- Email: [email protected]
Crystallographic data and magnetic properties of new ThSi2 and GdSi2 derivative compounds in the Gd–Ga–Ge system
Journal of Alloys and Compounds 305 (2000) 7–13
L
www.elsevier.com / locate / jallcom
Crystallographic data and magnetic properties of new ThSi 2 and GdSi 2 derivative compounds in the Gd–Ga–Ge system ` G. Venturini*, A. Verniere ´ , Universite´ Henri Poincare-Nancy ´ I, Associe´ au CNRS ( UMR 7555), B.P. 239, Laboratoire de Chimie du Solide Mineral 54506 Vandoeuvre les Nancy Cedex, France Received 3 January 2000; accepted 14 January 2000
Abstract The ThSi 2 and GdSi 2 derivative compounds in the Gd–Ga–Ge system have been investigated by mean of powder X-ray diffraction and magnetization measurements. A stoichiometric ThSi 2 -type compound and five ordered non-stoichiometric GdSi 2 derivative compounds have been characterized. The approximate crystal structure of Gd 24 (Ga,Ge) 43 is proposed. The evolution of the vacancy concentration seems to be closely related to the preservation of an optimal electron concentration which is consistent with the weak variation of the ordering temperatures of the antiferromagnetic Gd(Ga,Ge) 22x compounds (175T N 530 K). 2000 Elsevier Science S.A. All rights reserved. Keywords: Gd–Ga–Ge alloys; Gadolinium digermanides; Gadolinium digallides; Gallium substitution; Crystal structure; Magnetic properties
1. Introduction Powder X-ray diffraction studies of R(Ga 12x Ge x ) ¯2 compounds (R5Er, Y) have evidenced a rather complicated crystal chemistry [1,2]. In the Er–Ga–Ge system a new hexagonal AlB 2 derivative compound Er 4 (Ga,Ge) 7 has been discovered while the Y–Ga–Ge system displays four different AlB 2 derivative compounds, two different GdSi 2 derivative compounds and a stoichiometric ThSi 2 type compound according to the Ga(Ge) content. Thus, the increasing of the rare earth atomic size seems to enhance the stability of the ThSi 2 and / or GdSi 2 derivative compounds and it is expected that a still greater variety of GdSi 2 derivatives will be characterized in larger R system. In order to verify this assumption it has been planed to investigate a new R–Ga–Ge system involving a larger rare earth metal R. The evolution of the magnetic properties as a function of the vacancy concentration and / or Ga / Ge ratio has never been studied in these series. However, it might be interesting to examine the correlations between the two phenomena. The atomic size of gadolinium is slightly larger than that of yttrium and the compounds involving gadolinium have usually high magnetic ordering temperatures. For *Corresponding author. E-mail address: [email protected] (G. Venturini)
these reasons, it has been decided to study the crystallographic and magnetic properties of Gd(Ga,Ge) ¯2 compounds.
2. Experimental Powder samples have been prepared from mixtures of Gd 60 Ge 40 and GdGa 2 compounds (prepared in an induction furnace) and germanium powder. The corresponding mixtures were compacted into pellets, sealed in silica tubes under argon, annealed at 1103 K during one month and quenched into water. More than one hundred samples have been synthesized in the composition range 33–40%Gd, 2–67%Ga, 2–67%Ge. The annealed samples were checked by powder X-ray analysis (Guinier CoKa) with high purity silicon as ˚ The collection of the internal standard (a55.43082 A). diffracted intensities was made on a INEL CPS 120 curve detector. The refinement of the atomic coordinates has been done using the FULLPROF software [3]. The single phase samples have been studied by magnetic measurements carried out on a MANICS magneto-susceptometer (between 4.2 and 300 K) in applied fields up to 1.5T. The data collected in the paramagnetic state have been treated by a least square procedure.
0925-8388 / 00 / $ – see front matter 2000 Elsevier Science S.A. All rights reserved. PII: S0925-8388( 00 )00720-9
` / Journal of Alloys and Compounds 305 (2000) 7 – 13 G. Venturini, A. Verniere
8
3. Results The aim of this work was to study the crystallographic and magnetic properties of AlB 2 , ThSi 2 and GdSi 2 derivative compounds in the Gd–Ga–Ge system. Whatever the annealing duration, it has not been possible to obtain pure AlB 2 derivative compounds. The corresponding patterns always reveal the presence of GdSi 2 - and CrB-type phases as impurity and sometimes of unindexed diffracted intensities. This suggests that the AlB 2 derivative phases decompose eutectoidally or form peritectoidally during the quenching. For this reason, we just report on the properties of the GdSi 2 and ThSi 2 derivative compounds.
3.1. New ThSi2 and GdSi2 derivative compounds A pure ThSi 2 -type structure compound (S.G.: I4 1 / amd) has been obtained in the Gd 34 Ga 42 Ge 24 and Gd 35 Ga 38 Ge 27 samples while the Gd 34 Ga 44 Ge 22 one contains a small amount of AlB 2 -type Gd(Ga,Ge) 2 compound and the Gd 35 Ga 36 Ge 29 pattern displays weak lines belonging to a GdSi 2 -type compound. The cell parameters of the pure ThSi 2 phase are given in Table 1. The c parameter is very large and still larger than the values measured in the whole ˚ for LaGe 22x ). The binary RGe 22x compounds (c514.38 A c / a ratio is close to the ideal v12 value giving rise, with the ideal z Ge 513 / 24 coordinate, to Ge–Ge bonding angles close to 1208. The atomic coordinates and occupation factors have been refined from powder X-ray diffraction data ( x 2 56.4; R Bragg 513.8%). There are no significant deviation from the stoichiometry ( focc (Ge)50.99(1)) The refined coordinate z Ge 50.5396(3) is close to the ideal 13 / 24 value. The Ge rich side of the Gd(Ge,Ga) ¯2 solid solution is characterized by the presence of GdSi 2 -type compounds (S.G.: Imma). The corresponding powder diffraction patterns (Fig. 1) are all characterized by the presence of the (114) line (forbidden by the I4 1 /amd space group). The orthorhombic distorsion, giving rise to the splitting of the (200) line, is more or less pronounced (Fig. 1). The presence of a small amount of an AlB 2 -type phase is detected in the Gd 37 Ga 14 Ge 49 sample and the Gd 35 Ga 22 Ge 43 sample contains the ThSi 2 -type Gd 34 Ga 42 Ge 24 phase as impurity. The diffraction patterns of the other samples only display the characteristic lines of
the GdSi 2 -type and weak additional lines mainly located in the 35–508 2u range (Fig. 1). They can be indexed considering two type of propagating vectors. A three components (qx , 0.5, 0.5) propagating vector well accounts for the lines observed in the Gd 37 Ga 18 Ge 45 pattern. The indexation of the Gd 37 Ga 10 Ge 53 , Gd 37 Ga 12 Ge 51 , Gd 37 Ga 14 Ge 49 and Gd 35 Ga 22 Ge 43 patterns requires a two components (qx , qy , 0) propagating vector with different sets of qx and qy values. Hence, the Gd–Ga–Ge system is characterized by the presence of, at least, five GdSi 2 -type derivative compounds. The cell parameters and propagating vector components are summarized in Table 1. The cell volumes of the GdSi 2 derivative compounds are considerably smaller than that of the ThSi 2 -type Gd 34 Ga 42 Ge 24 compound. This should be related to the presence of non-metal vacancies in the GdSi 2 derivative compounds. The a / b and 2c /(a1b) ratios do not monotonically vary with the Ga / Ge ratio which might be related to different vacancy distributions in these compounds. The atomic coordinates and occupation factors in the GdSi 2 subcell have been refined from powder X-ray diffraction data. The 8(h) position (0, y, z) accounting for atomic displacements towards the created holes has been used for the description of the Ge(Ga) 2 site. Within the experimental accuracy, the refined atomic coordinates are very close each to the other (Table 2). The (Ge,Ga) 2 site is characterized by a partial occupation of about 4 / 5. It means that the chemical composition is close to R(Ge,Ga) ¯1.8 for the whole GdSi 2 derivative compounds.
3.2. Hypothetical GdSi2 superstructure found in the Gd37 Ga18 Ge45 sample A Q 5 (qx , 1 / 2, 1 / 2) propagating vector has been previously measured during investigations in the Y–Ga– Ge system [2]. However, the corresponding qx value cannot be simply expressed by an integer ratio. On the contrary, the GdSi 2 derivative compound found in the Gd 37 Ga 18 Ge 45 sample displays a propagating vector which may be expressed as Q5(5 / 12, 1 / 2, 1 / 2). This allows a commensurate description of the ordered structure in a new supercell with parameters a512a o , b52b o and c52c o . With such parameters, all the hkl indices related to the GdSi 2 subcell become even and the new indexation of the satellite lines is characterized by odd hkl indices. There-
Table 1 Crystallographic data of the ThSi 2 and GdSi 2 type derivatives in the Gd–Ga–Ge system (EC nm 5electron concentration provided by the non-metal sublattice (see Section 4)) Sample
˚ a (A)
˚ b (A)
˚ c (A)
a /b
2c(a 1 b)
˚ 3) V (A
qx
qy
qz
EC nm
Gd 37 Ga 10 Ge 53 Gd 37 Ga 12 Ge 51 Gd 37 Ga 14 Ge 49 Gd 37 Ga 18 Ge 45 Gd 35 Ga 22 Ge 43 Gd 34 Ga 42 Ge 24
4.128(1) 4.132(1) 4.122(1) 4.128(1) 4.141(2) 4.154(1)
4.101(1) 4.118(1) 4.089(1) 4.100(1) 4.138(1) 4.154(1)
13.912(3) 13.920(4) 13.997(4) 14.036(4) 13.962(5) 14.403(6)
1.0066 1.0034 1.0081 1.0068 1.0007 1.0000
3.3812 3.3745 3.4093 3.4118 3.3728 3.4673
235.5(2) 236.9(2) 235.9(2) 237.6(2) 239.3(3) 248.5(3)
0.5742(5) 0.5687(4) 0.6528(6) 0.4185(8) 0.5589(5) 0
0.5147(4) 0.4845(4) 0.5011(5) 0.5 0.4347(4) 0
0 0 0 0.5 0 0
6.694 6.696 6.609 6.651 – 6.727
` / Journal of Alloys and Compounds 305 (2000) 7 – 13 G. Venturini, A. Verniere
9
Fig. 1. Selected range of the Gd(Ga,Ge) 22x diffraction patterns showing the main superstructure lines (* ThSi 2 impurity in Gd 35 Ga 22 Ge 43 sample; ** AlB 2 impurity in Gd 37 Ga 14 Ge 49 sample).
fore, the structure should be described in an F centered cell. According to subcell refinements, the non-metal vacancies should be located on the Ge–Ge broken chains aligned along the b axis. The vacancy distribution along the a direction should be close to the wavevector periodicity i.e. five blocks with mean length 12 / 552.4. Such a pseudo-periodicity may be found considering three blocks with length 2a and two blocks with length 3a. Hence, the distribution of the vacancies along the a direction should
be related by the following sequency 0, 2 / 12, 4 / 12, 7 / 12, 9 / 12, 12 / 12 . . . The cell doubling along the b and c axis as well as the play of the F centered mode enable the location of the vacancies on one half part of the Ge–Ge chains. The other half part should be characterized by the same vacancies distribution. However, their relative positions with respect to the first part is undetermined and needs a trial method. There are three ways to describe the relative position of
Table 2 Refined parameters of GdSi 2 subcells (Gd and Ge 1 atoms in (0, 1 / 4, z) 4(e) position and Ge 2 in (0, y, z) 8(h) position Sample
z Gd
z Ge1
y Ge2
z Ge2
m Ge2
BG
x2
R Bragg
Gd 37 Ga 10 Ge 53 Gd 37 Ga 12 Ge 53 Gd 37 Ga 14 Ge 53 Gd 37 Ga 18 Ge 53 Gd 35 Ga 22 Ge 53
0.3740(2) 0.3740(3) 0.3747(2) 0.3758(2) 0.3736(5)
0.1987(4) 0.1990(4) 0.1990(4) 0.2008(4) 0.1993(6)
0.155(2) 0.157(2) 0.167(2) 0.175(2) 0.154(2)
0.0272(5) 0.0267(6) 0.0273(5) 0.0298(5) 0.0278(7)
0.208(3) 0.209(4) 0.197(3) 0.221(4) 0.222(6)
1.13(6) 0.88(6) 0.62(6) 1.07(6) 1.18(8)
5.9 5.3 6.3 5.6 6.9
12.2 12.9 12.5 12.8 13.9
` / Journal of Alloys and Compounds 305 (2000) 7 – 13 G. Venturini, A. Verniere
10
both half parts. All three yield the loss of the orthorhombic symmetry and lead to consider the non-conventional monoclinic space group F2 /m or the conventional one C2 /m with a512a o , b52b o , c5c o –6a o and b ¯1508. One of these ways gives rise to a significantly better reliability factor between observed and calculated spectra. Owing to the large number of free parameters, the refinement of the corresponding atomic coordinates does not satisfactorily converge. Therefore, we just report on the starting parameters (Table 3) and to the corresponding observed and calculated spectra (Fig. 2). It is obvious that the main relevant features of the superstructure lines are fairly reproduced by this approximate model. The formula deduced from the vacancies concentration is Gd 24 (Ga,Ge) 43 i.e. for such a propagating vector, the general formula is given by R 2 X 42qx . The approximate structure is depicted in Fig. 3.
3.3. Magnetic properties of the ThSi2 and GdSi2 derivative compounds The thermal variation of the susceptibility and the isotherm curves measured at 4.2 K are presented in Figs. 4 and 5. The magnetic data are summarized in Table 4. The isotherm curves of the Gd 34 Ga 42 Ge 24 , Gd 37 Ga 51 Ge 12 and Gd 34 Ga 49 Ge 14 compounds are characterized by a slight curvature in the highest applied fields suggesting the onset of metamagnetic transitions. All the studied compounds display an antiferromagnetic behaviour with pronounced ´ points. The ordering temperature of the ThSi 2 -type Neel Gd 34 Ga 42 Ge 24 compound (T N 530 K) is slightly higher
than those of the GdSi 2 derivative compounds (T N 517–24 K). The paramagnetic data have been calculated by a least square procedure taking into account the 2T N 2300 K region. The lowest paramagnetic Curie temperature is measured for the ThSi 2 -type compound. The effective moments are slightly larger than the Gd free ion value. Such a feature has been previously observed during the study of AlB 2 -type GdGa 22x Alx compounds [4].
4. Discussion Investigations in the R–Ga–Ge system enable the characterization of a stoichiometric ThSi 2 -type compound and five new GdSi 2 derivative compounds each of them being characterized by different ordering of the non-metal vacancies. Hence, the structural evolution along the ThSi 22 GdSi 2 series is much more complicated than that observed in the Y–Ga–Ge system [2]. The compounds with the lowest Ga concentration are characterized by (qx , qy , 0) wavectors and relatively small subcell volume. The Gd 37 Ga 18 Ge 45 compound displays a (qx , 1 / 2, 1 / 2) propagating vector and a subcell volume slightly larger than those of the former compounds. Increasing the Ga concentration yields the stabilization of a compound characterized, once again, by a (qx , qy , 0) wavevector and a significantly larger cell volume. Finally, a stoichiometric ThSi 2 -type compound exists for high Ga concentration. The global evolution of the cell volume strongly suggests a reduction of the non-metal vacancies with the Ga content. This is compatible with the results derived from the Y–
Table 3 ˚ c528.47 A, ˚ b 5150.48) Atomic coordinates of the Gd 24 (Ge,Ga) 43 structure. (S.G. C2 /m; a549.54a, b58.200 A, 4(i) Sites (x, 0, z) x
z
Gd 1 Gd 4 Gd 7 Gd 10 Ge 1 Ge 4 Ge 7 Ge 10 Ge 13 Ge 16 Ge 19
0.1258 0.8742 0.8722 0.8742 0.2798 0.4508 0.4680 0.5492 0.5692 0.7220 0.7055
y 0.25 0.25 0.25 0.302 0.198 0.25 0.25 0.25 0.25
0.0421 0.8746 0.2039 0.6246 0.0774 0.6629 0.0070 0.7538 0.0971 0.7569 0.5819
8( j) Sites (x, y, z) x Gd 13 0.1663 Gd 15 0.9996 Gd 17 0.1691 Ge 20 0.0476 Ge 22 0.2847 Ge 24 0.1264 Ge 26 0.4546 Ge 28 0.2779 Ge 30 0.1212
x
z
Gd 2 Gd 5 Gd 8 Gd 11 Ge 2 Ge 5 Ge 8 Ge 11 Ge 14 Ge 17
0.5421 0.2953 0.7079 0.0413 0.4941 0.0796 0.5070 0.1704 0.5971 0.1836
0.1258 0.8782 0.8742 0.8742 0.2798 0.4508 0.4680 0.5492 0.5692 0.7422
z 0.3742 0.3742 0.6258 0.2202 0.7778 0.7944 0.9508 0.9308 0.9508
Gd 14 Gd 16 Gd 18 Ge 21 Ge 23 Ge 25 Ge 27 Ge 29 Ge 31
x 0.0839 0.2504 0.0817 0.3681 0.1914 0.0347 0.3712 0.2126 0.0379
x
z
Gd 3 Gd 6 Gd 9 Gd 12 Ge 3 Ge 6 Ge 9 Ge 12 Ge 15 Ge 18
0.3746 0.7913 0.1246 0.5413 0.1629 0.5796 0.2538 0.6704 0.3403 0.0819
0.8742 0.8742 0.8742 0.8742 0.4508 0.4508 0.5492 0.5492 0.7220 0.7055
y 0.25 0.25 0.25 0.302 0.302 0.198 0.25 0.25 0.25
z 0.3742 0.6258 0.6258 0.7778 0.7578 0.7778 0.9508 0.9708 0.9508
` / Journal of Alloys and Compounds 305 (2000) 7 – 13 G. Venturini, A. Verniere
11
Fig. 2. Observed and calculated pattern of the Gd 37 Ga 18 Ge 45 sample. The Miller indices refer to the supercell. Insert shows the range where the main superstructure lines occur. (Tick 1: Gd 24 (Ga,Ge) 43 ; Tick 2: Gd 2 O 3 ).
Fig. 3. Projection of a half cell of the Gd 24 (Ga,Ge) 43 structure along the [10] direction. (Solid lines: Non-metal chains aligned along a and full non-metal chains aligned along b; Dotted lines: Partially filled non-metal chains aligned along b).
` / Journal of Alloys and Compounds 305 (2000) 7 – 13 G. Venturini, A. Verniere
12
Fig. 4. Thermal variation of the susceptibility of the Gd(Ga,Ge) 22x compounds (Happl 50.5T).
Ga–Ge study and suggests that an optimal electron concentration is held on along the involved series. The relation between the wavevectors and the chemical composition is not well understood. For the compound observed in the Gd 37 Ga 18 Ge 45 sample, we propose a structural hypothesis which rather well accounts for the observed superstructure lines and enables a relation between the qx value and the chemical composition. During the study of GdSi 2 -type RGe 22x compounds characterized by a two-component (qx , qy , 0) wavevector (R5La, Ce), a model relating the qy component to the vacancy concentration has been proposed through the formula R 2 Ge 42qy [5]. The close values of the cell volumes and qy components of the Gd 37 Ga 10 Ge 53 , Gd 37 Ga 12 Ge 51 and Gd 37 Ga 14 Ge 49 compounds suggest that a similar behaviour takes place giving rise to the approximate formula RGe ¯1.75 . It is worth noting that, in the binary germanides, such a composition is obtained through another mechanism as observed for the Nd 4 Ge 7 compound [5]. There remain some problems concerning the wavevector measured in the Gd 35 Ga 22 Ge 45 sample. In spite of a qy value greater than the q x value measured in the Gd 37 Ga 18 Ge 45 sample, its cell volume is significantly higher and suggests a lower vacancy concentration as depicted in Fig. 6. Hence, a different vacancy distribution, corroborated by the different indexation of the satellites (Fig. 1) should be assumed for this compound. The knowledge of the vacancy concentration, deduced from the wavevector components through the formula R 2 Ge 42q (q 5 qx or qy ), and the chemical composition of the corresponding sample R m Ga n Ge p allow a calculation of the valence electron concentration provided by the
Fig. 5. Magnetization versus applied field measured at 4.2 K.
Table 4 Summary of the magnetic data Sample
xo (emu / mole)
meff ( mB )
up (K)
T N (K)
Gd 37 Ga 10 Ge 53 Gd 37 Ga 12 Ge 51 Gd 37 Ga 14 Ge 49 Gd 37 Ga 18 Ge 45 Gd 35 Ga 22 Ge 43 Gd 34 Ga 42 Ge 24
0.0025(2) 0.0036(5) 0.0021(2) 0.0010(3) 0.0006(2) 0.0019(4)
8.18(8) 8.2(2) 8.08(6) 8.4(1) 8.18(7) 8.2(2)
236(1) 237(2) 223(1) 233(1) 239(1) 253(2)
20 22 17 22 24 30
Fig. 6. Variation of the cell volumes of the GdGa 22x subcells as a function of the non-metal concentration deduced from the wavevector component (The wavevector measured for the Gd 35 Ga 22 Ge 43 sample (arrow) does not fit the volume variation).
` / Journal of Alloys and Compounds 305 (2000) 7 – 13 G. Venturini, A. Verniere
non-metal sublattice. The mean valence Vm of the nonmetal element should be given by the formula Vm 5(3n1 4p) /(n1p). The electron concentration provided by the non-metal sublattice EC nm for a given RGe 22x formula is then EC nm 5(22x)Vm or (22q / 2)Vm . These values are given in Table 1. It is worth noting that they do not greatly vary in the whole ThSi 2 and GdSi 2 derivative compounds due to an interplay between the mean valence Vm and the vacancies concentration. Hence, the optimal electron concentration EC nm should be close to the mean value EC nm 5 6.67e 2 / f.u for the ThSi 2 and GdSi 2 derivative compounds Gd(Ga,Ge) 22x . This value is also close to those measured in the binary ThSi 2 derivative GdGe 22x compounds: between EC nm 56.55e 2 / f.u. for the Gd 168 Ge 275 compound and EC nm 56.82e 2 / f.u. for the Gd 17 Ge 29 compound [5]. The study of the magnetic properties provides interesting informations. Along the whole ThSi 2 –GdSi 2 series, the magnetic properties do not exhibit great variations with the Ga / Ge ratio. A quite different behaviour is observed in the Gd(Ga,Al) 2 solid solution within which a large variation of ordering temperature has been measured (15#T N #64 K) [4].This suggests that the conduction electron density does not greatly vary along the ThSi 2 –GdSi 2 series in spite of the replacement of Ga by non-isoelectronic Ge atoms. This is consistent with the previous remarks
13
concerning the electron concentration provided by the non-metal sublattice.
5. Conclusion The structural evolution along the ThSi 2 –GdSi 2 series in the Gd–Ga–Ge system seems to be driven by the preservation of an optimal electron concentration. This assumption is corroborated by the evolution of the magnetic properties. It should be now interesting to examine the evolution of other physical properties such as transport properties. It should also interesting to examine the magnetic properties of an AlB 2 series.
References ` B. Malaman, J. Alloys Comp. 291 (1999) [1] G. Venturini, A. Verniere, 201. ` J. Alloys Comp. 298 (2000) 213. [2] G. Venturini, A. Verniere, [3] J. Rodriguez-Carvajal, Physica B 192 (1993) 55. [4] L.D. Tung, N.P. Thuy, P.E. Brommer, J.J.M. Franse, K.H.J. Buschow, Physica B 266 (1999) 209. [5] G. Venturini, I. Ijjaali, B. Malaman, J. Alloys Comp. 289 (1999) 168.
L
www.elsevier.com / locate / jallcom
Crystallographic data and magnetic properties of new ThSi 2 and GdSi 2 derivative compounds in the Gd–Ga–Ge system ` G. Venturini*, A. Verniere ´ , Universite´ Henri Poincare-Nancy ´ I, Associe´ au CNRS ( UMR 7555), B.P. 239, Laboratoire de Chimie du Solide Mineral 54506 Vandoeuvre les Nancy Cedex, France Received 3 January 2000; accepted 14 January 2000
Abstract The ThSi 2 and GdSi 2 derivative compounds in the Gd–Ga–Ge system have been investigated by mean of powder X-ray diffraction and magnetization measurements. A stoichiometric ThSi 2 -type compound and five ordered non-stoichiometric GdSi 2 derivative compounds have been characterized. The approximate crystal structure of Gd 24 (Ga,Ge) 43 is proposed. The evolution of the vacancy concentration seems to be closely related to the preservation of an optimal electron concentration which is consistent with the weak variation of the ordering temperatures of the antiferromagnetic Gd(Ga,Ge) 22x compounds (175T N 530 K). 2000 Elsevier Science S.A. All rights reserved. Keywords: Gd–Ga–Ge alloys; Gadolinium digermanides; Gadolinium digallides; Gallium substitution; Crystal structure; Magnetic properties
1. Introduction Powder X-ray diffraction studies of R(Ga 12x Ge x ) ¯2 compounds (R5Er, Y) have evidenced a rather complicated crystal chemistry [1,2]. In the Er–Ga–Ge system a new hexagonal AlB 2 derivative compound Er 4 (Ga,Ge) 7 has been discovered while the Y–Ga–Ge system displays four different AlB 2 derivative compounds, two different GdSi 2 derivative compounds and a stoichiometric ThSi 2 type compound according to the Ga(Ge) content. Thus, the increasing of the rare earth atomic size seems to enhance the stability of the ThSi 2 and / or GdSi 2 derivative compounds and it is expected that a still greater variety of GdSi 2 derivatives will be characterized in larger R system. In order to verify this assumption it has been planed to investigate a new R–Ga–Ge system involving a larger rare earth metal R. The evolution of the magnetic properties as a function of the vacancy concentration and / or Ga / Ge ratio has never been studied in these series. However, it might be interesting to examine the correlations between the two phenomena. The atomic size of gadolinium is slightly larger than that of yttrium and the compounds involving gadolinium have usually high magnetic ordering temperatures. For *Corresponding author. E-mail address: [email protected] (G. Venturini)
these reasons, it has been decided to study the crystallographic and magnetic properties of Gd(Ga,Ge) ¯2 compounds.
2. Experimental Powder samples have been prepared from mixtures of Gd 60 Ge 40 and GdGa 2 compounds (prepared in an induction furnace) and germanium powder. The corresponding mixtures were compacted into pellets, sealed in silica tubes under argon, annealed at 1103 K during one month and quenched into water. More than one hundred samples have been synthesized in the composition range 33–40%Gd, 2–67%Ga, 2–67%Ge. The annealed samples were checked by powder X-ray analysis (Guinier CoKa) with high purity silicon as ˚ The collection of the internal standard (a55.43082 A). diffracted intensities was made on a INEL CPS 120 curve detector. The refinement of the atomic coordinates has been done using the FULLPROF software [3]. The single phase samples have been studied by magnetic measurements carried out on a MANICS magneto-susceptometer (between 4.2 and 300 K) in applied fields up to 1.5T. The data collected in the paramagnetic state have been treated by a least square procedure.
0925-8388 / 00 / $ – see front matter 2000 Elsevier Science S.A. All rights reserved. PII: S0925-8388( 00 )00720-9
` / Journal of Alloys and Compounds 305 (2000) 7 – 13 G. Venturini, A. Verniere
8
3. Results The aim of this work was to study the crystallographic and magnetic properties of AlB 2 , ThSi 2 and GdSi 2 derivative compounds in the Gd–Ga–Ge system. Whatever the annealing duration, it has not been possible to obtain pure AlB 2 derivative compounds. The corresponding patterns always reveal the presence of GdSi 2 - and CrB-type phases as impurity and sometimes of unindexed diffracted intensities. This suggests that the AlB 2 derivative phases decompose eutectoidally or form peritectoidally during the quenching. For this reason, we just report on the properties of the GdSi 2 and ThSi 2 derivative compounds.
3.1. New ThSi2 and GdSi2 derivative compounds A pure ThSi 2 -type structure compound (S.G.: I4 1 / amd) has been obtained in the Gd 34 Ga 42 Ge 24 and Gd 35 Ga 38 Ge 27 samples while the Gd 34 Ga 44 Ge 22 one contains a small amount of AlB 2 -type Gd(Ga,Ge) 2 compound and the Gd 35 Ga 36 Ge 29 pattern displays weak lines belonging to a GdSi 2 -type compound. The cell parameters of the pure ThSi 2 phase are given in Table 1. The c parameter is very large and still larger than the values measured in the whole ˚ for LaGe 22x ). The binary RGe 22x compounds (c514.38 A c / a ratio is close to the ideal v12 value giving rise, with the ideal z Ge 513 / 24 coordinate, to Ge–Ge bonding angles close to 1208. The atomic coordinates and occupation factors have been refined from powder X-ray diffraction data ( x 2 56.4; R Bragg 513.8%). There are no significant deviation from the stoichiometry ( focc (Ge)50.99(1)) The refined coordinate z Ge 50.5396(3) is close to the ideal 13 / 24 value. The Ge rich side of the Gd(Ge,Ga) ¯2 solid solution is characterized by the presence of GdSi 2 -type compounds (S.G.: Imma). The corresponding powder diffraction patterns (Fig. 1) are all characterized by the presence of the (114) line (forbidden by the I4 1 /amd space group). The orthorhombic distorsion, giving rise to the splitting of the (200) line, is more or less pronounced (Fig. 1). The presence of a small amount of an AlB 2 -type phase is detected in the Gd 37 Ga 14 Ge 49 sample and the Gd 35 Ga 22 Ge 43 sample contains the ThSi 2 -type Gd 34 Ga 42 Ge 24 phase as impurity. The diffraction patterns of the other samples only display the characteristic lines of
the GdSi 2 -type and weak additional lines mainly located in the 35–508 2u range (Fig. 1). They can be indexed considering two type of propagating vectors. A three components (qx , 0.5, 0.5) propagating vector well accounts for the lines observed in the Gd 37 Ga 18 Ge 45 pattern. The indexation of the Gd 37 Ga 10 Ge 53 , Gd 37 Ga 12 Ge 51 , Gd 37 Ga 14 Ge 49 and Gd 35 Ga 22 Ge 43 patterns requires a two components (qx , qy , 0) propagating vector with different sets of qx and qy values. Hence, the Gd–Ga–Ge system is characterized by the presence of, at least, five GdSi 2 -type derivative compounds. The cell parameters and propagating vector components are summarized in Table 1. The cell volumes of the GdSi 2 derivative compounds are considerably smaller than that of the ThSi 2 -type Gd 34 Ga 42 Ge 24 compound. This should be related to the presence of non-metal vacancies in the GdSi 2 derivative compounds. The a / b and 2c /(a1b) ratios do not monotonically vary with the Ga / Ge ratio which might be related to different vacancy distributions in these compounds. The atomic coordinates and occupation factors in the GdSi 2 subcell have been refined from powder X-ray diffraction data. The 8(h) position (0, y, z) accounting for atomic displacements towards the created holes has been used for the description of the Ge(Ga) 2 site. Within the experimental accuracy, the refined atomic coordinates are very close each to the other (Table 2). The (Ge,Ga) 2 site is characterized by a partial occupation of about 4 / 5. It means that the chemical composition is close to R(Ge,Ga) ¯1.8 for the whole GdSi 2 derivative compounds.
3.2. Hypothetical GdSi2 superstructure found in the Gd37 Ga18 Ge45 sample A Q 5 (qx , 1 / 2, 1 / 2) propagating vector has been previously measured during investigations in the Y–Ga– Ge system [2]. However, the corresponding qx value cannot be simply expressed by an integer ratio. On the contrary, the GdSi 2 derivative compound found in the Gd 37 Ga 18 Ge 45 sample displays a propagating vector which may be expressed as Q5(5 / 12, 1 / 2, 1 / 2). This allows a commensurate description of the ordered structure in a new supercell with parameters a512a o , b52b o and c52c o . With such parameters, all the hkl indices related to the GdSi 2 subcell become even and the new indexation of the satellite lines is characterized by odd hkl indices. There-
Table 1 Crystallographic data of the ThSi 2 and GdSi 2 type derivatives in the Gd–Ga–Ge system (EC nm 5electron concentration provided by the non-metal sublattice (see Section 4)) Sample
˚ a (A)
˚ b (A)
˚ c (A)
a /b
2c(a 1 b)
˚ 3) V (A
qx
qy
qz
EC nm
Gd 37 Ga 10 Ge 53 Gd 37 Ga 12 Ge 51 Gd 37 Ga 14 Ge 49 Gd 37 Ga 18 Ge 45 Gd 35 Ga 22 Ge 43 Gd 34 Ga 42 Ge 24
4.128(1) 4.132(1) 4.122(1) 4.128(1) 4.141(2) 4.154(1)
4.101(1) 4.118(1) 4.089(1) 4.100(1) 4.138(1) 4.154(1)
13.912(3) 13.920(4) 13.997(4) 14.036(4) 13.962(5) 14.403(6)
1.0066 1.0034 1.0081 1.0068 1.0007 1.0000
3.3812 3.3745 3.4093 3.4118 3.3728 3.4673
235.5(2) 236.9(2) 235.9(2) 237.6(2) 239.3(3) 248.5(3)
0.5742(5) 0.5687(4) 0.6528(6) 0.4185(8) 0.5589(5) 0
0.5147(4) 0.4845(4) 0.5011(5) 0.5 0.4347(4) 0
0 0 0 0.5 0 0
6.694 6.696 6.609 6.651 – 6.727
` / Journal of Alloys and Compounds 305 (2000) 7 – 13 G. Venturini, A. Verniere
9
Fig. 1. Selected range of the Gd(Ga,Ge) 22x diffraction patterns showing the main superstructure lines (* ThSi 2 impurity in Gd 35 Ga 22 Ge 43 sample; ** AlB 2 impurity in Gd 37 Ga 14 Ge 49 sample).
fore, the structure should be described in an F centered cell. According to subcell refinements, the non-metal vacancies should be located on the Ge–Ge broken chains aligned along the b axis. The vacancy distribution along the a direction should be close to the wavevector periodicity i.e. five blocks with mean length 12 / 552.4. Such a pseudo-periodicity may be found considering three blocks with length 2a and two blocks with length 3a. Hence, the distribution of the vacancies along the a direction should
be related by the following sequency 0, 2 / 12, 4 / 12, 7 / 12, 9 / 12, 12 / 12 . . . The cell doubling along the b and c axis as well as the play of the F centered mode enable the location of the vacancies on one half part of the Ge–Ge chains. The other half part should be characterized by the same vacancies distribution. However, their relative positions with respect to the first part is undetermined and needs a trial method. There are three ways to describe the relative position of
Table 2 Refined parameters of GdSi 2 subcells (Gd and Ge 1 atoms in (0, 1 / 4, z) 4(e) position and Ge 2 in (0, y, z) 8(h) position Sample
z Gd
z Ge1
y Ge2
z Ge2
m Ge2
BG
x2
R Bragg
Gd 37 Ga 10 Ge 53 Gd 37 Ga 12 Ge 53 Gd 37 Ga 14 Ge 53 Gd 37 Ga 18 Ge 53 Gd 35 Ga 22 Ge 53
0.3740(2) 0.3740(3) 0.3747(2) 0.3758(2) 0.3736(5)
0.1987(4) 0.1990(4) 0.1990(4) 0.2008(4) 0.1993(6)
0.155(2) 0.157(2) 0.167(2) 0.175(2) 0.154(2)
0.0272(5) 0.0267(6) 0.0273(5) 0.0298(5) 0.0278(7)
0.208(3) 0.209(4) 0.197(3) 0.221(4) 0.222(6)
1.13(6) 0.88(6) 0.62(6) 1.07(6) 1.18(8)
5.9 5.3 6.3 5.6 6.9
12.2 12.9 12.5 12.8 13.9
` / Journal of Alloys and Compounds 305 (2000) 7 – 13 G. Venturini, A. Verniere
10
both half parts. All three yield the loss of the orthorhombic symmetry and lead to consider the non-conventional monoclinic space group F2 /m or the conventional one C2 /m with a512a o , b52b o , c5c o –6a o and b ¯1508. One of these ways gives rise to a significantly better reliability factor between observed and calculated spectra. Owing to the large number of free parameters, the refinement of the corresponding atomic coordinates does not satisfactorily converge. Therefore, we just report on the starting parameters (Table 3) and to the corresponding observed and calculated spectra (Fig. 2). It is obvious that the main relevant features of the superstructure lines are fairly reproduced by this approximate model. The formula deduced from the vacancies concentration is Gd 24 (Ga,Ge) 43 i.e. for such a propagating vector, the general formula is given by R 2 X 42qx . The approximate structure is depicted in Fig. 3.
3.3. Magnetic properties of the ThSi2 and GdSi2 derivative compounds The thermal variation of the susceptibility and the isotherm curves measured at 4.2 K are presented in Figs. 4 and 5. The magnetic data are summarized in Table 4. The isotherm curves of the Gd 34 Ga 42 Ge 24 , Gd 37 Ga 51 Ge 12 and Gd 34 Ga 49 Ge 14 compounds are characterized by a slight curvature in the highest applied fields suggesting the onset of metamagnetic transitions. All the studied compounds display an antiferromagnetic behaviour with pronounced ´ points. The ordering temperature of the ThSi 2 -type Neel Gd 34 Ga 42 Ge 24 compound (T N 530 K) is slightly higher
than those of the GdSi 2 derivative compounds (T N 517–24 K). The paramagnetic data have been calculated by a least square procedure taking into account the 2T N 2300 K region. The lowest paramagnetic Curie temperature is measured for the ThSi 2 -type compound. The effective moments are slightly larger than the Gd free ion value. Such a feature has been previously observed during the study of AlB 2 -type GdGa 22x Alx compounds [4].
4. Discussion Investigations in the R–Ga–Ge system enable the characterization of a stoichiometric ThSi 2 -type compound and five new GdSi 2 derivative compounds each of them being characterized by different ordering of the non-metal vacancies. Hence, the structural evolution along the ThSi 22 GdSi 2 series is much more complicated than that observed in the Y–Ga–Ge system [2]. The compounds with the lowest Ga concentration are characterized by (qx , qy , 0) wavectors and relatively small subcell volume. The Gd 37 Ga 18 Ge 45 compound displays a (qx , 1 / 2, 1 / 2) propagating vector and a subcell volume slightly larger than those of the former compounds. Increasing the Ga concentration yields the stabilization of a compound characterized, once again, by a (qx , qy , 0) wavevector and a significantly larger cell volume. Finally, a stoichiometric ThSi 2 -type compound exists for high Ga concentration. The global evolution of the cell volume strongly suggests a reduction of the non-metal vacancies with the Ga content. This is compatible with the results derived from the Y–
Table 3 ˚ c528.47 A, ˚ b 5150.48) Atomic coordinates of the Gd 24 (Ge,Ga) 43 structure. (S.G. C2 /m; a549.54a, b58.200 A, 4(i) Sites (x, 0, z) x
z
Gd 1 Gd 4 Gd 7 Gd 10 Ge 1 Ge 4 Ge 7 Ge 10 Ge 13 Ge 16 Ge 19
0.1258 0.8742 0.8722 0.8742 0.2798 0.4508 0.4680 0.5492 0.5692 0.7220 0.7055
y 0.25 0.25 0.25 0.302 0.198 0.25 0.25 0.25 0.25
0.0421 0.8746 0.2039 0.6246 0.0774 0.6629 0.0070 0.7538 0.0971 0.7569 0.5819
8( j) Sites (x, y, z) x Gd 13 0.1663 Gd 15 0.9996 Gd 17 0.1691 Ge 20 0.0476 Ge 22 0.2847 Ge 24 0.1264 Ge 26 0.4546 Ge 28 0.2779 Ge 30 0.1212
x
z
Gd 2 Gd 5 Gd 8 Gd 11 Ge 2 Ge 5 Ge 8 Ge 11 Ge 14 Ge 17
0.5421 0.2953 0.7079 0.0413 0.4941 0.0796 0.5070 0.1704 0.5971 0.1836
0.1258 0.8782 0.8742 0.8742 0.2798 0.4508 0.4680 0.5492 0.5692 0.7422
z 0.3742 0.3742 0.6258 0.2202 0.7778 0.7944 0.9508 0.9308 0.9508
Gd 14 Gd 16 Gd 18 Ge 21 Ge 23 Ge 25 Ge 27 Ge 29 Ge 31
x 0.0839 0.2504 0.0817 0.3681 0.1914 0.0347 0.3712 0.2126 0.0379
x
z
Gd 3 Gd 6 Gd 9 Gd 12 Ge 3 Ge 6 Ge 9 Ge 12 Ge 15 Ge 18
0.3746 0.7913 0.1246 0.5413 0.1629 0.5796 0.2538 0.6704 0.3403 0.0819
0.8742 0.8742 0.8742 0.8742 0.4508 0.4508 0.5492 0.5492 0.7220 0.7055
y 0.25 0.25 0.25 0.302 0.302 0.198 0.25 0.25 0.25
z 0.3742 0.6258 0.6258 0.7778 0.7578 0.7778 0.9508 0.9708 0.9508
` / Journal of Alloys and Compounds 305 (2000) 7 – 13 G. Venturini, A. Verniere
11
Fig. 2. Observed and calculated pattern of the Gd 37 Ga 18 Ge 45 sample. The Miller indices refer to the supercell. Insert shows the range where the main superstructure lines occur. (Tick 1: Gd 24 (Ga,Ge) 43 ; Tick 2: Gd 2 O 3 ).
Fig. 3. Projection of a half cell of the Gd 24 (Ga,Ge) 43 structure along the [10] direction. (Solid lines: Non-metal chains aligned along a and full non-metal chains aligned along b; Dotted lines: Partially filled non-metal chains aligned along b).
` / Journal of Alloys and Compounds 305 (2000) 7 – 13 G. Venturini, A. Verniere
12
Fig. 4. Thermal variation of the susceptibility of the Gd(Ga,Ge) 22x compounds (Happl 50.5T).
Ga–Ge study and suggests that an optimal electron concentration is held on along the involved series. The relation between the wavevectors and the chemical composition is not well understood. For the compound observed in the Gd 37 Ga 18 Ge 45 sample, we propose a structural hypothesis which rather well accounts for the observed superstructure lines and enables a relation between the qx value and the chemical composition. During the study of GdSi 2 -type RGe 22x compounds characterized by a two-component (qx , qy , 0) wavevector (R5La, Ce), a model relating the qy component to the vacancy concentration has been proposed through the formula R 2 Ge 42qy [5]. The close values of the cell volumes and qy components of the Gd 37 Ga 10 Ge 53 , Gd 37 Ga 12 Ge 51 and Gd 37 Ga 14 Ge 49 compounds suggest that a similar behaviour takes place giving rise to the approximate formula RGe ¯1.75 . It is worth noting that, in the binary germanides, such a composition is obtained through another mechanism as observed for the Nd 4 Ge 7 compound [5]. There remain some problems concerning the wavevector measured in the Gd 35 Ga 22 Ge 45 sample. In spite of a qy value greater than the q x value measured in the Gd 37 Ga 18 Ge 45 sample, its cell volume is significantly higher and suggests a lower vacancy concentration as depicted in Fig. 6. Hence, a different vacancy distribution, corroborated by the different indexation of the satellites (Fig. 1) should be assumed for this compound. The knowledge of the vacancy concentration, deduced from the wavevector components through the formula R 2 Ge 42q (q 5 qx or qy ), and the chemical composition of the corresponding sample R m Ga n Ge p allow a calculation of the valence electron concentration provided by the
Fig. 5. Magnetization versus applied field measured at 4.2 K.
Table 4 Summary of the magnetic data Sample
xo (emu / mole)
meff ( mB )
up (K)
T N (K)
Gd 37 Ga 10 Ge 53 Gd 37 Ga 12 Ge 51 Gd 37 Ga 14 Ge 49 Gd 37 Ga 18 Ge 45 Gd 35 Ga 22 Ge 43 Gd 34 Ga 42 Ge 24
0.0025(2) 0.0036(5) 0.0021(2) 0.0010(3) 0.0006(2) 0.0019(4)
8.18(8) 8.2(2) 8.08(6) 8.4(1) 8.18(7) 8.2(2)
236(1) 237(2) 223(1) 233(1) 239(1) 253(2)
20 22 17 22 24 30
Fig. 6. Variation of the cell volumes of the GdGa 22x subcells as a function of the non-metal concentration deduced from the wavevector component (The wavevector measured for the Gd 35 Ga 22 Ge 43 sample (arrow) does not fit the volume variation).
` / Journal of Alloys and Compounds 305 (2000) 7 – 13 G. Venturini, A. Verniere
non-metal sublattice. The mean valence Vm of the nonmetal element should be given by the formula Vm 5(3n1 4p) /(n1p). The electron concentration provided by the non-metal sublattice EC nm for a given RGe 22x formula is then EC nm 5(22x)Vm or (22q / 2)Vm . These values are given in Table 1. It is worth noting that they do not greatly vary in the whole ThSi 2 and GdSi 2 derivative compounds due to an interplay between the mean valence Vm and the vacancies concentration. Hence, the optimal electron concentration EC nm should be close to the mean value EC nm 5 6.67e 2 / f.u for the ThSi 2 and GdSi 2 derivative compounds Gd(Ga,Ge) 22x . This value is also close to those measured in the binary ThSi 2 derivative GdGe 22x compounds: between EC nm 56.55e 2 / f.u. for the Gd 168 Ge 275 compound and EC nm 56.82e 2 / f.u. for the Gd 17 Ge 29 compound [5]. The study of the magnetic properties provides interesting informations. Along the whole ThSi 2 –GdSi 2 series, the magnetic properties do not exhibit great variations with the Ga / Ge ratio. A quite different behaviour is observed in the Gd(Ga,Al) 2 solid solution within which a large variation of ordering temperature has been measured (15#T N #64 K) [4].This suggests that the conduction electron density does not greatly vary along the ThSi 2 –GdSi 2 series in spite of the replacement of Ga by non-isoelectronic Ge atoms. This is consistent with the previous remarks
13
concerning the electron concentration provided by the non-metal sublattice.
5. Conclusion The structural evolution along the ThSi 2 –GdSi 2 series in the Gd–Ga–Ge system seems to be driven by the preservation of an optimal electron concentration. This assumption is corroborated by the evolution of the magnetic properties. It should be now interesting to examine the evolution of other physical properties such as transport properties. It should also interesting to examine the magnetic properties of an AlB 2 series.
References ` B. Malaman, J. Alloys Comp. 291 (1999) [1] G. Venturini, A. Verniere, 201. ` J. Alloys Comp. 298 (2000) 213. [2] G. Venturini, A. Verniere, [3] J. Rodriguez-Carvajal, Physica B 192 (1993) 55. [4] L.D. Tung, N.P. Thuy, P.E. Brommer, J.J.M. Franse, K.H.J. Buschow, Physica B 266 (1999) 209. [5] G. Venturini, I. Ijjaali, B. Malaman, J. Alloys Comp. 289 (1999) 168.