find significant application as components in optical temperature measurement systems.     

The effect of Li+ incorporation in Yb3+-Nd3+ co-doped CaF2 phosphors over the NIR photoluminescence emission excited under visible light

The structural and optical characteristics of Nd³⁺-Yb³⁺ doped CaF₂ phosphors with and without the addition of Li⁺ ions are described in this work. The phosphors synthetized by hydrothermal and co-precipitation methods showed near-infrared (NIR) luminescence emission associated with inter-electronic transition of the Yb³⁺ ion in the range of 900–1050 nm via energy transfer process from Nd³⁺ ions under visible light excitation. The addition of Li⁺ to these phosphors resulted in an improvement of the NIR luminescence intensity by a factor up to 5. The effect of the incorporation of Li⁺ ions into the CaF₂ crystallite structure, the reduction of luminescence quenching states, as well as the energy transfer mechanism involved are discussed.     

The role of the stabilizing agent on the structural and luminescent properties of hydrothermally synthesized ZrO2:Tb3+phosphors

Zirconium oxide powders doped with terbium, synthesized by hydrothermal route from a highly basic solution, were used to determine the role of the basic agent (NaOH, KOH or LiOH) utilized to carry out the hydrothermal synthesis on their morphology, crystalline structure, photoluminescent or cathodoluminescent properties. The synthesized powders showed an amorphous/polycrystalline nature with tetragonal phase crystallites of ZrO₂. The ratio of material undergoing the transformation from amorphous to crystalline is highly influenced by the kind of stabilizing agent used. As for the photoluminescence (PL) and cathodoluminescence (CL) results, the samples present the characteristic emission lines corresponding to inter electronic energy levels transitions for Tb³⁺ ions (⁵D₄ → ⁷F_J (J?=?3–6) transitions). The photoluminescence excitation spectra present a broad peak centered at 250?nm for all samples, however the sample prepared with LiOH as basic agent presented an additional peak at 290?nm which much likely is related to localized centers introduced by Li⁺ ions into the ZrO₂ crystallites.     

Investigation on Energy Transfer and Luminescent Properties of K3Gd(PO4)2:RE3+ (RE = Eu,Tb) Under UV and VUV Excitation

K₃Gd(PO₄)₂:RE³⁺ (RE = Eu, Tb) are prepared by solid‐state reaction and their photoluminescence (PL) properties are investigated under UV and VUV excitation, respectively. The obtained experimental data show that no energy transfer happens among the activator ions Tb³⁺ or Eu³⁺ under UV excitation. Under 147‐nm excitation, the strongest emission intensity of K₃Gd(PO₄)₂:RE³⁺ (RE = Eu, Tb) is obtained when the activator ions Tb³⁺ or Eu³⁺ concentration is 0.8 mol, the integrate emission intensity of K₃Gd_0.2(PO₄)₂:0.8Tb³⁺ is about 204% of commercial phosphor Zn_1.96SiO₄:0.04Mn²⁺ with chromaticity coordinates of (0.340, 0.561) and the decay time of about 5.09 ms under 147‐nm excitation. We analyze the experimental data and propose a possible energy‐transfer mechanism under 147‐nm excitation.     

Paramagnetic,NIR‐luminescent Nd3+‐ and Gd3+‐doped fluorapatite as contrast agent for multimodal biomedical imaging

Combining near infrared (NIR) luminescence and magnetic resonance (MR) contrasts in a crystal host is highly desirable for contrast agents in biomedical imaging technology, as it will enable multimodal imaging processes. In the present work, biocompatible luminescent and paramagnetic fluorapatite (FAp) nanoparticles were prepared via doping with neodymium (Nd³⁺) and gadolinium (Gd³⁺), respectively. While Nd³⁺‐doped FAp (Nd:FAp) exhibits dopant concentration‐dependent photoluminescence (PL) in the NIR spectral region, Gd³⁺‐doped FAp (Gd:FAp) shows paramagnetic behavior and strong transverse relaxation effects resulting in MR contrastive properties. Remarkably, multimodal co‐doped FAp (Nd:Gd:FAp) nanoparticles combine both properties in 1 single crystal enabling luminescence as well as MR contrast.     

Synthesis and characterization of Cu–doped Cs2KBiBr6 double perovskite phosphors for photoluminescent applications

In the present study, we report on the synthesis and photo-luminescent applications of hexagonal double perovskite Cs₂BIBiBr₆ (where BI = K, Li) doped with Cu ²⁺ ions. Powder XRD patterns were used to confirm the formation of single-phase compounds. Near-UV light was significantly assimilated by localized excitations focused on Bi ³⁺ ions in the host lattice. Only very faint photoluminescence was detected in the undoped host lattice, while energy transfer from Bi ³⁺ to Cu ²⁺ causes immense green photoluminescence in copper-doped materials. A photoluminescence emission peak was obtained at 415 nm for Cs₂KBiBr₆. PL peaks were gradually red-shifted to higher wavelengths of 417 nm and 419 nm for Cu-doped Cs₂ Li_0.5K_0.5BiBr₄Cl₂ and Cu-doped Cs₂KBiBr₄Cl₂, respectively. Their capacity to modify a phosphor system's excitation and emission spectrum has enhanced these novel classes of material.     

Precipitation Synthesis and Color‐Tailorable Luminescence of α‐Zr(HPO4)2: RE3+(RE = Eu,Tb) Nanosheet Phosphors

The rare earth (RE = Eu and Tb) ions‐doped α‐Zr(HPO₄)₂ (ZrP) nanosheet phosphors were synthesized by direct precipitation method, and their structures and photoluminescence properties were investigated. The results of X‐ray diffraction and scanning electron microscopy indicated that the systems of ZrP:RE³⁺ had similar nanosheet structure except with relatively larger interlayer spacing as compared with pure α‐ZrP. Under the excitation of UV light, the ZrP:RE³⁺ nanosheet phosphors showed red and green emission peaks corresponding to the ⁵D₀→⁷F₂ transition of Eu³⁺ and the ⁵D₄→⁷F₅ transition of Tb³⁺, respectively. After Eu³⁺ and Tb³⁺ were co‐doped in ZrP host, not only the red and green emission peaks were simultaneously observed, but also the luminescent intensity and fluorescence lifetimes of Tb³⁺ were gradually decreased with the increase in Eu³⁺‐doping concentration, which implied the energy transfer from Tb³⁺ to Eu³⁺ happened. It was deduced that the energy transfer from Tb³⁺ to Eu³⁺ occurred via exchange interaction. Through optimization to the samples, a nearly white‐light emission with the color coordinate (0.322, 0.263) was achieved under 377 nm excitation. The ZrP:RE³⁺ nanosheet phosphors may be a potential color‐tailorable candidate for fabricating optoelectronic devices such as electroluminescence panels.     

Mid‐IR to Visible Photoluminescence,Dielectric, and Ferroelectric Properties of Er‐Doped KNLN Ceramics

Two mole percentage Er‐doped (K_0.5Na_0.5)_1 ? xLi_xNbO₃ ceramics have been prepared and their dielectric, ferroelectric, and photoluminescence (PL) properties have been investigated. Under an excitation of 980 nm, the ceramics exhibit intense up‐conversion luminescent emission at 548 nm (green), weak emission at 660 nm (red) as well as strong down‐conversion luminescent emission in near‐infrared (NIR) (1.40–1.65 μm) and mid‐infrared (2.60–2.85 μm) regions. Probably due to the induced structure distortion and reduced local symmetry, the PL intensities of the green, red as well as mid‐infrared emissions are enhanced by the doping of Li⁺. Our results show that the Li‐doping is effective in establishing a dynamic circulatory energy process to further enhance the PL intensity of the mid‐infrared emission at the expense of the NIR emission. At the optimum doping level of Li⁺ (~6 mol%), the full bandwidth at half maximum of the mid‐infrared emission reaches a very large value of ~250 nm. The ceramics also exhibit good ferroelectric properties, and thus they should have great potential for multifunctional optoelectronic applications.     

Dazzling cool white light emission from Ce3+/Sm3+ activated LBZ glasses for W-LED applications

We synthesized a batch of co-doped (Ce³⁺+Sm³⁺): LBZ glass specimens by melt quenching process and their structural and radiation properties were studied by employing XRD, FE-SEM, optical absorption, photoluminescence and lifetime measurements. UV–Vis–NIR absorption studies of the co-doped (Ce³⁺+Sm³⁺): LBZ glassy matrix displays pertinent bands of both Ce³⁺ and Sm³⁺ ions. Individually doped Sm³⁺: LBZ glass exhibit bright orange emission at 603?nm (⁴G_5/2 → ⁶H_7/2) under the excitation of 403?nm. Nevertheless, the luminescence intensities pertaining to Sm³⁺ were extraordinarily increased by co-doping with Ce³⁺ ions to Sm³⁺: LBZ glassy matrices because of energy transfer from Ce³⁺ to Sm³⁺. The fluorescence spectra of co-doped (Ce³⁺+Sm³⁺): LBZ exhibits characteristic emission bands of Ce³⁺ (441?nm, blue) and Sm³⁺ (603?nm, reddish orange) under the excitation of 362?nm. Decay curves of Ce³⁺ and Sm³⁺ ions in co-doped glass has been fitted to double exponential nature. The decreasing lifetime of donor ion and rising lifetime of acceptor ion in double doped glass could support the energy transfer from Ce³⁺ to Sm³⁺ ions in the host matrix. The CIE coordinates and CCT values were calculated for all the obtained co-doped glassy samples from their luminescence spectra. By adding Ce³⁺ ions to individually doped Sm³⁺: LBZ glass matrix, the emitting color changes from reddish orange to white light which resembles the energy transfer from Ce³⁺ to Sm³⁺ ions. These studies, perhaps implied that attained co-doped (Ce³⁺+Sm³⁺): LBZ glassy samples are potential materials for white lighting appliances.     

The role of co-dopants on the luminescent properties of α-Al2O3:Mn4+ and BaMgAl10O17:Mn4+

Mn⁴⁺ doped aluminate materials with efficient red emission are promising components for warmer white light-emitting diodes. However, it still remains as a challenge on increasing its luminous efficiency. For Mn⁴⁺ doped aluminate phosphors, co-dopants such as Li⁺, Mg²⁺, Na⁺, Si⁴⁺, or Ge⁴⁺ ions are often added to tailor the photoluminescence properties of phosphors during preparing process. However, the role of the ions is still in debate. In this work we took BaMgAl₁₀O₁₇:Mn (BMA:Mn) and α-Al₂O₃:Mn as examples to study the effects of Li⁺, Mg²⁺, Na⁺, and Si⁴⁺ on their luminescent properties. The energy levels induced by the co-dopants and some possible intrinsic defects of hosts (Al₂O₃) were calculated using the first-principles method. It is found that the Mg²⁺ and Na⁺ ions, compared with Li⁺ and Si⁴⁺, can prefer to form hole-type defects which enhance the valence stability of Mn⁴⁺ and thus enhance the emission intensity of the as-prepared phosphors.     

Improvement of photoluminescence properties of Ce3+- doped CaSrAl2SiO7 phosphors by charge compensation with Li+ and Na+

In this work, we prepared CaSr_1-xAl₂SiO₇:xCe³⁺ (0.03 ≤ x ≤ 0.12) and CaSr_0.94Al₂SiO₇:0.03Ce³⁺,0.03 M⁺ (M⁺ = Li⁺ and Na⁺) phosphors via solid-state reaction method. Structural and photoluminescence (PL) properties of the phosphors were also investigated. The prepared phosphors formed an orthorhombic crystal structure with the P2₁2₁2₁ space group. CaSr_1-xAl₂SiO₇:xCe³⁺ phosphors were effectively excited by near-ultraviolet (UV) light (345 nm), which is suitable with the emission of near-UV light emitting diode chips. A broad blue emission (402 nm) was detected in CaSr_1-xAl₂SiO₇:xCe³⁺ and CaSr_0.94Al₂SiO₇:0.03Ce³⁺,0.03 M⁺ phosphors; this was attributed to the 4f⁰5d¹ → 4f¹ transition of Ce³⁺. To maintain charge equilibrium, charge compensators, such as monovalent Li⁺ and Na⁺ ions, were doped into the CaSr_0.97Al₂SiO₇:0.03Ce³⁺ phosphor, significantly improving its PL properties. The strongest emission intensity was achieved in CaSr_0.94Al₂SiO₇:0.03Ce³⁺,0.03Li⁺ phosphor. Addition of Li⁺ charge compensator was highly effective in improving PL properties of CaSr_0.97Al₂SiO₇:0.03Ce³⁺ phosphors.     

Tunable emission color of Li2SrSiO4:Tb3+ due to cross‐relaxation process and optical thermometry investigation

A series of Li₂SrSiO₄:xTb³⁺ (0.2%, 0.4%, 0.6%, 0.8%, 2%, 4%, and 6%) phosphors were prepared by conventional solid‐state reaction. It was found that this silicate phosphor has a wide excitation band at near‐ultraviolet region (230‐300 nm) due to spin‐allowed 4f ⁸→4f⁷5d¹ transitions of Tb³⁺ ions, with the exact position dependent on the crystal field of the lattice. The cross‐relaxation process originating from ⁵D₃→⁵D₄ and ⁷F₆→⁷F₀ happened between different Tb³⁺ ions. It leads to the luminescence color of Li₂SrSiO₄: xTb³⁺ tuning from blue to green just by controlling Tb³⁺ concentrations. Furthermore, concentration quenching mechanism, energy migration type, cross‐relaxation rate and efficiency, are discussed in detail. Finally, optical thermometry properties were investigated via temperature‐dependent emission spectra. The results show that low‐concentration‐doped sample (Li₂SrSiO₄:0.4%Tb³⁺) shows remarkable optical thermometry based on fluorescence intensity ratio (FIR) between the blue and green emission of Tb³⁺ ions, whereas the high‐concentration‐doped sample (Li₂SrSiO₄:4%Tb³⁺) demonstrates small emission intensity loss. It illustrates that terbium‐doped silicate phosphor is a multifunctional material with potential application for display field and optical thermometry .     

Preparation and photoluminescence properties with the site‐selected excitations of Bi3+‐activated Ba3Sc4O9 phosphors

A series of novel Bi³⁺‐doped Ba₃Sc₄O₉ phosphors were synthesized through the solid‐state reaction. Their photoluminescence, decay curves, and thermal quenching properties were investigated in detail. The Ba₃Sc₄O₉:Bi³⁺ phosphors could be efficiently excited in the ultraviolet and near‐ultraviolet region (300‐400 nm), and the photoluminescence properties possess an obvious site‐selected excitations phenomenon. When excited at the ultraviolet light (320‐360 nm), the phosphors present a green or a bluish green emission, and when excited at the near‐ultraviolet light (370‐390 nm), the phosphors always show a yellow emission. The emission spectra excited at the different wavelength can be decomposed into four components, which accord with the four cationic sites in the structure of Ba₃Sc₄O₉. The influence of the Bi³⁺ concentration on the photoluminescence properties is also investigated. Upon excitation at 330 and 377 nm, the Ba₃Sc₄O₉:Bi³⁺ both have good thermal quenching properties; their emission intensity of the peak at 150°C both exceed 60% of the initial value. The above results indicate that the Ba₃Sc₄O₉:Bi³⁺ phosphor is a promising candidate to provide green or yellow components for UV or near‐UV LEDs.     

Li3AlN2—a self‐activated yellow light emitting wide‐bandgap semiconductor used for LEDs

In allusion to the problems existing in the defect‐related luminescent materials, a series self‐activated light emitting semiconductors of Li₃AlN₂: R (R=0, Na⁺, Mg²⁺, Si⁴⁺, Tb³⁺, Eu³⁺) have been successfully synthesized by sample‐pressure sintering. Under the excitation at 422 nm, a yellow light peaked at 580 nm have been observed in the host lattice of Li₃AlN₂. The crystal structure and the electron structure of Li₃AlN₂ have been measured to investigate the defect‐related luminescent properties of Li₃AlN₂ using the Rietveld refinement on the basic of X‐ray diffraction data and the density functional theory (DET). The results show that Li₃AlN₂ crystallizes in cubic phase with full filled edge‐shared (Al/Li)N₄ tetrahedrons and is a wide‐bandgap semiconductor. The impurity defects produced by ions substitution have also been investigated, which leads to the red‐shift of the emission peak. Finally, the photoluminescence excitation (PLE) spectrum of Li₃AlN₂ with two excitation bands peaked at 300 nm and 422 nm has been detected, and the latter matches well with near‐UV LED chips. The thermal stability shows that integral intensity of Li₃AlN₂ at 150°C still has 60% of the initial intensity at room temperature. The results indicate their potential applications as the LED used phosphors.     

Augmenting the photocatalytic performance of cobalt ferrite via change in structural and optical properties with the introduction of different rare earth metal ions

In the present study, synthesis of different rare earth (RE) doped cobalt ferrite nanoparticles was done via facile sol-gel auto-combustion method using four different RE metal ions: Eu, Gd, Dy and Nd. The RE substituted cobalt ferrite nanoparticles were then characterized using FT-IR, powder XRD, HR-TEM, SAED, EDX, VSM and DRS techniques. From the characterization results, a significant variation in the structural, magnetic and optical properties of pure cobalt ferrite was observed with the introduction of different RE metal ions. This change in the properties was emerged due to the distortion of the ferrite crystal lattice due to replacement of smaller ionic radii Fe³⁺ ions with the comparatively larger ionic radii RE³⁺ metal ions. The catalytic activity of the fabricated RE doped cobalt ferrite nanoparticles was studied for the photo-Fenton degradation of cationic and anionic dyes. Under visible light irradiation, the as prepared RE doped nanoparticles exhibited great enhancement in the photo-Fenton degradation of dye molecules as compared to pure cobalt ferrite nanoparticles. The enhancement in the degradation rate was ascribed to the generation of defects in the crystal lattice, lower crystallite size and reduced band gap energy values which facilitated the facile transfer of photo-generated holes and electrons. Best catalytic results were obtained for CoNd_0.08Fe_1.92O₄ for SO dye (k?=?2.23?×?10^?1 min^?1) which were found to be around 9 times higher than the pure cobalt ferrite nanoparticles (k?=?0.23?×?10^?1 min^?1).     

Photoluminescence Properties of Er/Pr‐Doped K0.5Na0.5NbO3 Ferroelectric Ceramics

Er/Pr‐doped K_0.5Na_0.5NbO₃ ceramics have been fabricated and the effects of Pr³⁺ on their photoluminescence properties have been investigated systematically. The visible upconversion emissions, near‐infrared and mid‐infrared downconversion emissions of Er³⁺ ions under the excitation of 980 nm have been studied in detail. The effects of Pr³⁺ on PL properties and energy‐transfer processes have also been elucidated. By selecting an appropriate excitation source, simultaneous visible downconversion emissions of Er³⁺ and Pr³⁺ ions can be realized, and the emission colors of the ceramics can be tuned via the concentration of Pr³⁺ ions in a wide range from yellowish green to yellow. Our results also reveal that the photoluminescence emissions of the ceramics can be enhanced by the alignment of polarization of the ferroelectric host.     

Tunable Mission and Trichromatic White‐Emitting in Oxyfluoride Glasses by Utilization of Cu+ Ions as Multiple Energy‐Transfer Creators

A series of copper species, Tb³⁺, Mn²⁺ single‐ and co‐doped oxyfluoride glasses were synthesized by a melt‐quenching method. The photoluminescence properties of the glasses containing copper species were demonstrated. Results indicate that the blue‐green emission band peaking at 440 nm was observed, which was ascribed to the photoluminescence of Cu⁺ ions rather than the emissions of Cu²⁺ cations or Cu nano‐particles (Cu NPs) induced by local field effect (LFE) enhancement through surface plasmon resonance (SPR). The interaction mechanisms between Cu⁺ and Tb³⁺/Mn²⁺ have been systematically investigated, and significant enhancement of Cu⁺ emission and the energy‐transfer (ET) efficiencies of Cu⁺→Tb³⁺ and Cu⁺→Mn²⁺ were observed in glasses doped with SnO reducing agent. Furthermore, a wide‐range‐tunable emission and ideal white‐light fluorescence were realized in Cu⁺/Tb³⁺/Mn²⁺‐coactivated glasses by utilization of Cu⁺ cations as dual ET contributors from deep‐UV‐source to multiactivators. Our research further extends the understanding of the interactions between Cu⁺ and Tb³⁺/Mn²⁺ in amorphous materials.