Antonio C S Sabioni

Anne-Marie M Huntz
email: am.huntz@lemhe.u-psud.fr

A M J M ; Daniel

W A A Macedo

Measurement of Iron Self-Diffusion in Hematite Single Crystals by SIMS and Comparison of Cation Self-Diffusion in Corundum-Structure Oxides

Keywords: diffusion, anisotropy, SIMS, oxides user supplied): hematite, corundum structure, self-diffusion Fe 2 O 3, Hematite, Self-Diffusion, Anisotropy, Single Crystals, SIMS, Al 2 O 3, Cr 2 O 3

published or not. The documents may come

Measurement of iron self-diffusion in hematite single crystal by SIMS and comparison of cation self-diffusion

in corundum-structure oxides

Introduction

Alumina (Al 2 O 3 ), chromia (Cr 2 O 3 ) and even hematite (Fe 2 O 3 ) films are of great importance as the protection ensured by such films against oxidizing and aggressive atmospheres is efficient for long times at high temperatures. Moreover, these oxides have the same crystal structure of corundum and it is interesting to know how bulk cation self-diffusion differ in them and to try to understand the role of these diffusivities on their respective growth by oxidation of metallic alloys. Previous studies allowed to determine the cation bulk self-diffusion coefficients in these oxides either using a radioactive solution [1][2][3][4][5][6] or by SIMS [7] and it is important to compare results obtained by different methods. Indeed, two of the most accurate techniques to measure diffusion coefficients in solids are the radioactive techniques, using a radioactive isotope as tracer with depth profiling by sectioning and counting, and the secondary ion mass spectrometry (SIMS) used for depth profiling of stable tracers.

When adequately employed, both techniques should present the same performance, in spite of, due to its specificity, the radioactive techniques to be less susceptible to interpretation errors. On the other hand, SIMS is very attractive because there is not necessity to manipulate radioactive materials. It also offers the possibility of measuring very short depth profiles (from a few nanometers) and thus, it allows to use short annealing times and/or low temperatures, on very small samples, when compared to those used by radioactive techniques. Moreover, it may be applied to the depth profiling of all isotopes of the natural elements.

In fact, SIMS has shown to be a powerful technique to study diffusion in solids and has been extensively applied by a few authors of this work to determine self-diffusion and impurity diffusion coefficients in a wide variety of oxides used in different technological fields, such as UO 2 (nuclear fuel) [8,9], ZnO (electroceramic) [10], (Gd 0.9964 Ca 0.0036 )Sn 2 O 7 (solid electrolyte) [11], 2MgO.2Al 2 O 3 .5SiO 2 (glass) [12], Cr 2 O 3 (used to simulate oxide layer grown on Cr-alloys) [7,[13][14][15].

In order to make comparison between the performance of radioactive techniques and SIMS to measure diffusion coefficients in ceramic oxides, measurements of iron self-diffusion in hematite present a great interest as earlier works [1][2][3][4][5] determined self-diffusion coefficients by means of radioactive techniques and, though performed on samples from different sources, they show reasonable agreement above 900 o C.

In this study, iron self-diffusion in hematite single crystals has been determined for the first time by SIMS, using the 57 Fe stable isotope as iron tracer. To check the results obtained by SIMS, only the data previously determined by Atkinson and Taylor [5], and by Hoshino and Peterson [6] will be taken into account, because they are the most recent and show excellent agreement.

Afterwards, a comparison of the present results for iron self-diffusion in Fe 2 O 3 with the more recent data of cation bulk self-diffusion in Cr 2 O 3 [7] and in Al 2 O 3 [1] will be presented.

Experimental

Materials and Sample Preparation

The Fe 2 O 3 natural single crystals were supplied by the Department of Geology of the Federal University of Ouro Preto, Brazil. Mössbauer spectroscopy and X-ray diffraction analyses showed hematite to be the only phase in these crystals. A JXA-8900RL Jeol microprobe analyzer with EDS and WDS (PET, LiF, TAP and LDE crystals) detectors was employed in order to detect the presence of minor elements in the Fe 2 O 3 crystal. The detection limit of such a technique for the most common elements in iron oxide is about 100 ppm (~ 0.01 at %). In the present case, the photon detection statistics was improved by counting for 10 minutes on the peak positions and background positions. In these conditions, only Al was detected with a content of Al 2 O 3 equal to 0.16 ± 0.02 wt%.

The isotope 57 Fe was used as iron tracer. The natural iron has the following isotopic composition (atomic %): 54 Fe (5.8), 56 Fe (91.72), 57 Fe (2.2) and 58 Fe (0.28). The source of tracer used in this work was iron powder, which was enriched (95.8%) with the isotope 57 Fe. This iron was supplied by Chemotrade GmbH (Germany). The impurities in this iron were: C (<0.044%), and less than 0.01% for each of the following elements Mg, Al, Si, Cr, Ni, Cu and Zn.

The diffusion specimens have been used with the dimensions 4mm x 4mm x 1mm. These samples were polished with diamond suspensions of 9, 6, 3, 1 and 0.25µm using an automatic polisher Phoenix of Buhler. The polished surface was parallel or perpendicular to the basal plane of the crystal. After the polishing, the samples were cleaned in acetone under ultrasound, and then submitted to a pre-annealing to equilibrate them with the temperature and oxygen pressure to be used in the diffusion annealings.

After the pre-annealings, a 57 Fe film was deposited on the polished surface of the samples. The deposition of the 57 Fe film on Fe 2 O 3 was performed by molecular beam epitaxy, under a vacuum of 2x10 -9 mbar, with a deposition rate of 0.11 nm/min. The thickness of the film was about 10 nm as shown by figures 1 a and b.

Diffusion Experiments and Depth Profiling

The samples with the 57 Fe film were submitted to the diffusion annealings at 951 o , 1000 o , 1052 o , and 1100 o C for diffusion perpendicular to c-axis, and at 900 o , 1000 o , and 1100 o C for diffusion parallel to c-axis. A dynamic oxygen atmosphere of 10 5 Pa was used. These annealings were performed in a tubular furnace, with the samples in a Pt crucible placed inside a silica tube. At 1000 o and 1100 o C, a couple of samples were placed in the crucible, for simultaneous diffusion along and perpendicular to c-axis, exactly in the same experimental conditions. The 57 Fe depth profiles were established by secondary ion mass spectrometry (SIMS). These SIMS analyses were performed using a 4F-CAMECA apparatus at Laboratoire de Physiques des Solides et Cristallogenèse -CNRS/Meudon-Bellevue, France. The 57 Fe depth profiles were established by using a 10 keV Cs + primary beam. The analysis were performed at an area of 150µm x 150µm, and the signals of the ions 54 Fe -, 56 Fe -, 57 Fe -and 58 Fe -were taken from a central zone of 33µm in diameter. The 57 Fe concentration, [ 57 Fe], as function of the sputtering time, was determined from (1)

The penetration depths were obtained assuming a constant sputtering rate and measuring the depth of the crater by means of a Talystep profilometer. The diffusion profiles were determined parallel or perpendicular to the c-axis direction in Fe 2 O 3 crystal.

Results

Figure 2 shows a typical SIMS spectra of the iron isotopes in hematite after a diffusion annealing at 1000 o C. The 57 Fe depth concentrations profiles were deduced from the SIMS spectra using the methodology previously described.

Figures 3 shows the 57 Fe diffusion profile measured along c-axis at 900 and 1100°C (Fig. 3a andb, respectively), and perpendicular to c-axis after diffusion annealing at 1100 o C (Fig. 3c), under oxygen atmosphere, in hematite crystal.

For the conditions used in the diffusion experiments, i.e., diffusion from a thin film in a semiinfinite medium, the tracer concentration, C(x), as a function of the depth (x) is given by a Fick's second law solution as follows [START_REF] Philibert | Atom Movements, Diffusion, and Mass Transport in Solids[END_REF]:

C = [Q/(πDt) 1/2 ] exp(-x 2 /4Dt), (2)
where Q is the amount of tracer deposited on the surface per unit area, D is the diffusion coefficient, Fe 2 O 3 has the corundum structure, and is oxygen deficient, with a small non stoichiometry [START_REF] Kofstad | High Temperature Corrosion[END_REF]. The most important atomic point defect in Fe 2 O 3 should be oxygen vacancies and iron interstitial irons.

The formation of interstitial iron ion and of oxygen vacancies can be described by the following reactions:

) g ( O 4 3 ' e Fe Fe O 2 3 2 i x Fe x O + α + → + αo , and ' e ) g ( O 2 1 V O 2 O x O γ + + = γo , where x O
O and

x Fe Fe are oxygen ion and iron ion in their regular sites, respectively,

o α i Fe ( ) Fe or Fe , Fe , Fe i i i x i o o o o o o
is an interstitial iron, and

) V or V , V ( V O O x O O o o o o γ
is an oxygen vacancy. Therefore, there are four possible charge states (α = 4) for interstitial iron and three possible charge states (γ = 3) for oxygen vacancy.

In the literature, it is assumed that the iron self-diffusion mechanism in hematite takes place by means of iron interstitial [4][5][6], but the charge state of this defect is not clear yet.

Himmel et al. [3] have determined iron diffusion coefficients in natural hematite crystals. The impurity content was not informed. The radioactive isotope 55 Fe was used as iron tracer. The diffusion experiments were performed at two different temperatures: 1000 o and 1217 o C, in pure oxygen at 1 atm pressure, parallel and perpendicular to c-axis of the crystal. The iron diffusion coefficient was determined by means of the Decrease of Surface Activity Method [START_REF] Philibert | Atom Movements, Diffusion, and Mass Transport in Solids[END_REF]. This is an indirect method without depth profiling. In these experimental conditions, they found an activation energy of 381 kJ/mol, and the iron diffusion was independent of the crystallographic direction.

Chang and Wagner [4] have determined iron diffusion coefficients, along c-axis, in Fe 2 O 3 neutral single crystals as a function of oxygen partial pressure at 1200 o and 1300 o C. Chemical analysis of the crystals revealed at least 200 ppm (by wt) of impurities, being the most abundant the Ti (68), V(47), Mn (22), Mg [START_REF] Catlow | [END_REF], and Si (12). The radioactive isotope 55 Fe was used as iron tracer, and the diffusion coefficient was determined by the Gruzin'method [START_REF] Philibert | Atom Movements, Diffusion, and Mass Transport in Solids[END_REF], but apparently without depth profiling. The oxygen pressure dependence of the iron diffusion coefficient indicated that iron migrates interstitially in hematite crystals as triply-charged interstitial (

o o o i
Fe ), and the activation energy determined from the two temperatures, in 1 atm oxygen atmosphere, was 360 kJ/mol.

Atkinson & Taylor [5] have measured iron diffusion in synthetic crystals of hematite along c-axis direction. Chemical analysis of the crystals revealed 3% Pb and a total of 500 ppm for the transition metals Cr, Mn and Ni combined. The diffusion experiments were performed between 708 and 1303 o C using the radioactive isotope 59 Fe as iron tracer. The diffusion profiles were established by Figure 6 shows a comparison of our results with those of the literature [3][4][5][6], only taking into account data about iron diffusion along c-axis of the Fe 2 O 3 crystals, and above 900 o C. In general, in spite of the differences among the impurity contents of the samples, of the different techniques, and of the different temperature ranges used, the data about iron self-diffusion in hematite show reasonable agreement. In particular, the more reliable diffusion coefficients, obtained by using depth profiling, of Hoshino and Peterson [6], and Atkinson and Taylor [5], show very good agreement with our results, obtained by SIMS, which indicates that the iron self-diffusion coefficient is a well-defined property for hematite, along c-axis direction, above 900 o C, under oxygen atmosphere.]

Iron diffusion anisotropy

It was shown above that the iron diffusion along c-axis is greater than that perpendicular to c-axis and the diffusion coefficients are plotted in figure 7 as an Arrhenius graph. These results showing iron diffusion anisotropy are unequivocal due to the fact that the diffusion experiments for the two directions were performed exactly in the same experimental conditions. It is the first time that iron diffusion anisotropy in hematite is reported.

One way to understand the iron diffusion anisotropy, is to take into account the general expression for solid-state diffusion coefficients: D = γλ 2 Γ, where γ is a geometric factor, λ is the jump distance, and Γ is the jump frequency [START_REF] Philibert | Atom Movements, Diffusion, and Mass Transport in Solids[END_REF]. Usually, the geometric factor is given by γ = 1/N, where N is the number of neighbouring sites into which the ion can jump, while λ is the jump distance between these sites. In our experimental conditions (fig. 7), the ratio D //c / D ⊥c is greater than 20, at 1000 o C,

Cation self-diffusion in hematite, chromia and alumina

The results concerning cation bulk self-diffusion in Al 2 O 3 , Cr 2 O 3 and Fe 2 O 3 are gathered in figure 8a. Concerning alumina, the more recent results [1] were taken and they correspond to selfdiffusion along c-axis in alumina single crystals under air. Concerning chromia, it also concerns single crystals, but the surface plane was not a 0001 plane, but a 01 -1 2 plane (i.e. at 57.7° from 0001 plane). The diffusion treatment was performed in 10 -5 atm oxygen, but Sabioni et al. found that diffusion in chromia did not depend on the oxygen pressure [7,[13][14]. According to figure 8a, it looks like diffusion is much faster in hematite than in chromia and alumina. This could be due, at least for a part, to the differences in non-stoichiometry for the three oxides, but it is necessary also to consider that these oxides have different melting temperature and the representation of Fig. 8a is not satisfying. The comparison of self-diffusion in oxides having the same crystal structure and different melting temperature is more adequate in a normalized Arrhenius diagram (log D versus T m /T, where T m = melting temperature in Kelvin) [8]. This was done in figure 8b and, then, it appears that the differences between the three oxides are not so marked: alumina, which is the most stoichiometric of the three oxides, is characterised by smaller self-diffusion coefficients, while chromia and hematite are very close each other. Such results agree also with oxidation rates of materials developing one of these oxides as a protective film. The oxidation rate of alumina former alloys is smaller than the oxidation rate of chromia former alloys, while the growth rate of hematite is not far from that of chromia [START_REF] Kofstad | High Temperature Corrosion[END_REF]. It is just important to note that such bulk diffusion rates given in figures 8 cannot justify the oxidation rates of materials forming one of these three oxides as a protective film. Indeed, it indicates that the oxide growth is controlled by grain boundary diffusion [20][21].The differences between the various activation energies found for diffusion in these oxides will not be discussed for several reasons. First there is a great uncertainty in the determination of such activation energies especially when the number of experimental points is limited, and it is the case for most of the works mentioned here due to the difficulties encountered in these studies.

Moreover, amongst the various results in the literature, it can be remarked that the temperature range and the oxygen pressure are often varying from one study to another. So, the comparison of the activation energies does not seem satisfying.

Conclusions

For the first time iron diffusion has been simultaneously measured along and perpendicular to c-axis in hematite crystals. The measurements were performed using an original methodology based on the utilization of 57 Fe stable isotope as iron tracer, and depth profiling by secondary ion mass spectrometry (SIMS). The results obtained for the diffusion along c-axis show very good agreement with the more reliable diffusion coefficients previously determined by using radioactive techniques.

In the experimental conditions used in the present study, there is iron diffusion anisotropy in hematite crystals, the diffusion along c-axis being greater than that perpendicular to c: along c-axis, self-diffusion can be described by D //c (cm 2 /s)= 5.2x10 6

1. Iron profile as a function of the depth after an heat-treatment at 800°C, a) 57 Fe counts and b) 57 Fe concentration, showing that the thickness of the deposit was 10 nm maximum.

2. Evolution of the intensity of iron isotopes as a function of the sputtering time after a diffusion annealing at 1000°C.

  intensities (I) of the signals of the secondary negative ions 54 Fe -, 56 Fe, 57 Fe -and 58 Fe -by means of the following relationship:[ 57 Fe] = [I( 57 Fe -)/( I( 54 Fe -) + I( 56 Fe -)+ I( 57 Fe -)+ I( 58 Fe -)]

Discussion

  Figures 5a-b compares iron diffusion profiles determined parallel and perpendicular to caxis, at 1000 o C and 1100 o C, in the same experimental conditions. The diffusion along c-axis is greater than that perpendicular to c-axis, which shows that there is iron diffusion anisotropy in hematite.

  sectioning, above 900 o C, or argon ion sputtering at lower temperatures. Above 900 o C, Atkinson and Taylor obtained the following Arrhenius equation: D(cm 2 /s) = 1.6x10 9 exp [-577 (kJ/mol)/RT], while below 900 o C, they obtained the expression: D (cm 2 /s)= 2.8x10 -9 exp [-173(kJ/mol)/RT]. These authors proposed that in high-temperature region (above 900 o C), the iron diffusion behaviour is characteristic of pure Fe 2 O 3 , while at temperatures below 900 o C, the behaviour may have been influenced by impurities. Atkinson and Taylor [5] have reviewed and discussed the iron diffusion atomic mechanisms in hematite, without a conclusion about the charge state of the interstitial iron. Hoshino & Peterson [6] measured the iron diffusion in natural hematite single crystals along c-axis, with Ti, V, Mn and Ni being the major impurities, each about 30ppm by weight, Cl (10 ppm), As (7 ppm), Cr (3 ppm), Na (2 ppm) and Mg (2 ppm). The experiments were performed using the isotope 59 Fe as iron tracer and depth profiling by mechanical sectioning and counting. Between 1100 o C and 1300 o C, in an oxygen pressure of 10 5 Pa, they proposed the following Arrhenius equation for the iron volume diffusion in hematite: D(cm 2 /s) = 8.7x10 7 exp [-539 (kJ/mol)/RT], and suggested that interstitial iron ions diffuse in Fe 2 O 3 as doubly-charged interstitial ( o o i Fe ).

8 .

 8 50 at 1100 o C. As iron only occupies octahedral sites in corundum structure, the γ value is the same for diffusion in both directions considered in this work. On the other hand, there is no conclusive model describing the migration pathways for interstitial iron in hematite, which could give the λ values. Atomistic simulation of iron transport in hematite by means of interstitial migration was performed by Catlow et al[START_REF] Catlow | [END_REF]. They have investigated direct interstitial migration in which the interstitial iron ( through an anion triangle between nearest-neighbour interstitial sites. They found a unusual very high activation energy of more than 970 kJ/mol. They have also discussed several possible indirect interstitial pathways, i.e., interstitially mechanisms for iron diffusion in hematite, and have found activation energies ranging from 193 kJ/mol to 1024 kJ/mol. Each calculated activation energy was found to be different of the experimental values given above. The calculated activation energy nearest the experimental data shown above is 657 kJ/mol corresponding to a mechanism in which the interstitial iron moves in the ab plane to displace a lattice cation to the nearest interstitial site within that plane. No calculation was made for the migration of doubly-charged interstitial iron ( o o i Fe ). Whatever the mechanism investigated by Catlow et al., the difference between the λ values both along and perpendicular to c-axis is not enough to justify the ratio D //c / D ⊥c observed in this work. Therefore, values of γ or λ cannot explain the difference between the iron diffusion coefficients measured parallel or perpendicular to c-axis in Fe 2 O 3 crystals, and the interstitial iron diffusion anisotropy should be principally related to different jump frequencies (Γ) for the two different crystallographic directions used in this work, which is not surprising for an hexagonal structure like the corundum structure of hematite. It is worth noting that, the ratio D ⊥c / D //c , in the hexagonal structure, is found, experimentally, to be less than 1 as the ratio c/a is greater than 3 / 8 [16]. It is in good agreement with our results for which D ⊥c / D //c < 1, and c/a ≈ 2.7 > 3 / Other two important technological oxides, α-Al 2 O 3 and Cr 2 O 3 , have the same structure as Fe 2 O 3 . Diffusion anisotropy for the chromium self-diffusion in Cr 2 O 3 crystals was observed by Hoshino and Peterson [19] between 1490 o and 1570 o C, in different partial oxygen pressures. According to these authors, the value of the ratio D //c / D ⊥c for chromium self-diffusion in Cr 2 O 3 is ca. 1.7. They suggested that the chromium diffusion both parallel to and perpendicular to the c-axis takes place by means of triply-charged vacancies ( ' ' ' Cr V ), with different jump frequencies of chromium ions for the two directions. Thus, the difference between D //c and D ⊥c is small for chromium diffusion in Cr 2 O 3 crystals.As far as we know, there are no data available in the literature about aluminium diffusion anisotropy in Al 2 O 3 crystals.

  exp [-510 (kJ/mol)/RT], and, perpendicularly to c-axis, D ⊥c (cm 2 /s)= 83 exp [-430 (kJ/mol)/RT]. Comparison of self-diffusion in Al 2 O 3 , Cr 2 O 3 and Fe 2 O 3 , in a normalized Arrhenius diagram, showsthat cation self-diffusion in alumina, which is the most stoichiometric of these oxides, is smaller than in chromia and hematite.

3 . 4 . 7 . 8 .

 3478 Iron concentration profile versus penetration depth in Fe 2 O 3 single crystals, a) and b) along c-axis after diffusion at 900 and 1100°C respectively, c) perpendicular to c-axis after diffusion at 1100°C. Evolution of the logarithm of the iron concentration as a function of x 2 obtained from figure 3, a) and b) along c-axis after diffusion at 900 and 1100°C respectively, c) perpendicular to c-axis after diffusion at 1100°C. 5. Comparison of iron concentration profile versus penetration for diffusion along to and perpendicular to c-axis at a) 1000°C, b) 1100°C. The smaller the slope, the greater the diffusion coefficient. 6. Arrhenius plot of the diffusion coefficients obtained for iron diffusion along c-axis of hematite single crystals. Comparison with Atkinson et al. [5], Hoshino et al. [6], Himmel et al. [3] and Chang et al. [4] works. Arrhenius plot of the diffusion coefficients obtained for iron diffusion in hematite single crystals along to and perpendicular to c-axis. Comparison of cation self-diffusion in Fe 2 O 3 , Cr 2 O 3 and Al 2 O 3 single crystals, a) Arrhenius plot, b) plot of the diffusion coefficients versus Tm/T, T being the melting point of the oxide. ________________________________________________________________________________

  Fig.1a

  Fig.2

  Fig.3a

  Fig.3b

  Fig.4a

  Fig.4c

  Fig.5a

  Fig.6

  Fig.7

  Fig.8a

  Fig.8b

  Fig.1a

  Fig.2

  Fig.3b

  Fig.4a

  Fig.4b

  Fig.4c

  Fig.6

  Fig.7

  Fig.8a

  Fig.8b

Table I :

 I Iron self-diffusion coefficients measured in hematite single crystals

	F o
	r
	P
	e e r
	R e v i e w
	O n
	l y

Table 1 -

 1 Bulk diffusion coefficients of iron in Fe 2 O 3 single crystals

	Temperature ( o C) Time (s)	D ┴ (cm 2 /s)	D // (cm 2 /s)	D // / D ┴
	900	1.677x10 5		1.1x10 -16
	900	1.677x10 5		1.1x10 -16
	951	6.090x10 4	6.1x10 -17
	951	6.090x10 4	2.6x10 -17
	1000	1,800x10 4	1.8x10 -16	4.6x10 -15	25.6
	1000	1.800x10 4	2.2x10 -16	4.6x10 -15	20.9
	1052	5.640x10 3	7.9x10 -16
	1052	5.640x10 3	8.1x10 -16
	1100	1.020x10 4	4.1x10 -15	2.4x10 -13	58.5
	1100	1.020x10 4	4.1x10 -15	2.2x10 -13	53.4

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Acknowledgements

The authors are grateful to FAPEMIG & CNPq (Brazil) and CNRS (France) for financial support, and to F. Jomard for the SIMS analyses.


Ryszard Wawryk

Magnetic and transport properties of UBi 2 and USb 2 single crystals

Keywords: thermoelectric power, anisotropy, electronic transport, magnetic properties, resistivity Uranium dipnictides, Magnetic susceptibility, Resistivity, Thermoelectric power Uranium dipnictides, Magnetic susceptibility, Resistivity, Thermoelectric power

Magnetic and transport properties of UBi2 and USb2

single crystals

The UBi 2 and USb 2 compounds belong to group of the uranium dipnictides UX 2 (X=P, As, Sb, Bi) -they were, and are still intensively investigated due to their unusual transport properties. The magnetic properties of UBi 2 and USb 2 are described in Refs. [1] - [5], whereas the limited transport properties are presented in Refs. [START_REF] Henkie | Proc. Intern. Conf. on Solid Comp. of Transition Elements[END_REF][START_REF] Henkie | [END_REF]8]. The crystal structure and the Fermi surface [9] of both compounds are well defined. Therefore the aim of this work is to show how their features are reflected in the electrical transport coefficients.

UBi 2 and USb 2 crystallise in a tetragonal structure belonging to the anti-Cu 2 Sb-type with either P4/nmm or 7 4h D space group. The unit cell contains two formula units and the ratio of unit cell parameters c/a equals to 2.004 and 2.044 for UBi 2 and USb 2 , respectively. The neutron-diffraction study [3] showed that below the Néel temperature they order antiferromagnetically, along the c-axis, with alternating ferromagnetic sheets in the sequences (↑↓↓↑) for USb 2 and (↑↓) for UBi 2 . Such an ordering results in the magnetic unit cell of USb 2 , which is twice the chemical unit cell along the c-axis, while the magnetic and chemical unit cells of UBi 2 are of the same size. Hence the magnetic Brillouin zone for UBi 2 being fairly flat is the same as that of the chemical one. The ratio of the length k c along [001] to the length k a along [100] in the magnetic Brillouin zone of USb 2 and UBi 2 is 0.24 and 0.5, respectively. The de Haas-van Alphen and Shubnikov-de Haas experiments have allowed for constructing the Fermi surface for UBi 2 and USb 2 in the ordered state [9]. It consists of one spherical (α) and two cylindrical (β) sheets in UBi 2 and entirely cylindrical sheets in USb 2 . The magnetic Brillouin zone in USb 2 consists of one of each cylindrical sheets (α) and (δ), and two of each of cylindrical sheets (ε) and (γ). The Fermi surfaces of UBi 2 are the same in the paramagnetic and antiferromagnetic states. In the case of USb 2 the paramagnetic Fermi surfaces are related to those in UBi 2 , because the Brillouin zone in USb 2 is almost the same as that in UBi 2 and it is occupied by similar number of electrons. Thus, in the paramagnetic state 3 the spherical sheet (α) in UBi 2 corresponds to the corrugated cylindrical one in USb 2 (see figures 24c and 25a in Ref. [9]) and the cylindrical sheet (β) in UBi 2 corresponds to the long ellipsoidal Fermi surfaces in USb 2 (see figure 24d in Ref. [9]). The latter crosses over the Brillouin zone boundary, forming another corrugated cylindrical and a small-pocket ellipsoidal Fermi surfaces.

The paramagnetic to antiferromagnetic transition in USb 2 increases the number of the Fermi surface sheets and enhances their quasi-two dimensionality, as discussed in Ref. [9].

An angle-resolved photoemission study in single crystal of USb 2 at 15 K [10] showed the dispersion of extremely narrow bands situated near the Fermi level. The natural linewidth is less than 10 meV. In the normal emission spectrum there is also a dispersion observed of about 10 meV, which indicates a 3D character in electronic structure of USb 2 in contrast to the earlier evidence [9]. These resonant photoemission measurements confirm the 5f-electron hybridisation with the conduction electrons. This work presents results of measurements of the magnetic susceptibility χ(T), electrical resistivity ρ(T), and thermoelectric power S(T) down to 0.35 K, for UBi 2 and USb 2 single crystals. Their Fermi surfaces distinctly differ from each other.

We compare these data to those partially known from the literature and discuss the differences in the observed behaviours of USb 2 and UBi 2 . These observed differences are related to the variation in the Fermi surface topology of these two compounds. § 2. EXPERIMENTAL DETAILS USb 2 and UBi 2 single crystals were grown by the so called "molten metal solution" method [8].

They were grown in the form of plates with the dimensions of about 6×5×3 mm 3 along the a-, b-, and c-axes, respectively. For electrical resistivity and thermoelectric power examinations the specimens were cut out to the dimensions of about 4×0.5×0.5 mm 3 and 3×0.3×0.3 mm 3 for Deleted: ry Deleted: The investigation of hyperfine interactions at the uranium sites in the antiferromagnetic state of uranium dipnictides was done using 238 U Mössbauer spectroscopy [11]. In UBi2 the nuclear quadrupole interaction at 238 U is almost zero, whereas in USb2 the sign of these interactions is negative. This suggests that the nuclear quadrupole interactions in both compounds are correlated with their magnetic structures. carrying out the measurements along the a-and c-axes, respectively. The dc magnetic susceptibility in fields up to 5 T applied along the c-axis and in the temperature range 1.7 -400 K was measured with a superconducting quantum interference device magnetometer (Quantum Design). The electrical resistivity at temperatures of 0.35 -300 K was measured by a four point ac method. For the thermoelectric power measurements a modified set-up described in Ref. [11] has been used. § 3. RESULTS

Magnetic susceptibility

Magnetic susceptibility of a UBi 2 crystal, measured along the c-axis, shows the temperature dependence being typical for an antiferromagnet with a peak at T N = 180.8 K (figure 1, see also Ref. [START_REF] Troć | Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology[END_REF]). In the paramagnetic state the modified Curie-Weiss law is fulfilled: ( )

(
)

0 2 3 χ µ χ + Θ + = p B N T k T eff
, where N denotes the number of atoms in the unit cell, µ eff is the effective magnetic moment, k B is the Boltzmann constant, Θ p is the paramagnetic Curie temperature, and χ 0 is the temperature independent paramagnetic contribution. The parameters are as follows: µ eff = 3.36 µ B , Θ p = -17 K, and χ 0 = 2.7× 10 -3 emu/mol. Obtained from the fit of above equation to experimental data the µ eff value appears to be very close to that of 3.4 µ B , reported in Ref. [2]. The determined µ eff is however smaller from that of 3.62 µ B or 3.58 µ B expected for the free U +3 or U +4 ions, respectively.

[Insert figure 1 about here]

In the case of USb 2 , the χ(T) dependence, measured along the c-axis, displays a sharp maximum yielding the Néel temperature of 202 K (figure 1, see also Ref. [START_REF] Troć | Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology[END_REF]). In this case, the modified Curie-Weiss law is obeyed in paramagnetic region for Θ p = -59 K and µ eff = 3.32 µ B .

. Electrical resistivity

The electrical resistivity of UBi 2 single crystals were carried out, in the a and c directions, for two different samples having different purity. They were (figure 2), obtained in different syntheses. The resistivity ratio ρ 300 K / ρ 4.2 K = RR measured along the a-axis for the samples obtained in the first (1s) and second (2s) syntheses were 500 and 1110, respectively.

The room temperature resistivity, ρ 300 K , for both the (1s) and (2s) samples in the a direction was of 0.231 mΩ cm while in the c direction it was 3.88 mΩ cm. In the paramagnetic state the resistivity was found to be almost temperature independent, while that below T N decreases rapidly in both directions with decreasing temperature.

[Insert figure 2 about here] As seen in figure 2, distinct anisotropy in the temperature dependence of the resistivity is observed. Below T N , the anisotropy ratio (ρ c -ρ 0 )/(ρ a -ρ 0 ) increases with decreasing temperature down to about 27 K. It achieves a value of about 2.7 times larger than that in the paramagnetic range (figure 3), and then it decreases at lower temperatures.

The temperature dependence of the anisotropy ratio (ρ c -ρ 0 )/(ρ a -ρ 0 ) differs from the results presented in Ref. [9], where the anisotropy ratio defined as ρ c /ρ a achieves a maximum value of about 800 at the temperature of circa 80 K. In the present work the (ρ c -ρ 0 )/(ρ a -ρ 0 ) ratio reaches at 27 K a maximum value of about 50 while the ρ c /ρ a ratio is not larger than about 100 (figure 3).

[Insert figure 3 about here] This discrepancy in the anisotropy ratio probably arises from the difference in the sample purity. As mentioned above, the RR values for our samples in the a direction are 500 (1s) and 1110 (2s) compared to RR = 22 for the sample investigated by the authors of Ref. [9]. The RR values for the c direction in both cases were of the same order (i.e. 130 and 215 for our samples and 160 for the sample of Ref. [9]). Also the discrepancy in absolute values of the resistivity Deleted: In the low temperature antiferromagnetic range there is visible a shallow valley in the χ(T) dependence for UBi2 (the inset of figure 1). However, this valley is not as deep as that observed for USb2 (see also Ref. [START_REF] Wawryk | [END_REF]) or also for UNiSb2 and UPdSb2 there measured on the polycrystalline samples [15]. These minima in χ(T) curves, which occur at temperatures about 21 K and 50 K in UBi2 and USb2, respectively, may result from the crystal-field effects. In the ordered state, when the crystal field interaction is comparable with the exchange field interaction, anomalies in the χ(T) dependencies can occur. A crystal-field splitting (ground state is a doublet) of the order of the exchange interaction yields an anomalous temperature variation of the magnetic susceptibility as it was shown for CeSb and CeBi [16]. ¶ Deleted: the appears; for example, the room temperature resistivity of our samples along the a-and c-axes are of 0.23 mΩ cm and 3.9 mΩ cm, while that for the samples from Ref. [9] these values are considerably different and amount to 60 mΩ cm and 3.4 × 10 4 mΩ cm, respectively. The samples differ mainly in the magnitudes of the residual resistivity, ρ 0 .

According to the Matthiessen's rule the temperature dependence of the resistivity for an antiferromagnet can be written as follows:

m ph n n d ρ ρ ρ ρ ρ + + =       ∆ - ∆ + + - - Θ + = ∫ Θ - 0 / 0 0 exp ) / 2 1 ( ) 1 )( 1 ( ) / ( ) ( T T bT e e z z T a T T z z , (1)
where ρ ph is approximated by the generalised Bloch-Grüneissen equation for electron-phonon scattering with n = 3 (similarly as for another uranium compounds, e.g. for URhGa 5 [START_REF] Wawryk | [END_REF]). In Eq. ( 1) the ρ m denotes the magnon component, Θ is the Debye temperature, ∆ (= ε/k B ) is a gap in the magnons spectrum, and a and b are the fitting parameters. Whereas the third part of Eq.

(1), which concerns the electron-magnon scattering, is limited to temperatures below T N /3, the second part of Eq. ( 1) is valid in the whole temperature range (dashed line in figure 4).

[Insert figure 4 about here]

In figure 4 the fit of Eq. ( 1) to the experimental data is displayed by the solid line. The ρ m (T) equation was used previously for the fitting of the data in the case of the USb antiferromagnet [11].

The experimental ρ(T) data of a USb 2 single crystal are displayed in figure 5. The results are similar to those obtained and described earlier in Refs. [START_REF] Henkie | [END_REF]8] and [9], however a discrepancy in the anisotropy ratio is observed in comparison to the data of Ref. [9]. In the latter case a maximum value of about 90 is achieved in the ρ c /ρ a ratio at a temperature of circa 60 K, while for our sample this maximum value is found to be higher even than 190 and occurs at the temperature of 23 K (figure 3). In the paramagnetic state, near the critical temperature, ρ(T) in the c direction in the limit of 0 ≤ t ≤ 0.04 (t = (T -T N )/T N ) can be expressed as that in Ref. [15]:

ρ(T) = A t 1-α + B| t | + C , ( 2
)
where α is the critical exponent, A is the critical amplitude of the resistivity; B and C are the fitting parameters (first part of the solid curve 1 in figure 5). The exponent (1 -α) from Eq. (2)

becomes ½ in the limit 0.04 ≤ t ≤ 0.12 (second part). As seen from figure 5 (third part of the curve 1), formula (2) with α = 0.326 gives a good fit to the experimental data at temperatures above 225 K. For the a-axis the resistivity between T N and 260 K increases and then decreases slightly with increasing temperature to room temperatures.

[Insert figure 5 about here]

Below 70 K, for the ρ(T) data taken in a similar way like in UBi 2 along the a-axis a sufficient approximation is given by Eq. ( 1) (curve 2 in the inset of figure 5). A good fit in the antiferromagnetic range is given by the equation: ρ(T) = ρ 0 + ρ ph + aT 5/2 (dash-dotted line) [START_REF] Henkie | [END_REF].

For the c direction below T N /3 Eq. ( 1) gives rather a poor fit.

The behaviours of critical resistivity for the UBi 2 and USb 2 single crystals in the a and c directions are presented in figure 6 as a function of the reduced temperature t = (T -T N )/T N .

Using the classification from Ref. [16], the critical resistivity of a UBi 2 crystal in the a direction behaves like that for an antiferromagnetic semiconductor (figure 6a), while that along the c-axis as for an antiferromagnetic metal (figure 6b). This rule concerns USb 2 as well (figures 6c and 6d). The solid lines in figure 6 represent Eq. ( 2) fitted to the experimental data of the UBi 2 and USb 2 resistivities within the temperature limit -0.08 ≤ t ≤ 0.08 (for UBi 2 along the c-axis (figure 6b) this limit is equal to -0.04 ≤ t ≤ 0.08). The exponent (1-α) becomes ½ at boundary marked by t G .

[Insert figure 6 about here] The UBi 2 single crystals reveal a large anisotropy in the temperature dependence of the thermoelectric power S(T) (see figure 7). Above the Néel temperature, S(T) decreases and increases for the a and c directions, respectively. Below T N , a few extremes in S(T) are observed: for the a direction, after the change in slope at T N , the two maxima in the temperature dependence of the thermoelectric power occur, the first one: 1a S max = 30.6 µV/K at 1a T max = 130 K and the second maximum 2a S max = 2.5 µV/K at 2a T max = 3.5 K.

[Insert figure 7 about here]

For the c-axis two minima in S(T) exist: i.e. 1c S min = -5.9 µV/K and 2c S min = -1.0 µV/K at 1c T min and 2c T min of 103 K and 13.5 K, respectively. The S(T) curve for UBi 2 along the c direction changes its sign thrice, namely at temperatures: 33.5 K, 38 K, and 166 K.

The S(T) dependencies for a USb 2 single crystal along the a and c directions are presented in figure 8. They are similar to the results presented in Refs. [8,[START_REF] Troć | Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology[END_REF] along the a direction in the temperature range 50 -300 K and are similar to the results of Ref. [START_REF] Troć | Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology[END_REF] in the c direction in the temperature range 75 -300 K. However in the latter case they differ in absolute values of S at lower temperatures. In general, the thermoelectric power for USb 2 differs from that of UBi 2 , particularly in that taken along the a-axis. However, a maximum of a S max = 14.2 µV/K in the antiferromagnetic range exists, but it is single and appears at a T max = 25 K. This maximum can be explained if we assume that the total thermoelectric power is a sum of the two components: the diffusion one, S d , that increases linearly with temperature and the magnon/phonon-drag one, S g , which is pieaked. The phonon-drag thermoelectric power depends on temperature as T 3 before the maximum of the peak and as 1/T on the right hand side of S max [START_REF] Blatt | Thermoelectric Power of Metals[END_REF]. The solid curve 1 (the inset on the left hand side in figure 8 The temperature dependencies of the magnetic susceptibilities for UBi 2 and USb 2 single crystals reveal a similarity displaying a sharp maxima leading to the Néel temperatures of 180.8 K and 202 K, respectively. Below T N , at about T = 21 K and 50 K, in the χ(T) curves of UBi 2 and USb 2 there are observed small minima (for UBi 2 see the inset of figure 1), which may result from the crystal-field effects. In UBi 2 this valley is not as deep as that observed for USb 2 or also for UNiSb 2 and UPdSb 2 there measured on the polycrystalline samples [START_REF] Kaczorowski | [END_REF]. In the ordered state, when the crystal field interaction is comparable with the exchange field interaction, the anomalies in the χ(T) dependencies can occur. A crystal-field splitting (ground state is a doublet) of order of the exchange interaction yields an anomalous temperature variation of the magnetic susceptibility as was shown for CeSb and CeBi [20].

The electrical resistivity of UBi 2 measured along the c direction (figure 2) differs considerably from that of USb 2 (figure 5). A large hump in the resistivity curve observed in USb 2 just below T N in the c direction can be easy explained by the fact that the corrugated [9]. In UBi 2 the Fermi surface is not rebuilt during the transition from the paramagnetic to antiferromagnetic state and such a large hump in the resistivity is not observed, but only a small hump in ρ(T) occurs (figure 6b).

The genesis of six times greater resistivity anisotropy for USb 2 than that for UBi 2 (figure 3) is in the shape of the Fermi surface. The group velocity υ g for the electronic transport defined as ħ -1 (∂E/∂k) is zero at the band extrema and zone faces (see e.g. Ref.

[21]). Vector v g = ħ - 1 (∂E(k)/∂k) is in the direction normal to the energy surface. This condition cannot be fulfilled along the c direction for the cylindrical surface. This means that in the ordered state of USb 2 , for the c direction the group velocity of electrons should be zero. In practice, for USb 2 the cylindrical Fermi surfaces are corrugated [9] and a small component υ g along the c-axis exists.

In a real USb 2 crystal, at low temperatures the resistivity (in relation to the electron-magnon and electron-phonon interactions) in the c direction is almost 300 times larger than that in the a direction (figure 3).

Because of a hybridisation effect with the conduction band, the 5f-electrons, which are responsible for existing the magnetic moment in the uranium atoms, also contribute to the electronic transport properties of UBi 2 and USb 2 . They are considered to be partially localised and partially itinerant. It is known from the 238 U Mössbauer spectroscopy results [22] and measured large cyclotron masses, that the 5f-electrons in UBi 2 are more hybridised with the conduction electrons than those in USb 2 despite the larger d U-U distance for the former compound.

The electrical resistivity in both crystals: UBi 2 and USb 2 is satisfactorily described, below the best description for the ordered state is given by ρ ~ T 5/2 [START_REF] Henkie | [END_REF], but the mechanism yielding such a proportionality is as yet unknown.

T N /3,
Near the critical temperature in the a direction, the resistivity in USb 2 differs from that observed in UBi 2 which is firstly indicated by the temperature dependence of the derivative dρ/dT. Contrary to UBi 2 , the dρ/dT curve of USb 2 exhibits a peak at 202 K (the smaller inset in figure 5). Secondly, the critical exponent α in UBi 2 is negative. In UBi 2 the temperature dependence of ρ below T N is convex while in the case of USb 2 concave (figures 6a and 6c), probably due to the different values in the energy gap on the Brillouin zone boundary.

However, it should be noticed that in USb 2 the ellipsoidal (β) sheet crosses over the Brillouin zone boundary, while in UBi 2 such a case does not occur.

A metallic shape of ρ(T) in the critical region, characteristic for an antiferromagnet (in agreement with classification from Ref. [16]), is revealed for both the UBi 2 and USb 2 crystals only in the c direction. In view of the shape of the ρ(T) curve along the a-axis these two systems may be classified as antiferromagnetic semiconductors. This discrepancy in the classification may be caused by the fact that the authors of Ref. [16] assumed the spherical Fermi surface. In Ref.

[23] it is shown that the critical behaviour of the resistivity is very sensitive to the shape of the Fermi surfaces and the position of the point of instability, Q, in the Brillouin zone.

The large-q critical spin fluctuations grow in an antifferomagnet when the temperature decreases down through T N because the antiferromagnetic order is associated with the largewave-vector Q [15]. In a metallic aniferromagnet where Q ≈ k F this growth yields an increase in the resistance when the temperature is decreased through T N . This large momentum-transfer is consistent with the conservation of energy and momentum. The temperature dependence of the resistivity of an antiferromagnetic metal, predicted in the vicinity of the critical temperature [15], is confirmed by our results especially for those obtained in UBi 2 along the c direction (figure 6b) and also for USb 2 (figure 6d), where, as mentioned above, a large hump in the resistivity behaviour occurs.

In conclusion, the resistivity near the critical temperature for both the UBi 2 and USb 2 crystals observed along the a and c directions varies in a manner as predicted for the energy-like behaviour [15,16]: i.e. ρ ~ ± | t | 1-α and then it becomes proportional to ± | t | 1/2 close to the Ginsburg temperature, t G , at the vicinity of a transition from the critical to mean-field behaviour.

Looking at the temperature dependencies of the thermoelectric power (figure 8) and of the resistivity (figure 5) for USb 2 , both measured for the c direction, one sees that they have the extremes almost at the same temperature T(ρ max ) ≈ 1c T min . This can be explained if we take into account the fact, that in a two band model of a compensated metal the contribution of the particular band's thermoelectric power to the total thermoelectric power is weighted by the contribution of the particular band's conductivity to the total conductivity. The second minimum in the S(T) dependence occurs at the temperature 2c T min , which is close to the temperature of a maximum anisotropy ratio in the resistivity (the solid line in figure 3). This also confirms the influence of the conductivity on the thermoelectric power behaviour.

Similarly for UBi 2 (figure 7), 2c T min is close to the temperature of a maximum anisotropy ratio of the resistivity (dashed line in figure 3).

Undoubtedly, the shape of the Fermi surface is reflected in the temperature dependence of the thermoelectric power, e.g. for USb 2 , where only the cylindrical sheets exist along the c-axis (figure 8), the minima in S(T) are more strongly pronounced than those in the case of UBi 2 (figure 7), where besides the cylindrical sheets, a spherical one was also detected. This means, that in the case when only the cylindrical Fermi surfaces exist (USb 2 ), the electron transport along the c direction due to the temperature gradient is also limited, like in the case of the For good quality crystals, one cannot omit the magnon/phonon-drag contribution to the total thermoelectric power at low temperatures. This contribution is visible on the S(T) dependence especially along the a-axis for both the UBi 2 and USb 2 single crystals. In UBi 2 (figure 7) the small maximum 2a S max observed at 2a T max along the a-axis certainly arises from the magnon/phonon-drag effect. This thesis was confirmed in our measurements of the thermal conductivity, which will be published elsewhere, and the thermoelectric power data of two UBi 2 samples having a different purity. For the sample with a higher maximum of the thermal conductivity, a higher maximum in the thermoelectric power at 2a T max was observed. It is well known, that the magnon/phonon-drag effect often occurs and is large when crystals are of a high purity. Similarly for USb 2 (figure 8), in the a direction a S max at a T max should arise from the magnon/phonon-drag effect as well (see the left hand inset in figure 8). Obviously, this effect should exist also along the c-axis. Our calculations showed that the temperature T* at the vicinity of which the maximum value of S g is observed, for the a-axis, is close to the 2c T min .

This suggests that the 2c S min also originate from the magnon/phonon-drag effect.

Generally, the electron-magnon/phonon scattering (including normal as well as the Umklapp processes) will result in a negative magnon/phonon-drag thermoelectric power if the q vector of the absorbed magnon/phonon crosses an occupied region of the Brillouin zone, while S g will be positive if the q vector crosses an unoccupied region of the Brillouin zone [START_REF] Blatt | Thermoelectric Power of Metals[END_REF].

Thus, the charge transport in relation to a particular sheet of the Fermi surfaces may contribute with different magnitude and sign to the total thermoelectric power, including both the contributions: i.e. the diffusion and magnon/phonon-drag ones. Thus this gives such extremes, especially observed in USb 2 (figure 8) and in UBi 2 (figure 7) along the c direction.

Deleted: As mentioned above, the total thermoelectric power is the sum of diffusion and magnon/phonon-drag contributions. The former part can be dominant and in the c direction the latter part can be poorly visible. However in the case, when the magnon/phonon-drag is enhanced an extreme in the S(T) curve is possible to occur. (the second term in Eq. ( 1)); and the dash-dotted line displays the formula: ρ(T) = ρ 0 + ρ ph + aT 5/2 , where a = 1.424 × 10 -7 mΩ cm K -5/2 . In the inset the derivative dρ(T)/dT is given in mΩ cm K -1 unit.

Deleted

Deleted: 7 Deleted: 2

 72 Deleted: the Deleted: As mentioned above, USb2 exhibits an antiferromagnetic ordering below TN = 202 K.

  ) presents the equation: S(T) = S d + S g = aT + b/T fitted to the experimental data of S(T) within the temperature range 25 -90 K. The S d (straight line 2) was calculated from the above equation, S g (curve 3) was estimated as the difference between the experimental data and diffusion contribution. The maximum of S g appears at T* = 7.5 K.Similarly like for UBi 2 , S(T) in the c direction changes the sign in the antiferromagnetic ordering and passes through two minima: 1c S min = -18.4 µV/K and 2c S min = -19.2 µV/K at 1c T min = 78.5 K and 2c T min = 6.4 K. The two latter minima are deeper than those in the UBi 2 case and occur at lower temperatures.[Insert figure8about here] The lowest part of the S(T) data are well fitted by the equation: S(T) = a'T + b'T 3 being well known for the case of two components, i.e. for the diffusion and phonon-drag components in the thermoelectric power (the inset on the right hand side in figure8). In the ordered state one should consider rather the magnon/phonon-drag component. § 4. DISCUSSIONS AND CONCLUSIONS

  electrical field gradient. Additionally, in relation to the Umklapp processes, the electrons may drift in opposite direction to the temperature gradient.

  Figure 1

  Figure 7

Figure 1 .

 1 Figure 1. Magnetic susceptibility χ versus temperature of the UBi 2 (circles) and USb 2 (squares) single crystals measured in a magnetic field of 200 Gs parallel to the c-axis. Solid and dashed lines represent χ(T) = χ 0 + C/(T + θ p ) with χ 0 = 2.7 × 10 -3 emu/mol, Curie constant C = 1.41 emu K/mol, and θ p = -17 K for UBi 2 and χ 0 = 1.42 × 10 - 4 emu/mol, C = 1.38 emu K/mol, and θ p = -59 K for USb 2 . The inset displays the low temperature χ(T) data for UBi 2 (solid line is a guide for the eyes).

Figure 2 .

 2 Figure 2. Electrical resistivity versus temperature for two UBi 2 single crystals with different purity: 1s (RR = 500 and 130) and 2s (RR = 1110 and 215) measured for the a and c crystallographic directions, respectively.

Figure 3 .

 3 Figure 3. Temperature dependence of the anisotropy ratio (ρ c -ρ 0 )/(ρ a -ρ 0 ) for UBi 2 and USb 2 .

Figure 4 .

 4 Figure 4. Electrical resistivity of a UBi 2 single crystal versus temperature for the 1s sample along the a-axis. The solid line represents Eq. (1) with: ρ 0 = 4.05 × 10 -4 mΩ cm, a = 3.403 × 10 -2 mΩ cm, b = 5.73 × 10 -6 mΩ cm, Θ =

Figure 5 .

 5 Figure 5. Electrical resistivity of a USb 2 single crystal versus temperature along the a and c directions. The squares denote the experimental data. The solid line 1 represents Eq. (2) for the c-axis in the I part of the paramagnetic region with the following parameters: α = 0.452, A = -0.198 mΩ cm, B = 5.506 × 10 -5 mΩ cm, and C = 0.807 mΩ cm. These parameters in the II part are: α = 0.5, A = -0.206 mΩ cm, B = 0.012 mΩ cm, and C = 0.813 mΩ cm, while in the III part: α = 0.326, A = -0.223 mΩ cm, B = 1.553 × 10 -4 mΩ cm, and C = 0.796 mΩ cm. The inset shows the ρ(T) data along the a-axis; the solid line 2 presents Eq. (1) with ρ 0 = 1.178 × 10 -3 mΩ cm, a = 8.935 × 10 -2 mΩ cm, b = 2.025 × 10 -6 mΩ cm, Θ = 386 K, and ∆ = 2.73 K; the dashed line represents ρ ph (T)

Figure 6 .

 6 Figure 6. Electrical resistivity versus reduced temperature (t = (T -T N )/T N ) along the a and c directions for a UBi 2 crystal a), b) and a USb 2 crystal c), d).

Figure 7 .

 7 Figure 7. Thermoelectric power of the UBi 2 single crystal (1s) versus temperature measured along the a and c directions. The superscripts 1a and 2a at T max , and 1c and 2c at T min denote: the first and second maximum along the a-axis, and the first and second minimum along the c-axis, respectively.

Figure 8 .

 8 Figure 8. Thermoelectric power versus temperature for USb 2 single crystal along the a and c directions. Curve 1 in the inset on the left hand side displays the equation: S(T) = aT +b/T with the fitting parameters a and b equal to 0.216 µV/K 2 and 203 µV, respectively, determined along the a-axis. The straight line 2 and curve 3 present the diffusion and magnon/phonon-drag contributions to the total thermoelectric power, respectively. The inset on the right hand side presents the low temperature part of S(T) for the c-axis. The solid line displays the equation: S(T) = a'T + b ' T 3 , where a ' = -7.80 µV/K 2 and b ' = -1.36 µV/K 4 .

  by Eq. (1), although a better fitting is obtained for a UBi 2 crystal probably due to existence of the spherical Fermi surface. In USb 2 , where only cylindrical Fermi surfaces exist,

		Deleted: as well as
		Deleted: 2
	F o r
	P
	e
	e r
	R
	e
	v i e w	Deleted: [11]
	O n l
	y
	11

  In summary, the χ(T) results are similar for both compounds (figure1) so that the magnetic properties are alike, but the transport properties at low temperatures show interesting differences particularly if measured in the c direction. These differences can be explained in terms of the details of the two different Fermi surfaces dictated by the different magnetic structures found in these dipnictides. Tsutsui, M. Nakada, S. Nasu, Y. Haga, D. Aoki, P. Wiśniewski, Y. Ōnuki, Phys . Rev.

	[21] R. H. Bube, Electrons in Solids, (Academic Press, San Diego, 1988) pp. 120-121.
	[22] S. B 69 054404 (2004).
	[23] T. Kasuya and A. Kondo, Solid State Commun. 14 249, 253 (1974).
	F o r F o r F o r
	P P P
	e e e
	e r e r e r
	R R R
	e e e
	v i e v i e v i e	: 21
	w w w
	O n l O n l O n l
	y y y
	14 16

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ACKNOWLEDGEMENTS

Special thanks are expressed to Prof. Z. Henkie for helpful discussion and allowing the use of his samples. The author is also grateful to Prof. R. Troć and Dr. P. Wiśniewski for their critical reading the manuscript and M.Sc. R. Gorzelniak for his help in the magnetic susceptibility measurements. The Polish Committee for Scientific Research, Grant No. 1 P03B 073 27, supported this work.