Introduction

The thermal expansion compatibility of different component is a one of key problems for modern devices, such as thin film, multilayer chip capacitors (MLCCs), solid oxide fuel cell (SOFC), thermoelectric materials and high temperature piezoelectrics1,2,3,4. Thermal stress could give rise to material failure due to undesirable mismatch of coefficient of thermal expansion (CTE) of different components. The control of thermal expansion is an important topic for the material design. Negative thermal expansion (NTE) was recently found in some materials in the past two decades5,6,7,8,9,10,11. NTE materials have a promising potential application on tailoring CTE7. The overall thermal expansion can be tailored by either formation of composites or chemical modification of single-phase materials. For example, some composites were fabricated, such as ZrW2O8 with common materials12,13. The progress is, however, hampered mainly due to the poor thermal stability of ZrW2O8. It decomposes at a relatively low temperature (777°C)7. If the control of CTE could be achieved in single-phase materials, drawbacks in composites such as low binding capacity, thermal stress, or chemical reaction at interface, could be effectively overcame.

The control of NTE is an interesting topic for the studies on NTE especially of individual pure materials. Many kinds of chemical modifications have been carried out on various NTE materials. For example, ZrW2O8 based single-phase materials show little dependence of NTE on compositions and behave a very small varied range of CTE (αV = −2.2 ~ −2.6 × 10−5°C−1) by chemical modifications14. The control of NTE of ZrW2O8 is restricted by the fact of few suitable substitutions and low solubility limit. A single-phase ceramic material of Al2x(Hf,Mg)1-x(WO4)3 was found to have a bulk CTE range of −0.23 ~ 0.45 × 10−5°C−1, where a zero thermal expansion (ZTE) was also achieved8. Orthophosphate group of NaZr2(PO4)3 (NZP) of fast ionic conductivity have been widely studied with various substitutions at different sites to exhibit a CTE range of −0.17 ~ 0.19 × 10−5°C−115. The effect of cation size could play an important role in the thermal expansion property of NZP-based materials16. More recently, anti-perovskite Mn3AN (A = Zn and Ga) nitrides were found to have a giant NTE which was suggested to correlate with the coupling between the Γ5g antiferromagnetic spin configuration and lattice17,18. Many kinds of substitutions have been tried at three crystallographic sites in order for adjusting thermal expansion of Mn3AN. ZTE could be established in, for example, nanocrystalline Mn3Cu0.5Ge0.5N below −55 °C19 and Mn3(Ga0.5Ge0.4Mn0.1)(N1-xCx) in a temperature range of −83 ~ 0 °C20. The further studies on the complex interplay between magnetic exchange, cation radius and lattice would allow more precisely control NTE of Mn3AN materials, especially for a wide temperature range. The challenge still remains for the control of single-phase NTE materials. Especially, the control of NTE over a large range would benefit the practical applications of NTE materials.

Among the family of NTE materials, there is one branch of ferroelectrics which behave a general phenomenon that unit cell volume contracts during ferroelectric-to-paraelectric phase transition, such as perovskites of PbTiO3 (PT)21,22,23, BaTiO324, BiFeO325 and (Bi,La)NiO39, tungsten bronze PbNb2O626 and semiconductor GeTe27. It is important to note that all ferroelectrics except PT (RT ~ 490°C)23 exhibit NTE property within a narrow temperature range, e.g. 50°C for BiFeO325. Such large NTE temperature range of PT offers us an opportunity to control the NTE property. Our previous studies have revealed that the CTE can be adjusted by chemical substitutions for either Pb or Ti cations21,22,23. The temperature dependence of spontaneous polarization (PS) and lattice dynamics have approved that the ferroelectric behaviour plays an important role in the NTE nature of PT-based materials21,22. For future application of the NTE PT-based materials, however, one of main problems still remains. That is how to easily control the NTE over a large scale. Here, we report an effective way to control the NTE of ferroelectrics over a giant scale through a simple method by adjusting the ratio of cations with different ferroelectric activity which is defined as the PS displacement in the oxygen polyhedron28,29. The proposed system is the 0.5PbTiO3-0.5(Bi1-xLax)FeO3 (abbreviated as the 0.5PT-0.5BLxF, 0.0 ≤ x ≤ 0.2) whose Bi and La have essentially the same cation radius (1.34 Å for Bi3+ and 1.36 Å for La3+) however with much different ferroelectricity activity. Bi3+ has the strongest ferroelectric activity (0.8Å), while La3+ has the weakest one (0.05Å)28,29. The average bulk CTE can be controlled over a giant range from −7.0 to −0.71 × 10−5°C−1, which contains most known NTE materials. The detailed structure was investigated by both neutron powder diffraction based on Rietveld refinement and density function theory (DFT) calculation. A new concept of spontaneous volume ferroelectrostriction (SVFS) is proposed to elucidate the mechanism of NTE control in ferroelectrics.

Results

It is known that (1-x)PbTiO3-xBiFeO3 binary system can form a full range solid solution with a morphotropic phase boundary (MPB) around at x = 0.65 and exhibits unusual physical properties of much enhanced c/a, NTE and Curie temperature (TC)23,30,31. As the x = 0.0 for the 0.5PT-0.5BLxF, the c/a is significantly enhanced to 1.14 when compared with PT (c/a = 1.064). It is the highest in perovskites except those metastable compounds needed to be synthesized under high temperature and high pressure conditions. The extremely large lattice distortion is maintained by the strong Pb/Bi-O2 covalency which was evidenced by the experimental investigation on the electron-charge density distribution30. However, such giant lattice distortion is significantly reduced by the La substitution (see Supplementary Fig. S4). With increasing La content, the c axis is much reduced, while the a(b) axis is slightly increased. Thus, the c/a is significantly reduced. For example, the originally large c/a of 0.5PT-0.5BLxF is much reduced from 1.14 for the x = 0.0 to 1.057 for the x = 0.2. Since the coupling of PS and lattice is aligned along the c-axis direction, the large decrease in the c axis would imply weakened ferroelectric property. It is worth noting that even though the ionic radius of La3+ (1.36 Å) is essentially the same to Bi3+ (1.34 Å), the unit cell volume (V) apparently contracts by the substitution of La3+ (see Supplementary Fig. S4). The volume contraction is as large as 3.1% by the chemical modification from the x = 0.0 to 0.2. Such large volume contraction should dominate the NTE property.

The temperature evolution of unit cell volume for three compositions of 0.5PT-0.5BLxF (x = 0.0, 0.1 and 0.2) is shown in Fig. 1. It is interesting to observe that the NTE is significantly different from one another. Without the substitution of La, the 0.5PT-0.5BLxF with x = 0.0 represents a nonlinear and strong NTE in a wide temperature range of RT to 600 °C. It is similar to the composition of 0.4PT-0.6BF near the MPB23. In a lower temperature range (RT ~ 300°C), the unit cell volume shows little dependence on temperature with an average bulk CTE of = −0.83 × 10−5°C−1; However, it contracts dramatically at elevated temperatures with = −7.0 × 10−5°C−1 (300 ~ 600 °C). The average CTE of the overall temperature range (RT to 600 °C) is = −4.06 × 10−5 °C−1. The contraction of unit cell volume is as giant as −2.3% for the 0.5PT-0.5BLxF (x = 0.0). It worth noting that the NTE of 0.5PT-0.5BLxF (x = 0.0) is among the giant NTE materials, such as Mn3AN (−1.3%)17, BiNiO3 (−2.5 ~ −3.4%)9 and CuO nanoparticles (−1.1%)11. It also needs to note that the present giant NTE in the 0.5PT-0.5BLxF (x = 0.0) occurs in a wide temperature range (300 °C) which is broad than other giant NTE materials. For example, BiNiO3 has a colossal NTE over 80 °C9; (Mn0.96Fe0.04)3(Zn0.5Ge0.5)N shows a giant NTE over 70 °C17; and CuO nanoparticles exhibit a giant NTE over 170 °C11. It is interesting to observe that the giant NTE of 0.5PT-0.5BLxF can be distinctly weakened by the chemical substitution of La. For the x = 0.1, the NTE becomes linear below TC with a CTE of αV = −3.55 × 10−5°C−1 (RT ~ 500 °C). With further substitution of La content (x = 0.2), the unit cell volume only slightly contracts with increasing temperature. A very low thermal expansion is achieved in a wide temperature range (RT ~ 400 °C). Here, the CTE is αV = −0.71 × 10−5°C−1 for the x = 0.2. We can achieve that the NTE of 0.5PT-0.5BLxF can be tunable over a giant scale of CTE (−7.0 ~ −0.71 × 10−5°C−1) simply by adjusting La content. It is also important to note that such giant tunable range of CTE contains most known NTE materials7.

Figure 1
figure 1

Negative thermal expansion.

Unit cell volume of 0.5PbTiO3-0.5(Bi1-xLax)FeO3 (x = 0.0, 0.1 and 0.2) as function of temperature. FE and PE mean ferroelectric and paraelectric, respectively.

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What accounts for such giant-scale control of NTE in the single-phase 0.5PT-0.5BLxF? The NTE of the present 0.5PT-0.5BLxF, which is quantitatively described by the CTE in terms of , is actually dominated by the volume difference, , where and are unit cell volumes at RT and TC, respectively. As shown in Fig. 1, larger absolute value of means stronger NTE, while smaller one means weakened NTE. It is known that the unit cell volume reaches the minimum value at TC, due to the fact of NTE in the ferroelectric phase below TC whereas positive thermal expansion (PTE) in the paraelectric one above TC. Here, the is actually dominated by the ionic radius due to the loss of ferroelectricity. Above TC, the unit cell volume changes linearly, which is originated from lattice thermal vibration. The of the 0.5PT-0.5BLxF follows to a linear extrapolation of unit cell volume in paraelectric phase. However, the is strong different from one another. One can see that the strong NTE of the x = 0.0 is mainly due to considerably enhanced , while a near ZTE of the x = 0.2 is due to significantly reduced . The mechanism of NTE control over such giant scale would be elucidated according to the detailed studies on chemical bonding and hybridization, which will be discussed as follows.

The crystal structure at RT was refined based on Rietveld method by means of neutron powder diffraction. The experimental patterns can be well refined according to tetragonal structure model similar to PT and atomic positions could be stably calculated. It is known that the equilibrium lattice parameters of ferroelectricity are a balance of short-range repulsion favoring cubic paraelectric phase and long-range Coulomb force favoring ferroelectric one32. PS displacement is a key parameter to represent how ferroelectric property changes in a unit cell. Figure 2 represents the PS displacements at A-site (δzA) and B-site (δzB) for the 0.5PT-0.5BLxF as function of x. They are both reduced at a large content by the substitution of La, indicating a weakened ferroelectric property. For example, the δzA is reduced from 0.6903 Å of the x = 0.0 to 0.4619 Å of the x = 0.2 (Supplementary Table S1). The decrease in the PS displacements should originate from the significantly different ferroelectric activity of Bi and La atoms. It is known that Bi has the strongest ferroelectric activity (0.8 Å), whereas La has a very weak one (0.05 Å)29. The La substitution for Bi favors ionic bonding and would weaken the covalent hybridization of cations with oxygens, which can be also reflected from the change in the bond length (see Supplementary Fig. S5). With increasing content of La, chemical bonds of A-O2 and B-O1 (the shorter one) are elongated, indicating a weakened covalency and hybridization effect. For example, A-O2 and B-O1 of the x = 0.0 are 2.4287 Å and 1.7089 Å, respectively. However, those of the x = 0.2 are elongated to 2.5103 Å and 1.8268 Å, respectively. La substitution favors the formation of cubic paraelectric lattice and weakens the coupling between ferroelectricity and crystal lattice. Actually, there is a strong correlation between the PS displacement and the c axis (see Supplementary Fig. S6). The c axis is largely reduced by decreasing PS displacement. As a result, the VRT of 0.5PT-0.5BLxF is significantly reduced by the La substitution. Thus, the originally giant NTE of 0.5PT-0.5BLxF is strongly weakened by the La substitution.

Figure 2
figure 2

Spontaneous polarization property.

(a) PS displacements at A-site (δzA) and B-site (δzB) of 0.5PbTiO3-0.5(Bi1-xLax)FeO3 as function of La content (x). (b) The sketch of PS displacements of δzA and δzB in A-O12 and B-O6 polyhedra, respectively.

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The effect of La substitution on the covalent hybridization can be further supported by density function theory (DFT) calculation. Two compositions of 0.5PT-0.5BLxF (x = 0.0 and 0.25) were calculated in two 2 × 2 × 2 supercells of (Pb4Bi4)(Ti4Fe4)O24 and (Pb4Bi3La1)(Ti4Fe4)O24, respectively. The degree of hybridization can be quantitatively described by the value of minimum charge density (MED) of specific chemical bonds according to the valence-electron density distribution (Fig. 3). Without La substitution, there is a strong orbital hybridization for the strong NTE composition of 0.5PT-0.5BLxF (x = 0.0). The MED value of Bi-O2 bond is as high as 0.45 Å−3. However, the isovalent substitution of La for Bi weakens the hybridization behaviour for all chemical bonds, especially for the chemical bond of Bi-O2. Here, the MED value is reduced to 0.39 Å−3 for the composition of x = 0.25 which should have a similar low thermal expansion to the x = 0.2. The originally strong ferroelectric property cannot well be maintained anymore by the incorporation of weakly ferroelectric active La for strongly ferroelectric active Bi. And thus the PS displacements are all reduced (Supplementary Table S3). Therefore, due to the fact of much weakened ferroelectricity and a large reduction on the c axis, the of the 0.5PT-0.5BLxF significantly shrinks with increasing content of La.

Figure 3
figure 3

Valence electron-density distributions on the bc plane at x = 1/2 of supercell.

(a) (Pb4Bi4)(Ti4Fe4)O24 and (b) (Pb4Bi3La1)(Ti4Fe4)O24, which, respectively, corresponds to x = 0.0 and x = 0.25 of 0.5PbTiO3-0.5(Bi1-xLax)FeO3 through first-principle calculations. The dash line frame indicates the original lattice without La substitution. The 0% and 100% in color scale corresponds to 0.2 and 8Å−3, respectively and contours are from 0.2 to 4 Å−3 by step of 0.2 Å−3.

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Both detailed studies of crystal structure and first principle calculation have approved that there is a strong correlation between the ferroelectric property and the NTE for the 0.5PT-0.5BLxF. The present results further support the conclusion of the correlation between ferroelectricity and NTE, which was ever revealed by studies of lattice dynamics and temperature dependence of PS21,22. In order for quantitative characterization on the correlation between ferroelectricity and NTE, we introduce a new physical concept of spontaneous volume ferroelectrostriction to represent the contribution from ferroelectric property to NTE. Spontaneous volume ferroelectrostriction is defined as , where Vexp and Vnm are, respectively, unit cell volumes of experimental and nominal one. The nominal one of Vnm is calculated by extrapolation from paraelectric to ferroelectric phase. The Vnm can be basically considered as the volume component contributed from lattice thermal vibration. Therefore, the volume difference of Vexp − Vnm represents the quantitative contribution from ferroelectricity. Large value of means strong NTE, while small one means weak NTE. Similar to Landau theory33, here we plot the relationship of at RT for all investigated compositions of 0.5PT-0.5BLxF, where α is the coupling coefficient between and PS (Fig. 4). It is clearly to see that the shows a good correlation with the square of PS displacement (). On the one hand, strong ferroelectric property induces a large value of and thus produces a strong NTE such as for the x = 0.0 without La substitution. On the other hand, weakened ferroelectric property induces a small value of and produces a low thermal expansion such as for the composition of x = 0.2.

Figure 4
figure 4

The correlation between the spontaneous volume ferroelectrostriction () and spontaneous polarization.

There is a strong correlation of for the 0.5PbTiO3-0.5(Bi1-xLax)FeO3 ferroelectrics.

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Discussion

The present study gives a distinct guide to control thermal expansion of ferroelectrics. An effective way to control the NTE would benefit the CTE matching for different components of devices and composites. We can modulate the ferroelectric activity of cations to adjust the value of and thus control the thermal expansion of ferroelectrics. Strong NTE can be achieved by the substitutions of those cations with strong ferroelectric activity, such as Bi, Ti, Fe, Zn and Cd, while low thermal expansion by the substitution of cations with weak ferroelectric activity, such as La, Mg, Ni and Zr28. The present study also offers a useful way to achieve ZTE in the family of ferroelectrics. Actually, some of them have been previously experimentally observed to show such ZTE property, such as (Pb,La)TiO334 and well-known ferroelectric relaxor of Pb(Mg1/3Nb2/3)O315. It has been known for a long time that perovskite-type Pb-based relaxors exhibit near ZTE below the so-called Burns temperature (TB)15,35. Such near ZTE property could be understood according to the present concept of spontaneous volume ferroelectrostriction. As temperature cooling down from TB, the effect of spontaneous volume ferroelectrostriction is produced due to the frozen polar nanoregions (PNRs). Therefore, the normal thermal expansion is counteracted and thus near ZTE appears. Future studies could be focused on the precise control and fabrication of ZTE ferroelectric materials for technical application. The NTE control could be also extended to other important functional materials such as multiferroics, since NTE have both strong coupling with not only ferroelectric but also magnetic properties.

In summary, NTE of 0.5PT-0.5BLxF single-phase ferroelectrics is effectively controlled over a giant range from a strong NTE to a near ZTE by the chemical modification. The controllable NTE contains most NTE materials. The details of chemical bonds have been studied by neutron powder diffraction and DFT calculations. The facile control of NTE is strongly correlated to the tunable spontaneous volume ferroelectrostriction by modulating the ferroelectric activity of cations. Present study establishes an effective way to control thermal expansion of functional materials of ferroelectrics.

Methods

Sample preparation

Single-phase materials of 0.5PbTiO3-0.5(Bi1-xLax)FeO3 (x = 0.0, 0.1 and 0.2) were prepared by the conventional solid-state reaction method. The following raw materials were used: PbO, Bi2O3, TiO2, La2O3 and Fe2O3. The well-mixed raw materials were calcined at 750°C for 10 h. Then compacted pellets were sintered at 1100°C for 2 h covered with the powders of the same composition to compensate the loss of PbO and Bi2O3 during high temperature sintering process. The surface layers of sintered pellets were removed and then the sintered pellets were carefully crushed into fine powders.

Structure analysis

Room temperature neutron powder diffraction (NPD) was collected at the NIST Center for Neutron Research on the BT-1 high-resolution neutron powder diffractometer. The wavelength of synchrotron light was 1.5403 Å. The initial structural model of PbTiO3 (space group, P4mm) was adopted for the structural refinement performed on software Fullprof. The positions of Pb/Bi/La, Ti/Fe, O1 and O2 are 1a site at origin (0,0,0), 1b site at (1/2, 1/2, ZB), 1b site at (1/2, 1/2, ZO1) and 2c sites at (1/2, 0, ZO2)36, respectively. The high temperature X-ray diffraction (XRD) data were collected on an X-ray powder diffractometer (TTRIII, Rigaku, Japan) using Cu Kα radiation. The sample was maintained at a specified temperature for 10 min in order to reach thermal equilibrium. The scanning rate of angle 2θ was 4° min−1 and the heating rate was 10°C min−1. The lattice parameters were calculated using the software PowderX and TREOR.

DFT calculation

The electronic structure was calculated based on density functional theory (DFT) with generalized approximations (GGAs) performed with Vienna ab initio simulation package (VASP), in order to obtain the valence electron-density distribution of approximated 2 × 2 × 2 supercell of (Pb4Bi4)(Ti4Fe4)O24 and (Pb4Bi3La1)(Ti4Fe4)O24, corresponding to tetragonal compositions of 0.5PT-0.5BLxF (x = 0.0 and 0.25), respectively.