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paper/paper.md

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 # Summary
 
-Ferroelectric materials have an order parameter called polarization that can be toggled using an external electric field. Regions within the material that exhibit consistent polarization are known as domains, and the boundaries between different domains are referred to as domain walls (DWs).  These domain walls, which are only a few nanometers wide, possess unique properties with potential technological applications. DWs show promise for nanoscale electronic circuit elements and enable innovative design concepts because they can be created, erased, and manipulated using electric fields [@catalan2012domain],[meier2015functional],[@bednyakov2018physics] . DWs can also replicate the functions of key electronic components such as diodes [@whyte2015diode], transistors [@mundy2017functional] , and random access memory (RAM) [@sharma2017nonvolatile] .
+Ferroelectric materials have an order parameter called polarization that can be toggled using an external electric field. Regions within the material that exhibit consistent polarization are known as domains, and the boundaries between different domains are referred to as domain walls (DWs).  These domain walls, which are only a few nanometers wide, possess unique properties with potential technological applications. DWs show promise for nanoscale electronic circuit elements and enable innovative design concepts because they can be created, erased, and manipulated using electric fields [@catalan2012domain],[@meier2015functional],[@bednyakov2018physics] . DWs can also replicate the functions of key electronic components such as diodes [@whyte2015diode], transistors [@mundy2017functional], and random access memory (RAM) [@sharma2017nonvolatile] .
 
-Due to the small sizes and exciting properties of domain walls (DWs) in ferroelectric materials, there has been significant interest in studying how to control and manipulate them using atomistic simulations as discussed in [@schultheiss2020intrinsic], [@smaabraaten2020domain], and [@smaabraaten2018charged]. However, developing atomic DW structures is challenging and requires knowledge and understanding of the order parameter and DW types in ferroelectric materials. DWs can be ferroelectric, antiferroelectric, and/or ferroelastic, and they can vary depending on the allowed symmetry of the ferroelectric material. For instance, ferroelectric {BiFeO3} exists at room temperature as a rhombohedrally distorted perovskite with space group R3c and an internal angle of 89.23°. The spontaneous polarization is oriented along the [111]_P axis[@ederer2005effect], [@wang2003epitaxial]. The ferroelectric phase transition in BiFeO<sub>3</sub> causes lattice distortion along the <111>_P polarization direction, resulting in four types of DWs with polarization direction changes of 71°, 109°, or 180°[@wang2003epitaxial]. Similarly, other domain wall types have been identified in ferroelectric materials such as {BaTiO3}[@taherinejad2012bloch], PbTiO<sub>3</sub>[@meyer2002ab], YMnO<sub>3</sub> [@smaabraaten2018charged], and ferroelastic DWs in CaTiO<sub>3</sub>[@barone2014improper].
+Due to the small sizes and exciting properties of DWs in ferroelectric materials, there has been significant interest in studying how to control and manipulate them using atomistic simulations as discussed in [@schultheiss2020intrinsic], [@smaabraaten2020domain], and [@smaabraaten2018charged]. However, developing atomic DW structures is challenging and requires knowledge and understanding of the order parameter and DW types in ferroelectric materials. DWs can be ferroelectric, antiferroelectric, and/or ferroelastic, and they can vary depending on the allowed symmetry of the ferroelectric material. For instance, ferroelectric BiFeO$_3$ exists at room temperature as a rhombohedrally distorted perovskite with space group R3c and an internal angle of 89.23°. The spontaneous polarization is oriented along the [111]<sub>P</sub> axis[@ederer2005effect], [@wang2003epitaxial]. The ferroelectric phase transition in BiFeO<sub>3</sub> causes lattice distortion along the <111><sub>P</sub> polarization direction, resulting in four types of DWs with polarization direction changes of 71°, 109°, or 180°[@wang2003epitaxial]. Similarly, other domain wall types have been identified in ferroelectric materials such as BaTiO<sub>3</sub>[@taherinejad2012bloch], PbTiO<sub>3</sub>[@meyer2002ab], YMnO<sub>3</sub> [@smaabraaten2018charged], and ferroelastic DWs in CaTiO<sub>3</sub>[@barone2014improper].
 
 ``DWBuilder`` code is designed as a command-line tool to create DWs and interface structures from specific input unit cell geometries, as described in detail in the README file of the repository. The code comprises two main components: (i) a domain wall builder for similar materials and (ii) a heterogeneous interface builder for multi-material atomic interfaces.