- Email: [email protected]
Phase equilibria in the Er–Al–Si system at 873 K
CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 23–26
Contents lists available at ScienceDirect
CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry journal homepage: www.elsevier.com/locate/calphad
Phase equilibria in the Er–Al–Si system at 873 K Svitlana Pukas a , Wieslaw Łasocha b , Roman Gladyshevskii a,∗ a
Department of Inorganic Chemistry, Ivan Franko National University of Lviv, Kyryla i Mefodiya Street 6, 79005 Lviv, Ukraine
b
Faculty of Chemistry, Jagiellonian University, Ingardena Street 3, 30-060 Kraków, Poland
article
info
Article history: Received 8 June 2008 Received in revised form 7 July 2008 Accepted 9 July 2008 Available online 20 September 2008 Paper dedicated to the memory of Professor Ricardo Ferro.
a b s t r a c t The isothermal cross-section of the phase diagram of the system Er–Al–Si at 873 K was constructed based on X-ray powder diffraction. The existence of the compounds Er2 Al3 Si2 (Y2 Al3 Si2 -type structure), ErAlSi (YAlGe), Er2 AlSi2 (W2 CoB2 ), and Er2 Al1.5 Si1.5 (Mo2 FeB2 ) were confirmed and the formation of three new ternary alumosilicides was established: ErAl2.8 Si0.2 (HT-PuAl3 , hP24, P63 /mmc, a = 0.60295(4), c = 1.42308(9) nm), ∼Er5 Al6 Si4 (unknown structure), and Er6 Al3 Si (Tb6 Al3 Si, tI80, I4/mcm, a = 1.1436(2), c = 1.4854(2) nm). © 2008 Elsevier Ltd. All rights reserved.
Keywords: Alumosilicide Erbium X-ray powder diffraction Phase equilibrium Crystal structure
1. Introduction
2. Experimental
Detailed reviews of the current status of investigation of the phase diagrams of systems R–Al–Si where R—rare-earth element, can be found in [1,2]. Isothermal cross-sections of the phase diagrams have been constructed in the region 0–33.3 at.%R for La, Ce, Nd, Eu, and Gd (773 K), 0–40 at.%R for Ho (773 K), 0–50 at.%R for Tb and Pr (673 K). The interaction of the components at 873 K was investigated over the whole concentration range of the {Sm, Dy}–Al–Si systems [3,4]. The ternary compounds identified in the R–Al–Si systems crystallize with 16 different structure types [2,5], the majority of them being characterized by point compositions with rather simple stoichiometries. Exceptions are alumosilicides with homogeneity ranges along the line 33.3 at.%R (La, Ce, Pr, Nd, Sm, Eu, Gd, and Tb). Four more compounds of the {Ce,Sm,Tb}–Al–Si systems show variable compositions. Some solubility of the third element in the binary rare-earth compounds has been reported; the most extended homogeneity range is observed for the disilicide LaSi2 , which can incorporate up to 45 at.%Al. In this work we present the results of an investigation of the phase equilibria in the Er–Al–Si system at 873 K.
The investigation was carried out on eight two-component and 37 three-component alloys, which were prepared from high-purity elements (Er ≥ 99.83%, Al ≥ 99.99% and Si ≥ 99.999%) by arcmelting under argon atmosphere. The weight losses were less than 2%. The samples were annealed at 873 K in evacuated silica tubes for 720 h and then quenched into cold water. The phase analysis was performed based on X-ray powder diffraction data collected on a DRON-2.0M diffractometer (FeKα radiation), using the programs DICVOL [6], POWDER CELL [7], and the databases TYPIX [8] and PAULING FILE [5]. The crystal structures of some of the compounds were refined by the Rietveld method, using the program DBWS-9807 [9]. For this purpose, X-ray diffraction data for selected polycrystalline samples were collected on diffractometers HZG-4a and XPERT PRO (CuKα radiation).
∗
Corresponding author. Tel.: +380 32 2600388. E-mail address: [email protected] (R. Gladyshevskii).
0364-5916/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.calphad.2008.07.017
3. Results and discussion The isothermal cross-section of the phase diagram of the ternary system Er–Al–Si at 873 K is shown in Fig. 1. The existence of four binary compounds in the boundary system Er–Si at this temperature was confirmed: Er3 Si5−x (a new derivative of the AlB2 type with modulated structure; denoted in the literature as ErSi1.67 [10] or β -ErSi1.67 stable at T < 1048–1078 K [11]), ErSi (CrB-type structure) [12], Er5 Si4
24
S. Pukas et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 23–26
Fig. 2. Cell parameters of the solid solution of Al in ErSi, space group Cmcm.
Fig. 1. Isothermal cross-section of the phase diagram of the system Er–Al–Si at 873 K. Crosses show the nominal compositions of the samples used for the investigation. Equilibria indicated with dashed lines require confirmation. Table 1 Atom coordinates for the basic structure of Er3 Si4.76 Pearson symbol oS18, space group Amm2, cell parameters a = 0.40872(2), b = 1.13516(5), c = 0.65739(3) nm Site
Wyckoff position
x
y
z
Occupancy
Er1 Er2 Si1 Si2 Si3 Si4
2a 4d 2b 2b 4e 4e
0 0 1/2 1/2 1/2 1/2
0 0.3332(1) 0 0 0.1475(3) 0.3496(3)
0.0 0.0010(3) 0.3954(12) 0.6299(13) 0.1921(4) 0.3379(5)
1 1 0.47(2) 0.53(1) 1 0.88(1)
The real structure is modulated: superspace group Amm2(α 00), modulation vector q = 0.2223(1) a∗ .
(Sm5 Ge4 ) [13] and Er5 Si3 (Mn5 Si3 ) [14]. The silicide Er3 Si5−x is characterized by a narrow homogeneity range, which was found to be shifted into a Si-poorer region (60–61 at.%Si), in comparison with data reported in [10] (61–64 at.%Si). The cell parameters of the AlB2 -type subcell decrease with increasing number of vacancies on the Si site: a = 0.37943(4), c = 0.40911(7) nm for the polycrystalline sample Er39 Si61 and a = 0.37881(2), c = 0.40894(1) nm for Er40 Si60 . The crystallographic parameters for this phase at the composition Er3 Si4.76 , determined from X-ray single crystal diffraction data [15], are presented in Table 1. Concerning the compound ErSi, there was no indication of the formation of a FeB-type structure in any of the investigated samples. This is in contradiction with [11], where the coexistence of FeB-(composition ErSi) and CrB-(ErSi0.96 ) type structures was reported for the same temperature. Our results support the conclusions of [16], where the FeB- and CrB-type structures were assumed to be high- and low-temperature modifications. The existence of five binary compounds was confirmed in the system Er–Al at 873 K: ErAl3 (AuCu3 -type structure) [17], ErAl2 (MgCu2 ) [18], ErAl (DyAl) [19], Er3 Al2 (Zr3 Al2 ) [19], and Er2 Al (Co2 Si) [20]. The refined cell parameters of the erbium silicides and aluminides are listed in Table 2. The solubility of the third component in the binary compounds was investigated. It is not significant in Er3 Si5−x , Er5 Si4 , and the erbium aluminides, whereas the compound Er5 Si3 dissolves up to 10 at.%Al. The largest quantity of Al can be dissolved in ErSi (25 at.%); the cell parameters within the solid solution monotonically increase with increasing Al content, in agreement
with the larger atomic radius of Al (rAl = 0.143 nm, rSi = 0.132 nm). The variation of the cell parameters along the line 50 at.%Er is shown in Fig. 2. The existence of four previously reported ternary compounds was confirmed in the ternary system Er–Al–Si: Er2 Al3 Si2 (Y2 Al3 Si2 type structure) [21,22], ErAlSi (YAlGe) [23], Er2 AlSi2 (W2 CoB2 ) [24], and Er2 Al1.5 Si1.5 (Mo2 FeB2 ) [25]. The compounds ErAl2 Si2 (CaAl2 Si2 -type structure) [26], ErAl0.25 Si0.75 (CsCl) [27], and ErAl0.5−0.75 Si0.5−0.25 (FeB) [27] were not observed at 873 K, but three new ternary intermetallics, ErAl2.8 Si0.2 , ∼ Er5 Al6 Si4 , and Er6 Al3 Si, were found. The refined cell parameters of all the ternary compounds are listed in Table 3. The ternary erbium alumosilicides, despite the similar atomic radii of Al and Si, do now show any significant homogeneity ranges. According to [26], the compound ErAl2 Si2 was found in alloy annealed at 773 K for 150 h. Our studies showed that an alloy of the same composition, annealed at 873 K, contained the ternary compound Er2 Al3 Si2 , (Al), and (Si). We may conclude that ErAl2 Si2 exists at temperatures lower than 873 K and decomposes upon heating into the three phases mentioned above. A similar situation was observed in the Pr–Al–Si system, where PrAl2 Si2 was observed at 773 K, but had decomposed into Pr3 Al4 Si6 and (Al) at 873 K [28]. On the contrary, the erbium alumosilicides with CsCl- and FeB-type structures are probably stable only at high temperatures, since they were obtained by annealing alloys at 1273 K for 72 h [27]. The compound ErAl2.8 Si0.2 crystallizes with the hexagonal HT-PuAl3 structure type (Pearson symbol hP24, space group P63 /mmc) and forms two-phase regions with the ternary compounds Er2 Al3 Si2 , ErAlSi, and ∼Er5 Al6 Si4 , the binary compounds ErAl3 and ErAl2 , and (Al). The structure of this new compound was solved using X-ray powder diffraction data from a sample of composition Er20 Al70 Si10 , which contained three phases: 41% of the phase with the HT-PuAl3 -type structure, 45% ¯ ,a = Er2 Al3 Si2 (Y2 Al3 Si2 , mS14, C2/m) and 14% (Al) (Cu, cF 4, Fm3m 0.40462(3) nm). Because of the similar scattering factors of Al and Si, the Al/Si ratio on the sites in Wyckoff positions 6h and 12k was not refined, but was fixed according to data reported for the isotypic compound Yb1−y Al2.8 Si0.2 [29], the structure of which was investigated by the single-crystal method. The refined atom coordinates, listed in Table 4, are in good agreement with the data for the ytterbium compound. Our results do not allow us to confirm the stabilization of ErAl3 with trigonal HoAl3 -type structure by small quantities of Si, as reported in [30]. Diffraction lines that could not be attributed to any of the already known phases were observed in the samples Er30 Al60 Si10 , Er33.3 Al40 Si26.7 , Er36 Al31 Si33 , Er37 Al40 Si23 , and Er37.5 Al32.5 Si30 . The new compound was assigned the approximate composition
S. Pukas et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 23–26
25
Table 2 Crystallographic data of the binary compounds in the systems Er–Si and Er–Al, confirmed at 873 K Compound
Structure type
Er3 Si4.76 ErSi Er5 Si4 [13] Er5 Si3 ErAl3 [17] ErAl2 ErAl Er3 Al2 [19] Er2 Al
Pearson symbol
Er3 Si5−x CrB Sm5 Ge4 Mn5 Si3 AuCu3 MgCu2 DyAl Zr3 Al2 Co2 Si
Space group
oS18 oS8 oP36 hP16 cP4 cF 24 oP16 tP20 oP12
Cell parameters (nm)
Amm2 Cmcm Pnma P63 /mcm ¯ Pm3m ¯ Fd3m Pbcm P42 /mnm Pnma
a
b
c
0.40872(2) 0.4205(1) 0.727 0.8302(1) 0.4215 0.7798(1) 0.5791(2) 0.8123 0.6523(4)
1.13516(5) 1.0411(2) 1.432 – – – 1.1277(4) – 0.5024(6)
0.65739(3) 0.3792(1) 0.758 0.6210(2) – – 0.5574(1) 0.7484 0.9263(6)
Table 3 Crystallographic data of ternary compounds observed in the Er–Al–Si system at 873 K Compound
Structure type
ErAl2.8 Si0.2 Er2 Al3 Si2 ErAlSi ∼ Er5 Al6 Si4 Er2 AlSi2 Er2 Al1.5 Si1.5 Er6 Al3 Si
Pearson symbol
HT-PuAl3 Y2 Al3 Si2 YAlGe Unknown structure W2 CoB2 Mo2 FeB2 Tb6 Al3 Si
Space group
Cell parameters (nm) a
b
c
β 100.675(6)◦
hP24 mS14 oS12
P63 /mmc C 2/m Cmcm
0.60295(4) 1.00711(8) 0.39738(2)
– 0.40104(3) 1.01616(5)
1.42308(9) 0.65561(6) 0.56542(3)
oI10 tP10 tI80
Immm P4/mbm I4/mcm
0.40215(2) 0.68202(5) 1.1436(2)
0.57078(3) 0.42421(4) –
0.85441(5) 0.19732(3) 1.4854(2)
Table 4 Atom coordinates for ErAl2.8 Si0.2 : structure type HT-PuAl3 , Pearson symbol hP24, space group P63 /mmc, cell parameters a = 0.60295(4), c = 1.42308(9) nm, M1 = M2 = 0.93Al + 0.07Si (fixed) Site
Wyckoff position
x
y
z
Occupancy
Er1 Er2 M1 M2
2b 4f 6h 12k
0 1/3 0.829(3) 0.521(2)
0 2/3 0.658(3) 0.042(2)
1/4 0.0914(3) 0.0808(7) 1/4
1 0.95(1) 1 1
Table 5 Atom coordinates for Er6 Al3 Si: structure type Tb6 Al3 Si, Pearson symbol tI80, space group I4/mcm, cell parameters a = 1.1436(2), c = 1.4854(2) nm Site
Wyckoff position
x
y
z
Er1 Er2 Er3 Al1 Al2 Si1 Si2
2b 8h 8g 16l 8h 4c 4a
0.2029(5) 0.6657(8) 0 0.670(3) 0.126(4) 0 0
0.0645(5) 0.1657(8) 1/2 0.170(3) 0.626(4) 0 0
0.1324(4) 0 0.147(1) 0.205(2) 0 0 1/4
∼Er5 Al6 Si4 and its crystal structure is under investigation. This erbium alumosilicide forms two-phase regions with the ternary phases ErAl2.8 Si0.2 , ErAlSi, Er2 AlSi2 , and Er2 Al1.5 Si1.5 , and with binary ErAl2 . The determination of the crystal structure of the compound Er6 Al3 Si was carried out by X-ray powder diffraction. The powder pattern of the sample Er60 Al30 Si10 indicated that the new compound could be isotypic with tetragonal Tb6 Al3 Si (Pearson symbol tI80, space group I4/mcm) [31]. The compound forms twophase regions with the binary phases ErAl, Er3 Al2 , and Er2 Al, and solid solution of Al in Er5 Si3 . The refinement of the crystal structure of Er6 Al3 Si confirmed its isotypism with Tb6 Al3 Si. The investigated alloy, Er60 Al30 Si10 , contained, in addition to the main phase Er6 Al3 Si(Tb6 Al3 Si, I4/mcm, tI80), 22% ErAl (DyAl, oP16, Pbcm) and 21% Er5 Si3 (Mn5 Si3 , hP16, P63 /mcm). The atom coordinates of the structure of Er6 Al3 Si are given in Table 5. Table 6 summarizes the structure types reported in the ternary systems R–Al–Si. An almost complete row of isotypic compounds exists for the trigonal type CaAl2 Si2 . The compound ErAl2.8 Si0.2 is the second representative of the hexagonal type
Fig. 3. Cell parameters of R6 Al3 Si compounds with Tb6 Al3 Si structure type, space group I4/mcm. Y has been placed according to the best agreement with the variation of the cell parameters.
HT-PuAl3 , whereas the orthorhombic FeB- and cubic CsCl-type structures have so far only been reported for the system Er–Al–Si. Monoclinic Y2 Al3 Si2 -, orthorhombic YAlGe- and W2 CoB2 -, and tetragonal Mo2 FeB2 -type structures form only with late rare-earth elements. The erbium alumosilicide Er6 Al3 Si completes the row of representatives of the Tb6 Al3 Si structure type between Gd and Tm [32]. As can be seen from Fig. 3, the cell parameters of these isotypic compounds gradually decrease with increasing atomic number of the rare-earth element. A comparison of the systems Er–Al–Si and Er–Al–Ge, given in Table 7, shows that only two structure types, trigonal CaAl2 Si2 and orthorhombic YAlGe, are common to these systems. There are no isotypic compounds in the systems Er–Al–Si and Er–Ga–Si. It should be noted that the system Er–Al–Ge has been investigated in detail in the region 20–55 at.%Er and 0–33.3 at.%Al [33], whereas no systematic studies of the system Er–Ga–Si have been performed so far.
26
S. Pukas et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 23–26
Table 6 Representatives of 16 different structure types reported in the systems R–Al–Si (R—rare-earth element) Compound
RAl2 Si2 R3 Al4 Si6 R1−x Al2.8 Si0.2 RAlSi2 R2 Al3 Si2 RAl1.5 Si0.5 RAl1+x Si1−x RAlSi R2 AlSi2 R2 Al1.5 Si1.5 R2 Al1−x Si1+x
R6 Al3 Si R3 Al0.5 Si0.5
Structure type
CaAl2 Si2 Ce3 Al4 Si6 Mg3 Cd HT-PuAl3 CeAlSi2 Y2 Al3 Si2 AlB2 α -ThSi2 YAlGe W2 CoB2 Mo2 FeB2 FeB CrB CsCl Tb6 Al3 Si Cu3 Au
R La
Ce
Pr
Nd
Sm
Eu
Gd
Tb
Dy
Ho
Er
+
+ +
+ +
+
+
+
+
+
+
+
+
+
Yb
+
+
Lu
+ +
+
+
+
+ +
+ +
+ +
+ +
+
+
+
+
Structure type
MIII Al
+
+
+
+ +
+
Si
Ge
+ +
+
+ +
HT-PuAl3 Y2 Al3 Si2 ZrSi2
+ + +
+ +
Er2 MIII MIV 3
Y2 AlGe3
+
ErMIII MIV IV ErMIII 0.41−0.58 M1.21−1.11 IV ErMIII M 1.48 0.52 Er2 MIII MIV 2 IV Er2 MIII 1.5 M1.5 IV ErMIII 0.5−0.75 M0.5−0.25 IV ErMIII M 0.25 0.75 IV Er6 MIII 3 M
YAlGe α -GdSi2 α -ThSi2 W2 CoB2 Mo2 FeB2 FeB CsCl Tb6 Al3 Si
+
IV ErMIII 2 M2 IV Er2 MIII M 3 4
CaAl2 Si2 Hf2 Ni3 Si4
IV ErMIII 2.8 M0.2 IV Er2 MIII 3 M2 IV ErMIII M 0.15 1.92
+ +
+ + + + + + +
+ + + + + + + +
+
+
MIV Ga
+
+
+
+
+ + + +
+
+
Table 7 Compounds reported in the systems Er–MIII –MIV (MIII –Al, Ga, MIV –Si, Ge) Compound
Tm
+
4. Conclusions The interaction of erbium with aluminum and silicon at 873 K is similar to the interaction of the components in the corresponding systems with other late rare-earth elements, whereas replacement of Al by Ga or Si by Ge leads to the formation of compounds with different stoichiometry and crystal structure. Acknowledgements This work was supported by the Ministry of Ukraine for Education and Science under the grant No. 0106U001300. SP gratefully acknowledges Queen Jadwiga Fund at the Jagiellonian University. References [1] I. Melnyk, S. Pikus, N. Semus’o, R. Gladyshevskii, Arch. Mater. Sci. 25 (2004) 113–131. [2] I. Melnyk, S. Pikus, V. Kuprysyuk, N. Semuso, R. Gladyshevskii, Arch. Mater. Sci. 26 (2005) 279–301.
+
+
+
+ + +
+
+
+
+ +
+ + +
+ + +
+
[3] I. Melnyk, Ph.D. Thesis, Maria Curie-Skłodowska University, Lublin, 2005 (in Polish). [4] V. Kuprysyuk, Ph.D. Thesis, Maria Curie-Skłodowska University, Lublin, 2005 (in Polish). [5] P. Villars, K. Cenzual (Eds.), Pearson’s Crystal Data. Crystal Structure Database for Inorganic Compounds, ASM International, Materials Park, OH, 2007. [6] A. Boultif, D. Louër, J. Appl. Crystallogr. 24 (1991) 987–993. [7] W. Kraus, G. Nolze, PowderCell for Windows, Federal Institute for Materials Research and Testing, Berlin, 1999. [8] E. Parthé, L. Gelato, B. Chabot, M. Penzo, K. Cenzual, R. Gladyshevskii, TYPIX. Standardized Data and Crystal Chemical Characterization of Inorganic Structure Types, Springer-Verlag, Heidelberg, 1993–1994. [9] R.A. Young, A.C. Larson, C.O. Paiva-Santos, Rietveld Analysis of X-Ray and Neutron Powder Diffraction Patterns, School of Physics, Georgia Institute of Technology, Atlanta, GA, 1998. [10] T.B. Massalski (Ed.), Binary Alloy Phase Diagrams, second ed., ASM International, Materials Park, OH, 1990. [11] S.P. Luzan, V.E. Listovnichii, Yu.I. Buyanov, P.S. Martsenyuk, J. Alloys Compounds 239 (1996) 77–82. [12] E.I. Gladyshevskii, P.I. Kripyakevich, Zh. Strukt. Khim. 5 (1964) 853–859. Translated in J. Struct. Chem. 5 (1964) 789–794. [13] G.S. Smith, A.G. Tharp, Q. Johnson, Nature (London) 210 (1966) 1148–1149. [14] E.I. Gladyshevskii, Izv. Akad. Nauk SSSR, Neorg. Mater. 1 (1965) 868–872. Translated in Inorg. Mater. 1 (1965) 797–801. [15] S. Pukas, L. Akselrud, R. Cerny, R. Gladyshevskii, Coll. Abs. X Int. Conf. Cryst. Chem. Intermet. Compd., Lviv (2007) 123. [16] D. Hohnke, E. Parthé, Acta Crystallogr. 20 (1966) 572–582. [17] J.H.N. Vucht, K.H.J. Buschow, Philips Res. Rep. 19 (1964) 319–322. [18] J.H. Wernick, S. Geller, Trans. Am. Inst. Min. Metall. Pet. Eng. 218 (1960) 866–868. [19] K.H.J. Buschow, J. Less-Common Met. 8 (1965) 209–212. [20] K.H.J. Buschow, A.S. Van Der Goot, J. Less-Common Met. 24 (1971) 117–120. [21] X.-Z. Chen, B. Sieve, R. Henning, A.J. Schultz, P. Brazis, C.R. Kannewurf, J.A. Cowen, R. Crosby, M.G. Kanatzidis, Angew. Chem. Int. Ed. 38 (1999) 693–696. [22] S. Pukas, Yu. Lutsyshyn, R. Gladyshevskii, Coll. Abs. 9 Sci. Conf. Lviv. Chem. Readings, Lviv (2003) H13 (in Ukrainian). [23] S. Pukas, Yu. Lutsyshyn, M. Manyako, E. Gladyshevskii, J. Alloys Compounds 367 (2004) 162–166. [24] C. Kranenberg, A. Mewis, Z. Anorg. Allg. Chem. 626 (2000) 1448–1453. [25] T.I. Yanson, Ph.D. Thesis, Ivan Franko State University of Lviv, 1975 (in Russian). [26] A.O. Muravyova, O.S. Zarechnyuk, E.I. Gladyshevskii, Visn. Lviv. Univ. Ser. Khim. 13 (1972) 14–16 (in Ukrainian). [27] A. Raman, Inorg. Chem. 7 (1968) 973–976. [28] N. Muts, R. Gladyshevskii, E. Gladyshevskii, J. Alloys Compounds 402 (2005) 66–69. [29] J.T. Zhao, W. Schnelle, Yu. Grin, J. Solid State Chem. 163 (2002) 113–120. [30] J.H.N. Vucht, K.H.J. Buschow, Philips Res. Rep. 22 (1967) 233–245. [31] I.S. Dubenko, A.A. Evdokimov, V.N. Ionov, Kristallografia 32 (1987) 347–351. Translated in Sov. Phys. Crystallogr. 32 (1987) 201–203. [32] I.S. Dubenko, A.A. Evdokimov, Yu.N. Titov, Zh. Neorg. Khim. 30 (1985) 2994–2996. Translated in Russ. J. Inorg. Chem. 30 (1985) 1707–1708. [33] S. Pukas, R. Gladyshevskii, E. Gladyshevskii, Visn. Lviv. Univ. Ser. Khim. 45 (2004) 78–84 (in Ukrainian).
Contents lists available at ScienceDirect
CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry journal homepage: www.elsevier.com/locate/calphad
Phase equilibria in the Er–Al–Si system at 873 K Svitlana Pukas a , Wieslaw Łasocha b , Roman Gladyshevskii a,∗ a
Department of Inorganic Chemistry, Ivan Franko National University of Lviv, Kyryla i Mefodiya Street 6, 79005 Lviv, Ukraine
b
Faculty of Chemistry, Jagiellonian University, Ingardena Street 3, 30-060 Kraków, Poland
article
info
Article history: Received 8 June 2008 Received in revised form 7 July 2008 Accepted 9 July 2008 Available online 20 September 2008 Paper dedicated to the memory of Professor Ricardo Ferro.
a b s t r a c t The isothermal cross-section of the phase diagram of the system Er–Al–Si at 873 K was constructed based on X-ray powder diffraction. The existence of the compounds Er2 Al3 Si2 (Y2 Al3 Si2 -type structure), ErAlSi (YAlGe), Er2 AlSi2 (W2 CoB2 ), and Er2 Al1.5 Si1.5 (Mo2 FeB2 ) were confirmed and the formation of three new ternary alumosilicides was established: ErAl2.8 Si0.2 (HT-PuAl3 , hP24, P63 /mmc, a = 0.60295(4), c = 1.42308(9) nm), ∼Er5 Al6 Si4 (unknown structure), and Er6 Al3 Si (Tb6 Al3 Si, tI80, I4/mcm, a = 1.1436(2), c = 1.4854(2) nm). © 2008 Elsevier Ltd. All rights reserved.
Keywords: Alumosilicide Erbium X-ray powder diffraction Phase equilibrium Crystal structure
1. Introduction
2. Experimental
Detailed reviews of the current status of investigation of the phase diagrams of systems R–Al–Si where R—rare-earth element, can be found in [1,2]. Isothermal cross-sections of the phase diagrams have been constructed in the region 0–33.3 at.%R for La, Ce, Nd, Eu, and Gd (773 K), 0–40 at.%R for Ho (773 K), 0–50 at.%R for Tb and Pr (673 K). The interaction of the components at 873 K was investigated over the whole concentration range of the {Sm, Dy}–Al–Si systems [3,4]. The ternary compounds identified in the R–Al–Si systems crystallize with 16 different structure types [2,5], the majority of them being characterized by point compositions with rather simple stoichiometries. Exceptions are alumosilicides with homogeneity ranges along the line 33.3 at.%R (La, Ce, Pr, Nd, Sm, Eu, Gd, and Tb). Four more compounds of the {Ce,Sm,Tb}–Al–Si systems show variable compositions. Some solubility of the third element in the binary rare-earth compounds has been reported; the most extended homogeneity range is observed for the disilicide LaSi2 , which can incorporate up to 45 at.%Al. In this work we present the results of an investigation of the phase equilibria in the Er–Al–Si system at 873 K.
The investigation was carried out on eight two-component and 37 three-component alloys, which were prepared from high-purity elements (Er ≥ 99.83%, Al ≥ 99.99% and Si ≥ 99.999%) by arcmelting under argon atmosphere. The weight losses were less than 2%. The samples were annealed at 873 K in evacuated silica tubes for 720 h and then quenched into cold water. The phase analysis was performed based on X-ray powder diffraction data collected on a DRON-2.0M diffractometer (FeKα radiation), using the programs DICVOL [6], POWDER CELL [7], and the databases TYPIX [8] and PAULING FILE [5]. The crystal structures of some of the compounds were refined by the Rietveld method, using the program DBWS-9807 [9]. For this purpose, X-ray diffraction data for selected polycrystalline samples were collected on diffractometers HZG-4a and XPERT PRO (CuKα radiation).
∗
Corresponding author. Tel.: +380 32 2600388. E-mail address: [email protected] (R. Gladyshevskii).
0364-5916/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.calphad.2008.07.017
3. Results and discussion The isothermal cross-section of the phase diagram of the ternary system Er–Al–Si at 873 K is shown in Fig. 1. The existence of four binary compounds in the boundary system Er–Si at this temperature was confirmed: Er3 Si5−x (a new derivative of the AlB2 type with modulated structure; denoted in the literature as ErSi1.67 [10] or β -ErSi1.67 stable at T < 1048–1078 K [11]), ErSi (CrB-type structure) [12], Er5 Si4
24
S. Pukas et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 23–26
Fig. 2. Cell parameters of the solid solution of Al in ErSi, space group Cmcm.
Fig. 1. Isothermal cross-section of the phase diagram of the system Er–Al–Si at 873 K. Crosses show the nominal compositions of the samples used for the investigation. Equilibria indicated with dashed lines require confirmation. Table 1 Atom coordinates for the basic structure of Er3 Si4.76 Pearson symbol oS18, space group Amm2, cell parameters a = 0.40872(2), b = 1.13516(5), c = 0.65739(3) nm Site
Wyckoff position
x
y
z
Occupancy
Er1 Er2 Si1 Si2 Si3 Si4
2a 4d 2b 2b 4e 4e
0 0 1/2 1/2 1/2 1/2
0 0.3332(1) 0 0 0.1475(3) 0.3496(3)
0.0 0.0010(3) 0.3954(12) 0.6299(13) 0.1921(4) 0.3379(5)
1 1 0.47(2) 0.53(1) 1 0.88(1)
The real structure is modulated: superspace group Amm2(α 00), modulation vector q = 0.2223(1) a∗ .
(Sm5 Ge4 ) [13] and Er5 Si3 (Mn5 Si3 ) [14]. The silicide Er3 Si5−x is characterized by a narrow homogeneity range, which was found to be shifted into a Si-poorer region (60–61 at.%Si), in comparison with data reported in [10] (61–64 at.%Si). The cell parameters of the AlB2 -type subcell decrease with increasing number of vacancies on the Si site: a = 0.37943(4), c = 0.40911(7) nm for the polycrystalline sample Er39 Si61 and a = 0.37881(2), c = 0.40894(1) nm for Er40 Si60 . The crystallographic parameters for this phase at the composition Er3 Si4.76 , determined from X-ray single crystal diffraction data [15], are presented in Table 1. Concerning the compound ErSi, there was no indication of the formation of a FeB-type structure in any of the investigated samples. This is in contradiction with [11], where the coexistence of FeB-(composition ErSi) and CrB-(ErSi0.96 ) type structures was reported for the same temperature. Our results support the conclusions of [16], where the FeB- and CrB-type structures were assumed to be high- and low-temperature modifications. The existence of five binary compounds was confirmed in the system Er–Al at 873 K: ErAl3 (AuCu3 -type structure) [17], ErAl2 (MgCu2 ) [18], ErAl (DyAl) [19], Er3 Al2 (Zr3 Al2 ) [19], and Er2 Al (Co2 Si) [20]. The refined cell parameters of the erbium silicides and aluminides are listed in Table 2. The solubility of the third component in the binary compounds was investigated. It is not significant in Er3 Si5−x , Er5 Si4 , and the erbium aluminides, whereas the compound Er5 Si3 dissolves up to 10 at.%Al. The largest quantity of Al can be dissolved in ErSi (25 at.%); the cell parameters within the solid solution monotonically increase with increasing Al content, in agreement
with the larger atomic radius of Al (rAl = 0.143 nm, rSi = 0.132 nm). The variation of the cell parameters along the line 50 at.%Er is shown in Fig. 2. The existence of four previously reported ternary compounds was confirmed in the ternary system Er–Al–Si: Er2 Al3 Si2 (Y2 Al3 Si2 type structure) [21,22], ErAlSi (YAlGe) [23], Er2 AlSi2 (W2 CoB2 ) [24], and Er2 Al1.5 Si1.5 (Mo2 FeB2 ) [25]. The compounds ErAl2 Si2 (CaAl2 Si2 -type structure) [26], ErAl0.25 Si0.75 (CsCl) [27], and ErAl0.5−0.75 Si0.5−0.25 (FeB) [27] were not observed at 873 K, but three new ternary intermetallics, ErAl2.8 Si0.2 , ∼ Er5 Al6 Si4 , and Er6 Al3 Si, were found. The refined cell parameters of all the ternary compounds are listed in Table 3. The ternary erbium alumosilicides, despite the similar atomic radii of Al and Si, do now show any significant homogeneity ranges. According to [26], the compound ErAl2 Si2 was found in alloy annealed at 773 K for 150 h. Our studies showed that an alloy of the same composition, annealed at 873 K, contained the ternary compound Er2 Al3 Si2 , (Al), and (Si). We may conclude that ErAl2 Si2 exists at temperatures lower than 873 K and decomposes upon heating into the three phases mentioned above. A similar situation was observed in the Pr–Al–Si system, where PrAl2 Si2 was observed at 773 K, but had decomposed into Pr3 Al4 Si6 and (Al) at 873 K [28]. On the contrary, the erbium alumosilicides with CsCl- and FeB-type structures are probably stable only at high temperatures, since they were obtained by annealing alloys at 1273 K for 72 h [27]. The compound ErAl2.8 Si0.2 crystallizes with the hexagonal HT-PuAl3 structure type (Pearson symbol hP24, space group P63 /mmc) and forms two-phase regions with the ternary compounds Er2 Al3 Si2 , ErAlSi, and ∼Er5 Al6 Si4 , the binary compounds ErAl3 and ErAl2 , and (Al). The structure of this new compound was solved using X-ray powder diffraction data from a sample of composition Er20 Al70 Si10 , which contained three phases: 41% of the phase with the HT-PuAl3 -type structure, 45% ¯ ,a = Er2 Al3 Si2 (Y2 Al3 Si2 , mS14, C2/m) and 14% (Al) (Cu, cF 4, Fm3m 0.40462(3) nm). Because of the similar scattering factors of Al and Si, the Al/Si ratio on the sites in Wyckoff positions 6h and 12k was not refined, but was fixed according to data reported for the isotypic compound Yb1−y Al2.8 Si0.2 [29], the structure of which was investigated by the single-crystal method. The refined atom coordinates, listed in Table 4, are in good agreement with the data for the ytterbium compound. Our results do not allow us to confirm the stabilization of ErAl3 with trigonal HoAl3 -type structure by small quantities of Si, as reported in [30]. Diffraction lines that could not be attributed to any of the already known phases were observed in the samples Er30 Al60 Si10 , Er33.3 Al40 Si26.7 , Er36 Al31 Si33 , Er37 Al40 Si23 , and Er37.5 Al32.5 Si30 . The new compound was assigned the approximate composition
S. Pukas et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 23–26
25
Table 2 Crystallographic data of the binary compounds in the systems Er–Si and Er–Al, confirmed at 873 K Compound
Structure type
Er3 Si4.76 ErSi Er5 Si4 [13] Er5 Si3 ErAl3 [17] ErAl2 ErAl Er3 Al2 [19] Er2 Al
Pearson symbol
Er3 Si5−x CrB Sm5 Ge4 Mn5 Si3 AuCu3 MgCu2 DyAl Zr3 Al2 Co2 Si
Space group
oS18 oS8 oP36 hP16 cP4 cF 24 oP16 tP20 oP12
Cell parameters (nm)
Amm2 Cmcm Pnma P63 /mcm ¯ Pm3m ¯ Fd3m Pbcm P42 /mnm Pnma
a
b
c
0.40872(2) 0.4205(1) 0.727 0.8302(1) 0.4215 0.7798(1) 0.5791(2) 0.8123 0.6523(4)
1.13516(5) 1.0411(2) 1.432 – – – 1.1277(4) – 0.5024(6)
0.65739(3) 0.3792(1) 0.758 0.6210(2) – – 0.5574(1) 0.7484 0.9263(6)
Table 3 Crystallographic data of ternary compounds observed in the Er–Al–Si system at 873 K Compound
Structure type
ErAl2.8 Si0.2 Er2 Al3 Si2 ErAlSi ∼ Er5 Al6 Si4 Er2 AlSi2 Er2 Al1.5 Si1.5 Er6 Al3 Si
Pearson symbol
HT-PuAl3 Y2 Al3 Si2 YAlGe Unknown structure W2 CoB2 Mo2 FeB2 Tb6 Al3 Si
Space group
Cell parameters (nm) a
b
c
β 100.675(6)◦
hP24 mS14 oS12
P63 /mmc C 2/m Cmcm
0.60295(4) 1.00711(8) 0.39738(2)
– 0.40104(3) 1.01616(5)
1.42308(9) 0.65561(6) 0.56542(3)
oI10 tP10 tI80
Immm P4/mbm I4/mcm
0.40215(2) 0.68202(5) 1.1436(2)
0.57078(3) 0.42421(4) –
0.85441(5) 0.19732(3) 1.4854(2)
Table 4 Atom coordinates for ErAl2.8 Si0.2 : structure type HT-PuAl3 , Pearson symbol hP24, space group P63 /mmc, cell parameters a = 0.60295(4), c = 1.42308(9) nm, M1 = M2 = 0.93Al + 0.07Si (fixed) Site
Wyckoff position
x
y
z
Occupancy
Er1 Er2 M1 M2
2b 4f 6h 12k
0 1/3 0.829(3) 0.521(2)
0 2/3 0.658(3) 0.042(2)
1/4 0.0914(3) 0.0808(7) 1/4
1 0.95(1) 1 1
Table 5 Atom coordinates for Er6 Al3 Si: structure type Tb6 Al3 Si, Pearson symbol tI80, space group I4/mcm, cell parameters a = 1.1436(2), c = 1.4854(2) nm Site
Wyckoff position
x
y
z
Er1 Er2 Er3 Al1 Al2 Si1 Si2
2b 8h 8g 16l 8h 4c 4a
0.2029(5) 0.6657(8) 0 0.670(3) 0.126(4) 0 0
0.0645(5) 0.1657(8) 1/2 0.170(3) 0.626(4) 0 0
0.1324(4) 0 0.147(1) 0.205(2) 0 0 1/4
∼Er5 Al6 Si4 and its crystal structure is under investigation. This erbium alumosilicide forms two-phase regions with the ternary phases ErAl2.8 Si0.2 , ErAlSi, Er2 AlSi2 , and Er2 Al1.5 Si1.5 , and with binary ErAl2 . The determination of the crystal structure of the compound Er6 Al3 Si was carried out by X-ray powder diffraction. The powder pattern of the sample Er60 Al30 Si10 indicated that the new compound could be isotypic with tetragonal Tb6 Al3 Si (Pearson symbol tI80, space group I4/mcm) [31]. The compound forms twophase regions with the binary phases ErAl, Er3 Al2 , and Er2 Al, and solid solution of Al in Er5 Si3 . The refinement of the crystal structure of Er6 Al3 Si confirmed its isotypism with Tb6 Al3 Si. The investigated alloy, Er60 Al30 Si10 , contained, in addition to the main phase Er6 Al3 Si(Tb6 Al3 Si, I4/mcm, tI80), 22% ErAl (DyAl, oP16, Pbcm) and 21% Er5 Si3 (Mn5 Si3 , hP16, P63 /mcm). The atom coordinates of the structure of Er6 Al3 Si are given in Table 5. Table 6 summarizes the structure types reported in the ternary systems R–Al–Si. An almost complete row of isotypic compounds exists for the trigonal type CaAl2 Si2 . The compound ErAl2.8 Si0.2 is the second representative of the hexagonal type
Fig. 3. Cell parameters of R6 Al3 Si compounds with Tb6 Al3 Si structure type, space group I4/mcm. Y has been placed according to the best agreement with the variation of the cell parameters.
HT-PuAl3 , whereas the orthorhombic FeB- and cubic CsCl-type structures have so far only been reported for the system Er–Al–Si. Monoclinic Y2 Al3 Si2 -, orthorhombic YAlGe- and W2 CoB2 -, and tetragonal Mo2 FeB2 -type structures form only with late rare-earth elements. The erbium alumosilicide Er6 Al3 Si completes the row of representatives of the Tb6 Al3 Si structure type between Gd and Tm [32]. As can be seen from Fig. 3, the cell parameters of these isotypic compounds gradually decrease with increasing atomic number of the rare-earth element. A comparison of the systems Er–Al–Si and Er–Al–Ge, given in Table 7, shows that only two structure types, trigonal CaAl2 Si2 and orthorhombic YAlGe, are common to these systems. There are no isotypic compounds in the systems Er–Al–Si and Er–Ga–Si. It should be noted that the system Er–Al–Ge has been investigated in detail in the region 20–55 at.%Er and 0–33.3 at.%Al [33], whereas no systematic studies of the system Er–Ga–Si have been performed so far.
26
S. Pukas et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 33 (2009) 23–26
Table 6 Representatives of 16 different structure types reported in the systems R–Al–Si (R—rare-earth element) Compound
RAl2 Si2 R3 Al4 Si6 R1−x Al2.8 Si0.2 RAlSi2 R2 Al3 Si2 RAl1.5 Si0.5 RAl1+x Si1−x RAlSi R2 AlSi2 R2 Al1.5 Si1.5 R2 Al1−x Si1+x
R6 Al3 Si R3 Al0.5 Si0.5
Structure type
CaAl2 Si2 Ce3 Al4 Si6 Mg3 Cd HT-PuAl3 CeAlSi2 Y2 Al3 Si2 AlB2 α -ThSi2 YAlGe W2 CoB2 Mo2 FeB2 FeB CrB CsCl Tb6 Al3 Si Cu3 Au
R La
Ce
Pr
Nd
Sm
Eu
Gd
Tb
Dy
Ho
Er
+
+ +
+ +
+
+
+
+
+
+
+
+
+
Yb
+
+
Lu
+ +
+
+
+
+ +
+ +
+ +
+ +
+
+
+
+
Structure type
MIII Al
+
+
+
+ +
+
Si
Ge
+ +
+
+ +
HT-PuAl3 Y2 Al3 Si2 ZrSi2
+ + +
+ +
Er2 MIII MIV 3
Y2 AlGe3
+
ErMIII MIV IV ErMIII 0.41−0.58 M1.21−1.11 IV ErMIII M 1.48 0.52 Er2 MIII MIV 2 IV Er2 MIII 1.5 M1.5 IV ErMIII 0.5−0.75 M0.5−0.25 IV ErMIII M 0.25 0.75 IV Er6 MIII 3 M
YAlGe α -GdSi2 α -ThSi2 W2 CoB2 Mo2 FeB2 FeB CsCl Tb6 Al3 Si
+
IV ErMIII 2 M2 IV Er2 MIII M 3 4
CaAl2 Si2 Hf2 Ni3 Si4
IV ErMIII 2.8 M0.2 IV Er2 MIII 3 M2 IV ErMIII M 0.15 1.92
+ +
+ + + + + + +
+ + + + + + + +
+
+
MIV Ga
+
+
+
+
+ + + +
+
+
Table 7 Compounds reported in the systems Er–MIII –MIV (MIII –Al, Ga, MIV –Si, Ge) Compound
Tm
+
4. Conclusions The interaction of erbium with aluminum and silicon at 873 K is similar to the interaction of the components in the corresponding systems with other late rare-earth elements, whereas replacement of Al by Ga or Si by Ge leads to the formation of compounds with different stoichiometry and crystal structure. Acknowledgements This work was supported by the Ministry of Ukraine for Education and Science under the grant No. 0106U001300. SP gratefully acknowledges Queen Jadwiga Fund at the Jagiellonian University. References [1] I. Melnyk, S. Pikus, N. Semus’o, R. Gladyshevskii, Arch. Mater. Sci. 25 (2004) 113–131. [2] I. Melnyk, S. Pikus, V. Kuprysyuk, N. Semuso, R. Gladyshevskii, Arch. Mater. Sci. 26 (2005) 279–301.
+
+
+
+ + +
+
+
+
+ +
+ + +
+ + +
+
[3] I. Melnyk, Ph.D. Thesis, Maria Curie-Skłodowska University, Lublin, 2005 (in Polish). [4] V. Kuprysyuk, Ph.D. Thesis, Maria Curie-Skłodowska University, Lublin, 2005 (in Polish). [5] P. Villars, K. Cenzual (Eds.), Pearson’s Crystal Data. Crystal Structure Database for Inorganic Compounds, ASM International, Materials Park, OH, 2007. [6] A. Boultif, D. Louër, J. Appl. Crystallogr. 24 (1991) 987–993. [7] W. Kraus, G. Nolze, PowderCell for Windows, Federal Institute for Materials Research and Testing, Berlin, 1999. [8] E. Parthé, L. Gelato, B. Chabot, M. Penzo, K. Cenzual, R. Gladyshevskii, TYPIX. Standardized Data and Crystal Chemical Characterization of Inorganic Structure Types, Springer-Verlag, Heidelberg, 1993–1994. [9] R.A. Young, A.C. Larson, C.O. Paiva-Santos, Rietveld Analysis of X-Ray and Neutron Powder Diffraction Patterns, School of Physics, Georgia Institute of Technology, Atlanta, GA, 1998. [10] T.B. Massalski (Ed.), Binary Alloy Phase Diagrams, second ed., ASM International, Materials Park, OH, 1990. [11] S.P. Luzan, V.E. Listovnichii, Yu.I. Buyanov, P.S. Martsenyuk, J. Alloys Compounds 239 (1996) 77–82. [12] E.I. Gladyshevskii, P.I. Kripyakevich, Zh. Strukt. Khim. 5 (1964) 853–859. Translated in J. Struct. Chem. 5 (1964) 789–794. [13] G.S. Smith, A.G. Tharp, Q. Johnson, Nature (London) 210 (1966) 1148–1149. [14] E.I. Gladyshevskii, Izv. Akad. Nauk SSSR, Neorg. Mater. 1 (1965) 868–872. Translated in Inorg. Mater. 1 (1965) 797–801. [15] S. Pukas, L. Akselrud, R. Cerny, R. Gladyshevskii, Coll. Abs. X Int. Conf. Cryst. Chem. Intermet. Compd., Lviv (2007) 123. [16] D. Hohnke, E. Parthé, Acta Crystallogr. 20 (1966) 572–582. [17] J.H.N. Vucht, K.H.J. Buschow, Philips Res. Rep. 19 (1964) 319–322. [18] J.H. Wernick, S. Geller, Trans. Am. Inst. Min. Metall. Pet. Eng. 218 (1960) 866–868. [19] K.H.J. Buschow, J. Less-Common Met. 8 (1965) 209–212. [20] K.H.J. Buschow, A.S. Van Der Goot, J. Less-Common Met. 24 (1971) 117–120. [21] X.-Z. Chen, B. Sieve, R. Henning, A.J. Schultz, P. Brazis, C.R. Kannewurf, J.A. Cowen, R. Crosby, M.G. Kanatzidis, Angew. Chem. Int. Ed. 38 (1999) 693–696. [22] S. Pukas, Yu. Lutsyshyn, R. Gladyshevskii, Coll. Abs. 9 Sci. Conf. Lviv. Chem. Readings, Lviv (2003) H13 (in Ukrainian). [23] S. Pukas, Yu. Lutsyshyn, M. Manyako, E. Gladyshevskii, J. Alloys Compounds 367 (2004) 162–166. [24] C. Kranenberg, A. Mewis, Z. Anorg. Allg. Chem. 626 (2000) 1448–1453. [25] T.I. Yanson, Ph.D. Thesis, Ivan Franko State University of Lviv, 1975 (in Russian). [26] A.O. Muravyova, O.S. Zarechnyuk, E.I. Gladyshevskii, Visn. Lviv. Univ. Ser. Khim. 13 (1972) 14–16 (in Ukrainian). [27] A. Raman, Inorg. Chem. 7 (1968) 973–976. [28] N. Muts, R. Gladyshevskii, E. Gladyshevskii, J. Alloys Compounds 402 (2005) 66–69. [29] J.T. Zhao, W. Schnelle, Yu. Grin, J. Solid State Chem. 163 (2002) 113–120. [30] J.H.N. Vucht, K.H.J. Buschow, Philips Res. Rep. 22 (1967) 233–245. [31] I.S. Dubenko, A.A. Evdokimov, V.N. Ionov, Kristallografia 32 (1987) 347–351. Translated in Sov. Phys. Crystallogr. 32 (1987) 201–203. [32] I.S. Dubenko, A.A. Evdokimov, Yu.N. Titov, Zh. Neorg. Khim. 30 (1985) 2994–2996. Translated in Russ. J. Inorg. Chem. 30 (1985) 1707–1708. [33] S. Pukas, R. Gladyshevskii, E. Gladyshevskii, Visn. Lviv. Univ. Ser. Khim. 45 (2004) 78–84 (in Ukrainian).