Regularities of the property changes in the compounds EuLnCuS3 (Ln = La-Lu)

Article abstract of DOI:10.1016/j.jallcom.2021.159968

This work contains the results of complex experimental research of the compounds EuLnCuS₃ (Ln = La-Lu) enhanced by the DFT calculations. It is aimed at the data replenishment with particular attention to the revelation of regularities in the property changes, in order to extend the potential applicability of the materials of the selected chemical class. The ab initio calculations of the fundamental vibrational modes of the crystal structures were in good agreement with experimental results. The wavenumbers and types of the modes were determined, and the degree of the ion participation in the modes was also estimated. The elastic properties of the compounds were calculated. The compounds were found out to be IR-transparent in the range of 4000–400 cm^–1. The estimated microhardness of the compounds is in the range of 2.68–3.60 GPa. According to the DSC data, the reversible polymorphous transitions were manifested in the compounds EuLnCuS₃ (Ln = Sm, Gd-Lu): for EuSmCuS₃ T_α?β = 1437 K, ΔН_α?β = 7.0 kJ·mol^-1, T_β?γ = 1453 K, ΔН_β?γ = 2.6 kJ·mol^-1; for EuTbCuS₃ T_α?β = 1478 K, ΔН_α?β = 1.6 kJ·mol^-1, T_β?γ = 1516 K, ΔН_β?γ = 0.9 kJ·mol^-1, T_γ?δ = 1548 K, ΔН_γ?δ = 1.6 kJ·mol^-1; for EuTmCuS₃ T_α?β = 1543 K, T_β?γ = 1593 K, T_γ?δ = 1620 K; for EuYbCuS₃ T_α?β = 1513 K, T_β?γ = 1564 K, T_γ?δ = 1594 K; for EuLuCuS₃ T_α?β = 1549 K, T_β?γ = 1601 K, T_γ?δ = 1628 K. In the EuLnCuS₃ series, the transition into either ferro- or ferrimagnetic states occurred in the narrow temperature range from 2 to 5 K. The tetrad effect in the changes of incongruent melting temperature and microhardness conditioned on rLn³⁺ as well as influencing of phenomenon of crystallochemical contraction were observed. For delimiting between space groups Cmcm and Pnma in the compounds ALnCuS₃, the use of the tolerance factor t’ = IR(A)·IR(C) + a×IR(B)² was verified.

Full text of DOI:10.1016/j.jallcom.2021.159968

Journal of Alloys and Compounds 874 (2021) 159968
Contents lists available at ScienceDirect
Journal of Alloys and Compounds
journal homepage: www.elsevier.com/locate/jalcom
Regularities of the property changes in the compounds EuLnCuS3
(Ln = La-Lu)
Anna V. Ruseikinaa,⁎, Vladimir A. Chernyshev , Dmitriy A. Velikanov ,
b
c
c,d
c
d
Aleksandr S. Aleksandrovsky , Nikolay P. Shestakov , Maxim S. Molokeev ,
a
a
e
f,g
Maxim V. Grigoriev , Oleg V. Andreev , Alexander A. Garmonov , Alexey V. Matigorov ,
h
e
a
Ludmila V. Melnikova , Anatoliy A. Kislitsyn , Svetlana S. Volkova
a
Institute of Chemistry, University of Tyumen, Tyumen 625003, Russia
Institute of Natural Sciences and Mathematics, Ural Federal University, Ekaterinburg 620002, Russia
Kirensky Institute of Physics, Federal Research Center KSC SB RAS, Krasnoyarsk 660036, Russia
Siberian Federal University, Krasnoyarsk 660079, Russia
b
c
d
e
Institute of Physics and Technology, University of Tyumen, Tyumen 625003, Russia
f
Engineering Centre of Composite Materials Based on Wolfram Compounds and Rare-earth Elements, University of Tyumen, Tyumen 625003, Russia
Institute of Chemistry and Chemical Technology, Federal Research Center KSC SB RAS, Krasnoyarsk 660049, Russia
University of Tyumen, Tyumen 625003, Russia
g
h
a r t i c l e i n f o
a b s t r a c t
Article history:
This work contains the results of complex experimental research of the compounds EuLnCuS3 (Ln = La-Lu)
enhanced by the DFT calculations. It is aimed at the data replenishment with particular attention to the
revelation of regularities in the property changes, in order to extend the potential applicability of the
materials of the selected chemical class. The ab initio calculations of the fundamental vibrational modes of
the crystal structures were in good agreement with experimental results. The wavenumbers and types of
the modes were determined, and the degree of the ion participation in the modes was also estimated. The
elastic properties of the compounds were calculated. The compounds were found out to be IR-transparent
in the range of 4000–400 cm–1. The estimated microhardness of the compounds is in the range of
2.68–3.60 GPa. According to the DSC data, the reversible polymorphous transitions were manifested in the
Received 29 January 2021
Received in revised form 1 April 2021
Accepted 10 April 2021
Available online 16 April 2021
Keywords:
Inorganic materials
Ab initio calculations
Thermochemistry
Magnetic measurements
Microhardness
compounds EuLnCuS
3
(Ln = Sm, Gd-Lu): for EuSmCuS
3
T
α↔β = 1437 K, ΔНα↔β = 7.0 kJ·mol-1, Tβ↔γ = 1453 K,
-1
-1
ΔН
β↔γ
= 2.6 kJ·mol-1; for EuTbCuS3 Tα↔β = 1478 K, ΔН
α↔β
= 1.6 kJ·mol , Tβ↔γ = 1516 K, ΔНβ↔γ = 0.9 kJ·mol
,
Lattice dynamics
-1
T
T
γ↔δ = 1548 K, ΔНγ↔δ = 1.6 kJ·mol ; for EuTmCuS
3
T
α↔β = 1543 K, Tβ↔γ = 1593 K, Tγ↔δ = 1620 K; for EuYbCuS
3
α↔β = 1513 K, Tβ↔γ = 1564 K, Tγ↔δ = 1594 K; for EuLuCuS
3
Tα↔β = 1549 K, Tβ↔γ = 1601 K, Tγ↔δ = 1628 K. In the
EuLnCuS
3
series, the transition into either ferro- or ferrimagnetic states occurred in the narrow temperature
range from 2 to 5 K. The tetrad effect in the changes of incongruent melting temperature and microhardness
conditioned on rLn3+ as well as influencing of phenomenon of crystallochemical contraction were observed.
3
For delimiting between space groups Cmcm and Pnma in the compounds ALnCuS , the use of the tolerance
factor t’ = IR(A)·IR(C) + a×IR(B)2 was verified.
©
2021 Elsevier B.V. All rights reserved.
1
. Introduction
Copper-containing chalcogenides are important multifunctional
materials in such areas like photocatalysis, photovoltaics and proton
conductivity [3,8–16]. They are prospective as thermoelectric ma-
terials with exceedingly low thermal conductivities [12]. They can be
used in photoelectric equipment and as absorbers in solar cells
[17–21] and in nonlinear optical devices [22–24]. Synthesis of new
New compounds containing combination of d- and f-elements
are of great interest to solid state chemistry and materials science
due to their physical properties which make them prospective
materials in the field of infra-red and non-linear optics [1–7].
+2
+3
+1 -2
quaternary compounds of the type А
f-element, B = f- or d-element, X = chalcogen) has been carried out
for some decades [1,25–55]. Quaternary chalcogenides АLnCuХ
exert great variety of properties. Among them, there are
3
B Cu (X ) (A = s-, р- or
⁎
3
Corresponding author.
a
E-mail address: a.v.rusejkina@utmn.ru (A.V. Ruseikina).
https://doi.org/10.1016/j.jallcom.2021.159968
0925-8388/© 2021 Elsevier B.V. All rights reserved.

A.V. Ruseikina, V.A. Chernyshev, D.A. Velikanov et al.
Journal of Alloys and Compounds 874 (2021) 159968
ferromagnetics [28,29], ferrimagnetics [28,30], paramagnetics [1]
and diamagnetics [32]. The compounds are semiconductors with
bandgap energy from 1.63 eV to 2.61 eV [1,12,26,40,42,44]. The
europium-containing compounds possess narrower bandgap energy
that is associated with the presence of 4f-5d-transition in Eu2+ ion
demonstrating ability to control bandgap energy of chalcogenides
The X-ray diffraction measurements were performed by means of
an X-ray diffractometer PANalytical X'Pert PRO equipped with the
detector PIXcel (Co Kα-emission, graphite monochromator) and
DRON 7 (CuKα-emission and Ni filter) at 298 K. The X-ray diffraction
patterns were scanned at 298 K over the diffraction angles
o
10º≤ 2θ≤ 125(140)º in the increments of 0.013 and total accumula-
tion time 13 h. The crystal structures of the whole series of EuLnCuS
3
due to the embedded Eu [44]. PbLaCuS
3
possesses the conductivity
of p-type with the projected bandgap energy ≈1.5 eV [32]. The qua-
ternary chalcogenides are of various melting types like congruent
were previously refined in terms of the powder data by the deriva-
tive difference minimization method (DDM) and Rietveld method
[28,44,63], and the X-ray analysis was performed to determine
chemical composition and the phase purity of the synthesized
samples, that is important for the measurements of thermal, optical
and magnetic properties. According to the X-ray diffraction analysis,
the structural type of the compounds and the unit cell parameters
were consistent with the earlier data [28,44,63].
[52–55] and incongruent [26,30,44,49,56,57] ones. The phase equi-
libria in multicomponent systems Сu
2
2 3
Х–AX–B X
[49–55,58–60]
have complex nature, including peritectic, eutectic, eutectoid, peri-
tectoid interactions and formation of extensive solid solution areas.
The compounds ALnCuS
structural types of the orthorhombic system [26–28,30–33,40–42,
4,45,49,50,53,57,61–71]; see this table SI in Supplementary
Information for more detail.
Sulfides EuLnCuS (Ln = La-Nd, Gd, Dy-Er) melt incongruently
and three polymorphous transitions in the temperature range of
400–1610 K were detected for some of them [30,57,58]. The tran-
sition into the ordered magnetic state for EuLnCuS (Ln = Y, Eu, Tb,
Dy, Er-Lu) compounds occurs in the narrow temperature range from
3
(A = Sr, Ba, Eu, Pb) crystallize in four
4
The microstructure was observed on polished samples using the
AxioVert.A1 and Olympus GX-71 microscopes. Scanning electron
microscopy (SEM) was performed on a Philips SEM 515 and
JEOLJSM-6510 LV equipped with an energy dispersive spectrometer.
The differential scanning calorimetry experiments were carried
out on a Setsys Evolution 1750 (TG–DSC 1600) with the aid of the
PtRh 6%-PtRh 30% thermocouple. The complex was calibrated ac-
cording to the data of melting temperatures and melting enthalpies
of standard substances (Sn, Pb, Zn, Al, Ag, Au, Сu, and Pd). Prior to an
experiment, the working chamber of the complex was evacuated
and then filled with argon. The recording parameters were the fol-
lowing: the sample size: 100–110 mg, heating rate: 5 K/min, argon
flow rate: 25 ml/min, and alundum crucible capacity: 100 µl. The
heat absorption onset temperature was determined as the inter-
section point of a tangent with the baseline in the program package
Setsoft Software 2000 with a linear baseline from the first to last
point. The temperatures and enthalpies of the thermal events ap-
pearing in replica measurements were aligned with the thermo-
analytical error bar. While performing thermal analysis up to 1840 K,
the samples transformed into melt. The TG curves showed a 0.16 wt%
3
1
3
3
.4 to 5.5 K [28–30].
Despite the fact that the structure of the compounds EuLnCuS
3
(
Ln = La-Lu) was actually solved and refined previously, the data
concerning their properties and physicochemical characteristics are
still incomplete. This restricts the potentialities of their practical use.
The aim of this work is a comprehensive study of the compounds
3
EuLnCuS (Ln = La-Lu), in particular, the experimental determination
of thermal, optical, magnetic, durometric properties, the perfor-
mance of ab initio calculations of crystal structures, phonon spectra,
elastic properties, and the determination of regularities in their
property changes depending on rLn3+
.
2. Materials and methods
3
weight loss in the samples of EuLnCuS (Ln = Tb, Tm, Yb, Lu).
The graphical plottings were acquired by means of the program
Edstate 2d [72]. The crystal structures were visualized in the soft-
ware package Diamond 3 [73].
Durometric analysis of a polished sample was performed by the
Vickers method on an HMV-G21 [74]. The samples were used in the
cylindrical form and poured over with epoxy glue (EP resin and
solidifier in the ratio 100:12). Then, they were smoothed, and finally
polished by GOI polishing paste. The exposure time was 15 s and the
load was 10 kg-force (98.07 N).
2
.1. Materials
The rare-earth element oxides Ln
2
O
3
(Ln = La, Nd, Sm, Gd, Dy-Lu),
2 4 7
LnO (Ln = Ce, Pr) and Tb O (99.9%) were procured at the manu-
facture of Uralredmet (Russia). Elementary sulfur (99.99%) was
purchased in the Komponent-reactive manufacture (Russia).
Elementary copper (99.99%) was procured in Red Chemist, Ltd.
(
Russia). Argon (99.998%) was purchased from the technical gases
manufacture Kislorod-servis (Russia). Epoxy glue was procured in
OOO Scientific-Industrial Complex “Astat” (Russia). GOI polishing
paste was purchased in OOO “Tehnopayka” (Russia).
The low-temperature (1.8–50 K) magnetic susceptibilities of
EuLnCuS
magnetometer [75–77] in a 10 Oe magnetic field. Masses of the
samples were 0.0862 g (EuLaCuS ), 0.0475 g (EuCeCuS ), 0.1025 g
(EuPrCuS ), 0.0655 g (EuNdCuS ), 0.1055 g (EuSmCuS ), 0.0786 g
EuHoCuS ).
The dilatometric analysis was performed by means of a DIL 402
3
(Ln = La, Сe, Pr, Nd, Sm, Ho) were studied on a SQUID
3
3
2
.2. Methods
3
3
3
(
3
The compounds EuLnCuS
3
were synthesized by melting the in-
: 1Cu S. The
S was prepared from Cu and S by the ampoule
method according to the technique described earlier [49]. The
compounds EuS, Ln were synthesized at 1300 K from the rare-
earth element oxides in the flow of Н S and СS2, produced by de-
composition of аmmonium rhodanide (the carrier gas is argon) [30].
The powdered batch composed оf 2EuS: 1Ln :1Cu S was molten in
termediate sulfides mixed in the ratio 2EuS: 1Ln
compound Cu
S
2 3
2
РC in the following conditions: the temperature range for mea-
surements was 300–1240 K, heating rate was 5 K/min, pressure of
the puller contact was 30 сН, purge speed of argon was 25 ml/min.
The measurements were performed on the tablet with the diameter
2
2 3
S
2
0
of 6 mm and 1.28–3.3 mm thick. The initial length L of the samples
–3
was determined with the absolute error ± 5·10 mm, while per-
centage error of the initial length measurement is within the range
of 0.15–0.4%. The percentage error of the measurements of elonga-
tion ΔL during the thermal dilatation process was 5%, and the per-
S
2 3
2
the argon atmosphere in a graphite crucible placed in the silica
reactor. The synthesized samples were annealed in evacuated
and sealed-off silica glass ampoules at 1170 K for 1500 h [63]. No
interaction of the samples with silica was found during annealing.
0
centage error ΔL/L ranged from 5.15% to 5.4%. The dependencies of
the relative elongation of the samples on the temperature were
2

A.V. Ruseikina, V.A. Chernyshev, D.A. Velikanov et al.
Journal of Alloys and Compounds 874 (2021) 159968
Table 1
Lattice constants of EuLnCuS
3
(Å).
Compound S.G.
ST
Ba
a
b
c
Volume
a/c
Calc.
Exp.
EuPrCuS
EuSmCuS
EuGdCuS
3
Pnma
Pnma
Pnma
Pnma
Pnma
Pnma
Pnma
Pnma
2
MnS
CuS
3
7.9854
4.0540
4.0114
3.9901
3.9801
3.9714
3.9633
3.9233
3.9544
15.7090
12.7145
12.7571
12.7742
12.7908
12.8014
12.8996
12.8261
10.1150
10.0809
10.0403
509
535
528
524
521
518
509
515
512
509
508
0.5083
0.8257
0.8133
0.8075
0.8020
0.7968
0.7798
0.7914
0.3903
0.3909
0.3918
0.5100 [63]
0.8134 [63]
0.8041 [28]
0.7985 [28]
0.7932 [28]
0.7898 [57]
0.7925 [28]
0.7862 [30]
0.3889 [28]
0.3895 [28]
0.3898 [28]
3
Eu
2
3
10.4978
10.3755
10.3158
10.2579
10.2005
10.0590
10.1501
3.9477
3
EuTbCuS
EuDyCuS
3
3
EuHoCuS
EuYCuS
EuErCuS
EuTmCuS
EuYbCuS
EuLuCuS
3
3
3
3
Cmcm
Cmcm
Cmcm
KZrCuS
3
12.8220
12.8174
12.8562
3
3.9407
3.9337
3
approximated by some linear functions by the procedure described
in [78]. The approximation data were assessed by Fisher's ratio test:
bond, the valence basis sets "ECPnMWB-II" [91–94] were used. The
Gaussian primitives with orbital exponent values less than 0.1 were
removed from the valence basis set, since these calculations are
periodic. We used pseudo-potentials for the description of core
electronic shells of rare-earth ions, the 4f inclusive, with the valence
basic sets for outer orbitals involved in chemical bonding. Such ap-
proach makes it possible to reconstitute successfully both the lattice
structure and dynamics in the compounds that have a lanthanide ion
sublattice [95,96].
S
0
1
N
2
F =
,
S0 = N
(yiexp yiexp
)
–
the total variance,
S
1
i=1
1
N
i=
(yiexp yiappr )2 – the remainder variance [78]. We se-
S = N
1
1
lected both the values of the temperature range limits and the α(Т)
values, wherein the minimal values of the remainder variance con-
formed the determined polynomials.
The infrared absorption spectra were recorded in the range of
–
1
6
80–85 cm using an FTIR VERTEX 80 V spectrometer (BRUKER
The accuracy of calculating the self-consistent field was set at
OPTIK GMBH) equipped by an RT-DTGS FIR sensor. The sulfide
powders under investigation were grinded in agate mortar and then
mixed with ultrahigh molecular weight polyethylene (Mitsui
Petrochemical Ind., Japan) in a ratio 1:10 and pressed into 0.26 mm
thick pellets.
1
0-9 a.u. The accuracy of the calculation of the two-electron integrals
-8
was set at least 10 . Integration over the Brillouin zone was carried
out according to the Monkhorst-Pack scheme with a grid of k-points
equal to 8 × 8 × 8. The details of the calculation algorithm were
considered previously [95]. The calculations were done for all stoi-
3
The IR spectra of the compounds EuLnCuS were recorded in the
range of 4000–400 cm–1 using a FTIR spectrometer. The poly-
3
chiometric compounds EuLnCuS (Ln = Sm-Lu and Y). The modeling
of non-stoichiometric compounds requires an increase of the unit
cell and high computer costs. Therefore, the modeling of non-stoi-
crystalline sample was grinded in agate mortar and mixed with the
annealed potassium bromide powder to get a homogeneous mix,
and then pressed into a pellet in the mold PF13 using an automatic
hydraulic press Autotouch 9t. The pressure resistance time
was 2 min
3
chiometric compounds EuLnCuS (Ln = La, Ce, Pr, Nd) was not carried
out. For the crystal EuPrCuS , the calculations were done in the
3
stoichiometric approximation.
The crystal structure, phonon spectrum, and elastic properties of
the EuLnCuS
3
compounds were investigated at ab initio level of
3. Results and discussion
theory. The calculations were carried out in the framework of den-
sity functional theory (DFT) [79] by using the B3LYP hybrid func-
tional [80,81], which takes into account both local and nonlocal
Hartree-Fock exchanges. The functional allows to successfully de-
scribe complex compounds with an ionic-covalent bond [82,83]. The
calculations were performed in the CRYSTAL17 program designed to
simulate periodic structures [84,85]. The sequence of calculations
was as follows. First, the optimization of the crystal structure was
carried out. After that, the phonon spectrum (at the Г- point) or
elastic constants were calculated for the crystal structure corre-
sponding to the minimum energy.
3.1. The ab initio calculations of the EuLnCuS
3
crystal structure
(Ln = La-Lu) was ac-
The structure of the compounds EuLnCuS
3
tually solved and refined previously [28,29,44,63]. The calculated
lattice constants in comparison with the experimental data are given
in Table 1. The ratio a/c obtained from the calculation for the crystals
EuLnCuS
For the detailed observation, we synthesized the series of the
compounds EuLnCuS . The photos of obtained samples can be seen
in Fig. S1. Powdered compounds EuLnCuS consist of planar particles
3
is consistent with experimental data [28,30,57,63].
3
3
For europium, the ECP53MWB quasi-relativistic pseudo-potential
86,87] was used with the attached valence basis set ECP53MWB
88]. The Gaussian primitives with exponents less than 0.1 were
removed from the basis sets. The exponent in the outer d- orbital of
the valence basis set was set to 0.178. For copper, the full-electron
basis set [89] was used, as available on the CRYSTAL program site as
with linear sizes up to 20 µm (Fig. S2). The energy dispersive X-ray
spectrometric analysis was performed at 5 different locations on the
surface of each sample. The chemical compositions of the samplеs
were consistent with the theoretical contents of the elements
(Table 2) and with the XRD analysis data, presented earlier
[28,44,63].
[
[
"
Cu_86–4111(41D)G_doll_2000" [49]. For sulfur, the DURAND
pseudo-potential with the attached valence basis set was used
49,90]. The exponents in the two outer orbitals of the valence basis
3
In series of the compounds EuLnCuS (Ln = La - Lu), we can
clearly observe two regularities, they are periodicity and continuity.
The periodicity manifests itself in some changes of the ST com-
pounds, particularly in the segments of crystallochemical instability
(Тable S1), namely, the types of polyhedra cations. While transmit-
[
set were set to 0.20 and 0.22. The quasi-relativistic pseudopotentials
ECPnMWB were used to describe the inner shells of rare-earth ions
(n is the number of internal electrons replaced by the pseudopo-
ting from ST Ba
prism is transformed into the LnS
ment of transition of ST Eu CuS
polyhedron of europium with one-cap trigonal prism CN = 7 is
2
MnS
3
to ST Eu
2
CuS
octahedron (Fig. S3). In the seg-
to ST KZrCuS , the coordination
3 7
, the LnS one-capped trigonal
tential) [91,92]. For La n = 46, for Ce n = 47, etc. Thus, the inner shells
of the rare-earth ion, 4f including, were replaced by a pseudopo-
tential. To describe the outer shells 5s 5p involved in chemical
6
2
3
3
2
6
3

A.V. Ruseikina, V.A. Chernyshev, D.A. Velikanov et al.
Journal of Alloys and Compounds 874 (2021) 159968
Table 2
Elemental distribution over the surface of EuLnCuS
3
samples as probed by X-ray spectral microanalysis.
Ln
Соmpound
Eu
Cu
S
m
calcd
m
found
m
calcd
m
found
m
calcd
m
found
m
calcd
m
found
EuSmCuS
EuTmCuS
EuYbCuS
EuLuCuS
3
32.89
31.62
31.35
31.23
32.81
31.56
31.41
31.30
32.55
35.15
35.70
35.95
32.50
35.08
35.63
35.88
13.75
13.22
13.11
13.06
13.80
13.25
13.08
13.03
20.81
20.01
19.84
19.76
20.89
20.11
19.88
19.79
3
3
3
m
3
calcd and mfound are, respectively, the calculated mass percentage and the analyzed mass percentage of elements in EuLnCuS .
transformed into trigonal prism CN = 6. The changes of CN and co-
ordination polyhedra must cause discontinuities in all the compo-
(Fig. 1, Table 3). The type of the dependencies is consistent with the
structural changes of the compounds. In the limits of ST Ba MnS , a
slight change of microhardness was detected, if compared to the
compounds of the two other types. The structures of Eu CuS and
KZrCuS -type are described as 2D layers located in planes ab and ac,
respectively, with the Eu ions positioned between the layers. Since
the two-dimensional [LnCuS ] layers are formed by the distorted
LnS octahedra and CuS tetrahedra, the decrease in the radius of the
2
3
sition-property dependencies in
a number of the rare-earth
compounds EuLnCuS The continuous functions will manifest
3
.
2
3
themselves in monotonous changes of the unit cells parameters,
phase microhardness, phase transition temperature in dependence
3
2+
3
+
on rLn in a number of similar ST compounds.
3
6
4
3
.2. Microhardness and elastic constants of crystals EuLnCuS
3
rare-earth ion leads to the crystallochemical contraction of the two-
dimensional layers. This contraction is manifested in the decrease of
the average Ln‒S bond length, the changes in the unit cell para-
meters, and alteration of the local geometry around the Eu atom, as
The microhardness values of the compounds EuLnCuS
3
regularly
3
+
increase as rLn reduced within the limits of each structural type
3
Fig. 1. Dependencies of the unit cell parameters (Å): ○ – a, Δ – b, □ – c and × – the compounds EuLnCuS (microhardness values obtained in this research) on the radii of the rare-
3
+
earth ion rLn
.
4

A.V. Ruseikina, V.A. Chernyshev, D.A. Velikanov et al.
Journal of Alloys and Compounds 874 (2021) 159968
Table 3
3
Microhardness and color of the compounds EuLnCuS (Ln = La-Lu).
Compound
V
H , GPa
Color
Compound
H
V
, GPa
Color
Exp.
Calc.
Exp.
Calc.
EuLaCuS
EuCeCuS
EuPrCuS
EuNdCuS
EuSmCuS
EuGdCuS
EuTbCuS
3
3.33 ± 0.14
3.42 ± 0.26
3.49 ± 0.17
3.45 ± 0.23
2.68 ± 0.08
2.87 ± 0.21
2.92 ± 0.23
–
–
black
black
black
black
brown
brown
brown
EuDyCuS
EuHoCuS
EuYCuS
EuErCuS
EuTmCuS
EuYbCuS
EuLuCuS
3
3.08 ± 0.25
3.60 ± 24
–
2.85 [30]
2.73 ± 0.03
2.84 ± 0.21
2.94 ± 0.22
3.95
3.93
3.83
3.83
3.87
3.99
4.17
brown
brown
–
Red-brown
Red-brown
brown
3
3
3
4.63
–
4.37
4.30
4.15
3
3
3
3
3
3
3
3
3
Red-brown
Table 4
Temperatures (K) and enthalpies (kJ∙mol-1) of the phase transitions in EuLnCuS
3
(Ln = La-Lu).
or Tcra
ΔНсr or ΔH
a
Compound
α↔β
Т
β ↔ γ
Т
γ↔δ
Т
T
m
m
ΔН
ΔН
ΔН
EuLaCuS
EuCeCuS
EuPrCuS
EuNdCuS
EuSmCuS
EuGdCuS
EuTbCuS
EuDyCuS
3
[59]
[98]
[98]
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
1539 ± 4
1524 ± 3
1497 ± 3
1470 ± 4
1574 ± 8
1720 ± 5
23.3 ± 2.3
23.7 ± 2.3
20.1 ± 2.0
17.7 ± 1.8
4.2 ± 0.4
3
3
3
[60]
3
1437 ± 4
1460 ± 3
1478 ± 5
1500 ± 6
1516 ± 1
1524 ± 2
1543 ± 8
1513 ± 10
1549 ± 3
7.0 ± 0.7
2.6 ± 0.3
1.6 ± 0.2
4.4 ± 0.5
3.7 ± 0.4
2.3 ± 0.2
5.3 ± 0.5
2.3 ± 0.2
5.3 ± 0.5
1453 ± 5
1492 ± 5
1516 ± 3
1543 ± 4
1562 ± 2
1575 ± 3
1593 ± 7
1564 ± 7
1601 ± 2
2.6 ± 0.3
2.3 ± 0.3
0.9 ± 0.1
1.0 ± 0.1
1.2 ± 0.1
0.7 ± 0.1
1.3 ± 0.1
1.4 ± 0.1
1.5 ± 0.2
–
–
a
3
[99]
1525 ± 9
1548 ± 4
1568 ± 6
1591 ± 2
1602 ± 3
1620 ± 5
1594 ± 8
1628 ± 2
4.4 ± 0.4
1.6 ± 0.2
2.0 ± 0.2
2.2 ± 0.2
1.3 ± 0.1
2.4 ± 0.2
2.4 ± 0.2
2.4 ± 0.2
-3.8 ± 0.4
a
-3.3 ± 0.3a
3
1718 ± 6
1727 ± 7
1737 ± 7
a
3
[58]
[57]
-4.6 ± 0.4
-7.8 ± 0.8
a
a
EuHoCuS
EuErCuS
EuTmCuS
EuYbCuS
3
a
-3.5 ± 0.3a
3
[30]
1735 ± 10
a
a
3
1719 ± 6
-8.6 ± 0.8
a
a
3
1732 ± 6
-6.1 ± 0.6
a
-8.8 ± 0.8a
EuLuCuS
3
1735 ± 6
a
The data are based on the cooling curves.
well as the changes in the structure type and the space group. The
manifestation of the effect of the crystallochemical contraction of
two-dimensional layers is fully consistent with the increase of mi-
crohardness, also manifested in the isostructural compounds
is larger than 5 GPa, but gives overestimated values at lower hard-
ness. The experimental values of hardness are in the range of
2.7–3.6 GPa (Table 3). The formula (3.1) overestimates the hardness
3
of EuLnCuS by approx. 30% and does not describe the trend in the
(
SrSmCuS
crohardness change as a function of rLn confirms the manifesta-
tion of tetrad effect in series of complex sulfides EuLnCuS
Since experimental data on elastic constants are absent in re-
search papers, elastic constants of crystals EuLnCuS were also cal-
culated (Table S2). According to the calculations, the elastic
constants of crystals with a structural type of Eu CuS (Pnma) differ
significantly from the elastic constants of crystals with a structural
type of KZrCuS (Cmcm) (Table S2). The column "∆" in Table S2
shows the difference between the values of the elastic constants in
structures Eu CuS (Pnma) and KZrCuS (Cmcm). (The average values
3 3
2.7 GPa, SrErCuS 3.2 GPa [49]). Periodicity in the mi-
series La-Lu.
3+
3
.
3
.3. Thermal Properties
3
All the compounds melt incongruently to form polycrystalline
phase EuS and the melt. According to the XRD and SEM data, the
single-phase samples of the compounds EuLnCuS , crystallized from
the melt during DSC were found to change into the three-phase
samples. The microstructure of the samples contained primary
2
3
3
3
crystals of the EuS phase, surrounded by the EuLnCuS
tals. In the samples the eutectic consisting of the grains of the
EuLnCuS and CuLnS phases was observed between the grains of
the EuLnCuS phase [58–60].
On the thermal curve of the compounds EuLnCuS
Yb, Lu) the overlapping of endothermal melting effects of EuLnCuS
3
phase crys-
2
3
3
were calculated for the series Sm-Er and Tm, Yb, Lu, respectively.)
The values of C44 and C55 change several times. It is notable that the
bulk modulus of compounds with structure Eu
3
2
3
2 3
CuS (Pnma) differs
3
(Ln = Tb, Tm,
little from the bulk modulus of compounds with structure KZrCuS
3
3
(
Cmcm). The calculated bulk modulus, Young modulus and shear
and the primary crystals of EuS is observed (Fig. S5). On the cooling
curves, the thermal effects of the phase crystallization vary in tem-
peratures and overlap to a lesser extent. Therefore, the temperature
and enthalpy of incongruent melting were determined from the
cooling curve.
The temperature data of this phase transition are given ap-
proximately, as the supercooling effect is observed. The exothermal
effect of the crystallization process (ΔH = –24.8 J/g, e.g., for the
modulus in the Voigt, Reuss and Hill approximations for EuLnCuS
are given in Table S3. The dependence of Young modulus on the
crystallographic direction shows the anisotropy of elastic properties
3
(
Fig. S4).
The calculated values of the shear modulus and bulk modulus
make it possible to estimate the Vickers hardness for EuLnCuS . To
3
estimate the Vickers hardness, the known empirical formula (3.1)
was used [97]. This formula well describes the hardness in the series
of compounds with ionic and covalent types of chemical bond (about
3
compound EuLuCuS ) was separated into two peaks (ΔH = –6.6 J/g
and ΔH = –18.2 J/g). The first thermal effect manifested in the in-
terval 1740–1735 K characterizes the formation of primary crystals
EuS (ΔH = –1.2 kJ/mol), and the second one results from the inter-
action of primary crystals EuS with liquid to form the compound
4
0 compounds were considered in [97]).
G 1.137
B
HV = 0.92
G0.708
(3.1)
EuLuCuS
out for EuLnCuS
While performing DSC measurements of the initial single-phased
annealed samples of EuLnCuS , the phase transition peaks were
3
(ΔH = –8.8 kJ/mol). The analogous separation was carried
In (3.1), G and B are the bulk modulus and shear modulus by Hill
estimation, respectively. As it was shown in [97], formula (3.1)
provides good agreement with experimental values when hardness
3
(Ln = Tb, Tm, Yb) (Table 4).
3
5

A.V. Ruseikina, V.A. Chernyshev, D.A. Velikanov et al.
Journal of Alloys and Compounds 874 (2021) 159968
Nd and polymorphism and thermal stability improvement for REEs
Gd – Lu, were shown up. The abrupt changes of physicochemical
properties of the compounds EuLnCuS
the changes in the nature of the compounds as sulfide salts.
The compounds EuLnCuS are formed by basic sulfide EuS and
sulfides Cu S and Ln exerting acidic properties in relation to EuS
3
are the most likely caused by
3
2
2 3
S
sulfide. Acidity of sesquisulfides of rare-earth elements increases in
consequence of both rLn3+ reduction [71] and the increase of elec-
tronegativity of rare-earth atoms (XSm = 1.37; XTb = 1.40; XEr = 1.47;
XTm=1.48 [100]). Such increasing of Ln
base nature of complex sulfides EuLnCuS
In series of the compounds EuLnCuS , in the segment from Nd to
Sm, we observed the transformation of the structural type Ba MnS
being typical for the sulfide EuNdCuS , into the structural type
Eu CuS , which is intrinsic to EuSmCuS . The coordinal polyhedron
of lanthanide cation is transformed from one-cap trigonal prism
NdS into octahedron SmS . In the segment Nd–Sm–Gd, thermal
stability of the compounds EuLnCuS remarkably increases (Fig. 7).
The compounds EuLnCuS (Ln = La-Nd) are classified as thio-
cuprates because acidity of Cu S dominates over the Ln acidity.
With increase of acidity of Ln in series from La to Nd, the
temperature of incongruent melting of EuLnCuS decreases
appropriately. The compounds EuLnCuS (Ln = Sm-Lu) belong to
2 3
S acidity affects the acid-
3
.
3
2
3
,
3
2
3
3
7
6
3
3
Fig. 2. Phase-transition temperatures of EuLnCuS (Ln = La-Nd [98], Gd [99], Dy [58],
3
Ho [57], for the Sm, Tb, Tm, Yb and Lu compounds the phase transition temperatures
were measured in this work): Δ α→β; □ β→γ; and Ø γ→β polymorphic transitions and ○
incongruent melting.
2
2 3
S
2 3
S
3
detected for the first time. The compounds EuLnCuS
3
were sub-
3
divided into three groups for the rare-earth elements La-Nd, Sm and
Gd-Lu according to the number of the phase transitions.
thiolanthanate group as in series of these compounds both
polymorphous transition temperatures and their thermal stability
increases.
3
For the compounds EuLnCuS (Ln = La, Ce, Pr, Nd), the poly-
morphous transitions were not detected by the DSC method. The
decrease of the incongruent melting temperatures of complex sul-
3
According to the DSC data for the compounds EuLnCuS the
phenomenon of polymorphism, character of the compound melting,
regularities of the thermal characteristic changes of the phase
transitions in the series of compounds were determined.
fides EuLnCuS
lowering of thermodynamic stability of these compounds (Fig. 2).
The compound EuSmCuS was classified into a separate group
3
(Ln = La-Nd) and enthalpies of their melting indicates
3
since two polymorphous transitions resulted in thermal stability
improvement were found out.
3.4. Magnetic properties
In the compounds EuLnCuS
3
(Ln = Gd-Lu), three endoeffects
The temperature dependence of the inverse magnetic suscept-
(
Fig. 6, Table 4) reproduced in cooling of the samples were detected
3
ibility of the compounds EuLnCuS for Ln = La, Ce, Pr, Nd, Sm cor-
on the heating curves in the temperature range оf 1430–1640 K.
Within this temperature range, after the third endoeffect, the sam-
ples remain in polycrystalline state. The thermal effects defined in
responds to Curie-Weiss law that allows to classify these compounds
to ferromagnetics (Fig. S6). The calculated and experimental Curie
constants are in satisfactorily relation (Table 5). The Curie-Weiss
EuLnCuS
first type, i.e. polymorphous transitions. Similar transitions were
earlier detected in isostructural compounds SrLnCuS [56].
The polymorphous transitions are designated by Greek letters in the
order of increasing temperatures. Temperatures and enthalpies of
the phase transitions are determined according to heating curves
and they are presented in Table 4. The phase transitions proceed in
temperature interval up to 10 K. We were not succeeded in produ-
3
(Ln = Sm, Gd-Lu) resulted from the phase changes of the
parameters ϴ
W
were calculated and the values are listed in Table 5.
The dependence of inverse magnetic susceptibility on
3
temperature in EuHoCuS
ferrimagnetics:
3
is approximated by Neel’s relation for
1
T
C
1
=
+
T
(3.2)
0
The calculated parameters of the model are the following:
3
3
3
cing high temperature modifications of the compounds EuLnCuS
3
by
С = 0.217 K·m /kmol, 1/χ = 0.243 kmol/m , σ = 12.2 kmol·K/m ,
0
quenching into a coolant liquid since the polymorphous transitions
are classified as rapid ones and they can be detected by kinetic
method.
θ = 4.30 K. Curie point calculated from these parameters according to
the formula
2
In the series of compounds EuSmCuS
3
-EuLuCuS
3
, the tempera-
1
2
C
C
Tc =
+
+ 4C
+
,
tures of polymorphous transitions increase monotonously as a
0
0
0
3
+
(3.3)
function of rLn . The presence of local minimum for the compound
EuYbCuS correlates to 4f-electronic level occupation in Yb atom.
3
is equal to 4.8 K.
In the series of the compounds, two general regularities, such as
lowering of thermodynamic stability of the compounds for REEs La-
The study of magnetic properties of the compounds EuLnCuS3
(Fig. S6, Table 5) allows to determine common regularities of their
Table 5
W
The calculated and experimentally determined Curie constants (C), Curie-Weiss parameters (ϴ ), maximum inverse magnetic susceptibility temperature (Tmax), and the ar-
rangement type (F - ferromagnetic; Fe - ferrimagnetic).
Characteristics
EuLaCuS
3
EuCeCuS
3
EuPrCuS
3
EuNdCuS
3
EuSmCuS
3
EuHoCuS
3
3
С
С
ϴ
T
theor (K·m /kmol)
0.0990
0.0991
3.6
2.4
F
0.109
0.104
4.8
2.7
F
0.119
0.118
0.5
2.1
F
0.120
0.120
3.2
3.1
F
0.100
0.0994
5.3
3.1
F
0.276
0.228
–
4.8
Fe
3
exp (K·m /kmol)
W
, K
max, K
Arrangement type
6

A.V. Ruseikina, V.A. Chernyshev, D.A. Velikanov et al.
Journal of Alloys and Compounds 874 (2021) 159968
Table 6
Table 7
Thermal-expansion coefficient for some REEs compounds.
3
+
3
Magnetic moment of the Ln ion in EuLnCuS and type of magnetic ordering.
Iоn
Μ
theor, μ
B
Arrangement
Iоn
Μ
theor, μ
B
Arrangement
Compound Temperatures Tph
of discontinuous
Thermal expansion factor
Fisher's
variance
ratio
La3
+
0
F
F
F
F
Tb3+
9.72
10.63
10.60
9.59
7.57
4.54
0
Fe [28]
Fe [28]
Fe
Fe [30]
Fe [28]
F [28]
F [28]
Temperature
range, K
α (Т), 1/K
changes α, K
3
+
3+
Ce
Pr
2.54
3.58
3.62
2.68
0.84
7.94
Dy
3+
3+
Ho
EuDyCuS
EuHoCuS
EuYbCuS
3
1072 ± 5
1135 ± 5
1195 ± 5
300–1072
1072–1280
300–1135
1135–1280
300–1195
(1.76 ± 0.03)·10-5 649
(6.07 ± 0.07)·10
3
+
3+
Nd
Er
-
5
3
+
3+
Pm
No data
F
Fe [28]
Tm
-5
3
+
3+
3
(1.35 ± 0.02)·10
302
297
Sm
Yb
Lu
(7.47 ± 0.03)·10-
5
5
3
+
3+
Gd
(1.69 ± 0.02)·10-
(3.73 ± 0.04)·10-4
3
1195–1280
3
changes in series of REEs. In series of the compounds EuLnCuS , the
transition into the ordered magnetic state occurs in the narrow
-
1
temperature range from 2 to 5 K. Compounds, containing Ln3+ ions+,
to 125 cm . The highest involvement of copper in IR modes is pre-
-1
which magnetic moments are approximately equal to that of Eu2
dicted for the modes at ~72–81 cm (B2u) and at the row of IR modes
at about 100 cm-1. Thus, the strong participation of all three ions –
ion (7.94 μ
B
), exhibit ferrimagnetic properties (Table 6). If the mag-
-
1
3
+
2+
Eu, Ln and Cu appears in the low- wavenumber mode at ~72–81 cm
(B2u). Sulfur is involved in all IR modes. Sulfur is strongly involved in
modes with wavenumbers above 180 cm . Moreover, S1 ions are
most intensely involved. The ion S1 is mainly involved in the IR
mode with the maximum wavenumber ~ 300 cm-1 (B3u). S1 ions are
mainly involved in the two most intense IR modes at ~177–187 cm
(B2u) and ~200–201 cm (B1u). For example, the low-wavenumber IR
mode (~72–81 cm , B2u) strongly involves three ions (Eu, Ln and Cu),
and it is difficult to distinguish the dominant contribution of anyone
of them.
netic moment of Ln ion is lower than that of Eu ion, the com-
3
+
pound containing Ln is ferromagnetic.
-1
3.5. Vibrational properties
-
1
-1
The wavenumbers and types of phonon modes were determined
by the ab initio calculations. The results for the infrared active
modes are given in Tables S4–S5 and Fig. S7. The stoichiometric
-1
approximation for the EuPrCuS
3
allows to reproduce the lattice
constants well, but this approximation provides poor agreement
between the calculated IR spectrum and experimental data. The
The compounds EuLnCuS3 of all the REEs series are transparent
for IR radiation in the range of transition wavenumbers
4000–400 cm (Fig. S10).
–1
calculated wavenumbers of the IR modes for the EuPrCuS
shown in Fig. S7.
3
are not
On the basis of the analysis of displacement vectors obtained
from the ab initio calculations, the degree of participation of each
ion in a particular mode is estimated. The ions being significantly
shifted in the mode are listed in the column “Participants” of
Tables S4 and S5. The “S” index designates strong shift (“Strong”),
3
.6. Interpretation of dilatometry results
While performing dilatometric analysis of the samples EuLnCuS
3
(Ln = La-Nd, Sm, Gd [101], Dy, Ho, Yb, Table 7, Fig. S11) in the tem-
perature range of 900–1200 K, we observed sharp changes (2–3-
times/ twice-threefold) of the thermal expansion factor on the
constant field extension background. Moreover, the temperature of
the discontinuity Tph increases monotonously (Table 7).
“
W” designates weak shift (“Weak”). The maximum displacement of
ions reaches 0.03–0.04 Å. If displacement is higher than or equal to
0
0
0
.02 Å, it is indicated as “S”. If the displacement does not exceed
.01 Å, it is indicated as “W”, and if the displacement is lower than
.005 Å, then the ion is not mentioned in the column “Participants”.
3+
The dependence of Tph on ion radii r Ln , where the tetrad effect
is apparently observed, is shown in Fig. 3. The experimental points
are distinctly described by two straight lines with the parameters
determined by the least-squares deviation method. The left line
3
This information is given for crystals EuGdCuS (Pnma) and Eu-
YbCuS (Cmcm) in the column ''Participants". The calculated values
3
of the ion displacement in the modes are shown in Figs. S8 and S9.
The information of displacements of ions in the modes shows
Tph = a
1
+ b
1
r
indicated the compounds EuLaCuS
[101] and their regression constrants are equal to
= −3236 ± 35 K, = 4267 ± 34 K/Å (correlation index is
0.995). The right line Tph = a + b r indicated the compounds
[101], EuGdCuS [101], EuDyCuS , EuHoCuS , EuYbCuS
and their regression constrants are equal to = 3273 ± 24 K,
= −2392 ± 32 K/Å (correlation index is R = 0.987).
3
,
3
EuPrCuS ,
EuNdCuS
3
how much an ion is involved in the mode. In series EuLnCuS
3
(Ln =
a
1
b
1
R
1
Sm-Er), S.G. Pnma, europium ions are appreciably involved in the
=
2
2
-1
low-wavenumber modes with wavenumbers up to 160 cm , as well
as the Ln ion. The greatest involvement of europium in IR modes is
EuSmCuS
3
3
3
3
3
a
2
-1
predicted for the low-wavenumber mode at ~60 cm (B1u). The
b
2
2
greatest involvement of Ln3+ ion in IR modes is predicted for the
The discontinuous change of α(Т), as observed in our experi-
-1
low-wavenumber mode at ~75–80 cm (B2u). The vibrations of
ments, can be associated with neither high temperature poly-
morphous transitions, taking place at much higher temperatures
-1
copper are found in the IR modes with wavenumbers up to 130 cm .
The greatest involvement of copper is at the row of IR modes with
-1
wavenumbers about 100 cm . Sulfur is involved in all IR modes.
Sulfur ions S1, S2 and S3 are strongly involved in the IR modes with
-1
wavenumbers ~200, ~220 and ~250 cm . Both ions S1 and S2 are
-1
involved in an intense mode B3u at ~200 cm .
In series EuLnCuS (Ln = Tm, Yb, Lu), S.G. Cmcm, europium ions
are appreciably involved in low-wavenumber modes with wave-
3
-
1
-1
numbers up to ~130 cm , while the Ln ion – up to ~140 cm . The
highest involvement of europium in IR modes is predicted for the
-
1
low-wavenumber and low-intense modes at ~ 52–55 cm (B1u),
72–81 cm (B2u) and 125 cm (B3u). The highest participation of
Ln ion in IR modes is predicted for the same modes at ~ 52–55 cm
(B1u) and ~ 72–81 cm (B2u). In addition, Ln ions are strongly in-
volved in modes at ~ 91–98 cm (B1u) and ~ 135–138 cm (B3u). The
vibrations of copper appear in the IR modes with wavenumbers up
-
1
-1
~
3
+
-1
-
1
3+
-1
-1
3
+
Fig. 3. Dependence Tph on the ion radii of the lanthanoids r Ln
.
7

A.V. Ruseikina, V.A. Chernyshev, D.A. Velikanov et al.
Journal of Alloys and Compounds 874 (2021) 159968
Table 8
Temperatures of the expected structural transitions.
Compound
EuCeCuS
3
EuTbCuS
3
EuErCuS
0.890
3
EuTmCuS
3
EuLuCuS
0.861
3
Ion radii r, Å
1.010
0.923
0.880
T
ph, K
1025 ± 70
1065 ± 50
1144 ± 50
1168 ± 50
1213 ± 50
1
437–1594 K nor even more with the compound melting
them, and polyhedra СuS
4
, AS
7
(AS
6
), LnS
7
(LnS
6
) are jointed edge to
(
1539–1738 K) or oxidation, as the analysis was performed in the
edge [25,28–30,57,63], the crystal structure deformation and space
group changes are dependent on the ion radii rA2+, rLn and rCu . In
[26], for the determination of limits of the space groups Cmcm and
Pnma occurring in quaternary chalcogenides the dimensionless
3+
+
inert atmosphere. Besides, neither melting nor oxidation were not
registered by the DSC method, which, as mentioned above, was used
in the analysis process. Fracturing of the sample wasn’t observed as
well. The discontinuous change of the thermal expansion coefficient
is known to be a characteristic feature of the second type phase
transition [102]. Therefore, we suppose that, in the samples being
examined, in the indicated temperature range the structural tran-
sitions take place. With the use of the regression constrants a and b,
it is possible to predict the transition temperatures Tph for other
2
factor t = IR(A)·IR(C)/IR(B) was suggested. The critical value t = 0.908
governs the boundary line between space groups Cmcm and Pnma.
However, the calculation was based on the experimental data con-
cerning only the field of the space group change in the compounds
ALnCuS
for refinement of the structures PbLnCuS
contributions [31,33], it was mentioned that the samples of the
PbLnCuS (Ln = Tb, Dy,Tm, Y) compounds were multi-phase and,
besides the main phase, they contained LnCuS and PbS. Therefore,
3
(А = Pb, Ba), and we made an assumption of the necessity
3
(Ln = Tb, Dy, Y) [26]. In the
compounds EuLnCuS
vestigated in the dilatometric experiment (Table 8).
For the compounds EuPrCuS and EuNdCuS , the presence of
such transitions is confirmed by the XRS results [63]: EuPrCuS (SТ
CuS
MnS
, the phase transition takes
place in the temperature range of 970–1170 K (CТ BaLaCuS ) ↔ (СТ
Ba MnS ) [63], and expected temperature values are in the indicated
temperature range (Table 8, Fig. 3). As regarding to some other
compounds EuLnCuS (Ln = Sm - Lu) in the temperature range from
00 to 1300 K, the presence of the structural transitions has not been
3
(Ln = Ce, Tb, Er, Tm, Lu), which were not in-
3
3
3
2
3
the patterns have a lot of small impurity peaks and weak super-
structural peaks, which distinguish Pnma phase from Cmcm, can be
overlooked. For this reason, in the present work, we carried out the
calculations of t-factor resulted from the complete experimental
1
151±5K
BaLaCuS
3
)
EuPrCuS
(SТ BaLaCuS
According to the XRS data for EuСеCuS
3
(SТ Ba
2
MnS
3
), EuNdCuS
3
(SТ Eu
(SТ Ba
2
3
)
939±11K
1117±8K
EuNdCuS
3
3
)
EuNdCuS
3
2
3
).
3
data on the structures of the compounds A2+LnCuS
3
(А = Eu, Sr, Ba)
26–28,30,35,40,42,44,49,50,57,63–68], that allows to predict inter-
3
[
2
3
3
phase space group change in the PbLnCuS compounds. For this
purpose we suggest to use enhanced dependence t'= t + a, where a is
a variable parameter. As a result, the formula can be transformed to
3
9
2
be t’ = IR(A)·IR(C) + a × IR(B) , and, thus, the coefficient is as precise as
confirmed yet by XRS method, so our research will be moving
forward.
a = –0.6. The critical value t’ = 0.28 determines limiting date line
between orthorhombic space groups Cmcm and Pnma (Fig. 4).
As it is seen in Fig. (4), this new formula for the tolerance-factor
describes the demarcation line between phase fields for the com-
3.7. Symmetry prediction
In series A2+LnCuS
metal increases 1.2 Å (rEu ) < 1.21 Å (rSr ) < 1.23 Å (rPb ) < 1.35 Å
3 3
pounds ALnCuS (A = Ba, Sr, Eu), while many compounds PbLnCuS
3
(А = Eu, Sr, Pb, Ba), as the radius of divalent
2+ 2+ 2+
(Ln = Tb, Gd, Sm) can not be correctly classified by means of neither
t, nor t’ tolerance-factors. For these compounds, the dependences
assume the existence of Pnma phases; however, there is a mention in
the literature of Cmcm phases only. It should be noted that the Cmcm
phase can be easily confused with Pnma using only X-ray data as a
tool, since the difference is only in the presence of weak super-
structural peaks.
2
+
(
rBa ), gradual decrease of the number of compounds crystallized in
ST Ba MnS (space group Pnma): EuLnCuS (Ln = La, Ce, Pr, Nd) →
SrLnCuS (Ln = La, Ce) → PbLaCuS is observed (Table S1, Fig. 4).
2
3
3
3
3
Proximity of the ion radii of europium/strontium/plumbum to/with
REEs results in disorder of the A and Ln atoms in two crystal-
lographic positions that is typical for ST Ba MnS . Ba radius is much
2 3
Our data allowed to detect abnormity in behavior of the three
compounds PbLnCuS (Ln = Tb, Gd, Sm), and hence, for the last of
3
larger than those of light REEs, and, hence, each atom takes in-
dependent crystallographic positions, and the compounds crystallize
. As the radius rA2+ increases, the number of com-
in ST BaLaCuS
3
these, it is necessary to carry out thorough analyses of symmetry
using all kinds of experimental techniques. If the Cmcm symmetry
will be confirmed, then more detailed study of factors resulting in
this characteristic feature may be conducted to reach a clear
understanding.
2+
pounds crystallized in space group Сmcm also increases and A ions
transform faster into six-coordinated ones.
Since the compound structures of A2+LnCuS
(А = Eu, Sr, Pb, Ba)
2+
3
are described by 3D and 2D layers of LnCuS
3
with A ions between
4
. Conclusions
Generally, ab initio calculations of the structure and dynamics of
crystal lattice allow to determine the types of IR modes and assess
the degree of the ion participation in each mode. The elastic con-
stants of EuLnCuS , as the experimental data on those crystals are
3
not available in the literature, were also obtained by calculations.
Considerable difference of elastic constants for the compounds
EuLnCuS
3
(Ln = Sm-Er) and EuLnCuS
3
(Ln = Tm, Yb, Lu) was shown.
, the transition into ferro- or
In series of the compounds EuLnCuS
3
2
Fig. 4. Phase diagram of the compounds ALnCuS
3
in coordinates IR(B) , IR(A)×IR(C).
ferrimagnetic states takes place in the narrow temperature range
from 2 to 5 K. The effect of the decrease of the radius of the
rare-earth ion and crystallochemical contraction on the properties of
compounds is shown. The regularities of changes in the
temperatures of phase transformations, relative elongation, and
Critical value of a new tolerance-factor t’ = 0.28 fixes limiting date line between space
groups Cmcm and Pnma. The dependence is calculated for the compounds ALnCuS
A = Ba, Sr, Eu), while the compounds PbLnCuS are given solely for the evaluation.
Dashed limiting date line based on the previous formula for the tolerance-factor t [26]
is additionally shown. It is obvious that it describes demarcation less distinctly.
3
(
3
8

A.V. Ruseikina, V.A. Chernyshev, D.A. Velikanov et al.
Journal of Alloys and Compounds 874 (2021) 159968
microhardness of the compounds in the EuLnCuS
termined. The tolerance-factor t’ = IR(A)·IR(C) + a × IR(B) for the
3
series were de-
like to thank the staff of the Engineering Center of the Tyumen State
University for their help in carrying out physical and chemical tests.
2
prediction of the structural types of the compounds ALnCuS
3
was
verified.
Appendix A. Supporting information
Supplementary data associated with this article can be found in
the online version at doi:10.1016/j.jallcom.2021.159968.
Supporting information
Structural types and space groups of the compounds ALnCuS
A = Ln = La-Lu), Elastic constants of EuLnCuS , Bulk modulus,
, Calculated IR wavenumbers
3
(
3
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