Positive and negative electrocaloric effect in ${\mathrm{BaTiO}}_{3}$ in the presence of defect dipoles

Positive and negative electrocaloric effect in ${BaTiO}_{3}$ in the presence of defect dipoles

Yang-Bin Ma, Anna Grünebohm, Kai-Christian Meyer, Karsten Albe, and Bai-Xiang Xu

Phys. Rev. B 94, 094113 – Published 29 September 2016

Abstract

The influence of defect dipoles on the electrocaloric effect (ECE) in acceptor doped ${BaTiO}_{3}$ is studied by means of lattice-based Monte-Carlo simulations using a Ginzburg-Landau type effective Hamiltonian. Oxygen vacancy-acceptor associates are described by fixed local dipoles with orientation parallel or antiparallel to the external field. By a combination of canonical and microcanonical simulations the ECE is directly evaluated. Our results reveal that in the case of antiparallel defect dipoles the ECE can be positive or negative depending on the dipole density. Moreover, a transition from a negative to positive ECE can be observed when the external field increases. These transitions are due to the delicate interplay of internal and external fields and are explained by the domain structure evolution and related field-induced entropy changes. The results are in good qualitative agreement to those obtained by molecular dynamics simulations employing an ab initio based effective Hamiltonian. Finally, a modified electrocaloric cycle, which makes use of the negative ECE in the presence of defect dipoles, is proposed to enhance the cooling effect.

Received 11 September 2015
Revised 25 March 2016

DOI:https://doi.org/10.1103/PhysRevB.94.094113

Authors & Affiliations

Yang-Bin Ma^1,*, Anna Grünebohm², Kai-Christian Meyer¹, Karsten Albe^1,†, and Bai-Xiang Xu^1,‡

¹Institute of Materials Science, Technische Universität Darmstadt, 64287 Darmstadt, Germany
²Faculty of Physics and CENIDE, University of Duisburg-Essen, 47048 Duisburg, Germany

^*y.ma@mfm.tu-darmstadt.de
^†albe@mm.tu-darmstadt.de
^‡xu@mfm.tu-darmstadt.de

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Vol. 94, Iss. 9 — 1 September 2016

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Figure 1
Visualization of a simulation box with a fixed defect dipole (red) in the (a) 2D MC case and (b) 3D MD case (only one layer shown). Both simulations boxes have different sizes ( $8 \times 8$ and $4 \times 4 \times 4$ , respectively) but the same concentrations (1/64). As can be seen, the distances between the defect dipoles for the MC case are larger than for the MD case.
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Figure 2
Loading history in the (a) “Field off” and (b) “Field on” case for a MC (full line) and a MD (dashed line) simulation. Prepoling is neglected in the “Field on” case in the MD simulations, because at high defect concentrations the prepoled and unpoled sample are very similar. In the MC simulations the field is switched on or off instantaneously and in the MD simulations it is ramped. For details see Secs. 2c and 2d.
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Figure 3
Positive and negative ECE studied via MC for the “field on” case. (a) ECE in the presence of parallel aligned defect dipoles. Different defect concentrations are considered under a given external field $E^{ex}$ . (b) ECE as a function of $E^{ex}$ for a defect concentration of 6%. (c) Positive and negative ECE in the presence of antiparallel dipoles. When the defect density exceeds a critical value, the resultant internal antiparallel field overcomes $E^{ex}$ and a negative temperature change is observed (negative ECE). (d) Influence of $E^{ex}$ , while antiparallel defect dipoles with a concentration of 3% are present. When $E^{ex}$ surpasses the internal field induced by the antiparallel defect dipoles, a negative ECE appears only at lower temperatures, while a positive ECE dominates at higher temperatures, see the olive line (84.6 kV ${mm}^{- 1}$ ). The above phenomena are explained by the domain structures at the points I, II, III, A, and B in Fig. 4.
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Figure 4
Domain configurations at different points I, II, III, A, and B marked in Fig. 3. The external field $E^{ex}$ is applied in the horizontal direction and points to the right. (a) and (b) are the domain structure snapshots before and after the adiabatic stage for point I; (c) and (d) for point II; (e) and (f) for point III; (g) and (h) for point A; (i) and (j) for point B. The black dots with white arrows represent the defect dipoles which are either parallel or antiparallel to $E^{ex}$ . The red, blue, green and yellow dots represent the dipoles pointing to the left, to the right, to the bottom, and to the top, respectively.
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Figure 5
Comparison of $Δ T / E$ over $T$ obtained from the MC simulations with 3% antiparallel defect dipoles (top row) with the results of MD simulations with 1% antiparallel defect dipoles (bottom row). (a) and (b) are “Field on” cases, while (c), (d), (e), and (f) are “Field off” cases. A qualitative agreement between the MC and MD simulations is clearly visible. For the choice of parameters see Sec. 2d.
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Figure 6
Proposed modified ECE cycle to enhance the resultant $Δ T$ of a sample containing defect dipoles. The conventional cycle involves a-b-c-d-a (dashed arrows), and the proposed one includes a-b-c-e-a (solid arrows). Under adiabatic condition a field is applied rapidly parallel to the defect dipoles, taking the initial state (a) at $T_{0}$ to a state (b) with lower configurational entropy at $T_{1}$ . By transferring heat to a heat sink, the state (b) transforms to the state (c) with further lower configurational entropy at $T_{0}$ . Removing the field rapidly under adiabatic condition, from state (c) the system is cooled to state (d) at $T_{2}$ . By comparison, applying a field antiparallel to the defect dipoles the system is cooling further from state (c) to state (e) ( $T_{3} < T_{2}$ ). It should be noted that the magnitude of the external field should not be greater than the magnitude of the average internal field induced by the defect dipoles. Finally, by absorbing heat from a load, the system warms up to the state (a). The relation of the involved temperatures can be summarized as $T_{3} < T_{2} < T_{0} < T_{1}$ . It can be seen that by introduction of defect dipoles an enhancement of the electrocaloric cooling is achieved.
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Physical Review B

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Positive and negative electrocaloric effect in ${BaTiO}_{3}$ in the presence of defect dipoles

Yang-Bin Ma, Anna Grünebohm, Kai-Christian Meyer, Karsten Albe, and Bai-Xiang Xu

Phys. Rev. B 94, 094113 – Published 29 September 2016

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Physical Review B

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Positive and negative electrocaloric effect in BaTiO3 in the presence of defect dipoles

Yang-Bin Ma, Anna Grünebohm, Kai-Christian Meyer, Karsten Albe, and Bai-Xiang Xu

Phys. Rev. B 94, 094113 – Published 29 September 2016

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Positive and negative electrocaloric effect in ${BaTiO}_{3}$ in the presence of defect dipoles