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Mg$_x$Zn$_{1-x}$O solid solutions make it possible to tune the band gap of ZnO smoothly into the ultraviolet region. However, in ceramic materials the hexagonal wurtzite and cubic phases coexist over a wide composition range, so the nominal composition does not reflect the actual phase state that determines the optical and electrical properties. Infrared (IR) reflectance spectroscopy is sensitive both to lattice vibrations and to the phase state, which makes it an effective contactless diagnostic method. While the phonon modes of epitaxial MgZnO films have been well studied, an adequate dispersion model for ceramics over the entire composition range has not yet been proposed.
A series of Mg$_x$Zn$_{1-x}$O ceramic samples sintered at 1100 °C with a nominal MgO content of $0 \le x \le 1$ was studied. Specular IR reflectance spectra were recorded at room temperature with a Shimadzu IRTracer-100 FTIR spectrometer in the range 240–4000 cm$^{-1}$. The analysis was performed using a dispersion model for a polycrystalline two-phase material. The dielectric function of each phase is represented in factorized form with separate damping coefficients for the TO and LO phonons and includes two E$_1$ oscillators (ZnO-like and MgO-like) for the hexagonal phase and one F$_{1u}$ oscillator for the cubic phase. The two-phase mixture is described within the Bruggeman effective-medium approximation with the cubic-phase volume fraction fc, and the surface roughness is taken into account by the factor $\exp[-(4\pi\sigma\nu)^2]$. The model parameters were determined by the least-squares method.
For hexagonal ceramics ($x \le 0.30$) the model reproduces the experimental spectra with a root-mean-square deviation of 0.008–0.014. The reststrahlen band splits into ZnO-like ($\nu_{TO1} \approx$ 405–413 cm$^{-1}$, $\nu_{LO1} \approx$ 497–505 cm$^{-1}$) and MgO-like ($\nu_{TO2} \approx$ 508–514 cm$^{-1}$, $\nu_{LO2} \approx$ 618–630 cm$^{-1}$) modes, which shows that the two-mode behaviour of E$_1$ phonons known for films appears in ceramics already at $x = 0.03$. For pure ZnO ceramics the model gives $\nu_{TO} = 405$ cm$^{-1}$, $\nu_{LO} = 590$ cm$^{-1}$ and $\varepsilon_\infty = 3.71$, in good agreement with single-crystal data. The mode frequencies and $\varepsilon_\infty \approx$ 3.4–3.9 saturate at $x \ge$ 0.05–0.10 (corresponding to $x \approx$ 0.10–0.15 in films), which indicates limited solubility of Mg in the wurtzite lattice. At $x \ge 0.40$ the LO edge of the cubic phase appears near 700 cm$^{-1}$, and the cubic-phase fraction increases from fc ≈ 0.5 at $x = 0.40$ to $\approx 1$ at $x \ge 0.9$. For Mg-rich samples, qualitative agreement is achieved. The roughness parameter $\sigma \approx$ 0.25–0.33 µm hardly depends on composition, which reflects the quality of surface preparation rather than the properties of the material.
The proposed approach enables contactless estimation of the phonon parameters, the effective composition of wurtzite grains and the phase composition of oxide-based ceramic solid solutions.
Keywords: MgZnO ceramics, IR reflectance, two-mode phonon behaviour, dispersion analysis, phase composition.
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