Synthesis of ZnSe and ZnSe:Cu quantum dots by a room temperature photochemical (UV‐assisted) approach using Na2SeO3 as Se source and investigating optical properties

In this study, ZnSe and ZnSe:Cu quantum dots (QDs) were synthesized using Na₂SeO₃ as the Se source by a rapid and room temperature photochemical (UV‐assisted) approach. Thioglycolic acid (TGA) was employed as the capping agent and UV illumination activated the chemical reactions. Synthesized QDs were successfully characterized using X‐ray diffraction (XRD), transmission electron microscopy (TEM), photoluminescence (PL) and UV–visible (UV–vis) spectroscopy, Fourier transform‐infrared (FT‐IR), and energy dispersive X‐ray spectroscopy (EDX). XRD analysis demonstrated the cubic zinc blend phase QDs. TEM images indicated that round‐shaped particles were formed, most of which had a diameter of about 4 nm. The band gap of the ZnSe QDs was higher than that for ZnSe in bulk. PL spectra indicated an emission with three peaks related to the excitonic, surface trap states and deep level (DL) states. The band gap and QD emission were tunable only by UV illumination time during synthesis. ZnSe:Cu showed green emission due to transition of electrons from the Conduction band (CB) or surface trap states to the ²T₂ acceptor levels of Cu²⁺. The emission was increased by increasing the Cu²⁺ ion concentration, such that the optimal value of PL intensity was obtained for the nominal mole ratio of Cu:Zn 1.5%.     

Water‐soluble mercaptoundecanoic acid (MUA)‐coated CdTe quantum dots: one‐step microwave synthesis,characterization and cancer cell imaging

ABSTRACT: In this study, a one‐step approach for aqueous synthesis of highly luminescent semiconductors, CdTe quantum dots (QDs), using long‐chain thiols‐mercaptoundecanoic acid (MUA) as surface ligand, was developed in a microwave irradiation system. The synthetic conditions were systematically investigated. The as‐prepared MUA‐coated QDs were characterized by various spectroscopy techniques, transmission electron microscopy (TEM) and X‐ray powder diffraction (XRD). The experimental results document that MUA‐coated CdTe QDs have small diameter, good stability, high luminescence and long lifetime. Particularly, it was confirmed, using fluorescence correlation spectroscopy (FCS) that, compared with other ligand, MUA formed a thicker ligand layer on the QD surfaces, which will help their stability and conjugation with biomolecules. Furthermore, MUA‐coated QDs were successfully used for HeLa cell imaging. Copyright © 2011 John Wiley & Sons, Ltd.     

Aqueous synthesis of CdTe/CdS/ZnS quantum dots and their optical and chemical properties

In this paper, we described a strategy for synthesis of thiol‐coated CdTe/CdS/ZnS (core–shell–shell) quantum dots (QDs) via aqueous synthesis approach. The synthesis conditions were systematically optimized, which included the size of CdTe core, the refluxing time and the number of monolayers and the ligands, and then the chemical and optical properties of the as‐prepared products were investigated. We found that the mercaptopropionic acid (MPA)‐coated CdTe/CdS/ZnS QDs presented highly photoluminescent quantum yields (PL QYs), good photostability and chemical stability, good salt tolerance and pH tolerance and favorable biocompatibility. The characterization of high‐resolution transmission electron microscopy (HRTEM), X‐ray powder diffraction (XRD) and fluorescence correlation spectroscopy (FCS) showed that the CdTe/CdS/ZnS QDs had good monodispersity and crystal structure. The fluorescence life time spectra demonstrated that CdTe/CdS/ZnS QDs had a longer lifetime in contrast to fluorescent dyes and CdTe QDs. Furthermore, the MPA‐stabilized CdTe/CdS/ZnS QDs were applied for the imaging of cells. Compared with current synthesis methods, our synthesis approach was reproducible and simple, and the reaction conditions were mild. More importantly, our method was cost‐effective, and was very suitable for large‐scale synthesis of CdTe/CdS/ZnS QDs for future applications. Copyright © 2010 John Wiley & Sons, Ltd.     

High quantum yield and well‐dispersed quantum dots luminescent composite through sodium carboxymethyl starch

It is a challenging task to prepare well‐dispersed and highly luminescent quantum dots (QDs) powder and a new strategy is reported in this article. Sodium carboxymethyl starch (CMS‐Na) was employed in this work to prepare the QDs–starch composite. Ultraviolet (UV) light shows that the blank starches had no fluorescence, while the QDs‐starches were highly luminescent. Scanning electron microscopy (SEM) observation shows that the QDs–starch composite has the typical particle morphology with the diameter around 200 nm. Energy dispersive X‐ray spectroscopy (EDX) results show that there are intensive tellurium (Te) and cadmium (Cd) element signals. Combined fluorescent lifetime and steady‐state spectrometer show that the QDs–starch quantum yields (QYs) increase when the QDs loading increases from 1 × 10^?6 mol/g to 2 × 10^?6 mol/g, but when the loadings further increase, the QYs decrease slightly. For the red colour (λ_em = 660 nm) QDs, the QYs can reach to as high as 28.2%, and for the other colour QDs they can also have the QYs above 22%. Time‐resolved photobleaching experiments show that the fluorescent QDs–starch composite has a half‐decay time of 40.23 s. These results indicate that the CMS‐Na is a promising QDs dispersant to obtain high QY QD composites.     

Synthesis of highly luminescent and biocompatible CdTe/CdS/ZnS quantum dots using microwave irradiation: a comparative study of different ligands

We compared the effects of several ligands frequently used in aqueous synthesis, including L‐cysteine, L‐cysteine hydrochloride, N‐acetyl‐L‐cysteine (NAC), glutathione and 3‐mercaptopropionic acid, for microwave synthesis of CdTe quantum dots (QDs) in a sealed vessel with varied temperatures and times, and then developed a rapid microwave‐assisted protocol for preparing highly luminescent, photostable and biocompatible CdTe/CdS/ZnS core–multishell QDs. The effects of molecular structures of these ligands on QD synthesis under high temperatures were explored. Among these ligands, NAC was found to be the optimal ligand in terms of the optical properties of resultant QDs and reaction conditions. The emission wavelength of NAC‐capped CdTe QDs could reach 700 nm in 5 min by controlling the reaction temperature, and the resultant CdTe/CdS/ZnS core–multishell QDs could achieve the highest quantum yields up to 74% with robust photostability. In addition, the effects of temperature, growth time and shell–precursor ratio on shell growth were examined. Finally, cell culturing indicated the low cytotoxicity of CdTe/CdS/ZnS core–multishell QDs as compared to CdTe and CdTe/CdS QDs, suggesting their high potential for applications in biomedical imaging and diagnostics. Copyright © 2014 John Wiley & Sons, Ltd.     

A simple and sensitive label‐free fluorescence sensing of heparin based on Cdte quantum dots

A rapid, simple and sensitive label‐free fluorescence method was developed for the determination of trace amounts of an important drug, heparin. This new method was based on water‐soluble glutathione‐capped CdTe quantum dots (CdTe QDs) as the luminescent probe. CdTe QDs were prepared according to the published protocol and the sizes of these nanoparticles were verified through transmission electron microscopy (TEM), X‐ray diffraction (XRD) and dynamic light scattering (DLS) with an average particle size of about 7 nm. The fluorescence intensity of glutathione‐capped CdTe QDs increased with increasing heparin concentration. These changes were followed as the analytical signal. Effective variables such as pH, QD concentration and incubation time were optimized. At the optimum conditions, with this optical method, heparin could be measured within the range 10.0–200.0 ng mL^?1 with a low limit of detection, 2.0 ng mL^?1. The constructed fluorescence sensor was also applied successfully for the determination of heparin in human serum. Copyright © 2015 John Wiley & Sons, Ltd.     

Deposition of CdS,CdS/ZnSe and CdS/ZnSe/ZnS shells around CdSeTe alloyed core quantum dots: effects on optical properties

In this work, we synthesized water‐soluble L ‐cysteine‐capped alloyed CdSeTe core quantum dots (QDs) and investigated the structural and optical properties of deposition of each of CdS, CdS/ZnSe and CdS/ZnSe/ZnS shell layers. Photophysical results showed that the overcoating of a CdS shell around the alloyed CdSeTe core [quantum yield (QY) = 8.4%] resulted in effective confinement of the radiative exciton with an improved QY value of 93.5%. Subsequent deposition of a ZnSe shell around the CdSeTe/CdS surface decreased the QY value to 24.7%, but an increase in the QY value of up to 49.5% was observed when a ZnS shell was overcoated around the CdSeTe/CdS/ZnSe surface. QDs with shell layers showed improved stability relative to the core. Data obtained from time‐resolved fluorescence measurements provided useful insight into variations in the photophysical properties of the QDs upon the formation of each shell layer. Our study suggests that the formation of CdSeTe/CdS core/shell QDs meets the requirements of quality QDs in terms of high photoluminescence QY and stability, hence further deposition of additional shells are not necessary in improving the optical properties of the core/shell QDs. Copyright © 2015 John Wiley & Sons, Ltd.     

Do the cations in clay and the polymer matrix affect quantum dot fluorescent properties?

This paper studied the effects of cations and polymer matrix on the fluorescent properties of quantum dots (QDs). The results indicated that temperature has a greater impact on fluorescence intensity than clay cations (mainly K⁺ and Na⁺). Combined fluorescence lifetime and steady‐state spectrometer tests showed that QD lifetimes all decreased when the cation concentration was increased, but the quantum yields were steady at various cation concentrations of 0, 0.05, 0.5 and 1 M. Poly(ethylene oxide) (PEO), poly(vinyl alcohol) (PVA) and diepoxy resin were used to study the effects of polymers on QD lifetime and quantum yield. The results showed that the lifetime for QDs 550 nm in PEO and PVA was 17.33 and 17.12 ns, respectively; for the epoxy resin, the lifetime was 0.74 ns, a sharp decrease from 24.47 ns. The quantum yield for QDs 550 nm changed from 34.22% to 7.45% and 7.81% in PEO and PVA, respectively; for the epoxy resin the quantum yield was 2.25%. QDs 580 nm and 620 nm showed the same results as QDs 550 nm. This study provides useful information on the design, synthesis and application of QDs–polymer luminescent materials. Copyright © 2015 John Wiley & Sons, Ltd.     

Sensitization enhancement of europium in ZnSe/ZnS core/shell quantum dots induced by efficient energy transfer

Eu‐doped ZnSe:/ZnS quantum dots (formed as ZnSe:Eu/ZnS QDs) were successfully synthesized by a two‐step wet chemical method: nucleation doping and epitaxial shell growing. The sensitization characteristics of Eu‐doped ZnSe and ZnSe/ZnS core/shell QD are studied in detail using photoluminescence (PL), PL excitation spectra (PLE) and time‐resolved PL spectroscopy. The emission intensity of Eu ions is enhanced and that of ZnSe QDs is decreased, implying that energy was transferred from the excited ZnSe host materials (the donor) to the doped Eu ions (the acceptor). PLE reveals that the ZnSe QDs act as an antenna for the sensitization of Eu ions through an energy transfer process. The dynamics of ZnSe:Eu/ZnS core/shell quantum dots with different shell thicknesses and doping concentrations are studied via PL spectra and fluorescence lifetime spectra. The maximum phosphorescence efficiency is obtained when the doping concentration of Eu is approximately 6% and the sample showed strong white light under ultraviolet lamp illumination. By surface modification with ZnS shell layer, the intensity of Eu‐related PL emission is increased approximately three times compared with that of pure ZnSe:Eu QDs. The emission intensity and wavelength of ZnSe:Eu/ZnS core/shell quantum dots can be modulated by different shell thickness and doping concentration. The results provide a valuable insight into the doping control for practical applications in laser, light‐emitting diodes and in the field of biotechnology. Copyright © 2014 John Wiley & Sons, Ltd.     

Size‐dependent dual emission of Cu,Mn:ZnSe QDs: Controlling both emission wavelength and intensity

Cu,Mn:ZnSe quantum dots (QDs) of tunable size, controllable photoluminescence (PL) intensity ratio and PL range were prepared. A study of the experimental conditions confirmed that the size of Cu,Mn:ZnSe QDs is affected by the pH of the solution, the speed at which the Zn solution is injected and the reaction temperature. In general, high pH, low injection speed and high reaction temperature are optimal for preparing large QDs. Based on this knowledge, different sizes of Cu,Mn:ZnSe QDs were synthesized. Moreover, white emission Cu,Mn:ZnSe QDs were designed by controlling the experimental conditions and the feeding mole ratio of Mn:Cu.     

Sodium 4‐mercaptophenolate capped CdSe/ZnS quantum dots as a fluorescent probe for pH detection in acidic aqueous media

Development of the fluorescent pH detection method is promising due to the sensitivity, easy operation, and low‐cost, etc. However, traditional organic fluorophores have still some disadvantages such as the tedious preparation and purification as well as low photostability and water solubility, which limits the rapid detection application. Semiconductor quantum dots (QDs) have recently risen to prominence as an alternative for organic fluorophores in fluorescence analysis by virtue of their convenient synthesis and superior optical properties. In this study, we report on sodium 4‐mercaptophenolate functionalized CdSe/ZnS QDs (denoted as ^?OPhS‐QDs), which can serve as a selective “on–off” fluorescence probe for aqueous media pH. ^?OPhS‐QDs exhibit strong fluorescence in near neutral medium. As a Lewis organic base, ^?OPhS‐ moieties on QDs surface easily binds to proton under acidic conditions to yield 4‐mercaptophenol capped QDs (i.e. HOPhS‐QDs), which acts as an efficient hole trapper. As a result, the QDs photoluminescence (PL) is switched off. Under optimal conditions, the present probe exhibits a good linear relationship between fluorescence response and pH values in the pH range 3.0–5.2. Furthermore, the present probe exhibits a high selectivity for proton over other common cations and has been successfully used for pH detection in real water samples.     

Hydrothermal synthesis for high‐quality glutathione‐capped CdxZn1 – xSe and CdxZn1 – xSe/ZnS alloyed quantum dots and its application in Hg(II) sensing

High‐quality Cd_xZn_{1 – x}Se and Cd_xZn_{1 – x}Se/ZnS core/shell quantum dots (QDs) emitting in the violet–green spectral range have been successfully prepared using hydrothermal methods. The obtained aqueous Cd_xZn_{1 – x}Se and Cd_xZn_{1 – x}Se/ZnS QDs exhibit a tunable photoluminescence (PL) emission (from 433.5 nm to 501.2 nm) and a favorable narrow photoluminescence bandwidth [full width at half maximum (FWHM): 30–42 nm]. After coating with a ZnS shell, the quantum yield increases from 40.2% to 48.1%. These Cd_xZn_{1 – x}Se and Cd_xZn_{1 – x}Se/ZnS QDs were characterized by transmission electron microscopy, X‐ray diffraction, X‐ray photoelectron spectroscopy and Fourier transform infrared (FTIR) spectroscopy. To further understand the alloying mechanism, the growth kinetics of Cd_xZn_{1 – x}Se were investigated through measuring the fluorescence spectra and X‐ray diffraction spectra at different growth intervals. The results demonstrate that the inverted ZnSe/CdSe core/shell structure is formed initially after the injection of Cd²⁺. With further heating, the core/shell structured ZnSe/CdSe is transformed into alloyed Cd_xZn_{1 – x}Se QDs with the diffusion of Cd²⁺ into ZnSe matrices. With increasing the reaction temperature from 100 °C to 180 °C, the duration time of the alloying process decreases from 210 min to 20 min. In addition, the cytotoxicity of Cd_xZn_{1 – x}Se and Cd_xZn_{1 – x}Se/ZnS QDs were investigated. The results indicate that the as‐prepared Cd_xZn_{1 – x}Se/ZnS QDs have low cytotoxicity, which makes them a promising probe for cell imaging. Finally, the as‐prepared Cd_xZn_{1 – x}Se/ZnS QDs were utilized to ultrasensitively and selectively detect Hg²⁺ ions with a low detection limit (1.8 nM).     

Microwave‐assisted aqueous synthesis of new quaternary‐alloyed CdSeTeS quantum dots; and their bioapplications in targeted imaging of cancer cells

In this study, we report for the first time a one‐pot approach for the synthesis of new CdSeTeS quaternary‐alloyed quantum dots (QDs) in aqueous phase by microwave irradiation. CdCl₂ was used as a Cd precursor during synthesis, NaHTe and NaHSe were used as Te and Se precursors and mercaptopropionic acid (MPA) was used as a stabilizer and source of sulfur. A series of quaternary‐alloyed QDs of different sizes were prepared. CdSeTeS QDs exhibited a wide emission range from 549 to 709 nm and high quantum yield (QY) up to 57.7 %. Most importantly, the quaternary‐alloyed QDs possessed significantly long fluorescence lifetimes > 100 ns as well as excellent photostability. Results of high‐resolution transmission electron microscopy (HRTEM), energy dispersive X‐ray spectroscopy (EDX) and powder X‐ray diffraction (XRD) spectroscopy showed that the nanocrystals possessed a quaternary alloy structure with good crystallinity. Fluorescence correlation spectroscopy (FCS) showed that QDs possessed good water solubility and monodispersity in aqueous solution. Furthermore, CdSeTeS QDs were modified with alpha‐thio‐omega‐carboxy poly(ethylene glycol) (HS‐PEG‐COOH) and the modified QDs were linked to anti‐epidermal growth factor receptor (EGFR) antibodies. QDs with the EGFR antibodies as labeling probes were successfully applied to targeted imaging for EGFR on the surface of SiHa cervical cancer cells. We believe that CdSeTeS QDs can become useful probes for in vivo targeted imaging and clinical diagnosis. Copyright © 2012 John Wiley & Sons, Ltd.     

A highly selective and simple fluorescent sensor for mercury (II) ion detection based on cysteamine‐capped CdTe quantum dots synthesized by the reflux method

Cysteamine (CA)‐capped CdTe quantum dots (QDs) (CA–CdTe QDs) were prepared by the reflux method and utilized as an efficient nano‐sized fluorescent sensor to detect mercury (II) ions (Hg²⁺). Under optimum conditions, the fluorescence quenching effect of CA–CdTe QDs was linear at Hg²⁺ concentrations in the range of 6.0–450 nmol/L. The detection limit was calculated to be 4.0 nmol/L according to the 3σ IUPAC criteria. The influence of 10‐fold Pb²⁺, Cu²⁺ and Ag⁺ on the determination of Hg²⁺ was < 7% (superior to other reports based on crude QDs). Furthermore, the detection sensitivity and selectivity were much improved relative to a sensor based on the CA–CdTe QDs probe, which was prepared using a one‐pot synthetic method. This CA–CdTe QDs sensor system represents a new feasibility to improve the detection performance of a QDs sensor by changing the synthesis method. Copyright © 2014 John Wiley & Sons, Ltd.     

Aqueous synthesis of highly luminescent surface Mn2+‐doped CdTe quantum dots as a potential multimodal agent

Mn²⁺‐doped CdTe quantum dots (QDs) were synthesized directly via a facile surface doping strategy in aqueous solution. The best optical property emerged when the added amount of Mn²⁺ was 5% compared to Cd²⁺ in the CdTe nanoparticles and the reaction temperature was 60 °C. The fluorescence and magnetic properties of the QDs were studied. The as‐prepared Mn²⁺‐doped CdTe QDs have high quantum yield (48.13%) and a narrow distribution with an average diameter of 3.7 nm. The utility of biological imaging was also studied. Depending on the high quantum yield, cells in culture were illuminated and made more distinct from each other compared to results obtained with normal QDs. They also have a prominent longitudinal relaxivity value (r₁ = 4.2 mM^?1s^?1), which could indicate that the Mn²⁺‐doped CdTe QDs can be used as a potential multimodal agent for fluorescence and magnetic resonance imaging. Copyright © 2014 John Wiley & Sons, Ltd.     

Study of fluorescence quenching of mercaptosuccinic acid‐capped CdS quantum dots in the presence of some heavy metal ions and its application to Hg(II) ion determination

In this study, CdS quantum dots (QDs) capped with mercaptosuccinic acid (MSA) were prepared in one step. The size, shape, component and spectral properties of MSA‐capped CdS QDs were characterized by transmission electron microscopy (TEM), photoluminescence (PL) and infrared (IR) spectrometry. The results showed that the prepared QDs with an average diameter of 6 nm have favorable fluorescence, which is greatly influenced by the pH of the environment. The interaction of some heavy metal ions including Ag⁺, Hg²⁺, Cu²⁺, Ni²⁺ and Co²⁺ with MSA‐capped CdS QDs was investigated in different buffering pH media. Based on the fluorescence quenching of the QDs in the presence of each of the metal ions, the feasibility of their determinations was examined according to the Stern–Volmer equation. The investigations showed that Hg(II) ions can be determined in the presence of many co‐existing metal ions at a buffering pH of 5. This method was satisfactorily applied to the measurement of Hg(II) ions in some environmental samples. Copyright © 2014 John Wiley & Sons, Ltd.     

Near Infrared,Highly Efficient Luminescent Solar Concentrators

The fabrication of a low reabsorption emission loss, high efficient luminescent solar concentrator (LSC) is demonstrated by embedding near infrared (NIR) core/shell quantum dots (QDs) in a polymer matrix. An engineered Stokes shift in NIR core/shell PbS/CdS QDs is achieved via a cation exchange approach by varying the core size and shell thickness through the refined reaction parameters such as reaction time, temperature, precursor molar ratio, etc. The as‐synthesized core/shell QDs with high quantum yield (QY) and excellent chemical/photostability exhibit a large Stokes shift with respect to the bare PbS QDs due to the strong core‐to‐shell electrons leakage. The large‐area planar LSC based on core/shell QDs exhibits the highest value (6.1% with a geometric factor of 10) for optical efficiency compared to the bare NIR QD‐based LSCs and other reported NIR QD‐based LSCs. The suppression of emission loss and the broad absorption of PbS/CdS QDs offer a promising pathway to integrate LSCs and photovoltaic devices with good spectral matching, indicating that the proposed core/shell QDs are strong candidates for fabricating high efficiency semi‐transparent large‐area LSCs.     

Tunable excitation properties of ZnCdS:Mn/ZnS quantum dots for cancer imaging

Water‐soluble ZnS:Mn quantum dots (QDs) were synthesized using a hydrothermal method with 3‐mercaptopropionic acid as stabilizer. The optical properties of ZnS:Mn QDs were thoroughly investigated by tuning the doping concentration of Mn²⁺ and the Zn/S precursor ratio, to obtain an optimal parameter for QDs with excellent fluorescence characteristics. ZnS:Mn QDs excited at only one wavelength, however, which seriously limited their further application. Here, a trace Cd ion was doped into a ZnS host, resulting in QD excitation covering a wide adjustable waveband. Furthermore, when a ZnS shell was coated onto the surface of the ZnCdS:Mn QDs, photoluminescence intensity and stability were further enhanced. After coupling with an anti‐CK 19 antibody, the ZnCdS:Mn/ZnS core/shell QDs were able to function by labeling cancer cells, indicating that they could be considered as a suitable bio‐probe for cells and tissue imaging.     

Graphite oxide‐dispersed CdTe quantum dots nanocomposite for flexible display luminescent membranes

A quantum dot (QD) dispersant material was prepared using graphite oxide (GO). Luminescent films were prepared using polyvinyl alcohol as the polymer matrix. First, water‐soluble CdTe QDs were prepared by wet chemistry and GO was synthesized using a modified Hummers method. X‐Ray diffraction tests showed that the GO reflection peak [001] was 11.9°, which indicates that the d‐spacing is 0.7431 nm; atomic force microscopy showed a GO thickness of 200 nm. Fourier transform infrared spectra showed vibrations at 1624 cm^?1 for the carbonyl groups, and 3260 cm^?1 for the GO samples; the ‐C–O vibration was at 1320 cm^?1 and ‐COOH, ?OH vibrations were at 950 cm^?1. Fluorescent tests showed that pH had an impact on the QD colloidal stability. GO was neutralized before use as the host media for the GO/QDs nanocomposite. The results proved that the resultant nanocomposite is promising for use in brightness enhancement films in flexible displays.     

Simple synthesis of luminescent CdSe quantum dots from ascorbic acid and selenium dioxide

A simple, low‐cost and convenient method was developed for the synthesis of highly luminescent CdSe quantum dots (QDs) in an aqueous medium. Compared with previous methods, this synthesis was carried out in one pot using ascorbic acid (C₆H₈O₆) to replace NaBH₄ or N₂H₄ · H₂O as a reductant, and selenium dioxide to replace selenium or its other hazardous, expensive and unstable compounds as a precursor. The mechanism of CdSe QDs formation was elucidated. The influence of various experimental variables, including refluxing time, Cd/MSA and Cd/Se molar ratios, on the luminescent properties of the QDs were systematically investigated. X‐Ray powder diffraction and transmission electron microscopy characterization indicated that the QDs had a pure cubic zinc‐blended structure with a spherical shape. Copyright © 2015 John Wiley & Sons, Ltd.