energy

Grain
boundary (GB) can be defined as the interfacial region between two adjacent
crystals with different orientations. The microstructural properties of grain
boundaries have effect on physical and mechanical properties of polycrystalline
materials. Grain boundary structure and the excess energy per unit area that
exists in the system because of the presence of the grain boundaries often lead
to different properties or responses in the materials such as intergranular
fracture [1], corrosion
resistance [2], grain growth [3] and strength
of polycrystalline materials. Therefore the concept of ‘‘grain boundary design”
for the first time was suggested by Watanabe [4] that can be
defined as increase the number density of grain boundaries with favorable
properties, while decreasing the number density of boundaries that have
unfavorable properties. Due to Experimental difficulties off measuring precise
interfacial energies, many theoretical efforts have been made to model GB structures,
such as coincident-site-lattice (CSL) model [5], the
structural-unit (SU) model [6, 7] and the
displacement-shift-complete (DSC) model [8] and it is not
clear which model should be used for a calculation of a specific GB to achieve appropriate
results. Most researchers focused on face
centered cubic metals, while a few efforts on BCC metals has been made [9]. Wolf [10-12]
showed that the energy anisotropies of Fe and Mo were similar for symmetrical
tilt boundaries (STGBs). Morita and Nakashima [13] studied the GB
energy of <100> symmetric tilt boundaries in Mo, their results were
consistent with experimental GB energy. Olmsted
et al. [14] calculated the
energies of a set of 388 different grain boundaries for Al and Ni and they
found that GB energy had a correlation with the shear modulus. Recently Ratanaphan
et al. [15] computed the
energies of 408 different grain boundaries in bcc Fe and Mo and they found that
GB energy correlated with the cohesive energies. Tschopp et al. [16] studied a
large data set of grain boundary energies (about 170 GBs) and their
interactions with point defects in Fe using molecular dynamics. Yesilleten and Arias [17] investigated
effect of vacancies on the GB energies with
<110> tilt axis in Mo. Among the GBs of different metals, in this research body
centered cubic (BCC) Fe GBs is chosen due to wide range of industrial
applications of ferritic alloys. Despite the fact that role of inclination of the
grain boundary plane is important and this inclination results to form asymmetric
tilt grain boundaries (ATGBs) and ATGBs are usually observed in polycrystalline
materials [18], the researchers
mostly have focused on energy calculation of symmetric tilt grain boundaries [11,
19-21]. Vast
number of studies focused on the

 GBs with <110> tilt
axis [22-26],
because this GB is usually observed in polycrystalline iron.

In
this work energy of symmetric and asymmetric

,

 boundaries as typical <110> tilt GBs and

 as
representative of <100> tilt GBs is calculated using molecular dynamic
simulations based on embedded-atom method (EAM) potential developed by Mendelev
et al [27]. This potential
previously used to examine grain boundaries in iron [15,
16, 28-30]. A
new method is suggested for construction of GBs that cost of computations will
be efficiently lower than previous methods

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