Introduction

It is well established that anion polyhedra of small and high-valence cations are connected to each other via corner sharing in crystalline matters as postulated in Pauling’s third and fourth rules so as to minimize the Coulomb repulsion among cations. The validity of these rules is confirmed by a vast number of borates, silicates and phosphates as well. Exceptions are only met in borates synthesized under high pressures (HP) and high temperatures by Huppertz and coworkers recently. Typical compounds are Dy4B6O151, α-RE2B4O9 (RE = Eu, Gd, Tb, Dy)2, RE4B6O15 (RE = Dy, Ho)3 and HP-NiB2O44. A common feature in these borates is that they all contain BO4 tetrahedra connected to each other through edges instead of corners as in more than 1000 borate structures determined over the past decades. High pressure is essential in forming edge-sharing (es-) BO4 tetrehedra and even in inducing a conversion from BO3 planar triangle to BO4 tetrahedra5. But it is generally accepted that the pressure-driven formation of es-BO4 compounds is not thermodynamically favored; they are metastable over their ambient counterparts.

More recently, Chen’s group6 and Wu’s group7 independently reported the synthesis of a new borate KZnB3O6 under ambient pressure. This is the first borate with es-BO4 obtained without the aid of high pressures. Examination of its crystal structure reveals that BO4 tetrahedra in KZnB3O6 are nearly identical in B-O bond lengths and O-B-O angles to the previously reported HP borates1,2,3,4. First principles calculations6 show that es-KZnB3O6 is indeed more energy-favored than the hypothetical corner-sharing (cs-) one, which was constructed based on isostructural KCdB3O68. Yang and coworkers9 made a comparative study of es- and cs- KZnB3O6 by lattice dynamics and electronic-structure calculations and showed a soft-mode exists in the cs-isomorph, probably due to an overlong Zn-O bond in ZnO5 polyhedra, while there is none in the es-one. A study by nuclear magnetic resonance excludes the B-B bond10 in BO4. The origin, however, responsible for the formation of es-BO4 in es-KZnB3O6 in an energy-favorable way still remains unclear.

An interesting property in this newly-discovered KZnB3O6 is that its structure can be well preserved from room temperature up close to its melting point 1073 K, without any detectable phase transition occurring. This suggests that the structure or at least the fundamental building block (FBB) is very rigid to thermal attack. As is well-known, the way by which crystalline materials respond to changes in temperature offers a direct and straightforward measure of the nature of chemical bonds and structural peculiarities. In this work, we present the results of a study of the thermal expansions of KZnB3O6 from room temperature to 1013 K. It is found that unidirectional thermal expansion along the approximate [-3 0 2] direction exists over the entire measured temperature range from 298 K to 1013 K, which can fully accounts for the total volume thermal expansion; meanwhile, the expansions along other directions on the plane perpendicular to [-3 0 2] are negligibly small, i.e. the area shows zero expansion. By analyzing the variations in bond lengths, we show that the es-BO4 is virtually immune to changes in temperature thanks to the hinge rotations of B6O12 and Zn2O6 rigid groups, which only leads to a quasi-unidirectional expansion upon heating. The phonon dispersions and partial density of states (PDOS) calculations reveal a soft mode at 1013 K, due to transverse vibrations of the bridge oxygen whereby BO3 and B2O6 are connected, develops to cause the structure to dismantle at around its melting point. These results shed light on why KZnB3O6 can be stabilized over such a wide temperature range.

Results

KZnB3O6 powder samples were synthesized through solid state reactions from A.R. K2CO3, H3BO3 and ZnO. The preparing details can be consulted elsewhere6 or in Methods Section. This compound crystallizes in a triclinic unit cell with lattice constants a = 6.753 Å, b = 6.911 Å, c = 7.045 Å, α = 63.39 o, β = 72.584 o, γ = 69.13 o and space group P-1. Figure 1a shows the polyhedral view of its crystal structure, in which the metal-borate framework is built up from BO3 triangles, BO4 tetrahedra, ZnO4 tetrahedra. The FBB, B6O12 block, consists of two BO4 tetrahedra and four BO3 triangles. The BO4 tetrahedra are O1-O1 edge shared to each other and further corner-shared by BO3 trangles in their outer vertex O, see Fig. 1b. Two ZnO4 tetrahedra form a Zn2O6 polyhedron also through edge-sharing. Each FBB is bonded by six Zn2O6. K fills the voids left by these polyhedra.

Figure 1
figure 1

Structure of KZnB3O6.

(a) Polyhedral view of the KZnB3O6 crystal structure projected along the [01–1] direction, with tetrahedra ZnO4 in blue, triangular BO3 and tetrahedra BO4 units in green, adapted from Fig. 1a) in Ref.6. (b) Connection details of B6O12 and Zn2O6 blocks in the (-111) plane. The metal-borate framework is built up from BO3 triangles, BO4 tetrahedra, ZnO4 tetrahedra. The FBB consists of two es-BO4 tetrahedral and four vertexes-shared BO3 triangles.

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Figure 2 shows the powder X-ray diffraction patterns collected at 298 K, 373 K, 473 K, 573 K, 673 K, 773 K, 873 K, 973 K and 1013 K for KZnB3O6, respectively. A closer view of the enlargement of 2θ = 24 o ~ 31 o portion indicates that some peaks shift obviously towards low-angles, others nearly unshift, still others slightly towards high-angles, reflecting the changes in the unit cell are very anisotropic with increasing temperatures. All peaks can be indexed based on triclinic cells with high figure of merits by using Dicvol0611. As an example, the lattice constants for the 298 K pattern are a = 6.744 Å, b = 6.926 Å, c = 7.072 Å, α = 63.13 o, β = 72.40 o, γ = 69.07 o, in good consistency with ones obtained from the single crystal data. No phase transition occurs as no additional peaks emerge or disappear in the entire temperature range measured. The temperature dependent lattice constants a, b, c and cell volume are plotted in Fig. 3a. All the data along with the crystallographic angels are deposited in Supplementary Information, see Supplementary Table S1. We can clearly see lattice constants a and c linearly expand with the increasing temperatures, while b shrinks, resulting in volume expansion at a rate of (44.92 ± 1.5) × 10−6 K−1. This is an average thermal expansion rate for borates12,13.

Figure 2
figure 2

The powder X-ray diffraction patterns collected at 298 K, 373 K, 473 K, 573 K, 673 K, 773 K, 873 K, 973 K and 1013 K for KZnB3O6, respectively.

The inset is a closer view of the enlargement of 2θ = 24 o ~ 31 o portion indicates that some peaks shift obviously towards low-angles, others nearly unshift, still others slightly towards high angles.

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Figure 3
figure 3

Thermal expansion behavior of the KZnB3O6.

(a) The temperature dependence of lattice constants a, b, c and cell volume. (b) Normalized components of the principal axes versus temperature, where X1, X2 and X3 are (−1.06 ± 0.42) MK−1, (0.56 ± 0.31) MK−1 and (44.81 ± 0.79) MK−1, determined by the PASCal14 program. Inset: The thermal expansivity indicatrix, which describes the expansion rate in all directions in the set of orthogonal axes. It clearly shows the area of zero thermal expansion and a very large expansion along the X3 axis.

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Since the crystallographic axes of the present triclinic unit cell are chosen by convention, the variations in the lattice constants will not always reflect the fundamental thermal response of KZnB3O6. This is, in particular, true for the low symmetry compounds. It is established that a unique set of orthogonal axes, or the principal axes exist, along which the expansion or contraction describes the fundamental thermal response, including some nonzero shear components, or rather, the variation in the crystallographic angles of the unit cell for a given compound. To this end, we applied web-based software PASCal14 to find the set of orthogonal axes by inputting the unit cell data at all measured temperatures. Figure 3b gives the changes in length along the principal axes with the increasing temperatures. The principal coefficients of thermal expansions, their estimated standard deviations and the components of the principal axis relative to the crystallographic axes are summarized in Table 1. In comparison with the expansion data for the crystallographic axes, the variations of the principal axes with increasing temperatures are more anisotropic, the expansion rates for X1 and X2 being (−1.06 ± 0.42) × 10−6 K−1 and (0.56 ± 0.31) × 10−6 K−1, respectively, much smaller than one for the X3, (44.81 ± 0.79) × 10−6 K−1. Two facts are evident. First, the area expansion rate for the plane determined by X1 and X2 is virtually zero as αarea = αx1 + αx2 = (−0.5 ± 0.42) × 10−6 K−1. Second, the expansion rate for X3 is nearly equal to the volume expansion rate, αx3 ≈ αv ≈ 45 × 10−6 K−1. These facts suggest the volume expansion can be ascribed to the expansion occurring in the X3 axis, which is along approximate [-3 0 2] in the crystallographic coordinates. The inset of Fig. 3b is the thermal expansivity indicatrix which describes the expansion rates in all directions in Cartesian coordinate. It clearly shows an area zero thermal expansion and a very large expansion along the X3 axis. Although it is a common phenomenon that borates have large anisotropic thermal expansion12,13, such as recently-reported LiBeBO3 which shows an area negative expansion15 from 193 K to 273 K, the quasi-unidirectional thermal expansion for KZnB3O6 in such a wide temperature range is very rare and peculiar13,16,17.

Table 1 The expansivity, estimated standard deviation from room temperature to 1013 K for KZnB3O6 and the components of principal axes relative to the crystallgraphic axes.
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Discussion

To understand the peculiar thermal response and gain some insights on the thermal stability for KZnB3O6, we performed the geometry optimization and lattice dynamics study by density functional theory (DFT) calculations. We mimic the high temperatures by using the experimental lattice constants at high temperatures as constraints while allowing the geometry optimization of the atomic positions in the unit cell and subsequent lattice dynamics calculations. The calculating details and the results are archived in Supplementary Information. Careful examination of the bond lengths at 298 K and 1013 K reveals that the expansions in B-O and Zn-O bonds are generally below 0.5%, while up to 3.4% in K-O bonds (see Supplementary Table S2). Moreover, the Hirshfeld’s “rigid body” test18,19,20,21,22,23 indicated that the maximum differences in MSDA’s (mean square displacements of atoms) have magnitudes ∆ = 15 Å2 in group B6O12, ∆ = 9 Å2 in group Zn2O6. Meanwhile the maximum value is as large as ∆ = 108 Å2 for KO9 group (Table S3). It is then reasonable to take Zn2O6 and B6O12 as rigid groups and KO9 as an easily-deformable polyhedron in the temperature range from 298 K to 1013 K. We first consider the rigid rotations of bodies since they play a major role in negative- or zero-thermal expansions for compounds that contain rigid tetrahedra and octahedra24,25,26,27, etc., including B-O polyhedra12,13,28. For KZnB3O6, the rotations of rigid groups are shown in Fig. 4a. Reverse rotations are identified for B6O12 and Zn2O6 along the [1 0 1] direction, see Fig. 4a. Taking the angle between the normals of plane B3-B3 and Zn-Zn (see Figure caption for the definition of these planes) as an indicator for the relative rotation, it decreases by about 2.71 o from 298 K to 1013 K. These rotations can be better viewed in Fig. 4b, where the planes B2, B1 and B3-B3 generally rotate in an opposite way as the Zn-Zn plane does, for the angles between normals of the corresponding plane become smaller. For K-O bonds, we note that their elongations vary a lot, from 0.19% to 3.39%. The concerted effect of reverse rotations of rigid groups and very asymmetrical elongations in K-O bonds lead to expanding along roughly [–3 0 2], i.e., the X3 axis direction, leaving the other two directions, or rather, the plane perpendicular to [–3 0 2] almost unchanged upon heating (Supplementary Fig. S1). In addition, the FBB is found to become more flat with increasing temperatures. It can be seen that the angles between the B1, B2 and the B3-B3 planes decrease simultaneously, suggesting a reduced geometry distortion within the FBB upon heating. We think that these unusual thermal responses help secure the es-BO4 from disassociation.

Figure 4
figure 4

Hinge rotation of the KZnB3O6.

(a) The rigid groups’ rotations associate with the area zero thermal expansion. Top right: schematic of ‘hinge folding’ that simultaneously expands in a,c and contracts in b. (b) Left: The stereographic projection of B3-B3, B1, B2 and Zn-Zn planes at 298 K and 1073 K, rotations of those planes with increasing temperatures are indicated by arrows. Right: ‘hinge’ rotation of the contacted FBB and Zn2O6 units with temperature, where B3-B3 plane is defined by four O atoms bridging the BO4 and BO3 atoms, B1 and B2 planes are defined by two BO3 triangles, Zn-Zn plane is the brown plane defined by O2, O3, O2’ and O3’.

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Furthermore, the inversion symmetry of KZnB3O6 puts some limits on the deformation of B2O6. Since two B3 and two O1 are connected each other by –1, respectively, their only possible change in positions are either closer or away along their co-axial directions. Lengthening O1-O1 is unlikely because this kind of expansion will be inhibited by increasing B3-B3 repulsion as they become closer. Instead, the shortening O1-O1 is energy favored. Similar situation is for Zn2O6 polyhedra. This may explain why the es-BO4 polyhedra are stable at high temperatures.

The calculated phonon dispersions and PDOS at 298 K and 1013 K are shown in Supplementary Fig. S2. Most of vibrational branches shift towards low frequency when temperature increases from 298 K to 1013 K. Correspondingly, the PDOS at the low frequency band are enhanced. This can be better viewed from Supplementary Fig. S3, which shows the PDOS contributed by O4 for example. A few branches, however, shift a little or even towards high frequencies as see the PDOS contributed from O2. These results are consistent with our observations that KZnB3O6 expands in a very anisotropic way, large expansitivity along X3, zero along X1 and X2. Moreover, we find that an optical mode becomes negative at the Γ point in the Brillouin zone at 1013 K, implying a structural instability at this temperature. Meanwhile, the calculated vibration amplitudes associated with the negative optical mode reveal that the largest one resides on O4, which connects the BO3 triangles and the BO4 tetrahedra, see Supplementary Fig. S4. Accordingly, we speculate that the melting begins with the breakage of the link between BO3 and BO4 when temperature is close to its melting point.

Thermal responses of materials have been a hot research topic over the last decades. Many a compound was found to exhibit negative thermal expansions, others area negative expansions. The unidirectional thermal expansion reported here for KZnB3O6 is rarely known13,29. This unusual thermal response is related to the peculiar structure. This property may find future applications in its single crystal form in fields that require a very small change in diameters while expanding in the third dimension over a wide temperature range, such as a high precision optical lens.

In summary, the first borate with edge-sharing BO4 synthesized under ambient pressure, KZnB3O6, exhibits an unusual unidirectional thermal expansion: 45 × 10−6 K−1 with zero thermal expansion in the perpendicular direction over a temperature range from room temperature to 1013 K. The volume expansion can be regarded as coming from an expansion in one direction only. We determine that this unusual thermal behavior comes from rotations of rigid groups of B6O12 and Zn2O6, probably driven by very asymmetrical elongations of K-O bonds. In this way, the es-BO4 is secured from disassociation upon heating. Based on the present study, KZnB3O6 can be described as a 1-dimensional compound in the sense of thermal expansion. Other related properties of this compound merit further investigation.

Methods

Samples

The compound KZnB3O6 was prepared by grinding a mixture of K2CO3 (A.R.), ZnO (A.R.) and H3BO3 (99.99%) to a fine powder and then heating at 500 °C for 12 h to decompose the salt. In order to compensate for volatilization of alkali metals, 15% excess of K2CO3 (A.R.) is required. The sample was reground and annealed at 750 °C for 24 h and a single-phase white powder was readily obtained. The sample purity was verified by X-ray powder diffraction.

High temperature XRD measurements

Temperature-dependent in situ X-ray diffractometry was performed on an XPERT-PRO powder diffractometer system (CuKα1; 1.54056 Å) equipped with an Anton Paar HTK-1200N Oven Sample stage. The room-temperature diffraction pattern in the angular range from 10 o to 80 o with a scanning step width of 0.017 o was firstly obtained as a standard and then the sample was heated from 373 K to 1013 K at intervals of 100 K. Each diffraction pattern was obtained 30 min after the required temperature was reached. Unit cell parameters were then calculated by using the pattern indexing software Dicvol0611.

Additional Information

How to cite this article: Lou, Y. et al. Unidirectional thermal expansion in edge-sharing BO4 tetrahedra contained KZnB3O6. Sci. Rep. 5, 10996; doi: 10.1038/srep10996 (2015).