Structural Disorder of CuO, ZnO, and CuO/ZnO Nanowires and Their Effect on Thermal Conductivity

Abstract

In this work, the structural defects and the thermal conductivity of CuO, ZnO, and CuO/ZnO nanowires have been studied, using molecular dynamics simulation with COMB3 potential. The initial parameters and atoms positions were taken from reports of bulk materials with tenorite and wurtzite structures, respectively. Nanowires were grown along the c-axis, as observed experimentally. The results confirm the defects apparition in the systems after simulation with a formation of grains to reduce the energy of the nanowires. In the CuO nanowires case, the lack of periodicity in the basal plane causes a contraction effect over the network parameter b of the monoclinic structure with a Cu-O distance reduction. [A constriction effect on inclined planes, as a product of surface charges, deforms the nanowire, generating undulations. In ZnO nanowires, a decrease in the Zn-Zn distance produced a contraction in the nanowire length. A constriction effect was evident on the surface charges. It presented a bond reduction effect, which was larger at the ends of the nanowire. In CuO/ZnO nanowires, the structural defects come from the distortions of the crystalline lattice of the ZnO rather than CuO. The thermal conductivity of the nanowires was calculated at temperatures between 200 K and 600 K using the Green–Kubo equation. Results showed similar values to those reported experimentally, and the characteristic maximum with similar trends to those observed in semiconductors. Our results suggest that structural defects appear in nanowires grown on the free substrate, and are not related to the lattice mismatch.

1. Introduction

In recent years, much research has focused on understanding the physicochemical properties of one-dimensional (1D) nanostructures [1]. One-dimensional nanostructures are defined as linear structures with a diameter of less than 100 nm (nanowires, nanotubes, and nanorods). At these dimensions, a structural disorder appears near and at the surface. This structural disorder results from lattice symmetry breaking or surface dangling bond formation. It gives rise to site-specific surface anisotropy, weakened exchange coupling, and surface spin disorder [2]. In nanostructures, the effects of structural deviations on physicochemical properties remain a discrepancy due to experimental difficulties [2]. For example, structural defects, such as atomic vacancies, are related to the synthesis technique conditions for nanostructure production.

Among all one-dimensional nanostructures, cupric oxide (CuO) and zinc oxide (ZnO) are interesting due to their semiconductor properties (type p and n, respectively) and high demand for thermoelectric applications [3]. CuO is a semiconductor with a narrow indirect bandgap (1.2 eV in bulk), monoclinic structure (C2/c symmetry), and four formulas per unit cell [4]. In contrast, ZnO is a semiconductor with a wide direct bandgap (3.37 eV in bulk), hexagonal structure (P63mc symmetry), and two formulas per unit cell [5]. Cupric oxide and zinc oxide conductivities are associated with native defects [4,6]. The usual structural defects observed in cupric oxide and zinc oxide nanowires are twin planes, stacking faults, and inversion domain walls [7,8]. In general, twin planes result from crystals joining that grew on adjacent facets of performed grains [9]. Stacking faults appear by the changes in the stacking sequence of close-packed planes [8]. The other structural defects become increasingly important as the surface contribution to the total energy increases due to the size decreasing [8].

Experimentally, nanowires growing is associated with the differences in surface chemistry between two types of faces: polar faces and non-polar faces. In the former, the surface dipoles are thermodynamically less stable than in the latter [10]. In the simulation case, the atoms usually suffer from rearrangement to minimize their surface energy, and tend to grow stably. Structural defects show markable importance, for example:

• Cupric oxide nanowires growing by thermal oxidation exhibit compressive stress. It is the driving force in the growth mechanism [9];
• Structural defects play a fundamental role in improving the CO₂ electroreduction to ethylene [11].

Thermal conductivity has been widely investigated for zinc oxide nanowires, in theoretical studies [3], in simulations [12], and experimentally [13]. The focus in this case was:

• Determining the effect of confinement in the radial direction on thermal conductivity [3];
• Determining the surface effects on the thermal conductivity [14];
• Comparing the thermal conductivity among different nanostructures, such as gallium nitride [12];
• Determining the size dependence of the nanowires with thermal conductivity [15];
• Determining the effects of doping the nanowires and their relationship with thermal conductivity;
• Determining the thermal conductivity of zinc oxide nanowires embedded on polymeric matrices [13,16].

Most of the papers reporting on cupric oxide nanowires focus on enhanced thermal conductivity in nanofluids [4]. This property has been taken advantage of for applications in wastewater treatments [17]. Previous works have demonstrated that thermal conductivity depends on impurities, surface reconstruction, and structural disorder [18,19]. Modeling and simulating these nanostructured kinds is a low-cost method to study, understand, and predict their behavior. In the CuO nanowires case, some examples included the simulation of the mechanical [20] and optical [21] properties, and thermal growth [22]. In the ZnO nanowires case, the simulations included the bending and alignment of these nanostructures [23], mechanical properties [24], and electromechanical conversion [25]. Regarding structural properties, for nanostructured CuO, the unit-cell volume increases with a decrease in particle size, and the lattice becomes distorted as the crystal symmetry tends to increase [4]. Previous reports suggest that an amorphous layer covers the cylindrical body of the CuO [20] and ZnO [26] nanowires. ZnO/CuO core–shell nanowire heterojunctions have been grown and vertically aligned with a good p–n junction with promising performance as photodetectors [27]. Thus, to the best of our knowledge, a simulation using the molecular dynamics technique to focus mainly on the structural disorder of CuO, ZnO, and CuO/ZnO nanowires and their effect on the thermal conductivity has never been reported hitherto, and it is the aim of this work.

2. Methods

The simulations used the files of the potential COMB3 (charge-optimized many-body third generation) in LAMMPS [28,29]. The parameterization employed metallic units. In general terms, the total energy of the potential is described by

$$E_T={\sum }_i\left\{E_i^{Self}\left(q_i\right)+{\sum }_{j>i}\left[E_{ij}^{Short}\left(r_{ij},q_i,q_j\right)+E_{ij}^{Coul}\left(r_{ij},q_i,q_j\right)\right]+E^{polar}\left(r_{ij},q_i\right)+E_{ij}^{VDW}\left(r_{ij}\right)+E_i^{barr}\left(q_i\right)+E_i^{corr}\left(r_{ij},{\theta }_{ijk}\right)\right\}$$

(1)

where

• $E_i^{Self}\left(q_i\right)$ is the self-energy of atom i (including atomic ionization energies and electronic affinities);
• $E_{ij}^{Short}\left(r_{ij},q_i,q_j\right)$ is the bond order potential between the atoms i and j;
• $E_{ij}^{Coul}\left(r_{ij},q_i,q_j\right)$ is the Coulomb interactions;
• $E^{polar}\left(r_{ij},q_i\right)$ is the polarization term for organic systems;
• $E_{ij}^{VDW}\left(r_{ij}\right)$ is the Van der Waals energy;
• $E_i^{barr}\left(q_i\right)$ is a charge barrier function;
• $E_i^{corr}\left(r_{ij},{\theta }_{ijk}\right)$ is the angular correction term.

The COMB potentials are variable charge potentials. Therefore, the electronegativity equalization method (QEq) allowed for finding the equilibrium charge on each atom [30].

The initial sample consists of 400 nm long cylinders located in the z-direction, with diameters around 25 nm. Figure 1 shows initial crystalline structure examples for CuO (tenorite-type structure) and ZnO (Wurtzite-type structure).

Table 1. CuO and ZnO lattice parameters utilized for nanowire sample building [12,35] in Figure 1.

CuO		ZnO
Structure	Tenorite	Structure	Wurtzite
System	Monoclinic	System	Hexagonal
a	4.6837 Å	a	3.250 Å
b	3.4226 Å	c	5.207 Å
c	5.1288 Å
β	99.54°

shows the network parameters for both structures. Here, the lattice parameter c was in the z-direction. In tenorite, a parameter is in the x-axis and b parameter in the y-axis. Under a thermodynamic assembly type NVT, the instantaneous energy and temperature data were collected as time functions to verify the system’s stability. A time step of 5 fs was selected for a period of 100 ns. Different temperatures were used without using periodic conditions. Subsequently, under a thermodynamic assembly type NVE, by 100 ns at a time step of 0.2 fs, the thermal conductivity (κ) was calculated. The tensor κ is a measure of the propensity of a material to transmit thermal energy diffusively, according to Fourier’s law

$$\overrightarrow{\mathit{J}}=-\mathit{\kappa }\overrightarrow{\nabla }\mathit{T}$$

(2)

where J is the heat flux in units of energy per area per time, and $\overrightarrow{\nabla }\mathit{T}$ is the spatial temperature gradient. It is a quantity approximately isotropic; that is, as a scalar. Conductivity has an electronic and an acoustic component. Here, the last one was presented only along the nanowire. The electronic contribution to the thermal conductivity could be negligible because the carrier concentration for CuO [4] and ZnO [31] nanowires are lesser than 10¹⁹ cm⁻³ [32]. Despite the temperature dependence, Fourier’s law does not seem to agree with the nanoscale experimental results in semiconductor materials [33,34]. The method implemented to find κ used on stabilization under thermodynamic equilibrium conditions of the Green–Kubo equation is as follows:

$$\mathit{\kappa }=\frac{1}{{\mathit{K}}_{\mathit{B}}{\mathit{T}}^2\mathit{V}}{\int }_0^{\mathit{\infty }}〈{\mathit{J}}_{\mathit{z}}\left(0\right){\mathit{J}}_{\mathit{z}}\left(\mathit{t}\right)〉\mathit{d}\mathit{t}$$

(3)

where T is temperature, K_B is the Boltzmann constant, and V is the volume. This equation relates the average autocorrelation of the heat flux over time. The fluctuations of the kinetic and potential energies per atom allowed the heat flux determination (e_i) and the stress tensor per atom, according to the expression:

$$\overrightarrow{\mathit{J}}=\frac{1}{\mathit{V}}\left[{\sum }_{\mathit{i}}{\mathit{e}}_{\mathit{i}}{\overrightarrow{\mathit{v}}}_{\mathit{i}}-{\sum }_{\mathit{i}}{\overrightarrow{\mathit{S}}}_{\mathit{i}}{\overrightarrow{\mathit{v}}}_{\mathit{i}}\right]$$

(4)

3. Results

Figure 2 presents the final state of a CuO nanowire at 200 K. The comparison between the initial (Figure 1a) and final states evidences the deformation’s apparition. The radius of the nanowire contracts in the “y” direction, decreasing 16% after stabilization. Figure 3a compares the nanowire’s radial distribution function (RDF) among the initial and final states. The peak observed at the initial state at a distance equal to b = 3.4226 Å is finally reduced by approximately 6.2%. The shortest Cu-O distance showed a reduction of 17% compared with the bulk material [35]. These effects were observed independent of the temperature (not shown here). This situation arises from the loss of periodicity in the basal plane, which allows stronger Coulomb interactions (contraction in ionic bonds). A constriction effect occurs because of surface charges. Previous studies reported this effect in the simulations of materials with ionic bonds [14]. This stress produces a shear in the nanowire structure, given the monoclinic character of the crystalline lattice. Structural defects present in cupric oxide are associated with the formation of the grains in the nanowire, suggest a polycrystalline structure, and agree with experimental reports [36].

Figure 1 and Figure 2 show the inclined plane involved. Specifically, Figure 2 shows a diagonal plane crossing the wire width and defining the contour zones of the undulation. Moreover, these shear stresses cause pointed ends in the nanowire. The radial distribution also shows how crystallinity peaks decreased. Other peaks widening with low altitudes appear after stabilization. Such a situation is the reflection of a structural disorder that depends on the nanowire position:

• At the nanowire ending, there is a localized compression effect where some prominences appear at the edges;
• In the regions of maximum undulation, there are stress effects due to the increase and decrease in interatomic distances and tensile and compress stresses;
• In intermediate zones, there are stable crystalline structures;
• Due to the loss of coordination number, the surface atoms show deformations of the crystalline structure.

Figure 4 shows the final state of a ZnO nanowire at 200 K. Like CuO, the ZnO structure shows deformations concerning the initially raised cylinder. Here, the nanowire decreases its length by around 17.5%. The details of this observation are evident in the radial distribution function shown in Figure 3b. The distance between Zn-Zn ions, represented by the second peak, decreases by approximately 7.2%. Although the nanowire has high symmetry in the basal plane, the thickness in the “x” direction is lesser than that presented in “y”. The radius decreases by approximately 12% in the “x” direction and increases by 11% in the “y” direction. The constriction effect occurs by the attraction between surface charges. This constriction was reported in simulations of ZnO nanowires under the Buckingham potential [14]. This effect probably arises from the idealization of the sample in its initial state and the charge excess to side with the “x” direction. A movement generated after simulation on the surface atoms was observed, which favored an additional charge displacement. The first peak observed in the initial state corresponds to the Zn-O distance and increases by 6.6% after simulation. This is an unusual behavior because the interaction between charges should favor the decrease in distance. Such elongation preferably occurs in the “y” direction, where the thickness in that direction increases.

Experimentally wurtzite nanostructures have demonstrated a favorable growth direction along the c-axis [37]. Calculations of surface energies based on bond density reveal that the $\left\{01\stackrel{-}{1}0\right\}$ planes in the wurtzite structure are the energetically favorable surface in the 1D nanostructure system [38]. The wurtzite space group is described as several alternating planes composed of tetrahedrally coordinated cations and anions, stacking alternatively along the c-axis [39]. The oppositely charged ions produce positively charged $\left(001\right)$ and negatively charged $\left(00\stackrel{-}{1}\right)$ polar surfaces, resulting in a dipole moment and sometimes in spontaneous polarization along the c-axis, as well as a divergence in surface energy. Stacking faults can be easily formed in the I1 type of basal plane $\left[0001\right]$ [8], as in this case.

Additionally, the zooms sections of the nanowire presented in Figure 4 show that the planes between Zn and O ions tend to be closer. These structural transformations correspond to internal compression stress. The stress simulation predicts the Wurtzite-like structure instability at the nanoscale [40]. The radial distribution also shows how crystallinity peaks present a considerable width at middle heights. As can be seen in Figure 4, in a similar way to CuO nanowires, the structural disorder depends on the position of the wire, as follows:

(1)

At the ends of the nanowire, there is a localized compression effect with a considerable decrease in interatomic distances due to electrostatic attraction;

(2)

In the intermediate zones, there is a stable crystalline structure;

(3)

The surface atoms show a loss of crystallinity due to the low coordination number.

In some cases, this loss of coordination favored the appearance of superficial planes. This type of plane is observed in nanoparticles and originated by minimizing energy [41].

According to kinetic theory, the thermal conductivity associated with the lattice contribution by phonon scattering is proportional to the velocity sound, lattice-specific heat, and the phonon mean-free path. As the temperature increases, the lattice-specific heat increases until saturation. Moreover, the intrinsic temperature-dependent Umklapp processes becomes dominant. Additionally, in nanowires, the dispersion consists of two different mode types:

(1)

Cutting: corresponds to the transverse acoustic branch;

(2)

Expansion: corresponds to longitudinal acoustics and bending modes.

For a transverse mode in “x” and “y” directions, in the case of CuO and ZnO, the simulations showed that the thermal conductivity does not present any trend type with temperature (with values oscillating between 0.1 and 0.6 W/m·K). Then, phonon-boundary scattering limited the phonon conduction. In contrast, in the longitudinal direction, the thermal conductivity shows a clear trend with the temperature (Figure 5a,b) for CuO and ZnO. With this prevalence of longitudinal modes, where the values are higher than the cross-sections, it is possible to consider nanowires as thermally one-dimensional elements.

The bulk thermal conductivity at room temperature for cupric oxide and zinc oxide reported in the literature are 76.5 W/m·K [4] and 46 W/m·K [42], respectively. Size reduction in CuO and ZnO at the nanometric scale produces different changes in thermal conductivity. In the first case, a particle size reduction increases the thermal conductivity, compared with the bulk state, because of the long mean-free path of phonon vibration [43]. This observation agrees with the results obtained by our simulations for CuO nanowires at room temperature (135 W/m·K). In contrast, in the second one, a particle size reduction decreases the thermal conductivity, compared with the bulk state [12]. The ZnO nanowire’s thermal conductivity decreases with the diameter of the nanowires [15]. This observation agrees with the results obtained by our simulations for ZnO nanowires at room temperature and those reported in the literature for zinc oxide (

Table 2. Summary of the thermal conductivity of ZnO nanowires reported in the literature at room temperature with their diameter (d), length (L), and temperature maximum (T_max).

d (nm)	L (µm)	Thermal Conductivity (W/m·K)	Tmax	Reference
25	0.4	6	250	This work
0.1	0.0009	10	-	[46]
0.9	-	3	350	[45]
40	35	12	-	[13]
150	-	12	180	[47]
160	5	12	125	[3]
215	69	17	-	[13]
250	69	15	100	[16]
250	69	22	-	[13]
480	40	32	-	[13]

). The thermal conductivity of metal oxide particles decreases as the temperature increases because of the phonon–phonon scattering [44]. However, the grain boundaries will scatter phonons, and thus, the size of the crystalline domain acts as a limiting length for phonons [12]. The defects scattering and the phonon–phonon scattering affects the thermal conductivity; first in increases to a maximum and then decreases (Figure 5) [45]. The temperature of maximum thermal conductivity is sensitive to the nanowire diameter (Table 2).

Figure 6 presents the initial and final simulation states of ZnO/CuO nanowires at 200 K. In these, deformations were observed in the “xz” and “yz” planes when compared with the original structure. In the upper and lower parts of the nanowire, the atoms were located similarly to those previously presented for ZnO and CuO. Moreover, the analysis focuses on the deformations around the junction. The segment labeled A and B in Figure 6 show a higher level of deformation of the ZnO regions compared with CuO, where even the cylindrical deformation at the end of CuO, due to the constriction effect on the slip planes, is also observed in the interface.

Figure 7a presents a characterization of the interface using the radial distribution. The previous RDFs of the CuO and ZnO nanowires have been located below for comparative analysis. As can be seen, the peak located at 3.5 Å disappears, demonstrating a high degree of amorphicity. Additionally, peaks at distances below this value have not been shown to be consistent with CuO and ZnO. In particular, the peak corresponding to the first neighbors appears at an intermediate point concerning CuO and ZnO. This result seems to agree with previous research, where good adhesion of CuO nanoparticles on ZnO nanowires was reported [48].

Figure 7b,c present the radial distribution at distances close to the interface, around 20 Å above and below the initial interface. It was evaluated independently for the ZnO and CuO compounds. The isolated nanowires RDFs were included for comparative purposes. At these intermediate distances, a high degree of amorphicity is observed for ZnO as well. Moreover, CuO has been shown to preserve crystallinity peaks beyond the second neighbors, consistent with the values of the CuO RDF (Figure 4). Visually, these differences in crystallinity can be detailed in Figure 6. As a general result, any change in the properties of the composite nanowire, mainly in the conductive ones, should come from the distortions of the crystalline lattice of the ZnO rather than CuO.

4. Conclusions

A structural analysis of CuO, ZnO, and CuO/ZnO nanowires obtained by molecular dynamics was presented. The results for CuO indicate that although the dimensions of the network parameters in “xz” are approximately conserved, the “y” direction observed a considerable decrease. The loss of in-plane periodicity of the lattice would make the ionic bonds stronger and shorten the Cu-O distance. A constriction effect produced by the attraction of surface charges generates internal plane slippage, producing undulations in the shape of the nanowire. The results for ZnO show a contraction in the “z” direction. Moreover, the Zn-O distance enlarges and deforms the nanowire in one of the plane axes. These deformation effects are produced by periodicity loss in the plane, with a constrictor effect produced by the surface over the interior due to charge attraction. This surface effect also induces a high disorder at the ends of the nanowire by compression. Thermal conductivity as a temperature function agrees with previous simulations and experimental reports. Phonon scattering by structural disorder leads to a maximum in thermal conductivity. This maximum is shifting at higher temperatures.