text:
\section{Introduction}

High-throughput {\it ab initio} methods, capable of predicting
properties of an ample set of materials from quantum mechanics
calculations, are becoming important tools for scientists working in
rational materials development. These methods allow researchers to
correlate between different systems and to observe trends converging
toward the predictions of new materials
\cite{Ceder1998Nature,Johannesson2002PRL,Crespi,Curtarolo2003PRL,Curtarolo2005Calphad,Ceder2006NatureMaterials}.
The main difference between the ``several-calculations'' and the
``high-throughput'' philosophies is that the latter requires rapid
estimations of materials properties so that the correlations between
systems, even if roughly characterized, become the target
information instead of the throughout and accurate description of a
small subset. Clearly, to analyze the extensive amount of
information and to extract correlations, ad-hoc algorithms and
appropriate computer softwares have to be developed. Furthermore,
once the space of the search is narrowed, a detailed study can be
employed on the obtained reduced set of feasible candidate systems.

Several examples have appeared in literature in recent years, for
instance the ``data-mining of quantum calculations'' method leading
to the principle component analysis of the formation energies of
many alloys in several configurations
\cite{Curtarolo2003PRL,Curtarolo2005Calphad}, the evolutionary
approach for determining hamiltonian \cite{Hart2005NatMat}, the
``Pareto-optimal'' alloys and catalysts
\cite{Bligaard2003APL,Andersson2006JCatal} the prediction of the
lithium-boron superconductor \cite{artSC21}, the ``high-throughput
Kohn-anomalies'' search in ternary lithium-borides
\cite{artSC33,artSC37}, and the ``multi-optimization'' techniques
used in studying high-temperature reactions in multicomponent
hydrides
\cite{Wolverton2008JPCM,Siegel2007PRB,Akbarzadeh2007AdvMat}.

This manuscript focuses on the high-throughput formalism for the
calculations of solubility in binary alloys (solvus lines). The
knowledge of solubility is crucial for designing new alloys with
particular physical, chemical, and mechanical properties. For
example, if we have to enhance an alloy property by adding extra
specie as solute, it is necessary to know the equilibrium solubility
to understand if it is possible to dissolve the candidate specie,
and, if possible, to avoid supersaturation-precipitation and
subsequent modification of the target property (aging effect). In
superconducting materials research, the problem emerges frequently:
often expensive and difficult experiments are undertaken to enhance
the critical temperature \cite{Cava2003phisicaC,Singh08RbCs}. Even
in catalysis research, recent experiments and modeling have shown
that the solubility of carbon is responsible of thermodynamic
instabilities hindering the catalytic activity of very small Fe and
Fe:Mo clusters \cite{artSC36,artSC39}. The calculation of solubility
of Zr in Al has already been addressed with success within the
regular solution model \cite{SigliPROC} fit to {\it ab initio}
calculations \cite{SanchezPRB}. Solubility can also be extracted
from the knowledge of the phase diagram which, in the case of
lattice-conserving alloys, can be generated within the the cluster
expansion \cite{CD_deFontaine,CE_Ceder} and Monte Carlo
approaches\cite{Anton1,Anton2}. However, a straightforward
formalism leading to the estimation of equilibrium solubility for
general alloys is still lacking.

In the present paper we devised a statistical-thermodynamic approach
for the calculation of atomic solubility in alloys. The advantage of
our approach consists in taking into account all available ground
states rather than just the pure species configurations. To test the
method, we present calculations for a number of binary titanium systems.
The paper is organized as follows: In Sec. II we rewrite the
equations governing solubility in the case of vacancies and
substitutional impurities in binary alloys. Section III is devoted
to the discussions of capabilities and limits of our formalism.
Examples of phase diagrams and solubilities are addressed in Sec. IV
for the following test Ti-A systems (A=Ag,Au,Cd,Co,Cr,Ir,W,Zn).
Conclusions are given in Sec. V.

\section{Solubility formalism}
\label{Solubility}
\section*{Enthalpy}

Let us consider a disordered dilute solution of A-atoms and
vacancies (V) in a pure B-solid with a given Bravais crystal lattice
(labeled with the {\it ``dis''}). Without taking into account the
A-A, A-V, and V-V interactions and assuming that A and V
concentrations are small, the approximate enthalpy of the considered
alloy can be written as:
\begin{equation}\label{Eq:H}
    H^\texttt{\footnotesize dis}=E^\texttt{\footnotesize dis}+pV^\texttt{\footnotesize dis}=
    H_\texttt{\footnotesize B}^\texttt{\footnotesize at} N + H_{\texttt{\footnotesize A}_\texttt{\footnotesize B}} N_\texttt{\footnotesize A} +
    H_{\texttt{\footnotesize V}_\texttt{\footnotesize B}} N_\texttt{\footnotesize V},
\end{equation}
where $H_\texttt{\footnotesize B}^\texttt{\footnotesize at}$, $H_{\texttt{\footnotesize A}_\texttt{\footnotesize B}}$ and $H_{\texttt{\footnotesize V}_\texttt{\footnotesize B}}$ are the enthalpy of
the pure B solid per unit cell, the change in enthalpy of the solid
upon substitution of one B with an A-atom, and the change
in enthalpy upon removal of one B atom, respectively. In
addition, $N$ and $N_\alpha$ ($\alpha$=A,B,V) are the total numbers
of crystal lattice sites and of atoms of $\alpha$-type:
\begin{equation} \label{Eq:H1}
    \begin{array}{c}
    N=N_\texttt{\footnotesize A}+N_\texttt{\footnotesize B}+N_\texttt{\footnotesize V},\,\,\,\,\,
    H_\texttt{\footnotesize B}^\texttt{\footnotesize at}=E_\texttt{\footnotesize B}^\texttt{\footnotesize at}+pv_\texttt{\footnotesize B}^0,\\\\
    H_{\texttt{\footnotesize A}_\texttt{\footnotesize B}}=E_{\texttt{\footnotesize A}_\texttt{\footnotesize B}}^0+pv_{\texttt{\footnotesize A}_\texttt{\footnotesize B}}^0,\,\,\,
    H_{\texttt{\footnotesize V}_\texttt{\footnotesize B}}=E_{\texttt{\footnotesize V}_\texttt{\footnotesize B}}^0+pv_{\texttt{\footnotesize V}_\texttt{\footnotesize B}}^0,
    \end{array}
\end{equation}
$E_\alpha^\texttt{\footnotesize at}$ and $v_\alpha^0$ ($\alpha$=A,B) are energy and the
volume per atom of the $\alpha$-pure solid, $p$ is the
pressure, $v_{\texttt{\footnotesize A}_\texttt{\footnotesize B}}$ and $v_{\texttt{\footnotesize V}_\texttt{\footnotesize B}}^0$ represent the change of
volume of the B-pure solid upon introduction of one A-atom
or one vacancy. The framework introduced by Eq.
(\ref{Eq:H}) is similar to Wagner-Schottky model of a system of
non-interacting particles.\cite{WagnerSchottky30}. The quantities
with superscript ``0'' are considered to be temperature, pressure,
and composition independent being calculated at zero temperature and
pressure. Hence, the accuracy of the following results will be
better in the case of limited pressures or for systems with very
high bulk modulus, where the elastic energy fraction of
$E_\alpha^\texttt{\footnotesize at}$ is negligible.

The quantities in Eq. (\ref{Eq:H1}) can be easily approximated as
differences of first-principles energies and volumes between large
supercells (sc) with or without defects (substitutional A-atom or
vacancy):
\begin{equation} \label{Eq:H3}
    \begin{array}{c}
    E_{\texttt{\footnotesize A}_\texttt{\footnotesize B}}^0 \simeq E_\texttt{sc}[B_{n_\texttt{sc}-1}A]-E_\texttt{sc}[B_{n_\texttt{sc}}],\\
    v_{\texttt{\footnotesize A}_\texttt{\footnotesize B}}^0 \simeq V_\texttt{sc}[B_{n_\texttt{sc}-1}A]-V_\texttt{sc}[B_{n_\texttt{sc}}],\\\\
    E_{\texttt{\footnotesize V}_\texttt{\footnotesize B}}^0 \simeq E_\texttt{sc}[B_{n_\texttt{sc}-1}]-E_\texttt{sc}[B_{n_\texttt{sc}}],\\
    v_{\texttt{\footnotesize V}_\texttt{\footnotesize B}}^0 \simeq V_\texttt{sc}[B_{n_\texttt{sc}-1}]-V_\texttt{sc}[B_{n_\texttt{sc}}].
    \end{array}
\end{equation}
As the size of the supercell grows,
the approximate quantities in Eqs. (\ref{Eq:H3})
approach their exact values.
In literature\cite{Mishin} and in this paper,
$E_{\alpha_\texttt{\footnotesize B}}^0$, $v_{\alpha_\texttt{\footnotesize B}}^0$ and
$H_{\alpha_\texttt{\footnotesize B}}$ ($\alpha$=A,V) are called the ``raw''
(composition unpreserving) $\alpha$-defect formation energy, volume
and enthalpy, respectively.

The enthalpy per atom is obtained from Eq. (\ref{Eq:H}) as:
\begin{equation} \label{Eq:H4}
    \begin{array}{c}
    H^\texttt{\footnotesize dis}_\texttt{\footnotesize at}=H^\texttt{\footnotesize dis}/(N_\texttt{\footnotesize A}+N_\texttt{\footnotesize B})=\\\\
    H_\texttt{\footnotesize B}^\texttt{\footnotesize at} + H_{\texttt{\footnotesize A}_\texttt{\footnotesize B}} x_\texttt{\footnotesize A} +
    (H_{\texttt{\footnotesize V}_\texttt{\footnotesize B}}+H_\texttt{\footnotesize B}^\texttt{\footnotesize at}) x_\texttt{\footnotesize V},
    \end{array}
\end{equation}
where $x_\alpha$ ($\alpha$=A,B,V) are the atomic concentrations
\begin{equation}
x_\alpha=N_\alpha/(N_\texttt{\footnotesize A}+N_\texttt{\footnotesize B}).
\end{equation}
Then, we follow the convention of using the {\it formation}
enthalpy $\Delta H^\texttt{\footnotesize dis}_\texttt{\footnotesize at}$ calculated with respect to the pure A-
and B-solids \cite{Korzh00}:
\begin{equation} \label{Eq:H5}
    \Delta H^\texttt{\footnotesize dis}_\texttt{\footnotesize at} = H^\texttt{\footnotesize dis}_\texttt{\footnotesize at}-x_\texttt{\footnotesize A}
    H_\texttt{\footnotesize A}^\texttt{\footnotesize at}-(1-x_\texttt{\footnotesize A})H_\texttt{\footnotesize B}^\texttt{\footnotesize at},
\end{equation}
where $H_\texttt{\footnotesize A}^\texttt{\footnotesize at}=E_\texttt{\footnotesize A}^\texttt{\footnotesize at}+pv_\texttt{\footnotesize A}^0$
and $H_\texttt{\footnotesize B}^\texttt{\footnotesize at}$ has been defined
in Eq. (\ref{Eq:H1}).
Combining equations (\ref{Eq:H4}) and (\ref{Eq:H5}), we get
\begin{equation}\label{Eq:H7}
    \Delta H^\texttt{\footnotesize dis}_\texttt{\footnotesize at} = H_\texttt{\footnotesize A} x_\texttt{\footnotesize A}+H_\texttt{\footnotesize V} x_\texttt{\footnotesize V},
\end{equation}
where the quantities $H_\texttt{\footnotesize A}$ and $H_\texttt{\footnotesize V}$, defined as
\begin{equation}\label{Eq:H8}
    H_\texttt{\footnotesize A}=H_{\texttt{\footnotesize A}_\texttt{\footnotesize B}}-H_\texttt{\footnotesize A}^\texttt{\footnotesize at}+H_\texttt{\footnotesize B}^\texttt{\footnotesize at},
    \,\,\,\,\,\,\,\,H_\texttt{\footnotesize V}=H_{\texttt{\footnotesize V}_\texttt{\footnotesize B}}+H_\texttt{\footnotesize B}^\texttt{\footnotesize at}
\end{equation}
are usually called A-defect and V-defect ``true'' (composition
preserving)\cite{Mishin} formation enthalpies, which can be
obtained from\cite{Korzh00}
\begin{equation}\label{Eq:H9}
    H_\alpha=\left. \frac{\partial \Delta H^\texttt{\footnotesize dis}_\texttt{\footnotesize at}}{\partial x_\alpha}\right | _{x_\alpha \rightarrow 0}
    \,\,\,\,  (\alpha={\rm A,V}).
\end{equation}

\section*{Equilibrium Gibbs Free Energy}

The formation Gibbs free energy, $\Delta G^\texttt{\footnotesize dis}_\texttt{\footnotesize at}$, is defined as:
\begin{equation}\label{Eq:G1}
    \Delta G^\texttt{\footnotesize dis}_\texttt{\footnotesize at}=\Delta
    H^\texttt{\footnotesize dis}_\texttt{\footnotesize at}-T \Delta S^\texttt{\footnotesize dis}_\texttt{\footnotesize at},
\end{equation}
where $\Delta H^\texttt{\footnotesize dis}_\texttt{\footnotesize at}$ is described by Eq. (\ref{Eq:H7}) and the
formation entropy $\Delta S^\texttt{\footnotesize dis}_\texttt{\footnotesize at}=S^\texttt{\footnotesize dis}_\texttt{\footnotesize at}$ can be obtained
within the mean-field approximation as
\begin{equation}
\label{Eq:G2}
    \Delta S^\texttt{\footnotesize dis}_\texttt{\footnotesize at}= - \frac{k_\texttt{\footnotesize B} N}{N_\texttt{\footnotesize A}+N_\texttt{\footnotesize B}} \sum_{\alpha=\texttt{A,B,V}}
    c_\alpha \ln c_\alpha,
\end{equation}
where $T$, $k_\texttt{\footnotesize B}$, $c_\alpha$ ($\alpha$=A,B,V) are the temperature,
the Boltzmann constant, and the site concentrations of atoms:
\vspace{-4mm}
\begin{equation}\label{Eq:G3}
c_\alpha=N_\alpha/N.
\end{equation}
By changing variables from site concentrations $c_\alpha$ to atomic concentrations $x_\alpha$:
\begin{equation}\label{Eq:G4}
x_\alpha=N_\alpha/(N_\texttt{\footnotesize A}+N_\texttt{\footnotesize B}),\,\,\,\,\,\,c_\alpha=x_\alpha/(1+x_\texttt{\footnotesize V}),
\end{equation}
we rewrite Eq. (\ref{Eq:G1}) as
\begin{equation}\label{Eq:G5}\label{Eq:G6}
\begin{array}{c}
    \Delta G^\texttt{\footnotesize dis}_\texttt{\footnotesize at}=\Delta G^{\texttt{\footnotesize dis},\texttt{\footnotesize A}}_\texttt{\footnotesize at}+\Delta G^{\texttt{\footnotesize dis},\texttt{\footnotesize V}}_\texttt{\footnotesize at}, \\\\
    \Delta G^{\texttt{\footnotesize dis},\texttt{\footnotesize A}}_\texttt{\footnotesize at}=H_\texttt{\footnotesize A} x_\texttt{\footnotesize A}+k_\texttt{\footnotesize B} T[x_\texttt{\footnotesize A} \ln x_\texttt{\footnotesize A}+ (1-x_\texttt{\footnotesize A}) \ln
(1-x_\texttt{\footnotesize A})], \\\\
    \Delta G^{\texttt{\footnotesize dis},\texttt{\footnotesize V}}_\texttt{\footnotesize at}=H_\texttt{\footnotesize V} x_\texttt{\footnotesize V}+k_\texttt{\footnotesize B} T[x_\texttt{\footnotesize V} \ln x_\texttt{\footnotesize V} - (1+x_\texttt{\footnotesize V}) \ln
(1+x_\texttt{\footnotesize V})].
\end{array}
\end{equation}

In alloy with fixed atomic composition $x_\texttt{\footnotesize A}$,
the equilibrium concentration of vacancies $x_\texttt{\footnotesize V}^\texttt{\footnotesize eq}$
is determined by minimizing the formation Gibbs free energy:
\begin{equation}\label{Eq:G7}
    \left. \frac{\partial \Delta G^\texttt{\footnotesize dis}_\texttt{\footnotesize at}}{\partial
    x_\texttt{\footnotesize V}} \right|_{x_\texttt{\footnotesize A}}=\frac{\partial \Delta
    G^{\texttt{\footnotesize dis},\texttt{\footnotesize V}}_\texttt{\footnotesize at}}{\partial x_\texttt{\footnotesize V}}=0.
\end{equation}
The manipulation of Eqs. (\ref{Eq:G6})-(\ref{Eq:G7})
leads to:
\begin{equation}\label{Eq:G8}\label{Eq:G9}\begin{array}{c}
    x_\texttt{\footnotesize V}^\texttt{\footnotesize eq}=\left [\exp \left(\frac{H_\texttt{\footnotesize V}}{k_\texttt{\footnotesize B} T}\right)-1 \right]^{-1},\\\\
    \left. x_\texttt{\footnotesize V}^\texttt{\footnotesize eq}\right|_{k_\texttt{\footnotesize B} T \ll E_\texttt{\footnotesize V}}\simeq \exp \left(-\frac{H_\texttt{\footnotesize V}}{k_\texttt{\footnotesize B} T} \right ), \\\\
    \Delta G^{\texttt{\footnotesize dis},\texttt{\footnotesize V}}_\texttt{\footnotesize at}(x_\texttt{\footnotesize V}^\texttt{\footnotesize eq})= k_\texttt{\footnotesize B} T \ln \left[1-\exp \left(-\frac{H_\texttt{\footnotesize V}}{k_\texttt{\footnotesize B} T}\right)\right], \\\\
    \left.\Delta G^{\texttt{\footnotesize dis},\texttt{\footnotesize V}}_\texttt{\footnotesize at}(x_\texttt{\footnotesize V}^\texttt{\footnotesize eq})\right|_{k_\texttt{\footnotesize B} T \ll E_\texttt{\footnotesize V}} \simeq -k_\texttt{\footnotesize B} T \exp \left(-\frac{H_\texttt{\footnotesize V}}{k_\texttt{\footnotesize B} T} \right).
\end{array} \end{equation}
To conclude, the ``true'' vacancies formation enthalpy $H_\texttt{\footnotesize V}$ determines
the equilibrium concentration of vacancies with an Arrhenius-type
equation (see also Ref. \onlinecite{Korzh00}).
In the next section, we show that $H_\texttt{\footnotesize A}$ resolves the solubility
in the case of a phase-separating alloy having no intermediate ground states.

\section*{Solubility}

\begin{figure}  \vspace{-5mm}
  \includegraphics[width=0.5\textwidth]{fig01.eps}
  \vspace{-5mm}
  \caption{\small (Color online)
  (a) Temperature-concentration and (b) formation Gibbs free energy-concentration (at a given temperature $T_0$)
  graphs illustrating our solubility concepts.}\label{Fig:F-x}
\end{figure}

At a given temperature, the solubility of A-atoms in a B-solid
phase, $x_{\texttt{\footnotesize A}_\texttt{\footnotesize B}}^\texttt{\footnotesize sol}$, is defined as the maximum homogenously
achievable concentration of A without the formation of a new phase
(Fig. \ref{Fig:F-x}(a)). The accurate calculation of
$x_{\texttt{\footnotesize A}_\texttt{\footnotesize B}}^\texttt{\footnotesize sol}$ requires considering of the nearby ground state
(labeled as {\it``gs''}) with respect to the increase of $x_\texttt{\footnotesize A}$,
see the ``red line'' in Fig. \ref{Fig:F-x}(b). It is implemented by
minimizing the formation Gibbs free energy $\Delta G_\texttt{\footnotesize at}^\texttt{\footnotesize mix}(x)$ of
a mixture of (1) a disordered dilute solution of A-atoms and
vacancies in a B-rich solid phase at composition $x_{\texttt{\footnotesize A}_\texttt{\footnotesize B}}$ (the
``dis''-phase of the previous section), and (2) an on- or
off-stoichiometric ground state ``gs''-phase at composition
$x_{\texttt{\footnotesize A}_\texttt{\footnotesize gs}}$. The lever rule gives the fractions of the two phases:
\vspace{-4mm}
\begin{equation}\label{Eq:ComTang0}
  \begin{array}{c}
    \Delta G_\texttt{\footnotesize at}^\texttt{\footnotesize mix}(x)=\\\\
    \frac{x_{\texttt{\footnotesize A}_\texttt{\footnotesize gs}}-x}{x_{\texttt{\footnotesize A}_\texttt{\footnotesize gs}}-x_{\texttt{\footnotesize A}_\texttt{\footnotesize B}}} \Delta G^\texttt{\footnotesize dis}_\texttt{\footnotesize at}(x_{\texttt{\footnotesize A}_\texttt{\footnotesize B}})+
    \frac{x-x_{\texttt{\footnotesize A}_\texttt{\footnotesize B}}}{x_{\texttt{\footnotesize A}_\texttt{\footnotesize gs}}-x_{\texttt{\footnotesize A}_\texttt{\footnotesize B}}} \Delta G^\texttt{\footnotesize gs}_\texttt{\footnotesize at}(x_{\texttt{\footnotesize A}_\texttt{\footnotesize gs}}),
\end{array} \end{equation}
and the minimization is performed with respect to $x_{\texttt{\footnotesize A}_\texttt{\footnotesize B}}$ and
$x_{\texttt{\footnotesize A}_\texttt{\footnotesize gs}}$ ($x$ is the overall composition of A in the two-phase mixture, $x_{\texttt{\footnotesize A}_\texttt{\footnotesize B}}<x<x_{\texttt{\footnotesize A}_\texttt{\footnotesize gs}}$):
\begin{equation}\label{Eq:ComTang1}
    \frac{\partial \Delta G_\texttt{\footnotesize at}^\texttt{\footnotesize mix}}{\partial
    x_{\texttt{\footnotesize A}_\texttt{\footnotesize B}}}=0,\,\,\,\,\,\,\frac{\partial \Delta
    G_\texttt{\footnotesize at}^\texttt{\footnotesize mix}}{\partial
    x_{\texttt{\footnotesize A}_\texttt{\footnotesize gs}}}=0.
\end{equation}
Combining Eqs. (\ref{Eq:ComTang0}) and (\ref{Eq:ComTang1}) leads to
the usual {\it common-tangent} rule:
\begin{equation} \label{Eg:ComTang2}\begin{array}{c}
    \frac{\partial \Delta G^\texttt{\footnotesize dis}_\texttt{\footnotesize at}(x_{\texttt{\footnotesize A}_\texttt{\footnotesize B}})}{\partial
    x_{\texttt{\footnotesize A}_\texttt{\footnotesize B}}}= \frac{\partial
    \Delta G_\texttt{\footnotesize at}^\texttt{\footnotesize gs}(x_{\texttt{\footnotesize A}_\texttt{\footnotesize gs}})}{\partial
    x_{\texttt{\footnotesize A}_\texttt{\footnotesize gs}}}=\\\\
    \frac{\Delta G^\texttt{\footnotesize dis}_\texttt{\footnotesize at}(x_{\texttt{\footnotesize A}_\texttt{\footnotesize B}})-\Delta G_\texttt{\footnotesize at}^\texttt{\footnotesize gs}(x_{\texttt{\footnotesize A}_\texttt{\footnotesize gs}})}
    {x_{\texttt{\footnotesize A}_\texttt{\footnotesize B}}-x_{\texttt{\footnotesize A}_\texttt{\footnotesize gs}}}.
\end{array} \end{equation}
Substituting Eqs. (\ref{Eq:G5}) into Eqs. (\ref{Eg:ComTang2}), we obtain
\begin{equation}\label{Eq:Xsol1}
    x_{\texttt{\footnotesize A}_\texttt{\footnotesize B}}^\texttt{\footnotesize sol} = \left [\exp
    \left(H_\texttt{\footnotesize sol}/k_\texttt{\footnotesize B} T\right)+1 \right ]^{-1},
\end{equation}
which approximates as an Arrhenius-type relation at low temperature:
\begin{equation}\label{Eq:Xsol2}
    \left. x_{\texttt{\footnotesize A}_\texttt{\footnotesize B}}^\texttt{\footnotesize sol}\right|_{k_\texttt{\footnotesize B} T
    \ll H_\texttt{\footnotesize sol} } \simeq \exp \left(
    -H_\texttt{\footnotesize sol}/k_\texttt{\footnotesize B} T \right).
\end{equation}
The quantity $H_\texttt{\footnotesize sol}$ is defined as
\begin{equation}\label{Eq:Esol2}
    H_\texttt{\footnotesize sol} \equiv
    H_\texttt{\footnotesize A}-\frac{\Delta G^\texttt{\footnotesize dis}_\texttt{\footnotesize at}(x^\texttt{\footnotesize sol}_{\texttt{\footnotesize A}_\texttt{\footnotesize B}})-\Delta G_\texttt{\footnotesize at}^\texttt{\footnotesize gs}(x^\texttt{\footnotesize sol}_{\texttt{\footnotesize A}_\texttt{\footnotesize gs}})}
    {x^\texttt{\footnotesize sol}_{\texttt{\footnotesize A}_\texttt{\footnotesize B}}-x^\texttt{\footnotesize sol}_{\texttt{\footnotesize A}_\texttt{\footnotesize gs}}}.
\end{equation}
The non-linear problem described by Eqs.
(\ref{Eq:Xsol1}-\ref{Eq:Xsol2}) and (\ref{Eq:Esol2}) can be
linearized in the low-solubility limit (labeled as {\it ``ls''}):
\begin{equation}\label{Eq:LS}
    ls: \left\{\begin{array}{c}
    \,x^\texttt{\footnotesize sol}_{\texttt{\footnotesize A}_\texttt{\footnotesize B}}\simeq0,\,
    \Delta G^\texttt{\footnotesize dis}_\texttt{\footnotesize at}(x^\texttt{\footnotesize sol}_{\texttt{\footnotesize A}_\texttt{\footnotesize B}})\simeq
    \Delta G^{\texttt{\footnotesize dis},\texttt{\footnotesize V}}_\texttt{\footnotesize at}(x_\texttt{\footnotesize V}^\texttt{\footnotesize eq}),\\\\
    x^\texttt{\footnotesize sol}_{\texttt{\footnotesize A}_\texttt{\footnotesize gs}}\simeq
    x_{\texttt{\footnotesize A}_\texttt{\footnotesize gs}}^0,\,\,
    \Delta G_\texttt{\footnotesize at}^\texttt{\footnotesize gs}(x^\texttt{\footnotesize sol}_{\texttt{\footnotesize A}_\texttt{\footnotesize gs}})\simeq
    \Delta H_\texttt{\footnotesize at}^\texttt{\footnotesize gs}, \end{array} \right.
\end{equation}
where $\Delta H_\texttt{\footnotesize at}^\texttt{\footnotesize gs}$ is the formation enthalpy
of the ground state ``gs''.
In the low-solubility limit, $H_\texttt{\footnotesize sol}$  becomes:
\begin{equation} \label{Eq:EsolLS}
    H_\texttt{\footnotesize sol}^\texttt{\footnotesize ls} =
    H_\texttt{\footnotesize sol}^{\texttt{\footnotesize ls},\texttt{\footnotesize nv}}+\Delta
    G^{\texttt{\footnotesize dis},\texttt{\footnotesize V}}_\texttt{\footnotesize at}(x_\texttt{\footnotesize V}^\texttt{\footnotesize eq})/x_{\texttt{\footnotesize A}_\texttt{\footnotesize gs}}^0,
\end{equation}
where $H_\texttt{\footnotesize sol}^{\texttt{\footnotesize ls},\texttt{\footnotesize nv}}$ is the non-vacancy contribution (labeled as {\it ``nv''}):
\vspace{-3mm}
\begin{equation} \label{Eq:EsolLSNV}
    H_\texttt{\footnotesize sol}^{\texttt{\footnotesize ls},\texttt{\footnotesize nv}} =
    H_\texttt{\footnotesize A}-\Delta H_\texttt{\footnotesize at}^\texttt{\footnotesize gs}/x_{\texttt{\footnotesize A}_\texttt{\footnotesize gs}}^0.
\end{equation}
From the equilibrium vacancy concentration, Eq. (\ref{Eq:G9}),
the exponential part of Eqs. (\ref{Eq:Xsol1}-\ref{Eq:Xsol2}) becomes:
\begin{equation} \label{Eq:expV} \begin{array}{c}
    \exp \left(-H_\texttt{\footnotesize sol}^\texttt{\footnotesize ls}/k_\texttt{\footnotesize B} T \right)= \exp \left(-H_\texttt{\footnotesize sol}^{\texttt{\footnotesize ls},\texttt{\footnotesize nv}}/k_\texttt{\footnotesize B} T \right)\times \\\\
    \left[1-\exp \left(-\frac{H_\texttt{\footnotesize V}}{k_\texttt{\footnotesize B} T} \right) \right]^{-1/x_{\texttt{\footnotesize A}_\texttt{\footnotesize gs}}^0},
\end{array} \end{equation}
where the two contributions, non-vacancy and vacancy, are factorized.
The last expression indicates that the presence of vacancies effectively increases the solubility
by decreasing the number of host B-atoms in the solution.

\section{Interpretation of $H_\texttt{\footnotesize sol}^{\texttt{\footnotesize ls},\texttt{\footnotesize nv}}$}

\begin{figure}
  \vspace{-5mm}
  \includegraphics[width=0.45\textwidth]{fig02.eps}
  \vspace{-5mm}
  \caption{\small
  (Color online) The enthalpy-concentration graph demonstrating our concept of low-solubility formation enthalpy.
  A-pure, B-pure and "gs" are the ground states forming a convex hull.
  "sc" is a compound (supercell) with some intermediate enthalpy and composition.
  Compounds (B+A) and (B+gs) correspond to appropriate phase
  mixtures of the same general composition $x_\texttt{\footnotesize A}^\texttt{\footnotesize sc}$.} \label{Fig:E-x}
\end{figure}

For low-solubility calculations of non-interacting defects,
the framework can be implemented through first-principles calculation of $H_\texttt{\footnotesize sol}^\texttt{\footnotesize ls}$ (Eq. (\ref{Eq:EsolLS})).
It requires the knowledge of the enthalpy $\Delta H_\texttt{\footnotesize at}^\texttt{\footnotesize gs}$ and composition $x_{\texttt{\footnotesize A}_\texttt{\footnotesize gs}}^0$ of the ground-state ``gs'',
as well as the ``true'' defect formation enthalpies $H_\texttt{\footnotesize A}$ and $H_\texttt{\footnotesize V}$ (Eq. (\ref{Eq:H8})).

To capture the physical meaning of $H_\texttt{\footnotesize sol}^{\texttt{\footnotesize ls},\texttt{\footnotesize nv}}$,
let us consider an arbitrary
dilute solution ``sc'' at composition $x_\texttt{\footnotesize A}^\texttt{\footnotesize sc}$
(see Fig. \ref{Fig:E-x}).
The label ``sc'' indicates that the solution is generated as a {\it supercell} of the B-solid
upon insertion of defects, randomly distributed but not too close to avoid interactions.
The first part of Eq. (\ref{Eq:EsolLSNV}) can be rewritten according to Eq. (\ref{Eq:H9}) as:
\begin{equation}\label{Eq:Dis2}
    H_\texttt{\footnotesize A}=\frac{\partial \Delta
    H_\texttt{\footnotesize at}^\texttt{\footnotesize sc}(x_\texttt{\footnotesize A}^\texttt{\footnotesize sc})}{\partial
    x_\texttt{\footnotesize A}^\texttt{\footnotesize sc}}.
\end{equation}
The second part of Eq. (\ref{Eq:EsolLSNV}) becomes:
\begin{equation}\label{Eq:Dis1}
    \frac{\Delta
    H_\texttt{\footnotesize at}^\texttt{\footnotesize gs}}{x_{\texttt{\footnotesize A}_\texttt{\footnotesize gs}}^0}=
    \frac{\Delta
    H_\texttt{\footnotesize at}^{(\texttt{\footnotesize B}+\texttt{\footnotesize gs})}(x_\texttt{\footnotesize A}^\texttt{\footnotesize sc})}{x_\texttt{\footnotesize A}^\texttt{\footnotesize sc}}=
    \frac{\partial \Delta
    H_\texttt{\footnotesize at}^{(\texttt{\footnotesize B}+\texttt{\footnotesize gs})}(x_\texttt{\footnotesize A}^\texttt{\footnotesize sc})}{\partial x_\texttt{\footnotesize A}^\texttt{\footnotesize sc}},
\end{equation}
where $\Delta H_\texttt{\footnotesize at}^{(\texttt{\footnotesize B}+\texttt{\footnotesize gs})}(x_\texttt{\footnotesize A}^\texttt{\footnotesize sc})$ is the
formation enthalpy of the mixture of the pure B-solid with
the ground state ``gs'' with overall composition $x_\texttt{\footnotesize A}^\texttt{\footnotesize sc}$
(point (B+``gs'') in Fig. \ref{Fig:E-x}).
Thus, we obtain:
\begin{equation}\label{Eq:Dis3}
    H_\texttt{\footnotesize sol}^{\texttt{\footnotesize ls},\texttt{\footnotesize nv}}=
    \frac{\partial \left[\Delta
    H_\texttt{\footnotesize at}^\texttt{\footnotesize sc}(x_\texttt{\footnotesize A}^\texttt{\footnotesize sc})-
    \Delta
    H_\texttt{\footnotesize at}^{(\texttt{\footnotesize B}+\texttt{\footnotesize gs})}(x_\texttt{\footnotesize A}^\texttt{\footnotesize sc}) \right]}{\partial
    x_\texttt{\footnotesize A}^\texttt{\footnotesize sc}}.
\end{equation}
The comparison of Eq. (\ref{Eq:Dis2}) with Eq. (\ref{Eq:Dis3}) leads to the conclusion
that both $H_\texttt{\footnotesize A}$ and $H_\texttt{\footnotesize sol}^{\texttt{\footnotesize ls},\texttt{\footnotesize nv}}$ are derivatives of supercell
formation energies with respect to A-composition.
For $H_\texttt{\footnotesize A}$, the supercell formation enthalpy is determined with respect to pure A and B phases
(the distance between points ``sc'' and (B+A) in Fig. \ref{Fig:E-x}).
For $H_\texttt{\footnotesize sol}^{\texttt{\footnotesize ls},\texttt{\footnotesize nv}}$, the supercell formation enthalpy is determined
 with respect to B-pure and the ground state ``gs''
(the distance between points ``sc'' and (B+gs) in Fig.
\ref{Fig:E-x}). To conclude, $H_\texttt{\footnotesize A}$ and $H_\texttt{\footnotesize sol}^{\texttt{\footnotesize ls},\texttt{\footnotesize nv}}$ are
characterized by the angles $\alpha$ and $\beta$ between the
B-``sc''/B-A and B-``sc''/B-``gs'' lines, respectively. In analogy
with the $H_\texttt{\footnotesize A}$ definition in Eq. (\ref{Eq:H8}), $H_\texttt{\footnotesize sol}^{\texttt{\footnotesize ls},\texttt{\footnotesize nv}}$
can be considered as the ``low-solubility formation
enthalpy''.

The quantities $H_\texttt{\footnotesize A}$ and $H_\texttt{\footnotesize sol}^{\texttt{\footnotesize ls},\texttt{\footnotesize nv}}$ are identical only for
phase-separating alloys having no intermediate ground states (i.e. ``gs''$\equiv$ A).
In this case the low-solubility can be formally determined by minimizing $\Delta G^{\texttt{\footnotesize dis},\texttt{\footnotesize A}}_\texttt{\footnotesize at}$
(Eq. (\ref{Eq:G6})) with respect to $x_{\texttt{\footnotesize A}}$ (e.g. Ref. \onlinecite{Matysina}).
However, in the general case, the existence of ordered ground-states must be verified
so the appropriate formalism is used.
Generally, in ordering alloys $H_\texttt{\footnotesize A}$ and $H_\texttt{\footnotesize sol}^{\texttt{\footnotesize ls},\texttt{\footnotesize nv}}$ differ,
and might even have different signs.

Note that if the ``sc'' point is below (B+gs) in Fig. \ref{Fig:E-x}
($H_\texttt{\footnotesize sol}^{\texttt{\footnotesize ls},\texttt{\footnotesize nv}}<0$)
the solubility expressions (\ref{Eq:Xsol1}-\ref{Eq:Xsol2}) are not valid,
and there must exist an undetected ground state (it might be ``sc'' itself)
with concentration lower than $x_{\texttt{\footnotesize A}_\texttt{\footnotesize gs}}^0$.
In this case, such undetected ground state should be used for the calculation of solubility
rather than initial ``gs'' \cite{RomanMgBA}.

The expression for non-binary low-solubility within the regular
solution model derived in Refs. [\onlinecite{SigliPROC,SanchezPRB}]
coincides with our derivation in the case of binary alloys without
vacancies and high-temperature contributions. This is because the
regular solution model corresponds to our model for the free energy
in case of dilute solution.

\section{Ground states of selected Titanium alloys}

As an example of our formalism, we calculate the solubility of a set
of metals in titanium. First, we explore the possible ground states
of the A-Ti systems (A=Ag,Au,Cd,Co,Cr,Ir,W,Zn) and then we apply the
construction described in the previous section.

The low temperature stability of A-Ti is performed by using our
high-throughput quantum calculations framework
\cite{Curtarolo2005Calphad,Curtarolo2003PRL,artSC21,artSC37}, based
on first-principles energies obtained with the {\small VASP}
software \cite{kresse1993}. We use projector augmented waves (PAW)
pseudopotentials \cite{bloechl994} and exchange-correlation
functionals as parameterized by Perdew-Burke-Ernzerhof \cite{PBE}
for the generalized gradient approximation (GGA). Simulations are
carried out with spin polarization except Ti-Co, at zero temperature
and pressure \cite{enthalpy-energy}, and without zero-point motion.
All structures are fully relaxed (shape and volume of the cell and
internal positions of the atoms). The effect of lattice vibrations
is omitted. Numerical convergence to within about 1 meV/atom is
ensured by enforcing a high energy cut-off (357 eV) and dense 6,000
{\bf k}-point meshes.

The number of crystal structures considered for the
calculations of each A-Ti system \textbf{is} 194. In addition to the
176 described in Ref. \onlinecite{Curtarolo2005Calphad}, we
included the following prototypes A5, A6, A7, A11,
Ca$_7$Ge, NbNi$_8$ (Pt$_8$Ti), V$_4$Zn$_5$, C36 and the whole
complete set of hcp-superstructures with up to 4 atoms/cell. The
whole process is performed in an automatic fashion through the
software {\small AFLOW} which generates the prototypes, optimize the
parameters, perform the calculations, correct possible errors, and
calculate the phase diagrams \cite{Curtarolo2005Calphad,AFLOW}.

\begin{figure}[htb]
  \includegraphics[width=0.4\textwidth]{fig03.eps}
  \vspace{-4mm}
  \caption{\small
  (Color online) AgTi (silver-titanium) ground state convex hull.}
  \label{FIG:AgTi_GS}
\end{figure}

\begin{figure}[htb]
  \vspace{-3mm}
  \includegraphics[width=0.4\textwidth]{fig04.eps}
  \vspace{-4mm}
  \caption{\small
  (Color online) AuTi (gold-titanium) ground state convex hull.}
  \label{FIG:AuTi_GS}
\end{figure}

\begin{figure}[htb]
  \vspace{-3mm}
  \includegraphics[width=0.4\textwidth]{fig05.eps}
  \vspace{-4mm}
  \caption{\small
  (Color online) CdTi (cadmium-titanium) ground state convex hull.}
  \label{FIG:CdTi_GS}
\end{figure}

\begin{figure}[htb]
  \vspace{-3mm}
  \includegraphics[width=0.4\textwidth]{fig06.eps}
  \vspace{-4mm}
  \caption{\small
  (Color online) CoTi (cobalt-titanium) ground state convex hull.}
  \label{FIG:CoTi_GS}
\end{figure}

\begin{figure}[htb]
  \vspace{-3mm}
  \includegraphics[width=0.4\textwidth]{fig07.eps}
  \vspace{-4mm}
  \caption{\small
  (Color online) CrTi (cromium-titanium) ground state convex hull.}
  \label{FIG:CrTi_GS}
\end{figure}

\begin{figure}[htb]
  \vspace{-3mm}
  \includegraphics[width=0.4\textwidth]{fig08.eps}
  \vspace{-4mm}
  \caption{\small
  (Color online) IrTi (iridium-titanium) ground state convex hull.}
  \label{FIG:IrTi_GS}
\end{figure}

\begin{figure}[htb]
  \vspace{-3mm}
  \includegraphics[width=0.4\textwidth]{fig09.eps}
  \vspace{-4mm}
  \caption{\small
  (Color online) TiW (titanium-tungsten) ground state convex hull.}
  \label{FIG:TiW_GS}
\end{figure}

\begin{figure}[htb]
  \vspace{-3mm}
  \includegraphics[width=0.4\textwidth]{fig10.eps}
  \vspace{-4mm}
  \caption{\small
  (Color online) TiZn (titanium-zinc) ground state convex hull.}
  \label{FIG:TiZn_GS}
\end{figure}

Our results of ground state calculation are presented in Figs.
\ref{FIG:AgTi_GS}-\ref{FIG:TiZn_GS} and Table \ref{Tab:GS}. The
correspondence {\it ab initio} versus experimental results is very
good and typical for this type of calculations
\cite{Curtarolo2005Calphad}.

We propose degenerate results for:
1) Co$_2$Ti, experimentally reported as C15,
but with {\it ab initio} formation energies of
-311.4 meV/at. and -304.0 meV/at. for
C14 and C15, respectively;
2) CoTi$_2$, experimentally reported as NiTi$_2$,
but with {\it ab initio} formation energies of
-291.2 meV/at., -287.3 meV/at., and -285.7 meV/at. for
C37, CuZr$_2$, and NiTi$_2$, respectively;
3) TiZn, experimentally reported as B2,
but with {\it ab initio} formation energies of
-195.4 meV/at. and  193.4 meV/at. for
L1$_0$ and B2, respectively.

We propose the novel results for: 1) Ir$_7$Ti,
experimentally reported as a two phases region above 500{$^\circ$C}, but
with a possible {\it ab inito} low temperature ground state Ca$_7$Ge
with formation energy of -373.8 meV/at. 2) Ir$_2$Ti, experimentally
reported as a two phases region above 500{$^\circ$C}, but with a possible
{\it ab initio} low temperature ground state C11$_b$, with formation
energy of -716.0 meV/at. 3) TiW$_2$, experimentally reported as a
two phases region above 500{$^\circ$C}, but with a possible {\it ab initio}
low temperature ground state BCC$_{AB2}^{[211]}$, with formation
energy of -82.7 meV/at. (see notation for the prototype in Ref.
\cite{Curtarolo2005Calphad}). 4) TiW$_4$, experimentally reported as
a two phases region above 500{$^\circ$C}, but with a possible {\it ab
initio} low temperature ground state D1$_a$, with formation energy
of -83.8 meV/at. 5) Ti$_3$Zn, experimentally not explored, but with
a possible {\it ab initio} low temperature ground state A15, with
formation energy of -120.0 meV/at.

In particular, the results indicate that in the Ir-Ti system the low
temperature Ir-rich part of the known phase diagram is not complete,
and that the Ti-W alloy has an ordering tendency at low
temperature, in contrast to common belief \cite{Pauling,BB}. In
addition, in Ti-Zn there must exist a Ti-rich compound with Ti
composition higher than the reported Ti$_2$Zn, \cite{Pauling,BB}.

\begin{table}[htb]
  \caption{\small
    Low temperature phases comparison chart for Ag-Ti, Au-Ti, Cd-Ti, Co-Ti, Cr-Ti, Ir-Ti, Ti-V, and Ti-Zn.
    Experimental data correspond to the lowest available temperature \cite{Curtarolo2005Calphad}.
    The ``$^*$'' indicates the energy values used in solubility calculations.}
  \label{Tab:GS} \small
  \begin{tabular}{c|c|c|c|c} \hline\hline
    Experimental             &  {\it Ab initio}    & $\Delta E^{\texttt{\footnotesize gs}}_\texttt{\footnotesize at}$  & Space   & Pearson \\
    (Refs. \onlinecite{BB,Pauling})  & result      & (meV/at.)           &  group\cite{IntTabs}    & \\ \hline
    \multicolumn{5}{c}{{\bf Ag-Ti}} \\\hline
    AgTi-B11                 & B11                 & -67.6           &  P4/nmm  & tP4     \\ \hline
    AgTi$_2$-C11$_b$         & C11$_b$             &  -63.3$^*$ &  I4/mmm  & tI6     \\ \hline
    \multicolumn{5}{c}{{\bf Au-Ti}} \\\hline
    Au$_4$Ti-D1$_a$          & D1$_a$              & -283.2          &  I4/m    & tI10    \\ \hline
    Au$_2$Ti-C11$_b$         & C11$_b$             & -430.4          &  I4/mmm  & tI6     \\ \hline
    two-phase region         & Au$_4$Ti$_3$-       & -430.6          &  I4/mmm  & tI14    \\
    above 500{$^\circ$C}            & Cu$_4$Ti$_3$/tie    &                   &          &         \\ \hline
    AuTi-B11                 & B11                 & -429.8          &  P4/nmm  & tP4     \\ \hline
    AuTi$_3$-A15             & A15                 &  -356.1$^*$&  Pm$\bar{3}$n &  cP8  \\ \hline
    \multicolumn{5}{c}{{\bf Cd-Ti}} \\\hline
    CdTi-B11                 & B11                 & -62.0           &  P4/nmm  & tP4     \\ \hline
    CdTi$_2$-C11$_b$         & C11$_b$             &  -73.7$^*$      &  I4/mmm  & tI6     \\ \hline
    \multicolumn{5}{c}{{\bf Cr-Ti}} \\\hline
    Cr$_2$Ti-C15             & C15                 &  -120.3$^*$&  Fd$\bar{3}$m   & cF24    \\ \hline
    \multicolumn{5}{c}{{\bf Co-Ti}} \\\hline
    Co$_3$Ti-L1$_2$          & L1$_2$              & -254.8            & Pm$\bar{3}$m& cP4     \\ \hline
    Co$_2$Ti-C15             & C14                 & -311.4            & P6$_3$/mm & hP12   \\
                             & C15                 & -304.0            &  Fd$\bar{3}$m   & cF24    \\ \hline
    CoTi-B2                  & B2                  & -386.4            &  Pm$\bar{3}$m   & cP2     \\ \hline
    CoTi$_2$-NiTi$_2$        & C37                 &  -291.2$^*$&  Pnma    & oP12    \\
                             & CuZr$_2$            & -287.3            &  I4/mmm  & tI6     \\
                             & NiTi$_2$            & -285.7            &  Fd$\bar{3}$m   & cF96    \\ \hline
    \multicolumn{5}{c}{{\bf Ir-Ti}} \\\hline
    two-phase region         & Ir$_7$Ti-           & -373.8            &  Fm$\bar{3}$m   & cF32    \\
    above 500{$^\circ$C}            & Ca$_7$Ge            &                   &          &         \\ \hline
    Ir$_3$Ti-L1$_2$          & L1$_2$              & -720.3            & Pm$\bar{3}$m& cP4     \\ \hline
    IrTi-$\delta$            & L1$_0$              & -851.8            & P4/mmm   & tP4     \\ \hline
    two-phase region         & Ir$_2$Ti-           & -716.0            &  I4/mmm  & tI6     \\
    above 500{$^\circ$C}            & C11$_b$             &                   &          &         \\ \hline
    IrTi$_3$-A15             & A15/tie             &  -570.3$^*$& Pm$\bar{3}$n& cP8     \\ \hline
    \multicolumn{5}{c}{{\bf Ti-W}} \\\hline
    two-phase region         & TiW$_2$-            &  -82.7$^*$ & P$\bar{3}$m1    & hP3     \\
    above 500{$^\circ$C}            & BCC$_{AB2}^{[211]}$ &                   &          &         \\ \hline
    two-phase region         & TiW$_4$-            & -83.8             &  I4/m    & tI10    \\
    above 500{$^\circ$C}            & D1$_a$              &                   &          &         \\ \hline
    \multicolumn{5}{c}{{\bf Ti-Zn}} \\\hline
    non explored             & Ti$_3$Zn-A15        &  -120.0$^*$& Pm$\bar{3}$n& cP8     \\ \hline
    Ti$_2$Zn-CuZr$_2$        & CuZr$_2$            & -158.0            &  I4/mmm  & tI6     \\ \hline
    TiZn-B2                  & L1$_0$              & -195.4            & P4/mmm   & tP4     \\
                             & B2                  & -193.4            &  Pm$\bar{3}$m   & cP2     \\ \hline
    TiZn$_2$-C14             & C14/tie                 & -197.2            &  P6$_3$/mm & hP12  \\ \hline
    TiZn$_3$-L1$_2$          & L1$_2$              & -198.0            &  Pm$\bar{3}$m & cP4   \\ \hline
   \hline\hline \end{tabular}
  \vspace{-0.5mm}
\end{table}

\section{Results and discussion of solubility in Ti alloys}
\vspace{-2mm}

The ``raw'' formation enthalpies of Ti alloys with one
substitutional atom or a vacancy were obtained through Eqs.
(\ref{Eq:H3}) considering $3\times3\times3$ supercells of the hcp
Ti. Supercell dimensions were chosen to limit the defect-defect
interactions, being their distance at least three times larger than
the nearest neighbor Ti-Ti bond. The results are presented in Table
\ref{Tab:FormEn}. Solubilities temperature dependencies are
presented in Fig. \ref{FIG:Sol_T_theor}, while Fig.
\ref{FIG:Sol_theor_exper} illustrates a comparison of experimental
and theoretical data at T=700{$^\circ$C}.

\vspace{-3mm}
\begin{table}[thb]
  \caption{\small
    ``Raw'' formation enthalpies $H_{\texttt{\footnotesize A}_\texttt{\footnotesize Ti}}$,
    $H_{\texttt{\footnotesize V}_\texttt{\footnotesize Ti}}$ (from Eqs. (\ref{Eq:H1}-\ref{Eq:H3}) at
    zero pressure), ``true'' formation enthalpies $H_\texttt{\footnotesize A}$,
    $H_\texttt{\footnotesize V}$ (from Eq. (\ref{Eq:H8}) at zero pressure) and
    low-solubility (non-vacancy) formation enthalpy
    $H_\texttt{\footnotesize sol}^{\texttt{\footnotesize ls},\texttt{\footnotesize nv}}$ (from Eq. (\ref{Eq:EsolLSNV}) at
    zero pressure) of substitutional A-defects (A=Ag,Au,Cd,Co,Cr) and
    vacancies (V). The elements are ordered from low to high
    {\it ``low-solubility formation enthalpy''}.
    All quantities are in eV units.}\label{Tab:FormEn}
  \vspace{0.5mm}
  \begin{tabular}{c|ccc} \hline\hline
    A   &   $H_{\texttt{\footnotesize A}_\texttt{\footnotesize Ti}}$ &   $H_\texttt{\footnotesize A}$  &
    $H_\texttt{\footnotesize sol}^{\texttt{\footnotesize ls},\texttt{\footnotesize nv}}$ \\ \hline
    Zn  &   6.405   &   -0.262  &   0.218   \\
    Cd  &   7.267   &   0.24    &   0.461   \\
    Ag  &   5.412   &   0.304   &   0.494   \\
    Au  &   3.882   &   -0.781  &   0.643   \\
    W   &   -4.303  &   0.714   &   0.838   \\
    Ir  &   -2.059  &   -1.14   &   1.141   \\
    Co  &   1.138   &   0.316   &   1.19    \\
    Cr  &   -0.674  &   1.024   &   1.205   \\\hline
    \multicolumn{2}{c}{$H_{\texttt{\footnotesize V}_\texttt{\footnotesize Ti}}=10.002$,} &
    \multicolumn{2}{c}{$H_\texttt{\footnotesize V}=2.068$} \\ \hline\hline
\end{tabular} \end{table}

\begin{figure}
  \vspace{-5mm}
  \includegraphics[width=0.5\textwidth]{fig11.eps}
  \vspace{-12mm}
  \caption{\small
    (Color online)
    The solubilities of eight considered transition metals
    in titanium as functions of temperature (calculated through Eqs. (\ref{Eq:Xsol1},\ref{Eq:EsolLS})).
    Panel (b) is a magnified version of panel (a), to visualize the values for Ir, Co, and Cr.}
  \label{FIG:Sol_T_theor}
\end{figure}

\begin{figure}
  \vspace{-5mm}
  \includegraphics[width=0.5\textwidth]{fig12.eps}
  \vspace{-5mm}
  \caption{\small
  (Color online) Comparison of experimental\cite{Pauling,BB}
    and theoretical solubilities of eight considered transition metals
    in titanium at T=700{$^\circ$C}. From left to right, the elements are
    ordered from low to high low-solubility formation enthalpy (and
    correspondingly theoretical solubility) The error bars characterize
    the scattering of data measured in different experiments. We could
    not find the experimental data for solubilities in Ti-Zn.}
  \label{FIG:Sol_theor_exper}
\end{figure}

Table \ref{Tab:FormEn} shows negative ``true'' formation enthalpies
$H_\texttt{\footnotesize A}$ for A=Zn, Au, and Ir. This indicates that calculation of Zn,
Au, and Ir solubilities in Ti is not faceable without considering
nearby intermetallic ground states.

Figures \ref{FIG:Sol_T_theor}-\ref{FIG:Sol_theor_exper} show that
the highest theoretical solubilities in Ti occurs for Zn, Cd, Ag,
and Au as consequence of their low solubility formation enthalpies
(see Table \ref{Tab:FormEn}). This high solubility has also been
observed experimentally for Cd, Ag, and Au, whereas, to our best
knowledge, solubility of Zn does not seem to have been studied. High
solubility of late transition metals Zn, Cd, Ag, and Au in the early
transition metal titanium is due to the substantial localized
stability provided by the filling tendency of the $d$-band of Ti
(Ref. \onlinecite{Friedel}).

Because of the very high formation enthalpy of vacancies in Ti
(reported in Table \ref{Tab:FormEn}), the vacancy equilibrium
concentration was found to be very low at all considered
temperatures  (e.g. $x_\texttt{\footnotesize V}^\texttt{eq}<10^{-6}$ at $T < 1300${$^\circ$C} ).
Thus, the effect of vacancies on the solubilities of Ti
alloys should be negligible.

Although, theoretical and experimental results follow similar
trends, theoretical solubilities are considerably smaller for most
of the considered alloys. A similar discrepancy was also observed
for Al-Zr in Ref. \onlinecite{SanchezPRB}. The discrepancy could be
due to shortcomings of theory and/or experiment. The main
approximations of our model consist of (a) neglecting the defect
interaction, (b) neglecting the spatial defect correlation and (c)
assuming low concentration of defects. However, as such
approximations are somehow related, subsequent solubility
calculations suggesting low values validate the assumptions (the
mean-field approximation neglects the interatomic positional
correlations but it should work well when the deviation from
complete stoichiometric (pure Ti-solid in our case) is small - and
so is the solubility in our case - see Sec. 19 in Ref.
\onlinecite{KrivSm64}.) For all considered alloys except Ti-Zn, we
found that at intermediate temperatures the calculated solubilities
are small enough for our approximations to be valid, although
smaller than experiment, as mentioned before. In
Ref.\onlinecite{SanchezPRB}, the authors added the defect
interactions through the Cluster Expansion method but without
increasing the solubility considerably. Actually, our formalism
includes the solute-solvent ordering tendency by considering the
real intermetallic ground state other then the pure Ti-solid. Thus,
we conclude that our approximations (or those of the cluster
expansion method) are not responsible for the theory-experiment
solubility discrepancy.

In case of Ti-Zn, the formation enthalpy is very low (see Table
\ref{Tab:FormEn}). Correspondingly, the theoretically solubility at
intermediate temperatures is very high, violating the assumptions of
the model. Thus, for Zn in Ti, a more precise solute interaction and
correlation parameterizations is required, which can be obtained by
using, for example, Cluster Expansion and Monte Carlo simulations.
Hence, the presented formalism should be considered as an
appropriate starting point to determine if more computationally
expensive formalisms are needed.

The other approximation of our model is the assumed independence of
our model energy and volume parameters on temperature. The
dependence can be caused by non configurational degrees of freedom,
like vibrational or anharmonicity (magnetic ordering is not actual
for considered alloys). However, theory-experiment solubility
discrepancy is observed even at low enough temperatures (e.g. $T
\leq \Theta _\texttt{\footnotesize D}(\texttt{Ti})=$374-385 K \cite{Sundman01}), where the
vibrational contribution to the free energy is not important. In
fact, vibrational entropy is substantially smaller than the
configurational contribution \cite{AxelRMP}, so its inclusion can
not modify solubility results much. In fact, even in Ref.
\onlinecite{SanchezPRB}, the authors added phonon contribution
without increasing the solubility considerably.

On the other side, the experimental equilibrium solubility tends
usually to be overestimated. In fact, the formation of metastable
and/or unstable states which are subsequently frozen at low
temperatures, can make solubility measurements very challenging. In
such scenarios, the measured solubility may correspond to spinodal
concentration rather then actual binodal concentration or simply
characterize the frozen out of equilibrium solubility remaining from
the initial specimen preparation at higher temperature. Besides, the
segregation of defects into grain-boundaries, especially in
multicrystalline samples prepared through non optimal cooling
dramatically affect the amount of frozen defects and solutes.

\section{Conclusions}
Based on the statistical-thermodynamic theory of dilute lattice gas,
we developed an approach to calculate the atomic bulk solubility in
alloys. The advantage of our approach consists in considering all
the appropriate ground states rather than the pure species. It was
shown that the low-solubility follows simple Arrhenius-type
temperature dependence determined by a {\it ``low-solubility
formation enthalpy''}. This quantity is defined as the composition
derivative of the compound formation enthalpy with respect to nearby
ground states. ``Low-solubility formation enthalpy'' coincides with
the usual defect formation enthalpy only in the case of a
phase-separating alloy having no intermediate ground states and
vacancies. The key quantities of our model can be directly obtained
by first-principles calculations of by fitting experimental
temperature solubility dependence. Generalization of our model to
intermediate phases and/or to multicomponent, multisublattice,
interstitial-substitutional alloys is straightforward.

As examples, we applied the framework for a set ot eight Ti alloys
A-Ti (A=Ag,Au,Cd,Co,Cr,Ir,W,Zn). We have found that the highest
solubility for Zn, Cd, Ag, and Au is in qualitative
agreement with available experimental data and band structure
expectations. The quantitative differences between the theory and
experiment observed in the present and other similar studies are
discussed.

In conclusion, our formalism is correct in the limit of low-solubility and should be considered as an appropriate
starting point for determining if more computationally expensive formalisms are otherwise needed.

\section*{Acknowledgements}
We acknowledge Wahyu Setyawan, Mike Mehl, and Ohad Levy for fruitful discussions.
This research was supported by ONR (Grant No. N00014-07-1-0878)
and NSF (Grant No. DMR-0639822)
We thank the Teragrid Partnership (Texas Advanced Computing Center,
TACC) for computational support (MCA-07S005).

redpajama_set_name: RedPajamaArXiv


text:
import theano
from theano import tensor as T
from theano.tensor.nnet import conv
from theano.tensor.signal.downsample import max_pool_2d

import numpy as np

class Layer(object):

    def __init__(self, inputs, inputs_shape=None):
        """
        Useful to get outputs shape
        """

        if isinstance(inputs, Layer):
            self.inputs_shape = inputs.outputs_shape
        else:
            assert(inputs_shape is not None)
            self.inputs_shape = inputs_shape
        print '({0}) input shape {1}'.format(self.name, self.inputs_shape)

    def forward(self, inputs):
        raise NotImplementedError('This function has to be overloaded')

class RandFlip(Layer):

    def __init__(self, inputs, image_shape, name, theano_rng, mode_var):
        # one window for whole batch
        self.name = name
        super(RandFlip, self).__init__(inputs, image_shape)

        self.theano_rng = theano_rng
        self.mode = mode_var

        self.params = []

    def forward(self, inputs):
        flipped = inputs[:, :, :, ::-1]
        doflip = self.theano_rng.binomial(
            n=1, p=.5, size=(inputs.shape[0],))
        return T.switch(
            self.mode,
            inputs,
            T.switch(doflip.dimshuffle(0, 'x', 'x', 'x'),
                     flipped, inputs))

class ConvLayer(Layer):

    def __init__(self, rng, inputs, filter_shape,
                 name, image_shape=None, pad=0, init_scale=None):
        """
        Convolutional layer

        Args
        ----
        rng: instance of numpy.random.RandomState
        inputs: symbolic theano variable
        filter_shape: tuple of 4 ints (channels_out)
        """

        self.name = name
        super(ConvLayer, self).__init__(inputs, image_shape)
        assert self.inputs_shape[1] == filter_shape[1]

        self.rng = rng
        self.filter_shape = filter_shape
        self.pad = pad

        if init_scale is None:
            # if we don't specify a scale for weight initialization,
            # we use the formula
            # 1/sqrt(number of weights in each filter)
            init_scale = 1. / np.sqrt(
                filter_shape[1] *
                filter_shape[2] *
                filter_shape[3])

        self.init_scale = init_scale

        self.W = theano.shared(
            np.asarray(
                rng.uniform(low=-self.init_scale, high=self.init_scale,
                            size=self.filter_shape),
                dtype=theano.config.floatX
            ), name='{0}_W'.format(self.name)
        )

        self.params = [self.W]

        self.outputs_shape = (
            self.inputs_shape[0], self.filter_shape[0],
            self.inputs_shape[2] + 2 * self.pad - self.filter_shape[2] + 1,
            self.inputs_shape[3] + 2 * self.pad - self.filter_shape[3] + 1)

    def forward(self, inputs):
        # if padding is greater than zero, we insert the inputs into
        # the center of a larger zero array, effectively adding zero
        # borders
        if self.pad > 0:
            padded_inputs = T.set_subtensor(
                T.zeros((inputs.shape[0],
                         self.inputs_shape[1],
                         self.inputs_shape[2] + 2 * self.pad,
                         self.inputs_shape[3] + 2 * self.pad),
                        dtype=inputs.dtype)[:, :, self.pad:-self.pad, self.pad:-self.pad],
                inputs)
        else:
            padded_inputs = inputs
        padded_inputs_shape = (
            None,
            self.inputs_shape[1],
            self.inputs_shape[2] + 2 * self.pad,
            self.inputs_shape[3] + 2 * self.pad)

        return conv.conv2d(
            input=padded_inputs,
            filters=self.W,
            filter_shape=self.filter_shape,
            image_shape=padded_inputs_shape)

class MaxPoolLayer(Layer):

    def __init__(self, inputs, pool_size, name, ignore_border=True, stride=None):
        """
        Max pooling layer

        """
        self.name = name
        super(MaxPoolLayer, self).__init__(inputs)
        self.pool_size = pool_size
        self.ignore_border = ignore_border
        if stride is None:
            stride = pool_size
        self.stride = stride

        self.params = []

        self.outputs_shape = (
            self.inputs_shape[0],
            self.inputs_shape[1],
            (self.inputs_shape[2] - pool_size[0]) // stride[0] + 1,
            (self.inputs_shape[3] - pool_size[1]) // stride[1] + 1
        )

    def forward(self, inputs):
        return max_pool_2d(
            input=inputs,
            ds=self.pool_size,
            ignore_border=self.ignore_border,
            st=self.stride
        )

class ConvBiasLayer(Layer):

    def __init__(self, inputs, name):
        """
        Add bias
        """

        self.name = name
        super(ConvBiasLayer, self).__init__(inputs)

        self.b = theano.shared(
            np.zeros(
                (self.inputs_shape[1],), dtype=theano.config.floatX
            ), name='{0}_b'.format(self.name)
        )

        self.params = [self.b]

        self.outputs_shape = self.inputs_shape

    def forward(self, inputs):
        return inputs + self.b.dimshuffle('x', 0, 'x', 'x')

class RandCropAndFlip(Layer):

    def __init__(self, inputs, image_shape, patch_size, name, theano_rng, mode_var):
        # one window for whole batch
        self.name = name
        super(RandCropAndFlip, self).__init__(inputs, image_shape)

        self.patch_size = patch_size
        self.theano_rng = theano_rng
        self.mode = mode_var

        self.params = []

        print 'self.inputs_shape: {0}'.format(self.inputs_shape, )
        print 'patch_size: {0}'.format(patch_size, )
        print 'self.inputs_shape[2] - patch_size[0]: {0}'.format(self.inputs_shape[2] - patch_size[0], )
        print 'self.inputs_shape[3] - patch_size[1]: {0}'.format(self.inputs_shape[2] - patch_size[0], )

        self.outputs_shape = self.inputs_shape[:2] + self.patch_size

    def forward(self, inputs):
        rand_row_coord = self.theano_rng.random_integers(
            low=0, high=self.inputs_shape[2] - self.patch_size[0])
        rand_col_coord = self.theano_rng.random_integers(
            low=0, high=self.inputs_shape[3] - self.patch_size[1])

        center_row_coord = (self.inputs_shape[2] - self.patch_size[0]) // 2
        center_col_coord = (self.inputs_shape[3] - self.patch_size[1]) // 2

        row_coord = T.switch(
            self.mode, center_row_coord, rand_row_coord)
        col_coord = T.switch(
            self.mode, center_col_coord, rand_col_coord)

        patches = inputs[
            :, :,
            row_coord:row_coord + self.patch_size[0],
            col_coord:col_coord + self.patch_size[1]]

        flipped = patches[:, :, :, ::-1]
        doflip = self.theano_rng.binomial(
            n=1, p=.5, size=(inputs.shape[0],))

        # if train mode: randomly flip, else don't flip
        return T.switch(
            self.mode,
            patches,
            T.switch(doflip.dimshuffle(0, 'x', 'x', 'x'), flipped, patches))

class Dropout(Layer):

    def __init__(self, inputs, dropout_rate, name, theano_rng, mode_var, inputs_shape=None):
        """Dropout

        Args
        ----
        mode_var: symbolic variable, which has value 0 during training and 1
            during test time
        """

        self.name = name
        super(Dropout, self).__init__(inputs, inputs_shape)

        self.dropout_rate = theano.shared(
            dropout_rate, '{0}_dropout_rate'.format(name))
        self.theano_rng = theano_rng
        self.mode = mode_var

        self.params = []

        self.outputs_shape = self.inputs_shape

    def forward(self, inputs):
        mask = self.theano_rng.binomial(
            n=1, p=1 - self.dropout_rate, size=inputs.shape,
            dtype=theano.config.floatX)

        return T.cast(T.switch(
            self.mode,
            inputs * (1. - self.dropout_rate),
            inputs * mask), theano.config.floatX)

class AffineLayer(Layer):

    def __init__(self, rng, inputs, nouts,
                 name, init_scale=None, nins=None, with_bias=True,
                 inputs_shape=None):
        """
        Fully connected layer with bias option

        Args
        ----
        rng: instance of numpy.random.RandomState
        """

        self.name = name
        super(AffineLayer, self).__init__(inputs, inputs_shape=inputs_shape)
        self.rng = rng
        self.nins = self.inputs_shape[-1]
        self.nouts = nouts

        if init_scale is None:
            # if we don't specify a scale for weight initialization,
            # we use the formula
            # 1/sqrt(number of weights in each filter)
            init_scale = 1. / np.sqrt(self.nins)

        self.init_scale = init_scale
        self.with_bias = with_bias

        self.W = theano.shared(
            np.asarray(
                rng.uniform(low=-self.init_scale, high=self.init_scale,
                            size=(self.nins, self.nouts)),
                dtype=theano.config.floatX
            ), name='{0}_W'.format(self.name)
        )

        self.params = [self.W]

        if with_bias:
            self.b = theano.shared(
                np.zeros(
                    self.nouts, dtype=theano.config.floatX
                ), name='{0}_b'.format(self.name)
            )
            self.params.append(self.b)

        self.outputs_shape = (self.inputs_shape[0], self.nouts)

    def forward(self, inputs):
        outputs = T.dot(inputs, self.W)
        if self.with_bias:
            outputs = outputs + self.b
        return outputs

class Relu(Layer):

    def __init__(self, inputs, name):
        """
        Relu activation function
        """

        self.name = name
        super(Relu, self).__init__(inputs)

        self.params = []

        self.outputs_shape = self.inputs_shape

    def forward(self, inputs):
        return T.switch(inputs < 0, 0, inputs)

class Concat(Layer):

    def __init__(self, inputs_list, name, axis,
                 inputs_shape_list=None):
        """
        Concatenation layer
        """

        self.name = name
        self.axis = axis
        if inputs_shape_list is None:
            inputs_shape_list = [None] * len(inputs_list)
        assert len(inputs_shape_list) == len(inputs_list)

        self.inputs = []
        self.inputs_shape = []
        for i, inp in enumerate(inputs_list):
            if isinstance(inp, Layer):
                self.inputs.append(inp.outputs)
                self.inputs_shape.append(inp.outputs_shape)
            else:
                assert(inputs_shape_list[i] is not None)
                self.inputs.append(inp)
                self.inputs_shape.append(inputs_shape_list[i])

        self.params = []

        # concatenate the inputs
        self.outputs = T.concatenate(self.inputs, axis=axis)

        self.outputs_shape = list(self.inputs_shape[0])
        for i in range(1, len(self.inputs_shape)):
            self.outputs_shape[axis] += self.inputs_shape[i][axis]

class Softmax(Layer):

    def __init__(self, inputs, name):
        """
        Softmax
        """

        self.name = name
        super(Softmax, self).__init__(inputs)

        self.params = []

        self.outputs_shape = self.inputs_shape

    def forward(self, inputs):
        return T.nnet.softmax(inputs)

class Sigmoid(Layer):

    def __init__(self, inputs, name):
        """
        Sigmoid
        """

        self.name = name
        super(Sigmoid, self).__init__(inputs)

        self.params = []

        self.outputs_shape = self.inputs_shape

    def forward(self, inputs):
        return T.nnet.sigmoid(inputs)

class Reshape(Layer):

    def __init__(self, inputs, shape, name):
        """
        Reshaping
        """

        self.name = name
        super(Reshape, self).__init__(inputs)

        self.params = []

        assert(np.prod(self.inputs_shape[1:]) == np.prod(shape[1:]))

        self.outputs_shape = shape

    def forward(self, inputs):
        return T.reshape(inputs, (inputs.shape[0], ) + self.outputs_shape[1:])

class Composite(Layer):

    def __init__(self, layers, name):
        """
        Collection of layers used in fusion
        """

        self.layers = layers
        self.name = name
        super(Composite, self).__init__(self.layers[0].inputs,
                                        self.layers[0].inputs_shape)
        self.params = []
        for layer in self.layers:
            self.params.extend(layer.params)
        self.outputs_shape = self.layers[-1].outputs_shape

    def forward(self, inputs):
        for l, layer in enumerate(self.layers):
            if l > 0:
                layer_outp = layer.forward(layer_outp)
            else:
                layer_outp = layer.forward(inputs)
        return layer_outp

class Clip(Layer):

    def __init__(self, inputs, name, min_val, max_val):
        self.name = name
        super(Clip, self).__init__(inputs)
        self.min_val = min_val
        self.max_val = max_val

        self.params = []

        self.outputs_shape = self.inputs_shape

    def forward(self, inputs):
        return T.clip(inputs, self.min_val, self.max_val)

redpajama_set_name: RedPajamaGithub


Zoned R12 with development opportunities here for 6 plus houses or work with city to build more as attached homes (buyer to do due diligence). That equates to about $58k per lot. House of no value. Do not disturb tenant on site and do not go to property. Call Realtor for questions.
All information deemed reliable but not guaranteed. All properties are subject to prior sale, change or withdrawal. Neither listing broker(s) or information provider(s) shall be responsible for any typographical errors, misinformation, misprints and shall be held totally harmless. Listing(s) information is provided for consumers personal, non-commercial use and may not be used for any purpose other than to identify prospective properties consumers may be interested in purchasing. Information on this site was last updated 4/25/2019 7:05:43 AM. The listing information on this page last changed on 4/25/2019 7:05:43 AM. The data relating to real estate for sale on this website comes in part from the Internet Data Exchange program of RMLS (last updated 4/25/2019 7:05:43 AM) or Willamette Valley MLS (last updated 4/25/2019 7:05:43 AM). Real estate listings held by brokerage firms other than RE/MAX Equity Group may be marked with the Internet Data Exchange logo and detailed information about those properties will include the name of the listing broker(s) when required by the MLS.


This book contributes substantively to the current state-of-the-art of macroeconomics by providing a method for building models in which business cycles and economic growth emerge from the interactions of a large number of heterogeneous agents. Drawing from recent advances in agent-based computational modeling, the authors show how insights from dispersed fields like the microeconomics of capital market imperfections, industrial dynamics and the theory of stochastic processes can be fruitfully combined to improve our understanding of macroeconomic dynamics.
This book should be a valuable resource for all researchers interested in analyzing macroeconomic issues without recurring to a fictitious representative agent.


text:
Q: what is a good web app platform to build a VERY simple, single-purpose PDF "sign maker" We need something very trivial, yet apparently impossible to do with Rails...there is no full featured PDF library for ruby yet.
What I need to build is very simple:

*

*Web app, ideally hostable on Heroku or Godaddy

*ONE url: url specifies an existing PNG graphic file + a text string + an X,Y offset

*creates a PDF that simply overlays the text string (at X,Y) on top of the graphic

That's it, just a quick and dirty "sign customizer" to slap a string of text at a precise location on top of a graphic.
iText for Java is a nice library that does everything, but I don't know where to start to build a server-side Java web app... or to be more accurate, when I googled doing that my reaction was "is it really THAT complicated to deploy a web app using Java?" (spoiled by Rails I guess).
Any tips would be appreciated... it's an important function for my app that I'm disappointed to have to build outside by Rails app, but until there's a good PDF library for ruby I guess I'll have to learn a different way to do this!

A: For anyone who has a similar issue with ruby not handling pdf, an update: so far we've had great initial success with PHP + FPDF from http://www.fpdf.org/
The docs and tutorials for fpdf are awesome.

redpajama_set_name: RedPajamaStackExchange


text:
Uber's New Delivery Drone Absolutely Reeks of Vaporware [Updated]
Filed to:vaporware
Computer rendering of Uber's latest concept for a delivery drone
Graphic: Uber
Uber has announced it's developing a new drone it hopes to use for Uber Eats deliveries one day. Eric Allison, the head of Uber Elevate, talked about the new drone in Detroit yesterday at the Forbes Under 30 Summit. And while the mock-up design looks pretty cool, with rotating wings and six rotors, the details released so far raise some red flags.
According to Forbes (emphasis ours):
The new drone design can carry dinner for up two people and features six rotors, the company says. Its battery is designed for eight minutes, including loading and unloading, and it can only do relatively short hauls. The drone has a roundtrip range of 12 miles, or a total flight time of 18 minutes.
The battery lasts for just eight minutes but it has a total flight time of 18 minutes? How is that supposed to work? Your guess is as good as ours, since Uber did not reply to an email early Tuesday.
[Update 7:15 am ET: In an email this morning, Uber now says that Forbes isn't correct about its battery life but didn't provide an estimate to Gizmodo. Apparently Uber told Forbes that the drone is "designed to perform a maximum delivery leg in eight minutes including loading and unloading," which the Forbes author confused for battery life.]
[Update 8:30 am ET: Forbes appears to have changed its article without any notice of an update. The paragraph that we quoted above was in the original article.]
But even if you can successfully square that circle, it appears Uber Eats isn't banking on delivering food directly to your door anytime soon. The company has previously said that it will deliver food via drone to a central staging area and that Uber drivers in cars will pick them up and ultimately deliver the package to your door. Meanwhile, companies like Alphabet, under its Wing brand, have been successfully conducting drone delivery tests for food and medicine in Australia and will soon begin similar testing in Virginia. Unlike Uber, Wing is delivering its items directly to the customer's home.
According to Forbes, Uber Eats doesn't even plan to test this drone design until next summer in San Diego. But if Uber's history of failed promises are any indication, this thing is probably just vaporware—a futuristic product that won't actually get released into the real world. All we have from Uber is a computer rendering of the drone, and we've seen plenty of computer renderings from this company in the past, with absolutely no follow-through.
Remember back in February of 2017 when we heard that Uber's flying cars were just two years away? The company has had to revise that estimate again and again, but it hasn't stopped releasing promotional videos and flashy computer graphics promising that air taxis are just over the horizon.
Remember back in May of 2018 when Uber released that ridiculous design for an autonomous aerial taxi concept for passenger flight that we called the Spruce Goose of the 21st century? Again, we got plenty of splashy computer animations, but we have yet to see anything flying in the real world.
Uber CEO Dara Khosrowshahi told CBS News back in 2018 that his aerial taxis would soon be zipping around the country at up to 200 miles per hour. But Uber can't even get its autonomous vehicles on the ground working properly. Uber's self-driving car even killed a cyclist back in March of 2018.
Maybe Uber really needs to keep people hoping for something shiny and futuristic that's just around the corner. Because as it stands, Uber is losing billions of dollars every year. In fact, Uber Eats loses an estimated $3.36 on every single order that it fulfills. And analysts insist that it will keep losing a lot of money until at least 2024.
Delivery drones are an exciting field for companies that hope to get packages and food from point A to point B as quickly as possible. But any way you slice it, Uber seems to be way behind its rivals. And while Uber has gotten really good at making futuristic-looking computer animations, it will have to deliver a real drone at some point if it wants to succeed.
Is The Flying Car Finally Here?
It's that time of year again! Every six months or so, the media rave about the latest advancements…
Unless, of course, Uber plans to follow the flying car playbook that has worked for over a century. Keep telling the public that your product is just two years away. Forever.
Alphabet's Drone Unit Partners with FedEx and Walgreens for Drone Deliveries
Alphabet's Wing Lands 'World-First' Approval for Drone Deliveries of Food and Medicine in Australia
UPS Gets FAA Approval to Run America's First Drone Delivery Airline
Flying Cars Are Still Just Two Years Away, Now Brought to You by Uber™

redpajama_set_name: RedPajamaCommonCrawl


Excellent knowledge on human resources and human relations areas which includes manpower planning, recruitment and selection, induction, on the job and off the job training and development of different level of personnel, familiar with 360 degrees appraisal system, identifying the training need of personnel and planning the training programs, strong enough in conflict management, good at employee morale and motivation, easy to understand people and live with them with passion thick and thin on various situations. She should have a passion to pull out the talents of people, developing them, motivating them, training them and making them self sufficient in all aspects.
She should be fully familiar and hands on with all statutory matters and areas which includes factory inspector, minimum wages, labour office, pf and esi offices, mpcb, mseb and other agencies and closely to work with them, safety security of personnel and place should be her priority. She should be a strong believer in "legal and morale" aspects of business, no bribes, no entertaining of any politicians and political parties, etc. She comply all requirements of all legal authorities involved in a manufacturing company.
She should be a strict disciplinarian ensuring the employees vehicle reaches in office on time, employees facilities such as canteen, food, hygiene, cleanliness, both in shop floor and offices. Security personnel controlling, surprise checks in nights, maintaining the garden in its best, surrounding of the company premises and material should be kept update. Shop floor should be the highest priority when it comes to cleanliness and hygenie.


text:
Dieu et Mammon est un essai de François Mauriac publié pour la première fois en  aux éditions du Capitole. Il constitue une réponse de l'auteur à des interrogations que lui avait formulées André Gide par interpellation épistolaire – à la suite de la parution de l'essai de Mauriac La Vie de Jean Racine (1928) – qui intimait à Mauriac de choisir entre Dieu et ses passions humaines.

Résumé

Éditions
 Dieu et Mammon précédé de Étude de Ramon Fernandez, coll. « Faits et gestes de la vie contemporaine », éditions du Capitole, Bordeaux, 1929, 218 p.
 Dieu et Mammon préface de Ramon Fernandez, Éditions du Siècle, Paris, 1933, 208 p.
 Dieu et Mammon suivi de Souffrances et bonheur du chrétien, La Vie et la Mort d'un poète, Les Maisons fugitives et Hiver, Paris, éditions Grasset, 1958 et 1967, 302 p.

Notes et références

Essai de François Mauriac
Essai paru en 1929
Essai français des années 1920

redpajama_set_name: RedPajamaWikipedia


text:
Violation of 1974 accord: Pakistan vows to move UN on Bangladesh executions
Observer News Service | May 15, 2016
ISLAMABAD: Pakistan pledged on Friday to raise the issue of executions of Jamaat-i-Islami (JI) leaders in Bangladesh at appropriate United Nations forums, including its Human Rights Council (UNHRC), besides vowing to take the matter up at diplomatic level with other countries.
Members of the Senate were given details in this regard by Adviser to the Prime Minister on Foreign Affairs Sartaj Aziz.
Condemning the Bangladesh executions, he asked Bangladesh to reconsider its policy "not just in the interest of other Muslim countries, but also its own".
Terming executions of political opponents by Bangladesh government victimisation, he said that not only the Muslim world but the entire international community was expressing concerns in this regard.
Urging the international community to take notice of human rights violation in Bangladesh, Aziz said that the hangings were "in sheer violation of a 1974 agreement between Pakistan, India and Bangladesh".
Earlier, Senators Nehal Hashmi, Hamza, Chaudhary Tanvir Khan and Mushahidullah Khan praised Turkey for recalling its envoy from Bangladesh in protest and recommended that Pakistan should follow suit.Senator Hashmi paid tribute to the fallen political leaders, including Matiur Rehman Nizami, saying that Nizami had served as a parliamentarian and minister in Bangladesh.
He also said that the tribunal headed by Sheikh Hasina Wajid had executed JI leaders whose "only crime was their loyalty to Pakistan and the two-nation theory".
https://kashmirobserver.net/2016/05/15/violation-of-1974-accord-pakistan-vows-to-move-un-on-bangladesh-executions
Reminding lawmakers that Prof Ghulam Azam and Salahuddin Chaudhary were among those who met a similar fate, he said that their crime had not been established and they were not given a fair deal. "International organizations such as Amnesty International and Human Rights Watch had deemed the decision (to hang JI leaders) unacceptable," he added.
Senator Abdul Qayyum criticised what he termed 'kangaroo courts' which awarded death sentences to the leaders of JI's Bangladesh chapter and said the act amounted "to back-stabbing Pakistan as traitors".
He said if East Pakistan had "not become Bangladesh, such gallows would not have existed".
Senator Mushahidullah pointed out that Bangladesh's vast majority was Muslim and said that maybe the "regime in Dhaka or people with such a mindset could be against Pakistan, but it was impossible for an entire population to be against any one country".
Responding on a call-attention notice moved by Senator Kulsoom Parveen on the killing of a teenage girl in Abbottabad on 'orders' of a jirga, Minister of State for Parliamentary Affairs Shaikh Aftab Ahmed said both the federal and Khyber-Pakhtunkhwa governments had taken strict notice of the 'heinous incident'.
Senator Perveen condemned the girl's murder for just supporting elopement and urged the government to take prompt action against the culprits.
"Is there a law that allows such killing … Is there a law that allows such courts?" she asked.
Condemning the murder, Senator Mohsin Leghari pointed out that a bill moved by former Senator Sughra Imam and passed by the Senate, had lapsed during the previous government. He said that this issue had not been taken up during the joint parliamentary sittings.
He asked the law minister to look into the matter and urged the government to formulate new legislation if they could not work with the existing bill.
He said that urgent remedial measures were needed on the part of the federal and provincial governments.
Leader of the House Raja Zafarul Haq said that Muslim countries should join hands and stop the executions of political opponents in Bangladesh.
Members of the Opposition continued their boycott of the Senate session against what they termed the Prime Minister's delaying tactics over appearing before the House.


text:
NewsShow Jumping
Schwizer and Carlina make it a double in Helsinki
Switzerland's Pius Schwizer secured a superb back-to-back double when adding victory in the second leg of the Rolex FEI World Cup™ Jumping 2011/2012 series in Helsinki, Finland today to his opening-round success in Oslo, Norway last Sunday. Once again riding Carlina, the 49 year old rider was one of nine through to the second-round jump-off against the clock in which he set a target that could not be matched despite some heroic efforts from those who followed him.
Malin Baryard-Johnsson nearly stole his thunder with a feat of derring-do that would challenge even the trick-riding expertise of the Ukrainian Cossacks. In a heart-stopping "save" that had spectators on the edges of their seats, the Swedish rider managed to stay onboard her 11 year old gelding H&M Reveur de Hurtebise and finish third behind Holland's Michael Van der Vleuten while the host nation's Nina Fagerstrom slotted into fourth.
It was Schwizer who was wearing the biggest smile at the end of the day however, as, with the maximum 40 points already posting him to the top of the leaderboard, he is well on his way to the 2011/2012 series final in 's-Hertogenbosch, The Netherlands next April.
REAL WORLD CUP TRACK
"My compliments to the course designer – it was a real World Cup track" Schwizer said afterwards. Brazil's Jorge Guilherme set them a tough test in the small Helsinki arena. "You have to build top courses for the European World Cup events" he pointed out. "This is the Formula 1 of Jumping and it needs to be difficult enough while bearing in mind that we are still early in the season" he added.
In a starting field of 37 there were four retirements and two eliminations – the first of the latter taking out third-line rider Henk van de Pol and Kirfa de Kreisker from The Netherlands and the second occurring when Spain's Sergio Alvarez Moya and Kisby, going fifth from the end, ran into trouble at the last. This vertical proved influential. Ridden on a short five strides from the preceding double, the narrow stile consisting of just three white poles was merciless to those who, having had to push for the penultimate fence, arrived on a stride that was too forward.
Jorge however was quite satisfied when nine horse-and-rider combinations conquered his challenge to go through to the second-round decider.
SET THE PACE
Belgium's Ludo Philippaerts set the pace with a double-error from Kassini Jack and Austria's Iris Murray, who has coped admirably since stepping up in class with Night Flight in recent weeks, followed suit. But Schwizer and Carlina made no mistakes, setting off with purpose and setting the target with a great clear in 37.58 seconds. "I didn't take too much of a risk – I could have gone faster, but I knew it was pretty good" he said afterwards of his round.
Ireland's Billy Twomey was first to take that on, but took his foot off the gas after an early mistake with Romanov. The crowd went wild however when home-grown star, Nina Fagerstrom, left all the fences intact with Talent, although she was more than two seconds off Schwizer's target time. And she was immediately overtaken for runner-up spot by The Netherand's Maikel van der Vleuten and VDL Groep Verdo who clocked 38.30.
It was Frenchman Patrice Delaveau who looked most likely to oust the Swiss leader from his perch. Setting off like a whirlwind he was well up on the clock turning to the last with Ornella Mail, but paid a big price for a massive stand-off at the last. So when Germany's Daniel Deusser and Untouchable also left one on the floor, then only Baryard-Johnsson stood between Schwizer and an exceptional start to the new season.
The Swedish rider was looking good until she reached the former triple combination, now reduced to two jumping efforts. "I was too fast going in" she admitted afterwards, and the end result was a huge effort from her gelding that sent her into orbit over the second element. "I landed on the left-hand side of the saddle when I came back down, and it was quite scarey for a while!" she said. "I struggled to get back on, trying to get my stirrups, but I said to myself 'no, don't circle and no, forget about the stirrups, just keep going and try to stay in the saddle over the last three fences!" she added. Against all the odds she succeeded, and with the crowd bursting with admiration for her courage and determination, she galloped through the finish with the clock showing 40.62 and with all the poles still in place – "yeh, scarey – but good" she laughed afterwards.
This was good enough for third behind Van der Vleuten who was really pleased with his horse. "I've had him for four years now and he's one of the best I've ever had. "He's honest and always tries his best – no course is ever too high or too wide for him" he said of VDL Groep Verdi who is still only nine years old. Fagerstrom slotted into fourth having done "better than expected". "I always want to do well here in front of my family and my friends, but I didn't take too many risks – I preferred to finish with two clear rounds instead" said the rider who has now slotted into joint-eighth spot on the leaderboard ahead of the next leg of the Rolex FEI World Cup™ Jumping series in Lyon, France next Sunday.
1, Carlina (Pius Schwizer) SUI 0/0 37.58; 2, VDL Groep Verdi (Maikel van der Vleuten) NED 0/0 38.30; 3, H&M Reveur de Hurtebise (Malin Baryard-Johnsson) SWE 0/0 40.62; 4, Talent (Nina Fagerstrom) FIN 0/0 40.70; 5, Ornella Mail (Patrice Delaveau) FRA 0/4 35.14; 6, Untouchable 27 (Daniel Deusser) GER 0/4 37.40; 7, Romanov II (Billy Twomey) IRL 0/4 40.07; 8, Kassini Jac (Ludo Philippaerts) BEL 0/8 40.48; 9, Night Flight (Iris Murray) AUT 0/8 46.26; 10, Mic Mac du Tillard (Angelica Augustsson) SWE 4/- 58.97; 11, Nino des Buissonnets (Steve Guerdat) SUI 4/- 59.20; 12, VDL Bubalu (Jur Vrieling) NED 4/- 61.29; 13, Ciske van Overis (Edwina Tops-Alexander) AUS 4/- 61.53; 14, VDL Groep Quinara (Leopold van Asten) NED 4/- 62.02; 15, Bella Donna 66 (Meredith Michaels-Beerbaum) GER 4/- 62.88; 16, Copin van de Broy (Gregory Wathelet) BEL 4/- 63.38; =17, H&M Arctic Aurora Borealis (Peder Fredericson) SWE 4/- 63.45; =17, Eurocommerce Seoul (Wout-Jan van der Schans) NED 4/- 63.45.
Rolex FEI World Cup™ Jumping 2011/2012 Western European League
Standings After Round 2 at Helsinki (FIN):
1. Pius Schwizer SUI – 40
2. Maikel van der Vleuten NED – 26
3. Angelica Augustsson SWE – 18
4. Philipp Weishaupt GER – 17
5. Luciana Diniz POR – 15
5. Malin Baryard-Johnsson SWE – 15
5. Patrice Delaveau FRA – 15
8. William Funnell GBR – 13
8. Nina Fagerstrom FIN – 13
10. Denis Lynch IRL – 12
11. Daniel Deusser GER – 11
12. Meredith Michaels-Beerbaum GER – 10
12. Billy Twomey IRL – 10
12. Kevin Staut FRA – 10
12. Edwina Tops-Alexander AUS – 10
16. Ludo Philippaerts BEL – 9
17. Iris Murray AUT – 8
18. Rolf-Goran Bengtsson SWE – 7
This was the second round of the FEI World Cup™ Series 2011/12 and a back-to-back win for Switzerland's Pius Schwizer and Carlina.
37 riders from 16 different nations participated- AUS, AUT, BEL, DEN, ESP, FIN, FRA, GER, GBR, IRL, ITA, KSA, NED, NOR, SWE, SUI.
Current league leader is Pius Schwizer on the maximum 40 points.
The youngest horse competing was 8 years old, Meredith Michaels-Beerbaum's Bella Donna 66.
There were three 15 year old horses competing: Calandro (Sebastian Numminem), L'Espoir (Geir Gulliksen), Ideal de la Loge (Roger Yves Bost).
9 first-round clears.
4 double-clears.
4 retired – Anna-Julia Kontio (FIN), Sebastian Numminen (FIN), Jan Sprehe (GER), Cian O'Connor (IRL).
2 were eliminated- Henk van de Pol (NED), Sergio Alvarez Moya (ESP).


text:
Mathias Abraham Torstensen (born 1890s – 9 July 1975) was a Norwegian rower who competed in the 1912 Summer Olympics.

He was a crew member of the Norwegian boat, which was eliminated in the semi-finals of the coxed fours event. Listed as bronze medalists.

References

External links
profile

1890s births
Norwegian male rowers
Olympic rowers of Norway
Rowers at the 1912 Summer Olympics

1975 deaths


For people looking for reference material, please use the archives navigation bar on the right hand side.
Before I knew it, time had passed so slowly yet so quickly at the same time and it was already my final day in Venice.
Due to the packing, we missed the first boat out and caught the second one at 9am. As we entered the Venice city limits against the rising sun, an outline of a gigantic ship threatened to run us over. It was the huge Norwegian Jade cruise ship coming in under tow. For the record, our little motoscafi was producing more waves!
We started exploring the last bit of Venice which was the Dorsoduro area. This is the day's route.
The weather was very sunny and the haze of the first 3 days had cleared up which gave us a nice blue sky but also a blazing sun, the day being borderline hot in our winter clothes!
We took a peek at a Wine store where we had a sample taste of the local fragolino - strawberry wine. I'm actually a zero alcohol person so I do not know how to wine taste but it tasted fine to me. Glad to get the experience!
Near the wine store was a gondola shipyard, the Squero di San Trovaso which is apparently the oldest in the city and one of only three.
We headed westwards, heading deeper into the alleys and encountering less and less people, sitting inside a random beautiful church for 5 minutes to relax. With Venice's sights becoming more familiar and my memory card being almost full, pictures were sparse. The Lonely Planet map of Venice had proved rather reliable in previous days but it was totally lacking in accuracy for Dorsoduro, which with improvisation was not a problem.
We eventually looped back towards the east and encountered a nice wooden bridge. I was also surprised to find that despite the logistical nightmare of Venice, the city actually sorted it garbage with multiple rubbish bins for cans etc.
As we continued walking, we found ourselves at a Campo with a decapitated church tower!
It was at this very moment that I let my guard down, possibly due to fatigue. I folded the map and tried to navigate through the alleys by memory - and got lost unintentionally for the first time. There goes my theory that "It is possible to not get lost in Venice". Not all was a waste however, as we ended up at the Universita degli Studi Ca Foscari where Neko, a fellow ARIA pilgrim will study the next coming year! It had a nice courtyard with seats at the entrance where we munched down some sandwiches!
Another hour gone and I was hungry again. According to a friend's guidebook, Spaghetti ala Vongole (clamshell) is the recommended dish to have in Venice and I had been on the lookout for a place with a decent price (under €10) since Day 1. We finally found one and risking getting ripped off with tourist food, went in. The food was very good, if a little rich in oil and definately not tourist garbage. Unknown to me at that time, this tavern was recommended by that same guidebook.
One last place left to go in Dorsoduro which was the Chiesa di Santa Maria della Salute. The whole area was under restoration which also closed a traghetto route. Photography was constrained to wide-angle which I did not have and I already had pictures of that Church. I was a little dissapointed.
We took a traghetto to save 10 minutes...and who doesn't like gondola rides? Unfortunately, they didn't let me stand due to the low load factor of 3 passengers.
A final trip to Piazza San Marco, as we had "forgotten" to visit the Basilica 2 days earlier due to the long queue! The Norwegian Jade had emptied over 1000 lemmings and Piazza San Marco was like a rat race. I miss the quiet of the Piazza at 9am.
While there was a long queue for the Campanile due to the crowds, the line for the Basilica was almost empty despite the odds. No backpacks allowed - thanks Mr Terry Wrist. On top of it, no picture taking allowed. You will have to take my word for it that ARIA the Origination ep5.5 was an accurate depiction of the interior. The ceiling is lined with little bits of gold.
However unlike Neo-Venezia, the floor was uneven (long-term exposure to Aqua Alta?) and the main hall was full of seats and we could not freely roam about as sections were fenced off. While access to the main areas are free, a fee is charged if you want to see the chapels inside or more importantly, Akari's secret spot!
The time was approaching 3pm and it was time to take the boat back to our accomodation to collect our luggage, and go to the airport.
An interesting use of materials for this sign.
One last Gelato was consumed as we arrived at Zattere with 15 minutes to spare. I knew I had memory to burn so I finally started snapping away!
Our motoscafi-style boat, the San Giorgio in Alga which we took every morning. An appropriate name as it is named after an abandoned island which the boat passes a zillion times a day on the Fusina - Zattere route.
A motoscafi with old factories in the background.
The causeway from Mestre, with the day clear enough to see the Alps.
We arrived at Fusina with plenty of time to kill until the next bus to Mestre, so I went snapping pictures. Two views of Venice and the surrounding lagoon from Fusina, at approx 35mm and 300mm zoom.
Last picture but not the least, our accomodation! We got half of the trailerhome.
We then got our luggage and took the local ACTV bus to the airport, changing busses at Mestre station. This was a long, slow and crowded journey and I was totally knackered at the airport. Our flight was at 8pm and we arrived very early, taking into account Murphy's Law.
I am a bit of an aviation nut as well and was observing which runways were in use for departure. Winds negligible, planes taking off in both directions depending on destination. Gambling on a southwesterly runway departure for London, I grabbed the emergency exit row seat (legroom) on the left side of the aircraft and was victorious! I saw Venice and the navigation channels lit up by night in its full glory during climbout! I managed to get some sleep in the plane, despite the lack or recline, light dimming and the in-flight food marketing on Easyjet.
I finally arrived at my dormitory at 12am, feeling a little depressed that my trip to Venice had come to an end.
Hmm, I just wanted to ask about the blog today. So, last day, eh?
And, btw, this is the end of your blog, or you still have something to share?


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Transology: A Vehicle Manufacturing Plant for Southwark, London
Claudia White's project responds to the cultural context of a site in Southwark, London and the problems facing large cities. The proposal links underground, street, and sky to city—and invigorates and redefines the surroundings with an architectural language that delights in what could be.
Claudia White
Interior view from below; circulation of light and shadows immerse and extend through the layers of manufacture. © Claudia White.
Nigel Coates
Kent Jackson
Roger Kallman
Martha Schwartz
Ross Wimer
This scheme inserts an alternative transport system as an extension to the existing use of the site, with the concept of complete vehicle sharing across the city. The concept of Transology informs this architectural system and building. Transology is a "field of design concerned with the interrelationship of mobility and the environment." It introduces a conditioned environment and manufactures various modes of transport specific to the users' requirements and/or body contours. A roof top velodrome allows for vehicle test running, while providing an envelope to views across London. A person-specific transport structure extends the travel link from the tube station out onto London's roads, via sustainable means. It delivers an architectural catalyst for a wider structure for the city.
At night the site promotes itself, with the vehicles coming to life amongst the darkness. An influx of movement is highlighted. © Claudia White.
A double layered "velodrome" sits at roof level. Views across London's skyline can be enjoyed within the bowl. A panoramic photomontage compliments this detail. © Claudia White.
The proposal's insertion into the site, reveals a view east from the London Eye. © Claudia White.
is a technical project manager for the London-based software development company Can Factory. She has worked on a range of high-profile projects establishing herself within the design, architecture, and tech industries. Completing her architecture diploma at the Architectural Association, her interests lie in the crossover between design, science, and technology and how to develop intuitive ideas into buildable projects, both digital or physical. She previously worked with Amanda Levete and the late Jan Kaplicky at Future Systems, joining the team that developed the architectural design of Bangkok's Central Embassy Hotel. Working with Vicky Richardson at Blueprint Magazine and Eva Menz at her design studio further informed her interests of the facets and outlets of design.


of Lake Burragorang which stretches back 52 kilometres from the dam wall.
We use the water collected by the natural landscape (catchments) to help supply water for our needs, by building dams and weirs, or tapping into groundwater.
Rainfall in Greater Sydney's five drinking water catchments - Warragamba, Shoalhaven, Upper Nepean, Woronora and Blue Mountains - flows into creeks and rivers that flow into 11 major dams.
The dams are connected to each other by a complex system of rivers, weirs, canals and pipelines. This is called the water supply system.
When full, the dams hold more than 2.6 million megalitres of water.
WaterNSW manages the dams and raw (untreated) water supply system, and also helps protect the health of the water catchments.
which supplies 80% of Sydney's water.
WaterNSW supplies high quality raw water that is then treated to Australian drinking water guidelines and distributed to customers.
Most of the water WaterNSW helps protect is supplied to Sydney Water where it is treated at one of nine water filtration plants. More than 80% of Sydney's water comes from Warragamba Dam and is treated at Prospect water filtration plant.
After treatment, water enters Sydney Water's network of reservoirs, pumping stations and 21,000 kilometres of pipes to arrive at homes and businesses in Sydney, the Blue Mountains and the Illawarra.
WaterNSW also supplies water to Shoalhaven City Council for Kangaroo Valley, Goulburn Council for Goulburn residents and Wingecarribee Shire Council for Southern Highlands residents.
Screening - freshwater passes through fine screens to remove solid objects like fish, logs and leaves.
Flocculation - fine particles are removed using a chemical that makes the particles clump together (flocculate) and settle to the bottom.
Filtration - larger particles are caught and removed as the water moves through a layer of sand, or a combination of sand and crushed anthracite (coal).
Disinfection - chlorine is used to kill viruses, bacteria and microbes, then ammonia is added as a longer lasting disinfectant. Fluoride is added to meet NSW Health requirements.
Sydney's water supply system can also be topped up with water from the desalination plant at Kurnell. The plant operates when dam levels fall below certain levels.
The desalination plant can provide up to 250 megalitres of water a day - 15% of Sydney's needs.
The desalination plant uses reverse osmosis membranes to extract freshwater from saltwater, blocking particles and salts, so only freshwater can pass through.
Once treated, water from the plant travels through an 18 kilometre pipeline from Kurnell to join the city water supply at Erskineville.