Supporting information for:

Zero thermal expansion and semiconducting properties in

PbTiO3-Bi(Co,Ti)O3 ferroelectric solid solutions

Zhao Pan,1 Jun Chen,1,*) Xingxing Jiang,2 Zheshuai Lin,2 Linxing Zhang,1 Longlong Fan,1

Yangchun Rong,1 Lei Hu,1 Hui Liu,1 Yang Ren,3 Xiaojun Kuang,4 Xianran Xing1,*)

1
Department of Physical Chemistry, University of Science and Technology Beijing, Beijing 100083,

China

2
BCCRD, Key Laboratory of Functional Crystals and Laser Technology,Technical Institute of

Physics and Chemistry, Chinese Academy of Sciences,Beijing 100190, China

3
X-Ray Science Division,Argonne National Laboratory, Argonne, Illinois 60439, United States

4
College of MaterialsScience and Engineering, Guilin University of Technology, Guilin 541004

People’s Republic of China

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1. Structural analysis

Figure S1. The SXPD of 0.7PT-0.3BCT, 0.6PT-0.4BCT, 0.5PT-0.5BCT, and 0.6PT-0.4BCT5 in a

selected short range of 2θ at RT. All investigated samples keep the tetragonal symmetry.

Figure S2. Rietveld full profile refinement of 0.7PT-0.3BCT at room temperature. Final observed

(red solid circles) and calculated (black line) SPD patterns are shown. The blue solid line exhibits

the difference profile, and the green marks show the reflection positions.

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Figure S3. Rietveld full profile refinement of 0.6PT-0.4BCT at room temperature. Final observed

(red solid circles) and calculated (black line) SPD patterns are shown. The blue solid line exhibits

the difference profile, and the green marks show the reflection positions.

Figure S4. Rietveld full profile refinement of 0.5PT-0.5BCT at room temperature. Final observed

(red solid circles) and calculated (black line) SPD patterns are shown. The blue solid line exhibits

the difference profile, and the green marks show the reflection positions.

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Figure S5. Rietveld full profile refinement of 0.6PT-0.4BCT5 at room temperature. Final observed

(red solid circles) and calculated (black line) SPD patterns are shown. The blue solid line exhibits

the difference profile, and the green marks show the reflection positions.

Figure S6. Temperature evolution of unit cell volume of 0.7PT-0.3BCT, 0.6PT-0.4BCT,

0.5PT-0.5BCT, and 0.6PT-0.4BCT5, respectively.

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Figure S7. Lattice parameters and unit cell volume of 0.6PT-0.4BCT5 as a function of

temperature.

2. Impedance spectrum analysis

Electrical behavior of the compounds has been characterized over a wide

temperature range as a function of frequency by using ac impedance methods.

Frequency dependence of imaginary component of impedance (Z″) at different

temperatures of 0.6PT-0.4BCT5 is shown in Figure S8a. The impedance spectrum is

characterized by the appearance of semicircular arcs whose pattern of evolution

changes with rise in temperature. The high frequency semicircles are attributed to the

bulk effects whereas the low frequency semicircles are attributed to the grain

boundary.1 Each semicircular arc in the impedance pattern can be attributed to a

parallel combination of resistance (R) and capacitance (C). The bulk effect arises due

to parallel combination of bulk resistance (Rg) and bulk capacitance (Cg) and the grain

boundary effects arises due to parallel combination of grain boundary resistance (Rgb)

and grain boundary capacitance (Cgb).2 Here, each curve exhibits two broadening

peaks, which are corresponding to two electrical components (RC elements) of the
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bulk (Rg) and grain boundary (Rgb), respectively.3 It can be seen that the peaks of the

plot shift towards higher frequency with rise in temperature. The variation of Z″ with

frequency indicates a relaxation mechanism in the material.1 The broadening of peaks

on increasing temperature confirms the existence of temperature dependent relaxation

in the material, which might be resulted from the presence of immobile

species/electrons at low temperature and defects/vacancies at higher temperatures.4

Furthermore, the magnitude of Z″ decreases gradually, and has a tendency to merge in

the high-frequency region with rise in temperature. This is an indication of the

presence of space charge polarization at lower frequency and disappearance at higher

frequency.5

Complex modulus formalism is a very important and convenient tool to detect the

bulk phenomena properties as apparent conductivity relaxation times.6 It provides an

insight into the electrical processes characterized by the smallest capacitance of the

material. To characterize the temperature dependence of the bulk capacitance of

0.6PT-0.4BCT5, we inspected impedance spectrum data using spectroscopic plots of

the imaginary component of the electric modulus (M″) in the appropriate temperature

range (Figure S8b). It is noticeable that for the same change in temperature, the

change in Z″ is much more marked than that of the M″ plots (Figure S8). These plots

also show that a well-defined relaxation mechanism is in operation in the investigated

temperature range. The peaks shift systematically towards higher frequencies with

increasing temperatures. A shift in fmax at constant M″max would imply variation in R

but not in C. On the contrary, the change in the value of M″max with no variation in

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fmax would suggest a change in R and C.3 However, our data indicates variations in

both M″max and fmax indicating a variation in C. It is thus clear that the combined

usage of impedance and modulus spectroscopy permits one to clearly distinguish

whether the change in sample resistance is associated with change in resistivity or

with a variation in volume fraction.

The frequency explicit plots of the imaginary parts of impedance and electric

modulus indicate departures from the ideal Debye behavior.7 In the ideal case the Z″

and M″ peaks should be coincident on the frequency scale. As can be seen, there

might be two peaks in the M″ vs logf plots for temperatures higher than 150 °C.

However, this cannot be confirmed since data was not acquired beyond 10 MHz. The

decrease in values of M″ as a function of temperature is a direct indication of

increasing capacitance.

Figure S8. Complex impedance plots of 0.6PT-0.4BCT and 0.6PT-0.4BCT5 at room temperature

with equivalent circuit (inset).

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Figure S9. (a) Temperature dependence of Z*plots, and (b) modulus (M″) vs log (frequency) plots

for 0.6PT-0.4BCT5.

3. X-ray photoelectron spectroscopy (XPS)

Figure S10. XPS patterns of Co 2p for (a) 0.6PT-0.40BCT and (b) 0.6PT-0.4BCT5.

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 Figure S11. XPS patterns of Ti 2p for (a) PbTiO3 and (b) 0.6PT-0.4BCT.

Figure S12. XPS patterns of O 1s for (a) 0.6PT-0.4BCT, and (b) 0.6PT-0.4BCT5. The O 1s peak is

composed of lattice oxygen (M) and oxygen vacancy (S).8

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4. Uv-Vis absorption spectrum

Figure S13. Plot of (αhv)2 vs. hv of Uv-Vis spectrum of PT and 0.6PT-0.4BCT5 powders. The

linear extrapolation gives a band gap of 2.8 eV and 1.5 eV for PT and 0.6PT-0.4BCT5,

respectively. The band gaps are calculated with absorb data and Tauc’s elations.

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Table S1. Refined structural parameters of the 0.7PT-0.3BCT, 0.6PT-0.4BCT, 0.5PT-0.5BCT, and

0.6PT-0.4BCT5.

Lattice Parameters (Å)

0.7PT-0.3BCT 3.91733(2) 4.14109(9) 1.057 63.55 6.51 2.04 10.2

0.6PT-0.4BCT 3.92779(4) 4.11920(8) 1.049 63.55 7.20 2.22 10.5

0.5PT-0.5BCT 3.93746(8) 4.09559(5) 1.040 63.50 8.16 2.23 13.3

0.6PT-0.4BCT5 3.92253(3) 4.14441(1) 1.056 63.77 6.70 2.52 7.04

Table S2. The average CTEs of 0.7PT-0.3BCT, 0.6PT-0.4BCT, and 0.6PT-0.4BCT5.

CTE (×10-6 °C-1)

0.7PT-0.3BCT -17.25 RT ~ 500°C

0.6PT-0.4BCT -7.41 RT ~ 450°C

0.6PT-0.4BCT5 -6.34 RT ~ 530°C

0.33 RT ~ 500°C

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Table S3 CTEs and the corresponding temperature ranges of representative ZTE materials.

Sample α V (×10-6 °C-1) Temperature range (°C)

Invar alloys9 3.6 5 ~ 30

Fe[Co(CN)6]10 -4.41 -268.8 ~ 27

Zr0.4Sn0.6Mo2O811 -0.18 -261 ~ 327

Mn3Cu0.5Ga0.5N12 0.354 -261 ~ -43

TaO2F13 0.87 25 ~ 500

N(CH3)CuZn(CH3)414 0.6 -73 ~ 127

(Sc0.85Ga0.05Fe0.10)F315 0.702 27 ~ 627

0.6PT-0.4BCT5 0.33 25 ~ 500

Table S4. Spontaneous polarization (PS) of the 0.7PT-0.3BCT, 0.6PT-0.4BCT, 0.5PT-0.5BCT, and

0.6PT-0.4BCT5, determined by the structural refinement.

Composition δzA (Å) δzB (Å) PS (µC cm-2)

0.7PT-0.3BCT 0.5156 0.3263 60.3

0.6PT-0.4BCT 0.5076 0.3131 59.1

0.5PT-0.5BCT 0.5012 0.3090 58.9

0.6PT-0.4BCT5 0.5238 0.3080 59.4

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