Update paper.md

paper/paper.md

@@ -25,7 +25,7 @@ Ferroelectric materials have an order parameter called polarization that can be
 
 Due to the small sizes and exciting properties of DWs, there has been significant interest in studying how to control and manipulate them using atomistic simulations [@schultheiss2020intrinsic; @smaabraaten2020domain; @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]$_P$ axis[@ederer2005effect], [@wang2003epitaxial]. The ferroelectric phase transition in BiFeO$_3$ 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 BaTiO$_3$[@taherinejad2012bloch], PbTiO$_3$[@meyer2002ab], YMnO$_3$[@smaabraaten2018charged], and ferroelastic DWs in CaTiO$_3$[@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. Figure \fig:scheme shows the structure of the ``DWBuilder`` package. 
+``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. Figure 1 explains the structure and workflow of the ``DWBuilder`` package. 
 
 The first part, handled by the scripts ``dwbuilder.py`` and ``dbuilder.py``,  produces domain walls by first analyzing the input unit cell geometry and determining the space group of the structure. The space group is identified using the open-source Python library Pymatgen. If the space group matches the specified type, the script offers a range of possible domain wall types and ultimately creates the DW structures. If the space group of the input structure does not match, the script allows you to choose a desired space group type or manually define the domains by specifying lattice vectors. To generate different domains separately, you can use ``dbuilder.py`` to develop distinct domains, which can be useful for bulk and surface calculations of individual domains.