First-principles effective Hamiltonian calculations of the electrocaloric effect in ferroelectric BaxSr1−xTiO3

JID:PLA AID:126093 /SCO Doctopic: Condensed matter

[m5G; v1.261; Prn:28/10/2019; 13:19] P.1 (1-6)

Physics Letters A ••• (••••) ••••••

1

Contents lists available at ScienceDirect

67 68

2 3

Physics Letters A

4

69 70 71

5

72

6

www.elsevier.com/locate/pla

7

73

8

74

9

75

10

76

11 12 13 14 15 16 17 18

First-principles effective Hamiltonian calculations of the electrocaloric effect in ferroelectric Bax Sr1−x T i O 3

77

M. Tarnaoui, M. Zaim, M. Kerouad, A. Zaim ∗

81

Laboratoire de Physique des Matériaux et Modélisation des Systèmes (LP2MS), Unité Associée au CNRST-URAC: 08, University Moulay Ismail, Faculty of Sciences, B.P. 11201, Zitoune, Meknes, Morocco

83

23 24 25 26 27 28 29 30 31 32

80

84 85 86

20 22

79

82

19 21

78

a r t i c l e

i n f o

Article history: Received 17 July 2019 Received in revised form 22 October 2019 Accepted 22 October 2019 Available online xxxx Communicated by R. Wu Keywords: Effective Hamiltonian Adiabatic temperature Electrocaloric effect Barium strontium titanate

33 34 35 36 37 38

a b s t r a c t

87 88

Ferroelectric materials possess largest thermal response upon variations of the applied electric field, however, the magnitude corresponding to electrocaloric effect ( EC E ) is relatively too small for cooling applications. Theoretical insight is therefore required to provide additional information, leading to better understanding of the electrocaloric effect with enhanced performance. In this work, electrocaloric effect in Bax Sr1−x T i O 3 ( B S T ) ferroelectric ceramics is calculated from first-principles based effective Hamiltonian. The influence of the electric field and concentration on ferroelectric properties of Bax Sr1−x T i O 3 are investigated in detail. In particular, we have studied the polarization and pyroelectric coefficient as a function of temperature in order to examine the EC E. With increasing amount of Ba, the critical temperature T c is diffused and shifted towards higher temperature range. In addition, the adiabatic temperature change  T of Bax Sr1−x T i O 3 is also predicted with particular focus on the applied electric field and concentration x. Hence, the electrocaloric effect performance was determined by the feature of the phase transition. Our results also reveal particular contribution of the field gradient primary on the magnitude of adiabatic temperature change, leading to volume expansion, and thus improvement of EC E. Investigations in a wide temperature range also revealed large EC E shifted towards higher temperature to achieve  T  3.0 K for x = 1.0. An enhancement of EC E is therefore envisaged to show the usefulness of this material, which will be a step forward to experimentally synthesis this compound for more elucidations. © 2019 Elsevier B.V. All rights reserved.

89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104

39

105

40

106

41

107 108

42 43

1. Introduction

44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

In recent decades, ferroelectric materials based on Barium titanate ( BaT i O 3 ) have been successfully used in many manufactures due to its remarkable properties such as, the capacity of storage influenced by the dielectric constant. Among the ferroelectric materials, family Bax Sr1−x T i O 3 represents one of the attractive compositions with large contribution for many electronic applications of storage system such as, tunable microwave devices [1–3], multilayer capacitors [4,5], piezoelectric transducers [6] and energy storage [7–9]. Cooling devices of new generation based on electrocaloric effect ( EC E ) have attracted some attentions compared with the well-known refrigeration technologies due to its useful cooling applications [10–12], and could be more efficient, comfortable and environmentally friendly.

59 60 61 62 63 64 65 66

*

Corresponding author. E-mail addresses: [email protected] (M. Tarnaoui), [email protected] (M. Kerouad), [email protected] (A. Zaim). https://doi.org/10.1016/j.physleta.2019.126093 0375-9601/© 2019 Elsevier B.V. All rights reserved.

Recently, the increase demand for energy efficiency, cooling devices become more significant and require us to search more. In fact, the study of EC E and energy storage of B S T were in the top. Several studies of B S T materials were investigated using different techniques such as, molecular dynamic simulations [13], mean field theory [14] based on the transverse field Ising model and phenomenological thermodynamic theory [15] by the use of Landau-Devonshire approach. At the experimental level, Pe˘cnik et al. [16] have studied the dielectric properties and microstructure of B S T thin film. They have found that the dielectric properties of B S T thin film are strongly influenced by the grain size and residual stress. In Refs. [17,18], the structural and dielectric properties of B S T films were systematically investigated using different methods. Fan et al. [19] have investigated the thermal energy conversion of B S T ceramics with different curie temperature ( T c ). They have reported that materials possessing higher curie temperature begin to exhibit their superiority in energy conversion. Both experimental and theoretical works to analyze the electrocaloric performance have been tremendously found as evidenced by the reviews [20,21]. For instance, in Ref. [8], the energy storage properties and EC E of B S T ferroelectric ceramics were

109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132

JID:PLA

AID:126093 /SCO Doctopic: Condensed matter

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

[m5G; v1.261; Prn:28/10/2019; 13:19] P.2 (1-6)

M. Tarnaoui et al. / Physics Letters A ••• (••••) ••••••

2

experimentally studied, resulting large electrocaloric temperature change ( T max = 0.49 K). Lisenkov et al. [22] have examined EC E in Ba0.5 Sr0.5 T i O 3 from atomistic simulations. They have suggested that EC response presented in the material is mainly caused by the redistribution of the entropy between the part associated with the dipoles order and the one associated with the order in the kinetic energies of atomic vibrations. Motivation of this manuscript stems from ongoing studies of EC E in ferroelectric ceramics, however, thorough theoretical insight regarding ferroelectric properties and EC E of B S T thin film will be elucidated, leading to a step forward to provide guidance and better understanding of the usefulness of this material to possibly enhance electrocaloric performance. In the present paper, we investigate the EC E of Bax Sr1−x T i O 3 using the effective Hamiltonian and MD simulations. We will discuss the influence of the electric field and concentration x especially on the ferroelectric properties and electrocaloric response. In Section 2, we define the model. In Section 3 we present the results of simulation, while Section 4 is devoted to a brief conclusion. Followed by the work of Nishimatsu et al. [13], the effective Hamiltonian [23,24] is employed within molecular dynamic simulations to investigate EC E of Bax Sr1−x T i O 3 using feram code developed by Nishimatsu et al. [25,26], which is distributed freely under the GNU General Public License. We perform MD simulations in the canonical ensemble using Nosé-Poincaré thermostat [27] with small time step t = 2 fs. We thermalize the system for 20.000 time steps, and the properties were averaged for 60.000 time steps. A simulation box of 16 x 16 x 16 unit cells with small temperature steps in heating-up and cooling-down simulations (+2 K/step).

31 32

2. Model

33 34 35

The effective Hamiltonian used in the present calculation can be expressed as:

36 37 38 39 40 41 42 43

Hef f =

M∗

dipole

2



u˙ α ( R ) + 2

R ,α

46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

63 64 65 66

˙ α( R ) + V w

self

({u })

R ,α elas,homo

(1)

R

Where u ( R ) and w ( R ) are respectively the local soft-mode amplitude vector and acoustic displacement vector of each unit cell located at R. η1 ..η6 are the six-components local strain tensor. The first and second terms are the kinetic energy of the local soft ∗ modes and acoustic displacements with effective masses M dipole ∗ and M acoustic respectively. V self is the local mode self-energy, V dpl short

is the long-range dipole-dipole interaction energy, V is the short-range interaction energy, V elas,homo(inho) are respectively the homogeneous (inhomogenous) elastic energies, and V coup ,homo(inho) are respectively the coupling between the elastic deformations η1 ..η6 and local mode u, and between local mode u and acoustic mode w. The last term is the interaction between dipoles external electric field. Based on the Maxwell relation (∂ P /∂ T ) E = (∂ S /∂ E ) T , the adiabatic temperature change  T can be calculated as follows:

E 2

61 62

2

2

+ V dpl ({u }) + V short ({u }) + V ({u }, η1 ...η6 ) elas,inho coup ,homo ({ w }) + V ({u }, η1 ...η6 ) +V  ε .u ( R ) + V coup,inho ({u }, { w }) − Z ∗

44 45

∗  M acoustic

T = −T E1

1 C p, E

(

∂P )dE ∂T

(2)

Where the applied electric field is varied from E 1 to E 2 ( E = E 2 − E 1 ), and C p , E is the specific heat at constant pressure and

applied electric field. The value of the specific heat C E = 3.05 x 106 J K−1 m−3 corresponds to experimentally measured at room temperature [28], and reported for similar compound BaT i O 3 [29].

67 68 69 70

3. Results and discussions

71 72

In this section, we will investigate the influence of several parameters on the ferroelectric properties and electrocaloric effect of Bax Sr1−x T i O 3 ferroelectric ceramics. Fig. 1(a-f) show the temperature dependence of the longitudinal polarization P z and pyroelectric coefficient ρ under various applied electric fields ( E = 0, 100, 200, 300 and 400 cm), and selected concentrations of Ba (x = 0.0, 0.5 and 1.0 respectively). As it is known, barium titanate ( BaT i O 3 ) exhibits three distinct peaks, i.e. three phase transitions. It has a cubic phase, showing a paraelectric characteristic at higher temperature, then it transforms into a tetragonal phase (ferroelectric character) with spontaneous polarization ( P s ) along [001], then into orthorhombic phase (Ps // [011]), and finally to rhombohedral one. While strontium titanate SrT i O 3 is a centrosymmetric paraelectric material at room temperature. In order to combine this too materials, i.e. Bax Sr1−x T i O 3 . Nishimatsu et al. [13] have calculated the required parameters of the effective Hamiltonian for each material, and then combined them. Importantly, they have revealed relationship that connects hydrostatic pressure with concentration as discussed in [13]. From Fig. 1a, the longitudinal polarization P z in the vicinity of the critical temperature is dropped rapidly as the temperature increases and shows a continuous behaviour around T c in the absence of Ba content. However, Bax Sr1−x T i O 3 ferroelectric ceramics is still implicitly under pressure, which is the main reason we get a polarization exhibiting continuous behaviour in the vicinity of the critical temperature. In presence of electric field, the phase transition disappears, then the critical temperature is shifted to slightly higher temperature. Consequently, the system shows a smooth dependence of the longitudinal polarization on temperature. Distinction of the spontaneous polarization P s observed in Fig. 1a can be attributed mainly to difference in applied hydrostatic pressure used to induce the curie temperature. As can be seen from Fig. 1b in the absence of electric field, Ba0.5 Sr0.5 T i O 3 shows a characteristic feature of first-order transition around 200 K, i.e., the longitudinal polarization drops discontinuously to zero. Subsequently, the external electric field enhances the polarization and induces the dipoles to switch to be preferentially aligned. Moreover, at lower temperature, the increase in the applied electric field leads to a strong increase in the spontaneous polarization compared with the one formerly observed (Fig. 1a). Fig. 1c describes the case for x = 1. Our calculated spontaneous polarization is around 28 μC cm−2 in the absence of the electric field, which is slightly larger than reported in previous MD simulations [30], which is due significantly to difference in hydrostatic pressure taking into account. Hence, the applied electric field shifts the first-order transition character, and the transformation spreads over a larger temperature range, which means the ferroelectric behaviour also extends in term of transition temperature. In addition, the introduction of Ba content enlarges the phase transitions to some extent, and increases the critical temperature to ∼ 290 K. Consequently, the magnitude decreases and shifted towards higher temperature. Importantly, the concentration x is connected to the pressure as mentioned in [13]. The increase of x remains the pressure negative, therefore the phase transition is shifted to higher temperature range as discussed in detail in the review [30]. Hence, when the concentration increases (say x = 1), we get BaT i O 3 which is a ferroelectric material that exhibits 3 phase transitions and first-order character as already well-known in literature, which is the main reason we have observed the hump effect precisely in Fig. 1c to elucidate the first-order feature and phase transitions

73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132

JID:PLA AID:126093 /SCO Doctopic: Condensed matter

[m5G; v1.261; Prn:28/10/2019; 13:19] P.3 (1-6)

M. Tarnaoui et al. / Physics Letters A ••• (••••) ••••••

3

1

67

2

68

3

69

4

70

5

71

6

72

7

73

8

74

9

75

10

76

11

77

12

78

13

79

14

80

15

81

16

82

17

83

18

84

19

85

20

86

21

87

22

88

23 24

Fig. 1. (Color online) Temperature dependence of (a-c) the polarizations and (d-f) pyroelectric coefficients of Bax Sr1−x T i O 3 ferroelectric ceramics under various applied electric fields ( E = 0, 100, 200, 300 and 400 kV/cm), and for selected values of the concentrations (x = 0.0, 0.5 and 1.0 respectively).

27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

90 91

25 26

89

exhibited by BaT i O 3 , resulting a shift of T c towards higher temperature. Moreover, when x = 0.5, i.e. Ba0.5 Sr0.5 T i O 3 will result almost the same properties described formerly for x = 1, however, major distinction concerns only the phase transition temperature. Fig. 1(d-f) elucidate the influence of the applied electric fields up to a maximum of 400 kV/cm on the pyroelectric coefficient ρ for the same values used previously ( E = 0, 100, 200, 300, and 400 kV/cm). The pyroelectric coefficient (ρ = − ∂∂ TP ) exhibits a peak near the phase transition. The increase of the electric field reduces the maximum of ρ to some extent, and then shifts the transition temperature to slightly higher temperature range until it vanishes. Upon an increase of Ba content (Fig. 1e and 1f), the temperature corresponding to the maximum pyroelectric coefficient is shifted towards higher temperature, hence the critical temperature increases. In the absence of electric field, the pyroelectric coefficient increases a little bit (ρ  0.40 for x = 0.5, and ρ  1.2 for x = 1.0) and remains almost unchanged in the presence of the applied electric field. Consequently, it can be seen that large polarization gradient will induce better electrocaloric performance. In Fig. 2, we give snapshots of the switching process under selected applied electric fields ( E = 0, 100 and 300 kV/cm) for x = 0.5, and T = 300 K. In the absence of the external field, the system shows disorder character and P z ∼ 0. The increase in the applied electric field induces dipoling order-disorder behaviours to switch along the direction of the applied electric fields ( E = 100, and 300 kV/cm), resulting the appearance of induced polarization, which means P z increases. Hence, the disorder character is reduced and ferroelectric domains slightly appear ( E = 300 kV/cm). Consequently, the polarization is switched. In order to study the electrocaloric performance evaluated under various applied electric fields, we have depicted in Fig. 3 the adiabatic temperature change as a function of temperature for heating-up, and x = 0. We have fixed the final electric ( E 2 = 350 kV/cm) and ranging the initial one from 50 to 250 kV/cm at an increment of 50 kV/cm (Fig. 3a). Typically, EC E was carried out by analyzing the temperature dependence of spontaneous polarization during the application or removal of the electric field, and the change of ordering entropy. Following Eq. (2), the electrocaloric refrigeration  T can be examined in response to an applied electric field. As expected, the adiabatic temperature change increases rapidly with temperature until a maximum, then decreases gradu-

ally. The increase in the field range reduces the maximum of  T and thus the magnitude, which means the EC E will always occur above the Curie temperature. Furthermore, the maximum of adiabatic temperature change shifts slightly towards higher temperature when the initial field increases. The electrocaloric effect in this case is associated with the applied electric field induced dipoling order-disorder. Furthermore, it was mentioned that the overall magnitude of EC E depends on the field gradient as evidenced by the reviews reported in literature [31–34]. Fig. 3b describes the case of constant field gradient  E = 100 kV/cm. E 1 is varied from 100 to 350 kV/cm and E 2 from 200 to 450 kV/cm. Both  T and the magnitude change to a higher temperature even with constant electric field ( E = 100 kV/cm), showing substantial contribution of the external applied electric field primarily on the magnitude of adiabatic temperature change, and thus leading to volume expansion, and improvement of EC E. Moreover, our results indicate the importance of the initial and final electric fields to properly control the magnitude of the electrocaloric performance as reported in the review [29]. Therefore, by keeping the initial field E 1 small, it is possible to enhance the adiabatic temperature change, and therefore achieve large EC E. Pertinent example of EC E dealing with the present situation could be found in the review [35], which is mainly attributable to the initial electric field E 1 , and therefore resulting large  T for small  E. However, when E 1 becomes large, it is necessary to obtain large adiabatic temperature change. Importantly, by appropriately selecting the field gradient to induce EC E, the magnitude and temperature change can be improved. Fig. 4 displays variations in the polarization and pyroelectric coefficient as a function of temperature under constant electric field ( E = 100 kV/cm), and several values of x (x = 0.0, 0.2, 0.5, 0.8 and 1.0). From Fig. 4a, the increase of the concentration x vanishes the continuous behaviour (middle temperature range), resulting the appearance of the feature of first-order ferroelectric phase transition. Hence, the critical temperature increases, and the polarization drops continuously to higher temperature. Moreover, the increase of x enhances slightly the polarization and switches the dipoles along the polar axis. Fig. 4b describes the temperature dependence of the pyroelectric coefficient ρ . It is obvious that ρ exhibits a peak around the transition temperature with largest value (ρ ∼ 0.18 for x = 1.0), which will contribute to a large adiabatic tem-

92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132

JID:PLA

4

AID:126093 /SCO Doctopic: Condensed matter

[m5G; v1.261; Prn:28/10/2019; 13:19] P.4 (1-6)

M. Tarnaoui et al. / Physics Letters A ••• (••••) ••••••

1

67

2

68

3

69

4

70

5

71

6

72

7

73

8

74

9

75

10

76

11

77

12

78

13

79

14

80

15

81

16

82

17

83

18

84

19

85

20

86

21

87

22

88

23

89

24

90

25

91

26

92

27

93

28

94 95

29 30 31

Fig. 2. (Color online) Snapshots dipole configurations at 300 K for heating-up simulation projected into (011) plane for various electric fields ( E = 0, 100 and 300 kV/cm respectively), and for x = 0.5. The -z-polarized and +z-polarized sites are denoted by blue and red respectively.

96 97

32

98

33

99

34

100

35

101

36

102

37

103

38

104

39

105

40

106

41

107

42

108

43 44 45

Fig. 3. (Color online) Temperature dependence for heating-up simulation of (a) the adiabatic temperature change where E 1 is varied and E 2 is kept constant at 350 kV/cm, and (b) adiabatic temperature change where the applied electric field range is constant at 100 kV/cm and both E 1 and E 2 are varied.

109 110 111

46

112

47

113

48

114

49

115

50

116

51

117

52

118

53

119

54

120

55

121

56

122

57 58

123

Fig. 4. (Color online) Temperature dependence of (a) the polarization and (b) pyroelectric coefficient of Bax Sr1−x T i O 3 ferroelectric ceramics for constant electric field ( E = 100 kV/cm) and various concentrations (x = 0.0, 0.2, 0.5, 0.8 and 1.0).

59

62 63 64 65 66

125 126

60 61

124

perature change  T . Consequently, the increase of x destroys the disorder character and manifests more phases. To better understand the influence of x on the electrocaloric performance, Fig. 5 displays the temperature dependence of  T for various concentrations (x = 0.0, 0.2, 0.5, 0.8 and 1.0). We therefore use E 1 = 100 kV/cm and E 2 = 350 kV/cm as the initial

and finale electric fields to compute the EC E. According to Eq. (2), materials which possess larger pyroelectric coefficient would have higher EC E. The maximum of adiabatic temperature change | T max | which are mostly confined near the critical temperature varied rapidly with increasing the concentration x (| T max | = 0.92 K, 1.02 K, 1.55 K, 2.43 K and 2.96 K for x = 0.0, 0.2, 0.5, 0.8 and 1.0

127 128 129 130 131 132

JID:PLA AID:126093 /SCO Doctopic: Condensed matter

[m5G; v1.261; Prn:28/10/2019; 13:19] P.5 (1-6)

M. Tarnaoui et al. / Physics Letters A ••• (••••) ••••••

5

To explain this mechanism, we present in Fig. 6 snapshots of dipole configurations for some selected concentrations (x = 0.0, 0.5 and 1.0) under constant applied electric field  E = 100 kV/cm, and T = 300 K. From this figure, the increase of x appears gradually the order character (Fig. 6c), and the dipoles alignment evolve. Hence, the polarization is induced. Furthermore, the dipoles are still small and their alignment remain partially disordered (x = 0.5) and longranged ordered (x = 1.0).

1 2 3 4 5 6 7 8 10 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

37

69 70 71 72 73 74 76

4. Conclusion

Fig. 5. (Color online) Temperature dependence of the adiabatic temperature change for various concentrations (x = 0.0, 0.2, 0.5, 0.8 and 1.0), where E 1 and E 2 are kept constant at 100 kV/cm and 350 kV/cm respectively.

77 78

The EC E of Bax Sr1−x T i O 3 was investigated using first-principles based effective Hamiltonian implemented within MD framework. Our calculation points out that the adiabatic temperature change  T strongly depends on the magnitude of the applied electric field. However, by appropriately selecting the required initial and final electric fields, the EC E can be controlled. Moreover, a greater amount of Ba content increases the transition temperature to an even higher temperature and evolves the dipoles to switch to be aligned along the field axis, resulting an induced polarization. Hence, the observed EC E is shifted towards higher temperature and reaches in this case approximately ( T  2.4 K for x = 0.8) and ( T  3 K for x = 1.0). This work also reveals the contribution of the external electric field primarily on the magnitude of  T , leading to a larger volume expansion, and thus improvement of EC E, which will be a step forward to experimentally synthesis this material and may potentially open the door for practical applications.

respectively), and thus the magnitude. Among the Bax Sr1−x T i O 3 samples, the maximum  T (∼ 2.5 K) referring to Ba0.8 Sr0.2 T i O 3 has been obtained and reported almost similarly by Liu et al. [28] of compositionally graded B S T films with misfit strain and internal field caused by the oxygen vacancies, which is attributed to internal strains and space charge accumulation existing at the interfaces of the compositionally graded film according to their results. Moreover, upon an increase of the concentration x (adding Ba content), the order character improves and the dipoles realign, which in turn affects the entropy change and thus  T . Numerous references dealing with this compound have been discussed in the reviews [21,28,36–38]. Distinction with [21,28,36–38] is mainly attributed to difference in applied electric field taking into account, which enlarges the magnitude of EC E, as well as additional parameters such as internal strains and pressure which could induce large EC E. More comparison results with other reviews reported in literature are elcucidated in Table 1. Hence, this study provides estimation regarding the EC E in Bax Sr1−x T i O 3 ( B S T ) samples, which is slightly competitive in comparison with other compositions of B S T .

79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96

Declaration of competing interest

97 98

The authors declare no conflict of interest.

99 100 101

35 36

68

75

9 11

67

Table 1 Comparison of EC properties of Bax Sr1−x T i O 3 family ceramics reported in this work with other materials.

102 103 104

38 39

Material

E (kV/cm)

T (K )

T ( K )

Material

105

40

Ba0.8 Sr0.2 T i O 3 (present work)

250

406

2.46

Ceramic

106

41

Ba0.8 Sr0.2 T i O 3 (under strain) [28]

350

335

2.5

Film

107

42

Ba0.8 Sr0.2 T i O 3 (without strain) [28]

350

314

1.75

Film

108

43

Ba0.8 Sr0.2 T i O 3 [36]

33

338

0.83

Ceramic

109

44

Ba0.8 Sr0.2 T i O 3 [37]

50

344

1.67

Ceramic

110

45

Ba0.7 Sr0.3 T i O 3 [21]

10

299

0.18

Ceramic

111

46

Ba0.65 Sr0.35 T i O 3 [38]

90

303

2.10

Ceramic

112

47

Ba0.65 Sr0.35 T i O 3 [21]

20

296

0.42

Ceramic

113

48

114

49

115

50

116

51

117

52

118

53

119

54

120

55

121

56

122

57

123

58

124

59

125

60

126

61

127

62

128

63

129 130

64 65 66

Fig. 6. (Color online) Snapshots dipole configurations at 300 K for heating-up simulation projected into (011) plane at constant electric field ( E = 100 kV/cm), and for various concentrations (x = 0.0, 0.5 and 1.0 respectively). The -z-polarized and +z-polarized sites are denoted by blue and red respectively.

131 132

JID:PLA

AID:126093 /SCO Doctopic: Condensed matter

6

1

[m5G; v1.261; Prn:28/10/2019; 13:19] P.6 (1-6)

M. Tarnaoui et al. / Physics Letters A ••• (••••) ••••••

Acknowledgement

2 3 4

This work has been initiated with the support of URAC: 08 and the project PPR2: (MESRSFC-CNRST).

5 6

References

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

[1] K. Nadaud, C. Borderon, R. Gillard, E. Fourn, R. Renoud, H.W. Gundel, Thin Solid Films 591 (2015) 90. [2] C.V. Varanasi, K.D. Leedy, D.H. Tomich, G. Subramanyam, Thin Solid Films 517 (2009) 2878. [3] H.V. Alexandru, C. Berbecaru, F. Stanculescu, A. Ioachim, M.G. Banciu, M.I. Toacsen, L. Nedelcu, D. Ghetu, G. Stoica, J. Mater. Sci. Eng. B 118 (2005) 92. [4] C.-C. Ho, B.-S. Chiou, L.-C. Chang, C.-C. Chou, B.-H. Liou, C.-C. Yu, Surf. Coat. Technol. 201 (2006) 4163. [5] O.G. Vendik, S.P. Zubko, S.F. Karmanenko, M.A. Nikol’ski, N.N. Isakov, I.T. Serenkov, V.I. Sakharov, J. Appl. Phys. 91 (2002) 331. [6] T.T. Chen, M.S. Fu, B.W. Jia, Y.J. Wu, X.Q. Liu, X.M. Chen, Adv. Appl. Ceram. 112 (2013) 270. [7] W. Zhang, S. Xue, S. Liu, J. Wang, B. Shen, J. Zhai, J. Alloys Compd. 617 (2014) 740. [8] P.-Z. Ge, X.-G. Tang, Q.-X. Liu, Y.-P. Jiang, W.-H. Li, J. Luo, J. Mater. Sci., Mater. Electron. 29 (2018) 1075. [9] Y.H. Huang, J.J. Wang, T.N. Yang, Y.J. Wu, X.M. Chen, L.Q. Chen, Appl. Phys. Lett. 112 (2018) 102901. [10] S.-G. Lu, Q. Zhang, Adv. Mater. 21 (2009) 1983. [11] S. Kar-Narayan, N.D. Mathur, Ferroelectrics 433 (2012) 107. [12] X. Moya, E. Defay, N.D. Mathur, S. Hirose, Mater. Res. Soc. Bull. 43 (2018) 291. [13] T. Nishimatsu, A. Grünebohm, U.V. Waghmare, M. Kubo, J. Phys. Soc. Jpn. 85 (2016) 114714. [14] T. Yong-Mei, J. Qing, Chin. Phys. Soc. 13 (2004) 1149. [15] V.B. Shirokov, R.A. Shakhovoy, A.G. Razumnaya, Y.I. Yuzyuk, J. Appl. Phys. 118 (2015) 024101. [16] T. Pe˘cnik, S. Glin˘sek, B. Kmet, B. Mali˘c, J. Alloys Compd. 646 (2015) 766.

[17] X.H. Zhu, E. Defaÿ, B. Guigues, G. Le Rhun, C. Dubarry, M. Aïd, J. Eur. Ceram. Soc. 30 (2010) 471. [18] N.C. Pramanik, N. Anisha, P.A. Abraham, N.R. Panicker, J. Alloys Compd. 476 (2009) 524. [19] B. Fan, G. Yang, M.-Y. Li, P. Liu, S. Qiu, M. Shen, H. Liu, G. Zhang, Q. Wang, S. Jiang, Ceram. Int. 44 (2018) 8270. [20] X.Q. Liu, T.T. Chen, M.S. Fu, Y.J. Wu, X.M. Chen, Ceram. Int. 40 (2014) 11269. [21] Y. Bai, X. Han, K. Ding, L.-J. Qiao, Appl. Phys. Lett. 103 (2013) 162902. [22] S. Lisenkov, I. Ponomareva, Phys. Rev. B 80 (2009) 140102(R). [23] R.D. King-Smith, D. Vanderbilt, Phys. Rev. B 49 (1994) 5828. [24] W. Zhong, D. Vanderbilt, K.M. Rabe, Phys. Rev. B 52 (1995) 6301. [25] T. Nishimatsu, U.V. Waghmare, Y. Kawazoe, D. Vanderbilt, Phys. Rev. B 78 (2008) 104104. [26] J. Paul, T. Nishimatsu, Y. Kawazoe, U.V. Waghmare, Phys. Rev. Lett. 99 (2007) 077601. [27] S.D. Bond, B.J. Leimkuhler, B.B. Laird, J. Comput. Phys. 151 (1999) 114. [28] B.L. Liu, J.B. Wang, X.L. Zhong, K. Huang, B. Li, F. Wang, J. Xie, Y.C. Zhou, RSC Adv. 4 (2014) 24533. [29] G. Akcay, S.P. Alpay, J.V. Mantese, G.A. Rossetti, Appl. Phys. Lett. 90 (2007) 252909. [30] B. Luo, X. Wang, E. Tian, L. Wu, L. Li, J. Appl. Phys. 120 (2016) 074106. [31] B. Asbani, J.-L. Dellis, A. Lahmar, M. Courty, M. Amjoud, Y. Gagou, K. Djellab, D. Mezzane, Z. Kutnjak, M. El Marssi, Appl. Phys. Lett. 106 (2015) 042902. [32] V.S. Bondarev, I.N. Flerov, M.V. Gorev, E.I. Pogoreltsev, M.S. Molokeev, E.A. Mikhaleva, A.V. Shabanov, A.V. Es’kov, J. Adv. Dielectr. 7 (2017) 1750041. [33] A.S. Mischenko, Q. Zhang, J.F. Scott, R.W. Whatmore, N.D. Mathur, Science 311 (2006) 1270. [34] J. Shi, R. Zhu, X. Liu, B. Fang, N. Yuan, J. Ding, H. Luo, Materials 10 (2017) 1093. [35] S.P. Beckman, L.F. Wan, J.A. Barr, T. Nishimatsu, Mater. Lett. 89 (2012) 254. [36] K.S. Srikanth, S. Patel, R. Vaish, J. Aust. Ceram. Soc. 54 (2018) 439. [37] Y. Bai, F. Han, S. Xie, J. Li, S. Qin, J. Li, L. Qiao, D. Guo, J. Alloys Compd. 736 (2018) 57. [38] X.Q. Liu, T.T. Chen, Y.J. Wu, X.M. Chen, J. Am. Ceram. Soc. 96 (2013) 1021.

67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95

30

96

31

97

32

98

33

99

34

100

35

101

36

102

37

103

38

104

39

105

40

106

41

107

42

108

43

109

44

110

45

111

46

112

47

113

48

114

49

115

50

116

51

117

52

118

53

119

54

120

55

121

56

122

57

123

58

124

59

125

60

126

61

127

62

128

63

129

64

130

65

131

66

132