Influence of Er substitution for La on the thermal conductivity of (La1−xErx)2Zr2O7 pyrochlores

Accepted Manuscript Title: Influence of Er substitution for La on the thermal conductivity of (La1−x Erx )2 Zr2 O7 pyrochlores Author: Yonghe Zhang Min Xie Fen Zhou Xiangzhong Cui Xingeng Lei Xiwen Song Shengli An PII: DOI: Reference:

S0025-5408(14)00821-6 http://dx.doi.org/doi:10.1016/j.materresbull.2014.12.064 MRB 7931

To appear in:

MRB

Received date: Revised date: Accepted date:

23-1-2014 4-10-2014 23-12-2014

Please cite this article as: Yonghe Zhang, Min Xie, Fen Zhou, Xiangzhong Cui, Xingeng Lei, Xiwen Song, Shengli An, Influence of Er substitution for La on the thermal conductivity of (La1-xErx)2Zr2O7 pyrochlores, Materials Research Bulletin http://dx.doi.org/10.1016/j.materresbull.2014.12.064 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Influence of Er substitution for La on the thermal conductivity of (La1-xErx)2Zr2O7 pyrochlores Yonghe Zhanga, Min Xiea, Fen Zhoua, Xiangzhong Cuib, Xingeng Leib, Xiwen Songa,, Shengli Ana a

Inner Mongolia Key Laboratory of Advanced Ceramics and Device, School of Materials and

Metallurgy, Inner Mongolia University of Science and Technology, Baotou 014010, China Beijing Aeronautical Manufacturing Technology Research Institute, Beijing 100095, China

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 Corresponding author: Tel.: +86 4726896122; fax: +86 4725951571.

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E-mail. [email protected] (X.W.Song)

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Graphical abstract

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The substitution of Er3+ for La3+ effectively reduces the thermal conductivity of La2Zr2O7.

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With the increasing Er3+ content, the thermal conductivity significantly decreases at lower

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temperatures. At higher temperatures, however, the thermal conductivity of the

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(La1-xErx)2Zr2O7 becomes similar, indicating that the thermal conductivity is less sensitive to

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composition variation.

Highlights ► ● The substitution of Er3+ for La3+ reduces the thermal conductivity of La2Zr2O7. ► ● The thermal conductivity reveals a nearly temperature-independent behavior. ► ● A novel phonon scattering source (rattlers) was found in this study. ► ● The rattlers are more efficient in scattering low frequency phonons. ► ● The present study also provides a novel way to reduce the thermal conductivity.

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Abstract

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The influences of Er2O3 doping on the structure and thermo-physical properties of La2Zr2O7

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were investigated. The (La1-xErx)2Zr2O7 ceramics were synthesized by a solid state reaction method. The XRD results indicate that they all consist of the pure pyrochlore structure. The

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SEM results show that the microstructure of the sintered ceramics is dense and the grain

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boundaries are clean. The average thermal expansion coefficients of the (La1-xErx)2Zr2O7

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ceramics range from 9.57 ×10-6 K-1 to 9.66×10-6 K-1. The substitution of Er3+ for La3+

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effectively reduces the thermal conductivity of La2Zr2O7. With the increasing Er3+ content, the

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thermal conductivity significantly decreases at lower temperatures. At higher temperatures,

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however, the thermal conductivity of the (La1-xErx)2Zr2O7 becomes similar, indicating that the thermal conductivity is less sensitive to composition variation. In addition, for the

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composition with x=0.10, the thermal conductivity reveals a nearly temperature-independent

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behavior, which should be ascribed to the strong phonon scattering source (rattlers). Keywords: (La1-xErx)2Zr2O7 ceramics; Pyrochlore structure; Thermal conductivity; Thermal barrier coatings.

1. Introduction In order to further increase the operating temperature of gas engines, thermal barrier coatings (TBCs) are significantly applied to the surfaces of the blade, which can result in a higher system efficiency, lower emissions, and lower fuel consumption[1,2]. Moreover, thermal barrier coatings (TBCs) can also decrease the temperature of the metal substrate, which is beneficial for improving of the reliability and durability of the metallic components

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in advanced engines [3]. So far, the 6-8 wt.%Y2O3 partially stabilized ZrO2 (6-8YSZ) topcoat

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ceramic is the most widely used material in gas turbines. However, it is not suitable for the

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long-term application at temperatures above 1200 oC due to its low sintering resistance and

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poor phase structure stability, which will increase the thermal conductivity and significantly

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reduce the coatings durability [4-7]. Therefore, it is urgently desired to develop new topcoat

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applications higher than 1200 oC[5,6].

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ceramics with a remarkably lower thermal conductivity and better sintering resistance for

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Recently, the pyrochlore-type Ln2Zr2O7 (Ln=La,Nd,Sm,Eu,Gd,etc.) rare earth zirconates

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have been suggested an promising candidates for the topcoat ceramics due to their excellent

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thermophysical properties. For instance, the pyrochlore oxide of lanthanum zirconate

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(La2Zr2O7) exhibits high melting point, relatively high coefficient of thermal expansion, excellent thermal stability, low sintering rate and lower thermal conductivity, which make it

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more suitable for application as high-temperature thermal barrier coatings (TBCs)[8-11]. The La2Zr2O7 pyrochlore structure is considered to be a network consisting of corner linked of ZrO6 octahedral with La atoms filling the interstices[12]. The doping of La2Zr2O7 with one or more trivalent rare earth oxides will introduce point defects, enhance the point defect phonon

scattering and thereby lower the thermal conductivity [2,13-15]. Recently, a novel strong phonon scattering source (rattlers) has been suggested in Y2O3 or Yb2O3 doped La2Zr2O7 ceramics, which plays a dominant role in the glass-like thermal conductivity. The pyrochlore lattice has unique oversized oxygen cages AO8, if the smaller Yb3+ and Y3+ cations (rattlers) are introduced, they will occupy the AO8 cage centers, and AO8 cages become more spacious, resulting in the smaller Yb3+ and Y3+ ions vibrating locally and independently, which leads to

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a strong phonon scattering, and thus the thermal conductivity is significantly

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decreased[16,17]. Point defects are merely valid in scattering high frequency phonons

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(  D   4 ), however, the rattlers are more efficient in scattering low frequency phonons,

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significantly contributing to the reduction of the lattice thermal conductivity [18]. This

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provides a novel and quite intriguing approach to acquire low thermal conductivity. So far,

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the study on the association of rattlers scattering with the low thermal conductivity in this

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system is in the initial stage. The relation between the existence of rattlers and the substituting

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species of cations and the influence of various substituting cations on the thermal

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conductivity for this system have not been clearly understood. Therefore, it is essential to

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give further investigations on the effects of the A-site substitution on the rattling scattering

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and the glass-like thermal conductivity. The ionic radii Er3+ with eight-fold coordination (0.1004 nm) is similar to those of Yb3+ (0.0985 nm) and Y3+ (0.1019 nm) ions, which are all

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smaller than La3+ ion. In addition, Er3+ is more heavier than La3+. Thus, the smaller Er3+ ion is introduced into the La2Zr2O7 pyrochlore, the mass disorder and the ionic radius difference between the guest and the host ions will improve the phonon–point defect scattering[19,20]. Particularly, Er3+ potentially play a role similar to Y3+ and Yb3+, exiting strong phonon

scattering (rattlers scattering), and thereby a glass-like thermal conductivity will be obtained. To achieve this objective, the Er3+ ion was to partially substitute for the La3+ ion in the A-site. The phase structure and thermophysical properties of the (La1-xErx)2Zr2O7 (x=0, 0.02, 0.04, 0.06, 0.08 and 0.10, respectively) ceramics were investigated and the reason for the low thermal conductivity found in this system was discussed. 2. Experimental

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2.1 Sample preparation

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The (La1-xErx)2Zr2O7 (x=0, 0.02, 0.04, 0.06, 0.08 and 0.10) ceramics were synthesized by a

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solid state reaction method. The reactants of high-purity(≥99.99%) La2O3, ZrO2 and Er2O3

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were preheat-treated at 800 oC for 2h before weighing in order to remove any absorbed water.

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The stoichiometric constituents of (La1-xErx)2Zr2O7 were mixed by ball-milling in ethanol for

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24 h and dried at 70 oC for 12h, then the dried mixtures were sintered at 1500 oC for 6h for the

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solid state reaction. The calcined powders were again ball-milled in ethanol for 24h and dried

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at 70 oC for 12h to evaporate the ethanol. The resultant powders were dry-pressed into disk

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shapes at 20 Mpa, followed by cold isostatic pressing at 200 Mpa into pellets, then sintered at

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1600 oC for 5h in air.

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2.2 Structure characterization The phase structure of the synthesized samples was determined by X-ray diffraction(XRD,

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Bruker, D8 Advance) with Cu Kα radiation. The lattice parameters were determined by a slow scanning XRD over the range 20–80o with the rate of 0.02o s-1. The microstructure of the ceramics was examined using scanning electron microscopy (SEM, HITACHI JM-6510). The bulk density of the sintered samples was measured by Archimedes principle. The theoretical

densities of the solid solutions were calculated using the lattice volume and molecular weights of the unit cells. 2.3 Thermal properties measurement The linear thermal expansion coefficients (TECs) of these ceramics were measured with a high-temperature dilatometer (Netzsch DIL 402C) from ambient temperature to 1300 oC at a heating rate of 5 oC /min in air. The size of the samples was approximately

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25mm×3mm×4mm. The thermal diffusivity of the synthesized samples was measured by the

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laser-flash method (Netzsch LFA 457) in the range between ambient and 1000 oC in a vacuum.

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The present samples were about 12.5mm in diameter and 2mm in thickness. Before the

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thermal diffusivity measurements, both the front and rear surfaces of the ceramics were

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coated with a thin layer of colloidal graphite, which can enhance the absorption of the laser

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beam at the front surface and prevent direct transmission of the laser beam through the

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translucent specimens at high temperatures. The thermal diffusivity measurement was

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performed three times at each corresponding temperature. The specific heat capacity of the

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samples was calculated from one of the constituent oxides according to the Neumann–Kopp

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rule based on the reference specific heat values of La2O3, ZrO2 and Er2O3 [21,22]. The

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thermal conductivities (λ) of the samples were calculated by the following equation with the specific heat capacity(Cp), bulk density (ρ) and thermal diffusivity (α).

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   . .C P

(1)

Because the sintered samples were not fully (100%) dense, the measured values of the thermal conductivities were corrected for the actual data λ0 using the relation[7]: 4  0  1   3

(2)

where φ is the fractional porosity and determined by the relation   1    t , ρt is the theoretical density of the sintered specimens, and ρ is the bulk density. 3. Results and discussion 3.1 Phase structure The XRD patterns of the (La1-xErx)2Zr2O7(x=0, 0.02, 0.04, 0.06, 0.08, 0.10) ceramics sintered at 1600 oC for 5h are shown in Fig.1. The pure La2Zr2O7 ceramic has a single

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pyrochlore structure, which is characterized by the presence of superstructure peaks at 2θ

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values of about 27°(311), 37° (331) and 45° (511) using Cu Kα radiation[23]. It can be seen

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that the XRD patterns of the synthesized samples agree with the standard XRD spectra of La2Zr2O7. Therefore, Er3+ dissolves in the La2Zr2O7 lattice to form a pyrochlore-type solid

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solution. In addition, the partial substitution of Er3+ for La3+ results in a decreased lattice

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parameter, because the ionic radius of La3+(0.116nm) is greater than that of Er3+(0.1004nm).

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The lattice parameter and ionic radius for (La1-xErx)2Zr2O7 ceramics are listed in Table1.

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In the Ln2Zr2O7 system, the crystal structure is mainly determined by the ionic radius ratio

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r(Ln3+)/r(Zr4+) of the Ln and Zr cations. The pyrochlore structure in the zirconates is limited

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to the range of 1.46≤r(Ln3+)/r(Zr4+)≤1.78, and defective fluorite oxides will form if

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r(Ln3+)/r(Zr4+) is lower than 1.46,while it will transform into the monoclinic phase higher than 1.78[12,24]. For the complex rare-earth zirconates, the ionic radius ratio can be

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calculated by the following equation [25]:

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r ( Ln 3 ) (1  x)r ( La 3 )  xr ( Er 3 )  r ( Zr 4 ) r (Zr 4 )



(3)

The values of r(Ln3+)/r(Zr4+) of the (La1-xErx)2Zr2O7 (x=0,0.02,0.04,0.06,0.08,0.10) ceramics calculated according to Eq.(3) are 1.6111,1.6068,1.6024,1.5981, 1.5938 and 1.5894,

respectively. It also indicates that the (La1-xErx)2Zr2O7 ceramics have a pyrochlore crystal structure. 3.2 Microstructure Fig.2 shows the typical microstructure of the sintered ceramics, since the microstructure of these ceramics is very similar, Fig.2 (a) and Fig.2 (b) present the microstructure of the (La0.96Er0.04)2Zr2O7 and (La0.90Er0.10)2Zr2O7 ceramics, respectively. It can be seen from Fig.2,

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the size of grains of these ceramics is several micrometers and the grain boundaries are clean.

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It is also observed that the sintered ceramics are dense. In addition, the bulk densities (ρ) of

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(La1-xErx)2Zr2O7 ceramics measured by Archimedes principle are listed in Table 2, the

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measurement uncertainty is estimated to be about 0.5%. It can be seen from Table 2, the bulk

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densities of (La1-xErx)2Zr2O7 (x=0.02-0.10) ceramics are all higher than La2Zr2O7 ceramic,

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3.3 Thermal expansion coefficient

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and the relative densities (p) of (La1-xErx)2Zr2O7 ceramics are between 94.25 and 97.58%.

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The linear thermal expansion coefficients of the (La1-xErx)2Zr2O7 ceramics are drawn in Fig.3.

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The linear thermal expansion coefficients of (La1-xErx)2Zr2O7 increase as the temperature

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increases. The linear thermal expansion coefficient is determined by the average distance

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between the particles among the lattice for solid materials. Therefore, with the increase in temperature, the lattice vibration is intensified, the average distance between particles among

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the lattice is increased, which results in increasing linear thermal expansion coefficients. Fig.3 also indicates that the thermal expansion coefficients of (La1-xErx)2Zr2O7 and La2Zr2O7 are very similar at each temperature. For instance, their values range from 9.62 to 9.80×10-6 K-1 at 800 oC, and the average thermal expansion coefficients are 9.57 ~ 9.66×10-6

K-1. According to the thermal expansion theory of a solid, the thermal expansion coefficient is proportional to the average distance between particles among the lattice which is related to the intensity of the ionic bonds of elements composing the crystal [26]. The strength of the ionic bond is given by the following equation [27]:

I A B  1  e  ( x A  xB )

2

/4

(4)

where IA-B is the strength of the ionic bond between cations at sites A and B, xA is the average

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electronegativity of cations at site A, and xB is the average electronegativity of cations at site

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B. According to Eq.(4),the thermal expansion coefficients increase with the decreasing

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electronegativity difference between the cations at sites A and B. Because the electronegativity of Er3+ ions (1.24) is higher than La3+ ions (1.11), substituting the Er3+ ions

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for the La3+ ions partially increased the average electronegativity of ions at A sites, which

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results in the decreasing electronegativity difference between cations at sites A and B, that is,

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higher thermal expansion coefficients will be achieved. For the (La1-xErx)2Zr2O7

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(x=0,0.02,0.04,0.06,0.08,0.10) ceramics, the average electronegativity of the cations at site A

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are 1.11, 1.1126, 1.1152, 1.1178, 1.1204 and 1.123, respectively, and the average

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electronegativity of the cations at site B(Zr4+) is 1.33. Thus, the intensity of ionic bonds

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between cations at sites A and B calculated according to eq.(4) are 0.012, 0.0117, 0.0115, 0.0112, 0.0109 and 0.0107, respectively. Since the content of Er2O3 is low and the difference

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between the electronegativity between Er3+ ions (1.24) and La3+ ions (1.11) is tiny, which result in the strength of the ionic bonds between cations at sites A and B are very close. Consequently, the average thermal expansion coefficients of (La1-xErx) 2Zr2O7 ceramics are quite similar.

3.4 Thermal conductivity Fig.4 shows the composition-dependent thermal diffusivities of the (La1-xErx) 2Zr2O7 ceramics measured by the laser flash method. Before the calculation of the thermal conductivity, the specific heat capacities of the (La1-xErx)2Zr2O7 ceramics at various temperatures are calculated according to the Neumann-Kopp law[21,22]. The calculated thermal conductivities of the (La1-xErx)2Zr2O7 ceramics are shown in Fig.5.

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The thermal conductivity of La2Zr2O7 shows inverse temperature dependence, which suggests

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a dominant phonon conduction behavior in most polycrystalline materials [10]. In addition,

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the Er3+ doping effectively reduce the thermal conductivity of La2Zr2O7. With the increasing

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Er3+ content, the thermal conductivity significantly decreases at the lower temperatures, while

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the thermal conductivity of (La1-xErx)2Zr2O7 becomes close at the higher temperatures, that is,

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the thermal conductivity is less sensitive to the composition. Furthermore, for the composition

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x=0.10, the thermal conductivity shows a nearly temperature-independent behavior, which is

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unique for most polycrystalline solids. The marked features of the temperature-and

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composition-insensitive thermal conductivity mean that the (La1-xErx)2Zr2O7 ceramic with

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x=0.10 exhibit a glass-like thermal conductivity behavior.

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The lattice contribution of the thermal conductivity can be written as[28]:

1 max C ( , T ) v( )l ( , T ) d 3 0

(6)

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Where ω is the phonon frequency, C is the specific heat, v is the phonon velocity and l is the phonon mean free path. Based on the Debye approach, C is proportional to ω2 (C=X·ω2, X is a constant) when the temperature higher than Debye temperature, v equals the sound velocity and ωmax is the Debye frequency.

According to the phonon scattering mechanism of the thermal conductivity for insulated crystalline solids, the phonon-scattering processes mainly include phonon-phonon scattering, point defect scattering and grain boundary scattering [29]. Since the mean phonon free path of TBC materials is significantly smaller than the grain size [30], the effect of boundary scattering can be ignored. Thus, the phonon-phonon (Umklapp) scattering and point defect scattering dominate the mean phonon free path. However, there exists unique oversized

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oxygen cages, AO8, in the La2Zr2O7 pyrochlore lattice, and a strong phonon scattering

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(rattlers ) will be found when the La3+-site is substituted by other smaller rare earth

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cations(Yb3+ and Y3+).The rattlers can strongly scatter the low frequency phonons and thereby

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impede the heat transport[16,17]. As a result, the mean phonon free path l(ω) is determined by

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the phonon-phonon (Umklapp) scattering, point defect scattering and rattler scattering, their

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(7)

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1 1 1 1    l ( ) lU ( ) l P ( ) l R ( )

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relation is:

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Where, lU(ω), lP(ω) and lR(ω) are the phonon mean free path due to the phonon-phonon (Umklapp) scattering, point defect scattering and rattler scattering, respectively. The

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individual phonon mean free path can be expressed as[31,32]: (8)

1 c 4  l P ( ) D P

(9)

1 2  l R ( ) r (( R ) 2   2 ) 2

(10)

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1  2T  lU ( ) DU

where, DU and DP are parameters independent of the temperature and frequency, c is the

defects concentration, r is a constant and ωR is the resonant frequency. Considering the effect of point defects on the phonon mean free path, Eq. (6) can then be written as[33]:  A 0  arctan 1 T D  0

 A     D 1       3T1 1  1  0    1

2      1    D 

(11)

Where DP T DU c

Q

2 

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M  1 3 k B3  3D  3  2

(14)

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DU

T1 

(13)

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2

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1 1        2 4   0 

1   0

A

(12)

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0 

l min  D 

(15)

A

2

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In the above expressions, the coefficient A is determined by the fundamental constants,

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ωD is the Debye frequency, T1 is the characteristic temperature, lmin is the minimum mean free

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path of phonons, Q is a numerical constant, whose value were proposed by Klemens (Q=1.61),

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M is the average atom mass, Ω is the average atomic volume, kB is the Boltzmann constant,

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ΘD is the Debye temperature,  is Planck’s constant and γ is the Grüneisen constant .   has been proposed to be minimum phonon mean free path-related and can be written as:

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 

DU l min T

(16)

In summary, the Eq. (11) can also be rewritten as:





A A 2 2 2 A T1  0. 5 arctan  0.5  0.5 1  T1 T 2  1  1  T1 T 2 1.5 3T1 T 3 T 







1.5

(17)



4c D2 DU 2 c 0 M D  cNMv 2    0 . 544 DP 4 2 k B 2 kB 2

(18)

where, α is a temperature-sensitive parameter of the thermal conductivity, N is the number of atoms per unit cell, Ω0 is the unit cell volume and Г is the scattering coefficient. Since α = 0 for the La2Zr2O7 pyrochlore, Eq. (17) can be simplified to:



A 2 AT10.5  3T1 3T 1.5

(19)

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Following Wang,Y. F.[16], a very high value of α suggests a flat λ-T curve and thereby a

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temperature-insensitive λ. For this reason, we calculate the coefficient A firstly using equation

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(14), and then fit the thermal conductivity according to expressions (17) and (19). The

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essential fitting parameter values are listed in Table 2, in which E is the Young’s modulus. The

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fitting results are well in accordance with the calculated thermal conductivities, as presented

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in Fig.6. The fitting values are listed in Table 2, the α value remarkably increases with

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increasing of Er3+ ion content, which indicates a temperature-insensitive thermal conductivity

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behavior for the higher doping concentration of Er3+ ion. Furthermore, the equation (18)

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suggests that the parameter value α is directly related to the scattering coefficient Г. The

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phonon scattering coefficient Г can be expressed as[34,35]: (20)

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2  M  2       x1  x            M 

A

in which x is the concentration of Er3+, ε is a parameter describing the contributions of all the other factors other than the mass difference to the phonon scattering coefficient, which is less than 200 for typical ceramic materials[34,36]. M  M La  M Er , M  1  x M La  xM Er ,    La   Er and   1  x  La  x Er , where M and  are the mass and ionic radius of La or Er, respectively. The ε values are calculated using equation (20) along with the fitting

parameter α, are listed in Table 3. Extraordinarily high ε values (higher than 200) are obtained for the (La1-xErx)2Zr2O7 (x=0.02-0.10) solid solutions. This means that an extra strong phonon scattering source-rattler scattering is present in the (La1-xErx)2Zr2O7 ceramics[16,17]. Given that the variation in the thermal conductivity across the (La1-xErx)2Zr2O7 ceramics is mainly determined by point defect scattering, however, above the Debye temperature, the

containing defects and La2Zr2O7 ceramic can be expressed as[37]:

(21)

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 d tan 1 u   p u

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relation between the lattice thermal conductivity of (La1-xErx)2Zr2O7 (x=0.02-0.10) ceramics

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where  d and  p are the lattice thermal conductivity of (La1-xErx)2Zr2O7 (x=0.02-0.10) and

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La2Zr2O7 ceramics, respectively, and the parameter u is determined by the relation[37]: 1

(22)

A

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  2D 2  u     p 2 hv  

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in which h represent the Planck’s constant.

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First, using a normal ε value (ε =196) in equation (20), the scattering coefficient Г can be

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obtained, then the lattice thermal conductivity  d will be calculated according to equations

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(21) and (22), which are shown in Fig.7. It is known from Fig.7 that the thermal conductivity

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reduction ascribed to rattlers could be separated from point defect effects, if there are no rattler scattering in the thermal conductivity reductions, the two curves of thermal

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conductivity should be similar. Therefore, there exists a novel strong phonon scattering source (rattlers) in (La1-xErx)2Zr2O7 pyrochlores, and with increasing Er3+ content, the thermal conductivity remarkably decreases at the lower temperatures, which means rattlers are more efficient in scattering low frequency phonons[18]. However, the thermal conductivities

become similar ( A 3T1 ) at the high temperature, which is decided by expressions (17) and (19), and the influence of the rattler scattering becomes minimal. Meanwhile, it also provides a novel way to reduce the thermal conductivity by introducing rattlers into the A2B2O7-type pyrochlores lattice. 4. Conclusions Pure (La1-xErx)2Zr2O7 ceramics with a pyrochlore structure are synthesized by a solid state

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reaction at 1600 oC for 5h.The average thermal expansion coefficients of the (La1-xErx)2Zr2O7

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ceramics range from 9.57 ×10-6 K-1 to 9.66×10-6K-1. The substitution of Er3+ for La3+

SC

effectively reduces the thermal conductivity of La2Zr2O7. Particularly, for the composition

U

with x=0.10, the thermal conductivity shows a nearly temperature-independent behavior, and

N

a novel strong phonon scattering source (rattlers) is found in the (La1-xErx)2Zr2O7 pyrochlore,

A

which plays the dominant role in the extremely low thermal conductivity. The present study

TE

Appendices

D

peculiar pyrochlore structure.

M

also provides a novel approach to acquire a low thermal conductivity closely related to the

EP

The abbreviations are used in the manuscript

CC

1. a – The lattice parameter for (La1-xErx)2Zr2O7 ceramics 2. V – The lattice volume for (La1-xErx)2Zr2O7 ceramics

A

3. rA – The average ionic radius of cations at site A for (La1-xErx)2Zr2O7 ceramics 4. rB – The average ionic radius of cations at site B for (La1-xErx)2Zr2O7 ceramics 5. ρt – The theoretical density of the sintered specimens 6. ρ – The bulk density of the sintered specimens

7. p – The relative density of the sintered specimens 8. φ – The fractional porosity of the sintered specimens 9. Cp – The specific heat capacity of the sintered specimens 10. λ – The thermal conductivity of the sintered specimens 11. IA-B – The strength of the ionic bond between cations at sites A and B for (La1-xErx)2Zr2O7 ceramics

PT

12. xA – The average electronegativity of cations at site A for (La1-xErx)2Zr2O7 ceramics

RI

13. xB – The average electronegativity of cations at site B for (La1-xErx)2Zr2O7 ceramics

SC

14. M – The average atom mass of (La1-xErx)2Zr2O7 ceramics

U

15. Ω – The average atomic volume of (La1-xErx)2Zr2O7 ceramics

N

16. ΘD – The Debye temperature

M

18. v – The phonon velocity

A

17. γ – The Grüneisen constant

D

19. DU , DP – The parameters independent of the temperature and frequency

TE

20. c – The defects concentration

EP

21. ω – The phonon frequency

CC

22. ωR – The resonant frequency 23. N – The number of atoms per unit cell

A

24. Ω0 – The unit cell volume 25. l – The phonon mean free path 26. ωD – The Debye frequency 27. E – The Young’s modulus

28. T1 – The characteristic temperature 29. lmin – The minimum mean free path of phonons 30. α – A temperature-sensitive parameter of the thermal conductivity 31. Г– The scattering coefficient 32. ε – A parameter describing the contributions of all the other factors other than the mass difference to the phonon scattering coefficient

PT

33.  d ,  p – The lattice thermal conductivity of (La1-xErx)2Zr2O7 (x=0.02-0.10) and

SC

RI

La2Zr2O7 ceramics, respectively

U

Acknowledgements

N

The authors gratefully acknowledge the financial support for this research by the National

A

Natural Science Foundation of China under Grant No. 50974074, Program for New Century

M

Excellent Talents in University under Grant No. NCET-10-0910 and Natural Science

EP

TE

D

Foundation of Inner Mongolia under Grant No. 2011ZD09.

CC

References

[1] G. Suresh, G. Seenivasan, M. V. Krishnaiah, P. S. Murti, J. Alloy Compd. 269 (1998) 9-12.

A

[2] N. P. Bansal, D. M. Zhu, Mater. Sci. Eng. A 459 (2007) 182-195. [3] N. P. Padture, M. Gell, E. H. Jordan, Science 296 (2002) 280-284. [4] W. Beele, G. Marijnissen, A. Van Lieshout, Surf. Coat. Technol. 120-121 (1999) 61-67. [5] M. Belmonte, Adv. Eng. Mater. 8 (2006) 693-703.

[6] U. Schulz, J. Am. Ceram. Soc. 83 (2000) 904-910. [7] C. G. Levi, Curr. Opin. Solid State Mater. Sci. 8 (2004) 77-91. [8] X. Q. Cao, R. Vassen, D. Stoever, J. Eur. Ceram. Soc. 24 (2004) 1-10. [9] R. Vassen, X. Q. Cao, F. Tietz, D. Basu, D. Stover, J. Am. Ceram. Soc. 83 (2000) 2023-2028. [10] H. M. Zhou, D. Q. Yi, Z. M. Yu, L. R. Xiao, J. Alloys Compd. 438 (2007) 217-221.

PT

[11] B. Saruhan, P. Francois, K. Fritscher, U. Schulz, Surf. Coat. Technol. 182 (2/3) (2004)

RI

175-183.

SC

[12] M. A. Subramanian, G. Aravamudan, G. V. Subba Rao, Prog. Solid State Chem.15 (1983)

U

55-143.

N

[13] M. R. Winter, D. R. Clarke, J. Am. Ceram. Soc. 90 (2) (2007) 533-540.

A

[14] J. Wang, S. X. Bai, H. Zhang, C. R. Zhang, J. Alloy Compd. 476 (2009) 89-91.

M

[15] Z. G. Liu, J. H. Ouyang, Y. Zhou, J. Li, X. L. Xia, J. Eur. Ceram. Soc. 29 (2009) 647-652.

D

[16] Y. F. Wang, F. Yang, P. Xiao, Acta Mater. 60 (2012) 7024-7033.

TE

[17] C. L. Wan, W. Zhang, Y. F. Wang, Z. X. Qu, A. B. Du, R. F. Wu, W. Pan, Acta Mater.

EP

58 (2010) 6166-6172.

CC

[18] M. Zebarjadi, K. Esfarjani, J. Yang, Z. F. Ren, G. Chen, phys. rev. B 82 (2010) 195207-195212.

A

[19] X. G. Chen, S. S. Yang, H. S. Zhang, G. Li, Z. J. Li, B. Ren, X. D. Dang, H. M. Zhang, A. Tang, Mater. Res. Bull. 51 (2014) 171-175. [20] C. Bryan, C. A. Whitman, M. B. Johnson, J. F. Niven, P. Murray, A. Bourque, H. A. Dabkowska, B. D. Gaulin, M. A. White, Phys. Rev. B 86 (2012) 054303-054309.

[21] P. J. Spencer, Thermochim. Acta 314 (1998) 1-21. [22] J. Leitner, P. Chuchvalec, D. Sedmidubsky, A. Strejc, P. Abrman, Thermochim. Acta 395 (2003) 27-46. [23] B. P. Mandal, A. K. Tyagi, J. Alloys Compd. 437 (1–2) (2007) 260-263. [24] N. Hanako, H. Yamamura, T. Aarai, K. Kakinuma, K. Nomura, J. Ceram. Soc. Jpn. 112 (2004) 541-546.

PT

[25] H.Yamamura, H. Nishino, K. Kakinuma, K. Nomura, Solid State Ionics 158 (2003)

RI

359-365.

SC

[26] J. X. Wang, L. P. Li, B. J. Campbell, Z. Lv, Y. Ji, Y. F. Xue, W. H. Su, Mater. Chem.

U

Phys. 86 (2004) 150-155.

N

[27] H. S. Zhang, Z. J. Li, Q. Xu, F. C. Wang, L. Liu, Adv. Eng. Mater. 10 (2008) 139-142.

A

[28] P. G. Klemens, in: R. P. Tye. (Eds), Thermal Conductivity, Theory of the Thermal

M

Conductivity of Solids, Academic Press, New York, 1969, p. 1-68.

D

[29] P. G. Klemens, M. Gell, Mater. Sci. Eng. A 245 (2) (1998) 143-149.

TE

[30] D. R. Clarke, C. G. Levi, Annu. Rev. Mater. Res. 33 (2003) 383-417.

EP

[31] P. G. Klemens, Proc. Phys. Soc. 73 (1955) 1113-1128.

CC

[32] Y. G. Wang, X. F. Xu, J. H.Yang, Phys. Rev. Lett. 102 (2009) 175508-175511. [33] R. Mévrel, J. C. Laizet,

A. Azzopardi,

B. Leclercq,

M. Poulain, O. Lavigne, D.

A

Demange, J. Eur. Ceram. Soc. 24 ( 2004) 3081-3089. [34] B. Ables, Phys. Rev. B 131 (1963) 1906-1911. [35] G. A. Slack, Phys. Rev. 126 (1962) 427-441. [36] C. L. Wan, W. Pan, Q. Xu, Y. X. Qin, J. D. Wang, Z. X. Qu, M. H. Fang, Phys. Rev. B

74 (2006) 1-9. [37] J. Callayway, H. C. von Baeyer, Phys.Rev. 120 (4) (1960) 1149-1154.

Figure 1 X-ray diffraction patterns of the (La1-xErx)2Zr2O7 ceramics

PT

Figure captions

RI

Figure 2 Microstructure of the sintered ceramics (a) (La0.96Er0.04)2Zr2O7 and (b)

SC

(La0.90Er0.10)2Zr2O7

U

Figure 3 Thermal expansion cofficients of (La1-xErx)2Zr2O7 ceramics

N

Figure 4 Thermal diffusivity of (La1-xErx)2Zr2O7 ceramics

A

Figure 5 Thermal conductivity of (La1-xErx)2Zr2O7 ceramics

M

Figure 6 Simulated and measured thermal conductivity of (La1-xErx)2Zr2O7 ceramics

D

Figure 7 Calculated and measured thermal conductivity of (La1-xErx)2Zr2O7 ceramics with x is

A

CC

EP

TE

0.02, 0.04, 0.06, 0.08, 0.10, respectively

Table 1

Lattice parameter and ionic radius for (La1-xErx)2Zr2O7 ceramics

La2Zr2O7

10.7977

12.5891

(La0.98Er0.02)2Zr2O7

10.7892

(La0.96Er0.04)2Zr2O7

rA (Ǻ)

rA/rB

1.1600

0.7200

1.6111

12.5594

1.1569

0.7200

1.6068

10.7888

12.5580

1.1538

0.7200

1.6025

(La0.94Er0.06)2Zr2O7

10.7708

12.4952

1.1506

0.7200

1.5981

(La0.92Er0.08)2Zr2O7

10.7657

12.4775

1.1475

0.7200

1.5938

(La0.90Er0.10)2Zr2O7

10.7654

12.4764

1.1444

1.5894

A

CC

EP

TE

D

M

A

N

U

SC

a (Ǻ)

PT

rB (Ǻ)

RI

V (Ǻ3)

composition

0.7200

SC RI PT

Table 2

The basic parameters and fitting results for (La1-xErx)2Zr2O7 ceramics

ρt ρ p Ω v ωD ΘD γ E T1 lmin A M -3 3 -3 -26 -29 -1 13 (10 kg.m ) (10 kg.m ) (%) (10 kg) (10 m) (m.s ) (10 HZ) (K) (Gpa) (K) (Å) (W.m-1) 6.039 5.692 94.254 8.639 1.430 4749.774 7.624 582.428 2.07 180 146.5 4.047 570.3

U

x

A

α /

0.02

6.065

5.806

95.730

8.656

1.427

4739.583

7.614

581.626 2.07

180

145.7 4.047

541.0

4057

0.04

6.078

5.931

M

0

N

3

8.673

1.426

4734.511

7.606

581.035 2.07

180

145.7 4.047

523.9

10590

0.06

6.120

5.865

95.833

8.690

1.420

4718.237

7.592

579.987 2.07

180

144.7 4.047

519.8

16860

0.08

6.141

96.124

8.707

1.418

4710.163

7.583

579.274 2.07

180

144.5 4.047

482.5

19490

0.10

6.154

95.028

8.724

1.417

4705.186

7.575

578.691 2.07

180

144.4 4.047

473.7

21700

D

TE 5.903

EP

CC A

97.581

5.848

SC RI PT

Table 3

Scattering coefficient Г and the paremeter ε of the (La1-xErx)2Zr2O7 ceramics Г /

ε 196

5.674

15671

1.67×10-3+7.23×10-4ε

7.407

10242

0.06

2.50×10-3+1.09×10-3ε

7.900

7245

0.08

3.34×10-3+1.45×10-3ε

6.859

4728

6.111

3374

Г /

0.02

8.34×10-4+3.62×10-4ε

0.04

A

CC

N

A

M

D

TE

EP

0.10

U

x 0

4.17×10-3+1.81×10-3ε

D

TE

EP

CC

A Figure 1

A

M

N

U

SC RI PT

D

TE

EP

CC

A

Figure 2

A

M

N

U

SC RI PT

D

TE

EP

CC

A

Figure 2b

A

M

N

U

SC RI PT

D

TE

EP

CC

A Figure 3

A

M

N

U

SC RI PT

D

TE

EP

CC

A Figure 4

A

M

N

U

SC RI PT

D

TE

EP

CC

A Figure 5

A

M

N

U

SC RI PT

D

TE

EP

CC

A Figure 6

A

M

N

U

SC RI PT

D

TE

EP

CC

A

Figure 7

A

M

N

U

SC RI PT