Local and bulk melting of Cu at grain boundaries Page: 4 of 7
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3
0) 0.5
E
0.4
cO
a
, 0.3
0
- 0.2
(j 0.1-50 -25 0
Time (ps)25 5
FIG. 3: Temporal evolution of the global order parameter
of the Cu bicrystal, fi(t), at 1500 K (0-50 ps) and 1520 K
(50-100 ps). Inset: II versus temperature during incremental
heating.
1200 K 1300 K 1320 K
s
1360 K 1420 K 1460 K
1480 K 1500 K 1520 K
FIG. 4: Configurations of strict liquid atoms during incre-
mental heating of the Cu bicrystal after 50 ps thermalization
at respective temperatures. Color coding refers to the liquid
cluster size. Atoms in the first, second and third largest clus-
ters are colored yellow, black and gray, respectively; the rest
are colored red.
The high energy GBs reduce the amtotnt of superheating
from 0.22T,,, to 0.13T,,. Nonetheless, the hicrystal is still
superheated noticeably as fa.r as GB bulk melting is con-
tered. (See below for t1re liscussiot i 11lk teltiug
of GB.)
The tentprattre evolutions of the local order paramui-
ters (Fig. 1) and of the liquid atoits (Fig. 4) indicate that
heterogeneous nucleation and growth at the GBs domti-
nate melting. Disordering is pronounced along GBs and
its spatial variations can be regartdetd as one tiimensional
along the GB normal. To characterize the order parat-
eter across the planar GBs, we divide the simulation cell
along the interface nrmal (the .r direction) into small
bins and i is calculated for each bin, yielding a profile
i(.r). Shown in Fig. 5(a) is such art example obtained
at 1500 K atnd f = 47.5 ps. The profile of the order0.4
3- ~
(a)
50 100 150
x (A)100
50
(b)
0
0 50 100
Time (ps)0.8
0.4 -
0 500 1000 1500
T(K)parameter cau be described with a sigmdid function
tJ J ( .r ) ' t 1 - t a t :t n - o ) J
WM Wi+ ~2 1 ah 2u(3;)
Here alt is the center of a solid-liquid interface, and w
represents a characteristic length sale of the interface.
The subscripts 1 and 2 refer to the high and low plateau
values, respectively. We take the thickness of a GB, d,
as the full width at half naxiitunt (FVHM) of the ortler
paraetr profile.
Given the GB thickness defined above, we examine the
growth kinetics of telt originated at GBs. The temporal
evolution of the GB thickness at 1500 K during a 100 ps
rnt is shown in Fig. 5(b). and can be described withd(t) = dt + (d2 - d1 ) [1 - exp(-kt')] ,
(4)
where t. d2, k and tq are paratmters. Here subscripts
1 and 2 refer to the initial thickness antd that at cot-
plete melting, respectively, for a particular isobaric and
isothermal run. r' is characteristic of the growth kinetics
of the GB region, and is about 5.6 for growth of itelt
at 1500 K. (This equation is siitilar in formality to the
.Johnson-Mlcl-Avrami law.2526) The melting kinetics are
sensitive to temperature. A slight decrease in tempera-
ture slows down the kinetics. For example, bulk melting
aild growth occur at about 1.2 ns aiid 9/ ~ 4 at. 14Sf0
K. The corresponding values are about. 30 ps and 5.6,
respectively, at 1500 K. During melting, the solid-liquid
interface moves and its velocity is norimally consideredI to
be a costatt.t However. Fig. 5(b) shows the interface
velocity increases as bulk melting progresses and reaches
roghly a constant value before complete melting. This
velocity (for a single interface) is about 150 m s and
120 mist at 1500 K and 1480 K, respectively.
It is highly desirable to investigate in detail the char-
atteristics of GB during heating ii order to gain insight
iit GB mteting. The evolution of the GB width dr-
ing stepped heating is shown in Fig. 6(a); U increases
gradually from 300 K to 1480 K, and then abruptly froit
1481) K to 1500 K. The GB width increases froit about
5 A at 300 K to 6.5 A at 1300 K and then to 9.5 A at
1480 K. The abrupt increase in GB width at 1500 K isFIG. 5: (a) The order parameter profile along :r-axis of the
heated bicrystal at 1500 K and 47.5 ps. The solid curve is
the fit ting with Eq. (3). (b) GB width versus time at 1500 K.
0 The fitting (solid curve) refers to Eq. (4).i - , --
-
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Luo, Shengnian; Han, Li - Bo; An, Qi; Fu, Rong - Shan & Zheng, Lianqing. Local and bulk melting of Cu at grain boundaries, article, January 1, 2008; [New Mexico]. (https://digital.library.unt.edu/ark:/67531/metadc934814/m1/4/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.