3.1. Glass Transition
As a first indicator for differences between high and low boron concentration regimes, the glass transition temperature Tg
as an integral measure for the structure of a glass is considered. Table 1
lists the glass transition temperatures obtained by measuring average atomic volume changes by high energy X-ray scattering (Supplementary Figure S1
) for (Co6.8±3.9
with B concentrations between 22 and 85 at.%. The Co/Ta-ratio is constant at 6.8 ± 3.9. Tg
increases from 757 ± 1 K to 900 ± 1 K up to a B concentration of 46 at.%, then decreases to around 595 ± 1 K at 59 at.% B, and stays constant around 590 ± 14 K for higher B concentrations. These glass transition temperatures are lower than those reported in literature (Tg
= 975 K for Co55
], which may be attributed to the different synthesis routes.
is inversely proportional to the configurational entropy Sc
is larger for high B concentrations above 59 at.% compared to lower B concentrations. The constant Tg
and hence a constant Sc
corresponds to a constant number of degrees of freedom for (Co6.8±3.9
with more than 59 at.% B, despite the further incorporation of B into the material. This constant number of degrees of freedom suggests the existence of a B network in the high B concentration regime.
To further investigate the structural differences with focus on the short-range order, the reduced pair distribution functions G(r) of (Co6.8±3.9
as a function of B concentration are shown in Figure 1
a. For low B concentrations, the metal-metal (M-M) bonds with a distance of 2.6 Å at 22 at.% dominate G(r). At 3.1 Å, bonds with the second nearest neighbour are visible. The metal-boron (M-B) bonds result in a small peak at 2.1 Å for 22 at.% B, while the B-B bonds are not visible due to the low scattering power of B in X-ray scattering [42
With increasing B concentration, the intensity of the M-B bonds increases, while the intensity of the M-M peak decreases as it is expected for larger B concentrations and the corresponding lower metal concentrations in the sample. Hence, as the B concentration is increased, the metal atoms bond more often with B than with each other. Moreover, the bond lengths rM-B
increase with an increasing B concentration (Figure 1
b). Between 34 and 59 at.% B, the bond lengths increase by 4% for M-B and by 10% for M-M bonds. Above 59 at.%, rM-M
remains constant, while rM-B
decreases by 2.3%. This is consistent with the evolution of a B network, surrounding the metal atoms and separating them at a constant distance once the B network completely evolved at 59 at.% B. Simultaneously, the M-B bond length decreases upon further incorporation of B into the network, as the additional B atoms populate the B network and thereby surround the metal atoms more closely.
This B network evolution notion is supported by the calculated total and partial coordination numbers (CN). The total CN (Figure 2
a) remains constant around 12 up to 40 at.% B, then decreases between 40 and 70 at.% B down to 10 and stays constant at 7 for B concentrations larger 77 at.%. The low total CN above 77 at.% B is consistent with the formation of a B network structure. Further evidence for the B network evolution is given by the B concentration induced changes in partial CNs. Focusing on the metal coordination in Figure 2
b,c, a continuous decrease of metal-metal coordination is observed upon B addition. The decrease of Ta-Co coordination occurs predominantly between 40 and 70 at.%. B. Above 70 at.% B, the metal-metal CN is 0, since the metal-metal bonds are no longer formed and all remaining metal atoms form metal-B bonds. The opposite is observed for the metal-B coordination that increases from 0 to 9 for Co-B and from 0 to 10 for Ta-B in the composition range of 2 to 70 at.% B, being constant at 9 (Co-B) for larger B concentrations. The Ta-B CN above 70 at.% B scatters strongly, as only 3, 2 and 1 Ta atoms are present in the simulation cells for 77, 83, and 92 at.% B, respectively. Hence, these CN may not be significant due to lack of statistics. Finally, the B concentration induced changes in the B-B CN (Figure 2
d) give the strongest evidence for the formation of a B network. While the CN for B-B ranges from 0 to 1 for B concentrations lower 40 at.%, a jump of the B-B CN to 3.5 is observed at 40 at.%, which is consistent with the initiation of the B network formation proposed earlier based on the G(r) data shown in Figure 1
a. With further increasing B concentration, the CN increases up to 6 for 92 at.% B. The CN of 6 is close the CN of 5.6 for a perfect icosahedron in a crystalline structure [43
]. As an icosahedra-like structure with imperfect icosahedra has been predicted and experimentally verified for the amorphous Al0.75
], amorphous B4
], as well as for amorphous B [45
], the partial coordination numbers obtained here give evidence for the formation of an icosahedra-like B network starting to form at 40 at.% B.
Based on the short-range order and topology analysis carried out above, (Co6.8±3.9Ta)100−xBx is identified as metallic glass for B concentrations lower 40 at.% as the metals are predominantly coordinated with metals, while for B concentrations larger 70 at.% a network glass is present due to the presence of an icosahedral-like B network with metal atoms surrounded by B only. Within the concentration range of B concentrations between 40 and 70 at.%, the existence of a glass composite containing metallic glass and covalent glass-like regions is proposed, as the B network evolves in this region and the metal atoms are still coordinated with metals.
To compare physical and in-silico samples, G(r) of the ab initio models are depicted in Figure 1
a with open symbols. As the ab initio model can only cover the first coordination shell, bond distances smaller than 3.5 Å should be considered in the ab initio G(r). In the first coordination shell, however, the calculated G(r) exhibits peaks at the M-B, M-M and 2nd bond peak position of the experimentally obtained G(r). It is evident that the M-M peak splits into two peaks, indicating the presence of Co-Co and Co-Ta bonds. For large B concentrations, only the M-B are visible due to the low number of metal atoms in the cell. Considering the small cell size and the associated statistical limitations of the ab initio G(r), the ab initio configurations are consistent with the experiment. However, in contrast to the experimental G(r), also the B-B bonds at 1.71 Å for large B concentrations can be analysed. The B-B bond distances are consistent with icosahedral bonding, as reported in [13
To examine the medium-range order (MRO), the structure factor S(q) of (Co6.8±3.9
as a function of B concentration is shown in Figure 3
a. The S(q) shows clearly that samples are amorphous over the whole compositional range since Bragg peaks are absent. With increasing B concentration up to 62 at.% (Figure 3
b), the amorphous principal peak of the structure factor at 3.1 Å−1
shows a significant increase in full width at half maximum (FWHM), indicating the formation of less medium range ordered material. This observation is consistent with the higher configurational entropy notion at these B concentrations discussed in the context of the B concentration induced changes in glass transition temperature above. The vanishing double peak at 5.2 and 6.0 Å−1
between 22 and 59 at.% B underlines this enhanced disorder. In addition, a shoulder to the principal peak arises at 2.3 Å−1
and is clearly visible for B concentrations between 59 and 78 at.%, where the width of the principle peak increases strongly. The onset of the shoulder can already be seen in the asymmetry of the peak at 46 at.% B. This shoulder indicates that two types of medium-range order are present, being consistent with the glass composite regime proposed above.
3.3. Electronic Structure
In the next step, we critically appraise the glass composite formation notion by analysis of the electronic structure. According to the free electron model of Nagel and Tauc [47
], twice the Fermi vector kf
, which describes the Fermi sphere in amorphous materials, corresponds to the principal peak position of the structure factor qp
in a stable metallic glass:
Hence, the Fermi level Ef
can be experimentally determined from S(q) by inserting Equation (1) into Equation (2) [48
is the Planck constant divided by 2π and m the electron mass. As a comparison of experimentally and theoretically obtained absolute values of Ef
is not possible, the relative shift of Ef
as a function of B concentration is compared in Figure 4
. Based on ab initio data, Ef
is constant up to 63 at.% B and decreases for higher B concentrations. The experimentally obtained Ef
based on the free-electron model for metallic glasses [47
] remains constant for less than 62 at.% B and shifts to larger values for higher B concentrations. This deviation between the free electron model and the ab initio model indicates that the free-electron model is not applicable for B concentrations larger 62 at.%. Hence, the metallic character of the material is lost. This loss of metallic bonding character for B concentrations larger than 62 at.% is consistent with the proposal of a covalent network glass for large B concentrations made above.
The orbital overlap and bond strength give further insight into the change from metallic to covalent character by means of the integrated crystal orbital overlap population (ICOOP) [26
] and integrated crystal orbital Hamilton population (ICOHP) [27
] at Ef
. The latter is a measure of bond strength [28
]. Figure 5
a plots the partial ICOHP at Ef
for Co-B, B-B, Co-Co and Ta-B bonds. While the Co-Co contribution to the bond strength is low and constant up to 77 at.% (for higher B concentrations, Co-Co interaction cannot be found), the metal-B bond strength is between 1.5 and 2 eV, decreasing up to 32 at.% B and staying roughly constant for more than 32 at.% B. Significant changes are observed for the B-B bond strengths: Up to 32 at.%, the bonding contribution decreases down to −2.9 eV. Subsequently, the bond strength increases further up to –4.8 eV at 77 at.% and is constant for larger B concentrations (negative values are bonding, positive values anti-bonding contributions). The orbital overlap as quantified by ICOOP at Ef
b) is consistent with the ICOHP.
Summarizing the ab initio bonding analysis, the change of bonding from metal-metal to metal-B and B-B interactions is driven by increasing B-B bond strength and orbital overlap. Both the measure of bond strength ICOHP(Ef) and the integrated orbital overlap at Ef of B-B as a function of B concentration change slope two times at 32 at.% B and at 77 at.% B, being consistent with the metallic glass, composite, and B network glass regions defined above. The constant bond strength and overlap for B concentrations larger 77 at.% are consistent with the notion of a completely evolved B network in this composition range.
Investigating the B concentration induced changes in binding energy experimentally (Figure 6
), the results obtained by XPS are more complex to interpret. For samples with 16, 47 and 65 at.% B, the B 1s binding energy (Figure 6
a) exhibits a small but significant peak shift of 0.3 eV to larger binding energies consistent with the ab initio bonding analysis. The peak deconvolution indicates oxidation of the sample with 16 at.% B due to the presence of 16 at.% O in the sample. The B 1s peak, however, can neither be attributed to icosahedral nor to octahedral bonding or bonding in a solid solution, as the binding energies for the B 1s peak in the icosahedral AlMgB14
structure with 188.2 eV [49
], in Co-B bonds with 188.3 eV [50
], in Ta-B bonds with 188.7 eV [51
] and alpha-B with 188.0 eV [13
] are experimentally not resolvable. The B1s binding energy of icosahedrally bonded B in AlMgB14
is shown here as an example for B-rich solids.
The Co 2p3/2
peak (Figure 6
b) for samples with 16, 47 and 65 at.% B at a binding energy of 778.3 eV shows the presence of Co-B bonds as this binding energy is in between those for Co-B bonds in CoB (778.2 eV) and Co2
B (778.6 eV) [50
]. The observation of Co-B bonds is consistent with the ab initio bonding analysis. As for the B 1s peak, a small but significant peak shift of 0.2 eV towards higher binding energies between 16 and 65 at.% B is observed. A similar shift is obtained for the Ta 4f feature in the binding energy spectrum (not shown). The larger binding energy for the metals indicates an increased B coordination, consistent with the analysis of the coordination number.
It is well known that the soft-magnetism of Co-Ta-B is promising to reduce transformer losses [7
]. Hence, the influence of the enhanced B concentration on the volume magnetization is shown in Figure 7
. The total volume magnetization as well as the partial contributions of Co, Ta, and B based on ab initio data are compared with experimental data points of the saturation volume magnetization. The main contribution to volume magnetization comes from Co atoms, while B does not show a magnetic moment. With increasing B concentration, a decrease of magnetization is clearly visible due to the dilution of metal coupling by B. This decrease of magnetization is in agreement with literature [52
]. Above 63 at.% B the volume magnetization is approximately 0 due to the lack of metal-metal interactions, explainable by a B network surrounding the metals for high B concentrations. During the decrease from 0.1 to 0 µB
, a change in slope at 40 at.% B is observed, trending with the proposed onset of the region of the glass composite identified above.
Comparing the ab initio volume magnetization with experimental values, the measured near zero saturation magnetization for a sample with 75 at.% B agrees very well with the ab initio data. For a sample with 19 at.% B, the measured saturation volume magnetization of 0.098 µB
is 25 % larger than the ab initio volume magnetization. This enhanced volume magnetization may be caused by clustering of Co atoms in the physical sample in contrast to the homogenous distribution of Co atoms in the in-silico sample as well as by a different density. This clustering of Co atoms could lead to a phase separation as observed by Kontis et al. [11
]. The volume magnetization measurement (Supplementary Figure S2
) confirms the soft magnetism reported for the Co-Ta-B system [10
The B concentration induced transition from a metallic glass to a covalent B network glass has been investigated. It is revealed that these two composition regions are separated by a concentration region where the formation of a glass composite is inferred based on the glass transition temperature Tg
, topology, electronic structure, bonding and magnetization. Table 2
summarizes the critical B concentrations for the onset of a B network evolution as well as the beginning of a percolating B network based on each property.
Comparing the critical B concentrations in Table 2
, the critical B concentrations for the of onset of the B network evolution and percolation are consistent taking the large variety of quantities and methods as well as the discrete composition changes investigated into account. Hence, we can deduce from the mean concentration values in Table 2
is a metallic glass up to a B concentration of 39 ± 5 at.% B. For more than 69 ± 6 at.% B, the material is a network glass dominated by an amorphous icosahedra-like B network.
In between 39 ± 5 and 69 ± 6 at.% B, both metallic bonding and indicators for a B-network are observed. Hence, a glass composite is proposed consisting of metallically bonded regions and B network fragments. As the glass transition temperature changes in this composite regime, a material with defined processability may be designed by controlling the coordination and hence the fraction of icosahedral bonds. Additionally, this glass composite is promising in terms of mechanical properties, as it allows to combine the high strength and stiffness as well as plasticity of metallic glasses with the high stiffness and hardness of the amorphous borides. This combination of mechanical properties in the (Co6.8±3.9
system has been reported by Kontis et al. for a self-organized nanostructured material [11
]. The self-organized formation of a nanostructure may be enabled by the coexistence of metallic and covalently bonded regions in this concentration range.