**10. Ba(M2+1/3 M5+2/3)O3 – Based MW dielectrics (M2+ = Mg, Zn, Co, Ni; M5+ = Ta, Nb) with extremely high Q**

Ba(B2+1/3 B5+2/3) O3 compounds where B2+ = Mg, Zn, Co, Ni; B5+ = Ta, Nb (perovskite crystal structure) had been synthesized for the first time by the authors of [89,, , 92]. In these compounds, a 2:1- type ion ordering in the B sublattice is observed, in which two layers filled with B5+ ions alternate with a layer filled with B2+ ions. The authors [93, 94] showed that tantalum-containing materials possess a high Q value in the MW range. It should be noted that the synthesis of these materials involves many problems. Ceramics sinter at a high temperature, which may result in considerable evaporation of constituents (cobalt, zinc) and hence in the impairment of electrical properties. In the case of synthesis by the solid-state reaction method, extra phases Ba5Ta4O15, Ba4Ta2O9 are often present in ceramics [95], which affect adversely the Q value. To prevent this, the authors of [96] carried out synthesis from solutions, where solutions containing Mg2+, Ta5+ were used as starting substances, to which a solution of ammonia with oxyquinoline was added.

It had been found that in this case, the single-phase product Ba(Mg1/3Ta2/3)O3 is formed above 1300 0C without intermediate phases. Single-phase Ba(Mg1/3Ta2/3)O3 had been obtained by the solid-state reaction method too, using highly active reagents as starting substances [95-97].

When synthesizing tantalum-containing materials, the preparation of high-density ceramics was a difficult problem. Therefore, Nomura with coauthors [98] proposed to prepare dense ceramics (ρ ≈ 7520 kg/m3) by using additionally manganese impurities. Matsumoto and Hinga [99] used fast heating (330 0C/min) for the same purposes, which made it possible to achieve 96% of the theoretical density. To increase the rate of sintering and to order ions in the B sublattice, the authors of [100, 101] proposed preliminarily synthesized MTa2O6(M = Mg, Zn) as starting reagents. Renoult with coworkers [102] had synthesized fine-grained Ba(MgTa)O3 by the sol-gel method. In that case, dense ceramics could be obtained without additives.

The Q value in Ba(B2+1/3 B5+2/3)O3 perovskites is greatly affected by the type and degree of ion ordering in the B sublattice [103]. It had been found that by the partial substitution of Zr4+,

#### 132 Dielectric Material

Ti4+, W6+ ions for ions in the B sublattice, one can increase the degree of 1:2 - type ion ordering and hence increase the Q value [104, 105].

Microwave Dielectrics Based on Complex Oxide Systems 133

additional annealing. For instance, the Q × f value increased from 60000 to 168000 after

**Figure 17.** Schematic representation of 1:2 cation ordering in Ba(Zn1/3Ta1/3)O3. On the top left are shown two possible (111) directions for Zn and Ta orientation in the perovskite structure; on the right below is shown one of the possible variants of 1: 2 ordering. The oxygen ions were omitted for clarity [108].

Tamura et al [115] showed that Q in Ba(Zn1/3Ta2/3)O3 can be improved by adding BaZrO3(BZ) of low concentration (< 4 mol %). In this case, the ceramic sintering time is greatly reduced, which is required for the attainment of high Q values (Q × f = 105000 had been attained by

This was accounted for by the formation of defects in the B sublattice, the presence of which increased the rate of cation ordering in this sublattice. As the BZ concentration was increased, the type of ordering changed (when substitution reached 4 mol %), the system came to have 1:1 ordering and a double cell. Similar regularities were observed when small amounts of BaWO4 [116] and BaSnO3 [117] were added to Ba(Mg1/3Ta2/3)O3. The individual compounds Ba(Mg1/3Ta2/3)O3 and Ba(Zn1/3Ta2/3)O3 allow one to achieve high Q values, but their electrophysical properties have a low thermostability. Therefore, to increase the thermostability of electrical properties, materials are synthesized on the basis of solid solutions, where the end members have temperature dependences of permittivity of different sign. The materials based on solid solutions possess a higher thermostability, but the Q value is lower as compared with individual compounds, which may be attributed, in particular, to decrease in cation ordering in the B sublattice. On the basis of a solid solution, e.g. Ba(Zn1/3Ta2/3)O3, materials have been obtained which have a high level of electrophysical

The materials based on tantalum-containing perovskites possess today the highest Q values in the MW range among dielectrics with increased ε value. However, the difficulty of their synthesis: high sintering temperatures (Tsint > 1600 0C), the necessity of long additional

properties: ε = 30-40, TCε = (0-28) × 10-6 0C-1, Q8GHz = 15000 .

additional annealing at 1350 0C for 120 h [93].

adding 4 mol % BZ).

Ion ordering in the B sublattice is also affected by slight substitutions of ions in the A sublattice. For instance, Ref [104] showed that partial substitution of La2+ ions for Ba2+ ions in magnesium-barium tantalate results in the change of ion ordering in the B sublattice from the 2:1 type (space group Pm3I) to the 1:1 type (space group Fm3m). Similar changes of the type of ion ordering in the B sublattice were found in the case of partial substitution of lanthanum ions for barium ions in zinc-barium niobate with perovskite structure [105]. This result shows that the type of ion ordering in the B sublattice is very sensitive to chemical composition and preparation technique. The 1:1-type ion ordering in the B sublattice in Ba(B2+1/3 B5+2/3)O3 compounds was explained in terms of a "space-charge" model [106, 107], according to which only B2+ and B5+ ions can occupy the sites in the ordered Ba(β'1/2 β''1/2)O3 structure (1:1 type). Since in this case the electroneutrality condition is not satisfied in the crystalline phase, it may be assumed that the domains of the ordered crystalline phase (ordering type 1:1), which has an uncompensated charge, are in a disordered matrix rich in B5+ ions, as a result of which the electroneutrality condition is satisfied throughout the sample volume.

However, when investigating the system of solid solutions (1-x)Ba (Zn1/3Nb2/3)O3 xLa((Zn1/3Nb2/3)O3 (0 ≤ x ≤ 0.6), it was shown that 1:2 –type ordering persists in the interval 0 ≤ x ≤ 0.5 [105], whereas in the interval 0.05 ≤ x ≤ 0.6, 1:1 ion ordering in the B sublattice is observed. In this case, there is no aggregation. The investigation of the microstructure did not reveal the existence of disordered perovskite phase region, which was assumed in the "space-charge" model. Therefore, to describe the 1:1 ion ordering in the B sublattice, a "random-site" model was proposed [105, 108, , 110]. According to this model, 1:1 ordering in the above systems is described as follows. There are two alternating crystal planes, in which the B sublattice ions reside. One of them is occupied with B5+ cations and the other with B2+ cations and the remaining B5+ cations, which are disordered in this crystal plane.

Thus, in Ba(M2+1/3 M5+2/3)O3 compounds with perovskite structure, the B sublattice ions may be fully disordered as well as have 1:2 or 1:1 ordering. A calculation of the lattice energy of ordered and disordered structures showed [111] that ordered structure is characterized by lower Madelung energy, indicating this structure to be stable. Investigations of the electrophysical properties of Ba(B2+1/3 B5+2/3)O3 compounds showed that ion ordering in the B sublattice affects greatly the Q value [112].

It should be noted that Ba(B2+1/3 B5+2/3)O3 compounds with perovskite structure and 1:1 cation ordering in the B sublattice have, as a rule, a relatively low Q [113]. The largest Q value is observed in the Ba(Mg1/3Ta2/3)O3 and Ba(Zn1/3Ta2/3)O3 compounds. In these compounds, the B cations are stoichiometrically ordered in the hexagonal unit cell Pm3I (2:1ordering), in which the layers of Ta5+ and Zn(Mg)2+ cations are sequentially arranged along the (111) crystal plane (Fig 17). The layers of cations are separated by oxygen layers, which are displaced in the direction of small pentavalent tantalum cations [112]. The Q value is very sensitive to ordering in the B sublattice [93, 114]. It can be greatly increased by using additional annealing. For instance, the Q × f value increased from 60000 to 168000 after additional annealing at 1350 0C for 120 h [93].

132 Dielectric Material

sample volume.

Ti4+, W6+ ions for ions in the B sublattice, one can increase the degree of 1:2 - type ion

Ion ordering in the B sublattice is also affected by slight substitutions of ions in the A sublattice. For instance, Ref [104] showed that partial substitution of La2+ ions for Ba2+ ions in magnesium-barium tantalate results in the change of ion ordering in the B sublattice from the 2:1 type (space group Pm3I) to the 1:1 type (space group Fm3m). Similar changes of the type of ion ordering in the B sublattice were found in the case of partial substitution of lanthanum ions for barium ions in zinc-barium niobate with perovskite structure [105]. This result shows that the type of ion ordering in the B sublattice is very sensitive to chemical composition and preparation technique. The 1:1-type ion ordering in the B sublattice in Ba(B2+1/3 B5+2/3)O3 compounds was explained in terms of a "space-charge" model [106, 107], according to which only B2+ and B5+ ions can occupy the sites in the ordered Ba(β'1/2 β''1/2)O3 structure (1:1 type). Since in this case the electroneutrality condition is not satisfied in the crystalline phase, it may be assumed that the domains of the ordered crystalline phase (ordering type 1:1), which has an uncompensated charge, are in a disordered matrix rich in B5+ ions, as a result of which the electroneutrality condition is satisfied throughout the

However, when investigating the system of solid solutions (1-x)Ba (Zn1/3Nb2/3)O3 xLa((Zn1/3Nb2/3)O3 (0 ≤ x ≤ 0.6), it was shown that 1:2 –type ordering persists in the interval 0 ≤ x ≤ 0.5 [105], whereas in the interval 0.05 ≤ x ≤ 0.6, 1:1 ion ordering in the B sublattice is observed. In this case, there is no aggregation. The investigation of the microstructure did not reveal the existence of disordered perovskite phase region, which was assumed in the "space-charge" model. Therefore, to describe the 1:1 ion ordering in the B sublattice, a "random-site" model was proposed [105, 108, , 110]. According to this model, 1:1 ordering in the above systems is described as follows. There are two alternating crystal planes, in which the B sublattice ions reside. One of them is occupied with B5+ cations and the other with B2+

Thus, in Ba(M2+1/3 M5+2/3)O3 compounds with perovskite structure, the B sublattice ions may be fully disordered as well as have 1:2 or 1:1 ordering. A calculation of the lattice energy of ordered and disordered structures showed [111] that ordered structure is characterized by lower Madelung energy, indicating this structure to be stable. Investigations of the electrophysical properties of Ba(B2+1/3 B5+2/3)O3 compounds showed that ion ordering in the B

It should be noted that Ba(B2+1/3 B5+2/3)O3 compounds with perovskite structure and 1:1 cation ordering in the B sublattice have, as a rule, a relatively low Q [113]. The largest Q value is observed in the Ba(Mg1/3Ta2/3)O3 and Ba(Zn1/3Ta2/3)O3 compounds. In these compounds, the B cations are stoichiometrically ordered in the hexagonal unit cell Pm3I (2:1ordering), in which the layers of Ta5+ and Zn(Mg)2+ cations are sequentially arranged along the (111) crystal plane (Fig 17). The layers of cations are separated by oxygen layers, which are displaced in the direction of small pentavalent tantalum cations [112]. The Q value is very sensitive to ordering in the B sublattice [93, 114]. It can be greatly increased by using

cations and the remaining B5+ cations, which are disordered in this crystal plane.

sublattice affects greatly the Q value [112].

ordering and hence increase the Q value [104, 105].

**Figure 17.** Schematic representation of 1:2 cation ordering in Ba(Zn1/3Ta1/3)O3. On the top left are shown two possible (111) directions for Zn and Ta orientation in the perovskite structure; on the right below is shown one of the possible variants of 1: 2 ordering. The oxygen ions were omitted for clarity [108].

Tamura et al [115] showed that Q in Ba(Zn1/3Ta2/3)O3 can be improved by adding BaZrO3(BZ) of low concentration (< 4 mol %). In this case, the ceramic sintering time is greatly reduced, which is required for the attainment of high Q values (Q × f = 105000 had been attained by adding 4 mol % BZ).

This was accounted for by the formation of defects in the B sublattice, the presence of which increased the rate of cation ordering in this sublattice. As the BZ concentration was increased, the type of ordering changed (when substitution reached 4 mol %), the system came to have 1:1 ordering and a double cell. Similar regularities were observed when small amounts of BaWO4 [116] and BaSnO3 [117] were added to Ba(Mg1/3Ta2/3)O3. The individual compounds Ba(Mg1/3Ta2/3)O3 and Ba(Zn1/3Ta2/3)O3 allow one to achieve high Q values, but their electrophysical properties have a low thermostability. Therefore, to increase the thermostability of electrical properties, materials are synthesized on the basis of solid solutions, where the end members have temperature dependences of permittivity of different sign. The materials based on solid solutions possess a higher thermostability, but the Q value is lower as compared with individual compounds, which may be attributed, in particular, to decrease in cation ordering in the B sublattice. On the basis of a solid solution, e.g. Ba(Zn1/3Ta2/3)O3, materials have been obtained which have a high level of electrophysical properties: ε = 30-40, TCε = (0-28) × 10-6 0C-1, Q8GHz = 15000 .

The materials based on tantalum-containing perovskites possess today the highest Q values in the MW range among dielectrics with increased ε value. However, the difficulty of their synthesis: high sintering temperatures (Tsint > 1600 0C), the necessity of long additional

#### 134 Dielectric Material

annealing (Tann ≈ 1500 0C, 20-120 h), low reproducibility of properties, as well as the high price of tantalum (in 2000, the price of reagents containing tantalum increased by 500%) calls for search for new promising systems. Therefore, in recent years, attention has been given just to niobium-containing Ba(Nb2/3B2+1/3)O3 compounds (where B2+ = Mg, Zn, Co), which crystallize in perovskite structure [118, 119, 120].

Microwave Dielectrics Based on Complex Oxide Systems 135

When studying nonstoichiometry in barium sublattice (Ba1+xCo1/3Nb2/3O3+x at -0.03 <x <0.03), an extra phase Ba9CoNb14O45 appears, which makes a noticeable decreases greatly (Fig. 18(a)). Therefore, the highest Q values are observed for stoichiometric composition

Interesting properties are observed in the case of nonstoichiometry in the cobalt sublattice

Increasing the cobalt content of this system with reference to stoichiometry leads to a monotonic increase in relative density and corresponding slight increase in permittivity ε in the range 32 to 34 (Fig. 19a). At higher cobalt deficiencies (y < –0.02), the samples contained an additional phase Ba8CoNb6O24. In the range –0.03 ≤ у ≤ 0.01, the quality factor varies nonlinearly, with a maximum at −0.03 ≤ у ≤ −0.02. The Qf product exceeds that of

Electron diffraction data for the BaСo1/3+yNb2/3O3+y samples indicates that cobalt deficiencies in the range −0.03 ≤ у ≤ −0.02 are favourable for 1 : 2 B-site cation ordering in the cobaltcontaining perovskite (Fig. 20). As mentioned above, cation ordering is accompanied by an increase in quality factor, as observed in this system (Fig. 18b). The reduction in quality factor at large deviations from stoichiometry (y < –0.1) is due to the presence of a significant

**Figure 19.** Composition dependences of the (a) apparent density (ρ), permittivity (ε), (b) Qf product, and temperature coefficient of resonant frequency (τf) for Ba3Co1+yNb2O9+y materials; measurements at

The increase in Ba8CoNb6O24 content with increasing cobalt deficiency (y < 0) leads to a result of practical interest: the temperature coefficient of resonant frequency switches sign (Fig. 18 b). The reason for this is that BaCo1/3Nb2/3O3 and Ba8CoNb6O24 differ in the sign of τf: –7 and +16 ppm/K, respectively [129, 131]. Because of this, the BaСo1/3+yNb2/3O3+y materials exhibit a temperature compensation effect, whose magnitude can be tuned by varying the cobalt content. The present results, therefore, suggest that cobalt-deficient Ba(Co1/3Nb2/3)O3 is

stoichiometric BCN by 30–50%, reaching 80000–85000 GHz (Fig. 19b).

(BaCo1/3Nb2/3O3) (Fig. 18(b)).

amount of Ba8CoNb6O24.

10 GHz.

(BaCo1/3+yNb2/3O3+y, where -0.05 <y <0.01).

These materials sinter at lower temperature, and cheaper reagents are needed for them. However, their main disadvantage is a lower *Q* value as compared with tantalumcontaining perovskites [121, 122]. We have shown for the first time that Ba(Mg1/3Nb2/3)O3 – based materials can have in some cases an extremely high *Q* (*Q* × *f* ≈ 150000) [123]. New papers appeared [5, 124, 125], which show the creation of high-Q MW dielectrics based on niobium-containing perovskites to be worth-while.

Ba(Co1/3Nb2/3)O3 (BCN) offers a particularly attractive combination of properties. Polycrystalline Ba(Co1/3Nb2/3)O3 has high dielectric permittivity (ε =32) and *Qf* = 40000–60000 GHz [126, 127]. At the same time, centimeter and millimeter wave applications require higher *Q* values. The properties of BCN are very weak functions of temperature. In particular, the temperature coefficient of its resonant frequency (τ*f*) lies in the range –10 to – 7 ppm/K, suggesting that it can be used in the production of high-*Q*/low-τ*f* microwave materials [128, , 130]. The electrical properties of BCN, especially its *Q* (or its *Qf* product, where *f* is frequency), strongly depend on preparation conditions, in particular on the sintering temperature, heat-treatment time, and heating/cooling rate.

It is reasonable to assume that the observed variations in the properties of BCN are related to the ceramic microstructure evolution during the fabrication process, cation ordering, and lattice distortions. Such distortions can be produced in BCN via slight changes in its cation composition.

Therefore, we have studied the effect of partial nonstoichiometry in cation sublattices on the phase composition, microstructure and electrophysical properties of BCN.

**Figure 18.** Composition dependences of the (a) apparent density (ρ), permittivity (ε), (b) Qf product, and temperature coefficient of resonant frequency (τf) for Ba3+3xCoNb2O9+3x materials; measurements at10 GHz.

When studying nonstoichiometry in barium sublattice (Ba1+xCo1/3Nb2/3O3+x at -0.03 <x <0.03), an extra phase Ba9CoNb14O45 appears, which makes a noticeable decreases greatly (Fig. 18(a)). Therefore, the highest Q values are observed for stoichiometric composition (BaCo1/3Nb2/3O3) (Fig. 18(b)).

134 Dielectric Material

composition.

at10 GHz.

crystallize in perovskite structure [118, 119, 120].

niobium-containing perovskites to be worth-while.

sintering temperature, heat-treatment time, and heating/cooling rate.

phase composition, microstructure and electrophysical properties of BCN.

annealing (Tann ≈ 1500 0C, 20-120 h), low reproducibility of properties, as well as the high price of tantalum (in 2000, the price of reagents containing tantalum increased by 500%) calls for search for new promising systems. Therefore, in recent years, attention has been given just to niobium-containing Ba(Nb2/3B2+1/3)O3 compounds (where B2+ = Mg, Zn, Co), which

These materials sinter at lower temperature, and cheaper reagents are needed for them. However, their main disadvantage is a lower *Q* value as compared with tantalumcontaining perovskites [121, 122]. We have shown for the first time that Ba(Mg1/3Nb2/3)O3 – based materials can have in some cases an extremely high *Q* (*Q* × *f* ≈ 150000) [123]. New papers appeared [5, 124, 125], which show the creation of high-Q MW dielectrics based on

Ba(Co1/3Nb2/3)O3 (BCN) offers a particularly attractive combination of properties. Polycrystalline Ba(Co1/3Nb2/3)O3 has high dielectric permittivity (ε =32) and *Qf* = 40000–60000 GHz [126, 127]. At the same time, centimeter and millimeter wave applications require higher *Q* values. The properties of BCN are very weak functions of temperature. In particular, the temperature coefficient of its resonant frequency (τ*f*) lies in the range –10 to – 7 ppm/K, suggesting that it can be used in the production of high-*Q*/low-τ*f* microwave materials [128, , 130]. The electrical properties of BCN, especially its *Q* (or its *Qf* product, where *f* is frequency), strongly depend on preparation conditions, in particular on the

It is reasonable to assume that the observed variations in the properties of BCN are related to the ceramic microstructure evolution during the fabrication process, cation ordering, and lattice distortions. Such distortions can be produced in BCN via slight changes in its cation

Therefore, we have studied the effect of partial nonstoichiometry in cation sublattices on the

**Figure 18.** Composition dependences of the (a) apparent density (ρ), permittivity (ε), (b) Qf product, and temperature coefficient of resonant frequency (τf) for Ba3+3xCoNb2O9+3x materials; measurements

Interesting properties are observed in the case of nonstoichiometry in the cobalt sublattice (BaCo1/3+yNb2/3O3+y, where -0.05 <y <0.01).

Increasing the cobalt content of this system with reference to stoichiometry leads to a monotonic increase in relative density and corresponding slight increase in permittivity ε in the range 32 to 34 (Fig. 19a). At higher cobalt deficiencies (y < –0.02), the samples contained an additional phase Ba8CoNb6O24. In the range –0.03 ≤ у ≤ 0.01, the quality factor varies nonlinearly, with a maximum at −0.03 ≤ у ≤ −0.02. The Qf product exceeds that of stoichiometric BCN by 30–50%, reaching 80000–85000 GHz (Fig. 19b).

Electron diffraction data for the BaСo1/3+yNb2/3O3+y samples indicates that cobalt deficiencies in the range −0.03 ≤ у ≤ −0.02 are favourable for 1 : 2 B-site cation ordering in the cobaltcontaining perovskite (Fig. 20). As mentioned above, cation ordering is accompanied by an increase in quality factor, as observed in this system (Fig. 18b). The reduction in quality factor at large deviations from stoichiometry (y < –0.1) is due to the presence of a significant amount of Ba8CoNb6O24.

**Figure 19.** Composition dependences of the (a) apparent density (ρ), permittivity (ε), (b) Qf product, and temperature coefficient of resonant frequency (τf) for Ba3Co1+yNb2O9+y materials; measurements at 10 GHz.

The increase in Ba8CoNb6O24 content with increasing cobalt deficiency (y < 0) leads to a result of practical interest: the temperature coefficient of resonant frequency switches sign (Fig. 18 b). The reason for this is that BaCo1/3Nb2/3O3 and Ba8CoNb6O24 differ in the sign of τf: –7 and +16 ppm/K, respectively [129, 131]. Because of this, the BaСo1/3+yNb2/3O3+y materials exhibit a temperature compensation effect, whose magnitude can be tuned by varying the cobalt content. The present results, therefore, suggest that cobalt-deficient Ba(Co1/3Nb2/3)O3 is

#### 136 Dielectric Material

an attractive host for engineering advanced temperature-stable microwave dielectric materials with Qf on the order of 80000–90000 GHz and τf = –2 to +3 ppm/K.

Microwave Dielectrics Based on Complex Oxide Systems 137

**Figure 21.** Micrograph of the microsection of 0.93 [0.98Mg2TiO4 – 0.02 Co2 TiO4] -0.07CaTiO3 ceramic

The main attention in the analysis of the physical properties of MW dielectrics is given to the temperature coefficient of permittivity (TCε) and to dielectric loss (tg δ). The expression

*T*

3 *l l*

   

*T*  (4)

, in addition to the

( 1)( 2) 1

 

 

*TC a a*

It should be noted that polarization a in Eq (4) is equal to the sum of polarizations of all atoms of cell, whose volume is ν, only if all atoms of the structure have a cubic environment. This is the case, e.g. for alkali halide crystals. In more complex structures, effective polarization aeff is used [138]. For example, for perovskite structure, effective polarization aeff

electronic and ionic polarization of all atoms in the unit cell. In this case, the last term al in expression (4) must be written as al Δ ai [137]. An analysis of the TCε value of different materials as a function of chemical composition showed [139] that the large positive value of TCε in alkali halide crystals probably arises from high ionic polarizability ai and great thermal expansion al. There are compounds, e.g. LaAlO3, SrZrO3, the behavior of whose ε(T) differs from that of paraelectrics. This is attributed to the presence of nonferroelectric phase transitions [137], which are coupled with the rotation of oxygen octahedra. Similar nonferroelectric phase transitions were found, e.g. in the system (BaxSr1-x)(Zn1/3 – Nb2/3)O3 [140]. It was shown that structural transitions are accompanied by the reversal of the TCε sign, though the ε quantity does not undergo noticeable changes, which are typical of

**12. Analysis of the physical properties of MW dielectrics** 

for TCε can be derived directly from the Clausius-Mossotti equation [137]:

 

is obtained by introducing an ionic component of polarization, Δ ai

where al is linear thermal expansion coefficient.

**Figure 20.** [110] electron diffraction patterns of the Ba3Co1+yNb2O9+y samples with y = (a) –0.07 and (b) 0. The arrows mark superlattice reflections.
