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\DOI{10.5802/crchim.442}
\datereceived{2025-05-30}
\daterevised{2025-11-27}
\datererevised{2026-01-06}
\dateaccepted{2026-01-15}
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\dateposted{2026-03-12}
\begin{document}

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\title{Synthesis and structural study of new phosphates:
AMg\textsubscript{2}Fe(PO\textsubscript{4})\textsubscript{3} (A = Sr or Ba) with the \tralicstex{α}{$\upalpha$}-CrPO\textsubscript{4}
structure type}

\alttitle{Synth\`{e}se et \'{e}tude structurale de nouveaux  phosphates
: AMg\textsubscript{2}Fe(PO\textsubscript{4})\textsubscript{3} (A = Sr ou Ba) de type \tralicstex{α}{$\upalpha$}-CrPO\textsubscript{4}}

\author{\firstname{Ahmed} \lastname{Ould Saleck}\CDRorcid{0009-0002-3911-426X}\IsCorresp}
\address{Research Unit: Membranes, Mat\'eriaux, Environnement et
Milieux Aquatiques (2MEMA), BP 5026, FST, Universit\'e de
Nouakchott, Mauritanie}
\email[A. Ould Saleck]{ahmed.medlemine@univ-nkc.mr}

\author{\firstname{Abderrazzak} \lastname{Assani}\CDRorcid{0000-0002-4737-2966}}
\address{Laboratoire de Chimie Appliqu\'{e}e des Mat\'{e}riaux, Centre
des Sciences des Mat\'{e}riaux, Faculty of Science, Mohammed V
University in Rabat, Avenue Ibn Batouta, BP 1014, Rabat, Morocco}

\author{\firstname{Mohamed} \lastname{Saadi}\CDRorcid{0000-0003-2655-0230}}
\addressSameAs{2}{Laboratoire de Chimie Appliqu\'{e}e des Mat\'{e}riaux, Centre
des Sciences des Mat\'{e}riaux, Faculty of Science, Mohammed V
University in Rabat, Avenue Ibn Batouta, BP 1014, Rabat, Morocco}

\author{\firstname{Cyrille}\nobreakauthor\lastname{Albert-Mercier}\CDRorcid{0000-0001-9720-6184}}
\address{Univ. Polytechnique Hauts-de-France, INSA Hauts-de-France,
CERAMATHS- D\'{e}partement Mat\'{e}riaux et Proc\'{e}d\'{e}s,
Valenciennes, F-59313, France}

\author{\firstname{Claudine} \lastname{Follet-Houttemane}\CDRorcid{0000-0002-3102-5935}}
\addressSameAs{3}{Univ. Polytechnique Hauts-de-France, INSA
Hauts-de-France, CERAMATHS- D\'{e}partement Mat\'{e}riaux et
Proc\'{e}d\'{e}s, Valenciennes, F-59313, France}

\author{\firstname{Lahcen} \lastname{El Ammari}\CDRorcid{0000-0001-7980-974X}}
\addressSameAs{2}{Laboratoire de Chimie Appliqu\'{e}e des Mat\'{e}riaux, Centre
des Sciences des Mat\'{e}riaux, Faculty of Science, Mohammed V
University in Rabat, Avenue Ibn Batouta, BP 1014, Rabat, Morocco}

\shortrunauthors

\keywords{\kwd{Orthophosphate}
\kwd{Crystal structure}
\kwd{Solid-state reaction}
\kwd{X-ray diffraction}
\kwd{\tralicstex{α}{$\upalpha$}-CrPO\textsubscript{4}}
\kwd{Single crystal}}

\altkeywords{\kwd{Phosphate}
\kwd{Structure cristalline}
\kwd{R\'{e}action \`{a} l'\'{e}tat solide}
\kwd{Diffraction des rayons X}
\kwd{\tralicstex{α}{$\upalpha$}-CrPO\textsubscript{4}}
\kwd{Monocristal}}

\begin{abstract}
Single  crystals of new orthophosphates AMg\textsubscript{2}Fe(PO\textsubscript{4})\textsubscript{3}  (A
= Sr or Ba) have been synthesized by solid-state reaction. From
single crystal X-ray diffraction data, their corresponding crystal
structures were solved in the orthorhombic system, with the
\textit{Imma} space group and unit cell parameters \textit{a} = 10.3998 (2)
\AA{}, \textit{b} = 13.2000 (2) \AA{}, \textit{c} = 6.5364 (1) \AA{} for the
strontium compound and \mbox{\textit{a} = 10.4996 (2) \AA{}}, \textit{b} = 13.2696 (1)
\AA{},  \textit{c} = 6.6330 (2) \AA{} for the barium compound. Both phosphates
crystallize with the \tralicstex{α}{$\upalpha$}-CrPO\textsubscript{4} structure type. The
crystal structure of both orthophosphates is composed of MgO\textsubscript{6}
octahedra, FeO\textsubscript{6} octahedra, and PO\textsubscript{4} tetrahedra. The sharing of
{vertices} between those polyhedra leads to a three-dimensional network
defining hexagonal tunnels that are occupied by Sr\textsuperscript{2+} or Ba\textsuperscript{2+}
cations. 
\end{abstract}

\begin{altabstract}
Des monocristaux de nouveaux orthophosphates
AMg\textsubscript{2}{Fe(PO}\textsubscript{4})\textsubscript{3} (A = Sr ou Ba) ont \'{e}t\'{e}
synth\'{e}tis\'{e}s par r\'{e}action \`{a} l'\'{e}tat solide. Les
structures cristallines des deux compos\'{e}s ont \'{e}t\'{e}
r\'{e}solues dans le syst\`{e}me orthorhombique, groupe spatial
\textit{Imma}, \`{a} partir des donn\'{e}es de diffraction des
rayons X sur monocristal. La structure de ces deux compos\'{e}s est de
type \tralicstex{α}{$\upalpha$}-CrPO\textsubscript{4}. Les param\`{e}tres de maille valent
\textit{a}= 10,3998 (2) \AA{}, \textit{b}= 13,2000 (2) \AA{},
\textit{c}= 6,5364 (1) \AA{} pour le compos\'{e} au strontium et
\textit{a}= 10,4996 (2) \AA{}, \textit{b}= 13,2696 (1) \AA{},
\textit{c}= 6,6330 (2) \AA{} pour le compos\'{e} au baryum. La
structure cristalline de chacun des deux compos\'{e}s est
constitu\'{e}e d'octa\`{e}dres MgO\textsubscript{6}, d'octa\`{e}dres
FeO\textsubscript{6} et de t\'{e}tra\`{e}dres PO\textsubscript{4}. La jonction entre ces
poly\`{e}dres conduit \`{a} un r\'{e}seau tridimensionnel
d\'{e}finissant des tunnels hexagonaux qui sont occup\'{e}s par les
cations Sr\textsuperscript{2+} ou Ba\textsuperscript{2+}.
\end{altabstract}

\editornote{Submitted by invitation as part of the 13th edition of the Moroccan Meetings on Solid State Chemistry (REMCES-13).}
\alteditornote{Soumis sur invitation dans le cadre de la 13\textsuperscript{\`eme} \'edition des Rencontres Marocaines sur la Chimie de l'\'Etat Solide (REMCES-13)}

%\input{CR-pagedemetas}

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\section{Introduction}\label{sec1}
In the ${\upalpha}$-CrPO$_{4}$ structure~\cite{1}, the Cr$^{3+}$ and
P$^{5+}$  cations occupy four special positions of the \textit{Imma}
space group. Its corresponding framework is constructed on the basis of
[CrO$_{6}$] octahedra and [PO$_{4}$] tetrahedra, revealing vacant
channels along the [100] and [010] axis. Accordingly, this phosphate
can be formulated as A1A2Cr1Cr2$_{2}$(PO$_{4}$)$_{3}$, with the channel
vacant sites represented by A1, A2. As one of our points of interest is
to elaborate new ${\upalpha}$-CrPO$_{4}$-related open-framework
phosphates, we have {focused} our research on the mixed substitution of
di- and/or trivalent cations for Cr1 and/or Cr2. Such a substitution
leads to the charge compensation requiring the localization of
monovalent or divalent cations in the A1 and/or A2 channels. Hence,
using the hydrothermal process, we have managed to isolate new
phosphates Ag$_{2}$M$_{3}$(HPO$_{4}$)(PO$_{4}$)$_{2}$ (M ${=}$ Co or
Ni)~\cite{2,3}, besides the rarely encountered mixed-valence
\mbox{manganese} phosphates MMn(II)Mn(III)$_{2}$(PO$_{4}$)$_{3}$ 
(M~${=}$~Sr, Ba, or Pb)~\cite{4,5,6}. Moreover, the \mbox{solid-state}
reaction technique has allowed {us} to isolate a variety of new other
bi- and trivalent-cations-based phosphates with an
${\upalpha}$-CrPO$_{4}$ structure {type,} namely
${\upalpha}$-Na$_{2}$Ni$_{2}$Fe(PO$_{4}$)$_{3}$~\cite{7},
NaCuCr$_{2}$(PO$_{4}$)$_{3}$~\cite{8},
NaZnCr$_{2}$(PO$_{4}$)$_{3}$~\cite{9},
BaNi$_{2}$Fe(PO$_{4}$)$_{3}$~\cite{10,11,12}, and
M$'$Co$_{2}$Fe(PO$_{4}$)$_{3}$ (M$'$ ${=}$ Sr or Ba)~\cite{13,14}.

These {phosphates} exhibit interesting physicochemical properties. For
example,
NaCoCr$_{2}$(PO{$_{4}$}{)}{$_{3}$} and its isotypes
NaNiCr$_{2}$(PO{$_{4}$}{)}{$_{3}$} and
Na$_{2}$Ni$_{2}$Cr(PO$_{4}$)$_{3}$ can serve as cathode materials for
sodium-ion batteries, owing to their high discharge capacities of  352,
385, and 368~mAh$\cdot$g$^{-1}$, respectively~\cite{13}. Recently,
Matsaev \etal~have reported a novel series of iron-based phosphates,
${\upalpha}$-Fe$_{1-x}$Cr$_x$PO$_{4}$, adopting the ${\upalpha}$-CrPO$_{4}$
structure type, capable of Li-ion intercalation in a high potential
region.

The present work is devoted to the synthesis and crystal structure
study of the two new magnesium phosphates AMg$_{2}$Fe(PO$_{4}$)$_{3}$
(A ${=}$ Sr or Ba) with the $\upalpha$-CrPO$_{4}$ structure type. 

\section{Experimental}\label{sec2}

\subsection{Crystal growth}\label{sec21}

Single crystals of the two compounds AMg$_{2}$Fe(PO$_{4}$)$_{3}$  (A
${=}$ Sr or Ba) were grown by solid-state reaction. The crystals were
prepared from a stoichiometric mixture of ACO$_{3}$ (A ${=}$ Sr or Ba)
(BaCO$_{3}$: Sigma-Aldrich, 98\%; SrCO$_{3}$: BaCO$_{3}$:
Seelze--Hannover, 99\%), Mg(NO$_{3}$)$_{2}{\cdot}$6H$_{2}$O
(Sigma-Aldrich, 97\%), Fe(NO$_{3}$)$_{3}{\cdot}$9H$_{2}$O (Panreac,
98\%) and NH$_{4}$H$_{2}$PO$_{4}$ (Alfa Aesar, 98\%). The mixture was
progressively heated in a platinum crucible to 573, 673, 773, and
873~K,  maintaining each temperature for one night, combined with
intermediate grindings. The products were then heated slowly at a rate
of 5~\textdegree C/min, to 1473 K in the Sr case and to 1353~K for Ba.
The final product was maintained at the final temperature for 10 min
followed by cooling at room temperature at a rate of 5~\textdegree C/h.
Finally, green single crystals were isolated from the Sr-containing
preparation while brown crystals were obtained with Ba. 

\subsection{Crystal structure study}\label{sec22}

A single crystal of each preparation was chosen carefully under
microscope with suitable dimensions for X-ray diffraction (XRD)
studies. The XRD data were collected using a Bruker D8 Venture Super
DUO diffractometer with a PHOTON100 CMOS area-detector and
monochromatic MoK${\upalpha}$ radiation (${\lambda} = 0.71073$~\AA) at
room temperature. The APEX3~\cite{15} software was used for data
collection and the data were integrated with the SAINT-Plus program.
Absorption corrections were performed by a multiscan semi-empirical
method using SADABS~\cite{16}. The two crystal structures were
solved by the Patterson method and refined by the SHELXT
2014~\cite{17} and SHELXL 2018~\cite{18} programs incorporated in
the WinGX interface~\cite{19}. The structural graphics were drawn
using the DIAMOND {program}~\cite{20}. 

\section{Results and discussion}\label{sec3}

Table~\ref{tab1} summarizes the crystal data and structural refinement
results. For both structures AMg$_{2}$Fe(PO$_{4}$)$_{3}$ (A ${=}$ Sr or
Ba), the refinement of all ions in anisotropy led to good reliability
factors ($R_1 = 0.018$ and $wR_2 = 0.047$ for
SrMg$_{2}$Fe(PO$_{4}$)$_{3}$, $R_1 = 0.012$ and $wR_2 =0.032$ for
BaMg$_{2}$Fe(PO$_{4}$)$_{3}$).

\begin{table*}%tab1
\caption{\label{tab1}Crystal data and structure refinement of
AMg$_{2}$Fe(PO$_{4}$)$_{3}$ (A ${=}$ Sr or Ba)\vspace*{-2pt}}
\begin{tabular}{ccc}
\thead
Compound & SrMg$_{2}$Fe(PO$_{4}$)$_{3}$ & BaMg$_{2}$Fe(PO$_{4}$)$_{3}$ \\
\endthead
\multicolumn{3}{c}{{Crystal data}}\vspace*{4pt} \\
Crystal system & Orthorhombic & Orthorhombic \\
Space group & \textit{Imma} & \textit{Imma} \\
Cell dimension (\AA{}) & 10.3998 (2) & 10.4996 (2)\\
& 13.2000 (2) & 13.2696 (1)\\
&6.5364 (1)   & 6.6330 (2) \\
Cell volume (\AA{}$^3$) & 897.30 (3) & 924.15 (3) \\
Multiplicity ${Z}$ & 4 & 4 \\
Molecular weight (g/mol) & 477 & 526.72 \\
Density (g/cm$^{-3}$) & 3.531 & 3.786 \\
Coefficient absorption ${\mu}$ (mm$^{-1}$) & 8.31 & 6.53 \vspace*{4.5pt}\\
\multicolumn{3}{c}{{Data collection}} \vspace*{4.5pt}\\
Diffractometer~ & Br\"{u}ker X8 APEX- CCD & Br\"{u}ker X8 APEX- CCD \\
\parbox[t]{6cm}{\raggedright No.\ of measured, independent, and   observed [$I\geq 2\sigma(I)$] reflections} & 
9561, 892, 876 & 22556, 1671, 1595 \\
$R_{\mathrm{int}}$ & 0.035 & 0.032 \\
${\theta}_{\min}$--${\theta}_{\max}$ (\textdegree) & 3.1--32.5 & 3.1--41.5 \vspace*{4pt}\\
\multicolumn{3}{c}{{Refinement}} \vspace*{4.5pt}\\
$R[F^{2}> 2\sigma(F^{2})]$ & 0.018 &  0.012 \\
$wR_{2}(F^{2})$ & 0.047 &  0.032 \\
$S$ (Goodness-of-Fit): & 1.19 &  1.16 \\
No of refined parameters    & 54 & 58\\
No. of restraints & 0 &   \\
$\Delta\rho_{\max}, \Delta\rho_{\min}$ (e${\cdot}$\AA{}$^{-3}$) & 0.58, ${-}$0.82 & 1.38, ${-}$1.03
\botline
\end{tabular}
\vspace*{-2pt}
\end{table*}

\begin{table*}%tab2
\caption{\label{tab2}Atomic coordinates, occupancies, and equivalent
isotropic displacement parameters (\AA{}$^{2}$) of
SrMg$_{2}$Fe(PO$_{4}$)$_{3}$ and BaMg$_{2}$Fe(PO$_{4}$)$_{3}$*\vspace*{-2pt}}
\begin{tabular}{cccllll}
\thead
Atom & Site  & Occupation & \multicolumn{1}{c}{${x}$} & \multicolumn{1}{c}{$y$} & \multicolumn{1}{c}{$z$} & \multicolumn{1}{c}{$U_{\mathrm{\'eq}}$} \\
\endthead
Sr1 & \morerows{1}{$4e$}  & \morerows{1}{1}  & 0.0000  & 0.7500  & \mn0.59942 (3)  & 0.00871 (8)  \\
Ba1* &  &  & 0.0000  & 0.7500  & \mn0.60778 (2)  & 0.00789 (4)  \\
Fe1/Mg1 & \morerows{1}{$4a$}  & 0.{880 (1)}/0.{120 (1)} & 0.5000  & 0.5000  & \mn0.5000  & 0.00398 (9)  \\
Fe1/Mg1* &  & 0.{871 (1)}/0.{129 (1)} & 0.5000  & 0.5000  & \mn0.5000  & 0.00384 (5)  \\
Mg2/Fe2 & \morerows{1}{$8g$}  & 0.{940 (1)}/0.{060 (1)} & 0.7500  & 0.63349 (4)  & \mn0.2500  & 0.0053 (1)  \\
Mg2/Fe2* &  & 0.{871 (1)}/0.{129 (1)} & 0.7500  & 0.63293 (3)  & \mn0.2500  & 0.00283 (7)  \\
P1 & \morerows{1}{$4e$}  & \morerows{1}{1}  & 0.0000  & 0.7500  & \mn0.09209 (8)  & 0.0038 (1)  \\
P1* &  &  & 0.0000  & 0.7500  & \mn0.10104 (8)  & 0.00341 (8)  \\
P2 & \morerows{1}{$8g$}  & \morerows{1}{1}  & 0.7500  & 0.42840 (3)  & \mn0.2500  & 0.0043 (1)  \\
P2* &  &  & 0.7500  & 0.42840 (3)  & \mn0.2500  & 0.0043 (1)  \\
O1 & \morerows{1}{${8h}$}  & \morerows{1}{1}  & 0.0000  & 0.65613 (9)  & ${-}$0.0436 (2)  & 0.0071 (2)  \\
O1* &  &  & 0.0000  & 0.65524 (8)  & ${-}$0.0294 (2)  & 0.0065 (2)  \\
O2 & \morerows{1}{$8i$}  & \morerows{1}{1}  & 0.8822 (1)  & 0.7500  & \mn0.2362 (2)  & 0.0064 (2)  \\
O2* &  &  & 0.8813 (1)  & 0.7500  & \mn0.2390 (2)  & 0.0059 (2)  \\
O3 & \morerows{1}{$16j$}  & \morerows{1}{1}  & 0.71114 (9)  & 0.36450 (7)  & \mn0.0665 (1)  & 0.0081 (2)  \\
O3* &  &  & 0.71689 (9)  & 0.36643 (6)  & \mn0.0661 (1)  & 0.0082 (1)  \\
O4 & \morerows{1}{$16j$}  & \morerows{1}{1}  & 0.63860 (8)  & 0.50528 (6)  & \mn0.2950 (1)  & 0.0062 (2)  \\
O4* &  &  & 0.63800 (7)  & 0.50498 (6)  & \mn0.2930 (1)  & 0.0062 (1) 
\botline
\end{tabular}
\vspace*{-2pt}
\end{table*}

\begin{table*}%tab3
\caption{\label{tab3}Anisotropic displacement parameters (\AA{}$^{2}$) of
SrMg$_{2}$Fe(PO$_{4}$)$_{3}$ and BaMg$_{2}$Fe(PO$_{4}$)$_{3}$*\vspace*{-2pt}}
\begin{tabular}{cccclll}
\thead
{Atom} & $U^{11}$ & $U^{22}$ & $U^{33}$ & \multicolumn{1}{c}{$U^{12}$} & 
\multicolumn{1}{c}{$U^{13}$} & \multicolumn{1}{c}{$U^{23}$} \\
\endthead
Sr1 & 0.0091 (1)  & 0.0114 (1)  & 0.0056 (1)  & \mn0.000  & 0.000  & \mn0.000  \\
Ba1* & \00.00716 (6)  & \00.01205 (6)  & \00.00447 (5)  & \mn0.000  & 0.000  & \mn0.000  \\
Fe1/Mg1 & 0.0034 (2)  & 0.0041 (2)  & 0.0044 (2)  & \mn0.000  & 0.000  & \mn0.0003 (1)  \\
Fe1/Mg1* & 0.0034 (1) & 0.0040 (1)  & 0.0041 (1)  & \mn0.000  & 0.000  & \mn0.00011 (8)  \\
Mg2/Fe2 & 0.0051 (2)  & 0.0040 (2)  & 0.0067 (2)  & \mn0.000  & 0.0002 (2)  & \mn0.000  \\
Mg2/Fe2* & 0.0027 (2)  & 0.0013 (2)  & 0.0045 (2)  & \mn0.000  & 0.0003 (1)  & \mn0.000  \\
P1 & 0.0038 (2)  & 0.0034 (2)  & 0.0043 (2)  & \mn0.000  & 0.000  & \mn0.000  \\
P1* & 0.0033 (2)  & 0.0033 (2)  & 0.0036 (2)  & \mn0.000  & 0.000  & \mn0.000  \\
P2 & 0.0047 (2)  & 0.0038 (2)  & 0.0044 (2)  & \mn0.000  & 0.0005 (1)  & \mn0.000  \\
P2* & 0.0040 (1)  & 0.0039 (1)  & 0.0040 (1)  & \mn0.000  & 0.0005 (1)  & \mn0.000  \\
O1 & 0.0088 (5)  & 0.0050 (5)  & 0.0074 (5)  & \mn0.000  & 0.000  & ${-}$0.0018 (4)  \\
O1* & 0.0086 (4)  & 0.0039 (3)  & 0.0069 (4)  & \mn0.000  & 0.000  & ${-}$0.0018 (3)  \\
O2 & 0.0051 (5)  & 0.0071 (5)  & 0.0070 (5)  & \mn0.000  & 0.0015 (4)  & \mn0.000  \\
O2* & 0.0042 (4)  & 0.0076 (3)  & 0.0059 (4)  & \mn0.000  & 0.0016 (3)  & \mn0.000  \\
O3 & 0.0101 (4)  & 0.0074 (4)  & 0.0067 (3)  & ${-}$0.0018 (3)  & 0.0002 (3)  & ${-}$0.0022 (3)  \\
O3* & 0.0096 (3)  & 0.0085 (3)  & 0.0065 (3)  & ${-}$0.0021 (2)  & 0.0003 (2)  & ${-}$0.0027 (2)  \\
O4 & 0.0053 (3)  & 0.0059 (3)  & 0.0075 (3)  & \mn0.0012 (3)  & 0.0015 (3)  & \mn0.0006 (3)  \\
O4* & 0.0047 (3)  & 0.0064 (2)  & 0.0073 (3)  & \mn0.0011 (2)  & 0.0017 (2)  & \mn0.0008 (2)
\botline
\end{tabular}
\end{table*}

The two compounds crystallize in the \textit{Imma} space group with the
following unit cell parameters: $a = 10.3998$ (2)~\AA{}, $ b = 13.2000$
(2)~\AA{}, $c = 6.5364$ (1)~\AA{}, and $V = 897.30$ (3)~\AA{}$^3$ for
the strontium-based phosphate and $a = 10.4996$ (2)~\AA{}, $ b =
13.2696$ (1)~\AA{}, $c = 6.6330$~(2)~\AA{}, and $V = 924.15$ (3)
\AA{}$^3$ for the barium-based phosphate.

The atomic coordinates and equivalent isotropic displacement parameters
are given in Table~\ref{tab2}. The atomic anisotropic displacement
parameters are presented in Table~\ref{tab3}. The bivalent cation (site
${=}$ Ba1 or Sr1) is refined in the special position ($4e$). The P$^{5+}$
ions (sites named P1 and P2) are located in the special Wyckoff
positions ($4e$) and ($8g$), respectively. Two sites of the O$^{2-}$
ions, named O1 and O2, are refined in the special positions ($8h$) and
($8i$) respectively, while the other O$^{2-}$ ions (O3 and O4 sites)
are in the general position ($16j$). 


\begin{table*}%tab4
\caption{\label{tab4}Interatomic distances (\AA{}) and angles
(\textdegree) for AMg$_{2}$Fe(PO$_{4}$)$_{3}$ (A ${=}$ Sr or Ba)}
\tabcolsep 10pt
\begin{tabular}{ccc}
\tbody
\multicolumn{3}{c}{\raisebox{1pc}{}P--O distances (\AA) and O--P--O angles (\textdegree)}\vspace*{4pt} \\
\raisebox{1pc}{}Distance (\AA) & SrMg$_{2}$Fe(PO$_{4}$)$_{3}$ & BaMg$_{2}$Fe(PO$_{4}$)$_{3}$ \\
P1--O1 & 1.524 (1) & 1.526 (1) \\
P1--O1$^{\mathrm{ix}}$ & 1.524 (1) & 1.526 (1) \\
P1--O2$^{\mathrm{ix}}$ & 1.546 (1) & 1.546 (1) \\
P1--O2 & 1.546 (1) & 1.546 (1) \\
Average distances & 1.535 & 1.536 \\
P2--O3 & 1.521 (1) & 1.521 (1) \\
P2--O3$^{\mathrm{vii}}$ & 1.521 (1) & 1.521 (1) \\
P2--O4$^{\mathrm{vii}}$ & 1.568 (1) & 1.570 (8) \\
P2--O4 & 1.568 (1) & 1.570 (8)  \\
Average distances & 1.544 & 1.545  \\
Angle (\textdegree) & SrMg$_{2}$Fe(PO$_{4}$)$_{3}$ & BaMg$_{2}$Fe(PO$_{4}$)$_{3}$ \\
O1--P1--O1$^{\mathrm{ix}}$ & 108.8 (1) & 109.61 (3) \\
O1--P1--O2$^{\mathrm{ix}}$ & 110.77 (3) & 110.94 (9) \\
O1$^{\mathrm{ix}}$--P1--O2$^{\mathrm{ix}}$ & 110.77 (3) & 109.61 (3) \\
O1--P1--O2 & 110.77 (3) & 109.61 (3) \\
O1$^{\mathrm{ix}}$--P1--O2 & 110.77 (3) & 109.61 (3) \\
O2$^{\mathrm{ix}}$--P1--O2 & 104.91 (9) & 107.40 (9) \\
O3--P2--O3$^{\mathrm{vii}}$ & 112.62 (7) & 112.15 (4) \\
O3--P2--O4$^{\mathrm{vii}}$ & 114.04 (5) & 113.05 (7) \\
O3$^{\mathrm{vii}}$--P2--O4$^{\mathrm{vii}}$ & 108.10 (5) & 109.00 (5) \\
O3--P2--O4 & 108.10 (5) & 109.00 (5) \\
O3$^{\mathrm{vii}}$--P2--O4 & 114.04 (5) & 112.15 (4) \\
O4$^{\mathrm{vii}}$--P2--O4 & 99.34 (7) & 100.87 (6)  \vspace*{4pt}\\
\multicolumn{3}{c}{Fe1/Mg1--O distances (\AA) and O--Fe1/Mg1--O angles (\textdegree)}  \vspace*{4pt}\\
Distance (\AA) & SrMg$_{2}$Fe(PO$_{4}$)$_{3}$ & BaMg$_{2}$Fe(PO$_{4}$)$_{3}$ \\
Fe1/Mg1--O4$^{\mathrm{i}}$ & 1.9692 (8) & 1.9975 (8) \\
Fe1/Mg1--O4$^{\mathrm{ii}}$ & 1.9692 (8) & 1.9975 (8) \\
Fe1/Mg1--O4$^{\mathrm{iii}}$ & 1.9692 (8) & 1.9975 (8) \\
Fe1/Mg1--O4 & 1.9692 (8) & 1.9975 (8) \\
Fe1/Mg1--O1$^{\mathrm{iv}}$ & 2.081 (1) & 2.069 (1) \\
Fe1/Mg1--O1$^{\mathrm{v}}$ & 2.081 (1) & 2.069 (1)  \\
Average distances & 2.007 & 2.021  \\
Angle (\textdegree) & SrMg$_{2}$Fe(PO$_{4}$)$_{3}$ & BaMg$_{2}$Fe(PO$_{4}$)$_{3}$ \\
O1$^{\mathrm{iv}}$--Fe1/Mg1--O1$^{\mathrm{v}}$ & 180.0  & 180.000 (6) \\
O4$^{\mathrm{ii}}$--Fe1/Mg1--O1$^{\mathrm{v}}$ & 86.67 (3) & 88.18 (3) \\
O4$^{\mathrm{i}}$--Fe1/Mg1--O1$^{\mathrm{v}}$ & 93.33 (3) & 91.82 (3) \\
O4$^{\mathrm{iii}}$--Fe1/Mg1--O1$^{\mathrm{v}}$ & 93.33 (3) & 91.82 (3) \\
\tabularBreak{3}
O4--Fe1/Mg1--O1$^{\mathrm{v}}$ & 86.67 (3) & 88.18 (3) \\
O4--Fe1/Mg1--O1$^{\mathrm{iv}}$ & 93.33 (3) & 91.82 (3) \\
O4$^{\mathrm{i}}$--Fe1/Mg1--O1$^{\mathrm{iv}}$ & 86.67 (3) & 88.18 (3) \\
O4$^{\mathrm{iii}}$--Fe1/Mg1--O1$^{\mathrm{iv}}$ & 86.67 (3) & 88.18 (3) \\
O4$^{\mathrm{ii}}$--Fe1/Mg1--O1$^{\mathrm{iv}}$ & 93.33 (3) & 91.82 (3) \\
O4$^{\mathrm{i}}$--Fe1/Mg1--O4 & 85.90 (5) & 87.00 (5) \\
O4$^{\mathrm{i}}$--Fe1/Mg1--O4$^{\mathrm{iii}}$ & 94.10 (5) & 93.00 (5) \\
O4$^{\mathrm{ii}}$--Fe1/Mg1--O4$^{\mathrm{iii}}$ & 85.90 (5) & 87.00 (5) \\
O4$^{\mathrm{ii}}$--Fe1/Mg1--O4 & 94.10 (5) & 93.00 (5)  \vspace*{4pt}\\
\multicolumn{3}{c}{Mg2/Fe2--O distances (\AA) and O--Mg2/Fe2--O angles (\textdegree)}  \vspace*{4pt}\\
Distance (\AA) & SrMg$_{2}$Fe(PO$_{4}$)$_{3}$ & BaMg$_{2}$Fe(PO$_{4}$)$_{3}$ \\
Mg2/Fe2--O2 & 2.0647 (9) & 2.0784 (8) \\
Mg2/Fe2--O2$^{\mathrm{vi}}$ & 2.0647 (9) & 2.0784 (8) \\
Mg2/Fe2--O4 & 2.0719 (9) & 2.0849 (9) \\
Mg2/Fe2--O4$^{\mathrm{vii}}$ & 2.0719 (9) & 2.0849 (9) \\
Mg2/Fe2--O3$^{\mathrm{v}}$ & 2.1083 (9) & 2.1252 (8) \\
Mg2/Fe2--O3$^{\mathrm{viii}}$ & 2.1083 (9) & 2.1252 (8)  \\
Average distances & 2.082 & 2.096  \\
Angle (\textdegree) & SrMg$_{2}$Fe(PO$_{4}$)$_{3}$ & BaMg$_{2}$Fe(PO$_{4}$)$_{3}$ \\
O3$^{\mathrm{v}}$--Mg2/Fe2--O3$^{\mathrm{viii}}$ & 178.56 (6) & 179.55 (5) \\
O4--Mg2/Fe2--O3$^{\mathrm{v}}$ & 88.74 (4) & 87.75 (3) \\
O4$^{\mathrm{vii}}$--Mg2/Fe2--O3$^{\mathrm{v}}$ & 92.44 (4) & 92.62 (3) \\
O2--Mg2/Fe2--O3$^{\mathrm{v}}$ & 84.60 (4) & 85.59 (4) \\
O2$^{\mathrm{vi}}$--Mg2/Fe2--O3$^{\mathrm{v}}$ & 94.32 (4) & 94.07 (4) \\
O4--Mg2/Fe2--O3$^{\mathrm{viii}}$ & 92.44 (4) & 92.62 (3) \\
O4$^{\mathrm{vii}}$--Mg2/Fe2--O3$^{\mathrm{viii}}$ & 88.74 (4) & 87.75 (3) \\
O2--Mg2/Fe2--O3$^{\mathrm{viii}}$ & 94.32 (4) & 94.07 (4) \\
O2$^{\mathrm{vi}}$--Mg2/Fe2--O3$^{\mathrm{viii}}$ & 84.60 (4) & 85.59 (4) \\
O4--Mg2/Fe2--O4$^{\mathrm{vii}}$ & 70.47 (5) & 70.95 (4) \\
O2--Mg2/Fe2--O4$^{\mathrm{vii}}$ & 103.29 (3) & 103.28 (3) \\
O2--Mg2/Fe2--O2$^{\mathrm{vi}}$ & 83.70 (5) & 83.27 (5) \\
O2$^{\mathrm{vi}}$--Mg2/Fe2--O4 & 103.29 (3) & 103.28 (3)  \vspace*{4pt}\\
\multicolumn{3}{c}{A1--O distances (\AA) (A1 ${=}$ Sr or Ba)}  \vspace*{4pt}\\
Distance (\AA) & SrMg$_{2}$Fe(PO$_{4}$)$_{3}$ & BaMg$_{2}$Fe(PO$_{4}$)$_{3}$ \\
A1--O1$^{\mathrm{xi}}$ & 2.642 (1) & 2.715 (1) \\
A1--O2 & 2.672 (1) & 2.715 (1) \\
A1--O2$^{\mathrm{ix}}$ & 2.672 (1) & 2.745 (1) \\
A1--O3$^{\mathrm{v}}$ & 2.6744 (9) & 2.745 (1) \\
A1--O3$^{\mathrm{xii}}$ & 2.6744 (9) & 2.7658 (9) \\
\fourtabularBreak{3}
A1--O3$^{\mathrm{xiii}}$ & 2.6744 (9) & 2.7658 (9) \\
A1--O3$^{\mathrm{xiv}}$ & 2.6744 (9) & 2.7658 (9) \\
A1--O1$^{\mathrm{xi}}$ & 2.642 (1) & 2.7658 (9) \\
Average distances & 2.666 & 2.740
\botline
\end{tabular}
\tabnote{Symmetry codes: (i)~$x$, $-y+1$, $-z+1$; 
(ii)~$-x+1$, $y$, $z$; (iii)~$-x+1$, $-y+1$,
$-z+1$; (iv)~${x}-1/2$, $y$, $-z+1/2$; (v)~$-x+3/2$,
$-y+1$, $z+1/2$; (vi)~$-x+3/2$, $-y+3/2$, $-z+1/2$; (vii)~$-x+3/2$, 
$y$, $-z+1/2$; (viii)~${x}$, $-y+1$, $-z$; (ix)~$-x+2$, $-y+3/2$, $z$;
(x)~$-x+2$, $-y+3/2$, $z+1$; (xi)~$x$, $y$,
$z+1$; (xii)~$-x+3/2$, $y+1/2$, $z+1/2$; 
(xiii)~${x}+1/2$, $y+1/2$, $z+1/2$; (xiv)~$x+1/2$, $-y+1$,
$z+1/2$.}
\end{table*}

However, the position refinement of cations Fe$^{3+}$  and {Mg}$^{2+}$ 
in the special positions ($4e$) and (8\textit{g}), respectively,
results in negative atomic displacement parameters for Mg$^{2+}$, a
high-density residue in the vicinity of Mg$^{2+}$, and a density
deficit in the vicinity of Fe$^{3+}$, despite the very good $R_1$ and
{\textit{wR}}$_2$ factors {obtained.} {Those} facts suggest the
concomitant localization of Fe$^{3+}$  and Mg$^{2+}$ in the same site.
Such an assumption is established by the last {refinement} assuming,
firstly, the localization of both Fe$^{3+}$  and {Mg}$^{2+}$  in the
same crystallographic Wyckoff position ($4a$), initially
assigned only to Fe$^{3+}$. The occupancy rate {obtained} in this
site, hereafter named Fe1/Mg1 site, corresponds to 0.88{0 (1)} for
Fe$^{3+}$  and 0.12{0 (1)} for {Mg}$^{2+}$  {in} the strontium
compound. Likewise, the remaining amount of Fe accommodates the site of
Mg2 at the special Wyckoff position ($8g$), hereafter called Mg2/Fe2
site {in} the strontium phosphate. Such refinement led to an occupancy
of 0.94{0 (1)} for Mg$^{2+}$ and 0.06{0 (1)} for Fe$^{3+}$  at the
Mg2/Fe2 {site.} Therefore, refining the Fe/Mg site occupancy ratios in
the case of the Sr compound, taking into account the electrical
neutrality of the molecule, leads to a stoichiometric compound with a
Mg/Fe ratio of two and therefore a SrMg$_{2}$Fe(PO$_{4}$)$_{3}$
{formula.} In contrast, in the case of the {Ba} compound, the Mg/Fe
ratio is slightly less than {two} (7.482 (1)/4.518 (1)), and the
electrical neutrality of the molecule is no longer {maintained.} This
can be explained by the presence of a small amount of Fe$^{2+}$, and
consequently, the formula of the resulting compound will be
BaMg$_{1.87}$Fe$_{0.13}$Fe(PO$_{4}$)$_{3}$.\looseness=1

Selected bond lengths and angles in both compounds
AMg$_{2}$Fe(PO$_{4}$)$_{3}$ (A ${=}$ Sr or Ba) are listed in
\mbox{Table~\ref{tab4}.}

\begin{figure*}
\includegraphics{fig01}
\vspace*{-2pt}
\caption{\label{fig1}(A) Infinity chain of (Fe1/Mg1)P1O$_{9}$ formed by
sharing vertices of [Fe1Mg1O$_{6}$] octahedra and P1O$_{4}$ tetrahedra
(B) Sheet showing the {(Mg2/Fe2)}$_{4}${P2}$_{4}${O}$_{26}$ unit along
[010].}
\vspace*{-1pt}
\end{figure*}

In the two compounds SrMg$_{2}$Fe(PO$_{4}$)$_{3}$ and
BaMg$_{2}$Fe(PO$_{4}$)$_{3}$, the P$^{5+}$  ions located at the Wyckoff
positions ($4e$) and ($8g$) for P1 and P2 sites, respectively, have a
tetrahedral environment (P1O$_{4}$ and P2O$_{4}$) with a mean distance
$\langle \mathrm{P}\ndash \mathrm{O}\rangle$ of 1.540~\AA{}.

In both phosphates AMg$_{2}$Fe(PO$_{4}$)$_{3}$ (A ${=}$ Sr or Ba), the
cations Fe$^{3+}$  and Mg$^{2+}$ located in the Fe1/Mg1 site,
corresponding to the crystallographic Wyckoff position ($4a$), are
surrounded by six {O}$^{2-}$ ions forming an octahedron
(Fe1/Mg1)O$_{6}$ with a mean distance 
$\langle \mathrm{Fe1}/\mathrm{Mg1}\ndash \mathrm{O}\rangle$ of 2.007~\AA{}
for SrMg$_{2}$Fe(PO$_{4}$)$_{3}$ and 2.021~\AA{} for
BaMg$_{2}$Fe(PO$_{4}$)$_{3}$. 

\begin{figure*}
\includegraphics{fig02}
\caption{\label{fig2}Projection view along the $b$ direction of
the structure showing the hexagonal tunnels that accommodate Sr or Ba
in AMg$_{2}$Fe(PO$_{4}$)$_{3}$ (A ${=}$ Sr or Ba).}
\end{figure*}

For the Mg2/Fe2 site, the Mg$^{2+}$ and Fe$^{3+}$  cations are
statistically distributed in the Wyckoff position ($8g$) and adopt an
octahedral environment (Mg2/Fe2)O$_{6}$ with a mean distance
$\langle \mathrm{Mg2}/\mathrm{Fe2}\ndash \mathrm{O}\rangle $ 
of 2.082~\AA{} for SrMg$_{2}$Fe(PO$_{4}$)$_{3}$ and
2.096~\AA{} for BaMg$_{2}$Fe(PO$_{4}$)$_{3}$. 

Finally, for each compound, the A cation (Sr$^{2+}$ or Ba$^{2+}$) is
surrounded by eight O$^{2-}$ ions with a distance A--O ranging from
2.642(1)~\AA{} to 2.674 (1)~\AA{} for SrMg$_{2}$Fe(PO$_{4}$)$_{3}$ and
from 2.715 (1)~\AA{} to 2.766 (1)~\AA{} for
BaMg$_{2}$Fe(PO$_{4}$)$_{3}$. 

In the crystal structure of AMg$_{2}$Fe(PO$_{4}$)$_{3}$ phosphates (A
${=}$ Sr or Ba), (Fe1/Mg1)O$_{6}$ octahedra and P1O$_{4}$ tetrahedra are
connected via common vertices O1 alternately to form linear infinite
chains (Fe1/Mg1)P1O$_{9}$ along the \textit{b} axis
(Figure~\ref{fig1}A), while the octahedra (Mg2/Fe2)O$_{6}$ share the
O2--O2 edge to form dimers (Mg2/Fe2)$_{2}$O$_{10}$. Each dimer
(Mg2/Fe2)$_{2}$O$_{10}$ is linked to the two tetrahedral groups
{P2O}$_{4}$ by an O4--O4 edge to form the entity
(Mg2/Fe2)$_{2}$P2$_{2}$O$_{14}$. Those later entities share the O3
vertices to form sheets (Mg2/Fe2)$_{4}$P2$_{4}$O$_{26}$ parallel to the
(\textit{ac}) plane (Figure~\ref{fig1}B).

Vertices shared between sheets and chains lead to a three-dimensional
framework delimiting two types of tunnels in which the Sr$^{2+}$ or
Ba$^{2+}$ cations are located (Figure~\ref{fig2}).

Exploration of the crystallographic database shows that the structures
of both orthophosphates are similar to structures of the
${\upalpha}$-CrPO$_{4}$ type mentioned in literature such as
SrNi$_{2}$Fe(PO$_{4}$)$_{3}$~\cite{11},
SrCo$_{2}$Fe(PO$_{4}$)$_{3}$~\cite{13},
SrMn$^{\mathrm{II}}_{2}$Mn$^{\mathrm{III}}${(PO}$_{4}$)$_{3}$~\cite{4}, 
BaNi$_{2}$Fe(PO$_{4}$)$_{3}$~\cite{10}, and
BaMn$^{\mathrm{II}}_{2}$Mn$^{\mathrm{III}}$(PO$_{4}$)$_{3}$~\cite{5}.

\section{Conclusion}\label{sec4}

The single crystal X-ray diffraction study of these two new
orthophosphates, SrMg$_{2}$Fe(PO$_{4}$)$_3$ and
BaMg$_{2}$Fe(PO$_{4}$)$_3$ showed that these compounds
crystallize in an orthorhombic {system} (\textit{Imma} space group)
with unit cell {parameters} $a = 10.3998$ (2)~\AA{},  $b = 13.2000$
(2)~\AA{}, $c = 6.5364$ (1)~\AA{} for the strontium compound and $a =
10.4996$ (2)~\AA{}, $ b = 13.2696$ (1)~\AA{}, $c = 6.6330$ (2)~\AA{}
for the barium composition. Their structures are isotype to
${\upalpha}$-CrPO$_{4}$. The crystal structure of both compounds is
composed of MgO$_{6}$ \mbox{octahedra}, FeO$_{6}$ octahedra, and PO$_{4}$
tetrahedra. The sharing of vertices between those polyhedra leads to a
three-dimensional network delimiting hexagonal channels {that} are
occupied by Ba$^{2+}$ or Sr$^{2+}$ cations. 


\section*{CRediT authorship contribution statement}

\textbf{Ahmed Ould Saleck:} Investigation, Writing---Original draft,
Writing---Review \& editing.

\noindent
\textbf{Claudine Follet-Houttemane:} Investigation, Writing---Original
draft, Writing---Review \& editing.

\noindent
\textbf{Cyrille Albert-Mercier:} Investigation, Writing---Original
draft, Writing---Review \& editing.

\noindent
\textbf{Lahcen El Ammari:} Formal analysis, Writing---Original draft,
Writing---Review \& editing.

\noindent
\textbf{Mohamed Saadi:} Formal analysis, Writing---Original draft,
Writing---Review \& editing.

\noindent
\textbf{Abderrazzak Assani:} Formal analysis, Writing---Original draft,
Writing---Review \& editing.

\section*{Declaration of interests}

The authors do not work for, advise, own shares in, or receive funds
from any organization that could \mbox{benefit} from this article, and
have declared no affiliations other than their research organizations.

\section*{Data availability} 

All the data generated or analyzed during this study are included in
this published article. 

The data can be obtained free of charge from the Cambridge
Crystallographic Data Centre at
\url{http://www.ccdc.cam.ac.uk/structures}  with deposition number CCDC
2454547 for BaMg$_{2}$Fe(PO$_{4}$)$_{3}$ and CCDC 2454549 for
SrMg$_{2}$Fe(PO$_{4}$)$_{3}$.

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\refinput{crchim20250453-reference.tex}

\end{document}

