SCIENCE CHINA Physics, Mechanics & Astronomy • Research Paper •
October 2011 Vol.54 No.10: 1791–1795 doi: 10.1007/s11433-011-4453-3
Properties of CaB6 single crystals synthesized under high pressure and temperature XIN ShengWei, LIU ShaoCun, ZHAO ZhiSheng, YANG JianQing, XU Bo, TIAN YongJun & YU DongLi* State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, China Received April 11, 2011; accepted June 15, 2011; published online August 15, 2011
Pure CaB6 single crystals are synthesized under high pressure (1 GPa) and temperature (1050°C). The temperature-dependence of electric resistivity and Hall coefficient from 2 to 300 K shows that the CaB6 single crystals are conductors with semi-metallic behavior and electron carriers. Band structure calculations indicate that the conduction and valence bands meet at the X point at the Fermi level, which is consistent with the experimentally determined conducting behavior of CaB6 single crystals. Calculations of state density suggest that the states at the Fermi level originate from the 2p orbital of the B atoms and the 3d orbital of the Ca atom. Magnetization measurements show the paramagnetic nature of the CaB6. The micro-hardness of CaB6 is 24.39 GPa, and the Raman spectra of CaB6 yield three sharp peaks at around 780.9, 1138.9, and 1282.1 cm−1 for T2g, Eg, and A1g, respectively. The specific heat of the crystal is measured and found to be well described by the Debye and Einstein combined model. The fitting results show Debye and Einstein temperatures are 1119 and 199 K, respectively. high pressure, CaB6, semi-metallic, single crystals PACS: 75.40.-s, 72.15.-v, 78.30.-j
1
Introduction
While no magnetic elements have been found in calcium hexaborides, weak ferromagnetism has been observed in Ca1xLaxB6 (x = 0.005) at remarkably high temperatures (Tc = 600 K) [1]. This peculiar magnetic property has motivated numerous investigations into the properties of CaB6 crystals. In most studies on the physical or chemical properties of CaB6 crystals, polycrystalline compounds [2−5] or single crystals were prepared by the flux-growth method [6–8], an approach that has many advantages, including simple experiment conditions and ease of obtaining larger single crystals, among others. However, this method presents the unavoidable disadvantage of the flux medium easily introducing impurities into the CaB6 crystals, such as Al in the
*Corresponding author (email:
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case of the aluminum-flux-growth method [9]. Some properties of CaB6 crystals are highly sensitive to impurities and lattice defects, including electrical conductivity [10–19] and intrinsic magnetism [20−22]. The solution here is to use high-quality single crystals for the measurement of various crystal properties. In our previous work, CaB6 single crystals with high quality were synthesized using a liquid (Ca)-solid (B) reaction under high temperature and high pressure. Compared with the flux and floating zone methods, the HP-HT method can synthesize CaB6 crystals through only the direct reaction of pure B and Ca, yielding cleaner crystals. CaB6 single crystals obtained from this method were studied in detail in terms of their crystal structure and mechanism of growth [23]. In the current study, the resistivity , Hall coefficient RH, magnetism M, hardness H, Raman scattering spectra, and specific heat C of CaB6 single crystals prepared via the HP-HT method are examined. Analysis of the conductive phys.scichina.com
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behavior of these single crystals is also accomplished using first principles calculations.
2
Samples and experimental methods
Pure CaB6 single crystals were synthesized in a large-volume cubic-anvil press under high pressure (1 GPa) and high temperature (1050°C) for 3 h. By using a Physical Property Measurement System (PPMS), , RH, and the specific heat C of CaB6 single crystals were measured from 2 to 300 K. By using a microhardness tester (FM-700, Future-Tech Corp., Tokyo, Japan), the hardness of the (100) face of the CaB6 single crystals was measured at room temperature. The hardness was determined from indentation curves measured at loads ranging from 0.098 to 2.94 N. Raman spectra were obtained by a Raman spectrometer (RENISHAW, inVia, UK). Band structure and density of states (DOS) calculations were performed using the density functional theory implemented in CASTEP code, and based on a Perdew-Berke-Ernzerhof form of the generalized gradient approximation and ultra-soft Vanderbilt potential. The plane-wave cut-off, Ecut, was 270 eV, and the k-point mesh parameters were set to 6×6×6.
3
Results and discussion
Previous studies have shown that the purity of the boron powders can affect the electrical conductivity properties of CaB6 crystals [24]. In this work, two kinds of boron powders (with purities of 99.99% and 99.9999%) were adopted to synthesize two types of CaB6 single crystals, designated as (4N)CaB6 and (6N)CaB6, respectively. (T) of the CaB6 single crystals from 2–300 K are shown in Figure 1. (T) drops monotonically with decreasing temperature, such that those of (4N)CaB6 at 2 K and room temperature are 1.35 and 2.27 m·cm, respectively, while those of (6N)CaB6 are 3.42 and 6.24 m·cm, respectively. The residual resistance ratios (RRR) are 1.71 for (4N)CaB6 and 1.82 for (6N)CaB6. Compared with metallic conductors, the RRR of CaB6 single crystals is very low, and the absolute magnitude of (T) is rather large, indicating that the two types of crystals possess semi-metallic conducting behavior. (T) of (6N)CaB6 is about three times larger than that of (4N)CaB6. In the temperature range of 2–25 K, (T) of (6N)CaB6 single crystals is relatively constant. A declining trend with decreasing temperature was observed in the (T) curve of (4N)CaB6; this obvious discrepancy may have been caused by the impurities introduced by the (4N)B powder. The results of (4N)CaB6 are similar to those of FZ CaB6 crystals reported by Terashima et al. [25], which has been discussed in [23]. To understand the metallic conductivity of the CaB6 sin-
Figure 1 Resistivity of (4N)CaB6 and (6N)CaB6 crystals as a function of temperature. Inset (a) and (b) show (4N)CaB6 and (6N)CaB6 single crystals measured by the conventional four-probe method along the length-wise direction.
gle crystals, we made first principles calculations of the band structure. The conduction and valence bands just touch each other at the X point at the Fermi level; this supports the experimentally observed conduction behavior of CaB6 single crystals (Figure 2(a)). The results thus far are consistent with those presented in a previous study [14]. The total and partial DOS are presented in Figure 2(b), which shows that the Fermi level is located in a region of low DOS. From the calculated partial DOS, the dominant contributions to the states at the Fermi level originate from the 2p orbital of B and the 3d orbital of Ca. By calculating atomic populations, the s-d orbital hybridizations of Ca atoms were analyzed. The Ca atom lost just 1.75 electrons instead of 2 electrons in the 3s orbital for B–B bonding. The s-d orbital hybridizations led to the occupation of 0.51 electrons in the hybridized 3d orbital, which came from the 3s and 4s orbitals (0.51 electrons) of the Ca atom. Figure 3 presents the relationship of RH of CaB6 single crystals with temperature. Here, measurements were accomplished using a CaB6 single crystal measuring 0.24 mm along one axis (the inset of Figure 3). From 2 to 300 K, RH dropped monotonically with increasing temperature. The negative RH measured reveals that the majority of the conducting carriers are electrons that mainly come from the 2p orbital of the B atoms and the 3d orbital of the Ca atom. The density n of the conducting electrons in CaB6 single crystals can be estimated using the relation RH = 1/n·e, which is 6.32×1018 electron cm3 at room temperature. Room-temperature magnetization measurements indicate the paramagnetic nature of the CaB6 crystals. The susceptibility is 5.45×109 cm3·g1. This paramagnetic nature is much different from the investigation carried out by Meegoda et al. [26]. Their results show that the CaB6 crystals grown by the aluminum flux method possess ferromagnetism at 300 K. They considered the ferromagnetism was
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Figure 2 (a) Band structure and (b) DOS of CaB6.
Figure 3 Hall coefficient of a CaB6 single crystal. The inset shows the sample used in the experiment. Figure 4 Hardness of CaB6 crystals versus load. The inset shows the indentation on the (100) plane of CaB6.
attributed to the iron element in the surface of the CaB6 crystals, which may be deposited into the CaB6 surface during flux removal. The results in the current work confirmed that the pure CaB6 is paramagnetic. The hardness of the basic (100) face of a CaB6 crystal versus loading is shown in Figure 4; the inset shows the image of the indention (200 g). The exponential decay curve was fitted from six independent measurements. The hardness of the CaB6 single crystal is 24.39 GPa, indicating that CaB6 is a hard material. This value is very close to a Knoop hardness of 2600 kg/mm2 [27]. With its simple CsCl structure, CaB6 exhibits three Raman-active modes: A1g, Eg, and T2g. Because the Ca atom is located on an inversion center, the vibrations obtained can only be due to B octahedra. The assignment of observed active modes is given by the following polarization dependence: A1g+Eg modes appear in the (x; x) geometry, Eg in (x; x) and (x+y; xy), and T2g in (x; y), where x and y correspond to the directions of incident light polarization and scattered light polarization, respectively. Figure 5 displays the Raman spectra of a CaB6 single crystal. The geometry of the presented spectra is (x+y; xy), where all Raman-active phonons in the cubic symmetry
Figure 5 Raman spectra of a CaB6 single crystal. The inset shows the sample used in the experiment.
appear. The Raman spectra of CaB6 show sharp peaks at around 780.9, 1138.9, and 1282.1 cm−1 for T2g, Eg, and A1g, respectively. These are very close to the results reported by Norio et al. [4]. The line shapes of the T2g and A1g peaks are
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symmetric, but the Eg peak shows a doublet. Such a trend confirms the existence of anisotropic charge distributions on B octahedra without lattice distortions. Previous studies on the specific heat of CaB6 were restricted to low temperatures (below 20 K) [7,28,29]. In the current work, the specific capacity of CaB6 from 2 K to room temperature was measured. The specific heat of CaB6 increased as the temperature increased, as shown in Figure 6. The specific heat from 2 K to 20 K (black square in the inset (a)) are very close to those (grey dot) of CaB6 prepared by the Al flux method [29]. From their measurement results, the specific capacity increases firstly and decreases afterwards with increasing temperature in the range of 0.08–1 K, and reaches the maximum at 0.3 K. They considered that this phenomenon is associated with the low-lying magnetic excitations. The inset (b) of Figure 6 shows the relation of Cp/T 3 versus T. A peak at around 36 K can be found, which is similar to an abnormal phenomenon observed in glasses [30,31]. These compounds possess similarities in structure: relatively free atoms or ions located within a rigid cage. In a CaB6 crystal, the Ca atom is surrounded by the B octahedron. Hence, this metallic compound can be divided into two components: the B octahedron, which can be described by the Debye model, and the Ca ion, which can be described by the Einstein model. The specific capacity of metallic compounds is comparable with their electronic specific capacity when the temperature is very low. Thus, we adopt the Debye and Einstein combined model to describe the CaB6 specific heat as follows: C T nD CD nE CE ,
(1)
where T is the electronic specific heat, CD is the Debye model:
Figure 6 Heat capacity of CaB6 crystals versus temperature. The inset shows the curve of Cp/T 3 versus temperature.
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T CD 9nN A k TD
3
x4e x
TD T
e
0
x
1
2
dx,
(2)
CE is the Einstein model: 2
eTE T T , CE 3nN A k E 2 T eTE T 1
(3)
n is the magnitude of the same atom in one molecule, NA is Avogadro’s number, k is the Planck constant, and nD and nE are the coefficients of the Debye and Einstein models, respectively. Figure 7 presents the curve fitted by this model. As can be seen, good agreement is shown between the model simulation and the experimental results. The inset presents Cp/T versus T 2. The straight line was fitted by 11 experimental data points. The fitting results show the electronic specific coefficient = 0.1592 mJ·mol1·K2, and the slope of the straight line is b = 0.04818 mJ·mol1·K4. The Debye and Einstein temperatures are 1119 and 199 K, respectively, and coefficients of nD= 0.68 and nE=3.30 are obtained by fitting the experimental data. The curves fitted by the Debye and Einstein models are also shown in Figure 7. At about the liquid helium temperature, the specific heat almost only comes from the electronic specific heat, which is contributed to by the electrons near the Fermi surface, because the lattice heat capacity decreases quickly, following a T3 pattern, to approach zero at low temperature limits. The electronic specific heat is proportional to the temperature at low limits, and decreases slowly as the temperature decreases. At about 10–100 K, the vibration of Ca is dominant. At about 100–300 K, the specific heat of CaB6 is contributed to by its lattice heat capacity. According to the relationship between the Debye temperature and frequency, the vibration frequency is speculated to be about 1013–1014 s1. Such a
Figure 7 Heat capacity of CaB6 crystals fitted by the Debye and Einstein models. The inset shows the curve of Cp/T versus T2.
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high vibration frequency and Debye temperature imply that CaB6 possesses a high elastic modulus and low density.
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Conclusions
CaB6 single crystals were synthesized under high pressure (1 GPa) and temperature (1050°C). (T) and RH measurements show that the CaB6 single crystals obtained are conductive materials with semi-metallic behavior and electron carriers. The conducting electron density of CaB6 single crystals is 6.32×1018 electron cm3 at room temperature. The calculated band structure shows that the conduction valence bands just touch each other at the X point at the Fermi level, confirming the experimentally observed conducting behavior of CaB6 single crystals. The total and partial DOS also indicates that the dominant contributions to the states at the Fermi level originate from 2p orbital of B and 3d orbital of Ca. Magnetization measurements show that CaB6 is paramagnetic with a susceptibility of 5.45×109 cm3·g1, and microhardness measurements show that it is a hard material (24.39 GPa). The Raman spectra of CaB6 displayed sharp peaks at around 780.9, 1138.9, and 1282.1 cm−1 for T2g, Eg, and A1g, respectively. The specific heat of CaB6 was measured and may be well described by the Debye and Einstein combined model. This study was supported by the National Natural Science Foundation of China (Grant Nos. 51072174, 50772094 and 50821001) and the NBRPC (Grant No. 2011CB808205).
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