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Eur. J. Mineral., 36, 417–431, 2024
https://doi.org/10.5194/ejm-36-417-2024
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the Creative Commons Attribution 4.0 License.
Compressibility and thermal expansion of
magnesium phosphates
Catherine Leyx1, Peter Schmid-Beurmann2, Fabrice Brunet3, Christian Chopin1, and Christian Lathe4
1Laboratoire de Géologie, École normale supérieure–CNRS UMR8538, Université PSL, Paris, 75005, France
2Institut für Mineralogie, Universität Münster, 48194 Münster, Germany
3ISTerre, Univ. Grenoble Alpes, USMB, CNRS, IRD, UGE, Grenoble, 38048 CEDEX 9, France
4GeoForschungsZentrum Potsdam, 14473 Potsdam, Germany
Correspondence: Peter Schmid-Beurmann (psb@uni-muenster.de, psb48@yahoo.com)
Received: 13 August 2023 – Revised: 19 January 2024 – Accepted: 1 March 2024 – Published: 17 May 2024
Abstract. The ambient-temperature compressibility and room-pressure thermal expansion of two Mg3(PO4)2
polymorphs (farringtonite =Mg3(PO4)2-I, with 5- and 6-fold coordinated Mg, and chopinite =“Mg-
sarcopside” =[6]Mg3(PO4)2-II), three Mg2PO4OH polymorphs (althausite, hydroxylwagnerite and ε-
Mg2PO4OH, all with [5]Mg and [6]Mg) and phosphoellenbergerite ([6]Mg) were measured on synthetic powders
using a synchrotron-based multi-anvil apparatus to 5.5GPa and a laboratory high-temperature diffractometer,
with whole-pattern fitting procedures. Bulk moduli range from 64.5 GPa for althausite to 88.4 GPa for hydrox-
ylwagnerite, the high-pressure Mg2PO4OH polymorph. Chopinite, based on an olivine structure with ordered
octahedral vacancies (K0=81.6 GPa), and phosphoellenbergerite, composed of chains of face-sharing octahe-
dra (K0=86.4 GPa), are distinctly more compressible than their homeotypical silicate (127 and 133 GPa, re-
spectively). The compressibility anisotropy is the highest for chopinite and the lowest for phosphoellenbergerite.
First-order parameters of quadratic thermal expansions range from v1=2.19 ×10−5K−1for ε-Mg2PO4OH to
v1=3.58 ×10−5K−1for althausite. Phosphates have higher thermal-expansion coefficients than the homeo-
typical silicates. Thermal anisotropy is the highest for farringtonite and the lowest for hydroxylwagnerite and
chopinite. These results set the stage for a thermodynamic handling of phase-equilibrium data obtained up to
3 GPa and 1000 °C in the MgO–P2O5–H2O and MgO–Al2O3–P2O5–H2O systems.
1 Introduction
Magnesium phosphates may be of industrial interest – as
binder in refractories and mortars, as rapid-setting cements,
in 3D printing, and in the fertiliser industry – but are also
of medical interest as a constituent of human urinary stones
(e.g. Fang et al., 2022; Haque and Chen, 2019; Song and Li,
2021; Maurice-Estepa et al., 1999). As rock-forming min-
erals, although less common than other phosphates like ap-
atite or monazite, Mg-phosphates play an important role
in late-stage metasomatic processes around alkaline intru-
sive rocks (as shown by spectacular veins of bobierrite,
Mg3(PO4)2·8H2O, and kovdorskite, Mg2PO4OH ·3H2O,
on the Kola Peninsula, e.g. Liferovich et al., 2000); they are
also potential petrological indicators in metamorphic rocks
owing to their numerous polymorphic relations.
Indeed, early synthesis work has revealed five poly-
morphs of Mg2PO4OH (labelled αto ε; Raade, 1990)
and three polymorphs of Mg3(PO4)2(I to III, Nord and
Kierkegaard, 1968; Berthet et al., 1972; and Jaulmes et al.,
1997, respectively). Experimental phase-equilibrium stud-
ies (Brunet and Vielzeuf, 1996; Brunet et al., 1998; Leyx
et al., 2002; Leyx, 2004) have explored the relations of
the Mg3(PO4)2polymorphs with four of the Mg2PO4OH
polymorphs and the mineral phosphoellenbergerite, ideally
Mg14(PO4)6(HPO4)2(OH)6. The Mg3(PO4)2polymorphs in-
clude a low-pressure one (I), the mineral farringtonite found
in meteorites, and two high-pressure forms: (II), the Mg ana-
logue of the pegmatite mineral sarcopside, referred to as
“Mg-sarcopside” until it was discovered in nature as the min-
eral chopinite (Grew et al., 2007), and (III), the synthetic
Published by Copernicus Publications on behalf of the European mineralogical societies DMG, SEM, SIMP & SFMC.
418 C. Leyx et al.: Compressibility and thermal expansion of magnesium phosphates
high-pressure and high-temperature polymorph (Jaulmes et
al., 1997). The phase transitions and the high-temperature
behaviour of these three polymorphs were studied using syn-
chrotron radiation and Raman spectroscopy (Hu et al., 2022).
The polymorphs of Mg2PO4OH include the low-pressure
and high-temperature form ε-Mg2PO4OH; the intermediate-
pressure minerals holtedahlite (γ) and althausite (δ); and
hydroxylwagnerite (β), the hydroxyl analogue of wagner-
ite Mg2PO4F. Hydroxylwagnerite and phosphoellenbergerite
turned out to be high-pressure phases, actually encoun-
tered in ultrahigh-pressure metamorphic rocks (Chopin et al.,
2014; Brunet et al., 1998).
The dearth of thermodynamic data even in a simple sys-
tem like MgO–P2O5–H2O made the extraction of thermo-
dynamic properties (entropy, enthalpy of formation) from
the phase-equilibrium data an obvious target, this all the
more after calorimetric work on ε-Mg2PO4OH (Leyx et al.,
2005) and lazulite, MgAl2(PO4)2(OH)2(Brunet et al., 2004).
Given the broad pressure–temperature (P–T) range of the
phase-equilibrium experiments, performed at up to 3 GPa
and 1000 °C, knowledge of compressibility and thermal ex-
pansion for the relevant phases was a requirement for the
thermodynamic analysis of the experimental results. How-
ever, volume-property data for magnesium aluminium phos-
phate minerals are scanty: the few minerals concerned were
berlinite, the AlPO4analogue of quartz (Troccaz et al., 1967;
Sowa et al., 1990); farringtonite, Mg3(PO4)2-I (Schmid-
Beurmann et al., 2007); and chopinite, Mg3(PO4)2-II (Hu et
al., 2022). On such a narrow and structurally peculiar basis,
it proved hazardous to assume average compressibility and
thermal-expansion values for magnesium phosphates – or for
given structural groups of phosphates, as tentatively done for
silicates by Holland and Powell (1985) in their early thermo-
dynamic database. Indeed, although they all are orthophos-
phates, the relevant Mg-phosphates show a variety of struc-
tural types (Table 1): from the relatively open structures of
farringtonite and ε-Mg2PO4OH with 5- and 6-fold coordi-
nated Mg and packing efficiencies near 19–20 Å3per oxygen
to more densely packed phases (near 18 Å3per oxygen) like
althausite and hydroxylwagnerite with again 5- and 6-fold
coordinated Mg to compact structures (≤18 Å3per oxygen)
like chopinite with Mg in edge-sharing octahedra and phos-
phoellenbergerite with Mg in face-sharing octahedra.
The unknown behaviour of this structural variety
was the incentive for the present study, which reports
room-temperature compressibility measurements and room-
pressure thermal-expansion data obtained on powders of
synthetic farringtonite, chopinite, althausite, hydroxylwag-
nerite (referred to as OH-wagnerite in the following), ε-
Mg2PO4OH and phosphoellenbergerite (P-ellenbergerite in
the following).
2 Experimental techniques
2.1 Sample synthesis and characterisation
Farringtonite (=Mg3(PO4)2-I), chopinite (=“Mg-
sarcopside” =Mg3(PO4)2-II), ε-Mg2PO4OH, althausite,
OH-wagnerite and P-ellenbergerite were synthesised from
stoichiometric mixtures of MgO (Alfa Aesar, 99.95%, fired
at 1300 °C before weighing) added to NH4H2PO4(Sigma-
Aldrich, 99.999 %), reacted with water and heated at 600 °C
for 2 h (see Brunet et al., 1998). The mixtures were enclosed,
with 10 wt % deionised water for hydroxy-Mg-phosphate
synthesis and only water traces for anhydrous Mg-phosphate
synthesis, in gold capsules of 3 or 4 mm outer diameter,
sealed by arc welding.
Farringtonite and ε-Mg2PO4OH were synthesised in ex-
ternally heated Tuttle-type cold-seal pressure vessels (2d
at 550 MPa, 1000 °C, and 2 months at 60 MPa, 620 °C, re-
spectively); the other higher-pressure phases were synthe-
sised in a piston-cylinder apparatus, using a low-friction
1/2 in. (1.27 cm) diameter NaCl assembly (2 d at 2.2 GPa,
800 °C, for chopinite; at 1.2 GPa, 850 °C, for althausite; at
2.5 GPa, 850°C, for OH-wagnerite; and at 2GPa, 750°C, for
P-ellenbergerite).
Synthetic products were characterised by X-ray diffrac-
tion (cf. Sect. 2.3, “High-temperature X-ray diffraction”). All
the samples were single-phase except the chopinite sample
that contained traces of OH-wagnerite in spite of repeated
synthesis attempts. Upon heating, the althausite batch used
for thermal-expansion measurements also revealed traces of
OH-wagnerite which had not been detected before.
2.2 High-pressure X-ray diffraction
In situ high-pressure X-ray diffraction experiments were car-
ried out using a cubic multi-anvil high-pressure apparatus of
the Max-80 type, installed at the DORIS III storage ring of
HASYLAB (DESY, Hamburg, Germany). Pressure was gen-
erated quasi-isostatically by six tungsten-carbide anvils with
6 mm ×6 mm truncation in a cubic arrangement. Details of
the apparatus were given by Peun et al. (1995).
The diffraction measurements were performed in energy-
dispersive mode using a white synchrotron beam of
100 µm ×100 µm dimension at a fixed 2θangle, determined
for each run under ambient conditions from the diffraction
patterns of NaCl obtained at the top, in the middle and at
the bottom of the assembly. A radioactive 241Am source pro-
vided X-ray fluorescence Kα and Kβ lines from Rb, Mo, Ag,
Ba and Tb targets for energy calibration of the Ge solid-state
detector.
The sample assembly and the experimental technique were
similar to that of Grevel et al. (2000a). The cell assembly
contained two powdered samples sandwiched by pellets of
NaCl or of a NaCl–BN mixture; each sample was mixed with
vaseline. Grevel et al. (2000b) have shown that this procedure
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C. Leyx et al.: Compressibility and thermal expansion of magnesium phosphates 419
Table 1. Crystallographic properties of synthetic Mg-phosphates.
ε-Mg2PO4OH Althausite
δ-Mg2PO4OH
OH-wagnerite
β-Mg2PO4OH
Farringtonite
Mg3(PO4)2-I
Chopinite
Mg3(PO4)2-II
P-ellenbergerite
Mg13.8P8O38H8.4
Space group Pnma Pnma P21/c P 21/n P 21/a P 63mc
a(Å) 8.239 (1) 8.264 (1) 9.656 (3) 7.5957 (8) 10.25 (2) 12.426 (2)
b(Å) 6.135 (1) 6.065 (1) 12.859 (3) 8.2305 (5) 4.72 (1) 12.426 (2)
c(Å) 7.404 (1) 14.438 (3) 12.069 (4) 5.0775 (5) 5.92 (1) 5.0059 (9)
β(°) 108.49 (3) 94.05 (1) 90.9 (1)
Z4 8 16 2 2 1
V(Å3) 374.24 (8) 723.6 (2) 1421.2 (8) 316.63 (1) 286.37 (2) 669.4 (2)
Density (g cm−3) 2.850 2.951 3.002 2.74 3.05 2.979
Reference Raade and
Rømming
(1986a)
Rømming and
Raade (1980)
Raade and
Rømming
(1986b)
Nord and
Kierkegaard
(1968)
Annersten and
Nord (1980)
Amisano-Canesi
(1994)
results in hydrostatic high-pressure conditions. The pressure
was measured in the middle and at the ends of the cell
using the NaCl or NaCl–BN pellets as calibrants (Decker,
1971). Pressure gradients (due to internal stress) were found
to reach 0.1 to 0.2 GPa within the cell and are therefore the
major source of pressure uncertainty (Table 2), as compared
to those introduced by the refinement of NaCl cell volume
(around 10−3GPa) and by the determination of the 2θangle
(10−2to 5 ×10−2GPa).
The externally applied load was increased in most exper-
iments by steps of 10 up to 80 t, which corresponds to sam-
ple pressures of 5–5.5 GPa. Diffraction measurements were
performed after each loading increment, after a waiting time
of at least 10 min which had enabled the sample pressure
to reach a steady state. The first, “zero-load” measurement
was made after the anvils were brought into contact with the
cell, as indicated by an incipient rise of the load value, which
was then left to relax. Depending on the extent of this re-
laxation, the zero-load pressure value measured in situ may
depart more or less from the actual room pressure.
Several experimental runs under isothermal conditions at
ambient temperature (Table 2) were carried out for each
studied mineral (chopinite, althausite, OH-wagnerite and P-
ellenbergerite) to check the reproducibility and the con-
sistency of the measurements made over two campaigns
(September 2001 and May 2002, R and S run series in Ta-
ble 2, respectively).
2.3 High-temperature X-ray diffraction
High-temperature diffraction data were collected on a 17 cm
vertical Philips PW1050/25 goniometer in angle-dispersive
mode, using Ni-filtered CuKα radiation, at the Laboratoire
de Cristallochimie du Solide (Université Pierre-et-Marie-
Curie, Paris, France), employing a platinum-alloy plate as the
heating sample holder. Samples were ground, mixed with a
little xylene, spread on the Pt plate to form a thin continuous
film and then briefly heated to around 100 °C, at which tem-
perature the xylene evaporates, leaving a thin smooth pow-
der. The heating device and attached thermocouple used dur-
ing data collection were calibrated in situ by bracketing var-
ious structural phase transitions (KNO3(α→β), 139 °C;
BaCO3(γ→β), 811 °C) and melting reactions (KNO3,
337 °C; KCl, 776 °C; NaCl, 801 °C). Nominal temperatures
were corrected using the calibration; the corrected temper-
atures reported below are believed accurate to within 1%
above 200°C, within 2 °C below.
The diffraction patterns were recorded over the 20° <
2θ < 86° range. Four scans were obtained at each temper-
ature and merged, five at room temperature so as to im-
prove the counting statistics for the standard-volume de-
termination. Alloy peaks were not taken into account dur-
ing the refinement by ignoring some 2θintervals ([39, 41],
[45.5, 47.5], [67, 69.5] and [80.5, 83] at room temperature).
The data were collected up to 900 °C for anhydrous phases
and up to 400, 500 or 600 °C for hydrous phases, before or
until incipient dehydration.
2.4 Whole-pattern refinements
The lattice parameters of the samples were determined
by the Rietveld method. Two different programs were run
to refine the crystallographic and instrumental parameters:
GSAS (Larson and Von Dreele, 1988) for the high-pressure
diffraction patterns obtained by energy-dispersive methods
(Sect. 2.2) and the DBW program of Young et al. (1995) for
the high-temperature diffraction patterns, obtained in angle-
dispersive mode (Sect. 2.3).
Available literature data were used as input values for cell
parameters (Table 1) and atomic positions; the latter were
kept constant throughout the refinement procedure. The re-
fined data set included the cell parameters, the overall scale
factor, a profile shape factor, coefficients of the FWHM (full
width at half maximum) Caglioti’s polynomial and back-
ground parameters. Given the number of atoms in the unit
cells and the quality of our diffraction patterns, we did not
https://doi.org/10.5194/ejm-36-417-2024 Eur. J. Mineral., 36, 417–431, 2024
420 C. Leyx et al.: Compressibility and thermal expansion of magnesium phosphates
Table 2. Unit-cell parameters of studied Mg-phosphates as a function of pressure at ambient temperature.
P(GPa) a(Å) b(Å) c(Å) β(°) V(Å3)
Chopinite
a0,b0,c0,V010.180 4.478 5.90 285.13
R08, September 2001, 2θ=7.8634(75)
0.03 (9) 10.1601 (67) 4.7418 (29) 5.9154 (34) 90.05 (10) 284.98 (21)
0.03 (9) 10.1591 (66) 4.7411 (29) 5.9162 (34) 90.05 (10) 284.95 (21)
0.54 (13) 10.1667 (78) 4.7386 (26) 5.8815 (43) 90.14 (10) 283.34 (21)
0.54 (13) 10.2131 (77) 4.7400 (27) 5.8769 (43) 89.45 (7) 284.49 (21)
1.35 (16) 10.1843 (76) 4.7217 (25) 5.8503 (39) 89.22 (7) 281.30 (21)
1.87 (20) 10.1993 (86) 4.7208 (26) 5.8160 (43) 89.47 (11) 280.03 (21)
2.64 (23) 10.1794 (80) 4.7122 (32) 5.7767 (45) 89.50 (10) 277.08 (29)
3.20 (14) 10.1060 (79) 4.7134 (27) 5.8065 (37) 88.92 (6) 276.54 (23)
3.73 (12) 10.1008 (94) 4.7031 (32) 5.7915 (44) 88.88 (7) 275.07 (28)
4.18 (11) 10.0149 (80) 4.6877 (28) 5.8023 (42) 88.67 (6) 272.33 (26)
4.63 (12) 9.9807 (104) 4.6730 (37) 5.7869 (57) 88.64 (9) 269.82 (34)
Scale factors 1.0046 (14) 1.00033 (62) 1.0049 (10) 1.00157 (96)
R11, September 2001, 2θ=7.8622(63)
0.03 (8) 10.1809 (74) 4.7539 (35) 5.8969 (32) 89.87 (8) 285.40 (22)
4.28 (11) 10.0250 (49) 4.6876 (33) 5.7794 (24) 88.72 (4) 271.52 (17)
5.29 (11) 10.0055 (99) 4.6697 (85) 5.7413 (35) 88.97 (9) 268.20 (34)
Scale factors 1.0032 (22) 1.0011 (13) 0.9993 (14) 0.9993 (15)
S06, May 2002, 2θ=5.8055(13)
0.01 (2) 10.1852 (50) 4.7476 (16) 5.8943 (21) 89.29 (4) 285.00 (14)
1.07 (2) 10.1476 (47) 4.7199 (16) 5.8704 (26) 89.11 (4) 281.13 (15)
1.89 (4) 10.1196 (49) 4.7113 (17) 5.8528 (26) 89.08 (4) 279.00 (15)
2.93 (10) 10.0912 (49) 4.6932 (15) 5.8234 (24) 88.92 (3) 275.75 (15)
3.81 (5) 10.0606 (49) 4.6817 (16) 5.7994 (24) 88.77 (3) 273.10 (15)
4.57 (5) 10.0284 (49) 4.6800 (16) 5.7818 (32) 88.65 (3) 271.28 (17)
Scale factors 1.0039 (13) 0.99889 (53) 1.00074 (79) 0.99972 (65)
Althausite
a0,b0,c0,V08.2945 6.0881 14.4132 727.84
S02, May 2002, 2θ=5.7994(18)
0.0001 (110) 8.2925 (54) 6.0664 (33) 14.4153 (17) 725.18 (50)
1.05 (2) 8.2165 (35) 6.0608 (19) 14.3816 (31) 717.19 (35)
2.01 (4) 8.1847 (56) 6.0211 (28) 14.3091 (37) 705.16 (55)
2.69 (8) 8.1903 (57) 6.0114 (29) 14.2780 (34) 702.99 (58)
2.69 (8) 8.1725 (59) 6.0001 (30) 14.2566 (33) 699.08 (58)
Scale factors 0.9991 (18) 1.0012 (19) 1.00053 (40) 0.9993 (22)
S04, May 2002, 2θ=5.8048(63)
0.01 (4) 8.2965 (41) 6.1098 (20) 14.4111 (51) 730.50 (43)
0.99 (4) 8.2206 (41) 6.0438 (21) 14.3744 (35) 714.18 (41)
2.00 (5) 8.1731 (54) 6.0261 (30) 14.3108 (35) 704.84 (54)
3.16 (4) 8.1738 (66) 6.0052 (40) 14.2445 (38) 699.20 (66)
Scale factors 0.9992 (18) 1.0019 (18) 1.00062 (72) 1.0001 (26)
Eur. J. Mineral., 36, 417–431, 2024 https://doi.org/10.5194/ejm-36-417-2024
C. Leyx et al.: Compressibility and thermal expansion of magnesium phosphates 421
Table 2. Continued.
P(GPa) a(Å) b(Å) c(Å) β(°) V(Å3)
OH-wagnerite
a0,b0,c0,V09.6732 12.8600 12.0921 1426.91
S01, May 2002, 2θ=5.7959(23)
0.02 (3) 9.6672 (40) 12.8548 (23) 12.0965 (26) 108.43 (2) 1426.16 (40)
1.18 (6) 9.6284 (45) 12.8128 (24) 12.0470 (29) 108.58 (2) 1408.75 (44)
2.03 (2) 9.5907 (52) 12.7674 (25) 12.0078 (32) 108.60 (3) 1393.51 (46)
3.21 (4) 9.5266 (63) 12.7225 (29) 11.9820 (39) 108.45 (3) 1377.63 (51)
3.87 (3) 9.5014 (59) 12.6822 (28) 11.9533 (35) 108.37 (3) 1366.97 (49)
4.85 (14) 9.4860 (49) 12.6509 (26) 11.9167 (29) 108.45 (3) 1356.53 (45)
Scale factors 0.9999 (6) 0.9997 (3) 0.9999 (3) 0.9987 (7)
S05, May 2002, 2θ=5.8091(8)
0.01 (1) 9.6792 (87) 12.8651 (42) 12.0876 (56) 108.47 (5) 1427.66 (86)
1.18 (1) 9.6144 (58) 12.8164 (28) 12.0453 (36) 108.40 (3) 1408.35 (53)
1.99 (4) 9.5616 (65) 12.7938 (29) 12.0133 (39) 108.35 (3) 1394.85 (54)
2.98 (1) 9.5295 (63) 12.7546 (29) 11.9856 (38) 108.39 (3) 1382.43 (53)
4.01 (3) 9.4880 (60) 12.7011 (29) 11.9511 (37) 108.32 (3) 1368.62 (52)
4.77 (3) 9.4870 (63) 12.6749 (31) 11.9451 (39) 108.50 (3) 1362.10 (58)
5.57 (4) 9.4571 (65) 12.6535 (31) 11.9062 (40) 108.51 (3) 1351.03 (57)
Scale factors 0.9993 (8) 1.0012 (4) 1.0001 (4) 1.0004 (7)
P-ellenbergerite
a0,c0,V012.4176 5.0037 668.18
R07, September 2001, 2θ=7.8760(28)
0.01 (3) 12.4051 (9) 4.9994 (6) 666.27 (9)
1.06 (4) 12.3720 (9) 4.9750 (6) 659.49 (9)
1.78 (5) 12.3410 (10) 4.9571 (7) 653.83 (10)
2.44 (5) 12.3194 (9) 4.9444 (8) 649.86 (10)
3.14 (14) 12.2937 (9) 4.9316 (7) 645.49 (10)
3.80 (10) 12.2762 (10) 4.9193 (7) 642.03 (11)
4.43 (15) 12.2503 (10) 4.9074 (8) 637.79 (11)
4.99 (13) 12.2342 (10) 4.8975 (8) 634.83 (12)
5.45 (2) 12.2150 (11) 4.8884 (9) 631.67 (13)
Scale factors 0.9996 (2) 0.9991 (3) 0.9985 (5)
R10, September 2001, 2θ=7.8609(66)
0.02 (6) 12.4192 (8) 5.0026 (5) 668.21 (8)
1.50 (11) 12.3507 (11) 4.9670 (8) 656.15 (11)
3.48 (10) 12.2732 (13) 4.9235 (11) 642.27 (16)
5.26 (15) 12.2091 (15) 4.8904 (14) 631.32 (14)
Scale factors 0.9998 (4) 0.9995 (3) 0.9992 (10)
S01, May 2002, 2θ=5.7959(23)
0.02 (3) 12.4284 (19) 5.0091 (11) 670.06 (18)
1.19 (4) 12.3778 (18) 4.9864 (11) 661.62 (18)
2.06 (6) 12.3387 (20) 4.9637 (12) 654.44 (19)
3.20 (4) 12.3052 (19) 4.9473 (12) 648.75 (19)
3.88 (1) 12.2672 (17) 4.9294 (11) 642.42 (16)
4.67 (15) 12.2411 (14) 4.9146 (9) 637.77 (14)
Scale factors 1.0005 (3) 1.0017 (2) 1.0028 (6)
Note: values in brackets are 1σfor cell parameters and refer to the last decimal place. The terms a0,b0,c0and V0denote
the mean values for the lattice parameters and unit-cell volume under the lowest pressure of the different measurement runs
of each compound. The scale factors resulted from the fit using the Birch–Murnaghan equation of state (EoS) of second
order in EosFit7c 7.6.
https://doi.org/10.5194/ejm-36-417-2024 Eur. J. Mineral., 36, 417–431, 2024
422 C. Leyx et al.: Compressibility and thermal expansion of magnesium phosphates
refine the isotropic displacement parameters independently
but refined a common Biso variable for all the oxygen atoms
and another variable for the cations. The March–Dollase
preferred-orientation factor was also refined for chopinite,
ε-Mg2PO4OH, and althausite, which showed strong orien-
tation effects. When the samples were multi-phase (i.e. with
traces of a parasite compound), the cell parameters, the scale
factors, the profile shape factors and the FWHM polynomial
coefficients of both phases were refined simultaneously.
For the high-pressure experiments, the NaCl cell param-
eter was refined from the whole diffraction pattern for each
pressure condition and served as the input value to determine
pressure from Decker’s equation of state (EoS) (Decker,
1971).
For the high-temperature experiments, carried out on a
Bragg–Brentano diffractometer, a potential offset of the
2θzero point had to be considered. We first measured
diffraction patterns on the pure compounds and, follow-
ing Launay et al. (2001), refined the instrumental zero
shift simultaneously with the crystal parameters. The re-
sults at room temperature were then compared with those
obtained under the same conditions with the same com-
pounds mixed with α-Al2O3as internal standard. Refine-
ments indicated that the differences in the lattice parame-
ters were negligible (e.g. P-ellenbergerite with α-Al2O3:a=
12.426(5)Å, c=5.009(2)Å; P-ellenbergerite without α-
Al2O3:a=12.426(9),c=5.008(4)Å). Therefore, we chose
to go on performing the measurements without internal stan-
dard, refining the 2θ-zero shift at room temperature (e.g. P-
ellenbergerite: zero shift = −0.185(9)°2θ) and keeping this
value of the shift for the high-temperature refinements. The
sample displacement (due to holder expansion) was then re-
fined at each temperature step and showed a smooth varia-
tion with increasing temperature (e.g. from 0.126 at 101 °C
to 0.135 at 405 °C for P-ellenbergerite).
3 Results and discussion
3.1 Compressibility data
The experimental high-pressure data are presented in Figs. 1
to 3. The unit-cell parameters contained in Table 2 were
used to determine the room-temperature compressibility of
chopinite, althausite, OH-wagnerite and P-ellenbergerite.
The strong orientation effects along the (001) perfect cleav-
age of althausite, combined with the small number of peaks
in its diffraction patterns, prevented us from refining the al-
thausite cell parameters for pressures higher than 3.2 GPa.
We did not merge the several data sets into a single one for
each phase because the measured volumes at room pressure
(and temperature) differ by one or more cubic ångströms, e.g.
by 4 Å3in the case of P-ellenbergerite (Table 2). This indi-
cates that the P–Vdata of different runs have their own sys-
tematic error. This would bias the results if a common V0
Figure 1. Compressibility data of synthetic chopinite
(=Mg3(PO4)2-II =“Mg-sarcopside”), compared to the homeotyp-
ical forsterite. Error bars are from Table 2.
Figure 2. Compressibility data of Mg2PO4OH polymorphs. Error
bars are from Table 2.
were fitted to a combined data set. Therefore we chose to use
EosFit7c (Angel et al., 2014) version 7.6, which allows one
to apply individual “scale factors” to the data set of each mea-
surement run in combination with a fixed V0. The latter was
calculated as the mean value of the measured volume data of
the individual runs at room pressure and temperature. Such
a procedure is equivalent to a fit with individual V0values
of each data set. The volume data were weighted according
to the “effective variance method” (Orear, 1982) proposed by
Angel (2000): w=σ−2, where σ2=σ2
P+σ2
V·[(∂ P /∂V )T]2.
A Birch–Murnaghan equation of state truncated at second-
order in the energy (K0
0set to 4; Angel, 2000) was fitted to
the volume data by means of a weighted least-squares re-
gression: P=3/2K0[(V0/V )7/3−(V0/ V )5/3], where Vis
the unit-cell volume at high pressure P(in GPa), V0the
volume at ambient pressure and K0the bulk modulus. The
data scatter and the need to merge data from different ex-
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C. Leyx et al.: Compressibility and thermal expansion of magnesium phosphates 423
Figure 3. Compressibility data of synthetic phosphoellenbergerite,
compared to the homeotypical silicate. Error bars are from Table 2.
periments and refine scale factors made it impossible to re-
liably refine a third-order Birch–Murnaghan EoS. For in-
stance, application of a third-order instead of a second-order
EoS to the chopinite data results in a slightly lower w-χ2of
2.67 instead of 2.78 but in an unrealistic negative value for
K0= −0.6(2). For the other compounds, the w-χ2was in-
creased or unchanged using a third-order EoS (althausite and
P-ellenbergerite) and the uncertainty in the bulk modulus K0
was dramatically increased (althausite, OH-wagnerite and P-
ellenbergerite). Therefore we decided to use a second-order
Birch–Murnaghan EoS for the fits.
From the least-squares fit, the bulk moduli (Table 3)
are found to range between 64.5(62) GPa (althausite) and
88.4(19) GPa (OH-wagnerite). They show the gross correla-
tion that can be expected with the oxygen packing efficiency,
the more compact structures being less compressible. Com-
pared to other phosphate minerals, magnesium phosphates
are less compressible than berlinite (K0∼41 GPa, calculated
from Sowa et al., 1990) but more compressible than hydrox-
ylapatite (K0=97.5 GPa; Brunet et al., 1999), monazite-
(La) or xenotime (K0=144(2)and 149(2) GPa, respec-
tively; Lacomba-Perales et al., 2010). Besides, whereas the
silicates forsterite and ellenbergerite, homeotypical with
chopinite and P-ellenbergerite, respectively, are relatively in-
compressible (K0(forsterite)=127.4 GPa – Kroll et al., 2014;
K0(ellenbergerite)=133 GPa – Comodi and Zanazzi, 1993a)
and display 3 % average reduction in their molar vol-
ume at 5.0 GPa, chopinite and P-ellenbergerite are more
compressible with about 5 % volume reduction at 5.0 GPa
(K0(chopinite)=81.6 GPa; K0(P-ellenbergerite)=86.4 GPa). The
25 % octahedral vacancies in chopinite with respect to
forsterite (Berthet et al., 1972) may well account for its
higher compressibility. Indeed, in the olivine-type phosphate
series triphylite–heterosite, LiFe2+PO4to Fe3+PO4, the
50 % octahedral vacancies result in a drop of K0from 106 to
61 GPa (Dodd, 2007, confirming the first-principle modelling
Figure 4. Thermal-expansion data of synthetic farringtonite and of
synthetic chopinite compared to the homeotypical forsterite. Error
bars are from Table 3.
of Maxisch and Ceder, 2006). However, this line of argument
alone does not hold for the ellenbergerite series, in which
the number of vacancies (in the octahedral single chain) is
slightly lower in the softer phosphate (0.2 to 0.3“atoms” pfu;
Brunet et al., 1998; Brunet and Schaller, 1996) than in the
stiffer silicate (0.7 to 1.0 “atoms” pfu; Chopin et al., 1986).
For each of the Mg-phosphates studied, the pressure de-
pendence of unit-cell volumes normalised to Vref =V0·scale
factor was also fitted using a Berman-type polynomial
(Brown et al., 1989) for specific thermodynamic applications
(Table 3). We chose a second-order regression (except for
chopinite, first-order, v4being not significant): V (P )/Vref =
1+v3(P −1)+v4(P −1)2;Pis expressed in bars, and Vref
is the mean value of the room-pressure volumes V0of the
different measurement runs multiplied by the refined scale
factor derived from the fit using EosFit7 7.6. The v3and v4
Berman coefficients are listed in Table 3.
3.2 Thermal behaviour and expansion data
The experimental high-temperature data are presented in Ta-
ble 4 and Figs. 4 to 6. For the hydrous phases, the measure-
ments were limited by the breakdown of the minerals at high
temperature: both althausite and ε-Mg2PO4OH began to al-
ter and to form the anhydrous-phase farringtonite at 700 °C.
The high-pressure phases OH-wagnerite and P-ellenbergerite
showed no evidence of decomposition at 500 and 400°C, re-
spectively.
The unit-cell volumes all smoothly increase with a
parabolic dependence on temperature. The temperature de-
pendence of the unit-cell volume has been fitted to a Berman
second-order polynomial (Brown et al., 1989; Berman, 1988)
for each Mg-phosphate: V (T ) =V0(1+v1(T −T0)+v2(T −
T0)2), where T0is the standard temperature (293.15 K)
and V0the standard volume. The fits were done using
EosFit7c 7.6 with the implemented Berman EoS V0(1+
https://doi.org/10.5194/ejm-36-417-2024 Eur. J. Mineral., 36, 417–431, 2024
424 C. Leyx et al.: Compressibility and thermal expansion of magnesium phosphates
Table 3. Parameters of Berman thermal-expansion and compressibility functions, bulk moduli, and packing efficiencies for studied Mg-phosphates and their silicate equivalents (in
italics).
Thermal expansion Compressibility Bulk modulus Packing efficiency
v1×105
(K−1)
v2×109
(K−2)
w-χ2v3×106
(bar−1)
v4×1012
(bar−2)
R2K0
(GPa)
(Å3per oxygen)
ε-Mg2PO4OH 2.19(5) 11.4(7) 0.86 18.7
Althausite 3.58(26) – 12.2 −1.75(6)15(2) 0.962 64.5(62) 18.1
OH-wagnerite 2.42(32) 10(7) 2.10 −1.17(3)3.6(8) 0.996 88.4(19) 17.8
Farringtonite 2.39(5) 9.0(6) 1.68 −1.83(4)
Schmid-Beurmann
et al. (2007)
– 0.994 50(3)
Schmid-Beurmann
et al. (2007)
19.8
Mg3(PO4)2-I 2.85(5)
Hu et al. (2022)
7.4(6)
Hu et al. (2022)
6.58 19.8
Hu et al. (2022)
Mg3(PO4)2-II 3.52(6)
Hu et al. (2022)
8.2(8)
Hu et al. (2022)
3.08 17.8
Hu et al. (2022)
Mg3(PO4)2-III 2.75(7)
Hu et al. (2022)
10(1)
Hu et al. (2022)
0.54 17.6
Hu et al. (2022)
Chopinite 3.51(6) – 0.67 −1.08(1)– 0.992 81.6(18) 17.9
Forsterite 3.04(3)
Kroll et al. (2012)
6.3(3)
Kroll et al. (2012)
0.41 −0.653(3)
Finkelstein et al.
(2014)
0.485(8)
Finkelstein et al.
(2014)
0.999 127.4(2)
Kroll et al. (2014)
130.0(9)
Finkelstein et al.
(2014)
P-ellenbergerite 3.1(2) 20(4) 0.06 −1.13(4)2(1) 0.996 86.4(16) 17.6
Ellenbergerite 1.96(7)
Comodi and
Zanazzi (1993b)
2.90(8)
Amisano-Canesi
(1994)
11(1)
Comodi and
Zanazzi (1993b)
1.13
0.17
−0.74(1)
Comodi and
Zanazzi (1993a)
0.998 133.0(50)
Comodi and
Zanazzi (1993a)
Note: the thermal-expansion parameters v1and v2and the compressibility parameters v3and v4of this work and the mentioned literature were calculated using a Berman-type second-order polynomial (Brown et al., 1989; Berman,
1988) V (T ) =V0(1+v1(T −T0)+v2(T −T0)2+v3(P −P0)+v4(P −P0)2). The v1and v2values were retrieved from a fit using the function V (T ) =V0(1+α0(T −T0)+1/2α1(T −T0)2)implemented in EoSFit7c, where v1=α0
and v2=1/2α1. The v3and v4values were calculated from a fit of V (T ) =V0(1+v3(P −P0)+v4(P −P0)2)using OriginPro 7.5. T0is the standard temperature (293.15 K), V0is the standard volume and P0=1bar. For forsterite, the
thermal-expansion parameters v1and v2were derived from the data presented in Kroll et al. (2012, their Fig. 3) with the exception of the data of Bouhifd et al. (1996) >1200K and the low-temperature data of Kroll et al. (2012). The
bulk moduli were taken from the mentioned literature.
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C. Leyx et al.: Compressibility and thermal expansion of magnesium phosphates 425
Table 4. Unit-cell parameters of studied Mg-phosphates as a function of temperature.
T(°C) a(Å) b(Å) c(Å) β(°) V(Å3)
Farringtonite
a0,b0,c0,V07.6030 (9) 8.235 (2) 5.0788 (3) 317.48 (3)
25 7.6045 (5) 8.2389 (5) 5.0793 (3) 94.097 (4) 317.42 (3)
101 7.6103 (5) 8.2499 (5) 5.0803 (3) 94.122 (4) 318.14 (3)
202 7.6159 (5) 8.2631 (5) 5.0806 (3) 94.139 (4) 318.89 (3)
304 7.6228 (5) 8.2771 (5) 5.0825 (3) 94.168 (4) 319.83 (3)
405 7.6302 (5) 8.2929 (5) 5.0834 (3) 94.194 (4) 320.80 (3)
506 7.6369 (5) 8.3085 (5) 5.0848 (3) 94.218 (4) 321.76 (3)
607 7.6452 (5) 8.3254 (5) 5.0860 (3) 94.260 (4) 322.83 (3)
709 7.6538 (5) 8.3431 (5) 5.0882 (3) 94.298 (4) 324.00 (3)
810 7.6631 (5) 8.3620 (5) 5.0897 (3) 94.347 (4) 325.20 (3)
911 7.6718 (5) 8.3828 (5) 5.0912 (3) 94.395 (4) 326.46 (3)
Chopinite
a0,b0,c0,V010.215 (1) 4.7391 (3) 5.9069 (5) 285.95 (6)
25 10.2154 (8) 4.7393 (4) 5.9066 (4) 89.33 (1) 285.94 (7)
101 10.2237 (8) 4.7426 (4) 5.9128 (4) 89.34 (1) 286.68 (7)
202 10.2346 (9) 4.7473 (4) 5.9209 (4) 89.36 (1) 287.66 (7)
304 10.2466 (9) 4.7521 (4) 5.9274 (4) 89.36 (1) 288.60 (7)
405 10.2587 (9) 4.7581 (4) 5.9367 (4) 89.37 (1) 289.76 (7)
506 10.2760 (13) 4.7619 (6) 5.9422 (7) 89.39 (1) 290.76 (11)
ε-Mg2PO4OH
a0,b0,c0,V08.241 (4) 6.1333 (3) 7.409 (2) 374.70 (3)
25 8.2416 (3) 6.1338 (2) 7.4120 (3) 374.69 (3)
101 8.2456 (3) 6.1362 (2) 7.4186 (3) 375.36 (3)
202 8.2498 (3) 6.1400 (2) 7.4285 (3) 376.28 (3)
304 8.2550 (3) 6.1438 (2) 7.4392 (3) 377.29 (3)
405 8.2601 (4) 6.1471 (2) 7.4524 (3) 378.40 (3)
506 8.2659 (4) 6.1518 (2) 7.4663 (3) 379.66 (3)
607 8.2714 (4) 6.1561 (2) 7.4812 (3) 380.94 (3)
709 8.2777 (5) 6.1601 (3) 7.4966 (5) 382.26 (4)
Althausite
a0,b0,c0,V08.2838 (24) 6.0684 (42) 14.4431 (54) 726.58 (86)
25 8.2858 (24) 6.0741 (15) 14.4459 (22) 727.04 (30)
101 8.2892 (23) 6.0786 (15) 14.4542 (21) 728.30 (29)
202 8.2897 (19) 6.0764 (13) 14.4780 (22) 729.28 (25)
304 8.2901 (35) 6.0816 (20) 14.5212 (24) 732.12 (41)
405 8.2991 (21) 6.1050 (13) 14.5307 (22) 736.21 (27)
506 8.3113 (22) 6.1118 (14) 14.5569 (27) 739.45 (29)
607 8.3101 (17) 6.1212 (11) 14.5665 (29) 740.97 (25)
OH-wagnerite
a0,b0,c0,V09.6706 (12) 12.872 (1) 12.0903 (9) 1427.86 (41)
25 9.6717 (8) 12.8728 (9) 12.0912 (9) 108.461 (4) 1427.91 (32)
101 9.6782 (8) 12.8811 (9) 12.0971 (9) 108.454 (4) 1430.55 (32)
202 9.6859 (9) 12.8928 (11) 12.1071 (10) 108.434 (5) 1434.33 (37)
304 9.6962 (8) 12.9041 (10) 12.1168 (10) 108.430 (4) 1438.30 (35)
405 9.7101 (10) 12.9218 (12) 12.1302 (11) 108.425 (5) 1443.98 (41)
506 9.7179 (10) 12.9314 (12) 12.1374 (11) 108.373 (5) 1447.51 (41)
P-ellenbergerite
a0,c0,V012.4353 (3) 5.011 (1) 671.31 (7)
25 12.4354 (4) 5.0128 (2) 671.32 (8)
101 12.4447 (5) 5.0176 (2) 672.97 (8)
177 12.4548 (5) 5.0231 (2) 674.80 (9)
253 12.4650 (5) 5.0296 (2) 676.78 (9)
329 12.4745 (5) 5.0373 (2) 678.85 (9)
405 12.4844 (6) 5.0465 (3) 681.17 (10)
Note: values in brackets are 1σfor cell parameters and refer to the last decimal place. The terms a0,b0,c0and V0are fitted
values for the lattice parameters and unit-cell volume resulting from the fit using Berman’s (1988) EoS in EoSFit7 7.6.
https://doi.org/10.5194/ejm-36-417-2024 Eur. J. Mineral., 36, 417–431, 2024
426 C. Leyx et al.: Compressibility and thermal expansion of magnesium phosphates
Figure 5. Thermal-expansion data of Mg2PO4OH polymorphs. Er-
ror bars are from Table 4.
Figure 6. Thermal-expansion data of synthetic phosphoellen-
bergerite, compared to the homeotypical silicate. Error bars are
from Table 4.
α0(T −T0)+1/2α1(T −T0)2)using V0as well as α0and α1
as fit parameters. Then the coefficients of the second-order
Berman polynomial are v1=α0and v2=1/2α1. Their val-
ues are reported in Table 3, together with those obtained from
a fit of Hu et al. (2022) data. As can be realised from Fig. 4,
these authors have measured a slightly higher thermal expan-
sion of chopinite =Mg3(PO4)2–II.
Compared to other phosphate minerals, Mg-phosphate
thermal expansions are higher than those of monazite
(v1∼1×10−5K−1; e.g. Perrière et al., 2007), berlin-
ite (v1=1.9×10−5K−1; Troccaz et al., 1967) and hy-
droxylapatite (v1=1.79 ×10−5K−1; Brunet et al., 1999).
They are comparable to the expansion of compact sil-
icates like grossular (v1=2.38 ×10−5K−1) or pyrope
(v1=2.15 ×10−5K−1) (calculated from Thiéblot et al.,
1998) but exceed those of their silicate structural equiva-
lents: v1(chopinite)=3.51 ×10−5K−1> v1(forsterite)=3.04 ×
10−5K−1(calculated from Kroll et al., 2012), and
v1(P-ellenbergerite)=3.1×10−5K−1> v1(ellenbergerite)=1.96×
10−5K−1(calculated from Comodi and Zanazzi, 1993b).
3.3 Anisotropy
The anisotropy of compressibility and thermal expansion
of crystals can generally be described by the eigenvectors
Ev1,2,3of the second-rank tensors representing these prop-
erties (Nye, 1985). The components of the tensors were
determined by temperature- and pressure-dependent X-ray
diffraction measurements of the lattice parameters. The cor-
responding data of the Mg-phosphates and additional miner-
als are compiled in Tables 5 and 6. In the case of orthorhom-
bic and higher-symmetry compounds (Table 5), the eigenvec-
tors Ev1,2,3are oriented parallel to the crystallographic axes
a,band c. Therefore, in these cases the anisotropy of the
corresponding property can be evaluated by determining the
linear expansion αiand the linear moduli Miwith i=a,b,c
along the crystallographic axes. As the linear moduli Mi=
−xi(∂ P /∂xi)Twith xi=a,b,clattice parameter are the
inverse of the linear compressibility βi= −1/xi(∂xi/∂ P )T,
this procedure results directly in diagonalised tensors with
αa=α11,βa=β11 and so on.
The Mivalues were retrieved using EosFit7c 7.6 from the
pressure dependence of the lattice parameters and were cal-
culated in the same way as the bulk moduli K0of the volume
data.
The linear thermal-expansion coefficients αiwere calcu-
lated using the implemented Berman EoS of EosFit7c of
first-order V (T ) =V0(1+α0(T −T0)) using V0as well as
α0as fitting parameters.
In the case of the monoclinic compounds farringtonite,
chopinite and OH-wagnerite, the orientations of the orthog-
onal eigenvectors Ev1,2,3and therefore the axes of the repre-
sentation quadric (Nye, 1985) differ from those of the crys-
tallographic axes. One eigenvector must lie parallel to the
diad axis, which is the baxis in the settings used here. The
other two are oriented within the a–cplane. In order to quan-
tify the anisotropy, the values of the properties along the or-
thogonal eigenvectors were compared. The eigenvalues and
eigenvectors of the tensors of expansion and compressibil-
ity were calculated using the STRAIN routine in EosFit7c
in the range of highest- and lowest-temperature or highest-
and lowest-pressure data for each compound (Tables 2 and
4) under the condition that the eigenvectors are unit vectors.
In Table 6 the elements of the diagonalised tensors are given
together with the orientation of the eigenvectors towards the
nearest crystallographic axis (Tables 5 and 6).
In order to compare our results to the recently pub-
lished lattice parameters of Mg3(PO4)2-I (farringtonite) and
Mg3(PO4)2-II (chopinite) by Hu et al. (2022), the monoclinic
angle was calculated from their published lattice parameters
a,b,cand unit-cell volumes, as the mentioned authors did
not give data for the angle β.
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C. Leyx et al.: Compressibility and thermal expansion of magnesium phosphates 427
Table 5. Thermal-expansion and compressibility tensor elements of orthorhombic and hexagonal Mg-phosphates and silicates (in italics).
Thermal-expansion tensor elements Compressibility tensor elements
αii ×105(K−1)βi i ×103(GPa−1)
αa=α11 αb=α22 αc=α33 βa=β11 βb=β22 βc=β33
ε-Mg2PO4OH 0.63(1) 0.63(1) 1.66(7)
Althausite 0.56(8) 1.47(19) 1.60(12) 6.5(10) 6.6(10) 4.1(3)
Forsterite 1.45(2)
Kroll et
al. (2012)
0.88(1)
Kroll et
al. (2012)
1.23(1)
Kroll et
al. (2012)
3.73(3)
Finkelstein et
al. (2014)
1.46(2)
Finkelstein et
al. (2014)
2.66(2)
Finkelstein et
al. (2014)
P-ellenbergerite
Si-ellenbergerite
1.04(1)
0.77(2)
Comodi and
Zanazzi
(1993b)
0.87(3)
Amisano-
Canesi (1994)
=αa1.7(1)
1.11(2)
Comodi and
Zanazzi
(1993b)
1.22(13)
Amisano-
Canesi (1994)
3.38(9)
2.4(1)
Comodi and
Zanazzi
(1993a)
=βa4.73(7)
3.2(1)
Comodi and
Zanazzi
(1993a)
Note: data for forsterite and Si-ellenbergerite were recalculated from the cited literature. In the case of Kroll et al. (2012), data from their Table 1 were used with the exception
of the results below 20 °C. Forsterite was in the Pnam setting for consistency with that of chopinite (Table 6).
Table 6. Diagonalised thermal-expansion and compressibility tensor elements of monoclinic Mg-phosphates.
Thermal-expansion tensor elements Compressibility tensor elements
αii ×105(K−1)βi i ×103(GPa−1)
α11 α22 α33 β11 β22 β33
OH-wagnerite 1.01(5) 0.97(4) 0.82(3) 4.2(2) 2.98(8) 2.70(11)
Evi∀a, b,c 38(3)° // b20(3)° 12(4)° // b−7(4)°
∼[201] [010] ∼[102] ∼[100] [010] ∼[001]
Farringtonite 1.08(1) 1.95(1) 0.14(1)
Evi∀a, b,c −17.0(4)° // b−21.4(3)°
∼[201] [010] ∼[103]
Mg3(PO4)2-I 1.18(2)
Hu et al. (2022)
2.15(4)
Hu et al. (2022)
0.11(3)
Hu et al. (2022)
Evi∀a, b,c −17.3(9)° // b−21.8(6)°
∼[101] [010] ∼[103]
Mg3(PO4)2-II 1.31(4)
Hu et al. (2022)
1.18(4)
Hu et al. (2022)
1.51(5)
Hu et al. (2022)
Evi∀a, b,c 32(10)° // b33(10)°
∼[101] [010] ∼[103]
Chopinite 1.13(3) 0.99(3) 1.35(3) 2.54(15) 3.14(11) 5.12(15)
Evi∀a, b,c 42.1(4)° // b43(5)° 35(2)° // b36(2)°
∼[203] [010] ∼[102] ∼[101] [010] ∼[102]
Mg3(PO4)2-II in the P21/asetting for consistency with that of chopinite. The thermal expansions of Mg3(PO4)2-I and Mg3(PO4)2-II were recalculated from Hu et
al. (2022).
The compression is slightly anisotropic for the investi-
gated magnesium phosphates, with a maximum compress-
ibility contrast for chopinite (β33/β11 =2.02). Figure 7
shows a projection of the olivine-like chopinite structure
along the baxis (modified after Grew et al., 2007) to-
gether with the representation quadrics of compressibility
and the thermal-expansion tensor. The lengths of the axes
of the ellipsoids equal the inverse of the square root of
the property in that direction (Nye, 1985; Knight, 2010).
The directions of both the highest and the lowest com-
https://doi.org/10.5194/ejm-36-417-2024 Eur. J. Mineral., 36, 417–431, 2024
428 C. Leyx et al.: Compressibility and thermal expansion of magnesium phosphates
Figure 7. Projection of the chopinite structure along baxis (adapted
from Grew et al., 2007). The aand caxes are according to our set-
ting in Table 1. Representation quadric of the tensors of compres-
sion (blue) and thermal expansion (green) according to Nye (1985)
and Knight (2010).
pressibility do not match the crystallographic axes. The
highest compressibility appears near the [101] direction,
whereas the lowest is near [−102]. Compared to forsterite,
the tensor is rotated within the (010) plane by 54°. The
anisotropy of chopinite in this plane is about β33/β11 =
2.02, whereas in forsterite it is (β11 =βa)/(β33 =βc)=
1.40 (forsterite in the Pnam setting). The vacancies of
50 % of the M1 sites increase the anisotropy of chopinite
compared to forsterite. The anisotropy in P-ellenbergerite
(βc/βa=1.40) is about the same as in the homeotypical
silicate (Mg1/3,Ti1/3,1/3)2Mg6Al6Si8O28(OH)10 (βc/βa=
1.33) and can be related to the properties of the two main
structural elements, the octahedral single and double chains
running parallel to c. The dimers of face-sharing octahedra in
the double chain have their common face parallel to c, with
short Mg–Mg (or Mg–Al) distances across it; they should
therefore be least compressible perpendicular to c. This ef-
fect combines with the presence of vacancies in the face-
sharing octahedra of the single chain on the 6-fold screw axis,
which also make this chain easily compressible parallel to c.
Thermal expansion is slightly to moderately anisotropic
in the dense phases OH-wagnerite (α11/α33 =1.23), chopi-
nite (α33/α22 =1.36) and P-ellenbergerite (α33/α11 =1.63),
but it is more anisotropic in the low-pressure phases
ε-Mg2(PO4)OH (α33/α11 =2.63), althausite (α33/α11 =
2.86) and farringtonite (α22/α33 =13.9). Whereas the near-
isotropic behaviour of OH-wagnerite may reflect the three-
dimensional nature of its Mg polyhedral framework (Raade
and Rømming, 1986b), the high expansion along cin al-
thausite can be related to the existence of a perfect (001)
cleavage plane (space group Pnma, hence the preferred-
orientation problems). The strong anisotropy of farringtonite
thermal expansion is essentially due to the low expansion
along c. Along this direction, the Mg(2)O6octahedra are
connected to each other by two PO4tetrahedra and form
rather straight (Mg(PO4)2O2) chains, in which the sum of the
octahedral and tetrahedral edge lengths controls the crepeat
and cannot be much increased by polyhedral tilting.
4 Perspective
This exploratory survey will serve, in the first place, ther-
modynamic purposes but, together with results on Mg–
Al-phosphates (Schmid-Beurmann et al., 2007), allows a
few systematic remarks. The room-temperature thermal-
expansion coefficients obtained here for Mg-phosphates fall
within the range found by Schmid-Beurmann et al. (2007)
with MgAlPO5and lazulite MgAl2(PO4)2(OH)2(α0=0.9×
10−5K−1to α0=5.0×10−5K−1, respectively), which it-
self covers most of the range found in the silicate min-
erals (from α0=0.15 ×10−5K−1(prehnite) to α0=3.9×
10−5K−1(paragonite)). There seems to be a trend to-
wards higher thermal expansions for phosphate minerals as
compared to silicates, which we confirm here in the case
of isotypic compounds; however, this gross general fea-
ture should not obscure the fact that other groups of (syn-
thetic) phosphates do have very low thermal expansion (e.g.
Th4(PO4)4P2O7; Launay, 2001) or even negative volume
expansion for zeolite-type structures (e.g. Amri and Wal-
ton, 2009). As to compressibility, that of the Mg-phosphates
ranges between v3=1.0×10−6and 1.4×10−6bar−1and fits
within those found for the extreme structural types of berlin-
ite and apatite.
As mentioned before, Mg-containing phosphate minerals
have attracted increasing interest in experimental petrology
during the last few decades because of their potential as in-
dex minerals and the formation of solid solutions with sili-
cates (e.g. Cemiˇ
c and Schmid-Beurmann, 1995, and Schmid-
Beurmann et al., 2000, in addition to the references quoted
in the Introduction). However, for a successful application of
calculated phase equilibria to geobarometry and/or geother-
mometry, a resilient basis of thermodynamic data is required.
In this sense the current paper can be seen as one more step
towards an internally consistent database for phosphate min-
erals.
Eur. J. Mineral., 36, 417–431, 2024 https://doi.org/10.5194/ejm-36-417-2024
C. Leyx et al.: Compressibility and thermal expansion of magnesium phosphates 429
Data availability. Representative data shown in the figures are pro-
vided in the tables. The sources of literature data used in the figures
are cited in the captions and reference list.
Author contributions. FB, CC and PSB designed the study. CLe
prepared the samples and carried out the high-pressure experi-
ments together with FB and PSB, under the supervision of CLa at
DESY, and the high-temperature experiments at Université Pierre-
et-Marie-Curie. Data were analysed by CLe, FB, CC and PSB, and
reanalysed by PSB. CLe, FB and CC prepared an earlier version of
the manuscript, which was reshaped by PSB and CC after reanalysis
of the data and addition of the tensor analysis by PSB.
Competing interests. The contact author has declared that none of
the authors has any competing interests.
Disclaimer. Publisher’s note: Copernicus Publications remains
neutral with regard to jurisdictional claims made in the text, pub-
lished maps, institutional affiliations, or any other geographical rep-
resentation in this paper. While Copernicus Publications makes ev-
ery effort to include appropriate place names, the final responsibility
lies with the authors.
Acknowledgements. The help and hospitality offered by Michel
Quarton and Jean-Paul Souron at Laboratoire de Cristallochimie
du Solide, Université Pierre-et-Marie-Curie, Paris, for high-
temperature X-ray diffraction measurements were much appreci-
ated, as well as constructive comments by Ross Angel and the
anonymous referee.
Financial support. The PhD thesis of Catherine Leyx was funded
by the French Ministry of Higher Education. DESY (Hamburg, Ger-
many), a member of the Helmholtz Association HGF, provided ex-
perimental facilities and financial support.
Review statement. This paper was edited by Paola Comodi and re-
viewed by Ross Angel and one anonymous referee.
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