Stereospecific Synthesis of (Z,Z)-Isobenzofurans via Radical-Enabled Cleavage of C(sp3)?C(sp3) and C(sp2)-Halogen Bonds

Article abstract of DOI:10.1002/adsc.201900729

A novel radical-induced annulation/1,8-halosulfonylation of β-alkynyl ketones with haloaryl diazonium tetrafluoroborates and DABCO^.bis(sulfur dioxide) was first achieved via the cleavage/recombination of C(sp³)?C(sp³) and C(sp²)-halogen bonds, from which 47 examples of sulfone-containing 1,3-dimethylene-substituted (Z,Z)-isobenzofurans as single stereoisomers were synthesized in generally good yields. This multicomponent pathway is proposed to proceed through the in-situ generation of arylsulfonyl radicals, followed by selective radical addition-cyclization and ring-opening of the cyclopropyl unit as well as C(sp²)-halogen bond cleavage, resulting in the consecutive construction of three new chemical bonds, including C?S, C?O and C-halogen bonds. (Figure presented.).

Full text of DOI:10.1002/adsc.201900729

Journal of Materials Science: Materials in Electronics
https://doi.org/10.1007/s10854-019-02298-6
The infuence of various Mg contents on the microstructures,
mechanical properties and thermal expansion behaviors of P‑modifed
Al–50Si alloys
Tao Jiang1 · Chuang Yu1 · Boyue Xu1 · Hao Cheng1 · Guangming Xu1
Received: 2 June 2019 / Accepted: 30 September 2019
© Springer Science+Business Media, LLC, part of Springer Nature 2019
Abstract
In this work, the evolutions on the microstructure, mechanical performance as well as thermal expansivity of hypereutectic
Al–50Si alloys with diferent Mg contents were investigated in detail. Besides that, the growth mechanism of the fve-fold
branch-like primary Si crystal was also explained in the view of thermodynamics. The results indicated that the size of
primary Si crystal and the thermal expansivity showed upward trends with the increase of Mg content but the mechanical
property presented a downward trend. Moreover, as the Mg content rose, the morphologies of primary Si crystals in the
P-modifed Al–50Si–xMg (x=0, 5, 10 wt%) alloy changed from octahedron-like to plate-like and fvefold branch-like. The
reason of these adverse phenomena was attributed to the formation of Mg3P2 phase caused by the reaction between Mg ele-
ment and AlP compound, which will generate a poisoning efect and worsen the performances of the alloys.
1 Introduction
It was found in our previous research [9] that the primary
Si crystal in the unmodifed Al–50Si alloy showed coarse
lath-like and the coefcient of thermal expansion (CTE) of
the alloy reached up to 13.5×10−6/K. After modifcation,
the primary Si crystal was fne and uniform, moreover, the
CTE of the alloy dropped to 12.6 × 10−6/K, however, it is
still higher than the CTE of the Al–50Si alloy fabricated by
Osprey company (11.0×10−6/K). Therefore, it is necessary
to research a new modifcation process to refne the primary
Si crystal and reduce the CTE of the alloy.
The Al–Si alloy has expansive application prospect in the
realm of aerospace, automobile and electronics, which can
be ascribed to its excellent comprehensive performances,
such as light-weight, low thermal expansion, high wear
resistance and well corrosion resistance [1–3]. Neverthe-
less, as a result of the coarsening of Si crystal caused by
the increase of Si contents, the primary Si crystals exhibit
massive plate-like and star-like, which will deteriorate the
processability of the high-silicon aluminum alloy and limit
its application [4]. For the past few decades, extensive eforts
have been used to explore the methods in improving the
morphology of primary Si crystals. In general, the efec-
tive methods to refne primary Si crystal mainly comprise
modifcation treatment [5], melt-superheating treatment [6]
out-feld treatment [7] and rapid solidifcation [8], where
the modifcation treatment (especially with the use of phos-
phorus-containing modifer) is the most universal technique
applied in industry.
Mg, which can enhance the efect of aging strengthening
of materials, is one of the most commonly used strengthen-
ing elements in Al–Si alloys. Samuel et al. proposed that the
addition of Mg increased the yield strength and microhard-
ness of Al–Si alloy after aging treatment [10]. Furthermore,
the Mg and Si will also form the Mg2Si phase with high
elastic modulus (120 GPa), high strength (1670 MPa) and
low coefcient of thermal expansion (CTE, 7.5 ×10−6/K),
which will also improve the mechanical properties of Al–Si
casting alloys [11].
In our previous research, the addition of Mg can reduce
the size of primary Si crystal by decreasing the contents of
Si, moreover, the hardness of the hypereutectic Al–Si alloy
is also rose [12]. The phosphorus-containing admixture
is an efective modifer in refning primary Si, which is
widely used in commerce. Both Mg element and phospho-
rus-containing admixture can refne primary Si crystal,
* Guangming Xu
xu_gm@epm.neu.edu.cn
1
Key Laboratory of Electromagnetic Processing of Materials
of Ministry of Education, Northeastern University,
Shenyang 110819, China
Vol.:(0123456789)
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Journal of Materials Science: Materials in Electronics
Table 1 The experimental conditions of thermal expansion tests
however, the compound efects of two modifers have not
been investigated.
Experimental condi- Sample size Heating rate Temperature range
tions
With the intention of revealing the interaction between
Mg and P elements on the refning of primary Si crys-
tal, the Al–50Si–xMg alloys were manufactured by a
self-developed water-cooled copper mold. Moreover, the
efect of Mg content on the microstructure, mechanical
performance and thermal expansion of the alloys were also
investigated.
Ф4×10 mm 5 °C/min
50–500 °C
3 Results and discussions
3.1 Microstructures
Figure 1 shows the microstructure, grain-size and shape-
factor of primary Si crystal in the Al–50Si–xMg (x = 0,
5, 10) alloy with 3% Cu–P modifer. As a result of the
metamorphism of Cu–P alloy, the fne primary Si crystals
with polygon-like in shape distribute evenly in the Al–50Si
alloy. However, with the addition of Mg, the morphology
of primary Si crystal becomes irregular and the distribu-
tion is also inhomogeneous. The aggregations of primary
Si crystals are observed in Al–50Si–5Mg alloys, which
will separate the matrix and deteriorate the processability
of alloy. Besides that, some light-colored phases are also
found near primary Si crystals. When the Mg contents
rise to 10%, the fve-fold branch-like primary Si crystals
appear in the alloy, leading to an increasing rate of 45.7%
in grain size. The alloy should be in the state of over-
metamorphism with the increase of Mg content.
2 Experimental section
The Al–50Si–xMg (x = 0, 5, 10 wt%. Unless otherwise
stated, the percentages shown in this work all referred to
mass fractions.) alloys with 3% Cu–14P modifer were
prepared by a self-developed water-cooled copper mold
with the thickness of 25 mm. The raw materials used to
fabricate Al–50Si–xMg alloys included industrial pure Al
(99.7%), pure Mg (99%) and pure Si (98%). According
to our previous research, the optimal content of Cu–14P
modifer in Al–50Si alloy is 3%, thus, the Cu–14P admix-
ture with the content of 3% was added in the Al–50Si–xMg
alloy. The alloys were smelted in a graphite crucible which
was placed in the intermediate frequency furnace and
maintained at a temperature of 1200 °C for 20 min before
pouring into the mold.
At present, there are two viewpoints on the over-met-
amorphic phenomenon. On the one hand, partial modi-
fers will aggregate with each other, which will reduce the
efective nucleation sites of primary Si so that the refning
efect will be weakened. On the other hand, due to the
poisoning efect between modifers and alloying elements,
the valid contents of modifer will decrease, which will
eventually lead to the insufciency of refnement [14].
The scanning results show the elemental distribution
of Al, Si, Cu, Fe in Fig. 2a as well as the elemental dis-
tribution of Al, Si, Mg, Cu, Fe in Fig. 2e. Figure 2b, f
are the enlarged drawings of selected sections in Fig. 2a,
e, respectively. The results present that the Si crystals in
the P-modifed Al–50Si alloy are fne and homogeneous
but show coarse block-shape in Al–50Si–10Mg alloy.
Moreover, some cracks and pores can be seen clearly on
the surface of Si crystals in the Al–50Si–10Mg alloy. The
EDS results show that the compound at point i in Fig. 2f
is Mg2Si phase. Due to the addition of Mg element, the
Mg2Si phase with the morphology of polygon-like appear
in the alloy.
A feld emission scanning electron microscope was
employed to observed the morphology of Si crystal and
wear surface. Some samples were corroded in the NaOH
solution before observation. In order to quantitatively ana-
lyze the size of Si crystal, plenty of metallographs pho-
tographed by the Leica DMI5000 M optical microscope
were calculated with the use of the software (Image Pro
Plus). The mean-size and shape-factor were calculated
with the formulae of: [13]
F = 4ꢀA∕C2
(1)
ꢀ
A
(2)
S = 2
ꢀ
where F represents the shape factor, S is the dimension of
the Si crystallites, A means a medium section area of the Si
crystallites, C signifes a medium value of their perimeter.
The tensile tests of Al–50Si–xMg alloys were conducted
on an AG–X type universal testing machine at the stretching
rate of 0.2 mm/min. For the purpose of making the results
representative, fve tensile samples were tested at each con-
dition. The linear expansion coefcients of the alloys were
detected on a DIL805A/D type thermal dilatometer. Some
experimental conditions of thermal expansion tests were
presented in Table 1.
As presented in Fig. 3, the P elements are enriched at
region b and region c. The EDS results of point b and
point c show that both points have the elements of Mg,
Al, Si and P, meanwhile, the contents of Mg element are
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Journal of Materials Science: Materials in Electronics
Fig. 1 The microstructure, grain size and shape factor of primary Si crystals
dominant in the four elements. By comparing the elemen-
tal distribution of Mg and Si with EDS results shown in
Fig. 2, it can be inferred that the dark-grey phase sur-
rounding point b is Mg2Si phase. After subtracting the
infuence of Mg2Si phase and Al matrix on the EDS results
of point b, the atomic ratio of Mg/P in Fig. 3b is 1.61,
which is close to 3:2. This experimental result is similar
to the result of Hou et al. He believed that the Mg and P
will have reaction with each other and generate the Mg3P2
compound which can be used as the sites for the heteroge-
neous nucleation of Mg2Si phase [15].
are more active than Al. Mg and Sr are alkaline-earth ele-
ments, whose numbers of outermost electrons are the same.
Thus, the chemical properties of Mg and Sr are similar to
each other.
By comparing the chemical activities among the three
elements, it can be deduced that Mg can also react with AlP
phase and generate Mg3P2 phase. The reaction is shown as
follows.
3Mg + 2AlP → Mg3P2 + 2Al
(5)
Furthermore, because the standard free energy of forma-
tion for Mg3P2 is lower than that of AlP, the above reaction
is easy to generate [18].
As we all know, both Na and Sr will react with AlP phase.
The equations of two reactions are shown below [16, 17].
As the Mg contents increase, the Si crystals change from
regular polygon-like to long strip-like and fnally transform
into fve-fold branch-like. Moreover, due to the transforma-
tion of the morphology induced by the addition of Mg, the
mean size and the corresponding standard deviation of pri-
mary Si also increase. The mean factor of primary Si shows
a downward trend with the increasing of Mg content. The
3Na + AlP → Na3P + Al
(3)
3Sr + 2AlP → Sr3P2 + 2Al
(4)
According to the distribution law of elements in the peri-
odic table, Mg and Na are adjacent elements in the same
period. In addition, both chemical properties of two elements
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Journal of Materials Science: Materials in Electronics
Fig. 2 The elemental distribution and corresponding EDS results of Al–50Si and Al–50Si–10Mg alloys. a Al–50Si e Al–50Si–10Mg
less the content of Mg is, the smaller the grain size and the
corresponding standard deviation are, and the more regular
the shape is.
the samples such as triangles, quadrangles and pentagons
[19]. Therefore, it can be deemed that the polygon-like Si
crystals are the outlines of cut octahedrons.
Figure 4a shows the typical octahedron-like morpholo-
gies of Si crystals in the alloys without Mg content. During
the specimen preparation, the octahedral Si crystals are cut
into random angles, leaving a number of regular outlines on
As a result of the chemical reaction between AlP phase
with NaOH solution, a pore can also be seen in the center of
the polygon-like primary Si crystal. The P element added in
the Al–Si alloy will generate the AlP compound with a high
1 3

Journal of Materials Science: Materials in Electronics
Fig. 3 The elemental distribution and the EDS results
melting point. As presented in Fig. 5, the crystal structures
of Si crystal and AlP compound are diamond structure and
zinc blende structure, respectively. Both materials belong
to cubic structures. Their lattice constants (aSi =0.5428 nm,
aAlP =0.5451 nm) are close, moreover, the diference of min-
imum interatomic spacing (dSi =0.244 nm, dAlP =0.256 nm)
between two materials is less than 5%, which means that AlP
compounds will play a role of nucleation sites during solidi-
fcation [14]. The Si atoms will preferentially adsorb on the
preexistent AlP particles and develop into fne octahedral
primary Si crystals so that the refning efect is achieved.
Figure 4b shows the morphology of plate-like Si crystal in
the Al–50Si–5Mg alloys. As proposed by the Turnbull–Von-
negut formula, the two interfaces can form coherent inter-
face when the misft δ of them is lower than 5%, however,
when the conditions of ꢀ → ∞ and D → 0 are satisfed, the
two interfaces will form incoherent interface due to the high
dislocation density between them. The Turnbull–Vonnegut
formula is expressed as follows [20].
β phase at the two sides of interface, moreover, aꢀ is larger
than aꢀ.
The Mg3P2 compound belongs to cubic structure and the
lattice constant is 0.592 nm [21]. As presented in Table 2, the
misfts of the interfaces between AlP − Si and Mg3P2 − Si
satisfy the relation that ꢀAlP−Si < 5% < ꢀMg P −Si, moreo-
3
2
ver, the DAlP−Si is approximately twenty times as big as
DMg P −Si, which means that the nucleation efect of Mg3P2
3
2
compound to Si crystal is lower than that of AlP phase to Si
crystal. Due to the consumption of AlP particle caused by
the reaction between AlP particle with Mg element, numer-
ous Si crystals will do not contain nucleation sites, which
will make them grow with the mechanism of twin plane re-
entrant edge (TPRE) and develop into plate-like eventually.
Figure 4c shows the morphology of fve-fold branch-like
Si crystal in the Al–50Si–10Mg alloys. A large number of
Si clusters exist in the hypereutectic Al–Si alloy when the
melt is near the liquidus temperature of the alloy. During
the solidification process, these clusters with high sur-
face energy will gather with each other so that the surface
energy will be decreased. Because the crystal structure of
Si is diamond-type, some Si crystals are composed of the
crystal planes with lowest energy, i.e. {111} plane [22]. For
a face-centered cubic Si crystal, the simplest morphology
composed of {111} plane is tetrahedron or octahedron. The
tetrahedron-like primary Si is not found in this research,
(
)/
ꢀ = aꢁ − aꢂ aꢁ
D = aꢀ∕ꢁ
(6)
(7)
where δ represents the lattice misft, D signifes dislocation
spacing, aꢀ and aꢀ denote the lattice constant of α phase and
1 3

Journal of Materials Science: Materials in Electronics
Fig. 4 The evolution on the morphology, mean-size and shape-factor of primary Si crystal
Fig. 5 The crystal structures of Si crystal and AlP compound
however, the octahedron-like primary Si can be seen clearly
in the alloy. Hu believed that the fve-fold Si crystals were
the agglomeration of pre-existing octahedrons after satisfy-
ing certain thermodynamic conditions [23].
Table 2 The calculated results
of lattice misft and dislocation
spacing
AlP − Si Mg3P2 − Si
ꢀ (%)
0.42
8.31
6.53
D (nm) 129.24
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Journal of Materials Science: Materials in Electronics
As we all know, the external surfaces of octahedral Si crys-
tals are {111} planes. The energy used for the growth of an
octahedron with the side length of r can be described as [24]:
√
ΔU
The result of
is less than 0, which means that the
formation of fve-pyramid polyhedron coagulated by fve
octahedrons is a spontaneous behavior. The diference of
free energy between the fve-pyramid polyhedron and the
octahedron is:
√
2
r3ΔG + 2 3r2ꢀ(111)
(8)
U0 = −V0ΔG + A0ꢀ(111) = −
3
√
√
4
2
11
3
ΔU� = U�1 − U0 = −
r3ΔG +
r2ꢀ(111)
(12)
where U0 is the variation on the total free energy, V0 is the
volume of octahedron, A0 is the surface area of octahedron,
ΔG is the diference of free energy between liquid–solid
two-phase, ꢀ(111) is the free energy of {111} plane. The vari-
ation on the free energy for the coagulation of fve-pyramid
polyhedron is [24]:
3
2
It will be benefcial to form the fve-pyramid polyhedron
ΔU�
when the value of
i√s lower than 0. In other word, the
16ΔG
coagulation process of fve-pyramid polyhedron will occur
33 6ꢀ(111)
if the condition of r >
is satisfed.
√
√
√
√
5
2
15
3
5
3
5
2
r3ΔG +
r2ꢀ(111)
+
r2ꢀt +
r3Wd
(9)
U1 = −V1ΔG + A1ꢀ(111) + Atꢀt + V1Wd = −
3
2
2
3
V1 is the volume of fve-pyramid polyhedron, A1 is the sur-
face area of fve-pyramid polyhedron, At represent the total
areas of twin crystals, ꢀt is the free energy of twin crystal and
Wd is the density of elastic energy. A fve-pyramid polyhedron
composed of fve octahedrons need to overcome a misft of
7.5°, therefore, the elastic distortion energy will generate dur-
ing the coagulation process. In addition, the values of ꢀt and
Wd are extremely small compared with that of ΔG and ꢀ(111)
according to the previous research [24]. Thus, the formula 9
can be rewrote as:
Figure 6 shows the schematic diagram of fve-pyramid
polyhedral Si crystal and fvefold branch-like primary Si
crystal. During the solidifcation process, the preformed
octahedron-like primary Si crystals will agglomerate with
each other and form fve-pyramid polyhedral Si crystals
when the specifc thermodynamic condition is achieved. Due
to the fast growth rate along the direction of twinning plane,
the fve-pyramid polyhedron-like Si crystal will further grow
up and develop into fvefold branch-like eventually with the
falling of temperature.
√
√
5
2
15
3
U�1 = −V1ΔG + A1ꢀ(111) = −
r3ΔG +
r2ꢀ(111)
3.2 Properties
3
2
(10)
3.2.1 Mechanical performances
The diference of free energy between the fve-pyramid
polyhedron and fve octahedrons is:
Figure 7 shows the variation of mechanical properties of
Al–50Si alloy with diferent Mg contents. As the Mg content
increases, the ultimate tensile strength (UTS) of the alloy
declines from 92.87 MPa to 26.62 MPa and 9.09 MPa, show-
ing the decrease rates of 71.34% and 90.21%, respectively.
√
5
3
ΔU = U�1 − 5U0 = −
r2ꢀ(111) < 0
(11)
2
Fig. 6 The schematic diagram
of fve-pyramid polyhedron-like
Si crystal and fve-fold branch-
like Si crystal. a fve-pyramid
polyhedron-like Si crystal b
fvefold branch-like primary Si
crystal
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Journal of Materials Science: Materials in Electronics
in the Al–50Si–xMg (x = 5, 10) alloy, which will worsen
the mechanical properties, leading to the decrease of the
strength.
100
80
60
40
20
0
Figure 8 presents the fractographs of the tensile speci-
mens of Al–50Si alloy with diferent Mg content. The frac-
tographs listed in the right column of Fig. 8 are the enlarged
drawings of selected rectangular regions in the left column.
As seen in the Fig. 8, all fractures are dominated by brittle
fracture. The dimples appear in the local area of Al–50Si
alloy, which means that a small amount of plastic deforma-
tion feature still exists in the P-modifed Al–50Si alloy. Nev-
ertheless, the dimples basically disappear and are replaced
by the defects such as stomata and cracks with the increase
of Mg content. The appearance of stomata can be attrib-
uted to the oxidation and hydrogen absorption behaviors of
Mg element at elevated temperature and causes the stress
concentration in the vicinity of the defect region during the
test. With the action of tensile stress, the cracks will germi-
nate near the stomata and extend along the Si crystal until
they eventually penetrate the whole section, resulting in the
fracture of the alloys. Moreover, the secondary cracks are
also observed on the Si crystal, which further confrms the
occurrence of trans-granular fracture.
Al-50Si
Al-50Si-5Mg
Al-50Si-10Mg
Fig. 7 The variation of mechanical properties of Al–50Si alloys with
diferent Mg contents
The previous experimental results indicated that the strength
of high-silicon aluminum alloy was mainly infuenced by the
following factors: (1) the size and the distribution of primary
Si crystal; (2) the bonding strength between the Si crystal
and α-Al; (3) the sensitivity of Si crystal to cracks [25].
According to the Hall–Petch equation, the relationship
between the strength and the grain size can be express as:
3.2.2 Thermal expansion behaviors
√
The thermal expansion phenomenon of the material is the
variation of average distance of the lattice atom with temper-
ature in essence and express as thermal expansion behavior
at the macroscopic view. Figure 9 shows the experimental
results and theoretical models of the coefcient of thermal
expansion (CTE) with diferent Mg content. All the curves
in Fig. 9a show same trend with temperature, i.e., the CTE
of alloy increases frstly and then decreases with the increase
of temperature. In addition, the CTE of three alloys also
increase with Mg content when the temperature is lower
than 400 °C.
(13)
ꢀs = ꢀi + K∕
d
The ꢀs represents the yield strength of the material, ꢀi is
a constant and roughly equal to the yield strength of single
crystal, K is a constant which is related the grain bound-
ary structure, d signifes the average grain size of material.
The formula 13 suggests that the larger the grain size of the
material is, the smaller the strength of the alloy is, which is
also in line with our experimental results. Furthermore, the
stress concentration near the massive particle is more seri-
ous, which makes the cracking of Si phase easier, leading to
the decrease in strength.
The thermal expansion behavior of hypereutectic Al–Si
alloy is principally caused by Al matrix and restrained by Si
crystal. At a low temperature, the plastic deformation of the
α-Al matrix will not occur. With the increase of tempera-
ture, the thermal motions of atoms intensify and the bonding
forces between atoms are weakened, resulting in an increase
in the coefcient of thermal expansion. Nevertheless, as the
temperature keeps on rising, the thermal stress between the
interface of Al matrix and Si crystal continues to enhance
but the strength of the matrix decreases gradually. If the
thermal stress surpasses the yield strength of the α-Al, the
plastic deformation will generate in the matrix. Due to the
high porosity induced by the elevated melting temperature,
the plastically deforming Al matrix will move to the pores
so that the CTE of the alloy is decreased.
Except for the grain size mentioned above, the strength of
the alloy is also afected by the crack sensitivity of primary
Si. According to the Grifth equation [26], the maximum
tensile stress that primary Si crystal can withstand is:
√
ꢀf = 2Eꢁ∕ꢂC
(14)
where the E is the Young’s modulus of Si crystal, ꢀ denotes
the surface fracture energy, C signifes the internal crack
length. The Grifth equation believed that the maximum
tensile stress that primary Si crystal can withstand is in
inverse ratio to the internal defect lengths of Si crystal. As
seen in Fig. 8, some stomata caused by the hydrogen absorp-
tion of Mg element under high temperature were observed
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Journal of Materials Science: Materials in Electronics
Fig. 8 The fractographs of the tensile specimens of Al–50Si alloys with diferent Mg contents
da0
1
Except for the temperature and the porosity of the alloy, the
CTE of Al–Si alloys also depends on the solid solubility of Si
atom in Al matrix. The relation among the CTE with the lattice
constant and the solid solubility is expressed as [27]:
where ꢀ is the CTE of alloy,
refers to the variation of
RT
a0 dT
−ΔH
1
ΔH
RT2
inherent lattice expansion with temperature, Δa Ae
represents the efect of solid solubility on the tah0eΔrmC al expan-
sion of alloy, Δa and ΔC signify the variation of lattice
parameter and solid solubility with temperature,
respectively.
−ΔH
da0
1
1 Δa
ΔH
RT2
RT
ꢀ =
+
Ae
(15)
a0 dT
a0 ΔC
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Journal of Materials Science: Materials in Electronics
16
15
14
13
12
11
(a)
16
14
12
10
8
(b)
Al-50Si
Al-50Si-5Mg
Al-50Si-10Mg
Max value
ROM
Turner
0
100
200
300
400
500
6
Temperature ℃
Al-50Si
Al-50Si-5Mg
Al-50Si-10Mg
Fig. 9 The experimental results and theoretical models of CTE with diferent Mg content. a experimental results; b theoretical models
During the heating process, plenty of Si atoms will dis-
solve into the Al matrix and form supersaturated Al(Si) solid
solution. The solid solution can be divided into two type:
substitutional solid solution and interstitial solid solution.
Moreover, it is possible to form interstitial solid solution if
the radius ratio of two atoms are lower than 0.59. The radii
of the Al atom and the Si atom are 1.4318 Å and 1.1758 Å,
respectively [28]. The radius ratio of Si atom and Al atom
is 0.82, which is higher than 0.59. Thus, the Si atoms dis-
solved in the matrix will not form interstitial solid solution
with α-Al but form substitutional solid solution. As seen in
Fig. 10, because the radius of the Si atom is lower than that
of Al atom, the lattice constant of newly formed Al(Si) solid
solution will decline, which makes the value of Δa∕ΔC is
negative, resulting in the decreasing in CTE.
Figure 9b shows the max values of the experimental results
as well as the theoretical results predicted by ROM model and
Turner model. The max values of CTE for Al–50Si–xMg
alloys (x=5, 10) are 14.13×10−6/ °C and 15.73×10−6/ °C,
showing an increase rate of 11.87% and 24.49% compared
with Al–50Si alloy, respectively. However, it is noteworthy
that the change rules predicted by two models are absolutely
contrary to the experimental results.
The ROM model believes that the performance of alloy
only depends on the property and volume fraction of each
component and has nothing to do with the interaction between
each other. The ROM model is given as [29]:
ꢀ = ꢀ1V1 + ꢀ2V2 + ꢀ3V3
(16)
Fig. 10 Two types of substitutional solid solution
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Journal of Materials Science: Materials in Electronics
Table 3 The physical parameters of Al, Si and Mg2Si [9, 31]
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Si
Mg2Si
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28Si alloy. Mater. Des. 51, 383–390 (2013)
CTE (×10−6/°C)
Bulk modulus (K, GPa)
22.6
67.8
2.5
97.0
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where ꢀ1, ꢀ2, ꢀ3 andV1, V2, V3 represent the CTE and volume
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With a view to the microstructures shown in Fig. 1, a rea-
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Publisher’s Note Springer Nature remains neutral with regard to
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