Post-print of: Intermetallics Volume 19, Issue 11, November 2011, Pages 1688–1692
Formation of the complete range of Ti5Si3−xGex solid solutions via
mechanically induced self-sustained reactions
José M. Córdoba, Ernesto Chicardi, Miguel A. Avilés, Francisco J. Gotor
Instituto de Ciencia de Materiales de Sevilla, Centro Mixto CSIC-US, Américo
Vespucio 49, 41092 Sevilla, Spain
Abstract
The complete range of Ti5Si3–Ti5Ge3 solid solutions was synthesised from elemental
mixtures of Ti, Si, and Ge under an inert atmosphere via mechanically induced selfsustaining reactions (MSR). The stoichiometry of Ti5Si3−xGex solid solutions was
controlled by adjusting the Si/Ge ratio of the initial mixture. The chemical composition
and lattice parameters of the materials confirmed that Ti5Si3–Ti5Ge3 solid solutions
with good chemical homogeneity could be produced via MSR.
Keywords
A. Titanium silicides; A. Silicides, various; A. Ternary alloy systems; C. Mechanical
alloying and milling; C. Reaction synthesis
1. Introduction
Titanium silicides and germanides have attracted a significant amount of attention in
recent years due to their specific physical and chemical properties [1], [2] and [3]. In
general, titanium silicides and germanides are good electrical conductors and have
similar resistivities to metals and alloys. The potential use of silicides as conductors has
motivated thin-film silicide research [4] and [5], including applications such as (a)
Schottky barriers and ohmic contacts [6] and [7], (b) gates and interconnection metals,
and (c) epitaxial conductors in heterostructures [8].
Ti5Si3 and Ti5Ge3 have high melting points (2130 °C and 1960 °C, respectively) and
are difficult to process. Common methods for the synthesis of Ti5Si3 and Ti5Ge3
include chemical/physical vapour deposition, rapid thermal processing, and traditional
casting or powder metallurgical processes [9], [10], [11] and [12]. Due to the highly
exothermic heat of formation of these intermetallic compounds (−579 kJ/mol and −566
kJ/mol for Ti5Si3 and Ti5Ge3, respectively) [13] and [14], self-propagating hightemperature syntheses (SHS) have also been proposed.
Mechanically induced self-sustained reactions (MSR) [15] are a promising alternative to
conventional synthetic methods and have been used to produce advanced materials such
as borides, carbides, nitrides, carbonitrides, hydrides, silicides, aluminides, and other
intermetallic compounds [16], [17], [18], [19], [20], [21], [22] and [23]. MSR is a selfsustaining process due to the highly exothermic nature of the reactions; thus, MSR is
low cost, has low energy requirements, and yields highly pure products [24]. Moreover,
mechanochemical processes have shown several advantages such as small particles
sizes [25] and narrow size distributions. In general, mechanochemical syntheses refine
the microstructure of the product, which improves the superparamagnetic,
electromagnetic, electrical, optical (i.e., refractive index, transparency), and mechanical
properties (hardness, strength, toughness, plasticity) of the material.
Materials with superior or tailored properties can be produced from solid solutions [26]
and [27]. Ti5Ge3 and Ti5Si3 have the same structure, nearly equal lattice parameters
(both are hexagonal (P63/mcm) with a = b = 7.5370 Å, c = 5.2230 Å, and a = b =
7.4440 Å, c = 5.1430 Å, respectively), and similar atomic radii (Si, 1.32 Å; Ge, 1.37 Å)
and electronegativities (Si, 1.90; Ge 2.02); thus, Ti5Ge3 and Ti5Si3 should be totally
soluble and form a homogenous and complete solid solution [28].
Due to the great potential of titanium silicides/germanides, the objective of the present
study was to synthesise the complete range of Ti5Si3−xGex from stoichiometric
elemental powder mixtures via mechanically induced self-sustaining reactions.
2. Materials and methods
Titanium (99.98% pure, 325 mesh, Sigma Aldrich), silicon (99% pure, 325 mesh,
Sigma Aldrich), germanium (99.999% pure, 100 mesh, Sigma Aldrich), and high-purity
helium gas (99.999%, H2O ∼3 ppm, O2 ∼2 ppm, CnHm 0.5 ppm; Air Liquide) were
used in the present study. The reagents were combined in the appropriate proportions
(see Table 1) by hand grinding in an agate mortar, sonicated for 5 min in ethanol, and
ball milled under 6 bar of highly pure helium gas using a modified planetary ball-mill
(model Micro Mill Puverisette 7, Fritsch).
In each milling experiment, six tempered steel balls and 4 g of powder were placed in a
50-cc tempered steel vial (67Rc). The diameter and mass of the balls were 15 mm and
13.3 g, respectively, and the powder-to-ball mass ratio (PBR) was equal to 1/20. The
vial was purged with helium gas several times, and the desired helium pressure was
selected prior to milling. During the grinding experiments, the vial was permanently
connected to the gas cylinder by a rotary valve and a flexible polyamide tube. The
powder mixture was milled at a spinning rate of 600 rpm. The aforementioned rotation
rate was applied to both the supporting disc and the vial, which was spun in the opposite
direction. The pressure was continuously monitored with an SMC Solenoid Valve
(model EVT307-5DO-01F-Q, SMC) connected to an ADAM-4000 series data
acquisition system (Esis Pty Ltd.). When MSR was conducted, the temperature
increased due to the occurrence of exothermic reactions, which produced an
instantaneous increase in the total pressure of the system. The ignition time was
determined according to the time–pressure record, and the temperature inside the vial
was estimated from the change in pressure by applying the ideal gas law. The total
volume of the system was calibrated prior to the calculation. Upon ignition, milling was
prolonged for 10 min to ensure complete conversion.
X-ray diffraction patterns of the powders were obtained with a Philips X’Pert Pro
instrument equipped with a Θ/Θ goniometer. Cu Kα radiation (40 kV, 40 mA), a
secondary Kβ filter, and an X’Celerator detector were employed. The diffraction
patterns were scanned from 25° to 75° (2Θ) in step-scan mode, and a step of 0.05 and a
counting time of 120 s/step were applied. Using Fullprof computer program [29] and
assuming hexagonal symmetry, the lattice parameters (a and c) were calculated from the
entire set of peaks in the XRD diagram.
Scanning electron microscopy (SEM) and energy-dispersive X-ray (EDX) analysis were
performed with a Hitachi FEG S-4800 microscope equipped with an EDS detector
(EDAX Inc.) for chemical analysis. Powder samples were dispersed in ethanol and were
deposited onto a holey carbon grid.
3. Results and discussion
Table 1 shows the elemental analysis of mixtures submitted to high-energy ball milling
for the synthesis of Ti5Si3–Ti5Ge3 solid solutions with different Si/Ge atomic ratios
(2.4/0.6, 1.8/1.2, 1.5/1.5, 1.2/1.8, and 0.6/2.4). Samples TS and TG, which contained
pure Ti5Si3 and Ti5Ge3 phases, respectively, were synthesised for comparative
purposes. In all of the experiments, the effects of MSR were detected during the milling
process. The ignition times (tig) were determined from the time–pressure records and
are shown in Table 1. Similar values were obtained for all of the mixtures, except the
binary Ti/Ge sample, which presented a considerably shorter ignition time.
The XRD diagrams of the products after MSR were indicative of the formation of a
P63/mcm hexagonal phase (Fig. 1). The position of the XRD reflections in samples TS
and TG were identical to those in JCPDS data file 29-1362 (Ti5Si3) and 05-0684
(Ti5Ge3), respectively. However, when ternary mixtures of Ti, Si, and Ge were milled,
the XRD reflections of the resulting phases were between those of binary Ti5Si3 and
Ti5Ge3. The dotted red lines in Fig. 1 over the (002), (210), (311), (222), and (213)
characteristic reflections were indicative of a shift from pure Ti5Si3 (sample TS) to pure
Ti5Ge3 (sample TG). Therefore, the synthesised hexagonal phases can be described as a
solid solution with a molecular formula of Ti5Si3−xGex. Moreover, the continuous shift
in the XRD reflections (Fig. 1), which was attributed to different compositions in the
solid solution, proved that the stoichiometry of the solid solution could be controlled by
adjusting the initial Si/Ge atomic ratio.
The lattice parameters of the hexagonal phases of the Ti5Si3–Ti5Ge3 solid solution
were calculated from the XRD patterns and are shown in Table 2, along with the c/a
ratio and the cell volume. Fig. 2 shows the relationship between the initial composition
and lattice parameters of the milled samples. The similar trend followed by the lattice
parameters, a and c, in Fig. 2, suggests a random and homogeneous substitution
between both species independently of the atomic position in the lattice. It is remarkable
the asymmetrical character of the deviation of the Vergard’s law in comparison with the
approximately quadratic deviation in most binary alloy systems [30] and [31]. For
silicon-rich and germanium-rich compositions, a positive and negative deviation from
Vegard’s model was observed, respectively, producing an S-shaped variation of lattice
parameters with composition. The maximum deviation in a(=b) was 0.14%, and the
maximum deviation in c was 0.37%. The presence of secondary phases or unreacted
elements, which could account for the deviation between the presumed composition of
the solid solution and the estimated composition according to Vegard’s law, was not
detected. Careful examination of the XRD diagrams confirmed the formation of a
monophasic product. Both positive and negative deviations from linearity near the two
terminal compositions of the same system that leads to the anomalous S-shaped
violation of Vegard’s law has been found in some covalent pseudobinary alloys, and has
been attributed to the effect of bond-bending forces [32]. Moreover, this same S-shaped
deviation has also been predicted for alloy systems with large size-mismatched
constituents [33]. For Si-rich compositions, the Ti5Si3 lattice acts as a host structure for
Ge atoms. In contrast, for Ge-rich compositions, the host lattice is Ti5Ge3, and Si can
be considered an impurity. The substitution of Si or Ge generates local deformations in
the host structure. Because the atomic radii of Si and Ge are different, the host Ti5Ge3
lattice shrinks upon Si-substitution, and the Ti5Si3 lattice expands around Ge atoms.
In Fig. 3, the temperature increase inside the vial due to MSR is plotted against the
initial Si/Ge atomic ratio. As shown in the figure, the final temperature inside the vial
increased with an increase in the germanium content of the initial mixture. Due to the
fact that the heats of formation of the products in the solid solution (Ti5Si3, ΔH°for =
−579 kJ/mol and Ti5Ge3, ΔH°for = −566 kJ/mol) are nearly identical, the Ti5Si3−xGex
solid solutions have similar enthalpies of formation. Moreover, to obtain identical PBR
values for all of the milling runs, the total powder charge in the vial was held constant;
thus, the initial molar content decreased with an increase in the germanium content
(which is a heavier element than silicon), as shown in Fig. 3. Therefore, the maximum
temperature increase due to the substitution of silicon cannot be attributed to an increase
in the amount of heat released during MSR.
The aforementioned behaviour can be justified by considering that the germanium
reacts relatively fast, as indicated by the short ignition time, thus all the reaction heat is
released in a very short time, leading to a large temperature increase. The reaction is
more sluggish with silicon. Thus by the time all the reaction heat is available, a large
fraction is lost to the balls and the milling container, thus the temperature maximum is
lower. The change in the slope of the temperature profile observed in Fig. 3 from the
sample TS5G5 can be justified taking into account the specific heat (Cp) of the
Ti5Si3−xGex phases. The specific heat of the phases at different temperatures is
presented in Fig. 4. The Cp equation of Ti5Si3 and Ti5Ge3 was obtained from the
literature [13] and [34], and the Cp of the Ti5Si3−xGex solid solution phases was
determined by applying the law of mixtures. Fig. 4 shows how the Cp of the material
changes its trend as the temperature increases and the composition changes from Ti5Si3
to Ti5Ge3. At low temperatures, the Ge-rich phases have higher specific heat than Sirich phases and by contrast from ∼400 K the specific heat of the Si-rich phases is
higher. This temperature matched with that reached by the sample TS5G5 during its
reaction (Fig. 3, Te = ΔT + 298K = 422K), from which an increment in the temperature
slope was observed.
Fig. 5 shows the SEM micrographs of the powder samples after milling (samples TS,
TS8G2, TS6G4, TS4G6, TS2G8 and TG) and illustrates the morphological aspects of
the products. The SEM images revealed that the microstructures of the products are
similar and are characteristic of samples obtained by MSR [23], [24], [25] and [26].
Powdered Ti5Si3−xGe3 solid solution phases consisted of highly agglomerated submicrometric particles, and aggregates ranging from 1 to 3 μm were observed. Although
Ti5Si3 and Ti5Ge3 phases have similar fusion temperatures, the particles appeared
sintered when the solid solution was enriched in germanium due to the locally high
temperatures attained during the self-sustaining reaction and the lower specific heat of
germanium-rich phases, which induces relatively high local temperatures.
4. Conclusions
Monophasic Ti5Si3−xGe3 solid solutions were synthesised from blends of titanium,
silicon and germanium under helium atmosphere via mechanically induced selfsustaining reactions, and the stoichiometry of the Ti5Si3−xGe3 phases was controlled
by adjusting the initial Si/Ge atomic ratio. The temperature of the combustion process
was determined by applying the ideal gas law, and different behaviour was observed,
depending on the initial composition.
Acknowledgements
This work was supported by Spanish government under grant No. MAT2010-17046,
which is financed in part by European Regional Development Fund of 2007–2013. E.
Chicardi and J. M. Córdoba were supported by CSIC through JAE-Pre and JAE-Doc
grants, respectively, which are financed in part by European Social Fund (ESF).
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Figure captions
Figure 1. X-ray powder diffraction diagrams of products obtained from the initial
mixtures shown in Table 1 via mechanically induced self-sustaining reactions.
Figure 2. The lattice parameters (a and c) of the P63/mcm hexagonal Ti5Si3−xGe3
phases obtained by mechanically induced self-sustaining reactions.
Figure 3. Temperature inside the vial during MSR and initial molar quantities versus
the Si/Ge atomic ratio.
Figure 4. Specific heat (Cp) of the Ti5Si3–Ti5Ge3 system at different temperatures.
Figure 5. SEM micrographs showing the morphology of Ti5Si3−xGe3 samples. (a) TS;
(b) TS8G2; (c) TS6G4; (d) TS4G6; (e) TS2G8; (f) TG.
Table 1
Table 1. Summary of elemental mixtures submitted to milling, ignition times and pressure
changes observed during MSR. The change in temperature was calculated from the pressure.
Sample
TS
TS8G2
TS6G4
TS5G5
TS4G6
TS2G8
TG
Ti:Si:Ge Atomic Ratio
5:3:0
5:2.4:0.6
5:1.8:1.2
5:1.5:1.5
5:1.2:1.8
5:0.6:2.4
5:0:3
Powder charge (mol)
0.0124
0.0114
0.0106
0.0102
0.0099
0.0093
0.0087
tig (min)
40
40
34
41
30
34
19
ΔPressure (bar)
+2.53
+2.49
+2.36
+2.35
+2.67
+2.84
+3.10
ΔTemp. (K)
+109.6
+117.5
+119.5
+124.0
+145.0
+164.3
+191.3
Table 2
Table 2. Lattice parameters (a and c), c/a ratio, and cell volume (V) of hexagonal
Ti5Si3−xGe3 phases formed by MSR.
Sample
TS
TS8G2
TS6G4
TS5G5
TS4G6
TS2G8
TG
a = b (Å)
7.4396
7.4781
7.4902
7.5000
7.5024
7.5152
7.5349
c (Å)
5.1450
5.1630
5.1829
5.1876
5.1849
5.1952
5.2184
c/a
0.692
0.690
0.692
0.692
0.691
0.691
0.693
V (Å3)
246.613
250.043
251.820
252.708
252.739
254.105
256.580
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5