Introduction

The GeO2 melt is the archetype of various germanate melts. Its structure, particularly the local coordination environment of germanium, is of technological and geochemical importance and has been investigated extensively using various experimental methods or theoretical simulations1,2,3,4. It is widely accepted that germanium in the GeO2 melt is coordinated by four oxygen atoms at ambient conditions and by six oxygen atoms at extreme conditions5. However, the viewpoint still remains controversial. A long-standing puzzle arises from the Raman spectrum. The typical Raman spectrum of the GeO2 melt is dominated by a broad peak centered at 420 cm−1, with two shoulders (X1 and X2) present around 340 and 520 cm−1. About the structural origins of the two shoulders, the debates have continued for decades6,7,8,9,10. In this work, we investigate the Raman spectra and the bonding nature of a GeO2 melt by density functional theory (DFT) computation, focusing, in particular, on the structural origins of the two mysterious shoulders, and demonstrate threefold coordinated germanium occurring in the melt.

Results and discussion

Experimental Raman spectra

A polycrystalline GeO2 sample was heated in a Linkam TS1500 microscopic furnace. Its Raman spectra were recorded in situ from room temperature through its melting temperature (1388 K) on a Horiba Jobin Yvon LabRAM HR Evolution Raman spectrometer (for details, see Methods). The spectra, before melting, exhibit the typical features of quartz-type GeO211. After melting, some new Raman bands, centered at 340 (shoulder X1), 520 (shoulder X2), 735, and 805 cm−1, are present and systematically increase in intensity with temperature (Fig. 1).

Fig. 1: Raman spectra of GeO2 before and after melting.
figure 1

GeO2 melts at around 1388 K. X1 and X2 denote two characteristic Raman bands of the GeO2 melt. Source data are provided as a Source Data file.

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Structural transformation on melting

Recent studies have pointed out that heat-induced structural transitions of solids, including melting, often involve decreases in the coordination number of composed atoms12,13,14,15. For example, GeO2 undergoes the structural transition from the rutile- to quartz-type when heated at 1281 K (Fig. 2). Accompanying the transition, the coordination number of germanium decreases from six to four16. The decrease is probably associated with oxygen atom vibration (Fig. 2). At low temperatures, GeO2 is formed by octahedral [GeØ6] (rutile-type GeO2, Ø = bridging oxygen), and each germanium atom is coordinated by six oxygen atoms with small vibrational amplitudes. At 1281 K, the vibration of the oxygen atoms is enhanced, the space available around the germanium atom cannot accommodate six oxygen atoms, and thus octahedral [GeØ6] has to transform to tetrahedral [GeØ4] (the motif of quartz-type GeO2). For the same reason, the fourfold coordinated germanium in quartz-type GeO2 will convert to lower-coordinated germanium when heated at a higher temperature, such as at the GeO2 melting point (1388 K).

Fig. 2: Structural transformations of GeO2 during heating.
figure 2

Blue and orange spheres represent germanium and oxygen atoms, respectively. The orange wavy lines represent the vibration of oxygen atoms; their amplitude increases with temperature. Rutile-type GeO2 crystallizes in the P42/mnm space group (No. 136) with two GeO2 formulae in a tetragonal unit cell (a = 4.4066 Å and c = 2.8619 Å), and features a continuous [GeØ6]n network28. Quartz-type GeO2 belongs to the P3221 space group (No. 154) with three GeO2 formulae in a trigonal unit cell (a = 4.9870 Å and c = 5.6520 Å), and features a continuous [GeØ4]n network29. Rutile-type GeO2 transforms to the quartz-type at 1281 K and then melts at 1388 K.

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Figure 3 presents a possible structural transformation of GeO2 in the melting process. After melting, some Ge–Ø bonds in quartz-type GeO2 are broken (Fig. 3b), which yields the Ge–O bonds and threefold coordinated germanium atoms and finally the [GeOØ2]n chain (Fig. 3c). Thus, the GeO2 melt probably consists of the [GeOØ2]n chain and the [GeØ4]n network.

Fig. 3: GeO2 structures before and after melting.
figure 3

Blue and orange spheres represent germanium and oxygen atoms, respectively. a Quartz-type GeO2 (before melting). b Structural change occurring in the melting process. The fragmented bonds are broken in this process; as a result, fourfold coordinated germanium (in the form of [GeØ4]) converts to threefold coordinated germanium (in the form of [GeOØ2]). c A [GeOØ2]n chain formed after melting. d Structural model of the [GeOØ2]n chain.

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Structural model and computational Raman spectrum

DFT computation was used to study the structural features of the [GeOØ2]n chain and then to simulate its Raman spectrum (see Methods for computation details). Two [GeOØ2]n chains with four GeO2 formulae were placed into a three-dimensional, periodic, orthogonal unit cell, with fixed parameters a = 4.85 Å, b = 3.82 Å, and c = 8.15 Å, to construct the structural model. The model has \({D}_{2h}^{16}\) symmetry (space group Pnma). The reliability of the computational method was confirmed by comparing the computational Raman spectrum of quartz-type GeO2 to the experimental one (see Methods for details). The optimized structure of the [GeOØ2]n chain is shown in Fig. 3d (see Supplementary Fig. 1 and Supplementary Table 1 for more details). In this structure, each germanium atom is surrounded by five oxygen atoms (Fig. 3c); three of them are from the same chain with short Ge–O distances (dGe‒O1 = 1.84 Å, dGe‒O2 = 1.78 Å, and dGe‒O3 = 1.77 Å) and two from two neighboring chains with long Ge–O distances (dGe‒O4 = dGe‒O5 = 1.97 Å). 1.97 Å is greater than the length of a normal Ge–O single bond (usually no more than 1.92 Å17), indicating that the germanium atom is threefold coordinated.

The reliability of the chain structure was evaluated by DFT computation. The computational total energy of the chain model is −3868.22 eV; accordingly, each [GeOØ2] motif has an energy of −967.06 eV. The energy is slightly higher than that of the [GeØ4] motif in quartz-type GeO2 (−967.09 eV), revealing that [GeOØ2] is a metastable structure at low temperature and can coexist with [GeØ4] at high temperature.

The computational spectra of the [GeOØ2]n chain and the [GeØ4]n network (quartz-type GeO2), along with the GeO2 melt experimental spectrum (recorded at 1500 K), are shown in Fig. 4a. All of the experimental bands are produced in the computational spectra (see Supplementary Tables 2 and 3 for more details). The computational bands are in agreement with the experimental ones, not only in frequency but also in intensity, which confirms that the [GeOØ2]n chain coexists with the [GeØ4]n network in the GeO2 melt. To the best of our knowledge, the [GeOØ2]n chain is the first example of a species with threefold coordinated germanium.

Fig. 4: Computational results for the GeO2 melt.
figure 4

Blue and orange spheres represent germanium and oxygen atoms, respectively. a Computational Raman spectra of the [GeOØ2]n chain and the [GeØ4]n network, together with the experimental spectrum of the GeO2 melt (recorded at 1500 K). b Atomic vibrations for shoulder X1. c Atomic vibrations for shoulder X2. Source data are provided as a Source Data file.

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According to the DFT computational results, both the shoulders X1 and X2 are associated with the [GeOØ2]n chain and arise from the vibration of the bridging oxygen along the Ge–O–Ge angle bisection (Fig. 4b, c). Unlike X2, X1 involves the distinctive stretching vibration of the germanium atom along the Ge–O bond. Atomic vibrations for other strong Raman bands of the [GeOØ2]n chain are available in Supplementary Fig. 2. It is noteworthy that the Raman bands due to the Ge–O stretching vibrations are located at around 715 cm−1 (Supplementary Figs. 2b and 3b, c), significantly lower than the Ge‒O stretching frequency of the [GeO2Ø22−]n chain (located at around 815 cm−1)18,19, which reflects that the Ge‒O bonding in [GeOØ2]n is weaker than that in [GeO2Ø22−]n.

Electronic structures

Knowledge of the electronic structure is critical for understanding the nature of chemical bonding in the [GeOØ2]n chain. Here, only the valence electrons (Ge-4s24p2 and O-2s22p4) are considered for the DFT computation of the electronic structure. The total and projected densities of states (DOSs) of [GeOØ2]n are shown in Fig. 5a. All the bonding orbitals of the germanium atom are composed of the Ge-4s and Ge-4p orbitals and display some hybrid character, especially the orbitals in the energy range from −19.5 to −15.5 eV. The bonding orbitals from −9.0 to −6.0 eV and from −6.0 to 0.0 eV mainly derive from the Ge-4s and Ge-4p orbitals, respectively, apart from the O-2p orbitals. In comparison with quartz-type GeO2 (Fig. 5b), the [GeOØ2]n chain has more high-energy orbitals originating from the Ge-4p and O-2p atomic orbitals, which implies that the [GeOØ2]n chain has more weak- or non-bonding p orbitals. The electron localization function (ELF) is a measure of the probability of finding an electron pair in a space region and is an intuitive tool to identify the character of a chemical bond20. A valence ELF map of [GeOØ2]n is displayed in Fig. 5c. Most electron pairs are localized in the regions between Ge and O, which reveals the covalent nature of the Ge‒O/Ge‒Ø bonds. The population of the electron pairs between Ge and O in [GeOØ2]n resembles that in [GeØ4]n (Fig. 5d), further confirming that the Ge‒O/Ge‒Ø bonds have a similar character in the two structures.

Fig. 5: Electronic structures of the two structures in the GeO2 melt.
figure 5

Blue and orange spheres represent germanium and oxygen atoms, respectively. a Total and projected DOSs for the [GeOØ2]n chain. b Total and projected DOSs for the [GeØ4]n network. c A valence ELF map for the [GeOØ2]n chain. d A valence ELF map for the [GeØ4]n network. The maps are along the planes on which the Ge–O/Ge–Ø bonds lie. Source data are provided as a Source Data file.

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The trigonal planar geometry of the [GeOØ2] motif suggests that the germanium atom in the [GeOØ2]n chain is the sp2 hybridization. In the hybridization, the Ge-4s orbital mixes with two Ge-4p orbitals to form three Ge-sp² orbitals of equal energy. At the same time, a Ge-4s electron is excited to the empty Ge-4p orbital and results in the 4s14px14py14pz1 configuration (Fig. 6a). Each Ge-sp2 orbital electron pairs with an O-2p electron, forming three σ bonds (Ge–O/Ge–Ø bonds). The remaining perpendicular 4pz1 orbital is not involved in the bonding (Fig. 6b) but can interact weakly with two neighboring O-2p orbitals.

Fig. 6: Hybridization and bonding in the [GeOØ2] motif.
figure 6

a Hybridization scheme for the germanium atom. b Interactions between Ge-sp2 and O-2p orbitals (left), and the unhybridized Ge-4p orbital (right).

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Four representative bonding orbitals of [GeOØ2]n are shown in Fig. 7a. Except for the orbitals near the Fermi energy level, all of the bonding orbitals have the σ bond character. Since the O-2p orbital is significantly different in size from the Ge-4p orbital, the expected π bond, formed by laterally overlapping the Ge-4p orbital with the three O-2p orbitals, is not found. The [GeOØ2]n chain has similar bonding features to quartz-type GeO2 except for the orbitals in the energy range from −8.6 to −6.2 eV. In the energy range, each germanium atom interacts with two non-bridging O atoms in the adjacent [GeOØ2]n chains (Fig. 7a). Nonetheless, the interaction is weaker than the typical Ge–O covalent bonding (Fig. 7b) and thus easily appears and disappears in the GeO2 melt. We refer to the unique interaction as the fluxional bonding. The bonding can interpret the fluidity of the melt.

Fig. 7: Representative orbitals in different energy ranges for the two structures in the GeO2 melt.
figure 7

Blue and orange spheres represent germanium and oxygen atoms, respectively. a The [GeOØ2]n chain. b The [GeØ4]n network.

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More of the bonding characteristics of the [GeOØ2]n chain are revealed by the Hirshfeld charge population analysis21. The Hirshfeld charges of the germanium, non-bridging oxygen, and bridging oxygen atoms in the chain are +0.54 e, −0.25 e, and −0.29 e, respectively, indicating that all the Ge−O/Ge–Ø bonds are polar. According to the ELF analyses, the electron pairs around the Ge‒O bonds in the [GeOØ2]n chain are less than that in the [GeO2Ø22−]n chain (see Supplementary Fig. 4 for more details). The result is consistent with the Ge–O bond length data of the two chains (1.84 Å in [GeOØ2]n and 1.733 Å in [GeO2Ø22−]n) and further supports our inference that the Ge–O bonding in [GeOØ2]n is weaker than that in [GeO2Ø22−]n.

The threefold coordinated germanium, as well as the [GeOØ2]n chain, provides an insight into the structure of germanate melts, which is helpful for better understanding the melt behaviors in various technological processes such as crystal growth and glass production. Besides, the GeO2 melt is widely considered a chemical and structural analog of the SiO2 melt, the main constituent of magmas1,3,22. Hence the present GeO2 structure may have important implications for exploring the geochemical evolution occurring in Earth’s interior.

Methods

Raman spectroscopy

A GeO2 polycrystalline sample (rutile-type, 99.999%, Sinopharm Chemical Reagent) was placed into a platinum crucible which was heated in a Linkam TS1500 microscopic furnace. The Raman spectra of the sample were recorded on a Horiba Jobin Yvon LabRAM HR Evolution Raman spectrometer. The excitation source was the 355 nm line delivered by a Q-switched THG Nd:YAG pulsed laser with a power of about 10 mW. Raman scattering light was collected using an optical confocal system in a backscattering configuration. The Raman scattering light was analyzed with a single grating monochromator and detected with a CCD camera. The spectral resolution was about 1.3 cm−1. Prior to Raman measurements, the spectrometer was calibrated using a silicon wafer.

DFT computations

DFT computations within the plane-wave/pseudopotential scheme were performed using the Cambridge Sequential Total Energy Package (CASTEP)23. The generalized gradient approximation (GGA) in the Wu‒Cohen (WC) parametrization was adopted to treat the exchange and correlation effects. The use of the GGA-WC functional can significantly improve the computational accuracy relative to the most popular GGA-PBE (Perdew–Burke–Ernzerhof) functional24. Norm-conserving pseudopotentials were employed to describe the core–electron interactions. The valence electron configurations of germanium and oxygen were 4s24p2 and 2s22p4, respectively. An energy cutoff of 750 eV was used in all computations. The Brillouin zone integrations were performed over a 3 × 3 × 2 Monkhorst Pack grid for quartz-type GeO2 and over a 3 × 4 × 2 grid for the [GeOØ2]n chain. The two structural models were optimized until the total energy change, maximum displacement, maximum force, and maximum stress were less than 10−6 eV/atom, 0.001 Å, 0.03 eV/Å, and 0.05 GPa, respectively. For quartz-type GeO2, the cell parameters, as well as atomic positions, were optimized. For the [GeOØ2]n chain, all the atomic positions were optimized in a unit cell with fixed parameters a = 4.85 Å, b = 3.82 Å and c = 8.15 Å. After structure optimizations, the DOSs, ELFs, Hirshfeld charge populations, and bonding orbitals were computed with CASTEP for the two structural models.

CASTEP uses density functional perturbation theory (DFPT, also known as the linear response method) to compute the Raman spectra (modes, frequencies, and intensities at the Γ point) of quartz-type GeO2 and the [GeOØ2]n chain25. By constructing the Hessian matrix, Raman vibrational information was obtained. The eigenvectors of the matrix are the Raman modes; the square roots of the eigenvalues are the Raman frequencies. The intensity of each vibrational mode was computed from the derivative of the dielectric polarizability tensor with respect to the mode amplitude. Computational Raman intensities were corrected by the Bose–Einstein factors calculated with the excitation source wavelength (355 nm) and the experimental temperatures (300 K for quartz-type GeO2 and 1500 K for the [GeOØ2]n chain)25. Computational Raman lines were broadened by the Lorentzian line-shape function26 with a fixed full width at a half-maximum of 10 cm−1.

The reliability of the adopted computational method was confirmed by simulating the Raman spectrum of quartz-type GeO2. It is well-known that GGA often underestimates the computational Raman frequency due to the underbinding effect27. For this reason, all the computational Raman frequencies in this work were scaled by a uniform factor of 1.070. The scaled computational spectrum of quartz-type GeO2 is shown in Fig. 8, which is in good agreement with the experimental spectrum both in frequency and intensity.

Fig. 8: Computational and experimental Raman spectra of quartz-type GeO2.
figure 8

The computational frequencies are scaled by 1.070. Source data are provided as a Source Data file.

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Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.