# Crystallographic ordering of Al and Sn in -Ti

Felicity F. Worsnop  Susannah L. M. Lea  Jan Ilavsky  David Rugg  David Dye
Department of Materials, Royal School of Mines, Imperial College London,
Prince Consort Road, London, SW7 2BP, UK  Advanced Photon Source, Argonne
National Laboratory, 9700 S Cass Avenue, Argonne, IL, USA  Rolls-Royce plc.,
Elton Road, Derby, DE24 8BJ, UK

###### Abstract

Increasing attention is being paid to $\alpha_{2}$ Ti3(Al,Sn) precipitation
from the $\alpha$ phase of titanium alloys owing to its effect on slip band
formation, localisation and the implications for fatigue performance in jet
engine titanium. However, the early stages of $\alpha_{2}$ precipitation have
historically been difficult to observe in TEM, neutron diffraction or atom
probe analysis. Here, small angle X-ray scattering is used to reexamine the
phase boundary in binary Ti-Al and Ti-Sn alloys with around 500 ppmw O. It is
found that the phase boundaries in the literature are approximately correct,
at 6.2 wt.% Al and 16.9 wt.% Sn, and that this favours the use of Al as a
solid solution strengthener over Sn for ambient temperature applications.
However, once O content and phase partitioning in + alloys are taken into
account, this implies that Aleq limits for future alloy design of critical
rotating parts should be lowered substantially.

###### keywords:

Titanium alloys , Phase transformations

††journal: Scripta Mater.

Many + titanium alloys use Al and Sn to stabilise and strengthen the hcp
phase, producing materials that have excellent property combinations for
aerospace and industrial applications. Sn in particular is included for
retention of strength at elevated temperatures. However, these solutes are
known to undergo crystallographic ordering after exposure to temperatures
experienced during processing, forming the 2 Ti3(Al,Sn) phase [1]. For
instance, Ti–834 (Ti–5.8Al–4Sn–3.5Zr–0.7Nb–0.5Mo–0.35Si–0.06C) has been shown
to produce a fine dispersion of 2 precipitates after $24\text{\,}\mathrm{h}$
at $700\text{\,}\mathrm{\SIUnitSymbolCelsius}$ [2]. This ordered phase
promotes slip localisation that increases the risk of dwell fatigue crack
nucleation in critical rotating parts of jet engines. Under stress corrosion
cracking conditions, crystallographic ordering may arise around the crack
front as a result of corrosion reactions [3]. In both instances, deeper
understanding of the relative propensity of these solutes to undergo ordering
could aid alloy and processing design to mitigate potential failure
mechanisms.

In this study, binary Ti–Al and Ti–Sn alloys were investigated to evaluate the
relative propensity for crystallographic ordering of these widely used solutes
during isothermal exposure at $550\text{\,}\mathrm{\SIUnitSymbolCelsius}$.
Using SEM, TEM and small angle X-ray scattering (SAXS), the and (where
present) 2 microstructures were characterised. These data allowed analysis of
different strengthening contributions in each alloy, providing an assessment
of property trade-offs in the two alloying systems.

Sets of Ti–Al and Ti–Sn alloys were designed based on currently accepted phase
diagrams [1, 4] and a planned ageing temperature of
$550\text{\,}\mathrm{\SIUnitSymbolCelsius}$, with compositions chosen at and
either side of the /+2 boundary. Ingots were arc melted under argon from pure
elements, then hot-rolled and recrystallised using temperatures and times
suitable for each composition, Table 1, to produce equiaxed microstructures.
The bars were ice water quenched from the recrystallisation temperature, and
half of each bar was then encapsulated under argon and isothermally aged at
$550\text{\,}\mathrm{\SIUnitSymbolCelsius}$ for $80\text{\,}\mathrm{d}$.
Compositions were measured using ICP-OES and LECO at TIMET UK, Witton, UK.

Table 1: Compositions, processing details and grain sizes for the Ti–Al and Ti–Sn alloys. Nominal compositions are given in wt.%, and measured at.% compositions for the substitutional solutes (Al or Sn) are shown for reference. Rolling and recrystallisation temperatures for these steps were chosen according to the transus for each alloy. Ti–Al alloys were rolled at $1150\text{\,}\mathrm{\SIUnitSymbolCelsius}$. Ti–Sn alloys were rolled at $1050\text{\,}\mathrm{\SIUnitSymbolCelsius}$. All materials were ice water quenched (IWQ) after solutionising at the recrystallisation temperature. Alloy (nominal | Measured composition / wt.% | at.% Al or Sn |  $T_{\mathrm{roll}}$ / $\mathrm{\SIUnitSymbolCelsius}$ |  $T_{\mathrm{RX}}$ / $\mathrm{\SIUnitSymbolCelsius}$ |  $t_{\mathrm{RX}}$ / h | Grain size / $\mathrm{\SIUnitSymbolMicro m}$
---|---|---|---|---|---|---
composition) | Al | Sn | O | N |  |  |  |  |
Ti–3.5Al | 3.55 |  $<$0.01 | 0.04 | 0.01 | 6.12 | 980 | 900 | 1 | 50
Ti–5.3Al | 5.28 |  $<$0.01 | 0.03 | 0.01 | 8.99 | 980 | 900 | 2 | 49
Ti–7Al | 7.00 |  $<$0.01 | 0.08 | 0.01 | 11.76 | 980 | 900 | 3 | 57
Ti–7Sn |  $<$0.01 | 7.10 | 0.07 | 0.01 | 2.98 | 800 | 780 | 15 | 19
Ti–12Sn |  $<$0.01 | 12.02 | 0.06 | 0.01 | 5.21 | 800 | 780 | 12 | 20
Ti–17Sn |  $<$0.01 | 17.00 | 0.04 |  $<$0.01 | 7.62 | 800 | 780 | 4 | 13

Microstructures were characterised using backscatter SEM (Zeiss Sigma 300 FEG-
SEM, 8–$12\text{\,}\mathrm{kV}$ accelerating voltage) and conventional TEM
electron diffraction and dark field imaging (JEOL 2100F,
$200\text{\,}\mathrm{keV}$ accelerating voltage, with double-tilt specimen
holder). Microscopy specimens were prepared by electropolishing with a
solution of 3% perchloric acid, 40% butan-1-ol and 57% methanol, using an
applied voltage of 20.0–$21.5\text{\,}\mathrm{V}$, at temperatures between
$-45\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and
$-30\text{\,}\mathrm{\SIUnitSymbolCelsius}$. Mechanical properties were
characterised by tensile testing on an Instron 5967 load frame with a
$30\text{\,}\mathrm{kN}$ load cell and Instron 2620 extensometer, at a nominal
strain rate of $10^{-3}$ s-1, using a flat dogbone geometry with a
$19\text{\,}\mathrm{mm}$$\times$$1.5\text{\,}\mathrm{mm}$$\times$$1.5\text{\,}\mathrm{mm}$
gauge.

SAXS measurements were taken on the USAXS beamline [5] at the Advanced Photon
Source at Argonne National Laboratory, using a $21\text{\,}\mathrm{keV}$ beam
and a 800$\times$$800\text{\,}\mathrm{\SIUnitSymbolMicro m}$ beam area.
Samples were prepared by hand-polishing discs of $3\text{\,}\mathrm{mm}$
diameter and $300\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thickness with SiC
paper from 500 to 4000 grits, followed by neutralised colloidal silica
solution. After final thickness measurements and cleaning with detergent to
remove colloidal silica and with isopropanol to remove surface contaminants,
specimens were suspended in an amorphous, transparent tape for handling during
measurement. The data were reduced using the Nika package [6] and analysed
using the Irena package [7], informed by our previous analysis of 2
composition [8].

Equiaxed, single-phase microstructures were produced for each composition,
Fig. 1. Grain sizes were measured using the mean linear intercept method (per
ASTM E112 [9]), with grain sizes of around
$50\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and
$20\text{\,}\mathrm{\SIUnitSymbolMicro m}$ in the Ti–Al and Ti–Sn alloys
respectively, Table 1.

Figure 1: Microstructures of the Ti–Al and Ti–Sn binary alloys. (a)
Backscatter SEM showing equiaxed grains. The Ti–Sn alloys were found to be
susceptible to hydride formation during electropolishing, visible at some
grain boundaries in SEM. (b) Selected area diffraction patterns taken along B
= ¡0 1 -1 1¿. (c) Dark field images were recorded using a ¡2 -1 -1 0¿α2 two-
beam condition with B = ¡0 1 -1 1¿.

The IWQ and aged conditions were then compared using selected area diffraction
and dark field imaging in TEM for a qualitative indication of whether 2
formation had occurred. In the Ti–Al series, all three alloys showed no
superlattice reflections in the IWQ condition, indicating suppression of long-
range ordering during the quench from
$900\text{\,}\mathrm{\SIUnitSymbolCelsius}$. Only Ti–7Al developed clear
superlattice reflections after the ageing treatment. Dark field images showed
well formed Ti3Al 2 precipitates. No contrast could be observed in attempts to
take dark field images for aged Ti–3.5Al or Ti–5.3Al.

For the Ti–Sn alloys, the IWQ condition again showed no superlattice
reflections for any of the three alloys, with crystallographic disorder
maintained by the quench from $780\text{\,}\mathrm{\SIUnitSymbolCelsius}$.
Ageing produced faint superlattice reflections for the highest solute content
only, Ti–17Sn. Dark field imaging revealed a homogeneous distribution of much
finer precipitates in this specimen than in Ti–7Al.

For the two samples in which dark field imaging of 2 was possible, aspect
ratios were measured for use in SAXS data fitting. The clearly defined
precipitates in the Ti–7Al alloy allowed measurement of multiple separate
particles to give an average aspect ratio of 2.4, while an aspect ratio of 1.0
was assigned to the Ti–17Sn alloy’s precipitates, which were equiaxed in
appearance.

Further characterisation of precipitate dispersions (or absence thereof) was
conducted using SAXS, Fig. 2. The data were fitted using a model
microstructure containing a homogeneous dispersion of randomly-oriented
spheroids, representing the 2 precipitates, and a second population of thin
discs representing grain boundaries. The precipitate dispersions were modelled
as a homogeneous dispersion of spheroids, with aspect ratios informed by TEM.
Electron density contrast between and 2 phases for each alloy was calculated
in the Irena package [7] using a similar approach as in the authors’ previous
work on similar alloys [8]. The phase composition was taken to be that of the
alloy overall, the 2 phase composition was assumed to be stoichiometric Ti3Al
or Ti3Sn, and lattice parameters were assumed to be the same as for pure Ti.
This gave contrast values of
$2.2\text{\times}{10}^{20}\text{\,}{\mathrm{cm}}^{-4}$ for the Ti–Al alloys
and $53.6\text{\times}{10}^{20}\text{\,}{\mathrm{cm}}^{-4}$ for the Ti–Sn
alloys.

In Ti–3.5Al and Ti–5.3Al, both the IWQ and aged conditions gave no indication
of 2 Ti3Al formation, with a model describing the grain boundaries sufficient
for fitting in each case. In the Ti–7Al material, the small peak at
approximately
$4\text{\times}{10}^{-2}\text{\,}{\mathrm{\SIUnitSymbolAngstrom}}^{-1}$ was
modelled as a population of 2 Ti3Al nuclei, of mean diameter
$3.2\text{\,}\mathrm{nm}$ and with 0.4% volume fraction. This may indicate
that the quenching in this alloy was insufficient to suppress this early stage
of the phase separation process. Upon ageing, the peak shifted to higher
particle sizes and a volume fraction of 8.0% of particles with mean diameter
$25\text{\,}\mathrm{nm}$ was obtained through fitting spheroids of aspect
ratio 2.4.

Figure 2: SAXS curves and models for the Ti–Al and Ti–Sn binary alloys, IWQ
and aged. The presence of 2 precipitates was identified in Ti–7Al and Ti–17Sn
(wt.%). Below are shown the SAXS-derived volume fraction ($f_{\alpha{}2}$),
size ($d_{\mathrm{eq}}$), spacing ($s_{\mathrm{eff}}$) and number density
($n$) for each precipitate population, and the solubility limit (i.e. position
of the /+2 boundary on the Ti–X binary equilibrium phase diagram) for each
system.

Similarly, in the Ti–7Sn and Ti–12Sn materials, both IWQ and aged conditions
showed no signal from a precipitate phase. The Ti–17Sn alloy was also found to
have no second phase in the IWQ condition, but a clear peak had developed for
the aged specimen. This was ascribed to the 2 Ti3Sn phase identified in TEM
diffraction and imaging. This produced a fit for a volume fraction of 0.2%,
and a particle diameter of $13.7\text{\,}\mathrm{nm}$.

Tensile testing of the twelve materials in this study was performed to obtain
their 0.2% proof stresses, $\sigma_{\mathrm{0.2}}$, and strains at failure,
$\epsilon_{\mathrm{f}}$. The Hall–Petch relation was used to distinguish the
effects of solute content, ageing state and grain size:

$\sigma_{\mathrm{Y}}=\sigma_{\mathrm{0}}+\frac{k_{\mathrm{HP}}}{\sqrt{d}},$

in which $\sigma_{\mathrm{Y}}$ is the measured yield stress,
$\sigma_{\mathrm{0}}$ is a material constant, $k_{\mathrm{HP}}$ is the
material’s Hall–Petch coefficient (an empirically derived constant), and $d$
is the average grain diameter. The value of $\sigma_{\mathrm{0}}$ is given by
$\sigma_{\mathrm{0}}=\sigma_{\mathrm{Ti}}+\Sigma{}c_{i}\sigma_{\mathrm{i}}$,
where $\sigma_{\mathrm{Ti}}$ is the strength of pure Ti, $c_{i}$ is the
concentration of solute $i$ and $\sigma_{\mathrm{i}}$ is the strengthening
contribution per wt.% solute $i$. In this case, a $k_{\mathrm{HP}}$ value of
$230\text{\,}\mathrm{MPa}\text{\,}\mathrm{\SIUnitSymbolMicro m}$-1/2 was used
for all materials, being the reported value for both CP Ti [2] and for
equiaxed Ti–64 [10].

These Hall–Petch calculations of $\sigma_{0}$ enabled comparison of strengths
discarding the effects of grain size. The Ti–Al alloys showed the expected
trends in yield stress with solute content and ageing condition, Fig. 3(a). In
the IWQ condition, yield stresses were similar for the Ti–3.5Al and Ti–5.3Al
materials, at $540\text{\,}\mathrm{MPa}$ in each case, while the Ti–7Al alloy
showed a higher yield stress of $655\text{\,}\mathrm{MPa}$. Alongside solution
strengthening effects, the trace amount of 2 detected in SAXS for quenched
Ti–7Al may contribute to its higher yield stress.

After ageing, Ti–5.3Al and Ti–7Al saw an increase in $\sigma_{\mathrm{0}}$ of
$30\text{\,}\mathrm{MPa}$ and $50\text{\,}\mathrm{MPa}$ respectively. These
observations are explained by the formation of ordered domains in Ti–7Al, and
the possible formation of short-range order in Ti–5.3Al (for which no 2
precipitates were observable in TEM or SAXS). There was a slight softening of
the Ti–3.5Al material upon ageing, with a drop of around
$50\text{\,}\mathrm{MPa}$ in $\sigma_{\mathrm{0}}$ (intrinsic strength
property, discounting grain size effects). We attribute this to annealing of
dislocation density remaining after processing, and the absence of ordered
domains.

For the Ti–Sn alloys, Fig. 3(b), there was a clear trend of increasing yield
stress with increasing alloying content, in both the IWQ and aged conditions.
The Ti–12Sn and Ti–17Sn alloys both gained around $30\text{\,}\mathrm{MPa}$ in
yield stress upon ageing. The Ti–7Sn alloy showed slight softening upon
ageing; as for the Ti–3.5Al alloy, we attribute this to a lack of 2
precipitation and annealing out of defect density. For Ti–17Sn, loss of work
hardening ability is seen upon ageing (evident as flattening of its
stress–strain curve compared to the IWQ condition), consistent with the slip
band formation mechanism that is associated with 2 [11]. For Ti–7Al, the
effect is subtler and is mostly seen as a shortening of the yield region of
the stress–strain curve.

Figure 3: Tensile testing of (a) the Ti–Al binary alloys and (b) the Ti–Sn
binary alloys. (c) Resulting yield stresses $\sigma{}_{\mathrm{Y}}$,
calculated Hall–Petch intrinsic strengths $\sigma{}_{\mathrm{0}}$ (to discard
the effect of grain size), strains at failure $\epsilon{}_{\mathrm{f}}$, and
the measured grain sizes used for Hall–Petch analysis.

Based on the above results, the strengthening contributions of Al and Sn may
be compared. In the Ti–Al system, additions of Al were seen to provide a
moderate solid solution strengthening effect in the IWQ materials, offering an
increase in the Hall–Petch strength parameter $\sigma_{\mathrm{0}}$ of
approximately $115\text{\,}\mathrm{MPa}$ between the Ti–5.3Al and Ti–7Al
alloys. This corresponds to a gain of
$61\text{\,}\mathrm{MPa}$/$\mathrm{wt.\%}$ Al, or
$38\text{\,}\mathrm{MPa}$/$\mathrm{at.\%}$ Al. By comparison, the Ti–Sn alloys
showed stronger solid solution strengthening, with an increase from
$340\text{\,}\mathrm{MPa}$ to $660\text{\,}\mathrm{MPa}$ between the Ti–7Sn
and Ti–17Sn materials in the IWQ condition. This corresponds to
$30\text{\,}\mathrm{MPa}$/$\mathrm{wt.\%}$ Sn, or
$64\text{\,}\mathrm{MPa}$/$\mathrm{at.\%}$ Sn.

For the compositions that underwent 2 formation, age hardening effects may
also be compared. A $\sigma_{\mathrm{0}}$ increase of
$55\text{\,}\mathrm{MPa}$ for Ti–7Al was found, in which an 8% volume fraction
of 2 was produced. In the Ti–17Sn material, ageing produced a low volume
fraction (0.2%) of 2, with a resulting small increase of $\sigma_{\mathrm{0}}$
by $30\text{\,}\mathrm{MPa}$.

Orowan strengthening is approximately given by
$\Delta\tau_{\mathrm{bowing}}=Gb\sqrt{(3f/2\pi)}$/r, where $G$ is the shear
modulus, $b$ the Burgers vector and $r$ the precipitate radius [12]. From the
SAXS analysis, the ratio of expected precipitate hardening contributions given
by $\sqrt{f}/r$ was 3.5, whereas the tensile test measurements showed that the
Ti–7Al alloy had a 1.8$\times$ greater increase in yield strength on ageing
than Ti–12Sn. Given the uncertainties in the analyses, and the removal of
solute from the matrix (non-diluteness), this order-of-magnitude agreement is
felt to provide confidence to the SAXS analysis.

For assessment of the Ti–Al and Ti–Sn binary equilibrium phase diagrams, the
lever rule was used to calculate the position of the /+2 boundary at
$550\text{\,}\mathrm{\SIUnitSymbolCelsius}$ in each system. For a two-phase
system, $f_{1}(c-c_{1})=f_{2}(c-c_{2})$, where $c$ is the alloy composition,
$c_{1}$ and $c_{2}$ are the compositions of phases 1 and 2, and $f_{1}$ and
$f_{2}$ are the volume fractions of each phase. The composition at the single-
phase boundary is then $c_{\alpha}=(c-f_{\alpha{}2}c_{\alpha{}2})/f_{\alpha}$.
For the Ti–7Al and Ti–17Sn alloys for which 2 was formed, stoichiometric Ti3X
compositions were assumed for the 2 phase. The solubility limit at
$550\text{\,}\mathrm{\SIUnitSymbolCelsius}$ was found to be
$10.6\text{\,}\mathrm{at.\%}$ or $6.2\text{\,}\mathrm{wt.\%}$ Al in the Ti–Al
system, and $7.6\text{\,}\mathrm{at.\%}$ or $16.9\text{\,}\mathrm{wt.\%}$ Sn
in the Ti–Sn system, in close agreement with previous studies [1, 13].

This measurement of solubility limits may be used to reassess the widely used
convention of aluminium equivalent, a metric that aims to capture an alloy’s
overall likelihood of straying into the two-phase +2 field. The principle,
initially put forward by Rosenberg et al. [14], calculates a value
$\mathrm{Al}_{\mathrm{eq}}=\sum_{i}x_{i}c_{i}$, where $c_{i}$ are wt.%
compositions of each element in the alloy, and $x_{i}$ are empirically derived
constants, calculated as the ratio of the solubility limit of element $i$ to
that of Al. Current literature gives this as $\mathrm{Al}_{\mathrm{eq}}$ =
[Al] + 0.33[Sn] + 0.17[Zr] + 10[O]. Based on the present results, however, the
prefactor for Sn might be modified very slightly from 0.33 to
$0.36\text{\,}{\mathrm{wt.\%}}^{-1}$, i.e. a 10% increase in its value.

Binary alloys at the solubility limit in each system, i.e. Ti–6.2Al and
Ti–16.9Sn (wt.%), may be further considered in terms of the trade-off between
solution strengthening, propensity for ordering and density. The density of
these alloys based on the average atomic mass (i.e. assuming no change in
lattice parameters from pure Ti) would be
$4.30\text{\,}\mathrm{g}\text{\,}{\mathrm{cm}}^{-3}$ and
$5.01\text{\,}\mathrm{g}\text{\,}{\mathrm{cm}}^{-3}$ respectively, the Sn
alloy being denser. Yield stresses were calculated based on Hall–Petch
parameters for these two alloy compositions, interpolating a value of
$\sigma_{\mathrm{0}}$ for the compositions at the solubility limit. For
Ti–6.2Al, this gave a $\sigma_{\mathrm{0}}$ of $571\text{\,}\mathrm{MPa}$, and
for Ti–16.9Sn this was slightly higher at $590\text{\,}\mathrm{MPa}$. A grain
size of $20\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and a Hall–Petch
coefficient of $230\text{\,}\mathrm{MPa}\text{\,}\mathrm{\SIUnitSymbolMicro
m}$-1/2 [10] were assumed. These calculations gave predicted yield stresses of
$623\text{\,}\mathrm{MPa}$ and $642\text{\,}\mathrm{MPa}$ for Ti–6.2Al and
Ti–17Sn respectively. The calculated specific strengths of alloys at the
solubility limit in each system were then found to be
$145\text{\,}\mathrm{MPa}\text{\,}{\mathrm{g}}^{-1}\text{\,}{\mathrm{cm}}^{3}$
for Ti–6.2Al and
$128\text{\,}\mathrm{MPa}\text{\,}{\mathrm{g}}^{-1}\text{\,}{\mathrm{cm}}^{3}$
for Ti–16.9Sn, a 13% benefit for Al over Sn.

Multiple properties must be considered together to evaluate the best trade-off
for a given application. These include strength, density, fatigue resistance,
corrosion and oxidation resistance, and the retention of mechanical properties
at elevated temperature. In the case of rotating parts for jet engines, Al
provides a clear density (i.e. specific strength) advantage. Considering
fatigue properties, higher propensity for crystallographic ordering is linked
to increased dwell sensitivity, on account of the contribution to
micromechanical stress localisation due to slip band formation [11, 15].

The inclusion of higher -stabiliser content (particularly Sn) for high
temperature alloys such as Ti–834 or Ti–6242 is partly motivated by reduction
of volume fraction. The phase is more susceptible to degradation of its
mechanical properties and environmental resistance at elevated temperature due
to the higher diffusion rates in the bcc phase [2, 16], so that reducing its
volume fraction provides better retention of properties to higher temperatures
for an + alloy. Alloys known to experience a dwell fatigue life debit include
Ti–64, Ti–6246 and Ti–834 [17]. The Aleq values for these alloys are 7.5, 8.9
and 9.3 wt.%, respectively. Additionally, ageing treatments in the +2 field
are often used to strengthen the phase, despite the potential impact on dwell
fatigue resistance.

A guideline that has been commonly referenced in titanium alloy design and
industry for several decades has been that an alloy will be stable and
“unlikely” to form 2 if Al${}_{\mathrm{eq}}\leq$ $9\text{\,}\mathrm{wt.\%}$
[14, 18]. However, it has been demonstrated in this study that this is
comfortably within the 2-forming regime for the binary Ti–Al and Ti–Sn
systems. The mixed ordered phase Ti3(Al,Sn) can also form in alloys containing
both solutes [19]. This study has considered model alloys with single-phase
microstructures, so that the alloy Aleq is the same as the phase’s Aleq
content. It may be noted that the phase in + alloys will be enriched in
-stabilising solutes relative to the alloy composition.

Typical rotor alloys contain anywhere up to 2000 ppmw O (0.2 wt%), an Aleq
increment of 2. Here, the solubility limit of 6.2 wt.% in an alloy containing
0.08 wt% O implies an Aleq limit of 7.0 wt%. This implies that a Ti–$x$Al–4V
alloy containing 0.2 wt% O should contain no more than 5 wt.% Al. If, in an +
alloy such as Ti–6Al–4V, a 10% volume fraction of Al-depleted $\beta$ phase is
assumed, then this implies an lower Aleq limit of 6.5 wt% or less, or an Al
limit of 4.5 wt.% once O is taken into account. Thus, even alloys such as
Ti-5Al-7.5V (Ti-575) may not be entirely safe from $\alpha_{2}$ precipitation.

From an alloy design perspective, we therefore suggest that current structural
+ alloys for aerospace applications (especially critical rotating parts
subject to dwell fatigue loading) contain too high an aluminium equivalent to
avoid deleterious crystallographic ordering.

In summary, SAXS was used to examine the solubility limits for Al and Sn in
$\alpha$-Ti against Ti3(Al,Sn) precipitation. The /+2 boundary was found to
lie at $6.2\text{\,}\mathrm{wt.\%}$ ($10.6\text{\,}\mathrm{at.\%}$) for the
Ti–Al system and $16.9\text{\,}\mathrm{wt.\%}$ ($7.6\text{\,}\mathrm{at.\%}$)
for the Ti–Sn system, for alloys containing around 500 ppmw O, in agreement
with literature [1, 13]. Tensile testing combined with a Hall-Petch analysis
showed that, due to the density penalty associated with Sn additions, Al is a
slightly more efficient solution strengthener than Sn, even at the solubility
limit. Counter to the compositional design of several widely-used + and near-
alloys in use today, it is suggested that a ‘safer’ Aleq limit may be as low
as $6.5\text{\,}\mathrm{wt.\%}$, or an alloy Al limit of 4.5 wt.%, compared to
the limit of Al${}_{\mathrm{eq}}=9$ wt.% used traditionally.

## Acknowledgements

FFW was funded by Rolls-Royce plc and by the EPSRC Centre for Doctoral
Training in the Advanced Characterisation of Materials (EP/L015277/1). DD was
funded by a Royal Society Indstrial Fellowship and EPSRC (EP/K034332/1). We
thank Dr T.W.J. Kwok and Dr I. Bantounas at Imperial College London for their
assistance with alloy processing, and TIMET for their support with the
composition measurements. This research used resources of the Advanced Photon
Source, a U.S. Department of Energy (DOE) Office of Science User Facility
operated for the DOE Office of Science by Argonne National Laboratory under
Contract No. DE-AC02-06CH11357.

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