Chemical transformation of Te into new ternary phase Pb_mCu_nTe_m+n nanorods and their surface atom diffusion and optical properties

Abstract

A new stable phase of ternary Pb_mCu_nTe_m+n with rough surface, including one-dimensional (1D) bamboo-like shaped and curved nanorods with short branches, was first synthesized using Te as a sacrificial template. The structure does not exist in the bulk Cu₂Te–PbTe phase diagram. It is revealed that the optimal Pb²⁺/Cu²⁺ chemical reactivity synergistic effect can preserve the initial shape of the Te nanorod parent template, which involves small volume changes and secondary nucleation phenomenon along the entire length of the nanorods. Furthermore, the diffusion of surface atoms and a surface pre-melting on the short branches of the nanorods were observed upon in situ electron-beam irradiation. The average Cu atom diffusion distance calculated (3 × 10⁻¹¹ m s⁻¹) is higher than the reported value (1.34 × 10⁻¹² m s⁻¹) in Cu₂O at 373 K, which is attributed to the local high temperature created by the incident electron irradiation and large surface to volume ratio of the nanomaterials. In addition, the Pb_mCu_nTe_m+n nanorods exhibit well-defined and size-dependent optical band gaps (E_g) in the near-IR region. We envision that the Te template strategy is general and robust and offers easy access to other new phase ternary PbTe-based nanomaterials via carefully balancing the chemical reactivity of the precursor.

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1. Introduction

Since 1928, bulk lead telluride (PbTe) with narrow band gaps (0.32 eV) and face-centered cubic structures have been studied as thermoelectric materials.¹ Recently, currently known alloying or dopant species such as MnTe, MgTe, CdTe, YbTe, Ag₂Te, PbSe and PbS in bulk PbTe have been intensely studied as state-of-art thermoelectric materials at moderate temperature ranges (500–700 K).^1,2 Different from the high temperature solid state reaction in vacuum, solution routes to semiconductor inorganic doping nanocrystals (NCs) have made dramatic advancements over the last two decades.^3,4 Effective doping incorporation means that the dopants are actually substituting the host atoms in the NC core rather than just being adsorbed on the nanocrystal surface. However, there have not been many successes due to the “self-purification” of impurities in the semiconductor nanocrystals. In the “self-purification” mechanism, the impurity formation energy in the nanocrystals is much higher than in the bulk materials. Furthermore, from the kinetics perspective, the distance that impurities need to travel to reach the surface of the nanocrystals is very short. Both these facts cause a decrease in the solubility of the dopant impurities in the nanocrystals.^5,6 However, kinetics rather than thermodynamics govern NC growth at the relatively low temperatures (<400 °C) at which the solution phase syntheses are typically conducted. This implies that kinetic factors will limit or control the dopant incorporation in the host NCs. Therefore, impurities will be incorporated in the NCs only if a careful balance is established between the host and dopant growth rates.

Recently, there are some literature reports published on PbTe-based alloy nanocrystals with different elements. Halogen element-doped PbTe nanocrystals have been reported. For instance, a simple and effective method to introduce Cl doping in PbTe_xSe_yS_1−x−y nanomaterials with high thermoelectric performance produced from the bottom-up assembly of colloidal nanoparticles (NPs) was described.⁷ Fang et al. demonstrated a successful synthesis of colloidal n-type lead telluride nanocrystals doped with iodine(I).⁸ The successful application of the same iodine dopants to nanocrystal systems greatly depends on the synthetic methods used and includes the dopant impurities in the precursor solutions used during the colloidal synthesis, which has been proven to be the most effective way. Moreover, doping transition metal ions into PbTe semiconductor (metal-doped PbTe) nanocrystals (NCs) by the intentional insertion of impurities, such as In, Au and Ag ions, has gathered enormous interests over the past two decades. For instance, Kade et al. synthesized PbTe with In doping and found that the In atoms were more likely to replace lead (Pb) rather than to take the interstitial sites.⁹ It is reported that the shape and thermoelectric properties of PbTe nanocrystals can be tuned by bismuth doping.¹⁰ Colloidal PbTe–Au nanocrystal heterostructures have been fabricated via the reaction of PbTe nanocrystals with a AuCl₃ solution.¹¹ Interestingly, it is found that in the nanostructures, the most stable energetic configurations might be very different from those observed in the bulk materials. The remaining amorphous regions (the “shell”), still under low dose, have roughly a Pb₃₅Te₅₇Au₈ stoichiometry. Such a metastable Au₃Te phase was never observed before in the bulk material. Unfortunately, with the exception of the PbTe-based alloy nanocrystal mentioned above, although several solution phase approaches have been attempted to prepare Cu doping metal telluride such as Cu-doped Bi₂Te₃ hexagonal nanoplates,¹² to date, reports on Cu doped PbTe nanomaterials are very rare.

On the other hand, Kanatzidis's group paid attention to the possibility of using PbMX (X = S, Te, M = Sb, Sn)-based ternary alloy nanomaterials as a tool to discover new phase materials. For example, they reported the synthesis of a series of narrowly disperse solid solutions of Pb_1−xSn_xTe nanocrystals with a cubic NaCl-type structure by employing a colloidal synthetic strategy. It is found that in the nanocrystalline state, the NaCl rock salt structure of Pb_2−xSn_xS₂ is stable in a particular composition range, which does not exist in the bulk form.¹³ Next, a series of Pb_mSb_2nTe_m+3n nanocrystals and Pb_mSb_2nSe_m+3n flower-like nanocrystal aggregates with cubic rock-salt type structures, which are new phases within the PbTe(Se)–Sb₂Te(Se)₃ system, were stabilized in the nanoscale regime.^14,15 New phases of homologous Pb_mBi_2nTe_3n+m nanosheets were fabricated by Arindom Chatterjee et al.¹⁶ Previous study by our group demonstrated the synthesis of a new stable phase of ternary Pb_mSb_2nTe_m+3n one-dimensional (1D) nanorods with a rough surface, using Te as a sacrificial template.¹⁷ As we all know, Cu atoms and ions have a lot of similarities with those of Au, including similar positive redox potentials.¹¹ However, according to the bulk Cu₂Te–PbTe phase diagram data, the solubility of Cu in PbTe is much lower and there is no Pb–Te–Cu ternary compound reported (Fig. S1, ESI†).¹⁸ To our surprise, as a matter of fact, based on X-ray analysis, Snyder et al. found that the crystal structure of Pb–Te–Cu is present as a NaCl prototype, indicating that it was a PbTe phase with Cu solubility at high temperature.¹⁹ Although there is some deviation error in the PbTe–Cu composition variation, the Cu solubility detected in the PbTe phase was still high (about 20–50 at%), which is larger than that of the phase diagram data.¹⁹ Therefore, according to the general formula related to the PbTe-based new phases with cubic rock-salt type structure, the solid solution phase with Pb_mCu_nTe_m+n stoichiometry may exist in the nanoscale. However, to the best of our knowledge, there is no report on the facile synthesis and systematical investigation of the new ternary solid solution phase Pb_mCu_nTe_m+n nanorods and their thermal and optical properties. We describe herein that the cubic structural form for the particular composition range reported for Pb_mCu_nTe_m+n does not exist in the bulk form. The diffusion of surface atoms and a surface pre-melting were observed upon in situ electron-beam irradiation. In addition, the size-dependent optical band gaps (E_g) of Pb_mCu_nTe_m+n were investigated.

2. Experimental section

2.1. Synthesis

In a typical preparation of Pb_mCu_nTe_m+n nanorods via a two-step solvothermal procedure, 0.320 g of sodium tellurite (Na₂TeO₃) and 0.250 g of ethylenediaminetetraacetic acid disodium salt (EDTA) were added into a beaker, injecting 10 mL ethylene glycol (EG) subsequently. After constantly stirring for 10 min with the injection of 6 mL of 80% hydrazine hydrate (N₂H₄·H₂O), the mixture was transferred into a 20 mL stainless teflon-lined autoclave, sealed and maintained in an oven at a planned temperature of 180 °C for 0.5 h. The autoclave was cooled down to room temperature naturally after the reaction and then 0.5 g of lead acetate (Pb(CH₃COO)₂·3H₂O), two dosages of copper dichloride (CuCl₂·2H₂O, samples with different amounts of Cu²⁺ were named, 0.3 g refers to sample 1; 0.5 g refers to sample 2) and 1.0 g of potassium hydroxide (KOH) were added into a dry beaker, into which the products obtained were transferred. After stirring for 20 min until all the chemicals were dispersed thoroughly, they were transferred into a 20 mL stainless teflon-lined autoclave, which was heated at 180 °C for 5.5 h and cooled to room temperature. Finally, the sample was washed three times with pure water and ethanol, dried in a vacuum oven at 80 °C for 4 h. The synthesis procedure and images of each stage are shown in Fig. 1.

Fig. 1 Schematic of the reaction process of Pb_mCu_nTe_m+n.

2.2. Characterization

The morphologies were characterized using a HITACHI SU 8000 field emission scanning electron microscope (FESEM) and energy-dispersive X-ray spectroscopy (EDX) implemented by FESEM was used to analyze the chemical composition of the prepared products. The X-ray diffraction (XRD) patterns of the products collected at room temperature were performed on a Rigaku D/max-2000 diffractometer equipped with Cu Kα radiation from 20° to 80° with steps of 0.02° at a scanning rate of 5° min⁻¹. High-resolution transmission electron microscopy (HRTEM, FEI, Tecnai G2 F30) was used to characterize the arrangement of atoms in the product. Inductively coupled plasma-atomic emission spectroscopy (ICP-AES) was used to determine the elemental composition of the prepared series of Pb_mSb_2nTe_m+3n nanocrystals. Only Pb²⁺ and Sb³⁺ were analyzed as Te is liberated as H₂Te gas during the dissolution process in aqua regia. The reported amounts of Te are only estimated, assuming charge-balanced compositions. The binding energy and surface oxidation of the prepared products were explored on an X-ray photoelectron spectrometer (XPS) (PHI 5700 ESCA40) using Al Kα radiation as the excitation source. In addition, infrared (IR) analysis of the products was performed using an FTIR spectrometer (Shi-madzu) in the range of 400–4000 cm⁻¹ in the form of KBr pellets. The optical properties of the products were measured based on the obtained data.

3. Results and discussion

3.1. Structure and morphology characterization

The morphology of sample 1 prepared via a two-step solvothermal method was characterized by FESEM. The as-synthesized Pb_mCu_nTe_m+n nanorods were in bamboo-like shapes with diameters of 40 to 60 nm and lengths of 800 to 1000 nm in the homogeneous dispersion with uniform size and high yield (Fig. 2a–b). The energy dispersive X-ray spectrometry (EDS) analysis shown in the inset of Fig. 2a shows that Cu, Pb, Te exist in all the samples. Fig. 2c–d reveal that sample 2 was composed of curved nanorods with one or two short branches and the average length and diameter becomes 500 nm and 50 nm, respectively. The large volume expansion from hexagonal Te to cubic Pb_mCu_nTe_m+n introduces significant mechanical stress during the transformation, which is released by the breaking and curving of the nanorods. Fig. 2d shows an HRTEM image at the edge of a curved nanorod, which clearly shows a lattice spacing of approximately 0.23 nm, corresponding to the (220) plane of PbTe. The lattice distortion structure marked by the arrow is more clearly observed, which was generated from either the substitution of Pb²⁺ by Cu²⁺ or the insertion of interstitial Cu²⁺ into the PbTe matrix, indicating the formation of the Pb_mCu_nTe_m+n solid solutions. The nanorod powders were measured by X-ray diffraction (XRD) to determine the composition phase and crystallinity (Fig. 2e). Illustrated in the XRD pattern of the as-prepared sample 1 and sample 2, all the diffraction peaks can be indexed exclusively as the face-centered-cubic (fcc) structures of PbTe with the space group Fm3̄m (225) (JCPDS# 38-1435). No characteristic peaks of Cu-related impurities are detected in the XRD patterns, indicating that the Cu ions are successfully doped into the cubic PbTe lattices. Moreover, the average elemental compositions of the prepared two samples were determined by energy dispersive spectroscopy and inductively coupled plasma-atomic emission spectroscopy. The results show the agreement of the values obtained from both analyses. When compared to the XRD pattern of pure PbTe, a slight shift towards higher angles occurs upon increasing the Cu concentration, indicating lattice shrinking due to the substitution of Pb (covalent radius ≈ 1.80 Å) ions by smaller Cu (covalent radius ≈1.35 Å). This is further proved by the decrease in the lattice constants, as shown in Fig. 2f, which verifies the effective solution of Cu atoms into the PbTe matrix. It should be noted that the lattice constants are calculated using the Bragg equation 2d sin θ = nλ, where the wavelength λ adopted (0.15406 nm). The accuracy of the resulting lattice constants may be affected by the chosen peaks whose 2θ are lower than 70°.

Fig. 2 (a and b) SEM images of sample 1 and the EDS spectrum of the sample inset in (a); (c) SEM images of sample 2. (d) TEM and HRTEM images of sample 2. (e) Comparative XRD patterns of Pb_mCu_nTe_m+n solid solution samples and a standard PbTe powder shown as vertical lines. (f) Plot showing the variation of the cell parameters with a nominal atomic composition of Pb_mCu_nTe_m+n nanocrystals following Vegard's law.

To further confirm that the prepared nanorods are solid solutions, elemental maps were measured. Fig. 3a shows a high angle annular dark-field (HAADF) micrograph of a selected dense and intact area of an individual bamboo-like nanorod, which is in agreement with the FESEM observations. From the associated elemental maps of Pb, Cu and Te shown in Fig. 3b–e, it is clearly seen that Cu is evenly distributed throughout the entire PbTe lattice within the nanorod, confirming the homogeneous solid solution phase behavior of the nanocrystals, which is in line with the experimental XRD observations in the current study. Similar results were obtained from the corresponding elemental maps recorded from a single curved nanorod with a small branch shown in Fig. 3f–j, which supports the view that nanorods prepared via this route are homogeneous solid solutions and not a phase-separated collection of PbTe and Cu_2−xTe nanocrystals.

Fig. 3 (a, b, f and g) HAADF STEM images and (c–e) and (h–j) the spatially resolved Cu, Pb and Te elemental maps of the bamboo-like and curved nanorods, respectively.

The doped Pb_mCu_nTe_m+n samples were further verified using X-ray photoelectron spectroscopy (XPS) analysis in order to understand the doping state of Cu and their bonding behavior. Fig. 4a shows the XPS survey spectra of the two samples with different amounts of Cu, from which the XPS signals of Cu can be observed unambiguously for both samples. The peaks for O and C should be attributed to air exposure of the sample and therefore, the absorption of gaseous molecules, e.g., H₂O, O₂ and CO₂. Fig. 4b–d exhibits the high-resolution spectra of Pb 4f, Te 3d and Cu 2p, respectively. The predominant measured binding energies for Te are 586.3 eV, 583.2 eV, 576.1 eV and 572.3 eV, in which 586.3 eV and 576.1 eV correspond to Te 3d_3/2 and Te 3d_5/2, respectively, as well as 583.2 eV and 572.3 eV for Te⁴⁺ indicating the existence of a surface oxide layer (Fig. 4b).¹⁷ Two sets of peaks at 143.1 eV and 138.4 eV were assigned to Pb 4f_5/2 and Pb 4f_7/2 without any shoulder peaks (Fig. 4c).²⁰ The binding energies of Cu 2p for the two samples were compared as shown in Fig. 4b, confirming the presence of the same chemical environment Cu²⁺ ions in the as-prepared samples and clearly demonstrating the successful incorporation of Cu species in the PbTe crystal structure. The binding energies of the Cu 2p_1/2 and Cu 2p_3/2 peaks at 932.8 eV and 952.9 eV with two obvious satellite peaks (Fig. 4d) can be indexed as the oxidation state of Cu²⁺, not Cu⁰.¹² Moreover, two shakeup and satellite peaks at 943.5 eV and 962.9 eV can be assigned to the paramagnetic state of Cu²⁺.²¹ Similarly, it is reported that Cu²⁺ chemical state doping could give rise to the formation of nanosized Cu_1−xZn_xS solid solutions.²² The composition determined by XPS is also in accordance with the Cu element mapping results, as shown in Fig. 3. Based on the detailed structural, chemical, and bonding characterization outlined above, we achieved Cu doped PbTe nanorods with Cu²⁺ replacing Pb²⁺.

Fig. 4 X-ray photoelectron spectroscopy (XPS) spectra for sample 1 and sample 2: (a) survey spectra of the two samples. The high-resolution XPS peaks for the (b) Te 3d, (c) Pb 4f and (d) Cu 2p regions.

3.2. Investigation of parameters influencing the formation of Pb_mCu_nTe_m+n nanorods

A two-step solvothermal method was used to synthesize the Pb_mCu_nTe_m+n nanorods via a Te template that was formed in the first step. Then, Pb²⁺/Cu²⁺ was injected into the solution to generate the target products. To elucidate the fact that the shape, size and structure of the final nanocrystals can be modified upon metal ion doping with a synergistic effect, a series of nanocrystals have been prepared under the same reaction conditions as shown in the typical synthesis process except for a variation in the concentration of the Pb/Cu precursors and a group of SEM images have been collected for the different shapes, as shown in Fig. 5. When excess Cu was present in the reaction mixture from 0.15 g to 1.5 g (0.9 mmol to 9.0 mmol) (Fig. 5a–d) with a fixed concentration of Pb²⁺ (1.3 mmol), the nanocrystal shape evolved from irregular nanocubes/nanocrystals (NC) (0.15 g, 0.9 mmol) to bamboo-like nanorods/nanorods (NR) (0.3 g, 1.8 mmol for sample 1), curved NR (0.5 g, 2.9 mmol for sample 2), NR with NC and finally, only NC can be collected as the dosage of Cu source increases to 1.5 g (9.0 mmol). Moreover, the variation of the amount of Pb with a fixed concentration of Cu²⁺ (1.8 mmol) was designed to further investigate the role of the metal precursors in forming the bamboo-like NR. The similar evolution of their shapes from NC to bamboo-like and final NC has been observed while varying the Pb source from 0 g to 1.5 g (0 mmol to 3.9 mmol) (Fig. 5e–h). The curves that reveal the tendency of certain morphologies by the amount of metal sources used are shown in Fig. 5i.

Fig. 5 SEM images of the as-prepared samples synthesized with different amounts of metal source: Cu source with (a–d) 0 g; 0.5 g; 1.0 g; 1.5 g; Pb source with (e–h) 0 g; 0.5 g; 1.0 g; 1.5 g. (i) The tendency of sample 1 with varying metal sources (nanocube (NC), nanorod (NR)). (j) Schematic of the proposed growth mechanisms of the Pb_mCu_nTe_m+n nanorods (NR).

To depict the phenomenon, we propose a kinetics-controlled competition process for the formation of bamboo-like shaped and curved Pb_mCu_nTe_m+n nanorods, as shown schematically in Fig. 5j. It is a simulative and ideal model to express the abovementioned conjecture, which can be regarded as following classical precipitation composed of three stages: nucleation, growth and coarsening process. In general, lattice distortion can be caused by ion doping.²³ Moreover, the limited availability of suitable and compatible precursors in the reaction medium for the formation of multinary PbTe-baded alloys still remains a great challenge. It is well known that the most common way to dope nanomaterials is to include impurities in the precursor solutions and requires a lot of fine-tuning of the reaction reactivity.^4,24 Unlike the situation of our Pb–Te–Cu alloy, Yu's research group reported a series of multimetal chalcogenide alloys and hybrid nanowires, among them, Cu/Pb metal chalcogenide hybrid nanowires were obtained when the Cu and Pb precursors were added into the Te_xSe_y@Se nanowire solution batch.²⁵ In a single nanowire, Se and Te atoms are uniformly distributed, whereas the Cu and Pb atoms randomly distribute on the nanowires. This is may be attributed to the short diffusion pathway due to their ultrathin Te_xSe_y nanowires and the easier released strain. Another possible reason is that a suitable Pb/Cu precursor reactivity is not well balanced without using selection ligands. Recently, it is reported that the Pb/anion ratio is size- and composition-dependent in all the alloys, which allow for the homogeneous incorporation of anions of the samples (high Te content or Pb-rich zone). A more reactive anion precursor results in a lower Pb/anion ratio.²⁶ A detailed understanding of the alloying mechanism is essential for developing better synthetic strategies for producing these alloyed nanomaterials. However, reports on these nanoalloys rarely include analysis of the alloying process. Herein, three key aspects, including the reactions, formation constants and solubility, contributed to the success of new phase Pb_mCu_nTe_m+n solid solution nanorods. First, Pb and Cu ions, while still being well dispersed in a solution, are readily available for the reaction, which should make the overall reaction thermodynamically favored. In our present study, to maintain the chemical state of two free metal ions to obtain a solid solution, EDTA was selected to complex all metal ions in the solution. It is well known that the EDTA ion has a strong chelating ability with metal ions in solutions. The EDTA ligand reacts with metal ions to form a stable complex, which is sexadentate binding through four oxygens and two nitrogens. Second, the formation constant K (stability constant) is a measure of the strength of the interaction between the reagents that come together to form the complex. The values of log K for the Pb–EDTA and Cu–EDTA complex are 18.0 and 18.8, respectively.²⁷ According to the standard reduction potential, N₂H₄/N₂ in an alkaline solution is 1.16 V, Te/Te²⁻ is −1.143 V and TeO₃²⁻/Te²⁻ is −0.57 V, respectively. These are standard state values taken from the CRC Handbook of Chemistry and Physics, 90th edition (CRC Press, 2010).²⁵ It is to be noted that ligands and surrounding solvent interactions can greatly shift the redox potentials. Therefore, the chemical environment is mainly responsible for adjusting the reduction potential to an appropriate value.²⁸ Thus, the overall chemical reaction involved in the hydrothermal synthesis can be described by the following eqn (1)–(4):

3TeO₃²⁻ + 3N₂H₄ → 3Te + 3N₂ + 3H₂O + 6OH⁻ (1)

[Pb(EDTA)]²⁻ → Pb²⁺ + (EDTA)⁴⁻ log K = 18.0 (2)

[Cu(EDTA)]²⁻ → Cu²⁺ + (EDTA)⁴⁻ log K = 18.8 (3)

2Pb²⁺(Cu²⁺) + 2Te + N₂H₄ + 4OH⁻ → 2PbTe(Cu) + N₂ + 4H₂O (4)

Third, it is known that a less soluble final compound is easy to precipitate. Unfortunately, the solubility data of metal tellurides in solution are not available. In general, it is well accepted that the solubility products of metal chalcogenides have a lower value as the ionic radius of the chalcogen increases: K_sp(M_xS_y) > K_sp(M_xSe_y) > K_sp(M_xTe_y). As the solubility product of CuS, CuSe, PbS and PbSe is in the order: K_sp(CuS) = 5 × 10⁻³⁶, K_sp(PbS) = 1 × 10⁻²⁸, K_sp(CuSe) = 2 × 10⁻⁴⁰ and K_sp(PbSe) = 1 × 10⁻³⁷, we can conclude that the solubility products of the metal tellurides have a lower and closer value, and the order of magnitude K_sp(CuTe) = K_sp(PbTe) causes the Pb ions and Cu ions to distribute well in the PbTe lattice.²⁹ Upon increasing the reaction temperature, the Pb/Cu ions released by the decomposition of the complex are diffused into the Te template matrix through topotactic transformation along with competitive formation rate of CuTe and PbTe. By referring to the PbTe crystal lattice, the (111) planes consist of monoatomic planes and the Te and Pb atomic planes are consecutively stacked along the [111] direction. Furthermore, the interdistance between the basal (222) planes is 1.865 Å for PbTe and the (003) planes is 1.975 Å for Te, i.e. a difference of about 6%. This is supported by both the epitaxial relationship between the (001) planes of Te and the (111) planes of fcc-PbTe and the observed preferential growth of PbTe along the (111) direction. Therefore, at a low Cu content, bamboo-like NRs were obtained because of the formation of a cubic PbTe phase that performs [111]-directed growth, which is different from the [001]-direct growth of Te. On the other hand, at a high Cu content, the fast diffusion of Cu²⁺ becomes dominant and lattice strain started to accumulate through an ion-exchange process. The continued accumulated stress should be released by cracking the surface and even secondary nucleation to form short nanorods through absorbing the nutrition on the newly exposed active site, which caused the formation of curved NRs with short branches. Sounart et al. systematically studied the secondary nucleation phenomenon of hexagonal ZnO crystals in a solution.³⁰ Overall, Pb²⁺/Cu²⁺ has been illustrated to have a cooperative effect and the amount of Pb/Cu precursor kept in a reasonable range is essential to control ion diffusion and reaction activity towards Te, thereby leading to the retention of the shape of the parent nanorod template and heterogeneous nucleation.

4. Surface atom diffusion upon in situ electron beam irradiation

For sample 2 with a high Cu concentration, in situ electron-beam irradiation on the short branch of a nanorod was performed using a transmission electron microscope operating at 300 keV. Under a few minutes of exposure to the electron beam during TEM, the incident electron irradiation can create a significant local high temperature increase in the material due to electron thermal spikes and poor thermal conduction away from the particles.³¹ It is well known that the melting point of the nanomaterials decreases with a reduction in size when compared to the bulk counterparts. In general, the melting of the nanoparticles starts at their surfaces at reduced temperatures.³² The surface melting of gold nanorods with large surface to volume ratio can be directly studied by in situ transmission electron microscopy (TEM).³³ Therefore, it is reasonable to assume that the 300 keV electron beam can result in the diffusion of the surface atoms and a surface pre-melting of the short branches, indicating that the atoms in the monoatomic layer interact with the adjacent atoms to form bigger clusters. Recently, Xu and co-workers observed that local melting in a single-crystalline Ag nanowire under the irradiation of a high-intensity electron beam (HIEB) enhances the diffusion of atoms along the surface of the Ag nanowire.³⁴ Furthermore, it was revealed by our group that Zn single crystalline nanowires to polycrystalline nanowires consisted of about 5 nm nanoparticles structure transition, which can also be directly observed after exposure to an electron beam.³⁵ In our present study, Fig. 6 shows the changes in the two tips region during the process. The original clear round and smooth tip became sharp after 6 min, whereas the spacing between the tips, marked by arrows, is shortened from 28 nm (Fig. 6a) to 20 nm (Fig. 6d), showing the atom movement rate is 0.03 nm s⁻¹ (3 × 10⁻¹¹ m s⁻¹). Similar behavior is not observed in sample 1 with a low content of Cu, so it can be concluded that the doping amount of Cu appears to enhance the diffusion of atoms along the surface. Anderson et al. found that although Pb is immiscible in bulk Cu, at a low coverage, it is energetically favorable for a Pb to replace a Cu atom in the outermost layer of the crystal, forming a surface alloy.³⁶ Vacancy-mediated diffusion and atom exchange are responsible for the mass transport on different length scales. In addition, it is well known that Cu diffuses much faster than Pb, and the self-diffusion coefficients of Cu ions, D_Cu, in Cu₂O at 373 K are calculated to be 1.8 × 10⁻²⁴ m² s⁻¹.³⁷ The average diffusion distance, (D_Cut)^1/2, at 373 K is estimated to be 1.34 × 10⁻¹² m s⁻¹, which are one order of magnitude smaller than the value (3 × 10⁻¹¹ m s⁻¹) obtained in our case. It seems likely that the local high temperature created by the incident electron irradiation is higher than 373 K, which may lead to Cu migration much faster than that in Cu₂O at 373 K. Of course, the nanomaterials with large surface to volume ratio on the promotion of Cu migration cannot be neglected when compared to Cu₂O. Some defects could exist on the surface of the nanorod, leading to the chemical bonds of surface Pb, Cu and Te atoms dangling outside the solid. These unsaturated “dangling” bonds are of high reactivity and extremely sensitive to temperature to reduce the surface energy.

Fig. 6 Sequential snapshots from in situ HRTEM showing the different stages of the atom movement process, as marked by the arrows.

5. Optical properties

The optical properties of the nanocrystals of sample 1 and sample 2 prepared with different amounts of Cu were measured using FTIR spectroscopy before showing the plot of (αhν)² vs. photon energy (hν) for the bamboo-like nanorods (sample 1) and curved nanorods (sample 2) in Fig. 7. According to the data for the absorption spectra, the optical band gaps (E_g) of sample 1 and sample 2 can be calculated using the equation:

(αhν)² ∼ (hν − E_g)

Fig. 7 Plot of (αhν)² versus hν used for the determination of the band gap of sample 1 and sample 2. The insets are the corresponding SEM images and average length of the two samples.

Then, E_g can be estimated by extending the linear part of the curve to zero absorption, which showed that E_g of sample 1 and sample 2 was 0.298 eV and 0.305 eV, respectively. The band energies of Pb_mCu_nTe_m+n nanorods are significantly smaller than the ternary new phase Pb_mSb_2nTe_m+3n nanocrystals with sizes of 10–12 nm and nanorods reported in the literature with values in the range of 0.41–0.45 eV and 0.316–0.375 eV, respectively.^14,17 Moreover, it is clearly seen that sample 2 showed a higher band gap value than sample 1. It is well known that band gap engineering, as a powerful technique in the development of new semiconductor materials, particularly at the nanoscale, has aroused a great deal of interest. It has been widely accepted that altering three factors, including the nanocrystal morphology, composition and size, is accompanied by changes in the optical properties. First, since the surface microstructure of our nanorod sample does not have a big difference, they are expected to exhibit weak effects on the morphology-dependent optical properties and the influence of the morphology on the band gaps of the ternary alloys can be neglected. Second, another means of tailoring the semiconductor band gap is by changing the particle composition via control of the constituent stoichiometries.^13,38 A non-linear relationship between the band gap energy and the composition, known as “optical bowing”, was also observed for the homogeneous alloys nanocrystals and its origin is usually attributed to the structural relaxation effect arising from the difference in the lattice constants and bond lengths.³⁸ For instance, ZnSe_xTe_1−x nanowires exhibit strong band bowing with the band gap minimum occurring at x = 0.30.³⁸ In addition, it is reported that Pb_1−xSn_xTe nanocrystals obey the band inversion model, but at the crossover point of x = 0.67, there is a huge “avoided crossing” as a result of the quantum confinement effect.¹³ It is likely that the Pb_mCu_nTe_m+n nanorods follow a similar trend. Usually, sample 2 should show a lower band gap value than sample 1 with an increase in the mole fraction of Cu before the band gap minimum. However, it is not the case in the present study. Therefore, the factor can be ruled out. Of course, further experimental and theoretical studies, which are beyond the scope of current work, are needed to conclusively confirm this transition. Specific studies used to probe the evolution of the band structure as a function of Cu composition are currently underway. Last but not the least, reducing the dimensions of a semiconductor to a size comparable to or smaller than its exciton Bohr radius effectively widens its energy gap. The most possible reason is that the sizes of sample 2 are smaller than those of sample 1 based on the quantum confinement effect, as shown in the inset of Fig. 7. The exciton Bohr radius plays an important role in the quantum confinement effect. Murphy et al. reported on the high anisotropy of the electronic band of PbTe and reported exciton Bohr radii of 12.9 nm and 152 nm in the longitudinal (111) and transverse directions, respectively.³⁹ By comparison, these values are significantly different from the band gaps of the individual binary end members. These band gap values were all bigger than the previously reported values for binary PbTe dendritic structures (0.272 eV), hopper crystals (0.268 eV) and were similar to those of nanowires (0.308 eV) and nanoparticles (0.31 eV).^40–42 On the other hand, these band gap values were obviously different from a direct band gap between 1.1 eV and 1.5e V for copper telluride.⁴³ Copper telluride (Cu_xTe, 1 < x < 2) is known to exist in a wide range of compositions and phases whose properties are controlled by the Cu : Te ratio. There are different crystal structures depending on the relative stoichiometry (e.g., CuTe, Cu₃Te₂, Cu₃Te₄, Cu₇Te₄, Cu₇Te₅ and Cu₂Te) and in the non-stoichiometric Cu_2−xTe cases. It should be noted that because Pb_mCu_nTe_m+n nanorods are new compounds, there is no corresponding bulk Pb_mCu_nTe_m+n counterparts to compare them with. Table 1 shows a comparison of the ternary PbTe-based composite with various reported band gap values. In a word, the stabilization of a new crystal form on the nanoscale is of fundamental interest in understanding the limits of phase stability as a function of size. The advantages of these alloyed nanomaterials may show interesting properties that are not observed in the simpler binary systems and give rise to a multitude of potential applications, including optoelectronics, catalysis, photovoltaics and biological imaging. In contrast, the disadvantage may be the thermal stability of the new phase, which should be further studied in the future.^14,15

Table 1 A comparison of the ternary PbTe-based composite and various reported band gap values

Material	Band gap	Reference
PbmCunTem+n nanorods	0.298 and 0.305 eV	Present work
PbmSb2nTem+3n nanocrystals	0.41–0.45 eV	14
PbmSb2nTem+3n nanorods	0.316, 0.341 and 0.375 eV	17
PbBi2Te4 and PbBi6Te10	0.7 and 0.25 eV	16
PbTe dendritic structures	0.272 eV	40
PbTe hopper crystals and nanowires	0.268 eV, 0.308 eV	41
PbTe nanoparticles	0.31 eV	42

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6. Conclusions

In conclusion, we first achieved the selective synthesis of new phase Pb_mCu_2nTe_m+3n nanorods with a rough surface via a Pb²⁺/Cu²⁺ chemical reactivity synergistic effect, which can preserve the initial morphology of the Te nanorod template. The transformation involving small volume changes is considered to be homogeneous along the entire length of the nanorods, leading to single crystallinity nanorods with curved surface. The diffusion of surface atoms and a surface pre-melting on the short branch of a nanorod was observed upon in situ electron-beam irradiation. In addition, the optical band gaps (E_g) of Pb_11.4CuTe_12.4 and Pb_6.29CuTe_7.29 were 0.298 eV and 0.305 eV, respectively. We envision that the Te template strategy is general and robust and offers easy access to other ternary PbMX (M = Bi, La, Sn, Ag; X = S, Se, Te) new phase nanomaterials with well-defined structure and unique properties by carefully balancing the Pb²⁺/Cu²⁺ reaction reactivity.

Acknowledgements

This study was supported by the National Natural Science Foundation of China (Project No. 21101044), the Independent Subject of State Key Laboratory of Advanced Welding and Joining, the Fundamental Research Funds for the Central Universities (Grant No. AUGA5710013115 and IBRSEM. 201330) and the Program for Innovation Research of Science in Harbin institute of Technology (PIRS of HIT No B201507).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra07779j

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