Recent progress in nanostructured silver sulfide: from synthesis and nonstoichiometry to properties

D g s t U c S N i C t S s ties of nanostructured semiconduc years. He is mostly recognized as an sulde synthesis. He is an author o 60 scientic articles, and seven p and silver suldes. His current re the development of new methods heteronanostructures for optoel biosensing. Institute of Solid State Chemistry, Ural Bra 620990 Ekaterinburg, Russia. E-mail: sadovn Cite this: J. Mater. Chem. A, 2017, 5, 17676


Introduction
The synthesis and properties of nanostructured chalcogenides, including semiconducting lead sulde (PbS), cadmium sulde (CdS), mercury sulde (HgS), copper(II) sulde (CuS), Cu 2 S, and Dr Stanislav I. Sadovnikov graduated in the materials science of semiconductors from the Ural State Technical University, Russia. He is currently a Senior Research Scientist at the Laboratory of Nonstoichiometric Compounds in the Institute of Solid State Chemistry of the Ural Branch of the Russian Academy of Sciences. He has studied the synthesis, structure and properties of nanostructured semiconducting suldes for more than 10 years. He is mostly recognized as an expert in the eld of nanosized sulde synthesis. He is an author of two review articles, more than 60 scientic articles, and seven patents on nanostructured lead and silver suldes. His current research interests are focused on the development of new methods of synthesis of semiconductor heteronanostructures for optoelectronics, photocatalysis and biosensing.
Professor Dr Aleksandr I. Gusev graduated in physical chemistry from the Ural State Technical University, Russia. He is Chief Research Scientist at the Laboratory of Nonstoichiometric Compounds in the Institute of Solid State Chemistry of the Ural Branch of the Russian Academy of Sciences. He has been exploring crystal and electronic structures and the properties of novel nonstoichiometric compounds such as carbides, suldes, and oxides, and nanostructured advanced materials for more than 40 years. He is an author of 16 monographs including Disorder and Order in Strongly Nonstoichiometric Compounds (Springer, 2001), Nanocrystalline Materials (Cambridge, 2004), and Tungsten Carbides: Structure, Properties and Application in Hardmetals (Springer, 2013), 23 review articles and more than 350 scientic articles. His current interests lie in the materials science of nanostructured semiconductor suldes. silver sulde (Ag 2 S), have been described in a number of review articles and books. [1][2][3][4][5][6][7][8][9][10] However, too broad range of objects inevitably made the discussion too compact. Nanostructured Ag 2 S has been mentioned in these works very briey. Nonstoichiometry (i.e., deviation from stoichiometric composition) of Ag 2 S has not been considered at all.
Nonstoichiometry is a fundamental characteristic of inorganic substances, which affects the structure and properties of compounds, on the one hand, and depends on the size of structural elements (particles, grains, crystallites, domains) of compounds, on the other hand. Until recently, the relationship and interdependence between nonstoichiometry and particle size at the nanometer scale has been scarcely examined or discussed only as an example of strongly nonstoichiometric compounds (e.g., carbides, oxides, nitrides of transition metals). Certainly the nonstoichiometry in nanostructured suldes, which in the conventional bulk (coarse-grained) state are traditionally considered to be stoichiometric compounds, has never been discussed. Indeed, at present the number of studies devoted to nonstoichiometry of sulde nanoparticles is extremely limited.
Modern solid-state physics, physical material science and electronics are inconceivable without semiconducting heterostructures. Such semiconducting heterostructures as quantum wells, quantum wires and quantum dots allow control of fundamental parameters of semiconducting crystals as the forbidden band width, effective mass and mobility of charge carriers and electronic energy spectrum. 6, [11][12][13] Heteronanostructures combining the properties of semiconductors in the nanocrystalline state, on the one hand, and nonstoichiometry, on the other hand, are the next step in the development of quantum electronics.
We have tried to take into account both the purely scientic, fundamental interest in the problem of nanostructured Ag 2 S and some applied aspects of this problem that are of considerable importance for practical application of Ag 2 S.
The well-known Ag 2 S is one of the most requisite semiconducting suldes 1,2,14-19 along with lead, zinc, cadmium and copper suldes. [3][4][5][20][21][22][23][24][25] Ag 2 S is the only semiconducting sulde (except for HgS) having three polymorphous modications (a-Ag 2 S, b-Ag 2 S and g-Ag 2 S) within rather close temperature intervals. 26 These modications of Ag 2 S differ greatly in their structure and properties. The unique character of Ag 2 S has to do also with the transition between semiconducting a-Ag 2 S and superionic b-Ag 2 S phases. The presence of this transformation makes it possible to use Ag 2 S in Ag 2 S/Ag heteronanostructures intended for new-generation microelectronic devices such as resistance nanoswitches and nonvolatile memory nanodevices.
Low-temperature semiconducting-phase a-Ag 2 S (acanthite) with monoclinic crystal structure exists at temperatures below $450 K. Under equilibrium conditions, cubic phase b-Ag 2 S (argentite) exists in the temperature range 452-859 K, has a body centered cubic (bcc) sublattice of sulfur (S) atoms and has a superionic conductivity. High-temperature cubic g-Ag 2 S phase with a face centered cubic (fcc) sublattice of S atoms is stable from $860 K up to melting temperature.
It is thought that the monoclinic a-Ag 2 S phase is stoichiometric, whereas cubic b-Ag 2AEd S and g-Ag 2AEd S with d y 0.002 are nonstoichiometric phases having either a small deciency or small excess of silver. The homogeneity intervals of cubic allotropic forms of Ag 2 S have been determined. [27][28][29][30][31][32][33] According to, 34 nonstoichiometric body centered cubic b-Ag 2+d S (d # 0.002) is characterized by high electronic conductivity of about 1.3 Â 10 3 U À1 cm À1 that is 10 6 times higher than that in the monoclinic a-Ag 2 S phase. Owing to high electronic conductivity, bcc b-Ag 2 S can be used in photography. 34 In normal conditions, bulk coarse-crystalline Ag 2 S with an a-Ag 2 S acanthite-type structure is a direct semiconductor which possesses a wide band gap E g and low charge-carrier mobility. The band gap E g of a-Ag 2 S depends on temperature. According to, 35,36 the band gap of acanthite a-Ag 2 S at 300 K is about 0.9 eV, and its temperature coefficient vE g /vT ¼ À(1.2 À 1.5) Â 10 À3 eV K À1 . 36 The conventional band gap of acanthite a-Ag 2 S at 300 K is 0.9-1.1 eV.
For bulk coarse-crystalline acanthite a-Ag 2 S, the electron and hole effective masses are m e ¼ 0.286m 0 and m h ¼ 1.096m 0 , respectively. 37 Taking this into account, the reduced exciton mass m ex ¼ m e m h /(m e + m h ) for acanthite a-Ag 2 S is $0.23m 0 ¼ 2.06 Â 10 À31 kg.
The characteristic size of the Wannier-Mott exciton (or the Bohr radius of the exciton) in the macroscopic (bulk) semiconductor has been determined to be R ex z n 2 ħ 2 3/m ex e 2 ¼ (n 2 3m 0 /m ex )a B , where a B ¼ ħ 2 /m 0 e 2 ¼ 0.0529 nm is the Bohr radius. For reduced exciton mass m ex ¼ 0.23m 0 and dielectric constant 3 ¼ 5.95, 38 the radius R ex of the rst exciton state with n ¼ 1 in coarsecrystalline acanthite a-Ag 2 S is equal to (26 AE 1)a B or $1.4 AE 0.1 nm and the exciton diameter D ex is about 2.8 nm.

Methods of synthesis of nanostructured Ag 2 S
Nanostructured Ag 2 S has been investigated intensively in recent years due to possible application in optoelectronics, biosensing and catalysis. [39][40][41][42] It is an excellent substance for the preparation of heterostructures. 43 Nanostructured Ag 2 S can be used in photochemical cells, 44 infrared detectors, [45][46][47] in resistanceswitches and nonvolatile memory devices. [48][49][50] Ag 2 S is a promising material for conversion of solar energy into electrical energy. 51,52 Recently, three-dimensional nanoparticle superlattices were built up with Ag 2 S hollow nanospheres and nanodiscs as building blocks. 53 Ag 2 S nanoparticles possess antibacterial action. 54,55 Creation of isolated, stable Ag 2 S quantum dots to be used as biomarkers holds much promise. 56,57 Nanostructured silver chalcogenides including Ag 2 S also have been showing promising applications in thermoelectrics. 58 The thermoelectric effect refers to phenomena by which either a temperature difference creates an electric potential or an electric potential creates a temperature difference. The dimensionless gure of merit (thermoelectric performance) ZT of any material is determined as sS 2 T/k, where s is the electrical conductivity, S is the Seebeck coefficient, k is the thermal conductivity of the material, and T is the absolute temperature. Tellurides, selenides, suldes, and their solid solutions are the most attractive thermoelectric materials. [58][59][60][61] Silver chalcogenides Ag 2 Se and Ag 2 S have attracted much interest due to reversible transformation between semiconductor and superionic phases. In study, 58 it has been shown that the Seebeck coefficient and ZT for Ag 2 S nanocrystal are equal to À76 mV K À1 and 0.12 at the temperature of the transition from a-Ag 2 S to b-Ag 2 S. For nanocrystalline Ag 2 Se and Ag 4 SeS, values of ZT are 0.23 and 0.33, respectively. According to, 60 the Seebeck coefficient of Ag 2 S nanocrystalline lm is À198 mV K À1 at 400 K; therefore, enhanced ZT for Ag 2 S nanolms can be anticipated. According to, 58 the cooperative contribution of superionic phase transition, reduced grain size, and alloying opens up a promising new approach to "tailor" sulde materials for optimal thermoelectric performance.
Nanostructured Ag 2 S in the form of nanopowders, quantum dots, and heteronanostructures based on Ag 2 S has been successfully produced by different methods such as hydrochemical deposition, template method, sol-gel method, synthesis in microemulsions, as well as by sonochemical, hydrothermal, solvothermal, electrochemical, microwave and other techniques. Every method has both advantages and limitations.
Sodium sulde (Na 2 S) 30 Recently, much attention has been devoted to the production of different hybrid heteronanostructures of the core-shell type, which include Ag and its compounds (Ag 2 O@Ag 2 S, Ag@SiO 2 , etc.). [79][80][81] In particular, familiar core-shell nanostructures can be formed by two different semiconductors (CdSe@CdS, CdSe@ZnS, CdS@Ag 2 S, CdS@ZnS, GaAs@AlS, etc.). [82][83][84][85][86] The nanosized particles are not stable. The high surface energy will impel the nanoparticles to aggregate. Therefore, creation of core-shell particles can be due to the necessity of xing of specic groups (organic ligands) on the surface of the core, which would prevent agglomeration, growth, and oxidation of particles and provide the production of stable isolated nanoparticles. Using the protective shell, it is possible to control the size of isolated nanoparticles. Stabilizing and capping agents such as trioctylphosphine oxide, 87,88 L-cysteine, [89][90][91] glutathione, 92 long-chain amines (hexadecylamine, octylamine, dioctylamine, ethylenediamine), 39 ethylenediaminetetraacetic acid (EDTA) and EG 75,93 are used for the creation of a protective shell. However, most of the listed stabilizing agents are hazardous to human health and have a serious impact on the environment. One of the most commonly requested non-toxic capping agents which has a high degree of electrostatic stabilization is sodium citrate (Na 3 C 6 H 5 O 7^N a 3 Cit). 55,68,69,[94][95][96] Several investigations 97-100 have shown that extracts or aqueous solutions of natural products (leaves, seeds, fruits, roots, honey, royal jelly, gum of trees, bovine serum albumin, etc.) can be used as stabilizing agents for the preparation of isolated nanoparticles of Ag 2 S and Ag with a protective shell. Such exotic stabilizing agents are non-toxic and do not exert a harmful impact on the environment due to their high antioxidant potential. However, the complete identication of the complex composition of listed natural stabilizing agents has been an open and undecided problem until now. Therefore, real application of natural stabilizing agents is rather limited.
The most pronounced part in the formation of Ag 2 S nanoparticles has been played by complexing agents. Na 3 Cit is the main complexing agent for Ag + . One must point out that the Na 3 Cit is the completely harmless standardized food additive E331.

Synthesis by decomposition of molecular precursors
Application of molecular precursors has some attractive features. On the one hand, it provides such important advantages as simplicity, safety and compatibility with metal organic chemical vapor deposition. 101 On the other hand, the use of molecular precursors may lead to the unusual selectivity in crystal growth or formation of the metastable phase of the nal products, which are not always achievable by conventional synthetic methods.
Among the solution methods, the injection of an organometallic precursor into a hot solvent provides a simple route to produce particles with desirable properties (e.g., high crystallinity, and uniform shapes and sizes with a high degree of monodispersity).
Lim et al. 39 discovered that air-stable precursors such as silver thiobenzoate (Ag(SCOPh)) meets these requirements. The precursor crystals were found to decompose in amine at room temperature to give Ag 2 S nanoparticles. The most important parameters of synthesis are the reaction temperature, type of amine, relative concentration of the reagents, and reaction time. Lim et al. 39 found that by increasing the injection temperature to 393 K, cube-shaped Ag 2 S nanocrystals are obtained exclusively (Fig. 1). The uniform Ag 2 S nanocubes selfassemble into ordered two-dimensional arrays on the surface of the transmission electron microscope grid (Fig. 1a). The average size of these nanocubes is 44 AE 4 nm. The scanning electron microscopy (SEM) image in Fig. 1b illustrates that large quantity of these nanocubes can be obtained using this approach. High-resolution transmission electron microscopy (HRTEM) images ( Fig. 1c and d) clearly show that Ag 2 S nanocubes are single crystals.
Later, spherical Ag 2 S nanocrystals were obtained via a modied hot-injection process of the same single-source molecular precursor Ag(SCOPh), which can potentially generate both Ag* and AgS* fragments simultaneously. 102 Wang et al. 103 obtained Ag 2 S nanocrystallites by heating molecular precursors such as silver diethyldithiocarbamate (Ag-DDTC) in air at 473 K for 3 h, and used this air-stable molecular precursor as the reactant source. The proposed method was both costeffective and non-toxic. Monodisperse Ag 2 S nanoparticles with controlled size were successfully synthesized by thermolysis of harmless silver xanthates as a single-source molecular precursor. 104 In one experiment, 104 the diameter of the Ag 2 S nanoparticles ranged from 8.9 AE 1.2 nm to 48 AE 4 nm (Fig. 2). Control of the particle size has been achieved by simply changing the alkyl chain length in the precursors.

Synthesis of nanostructured Ag 2 S with different morphology
Recently, great efforts have been focused on the preparation of Ag 2 S nanoparticles of various morphology, and on the morphology control of the semiconductor nanocrystals. 105 For example, Zhao et al. 106 prepared rod-like Ag 2 S nanocrystals using Na 2 S 2 O 3 as a S source via gamma-ray irradiation of aqueous solutions at room temperature.
An alcohol solution method to synthesize nanostructured Ag 2 S using carbon bisulde (CS 2 ) as the S source has been described. 107 All the products were irregular Ag 2 S microstructures and nanostructures. When the reaction medium was changed from water and alcohol-water to alcohol, the morphology of synthesized Ag 2 S changed from big irregular nanosheets to leaf-like nanosheets, elliptical, and Y-shaped aked Ag 2 S nanoparticles.
Later, Chen et al. 108 reported that leaf-like Ag 2 S nanosheets were prepared successfully by a facile hydrothermal method from a mixture of alcoholic CS 2 solution with an aqueous solution of AgNO 3 and NH 3 . Ag 2 S microstructures and nanostructures with different morphologies, including micrometer bars, nanowires, and nanopolyhedrons, have been synthesized by a facile one-step method at room temperature. 109 In the proposed method, no organic template materials were added to the reaction mixture, which contained aqueous solutions of AgNO 3 , NH 3 , and N 2 H 4 CS. By changing the reactant concentration ratio, the size and morphology of prepared Ag 2 S particles can be easily tuned.
In recent years, polyhedral nanocrystals, including facecentered cubic sulde nanocrystals, 39,110 have been successfully fabricated. Wang et al. 110 prepared Ag 2 S nanocrystals by thermolysis of an organometallic precursor Ag[S 2 P(OR) 2 ] (R ¼ C n H 2n+1 ). The above-mentioned hydrothermal method has been improved by Dong et al. 111 Most of the observed Ag 2 S nanoparticles looked hexagonal. Ag 2 S-poly(N-isopropylacrylamide-co-methacrylic acid) (PNI-PAM-MAA) and Ag 2 S-PNIPAM composite microspheres with patterned surface structures have been synthesized by a polymeric minigel template method. 112 The surface structure of Ag 2 S-PNIPAM-MAA microspheres looks like owers.
Single-crystalline Ag 2 S hollow nanohexagons with narrow size distribution were successfully synthesized in aqueous solutions of AgNO 3 , N 2 S 2 O 3 , and C 19 H 42 BrN (CTAB) at 318 K. 113 Tetrahedral colloidal crystals of Ag 2 S nanoparticles have been synthesized from aqueous solutions of AgNO 3 , NH 3 , and 1-dodecanethiol (CH 3 (CH 2 ) 11 SH) in an autoclave at 473 K for 5 h. 114 Due to the high uniformity and van der Waals interactions, Ag 2 S nanoparticles spontaneously assemble into tetrahedral colloidal aggregates comprising a perfectly ordered 3D superlattice structure (Fig. 3).
A sacricial core of S nanoparticles is used to synthesize Ag 2 S hollow nanospheres via a wet chemical method at room temperature. 115 S nanoparticles as cores were synthesized from Na 2 S 2 O 3 in the presence of cetyltrimethyl ammonium bromide aqueous solution. Aer completion of the formation of cores, the AgNO 3 solution was added. Then, the produced particles were washed by a water-ethanol mixture and treated with CS 2 for the complete conversion of AgBr to Ag 2 S, as well as to remove the cores to form Ag 2 S hollow nanospheres (Fig. 4).
Worm-like Ag 2 S nanobers with lengths up to several micrometers and diameters of 25-50 nm have been prepared in reverse microemulsions in the presence of CH 3 C(S)NH 2 as a S source and EDTA as a chelating ligand. 116 In study, 117 rice-shaped Ag 2 S nanoparticles were produced by the reaction between Ag(NH 3 ) 2 + and Na 2 S in the presence of  polyvinylpyrrolidone (C 6 H 9 NO) n (PVP) through a hydrothermal method. Large, rice-shaped Ag 2 S particles have been synthesized by hydrochemical bath deposition from aqueous reaction mixture of silver nitrate (AgNO 3 ), Na 2 S, and Na 3 Cit. 118 Reaction mixture was heated in closed vessel at a temperature of 373 K under the pressure $2 Â 10 5 Pa within 2 h.

Synthesis of Ag 2 S nanowires
The one-dimensional (1D) nature of Ag 2 S nanowires endows their unique electrical, optoelectronic, and mechanical properties. Single-crystalline Ag 2 S nanowires can be expected to have superior properties owing to their anisotropic geometry, and carrier and photon connement in two dimensions.
Conventional nanowire synthesis oen requires high temperature and/or various templates.
According to, 119,120 there are two different routes for the synthesis of 1D nanomaterials, namely, "hard" and "so" approaches. The rst approach includes template-directed synthesis and the vapor-liquid-solid and vapor-solid techniques, which usually require high temperature and pressure. In comparison, the so approaches, such as hydrothermal/ solvothermal processes, the solution-liquid-solid mechanism, and capping agents/surfactant-assisted synthesis, provide a convenient and low-temperature pathway for the fabrication of 1D nanomaterials.
Recently, Ag 2 S nanowires have been synthesized through the gas-solid reaction route, 121 anodic aluminum oxide template method, 122 microwave irradiation-assisted method, 123 and hydrothermal method with amine ligand. 120 Wen et al. 121 reported on the successful synthesis of Ag 2 S nanowires by a simple and mild gas-solid reaction method on Ag substrates. For the nanowire synthesis, the cleaned Ag foil was subjected to preoxidation and suldizing by an exposition in an atmosphere of an O 2 /H 2 S mixture from room temperature to 313 K in a water bath. The resulting Ag 2 S nanowires contained one-phase monoclinic acanthite a-Ag 2 S and had diameter of 40-150 nm and lengths up to 100 mm.
In other syntheses, 120 AgNO 3 was dissolved in warm octadecylamine solvent, forming silver ammines that were rapidly converted to Ag 2 S nuclei upon the addition of S powder. Aer stirring, the system was maintained at 393 K for further growth and crystallization. This process resulted in the generation of ultralong Ag 2 S nanowires with diameters in the range of 10-30 nm and lengths up to hundreds of micrometers. Authors 120 could only obtain uniform nanowires at a temperature neither lower nor higher than 393 K. Synthesized Ag 2 S nanowires are very sensitive to oxygen and there is a quasi-linear ratio between the current and the logarithm of oxygen pressure. These excellent performances indicate that Ag 2 S nanowires are promising candidates for photoswitches and room-temperature oxygen sensors.
In work, 124 Ag 2 S nanowires were prepared in anhydrous ethanol through a simple and sacricial templating solvothermal route. The experimental results 124 demonstrated that the reaction temperature, Ag + concentration, reaction time and solvent played crucial parts in the formation of the Ag 2 S nanowires. In a typical procedure, a mixture of S powder and Cd(CH 3 COO) 2 were dissolved consecutively in ethylenediamine. The resulting mixture was heated in the autoclave at 473 K for 2 h. Then, as-prepared CdS nanowires and AgNO 3 were dissolved in anhydrous ethanol. The resulting mixture was heated in the autoclave at 473 K for 12 h. The addition of excess Ag + leads to the complete transformation of CdS nanowires to the Ag 2 S nanowires.
Later, 125 a cation-exchange process was used for fabrication of Ag 2 S nanowires. Authors 125 reported a sequential two-step cation exchange process which transformed single-crystal nanowires to twinning nanowires. Specically, CdS nanowires were used as a template to form CdS-Cu 2 S core shell nanowires and subsequently twinning Cu 2 S nanowires through cation exchange. Then, twinning Cu 2 S nanowires were transformed to Cu 2 S-Ag 2 S superlattice nanowires with tunable segment  lengths via further cation exchange of Cu + by Ag + . Fig. 5 shows the schematic synthetic sequence to form Cu 2 S-Ag 2 S superlattice nanowires from CdS nanowires. Thus, authors 125 have demonstrated that twins created in the cation exchange process of nanowires can be utilized to generate heterostructures in the chain cation exchange steps.

Preparing Ag 2 S nanoparticles and quantum dots
Ag 2 S quantum dots are treated as an ideal optical probe with uorescence emission from UV to NIR region because these quantum dots have lower toxicity compared with chalcogenide quantum dots of such heavy metals as Pb, Ca, and Hg. 126,127 The synthesis of quantum dots, which can be used as optical probes for in vitro and in vivo molecular imaging, has made great progress. 128 The rst synthesis of Ag 2 S quantum dots with emission in the NIR-II region was demonstrated by Du and coauthors. 127 In a typical reaction, Ag-DDTC was mixed with oleic acid (CH 3 (CH 2 ) 7 CH]CH(CH 2 ) 7 COOH), 1-octadecane (CH 3 (CH 2 ) 16 CH 3 ) and octadecylamine (CH 3 (CH 2 ) 17 NH 2 ).
In study, 129 highly monodisperse and water-soluble clusters representing Ag 2 S quantum dots, covered by ribonuclease-A, were synthesized in aqueous medium via a biomimetic route (i.e., by a method that mimics biochemical processes).
Siva et al. 130 noted that the biomolecules assisted the formation of inorganic nanostructures, facilitated electrostatic stabilization, and improved the optical properties of nanoparticles. In study, 130 aqueous solutions of AgNO 3 and aurochloric acid (HAuCl 4 ) and also a solution of L-cysteine in a mixture of water, ethylene glycol, and ethanol were used for synthesis of L-cysteine-capped Ag 2 S and Ag 3 AuS 2 nanocrystals. Ag 2 S nanocrystals were prepared using Ag nuclei as a core. Siva et al. 130 proposed the following scheme of formation of Ag 2 S particles: There are many other methods for synthesis of nanostructured Ag 2 S. In study, 131 Ag 2 S nanoparticles were prepared by pyrolysis using AgNO 3 and S powder as precursors, and oleylamine C 18 H 35 NH 2 as a solvent. Oleylamine acts as both a reducing agent and stabilizer during the synthesis. Ag 2 S nanoparticles of uniform size were prepared by controlling the ratio amounts of AgNO 3 : S and ripening time.
Shakouri-Arani and Salavati-Niasari 132 produced Ag 2 S nanoparticles by a solvothermal process via reaction of AgNO 3 and a new sulfuring agent from the class of thio Schiff-base (2-(benzylidene amino)benzenethiol C 13  Experimental results 132 indicate that the reaction temperature, presence of surfactant, and type of solvent affect the size of Ag 2 S nanoparticles. Fig. 6 illustrates the inuence of various conditions of synthesis on the formation of Ag 2 S nanoparticles.
An improved hydrothermal/solvothermal method has been developed by Wang et al. 133 to prepare nanostructured Ag 2 S. Using a liquid-solid-solution (LSS) system consisting of an ethanollinoleic acid liquid phase, solid metal linoleate, and a waterethanol solution under hydrothermal conditions, monodisperse Ag 2 S nanocrystals of size 7.3 nm were successfully synthesized.
Biocompatible Ag 2 S quantum dots were prepared through thermal decomposition of a single-source precursor, Ag-DDTC with CH 3 (CH 2 ) 11 SH as a covalent ligand and solvent. 134 The reaction mixture was heated to 483 K at a heating rate of 15 K min À1 and kept for 1 h under a N 2 atmosphere. As a result, hydrophobic Ag 2 S quantum dots with an average diameter from 5.4 to 10.0 nm coated with CH 3 (CH 2 ) 11 SH as the surface ligand were obtained.
Stable and highly luminescent near-IR emitting Ag 2 S colloidal quantum dots were prepared by a simple aqueous method using 2-mercaptopropionic acid (C 3 H 6 O 2 S; 2-MPA) as a coating. 135 Nanoparticle size can be tuned between 2.3 and 3.1 nm with an emission maximum between 780 and 950 nm.
A similar one-step method was reported by Jiang et al. 56 using 3-mercaptopropionic acid (3-MPA) and EG rather than 2-MPA. In this case, the quantum dot surface was terminated with carboxyl groups. The PL emission wavelength of Ag 2 S quantum dots was broadly tunable, from 510 to 1221 nm, by varying the growth time. Li et al. 57 demonstrated that Ag 2 S quantum dots can be used as NIR luminescent probes for in vivo monitoring of lymphatic and vascular networks with deep penetration. They reported that Ag 2 S quantum dots can provide spatial resolution of 40 mm during in vivo photoluminescence (PL) imaging, and this allowed them to monitor angiogenesis.

Hydrochemical deposition of different forms of nanostructured Ag 2 S
Chemical deposition from aqueous solutions (also termed "chemical condensation method", and one-pot synthesis in aqueous solutions) and hydrochemical bath deposition are the most popular methods used for the synthesis of nanocrystalline sulde powders.
Hydrochemical bath deposition is a well-known method which allows preparation of colloidal solutions of Ag 2 S nanoparticles and quantum dots, nanocrystalline and coarsecrystalline Ag 2 S powders, isolated Ag 2 S nanoparticles, and different heteronanostructures with Ag 2 S.
Usually, nanostructured Ag 2 S synthesizes by hydrochemical deposition from aqueous solutions of AgNO 3 and Na 2 S. Solutions of Na 3 Cit or the disodium salt of EDTA (Trilon B) are used as complexing agents. Coarse-crystalline Ag 2 S powder is prepared by hydrothermal synthesis from an aqueous reaction mixture of AgNO 3 , Na 2 S and Na 3 Cit with subsequent heating of a matrix solution with the precipitated powder in a closed vessel at elevated temperature and pressure.
Hydrochemical deposition of Ag 2 S nanopowders using of Trilon B, and also hydrothermal synthesis of Ag 2 S powder, are described in study. 67 Ag 2 S deposition in the presence of Trilon B occurs according to the following reaction scheme: Trilon B was added with constant stirring to AgNO 3 solution, and the prepared solution was then mixed with Na 2 S solution. During mixing of the solutions, a sulde formation reaction occurred instantaneously. All nanoparticles were deposited during 2 days. The average size D of Ag 2 S nanoparticles in the deposited Ag 2 S nanopowders was 58 AE 8 nm.
Disadvantages of the chemical deposition of Ag 2 S from aqueous AgNO 3 , Na 2 S, and Trilon B solutions are the large size of prepared Ag 2 S nanoparticles and the presence of a considerable amount of metallic Ag impurity.
Hydrochemical bath deposition using Na 3 Cit is a wellknown, simple and reliable universal "green" method which allows preparation of non-toxic colloidal solutions of Ag 2 S nanoparticles, isolated Ag 2 S nanoparticles and quantum dots with protective shells, Ag 2 S/Ag heteronanostructures, nanocrystalline and coarse-crystalline powders of Ag 2 S. 76,136-139 A weak aqueous solution of AgNO 3 , which is widely applied in pharmacology and medicine and possesses antibacterial action, is usually used as a source of Ag + for Ag 2 S synthesis. Conditions of hydrochemical bath deposition for preparing different forms of nanostructured Ag 2 S, and the previously unknown possibilities of this method are generalized in study. 136 Hydrochemical deposition of nanostructured Ag 2 S with using Na 3 Cit is an example of green chemistry because of the design of chemical products and processes that reduce or eliminate the use and generation of hazardous substances. 140 Indeed, hydrochemical bath deposition allows one to obtain valuable products from harmless substances using environmentally friendly methods.
In study, 136 different forms of nanostructured Ag 2 S was synthesized by hydrochemical bath deposition from aqueous solutions of AgNO 3 and Na 2 S used as sources of Ag + and S 2À . Na 3 Cit was used as a complexing agent and electrostatic stabilizer.
The solubility product (K sp ) of Ag 2 S is very small (according to, 141 at 298 K, K sp ¼ 6.3 Â 10 À50 ), and Ag 2 S is formed from an aqueous solution of AgNO 3 and Na 2 S in a simple reaction where concentrations of S 2À and Ag + are related by C S 2À ¼ C Ag +/2. Small variation in the ratio of reagent concentrations as compared with the perfect reaction (4), introduction of a complexing agent, and control over synthetic conditions allow preparation of different forms of Ag 2 Sfrom coarse-crystalline powder to colloidal nanoparticles. A generalized scheme of synthesis of different types of nanostructured Ag 2 S and Ag 2 S/Ag heteronanostructures is shown in Fig. 7.
Coarse-crystalline Ag 2 S powders are deposited almost instantly from an aqueous solution of AgNO 3 and Na 2 S with a large excess concentration of S 2À (C S 2À $ C Ag + ) both without and with addition of Na 3 Cit as a complexing agent at room temperature in the dark (Fig. 7a). Synthesis with excess Na 2 S and without addition of Na 3 Cit led to the deposition of Ag 2 S powder of particle size $1000 nm. When Na 3 Cit was added to reaction mixtures having excess Na 2 S, the average size of Ag 2 S particles decreased to $200 nm.
If the concentration of S 2À is sufficient or differs slightly from the concentration required for the chemical bonding, all Ag + (i.e. C S 2À z C Ag + /2 + d), then addition of Na 3 Cit to the solution promotes the formation of Ag 2 S nanoparticles and quantum dots (Fig. 7b). Deposition of Ag 2 S takes place in neutral medium at pH z 7 by the following reaction scheme where d $ 0. Some excess of Na 2 S is necessary for synthesis of Ag 2 S without an impurity of metallic Ag nanoparticles. Synthesis was carried out in a dark room. Na 3 Cit has a triple role in aqueous solutions of AgNO 3 and Na 2 S.
First, it is a complexing and stabilizing agent during deposition of Ag 2 S nanoparticles, which occurs both in the light and dark (Fig. 7b). Second, during deposition in the dark, Na 3 Cit is adsorbed on Ag 2 S nanoparticles, impeding their agglomeration. In this case, an increased duration of deposition and use of reaction mixtures with an enhanced concentration of Na 3 Cit leads to the formation of a protective citrate shell on the surface of Ag 2 S nanoparticles (Fig. 7c). Third, during deposition in the light in aqueous solutions with lowered content of S 2À , Na 3 Cit can reduce Ag + to metallic silver. 142 During deposition in the light, Na 3 Cit, as a reducing agent, takes part in a photochemical reaction ). In this case, selection of the concentrations of AgNO 3 , Na 2 S, and Na 3 Cit in the initial solution meeting the condition C S 2À # C Ag + /2 makes it possible to deposit Ag nanoparticles along with Ag 2 S nanoparticles and to synthesize Ag 2 S/Ag heteronanostructures (Fig. 7d).
In principle, citric acid (harmless standardized food additive E330) can be used as a complexing agent for Ag + , but its application in Ag 2 S synthesis displaces the equilibrium into the acidic region, which is not desirable.
Nanosized Ag 2 S powders were prepared from aqueous solutions of AgNO 3 and Na 2 S containing Na 3 Cit. The concentration of AgNO 3 was 50 mmol l À1 . The concentration of Na 2 S in the initial reaction mixtures was slightly over half of the AgNO 3 concentration, i.e., C Na 2 S ¼ (C AgNO 3 /2) + d with d ¼ 0.5 mmol l À1 . 136 The average particle size (D) in the examined Ag 2 S nanopowders was about 46 AE 7 nm.
The technology for the production of Ag 2 S nanopowders with preset nanoparticle size from 20 to 500 nm by hydrochemical deposition has been patented. 143 Stable colloidal solutions of Ag 2 S quantum dots were prepared from the reaction mixtures with AgNO 3 concentrations (C AgNO 3 ) from 0.3125 to 2.5 mmol l À1 . The Na 2 S concentration (C Na 2 S ) in the reaction mixtures was slightly over half of the AgNO 3 concentration (i.e., C Na 2 S ¼ (C AgNO 3 /2) + d, where d ¼ 0.01 mmol l À1 ). 136 According to the dynamic light scattering (DLS) data, the size of Ag 2 S quantum dots in colloidal solutions was #20 nm. The DLS zeta-potential measurements of colloidal solutions conrmed that these solutions remained stable for >100 days. The particle size distributions for the colloidal solutions with different size of Ag 2 S quantum dots and the appearance of these colloidal solutions are shown in Fig. 8a and b. The zeta potential (z) of quantum dots in a solution is an indicator of the system stability. The DLS measurements revealed that 3 days aer synthesis, the z was À45 to À28 mV, and the quantum dot size was 2-13 nm. The z and size of Ag 2 S quantum dots measured 100 days aer synthesis of colloidal solutions remained almost unchanged. 136 The comparison of the z with the average size (D DLS ) of quantum dots for synthesized colloidal solutions 100 days aer synthesis is displayed in Fig. 8c. The D DLS of quantum dots was 2 to 17 nm, the value of z varied from À49 to À29 mV, and the average z was À35 AE 10 mV. It can be seen that, the smaller is the absolute value of z, the larger is the size of Ag 2 S quantum dots. Fig. 9 presents the size-dependent PL emission spectra of Ag 2 S colloidal solutions in which the uorescence of Ag 2 S quantum dots is tunable from $1176 to $960 nm by decreasing the nanoparticle D DLS from 15.0 to 2.3 nm. According to, 56 the PL peak for Ag 2 S quantum dots with a size about 1.5 nm was observed at $640 nm (see Fig. 9). The PL emission peaks shied from $960 to $1170 nm with the size of Ag 2 S quantum dots increasing from $2.3 to 4.2 nm and remained constant at 1166-1176 nm with an increase of the quantum dot size from $4.2 to >15 nm. The continuous blue shi of the PL emission of Ag 2 S quantum dots from $1176 to $640 nm can be attributed to the strengthened quantum connement effect and increase in band gap E g which resulted from the decreasing size of Ag 2 S quantum dots. This hypothesis is in agreement with experimental data 144 on the size-dependent band gap of Ag 2 S nanopowders. An almost constant position of the PL emission peaks at $1166 to 1176 nm for the Ag 2 S quantum dots with a boundary value of $4.2 nm is evidence for transition from the strong quantum connement regime to a weak quantum connement regime. According to this hypothesis, the estimated Ag 2 S exciton radius (R exc ) is less than half of boundary size of 4.2 nm (i.e., #2.1 nm).
The R exc for Ag 2 S, which is calculated by formula (1), is about 1.4 AE 0.1 nm, and the exciton diameter is about 3 nm. According to an analogous estimation, 145 the Ag 2 S exciton diameter ranges from 3.0 to 4.4 nm. A strong blue shi for a quantum dot of size 1.5 nm agrees with data 145 on the Ag 2 S exciton diameter. An estimated exciton diameter $3 nm for Ag 2 S is in satisfactory agreement with the experimental result (4.2 nm), 136 which follows from the size-dependent PL emission spectra (see Fig. 9).
The technology for preparing aqueous colloidal solutions of stable Ag 2 S quantum dots has been patented. 146 Ag 2 S@C nanoparticles with a carbon-containing citrate shell were found in colloidal solutions prepared from an aqueous solutions of AgNO 3 and Na 2 S at concentrations of 5.0 and   56 The wavelengths corresponding to the maxima of the PL peaks are indicated. The inset presents a fluorescence image of Ag 2 S colloidal solution of quantum dot size $8 nm.
2.5 mmol l À1 or 50 and 25 mmol l À1 , respectively; the Na 3 Cit concentration varied from 5 to 100 mmol l À1 . 68,136,147 Synthesis was carried out at room temperature in the dark.
The X-ray diffraction (XRD) patterns of Ag 2 S nanopowders deposited from a reaction mixture of AgNO 3 , Na 2 S and Na 3 Cit with concentrations of 5.0, 2.5 and 5.0 mmol l À1 , respectively, are shown in Fig. 10A. These nanopowders can be distinguished by their dwell time in the solution (from 20 to 1200 min). The quantitative analysis of the XRD patterns and comparison with data 148 have shown that the observed set of diffraction reections corresponds to nonstoichiometric monoclinic (space group P2 1 /c) acanthite $Ag 1.93 S. The amorphous carboncontaining shell is not visible on the XRD patterns.
The Ag 2 S nanoparticles extracted from the colloidal solutions have an amorphous shell (Fig. 10B). Other things being equal, the thickness of the shell grows when the nanoparticle dwell time in the colloidal solution containing C 6 H 5 O 7 3À ( Fig. 10B(a)-(d)) increases, and when the concentration of Na 3 Cit in the solution increases. A ltered image of area 1 isolated by a white square is shown in Fig. 10B(a). The determination of the interplanar distances of cores conrmed a monoclinic structure of the colloidal Ag 2 S nanoparticles. Fig. 10C(e) shows as an example of the XRD pattern of the core of the nanoparticle presented in Fig. 10B(a). The observed set of spots (À1À11), (À111), (020), and (À212) corresponds to the [101] plane of the reciprocal lattice of the monoclinic (space group P2 1 /c) a-Ag 2 S phase with an acanthite structure.
According to the energy-dispersive X-ray spectroscopy (EDX) results, the content of Ag and S in the colloidal core-shell nanoparticles corresponds to Ag 1.95-1.98 S (Fig. 10C(f)-(h)). The content of carbon is proportional to the intensity of the C Ka line and increases with growth of the shell thickness ( Fig. 10C(f)-(h)). Hence, the shell of sulde nanoparticles contains carbon and is a citrate shell.
Indeed, the three carboxylate groups of Na 3 Cit have strong affinity for Ag + , which favors the attachment of citrate groups on the surface of the Ag 2 S nanoparticles and prevents them from aggregating into large particles. In other words, C 6 H 5 O 7 3À are adsorbed on the surface of nanoparticles and form a citrate carbon-containing shell that prevents the growth and agglomeration of the nanoparticles.
In the solutions with Na 3 Cit, the C 6 H 5 O 7 3À are adsorbed on the surface of Ag 2 S nanoparticles and rst form an uneven, discontinuous shell. As the Ag 2 S nanoparticle dwell time in the solution increases, the discontinuities are gradually lled with citrate complexes, and a continuous carbon-containing shell is formed. Gradual adsorption of the citrate complexes by the formed coating promotes smoothing of the shell surface and the growth of the shell thickness. 68,136 A continuous shell is formed when The presence of a protective citrate shell is important for the PL of Ag 2 S nanoparticles. A decrease in nanoparticle size should be accompanied by a blue shi of the PL peak. However, the observed shi may be less than expected because of the formation of surface trap states in the band gap and electron-phonon coupling. To induce a blue shi, one should suppress the formation of surface trap states in the band gap of Ag 2 S nanoparticles. If the core size is constant, a growth of the protective carbon-containing citrate shell thickness leads to weak intensity enhancement of the PL peaks and a small shi of peaks into the region of lower wavelength (Fig. 11). The position of PL peaks does not depend on the size of an Ag 2 S core of $12 nm.
According to, 68,136,147 hydrochemical bath deposition allows preparation of Ag 2 S@C core-shell nanoparticles with pre-assigned sizes of the Ag 2 S core from 10 and 50 nm and pre-assigned carboncontaining citrate shell thickness from 1.5 to 10 nm.
The process of manufacture of Ag 2 S@C core-shell nanoparticles with a protective citrate carbon-containing shell by hydrochemical deposition has been patented. 149 Comparison of advantages and disadvantages of the main methods for synthesis of different forms of nanostructured Ag 2 S is presented in summary Table 1.
From a comparison of different methods for the synthesis of nanostructured Ag 2 S, it follows that the most universal method is hydrochemical deposition. This method allows synthesis of colloidal solutions of Ag 2 S nanoparticles, isolated Ag 2 S nanoparticles and quantum dots with protective shells, Ag 2 S/Ag heteronanostructures, nanocrystalline and coarse-crystalline powders of Ag 2 S. All the forms of nanostructured Ag 2 S with controllable size can be prepared from the same chemical reagents by varying only their concentrations in solution and the conditions of synthesis. The important advantage of hydrochemical deposition in comparison with other methods is the reproducibility of obtained results.
Hydrothermal and solvothermal synthetic methods are most promising for the preparation of Ag 2 S in the form of sufficiently large objects with different morphologies (e.g., leaf-like nanosheets, ake or star-shaped crystallites, faceted crystals, tetrahedral and hexagonal particles, hollow particles, etc.). Such objects can have the size from hundreds of nanometers to tens of micrometers.
The preferred method for preparation of Ag 2 S nanowires with a high aspect ratio (length/diameter) is template synthesis using silver foil or an aluminum oxide template.
3. Crystal structure of Ag 2 S phases Ag 2 S has three basic polymorphic modications: monoclinic a-Ag 2 S acanthite, cubic b-Ag 2 S argentite, and high-temperature cubic g-Ag 2 S sulde. Structures of the different phases of Ag 2 S were dened originally in studies [150][151][152] and specied later in works. [153][154][155] In works, 150-153 the structure of different Ag 2 S phases was determined on samples of natural minerals such as acanthite and also pseudomorphic acanthite that preserved the cubic morphology of argentite. In works, 154,155 an articial crystal or a powder of Ag 2 S were used for structure determination. In all cases, these were coarse-grained samples with grain (particle) size of 5-10 mm or larger.
Crystal structures of these phases are fairly complex. Hence, in most experimental works devoted to synthesis and properties of Ag 2 S, description of the crystal structure of the synthesized sulde is lacking 57,156,157 or it is made by comparing experimental XRD or TEM results 46,49,56,57,70,73,100,117,[158][159][160] with old XRD data. 150 So, in studies, 46,49,[159][160][161] without performing full-prole structure renement, it was suggested that Ag 2 S synthesized in the form of a lm, nanocrystalline powder or nanoparticles has a crystal structure of natural acanthite, whereas in work 75 it was assumed that synthesized Ag 2 S lm had the structure of argentite. However, the crystal structure of synthetic Ag 2 S may have considerable differences that affect the properties of Ag 2 S. For example, with regard to the XRD patterns of Ag 2 S nanoparticles, authors 159 found a set of spots corresponding to the monoclinic a-Ag 2 S phase with an acanthite structure, as well as several spots that could not be identied in a monoclinic acanthite-type structure. According to, 159 the atomic ratio of Ag to S was estimated to be 1.7 and even 1.1 for nanoparticles with a size of $10 and $6 nm, respectively. In other words, the examined nanoparticles had the nonstoichiometric chemical composition Ag 1.7 S and even Ag 1.1 S.
Careful determination of crystal structures of coarsecrystalline and nanocrystalline acanthite a-Ag 2 S and argentite b-Ag 2 S has been performed recently in studies. 118,148,[162][163][164][165][166] 3.1 Articial coarse-crystalline a-Ag 2 S According to, 150,153 the structure of acanthite a-Ag 2 S can be interpreted as a result of distortion of the b-Ag 2 S argentite structure. Indeed, the unit cells of a-Ag 2 S acanthite proposed in studies 150,153 have axes that can be represented as a combination of axes a bcc , b bcc and c bcc of the unit cell of bcc argentite.
Recently, 118,163 the crystal structure of a-Ag 2 S acanthite was rened for the rst time on synthesized articial samples of coarse-crystalline powder of Ag 2 S with the use of full-prole analyses of XRD data. The average particle size D of coarsecrystalline Ag 2 S powder was estimated from the value of specic surface area S sp ¼ 1.6 AE 0.1 m 2 g À1 and was $515 nm.
According to EDX results, the content of Ag and S in the synthesized coarse-crystalline Ag 2 S powder was 86.8 AE 0.4 and 12.9 AE 0.1 wt%, which corresponds to stoichiometric Ag 2 S.
The renement of the crystal structure of synthesized Ag 2 S provided the following results: synthesized Ag 2 S had a crystal structure of a-Ag 2 S acanthite type; monoclinic (space group Fig. 11 Effect of citrate shell thickness on the PL emission spectra of Ag 2 S@C core-shell nanoparticles. The wavelengths corresponding to the maxima of the PL peaks are indicated. The wavelength of excitation is 658 nm.  These unit cell parameters were in good agreement with the data. 153 Thus, articial coarse-grained Ag 2 S is stoichiometric. The arrangement of Ag and S atoms in the unit cell of articial monoclinic (space group P2 1 /c) Ag 2 S with an a-Ag 2 S acanthite type structure is displayed in Fig. 12. 3.2 Crystal structure and nonstoichiometry of nanostructured a-Ag 2 S Determination of the inuence of nanoparticle size on their nonstoichiometry is a fundamental scientic problem.
A nanostructured Ag 2 S has been studied extensively in the past two decades. However, until lately, there were no experimental works on the determination of the crystal structure of nanocrystalline Ag 2 S.
Determination of the structure of nanocrystalline Ag 2 S has been done in study. 148 The nanocrystalline powder of Ag 2 S was synthesized by chemical deposition from aqueous solution of AgNO 3 and Na 2 S containing Na 3 Cit as a complexing and stabilizing agent.
The XRD pattern of synthesized Ag 2 S nanopowder is shown in Fig. 13. According to the BET data, the particle size of the nanopowder was 44 AE 5 nm.
Preliminary analysis revealed that the synthesized nanocrystalline powder had a monoclinic (space group P2 1 /c) a-Ag 2 S acanthite-type structure. The XRD reections of the nanopowder were broadened and, therefore, the reections located close to each other overlapped. The average size D of coherent scattering region (CSR) estimated from broadening of nonoverlapping diffraction reections (À102), (110), (À113), (À104), (031) and (014) was 43 AE 6 nm.
The coordinates of Ag and S atoms and unit cell parameters for Ag 2 S nanopowder ( Table 2) are close to those for coarsecrystalline Ag 2 S. However, the occupancy of crystallographic positions 4(e) by Ag1 and Ag2 atoms was $0.97 and $0.96, respectively (Table 2). Hence, Ag 2 S nanoparticles of size less than $50 nm are nonstoichiometric, have a composition of $Ag 1.93 S and contain vacant sites in the metal sublattice.

Acanthite a-Ag 2 S-argentite b-Ag 2 S phase transformation
For the rst time, complex in situ high-temperature XRD and SEM study of the a-Ag 2 S (acanthite) to b-Ag 2 S (argentite) phase transformation in nanocrystalline and coarse-crystalline powders of Ag 2 S has been carried out in works. 162,165,166 Until lately, few data on acanthite-argentite phase transformation were obtained only on bulk coarse-crystalline Ag 2 S samples.
The low-temperature monoclinic phase a-Ag 2 S (acanthite) exists at temperatures below $450 K. Argentite b-Ag 2 S has a bcc sublattice of S atoms and exists in the temperature interval 452-859 K.
When argentite b-Ag 2 S is cooled below 450 K under equilibrium conditions, a polymorphous phase transformation takes place that gives rise to monoclinic acanthite a-Ag 2 S. This transformation is accompanied by distortion of the bcc sublattice of S atoms to the monoclinic sublattice. The Ag atoms statistically distributed in positions of the bcc structure of argentite are concentrated in the positions of the monoclinic structure of acanthite, and occupy them with probability close to 1.
To precisely determine the phase transformation temperature, Ag 2 S powders were studied via differential thermal analysis-differential thermal gravimetry (DTA-DTG) upon heating and cooling. During heating, the DTA curves had one endothermic peak at about 449-450 K, which corresponded to the a-Ag 2 S (acanthite)-b-Ag 2 S (argentite) phase transformation. In cooling from 500 K to room temperature, the DTA dependencies exhibited an exothermal peak related to the argentite-  to-acanthite phase transformation towards a lower temperature range by $20 K. The presence of the temperature hysteresis (T trans ) means this was a rst-order reversible acanthite-argentite transformation. The enthalpy of the phase transformation (DH trans ) was $3.7-3.9 kJ mol À1 , which is very close to that determined in works [167][168][169][170] The XRD patterns for coarse-crystalline Ag 2 S powder collected at 300, 433, 453 and 503 K, and the XRD patterns for nanocrystalline Ag 2 S powder at 300, 398 and 463 K are shown in Fig. 14. The XRD patterns recorded at T < 450 K (Fig. 14a and c) contained the diffraction reections of monoclinic (space group P2 1 /c) a-Ag 2 S acanthite. The average particle size D in the nanopowder estimated from broadening of diffraction reections was $60 nm. According to the DTA data, the transformation of acanthite a-Ag 2 S into argentite b-Ag 2 S takes place at $449-450 K. Indeed, the XRD patterns recorded at T $ 453 K contained diffraction reections of cubic (space group Im 3m) b-Ag 2 S argentite. The renement of the XRD pattern (Fig. 14b) showed that coarse-crystalline Ag 2 S at 503 K contained one phase with a cubic (space group no. 229 -Im 3m (I4/m 32/m) (O 9 h )) structure of b-Ag 2 S argentite (Table 3). According to hightemperature XRD data, 162,166 the unit cell of b-Ag 2 S argentite includes two Ag 2 S formula units. Two S atoms occupy crystallographic positions 2(a) and form a bcc sublattice. Four Ag atoms in b-Ag 2 S argentite are statistically distributed in 54 positions 6(b) and 48(j) with the occupation probabilities $0.0978 and $0.0711, respectively (Table 3).
A structure with such small occupancies can be stable only if the mobility of Ag atoms/ions is very high. The amount of Ag + in argentite b-Ag 2 S is much smaller than the number of sites of the cation sublattice. Therefore, signicant positional disorder in an arrangement of Ag + and a gigantic (>92%) concentration of vacant sites facilitate the "jumping" of cations and provide the superionic conductivity of the b-Ag 2 S phase.
The unit cell of cubic (space group Im 3m) b-Ag 2 S argentite is shown in Fig. 15. Detailed crystallographic information on b-Ag 2 S argentite presented as "Crystal structure data" in the CIF-le attached to article. 162 This CIF number 1062400, which was placed on the Cambridge Crystallographic Data Centre (CCDC) website, can be found at the following electronic address. 171 Thus, heating of monoclinic a-Ag 2 S acanthite up to $449-450 K leads to a polymorphic phase transition with the formation of bcc b-Ag 2 S argentite.
SEM images of the acanthite-to-argentite transformation occurring in nanocrystalline and coarse-crystalline Ag 2 S powders are shown in Fig. 16. Table 2 Refined crystal structure of monoclinic (space group no. 14 -P2 1 /c (P12 1 /c1)) Ag 1.93 S nanopowder with an a-Ag 2 S acanthite-type structure and particle size $45 nm: 148 (5)  XRD pattern of coarse-crystalline silver sulfide with a monoclinic (space group P2 1 /c) a-Ag 2 S acanthite-type structure at 300 and 433 K, and with a cubic (space group Im 3m) b-Ag 2 S argentite-type structure at 453 K. (b) Experimental ( ) and calculated ( ) XRD patterns of coarse-crystalline silver sulfide with cubic (space group Im 3m) b-Ag 2 S argentite-type structure at 503 K and the difference (I obs À I calc ) between the experimental and calculated XRD patterns; the ticks correspond to reflections of cubic argentite b-Ag 2 S. (c) XRD patterns of nanocrystalline Ag 1.93 S with a monoclinic (space group P2 1 /c) acanthite-type structure at 300 and 398 K, and with a cubic (space group Im 3m) b-Ag 2 S argentite-type structure at 463 K, respectively. Reproduced from ref. 162 and 166 with permission from the PCCP Owner Societies.
In the upper row (Fig. 16a-c) the initial nanopowder with a surface area (for which the elemental chemical composition was determined by EDX) as well as the cumulative elemental EDX pattern of the initial powder are shown. According to the EDX data (Fig. 16c), the content of Ag and S in the Ag 2 S nanopowder determined from the integral intensities AgL and SK lines were 86.8 AE 0.4 and 13.1 AE 0.1 wt%. This corresponds to a sulde which is close to the stoichiometric composition of Ag 2 S but with small deciency of silver. The second row ( Fig. 16d-f) show a SEM image of the electron beam-heated surface area, upon which argentite particles are growing, and of the same area (side view) with grown argentite crystals.
Short pyramidal nuclei of argentite crystallites (whose base was about 50-80 nm in thickness) appeared on the surface of Ag 2 S powder particles $30 s aer the start of heating. As a result of heating, the nuclei grew quickly, taking the shape of whiskers, and in $5 min covered the entire surface of the acanthite particle.
The sequence of formation and growth of argentite nanoparticles can be conventionally divided into four stages. First, as a result of electron-beam irradiation of acanthite, the particles are heated. Second, the phase transformation leads to the formation of argentite, so the appearance and growth of argentite nuclei take place on the surface of acanthite particles. The third stage is connected with the growth of argentite particles as a result of further heating and the argentite nuclei interacting with the low-temperature phase of acanthite acting as a donor. The growth of argentite particles ends at the fourth stage when no low-temperature acanthite remains in the surface layer.
The formation of argentite was also conrmed by HRTEM data. Fig. 17 demonstrates the HRTEM and TEM images of Ag 2 S nanopowder before and aer radiation heating. 162 In Fig. 17a, the interplanar distance is 0.309 nm and clearly visible, which Table 3 Refined crystal structure of cubic (space group no. 229 -Im 3m (I4/m 32/m) (O 9 h )) coarse-crystalline silver sulfide b-Ag 2 S (b-Ag 2.01 S) with an argentite-type structure at 503 K: 162,166,166 (1)   coincides with the distance d (110) between atomic planes (110) of Ag 2 S with a monoclinic (space group P2 1 /c) a-Ag 2 S acanthite structure. Upon radiation heating of the nanopowder, the HRTEM image exhibits an interplanar distance of 0.245 nm (Fig. 17b). This corresponds to the distance between the atomic planes (200) of cubic (space group Im 3m) Ag 2 S with a b-Ag 2 S argentite structure. The insets in Fig. 17 correspond to the TEM images of these nanopowders of Ag 2 S before and aer heating.  (Table 4). According to, 155 at 923 K, eight Ag atoms are statistically distributed in 88 positions 8(c), 32(f) and 48(i) with the occupation probabilities $0.088, $0.15, and $0.027, respectively. Model 155 suggests some Ag deciency in the g-phase corresponding to nonstoichiometric Ag 1.7 S. Fig. 15 shows the crystal structure of g-Ag 2 S proposed in study. 155 Using the temperature dependences of the crystal lattice parameters of monoclinic acanthite a-Ag 2 S, cubic argentite b-Ag 2 S, and cubic phase g-Ag 2 S, it is possible to estimate the interatomic distances in these phases at comparable temperatures close to the a-Ag 2 S-b-Ag 2 S and b-Ag 2 S-g-Ag 2 S transformation temperatures. The least distance between the Ag1 and Ag1 atoms in the crystal lattice of monoclinic a-Ag 2 S acanthite at 433 K is 0.3351 nm, and the least distance between the Ag1 and Ag2 atoms is in the interval from 0.3085 to 0.3200 nm. 166,173 The covalent diameter of the Ag atom is $0.292 nm. With that in mind, it is clear that Ag atoms in monoclinic acanthite are at rather large distances from each other and, therefore, occupy their crystallographic sites with a probability $1. According to, 166,173 in the crystal lattice of cubic b-Ag 2 S argentite at 443 K, the least possible distance between the Ag1 and Ag1 atoms is 0.2428 nm, between the Ag1 and Ag2 atoms is from 0.0927 to 0.2971 nm, and between the Ag2 and Ag2 atoms is from 0.0988 to 0.2998 nm. Thus, in cubic argentite, the possible distances between Ag atoms are too small for the 6(b) and 48(j) positions to be occupied by Ag atoms with a probability of 1. Indeed, the occupancies of the 6(b) and 48(j) positions by Ag atoms in b-Ag 2 S (in other words, the probabilities of nding Ag atoms in the 6(b) and 48(j) sites) are very small and equal to $0.0978 and $0.0711, respectively. In the cubic g-Ag 2 S phase, the possible distances between Ag atoms are too small for the 8(c), 32(f) and 48(i) positions to be occupied by Ag atoms with a probability of 1. Therefore, the probabilities of lling of the 8(c), 32(f) and 48(i) sites by Ag atoms are <0.1. Physically, this means that Ag atoms in the lattices of cubic b-Ag 2 S and g-Ag 2 S phases are in constant motion over all possible crystallographic positions. It is this constant motion of Ag atoms that provides the stability of crystal lattices of cubic b-Ag 2 S and g-Ag 2 S phases, and their superionic conductivity as distinct from the semiconducting a-Ag 2 S acanthite.

Effect of small particle size on the thermal expansion and heat capacity of Ag 2 S
For the application of nanocrystalline Ag 2 S in infrared equipment, solar-energy converters and resistive switches, it is necessary to have information about the variation in the thermal expansion coefficient of different Ag 2 S phases versus the temperature, and about the effect of particle size on such lattice properties of Ag 2 S as heat capacity and thermal expansion.
According to, 169 the linear thermal expansion coefficient a ac of acanthite is $20 Â 10 À6 K À1 . According to, 174 in the temperature range 293-450 K, the a ac of bulk acanthite is 16.8 Â 10 À6 K À1 , and the linear thermal expansion coefficient a arg of bulk argentite is 45.8 Â 10 À6 K À1 from $460 to 570 K.
A systematic in situ study of the thermal expansion of coarsecrystalline and nanocrystalline powders of Ag 2 S in the region of existence of monoclinic a-Ag 2 S acanthite and cubic b-Ag 2 S argentite has been done for the rst time in works 166,173 via a high-temperature XRD method. Recently, direct dilatometric measurements of the thermal expansion of coarse-crystalline and nanocrystalline Ag 2 S at 290 to 970 K in the region of existence of monoclinic acanthite a-Ag 2 S, argentite b-Ag 2 S, and g-Ag 2 S phases, as well as the heat capacity of nanocrystalline Ag 2 S in the temperature interval from 300 to 930 K, have been carried out in study. 175 The average particle size in coarse-and nanocrystalline Ag 2 S powders was $430 and $66 nm.
The effect of temperature on the evolution of XRD patterns of nanocrystalline Ag 2 S is shown in Fig. 14. The XRD patterns of Ag 2 S recorded at <450 K contain the diffraction reections of monoclinic (space group P2 1 /c) acanthite a-Ag 2 S, and the XRD patterns recorded at >450 K contain the diffraction reections of cubic (space group Im 3m) argentite b-Ag 2 S. Thus, a polymorphous phase transformation of monoclinic acanthite a-Ag 2 S into bcc argentite b-Ag 2 S takes place at $448-453 K.
According to data from high-temperature XRD studies, 166,173 the isotropic (averaged in all crystallographic directions) linear thermal expansion coefficient a ac-nano of nanocrystalline acanthite in the temperature range 300-400 K is The a ac-nano of nanocrystalline acanthite is $25% larger than the analogous coefficient a ac of coarse-crystalline acanthite. The difference in the coefficients a ac-nano and a ac is due to the small particle size in nanocrystalline acanthite. Earlier, a similar difference in the linear thermal expansion coefficients of nanocrystalline lm and coarse-grained sample was observed for PbS. 4,176,177 According to, 166,173 the dependence of a arg on the annealing temperature T in the range 443-623 K can be represented as a arg (T) ¼ 84.5 Â 10 À6 À 6.9 Â 10 À8 T AE 3 Â 10 À6 [K À1 ]. (8) The temperature dependences of a aver (T) for coarse-and nanocrystalline Ag 2 S measured by dilatometry are demonstrated in Fig. 18. The largest coefficient a aver (T) in the examined temperature range 293-970 K belonged to nanocrystalline Ag 2 S produced from a powder with an average particle size of $66 nm. The average linear thermal expansion coefficients a aver of coarse-crystalline and nanocrystalline acanthite a-Ag 2 S and argentite b-Ag 2 S measured in works 166,173 by high-temperature XRD are shown in Fig. 18 for comparison. The results of dilatometric and high-temperature XRD measurements of a aver agree with each other satisfactorily.
The heat capacity of Ag 2 S nanopowder changes monotonically with rising temperature, except for the transition regions (Fig. 19). In the temperature range 300-450 K, the heat capacity increases and then, near the transition temperature T a-b , it experiences a discontinuity. In the region of existence of the b-Ag 2 S phase, in the temperature interval from $470 to $840 K, the heat capacity rst decreases slightly to $670 K and then grows slightly to the transition temperature T b-g , where it discontinues. As the temperature increases further to $890 K, a small reduction of the heat capacity is observed and, at T > 890 K, the heat capacity increases slightly. According to the heat capacity measurements, the transition temperatures T a-b and T b-g were 451 and 858 K, respectively.
The peaks of the heat capacity C p of Ag 2 S nanopowder in the a-Ag 2 S-b-Ag 2 S and b-Ag 2 S-g-Ag 2 S transformation regions were symmetric rather than l-shaped (Fig. 19, inset). A symmetric shape of the observed peaks is more characteristic of rst-order phase transitions. The heat capacity peaks were very narrow (the width of peak base was about 8 K), which is also typical for rstorder phase transitions.
The enthalpy of the phase transformations a-Ag 2 S-b-Ag 2 S and b-Ag 2 S-g-Ag 2 S was estimated to be DH a-b ¼ 4.2 AE 0.4 and  DH b-g ¼ 1.2 AE 0.3 kJ mol À1 , respectively. According to data, 167,168,170 the enthalpy DH a-b is 3.98, 3.93, and 4.06 kJ mol À1 , respectively. According to, 162,165,166 the enthalpy DH a-b is 3.7-3.9 kJ mol À1 . As reported in, 168,170 the enthalpy DH b-g of the transformation of argentite b-Ag 2 S into the g-Ag 2 S phase was $0.50 and $0.78 kJ mol À1 , respectively. Within the measurement error, the obtained values of enthalpies DH a-b and DH b-g were close to the literature data.
For comparison, Fig. 20 presents experimental data on the heat capacity C p of nanocrystalline Ag 2 S 175 and the most reliable experimental data from the literature on the C p of coarsegrained Ag 2 S 170 obtained with the use of adiabatic-shell calorimetry. In the whole temperature region, the heat capacity of nanocrystalline Ag 2 S measured in study 175 was 1-4% larger than the heat capacity of coarse-crystalline sulde. 170 The measured heat capacity C p peaks of Ag 2 S nanopowder was slightly broadened in temperature as compared with those for bulk Ag 2 S obtained in study. 170 The main reason of variation of the lattice properties of nanocrystals in comparison with bulk substances is variation of the shape and boundaries of the phonon spectrum, i.e. change of the frequency distribution function of atomic vibrations. 176 According to, 178,179 waves can occur in nanoparticles whose length does not exceed the doubled maximum size of the particle D, i.e., l # 2D. Hence, on the side of low-frequency vibrations, the phonon spectrum is limited by a certain minimal frequency u min $ 2p c t 2D , where c t is the velocity of propagation of transverse elastic vibrations (i.e., transverse velocity of sound). In bulk crystals, there is no limitation like this. Besides, the phonon spectrum is limited on the side of high frequencies.
Studies, 176,177 took into consideration the restrictions of the phonon spectrum of the small particles and used the approach 180 for the upper boundary u max of the phonon spectrum of small particles. They showed that the molar heat capacity of a model nanocrystalline substance with particles of a cubic shape with edges in length D can be presented as a function not only of the temperature T, but also of the size D of the small particle: where the rst summand represents the Debye heat capacity of bulk crystal in the low-temperature region. The values k 1 ¼ (k B 2 c 1 À1 /8pħ)I 2 and k 2 ¼ (k B 3 c 2 À1 /2pħ 2 )I 3 are positive constants, including the Riemann zeta functions and effective propagation velocities of elastic vibrations, c 1 À1 and c 2 À1 .
The linear thermal expansion coefficient a(T) is related to heat capacity C V by the known relationship where B is the bulk modulus, v m is the molar volume, and g is the Grüneisen constant.
With allowance for eqn (9) and (10), the thermal expansion coefficient of nanocrystalline substance can be presented as Thus, the heat capacity and the thermal expansion coefficient of a nanocrystalline substance include an additional positive contribution as compared with the same properties of a coarse-grained (bulk) substance. Exactly this result was observed for the heat capacity and the thermal expansion coefficient of nanocrystalline and coarse-grained (bulk) Ag 2 S. The appearance of a positive contribution is due to the restriction of the phonon spectrum on the side of low and high frequencies.
According to, 166 the reduction of the particle size in Ag 2 S is accompanied by enhancement of the anharmonicity of atomic vibrations. Anharmonicity results in enhanced phononphonon scattering, which reduces the thermal conductivity k and increases the ZT of nanostructured Ag 2 S. This conrms the possibility of application of nanostructured Ag 2 S as a thermoelectric material that it was noted in study. 58

Heteronanostructures based on Ag 2 S
Semiconductor-metal hybrid heteronanostructures may exhibit not only a combination of properties of the separate components but also further enhanced property tunability. It is supposed that, owing to synergetic effects, new improved properties will arise from the interactions between the metal and semiconductor.
Among semiconductor-metal nanocomposites, the heteronanostructures based on Ag 2 S have attracted special attention and are very useful for manifold applications. Ag 2 S-based heteronanostructures can be used in infrared detectors, in resistance-switches and nonvolatile memory devices, and for bioimaging as biomarkers. 2  Ag 2 S-based heteronanostructures exhibit an excellent bactericidal effect against many types of bacteria. In recent years, Ag 2 Sbased semiconductor-metal heterostructures have emerged as one of the leading materials for photocatalytic conversion of sunlight energy. [186][187][188] Synthesis of Ag 2 S/M (M ¼ Ag, Au, Pt, Pd, Os) heteronanostructures was studied in detail by Yang, Ying and coauthors. 16,40,189,190 They developed a general scheme for transferring the transition metal ions from water to an organic medium using an ethanol-mediated route, which was extended to preparation of a variety of semiconductor/noble-metal heteronanostructures.
A room-temperature method was developed to rst derive aqueous-dispersible Ag 2 S nanocrystals. Typically, C 18 H 17 K 2 O 8 PS 2 salt was added to aqueous AgNO 3 solution. The mixture was stirred for 1 h to form Ag-complexes, with subsequent prompt addition of aqueous Na 2 S solution, which resulted in Ag 2 S hydrosol being produced. 40 Then, Ag 2 S nanocrystals were used as seeds for the formation of nanocomposites with different metals. By using 7 nm Ag 2 S nanocrystals, Na 3 Cit, and various noble-metal precursors at 378 K (for gold) and 383 K (for other noble metals), a set of Ag 2 S/M heteronanostructures were obtained, such as Ag 2 S/Au and Ag 2 S/Ag (Fig. 21), Ag 2 S/Pt, Ag 2 S/ Os, and Ag 2 S/Pd. In the presence of Ag 2 S seeds, the metals nucleated preferentially on the existing Ag 2 S seeds rather than homogeneously.
Cation-exchange reactions can also be used to prepare heteronanostructures through the partial transformation of ionic nanocrystals. 2 The chemical transformation of nanocrystalline solids has emerged as a very promising strategy for inorganic nanostructure synthesis. Among various chemical transformations, the cation-exchange reaction is especially interesting because it can alter the composition of the existing ionic nanocrystal by replacing the cations within the crystal lattice with a different metal ion.
The cation exchange at the nanoscale can transfer one material into another while retaining its morphology. If the exchange only takes place partially in the nanostructure, alloy or core-shell structures are formed. However, by carefully controlling the reaction, heterostructures may also be obtained. Alivisatos and co-authors 191 gave an example of partial change of CdS nanorods into Ag 2 S to form CdS-Ag 2 S superlattices. CdS nanorods in toluene were added to a solution containing toluene, AgNO 3 and methanol at very low temperature and then warmed to room temperature slowly to allow the replacement reaction. The lattice mismatch strains induced the spontaneous formation of periodic structures. The product showed an array of Ag 2 S quantum dots separated by conning regions of CdS. Such an array has potential applications as nanometer-scale optoelectronic devices. Ag 2 S/ZnS heteronanostructures having a matchstick shape with Ag 2 S quantum dots as the heads and ZnS quantum rods as the stems were synthesized in study. 192 These hybrid quantum rods were synthesized by a one-pot thermal decomposition method, and their size could be tuned by changing the ratio between the Ag-DDTC and zinc diethyldithiocarbamate (Zn [S 2 CN(C 2 H 5 ) 2 ] 2 or Zn(DDTC) 2 ) precursors. The diameter of the Ag 2 S head in the Ag 2 S/ZnS heterostructures was around 8.5 nm and the stem size was $7.8 Â 35 nm when a 1 : 2 Ag(DDTC) : Zn(DDTC) 2 molar ratio was used in the synthesis. With an increased molar ratio of 2 : 1, the diameter of the Ag 2 S head in the heteronanostructures was about 4.5 nm and the stem size was $4 Â 48 nm (Fig. 22). The Ag 2 S/ZnS heteronanostructures exhibited appealing PL in UV/blue and NIR regions. Later, Shen et al. 43 modied the synthetic approach to demonstrate one-pot fabrication of Mn-doped Ag 2 S/ZnS quantum rods with multicolor PL in three wavelength regions (blue, orange, and NIR).
A convenient room-temperature method for preparation of a new type of Ag 2 S/Ag heterodimers was devised in study. 55 At rst, monodisperse CdS colloidal nanospheres were synthesized through a modied polyol process (i.e., synthesis of a metal-containing compound in PEG). The CdS nanospheres were used as solid precursors for subsequent chemical transformation to Ag 2 S nanospheres via cation exchange and as a template for deposition of metallic silver. As a result, each Ag 2 S nanosphere was grown with a triangular prism of a Ag crystal, leading to formation of a novel type of asymmetric semiconductor/metal photosensitive heterodimers. According to, 55 these Ag 2 S/Ag semiconductor/metal heterodimers exhibited remarkable bactericidal activity under visible-light illumination and may nd future applications, including bacterial deactivation, bioimaging and sensing, as well as heterogeneous catalysis under ambient conditions. According to study, 193 mono-dispersed Ag 2 S@Ag hybrid nanocomposites exhibit superior adsorption performance for the removal of such organic contaminants as methyl blue and methyl orange from wastewater. Mono-dispersed Ag 2 S@Ag nanoparticles have been synthesized using laser ablation of bulk Ag targets in activated aqueous solution containing C 2 H 5 NS and hexadecyl trimethyl ammonium bromide.
Comparison of the advantages and disadvantages of the main methods for synthesis of Ag 2 S/Ag heteronanostructures is presented in Table 5.
Nonvolatile memory unit represents one of the most important components in state-of-the-art microelectronic/ nanoelectronic devices and has been subject of intensive investigations in the past decades. 16,[48][49][50]181,194 Among different concepts memories, resistive switching memories, whose operation is primarily based on ion migrations that can result in reversible formation and breakage of a conductive lament in the sandwiched metal-insulator-metal structure, are particularly intriguing because they have a low production cost, offer reduced power consumption, and a switching rate as fast as semiconductor devices currently used and, in principle, can be made arbitrarily small. The Pt/Ag 2 S/Ag is an interesting structure exhibiting well-dened resistive switching behavior. 181 For example, Aono and co-authors 181,195 demonstrated basic logic gate operations and fabricated a 1 kbit nonvolatile memory chip based on a Pt/Ag 2 S/Ag heteronanostructure. Recently, they further claried the rate-limiting processes determining the switching time in a Pt/Ag 2 S/Ag system, thus providing a deeper understanding toward the switching mechanism. 196 Despite much recent progress, for future applications, an extended array of Ag 2 S/Ag resistive switches with smaller feature size as well as compatibility with conventional Si-based technology would be more favorable, but has not been realized.
The semiconductor/metal Ag 2 S/Ag heteronanostructures are interesting for the production of resistive switches and nonvolatile memory devices.
The electrical properties of Ag 2 S/Ag heteronanostructure of the heteronanowire type have been studied in work. 48 An anodic aluminum oxide (AAO) template-assisted electrochemical strategy was used for synthesizing a Ag 2 S/Ag heteronanowire array. The porous AAO membrane was deposited partially with Ag nanowires, and then Ag 2 S nanowires were grown by electrochemical sulfurization. Liang et al. 48 assumed that the main reason for the resistance-switching phenomenon in this Ag 2 S/ Ag heteronanostructure was the creation and dissolution of a lament-like Ag conducting bridge.
Recently, authors of study 194 reported the fabrication of an extended array of Ag 2 S/Ag nanodots with a density of 60 Gbit in À2 , which was accomplished by sputtering Ag onto a Si substrate using an ultrathin porous AAO membrane as a shadow mask, followed by room-temperature sulfurization (Fig. 23). This resulted in the formation of a high density of Ag 2 S/Ag bilayer nanodots with a feature size of 45 nm.
The resistance switching behavior of an Ag/Ag 2 S/W nanoscale heterostructure of sandwich type was studied by Xu et al. 49 To synthesize Ag 2 S, an Ag wire of diameter of 0.5 mm heated with S powder to 470 K for 30 min. The suldized Ag wire was scratched by an Ag wire so that some small pieces of Ag 2 S were transferred to the Ag wire. For observation, the Ag wire with the Ag 2 S tip-end was mounted on a high-resolution transmission electron microscope opposite the sharp tungsten W tip. Xu et al. 49 directly observed the formation and breakage of a conducting pathway in a superionic solid electrolyte resistance  nanoswitch with complete reproduction of its performance (Fig. 24). They found that the transition of semiconducting acanthite a-Ag 2 S into conducting argentite b-Ag 2 S took place at room temperature and only within a conductive pathway. The argentite not only formed part of the conducting channel but also provided the pathway for the migration of Ag + . In fact, the Ag + could migrate only in the argentite phase and not in the acanthite a-Ag 2 S phase.
In study, 197 a wet chemical process was used for fabrication of Ag 2 S at thin lms on Ag electrodes utilized for an atomic Ag 2 S/Ag switch. A counter electrode made of Ag with a gap of $1 mm was fabricated using conventional UV-lithography on a Si substrate. The substrate with Ag was dipped into an aqueous solution of Na 2 S for sulfurization. As a result, Ag 2 S was formed on the Ag surface.
In study, 50 the resistive switches Ag 2 S/Ag nanoclusters for memory cells were formed by sulfurization of melting-dispersed thin continuous Ag lms. Ag nanocluster arrays were formed by thermal annealing of 10 nm-thick Ag lms at 500 K during 40 min immediately aer vacuum thermal evaporation. Lowtemperature sulfurization in a H 2 S atmosphere in an airtight chamber was used to obtain Ag 2 S particles. Gubicza et al. 198 demonstrated stable resistive switchings in metallic Ag-Ag 2 S-Ag heteronanojunctions created by an scanning tunneling microscope (STM). An 80 nm-thick Ag layer was deposited onto a Si substrate followed by a 5 min sulfurization in a H 2 S atmosphere at 333 K. As a result, a 30 nm-thick stoichiometric Ag 2 S cap layer on the planar Ag electrode was obtained. Nanometer-scale junctions were created between the Ag 2 S surface and a mechanically sharpened Ag wire of 0.35 mm in diameter in STM geometry. According to, 198 fast and highly integrable memory cells are the merits of lithographically designed Ag-Ag 2 S-Ag heteronanostructures.
The synthesis of multifunctional nanocomposite systems is of great interest. In particular, heteronanostructures such as Ag 2 S/Ag consisting of a semiconductor and a noble metal are very useful for various applications. This type of heterostructures that contain Ag and Ag 2 S nanowires or an Ag lm with Ag 2 S/Ag nanoclusters are considered for the production of biosensors, 183 resistive switches, and nonvolatile memory devices. [48][49][50]194,197,199 The action of the resistive switch is based on the phase transformation between nonconducting a-Ag 2 S acanthite and superionic b-Ag 2 S argentite.
Hydrochemical deposition has been applied for the rst time to the synthesis of Ag 2 S/Ag heteronanostructures in studies. 136,[200][201][202][203] Ag 2 S/Ag heteronanostructures have been synthesized by chemical deposition from aqueous solutions of AgNO 3 , Na 2 S, and Na 3 Cit with a reduced concentration of Na 2 S (C Na 2 S < C AgNO 3 /2). Synthesis was carried out under illumination of solutions by a light-emitting diode with a 450 nm wavelength and an irradiation intensity of 15 mW cm À2 . Two processes take place simultaneously in such mixtures: formation of Ag 2 S and appearance of Ag nanoparticles as a result of photochemical reduction reaction (6) of Ag 2+ by C 6 H 5 O 7 3À . At certain synthesis conditions, Ag and Ag 2 S nanoparticles are united in Ag 2 S/Ag nanocomposites.
The scheme of deposition of Ag 2 S/Ag heteronanostructures from aqueous solutions of AgNO 3 , Na 2 S and Na 3 Cit, TEM and HRTEM images of Ag 2 S, Ag and Ag 2 S/Ag particles and their diffraction patterns, as well as EDX analysis of Ag 2 S, Ag particles and Ag 2 S/Ag heteronanostructures are shown in Fig. 25.
Synthesis was carried out in a particular sequence. Briey, a complexing agent was added to AgNO 3 in the dark. Then, a solution of Na 2 S was poured into the prepared solution (Fig. 25a). As a result, deposition of Ag 2 S powder occurred. Then, the solution was irradiated with monochromatic light at wavelength 450 nm. In accordance with the photochemical reaction (6) C 6 H 5 O 7 3À reduced the Ag + to Ag nanoparticles in aqueous solutions (Fig. 25b). The reduction of Ag at the surface of Ag 2 S nanoparticles leads to the formation of Ag 2 S/Ag heteronanostructures (Fig. 25c). The HRTEM images of deposited Ag 2 S, Ag and Ag 2 S/Ag particles are shown in Fig. 25d-f, respectively. In studies, 136,200,201,203 the diffraction patterns (selected area of electron diffraction (SAED)) ( Fig. 25g-i) of these particles were obtained by fast Fourier transformation (FFT) of their HRTEM images.
The observed set (Fig. 25g) of diffraction reections and interplanar distances of Ag 2 S nanoparticles corresponded to monoclinic (space group P2 1 /c) nanocrystalline acanthite a-Ag 1.93 S. 148 The Ag nanoparticle (Fig. 25e) had a cubic (space group Fm 3m) structure with microtwinning in the direction of the [111] planes (Fig. 25h). Diffraction patterns (Fig. 25i) obtained by FFT of HRTEM images (Fig. 25f) of Ag 2 S/Ag heteronanostructures revealed reections of monoclinic Ag 2 S and twinned reections of cubic Ag.
According to the EDX results ( Fig. 25j-l), the content of Ag and S in Ag 2 S nanoparticles was $86.3 AE 0.4 and $12.9 AE 0.1 wt% and corresponded to $Ag 1.95-1.98 S. Ag nanoparticles contained Ag only, and Ag 2 S/Ag heteronanostructure contained about 87.8 and 11.5 wt% of Ag and S, respectively.
The XRD pattern and HRTEM images of Ag 2 S/Ag heteronanostructures are shown in Fig. 26. Areas (1) and (3) correspond to Ag and Ag 2 S nanoparticles, respectively. The Ag nanoparticle clearly exhibited microtwinning in the direction of the [01À1] planes. Area (2) corresponded to that part of heteronanostructure where the Ag 2 S and Ag nanoparticles are in Fig. 24 (a) Off-and (b) on-states of a narrow and thin Ag 2 S/Ag device regions. The Ag electrode is located on the top part of the image, and the W electrode is in the bottom part. When the device is switched from the off-to on-states, an area 1 has almost no change, the argentite appears in area 2, the argentite and Ag appear in area 3, and no changes are seen in area 4. Reproduced from ref. 49 with permission from ACS. direct contact. Indeed, a set of spots (Fig. 26b) contains diffraction reections of both phases: Ag 2 S and Ag. The interplanar distances for area (3) and the set of eight spots (Fig. 26c) corresponded to monoclinic (space group P2 1 /c) a-Ag 2 S acanthite.
The Ag 2 S/Ag heteronanostructures combine ionic and electronic conductors and can be used to create biosensors, resistive switches and nonvolatile memory devices.
Let us turn to a discussion of Ag 2 S/Ag heteronanostructures prepared by the hydrochemical deposition method.
A typical Ag 2 S/Ag heteronanostructure contained in the colloidal solution prepared from aqueous solutions of AgNO 3 , Na 2 S and Na 3 Cit is shown in Fig. 27 as an example. As can be seen, the Ag 2 S and Ag nanoparticles are in immediate contact. The Ag nanoparticle clearly exhibits microtwinning in the direction of the [111] planes. According to the EDX data, the nanoparticle contains only Ag. The interplanar distances observed for Ag 2 S nanoparticles correspond to monoclinic acanthite. The zone axis of the Ag 2 S nanoparticle matrix is The resistive switches of Ag 2 S/Ag types consist of a superionic conductor located between two metal electrodes. In the case of Ag 2 S/Ag heterostructures, one of the electrodes is Ag, and the second electrode can be Pt, Au, Cu, or W. The conductivity of Ag was 6.3 Â 10 5 ohm À1 cm À1 , that of the b-Ag 2 S argentite and a-Ag 2 S acanthite phases were about 1.6 Â 10 3 and only 2.5 Â 10 À3 ohm À1 cm À1 at room temperature, 35 respectively. Thus, the conductivity of acanthite was 6 orders of magnitude lower than that for the argentite phase. It is, thus, reasonable to conclude that the conducting channel in Ag 2 S/Ag heterostructures can be made of a mixture of Ag and b-Ag 2 S argentite. In studies, 136,[200][201][202][203] Ag 2 S/Ag heteronanostructures formed by Ag 2 S and Ag nanoparticles were produced by a simple method of hydrochemical bath deposition. Deposition of Ag 2 S/Ag heterostructures on a substrate coated with a thin conducting metallic layer will make it possible to form a structure that can work as a resistive switch. The action of the switch is based on the phase transformation of nonconducting a-Ag 2 S acanthite into b-Ag 2 S argentite exhibiting superionic conduction. The transition into a high-conduction state is due to abrupt disordering of the cationic sublattice. Authors of studies 204,205 have shown that a high-conduction state of a crystal can be achieved by external electric eld-induced "melting" of the cationic sublattice taking place without heating of the crystal. Such transformation occurring as a result of applied external electric eld was conrmed with respect to nanocrystalline Ag 2 S in studies. 49,50,194,199 The effect of an external electric eld induced abrupt disordering, allowing the realization of the superionic state of Ag 2 S at room temperature. This opens up the possibilities for the practical use of materials based on Ag 2 S.
Authors of works [200][201][202][203] studied preliminarily the switching processes in Ag 2 S/Ag heteronanostructures. For this purpose, a metallic Pt microcontact was supplied to Ag 2 S/Ag heteronanostructure and bias voltage was impressed so that the Ag electrode was charged positively. When positive bias voltage increased to 500 mV, the conduction of the heteronanostructure grew and the nanodevice transformed into the conducting state (i.e., the on-state). The bias back to negative values decreased the conduction and the nanodevice transformed into the offstate. Fig. 28 displays a region of an Ag 2 S/Ag heteronanostructure where change of crystal structure at the transition from the offstate (Fig. 28a) to the on-state (Fig. 28b) can be observed. Using FFT of HRTEM images, authors of studies 200,202,203 obtained the selected areas of electron diffraction (SAEDs) (Fig. 28c and d).
The electron diffraction pattern of an Ag 2 S/Ag heteronanostructure in the off-state is shown in Fig. 28c. This SAED contains (111), (11À1) spots and twinning reection (111)* corresponding to cubic (space group Fm 3m) Ag, as well as (2À12) and (030) spots corresponding to monoclinic (space group P2 1 /c) a-Ag 2 S acanthite. The observed angle of 100.3 between (2À12) and (030) spots of monoclinic acanthite coincided within the measurement error with the theoretical value 100.7 . Experimental angles between diffraction spots of cubic Ag coincided with the theoretical values.
Then, a positive bias was applied to the Ag 2 S/Ag heteronanostructure to turn it on. HRTEM images of an Ag 2 S/Ag heteronanostructure in the on-state and its selected electron diffraction patterns are presented in Fig. 28b and d, respectively. The electron diffraction pattern (Fig. 28d) contains two sets of spots corresponding to cubic (space group Fm 3m) Ag, and cubic (space group Im 3m) b-Ag 2 S argentite. The observed angle of 30.1 between the (011) and (112) spots of cubic b-Ag 2 S argentite coincides with the theoretical value of 30 .
Thus, the applied bias leads to the appearance of conducting b-Ag 2 S argentite instead of nonconducting a-Ag 2 S acanthite and the formation of conductive channel from argentite b-Ag 2 S and Ag.
The current-voltage I(V) characteristics of the resistive switches based on Ag 2 S/Ag heteronanostructures produced by different methods are presented in studies. [48][49][50]194,199 As a rule,  the bias voltage is from AE150 to AE500 mV. According to, 49 the minimum energy barrier for an Ag cation jumping from one atomic site to the other is about 130 meV.
An I(V) characteristic of the resistive switch based on an Ag 2 S/Ag heteronanostructure produced by hydrochemical deposition in studies 200,202,203 is shown in Fig. 29a. The schematic operation of this switch is shown in Fig. 29.
The initial Ag 2 S phase was a nonconducting acanthite a-Ag 2 S (Fig. 29(1)). When a positive bias was applied, Ag + started to move towards the negatively charged cathode M and were reduced to Ag during their transport. Simultaneously, the a-Ag 2 S phase transformed into superionic b-Ag 2 S argentite ( Fig. 29(2)), and a continuous conductive channel was formed (Fig. 29(3)). The continuous conductive channel that was formed from argentite b-Ag 2 S and Ag was retained when the external eld is turned off. This phenomenon can be considered to be a memory effect (Fig. 29(3)). If a negative (reverse) bias is applied to the switch, the Ag nanocrystals start dissolving in argentite, the Ag + move to the anode, argentite transforms into the initial acanthite again, the conductive channel breaks down, and an off-state is realized (Fig. 29(4 and 5)). Because of the formation of nonconducting acanthite, the conductive channel disappears, the switch transforms into the initial state and is turned off (Fig. 29(6)). If positive bias is applied once again, the destroyed conductive channel is restored due to the appearance of argentite and the formation of Ag.
According to, 49,50,202,203 the bias voltage which is sufficient to turn on and turn off the switch is from AE0.2 to AE10.0 V depending on the metal M used as the second electrode.
The UV-vis optical absorption spectra of colloidal solutions containing Ag 2 S/Ag composite nanoparticles 200 contain a broad intensive absorption band in the region of $360 to 450 nm, which corresponds to Ag nanoparticles and is due to surface plasmon resonance (SPR). 55,100,206,207 Also, the weakly diffused absorption peak observed at $312-320 nm corresponds to Ag 2 S nanoparticles.
Ag 2 S/Ag nanocomposites can be applied as promising biosensing probes. Ag nanoparticles can be used as biosensors owing to their unique SPR, which depends on the size and shape of particles. 183,208,209 However, Ag nanoparticles are easily oxidized, which is why they should be protected. The combination of Ag nanoparticles and chemically stable Ag 2 S allows one to increase the stability of Ag nanoparticles and to use Ag 2 S/Ag nanocomposites and Ag@Ag 2 S core-shell structures for biosensing applications in the future.
According to, 186,210 Ag 2 S/Ag heteronanostructures possess considerable antibacterial activity and can be used in biology and medicine. This agrees with data 54,55,144 on the antibacterial activity of Ag 2 S colloidal solutions and nanopowders.

Conclusions and outlook
This review presented the major advances in the controlled synthesis of nanostructured Ag 2 S in the form of nanopowders, stable colloidal solutions, quantum dots, isolated nanoparticles with a protective shell, and heteronanostructures. Also, the main results on the study of crystal structure, nonstoichiometry and properties of nanostructured Ag 2 S were detailed.
An increasing variety of semiconductor nanostructured Ag 2 S with various sizes and shapes can now be prepared. Along with the development of synthetic methods, the applications of nanostructured Ag 2 S have become wider.
Investigations over recent years have shown that nanostructured materials based on Ag 2 S are more effective than their bulk counterparts due to the following advantages: higher specic surface areas and more active sites for catalysis; longer cycle life; enhanced band gap of the semiconductor Ag 2 S phase; higher electric conductivity of high-temperature Ag 2 S phases; shorter path lengths for the transport of charge carriers (electrons and holes). Experimental studies of the quantum connement effect of Ag 2 S quantum dots have shown that the exciton diameter of Ag 2 S is about 4 nm.
Synthesized forms of nanostructured Ag 2 S have several possible applications. First, stable Ag 2 S colloidal solutions and Ag 2 S quantum dots are suitable for biological and medical application as biomarkers because these solutions are non-toxic and do not contain hazardous substances. Ag 2 S quantum dots exhibit bright photoluminescence and excellent photostability. Therefore, Ag 2 S quantum dots of size less than 3-4 nm could be used for NIR applications in the biomedical eld as luminophores or biomarkers. The creation of a protective shell on Ag 2 S quantum dots helps to prevent the agglomeration and growth of quantum dots and to retain their optical properties.
Nanocrystalline Ag 2 S powders can be used for production of electronic devices such as photovoltaic cells, photoconductors, and infrared detectors. Ag 2 S/Ag heteronanostructures unite ionic and electronic conductors. A high-conducting state of such heteronanostructures can be induced by an external electric eld without heating of this composite owing to phase transformation of nonconducting acanthite into argentite and the exhibition of superionic conduction. Ag 2 S/Ag heteronanostructures are intended for application in fast-acting resistive switches and nonvolatile memory devices. Also, Ag 2 S/ Ag nanocomposites can be applied as promising biosensing probes and photocatalysts. Composite heteronanostructures based on Ag 2 S not only combine the properties of the individual nanocrystals, but also lead to new collective properties due to synergetic effects. Recent studies have shown that the synergetic effect can considerably enhance the properties of composite nanomaterials based on nanostructured Ag 2 S.
All the forms of nanostructured Ag 2 S possess signicant potential antibacterial activity, and can be used as effective agents against asepsis and for disinfection.
Thus, recent advances have shown that nanostructured Ag 2 S possesses great possibilities for potential application in different areas, from optoelectronics to biomedicine, because of its unique physical and chemical properties and "nanosized" effects.
The exploration and development of new synthetic methods and techniques to prepare nanostructured Ag 2 S with better performance, and understanding of its structure-related properties, is an ongoing task for researchers.
Although the last decade has witnessed great progress in the synthesis of nanostructured Ag 2 S and its application, challenges still exist. The discussion below illustrates some of the challenges that scientists and technologists are facing in the synthesis and application of nanostructured Ag 2 S.
Stable colloidal solutions contain the nest Ag 2 S nanoparticles of size about 2-16 nm but the concentration of such nanoparticles is 0.01-0.02 mg mL À1 and rather small. That is why an important problem in the synthesis of different forms of nanostructured Ag 2 S remains the preparation of more concentrated colloidal solutions that retain their long-term stability and small size of nanoparticles.
Obtaining a narrow size distribution of synthesized Ag 2 S nanoparticles (i.e., the synthesis of uniform-sized nanoparticles) is another important challenge. Indeed, the synthesis of monodisperse Ag 2 S nanoparticles (with size variation <5%) is of key importance because the properties of the nanoparticles depend strongly on their sizes and uniformity.
One of the major challenges of using Ag 2 S quantum dots in electronics is the creation of large arrays of the quantum dots homogeneous in size and shape. The synthesized quantum dots are located on the substrate surface in a random way. For application in electronics, the prepared arrays of Ag 2 S quantum dots should be well ordered, preferably by self-organization, and should be compatible with optical devices and detectors. Another important problem facing Ag 2 S quantum dot arrays is improvement of the electric conductivity reduced by the organic ligands used in colloidal synthesis. Achieving the necessary performances of Ag 2 S quantum dot assemblies is an attainable aim in the next years.