Unique Structural Features of NbS₃ Ribbon Whiskers

The X-ray diffraction analysis of NbS₃ ribbon whiskers has revealed three structural features: (i) a fine-crystalline structure throughout the entire volume with the preferred orientation along the [001] direction perpendicular to the long b axis of the whisker, (ii) the combination of crystalline macroblocks with a length up to 0.5 mm with small crystallites of various orientations, and (iii) the combination of crystalline macroblocks with the left-hand twisting of planes around the b axis with a pitch angle of 1.25° per every 0.2 mm and with the return to the initial orientation in the next block. Structural features (ii) and (iii) of NbS₃ whiskers have not yet been observed, and inorganic crystals with such properties are absent to the best of our knowledge. All crystallites have a unit cell with almost right angles and approximately the same lattice constant c (18.130 Å), whereas the lattice constants a and b are noticeably different in a single sample. All crystallites can be referred to phase IV rather than to phase I, as expected. The right angle between the a and c axes can be explained by the twinning of phase I along the c axis. Differences in the lattice constants in macroblocks indicate large stresses in structures. Such stresses near twins (and/or stacking faults) can significantly affect the free electron density and play a key role in the formation of charge density waves in various phases of NbS₃.

The NbS₃ compound was obtained in the form of numerous polymorphs [1–3] (Table 1), and a number of polymorphs were predicted theoretically [4]. The triclinic (NbS₃-I) [5] and monoclinic (NbS₃-II) [6] phases are most studied. The monoclinic phase is of interest due to three charge density waves observed in it; two of them are formed above room temperature. The NbS₃-II compound is unique in this respect: in contrast to other related compounds (NbSe₃, TaS₃), where charge density waves are also observed, the structural transition with the formation of charge density waves above room temperature is observed only in NbS₃, which allows the application of these whiskers. The first results for phase II were obtained in the 1980s, but the intensive study of NbS₃-II began approximately in 2009, when reproducible conditions for the synthesis of this phase were achieved [7, 8]. Previously, phase I usually prevailed in grown “pods.” Charge density waves, which could carry the current, are absent in this phase. The doubling of the period along the b direction of whisker growth can be considered as a specific charge density wave that cannot slide in principle. Nevertheless, the nonlinear conductivity depending on the synthesis conditions was observed in NbS₃-I [9, 10]. The nature of this phenomenon is incompletely clear.

Table 1. Unit cell parameters of NbS₃ polymorphs known from previous experiments. The a and b axes for phase IV from [1] are exchanged¹

Phase I has the simplest structure among known polymorphs [11]. Its unit cell contains only two Nb chains and, therefore, can be treated as an elementary “building block.” Combining four such blocks, one can compose the unit cell of phase II containing eight chains [12, 13]. The features of NbS₃-I listed above are reasons for the necessity of the exact knowledge of the structural properties of this phase. Furthermore, recent results obtained in [1–4] indicate that the structure of NbS₃-I should be at least reexamined. It would also be of interest to study the defect structure of this phase.

The aim of this work is to study whiskers that were grown at the Kotelnikov Institute of Radioengineering and Electronics, Russian Academy of Sciences and were nominally classified as phase I according to their electrophysical properties. We found that whiskers of this phase, according to the classification in [1], belong to the type-IV polymorphic structure and can be crystallized in three forms: (i) small crystallites, (ii) the combination of large and small crystallites, and (iii) only large macroblocks up to 0.5 mm in the direction of the long axis. In the last case, the crystal lattice is left-hand twisted around the b axis coinciding with the long axis of the whisker.

The structural studies were carried out on a Panalytical X’Pert MRD diffractometer with a primary hybrid monochromator.

All studied samples were obtained in a single growth cycle from a gas phase. Niobium and sulfur (in a small excess) were placed in an ampule and a temperature gradient of 570–610°C was maintained. Among seven ribbon whiskers, which were parallel to each other and were separated from each other by a distance of about 2 mm, sample no. 1 was 2 mm longer than the other six samples, which made it possible to determine its structural parameters. However, an attempt to transport it to a separate crystal holder for recording the diffraction pattern resulted in its transformation to a coil of entangled fibers. The other six samples were close in structure to sample no. 2, whose characteristics are presented in detail in this work, and had various concentrations of small crystallites. Attempts to remove these whiskers for the analysis of sample no. 2 with the best morphology also led to their transformation to fiber coils. Thus, we studied three samples; sample no. 3 was initially selected as the most visually perfect without visible defects, i.e., signatures of small crystallites.

The top and bottom diffraction patterns shown in Fig. 1 are obtained from whisker no. 3, which consists of only large crystal blocks, and from whisker no. 2, which also contains small misoriented crystallites, respectively. The side surface of both whiskers, which are slightly flattened ribbons, coincides with the (001) face. This face is perpendicular to a weak van der Waals bond between double arrays of triangular prisms. Diffraction patterns were recorded from this face. The top diffraction pattern from sample no. 3 demonstrates only (00l) reflections, whereas the bottom diffraction pattern from sample no. 2 includes not only these reflections but also weaker reflections from small crystallites and the strong (1 0 14) reflection from a block with a different orientation.

Fig. 1.

(Color online) Diffraction patterns of sample nos. (bottom) 2 and (top) 3. The top pattern contains only (00l) reflections. In addition to these reflections, the bottom pattern includes a number of reflections from misoriented crystallites and the strong (1 0 14) reflection from a block with a different orientation.

Figure 2 shows rocking curves of sample no. 2 in the ω – θ angle range from –4° to +4°, where ω is the angle of incidence of X rays on the sample and θ is the diffraction angle. The top (008) curve contains only the peak from the single-crystal block, whereas the middle (0 0 12) curve includes not only this peak from the same single-crystal block but also weak peaks from small crystallites, which completely dominate in sample no. 1 and do not give the (002), (004), and (008) reflections. The inset of Fig. 2 presents (2θ–ω)-scanning curves with the third analyzer crystal on the (0 0 12) reflection for the main block and one of the small crystallites. The peak from the small crystallite is broadened due to a small thickness and its maximum is shifted towards smaller angles compared to the maximum of the peak from the main crystal. Upon the grazing incidence of X rays on the ribbon, the intensity and the number of peaks from small crystallites increase (bottom curve in Fig. 2) after the rotation of the sample by 88° about the horizontal axis.

Fig. 2.

(Color online) Rocking curves of sample no. 2 on (top) (008) and (middle) (0 0 12) reflections, as well as (bottom) (0 2 12) reflection after the deviation of the sample from the vertical by 88°. Inset: (2θ–ω)-scanning curves with the third analyzer crystal on the (0 0 12) reflection to determine the lattice parameters c of large and small crystallites.

To determine the lattice parameters along the a and b axes, as well as the angles between these axes and the c axis, we used the $(1 0 12){-} (\overline 1 0 12)$ and $(028){-} (0\overline 2 8)$ asymmetric reflection pairs, respectively.

Figure 3 presents (2θ–ω)-scanning curves with the third analyzer crystal on the (black) (0$\overline 2$8) and (red) (028) reflections from sample no. 2. A small monoclinic distortion of the angle between the b and c axes is present. Crystallography formulas for the monoclinic lattice with the known lattice constant с_sc(004) = 18.1312 Å give b_sc = 6.7518 Å and α_sc = 90.087°. Figure 4 shows (2θ–ω)-scanning curves with the third analyzer crystal with a slit of 0.1 mm for the same sample on the (black) ($\overline 1$ 0 14) and (red) (1 0 14) asymmetric reflections with inclination angles of ${{\psi }_{1}}$ = –15.5° and ψ₂ = 18.4°. With the average value 2θ = 76.874° and under the assumption that the а and с axes are perpendicular to each other, crystallography formulas give the lattice constant a_sc = 4.260 Å and the inclination angle ψ_{(001)/(1 0 14)} = 16.9°, which is in good agreement with the average experimental inclination angle.

Fig. 3.

(Color online) (2θ–ω)-scanning curves with the third analyzer crystal on (black) (0$\overline 2$8) and (red) (028) reflections of sample no. 2. A small monoclinic distortion of the angle α between the b and c axes is present.

Fig. 4.

(Color online) (2θ–ω)-scanning curves with the third analyzer crystal with a slit of 0.1 mm on the (black) ($\overline 1$  0 14) and (red) (1 0 14) asymmetric reflections of sample no. 2. The angle β between the a and c axes is right.

The results are summarized in Table 2.Footnote

Our experiment does not reveal yet the doubling of the lattice constants b and c. We coordinated our results with the known data for phase IV [1]. A high resistivity of the samples also indicates doubling along the b axis.

All crystallites correspond to the type-IV structure in terms of the classification in [1].²

Table 2. Unit cell parameters of thee NbS₃ whisker samples, where 2_sc and 2_p are the single-crystal and polycrystalline parts of sample no. 2

According to Table 2, the angle β = 90° is the same for all crystallites, whereas the NbS₃-I phase implies that the angle between the a and c axes is β = 97.17° [5, 11]. The unit cell of phase IV can be represented as the combination of two unit cells of phase I, which are in the twinning position with respect to each other along the c axis (Fig. 5).³ In this case, the lattice constant c is doubled and the angle β becomes right. Thus, although the studied samples do not belong to phase I, phase IV apparently consists of two unit cells of phase I, which can be treated as the building block [12, 13].

Fig. 5.

(Color online) Projections of the unit cells of NbS₃‑I and NbS₃-IV along niobium chains located in the centers of triangular prisms. The angle between the a and c axes in phase IV is right probably because of the twinning position of the second pair of chains upon the doubling of the lattice constant c.

We emphasize that all three angles of the unit cell are close to 90° only in phase IV among all known polymorphs of NbS₃, whereas one of the angles in the other phases is close to either 97° or 110° [1].

We used (1 0 12)–($\overline 1$ 0 12) and (0 2 12)–(0 $\overline 2$ 12) reflection pairs from small crystallites in sample no. 2 to determine the lattice constants a and b, respectively. The results a_p = 4.759 Å and b_p = 6.5964 Å correspond to the orthorhombic structure and are noticeably different from the lattice constants of the main crystal blocks in this sample.

Figure 6 shows X-scanning curves obtained with a slit of 0.1 mm on the (0 0 12) reflection along the long horizontal axis of the whisker in sample no. 3 at various angles of deviation ψ of the crystal holder from the vertical. It is seen in Fig. 6 that the whisker consists of at least four blocks. Indeed, the most intense peak at the position X = –0.2 mm corresponds to two slightly misoriented blocks. For this reason, the measurements were performed on the farthest separate block with X ≈ 1.6 mm. Figure 7 presents ψ-scanning curves at local points of this block obtained with a slit of 0.1 mm and a step of 0.2 mm along the X axis. Despite a low sensitivity of the intensity to the angle of rotation of the sample about the horizontal axis, it is clearly seen that the average angle ψ increases when the measurement point is shifted towards larger X values. This corresponds to the left-hand twisting of the (001) crystal planes in the measured block near its center by 1.25° per 0.2 mm. Twisting is observed in each block of the studied sample, but it is less pronounced in other blocks because of the partial imposition of blocks on each other. Nevertheless, it is clearly seen that the block with the maximum intensity at X = 1.0 mm in Fig. 6 has the minimum value $\psi = - 5^\circ$, and the shine from the face in the optical microscope demonstrates that the average position of the (001) plane in this whisker remains unchanged over the entire its length. Consequently, it can be assumed that left-hand twisting is periodically discharged in the opposite direction, which can be responsible for the separation of the whisker into blocks.

Fig. 6.

(Color online) X-scanning curves obtained with a slit of 0.1 mm on the (0 0 12) reflection of horizontal whisker no. 3 at the angles of deviation of the sample around the horizontal axis (black) ${{\psi }_{1}} = - 3.5^\circ$, (blue) ${{\psi }_{2}} = - 5^\circ$, and (red) ${{\psi }_{3}} = - 2^\circ$.

Fig. 7.

(Color online) ψ-scanning curves obtained with a slit of 0.1 mm on the (0 0 12) reflection for the rightmost block at points X = (green) 1.35, (black) 1.55, (red) 1.75, and (blue) 1.95 mm. As approaching the end of whisker no. 3, the (001) plane is left-hand twisted around its axis.

The twisting of crystal planes around the axis of the whisker noticeably reduces the intensity of asymmetric reflections having the a component, whereas the intensity of the other reflections hardly changes. Therefore, the weakest bond in the IV-NbS₃ structure is the bond between niobium and sulfur atoms from neighboring triangular prisms. For this reason, to determine the lattice constant a, we used a parallel analyzer instead of the third analyzer crystal; its angular accuracy is an order of magnitude lower, but the intensity of the reflection is an order of magnitude higher. The resulting lattice constant is 5.025 Å, which is noticeably different from a value of 4.260 Å in crystal no. 2, whereas the other unit cell parameters are close (b = 6.7682 Å, c = 18.1312 Å, and α = 90.093°).

Variations of the lattice constants b and, more significant, a (see Table 1) indicate high internal stresses in whiskers. The transformation of crystals to fiber coils even upon tender touch to them also evidences these stresses. Variations of the lattice constants are reasonably attributed to deviations from stoichiometry, which lead to the appearance of twins and stacking faults. The monoclinic lattice promotes the appearance of internal stresses upon the collision of growing fragments of twins. This effect can be a key to understand the physics of formation of charge density waves in various phases of NbS₃. Thus, the lattice constant а is related to the distance between sulfur atoms in neighboring triangular prisms, and the probability that one electron in each sulfur atom belongs to the conduction band increases with this lattice constant. Thus, the free electron density can significantly vary even within a single polymorph. This possibly explains the difference between low-resistance NbS₃-II samples, where the second charge density wave is formed at 150 K, and high-resistance samples of the same phase, where the second charge density wave is not formed [14, 15]. The maximum stresses can be expected near twins or stacking faults, which can result in the formation of charge density waves in them with a thickness of several atomic layers [16].

To summarize, it has been established that NbS₃ whiskers, which were nominally classified as phase I, belong to polymorph IV with a small monoclinic admixture (deviation of the angle between the b and c axes from the right angle is less than one tenth degree). The unit cell of this polymorph can most probably be represented as a combination of two unit cells of phase I, which are located in the twin positions with respect to each other. We have revealed three types of whiskers:

• those consisting of only small crystallites with the preferred orientation along the c axis,

• whiskers combining large blocks with a size up to 0.5 mm and small crystallites surrounding them,

• those consisting of only large blocks whose crystal planes are left-hand twisted around the axis of the whisker.

The combination of large crystal blocks with small misoriented crystallites in a single whisker, as well as left-hand twisting with a periodic return to the average azimuth position, has been observed for the first time. Since internal stresses were high, NbS₃-IV whiskers of all three detected types could be affected by the post-growth transformation of the depth depending on their stoichiometric composition. Internal stresses, which are responsible for enormous variations of the lattice constant within one phase (more than 30% along the a axis) and, thereby, of the free electron density, can play a key role in the formation of charge density waves in various polymorphs of NbS₃, in particular, on twins and/or stacking faults.