Experimental Part

Abstract

All chemicals were of analytic-grade purity obtained from Sinopharm Chemical Reagent Co., Ltd and used as received without further purification.

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7.1 Materials

All chemicals were of analytic-grade purity obtained from Sinopharm Chemical Reagent Co., Ltd and used as received without further purification.

7.2 Samples Preparation

7.2.1 Synthesis of Ag₂Se and Ag₂S Nanocrystals

Ag₂Se and Ag₂S nanocrystals were synthesized using a modification of the method proposed by Wang et al. [1]. Briefly, 20 ml octadecylamine was heated to 180 °C, and then, 0.5 g of AgNO₃ was added. After the mixture was magnetically stirred for 10 min, 0.13 g selenium or 0.06 g sulfur powders was added into the system. The mixture was maintained at 180 °C for 3 h under stirred conditions, and then the reaction was quickly stopped. The nanocrystals were separated from the resulting solution by centrifuge and washed for several times with ethanol and cyclohexane. All the samples were dried in a vacuum at 60 °C for 6 h.

7.2.2 Synthesis of Ag₄SeS Nanocrystals

20 ml octadecylamine was heated to 180 °C, and then, 0.5 g of AgNO₃ was added. After the mixture was magnetically stirred for 10 min, 0.063 g selenium and 0.026 g sulfur powders were added into the system. The mixtures were maintained at 180 °C for 3 h under stirred conditions, and then the reaction was quickly stopped. The nanocrystals were separated from the resulting solution by centrifuge and washed for several times with ethanol and cyclohexane. All the samples were dried in a vacuum at 60 °C for 6 h.

7.2.3 Synthesis of AgBiSe₂ Nanocrystals

AgBiSe₂ nanocrystals were synthesized through a simple colloidal method. Briefly, slurry of bismuth (III) citrate (0.199 g) in 20 ml oleylamine was heated at 120 °C for 30 min under an N₂ atmosphere to remove oxygen and water. The solution was then heated to 180 °C under vigorous magnetic stirred conditions, and 0.085 g of AgNO₃ was quickly added at this temperature. After the mixture was magnetically stirred for 10 min, 0.079 g selenium powder was quickly added into the system. The mixture was maintained at 180 °C for 3 h under magnetic stirred conditions. After cooling the resulting solution to room temperature, the nanocrystals were separated from the resulting solution by centrifuge and washed for several times with ethanol and cyclohexane. All the samples were dried in a vacuum at 60 °C for 6 h.

7.2.4 Synthesis of AgBi_1−xSb_xSe₂ Solid Solution Nanoplates

In this study, we have synthesized a series of AgBi_1−x Sb _x Se₂ (x = 0, 0.25, 0.5, 0.75, and 1) solid-solutioned nanoplates. Taking AgBi_0.5Sb_0.5Se₂ as an example, firstly, Bi(III)-complex and Sb(III)-complex precursor solution was prepared by adding 0.193 g of bismuth acetate and 0.149 g antimony acetate to 2 ml 2-ethylhexanoic acid in a flask, respectively. The mixture was kept at 80 °C and stirred for 30 min until a uniform mixture was formed, then cooled to room temperature. Secondly, selenium precursor solution was prepared in a separate flask, where 0.2 g of Se powder was mixed with 20 ml oleylamine, and kept at 180 °C, then stirred for 30 min. Thirdly, Bi(III)-complex and Sb(III)-complex precursor solution was swiftly injected into the Se-precursor solution, and 0.170 g AgNO₃ also was added into the Se-precursor solution. The mixture was maintained at 180 °C for 3 h under stirring, and then the reaction was quickly stopped. The nanoplates were separated from the resulting solution by centrifuge and washed for several times with ethanol and cyclohexane. All the samples were dried in a vacuum at 60 °C for 6 h.

7.2.5 Synthesis of AgBi_0.5Sb_0.5Se₂ Solid-Solutioned Homojunction Nanoplates

In a typical synthesis of AgBi_0.5Sb_0.5Se₂ homojunction, 0.193 g of bismuth acetate and 0.149 g antimony acetate were added into 20 ml oleylamine and kept at 80 °C under stirred for 30 min. Then 0.2 g of Se powder was added into the mixture after the mixture was heated up to 180 °C. The mixture was maintained at 180 °C for 1 h under stirred, and then 0.170 g AgNO₃ was added. After the mixture being maintained at 180 °C for 1 h under stirred conditions, the reaction was quickly stopped. The samples were separated from the resulting solution by centrifuge and washed for several times with ethanol and cyclohexane. All the samples were dried in a vacuum at 60 °C for 6 h.

7.2.6 Synthesis of Cu₂XSnS₄ Nanocrystals

Briefly, 0.07 g of sulfur powders was dissolved into 20 ml octadecylamine at 80 °C. Then, 0.262 g of copper acetylacetonate, 0.132 g of zinc acetylacetonate, and 0.177 mL dibutyltin bis(2,4-pentanedionate) were added into the S-precursor solution. After the complex solution stirred at 120 °C for 30 min under N₂ atmosphere, the temperature was slightly heating up to 230 °C. The mixture was maintained at 230 °C for 1.5 h under stirred conditions, and then the reaction was quickly stopped. The nanocrystals were separated from the resulting solution by centrifuge and washed for several times with ethanol and cyclohexane. For the Ni-doped Cu₂ZnSnS₄ nanocrystals, the nickel acetylacetonate as the nickel source was added into the S-precursor solution together with zinc source. For the magnetic ions fully substituted quaternary Cu₂XSnS₄ (X = Mn, Fe, Co) nanocrystals, the manganese (II) acetylacetonate, or iron (II) acetylacetonate, or cobalt (II) acetylacetonate was respectively used to replace zinc acetylacetonate while other conditions remain the same. All the samples were dried in a vacuum at 60 °C for 6 h.

7.2.7 Surfactants Removal Process and Bulk Samples Preparation

The organic surfactants were removed via the procedure of previously reports [2] before fabrication of bulk samples for thermoelectric measurement. Briefly, as-prepared silver chalcogenides were dispersed in cyclohexane with hydrazine solution (85 % v/v) and stirred vigorously until all the nanocrystals precipitated. The supernatant is decanted and the precipitate is washed with ethanol three to four times to remove hydrazine and collected by centrifugation, and then dried in vacuum at 65 °C. After the hydrazine treatment, the nanocrystals are hot-pressed into rectangular (10 mm × 4 mm × 1.5 mm) and round disk bulk samples (with diameter of about 13 mm and thickness of 2 mm) under 60 MPa at 400 °C for 30 min.

7.3 Characterizations

The structure of these obtained samples was characterized with the X-ray diffraction (XRD) pattern, which was recorded on a Rigaku Dmax diffraction system using a Cu Kα source (λ = 1.54187 Å). Temperature-dependent XRD (X-ray diffraction) patterns of the samples were recorded between 27 and 330 °C by the Shimadzu XRD-7000 with Cu Kα radiation (λ = 1.54187 Å). X-ray photoelectron spectroscopy (XPS) measurements were performed on a VGESCALAB MK II X-ray photoelectron spectrometer with an excitation source of Mg Kα = 1253.6 eV. Electron microscopy observations were carried out with a Hitachi H-800 transmission electron microscope at 100 kV. High-resolution transmission electron microscopy (HRTEM) images were taken on JEOL-2010 transmission electron microscope at 200 kV. The field emission scanning electron microscopy (FE-SEM) images were taken on a JEOL JSM-6700F SEM. Temperature-dependent Raman spectra were recorded by a LABRAM-HR Confocal Laser MicroRaman Spectrometer 750 K with a laser power of 0.5 mW. The temperature-dependent EPR measurement of the powder sample was performed using a Bruker EMX Plus model spectrometer operating at X-band frequencies (9.4 GHz) at different temperatures.

7.4 Thermoelectric Properties Measurements

Rectangular shape samples with typical sizes of 10 mm × 4 mm × 1.5 mm were employed to simultaneously measure electrical conductivity σ and Seebeck coefficient S by the standard four-probe methods in a He atmosphere (ULVAC-RIKO ZEM-3). Thermal conductivity κ was calculated using the equation κ = aρC _p from the thermal diffusivity a obtained by a flash diffusivity method (LFA 457, Netzsch) on a round disk sample with diameter of about 13 mm and thickness of 2 mm, and specific heat C _p was determined by a differential scanning calorimeter method (DSC Q2000, Netzsch).

7.5 Positron Annihilation Spectroscopy

The positron lifetime experiments were carried out with a fast-slow coincidence ORTEC system with a time resolution of about 230 ps full width at half maximum. A 5mCi source of ²²Na was sandwiched between two identical samples, and the total count was one million. The temperature-dependent Doppler broadening energy spectroscopic (DBES) spectra were measured using an HP Ge detector at a counting rate of approximately 800 cps. The energy resolution of the solid-state detector was 1.5 keV at 0.511 MeV (corresponding to positron 2γ annihilation peak). The total number of counts for each DBES spectrum at different temperature was 8 million. Because of the high temperature, the hpGe detector should be put a little far away from the sample and the ²²Na source was dropped on a nickel membrane. Considering the problem of counting rate, the positron single Doppler broadening experiment was adopted.

7.6 Calculation Details

7.6.1 Calculation Details for Ag₂Se

The band structure calculations of orthorhombic and cubic Ag₂Se were performed using the CASTEP program package with the Perdew–Burke–Ernzerhof (PBE) GGA functional.

7.6.2 Calculation Details for AgBiSe₂

The structural optimization, total energies, and electronic structure calculations were performed by using VASP code [3] with the projector-augmented wave (PAW) potentials [4]. Generalized gradient (GGA) corrections were applied to the exchange–correlation function within the implementation of PBE [5]. After the full convergence test, the kinetic energy cut-off of the plane-wave basis was chosen to be 450 eV. The Brillouin zone of hexagonal unit cell and cubic supercell are sampled in the k-space within the Monkhorst-Pack scheme [6] by (15 × 15 × 3) and (4 × 4 × 4) mesh points for the self-consistent structure optimizations, (21 × 21 × 5) and (5 × 5 × 5) mesh points for the total energy calculations, respectively. All atomic positions and lattice parameters are optimized by using the conjugate gradient method where total energy and atomic forces are minimized. The convergence for energy is chosen as 10⁻⁵ eV between two ionic steps, and the maximum force allowed on each atom is 0.01 eV/Å. The band-decomposed charge density is obtained by summing up the local density of states for the eigenvalues at a specified band, which is provided to analyze the orbital characters near Fermi surface, including VBM and CBM in the semiconductor. The 3D charge density iso-surfaces have been drawn by VESTA [7].

Relational structures at different temperatures in the rhombohedral–cubic phase transition. As temperature increases, AgBiSe₂ crystallized in the hexagonal phase is observed to undergo continuous phase transition to rhombohedral phase around 410 K and then to cubic phase around 580 K. Also the phase transitions take place reversibly as temperature decreases, that is, the cubic phase undergoes the continuous phase transition to rhombohedral phase around 560 K and then to the hexagonal phase around 390 K during cooling process. Our optimized lattice parameter for rhombohedral structure of the AgBiSe₂ intermediate-temperature phase is a = 7.076 Å. The corresponding band structure and density of states is then calculated using this structure, and indirect narrow band-gap ~0.5 eV is found (Fig. 7.1a, b). According to the PDOS (Fig. 7.1c–e), the valance bands near Fermi level of AgBiSe₂ are mainly composed of d states of Ag atoms while the conduction bands are composed of p states of Bi atoms, where both hybridize with p states of Se atoms.

Fig. 7.1

a The band structure and b total density of states for rhombohedral phase AgBiSe₂. Projected density of states (PDOS) of each atom: c for Ag, d for Bi, and e for Se, respectively. The Fermi level (E _f , red dashed line) is set at 0 eV

Focusing on the high-temperature cubic phase, the high degree of disorder in the Ag and Bi atoms makes the exact electronic band structure calculations impossible. For treating such materials systems by first principles methods, two general methods have been usually carried out, i.e., the supercell method and the virtual crystal approximation (VCA) method [8], but the VCA method is not well suited to simulate the details of this phase transition although it is simpler and more efficient. So, in our case, a cubic supercell with 64 atoms is used for the disordered phase in the supercell approximation.

Structural analysis (Fig. 7.2) based on original structural model revealed that, in hexagonal AgBiSe₂ lattice, the atomic arrangement can be considered as repeating units with each consisting of eleven atomic Se–Ag–Se–Bi–Se–Ag–Se–Bi–Se–Ag–Se chain (denoted as Ag–Bi–Se chain) along the c axis, which is then separated by a layer of Bi. Obviously, two crystallographically distinct Bi atoms are observed in this structure: Bi₂ is bonded to Se atoms with distance of 2.993 and 2.981 Å, whereas Bi1 is isolatedly inserted to two Ag–Bi–Se layers and weakly bonded with Se atoms with distance of 3.04 Å. While in the rhombohedral phase, the Bi₂–Se bonds are weakened and all Bi atoms locate at the same chemical environment.

Fig. 7.2

Crystalline structure of AgBiSe₂ during the phase transition. The change of Ag–Bi–Se chain is indicated

Lots of theoretical works about the similar disordered materials, such as Ag–Sb-based and Tl-based I–V–VI₂ ternary chalcogenides, have been done by Khang Hoang et al. [9–11]. According to their single-crystal XRD results, the AF-I, AF-II, AF-IIb, and AF-III structures are been observed in the disorder phase (Fig. 7.3). The calculation results show that the near degeneracy of AF-II and AF-IIb mixed phases exist in the high-temperature disordered phase. We also compared these structures in high-temperature phase of AgBiSe₂, the results are given in Table 7.1.

Fig. 7.3

Possible ordered structures of AgBiSe₂: a AF-I (space group: Pm-3m, P4/mmm), b AF-II (R-3m), c AF-IIb (F-3dm), and d AF-III (I4₁/amd)

Table 7.1 Structural parameters information

The total energies for all the structures are AF-IIb, AF-II < AF-III < AF-I; AF-IIb and AF-II have almost the same total energy. From careful analysis of structure, AF-IIb is obtained by rotating the second and the fourth layers of AF-IIb by 90° around the z axis. AF-II and AF-IIb have alternate Ag–Se–Bi–Se–… chains in all periodic directions, but no Ag–Se–Bi–Se–… chains can be found in AF-I while it is only presented in the c direction in AF-III. The total energy is lower when more alternate Ag–Bi–Se chains existed. Furthermore, the AF-II structure has the consistent order of layer alternately stacking (Ag–Se–Bi–Se–…) with the intermediate-temperature phase of AgBiSe₂ in the direction (111) (Fig. 7.3b, c). Since the lattice difference between AF-II and rhombohedral is less than 2 % (Table 7.1), the differences of energy and electron structure between them are also small, ΔE ~ 7.4 meV/f.u. (f.u. = formula unit), where the electron structure is shown later. It is not possible to change the structure from rhombohedral to AF-IIb without reconstruction of the layers because of the completely different order in the direction (111) between them. Based on the above reasons, the AF-II and AF-IIb structures are treated as the intermediate-temperature and high-temperature phase in our next calculations, respectively, which is different from the work by Hoang et al. [9]. Since the disorder between Ag band Bi atoms exists in AgBiSe₂ when heating, the structure of AgBiSe₂ is possible to change from AF-II to AF-IIb through the diffusion of vacancies.

To study the effect of the Ag–Se–Bi–Se–… chains, the total DOS of different structures of AgBiSe₂ were carried out in Fig. 7.4, which shows that AgBiSe₂ is an indirect narrow band-gap semiconductor (E_g ~ 0.5 eV) in both AF-II and AF-IIb structure. However, no gap can be found in AF-I while a very small gap (~0.1 eV) in AF-III, which indicates that the sequence of Ag–Se–Bi–Se–… chains play an important role in AgBiSe₂. AF-II and AF-IIb AgBiSe₂ tend to identical both in total energy and electronic structure due to the same sequence of Ag–Se–Bi–Se–… chains in all directions, which also reveals that the influence of simple change in structure is quite subtle unless a rearrangement of the chains.

Fig. 7.4

Total DOS of AgBiSe₂ in different possible structure of AF-I, AF-II, AF-IIb, and AF-III. The Fermi levels (E _f , black dashed line) is set at 0 eV, f.u. = AgBiSe₂ (4 atoms). It is clearly shown that the structural model of AF-II and AF-IIb behave as semiconductor with narrow band-gap of 0.5 eV

Defects for p -type conductivity. Since the intermediate-temperature and high-temperature phase show p-type conduction, the different point and disorder defects in AgBiSe₂ are studied here. A finite-sized supercell model is used to calculate the formation energy. Although the defect formation energy of charged defects is dependent on the Fermi energy [12], here we just consider the neutral defects which are independent of Fermi level. A vacancy was created by removing one atom from the supercell. After relaxation, the formation energy ($E_{f}^{v}$) of a vacancy V _X at the X site is defined as

$$ E_{f}^{v} = E_{\text{tot}}^{v} - E_{\text{tot}} - \mu_{x} $$

(1)

where $E_{\text{tot}}^{v}$ and $E_{\text{tot}}$ are the total energy of the supercell with and without the vacancy V _x ; $\mu_{x}$ is the chemical potential of X, which was calculated as the energy per atom in each elementary state. $X_{Y}$ and (X,Y) denotes that the defect X atom site is replaced by extra Y atom and the one X atom change with Y atom, respectively.

The formation energy of an Ag vacancy is the lowest among all defects discussed here, which suggest that Ag vacancy is most likely the native defect in AgBiSe_2. The defect of disorder between Ag and Bi is also possible to occur when heated as the formation energy is also low.

To search for the effect of Ag vacancy, the band structure of AgBiSe₂ with an Ag vacancy in AF-II and AF-IIb structure are presented in Fig. 7.5. The Fermi level of these defective AgBiSe₂ is obviously seen to penetrate into the valance bands comparing to perfect AgBiSe₂. The band-decomposed charge density analysis (Fig. 7.5d, f) indicates that these half-filled bands originate predominantly from the d states of the six Ag atoms around vacancy. The Ag vacancy is actually acceptor with shallow acceptor levels with holes as charge carriers, which results in p-type conduction both in AF-II and AF-IIb.

Fig. 7.5

Crystals structure, band structure, and band-decomposed charge density plots for AgBiSe₂ with Ag vacancy in AF-II (a, d, g), intermediate (b, e, h) and AF-IIb (c, f, i) structure with 64 atoms, respectively. The Fermi level (E _f , red dashed line) is set at 0 eV. The empty defects states summed between 0 and +0.2 eV with Ag vacancies. The iso-surfaces for band-decomposed charge density plots correspond to a value of 0.007 e × Å⁻³

The order–disorder transition accompanied by a p – n – p switching. The phase transformation of the ternary compounds AgBiSe₂ has been reported by Manolikes et al. [13]. According to their experiments, this order–disorder transition proceeds through the formation of microdomains and their subsequent growth. The striations observed during the transition reveal that a large number of APBs parallel c-planes is formed, which cause the cations disordered. In our calculations, AgBiSe₂ of surface defects with APBs is constructed by changing the sequent of Ag and Bi layers along c-direction in the hexagonal cell. After full relax of ions, the structure corresponding to r-c phase in Fig. 7.5 is obtained, the PDOS and the band-decomposed charge density plots near Fermi level are given in Figs. 3.6 and  3.7 respectively. A metallic state is found in this structure.

Since the effect of a low-volume change during the transitions is not obvious to the electronic structure, several assumed structures of the same volume including Ag vacancy and Ag–Bi disorder of defects can be established to study the process of phase transition from AF-II to AF-IIb. Focusing on the middle structure Fig. 7.5b, the conduction and valence bands near the Fermi energy tend to overlap each other. From band structure and band-decomposed charge density analysis (Fig. 7.5e, h), the unoccupied states near Fermi level are predominantly distributed at the Ag atoms of Ag–Se–Ag–Se–… chains, and it will be extend when these chains spread over the entire crystal. The middle structure Fig. 7.5b can be treated as a possible intermediate n-type phase. We can understand that the formation of the Ag–Se–Ag–Se–… chains due to the exchange between the Ag and Bi atoms results in continuous electronic bands distributed in the chains to form an intermediate quasi-metallic state. The indistinguishability of cations sited in the Na positions make the Ag–Se–Bi–Se–… chains still uniform and semiconductive in the completely disordered case described by the AF-IIb structure. This temperature-dependent p–n–p switching is the result of disordering partially between the Ag and Bi atoms in case of Ag vacancy.

7.6.3 Calculation Details for Cu₂XSnS₄

All calculations were done by performing density functional theory as implemented in the Vienna ab initio Simulation Package (VASP) [14]. In our calculations, the hybrid functional Heyd–Scuseria–Ernzerhof (HSE06) [15] was employed, in which the mixing parameter of 0.25 was selected. The single-particle equations were solved using the projector-augmented wave (PAW) [16] method with a plane-wave cut-off of 600 eV. A k-points mesh of 1 × 1 × 2 was used to sample the Brillouin zone of the supercell. For the electronic self-consistency loop, a total energy convergence criterion of 1 × 10⁻⁴ eV was required. Lattice constants and internal coordinates were fully optimized until residual Hellmann–Feynman forces were smaller than 0.01 eV/Å.