Influence of the Carbon Allotropes on Dilatometric Properties …
661
compounds thermal decomposition, the processes of sintering; and, conversely, the
degradation of the composite grains in rolled materials, etc. From the point of view
of the micro/nanoscale phenomena, it should be noted that a large number of possible
combinations where these mechanisms can be actual. There can be the interaction of
grains/particles: iron–iron, copper–copper, and iron–copper, as well as some influence of uncontrolled factors (pores, defects, impurities, etc.). Besides, the effect of
high local temperatures under mechano-chemical activation can result in the presence in investigated composites of iron particles, where the surface layer is a solid
copper solution in iron, and vice versa,copper particles, where the surface layer is
a solid solution of iron in copper [31]. The interaction between iron and copper
particles and their interaction with the particles of the above-mentioned core–shell
type are also a factor that complicates the dilatometric behavior of the materials
under study. It should be also emphasized that the activity of these processes can
essentially depend on the size of the grains/particles of the material. More precisely,
it has to say, that the ratio of the volume of the surface layer to the volume of the
central core of the particle changes depending on the particles size, and therefore
the role of the corresponding zones of the particles in the dilatometric processes also
varies. It is clear that a detailed analysis of all these factors, at this moment, cannot
be made especially in the case of so multicomponent samples. Therefore, we will
try to distinguish the most significant of them and analyze their role initially on the
simplest of the composition of the studied systems: Fe–Cu.
“Pure” thermal expansion effects are those caused by an increase in the equilibrium
distance between atoms of solid state due to the increase of their vibrations amplitude
when the temperature rises. For most of solids, their expansion occurs if temperature
increases. Obviously, the temperature ranges, where the contribution of the “pure”
thermal expansion of the samples studied by us is preferable, should be those where
the L/L 0 (T) dependence is close to the linear and, at the same time, the CTE in this
range does not change. An approximation of the L/L 0 (T) experimental dependence
for the Fe–Cu composite (Fig. 12, curve 1) was made by assuming a linear expansion
of this material. To do this, the above calculated <α i (T)> values were used (Table 1). In
this case, the initial values of the sample length L 0i on each of the temperature ranges
(T) i (i = 1 ÷ 5) were selected as the parameter corresponding to the actual sample
length at the initial temperature of the corresponding range, T 0i . The normalized
values of those parameters, L
∗
oi = L 0i /L 0 , are also given in Table 1. It was assumed
for such approximation that the L(T) value is an additive sum of the straight lines
L i (T) = L
∗
oi + L
∗
oi <α i (T)> · (T – T 0i ), and each of which is relevant in the appropriate
range of temperatures (T) i :
L(T) = SUM
L
∗
oi + L
∗
oi · < α i (T) · (T − TL 0i )
.
(2)
The line segments (L i (T)−L 0i (T))/L 0i (T)) constructed in this way are shown in
Fig. 12. It is evident that they well describe the behavior of the L/L 0 (T) experimental
dependence on the first three low-temperature ranges (35–550 °C), while in the hightemperature range (575–800 °C), the calculated <α i (T)> values using and hence the
consideration of the Fe–Cu composite expansion in a linear approximation does not
661
compounds thermal decomposition, the processes of sintering; and, conversely, the
degradation of the composite grains in rolled materials, etc. From the point of view
of the micro/nanoscale phenomena, it should be noted that a large number of possible
combinations where these mechanisms can be actual. There can be the interaction of
grains/particles: iron–iron, copper–copper, and iron–copper, as well as some influence of uncontrolled factors (pores, defects, impurities, etc.). Besides, the effect of
high local temperatures under mechano-chemical activation can result in the presence in investigated composites of iron particles, where the surface layer is a solid
copper solution in iron, and vice versa,copper particles, where the surface layer is
a solid solution of iron in copper [31]. The interaction between iron and copper
particles and their interaction with the particles of the above-mentioned core–shell
type are also a factor that complicates the dilatometric behavior of the materials
under study. It should be also emphasized that the activity of these processes can
essentially depend on the size of the grains/particles of the material. More precisely,
it has to say, that the ratio of the volume of the surface layer to the volume of the
central core of the particle changes depending on the particles size, and therefore
the role of the corresponding zones of the particles in the dilatometric processes also
varies. It is clear that a detailed analysis of all these factors, at this moment, cannot
be made especially in the case of so multicomponent samples. Therefore, we will
try to distinguish the most significant of them and analyze their role initially on the
simplest of the composition of the studied systems: Fe–Cu.
“Pure” thermal expansion effects are those caused by an increase in the equilibrium
distance between atoms of solid state due to the increase of their vibrations amplitude
when the temperature rises. For most of solids, their expansion occurs if temperature
increases. Obviously, the temperature ranges, where the contribution of the “pure”
thermal expansion of the samples studied by us is preferable, should be those where
the L/L 0 (T) dependence is close to the linear and, at the same time, the CTE in this
range does not change. An approximation of the L/L 0 (T) experimental dependence
for the Fe–Cu composite (Fig. 12, curve 1) was made by assuming a linear expansion
of this material. To do this, the above calculated <α i (T)> values were used (Table 1). In
this case, the initial values of the sample length L 0i on each of the temperature ranges
(T) i (i = 1 ÷ 5) were selected as the parameter corresponding to the actual sample
length at the initial temperature of the corresponding range, T 0i . The normalized
values of those parameters, L
∗
oi = L 0i /L 0 , are also given in Table 1. It was assumed
for such approximation that the L(T) value is an additive sum of the straight lines
L i (T) = L
∗
oi + L
∗
oi <α i (T)> · (T – T 0i ), and each of which is relevant in the appropriate
range of temperatures (T) i :
L(T) = SUM
L
∗
oi + L
∗
oi · < α i (T) · (T − TL 0i )
.
(2)
The line segments (L i (T)−L 0i (T))/L 0i (T)) constructed in this way are shown in
Fig. 12. It is evident that they well describe the behavior of the L/L 0 (T) experimental
dependence on the first three low-temperature ranges (35–550 °C), while in the hightemperature range (575–800 °C), the calculated <α i (T)> values using and hence the
consideration of the Fe–Cu composite expansion in a linear approximation does not