Journal of Physics and Chemistry of Solids 73 (2012) 1191–1195

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Crystal structure, thermal expansion and magnetic properties of Nd2Cu0.8Ge3 compound Xingwen Lu a,b, Lingmin Zeng a,c, Kaimin Shih b,n a

Key Laboratory of New Processing Technology for Nonferrous Metal and Materials, Ministry of Education, Guangxi University, Nanning, Guangxi, China Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China c College of Materials Science and Engineering, Guangxi University, Nanning, Guangxi, China b

a r t i c l e i n f o

abstract

Article history: Received 28 February 2012 Received in revised form 20 April 2012 Accepted 22 April 2012 Available online 1 May 2012

A new ternary intermetallic compound, Nd2Cu0.8Ge3, was synthesized and its crystal structure was determined by Rietveld refinement of X-ray powder diffraction data. The Nd2Cu0.8Ge3 compound crystallizes in space group I41/amd (No. 141), with a tetragonal a-ThSi2 structure type, and a ¼0.41783(2) nm, c¼ 1.43689(9) nm, Z ¼ 2 and Dcalc ¼7.466 g/cm3. Using the high temperature powder X-ray diffraction (HTXRD) technique, the lattice thermal expansion behavior of the compound was investigated in the temperature range of 298–648 K, and the result shows that its unit-cell parameters increased anisotropically when temperature increased. The magnetic susceptibility measured in the temperature range of 5–300 K indicated antiferromagnetic order of Nd2Cu0.8Ge3 at low temperatures, and the magnetic susceptibility can be well described over the range of 50–300 K using Curie–Weiss law. The calculated effective magnetic moment (meff) is 3.53 mB and dominated by the contribution of the Nd3 þ ions. & 2012 Elsevier Ltd. All rights reserved.

Keywords: C. X-ray diffraction D. Crystal structure D. Thermal expansion

1. Introduction Compounds in R–T–X systems, where R¼rare earth metals, T¼transition metals and X¼Si, Ge or Sn, have received strong attention in recent years because of their important role in many technological applications such as microwave devices, permanent magnets, and magnetic and optical recording devices. Thus, new ternary compounds with superior properties have been intensively explored. Previous studies of the Nd–Cu–Ge system reported five ternary compounds with distinct structures: NdCuGe (AlB2-type), NdCuGe2 (CeNiSi2-type), NdCu2Ge2 (ThCr2Si2-type), Nd2CuGe6 (Ce2CuGe6-type), and Nd3Cu4Ge4 (Zr3Cu4Si4-type) [1–3]. The magnetic properties of NdCuGe, Nd2CuGe6 and Nd3Cu4Ge4 have also been investigated, and the results have indicated the Curie–Weiss paramagnetic behavior for all compounds at high temperatures [4–7]. Moreover, the Ce(CuxGey)2 (xþy¼0.90, 0.95 and 1.0) system has been detailedly examined by Nakamoto et al. [8] to determine the phase constitution of the Ce(CuxGey)2 alloy. They found that alloy Ce(Cu0.20Ge0.75)2 (i.e. Ce2Cu0.8Ge3) is a single phase with a-ThSi2-type structure, whereas alloy Ce(Cu0.15Ge0.80)2 (i.e. Ce2Cu0.6Ge3.2) with smaller Cu:Ge ratio is multiphase (unidentified phase(s) and a a-ThSi2-type phase). During our recent study of Nd–Cu–Ge system, the results of XRD patterns analysis of Nd2Cu0.6Ge3.2 agree well with

n

Corresponding author. Tel.: þ852 28591973; fax: þ852 25595337. E-mail address: [email protected] (K. Shih).

0022-3697/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jpcs.2012.04.015

those reported by Nakamoto et al. on Ce2Cu0.6Ge3.2. Thus, an Nd–Cu–Ge compound with a stoichiometric ratio of 2:0.8:3, i.e. Nd2Cu0.8Ge3, was synthesized with its crystal structure identified. Given that both the thermal and magnetic properties of the compound are crucial for its industrial applications, this study also reports information on its lattice thermal expansion and temperature-dependent magnetic susceptibility.

2. Material and methods 2.1. Sample preparation A polycrystalline sample of Nd2Cu0.8Ge3 with a total weight of 3 g was prepared by arc melting the ingots of its elemental constituents (99.9 wt% Nd, 99.9 wt% Cu, 99.99 wt% Ge) under a high purity argon atmosphere. To ensure the homogeneity of the sample, several melting treatments were performed and the total mass loss was less than 1 wt%. After melting, the sample was enclosed in an evacuated quartz tube, annealed at 673 K for 800 h, cooled to 473 K at a rate of 0.15 K/min, kept at that temperature for 360 h, and finally quenched by liquid nitrogen. The ingot was then ground to powder by agate mortar, and annealed again at 473 K for 48 h to remove the residual stress. The final product was ground to particle size less than 10 mm measured by a particle size analyzer (Coulter Multisizer II, Beckman, Fullerton, CA).

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The chemical composition of the synthesized sample was inspected by a scanning electron microscope (SEM; Model S-3400N, Hitachi, Japan) equipped with an energy dispersive X-ray spectrometer (EDXS). The result derived from the SEM-EDXS with ZAF matrix correction (36.02 at% Nd, 12.42 at% Cu and 51.56 at% Ge) was generally consistent with the nominal composition of Nd2Cu0.8Ge3 (34.48 at% Nd, 13.79 at% Cu and 51.72 at% Ge). 2.2. Data collection The powder diffraction data of Nd2Cu0.8Ge3 were obtained with a Rigaku D/max 2500V powder diffractometer equipped with a Cu Ka radiation and a graphite monochromator at room conditions. The scan range was from 101 to 1101 (2y) with a step size of 0.021 and a count time of 2 s per step. The indexing of the XRD pattern of the sample was carried out by using a Jade 6.0 program [9]. The crystal structural refinement of the new compound Nd2Cu0.8Ge3 was performed by using Rietveld method on the obtained XRD data. To study the thermal expansion property of Nd2Cu0.8Ge3, HTXRD data were collected at an interval of 50 K between 298 K and 648 K. The HTXRD experiment was performed on a Rigaku D/ max2500V powder diffractometer equipped with a high-temperature attachment. The diffractometer was operated at 40 kV and 200 mA using Cu Ka radiation. The 2y scan range was from 201 to 601 with a speed of 41 min  1. The temperature was monitored with a Pt–Rh thermocouple and controlled to an accuracy of about 71 K with a PTC-20A temperature controller. The sample was heated to the designated temperature at a rate of 15 K min  1 and was held for 20 min. All measurements were carried out in a near-vacuum environment (  2 Pa). The observed 2y values for each pattern were corrected for instrumental errors using the polynomial equation obtained from the calibrating standard SRM 640c. The lattice parameters were obtained by a least-squares refinement of the corrected data at each temperature. Magnetic susceptibility was determined using a superconducting quantum interference device magnetometer (MPMS-5.5T, Quantum Design, San Diego, CA) from 5 to 300 K in a magnetic field 50 Oe.

Fig. 1. Experimental (crosses), calculated (solid line) and the difference between experimental and calculated (solid line at the bottom) data for the X-ray powder diffraction patterns of the Nd2Cu0.8Ge3 sample. Vertical bars indicate the positions of hkl reflections for Nd2Cu0.8Ge3 phase.

Table 1 Refinement parameters obtained from the Rietveld analysis of Nd2Cu0.8Ge3 compound. Formula

Nd2Cu0.8Ge3

Space group Lattice parameters (nm) Unit-cell volume (nm3) Calculated density (g/cm3) Formula units per unit cell RP RWP RB RF

I41/amd (No. 141) a¼ 0.41778(2) c¼ 1.43654(9) 0.25074 7.476 2 9.57% 12.41% 7.29% 5.47%

 Y i ðobsÞY i ðcalcÞ P Y i ðobsÞ  P  IH ðobsÞIH ðcalcÞ P RB ¼ IH ðobsÞ

RP ¼

3. Results and discussion 3.1. Crystal structure The indexing result of the powder diffraction pattern of Nd2Cu0.8Ge3 indicated a tetragonal cell with the lattice parameters of a¼0.41809(2) nm and c¼ 1.43782(3). The value of FN, the Smith and Snyder figure of merit [10], was obtained as F30 ¼79.4(72). Extinction conditions were: (hkl: hþkþla2n; hk0: h, ka2n; 0kl: kþla2n; hhl: 2hþla4n; 00l: la4n; h00: ha2n; hh0 : h a 2n). The only space group that can satisfy these extinction conditions is I41/amd (No. 141). The unit-cell parameters obtained from the indexing and atomic parameters of a-ThSi2 [11] were taken as the initial model to refine the structural parameters. The Rietveld refinement of Nd2Cu0.8Ge3 was performed by using the DBWS9807a [12] program, and the DMPLOT plot view program [13] was used to illustrate the refinement results. The pseudo-Voigt function was selected as the profile fitting function. In the final refinement cycle, 24 parameters were allowed to vary, including the lattice constants, full width at half maximum intensity, preferred orientation, atomic position parameters, and thermal parameters. The observed and calculated diffraction patterns of Nd2Cu0.8Ge3, together with the difference between them, are shown in Fig. 1. The key refinement parameters obtained from the Rietveld analysis are shown in Table 1. The atomic coordinates, occupancy, and isotropic thermal displacement parameters for the compound Nd2Cu0.8Ge3 are summarized in Table 2.

P 

(P RWP ¼ P RF ¼



oi Y i ðobsÞY i ðcalcÞ  P  oi Y i ðobsÞ 2

2 )1=2

½IH ðobsÞ1=2 ½IH ðcalcÞ1=2 P ½IH ðobsÞ1=2

Table 2 Atomic coordinates, occupancies and isotropic thermal displacement parameters (Beq) of Nd2Cu0.8Ge3 compound. Atom

Site

x

y

z

Occupancy

Beq (nm2)

Nd Cu Ge

4a 8e 8e

0 0 0

0.75 0.25 0.25

0.125 0.2929(7) 0.2929(7)

1 0.2 0.75

0.0421(8) 0.1205(1) 0.0876(3)

The bond lengths and the number of the nearest neighbors of each atom in the tetragonal structure of Nd2Cu0.8Ge3 are listed in Table 3. The values of the interatomic distances agree well with the sums of the atomic radii of the respective components (rNd ¼0.182 nm, rCu ¼0.128 nm, and rGe ¼0.139 nm [14]). The structure shows the shortest M–M distance of 0.2359(4) nm, which corresponds to  92% of the sum of the atomic radii. The Nd–M separations are 0.3181(3) nm and 0.3191(4) nm, and they are close to the sum of the metallic single-bond radii. The Nd–Nd interatomic distance is 0.4155(6) nm, which is slightly longer than the sum of the metallic single-bond radii (0.364 nm).

X. Lu et al. / Journal of Physics and Chemistry of Solids 73 (2012) 1191–1195

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Table 3 Interatomic distances (d) and coordination numbers (CN) of atoms in the Nd2Cu0.8Ge3 structure. Atoms

Neighbor atoms

d (nm)

CN

Nd

4  Nd 8M

0.4155(6) 0.3181(3)

12

M

1M 2M 6  Nd

0.2425(8) 0.2359(4) 0.3191(4)

9

M¼ Cu or Ge.

Fig. 3. Temperature dependency of the lattice parameters (a and c) and unit cell volume (V) of Nd2Cu0.8Ge3.

Fig. 2. HTXRD patterns of Nd2Cu0.8Ge3 collected at different temperatures.

3.2. Lattice thermal expansion A comparison of the HTXRD patterns of Nd2Cu0.8Ge3 obtained at temperatures ranging from 298 K to 648 K indicates that no phase transformation had occurred in the tested temperature range except with the effect of lattice expansion (Fig. 2). The temperature-dependent lattice parameters, i.e. a, c and volume (V), of Nd2Cu0.8Ge3 sample are plotted in Fig. 3. At relatively lower temperatures (298–498 K), the obtained lattice parameters (a, c and volume V) increase nearly linearly with the increase of temperature. However, the variation of a, c and V over the entire temperature range (298–648 K) is better fitted by a non-linear function of temperature. Therefore, the data in Fig. 3 were fitted by the method of least squares giving third degree polynomial functions: aðnmÞ ¼ 0:41202 þ 3:37264  105 T27:55084 108 T 2 þ 6:94545  1011 T 3

ð1Þ

cðnmÞ ¼ 1:39291þ 1:50015  104 T21:30223 107 T 2 þ 3:21212  1011 T 3 :

ð2Þ

Vðnm3 Þ ¼ 0:23628 þ6:63953  105 T21:13329 107 T 2 þ8:9445  1011 T 3 :

ð3Þ

where T is the temperature, which ranges from 298 K to 648 K. The lattice parameters a and c increase non-linearly in the temperature range of 298–648 K, implying the anharmonic nature of Nd2Cu0.8Ge3 crystal field and the temperature-dependence of its vibrational frequency. Once the lattice parameter a is expressed as a function of temperature, its instantaneous thermal expansion coefficients ðaia Þ and the percentage of the mean linear thermal expansion can be estimated as follows:

aia ¼ ð1=aT Þ  ðdaT =dTÞ:

ð5Þ

MLTE ¼ 100  ððaT a298 Þ=a298 Þ:

ð6Þ

In the above expressions, aT represents the lattice parameter at temperature T, and a298 refers to the value of lattice parameter taken at 298 K. Similarly, aic and aiV can also be defined according to Eq. (5) and the percentage linear thermal expansion of Nd2Cu0.8Ge3 were calculated using Eq. (6), as reported in Table 4. These results have collectively led to a conclusion that the unit cell volume of this compound increases progressively as a function of the absolute temperature. The average thermal expansion coefficients were found to be 2.78  10  5 K  1 and 3.46  10–5 K  1 for aia and aic , respectively, and the average relative bulk thermal expansion coefficient ðaiV Þ was 9.01  10  5 K  1. These results revealed the anisotropic thermal expansion characteristic of the Nd2Cu0.8Ge3 compound. The different thermal expansion behavior along the a- and c-axes can be realized due to the crystallographic anisotropy of Nd2Cu0.8Ge3. Fig. 4 shows the crystal structure of Nd2Cu0.8Ge3

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Table 4 Temperature dependency of the lattice parameters (both measured and fitted a, c and V), instantaneous thermal expansion coefficients (aia ,aic ,aiV ), and mean linear thermal expansions (MLTE) of the Nd2Cu0.8Ge3 compound. T (K)

a (nm)

a (nm) (fitted)

aia 105 ðK 1 Þ MLTE (%) c (nm)

c (nm) (fitted)

3 aic 105 ðK 1 Þ MLTE (%) V (nm )

V (nm3) (fitted)

aiV 105 ðK 1 Þ MLTE (%)

298 348 398 448 498 548 598 648

0.41724 0.41747 0.41780 0.41830 0.41875 0.41922 0.41995 0.42112

0.41720 0.41754 0.41786 0.41822 0.41867 0.41926 0.42004 0.42107

1.73 1.53 1.59 1.89 2.43 3.23 4.27 5.55

1.42690 1.43070 1.43401 1.43687 1.43929 1.44130 1.44292 1.44418

5.67 4.97 4.30 3.67 3.07 2.51 1.99 1.50

0.24837 0.24943 0.25039 0.25132 0.25229 0.25335 0.25459 0.25605

9.13 8.03 7.47 7.44 7.95 8.99 10.54 12.57

– 0.05 0.13 0.25 0.35 0.47 0.64 0.92

1.42696 1.43050 1.43423 1.43682 1.43923 1.44135 1.44289 1.44419

– 0.25 0.51 0.69 0.86 1.01 1.12 1.21

0.24842 0.24931 0.25035 0.25141 0.25237 0.25331 0.25447 0.25612

– 0.34 0.76 1.19 1.58 1.95 2.42 3.08

Fig. 5. The temperature dependence of the magnetic susceptibility w(T) of Nd2Cu0.8Ge3 compound. The inset shows the reciprocal magnetic susceptibility w  1(T) with the solid line representing the fit to the Curie–Weiss law.

Fig. 4. Projection of Nd2Cu0.8Ge3 crystal structure along b-axis, and M represents the Cu or Ge atoms.

projected on the a–c plane. It can be observed that zigzag y M–M–My (with bond angles of 1201) andy Nd–M–Ndy (with bond angles of 1301) chains form 3D networks along the a-axis; while the M–M–M and Nd–Nd chains are along the c-axis. Since stretching force constants are in general higher than bending forces [15], elongation along the c-axis will take place under a thermal load, resulting in the bending of bonds along c-axis, which may reduce the thermal expansion along a-axis. Therefore, the overall increase of chain length along a-axis due to the increase of temperature is smaller than that of M–M?M–M and Nd–Nd chains along c-axis, and the anisotropic thermal expansion behavior of Nd2Cu0.8Ge3 can be expected. 3.3. Magnetic property The magnetic susceptibility of polycrystalline Nd2Cu0.8Ge3 was determined in the 5–300 K temperature range using a superconducting quantum interference device (SQUID) magnetometer (Quantum Design, Inc.) under an applied magnetic field of 200 Oe. Temperature dependence of the magnetic susceptibility w(T) is shown in Fig. 5. At lower temperatures, the Nd2Cu0.8Ge3 compound orders antiferromagnetically and the corresponding the Ne´el temperature TN ¼10.6 K was determined from the midpoint of the jump in dw/dT curve. The reciprocal of magnetic susceptibility versus temperature (1/w–T curve) for the Nd2Cu0.8Ge3

compound is plotted in the inset of Fig. 5. The result shows a linear increase with temperatures above 50 K and indicates the paramagnetic behavior of Nd2Cu0.8Ge3 at high temperatures. In addition, the experimental data fit well to the Curie–Weiss law with the form of w ¼C/(T  yp) [16], in which C is the Curie constant and yp is the paramagnetic Curie temperature. The Curie constant (C) can be written as C¼n NAm2eff/3kB, where n is the concentration of Nd3 þ per formula unit, NA is the Avogadro number, meff is the effective magnetic moment, and kB represents the Boltzmann constant. The magnetic susceptibility fitted by the least-squares method in the temperature ranges of 50–300 K gave a paramagnetic Curie temperature (yp) of 6.58 K and a Curie constant (C) of 0.52. This result yielded an effective paramagnetic moment of 3.53 mB, which is very close to the Russell–Saunders value calculatedffi from the 4I9/2 state of a free Nd3 þ ion pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðg JðJ þ 1Þ ¼ 3:62Þ [17]. Hence, the overall result of analyzing the magnetic property of Nd2Cu0.8Ge3 suggests that the magnetism of this compound is mainly due to its trivalent rare earth atoms.

4. Conclusions The result of Rietveld refinement on the powder XRD data supports that the Nd2Cu0.8Ge3 compound crystallizes in the tetragonal a-ThSi2-type structure with the space group I41/amd (No. 141). The lattice parameters of this compound were identified as a¼0.41783(2) nm and c¼1.43689(9) nm. Within the temperature range of 298–648 K, the lattice parameters and the unit cell volume

X. Lu et al. / Journal of Physics and Chemistry of Solids 73 (2012) 1191–1195

showed a gradual increase when temperature increases. The average thermal expansion coefficients are aia ¼ 2:78  105 K 1 , aic ¼ 3:46  105 K 1 , and aiV ¼ 9:01  105 K 1 . Furthermore, the experimentally determined effective paramagnetic moment (meff) is 3.53 mB, and this result indicates the dominant contribution of Nd3 þ ions in the magnetic property of Nd2Cu0.8Ge3 compound.

Acknowledgments This work was supported by the National Natural Science Foundation of China (nos. 50861005 and 50961002). References [1] P. Villars, Pearson’s Handbook: Crystallographic Data for Intermetallic Phases, Desk Edition, ASM International, Materials Park, OH, 1997. ¨ [2] E. Wawrzynska, M. Balanda, S. Baran, J. Leciejewicz, B. Penc, N. Stußer, A. Szytula, J. Phys. Condens. Matter 17 (2005) 1037–1047. [3] S. Tsuduki, A. Onodera, K. Ishida, Y. Kitaoka, A. Onuki, N. Ishimatsu, O. Shimomura, Solid State Commun. 134 (2005) 747–751.

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