660
M. C. Bouleklab et al.
The performed description of dilatometric characteristics, without a doubt, shows
that their complex behavior should be associated with the multicomponent composition of Fe–Cu-MWCNTs composites. Therefore, further analysis of the dilatometric
data, of course, should start with the simplest case—the Fe–Cu composite.
Analysis of the data on the temperature dependence of the CTE, α(T), for the
Fe–Cu composite allows us to select at least five ranges with different temperature
behavior of the α(T) value (i = 1 ÷ 5): i T = ~ 65–120, 165–260, 310–525, 575–650,
and 725–790 °C, respectively. The average values of α(T) in these ranges, <α i (T)>
were determined by us according to the usual formula for calculating averages values:
α i (T ) =
1
i (T )
T i+1
T i
α(T )dT
(1)
The resulting values of the <α i (T)> thus obtained for each temperature range
are given in Table 1. These <α i (T)> values can be compared to the values of previously known for similar systems. First of all, we note that for iron and copper, the
components of such systems, the coefficients of thermal expansion for bulk samples
lie in rather wide limits and depend on the composition (brand) and therefore on
the structure of the lattice and the state of the metal (temperature, etc.). Thus, in
the temperatures range 100–300 °C for α-Fe it is possible to give for α the values
(12.8–14.4)·10
−6
K
−1 and (12.4–14.1)·10
−6
K
−1 with a carbon content of 0.05 and
0.5%, respectively. The α value for Cu in the temperature range 0–100 °C is 17·10
−6
K
−1 . It is evident that these values are significantly (in 4.3 and 5.5 times) more than
the value we estimated for the CTE coefficient or the investigated Fe–Cu composite
in the same range of temperatures (~100–300 °C). Approximately the same, these
relationships remain at higher temperatures (300–550 °C (Table 1). If to compare
that with powder compact compositions of iron or Fe–Cu composites, then these
ratios, according to our estimations of the data (taken from [25, 27, 34, 45–48]),
may vary widely, and they may be characteristic for massive samples of Iron, that is,
they vary greatly from our data (4.0 and 5.5 [46], 3.0–4.0 [34], 5.0 [25]), and to be
close to them: 1.4 (see, for example, [41]). So, we must conclude that a comparative
analysis of own and literature data regarding the absolute values of the coefficients of
thermal expansion is not constructive due to significant differences in the conditions
of obtaining and characteristics of the studied samples, while the consideration of
the L/L 0 and α(T) values temperature changes is more attractive from this point of
view.
Obviously, there is a significant number of reasons for the complex temperature
behavior of these dilatometric characteristics for composite materials. The mechanisms of their thermal expansion/reduction can be considered both from a macroscale
and from a microscale point of view. Those possible mechanisms are thermal expansion of the crystalline solid state lattice; transformation of the crystal lattice structure and phase transformation; reduction/shrinkage due to the temperature-activated
release of the initial adsorbed gases and gases formed as a result of the adsorbed
M. C. Bouleklab et al.
The performed description of dilatometric characteristics, without a doubt, shows
that their complex behavior should be associated with the multicomponent composition of Fe–Cu-MWCNTs composites. Therefore, further analysis of the dilatometric
data, of course, should start with the simplest case—the Fe–Cu composite.
Analysis of the data on the temperature dependence of the CTE, α(T), for the
Fe–Cu composite allows us to select at least five ranges with different temperature
behavior of the α(T) value (i = 1 ÷ 5): i T = ~ 65–120, 165–260, 310–525, 575–650,
and 725–790 °C, respectively. The average values of α(T) in these ranges, <α i (T)>
were determined by us according to the usual formula for calculating averages values:
α i (T ) =
1
i (T )
T i+1
T i
α(T )dT
(1)
The resulting values of the <α i (T)> thus obtained for each temperature range
are given in Table 1. These <α i (T)> values can be compared to the values of previously known for similar systems. First of all, we note that for iron and copper, the
components of such systems, the coefficients of thermal expansion for bulk samples
lie in rather wide limits and depend on the composition (brand) and therefore on
the structure of the lattice and the state of the metal (temperature, etc.). Thus, in
the temperatures range 100–300 °C for α-Fe it is possible to give for α the values
(12.8–14.4)·10
−6
K
−1 and (12.4–14.1)·10
−6
K
−1 with a carbon content of 0.05 and
0.5%, respectively. The α value for Cu in the temperature range 0–100 °C is 17·10
−6
K
−1 . It is evident that these values are significantly (in 4.3 and 5.5 times) more than
the value we estimated for the CTE coefficient or the investigated Fe–Cu composite
in the same range of temperatures (~100–300 °C). Approximately the same, these
relationships remain at higher temperatures (300–550 °C (Table 1). If to compare
that with powder compact compositions of iron or Fe–Cu composites, then these
ratios, according to our estimations of the data (taken from [25, 27, 34, 45–48]),
may vary widely, and they may be characteristic for massive samples of Iron, that is,
they vary greatly from our data (4.0 and 5.5 [46], 3.0–4.0 [34], 5.0 [25]), and to be
close to them: 1.4 (see, for example, [41]). So, we must conclude that a comparative
analysis of own and literature data regarding the absolute values of the coefficients of
thermal expansion is not constructive due to significant differences in the conditions
of obtaining and characteristics of the studied samples, while the consideration of
the L/L 0 and α(T) values temperature changes is more attractive from this point of
view.
Obviously, there is a significant number of reasons for the complex temperature
behavior of these dilatometric characteristics for composite materials. The mechanisms of their thermal expansion/reduction can be considered both from a macroscale
and from a microscale point of view. Those possible mechanisms are thermal expansion of the crystalline solid state lattice; transformation of the crystal lattice structure and phase transformation; reduction/shrinkage due to the temperature-activated
release of the initial adsorbed gases and gases formed as a result of the adsorbed