CEJP 3(3) 2005 395–408
Study of solid-solution hardening in binary
aluminium-based alloys
Mohamed Draissia∗, Mohamed-Yacine Debili
Département de Physique, Faculté des Sciences,
Université Badji-Mokhtar,
BP 12 Annaba, 23000 Algérie
Received 19 September 2004; accepted 22 March 2005
Abstract: Solid-solution formation in binary aluminium-based alloys is due essentially
to the combined effects of the size and valence of solvent and solute atoms, as expected by
the four Hume-Rothery rules. The lattice parameter of aluminium in the solid solution of
the sputtered Al-Fe films is [Al-a (Å) = 4.052–6.6×10−3 Y]. The increasing and decreasing
evolution of the lattice parameter of copper [Cu-a (Å) = 3.612+1.8×10−3 Z] and aluminium
[Al-a (Å) = 4.048-1.6×10−3 X] in the sputtered Al-1.8 to 92.5 at. % Cu films is a result
of the difference in size between the aluminium and copper atoms. The low solubility of
copper in aluminium (< 1.8 at. % Cu) is due to the valences of solvent and solute atoms
in contrast with other sputtered films prepared under similar conditions, such as Al-Mg
(20 at. % Mg), Al-Ti (27 at. % Ti), Al-Cr (5at. % Cr) and Al-Fe (5.5 at. % Fe) where
the solubility is due to the difference in size.
c Central European Science Journals. All rights reserved.
Keywords: Aluminium alloys, sputtering, x-ray diffraction, solid solutions, lattice
parameter
PACS (2000): 61.10.Nz
1
Introduction
Aluminium and aluminium alloys represent an important category of materials due to
their high technological value and their wide application - especially in the aerospace
field, motorized vehicles and domestic industry. The formation of metastable phases in
thin films occurs generally because of the fast speeds of solidification applied during the
transformation of the vapor to solid film [1-3]. The aluminium-based films prepared by
cathodic magnetron sputtering such as Al-Mg, Al-Ti, Al-Cr and Al-Fe [4-7] exhibit sig∗
E-mail: [email protected]
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M. Draissia, M.-Y. Debili / Central European Journal of Physics 3(3) 2005 395–408
nificant mechanical and electrochemical properties which make them candidates for wide
employment as hard and anti-corrosive consumable coatings for corresponding traditional
alloys. These films present a notable extension of the aluminium solid solution, testifying
to a great solubility of the alloying elements in aluminium in contrast to copper in the
Al-Cu films [8-11] prepared under similar conditions - where we note only a very low
solubility of copper in aluminium as predicted by the Al-Cu equilibrium diagram.
In this present work, the lattice parameters of aluminium and copper in sputtered
binary films are studied by means of X-ray diffraction diagrams and compared to those
of bulk binary alloys [12-16].
2
Composition evolution in the films
The atomic or mass compositions (at.% or m.%) of binary A-B alloy systems generally
represent the percentage in atoms or mass of B compared to the sum of the atoms or
masses of A and B. By calling X the atomic percentage and M the mass percentage of
the element B in A-B alloy, the compositions are:
X (at. % B ) = NA× 100/(NA + NB )
(1)
M (m. % B) = mB× 100/(mA + mB )
(2)
Where N and m represent the number of atoms and the mass of the element B in the
alloy A-B respectively. By taking x = X/100, the composition of a binary A-B alloy will
be represented by A1−x Bx
The composite targets used in preparation by radio frequency (13.56 MHz) magnetron
cathodic sputtering of the binary aluminium-based films Al-Mg, Al-Ti, Al-Cr, Al-Fe and
Al-Cu consist of an aluminium crown in which is inserted a disc of the alloying element.
The aluminium and alloying element are both used either in a bulk state or a compacted
powder. The use of material in a bulk state in cathodic sputtering minimizes the presence
of oxygen in the films; only the composite targets Al-Cu were used in a bulk state. This
configuration shape for the composite target allows for a simple approach to control the
alloy element composition in the co-sputtered films. This evolves as a parabolic form
with the insert diameter (Figure 1).
The concentration X (at %) of the alloy element is:
X (at %) = (N × 100)/(N + NAl ).
(3)
Where N and NAl are the number of atoms of alloying element and aluminium in the
target respectively.
For a composite target with a 70 mm diameter the evolution of the atomic concentration (at. %) with the insert diameter “d” is:
X (at. %) = R × d2 × 100/[R × d2 + (490 − 0.1 × d2 )].
With surface fraction “F” it is:
(4)
M. Draissia, M.-Y. Debili / Central European Journal of Physics 3(3) 2005 395–408
X (at. %) = R × F × 100/[R × F + (0.1 − 0.1 × F)].
397
(5)
And for the mass concentration are:
M (m. %) = ρ × d2 × 100/[ρ × d2 + (13230 − 2.7 × d2 )].
(6)
M (m. %) = ρ × F × 100/[ρ × F + (2.7 − 2.7 × F)].
(7)
Where R is the ratio between the density ρ and the atomic mass At for each aluminiumalloying element (Table 1).
Element
Al
Mg
Ti
Cr
Fe
Cu
Atomic Mass (At )
Density (ρ)
R = ρ/At
27
2.70
24.3
1.74
0.07
48
4.51
0.09
52
7.19
0.14
55.8
7.86
0.14
63.5
8.96
0.14
Table 1 Ratio between mass density and atomic mass of Al and the Al-alloying elements.
Figure 1 shows the parabolic form of the atomic concentration evolution in the composite targets for the aluminium-alloying elements with respect to their insert diameter.
As R has almost the same value for the alloying elements Cr, Fe and Cu the atomic
concentration evolution for these elements is also the same, and this leads us to predict
that structural properties are almost the same for the aluminium-based alloy films with
these elements.
The atomic and mass compositions for the Al-Cu films are:
X ≈ 100 × d2 /(3500 + 0.28 × d2 ) ≈ 100 × F/(0.71 + 0.28 × F).
(8)
M ≈ 100 × d2 /(1470 + 0.7 × d2 ) ≈ 100 × F/(0.3 + 0.7 × F).
(9)
Fig. 1 Atomic composition evolution with insert diameter in composite targets.
398
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M. Draissia, M.-Y. Debili / Central European Journal of Physics 3(3) 2005 395–408
Solid solution formation
3.1 Hume-Rothery relations
Figure 2 shows microstructure evolution with the Cu concentration for the radio frequency (13.56 MHz) cathodic magnetron sputtering where the limits are approximate.
We observe a vast field of the microstructure containing the intermetallic Al(Cu) compound reaching approximately 80 at. % Cu compositions. No intermetallic compounds
have been observed in the Al-Mg, Al-Ti, Al-Cr and Al-Fe films; on the other hand, an
amorphous phase field is detected in these films.
ĮAl + Al2Cu
Al
20
40
ĮAl
+
ĮCu
+
Cu3Al
ĮAl
+
Cu3Al
at.%Cu
60
ĮCu
80
Cu
Fig. 2 Structural evolution of the sputtered Al-Cu films system [8,9].
Some simple empirical laws on solid solution formation in the binary A-B alloys have
been given by Hume-Rothery. These four laws are based on the size factor, the structure,
the electronegativity and the valences.
(1) If the difference in size of the elements is greater than ±15 % the lattice distortions
(for example the local lattice constraints) are so important that the solid solution
formation is restricted.
(2) If the two elements, solvent and solute, have the same structure there could be
formation of a solid solution.
(3) If the electronegativities (ionization energy) of the two elements are close, the solid
formation is favoured. The great electropositivity of an element and the great electronegativity of the other would give rise to the formation of intermetallic compounds.
(4) A metal will dissolve another metal of greater valence much more than a metal of
lower valence.
The limit extension of the fcc copper solid solution α Al (< 1,8 at. % Cu) [8,9] is much
lower than that already observed in the Al-based films with the presence of chromium
or iron (5 at. % Fe) [6,7] and much lower than that observed in the deposits Al-Mg (20
at. % Mg) [4] or Titanium (27 at. % Ti) [5]. This is in agreement with the binary
Al-Cu equilibrium diagram where the limit of solubility of copper in aluminium does not
M. Draissia, M.-Y. Debili / Central European Journal of Physics 3(3) 2005 395–408
399
exceed 0.3 at. % Cu (Figure 3). These differences in solubility of the alloying elements
in aluminium (αAl solid solution) are probably due to the differences in size between the
solvent (aluminium) and the solute atoms (alloying elements).
Fig. 3 Equilibrium Diagram of the binary Al-Cu system.
- Al-Cu alloys
1st law: rAl = 1.43 Å and rCu = 1.28 Å. ∆R% = -10.5%
favourable
2nd law: Al and Cu both have the fcc structure
favourable
3rd law: EAl = 1.38 et ECu = 1.78. ∆E% = 29%
Not favourable
4th law: The valence of Al is +3 and Cu +1
Not favourable
- Cu-Al alloys
1st law: ∆R% = -11.7%
favourable
2nd law: Al and Cu have the fcc structure
favourable
3rd law: ∆E% = -22.5%
Not favourable
4th law: The valence of Cu is +1 and Al +3
favourable
These four factors control the tendency of the formation of substitutional solid so-
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M. Draissia, M.-Y. Debili / Central European Journal of Physics 3(3) 2005 395–408
lution. According to these results, aluminium is substituted in copper and the reverse
is also true in spite of the difference of the atomic radii, rAl = 1.43 Å and rCu = 1.28 Å.
When the size factor, the 1st law, differs by less than 15 % the solid solution formation
is favourable. However, when it differs by more than 15 % the extension of the solid
solution is restricted to usually less than 1 %.
The calculated size difference of aluminium and copper elements in both binary Al-Cu
and Cu-Al alloys differ by less than 15 %, this means that the two elements are soluble
one in the other. For the Cu(rich)-Al, we observe a notable extension of solid solution of
aluminium in copper in good agreement with bulk equilibrium diagram (Figure 3) and
deposits phase diagram (Figure 2) of binary Al-Cu alloy systems. For the Al(rich) side,
the extension of the solid solution is lower than 1.8 at. % Cu in the co-sputtered Al-Cu
deposits and 0.3 at. % Cu in the bulk Al-Cu system in spite of the fact that aluminium
and copper have the same structure fcc and also that the atomic size of copper with
a volume of lattice of 8.784 Å3 is definitely lower than that of the aluminium which is
12.248 Å3 . These properties would normally allow solubility by substitution of copper in
aluminium.
Solid-solution formation in Al(rich)-Cu alloys is not favourable and was less than 2
at. % Cu as envisaged by Hume-Rothery in the 4th law of electronegativity (difference
between ionization energies) and especially the 3rd law pertaining to valences. This is due
to the strong tendency to form intermetallic compounds in the aluminium-copper alloys.
The valence of aluminium is +3 and that of copper is +1, therefore aluminium is more
soluble in copper than copper in aluminium. The extension of the solid solution for the
copper rich-side can reach 21 at. % Cu for bulk Al-Cu and exceeds 13.83 at. % Cu for
Al-Cu films (with a presence of the intermetallic phase Cu3 Al with ordered sc structure
Cu3 Au [17] in the films of composition 33.36 at. % Cu [1-3]). Thus, the size factor alone
cannot explain the formation of solid solution in binary alloys and the valence factor also
needs to be considered.
Table 2 gathered the solubility extends of the alloying elements in the aluminium (αAl
solid solution) with the ratio of the atomic radii and the structures of pure aluminium
and its alloying elements.
Element
Atomic radius r (Å)
Ratio r/rAl
Structure
Solubility limit (at. %)
Reference
Al
Mg
Ti
Cr
Fe
Cu
1.43
1
fcc
1.60
1.118
hcp
20
[4]
1.47
1.027
hcp
27
[5]
1.27
0.888
cc
5
[6]
1.26
0.881
cc
∼ 5.5
[7]
1.28
0.895
fcc
< 1.8
[8,11]
Table 2 Extension limits of the solid solution αAl in the Al-based alloys films.
The effect of the difference in size between solvent and the solute can indeed be
shown clearly by plotting the curve logarithm of the variation of hardness H with the
composition X [Log(dH/dX)] according to the difference between the atomic diameters
M. Draissia, M.-Y. Debili / Central European Journal of Physics 3(3) 2005 395–408
&X
/RJ>G+G;[ @
&U
)H
7L
401
/RJ''[ Fig. 4 Relation between solid solution hardness and atomic diameters difference of the solvent
and solute.
(∆D) of solvent and the solute [18]. For extension limits of solid solution (Table 2) of
about 5 at. % the Al-Cr and Al-Fe films, 27 at.% for Al-Ti, a straight line is obtained
for the alloying elements where the difference in atomic size with aluminium are close:
∆DT i = |DAl –DT i| = |2.86 − 2.94| = 0.08Å, ∆DCr = 0.32 Å, ∆DF e = 0.34 Å, ∆DCu =
0.30 Å. The limited effect of the difference in size with Ti appears in the field of the
corresponding solid solution owing to the fact that its atomic diameter is larger than that
of aluminium (Figure 4).
7000
0
5
15
20
25
30
7000
6000
H 0.01 N (MPa)
10
6000
Al-C u
5000
5000
4000
4000
3000
3000
2000
2000
1000
1000
0
0
0
5
10
15
20
25
30
at.% Cu
Fig. 5 Evolution of the microhardness with copper composition in the Al(rich)-Cu deposits.
The extrapolation of Vickers hardness Hv (10g) corresponding to the limit of extension of solubility of copper in aluminium is about 1430 MPa, as Hv (10g) of sputtered
pure aluminium is 1300 MPa, which corresponds to a Hv hardness of 2700 MPa for the
compositions close to the limit of extension of the solid solution of the Al-Cu deposits
402
M. Draissia, M.-Y. Debili / Central European Journal of Physics 3(3) 2005 395–408
system. Measurements of the hardness Hv for bulk pure copper under various loads [10]
give the possibility of obtaining hardness Hv (1g) for the limit of solubility of copper in
the aluminium and that will be about 4000 Mpa, which corresponds a concentration of
about 10 at. % Cu (Figure 5). This 10 at. % Cu composition should be the limit of
extension of the aluminium solid solution in the co-sputtered Al-Cu films.
3.2 Evolution of the lattice parameter
3.2.1 Lattice parameter of aluminium
Figure 6 shows the X-ray diffraction (XRD) diagrams of the co-sputtered Al(rich)-Cu
films. Contrary to the deposits Al-Ti, Al-Cr and Al-Fe prepared under similar conditions,
the Al-Cu films containing a low amount of the alloying element (1,8 at. % Cu) are a
mixture of the αAl + Al2 Cu phases and this is in agreement with the equilibrium diagram.
The measured lattice parameters for aluminium in the Al-0 to 21.95 at. % Cu films are
represented in Table 3.
at. % Cu
0
1.80
(2 phases)
7.21
(2 phases)
21.95
(2 phases)
Structure
Al-a (Å)
Al
4.049
Al + Al2 Cu
4.043
Al + Al2 Cu
4.038
Al + Al2 Cu
4.012
Table 3 Experimentally measured Al-lattice parameters in the Al(rich)-Cu films at 25 ◦ C.
Fig. 6 XRD diagrams of the co-sputtered Al(rich)-Cu films: (a) 1.8 at.%C, (b) 7.21 at.%Cu,
Fig. 6 XRD diagrams of the co-sputtered Al(rich)-Cu films: (a) 1.8 at. % Cu, (b) 7.21 at. %
Cu, (c) 21.95 at. % Cu.
The equation which governs the evolution of the Al-lattice parameter with the com-
M. Draissia, M.-Y. Debili / Central European Journal of Physics 3(3) 2005 395–408
403
position X (at. % Cu) is:
Al-a(Å) = 4.048 − 1.6 × 10−3 X.
(10)
at. % Cu
0
0.06
0.40
0.80
1.23
1.37
1.62
Al-a (Å)
4.0413
4.0411
4.0394
4.0372
4.0354
4.0348
4.0336
Table 4 Experimental data of the Al-lattice parameter in bulk Al-Cu solid solution alloys
measured at 25 ◦ C [12].
m. % Cu
0
0.95
1.95
2.98
3.96
4.97
Al-a (Å)
4.0409
4.0390
4.0368
4.0349
4.0328
4.0306
Table 5 Experimental data of the Al-lattice parameter in bulk Al-Cu solid solution alloys
measured at 18 ◦ C [13].
Figure 7 shows the evolution of the lattice parameter of aluminium in the solid solutions of some binary Al-Cu alloys as films (Table 3 Figure 7a) and bulk (Table 4 Figure
7b and Table 5 Figure 7c). The lattice parameter of aluminium decreases regularly with
copper concentration; this decrease is very clear owing to the fact that there is a difference
in size between the atoms of solvent (aluminium) and solute (copper). As the aluminium
radius (rAl = 1.43 Å) is greater than that of copper (rCu = 1.28 Å), the copper dissolves
in aluminium. During the crystallization of vapour to solid films there is a substitution
of aluminium atoms (atomic volume of 12.248 Å3 and lattice volume of 66.38 Å3 ) by
smaller copper atoms (atomic volume of 8.784 Å3 and lattice volume of 47.24 Å3 ). However, the solid solution formation in the Al(rich)-Cu films is lower than 1.8 at.%Cu as
confirmed by Figure 6 XRD diagrams, so we can say that there was contraction of the
aluminium lattice under the effect of the elastic interactions of the phase θ(Al2 Cu) with
a lattice volume of 179.43 Å3 which is greater than that of aluminium (66.38 Å3 ). This
phenomenon is explained by the main tendency of binary Al-Cu alloys to the formation
of intermetallic compounds in contrast with other binary Al-based films prepared under
similar conditions, such as Al-Fe where the solubility of iron in aluminium extends up to
about 5 at. % Fe (Table 6).
at. % Fe
0
4
7.5 (2 phases)
Al-a (Å)
4.05
4.03
4.00
Table 6 Experimentally measured Al-lattice parameter in the solid solutions of the Al-Fe films
[7].
The lattice parameter evolution is as:
Al-a(Å) = 4.052 − 6.6 × 10−3 Y.
Where Y is the iron composition.
(11)
404
M. Draissia, M.-Y. Debili / Central European Journal of Physics 3(3) 2005 395–408
a (Angstron)
0
5
10
15
20
25
4.05
4.05
4.04
4.04
4.03
4.03
(a)
4.02
4.02
(b)
4.01
4.01
(c)
4.00
4.00
0
5
10
15
20
25
at.%Cu
Fig. 7 Evolution of the Al-lattice parameter in solid solutions of binary Al-Cu alloys: (a) films,
(b) bulk [12], (c) bulk [13].
3.2.2 Lattice parameter of copper
Figure 8 shows that the as-sputtered Al-Cu(Rich) films structure, also examined by XRD,
consisted of fcc peaks of the copper solid solution for the compositions extending over
13.83 at. % Cu. For the 33.36 at. % Cu composition films it consisted of a fcc copper
matrix in which are dispersed the unexpected cubic Cu3 Al phase particles (See Figure 2).
Fig. 8 XRD diagrams of the co-sputtered Al-Cu(rich) films: (a) 7.5 at.%Cu, (b) 13.83 at.%Cu,
Fig. 8 XRD diagrams of the co-sputtered Al-Cu(rich) films: (a) 7.5 at. % Al, (b) 13.83 at. %
Al, (c) 33.36 at. % Al.
M. Draissia, M.-Y. Debili / Central European Journal of Physics 3(3) 2005 395–408
at. % Al
0
07.50
13.83
33.36 (2 phases)
Structure
Cu-a (Å)
αCu
3.615
αCu
3.626
αCu
3.637
αCu + Cu3 Al
3.672
405
Table 7 Measured Cu-lattice parameter in the solid solutions of the Al-Cu(rich) films.
The relation between the Cu-lattice parameter and the composition Z (at. % Al) is:
Cu-a(Å) = 3.612 + 1.8 × 10−3 Z.
(12)
at. % Al
0
5
10
15
21 (2 phases)
Cu-a (Å)
3.6075
3.6195
3.6318
3.6433
3.6551
Table 8 Cu-lattice parameter in solid solutions of bulk Cu-Al alloys [14].
at.%Al
Cu-a (Å)
0
4.63
6.97
11
17.26
18.98
20.92
(2 phases)
24.57
(2 phases)
3.6079
3.6199
3.6260
3.6363
3.6515
3.6563
3.6580
3.6582
Table 9 Cu-lattice parameter in solid solutions of bulk Cu-Al alloys [15].
0
5
10
15
20
25
30
35
40
3 .6 8
3 .6 8
(b )
(c )
3 .6 7
a (Angstron)
3 .6 6
3 .6 7
3 .6 6
(a )
3 .6 5
3 .6 5
3 .6 4
3 .6 4
3 .6 3
3 .6 3
3 .6 2
3 .6 2
C u -a (A l-C u film s )
3 .6 1
3 .6 1
3 .6 0
3 .6 0
0
5
10
15
20
25
30
35
40
a t.% A l
Fig. 9 Evolution of the lattice parameter of copper in solid solutions of binary Al-Cu alloys: (a)
films, (b) bulk [14], (c) bulk [15].
at. % Al
6
8
10
Cu-a (Å)
3.6291
3.6265
3.6319
Table 10 Lattice parameter data of copper in solid solutions of bulk Cu-Al alloys at 18 ◦ [16].
406
M. Draissia, M.-Y. Debili / Central European Journal of Physics 3(3) 2005 395–408
The evolution of the copper-lattice parameter with the aluminium composition is
illustrated in Figure 9, where it is compared with other results. The lattice parameter
increases regularly with the aluminium concentration, this variation is obvious owing to
the fact that there is a difference in size between the solvent atoms of aluminium and the
solute atoms of copper (Table 11). As the atomic radius of aluminium (rAl = 1.43 Å) is
greater than that of copper (rCu = 1.28 Å), copper dissolves in aluminium and there is
substitution of the copper atoms (atom volume of 8.784 Å3 and lattice volume of 47.24
Å3 ) by larger aluminium atoms (atom volume 12.248 Å3 and lattice volume of 66.38 Å3 ).
Thus, during crystallization [19], there is an increase in the volume of the copper lattice
matrix by substitutional incorporation of aluminium atoms, therefore there is dilation of
the copper lattice from where the lattice parameter of copper is increased in the solid
solutions of binary Cu-Al alloys. Other results (Table 10) show that the lattice parameter
of copper decreases in the solid solutions when increasing the concentration from 6 to 8
at.% of aluminium, then it increases for composition 10 at. % Al. The authors [16]
recognize that there is insufficiency in the obtained results.
A similar evolution of the Cu-lattice parameter was also observed in the Cu-0 to 18 at.
% Ta thin films deposited at 120 ◦ C [20]. This parameter increases with Ta composition
in the films where the structure is two phases as a copper matrix in which are distributed
fine particles of tantalum. The equation that governs this evolution is:
Cu-a(Å) = 3.613 + 00016 × W.
(13)
Where W is the atomic tantalum composition (at. % Ta). The equation provides
further evidence of an increase in the lattice parameter with increasing tantalum concentration. This increase in the lattice parameter is also due to the difference in size between
the solvent atoms (copper) and the solute atoms (tantalum) (Table 11).
Al
Cu
Ta
r (nm)
01.43
1.28
1.46
∆r = | rCu - rX |(nm)
0.15
0
0.18
Structure
Fcc
fcc
bcc
4.049
3.615
3.305
[21]
[22]
[23]
a∗ (Å)
∗ Reference
Table 11 Structural characteristics of Al, Cu and Ta.
4
Conclusion
Both aluminium and copper lattice parameter results extrapolated from the XRD of
the co-sputtered aluminium-copper diagrams are in agreement with experimental data
concerning the solid solutions of bulk binary aluminium-copper alloys. This decreases or
M. Draissia, M.-Y. Debili / Central European Journal of Physics 3(3) 2005 395–408
407
increases linearly with the atomic aluminium or copper concentration respectively. The
notable extension of the solid solution observed in the Al-Cu(rich) films is essentially due
to the difference in size between the copper and aluminium atoms. The very low solubility
of copper in aluminium can be explained by the laws of Hume-Rothery as being due to
the difference of the valences of the solvent and solute atoms. This work should be
supplemented by a study of the co-sputtered Al(rich)-Cu films after heating at 400 ◦ C to
see if the solubility of copper in aluminium changes.
References
[1] M. Draissia: Structure et physico-chimie des dépôts métastables aluminium-cuivre
élaborés par pulvérisation cathodique magnétron, Thesis (PhD) , Université BadjiMokhtar Annaba (Algérie), 2004.
[2] M. Draissia, H. Boudemagh and M.Y. Debili: “Structure and Hardness of the
Sputtered Al-Cu Thin Films System”, Physica Scripta, Vol. 69, (2004), pp. 348–350.
[3] M. Draissia and M.Y. Debili: “Atomic size effects on the hardness of r.f. Sputtered
Al-Cu(Rich) thin films”, Journal of Crystal Growth, Vol. 270, (2004), pp. 250–254.
[4] R.D. Arnell and R.I. Bates: “The deposition of highly supersaturated metastable
aluminium-magnesium by unbalanced magnetron sputtering from composite target”,
Vacuum, Vol. 43, (1992), pp. 105–109.
[5] F. Sanchette, Tran Huu Loı̈ and C. Frantz: “Structure-properties relationship of
metastable Al-Cr and Al-Ti alloys deposited by r.f. magnetron sputtering: role of
nitrogen”, Surf. Coat. Technol., Vol. 74-75, (1995), pp. 903–909.
[6] F. Sanchette, Tran Huu Loı̈, A. Billard and C. Frantz: “Deposition of metastable
aluminium-chromium alloys by r.f. magnetron sputtering from mixed-powder
targets”, Surf. Coat. Technol., Vol. 57, (1993), pp. 179–182.
[7] M.Y. Debili, Tran Huu Loı̈ and C. Frantz: “Caractérisation chimique et structurale de
dépôts métastables aluminium-fer obtenus par pulvérisation cathodique magnétron”,
La revue de Métallurgie-CIT/Science et Génie des Matériaux, Vol. 12, (1998), pp.
1501–1509.
[8] Unpublished results: M. Draissia, H. Boudemagh and M.Y. Debili: “Observation
d’une démixtion dans des films minces nanostructurés Al-66.64 at.%Cu obtenus par
dépôt physique en phase vapeur (PVD)”, presented at the conference: The 3rd Int.
Cong. on Mat. Sci.& Eng., Jijel (Algérie) 25-27 May 2004.
[9] Unpublished results: M. Draissia, H. Boudemagh and M.Y. Debili: “Unexpected
phase separation in magnetron sputter-deposited Al-Cu thin films system”, presented
at the conference: IXmes Journées Maghrébines des Sciences des Matériaux JMSM,
Oran (Algérie) 8-10 May 2004.
[10] Unpublished results: M. Draissia and M.Y. Debili: “Corrosion behaviour of
nanostructured aluminium-based alloys”, presented at the conference: 7mes Journées
Francophones des Jeunes Physico-Chimistes, Monastir (Tunisie) 19-21 March 2004.
[11] Unpublished results: M. Draissia, M.Y. Debili and J.P. Millet: “Structural and
chemical properties of sputtered Al-Cu deposits”, presented at the conference:
Eurocorr 2004, Nice (France) 12-16 September 2004.
[12] J. Axon and W. Hume-Rothery: Proc. Roy. Soc. A., Vol. 193, (1948), p. 1.
408
M. Draissia, M.-Y. Debili / Central European Journal of Physics 3(3) 2005 395–408
[13] C. Ellwood and J.M. Silcock: J. Ins. Met., Vol. 74, (1948), p. 457.
[14] A.J. Bradley and H.J. Goldschmidt: J. Inst. Met., Vol. 65, (1939), p. 389.
[15] I. Obinata and J. Wassermann: Naturwiss, Vol. 21, (1933), p. 382.
[16] H. Stirling and G.V. Raynor: Private communication and J.Inst. Met, Vol. 84, (1955),
p. 57.
[17] V. Fournée, I. Mazin, D.A. Papaconstantapoulos and E. Belin-Ferré: “Electronic
structure calculations of Al-Cu alloys : comparison with experimental results on
Hume-Rothery pahases”, Philosophical Magazine B, Vol. 79(2), (1999), pp. 205–221.
[18] R.W.K. Honeycombe: The Plastic Deformation of Metals, 2nd ed., Arnold, UK,
1984.
[19] M. Draissia, N. Boukhris and M.Y. Debili: “Thermomechanical behavior of rapidly
solidified Fe-25Cr-20Ni”, Materials Science Forum, Vol. 467-470, (2004), pp. 247–250.
[20] H. Wang, M.J. Zaluzec and J.M. Rigsbee: “Microstructure and Mechanical Properties
of Sputter-Deposited Cu1−x Tax Alloys”, Metall. Trans. A, Vol. 28, (1997), pp. 917–
925.