A series of layered CuCr_1-xMg_xO₂ (0 ≤ x ≤ 0.08) polycrystalline ceramics were prepared. The effects of substituting Mg²⁺ cations for Cr³⁺ cations on the grain composition, grain size, grain quantity, and electrical conductivity were investigated. When x = 0–0.04, the distinct layered structure grain grew rapidly with the increase of magnesium in the composition, and the average grain size increased from 2.5 μm (x = 0) to 15 μm (x = 0.04) due to the decrease of activation energy. Furthermore, the bulk density and lattice constant also reached the maximum and minimum values of 4.367 g/cm³ and 17.083 respectively at x = 0.04. When x = 0.05–0.08, the average grain size slightly decreased due to the grown-up second-phase MgCr₂O₄ hindering of grain growth. The results showed that the average size of the second-phase MgCr₂O₄ had reached 1.3 μm when x = 0.04. In general, the larger the grain size of polycrystalline ceramics, the more defects in the grain boundaries, and the better its electrical conductivity. Therefore, the solid-phase reaction, which can obtain larger grain size and more grain boundary defects, was chosen here to prepare CuCr_1-xMg_xO₂ polycrystalline ceramics, so as to obtain a highly conductive CuCr_1-xMg_xO₂ ceramic material. The minimum resistivity of the obtained CuCr_0.6Mg_0.4O₂ polycrystalline ceramic is only 0.091 Ω·cm, which is of great significance for the development of transparent conductive oxides

Keywords: CuCr_1-xMg_xO₂ grain composition grain size grain quantity electrical conductivity

Since the discovery of p-type CuCr_1-xMg_xO₂ materials, studies have primarily focused on their thermoelectric, photoelectric, and catalytic properties [1-7], while the crystal structure of CuCr_1-xMg_xO₂ and the second phase have been less frequently studied. As a p-type transparent conductive oxide, CuCr_1-xMg_xO₂ ceramics have been prepared by hydrothermal synthesis, solid-state reaction, et al. [1, 4, 5, 7, 8], and CuCr_1-xMg_xO₂ films have been prepared by reactive magnetron sputtering deposition, sol-gel processing, ALD (atomic layer deposition), et al. [3, 9, 10]. Maignan et al. [1] obtained the microstruc- ture images of CuCr_1-xMg_xO₂ ceramics and measured its composition using energy-dispersive X-ray spectro- scopy. Yu et al. [3] obtained the microstructure images of CuCr_1-xMg_xO₂ films and analyzed their surface topography, root mean square roughness, and optical and electrical properties. Kaya et al. [4] compared the images, resistivity and calculated particle-size distribu- tions of Mg- and Fe-doped CuCrO₂ nanocrystals prepared by hydrothermal synthesis. Furthermore, Okuda et al. published a series of research papers on the properties of doped CuCrO₂ ceramics [5, 7 ,8]. H.-Y. Chen et al. [9] analyzed the morphologies, and the optical, electrical properties. In this paper, we summarized the statistical grain distribution of the main-phase CuCr_1-xMg_xO₂ and second-phase MgCr₂O₄ based on electron microscope images. Moreover, we analyzed the characteristics of the grain structure and its correlation with electrical resistivity.

The CuCr_1-xMg_xO₂ ceramic samples were prepared in two steps using a standard solid-state reaction in air. First, the raw materials (Cu₂O [99.9%], Cr₂O₃ [99.95%], and MgO [99.99%]) were weighed according to the stoichiometric ratio, mixed well, and ground. Then, the powders were pressed into pellets and pre-sintered at 1,100 ^oC for 12 h. In the second step, the sintered pellets were ground and pressed into pellets again, sintered at 1,100 ^oC for 12 h, and finally, cooled to room temperature.
The polycrystalline structures of the obtained samples were characterized by BDX3200 X-ray diffraction (XRD). The microstructures were observed using an XL30E scanning electron microscope (SEM). The resistivity-temperature (ρ–T) curves were studied using the four-probe method between 100 and 300 K.

Phase structure
The XRD patterns of CuCr_1-xMg_xO₂ (x = 0, 0.005, 0.01, 0.02, 0.03, 0.04, 0.05, 0.08) are shown in Fig. 1(a). The figure shows that bulk ceramics comprise a 3R-delafossite structure and a high c-axis orientation. Compared to the CuCrO₂ standard spectrum (PDF 89-0539), the strongest (006) diffraction peaks indicate a shift to the right. This implies that the lattice parameter c has a decreasing trend. In addition, The spinel phase of MgCr₂O₄ with a (311) peak at 2θ = 35.674^o was detected in some of the samples (x = 0.04–0.08). These results are in good agreement with existing studies [5, 6]. Fig. 1(b). shows the relationship between bulk density, lattice parameter c and the magnesium doping amount x. As you can see from the Fig. 1(b), substituting magnesium for chromium will produce more crystallizable CuCr_1-xMg_xO₂ phase. With the increase of the doping amount of magnesium, the bulk density displayed an increasing trend, while the lattice constant displayed a decreasing trend. When x = 0.04, the bulk density and lattice constant reached the maximum and minimum values of 4.367 g/cm³ and 17.083 respectively, which is consistent with the reports [1, 11]. This may be mainly due to the saturation of magnesium doping.

Vertical section morphology observation
Scanning electron microscope (SEM) images of CuCr_1-xMg_xO₂ samples are shown in Fig. 2. As you can see from the Fig. 2, all samples have layered grains. At a low doping level (x≤ 0.04), small grains are loosely distributed and sufficiently grow in the ab-plane with a reduction in grain boundaries and pores; At a high doping level (x= 0.05 and 0.08), the grains size and grain boundaries hardly changed. Similar results have previously been reported for Fe- and Mg-doped CuCrO₂ nanocrystals [4]. At the same time, the doping of magnesium also introduces the second phase of MgCr₂O₄ spinel [1]. When x = 0.005–0.03, fine second-phase MgCr₂O₄ grains are observed among the CuCr_1-xMg_xO₂ grains; When x = 0.04–0.08, MgCr₂O₄ grains have obviously grown in size and reach maximum average value at x = 0.08.
In order to quantitatively describe the crystallization of the CuCr_1-xMg_xO₂ samples. The grain size and quantity of CuCr_1-xMg_xO₂ phase and MgCr₂O₄ phase are counted. Fig. 3 shows the grain size distribution of CuCr_1-xMg_xO₂ (0 ≤ x ≤ 0.08) samples. As you can see from Fig. 3, the average grain size is about 2.5 μm at low doping (x = 0, 0.005, 0.01), increase to 15 μm at moderate doping (x = 0.02, 0.03, 0.04), and fall to 11 μm at high doping (x = 0.05, 0.08). When x = 0.04, the average size of CuCr_1-xMg_xO₂ phase reaches maximum value (15 μm). Further, in order to clarify the reasons for affecting the grain size distribution of the main-phase CuCr_1-xMg_xO₂, the associated second-phase MgCr₂O₄ was studied. Fig. 4 shows the grain quantity of MgCr₂O₄ phase. As you can see from Fig. 4, although the grain quantity is the largest when x = 0.005, the average grain size is only about 0.8 μm, which hardly hinders the growth of CuCr_1-xMg_xO₂ grains. But when x = 0.04, the average size of the second-phase MgCr₂O₄ has reached 1.3 μm, and the hindrance to the average grain size of CuCr_1-xMg_xO₂ gradually appears. We speculate that this may be the reason why CuCr_1-xMg_xO₂ phase has the largest size when x = 0.04. In addition, this may be the reason why the bulk density and lattice constant reached extreme when x = 0.04. This follows the kinetic grain-growth equation, G_n - G₀ⁿ = At exp  (- (Q/RT)), and it is in good agreement with existing reports [12-14]. Changes in the apparent activation energy Q and kinetic grain-growth exponent n in CuCr_1-xMg_xO₂ with increase of the magnesium content are thought to be responsible for the crystalline grains size distribution. As the main-phase CuCr_1-xMg_xO₂ increases, the acute angles of the grains turned into obtuse angles, indicating a decrease in the crystalline melting point and the liquid precipitation of the polycrystalline grains, which can explain the reason for the increase of CuCr_1-xMg_xO₂ grain size too.

Electric transport properties
Fig. 5 shows the resistivity-temperature (ρ-T) curves of CuCr_1-xMg_xO₂ (0.01 ≤ x ≤ 0.08) polycrystals. The resistivity is measured by a four-probe method and the resistivity is calculated by formula for volume resistivity (ρ = RS/L, where R is the resistance, S is the area, and L is the length). All the samples show semiconducting electrical transport behavior. When x = 0–0.04, the re- sistivity rapidly decreases with the increase of magnesium doping amount. The room-temperature resistivity reaches a minimum of 0.091 Ω·cm at x = 0.04, which is com- parable to the results of existing reports shown in Table 1 [4, 15, 16]. When x = 0.05–0.08, the resistivity is almost unchanged. This is because the grain size reaches its highest level, resulting in the best integrity of the lattice at x = 0.04. Thus, the reduction of grain boundaries may also have been responsible for the decrease in resistivity.

In this study, CuCr_1-xMg_xO₂ (0 ≤ x ≤ 0.08) polycry- stalline ceramics were prepared using a solid-state reaction. And the effects of magnesium doping on lattice constant c, bulk density, average grain size, resistivity and associated second phase of CuCr_1-xMg_xO₂ polycry- stalline ceramics were also discussed. It was found that the increase of magnesium content in CuCr_1-xMg_xO₂ polycrystalline ceramics led to the decrease of activation energy and the growth of the second-phase MgCr₂O₄ grains, which in turn affected the size and number of CuCr_1-xMg_xO₂ grains. Furthermore, the electrical con- ductivity of CuCr_1-xMg_xO₂ polycrystalline ceramics was affected. The results show that CuCr_0.6Mg_0.4O₂ polycrystalline ceramics had the smallest lattice constant c (17.083), the highest bulk density (4.367 g/cm³), the largest average grain size (15 μm), and the smallest resistivity (0.091 Ω·cm). This is one of the best results reported so far. It has important guiding significance for the development of transparent conductive oxides with high conductivity.