**1. Introduction**

Bulk metallic glasses (BMGs) possess a unique set of properties such as an unrivalled combination of toughness and strength [1], very high elastic limit and elastic energy capacity [2], biocompatibility [3], corrosion resistance, etc. [4]. One of the main disadvantages is the localisation of the BMG plastic deformation at room temperature in the shear bands (SB) [5]. SB is a planar defect with a thickness of about 10–20 nm [6] accumulating the excess-free volume (EFV) during deformation [7]. Such a "decompaction" of the SB structure induces strain softening [8], with the formation of voids and microcracks merging into the main crack as load increases [9,10]. However, significant experimental evidence has been put forward on strain hardening and material densification occurring in BMGs in association with shear bands during mechanical compression [11], tension [12], and rolling [13]. Moreover, the presence of EFV trapped in the glassy state does not necessarily lead to strain softening. The finite element modelling shows that the plasticity of metallic glasses can be enhanced with the EFV-induced heterogeneity, and even apparent hardening can be achieved [14]. The cyclic loading of BMGs in the range of apparently elastic strains leads to the formation of the elastic nano-scale heterogeneity in the bulk [15]. The nano-scale heterogeneity, which is inherent to SB, has been widely approved not only by modelling [16], but also experimentally by high-resolution transmission electron microscopy (HRTEM) and digital image correlation (DIC). In particular, it was convincingly demonstrated that the SB structure consists of alternating ~0.1–0.4 μm-long segments representing compressed and stretched areas with the density, which is either larger or smaller than that in the matrix, respectively [17,18]. Thus, the material within the SB can experience both local softening due to decompaction, and hardening due to compaction of atoms.

The successful observations of the deformation hardening in BMGs commonly refer to the high density of SBs. The greater the number of SBs and the total sheared area, the larger the deformation capacity and the apparent ductility [1,11]. The emergence of the primary SB always leads to softening and failure due to the concentration of all shear deformation in one band [19]. The intermittent hardening of BMG is witnessed by multiple observations of intersecting SBs blocking each other similarly to slip bands in crystals [11,13]. Thus, the hardening/softening behaviour is governed by the development of SBs and their interactions with each other as well as with the applied stress.

The underlying mechanism of non-uniform deformation of BMGs is still under debates due to a grea<sup>t</sup> complexity of direct observations. Currently, the most widespread concept is based on the hypothetical elementary deformation units—the shear-transformation zones (STZ) [20]. Microscopic STZs are supposed to interact elastically by triggering slip avalanches and forming macroscopic SBs. Ironically, the critical interaction parameter—the elastic field of the STZ—is a priori undefinable in the static state [5]. One can approximate the STZ-induced elastic fields by the infinite-range mean-field [21], which is in good numerical agreemen<sup>t</sup> with experiments even though it is still largely speculative. Along with the family of STZ models, the approaches based on atomistic simulations are actively discussed and used for the interpretation of the SB behaviour in metallic glasses [22]. Among these approaches, the dislocation-based model [23], the free volume model [24], and the percolation approach [25] are particularly noteworthy.

The alternative to simulations is the use of empirical studies of elastic displacements created by SB. The recently disclosed long-range elastic fields around the SB tip [26] allow assuming reasonably that the interaction between SBs occurs across the scales not only on the atomic level but also on the macroscopic scale, which resembles the behaviour of dislocations in crystals, despite fundamental microstructural di fferences between crystals and amorphous solids.

The SB activity manifests itself as shear steps on a polished surface of a deformed sample and can be revealed with the surface profile analysis. The surface morphology of sheared BMGs has been frequently observed in the 2D-mode by means of scanning electron microscopy (SEM) [27–29], or in the 3D-mode by atomic force microscopy (AFM) [30–32] or confocal laser scanning microscopy (CLSM) [33]. In comparison with CLSM and AFM, scanning white light interferometry (SWLI) is more suitable for the 3D mapping of the SB topology due to a combination of the unbeatable vertical resolution up to 0.1 nm and rapid scanning of the area up to 1 cm<sup>2</sup> [34].

Both AFM and SWLI methods have been used to investigate the influence of the applied stress and pre-strain history on the SB morphology during BMG indentation [32,34]. The results clearly sugges<sup>t</sup> that the interaction exists between the developing SBs, previously formed SBs and residual stresses, which results in SB reactivation, blockage, intersection, and termination. However, all these e ffects were described without taking into account that the SB is the imperfection with its own self-induced elastic stress field. The present work reports on the results of detailed investigations of the macro-scale 3D surface topology of the deformed BMG aiming at shedding light on the formation of SB's features and mutual SBs interactions on account of their long-ranged elastic stresses.

The paper is organised as follows. In the following section, the material properties and testing methods are briefly described. For the sake of consistency, the results and discussion are provided together within each sub-section of Section 3. Section 3.1 highlights the experimental evidence to date supporting the presence of long-range elastic fields. SBs morphologically classified as shear and tear mode types in Section 3.1 are further analysed by means of the 3D surface mapping in Sections 3.2 and 3.3, respectively. Section 3.4 is focused on the local o ffset and path deviations within SBs. Whereas Sections 3.1–3.4 describe the results of SB investigations after mechanical compression, Section 3.5 reveals new facts of the interaction between SBs formed during micro-indentation of BMGs. Lastly, all findings are summarised in Section 4.
