Structure and microwave dielectric characteristics of Sr(La_1−xSm_x)₂Al₂O₇ ceramics

Abstract

Sr(La_1−xSm_x)₂Al₂O₇ (0 ≤ x ≤ 1) ceramics were synthesized by a standard solid-state reaction method, and the microwave dielectric characteristics were investigated together with the densification behavior, microstructure and phase composition. X-ray diffraction analysis indicated that the matrix phase with Ruddlesden–Popper structure of n = 2 was obtained in the entire composition range. Dense ceramics with relative density of over 96% theoretical density were obtained by sintering at over 1575 °C in air for 3 h. With increasing Sm³⁺ substitution, the relative dielectric constant increased from 18.8 to 21.3, and the temperature coefficient of resonant frequency was adjusted from −21.7 to 4.8 ppm per °C, while though the Qf value should theoretically decrease with Sm substitution because of the increased interlayer polarization charge, the high Qf was maintained for x < 0.5 and even increased slightly at x = 0.5 due to some extrinsic reasons such as large grain size. The best combination of microwave dielectric characteristics was achieved at the composition of x = 0.5: ε_r = 21.0, Qf = 115 900 GHz, τ_f = −3.7 ppm per °C.

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Introduction

Over the past few decades, with the rapid development of modern wireless communication technology such as satellite communications, base station and mobile communication systems, high-performance microwave dielectric ceramics which play the key roles in microwave resonators, filters and antennas have attracted numerous attentions of researchers.^1,2 It is well-known that three key characteristics are required in microwave dielectric ceramics: appropriate relative dielectric constant (ε_r), high unloaded quality factor (Q) and near-zero temperature coefficient of resonant frequency (τ_f).^3,4 As the important commercial microwave dielectric ceramics with low ε_r (ε_r < 30), ceramics in MgTiO₃–CaTiO₃ system (ε_r = 21, Qf = 56 000 GHz, τ_f = 0 ppm per °C) with low cost are well-known as the materials for dielectric resonator and patch antenna,⁵ but their Qf values are not high enough for high-performance microwave applications. On the other hand, Ba-based complex perovskite ceramics such as Ba(Mg_1/3Ta_2/3)O₃, Ba(Zn_1/3Ta_2/3)O₃ and Ba(Zn_1/3Nb_2/3)O₃ are well known as the ultralow loss microwave dielectric ceramics.^6–9 However, their high cost due to the noble elements such as Ta and Nb, poor sintering ability and strong processing dependence because of the volatile element such as Zn are serious limitations, considering their continued practical applications. Therefore, searching for a new candidate with desired properties and low cost is a crucial issue.

In the past few decades, Ruddlesden–Popper (R–P) compounds with the general formula of A′₂[A_n−1B_nO_3n+1] (A, A′ = alkaline or rare earth metal ions, B = metal ion)¹⁰ have attracted much attentions because of their rich properties such as low thermal conductivity, oxide-ion conductivity, superconductivity, ferroelectricity, colossal magnetoresistance, catalytic activity and magnetic transport property.^11–15 The stability of the structure depends on the crystal-chemical constraint that is the n/1 intergrowth of n ABO₃ perovskite layers (P_n) alternating with one AO rock-salt layer (RS) along c axis. Recently, MLnAlO₄ (M = Sr, Ca; Ln = La, Nd, Sm) ceramics with R–P structure of n = 1, namely K₂NiF₄ structure without noble elements such as Ta and Nb have been investigated, and they have attracted wide attentions as potential candidates for low-loss microwave dielectric applications.^16–20 Wise et al.²¹ reported the relation between the structure and property of (Sr_xCa_1−x)_n+1Ti_nO_3n+1 with different n value. Thus, the microwave dielectric characteristics of R–P compounds could be controlled by adjusting the n value.

In the previous work, SrLn₂Al₂O₇ (Ln = La, Nd, Sm) ceramics with R–P structure of n = 2 were prepared, and their excellent microwave dielectric properties (ε_r = 18.2–21.6, Qf = 64 680–71 680 GHz and τ_f = −22.1 to +4 ppm per °C) were obtained.²² Referring to the MLnAlO₄ (M = Sr, Ca; Ln = La, Nd, Sm) ceramics, their microwave dielectric characteristics can be improved by cation substitution. Zvereva et al.^23,24 have researched the formation of (Sr_1−xCa_x)Ln₂Al₂O₇ (Ln = La, Nd) solid solution with x < 0.5, and have found that the solid solution with Ca substitution was formed easily. According to Yi and Liu et al.,^25,26 the more excellent microwave dielectric characteristics of SrLn₂Al₂O₇ (Ln = La, Nd, Sm) ceramics can be expected by proper amount of Ca²⁺ and Ti⁴⁺ substitution for Sr²⁺ and Al³⁺, respectively. SrLa₂Al₂O₇ possesses the best Qf value among SrLn₂Al₂O₇ (Ln = La, Nd, Sm) ceramics due to the minimum interlayer polarization charge,²² but its τ_f is too negative for practical application. Therefore, SrSm₂Al₂O₇ is chosen to adjust the Qf and τ_f values of SrLa₂Al₂O₇ because of its same crystal structure as SrLa₂Al₂O₇ and positive temperature coefficient of resonant frequency.

In the present work, Sr(La_1−xSm_x)₂Al₂O₇ (x = 0, 0.25, 0.5, 0.75, 0.85, 0.95, 1) microwave dielectric ceramics are prepared by a standard solid-state reaction method. The microwave dielectric properties are investigated together with their structure, and the relationship between them are also discussed. The effects of interlayer polarization charge, grain size, secondary phase and stacking fault on the properties are emphasized.

Experimental

Sr(La_1−xSm_x)₂Al₂O₇ (x = 0, 0.25, 0.5, 0.75, 0.85, 0.95, 1) ceramics were prepared using high purity SrCO₃ (99.95%), La₂O₃ (99.99%), Sm₂O₃ (99.99%) and Al₂O₃ (99.99%) powders as raw materials. Here, La₂O₃ and Sm₂O₃ raw powders were preheated at 900 °C in air for 2 h before weighing because of the hygroscopicity of the rare earth oxide. The stoichiometric raw powders were mixed by ball-milling with zirconia media in ethanol for 24 h. The slurries were dried and then calcined at relevant temperature range from 1425 °C to 1575 °C in air for 6 h. Then, the calcined powders were mixed by ball-milling and dried again. After mixing and grinding with the organic binder (about 8 wt% polyvinyl alcohol), the powders were pressed into cylinders of 12 mm in diameter and 2–6 mm in height under a uniaxial pressure of 98 MPa. Then the cylinders were sintered at 1525–1600 °C in air for 3 h to form the dense ceramics with the heating rate of 5 °C min⁻¹. After sintering, the cylinders were cooled to 1000 °C at a rate of 2 °C min⁻¹ and further cooled inside the furnace.

The bulk densities of sintered ceramics with regular shape were measured by the Archimedes method. After crushing and grinding the sintered ceramics, their crystal structures were characterized by powder X-ray diffraction analysis (XRD) (RIGAKU D/max 2550PC, Rigaku Co., Tokyo, Japan) with CuK_α (λ = 0.15418 nm) radiation. After polishing and thermal etching at 1525 °C for 30 min, the microstructures of the sintered ceramics were observed by scanning electron microscopy (SEM) (SIRION-100; FEI Co., Eindhoven, Netherlands). For Rietveld refinement analysis, the XRD data were collected over the 2θ range from 8° to 130° with a step width of 0.02° and a count time of 2 s at room temperature. FULLPROF program was chosen to calculate the Rietveld structure. Samples for transmission electron microscopy observation were cut ultrasonically to disks of 3 mm in diameter and then mechanical polished to a thickness of about 10 μm. The final perforation of the samples was conducted by precision argon-ion milling. The selected area electron diffraction (SAED) patterns and high-resolution TEM (HRTEM) images were obtained using a transmission electron microscopy (Tecnai G² F20, FEI Co., Hillsboro, OR).

The relative dielectric constant (ε_r) and the temperature coefficient of resonant frequency (τ_f) were determined by the Hakki–Coleman method,²⁷ using a vector network analyzer (E8363B, Agilent Technologies, Palo Alto, CA). The τ_f value was measured in the temperature range of 20–80 °C at microwave frequency and calculated by the following equation:

where, the f₂₀ and f₈₀ were the TE₀₁₁ resonant frequencies at 20 °C and 80 °C, respectively. The quality factor (Q) was determined at around 7 GHz by the closed cylindrical resonant cavity method, using a silver-coated cavity connected to the network analyzer.²⁸ Here, the product Qf was used to evaluate the dielectric loss instead of Q alone, because the Q factor generally varied inversely with frequency (f) in the microwave range.

Results and discussion

Fig. 1 shows the relative densities of Sr(La_1−xSm_x)₂Al₂O₇ (0 ≤ x ≤ 1) ceramics as functions of the sintering temperature. In the entire composition range, the relative density increases with increasing sintering temperature and over 96% theoretic density (T.D.) is reached at 1575 °C. Moreover, the maximum relative density of over 99% T.D. is obtained at x = 0.5. Fig. 2 shows the microstructures of the present ceramics sintered at 1575 °C in air for 3 h. The grains generally exhibit long strip-shaped and plate-shaped morphology in the first three compositions (x = 0–0.5) and the different shapes indicate the different sections of the grains. In contrast, the rest compositions exhibit short rod-shaped morphology. As for the grain size, the lengths of the grains are nearly 10–15 μm at x = 0–0.5, however that of the rest compositions (x = 0.75–1) are about 2–5 μm. Besides, visible pores exist in the thermally etched surfaces of all ceramics, but the minimum amount is obtained at x = 0.5.

Fig. 1 Relative densities of Sr(La_1−xSm_x)₂Al₂O₇ ceramics as functions of sintering temperature.

Fig. 2 SEM micrographs of thermally etched surfaces of Sr(La_1−xSm_x)₂Al₂O₇ ceramics with various compositions sintered at 1575 °C in air for 3 h: (a) x = 0, (b) x = 0.25, (c) x = 0.5, (d) x = 0.75, (e) x = 0.85, (f) x = 0.95 and (g) x = 1.0.

Fig. 3(a) shows the XRD patterns of the present ceramics sintered at 1575 °C in air for 3 h. In the entire composition range, the reflection peaks of the major phase along with the relevant indices of the crystallographic planes can be matched with those for SrLa₂Al₂O₇, indicating that the structure of the major phase is tetragonal Ruddlesden–Popper structure in space group I4/mmm. Different secondary phases appear in different compositions: Al₂O₃ in space group R3̄c at x = 0–0.5; SrSmAl₃O₇ and SmAlO₃ in space group P4̄2₁m and Pbnm, respectively at x = 0.75–1. As shown in Fig. 3(b), the diffraction patterns of the enlarged (006) and (110) peaks shift slightly toward higher angle with the increasing x, indicating that the lattice parameters (a, c and V) are decreasing.

Fig. 3 (a) XRD patterns of Sr(La_1−xSm_x)₂Al₂O₇ ceramics with various compositions sintered at 1575 °C in air for 3 h; (b) enlargement of the peaks at (006) and (110) crystallographic plane.

Fig. 4 illustrates the profile fit of the calculated and observed X-ray diffraction patterns of the ceramic (x = 0.5) together with the Bragg positions of the secondary phases. The Rietveld refinement results are listed in Table 1, including refined the structural parameter, reliability factor, ion occupation distribution and bond length. According to the results, as shown in Fig. 5, with the increment of Sm³⁺ substitution, the lattice parameters (a, c and V) of the present ceramics decrease linearly due to the decreasing effective ionic radius (R_La³⁺ > R_Sm³⁺), which is in consonance with the variations of the corresponding peaks in XRD patterns.

Fig. 4 Profile fit for the Rietveld refinement of Sr(La_1−xSm_x)₂Al₂O₇ (x = 0.5) ceramics sintered at 1575 °C in air for 3 h.

Table 1 The refined structural parameter, reliability factor, ion occupation distribution and bond length for Sr(La_1−xSm_x)₂Al₂O₇ ceramics sintered at 1575 °C for 3 h^a

	0	0.25	0.5	0.75	0.85	0.95	1
a The refined atomic fractional coordinate positions are A(1)[2b] (0, 0, 0.5), A(2)[4e] (0, 0, z), Al[4e] (0, 0, z), O(1)[2a] (0, 0, 0), O(2)[8g] (0, 0.5, z), O(3)[4e] (0, 0, z) in space group I4/mmm.
a (Å)	3.7741(4)	3.7611(5)	3.7460(4)	3.7316(5)	3.7252(5)	3.7192(5)	3.7165(5)
c (Å)	20.2082(2)	20.1227(3)	20.0369(2)	19.9589(3)	19.9261(3)	19.9026(3)	19.8901(3)
V (per unit cell) (Å^3)	287.845	284.653	281.161	277.930	276.515	275.305	274.722
Z(Sr, Ln)(2) (Å)	0.3185(3)	0.3184(3)	0.3183(3)	0.3184(2)	0.3185(2)	0.3185(2)	0.3185(2)
ZAl (Å)	0.0954(12)	0.0953(2)	0.0950(15)	0.0949(12)	0.0946(11)	0.0942(12)	0.0941(12)
ZO(2) (Å)	0.0961(14)	0.0975(3)	0.0979(19)	0.0988(15)	0.0994(14)	0.0993(15)	0.0992(15)
ZO(3) (Å)	0.1944(3)	0.1962(2)	0.1983(3)	0.1995(2)	0.1998(2)	0.2005(2)	0.2003(2)
Rp	5.73%	5.30%	6.18%	4.95%	4.54%	4.76%	4.83%
Rwp	8.13%	7.91%	8.45%	6.71%	6.21%	6.54%	6.59%
RB	3.57%	3.28%	3.97%	4.27%	3.75%	3.91%	3.96%
χ^2	5.20	5.80	4.52	2.47	2.74	2.80	2.77
Ion occupation distribution of A sites
Sr1^2+	0.232	0.252	0.365	0.482	0.509	0.566	0.577
La1^3+	0.768	0.739	0.532	0.232	0.239	0.061	0
Sm1^3+	0	0.009	0.103	0.286	0.252	0.373	0.423
Sr2^2+	0.768	0.747	0.634	0.517	0.491	0.433	0.423
La2^3+	1.232	0.761	0.468	0.268	0.061	0.041	0
Sm2^3+	0	0.492	0.898	1.215	1.448	1.526	1.577
Bond length
(Sr, Ln)(1)–O(1) × 4 (Å)	2.6687(20)	2.6595(2)	2.6488(20)	2.6387(2)	2.6341(2)	2.6299(2)	2.6279(2)
(Sr, Ln)(1)–O(2) × 8 (Å)	2.708(2)	2.717(2)	2.711(3)	2.715(2)	2.719(2)	2.714(2)	2.710(2)
(Sr, Ln)(2)–O(3) × 1 (Å)	2.496(6)	2.451(4)	2.405(6)	2.374(4)	2.365(4)	2.352(4)	2.349(4)
(Sr, Ln)(2)–O(3) × 4 (Å)	2.6851(5)	2.6721(6)	2.6696(8)	2.6628(5)	2.6592(5)	2.6569(6)	2.6545(6)
(Sr, Ln)(2)–O(2) × 4 (Å)	2.5575(20)	2.530(2)	2.516(3)	2.492(2)	2.4793(19)	2.4766(20)	2.4762(20)
Al–O(3) × 1 (Å)	1.990(7)	2.037(5)	2.071(7)	2.087(5)	2.097(5)	2.113(5)	2.115(5)
Al–O(1) × 1 (Å)	1.927(2)	1.922(3)	1.903(3)	1.895(2)	1.884(2)	1.876(2)	1.871(2)
Al–O(2) × 4 (Å)	1.8871(4)	1.8810(10)	1.8739(15)	1.8674(16)	1.8651(18)	1.8624(2)	1.8610(2)

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Fig. 5 Lattice parameters (a, c and cell volume) of Sr(La_1−xSm_x)₂Al₂O₇ ceramics with various compositions.

Crystal structure of the present ceramics is shown in Fig. 6(a) according to the refined results. From the diagrammatic sketch, there are two kinds of A sites occupied by Sr²⁺, La³⁺ and Sm³⁺ ions with different proportions—one is (Sr, Ln) ion with twelve coordination number (A₁) in the middle of the P₂ layer and the other is (Sr, Ln) ion with nine coordination number (A₂) in the RS layer, and three kinds of oxygen sites—O(1), O(2), O(3) shown in Fig. 6(c). Because of the layered structure of Sr(La_1−xSm_x)₂Al₂O₇ ceramics, it can be regarded as different parallel charged layers stacking alternately along the c axis, i.e., -AlO₂-(Sr, La, Sm)O-(Sr, La, Sm)O–AlO₂-(Sr, La, Sm)*O–AlO₂-(Sr, La, Sm)O-(Sr, La, Sm)O–AlO₂- (see Fig. 6(b)). Benabbas²⁹ have handled the layers along c axis in the R–P structure with n = 1 as uniform blocks according to the superposition principle and have summarized their interlayer polarization charges. In this case, because the difference between Sr²⁺ and Ln³⁺ in charge and radius, the ratio of Sr²⁺ to Ln³⁺ at different A site is not exactly equal to 1 : 2 (see Table 1). Therefore, the formal charge of each layer can be obtained by eqn (2) on the basis of the corresponding formal ionic charges. The results are shown in Fig. 6(b).

where, C represents the polarization charge of corresponding layer, C_i and C₀ represent the valence of corresponding cation and oxygen, respectively, and x_i represents the proportion of corresponding cation on the basis of the ion occupation distribution shown in Table 1. In the present ceramics, every layer experiences the electric field created, as a first approximation, by the neighboring layers, and the interlayer polarization creates as a consequence of these polarization charges. Moreover, with increasing the substitution of Sm³⁺ ion with smaller radius, Ln³⁺ ions trend to occupy A₂ site, while Sr²⁺ ion trends to occupy A₁ site according to the refined results, resulting in the increasing interlayer polarization especially in RS layer.

Fig. 6 (a) Crystal structure of Sr(La_1−xSm_x)₂Al₂O₇ ceramics; (b) interlayer polarization charges of Sr(La_1−xSm_x)₂Al₂O₇ ceramics with various compositions ((Sr, Ln) ion with twelve coordination number is marked by asterisk); (c) atom displacements of Sr(La_1−xSm_x)₂Al₂O₇ ceramics along c axis.

In order to minimize the interlayer polarizations, the corresponding ions drove by the electric field created and the signs of their charges will move along c axis until they reach their equilibrium (real) positions. As shown in Fig. 7, the normalized bond length (NBL) is used to describe the state of cations. NBL is defined as the ratio of the actual bond length to the ideal bond length which is calculated using the effective ionic radii.³⁰ As shown in Fig. 6(c), because the polarization charges of neighboring layers in RS layer are positive, the A₂ cations move towards neighboring -AlO₂- layer along c axis, on the contrary, the apical oxygen (O(3)) anions move closer along c axis. As a result, the A₂ ion is in “compressed” state along c axis with NBL of A₂–O(3) shorter than 1, while the Al ion is in “elongated” state along c axis with NBL of Al–O(3) larger than 1. In summary, the A₁O₁₂ polyhedron is compressed along and perpendicularly to c axis, and the AlO₆ octahedron is elongated along c axis and compressed perpendicularly to c axis, while the A₂O₉ polyhedron is opposite to AlO₆ octahedron.

Fig. 7 Normalized bond length of Sr(La_1−xSm_x)₂Al₂O₇ ceramics with various compositions.

The stability of the structure can be characterized by tolerance factor (t). The tolerance factors are calculated first from two extreme aspects based on the assumptions that the cations of A site in one perovskite block are all twelvefold (represented by t_A1) or ninefold (represented by t_A2) by the following eqn (3).²² Because the ratio of A₁ to A₂ is 1 : 2, the final tolerance factors are calculated by the following eqn (4).²² The result as a function of x is shown in Fig. 8. The coordination numbers and effective ionic radii of atoms are based on the research of Shannon.³⁰

where, R_Sr²⁺, R_La³⁺, R_Sm³⁺, R_Al³⁺, R_O²⁻ are the effective ionic radii of corresponding ions; x, y and z are the proportions of Sr²⁺, La³⁺ and Sm³⁺ ions on the basis of the ion occupation distribution shown in Table 1. As shown in Fig. 8, with increasing x, the tolerance factor decreases linearly. The stability of the structure could be related to the internal stresses. With increasing x, the distortions of most of the bonds and the three polyhedrons become serious (see Fig. 7), which can lead to the increased internal stress. As a result, the stability (characterized by the tolerance factor) decreases.

Fig. 8 Tolerance factor of Sr(La_1−xSm_x)₂Al₂O₇ ceramics with various compositions.

Fig. 9 shows the microwave dielectric characteristics of Sr(La_1−xSm_x)₂Al₂O₇ ceramics sintered at 1575 °C for 3 h as functions of composition. As shown in Fig. 9(a), with increasing x, the relative dielectric constant increases slightly from 18.8 to 21.3. On the basis of the structure parameters, the molecule polarizability (α) of the present ceramics is calculated by the microscopic Clausius–Mosotti equation³¹ as follow:

where, V represents the volume per unit cell, Z represents the number of molecule per unit cell. As shown in Table 2, with increasing x, variation trend of the calculated molecule polarizability (α_c) based on eqn (5) is similar to that of predicted molecule polarizability (α_p) according to the oxide additivity law.³² There is a deviation between α_c and α_p because α_p is given by ion polarizability of oxide. The cations in actual Sr(La_1−xSm_x)₂Al₂O₇ structure are in “elongated” or “compressed” state which are very different from that in oxides. According to Shannon, the cation polarizability will be increased or decreased as a result of the presence of “elongated” or “compressed” state, respectively.³² In this case, most of NBL are shorter than 1, which means the α_p listed in Table 2 is larger than that in the actual condition, resulting in the negative sign of Δ. In addition, the larger deviation should be related to larger volume of A₁O₁₂, AlO₆ and A₂O₉ polyhedrons which also can reflect the surroundings of A₁, Al and A₂ cations.

Fig. 9 Microwave dielectric characteristics of Sr(La_1−xSm_x)₂Al₂O₇ ceramics sintered at 1575 °C in air for 3 h as functions of composition: (a) relative dielectric constant, (b) Qf value and (c) temperature coefficient of resonant frequency.

Table 2 The calculated and predicted molecule polarizability in Sr(La_1−xSm_x)₂Al₂O₇ ceramics sintered at 1575 °C for 3 h^a

x	αp (Å^3)	Observed (Z = 2)			Δ (%)
		εr	Vunit cell (Å^3)	αc (Å^3)
a Δ (%) = ((αc − αp)/αc) × 100.
0	32.03	18.8	287.845	29.42	−8.88%
0.25	31.37	19.5	284.653	29.25	−7.22%
0.5	30.70	21.0	281.161	29.20	−5.14%
0.75	30.04	21.1	277.930	28.88	−3.99%
0.85	29.77	21.2	276.515	28.75	−3.53%
0.95	29.50	21.3	275.305	28.65	−2.99%
1	29.37	21.3	274.722	28.58	−2.75%

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As shown in Fig. 9(b), the Qf value of Sr(La_1−xSm_x)₂Al₂O₇ ceramics trends to decrease in general with increasing the substitution of Sm³⁺ ion but indicates a slight increment at x = 0.5. The Qf values of the first three compositions (x = 0–0.5) are much larger than that of the rest compositions (x = 0.75–1). Fan et al. have done lots of research about the effect of interlayer polarization charge on dielectric loss.^16,33,34 In this case, the theoretical decreasing trend of Qf value is associated with the interlayer polarization effect and the stability of the structure (characterized by the tolerance factor). As x increases, the interlayer polarization charge increases, leading to the increasing damage to the charge balance between each layer. Besides, the degree of the actual bond length away from ideal value, namely the deviation of NBL from 1 increases, especially the bond lengths of Al–O(3), A₂–O(3) (see Fig. 8) in the RS layer, resulting in the increasing internal stresses. Meanwhile, the stability of the structure decreases. In conclusion, the Qf value should decrease theoretically with increasing x.

Actually, high Qf value is maintained for x < 0.5, and the Qf value even increases slightly at x = 0.5 (Qf = 115 900 GHz), then decreases rapidly at x = 0.75 (Qf = 76 590 GHz). It is well known that the extrinsic factors such as grain size, secondary phase, porosity and stacking fault also affect the Qf value significantly, and even play the dominating role in some cases.^6,35–38 The extraordinary high relative density at x = 0.5 (about 99% T.D.) may contribute to the slight increment at x = 0.5. Kim et al. have pointed out that the Qf value decreased obviously with the decreasing grain size.³⁵ In this case, the smaller grain size at x = 0.75–1 (see Fig. 2) also has adverse effect on the Qf value. Meanwhile, the increasing amount and type of secondary phases with lower Qf value such as SmAlO₃ (ε_r = 20.4, Qf = 65 000 GHz, τ_f = −74 ppm per °C)³⁹ could also lead to the deterioration of Qf value at x = 0.75–1. Besides, Fig. 10 shows the HRTEM images viewed along the [010] direction which is the most readily interpretable zone axis for direct illustration of the stacking fault. As shown in Fig. 10(a) and (b), compared to the ceramic at x = 0.5, the stacking faults appeared at x = 0.75 are obvious. Using FFT analysis, as shown in Fig. 10(c) and (d), the diffraction spots of x = 0.75 elongate along c axis, while that of x = 0.5 are round dots, which indicates one-dimensional (1D) disorder as the appearance of the stacking faults where the n values of the layered structure are not equal to 2.²⁵ The stacking faults can be regarded as the secondary phases implanted to the matrix phase, resulting in the inhomogeneous microstructure of the ceramics, and they could do harm to Qf value.

Fig. 10 TEM microanalysis for Sr(La_1−xSm_x)₂Al₂O₇ ceramics (x = 0.5, 0.75). (a) and (b) HRTEM images viewed along [010] zone axis, and the insets are the corresponding selected diffraction patterns taken along the same zone axis; (c) and (d) the simulated diffraction patterns of white square areas of (a) and (b) by using FFT respectively.

As shown in Fig. 9(c), the temperature coefficient of resonant frequency (τ_f) increases from −21.7 to 4.8 ppm per °C with increasing x. It is correlated to the temperature coefficient of ε_r (τ_ε) and the linear thermal expansion coefficient (α_L) through the following equation.³

For the perovskite-type ceramics, the effect of α_L can be ignored because it is almost a constant about 8 to 10 ppm per °C.⁴⁰ Therefore, τ_f is mainly affected by τ_ε which is related to ε_r. According to Reaney et al.,³ the variation of τ_ε with t is strongly affected by the structural phase transition. However, no diffraction spot which represents inphase or antiphase tilting of oxygen octahedron is observed (see Fig. 10), even though the t is less than 0.985. Consequently, τ_ε decreases with the decreasing t, resulting in the increment of τ_f according to eqn (6), and the relationship between ε_r and τ_f is monotonous. Therefore, the τ_f value of SrLa₂Al₂O₇ ceramic can be adjusted to near-zero by Sm³⁺ ion substitution.

Conclusions

Low-loss and temperature-stable Sr(La_1−xSm_x)₂Al₂O₇ solid solution ceramics with R–P structure of n = 2 can be prepared through a standard solid-state sintering method. The crystal structure of matrix phase evolves linearly with x. With increasing Sm³⁺ substitution, ε_r value increases slightly, while τ_f value can be adjusted from negative towards positive. Though the Qf value should theoretically decrease with increasing interlayer polarization charges which is influenced by the enhancive occupation ratio of Ln ions in the RS layer, the extrinsic factors such as large grain size and high relative density could benefit to the Qf value, resulting in the high Qf value for x < 0.5 and even leading to a slight increment at x = 0.5. The best combination of microwave dielectric characteristics is achieved at the composition of x = 0.5: ε_r = 21.0, Qf = 115 900 GHz and τ_f = −3.7 ppm per °C, making this material potential for commercial microwave applications.

Note added after first publication

This article replaces the version published on 10th October 2016, which, owing to an editorial office error, referred to the product of the quality factor (Q) and the frequency (f) by the term Q_f rather than the correct form Qf.

Acknowledgements

The present work was financially supported by the Chinese National Basic Research Program under grant number 2015CB654601.

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