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Crystal structure and thermal expansion properties of new compound La2Cu0.8Ge3
Journal of Alloys and Compounds 485 (2009) 739–742
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Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Crystal structure and thermal expansion properties of new compound La2 Cu0.8 Ge3 Jialin Yan a,b,1 , Xingwen Lu a,b , Wenjun Shen a,b , Lingmin Zeng a,b,∗ , Liangqin Nong c a b c
Key Laboratory of New Processing Technology for Nonferrous Metal and Materials, Ministry of Education, Guangxi University, Nanning, Guangxi 530004, China College of Materials Science and Engineering, Guangxi University, Nanning, Guangxi 530004, China College of Physics and Electronic Engineering, Guangxi University for Nationalities, Nanning, Guangxi 530006, China
a r t i c l e
i n f o
Article history: Received 31 May 2009 Accepted 10 June 2009 Available online 18 June 2009 Keywords: Intermetallics Crystal structure Thermal expansion High-temperature X-ray diffraction
a b s t r a c t A new ternary compound La2 Cu0.8 Ge3 was synthesized and studied. The crystal structure of La2 Cu0.8 Ge3 was refined from X-ray powder diffraction data by Rietveld method. The new compound was found to have a tetragonal ˛-ThSi2 structure with space group I41 /amd (No. 141), and a = 0.42807(2) nm, c = 1.45626(6) nm, Z = 2 and Dcalc = 6.931 g/cm3 . The thermal expansion properties of La2 Cu0.8 Ge3 were investigated using high-temperature powder X-ray diffraction technique in the temperature range from 321 K to 753 K. Results show that its unit-cell parameters increase with increasing temperature. The −5 −5 coefficients of average lattice thermal expansion are ˛ ¯m K−1 , ˛ ¯m K−1 and a = 1.17 × 10 c = 1.09 × 10 ˛ ¯m = 3.42 × 10−5 K−1 . V © 2009 Published by Elsevier B.V.
1. Introduction Compounds in R–T–X systems where R = rare earth metals, T = transition metals and X = Si, Ge or Sn are known to exhibit excellent physical properties and are the subject of intensive investigations. In the La–Cu–Ge system, four ternary compounds, namely LaCuGe [1], LaCuGe2 [2], La2 CuGe6 [3] and LaCu2 Ge2 [4] have been reported in the Pearson’s Handbook [5]. In his paper on the study of the magnetic, electric and thermal properties of Ce2 CuGe3 , Tien et al. [6] showed the X-ray diffraction (XRD) pattern of La2 CuGe3 , and reported that La2 CuGe3 crystallizes in an orthorhombic structure with a = 0.7260 nm, b = 0.4608 nm and c = 0.4465 nm. Later Nakamoto et al. [7] examined carefully the phase constitution of the Ce(Cux Gey )2 (x + y = 0.90, 0.95 and 1.0) alloy system by XRD. They found that alloy with a stoichiometry of 2:1:3 is multiphase, whereas alloy Ce(Cu0.20 Ge0.75 )2 (i.e. Ce2 Cu0.8 Ge3 ) is single phase with the ˛-ThSi2 -type structure. During our recent study of the La–Cu–Ge system, we obtained the XRD pattern of La2 CuGe3 , which is similar to those reported by Tien et al. [6]. Our analysis of the XRD pattern of La2 CuGe3 indicated that this pattern consists of three phases (the AlB2 -, ˛-ThSi2 - and ThCr2 Si2 -type phases). These results agree well with those reported by Nakamoto et al. [7] on
∗ Corresponding author at: College of Materials Science and Engineering, Guangxi University, Nanning, Guangxi 530004, China. Tel.: +86 771 3275918; fax: +86 771 3233530. E-mail addresses: [email protected] (J. Yan), [email protected] (L. Zeng). 1 Co-author: Tel.: +86 771 3233530; fax: +86 771 3233530. 0925-8388/$ – see front matter © 2009 Published by Elsevier B.V. doi:10.1016/j.jallcom.2009.06.069
Ce(Cu0.25 Ge0.75 )2 . A new ternary compound with a stoichiometry of 2:0.8:3 was found. In this paper, we reported the crystal structure and thermal expansion properties of the new compound La2 Cu0.8 Ge3 . 2. Experimental The sample button of La2 Cu0.8 Ge3 , weighted 3 g, was arc-melted in an argon atmosphere using 99.8 wt.% pure La, 99.99 wt.% pure Cu and 99.999 wt.% pure Ge. To improve the homogeneity, the sample was turned over and remelted several times. The total mass loss after arc melting was less than 1 wt.%. After melting, the sample was enclosed in an evacuated quartz tube and annealed at 673 K for 800 h, then cooled down to 473 K at a rate of 0.15 K/min and kept for 360 h before being quenched in liquid nitrogen. The ingot was ground in an agate mortar and pestle to a particle size of no more than 10 m and finally annealed again at 473 K for 48 h to remove residual stresses. Before X-ray measurements, sample composition was examined by means of scanning electron microscope (SEM) and energy dispersive X-ray spectroscopy (EDXS). The sample composition (35.97 at.% La, 12.62 at.% Cu and 51.41 at.% Ge) analyzed by SEM-EDXS with ZAF matrix corrections was very close to the nominal composition of La2 Cu0.8 Ge3 (34.48 at.% La, 13.79 at.% Cu and 51.72 at.% Ge). XRD data of the specimen was collected on a Rigaku D/max 2500 V powder diffractometer equipped with CuK˛ radiation and a diffracted-beam graphite monochromator. The 2 scan range was from 20◦ to 110◦ with a step size of 0.02◦ and a counting time of 2 s per step. The 2 obs values of the peaks were determined by the second derivative method using Jade 5.0 XRD Pattern Processing software [8] after smoothing the pattern, fitting and removing background and stripping K˛2 . Values of unit-cell parameters were obtained by the least-squares method using Jade 5.0. The Rietveld refinement of La2 Cu0.8 Ge3 was performed using the DBWS9807a program [9]. The DMPLOT-plot view program [10] was used to plot the refinement results. The lattice thermal expansion properties for La2 Cu0.8 Ge3 were investigated using the high-temperature X-ray powder diffraction technique (HTXRD) in the temperature range from 321 K to 753 K with a 2 scan range from 20◦ to 65◦ and a scan speed
740
J. Yan et al. / Journal of Alloys and Compounds 485 (2009) 739–742
Table 1 Rietveld refinement results for La2 Cu0.8 Ge3 .
3. Results and discussion
Formula
La2 Cu0.8 Ge3
Space group Lattice parameters (nm)
I41 /amd (No. 141) a = 0.42807(2) c = 1.45626(6) 0.26685 6.931 2 9.56% 12.56% 7.06% 5.22%
Unit-cell volume (nm3 ) Calculated density (g/cm3 ) Formula units per unit-cell Rp Rwp RB RF
1/2 2 ωi [Yi (obs)−Yi (calc)] , Rwp = , 2 Yi (obs) ωi [Yi (obs)] [IH (obs)]1/2 −[IH (calc)]1/2 RF = . 1/2
Rp =
|Yi (obs)−Yi (calc)|
3.1. Crystal structure
RB =
|IH (obs)−IH (calc)|
Indexing the XRD pattern of La2 Cu0.8 Ge3 using Jade 5.0 shows that La2 Cu0.8 Ge3 is tetragonal and the unit-cell parameters are a = 0.42791(2) nm, c = 1.45578(7) nm. Extinction conditions were found to be: h k l: h + k + l = / 2n; h k 0: h, k = / 2n; 0 k l: k + l = / 2n; h h l: 2h + l = / 4n; 0 0 l: l = / 4n; h 0 0: h = / 2n; h h 0 : h = / 2n). The only space group, which can satisfy these extinction conditions, is I41 /amd (No. 141). The figure of merit for indexing FN [11] is F30 = 119.1(0.007, 36). ,
IH (obs)
[IH (obs)]
Table 2 Atomic and thermal factors for La2 Cu0.8 Ge3 . Atom
Sites
x
y
z
Occupancy
Beq (nm2 )
La Cu Ge
4a 8e 8e
0 0 0
3/4 1/4 1/4
1/8 0.2931(2) 0.2931(2)
1 0.20(3) 0.75(5)
0.0266(9) 0.0182(6) 0.0535(4)
Table 3 Selected interatomic distances in the crystal structure of La2 Cu0.8 Ge3 . Atom
Neighbor atom
Distance (nm)
La M
M × 12 M×1 M×2 La × 6
0.3252(3) 0.2385(3) 0.2481(1) 0.3252(1)
M = Ge or Cu.
of 4◦ min−1 . The temperature was monitored with a Pt–Rh thermocouple and controlled to an accuracy of ±1 K with a PTC-20A temperature controller. The specimen was heated to the desired temperatures at a rate of 15 K min−1 and held for 30 min. All measurements were carried out in vacuum of about 2 Pa.
Fig. 2. Crystal structure of La2 Cu0.8 Ge3 .
Fig. 1. Observed, calculated and residuals of the powder diffraction patterns of La2 Cu0.8 Ge3 .
J. Yan et al. / Journal of Alloys and Compounds 485 (2009) 739–742
741
Fig. 3. HTXRD patterns of La2 Cu0.8 Ge3 recorded at different temperatures. Table 4 The temperature dependence of unit-cell parameters a and c, both measured and fitted; mean and relative linear thermal expansion coefficient and LPTE for La2 Cu0.8 Ge3 . T (K)
a (nm)
a (nm) (fitted)
−6 ˛m (K−1 ) a × 10
˛ra × 10−6 (K−1 )
LPTE (%)
c (nm)
c (nm) (fitted)
−6 ˛m (K−1 ) c × 10
˛rc × 10−6 (K−1 )
LPTE (%)
321 353 403 453 503 553 603 653 703 753
0.42813 0.42817 0.42836 0.42871 0.42900 0.42928 0.42949 0.42994 0.43041 0.43081
0.42809 0.42821 0.42842 0.42866 0.42894 0.42924 0.42958 0.42996 0.43037 0.43081
– 8.76 9.40 10.1 10.9 11.6 12.3 13.2 13.9 14.7
8.02 9.00 10.5 12.1 13.6 15.2 16.7 18.2 19.8 21.3
– 0.03 0.08 0.13 0.20 0.27 0.35 0.44 0.53 0.64
1.45578 1.45633 1.45724 1.45808 1.45871 1.45940 1.46016 1.46073 1.46126 1.46186
1.45580 1.45636 1.45721 1.45800 1.45876 1.45946 1.46012 1.46074 1.46130 1.46183
– 12.0 11.8 11.4 11.2 10.8 10.5 10.2 9.89 9.59
12.3 11.9 11.3 10.6 10.0 9.38 8.75 8.12 7.48 6.85
– 0.04 0.10 0.15 0.20 0.25 0.30 0.34 0.38 0.41
−5 −5 Average lattice thermal expansion coefficients ˛ ¯m K−1 , ˛ ¯m K−1 and ˛ ¯m = 3.42 × 10−5 K−1 . a = 1.17 × 10 c = 1.09 × 10 V
The crystal structure of La2 Cu0.8 Ge3 was refined by using the program DBWS9807a [9]. The unit-cell parameters obtained from indexing and the atomic position parameters of ˛-ThSi2 [12] were used as starting values. The Pseudo-Voigt function was selected as the profile fitting function. A total of 24 parameters, including unit-cell parameters, full width at half maximum (FWHM), preferred orientation, atomic position and thermal parameters were refined. Successfully structural refinement yielded unit-cell parameters of a = 0.42807(2) nm, c = 1.45626(6) nm with a reliability R-factor Rp = 9.56% and a weighted R-factor Rwp = 12.56%. Crystal data and refinement results of the compound La2 Cu0.8 Ge3 are given in Table 1. The observed and the calculated powder XRD patterns as well as the difference curve are plotted in Fig. 1 using the DMPLOTplot view program [10]. The atomic positions and isotropic atomic displacement parameters of this compound are listed in Table 2. The
crystal structure of La2 Cu0.8 Ge3 is shown in Fig. 2. Selected interatomic distances are listed in Table 3. It can be seen from Table 3 that the shortest distance dM–M = 0.2385(3) nm, which corresponds to 89.4% of the sum of the atomic radii. The La-M distance in the structure is 0.3252(1) nm. 3.2. Thermal expansion HTXRD patterns of La2 Cu0.8 Ge3 recorded at different temperatures in the range of 321–753 K are plotted in Fig. 3. A comparison of the HTXRD patterns reveals that there is no phase change in the XRD patterns, except shifts in the positions of Bragg reflections towards lower 2 angles, indicating lattice expansions. The unitcell parameters at high temperatures were calculated using the Jade 5.0 program, and the results are listed in Tables 4 and 5. Values of
Table 5 The temperature dependence of unit-cell volume, both measured and fitted, mean and relative volume thermal expansion coefficient and VTE for La2 Cu0.8 Ge3 . T (K)
V (nm3 )
V (nm3 ) (fitted)
˛m × 10−6 (K−1 ) V
˛rV × 10−6 (K−1 )
VTE (%)
321 353 403 453 503 553 603 653 703 753
0.26684 0.26699 0.26739 0.26798 0.26847 0.26894 0.26935 0.27001 0.27070 0.27131
0.26679 0.26704 0.26746 0.26791 0.26839 0.26891 0.26946 0.27004 0.27065 0.27130
– 29.3 30.6 31.8 33.0 34.3 35.5 36.7 37.9 39.1
28.3 29.9 32.4 34.9 37.4 39.9 42.4 45.0 47.5 50.0
– 0.09 0.25 0.42 0.60 0.79 1.00 1.22 1.45 1.69
742
J. Yan et al. / Journal of Alloys and Compounds 485 (2009) 739–742
Values of the measured unit-cell parameters have been used to calculate the mean linear thermal expansion coefficient (˛m a ), the relative linear thermal expansion coefficient (˛ra ) and the percentage of the unit-cell parameter thermal expansion (LPTE) by the following relations: ˛m a =
1 aT − a321 × a321 T − 321
(4)
˛ra =
1 daT × a321 dT
(5)
LPTE (%) =
aT − a321 × 100 a321
(6)
where aT is the unit-cell parameter a at temperature T and a321 is the value of the unit-cell parameter at the temperature 321 K. m Parameters ˛m c , ˛c and ˛V , ˛V are also defined similarly to Eqs. (4) and (5). The percentage of the volume thermal expansion (VTE) can be defined similarly to Eq. (6). The temperature dependence of m r m r ˛m a , ˛a ˛c , ˛c and ˛V , ˛V between 321 K and 753 K are also given in Tables 4 and 5. From these values the average mean thermal expansion coefficients along the a and the c axes in the tempera−5 ture range of 321–753 K are calculated to be ˛ ¯m K−1 , a = 1.17 × 10 −5 −1 m ˛ ¯ c = 1.09 × 10 K and the average unit-cell volume thermal expansion coefficient to be ˛ ¯m = 3.42 × 10−5 K−1 . V 4. Conclusions The new ternary compound La2 Cu0.8 Ge3 was found to crystallize in tetragonal with the defect ˛-ThSi2 type structure with space group I41 /amd (No. 141) and unit-cell parameters a = 0.42807(2) nm and c = 1.45626(6) nm. In the temperature range of 321–753 K, the sample is stable and no phase transformation was observed. The unit-cell parameters increase with increasing temperature. The coefficients of average mean thermal expansion along the a and the −5 −5 c axes are ˛ ¯m K−1 and ˛ ¯m K−1 , respeca = 1.17 × 10 c = 1.09 × 10 tively. The average thermal expansion coefficient of the unit-cell volume is 3.42 × 10−5 K−1 . Acknowledgement This work was supported by the Natural Science Foundation of Guangxi (No. 0648039). References
Fig. 4. The temperature variations of the unit-cell parameters and unit-cell volume for La2 Cu0.8 Ge3 .
unit-cell parameters were found to increase with increasing temperature. Variations in unit-cell parameters and unit-cell volume with temperature from 321 K to 753 K for La2 Cu0.8 Ge3 are plotted in Fig. 4. Data points in Fig. 4 can be represented by the following polynomial functions: a(nm) = 0.42767 − 7.98628 × 10−7 T + 6.59086 × 10−9 T 2 −5
c(nm) = 1.44909 + 2.38547 × 10 3
T − 9.21688 × 10
−6
V (nm ) = 0.26506 + 3.25318 × 10
−9 2
T
−9 2
T + 6.69223 × 10
where T is the temperature in Kelvin.
T
(1) (2) (3)
[1] A. Iandelli, J. Alloys Compd. 198 (1993) 141–142. [2] M. Francois, G. Venturini, B. Malaman, B. Roques, J. Less-Common Met. 160 (1990) 197–213. [3] M.B. Konyk, P.S. Salamakha, I.O. Bodak, V.K. Pecharskii, Soviet PhysicsCrystallography, translated from Kristallografiya., 33 (1988) 494–495. [4] W. Rieger, P.E. Monatsh, Chemistry 100 (1969) 444–454. [5] P. Villars (Ed.), Pearson’s Handbook: Crystallographic Data for Intermetallic Phases, Desk Edition, ASM International, Materials Park, OH, 1997. [6] C. Tien, C.H. Feng, C.S. Wur, J.J. Lu, Phys. Rev. B 61 (2000) 12151. [7] G. Nakamoto, T. Hagiuda, M. Kurisu, Physica B 312–313 (2002) 277– 279. [8] X.p.p. Materials Data JADE Release 5, Materials Data Inc., Livermore, CA., Materials Data JADE Release 5, XRD pattern processing, Materials Data Inc., Livermore, CA. [9] R.A. Young, A.C. Larson, C.O. Paiva-Santos, User’s Guide to Program DBWS-9807a for Rietveld Analysis of X-ray and Neutron Powder Diffraction Patterns with a PC and Various Other Computers, School of Physics, Georgia Institute of Technology, Atlanta, GA, 2000. [10] H. Marciniak, R. Diduszko, DMPLOT-Plot View Program for Rietveld Refinement Method, Version 3, 1997, Computer Software. [11] G.S. Smith, R.L. Snyder, J. Appl. Crystallogr. 12 (1979) 60–65. [12] G. Brauer, A. Mitins, Z. Anorg. Allg. Chem. 249 (1942) 325–339.
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Crystal structure and thermal expansion properties of new compound La2 Cu0.8 Ge3 Jialin Yan a,b,1 , Xingwen Lu a,b , Wenjun Shen a,b , Lingmin Zeng a,b,∗ , Liangqin Nong c a b c
Key Laboratory of New Processing Technology for Nonferrous Metal and Materials, Ministry of Education, Guangxi University, Nanning, Guangxi 530004, China College of Materials Science and Engineering, Guangxi University, Nanning, Guangxi 530004, China College of Physics and Electronic Engineering, Guangxi University for Nationalities, Nanning, Guangxi 530006, China
a r t i c l e
i n f o
Article history: Received 31 May 2009 Accepted 10 June 2009 Available online 18 June 2009 Keywords: Intermetallics Crystal structure Thermal expansion High-temperature X-ray diffraction
a b s t r a c t A new ternary compound La2 Cu0.8 Ge3 was synthesized and studied. The crystal structure of La2 Cu0.8 Ge3 was refined from X-ray powder diffraction data by Rietveld method. The new compound was found to have a tetragonal ˛-ThSi2 structure with space group I41 /amd (No. 141), and a = 0.42807(2) nm, c = 1.45626(6) nm, Z = 2 and Dcalc = 6.931 g/cm3 . The thermal expansion properties of La2 Cu0.8 Ge3 were investigated using high-temperature powder X-ray diffraction technique in the temperature range from 321 K to 753 K. Results show that its unit-cell parameters increase with increasing temperature. The −5 −5 coefficients of average lattice thermal expansion are ˛ ¯m K−1 , ˛ ¯m K−1 and a = 1.17 × 10 c = 1.09 × 10 ˛ ¯m = 3.42 × 10−5 K−1 . V © 2009 Published by Elsevier B.V.
1. Introduction Compounds in R–T–X systems where R = rare earth metals, T = transition metals and X = Si, Ge or Sn are known to exhibit excellent physical properties and are the subject of intensive investigations. In the La–Cu–Ge system, four ternary compounds, namely LaCuGe [1], LaCuGe2 [2], La2 CuGe6 [3] and LaCu2 Ge2 [4] have been reported in the Pearson’s Handbook [5]. In his paper on the study of the magnetic, electric and thermal properties of Ce2 CuGe3 , Tien et al. [6] showed the X-ray diffraction (XRD) pattern of La2 CuGe3 , and reported that La2 CuGe3 crystallizes in an orthorhombic structure with a = 0.7260 nm, b = 0.4608 nm and c = 0.4465 nm. Later Nakamoto et al. [7] examined carefully the phase constitution of the Ce(Cux Gey )2 (x + y = 0.90, 0.95 and 1.0) alloy system by XRD. They found that alloy with a stoichiometry of 2:1:3 is multiphase, whereas alloy Ce(Cu0.20 Ge0.75 )2 (i.e. Ce2 Cu0.8 Ge3 ) is single phase with the ˛-ThSi2 -type structure. During our recent study of the La–Cu–Ge system, we obtained the XRD pattern of La2 CuGe3 , which is similar to those reported by Tien et al. [6]. Our analysis of the XRD pattern of La2 CuGe3 indicated that this pattern consists of three phases (the AlB2 -, ˛-ThSi2 - and ThCr2 Si2 -type phases). These results agree well with those reported by Nakamoto et al. [7] on
∗ Corresponding author at: College of Materials Science and Engineering, Guangxi University, Nanning, Guangxi 530004, China. Tel.: +86 771 3275918; fax: +86 771 3233530. E-mail addresses: [email protected] (J. Yan), [email protected] (L. Zeng). 1 Co-author: Tel.: +86 771 3233530; fax: +86 771 3233530. 0925-8388/$ – see front matter © 2009 Published by Elsevier B.V. doi:10.1016/j.jallcom.2009.06.069
Ce(Cu0.25 Ge0.75 )2 . A new ternary compound with a stoichiometry of 2:0.8:3 was found. In this paper, we reported the crystal structure and thermal expansion properties of the new compound La2 Cu0.8 Ge3 . 2. Experimental The sample button of La2 Cu0.8 Ge3 , weighted 3 g, was arc-melted in an argon atmosphere using 99.8 wt.% pure La, 99.99 wt.% pure Cu and 99.999 wt.% pure Ge. To improve the homogeneity, the sample was turned over and remelted several times. The total mass loss after arc melting was less than 1 wt.%. After melting, the sample was enclosed in an evacuated quartz tube and annealed at 673 K for 800 h, then cooled down to 473 K at a rate of 0.15 K/min and kept for 360 h before being quenched in liquid nitrogen. The ingot was ground in an agate mortar and pestle to a particle size of no more than 10 m and finally annealed again at 473 K for 48 h to remove residual stresses. Before X-ray measurements, sample composition was examined by means of scanning electron microscope (SEM) and energy dispersive X-ray spectroscopy (EDXS). The sample composition (35.97 at.% La, 12.62 at.% Cu and 51.41 at.% Ge) analyzed by SEM-EDXS with ZAF matrix corrections was very close to the nominal composition of La2 Cu0.8 Ge3 (34.48 at.% La, 13.79 at.% Cu and 51.72 at.% Ge). XRD data of the specimen was collected on a Rigaku D/max 2500 V powder diffractometer equipped with CuK˛ radiation and a diffracted-beam graphite monochromator. The 2 scan range was from 20◦ to 110◦ with a step size of 0.02◦ and a counting time of 2 s per step. The 2 obs values of the peaks were determined by the second derivative method using Jade 5.0 XRD Pattern Processing software [8] after smoothing the pattern, fitting and removing background and stripping K˛2 . Values of unit-cell parameters were obtained by the least-squares method using Jade 5.0. The Rietveld refinement of La2 Cu0.8 Ge3 was performed using the DBWS9807a program [9]. The DMPLOT-plot view program [10] was used to plot the refinement results. The lattice thermal expansion properties for La2 Cu0.8 Ge3 were investigated using the high-temperature X-ray powder diffraction technique (HTXRD) in the temperature range from 321 K to 753 K with a 2 scan range from 20◦ to 65◦ and a scan speed
740
J. Yan et al. / Journal of Alloys and Compounds 485 (2009) 739–742
Table 1 Rietveld refinement results for La2 Cu0.8 Ge3 .
3. Results and discussion
Formula
La2 Cu0.8 Ge3
Space group Lattice parameters (nm)
I41 /amd (No. 141) a = 0.42807(2) c = 1.45626(6) 0.26685 6.931 2 9.56% 12.56% 7.06% 5.22%
Unit-cell volume (nm3 ) Calculated density (g/cm3 ) Formula units per unit-cell Rp Rwp RB RF
1/2 2 ωi [Yi (obs)−Yi (calc)] , Rwp = , 2 Yi (obs) ωi [Yi (obs)] [IH (obs)]1/2 −[IH (calc)]1/2 RF = . 1/2
Rp =
|Yi (obs)−Yi (calc)|
3.1. Crystal structure
RB =
|IH (obs)−IH (calc)|
Indexing the XRD pattern of La2 Cu0.8 Ge3 using Jade 5.0 shows that La2 Cu0.8 Ge3 is tetragonal and the unit-cell parameters are a = 0.42791(2) nm, c = 1.45578(7) nm. Extinction conditions were found to be: h k l: h + k + l = / 2n; h k 0: h, k = / 2n; 0 k l: k + l = / 2n; h h l: 2h + l = / 4n; 0 0 l: l = / 4n; h 0 0: h = / 2n; h h 0 : h = / 2n). The only space group, which can satisfy these extinction conditions, is I41 /amd (No. 141). The figure of merit for indexing FN [11] is F30 = 119.1(0.007, 36). ,
IH (obs)
[IH (obs)]
Table 2 Atomic and thermal factors for La2 Cu0.8 Ge3 . Atom
Sites
x
y
z
Occupancy
Beq (nm2 )
La Cu Ge
4a 8e 8e
0 0 0
3/4 1/4 1/4
1/8 0.2931(2) 0.2931(2)
1 0.20(3) 0.75(5)
0.0266(9) 0.0182(6) 0.0535(4)
Table 3 Selected interatomic distances in the crystal structure of La2 Cu0.8 Ge3 . Atom
Neighbor atom
Distance (nm)
La M
M × 12 M×1 M×2 La × 6
0.3252(3) 0.2385(3) 0.2481(1) 0.3252(1)
M = Ge or Cu.
of 4◦ min−1 . The temperature was monitored with a Pt–Rh thermocouple and controlled to an accuracy of ±1 K with a PTC-20A temperature controller. The specimen was heated to the desired temperatures at a rate of 15 K min−1 and held for 30 min. All measurements were carried out in vacuum of about 2 Pa.
Fig. 2. Crystal structure of La2 Cu0.8 Ge3 .
Fig. 1. Observed, calculated and residuals of the powder diffraction patterns of La2 Cu0.8 Ge3 .
J. Yan et al. / Journal of Alloys and Compounds 485 (2009) 739–742
741
Fig. 3. HTXRD patterns of La2 Cu0.8 Ge3 recorded at different temperatures. Table 4 The temperature dependence of unit-cell parameters a and c, both measured and fitted; mean and relative linear thermal expansion coefficient and LPTE for La2 Cu0.8 Ge3 . T (K)
a (nm)
a (nm) (fitted)
−6 ˛m (K−1 ) a × 10
˛ra × 10−6 (K−1 )
LPTE (%)
c (nm)
c (nm) (fitted)
−6 ˛m (K−1 ) c × 10
˛rc × 10−6 (K−1 )
LPTE (%)
321 353 403 453 503 553 603 653 703 753
0.42813 0.42817 0.42836 0.42871 0.42900 0.42928 0.42949 0.42994 0.43041 0.43081
0.42809 0.42821 0.42842 0.42866 0.42894 0.42924 0.42958 0.42996 0.43037 0.43081
– 8.76 9.40 10.1 10.9 11.6 12.3 13.2 13.9 14.7
8.02 9.00 10.5 12.1 13.6 15.2 16.7 18.2 19.8 21.3
– 0.03 0.08 0.13 0.20 0.27 0.35 0.44 0.53 0.64
1.45578 1.45633 1.45724 1.45808 1.45871 1.45940 1.46016 1.46073 1.46126 1.46186
1.45580 1.45636 1.45721 1.45800 1.45876 1.45946 1.46012 1.46074 1.46130 1.46183
– 12.0 11.8 11.4 11.2 10.8 10.5 10.2 9.89 9.59
12.3 11.9 11.3 10.6 10.0 9.38 8.75 8.12 7.48 6.85
– 0.04 0.10 0.15 0.20 0.25 0.30 0.34 0.38 0.41
−5 −5 Average lattice thermal expansion coefficients ˛ ¯m K−1 , ˛ ¯m K−1 and ˛ ¯m = 3.42 × 10−5 K−1 . a = 1.17 × 10 c = 1.09 × 10 V
The crystal structure of La2 Cu0.8 Ge3 was refined by using the program DBWS9807a [9]. The unit-cell parameters obtained from indexing and the atomic position parameters of ˛-ThSi2 [12] were used as starting values. The Pseudo-Voigt function was selected as the profile fitting function. A total of 24 parameters, including unit-cell parameters, full width at half maximum (FWHM), preferred orientation, atomic position and thermal parameters were refined. Successfully structural refinement yielded unit-cell parameters of a = 0.42807(2) nm, c = 1.45626(6) nm with a reliability R-factor Rp = 9.56% and a weighted R-factor Rwp = 12.56%. Crystal data and refinement results of the compound La2 Cu0.8 Ge3 are given in Table 1. The observed and the calculated powder XRD patterns as well as the difference curve are plotted in Fig. 1 using the DMPLOTplot view program [10]. The atomic positions and isotropic atomic displacement parameters of this compound are listed in Table 2. The
crystal structure of La2 Cu0.8 Ge3 is shown in Fig. 2. Selected interatomic distances are listed in Table 3. It can be seen from Table 3 that the shortest distance dM–M = 0.2385(3) nm, which corresponds to 89.4% of the sum of the atomic radii. The La-M distance in the structure is 0.3252(1) nm. 3.2. Thermal expansion HTXRD patterns of La2 Cu0.8 Ge3 recorded at different temperatures in the range of 321–753 K are plotted in Fig. 3. A comparison of the HTXRD patterns reveals that there is no phase change in the XRD patterns, except shifts in the positions of Bragg reflections towards lower 2 angles, indicating lattice expansions. The unitcell parameters at high temperatures were calculated using the Jade 5.0 program, and the results are listed in Tables 4 and 5. Values of
Table 5 The temperature dependence of unit-cell volume, both measured and fitted, mean and relative volume thermal expansion coefficient and VTE for La2 Cu0.8 Ge3 . T (K)
V (nm3 )
V (nm3 ) (fitted)
˛m × 10−6 (K−1 ) V
˛rV × 10−6 (K−1 )
VTE (%)
321 353 403 453 503 553 603 653 703 753
0.26684 0.26699 0.26739 0.26798 0.26847 0.26894 0.26935 0.27001 0.27070 0.27131
0.26679 0.26704 0.26746 0.26791 0.26839 0.26891 0.26946 0.27004 0.27065 0.27130
– 29.3 30.6 31.8 33.0 34.3 35.5 36.7 37.9 39.1
28.3 29.9 32.4 34.9 37.4 39.9 42.4 45.0 47.5 50.0
– 0.09 0.25 0.42 0.60 0.79 1.00 1.22 1.45 1.69
742
J. Yan et al. / Journal of Alloys and Compounds 485 (2009) 739–742
Values of the measured unit-cell parameters have been used to calculate the mean linear thermal expansion coefficient (˛m a ), the relative linear thermal expansion coefficient (˛ra ) and the percentage of the unit-cell parameter thermal expansion (LPTE) by the following relations: ˛m a =
1 aT − a321 × a321 T − 321
(4)
˛ra =
1 daT × a321 dT
(5)
LPTE (%) =
aT − a321 × 100 a321
(6)
where aT is the unit-cell parameter a at temperature T and a321 is the value of the unit-cell parameter at the temperature 321 K. m Parameters ˛m c , ˛c and ˛V , ˛V are also defined similarly to Eqs. (4) and (5). The percentage of the volume thermal expansion (VTE) can be defined similarly to Eq. (6). The temperature dependence of m r m r ˛m a , ˛a ˛c , ˛c and ˛V , ˛V between 321 K and 753 K are also given in Tables 4 and 5. From these values the average mean thermal expansion coefficients along the a and the c axes in the tempera−5 ture range of 321–753 K are calculated to be ˛ ¯m K−1 , a = 1.17 × 10 −5 −1 m ˛ ¯ c = 1.09 × 10 K and the average unit-cell volume thermal expansion coefficient to be ˛ ¯m = 3.42 × 10−5 K−1 . V 4. Conclusions The new ternary compound La2 Cu0.8 Ge3 was found to crystallize in tetragonal with the defect ˛-ThSi2 type structure with space group I41 /amd (No. 141) and unit-cell parameters a = 0.42807(2) nm and c = 1.45626(6) nm. In the temperature range of 321–753 K, the sample is stable and no phase transformation was observed. The unit-cell parameters increase with increasing temperature. The coefficients of average mean thermal expansion along the a and the −5 −5 c axes are ˛ ¯m K−1 and ˛ ¯m K−1 , respeca = 1.17 × 10 c = 1.09 × 10 tively. The average thermal expansion coefficient of the unit-cell volume is 3.42 × 10−5 K−1 . Acknowledgement This work was supported by the Natural Science Foundation of Guangxi (No. 0648039). References
Fig. 4. The temperature variations of the unit-cell parameters and unit-cell volume for La2 Cu0.8 Ge3 .
unit-cell parameters were found to increase with increasing temperature. Variations in unit-cell parameters and unit-cell volume with temperature from 321 K to 753 K for La2 Cu0.8 Ge3 are plotted in Fig. 4. Data points in Fig. 4 can be represented by the following polynomial functions: a(nm) = 0.42767 − 7.98628 × 10−7 T + 6.59086 × 10−9 T 2 −5
c(nm) = 1.44909 + 2.38547 × 10 3
T − 9.21688 × 10
−6
V (nm ) = 0.26506 + 3.25318 × 10
−9 2
T
−9 2
T + 6.69223 × 10
where T is the temperature in Kelvin.
T
(1) (2) (3)
[1] A. Iandelli, J. Alloys Compd. 198 (1993) 141–142. [2] M. Francois, G. Venturini, B. Malaman, B. Roques, J. Less-Common Met. 160 (1990) 197–213. [3] M.B. Konyk, P.S. Salamakha, I.O. Bodak, V.K. Pecharskii, Soviet PhysicsCrystallography, translated from Kristallografiya., 33 (1988) 494–495. [4] W. Rieger, P.E. Monatsh, Chemistry 100 (1969) 444–454. [5] P. Villars (Ed.), Pearson’s Handbook: Crystallographic Data for Intermetallic Phases, Desk Edition, ASM International, Materials Park, OH, 1997. [6] C. Tien, C.H. Feng, C.S. Wur, J.J. Lu, Phys. Rev. B 61 (2000) 12151. [7] G. Nakamoto, T. Hagiuda, M. Kurisu, Physica B 312–313 (2002) 277– 279. [8] X.p.p. Materials Data JADE Release 5, Materials Data Inc., Livermore, CA., Materials Data JADE Release 5, XRD pattern processing, Materials Data Inc., Livermore, CA. [9] R.A. Young, A.C. Larson, C.O. Paiva-Santos, User’s Guide to Program DBWS-9807a for Rietveld Analysis of X-ray and Neutron Powder Diffraction Patterns with a PC and Various Other Computers, School of Physics, Georgia Institute of Technology, Atlanta, GA, 2000. [10] H. Marciniak, R. Diduszko, DMPLOT-Plot View Program for Rietveld Refinement Method, Version 3, 1997, Computer Software. [11] G.S. Smith, R.L. Snyder, J. Appl. Crystallogr. 12 (1979) 60–65. [12] G. Brauer, A. Mitins, Z. Anorg. Allg. Chem. 249 (1942) 325–339.