77 research outputs found
Ab-initio elastic tensor of cubic TiAlN alloy: the dependence of the elastic constants on the size and shape of the supercell model
In this study we discuss the performance of approximate SQS supercell models
in describing the cubic elastic properties of B1 (rocksalt)
TiAlN alloy by using a symmetry based projection technique. We
show on the example of TiAlN alloy, that this projection
technique can be used to align the differently shaped and sized SQS structures
for a comparison in modeling elasticity. Moreover, we focus to accurately
determine the cubic elastic constants and Zener's type elastic anisotropy of
TiAlN. Our best supercell model, that captures accurately both
the randomness and cubic elastic symmetry, results in GPa,
GPa and GPa with 3% of error and for Zener's
elastic anisotropy with 6% of error. In addition, we establish the general
importance of selecting proper approximate SQS supercells with symmetry
arguments to reliably model elasticity of alloys. In general, we suggest the
calculation of nine elastic tensor elements - , , ,
, , , , and , to evaluate and
analyze the performance of SQS supercells in predicting elasticity of cubic
alloys via projecting out the closest cubic approximate of the elastic tensor.
The here described methodology is general enough to be applied in discussing
elasticity of substitutional alloys with any symmetry and at arbitrary
composition.Comment: Submitted to Physical Review
Elinvar effect in Ti simulated by on-the-fly trained moment tensor potential
A combination of quantum mechanics calculations with machine learning (ML)
techniques can lead to a paradigm shift in our ability to predict materials
properties from first principles. Here we show that on-the-fly training of an
interatomic potential described through moment tensors provides the same
accuracy as state-of-the-art {\it ab inito} molecular dynamics in predicting
high-temperature elastic properties of materials with two orders of magnitude
less computational effort. Using the technique, we investigate high-temperature
bcc phase of titanium and predict very weak, Elinvar, temperature dependence of
its elastic moduli, similar to the behavior of the so-called GUM Ti-based
alloys [T. Sato {\ it et al.}, Science {\bf 300}, 464 (2003)]. Given the fact
that GUM alloys have complex chemical compositions and operate at room
temperature, Elinvar properties of elemental bcc-Ti observed in the wide
temperature interval 1100--1700 K is unique.Comment: 15 pages, 4 figure
Origin of the anomalous piezoelectric response in wurtzite ScAlN alloys
The origin of the anomalous, 400% increase of the piezoelectric coefficient
in ScAlN alloys is revealed. Quantum mechanical calculations show
that the effect is intrinsic. It comes from a strong change in the response of
the internal atomic coordinates to strain and pronounced softening of C
elastic constant. The underlying mechanism is the flattening of the energy
landscape due to a competition between the parent wurtzite and the so far
experimentally unknown hexagonal phases of the alloy. Our observation provides
a route for the design of materials with high piezoelectric response.Comment: 10 pages, 4 figures, accepted for publication in Phys. Rev. Let
Significant elastic anisotropy in TiAlN alloys
Strong compositional-dependent elastic properties have been observed
theoretically and experimentally in TiAl N alloys. The elastic
constant, C, changes by more than 50% depending on the Al-content.
Increasing the Al-content weakens the average bond strength in the local
octahedral arrangements resulting in a more compliant material. On the other
hand, it enhances the directional (covalent) nature of the nearest neighbor
bonds that results in greater elastic anisotropy and higher sound velocities.
The strong dependence of the elastic properties on the Al-content offers new
insight into the detailed understanding of the spinodal decomposition and age
hardening in TiAlN alloys.Comment: 3 figures, 3 page
Does timing of decisions in a mixed duopoly matter?
We determine the endogenous order of moves in a mixed pricesetting duopoly. In contrast to the existing literature on mixed oligopolies we establish the payo equivalence of the games with an exogenously given order of moves if the most plausible equilibrium is realized in the market. Hence, in this case it does not matter whether one becomes a leader or a follower. We also establish that replacing a private firm by a public firm in the standard Bertrand-Edgeworth game with capacity constraints increases social welfare and that a pure-strategy equilibrium always exists
Tunable Lyapunov exponent in inverse magnetic billiards
The stability properties of the classical trajectories of charged particles
are investigated in a two dimensional stadium-shaped inverse magnetic domain,
where the magnetic field is zero inside the stadium domain and constant
outside. In the case of infinite magnetic field the dynamics of the system is
the same as in the Bunimovich billiard, i.e., ergodic and mixing. However, for
weaker magnetic fields the phase space becomes mixed and the chaotic part
gradually shrinks. The numerical measurements of the Lyapunov exponent
(performed with a novel method) and the integrable/chaotic phase space volume
ratio show that both quantities can be smoothly tuned by varying the external
magnetic field. A possible experimental realization of the arrangement is also
discussed.Comment: 4 pages, 6 figure
THE WAIT-AND-SEE OPTION IN ASCENDING PRICE AUCTIONS
Cake-cutting protocols aim at dividing a ``cake'' (i.e., a divisible
resource) and assigning the resulting portions to several players in a way that
each of the players feels to have received a ``fair'' amount of the cake. An
important notion of fairness is envy-freeness: No player wishes to switch the
portion of the cake received with another player's portion. Despite intense
efforts in the past, it is still an open question whether there is a
\emph{finite bounded} envy-free cake-cutting protocol for an arbitrary number
of players, and even for four players. We introduce the notion of degree of
guaranteed envy-freeness (DGEF) as a measure of how good a cake-cutting
protocol can approximate the ideal of envy-freeness while keeping the protocol
finite bounded (trading being disregarded). We propose a new finite bounded
proportional protocol for any number n \geq 3 of players, and show that this
protocol has a DGEF of 1 + \lceil (n^2)/2 \rceil. This is the currently best
DGEF among known finite bounded cake-cutting protocols for an arbitrary number
of players. We will make the case that improving the DGEF even further is a
tough challenge, and determine, for comparison, the DGEF of selected known
finite bounded cake-cutting protocols.Comment: 37 pages, 4 figure
Temperature-dependent elastic properties of Ti_(1−x)Al_xN alloys
Ti_(1−x)Al_xN is a technologically important alloy that undergoes a process of high temperature age-hardening that is strongly influenced by its elastic properties. We have performed first principles calculations of the elastic constants and anisotropy using the symmetry imposed force constant temperature dependent effective potential method, which include lattice vibrations and therefore the effects of temperature, including thermal expansion and intrinsic anharmonicity. These are compared with in situ high temperature x-ray diffraction measurements of the lattice parameter. We show that anharmonic effects are crucial to the recovery of finite temperature elasticity. The effects of thermal expansion and intrinsic anharmonicity on the elastic constants are of the same order, and cannot be considered separately. Furthermore, the effect of thermal expansion on elastic constants is such that the volume change induced by zero point motion has a significant effect. For TiAlN, the elastic constants soften non-uniformly with temperature: C_(11) decreases substantially when the temperature increases for all compositions, resulting in an increased anisotropy. These findings suggest that an increased Al content and annealing at higher temperatures will result in a harder alloy
High temperature decomposition and age hardening of single-phase wurtzite TiAlN thin films grown by cathodic arc deposition
We investigated the high temperature decomposition behavior of wurtzite phase
TiAlN films using experimental methods and first-principles
calculations. Single phase metastable wurtzite TiAlN (x = 0.65,
0.75, 085 and 0.95) solid solution films were grown by cathodic arc deposition
using low duty cycle pulsed substrate-bias voltage. First-principles calculated
elastic constants of the wurtzite TiAlN phase show a strong
dependence on alloy composition. The predicted phase diagram shows a
miscibility gap with an unstable region. High resolution scanning transmission
electron microscopy and chemical mapping demonstrate decomposition of the films
after high temperature annealing (950C), which resulted in nanoscale
chemical compositional modulations containing Ti-rich and Al-rich regions with
coherent or semi coherent interfaces. This spinodal decomposition of the
wurtzite film causes age hardening of 1-2 GPa
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