Michael Schöneich

Marcus P Schmidt

Peer Schmidt
email: peer.schmidt@chemie.tu-dresden.de[

Prof. Dr Bernd Harbrecht

Chemical vapour transport of bismuth and antimony chalcogenides M 2 Q 3 (M = Sb, Bi, Q = Se, Te)

Keywords: chemical vapour transport, antimony , bismuth, selenide, telluride antimony selenide, antimony telluride, bismuth selenide, bismuth telluride, chemical vapour transport, thermodynamic modelling

Thermodynamic modelling of the ternary systems M/Q/I (M = Sb, Bi, Q = Se, Te) indicated solid-gas equilibria suitable for chemical vapour transport of bismuth and antimony chalcogenides. The predictions of the modelling were confirmed by transport experiments on a transport balance. The optimum transport conditions using iodine as transport agent were determined for all systems to: ϑ source = 500 °C and ϑ sink = 450 °C. For ∆T > 50 K the sequential transport of chalcogenide iodides MQI followed by M 2 Q 3 occurs. Thermodynamic standard data of the gas species SbI(g) were concluded from equilibrium calculations: ∆H 0 f,298 (SbI(g)) = 106 ±3 kJ•mol -1 ; S 0 298 (SbI(g)) = 255 ±3 J•mol -1 •K -1 ; C p (SbI(g)) = 37±1 J•mol -1 •K -1 ____________

Introduction

The vapour transport of selenides and tellurides is fairly well investigated. First reports on chemical transport of chalcogenides are related to the systematic development of this synthesis method [1 -4]. To date a large number of chemical vapour transport experiments concerning transition metal chalcogenides as well as chalcogenides of main group elements have been described. Hence, chemical vapour transport of chalcogenides of elements of groups 13, and 14 are reported (Al [1], Ga [3, 5 -7], In [8,9], Si [10 -12], Ge [13 -15], Sn [3, 16 -18], Pb [19 -21]). Transport experiments for crystal growth of Sb 2 Te 3 using iodine are described to produce multiphase mixtures of Sb 2 Te 3 and unknown phases [22]. Apart from this report no attention has been given to the transport behaviour of compounds M 2 Q 3 of group 15 elements, despite their importance as thermoelectric materials. The "closed space vapour transport" of M 2 Q 3 as a kind of Physical Vapour Deposition (CVD) process has been investigated [23].

Recent investigations are demonstrating the possibility of detailed thermodynamic modelling of gas phase equilibria and the vapour transport behaviour even for chalcogenides of complex composition, such as phases with homogeneity range or solid solutions. Using these calculations prior to the experiment, meticulous prediction of experimental transport conditions becomes possible [24,25].

Our investigation on antimony and bismuth chalcogenides proves the power of thermodynamic modelling for the prediction of chemical vapour transport properties. The calculations concerning the solid-gas equilibria are presented at different levels of complexity.

Results and Discussion

Thermodynamic modelling of the vapour transport

Prior to the experiments, various thermodynamic calculations concerning the vapour transport behaviour of binary compounds M 2 Q 3 (M = Sb, Bi, Q = Se, Te) were performed. The transport behaviour of chalcogenides of antimony and bismuth is discussed for the system Bi 2 Se 3 /I 2 as example.

In a first step, calculation of equilibrium constants K p of individual equilibria were utilised to estimate the conditions of chemical vapour transport of M 2 Q 3 . The vapour transport appears possible, if the equilibrium constant is not extreme (10 -4 < K p < 10 4 ). The direction of transport depends on the heat of reaction (T 2 → T 1 if ∆H 0 r > 0 and T 1 → T 2 if ∆H 0 r < 0). The transport of bismuth selenide using iodine as transport agent was examined according the equilibria (1), (2).

2/5 Bi 2 Se 3 (s) + 2/5 I 2 (g) ⇌ 4/5 BiI(g) + 3/5 Se 2 (g) (1) ∆H 0 R,800 = +168.2 kJ•mol -1 ; ∆S 0 R,800 = +155.9 J•mol -1 •K -1 ∆G 0 R,800 = 43.5 kJ•mol -1 ; K p, 800 = 10 -3 bar 2 Bi 2 Se 3 (s) + 6 I 2 (g) ⇌ 4 BiI 3 (g) + 3 Se 2 (g) (2) ∆H 0 R,800 = +242.3 kJ•mol -1 ; ∆S 0 R,800 = +296.9 J•mol -1 •K -1 ∆G 0 R,800 = 4.8 kJ•mol -1 ; K p, 800 = 5 • 10 -1 bar
In contrast, vapour transport using bromine or chlorine is unfavourable due to its extreme equilibrium constants K p,800 > 10 4 bar. These result from the higher stability of the involved chlorides and bromides (compare: ∆H 0 800 (BiI) = 93.7 kJ•mol -1 ; ∆H 0 800 (BiBr) = 72.4 kJ•mol -1 ; ∆H 0 800 (BiCl) = 43.8 kJ•mol -1 ; and ∆H 0 800 (BiI 3 ) = +25.2 kJ•mol -1 ; ∆H 0 800 (BiBr 3 ) = -115.5 kJ•mol -1 ; ∆H 0 800 (BiCl 3 ) = -224.2 kJ•mol -1 [START_REF] Barin | Thermochemical Data of Pure Substances[END_REF]) Relating to the equilibria (1) and ( 2) the transport is expected to occur from the higher temperature in the source to the lower temperature in the sink (T 2 → T 1 ; ∆H 0 R,800 > 0). Second, to obtain more detailed predictions on the experimental transport conditions as well as to reveal more complex interactions of different solid-gas equilibria, thermodynamic modelling of the ternary systems was performed by using the program TRAGMIN [25]. For the system Bi 2 Se 3 /I 2 the condensed phases Bi(s), BiI 3 (s), Bi 2 S e 3 (s), BiSeI(s), I 2 (s) and Se(s,l) and the gaseous species Bi(g), Bi 2 (g), BiSe(g), BiI(g), BiI 3 (g)¸ I(g), I 2 (g), Se x (g) (1 ≤ x ≤ 8) were taken into account. The calculations show, that apart from Se 2 (g) all other species Se x (g) can be neglected, because their pressures are just too low. For the formation of gaseous BiSeI(g) in minor quantity, mass spectrometric experiments provide evidence [START_REF] Binnewies | [END_REF], see also [START_REF] Schmidt | [END_REF]. Nevertheless, its partial pressure is at least two orders of magnitude lower than those of BiI(g) and BiI 3 (g). Since thermodynamic data have not yet been determined, the species BiSeI(g) has been neglected in our calculations.

The calculated composition of the equilibrium gas phase of an initial solid BiSeI(s)/Bi 2 Se 3 (s) (n(Bi 2 Se 3 ) = 1 mmol; n(I 2 ) = 0.1 mmol; V = 20 ml) is shown in Fig. 1. The break of the pressure curves at 450 °C is related to the existence of BiSeI under the given conditions. At ϑ < 450 °C BiSeI condenses, while the compound is completely evaporated at ϑ > 450 °C. Since only species with partial pressures p ≥ 10 -5 bar are regarded as relevant for chemical vapour transport, the selenium-containing species Se 2 (g), and the bismuth-containing species BiI 3 (g), BiI(g) can contribute to the transport. Accordingly, vapour transport of Bi 2 Se 3 should be possible at temperatures above 375 °C (650 K, respectively). Neither iodides of selenium nor gaseous species of elemental bismuth could be found with relevant partial pressures. Figure 1. Composition of the gas phase over Bi 2 Se 3(s) /I 2(s)calculated using the program TRAGMIN [START_REF]GMIN Version 5.0b, package TRAGMIN for calculation of thermodynamic equilibrium[END_REF] (n(Bi 2 Se 3 ) = 2 mmol; n(I 2 ) = 1 mmol; V = 20 ml) . Grey marked area: transport relevant region.

Third, for the estimation of transport conditions the pressure behaviour of coexistent phases in the pertinent system has to be considered: Fig. 2 shows the barogram of the system Bi 2 Se 3 (s)/I 2 (g) with thermal decomposition pressures of BiSeI(s) according to (3), [29] and Bi 2 Se 3 (s) (4), [30].

3 BiSeI(s) ⇌ Bi 2 Se 3 (s) + BiI 3 (g) (3) 2/5 Bi 2 Se 3 (s) ⇌ 4/5 BiSe(g) + 1/5 Se 2 (g) (4)
The transport of Bi 2 Se 3 in the above estimated temperature region follows schematically the arrows in Fig. 2. Depending on the temperature gradient and the amount of the transport agent iodine (or more specifically its partial pressure) different transport results can be predicted.

Case I:

Phase pure transport of Bi 2 Se 3 is possible with ϑ source = 500 °C and a transport gradient ∆T = 100 K. The equilibrium pressure of BiI 3 (g) must not exceed 10 -3 bar. For this reason the initial amount of iodine needs to be restricted to m iodine /V ampoule ≤ 0.5 mg/ml.

Case II:

Transport experiments with Bi 2 Se 3 at ϑ source = 500 °C as starting material and transport gradients ∆T ≤ 100 K will result in the deposition of various solids in the growth zone depending on the amount of added iodine. If the equilibrium pressure of BiI 3 (g) reaches 10 -2 bar, the existence condition of BiSeI is fulfilled and its condensation in the sink occurs. With proceeding deposition of BiSeI in the sink the total pressure of BiI 3 decreases until in a second step transport of Bi 2 Se 3 can be predicted (case II * , Fig. 2).

Case III: Keeping the equilibrium pressure of BiI 3 (g) constant at p(BiI 3 (g)) < 10 -3 bar (initial amount of iodine m iodine /V ampoule ≤ 0.5 mg/ml and the temperature gradient at ∆T = 100 K, the phase pure transport of Bi 2 Se 3 is dependent on the source temperature: with decreasing ϑ source ≤ 450 °C the existence condition of BiSeI is fulfilled again and the condensation of BiSeI in the sink occurs.

Case IV:

In the special case of varying the source temperatue by ϑ source ≤ 450 °C jointly with an increase of the temperature gradient by ∆T ≥ 100 K the transport can be expanded to the existence condition of selenium, resulting in a simultaneous condensation of BiSeI and Se in the sink.

The phase relations and equilibrium pressures for the analogous systems M 2 Q 3 /I 2 including the ternary phases BiTeI [29], SbSeI [31], and SbTeI [32] can be assumed to be similar. For this reason, the temperature conditions and the amount of transport agent (iodine) has to be restricted in the same way. With hindsight the former transport experiments of Sb 2 Te 3 using iodine (m iodine /V ampoule = 7.5 mg/ml; ϑ = 610 … 470 °C [22]), the sequential transport of SbTeI and Sb 2 Te 3 can be supposed analogous to case II. The described transport behaviour is finally to consider by discussion of the temperature dependent transport efficiency ∆(p i /p * L ) of gaseous components The transport efficiency is defined as the difference of a compounds partial pressure in the source and its partial pressure in the sink normalized by the partial pressure of a solvent L at both temperatures (here inert nitrogen gas, see equation ( 5)). This is attributed to the fact, that transport effective species exhibit positive and the transport agent negative

T L i T i L i p p p p p p         -         = ∆
transport efficiencies respectively, whereas transport efficiencies are zero for species that are not involved in the transport reaction [33].

(5)

The detailed calculation of the solid-gas equilibria over solid Bi 2 Se 3 in the temperature gradient ϑ source = 500 °C, ∆T = 10…50 K only shows efficiencies for the species BiI(g), BiI 3 (g), Se 2 (g), I(g), and I 2 (g) as already concluded from the Figure 1. The phase pure transport of Bi 2 Se 3 proceeds according to the dominant equilibrium (1) by formation of BiI(g) and Se 2 (g) as the transport efficient species (∆(p i /p * L ) > 0), while iodine acts as the transport agent (∆(p i /p * L ) < 0), Fig. 3. Beside the solid-gas-reaction additional homogenous gas phase equilibria exist (6 -8).

Se x(g) ⇌ x/2 Se 2(g) (6) I 2(g) ⇌ 2 I (g) (7) BiI 3(g) ⇌ BiI (g) + I 2(g) (8)
As a result of our calculations, the formation of BiI 3 (g) ( 2) does not show a significant temperature dependence. Hence, its transport efficiency, which is proportional to ∆(p(BiI 3 )/p * L ), is rather low. In contrast, the partial pressure of BiI(g) changes more distinctly and thus effects the transport reaction. According to the detailed modelling for all the investigated systems M 2 Q 3 (M = Sb, Bi, Q = Se, Te), the chemical vapour transport can be described by the general equilibrium (9):

M 2 Q 3(s) + I 2(g) ⇌ 2 MI (g) + 3/2 Q 2(g) (9) 2/5 M 2 Q 3 (s) ⇌ 4/5 MQ(g) + 1/5 Q 2 (g) (10)
The decomposition sublimation reactions of all compounds M 2 Q 3 according to equation (10) only have a petty contribution to the vapour transport in the considered temperature range (K p, 800 ≈ 10 -6 bar; ∆(p(MQ)/p * L ) = 0, Figure 3). By increasing the amount of the transport agent iodine and varying the temperature gradient BiSeI can be deposited at the sink, as predicted from the barograms (Fig. 2). Figure 4 shows the transport efficiency of one of these calculations: With increasing temperature gradient ∆T = 10…50 K a change in the slope of the transport efficiency curves of the iodine rich species appears, which indicates a change of the transport equilibrium. With a gradient ∆T ≥ 50 K the transport equilibrium (11) for the condensation of BiSeI occurs: 2 BiSeI(s) + 2 I 2 (g) ⇌ 2 BiI 3 (g) + Se 2 (g) (11) Further calculations with variation of the initial amount of iodine show a shift in the temperature gradient for phase pure transport of Bi 2 Se 3 or condensation of BiSeI, respectively. Thus the detailed calculations of the transport efficiency substantiate the dependence of the transport on the initial iodine quantity, as stated from the barograms (Fig. 2).

Figure 4. Transport efficiency ∆(p i /p * L ) with higher iodine quantity (m iodine /V ampoule ≥ 0.5 mg/ml): transport of Bi 2 Se 3 at ϑ source = 500 °C, ∆T < 40 K and transport of BiSeI at ϑ source = 500 °C, ∆T > 40 K.

Transport experiments

All chemical vapour transport experiments were conducted with identical amounts of samples M 2 Q 3 and iodine (m iodine /V ampoule = 0.44 mg/ml) in silica ampoules. In order to verify the calculations, chemical vapour transport was performed at various source temperatures and temperature gradients by using a transport balance [34], which permits in situ measurements of the mass flow by time.

Figure 5 shows the experimental mass flow for Sb 2 Se 3 , Sb 2 Te 3 , Bi 2 Se 3 , and Bi 2 Te 3 under similar transport conditions of ϑ source = 500 °C, and ∆T = 50 K. Basically transports are feasible for all M 2 Q 3 compounds (M = Sb, Bi, Q = Se, Te) with the sink temperature above 450 °C. The maximum in temperature is limited by the respective melting points of the compounds. The ideal gradient is -dependent on the amount of iodine -∆T = 20 -100 K. Large gradients result in a large amount of transported polycrystalline material. Smaller gradients allow the formation of well formed crystals (Figures 78910). At an average gradient of ∆T = 50 K mass flow rates of 0.9 mg•h -1 for Sb 2 Te 3 , 0.6 mg•h -1 for Sb 2 Se 3 , 0.3 mg•h -1 for Bi 2 Te 3 , and 0.1 mg•h -1 for Bi 2 Se 3 result. The higher rates of antimony chalcogenides are the consequence of slightly higher equilibrium constants (12) + (13). The calculated transport rates agree with the experimental ones in the order of magnitude: 4.9 mg•h -1 for Sb 2 Te 3 , 3.7 mg•h -1 for Sb 2 Se 3 , 3.7 mg•h - 1 for Bi 2 Te 3 , and 0.3 mg•h -1 for Bi 2 Se 3 . More precise predictions are inappropriate for transport rates of about 1 mg•h -1 .

T source T sink T/K ϑ /°C
Specific measurements have been devised regarding the predicted problem of condensation of compounds MQI (M = Sb, Bi, Q = Se, Te [29]) by using sink temperatures below 450 °C in combination with higher amounts of iodine (m iodine /V ampoule ≥ 0.5 mg/ml). For a representative transport experiment with Bi 2 Se 3 at ϑ source = 500 °C, and ∆T = 75 K two regions with different linear mass flow were detected, Fig. 6. In the first region BiSeI is deposited at the sink. As a result of the formation of BiSeI the iodine partial pressure in the systems decreases, entailing a change of the transport equilibrium by the lowered iodine pressure. Phase pure transport of Bi 2 Se 3 results, which is indicated by the smaller slope of the curve in the second transport region of figure 6. The observed behaviour can be explained with the help of the barogram (Figure 2): The transport starts under conditions similar to case II. During condensation of BiSeI the pressure decrease and the transport drifts in chronological sequence to case I.

Conclusions

The present work shows the investigation of the vapour transport of M 2 Q 3 chalcogenides (M = Sb, Bi, Q = Se, Te) on the basis of thermodynamic modelling and experimental data. The results of modelling of solid-gas equilibria have been examined and validated by experiments on a transport balance. It could be shown, that a phase pure transport of M 2 Q 3 chalcogenides is possible in a temperature range above 450 °C with gradients ∆T ≤ 100 K. The optimum transport temperatures have been determined for all systems to be ϑ source = 500 °C and ϑ sink = 450 °C.

The modelling of solid-gas equilibria also predicts a pressure-and temperature-dependent change of the transport equilibrium regarding M 2 Q 3 and MQI. It could be demonstrated, that the quantity of iodine is the controlling parameter of this change in the transport equilibrium.

Experimental Section

Starting materials used to produce the chalcogenides were antimony (Chempur, 99.999 %), bismuth (Chempur, 99.9999 %), selenium (Heraeus, 99.999 %) and tellurium (Sigma Aldrich, 99,999 %).

Pre-synthesis of the chalcogenides M 2 Q 3 (M = Sb, Bi, Q = Se, Te) were performed by solid-state reaction of stochiometric mixtures of the elements in a sealed, evacuated silica tube. The mixtures have been heated for 2 h up to 500 °C and slowly cooled down to room temperature. By this method single phase powder samples, identifiable by powder XRD, has been obtained.

For all attempts of chemical vapour transport, 300 mg of M 2 Q 3 powder and 7 mg of iodine (Grüssing, 99,5%, double sublimated over BaO) were stacked in a large silica ampoule (V = 16 ml; l = 12 cm, A = 1.2 cm 2 ). In order to verify the calculations, chemical vapour transport was performed at various source temperatures and temperature gradients by using a transport balance [34], which permits in situ measurements of the mass flow over time.

Phase identification of products has been realised by powder XRD. Patterns of synthesised compounds and mixtures were collected with a STOE Stadi P diffractometer using CuK αradiation (transmission mode, Ge-monochromator) with an acceleration voltage of 40 kV and a filament current of 30 mA. The diffractometric scans were obtained between 5 and 110° 2θ; step width 0.03° 2θ.

Thermodynamic modelling of phase equilibria were accomplished using Calphad-methods based on the Eriksson Gibbs energy minimizer implemented in the program Tragmin [START_REF]GMIN Version 5.0b, package TRAGMIN for calculation of thermodynamic equilibrium[END_REF]. The solid-gas equilibria in the ternary system M/Q/I (M = Sb, Bi, Q = Se, Te) have been calculated for different compositions isothermally in the temperature range of 400 -900 K with ∆Τ = 20 K. The thermodynamic data of condensed phases used are displayed in Table 3. Data sets of all gaseous species containing the components M, Q and I were adopted from [START_REF] Knacke | Thermochemical Properties of Inorg. Substances[END_REF] and [START_REF] Barin | Thermochemical Data of Pure Substances[END_REF]. Merely the formation of gaseous antimony monoiodide is borrowed from [START_REF] Ustinov | [END_REF]. The enthalpy of formation results in evaluation of the function of equilibrium constant (14). The entropy is concluded from the gas phase equilibrium (15). The obtained value is well consistent with pertinent standard entropies of similar species: S 0 298 (BiI(g)) = 275.4 [START_REF] Knacke | Thermochemical Properties of Inorg. Substances[END_REF]; S 0 298 (InI(g)) = 267.3 [START_REF] Knacke | Thermochemical Properties of Inorg. Substances[END_REF]; S 0 298 (TlI(g)) = 274.8 [START_REF] Knacke | Thermochemical Properties of Inorg. Substances[END_REF]; S 0 298 (BiSe(g)) = 269.0; J•mol - 1 •K -1 [START_REF] Knacke | Thermochemical Properties of Inorg. Substances[END_REF]; S 0 298 (BiTe(g)) = 273.0 [START_REF] Knacke | Thermochemical Properties of Inorg. Substances[END_REF]; S 0 298 (SbSe(g)) = 255.9 [START_REF] Barin | Thermochemical Data of Pure Substances[END_REF]; S 0 298 (SbTe(g)) = 262.4 [START_REF] Mills | Thermodynamic Data for Inorganic Sulphides, Selenides and Tellurides[END_REF]. The average molar heat capacity of SbI(g) is deduced in comparison with similar known species. Table 1: Thermodynamic data of condensed species used for modelling of the systems Sb/Se/I, Sb/Te/I, BiSe/I, and Bi/Te/I.

C p / J•mol -1 •K -1 [a] Species 0 T H ∆ / kJ•mol -1 0 T S / J•mol -1 •K -1 T / K A b c

Figure 2 .

 2 Figure 2. Transport regions depending on source temperature and the coexistence pressure of BiI 3 (g) (in dependence of initial amount of iodine). I -phase pure transport of Bi 2 Se 3 ; II + III sequential transport of BiSeI and Bi 2 Se 3 ; IV simultaneous transport of BiSeI and selenium.

Figure 3 .

 3 Figure 3. Transport efficiency ∆(p i /p * L ) for the transport of Bi 2 Se 3 at ϑ source = 500 °C, ∆T = 10…50 K with low iodine quantity (m iodine /V ampoule ≤ 0.5 mg/ml).

2/ 5

 5 Sb 2 Te 3 (s) + 2/5 I 2 (g) ⇌ 4/5 SbI(g) + 3/5 Te 2 (g) (12) ∆G 0 R,800 = 57.4 kJ•mol -1 ; K p, 800 = 2 • 10 -4 bar 2 Sb 2 Te 3 (s) + 6 I 2 (g) ⇌ 4 SbI 3 (g) + 3 Te 2 (g) (13) ∆G 0 R,800 = -9.7 kJ•mol -1 ; K p, 800 = 4 • 10 0

Figure 5 .

 5 Figure 5. Mass flow for transports of M 2 Q 3 with constant experimentally conditions: ϑ source = 500 °C, ∆T = 50 K.

Figure 6 .

 6 Figure 6. Sequential transport of BiSeI and Bi 2 Se 3 on the transport balance ϑ source = 500 °C, ∆T = 75 K.

Figure 7 .

 7 Figure 7. Crystals of Sb 2 Se 3 grown at conditions: ϑ source = 500 °C, ∆T = 50 K, (m iodine /V ampoule = 0.44 mg/ml).

Figure 8 .

 8 Figure 8. Intergrown crystals of Sb 2 Te 3 obatined at conditions: ϑ source = 500 °C, ∆T = 50 K, (m iodine /V ampoule = 0.44 mg/ml).

Figure 9 .

 9 Figure 9. Crystals of Bi 2 Se 3 grown at conditions: ϑ source = 500 °C, ∆T = 50 K, (m iodine /V ampoule = 0.44 mg/ml).

Figure 10 .

 10 Figure 10. Crystals of Bi 2 Te 3 grown at conditions: ϑ source = 500 °C, ∆T = 50 K, (m iodine /V ampoule = 0.44 mg/ml).

SbI 3 ( 1 C

 31 g) + 2 Sb(s, l) ⇌ 3 SbI(g) (14) lg(K p /bar 2 ) = (10.5 ± 0.4) -(16290 ± 500)/T [38] ∆H 0 f,298 (SbI(g)) = 106 ± 3 kJ•mol -1 SbI 3 (g) + 2 Sb(g) ⇌ 3 SbI(g) (15) ∆S 0 R,298 ≈ 0 ± 10 J•mol -1 •K -1 S 0 298 (SbI(g)) = 255 ± 3 J•mol -1 •K -p (SbI(g)) = 37 ± 1 J•mol -1 •K -1

Acknowledgments

The authors thank Mrs. P. Scheppan, Max Planck Institute for Chemical Physics of Solids, Dresden, for performing the REM measurements. Financial support by the Deutsche Forschungsgemeinschaft is gratefully acknowledged.


Gregor ; Koch

Dr Michael Ruck
email: michael.ruck@chemie.tu-dresden.de

Dipl.-Chem G Koch

The Layered Coordination Polymer Bi(SCN) 3 •½H 2 O

Keywords: Bismuth, Coordination polymer, Hydrate, Thiocyanate Bismuth, Coordination polymer, Hydrate, Thiocyanate

Yellow crystals of Bi(SCN) 3 •½H 2 O are obtained by reacting (BiO) 2 CO 3 and HSCN in aqueous solution. X-ray diffraction on a single-crystal revealed a triclinic lattice (space group P1 ) with a = 843.6(2) pm, b = 920.4 (2) pm, c = 1210.7(2) pm, α = 109.16(3) °, β = 109.06(3) °, γ = 90.22(3) °, V = 832.8(3)•10 6 pm 3 , and Z = 4.

All thiocyanate anions bind with both ends to different cations. The coordination network expands in plane layers parallel (1 1 0). The water molecule coordinates one of the two independent Bi 3+ cations. Dehydration sets in at 100 °C, followed by stepwise thermal decomposition to Bi 2 S 3 .

Introduction

The thiocyanate anion belongs to the so-called pseudohalogenides. Salts with such monovalent bi-or triatomic anions show extensive chemical similarity to the corresponding halogenides. In the context of metal-rich compounds, however, the number of corresponding lowvalent pseudo-halogenides is much smaller than would be expected. Most examples are found with thiocyanate or azide as terminal ligands of Nb 6 Cl 12 cluster cores [1]. In analogy to the chemistry of bismuth-rich halogenides [2], the synproportionation of Bi with Bi(SCN) 3 could be a potential synthetic approach to low-valent thiocyanates. Surprisingly, reliable information on Bi(SCN) 3 , including its crystal structure, is not available.

The existence of bismuth thiocyanate has already been suggested in the 19 th century by Bender [3]. In 1906, Rosenheim and Vogelsang mentioned a hydrate with the (unlikely) composition Bi(SCN) 3 •14H 2 O [4]. Later the structures of complex salts like RbBi(SCN) 4 [5] or Cs 2 Na[Bi(SCN) 6 ] [6] have been reported. In accordance to the HSAB principle the bismuth cation is coordinated by the "soft" sulfur atom, while the "hard" nitrogen atom binds preferably to the alkaline metal cation. The first structural information on Bi(SCN) 3 , which was synthesized by the method of Gallais and Familiades [7], was provided by Bensch et al., who proposed a triclinic cell (space group P1 , a = 662.9(3) pm, b = 1178.4(6) pm, c = 1200.8(5) pm, α = 114.18(4) °, β = 102.33(5) °, γ = 98.59(5) °, V = 805.9•10 6 pm 3 ) [8].

In view of this, we attempted to grow crystals of bismuth thiocyanate following diverse synthetic strategies. What we were able to characterize by single-crystal diffraction turned out to be the semi-hydrate Bi(SCN) 3 •½H 2 O.

____________

Experimental Section

Synthesis: Bi(SCN) 3 •½H 2 O was synthesized from (BiO) 2 CO 3 and HSCN according to [7]:

(BiO) 2 CO 3 + 6HSCN → 2Bi(SCN) 3 •½H 2 O + CO 2 + 2H 2 O.
In a three-necked flask 40 g (NH 4 ) 2 SO 4 (Grüssing, 99.5 %) were dissolved in 10 mL H 2 O. Two dropping funnels with (a) 75 g NH 4 SCN (Grüssing, 99 %) dissolved in 300 mL H 2 O and (b) 120 mL of an aqueous solution of 100 g H 2 SO 4 (Biesterfeld, 95 -97 %) were mounted. 30 g H 2 SO 4 (95 -97 %) were added to the (NH 4 ) 2 SO 4 and the flask was heated to 60 °C. Simultaneously, both solutions were added dropwise. The freshly produced HSCN was distilled at reduced pressure (20 -50 Pa) and condensed into an ice-cooled receiver. Addition of (BiO) 2 CO 3 (Schering) to the distillate resulted in the evolution of gas and the solution turned orange. After 1 h of stirring, the solution was separated from the excess of (BiO) 2 CO 3 . Fractions of the orange solution were used for probing several crystallization methods. Evaporation at ambient conditions yielded yellow crystals, the use of a rotary evaporator resulted in yellow powder. Yellow crystals and orange powder were obtained by extraction with MeCN, DMF, THF, Et 2 O, or ethyl acetate and subsequent evaporation of the solvent. Tests with DMSO, toluene, or hexane were not successful. Alternatively, the metathesis reaction of bismuth halogenides with thiocyanates of the alkaline metals [9] in the eutectic mixture n(NaSCN) : n(KSCN) = 7 : 3 (melting point 122 °C) [10], following the reaction BiX 3 + 3MSCN → Bi(SCN) 3 + 3MX, as well as the corresponding Finkelstein reaction in dry acetone were tested. In both cases, the precipitation of MX was observed, but suitable crystals of bismuth thiocyanate were not obtained.

Vibrational Spectroscopy: The infrared spectrum of a pressed pellet of Bi(SCN) 3 •½H 2 O with KBr was recorded with a Nicolet Magna-IR 550 Series II spectrometer. The spectrum of a pure KBr sample was subtracted. The Raman spectrum of a Bi(SCN) 3 •½H 2 O crystal was measured using a Raman microscope Renishaw RM 2000 equipped with a CCD detector and an 800 L/mm lattice monochromator. The wavelength of the laser was 632.9 nm, the power of the beam on the sample was 0.3 mW.

Thermal Analysis: Bi(SCN) 3 •½H 2 O was heated to 700 °C (rate 5 K/min) in an open Al 2 O 3 crucible inside a thermobalance (Netzsch STA 409 PC Luxx). The atmosphere was a stream (100 mL/min) of Ar (99.999 %).

X-ray Crystallography: Intensity data of a single-crystal (yellow flat needle) were collected at 293(2) K on an imaging plate diffraction system IPDS-II (Stoe) using graphite-monochromated Mo-Kα radiation. The raw-data were corrected for background, polarization and Lorentz factor. The microscopic description of the crystal shape, which was later used in the numerical absorption corrections (µ(Mo-Kα) = 21.9 mm -1 ; max./min. transmission: 0.864/0.161) [START_REF]Data Reduction Program, version 1.01[END_REF], was optimized using sets of reflections that are equivalent in the triclinic Laue class [START_REF]Crystal Optimisation for Numerical Absorption Correction Program, version 1.06[END_REF]. The structure was solved with direct methods [13] and subsequent difference Fourier syntheses in the space group P1 (no. 2). Even the hydrogen atoms could be localized, although with high standard deviations of their parameters. For the hydrogen atoms a common isotropic displacement parameter could be refined, while anisotropic displacement parameters were determined for the other atoms. Atomic parameters are listed in Table 1, selected interatomic distances in Table 2. Data in brief: 15033 reflections measured, 5406 unique; -12 ≤ h ≤ 12, -13 ≤ k ≤ 13, -17 ≤ l ≤ 17, 2θ max = 64°; R int = 0.043, R σ = 0.076; extinction parameter: 145(6)•10 -5 ; 198 parameters; R 1 = 0.033 for 3444 F o > 4σ(F o ), R 1 = 0.066 for all F o , wR 2 = 0.045; residual electron density 1.5 to -1.9 e/(10 6 pm 3 ). The experimental powder diffractogram, which was measured with a Stadi-P powder diffractometer (Stoe) using Cu-Kα 1 radiation, nicely matches the calculated pattern. Further data, in the form of a CIF, have been deposited with the Fachinformationszentrum Karlsruhe, D-76344 Eggenstein-Leopoldshafen, Germany (E-mail address: crysdata@fiz-karlsruhe.de), as supplementary material no. CSD-421612, and can be obtained by contacting the FIZ quoting the article details and the CSD number. Graphic representations of the crystal structure were developed with the program Diamond [START_REF] Brandenburg | Diamond 3.2d, Crystal and Molecular Structure Visualization[END_REF].

Results and Discussion

Yellow transparent crystals of bismuth trithiocyanate semi-hydrate, Bi(SCN) 3 •½H 2 O, were crystallized following the route of Gallais and Familiades [7]. Single-crystal X-ray diffraction revealed a triclinic lattice (space group P1 ) with 3 , and Z = 4. The powder pattern of the yellow crystals, which matches the results of the singlecrystal structure determination, deviates significantly from the pattern of the microcrystalline orange by-product, which was described by Bensch et al. [8]. The unit cell volumes of the probably water-free orange powder and the yellow semihydrate differ by 26.9•10 6 pm 3 , which corresponds to 8.1 cm 3 /mol(H 2 O). Biltz has listed volume increments between 8 and 11 cm 3 /mol(H 2 O) [START_REF] Blitz | Raumchemie der festen Stoffe[END_REF].

The crystal structure of Bi(SCN) 3 •½H 2 O consists of twodimensional coordination networks that form plane layers parallel (11 0). The full width of one layer is 623 pm, which includes an estimated van der Waals gap of about 237 pm. Two-dimensional coordination networks were also found for M(SCN) 2 with M = Zn [START_REF] Aslanov | [END_REF], Sn [17], and Hg [18], while M(SCN) 2 with M = Eu, Sr, Ba [9], Ni [19], Cd [20], and Pb [21] prefer three-dimensional connectivity.

The thiocyanate anions and the water molecules constitute the surface of the layer, while the Bi 3+ cations are situated inside (Figure 1). The axes of thiocyanate anions are inclined to the plane with the N atoms pointing to the interior. All thiocyanate anions coordinate with both ends to different cations. Except for S4, which is µ 2 -bridging, all S and N atoms are non-bridging. The bond angle in the thiocyanate anions differs by 1.2(7) ° to 4.7(6) ° from 180 °. The S-C bond lengths range from 164.0(7) to 166.3(6) pm, the N-C bond lengths from 112.8 (7) to 114.8(8) pm. Considering the given accuracy, these distances and angles agree with literature data [9]. For the orientation of the water molecule, the bonding of the O atom to the Bi2 cation seems to be the determining factor; the secondary bond to Bi1 is almost 60 pm longer (Figure 2). The hydrogen atoms, which were (approximately) localized by X-ray diffraction, are situated on the reverse site of the donating lone-pairs of the oxygen atom and point in the opposite direction of the Bi2-O bond. Thus the potential hydrogen bridge O-H1•••N5, which is strongly bend (O•••N5 276 pm, H1•••N5 ~200 pm, angle at H1 < 135°), is most likely not essential for the structure. The coordination number of both symmetry independent Bi 3+ cations is seven. Bi1 is coordinated by four S and three N atoms. Bi2 binds to three S, and three N, and one O atom. Applying the bond-length bond-strength concept [22] in the version of Brese and O'Keeffe [23] and bond valence parameters R BiS = 255 pm, R BiN = 224 pm, and R BiO = 209 pm, results in bond valence sums of 3.17(3) for Bi1 and 3.34(3) for Bi2. Even in view of the error limits of the concept, the formula, and the parameters, the calculated valence sum of Bi2 is too large (the given standard deviation is based only on the standard deviations of the distances). It can be argued that the dative bond of the O atom, which contributes about 0.23 to the sum, is not properly handled. In particular, the H atoms do not bind to any other atom and thus, in strict application of the principle, the O atom of the water molecule should have no remaining valence. The vibrational spectra of Bi(SCN) 3 •½H 2 O (Figure 3) can be interpreted in analogy to the detailed analysis of the Ba(SCN) 2 spectra by Wickleder [9]. The low-frequency Raman bands below 250 cm -1 are attributed to modes that include Bi atoms. The bands at higher frequencies in both spectra can be assigned to internal vibrations of the thiocyanate anion: δ(SCN) between 432 cm -1 and 460 cm -1 ; ν(CS) between 719 cm -1 and 787 cm -1 ; 2δ(SCN) between 889 cm -1 and 997 cm -1 ; ν(CN) between 2003 cm -1 and 2144 cm -1 . The IR absorption at 1620 cm -1 originates from the bending mode of the H 2 O molecule [START_REF] Socrates | Infrared Characteristic Group Frequencies, Tables and Charts[END_REF]. In contrast to the water-free thiocyanates M(SCN) 2 with M = Eu, Sr, Ba [9], the semi-hydrate Bi(SCN) 3 •½H 2 O does not melt congruently, but decomposes in several steps in the course of heating. In a dynamic thermogravimetric heating experiment (Figure 4) the sample lost 1.9 wt.-% above 70 °C, which is assigned to adherent moisture. The following weight loss of again 1.9 wt.-% is probably caused by the coordination water (calc. 2.3 wt.-%). The product of the dehydration step, which is completed at 190 °C, proved to be amorphous in the X-ray diffraction experiment. Above 260 °C, the thiocyanate anions decompose successively into sulfide anions and gas phase species, probably CS 2 , (CN) 2 , and N 2 [25]. For the decay of one of the six crystallographically distinct thiocyanate anions a weight loss of 5.35 wt.-% is anticipated. Starting at 260 °C, 310 °C, and 610 °C, one, another three, and the last two groups undergo decomposition. The product after heating to 700 °C and cooling to room temperature is Bi 2 S 3 , which was identified by powder diffraction. The integral weight loss matches quite nicely.

Conclusions

Bi(SCN) 3 •½H 2 O has been characterized as one product of the aqueous synthesis of bismuth thiocyanate. Thermal dehydration is possible, but degrades the crystals to amorphous powder. Nevertheless this material can be used for further synthesis, although not in reactions above 260 °C. Mild solvothermal methods or the use of ionic liquids [START_REF] Ahmed | )3½H2O. The S atoms of the thiocyanate anions and the water molecules[END_REF] are recommended.

a

  = 843.6(2) pm, b = 920.4 (2) pm, c = 1210.7(2) pm, α = 109.16(3) °, β = 109.06(3) °, γ = 90.22(3) °, V = 832.8(3)•10 6 pm

Figure 1 .

 1 Figure 1. Layered coordination network parallel (1 1 0) in the crystal structure of Bi(SCN) 3 •½H 2 O. The S atoms of the thiocyanate anions and the water molecules constitute the layer surface.

Figure 2 .

 2 Figure 2. Coordination of the Bi 3+ cations in Bi(SCN) 3 •½H 2 O. Ellipsoids indicate 70 % probability. Distances are given in pm.

Figure 3 .

 3 Figure 3. IR (top) and Raman spectra (below) of Bi(SCN) 3 •½H 2 O.

Figure 4 .

 4 Figure 4. Thermogravimetry of Bi(SCN) 3 •½H 2 O in a flow of Ar.

Table 1 .

 1 Coordinates and equivalent isotropic displacement parameters of the atoms in Bi(SCN) 3 •½H 2 O at 293(2) K. U eq (in pm 2 ) is defined as one third of the trace of the orthogonalized tensor U ij .

	Atom	x	y	z	Ueq/Uiso
	Bi1	0.30158(3)	0.26911(2)	0.07828(2)	281.7(7)
	Bi2	0.23536(3)	0.19707(2)	0.44276(2)	309.4(7)
	S1	-0.0248(2)	0.2613(2)	-0.0659(2)	394(4)
	S2	0.3864(2)	0.0909(2)	-0.1091(1)	388(3)
	S3	0.6741(2)	0.3516(2)	0.1469(2)	385(4)
	S4	0.5234(2)	0.2272(2)	0.3392(1)	315(3)
	S5	0.4844(2)	0.1659(2)	0.6417(2)	429(4)
	S6	0.0470(3)	0.3175(2)	0.5810(2)	498(5)
	N1	-0.1971(7)	-0.0102(6)	-0.0843(6)	434(14)
	N2	0.0704(8)	-0.0653(7)	-0.2804(5)	517(15)
	N3	0.6991(8)	0.5413(7)	0.0139(6)	468(15)
	N4	0.6647(7)	0.5370(6)	0.4637(5)	378(12)
	N5	0.7020(9)	0.4406(7)	0.7361(6)	544(17)
	N6	-0.1674(8)	0.0551(6)	0.5349(6)	447(14)
	C1	-0.1220(8)	0.0992(7)	-0.0729(6)	320(14)
	C2	0.1978(9)	0.0001(7)	-0.2081(6)	346(14)
	C3	0.6862(8)	0.4642(7)	0.0669(6)	305(13)

Table 2 .

 2 Selected

			interatomic distances (in pm) for
	Bi(SCN) 3 •½H 2 O. Symmetry operators: (i): x, y, z; (ii): 1-x, 1-y, -z;
	(iii): -x, -y, -z; (iv): 1-x, 1-y, 1-z; (v): -x, -y, 1-z.
	Bi1-N3 ii 235.9(5)	Bi2-N4 iv 235.1(5)
	N1 iii 256.9(5)	N6 v	250.8(5)
	S2 i	264.1(2)	O i	262.6(5)
	S1 i	272.2(2)	S6 i	266.2(2)
	N5 iv 288.0(7)	N2 iii 266.3(6)
	S3 i	300.1(2)	S5 i	273.0(2)
	S4 i	325.2(2)	S4 i	312.4(2)
	S-C	164.0(7) -166.3(6) N-C	112.8(7) -114.8(8)

Wiley-VCH

Acknowledgement

We thank Hannelore Dallmann, Inge Schubert, Philipp Wollmann, and Christoph Ziegler for experimental support.

Entry for the


Dr Rainer Pöttgen
email: pottgen@uni-muenster.de

on Intermetallics -An Overview

Keywords:

Gd Mössbauer spectroscopy on intermetallic compounds is a useful complementary spectroscopic tool for the determination of magnetic structures, since the high absorption cross-section strongly hampers neutron diffraction experiments for compounds containing natural gadolinium. The recent trends applied to solid state chemistry and materials sciences for that spectroscopic technique are reviewed.

Introduction

The half-filled 4f shell leads to remarkable magnetic properties for the rare earth metal gadolinium. It has a quite high paramagnetic moment of 7.94 µ B /Gd atom and has been described as a ferromagnet [START_REF] Szytuła | Handbook of Crystal Structures and Magnetic Properties of Rare Earth Intermetallics[END_REF]. The complex temperature dependence of its magnetic structure, however, has been controversially discussed since the early description [START_REF] Belov | [END_REF]. New investigations on high-purity gadolinium crystals [3] ordering between the spin-reorientation and the Curie temperature and weaken hints for helical antiferromagnetic ordering. This basic knowledge on the magnetic ground state of gadolinium strongly underlines the necessity for basic research. The spin reorientation around 260 K, however, is not detectable via 155 Gd Mössbauer spectroscopy due to the vanishing f-factor at higher temperature.

The Curie temperature of gadolinium amounts to 294(1) K [4]. The accompanied phase transition to a paramagnetic state has large importance for magnetic cooling, respectively heating near room temperature, an important technological aspect. Determination of the magnetocaloric effect shows that the purity of the sample is essential for determination of the intrinsic properties.

Ingoing from elemental gadolinium, a variety of binary and ternary intermetallic gadolinium compounds has been synthesized and characterized with respect to their magnetocaloric properties, in order to transfer these properties to new compounds for modulating application oriented properties. Recent results confirm this hope. To give an example, Gd 5 Si 2 Ge 2 [5] has a 30 % higher adiabatic temperature with respect to elemental gadolinium. This important parameter of magnetocaloric properties of a given compound specifies the temperature change of the material upon an adiabatic change of the magnetic field. The extensive investigation of the giant magnetic caloric (GMC), giant magnetoresistance (GMR) or giant magnetostrictive (GMS) effects is a main field in current gadolinium-based research. Further examples are GdFeSi [6], GdMgX (X = Al, Ga, In) [7] or GdFe 2 and GdCo 2 [8], which have also been studied with respect to their magneto-optical properties. Some of the ternary compounds might be suitable for technical processes. Based on its magnetocaloric performance, ferromagnetic GdNiGa [9] is taken into consideration for magnetic cooling of hydrogen gas.

Although such gadolinium intermetallics show promising magnetocaloric properties, determination of their magnetic structure is not an easy task. With 49000 barns, gadolinium has the highest cross-section for thermal neutrons, drastically hampering classical neutron diffraction experiments. Besides magnetic measurements on oriented single crystals, 155 Gd Mössbauer spectroscopy is a useful complementary tool for elucidation of the magnetic structures. A concise overview on the theoretical background of 155 Gd Mössbauer spectroscopy can be found in a review article by Czjzek [START_REF] Czjzek | Mössbauer Spectroscopy of New Materials Containing Gadolinium[END_REF].

Within SPP 1166 Lanthanoidspezifische Funktionalitäten in Molekül und Material we have investigated the structures, magnetic properties and 155 Gd Mössbauer spectroscopic data of a variety of gadolinium intermetallics [START_REF] Pöttgen | [END_REF][12][13][14][15][16][17][18][19][20][21][22][23]. These results and parallel data from literature on intermetallic gadolinium compounds are reviewed herein. Some intermetallic compounds have already been included in the older review by Czjzek [START_REF] Czjzek | Mössbauer Spectroscopy of New Materials Containing Gadolinium[END_REF].

The latter review and an article by Silver and Withnall [24] give good literature overview on 155 Gd data of different gadolinium based oxides. Herein we have only considered literature later then 1993.

Our report is written from a synthetic solid state chemist's point of view. We do not go into physical details, but we use the information supplied by the 155 Gd spectra in order to better understand structure-property relationships.

Experimental

Synthesis techniques

The various Gd x T y X z intermetallics reviewed herein have all been prepared from the pure elements under suitable argon atmosphere in order to avoid side reactions with residual oxygen. Most compounds melt congruently and they have been obtained via arcmelting. This is especially possible if all three elements have comparable melting and boiling points. If elements with comparatively low boiling points, e. g. magnesium or cadmium, are used, arc-melting leads to large weight losses upon evaporation. In those cases the samples can be prepared by induction melting of the elements in sealed highmelting metal tubes. Mostly niobium and tantalum have been used as inert container material. The X components Ga, Al, In, and Sn have high liquidus ranges. This is an excellent prerequisite for metal flux growth techniques [25]. The low melting point of these elements enables, besides solubility of the reactants, low reaction temperatures, while the high boiling temperatures avoid evaporations. The largest advantage of the flux techniques is the availability of larger single crystals for property measurements.

For the detailed synthesis conditions we refer to the original articles.

The 155 Gd Mössbauer Spectroscopic Source

Gadolinium has several isotopes of which the Mössbauer effect has been observed for 154 Gd, 155 Gd, 156 Gd, 157 Gd, 158 Gd, and 160 Gd. For physical reasons, 155 Gd is the best choice for an extensive use (half-life (linewidth), transition energy, source half life etc.) [26]. The source isotope 155 Eu, see Fig. 1, decays into three excited states of 155 Gd with Mössbauer transitions at 105, 86, and 60 keV. The 86.5 keV gamma rays (Ig = 3/2, E1, Ie = 5/2) are used for the present experiments. In natural gadolinium the abundance of 155 Gd is 14.8 %. The half-life of the source is 4.96 years. The sources used are composed of neutron-activated powders of SmPd 3 enriched up to 90 % with the 154 Sm isotope. For the 155 Eu:SmPd 3 sources lead foils of 0.9 mm thickness are applied as a critical absorber to suppress the intensity of the higher 105.3 keV gamma ray transition. A NaI(Tl) scintillation counter or Ge(Li) semiconducting detector is used to measure the 86.5 keV resonance transition gamma rays. The absorber thickness needs to be optimized due to high-energy elements of the gamma rays [27].

Analyses of the Data

For the proper description of the recorded 155 Gd Mössbauer spectra in the magnetically ordered state a least-squares fitting procedure which includes the diagonalization of the full hyperfine Hamiltonian within the transmission integral approximation is necessary [START_REF] Czjzek | Mössbauer Spectroscopy of New Materials Containing Gadolinium[END_REF]. The Hamiltonian written in the principal axes system of electric field gradient (EFG) tensor is given by the formula [START_REF] Czjzek | Mössbauer Spectroscopy of New Materials Containing Gadolinium[END_REF]:

)] I + I ( + I Î 3 [ 1) - 4I(2I E + ] sin ) I + I ( + cos I [ H = ˆ2 - 2 + 2 2 2 z Q - + 2 1 z hf η ϕ ϕ θ θ µ ∆ i i B e e g H
The numerical diagonalization of this Hamiltonian gives eigenvalues and eigenvectors wherefrom the energies of the individual line positions and the relative line intensities can be calculated, respectively (see [START_REF] Czjzek | Mössbauer Spectroscopy of New Materials Containing Gadolinium[END_REF] and references therein).

As a result of least-squares fits to the experimental spectra the following parameters can be derived: the isomer shift δ IS ; the quadrupole interaction constant ∆E Q = eQ g V zz , where Q g = (1.30 ± 0.02) b [28], the magnetic hyperfine field H hf , the asymmetry parameter η = (V xx -V yy ) / V zz , and the polar angles θ and ϕ giving the direction of the magnetic hyperfine field with respect to the principal axes of the electric field gradient (EFG) tensor. If the direction of the magnetic hyperfine field follows the magnetic moment well then the polar angles θ and ϕ contribute to our knowledge concerning realized magnetic ordering.

It has to be emphasized that from a spectrum obtained in the paramagnetic state only the effective absolute quadrupole interaction value

∆ eff Q E = eQ g V zz •(1 + η 2 /3) 1/2 can
be inferred, because of the small magnitude of the excited quadrupole moment Q ex [START_REF] Czjzek | Mössbauer Spectroscopy of New Materials Containing Gadolinium[END_REF]. In contrast, magnetic hyperfine split spectra have to be fitted with independent ∆E Q = eQ g V zz and η parameters in a self-consistent way since they are usually correlated. It has to be stressed, here, that it is a common practise to keep the absolute value of ∆E Q as equal to ∆ eff Q E when fitting the magnetically split spectra since the values of ∆E Q , η, θ and ϕ are usually strongly correlated in a magnetic region and they can not be determined independently for this case. However, this procedure can lead, when η ≠ 0, to a remarkable higher V zz value.

For our own measurements, the source width Γ S of the recoil-free emitted gamma line and the background reduced Debye-Waller factor of the source, f S , was determined from an independent measurement with a standard GdFe 2 absorber and kept constant during the fits to the experimental spectra while the nuclear g-factor ratio, g ex / g g and the ratio of nuclear quadrupole moments, Q ex / Q g were constrained to 1.235 and 0.087 [29], respectively. The interference ξ-factor for the E1 transition of 86.5 keV was fixed to the value ξ = 0.0275 [30] in the absorption cross-section.

The 155 Gd Mössbauer spectroscopic data can be systemized in several ways [START_REF] Stevens | Mössbauer Effect Data Index[END_REF]. An interesting approach was performed by de Vries et al. who interpreted data in terms of the model of Miedema and van der Woude [START_REF] De Vries | [END_REF]. Besides normal pressure data, 155 Gd Mössbauer spectroscopy under pressure is an interesting tool. Elemental gadolinium has been investigated up to 17 GPa [33]. Such data are especially interesting, since the comparison of 155 Gd and 151 Eu Mössbauer spectroscopic measurements gives valuable information about the stability of Eu II under pressure. An extensive high-pressure 155 Gd Mössbauer spectroscopic study was also performed for GdCo 5 , GdRu 2 Si 2 , and Gd 2 Fe 17 N 3 [34], and the extensive results have been discussed in comparison to the high-pressure data of gadolinium metal.

Selected Intermetallic Compounds

In the following chapters, the intermetallic gadolinium compounds are discussed in groups, depending on their structure types. The basic 155 Gd Mössbauer spectroscopic data (isomer shift, electric quadrupole splitting parameter, magnetic hyperfine field) are listed in Table 1.

Equiatomic Compounds with AlB 2 -Related Structures

The stannide GdAuSn has repeatedly been studied by 155 Gd Mössbauer spectroscopy [35][36][37]. GdAuSn crystallizes with the NdPtSb type structure, space group P6 3 mc, an ordered version of AlB 2 . Each gadolinium atom is surrounded by two puckered Au 3 Sn 3 hexagons. For crystal chemical details of AlB 2 related superstructures we refer to a review article [38]. The antiferromagnetic ordering in GdAuSn is paralleled by magnetic hyperfine field splitting in the 155 Gd spectrum. Data taken down to 4.2 K show approximately a Brillouin function. The Au-Sn ordering has an influence also on the magnetic homogeneity of the samples, as discussed in [35][36][37].

GdCuSn [35] with the same structure type shows a significantly higher quadrupole splitting parameter (Table 1), indicating lower site symmetry (stronger structural distortion) for the gadolinium atoms as compared to the gold compound. Isotypic GdAuGe [START_REF] Pöttgen | [END_REF] has an almost equal isomer shift, indicating similar electron density at the gadolinium nuclei. The highest transferred hyperfine field of 4.87 T, as observed by 119 Sn Mössbauer spectroscopy, occurs for GdAgSn [39], although an even higher field occurs in the structurally related Zintl phase EuZnSn (12.8 T) [40]. GdAu 0.44 In 1.56 [START_REF] Pöttgen | [END_REF] shows a statistical occupancy of the gold and indium atoms on the hexagonal network. This has a peculiar effect on the temperature dependence of the magnetic hyperfine field. One does not observe a Brillouin function. The hyperfine field decreases in an almost linear fashion with increasing temperature with a hyperfine field of 19.8 T at 4.2 K. This unusual behavior had been ascribed to a percolative demagnetization process with a coexistence of magnetically ordered and disordered (or differently ordered) domains.

The stannide GdNiSn [41] with the orthorhombic TiNiSi type structure shows much stronger distortion of the gadolinium coordination sphere as the hexagonal AlB 2 super-structures. This low site symmetry is reflected in enhanced electric quadrupole splitting of 1.81 mm/s. Thus, the 30 K spectrum of GdNiSn shows a well resolved doublet. The 155 Gd spectrum in the magnetically ordered state led to two plausible models for the magnetic structure of GdNiSn. Either the magnetic moments are all collinear and lie in the ab-plane (or cb-plane) or non-collinear and deviate from the crystallographic b axis by 54(2)°. In this case the spectroscopic data helped to get an idea of the magnetic structure. Quite well resolved 155 Gd spectra were also obtained for a Gd 0.1 Tb 0.9 NiSn sample (Figure 2). Doping with 10 % gadolinium is sufficient to get a good signal-to-noise ratio.

Also for Gd 2 PdSi 3 [42] the 155 Gd data underlined the magnetic susceptibility and resistivity results. However, the Mössbauer spectroscopic data have only been published graphically. In the magnetically ordered state the gadolinium atoms exhibit a huge hyperfine field larger than 30 T and one observes an abrupt jump in the temperature dependence of the hyperfine field near 15 K, related to the magnetic ordering of one of the two crystallographically inequivalent gadolinium sites. Gd 2 RhSi 3 [43] crystallizes with an ordering variant of AlB 2 with two crystallographically independent gadolinium sites. One gadolinium site has 12 Si neighbors, while the other has 6 Si + 6 Rh neighbors, resulting in drastically different crystal field interactions. Most likely the mixing of gadolinium 5d, 6p states with the Rh 4d states is responsible for the prevailing 5d, 6p electron asphericity and thus the enhanced quadrupole splitting parameter. GdCuSi (T N = 14 K), GdCuGe (T N = 19 K), and GdGaAl (T N = 50 K) [44] crystallize with AlB 2 subcells [38]. At least for GdCuGe [45], weak superstructure reflections (single crystal data) reveal the Cu / Ge ordering in a NdPtSb type fashion. Among the three compounds GdGaAl has the smallest c/a ratio of the unit cell parameters. This is reflected in the highest quadrupole splitting parameter (Table 1). In a parallel work Mulder et al. investigated the 155 Gd Mössbauer spectra of the whole AlB 2 type solid solution GdGa 2-x Al x [46]. As a result of the changing c/a ratio within the solid solution the quadrupole splitting parameter changes from positive to negative for x > 0.5 in GdGa 2-x Al x . At 4.2 K, the isomer shifts decrease from 0.59 mm/s for x = 0 to 0.51 mm/s for x = 1.20. Similar trend is observed for the hyperfine field (33.3 → 25.7 T), however, the x = 0.75 sample showed 34.9 T.

The antimonides GdNiSb and GdPdSb both crystallize with the cubic MgAgAs and the hexagonal NdPtSb type structure, respectively. These structures just differ in the stacking sequence of the Ni 3 Sb 3 , respectively Pd 3 Sb 3 hexagons, i. e. ABC for the MgA-gAs and AB for the NdPtSb type. The spectroscopically derived parameters [47] are comparable to the structurally related stannides (Table 1). GdNiSb, however, shows an AlB 2 related high-temperature modification. The higher quadrupole splitting parameter and the smaller hyperfine field are indicative for substantial structural disorder (Ni-Sb mixing) with respect to the cubic low-temperature phase.

Equiatomic Compounds with ZrNiAl Structure

GdAgGe crystallizes with the hexagonal ZrNiAl type structure [START_REF] Pöttgen | [END_REF]. The gadolinium atoms have significantly lower site symmetry as compared to the AlB 2 related materials discussed above. This is reflected in a much larger quadrupole splitting parameter. Similar to GdAuGe, and isotypic GdAuIn, the temperature dependence of the magnetic hyperfine field nicely follows a Brillouin function with S = 7/2 behavior (Figure 3). A significant difference of equiatomic GdAuIn with respect to GdAu 0.44 In 1.56 (vide ultra) concerns the isomer shift, i. e. 0.452 mm/s for GdAu 0.44 In 1.56 vs. 0.355 for GdAuIn, indicating a higher electron density at the gadolinium nuclei in GdAuIn.

GdPdMg (T C = 95.7 K), GdAgMg (T C = 39.3 K), GdPtMg (T C = 97.6 K) [14], GdAuMg (T N = 81.1 K) [15], GdPdCd (T C = 62.5 K) [13], and GdAuCd (T N = 66.5 K) [16] show all comparatively high magnetic ordering temperatures, accompanied by substantial magnetic hyperfine field splitting in the 4.2 K 155 Gd spectra. Among the many equiatomic compounds investigated (Table 1), those with magnesium and cadmium shows the smallest isomer shifts. These trends are discussed in detail below. The quadrupole splitting parameter of these compounds shows also significant differences. In that series of compounds, with increasing valence electron concentration, the c/a ratio of the cell increases which is paralleled by an increase of ∆E Q . Thus, the structural distortion is readily expressed in the 155 Gd spectra. The spectroscopic data of GdAuCd [16] in com-bination with susceptibility measurements point to a propagation vector k = (1/2, 0, 1/2).

Equiatomic Compounds with CeFeSi Type

The silicides GdMnSi, GdFeSi, and GdCoSi [48] adopt the tetragonal CeFeSi type structure, space group P4/nmm, a ternary ordered version of La 2 Sb. The three compounds have almost similar isomer shift values (Table 1), but the electric quadrupole parameters increase with increasing electron count. Such a behavior might be explained in terms of a decreasing hybridization of the gadolinium valence states with the transition metal 3d states. The magnetic hyperfine field increases in the same sequence and can be interpreted as a decreasing contribution of the conduction electron in the sequence Mn→Fe→Co.

ThCr 2 Si 2 Type and Related Compounds

The whole series of GdT 2 Ge 2 germanides (T = Mn, Fe, Co, Ni, Cu, Ru, Rh, Pd, Ag) with the tetragonal ThCr 2 Si 2 type structure has been studied by temperature dependent 155 Gd Mössbauer spectroscopy [49]. The diverse parameters are listed in Table 1. This extensive study nicely demonstrated that the sign of the V zz parameter derived from the quadrupole splitting helps to predict the magnetic macroscopic anisotropy behavior of the gadolinium atoms. For the GdT 2 Ge 2 series a nice correlation between the difference between the average charge densities ∆n WS = n WS (T) -n WS (Ge) at the edge of the atomic shells and the V zz values is observed (Figure 4). Indeed, this is a function of the valence electron concentration (VEC); increasing V zz values are observed for an increasing VEC.

The germanide GdAl 2 Ge 2 with the hexagonal CaAl 2 Si 2 type structure [43,50] has quite high site symmetry for the gadolinium atoms. No quadrupole splitting was needed for fitting the 155 Gd spectrum. In agreement with the general trends (vide infra), GdAl 2 Ge 2 shows a comparatively high isomer shift of 0.57 mm/s. In agreement with the antiferromagnetic ordering at 19.7 K GdAl 2 Ge 2 shows full magnetic hyperfine field splitting with H hf = 26.9 T. Further ThCr 2 Si 2 type compounds studied by 155 Gd Mössbauer spectroscopy are GdNi 2 Sb 2 (T N = 6.5 K), GdCu 2 Sb 2 (T N = 15.8 K), and GdGa 2 Al 2 (T N = 42.4 K) [51].

The three compounds show full magnetic hyperfine field splitting in the magnetically ordered regime. The sign and value of the V zz parameters again scales with the VEC as discussed above. BaNiSn 3 type GdIrSi 3 [52] can be considered as a non-centrosymmetric occupancy variant of the ThCr 2 Si 2 family [53]. In contrast to the 81 K antiferromagnet GdIr 2 Si 2 with ThCr 2 Si 2 type, GdIrSi 3 shows a much lower Néel temperature of 15.5 K. This might be a consequence of the non-centrosymmetric iridium-silicon coordination around the gadolinium atoms. The higher silicon content in GdIrSi 3 with respect to GdIr 2 Si 2 is reflected in a much higher isomer shift, i. e. 0.640 vs. 0.533 mm/s. The lower site symmetry leads to a higher quadrupole splitting parameter for GdIrSi 3 .

Further BaNiSn 3 type gadolinium intermetallics have been studied [54]. The 155 Gd Mössbauer spectroscopic data are listed in Table 1. The four compounds GdCoSi 3 (T N = 9.6 K), GdNiGa 3 (T N = 14.5 K), GdCuGa 3 (T N = 10.1 K), and GdCuAl 3 (T N = 10 K) all show magnetic hyperfine field splitting at 4.2 K, in full agreement with the susceptibility measurements. The most interesting sample in this series of four compounds is GdCuAl 3 . Its 155 Gd Mössbauer spectrum at 4.2 K was well reproduced with three spectral components at the same isomer shift, but with distinctly different magnetic hyperfine fields. This is certainly a consequence of structural disorder, indicating different domains with varying magnetic long-range ordering. The course of the isomer shifts as a function of the p-element content and the VEC is discussed below.

Borides, Carbides, and Borocarbides

The rhodium-rich borides GdRh 3 B and GdRh 3 B 0.706 have been studied by 155 Gd Mössbauer spectroscopy at 12 K [55], resulting in isomer shifts of 0.11 and 0.08 mm/s, respectively. The decrease in boron concentration is directly reflected in a decrease of the isomer shift. This is consistent with a slightly larger s electron density at the gadolinium nuclei. Antiferromagnetic ordering has been observed for the complex carbides GdCoC 2 (T N 15.6 K) and GdNiC 2 (T N = 20.0 K) [56,57]. In agreement with the full magnetic saturation observed in the magnetization experiments, both samples showed substantial magnetic hyperfine field splitting at 4.2 K (Table 1). The 155 Gd data allowed for a determi-nation of the crystal field parameters of A 0 2 = -498 and 277 K / a 2 0 for GdCoC 2 and GdNiC 2 , respectively.

A complex magnetic behavior has been observed for the silicide carbide GdRu 2 SiC [21]. This DyFe 2 SiC type compound orders antiferromagnetically at 10 K shows an S = 7/2 Brillouin type increase of the magnetic hyperfine field with decreasing temperature, leading to a saturation value of 30.4 T. Below 4.2 K one observes a drastic change of the magnetic structure. The 155 Gd Mössbauer spectrum shows a complex field distribution with five maxima (Figure 5), indicating a non-collinear magnetic structure.

The borocarbides GdCo 2 B 2 C and GdNi 2 B 2 C [58,59] order magnetically below 21 and 5.5 K, respectively. The ordering temperatures have been determined from the temperature dependence of the magnetic hyperfine field at the gadolinium nuclei. Quantitative evaluation of the quadrupole splitting parameters led to an estimate of the secondorder crystal field parameters A 0 2 = -428 and -346 K / a 2 0 for GdNi 2 B 2 C and GdCo 2 B 2 C, respectively. More detailed temperature dependent studies [59] then revealed a more complex magnetic ordering behavior. Below ca. 14 K GdNi 2 B 2 C shows a spiral-like magnetic structure with gadolinium magnetic moments rotating within the bc plane. In the temperature range between 14 K and the Néel temperature (ca. 20 K), the magnetic structure becomes a sine-modulated one with the gadolinium magnetic moments perpendicular to the tetragonal c axis.

Complex Silicides

Ternary silicides and germanides Gd 5 Si 2 Ge 2 have intensively been studied in the last 15 years with respect to their outstanding magnetocaloric properties. In a recent study the solid solution Gd 5 Ge 2 (Si 1-x Sn x ) 2 (x = 0.23 and 0.40) has been investigated with respect to 155 Gd Mössbauer spectroscopy [60]. The spectra showed two independent spectral contributions which correspond to the two crystallographically independent gadolinium sites. This is in agreement with the low-temperature structure determined from Xray powder diffraction. Gd 2 Fe 3 Si 5 contains one gadolinium site with site symmetry m [61]. Consequently no axial symmetry is observed and the 155 Gd spectrum at 10 K, slightly above the Néel temperature of 8.6 K shows substantial quadrupole splitting of -3.3 mm/s. In the mag-netically ordered state (4.2 K data), Gd 2 Fe 3 Si 5 shows full magnetic hyperfine field splitting with a refined hyperfine field of 26(3) T.

Complex Ternary Indium Compounds

Gd 4 Pd 10 In 21 [20] crystallizes with the monoclinic Ho 4 Ni 10 Ga 21 type structure with two crystallographically independent gadolinium sites in the unit cell which can be resolved in the 155 Gd spectrum. At 20 K, slightly above the Néel temperature of 14.2 K, the spectrum could be well reproduced with two spectral components and the parameters listed in Table 1. In the magnetically ordered state a reliable fit to the experimental data was not possible. Nevertheless, the 155 Gd data clearly manifest the magnetic ordering of the gadolinium atoms.

Strong quadrupole splitting has also been observed for the 60.5 K ferromagnet LT-GdNiIn 2 (MgCuAl 2 type) [19]. The structure contains only one crystallographic gadolinium site with site symmetry m2m. The refined experimental line width of 0.61(4) mm/s is greater than the natural one, pointing to structural imperfections in the investigated sample. In the magnetically ordered state the spectrum is well described by a single magnetic component without any hyperfine field distribution. The resolution of the spectrum, however, did not allow for a determination of the magnetic structure of LT-GdNiIn 2 .

GdRhIn 5 [17] with the tetragonal HoCoGa 5 structure shows an almost cuboctahedral indium coordination for the gadolinium atoms. The tetragonal distortion is only very small, as is expressed by the small quadrupole splitting parameter of 0.171 mm/s. The high indium content leads to a very high isomer shift of 0.657 mm/s. This is discussed in the context with other gadolinium intermetallics in the last chapter. In the antiferromagnetic state GdRhIn 5 shows full hyperfine field splitting with H hf = 23.3 T. The magnetic and 155 Gd Mössbauer spectroscopic data point to a simple collinear antiferromagnetic structure with the gadolinium magnetic moments aligned in-or close to the basal plane. It was pointed out that the magnetic structure in this case could consist of ferromagnetic Gd planes perpendicular to the c-axis with a stacking sequence +-+-leading to the net antiferromagnetic ordering. GdCu 5.1 In 6.9 is a ternary ordered version of the ThMn 12 type [62]. Again, similar to GdRhIn 5 discussed above, also GdCu 5.1 In 6.9 shows a high isomer shift of 0.597 mm/s. The tetragonal distortion of the gadolinium coordination polyhedron leads to a quadrupole splitting parameter of 0.59 mm/s. GdCu 5.1 In 6.9 is a 13.4 K antiferromagnet. Below the Néel temperature, the magnetic hyperfine field detected at the gadolinium nuclei continuously increase up to 25 T at 4.2 K as a S = 7/2 Brillouin function. The 155 Gd data point to an alignment of the gadolinium magnetic moments within the ab-plane.

The half-Heusler compound GdCu 2 In [63] is a 9.6 K antiferromagnet. Below the ordering temperature, the temperature dependence of the magnetic hyperfine field follows a J = 7/2 Brillouin function. Based on these detailed temperature dependent investigations, the total contribution to the magnetic hyperfine field at the 155 Gd nuclei in gadolinium containing Heusler compounds resulting from the conduction electron polarisation is +9.8(2.5) T. GdPt 4 In [23] crystallizes with the cubic MgCu 4 Sn type structure and orders ferromagnetically at T C = 21.9 K. In agreement with the high platinum content, one observes a low isomer shift of 0.32 mm/s at 4.2 K. Although the structure is cubic, due to a small degree of Gd / In statistics, one observes electric quadrupole splitting of 1.28 mm/s. This structural disorder is also reflected in a lower hyperfine field of only 16.5 T at 4.2 T. Similar disorder has been observed for GdCu 4 In [64,65], however, the hyperfine field of 22 T is larger.

A peculiar compound is the icosahedral quasicrystal of composition Gd 14 Ag 50 In 36 [66,67]. This quasicrystal is a spin-glass system. 155 Gd Mössbauer spectra show a distribution of electric quadrupole splitting, underlining the existence of a multiplicity of gadolinium sites. In the 155 Gd Mössbauer spectra magnetic hyperfine field splitting sets in at a temperature slightly higher than the freezing temperature. The spectra confirm that the gadolinium spins are frozen at 1.5 K and are fluctuating at 4.6 K.

Stannides

Gd 3 Cu 4 Sn 4 [22] with the orthorhombic Gd 3 Cu 4 Ge 4 type structure shows two successive magnetic ordering temperatures of 13 and 8.6 K. The structure contains two crystallographically independent gadolinium sites 4e and 2d which can be resolved in the 155 Gd spectra. The magnetic hyperfine fields at the two gadolinium nuclei follow S = 7/2 Brillouin functions with saturated magnetic hyperfine fields of 26.8 T for the lower and 32.0 T for the higher magnetic ordering temperature.

The GdT x Sn 2 [T = Fe (x = 0.17), Co (x = 0.27), Ni (x = 0.32), Cu (x = 0.17)] stannides show significant defects on the transition metal positions [68]. Although one observes different VEC, the isomer shifts (Table 1) are very close and there is no clear trend either with x or VEC. The domain character of these partially filled structures is expressed by a slightly enhanced experimental line width. Nevertheless, full magnetic hyperfine field splitting is observed in the magnetically ordered state.

Metal-Rich Gadolinium Compounds

The metal-rich gadolinium compounds GdCo 11 Ti, GdFe 9 Ti 2 , GdNi 9 In 2 , and Gd 2 Cu 7 Al 10 [43] have quite complex crystal structures, however, these materials are quite interesting since at least GdCo 11 Ti (T C ≈ 100 K) and GdFe 9 Ti 2 (T C = 280 K) have high magnetic ordering temperatures. Among these compounds GdNi 9 In 2 shows the largest quadrupole splitting parameter, while the V zz component observed for Gd 2 Cu 7 Al 10 is almost zero. GdFe 11 Ti with ThMn 12 type structure forms a hydride of composition GdFe 11 TiH 1-δ [69]. The hydride formation strongly affects the electronic situation of the gadolinium atoms. First one observes an increase of the isomer shift, but also a significant increase of the quadrupole splitting parameter. Hydrogenation thus induces an increase of the second-order anisotropy term. Gd 2 Ni 2 Mg [12] (tetragonal Mo 2 B 2 Fe type) has one of the lowest isomer shift values (0.13 mm/s) observed for intermetallic gadolinium compounds. The low site symmetry (m.2m) of the gadolinium atoms is reflected by a large quadrupole splitting parameter of 2.87 mm/s, even larger than the one observed for GdNiSn (Table 1) [41].

The Laves phase GdMn 2 [70] has two different magnetic substructures arising from the gadolinium and manganese atoms. The manganese substructure is a frustrated threedimensional one. The magnetic ordering of the gadolinium atoms was monitored through 155 Gd Mössbauer spectroscopy, indicating that the gadolinium substructure remains ordered up to ca. 80 K. Another interesting spillover of this study concerns the resolution of 155 Gd Mössbauer spectroscopy. A 2.5 % Gd 2 O 3 impurity component was clearly detectable in the spectrum. GdMn 2 and also the isotypic Laves phases GdFe 2 and GdAl 2 have furthermore been studied under high-pressure conditions [71], underlining the pressure dependence of the hyperfine fields. GdMn 2 [72] absorbs a distinct amount of hydrogen. The influence of hydrogen sorption on the 155 Gd spectra in the range GdMn 2 H x up to x = 4.3 has been studied. The hydrogenation drastically changes the isomer shift from 0.073 for x = 0 to 0.615 for x = 4.3 and one also observes a maximum of the magnetic hyperfine field for x = 3.0. For smaller hydrogen contents the spectra showed two spectral components, most likely due to domain formation.

Germanides and Stannides with HfFe 6 Ge 6 Type Structure

First 155 Gd Mössbauer spectroscopic data on GdMn 6 Ge 6 and GdMn 6 Sn 6 have been reported by Mulder et al. [73]. Magnetic hyperfine field splitting with moderate values (Table 1) has been observed for both compounds. The quadrupolar splitting in the germanide is substantially larger than in the stannide. Later on field dependent studies have been performed for GdMn 6 Sn 6 [74] in order to determine the sign of the hyperfine field.

The Mössbauer spectroscopic data of the germanide are in agreement with a nuclear magnetic resonance analysis [75]. The gadolinium substructure of GdFe 6 Ge 6 [76] shows the higher Curie temperature of 30.8 K. This reference gives a complete overview on diverse intermetallic gadolinium compounds with HfFe 6 Ge 6 type structure.

Complex Aluminides

The complex aluminide GdPd 2 Al 3 [77] GdNiAl 4 [79] shows two magnetic transitions at the Néel temperatures of 24.7 and 20.8 K. The 155 Gd Mössbauer spectrum at 27 K, slightly above the magnetic ordering temperature could be well reproduced with a single, quadrupole-split signal. Below the first magnetic ordering temperature the magnetic hyperfine field continuously increases with decreasing temperature and saturates at a value of 30 T. Based on a point charge model estimation of the EFG, the gadolinium magnetization is aligned preferentially with either the b-or the c-axis.

Iron-Arsenide Superconductors

From the large family of ZrCuSiAs type materials [80], GdFeAsO and the slightly overdoped superconductor Gd 0.84 Th 0.16 FeAsO [81] have recently been studied by 57 Fe and 155 Gd Mössbauer spectroscopy. The 57 Fe data clearly show that the supeconducting sample of Gd 0.84 Th 0.16 FeAsO shows no long-range magnetic ordering of the iron magnetic moments, while GdFeAsO shows full magnetic hyperfine field splitting in the magnetically ordered state. In contrast, the 155 Gd Mössbauer spectra show magnetic ortdering of the gadolinium moments in both compounds with an almost similar hyperfine field at 1.5 K (Table 1). The low site symmetry of the gadolinium atoms is reflected by substantial quadrupole splitting.

Trends in the Isomer Shifts

The various isomer shifts of the gadolinium intermetallics cover a broad range. They strongly depend on the nature of the elements coordinating the gadolinium atoms [82].

The values are relatively small if more transition metal atoms built up the coordination sphere (around 0.3 mm/s) and become larger for higher amounts of s, p elements like aluminum (around 0.6 mm/s) or silicon / germanium (up to 0.8 mm/s).

In the last thirty years, besides some intermetallic compounds, also a variety of gadolinium containing oxides has been studied by 155 Gd Mössbauer spectroscopy. These results have been summarized in several papers on isomer shift scales [START_REF] Czjzek | Mössbauer Spectroscopy of New Materials Containing Gadolinium[END_REF][83][84][85]. In total, the isomer shift scale for 155 Gd covers a range of more than 1 mm/s. Extreme compounds are an amorphous Gd 80 Au 20 alloy with an isomer shift lower then -0.2 mm/s and GdB 6 with an isomer shift of almost 0.9 mm/s [START_REF] Czjzek | Mössbauer Spectroscopy of New Materials Containing Gadolinium[END_REF]. Selected compounds listed in Table 1 are plotted in an isomer shift scale in Figure 6.

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Wiley-VCH

ZAAC

Examining the many data listed in Table 1 we can observe a clear trend. Especially for the series of GdTX and GdT 2 X 2 compounds, the isomer shift increases with increasing VEC either within the 3d, 4d, or 5d row of transition metals, or with increasing VEC of the p element. The manganese containing compounds deviate from this correlation, possibly due to a different electronic structure.

An increasing electron density at the gadolinium nuclei leads to a shift of the δ IS values towards negative velocities. Over the whole range, for these intermetallic compounds we observe a considerable variation of the conduction electron character, with the largest 6s contributions for the smallest isomer shift, and strong 5d and / or 6p predominance for the largest δ IS values.

Crystal Field Parameters derived from 155 Gd Spectra

The experimental determination of the quadrupole interaction at the Gd nuclei is of general interest for a deeper insight into the electronic properties of rare earth compounds. The trivalent gadolinium ion in the 8 S 7/2 electronic state with a spherical distribution of the 4f electronic charge is insensitive to crystal field effects (CFE); hence the 155 Gd nucleus is a good probe for a lattice contribution to the electric field gradient.

The crystal electric field parameter (CEF) 0 2 A is commonly given by the relation [START_REF] Czjzek | Mössbauer Spectroscopy of New Materials Containing Gadolinium[END_REF]86]:

0 2 A = -V zz (1-σ 2 )/[4(1-γ ∞ )]
Here, σ 2 is a screening coefficient estimated to be about 0.6 for any rare earth ion and γ ∞ (and (1-γ ∞ ) is about 60) is the Sternheimer antishielding factor of the EFG produced by the lattice charges (i.e. the polarisation of the core electrons). Although the last relation has no fundamental basis from a theoretical point of view [87,88] it was shown, however, that the proportionality between V zz and 0 2

A keeps rather well for individual rare earth series of different compounds [START_REF] Czjzek | Mössbauer Spectroscopy of New Materials Containing Gadolinium[END_REF]43,44,49,51,78,86]. The quantity 0 2

A is then a universal factor applicable to all isostructural compounds of rare earths, provided that the structural parameters do not significantly vary with the rare earth. V zz itself, which is an important solid state property, can be obtained easily from the quadrupole constant ∆E Q ( 155 Gd) using the following formula:

V zz = 2.2206⋅10 21 ∆E Q [mm/s] V/m 2 . The next term of CEF, i.e. 2 2
A is directly related to the asymmetry parameter η in the form:

2 2 A = η 0 2

A

This term is always zero for a site with axial symmetry since then η = 0.

Hyperfine interactions and magnetic structures

Generally, to get a complete description of the magnetic structure for a given solid, several experimental methods must be combined together. Among them there are mac- First of all to answer this question, the knowledge of the direction of the EFG principal axis V zz should be known for all possible Gd sites in the structure what could be sometimes a serious task. Here, however, the symmetry conditions and the quality of the trial fits can be decisive in establishing mutual orientations of principal axes for the EFG tensor [21,41].

Secondly, a magnetically split Gd spectrum has to be well resolved to allow its careful analysis and this second condition is usually not fulfilled in the case of 155 Gd Mössbauer spectroscopy. Obviously, this analysis is easier if Gd occupies only one crystallographic site with relatively high symmetry (for example tetragonal or hexagonal) and if the magnetically split spectrum can be fitted with a low number of magnetic components. However, the situation is not hopeless and there are many examples where this spectroscopy is successful in determining at least some of elements of magnetic ordering [14,17,21,41,59] even for compounds with non-collinear magnetic structures. As a most spectacular example one can serve the tetragonal carbide GdNi 2 B 2 C [59], where the application of 155 Gd Mössbauer spectroscopy and a sophisticated analysis of the recorded spectra at the magnetic regime revealed that below T R = 14 K this compound orders in the bunched spiral-like structure with gadolinium magnetic moments rotating within the bc-plane while between T R and T N = 20 K the existence of a sine-modulated type of structure was confirmed with the gadolinium magnetic moments perpendicular to the tetragonal c axis.

As mentioned above, for the hexagonal antiferromagnetic stannide GdNiSn [41] two possible magnetic structures have been proposed for all temperatures below T N . The first structure was described as a collinear one with the Gd magnetic moments lying in the ab-plane (or cb-plane) and the second as non-collinear structure with the Gd magnetic moments slightly deviated from the cb-plane. In the case of the antiferromagnetic carbide GdRu 2 SiC [21], magnetically split spectra between T N and 4.2 K can be well fitted with only one magnetic component but the spectrum recorded at 2.15 K can be effectively fitted with a characteristic distribution of magnetic hyperfine fields (Fig. 5).

From the analysis of the obtained Mössbauer spectra it was shown that in the temperature region 4.2 K ≤ T ≤ T N a collinear magnetic structure is realized with the Gd magnetic moments ordered along the a-axis (being the V zz axis of the EFG tensor) or close to it, while at T = 2.15 K, a non-collinear magnetic structure appears resulting with the distribution of magnetic hyperfine fields. 155 Gd Mössbauer spectroscopic studies carried out for the ferromagnetic GdTMg (T = Pd, Ag, Pt) intermetallics [14] show that the derived θ angles are neither 0° nor 90° and these results point to a magnetic structure where the magnetic moments deviate from the crystallographic c axis. In particular, if V zz is perpendicular to the c axis then the magnetic moments would be confined within the basal ab-plane.

The presence of tin in ternary Gd stannides gives an exceptional opportunity to follow the magnetic phase transformations and magnetic interactions simultaneously at two different sites by means of two microscopic probes, namely the 155 Gd and 119 Sn isotopes. Such investigations showed, for example, that the magnetic structure of GdAgSn [35,39] is not homogenous and the fact that the temperature dependence of the average magnetic hyperfine field <H hf > at the Sn site does not follow an S 7/2 Brillouin-function indicates more complex magnetic interactions, reflecting its more complex magnetic structure. In this context it is worth to note that tin is a diamagnetic atom and therefore 119 Sn Mössbauer spectroscopy is an ideal tool to study the so-called transferred hyper-fine field, i.e. the magnetic hyperfine field induced at the 119 Sn Mössbauer nucleus by the surrounding magnetic gadolinium atoms.

The magnetic hyperfine field at the gadolinium site H hf is usually presented in the form:

H hf = H CP + H CE + H D where H CE = H S + H TR .
The core-polarisation field H CP is caused by exchange interactions between 4f and core electrons. Its value, H CP = (-340±20) kOe [START_REF] Watson | Hyperfine Interactions[END_REF][START_REF] Gegenwarth | [END_REF] is assumed not to be dependent on the gadolinium environment in solids. H CE is the conduction electron contribution to the magnetic hyperfine field. The H S term is the self-polarisation field ascribed to polarisation of conduction electrons polarised by the given local Gd magnetic moment while H TR is the transferred field contribution due to the conduction electron polarisation by magnetic atoms in the surroundings. H D is the dipole field but its amplitude is usually small and therefore can be neglected in most cases. Hence, the conduction electron contribution H CE can be estimated from the experimental result obtained for H hf as

H CE = H hf -H CP .
Orientations of rare earth magnetic moments as anticipated from 155 Gd spectra Some useful information about the preferred arrangements of the magnetic rare earth moments can be derived from the analysis of the quadrupole interactions observed at the Gd nuclei.

m B 2 = Q 4f m A 2 = α J ⋅ <r 2 > 4f ⋅ m A 2
where Q 4f = α J ⋅ <r 2 > 4f is the quadrupole moment of the 4f state and here α J ⋅is the Stevens factor while <r 2 > 4f is the mean squared radius of the 4f wave function.

Both m B 2 parameters can be then expressed by the following formulae: 0 states with the possible smallest J z  contribute to the electronic ground state and the magnetic moment is aligned in the basal plane (⊥z). Such a procedure was satisfactorily applied in the case of compounds with tetragonal [START_REF] Czjzek | Mössbauer Spectroscopy of New Materials Containing Gadolinium[END_REF]17,49,91] and hexagonal symmetry [74] giving a good agreement between predicted and experimentally observed directions of magnetic rare earth moments by neutron diffraction methods and (or) single crystal magnetizations studies. Obviously, this procedure is usually not applicable for lower symmetries where higher terms of the Stevens expansion have to be taken into account to get proper prediction concerning the easy direction or easy plane of magnetic rare earth moments. * Please note that presented here quadrupole spiltting constants (QSC) ∆

2 B (K) = - 90.2 ⋅ α J ⋅ <r 2 > 4f ⋅ ∆E Q ( 155 Gd
eff Q E = eQ g V zz •(1 + η 2 /3) 1/2 or ∆E Q are defined in a uniform way as ∆

eff Q E = eQ g V zz •(1 + η 2 /3) 1/2 and ∆E Q = eQ g V zz . The lack of an error at a given QSC means that its absolute value was kept constant during the fitting procedure to that obtained at the paramagnetic state while its sign was varied to get the best fit to the spectra recorded below a magnetic transition temperature.

± -means that the sign of QSC was undetermined.

** The analysis of the spectra obtained below T = 14 K leads to the complex bunched spiral-like magnetic structure with the different magnetic hyperfine fields at the nth gadolinium site. For details see [59].

Figure Captions

Fig. 1 γ-ray transition scheme for 155 Gd, redrawn from [START_REF] Stevens | Mössbauer Effect Data Index[END_REF].

Fig. 2 155 Gd Mössbauer spectra of Gd 0.1 Tb 0.9 NiSn taken above and below the Néel temperature. Reproduced from [41] with permission of Elsevier.

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Wiley-VCH ZAAC Fig. 3 Temperature dependence of the internal magnetic hyperfine fields of GdAgGe, GdAuGe, and GdAuIn. Reproduced from [START_REF] Pöttgen | [END_REF] with permission of Elsevier.

  with PrNi 2 Al 3 type structure shows a huge quadrupole splitting parameter of 5.64 mm/s in the paramagnetic regime, emphasizing the strongly asymmetric charge distribution around the gadolinium nuclei. Full magnetic hyperfine field splitting occurs at 4.2 K. Slightly different Mössbauer parameters have been observed by Mulder et al. [78]. Although the PrNi 2 Al 3 type contains only one crystallographic rare earth position, the spectra for this second GdPd 2 Al 3 sample were fitted with two signals in 81 : 19 ratio with distinctly different V zz values and also substantially different hyperfine fields in the magnetically ordered regime. The origin of this discrepancy remains unclear.

  roscopic and microscopic techniques, such as magnetization and susceptibility measurements, neutron diffraction investigations, solid state NMR and of course Mössbauer spectroscopy. Hereafter, we would like to discuss the question what we can learn from 155 Gd Mössbauer spectroscopy concerning the spin configuration i.e. what are the spatial orientations of individual magnetic moments with respect to the crystallographic axes.

2 B and 2 2 B

 22 The quantities ∆E Q and η obtained from155 Gd Mössbauer spectroscopy can provide estimates for the quadrupolar terms 0 in the Stevens expansion Σ m n B m n O of a coupling of the 4f shell of rare earths with non-zero orbital angular momentum to the crystal field. Please note that these two quadrupolar terms m B 2 are closely related to the previously defined m A 2 CEF parameters by the expression [10]:

) and 2 2 B = η ⋅ 0 2 B 2 B 2 H 2 B 2 B

 222222 , where the mean squared radius of the 4f wave function <r 2 > 4f for a given rare earth is expressed in atomic units and ∆E Q in units of mm/s. Providing that 0 is the leading term in the crystal field Hamiltonian, then when translated for other rare earth ions in the family of isostructural compounds, its sign gives information about the magnetocrystalline anisotropy, since then 0 the ground state doublet is built up of states with a maximum absolute value of J z which means that the magnetic moment is pointed in the direction of the z-quantization axis. In contrary, for positive values of 0 only

Fig. 4

 4 Fig.4 Dependence of experimentally derived V zz values of the germanides GdT 2 Ge 2 on the difference of the electron density n WS at the edge of the atomic shell of the T and Ge atoms using Miedema's model. Reproduced from[49] with permission of Elsevier.

Fig. 5

 5 Fig.5 Field distribution function F(H hf ) obtained for the 155 Gd spectrum of GdRu 2 SiC recorded at T = 2.15 K. Solid lines denote Gaussian profiles fitted to the distribution. Reproduced from[21] with permission of ACS. Please note that the last profile above 425 kOe can be an artefact of the fitting procedure.

Fig. 6

 6 Fig. 6 Isomer shift scale (with respect to a 155 Eu:SmPd 3 source) for the 86.5 keV transition of 155 Gd for selected compounds ofTable1. For details see text.

Table 1 .

 1 155 Gd Mössbauer spectroscopic data of diverse intermetallic compounds: isomer shift, δ [mm/s]; electric quadrupole splitting parameters, ∆ eff Q E or ∆E Q [mm/s]; magnetic hyperfine field, H hf[T]. The temperature of the measurements is given in parentheses. Parameters without standard deviations had been constrained. In the case of two isomer shifts listed, the spectra were fitted with a superposition of two spectral components. The magnetic ordering temperatures T M derived from susceptibility measurements (when available) are listed in a separate column.

	Compound	structure type	δ [mm/s] ∆	eff Q E or ∆E Q [mm/s]* H hf [T]	T M [K] Reference
	aluminides
	GdGaAl	AlB 2	0.52	-2.071	26.1	50	[44]
	GdGa 2 Al 2 (4.2 K)	ThCr 2 Si 2	0.58	1.306	29.2	42.4	[51]
	GdCuAl 3 (4.2 K)	BaNiSn 3	0.57 (51 %)	3.828	18.5	10.0	[54]
			0.57 (37 %)	2.702	28.7		[54]
			0.57 (12 %)	0.811	14.5		[54]
	GdPd 2 Al 3 (20 K)	PrNi 2 Al 3	0.482(6)	5.64(3)	-		[77]
	GdPd 2 Al 3 (4.2 K) GdNiAl 4 (4.2 K)	PrNi 2 Al 3 YNiAl 4	0.482(11) 0.528(2)	5.64 3.594(9)	27.1(3) 30 saturation field	24.7	[77] [79]
	gallides
	GdNiGa 3 (4.2 K)	BaNiSn 3	0.59	2.792	28.5	14.5	[54]
	GdCuGa 3 (4.2 K)	BaNiSn 3	0.62	3.422	28.7	10.1	[54]
	indium compounds
	GdAuIn (4.2 K)	ZrNiAl	0.355(4)	-2.828(16)	18.4(2)	12.5	[11]
	GdAu 0.44 In 1.56	NdPtSb	0.452(10)	-3.368(16)	19.8(1)	21.0	[11]
	Gd 4 Pd 10 In 21 (20 K)	Ho 4 Ni 10 Ga 21	0.56(2)	1.98(1)	-	14.2	[20]
			0.57(1)	4.48(1)	-
	LT-GdNiIn 2 (78 K)	MgCuAl 2	0.47(1)	4.16(5)	-	60.5	[19]
	LT-GdNiIn 2 (4.2 K)	MgCuAl 2	0.46(1)	4.16	25.4(3)		[19]
	GdRhIn 5 (47 K)	HoCoGa 5	0.657(2)	0.684(8)	-	41.0	[17]
	GdRhIn 5 (4.2 K)	HoCoGa 5	0.660(2)	-0.684	23.34(7)		[17]
	GdCu 5.1 In 6.9 (4.2 K)	ThMn 12	0.590(6)	0.60(12)	25.0(3)	13.4	[62]
	GdCu 2 In (1.5 K)	MnCu 2 Al	0.414(5)	-	22.7(3)	9.6	[63]
	GdPt 4 In (30 K)	MgCu 4 Sn	0.34(1)	1.28(2)	-	21.9	[23]
	GdPt 4 In (4.2 K)	MgCu 4 Sn	0.32(1)	±1.28(4)	16.5(2)		[23]
	Gd 14 Ag 50 In 36 (1.5 K)	quasicrystal	0.52(2)	-2.4(1)	12(1)	4.25	[66, 67]
	carbides
	GdNiC 2 (4.2 K)	CeNiC 2	0.66(3)	-1.43(5)	34.0(5)	20.0	[56, 57]
	GdCoC 2 (4.2 K)	CeCoC 2	0.61(3)	2.57(5)	25.7(5)	15.6	[56, 57]
	GdRu 2 SiC (4.2 K)	DyFe 2 SiC	0.516(3)	-1.03	27.3(1)	10	[21]
	GdCo 2 B 2 C (4.2 K)	LuNi 2 B 2 C	0.50	3.332	-45.6		[58]
	GdNi 2 B 2 C (4.2 K)	LuNi 2 B 2 C	0.56	5.44	-27.9		[58]
	GdNi 2 B 2 C (4.2 K)	LuNi 2 B 2 C	0.54	5.38	**		[59]
	silicides
	GdMnSi (4.2 K)	CeFeSi	0.37	-1.441	22.6		[48]
	GdFeSi (4.2 K)	CeFeSi	0.35	-0.811	24.0		[48]
	Gd 2 Fe 3 Si 5 (4.2 K)	U 2 Mn 3 Si 5	0.54(3)	-3.7(1)	26(3)	8.6	[61]
	GdCoSi (4.2 K)	CeFeSi	0.35	2.207	28.5		[48]
	GdCuSi (4.2 K)	AlB 2	0.45	-1.441	30.5	14	[44]
	Gd 2 RhSi 3 (0.5 K)	Er 2 RhSi 3	0.44 (70 %)	4.728	24.0	14	[43]
			0.63 (30 %)	1.171	28.2
	Gd 5 Ge 2 Si 1.54 Sn 0.46 (4.2 K)	Gd 5 Si 2 Ge 2	0.51 (87 %)	0.87	-		[60]
			0.61 (13 %)	3.47	-
	Gd 5 Ge 2 Si 1.20 Sn 0.80 (4.2 K)	Gd 5 Si 2 Ge 2	0.34 (79 %)	0.53	-		[60]
			0.48 (21 %)	1.99	-
	GdCoSi 3 (4.2 K)	BaNiSn 3	0.57	1.756	25.6	9.6	[54]
	GdIrSi 3 (4.2 K)	BaNiSn 3	0.640(12)	2.03(18)	28.0(6)	15.5	[52]

Table

Wiley-VCH ZAAC

This work was financially supported by the Deutsche Forschungsgemeinschaft through SPP 1166 Lanthanoidspezifische Funktionalitäten in Molekül und Material and by Poland's Committee for Scientific Research grant under contract No: 1 P03B 084 28.