662
M. C. Bouleklab et al.
give a satisfactory result. (The constructed lines on this temperature range are given
by dots.)
Taking into account the above-made analysis of the L/L 0 (T) and α(T) experimental dependences on temperature and approximation of the L/L 0 (T) dependence
on the calculated lines as well, we go to the conclusion that the mechanism of “pure”
thermal expansion of the Fe–Cu composite dominates in the range of temperatures
375–550 °C.
There are cases in the solids dilatometry when the size of the solid body decreases
with temperature increasing. That dependence may be caused by a sharp increasing
the repulsion forces if compare with attraction forces increasing. It is obvious that
such cases are more likely for solids which include three or more types of atoms [49].
It is clear that the same behavior is quite possible to observe for multicomponent
and multiphase solids: alloys, compacts, composites, etc. where the role of atoms is
already played by separated grains/particles of such composite materials.
Among the results presented in this paper, the decrease in the L/L 0 value with
temperature increasing also takes place at some temperature intervals. These are the
ranges 35–75, 135–200 °C for the Fe–Cu samples; the range 50–150 °C for the Fe–
Cu-MWCNT (0.5), and the range 500–625 °C for the Fe–Cu-MWCNT (1.0) samples
(Fig. 12). However, it should be emphasized that other mechanisms of the complex
dilatometric behavior, which are caused by the multicomponent composition of the
investigated composites, can give a stronger temperature effect than described above.
In general, the temperature behavior of the dimension of compacted powders,
composite materials, etc. can be largely due not so much to “pure” thermal effects,
but as a manifestation of the structural and phase transformations of such materials
components, that is, it may be the result of their multi-component composition. So,
if we consider the simplest model case of a composite material containing only
two components that do not interact with each other, for example, powders of two
metals, then for such material, at a certain temperature range, the thermal expansion
coefficient α m can be considered by so-called “rule of mixture”:
α m = α 1 (1 − v 2 ) + α 2 v 2 ,
(3)
where α 1 is the CTE of the main phase 1 of the material, and α 2 and v 2 are the CTE
and the volume contribution of phase 2 to which the first phase is transformed. From
the following form of formula (3):
α m = α 1 − (α 1 − α 2 )v 2
(4)
It is easy to see that for a case α 1 > α 2 , the v 2 increasing leads to a decrease in
the value of α m at a rate (α 1 −α 2 ), whereas in the case of α 1 < α 2 , the v 2 increasing is
accompanied by the α m increase with the same rate: (α 1 −α 2 ). The inserts in Fig. 2
illustrate the described influence. Thus, the above-mentioned transitions to the ranges
of increase (decrease) of the CTE on the α(T) curves may be due to phase transformations in the compositions of the samples. Taking into account the diffusion between
phases and the formation of phase interfaces (e.g., by using instead of the ratio
M. C. Bouleklab et al.
give a satisfactory result. (The constructed lines on this temperature range are given
by dots.)
Taking into account the above-made analysis of the L/L 0 (T) and α(T) experimental dependences on temperature and approximation of the L/L 0 (T) dependence
on the calculated lines as well, we go to the conclusion that the mechanism of “pure”
thermal expansion of the Fe–Cu composite dominates in the range of temperatures
375–550 °C.
There are cases in the solids dilatometry when the size of the solid body decreases
with temperature increasing. That dependence may be caused by a sharp increasing
the repulsion forces if compare with attraction forces increasing. It is obvious that
such cases are more likely for solids which include three or more types of atoms [49].
It is clear that the same behavior is quite possible to observe for multicomponent
and multiphase solids: alloys, compacts, composites, etc. where the role of atoms is
already played by separated grains/particles of such composite materials.
Among the results presented in this paper, the decrease in the L/L 0 value with
temperature increasing also takes place at some temperature intervals. These are the
ranges 35–75, 135–200 °C for the Fe–Cu samples; the range 50–150 °C for the Fe–
Cu-MWCNT (0.5), and the range 500–625 °C for the Fe–Cu-MWCNT (1.0) samples
(Fig. 12). However, it should be emphasized that other mechanisms of the complex
dilatometric behavior, which are caused by the multicomponent composition of the
investigated composites, can give a stronger temperature effect than described above.
In general, the temperature behavior of the dimension of compacted powders,
composite materials, etc. can be largely due not so much to “pure” thermal effects,
but as a manifestation of the structural and phase transformations of such materials
components, that is, it may be the result of their multi-component composition. So,
if we consider the simplest model case of a composite material containing only
two components that do not interact with each other, for example, powders of two
metals, then for such material, at a certain temperature range, the thermal expansion
coefficient α m can be considered by so-called “rule of mixture”:
α m = α 1 (1 − v 2 ) + α 2 v 2 ,
(3)
where α 1 is the CTE of the main phase 1 of the material, and α 2 and v 2 are the CTE
and the volume contribution of phase 2 to which the first phase is transformed. From
the following form of formula (3):
α m = α 1 − (α 1 − α 2 )v 2
(4)
It is easy to see that for a case α 1 > α 2 , the v 2 increasing leads to a decrease in
the value of α m at a rate (α 1 −α 2 ), whereas in the case of α 1 < α 2 , the v 2 increasing is
accompanied by the α m increase with the same rate: (α 1 −α 2 ). The inserts in Fig. 2
illustrate the described influence. Thus, the above-mentioned transitions to the ranges
of increase (decrease) of the CTE on the α(T) curves may be due to phase transformations in the compositions of the samples. Taking into account the diffusion between
phases and the formation of phase interfaces (e.g., by using instead of the ratio