x Cis valid
0xxxx . If we pay attention to only
one side of I
C or II
C, thtion occurs via
the ran the other hand, if we pay at-
tention to boI
C and II
,,Ctx Ctx C is actually valid, because we
cannot know in a pure mrial whher a
etn atom between
th sides of
is one of
e early stage, we
C or II
C in the initial state.
That (24) is independent of t means the time-averaged
n profile caud bye Brownian motion.
Therefore, the diffusion occus as a result of the random
movement even in a pure material. Equation (24) thus
gives the evid ence of the Brownian motion in a pure ma-
From the historical point of view, if the FFL had been
might have understood the
bhavior of Brownian motion before the Einstein theory.
As can be seen from the above 1) - 4), the diffusivity
depends on the concentration when
t depends on
t. The concentration dependence of diffusivity is thus
caused by the material source on the dion boundary
terface at A
x or B
x. In consideration of the
above 1) - 4), the FFL is obviously incomplete without
t for FSversal.
Hereinbefore, it was clarified that we can revise the
o it is applicable to various diffu
L and it is not u
divergence theorem sh
tion law. On the other
as also shown that the NDF plays an extremely impor-
tant role to understan d diffusion problems. Hereafter, the
diffusion problems should be analyzed by using the NDF
for a diffusion system as an additional condition equation
The FSL consistent
be exactly valid as aould
the FFL should be replaced by the NDF which is not only
exactly valid in mathematics but also extremely useful
for physics. The obtained novel results in the present
study are as follows:
1) Even if a material source independent of the space
yz is contained in the diffusion system, the FSL is
applicable to analyzing the diffusion problems as it is.
t plays an extremely impor-
tant role in the diffusion problems.
2) A law must be universal. The NDF is systematically
applicable to the problems of interdiffusion, one-way
n coefficients can be
ion study. Equation (21) is dominant in the techno-
 J. B. J. Fourier la Chaleur,” Chez
, 1855, pp. 31-39.
hte, Vol. 66,
rte Bewegung von in Ruhenden Flus-
diffusion, impurity diffusion and self-diffusion. Further,
the NDF of (14) or (22) is applicable to analyzing diffu-
sion problems, for instance as seen from the derivations
of (21) and (24). However, the FFL has not ever been
used for analyzing the diffusion problems because of its
incompleteness. The NDF is thus universal to the diffu-
sion problems, but the FFL is not.
3) The NDF reveals that the K-effect is reasonably
obtained as (19). The interdiffusio
tained by applying (21) to the experimental results. On
the contrary, (19) can predict the behavior of K-effect
using various combinations of the obtained diffusivities.
As a result, the intrinsic diffusion conception inconsistent
with the FSL is thus not only unnecessary but also un-
The NDF derived here is a fundamental equation in the
gical material science, since the atomic diffusivity val-
ues in alloy are obtained by using it for the interdiffusion
experimentation. Although the present study was dis-
cussed in relation to diffusion problems between metal
plates, the results obtained here are also applicable to
various material problems described by the FSL. Hereaf-
ter, the new findings obtained here may make a funda-
mental change to the existing diffusi on theory.
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