1. Introduction
One of the most fundamental questions regarding matter, whether a new reaction will
or will not occur, and how quickly it will occur, led to the emergence of thermodynamics
[1,2]. At the basis of thermodynamics is the fact that all physicochemical reactions that
occur between materials proceed in a manner that lowers their total energy; the larger
the gradient, the faster the reaction proceeds. Moreover, these energies can have
different forms, such as Helmholtz energy (F) [3], internal energy (U) [4], Gibbs energy (G) [5], enthalpy (H) [6], and external energy (PV) [7]. Most of these energies are not path functions, which depend on the path taken to
reach a specific value, but are state functions that are not path dependant. A reaction
between a reactant and product means that there is an energy non-equilibrium between
them, which indicates that a dynamic energy transfer is required to reach an energy
equilibrium. However, in the most cases, the understanding of a reaction is based
on room temperature. That is, if the reference point is changed, all physicochemical
reactions can reach energy equilibrium at every moment. Therefore, since energy equilibria
based on different criteria are considerably different from each other, theoretically,
an energy non-equilibrium cannot exist. This can be easily understood from the following
example (Fig 1).
One often describes G [5] as shown in Fig 1a. In other words, a car parked on a slope (non-equilibrium state) must be moved to
a flat area (equilibrium state) along the slope because the car is in an energetically
unstable state when parked on the slope. Accordingly, any material in a non-equilibrium
state is like the car unstably parked on the slope. Since this possibility reverses
the energy concept shown in Fig 1a, this theory actually cannot be established. A non-equilibrium state is nothing but
a deviation from a particular criterion of equilibrium in an already established state,
although each state strictly corresponds to a local energy equilibrium.
Fig 1b shows an example of equilibrium at each moment (local equilibrium), and a collection
of images captured successively at a given time. Here, the first and last images can
be regarded as pre-reaction and post-reaction states that appear to be stationary,
and the images between the first and last images can be regarded as reaction states,
each of which looks like a moving state. However, every moment has images showing
equilibrium at that moment, with a one-to-one correspondence. In other words, the
reaction at each moment corresponds to a static local equilibrium. If there is energy
non-equilibrium from a relative point of view and only an energy balance is achieved
from an absolute point of view, how can we explain the changes in materials that have
different compositions, sizes, and shapes depending on the surrounding environment?
Here, we propose an absolute energy equilibrium law in which a material represented
by a mass is always in energy equilibrium with a space represented by a temperature.
This is an extension of the mass–space energy conservation law that includes the existing
energy conservation laws; this law allows many physicochemical phenomena that are
considered to exist in a state of energy non-equilibrium to be analyzed from a new
viewpoint. To support this argument, we applied the objective causal relation in terms
of a one-to-one correspondence between the structural change in steel (mass) and temperature
(space) in the iron—carbon phase diagram [8]. In particular, this showed that the morphological and microstructural changes in
non-equilibrium states could be consistently explained using the extended energy law
as a major premise. From this fact, we were able to rectify the contradictory interpretation
based on the present energy balance concept, that an unstable state of energy non-equilibrium
can continue.
2. Results and Discussion
2.1. Reinterpreting temperature and equilibrium
What is the temperature that we often employ in scientific and engineering processes?
Apart from understanding its basic definition, we need to first briefly review the
characteristics of temperature that are common in everyday life. According to the
third law of thermodynamics [9] space and mass do not exist without temperature. Here, mass is considered a special
type of space because it has a volume within a certain area from the moment it is
formed, and it can be a part of space. In other words, mass can be considered as space
with properties and forms different from the surrounding space. Thus, space can be
considered as the area of the environment surrounding the object of interest (mass).
For example, in the case of fish, the sea can become space, for humans, the atmosphere
can become space, and for astronauts, vacuum can be space. The important point here
is that temperature exists in a vacuum even without a medium such as water or air;
this is evident in many experiments using ultra-high vacuum [10-12]. However, because temperature change is proportional to the change in thermal energy
according to the relation ΔQ = cmΔT (where ΔQ, c, m, and ΔT represent the change in heat energy (calorie), specific heat, mass, and change in
temperature, respectively) [13,14], temperature may be regarded as energy. In other words, temperature can be thought
of as energy representing space. This energy can be considered to be the product of
temperature (T in K) and entropy (S in J/K), which is the energy corresponding to that temperature. If so, it is expected
that there will be an energetic entry or exit to equilibrate with the mass energy
present in such a space. Then, the mass energy can be easily deduced from the known
mass–energy equivalence (E = mc2) [15].
A perfect example of this plausible assumption is that as temperature changes, the
state of a material changes sequentially as follows: solid→liquid→gas→plasma. This
can be seen as the levelling (energy levelling) of temperature, starting from low
to high; there is a one-to-one correspondence with the state of the material at each
temperature, as the mass energy changes with respect to the spatial energy.
2.2 Spatial energy–mass energy relationship
Let us apply the above-mentioned relationship between temperature and mass to changes
in morphologies and microstructures in the Fe–C phase diagram according to temperature
[8] (Fig 2a). The original x-axis shows the compositional changes of Fe and C; however, if the
x-axis becomes the temperature axis, the phase diagram is as shown in Fig 2b. This can be interpreted as an equilibrium composition with respect to temperature.
That is, it is the equilibrium mass energy corresponding to a particular space energy.
At this point, observing the green points in Fig 2b, it is possible that the simultaneous mixing of Fe and C does not correspond to temperature
on a one-to-one basis. However, even if the two elements are mixed, the contents of
Fe and C are different at each temperature, and the composition is determined using
the lever rule [16] (Fig 3). That is, each temperature has its own composition. Thus, considering a mass basis,
it can be seen that different mass energies, according to composition, have corresponding
spatial equilibrium energies. Specifically, the main structures in agreement with
temperature are as follows [8] (Fig 1b):
(1) The austenite (γ) phase of the face-centered cubic structure, which is stable
between 727 and 1493 °C, below 2.14 wt% C
(2) The ferrite (α) phase of the body-centered cubic structure, which is stable up
to 912 °C, below 0.022 wt% C
(3) A mixed phase of austenite (γ) and cementite (θ), which is stable between 727
and 1147 °C, with C content above 2.14 wt%
(4) A pearlite phase consisting of ferrite (α) and cementite (θ), which is stable
below 727 °C, with C content above 0.022 wt%
These results show that the spatial energy at each temperature corresponds to the
mass energy, which changes in each phase to maintain the energetic equilibrium between
the two terms.
2.3 Non-equilibrium spatial energy–mass energy relation
In the previous section, we examined the temperature and phase based on the equilibrium
state of Fe–C. However, as is already known, new structures of bainite [17] and martensite [18] can be obtained, depending on the cooling conditions, (i.e., how the temperature
is controlled), although not in the equilibrium state (i.e., the phase diagram). These
phases can be observed in a separate time-temperature-transformation (TTT) curve [19] (Fig 4a) or a continuous cooling transformation (CCT) curve [20] (Fig 4b).
What is interesting here is that the same austenite phase has caused a bainite or
martensite transformation, instead of a ferrite or pearlite transformation. In other
words, the cause (austenite source) is the same, but the results (phases) are different.
Therefore, from the present point of view, when one state (ferrite or pearlite) is
fixed as the equilibrium basis, the other one (bainite or bartensite) becomes the
non-equilibrium basis. The possible phase changes are explained as follows:
(1) At relatively high temperatures, it is possible to atomically diffuse into the
ferrite or pearlite phase with time.
(2) It is difficult to atomically diffuse into the equilibrium phase with time at
relatively low temperatures, which may result in a non-equilibrium bainite or martensite
transformation.
If so, as described above, are these non-equilibrium phases able to remain static
and stable in a dynamic unstable state? If not, like the half-life [21] of a radioactive element, do they change to ferrite or pearlite, which are equilibrium
phases, with time? It is difficult to provide a clear answer to these two questions.
This is because, ultimately, maintaining an energetically unstable state is not feasible.
Furthermore, no results have been reported to date indicating that bainite or martensite
phases have transformed to ferrite or pearlite phases.
This phenomenon can be interpreted as follows. As mentioned earlier, space energy
and mass energy always try to maintain equilibrium, and in general, each temperature
has an equilibrium state corresponding to the material. As an easy example, in the
case of water, water below 0 °C s is present as a solid; from 0 up to 100 °C, it is
a liquid, and above 100 °C, it exists as a gas. At this time, the boundary between
water and space has an unusual physicochemical property different from existing water
and existing space because this is the area where mass and space with different energies
achieve energy equilibrium. In other words, boundaries, surfaces, and interfaces can
be seen as having both mass and space, and they are the points where the two different
energies are uniquely equal. Hence, the implications of the boundary itself can be
seen as sharing different parts.
Therefore, since the difference between two energies must be minimized at the boundary,
it can be expressed as a mean value, such as (a + b) / 2 = c, where a and b correspond to the respective energies (of mass and space), and c corresponds to a
boundary energy. Based on these facts, the bainite and martensite phases, which are
not shown in the present equilibrium diagram, can be said to maintain energy equilibrium
based on the mass–space energy conservation law. In other words, as shown in Figs 1, 2, 4, whatever the phases are, the appearance of a boundary means that the energies of
the symmetrical factors are balanced equally.
Here, the difference in morphology is only the difference between the energy of each
space or mass and the original equilibrium energy at which the space and mass show
a one-to-one correspondence. Namely, whether the energy difference between mass and
space is small or large, it is evident that it is equally a space-mass energy equilibrium.
Therefore, the larger the space-to-mass energy difference, the higher the energy equilibrium
at the boundary will be. For this reason, in the case of martensite formed by quenching
with a large temperature difference, the energy at the surface is high and the hardness
of the steel increases. That is, martensite is not a phase with energy non-equilibrium
but one with an energy equilibrium where there is a large difference between the initial
spatial energy and mass energy.
2.4 Heat treatment types and energy balance
Even though the mass–space energy equilibrium is not elaborately discussed, the heat
treatment [22] of metals has long been studied empirically in efforts to improve their mechanical
properties, processability, and physical and chemical properties before the effects
of heat treatment were scientifically proven [23,24]. However, various types of heat treatments, such as quenching and annealing, are
derived from the viewpoint of mass–space energy equilibrium. In other words, they
can change mass energy by changing spatial energy through changes in the heating temperature,
holding time, and cooling rate. The most commonly used types of heat treatment methods
are quenching [25,26], tempering [27,28], normalizing [29,30], and annealing [31,32], and the rough process conditions for these heat treatment methods are shown in
Fig 5. The purpose of these various heat treatments can be analyzed in terms of the space-mass
energy equilibrium as follows.
(1) Quenching: In this method for increasing the hardness and strength of steel, the
difference between the spatial energy and mass energy, is too large as mentioned above.
Therefore, only the surface of the mass can become thick and hard because the energies
are concentrated at the surface (Fig 5a).
(2) Tempering: To compensate for the brittleness caused by quenching, internal stress,
accumulated upon reaching equilibrium, is eliminated; the material becomes tough by
cooling in air after heating to a temperature below the transformation point (< 723
°C). In other words, the equilibrium attained during quenching (from the large difference
between space energy and mass energy) disappears (Fig 5b).
(3) Normalizing: The steel is heated to the austenite temperature and then air-cooled.
This heat treatment is capable of reducing the deformation caused during quenching.
The difference between the mass and space energies is usually considered to be in
between that of quenching and annealing (Fig 5c).
(4) Annealing: The steel is heated and cooled in the furnace. Since the energy balance
is such that the difference between the space energy and mass energy is the smallest,
the probability of stress accumulating inside and outside the material is the least
(Fig 5d).
Based on the above discussion, it is necessary to clarify that many amorphous materials
[33], antimatter [34], and supersaturated [35] and supercooled [36] materials, which are currently defined as non-equilibrium materials, are non-equilibrium
materials with respect to only one fixed criterion among various criteria. In principle,
according to the major premise of the space–mass energy conservation law, it is reasonable
to assume that all the states of the continuum material are energy balance states.
Thus, just as mass can be controlled through space, bidirectional energy transfer
that can control space through mass will be possible.