Elemental pieces with purity higher than 99.9 wt% were used as the starting materials. The master alloy ingots with desired nominal compositions were prepared by arc melting under a Ti-gettered argon atmosphere in a water-cooled copper hearth. The alloy ingots were re-melted several times to ensure compositional homogeneity. The BMG cylindrical samples of 4 mm in diameter were fabricated by the copper mold casting of the arc-melted alloys. The details are described elsewhere^{[33, 34]}. Using the disc samples taken from the cross-sectional surface of the as-cast rods, the amorphous features of the as-cast cylinders were confirmed using X-ray diffraction (XRD) under a Rigaku D/max 2500 diffractometer (Rigaku, Tokyo, Japan) with monochromatic Cu Kα radiation. Commercial pure titanium (99.98%) and CoCrMo alloy were obtained in plate and bulk form, respectively. The cylinder specimens for MRI examination were machined into a desired dimension of 3 mm in diameter and 25 mm in length. For comparison, mechanical and thermal properties of the investigated BMGs are listed in Table 1.

Table 1

Table 1

Table 1 Mechanical and thermal properties given in literatures for the investigated bulk metallic glasses Properties Au-based[32] and [37] Cu-based[35] and [38] Zr-based[33] and [34] Ti-based[36] Critical diameter, Dc (mm) 5 6 10 7 Yield strength, σ y (MPa) 1049 2050 1600 2010 Youngs modulus, E (GPa) 74.4 102.1 82.8 100.4 Shear modulus, G (GPa) 26.45 37.4 30.2 - Bulk modulus, B (GPa) 132.31 126.5 104.1 - Poisson ratio, ν 0.406 0.365 0.367 - Glass transition temperature, Tg (K) 401 695 652 641 Crystallization temperature, Tx (K) 459 724 719 693 Density, ρ (g/mm3) 11.6 7.0 6.5 6.3

Table 1 Mechanical and thermal properties given in literatures for the investigated bulk metallic glasses

Note: Au-based = Au₄₉Ag_5.5Pd_2.3Cu_26.9Si_16.3, Cu-based = Cu_50.4Ni_5.6Ti₃₁Zr₁₃, Zr-based = Zr₆₁Ti₂Cu₂₅Al₁₂, Ti-based = Ti₄₇Cu₃₈Zr_7.5Fe_2.5Sn₂Si₁Ag₂.

The volume magnetic susceptibility (χ _v) of the investigated metals and phantom gel was measured using the MPMS-7S superconducting quantum interference device (SQUID, Quantum Design, San Diego, USA). A piece of sample of approximately 0.6 g in weight was taken from each metal. Then, the samples were polished and weighed. The measurements were conducted at room temperature and in the applied external magnetic field with a strength that increased from 0 to 3 T. The ratio of magnetic moment to applied magnetic field strength at 3 T was calculated as magnetic susceptibility. The measurements were repeated at least three times for a given alloy specimen.

A polymethyl methacrylate container with inner dimensions of 135 mm ×  90 mm ×  55 mm was used, and filled with the nickel-doped agarose gel as a phantom. The phantom consisted of de-ionized, distilled water, a stock solution of 10 mmol/L Ni(NO₃)₂ and a 2% polysaccharide agarose powder (BIOWEST, Spain)^[39]. A cylindrical BMG sample for MRI examination was embedded in the middle of the phantom, as shown in Fig. 1. The longitudinal axis of the phantoms was set both parallel and perpendicular to the static magnetic field (B₀) under a laser beam guide to ensure the nearly identical location for every imaging acquisition.

Fig 1.

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	Fig 1. Phantom used for in vitro MR examination showing that a cylinder specimen placed in the container center was embedded in the Ni-doped agarose gel.

MRI was performed in a 3-T system (HDx Twinspeed; GE, NY, USA) using an 8-channel transmit/receive head coil. Two types of radiofrequency pulse sequences were applied for imaging as follows: (1) T1-weighted, FSE pulse sequence; repetition time (TR), 400 ms; echo time (TE), 27.3 ms; bandwidth (BW), 19.2 kHz; matrix size, 512 ×  512; slice thickness, 1 mm; FOV, 150 mm ×  150 mm; number of excitations (NEX), 3 times; (2) GRE pulse sequence; TR, 20 ms; TE, 5.5 ms; BW, 31.2 kHz; matrix size, 512 ×  512; slice thickness, 1 mm; FOV, 150 ×  150 mm; NEX, 4 times; flip angle 60° . The frequency encoding direction started from the head and travelled down to the feet (HF), parallel to B₀ and the slicing moved from anterior to posterior.

According to the specification of ASTM F2119-07^[40], the extent of the artifact in MRI was defined as the distance from the specimen boundary to the fringe of the artifact in which signal intensity (SI) varied within ± 30% with respect to the mean value of SI. To determine the mean SI, it was necessary to fix four ROIs in each MR image, which should be as close to the specimen as possible without involving any artifacts. This methodology were used in several studies, and rendered a comparison with other metals under similar evaluations of artifacts^{[41, 42, 43]}. To avoid underestimation of artifacts, the imaging locations acquired through the specimens were chosen from a complete set of MR images that covered the largest or worst case of artifacts. Data in the images were processed and analyzed using the authorized data visualization software (Avizo Fire, VSG, USA). With the original 2D images at a number of individual slices, 3D renderings were constructed from all slices of MR images with the corresponding criteria.

Fig. 2 shows XRD patterns taken from the cross-sectional surface of as-cast 4-mm-diameter BMGs for four alloys, including Au₄₉Ag_5.5Pd_2.3Cu_26.9Si_16.3 (AuAgPdCuSi), Zr₆₁Ti₂Cu₂₅Al₁₂ (ZrTiCuAl), Cu_50.4Ni_5.6Ti₃₁Zr₁₃ (CuNiTiZr) and Ti₄₇Cu₃₈Zr_7.5Fe_2.5Sn₂Si₁Ag₂ (TiCuZrFeSnSiAg). For the Au-, Zr- and Cu-based alloys rods, no Bragg peaks from any crystalline phase are detectable but a broad diffusive diffraction maximum at 2θ  = 35° -50° , indicating the formation of monolithic metallic glasses. In the case of Ti-based alloy, however, trace amount of crystalline phase remains, showing visible diffraction lines overlapped with main diffusive peak, but the amorphous phase is predominant in structure.

Fig 2.

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	Fig 2. XRD patterns taken from cross-section surface of as-cast BMG cylinders of 4 mm in diameter.

As the representative, Fig. 3 displays fifteen successive slices of 2D MR images around the ZrTiCuAl BMG cylinder, which were taken with FSE and GRE sequences as shown in Fig. 3(a) and (b), respectively. The specimen was set in an orientation parallel to B_0. In the case of FSE, the artifacts consisted of the light region due to signal pile-up (hyperintensity) and the dark region caused by a signal loss (hypointensity), taken as a larger area fraction as shown in Fig. 3(a). The former could be the combination of in-plane and through-plane displacement of the signal from multiple locations to one location, while the latter could be due to dephasing or from the signal being shifted away from region^[3]. In contrast, only dark artifacts appeared in the GRE-mode images, as shown in Fig. 3(b). Additionally, a blooming ball shaped intensity void at two ends of the cylinder was more remarkable in comparison with the FSE scenario. As suggested, such a shape distortion was caused by the inhomogeneous dipole field^[5]. As indicated on all slices, the artifacts were distributed symmetrically from the geometric center of the specimen. Of the entire set of scanning images, the central image at the coronal plane exhibited the worst case, i.e., with the most severe artifacts.

Fig 3.

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	Fig 3. Successive 2D MR images of (a) FSE and (b) GRE at 3-T field strength for a ZrTiCuAl BMG cylinder. The cylinder specimen in the phantom was parallel to B0. Slices were distributed symmetrically around the specimen center.

In parallel, as the representative, Fig. 4(a) and (b) shows 2D MR images around the ZrTiCuAl BMG cylinder under a condition that the specimen was perpendicular to B₀, which were also taken with FSE and GRE sequences, respectively. Similarly, the artifacts consisting of signal void and signal pile-up appeared in the FSE image, whereas only signal void is present in the GRE image. It is noteworthy that the change in orientation of the longitudinal axis of specimen from parallel to perpendicular results in more severe distortion and exaggeration in the artifacts, if the rest of imaging parameters were fixed. As shown in Fig. 4(a), both the signal void and geometric distortion were extended over a wide range around the cylindrical specimen and wrapped it up tight into an elliptical shape, together with high signal rims partially surrounding the area of signal loss. Nevertheless, such high signal rims do not take place in the GRE case, as shown in Fig. 4(b).

Fig 4.

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	Fig 4. Successive 2D MR images of (a) FSE and (b) GRE at 3-T field strength for a ZrTiCuAl BMG cylinder. Cylinder specimen in the phantom was perpendicular to B0. Slices were distributed symmetrically around the specimen center.

Using these successive 2D slices, a 3D configuration of the artifact was constructed for each metal. Fig. 5 and Fig. 6 show a group of reconstructed 3D images for six investigated metals, together with 2D images with the largest artifact. The longitudinal axes of the metal cylinders were parallel and perpendicular to the B₀, respectively, as the two terminal conditions.

In contrast to the 2D images, the 3D image displayed a clear and complete artifact configuration. As shown in Fig. 5, the FSE case of the ZrTiCuAl as the typical, the signal void and signal pile-up were colored by the yellow and the red, respectively, which were equivalent to dark and light contrast in the 2D image, respectively. The artifact profile is less-changed in the middle of cylindrical sample. A significant distortion appears at the end of sample, showing a matchstick-like shape. The sections marked in the red alternatively appeared at the location of the top, middle and bottom of sample. It was noteworthy that the global shape of artifact configuration was markedly asymmetric along the longitudinal direction of cylinder from bottom to top. In the GRE case, the artifact configuration in 3D image displayed appearance of a “ dumbbell” shape. Similar to the 2D GRE images, signal pile-up as displayed by red area was unable to resolute even in the 3D GRE images.

Fig 5.

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Fig 5. Artifacts in 2D MR and reconstructed 3D images from six investigated metals. 2D MR images were taken in FSE (upper) and GRE (lower) at 3-T field strength. The direction of B0 indicated by the arrow was parallel to the specimen longitudinal axis. The 2D image was representative of maximum artifact in plane among the set of scanning slices. The 3D image was taken from anterior view, showing artifact configuration constructed in space.

It was of interest to note that the configurations for the CuNiTiZr, TiCuZrFeSnSiAg and CP-Ti were substantially the same as that for the ZrTiCuAl, even in both imaging sequences. But, it is evident that CoCrMo alloy generated more appreciable distortions and artifacts in both the FSE and GRE images, in which the extent of image degradation was at a more detrimental level with respect to all BMGs and CP-Ti. Location of the signal hypointensity and hyperintensity were almost comparative to that of the ZrTiCuAl, CuNiTiZr, TiCuZrFeSnSiAg and CP-Ti. Nevertheless, the distortion location seems irrespective of distortion severity and artifacts volume. By carefully viewing, it is noticed that the signal pile-up, as displayed by red section in the 3D GRE image and surrounded by signal void, was slightly enhanced, as shown in Fig. 5 and Fig. 6, which did not occur at the remainder metals.

Owing to the diamagnetic feature, Au-based BMG manifests significantly distinct scenario. Its artifact configuration is completely reversed with respect to the other BMGs. As indicated, the artifacts signs such as signal locations, and the direction distortions are opposite to paramagnetic BMGs. Compared with the ZrTiCuAl BMG, matchstick-like configuration of artifact in reconstructed FSE image for the AuAgPdCuSi exhibits upside-down feature in all three dimensions, as shown in Fig. 5. As is well known, artifacts extent in MRI is mainly determined by homogeneity of static magnetic field. In the current situation, difference in magnetic susceptibility between adjacent substances, such as metals and Ni-doped agarose gel phantom, yielded inhomogeneous magnetic field, and then perturbation. The induced disturbance alters the static magnetic field, either by strengthening the field via pulling the static field lines into paramagnetic metal or by weakening the field via deflecting the lines away from diamagnetic metal^[44]. This is a reason why the opposite artifacts configurations in space are generated by the diamagnetic and paramagnetic metals.

In a scenario where the longitudinal axes of cylinders were perpendicular to B₀, the shapes and extents of either distortions or artifacts in the images were significantly different from the case parallel to B₀ under identical imaging conditions, as shown in Fig. 6. Typically, artifact configuration in the FSE 3D image displayed a belly-shaped deformation, engulfing the cylindrical specimen, which made it impossible to delineate the contour and location of the specimen. As such, the configuration consisted of red and yellow parts that were associated with the hyperintensity and hypointensity of artifacts, respectively. As indicated, volume of yellow part was larger by approximately a factor of two to four with respect to the red part. In contrast, the hyperintensity effect is insignificant in the GRE 3D image, as shown by the nearly invisible response to the red-colored.

Fig 6.

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	Fig 6. Artifacts of six investigated metals in FSE (upper) and GRE (lower) images at 3-T field strength presented in 2D and reconstructed 3D views. Longitudinal axis of specimen was orientated perpendicular to B0. 2D and reconstructed 3D images showing maximum extent and spatial configuration of artifacts.

Similar to the situation that the cylinder specimens were set parallel to the B0, artifact appearance of the ZrTiCuAl, CuNiTiZr, and TiCuZrFeSnSiAg were nearly similar to that of the CP-Ti, as shown in Fig. 6. For the CoCrMo alloy, however, geometric distortion and spatial configuration of the artifact in the 2D and 3D images were much more severe with respect to the five remainders by orders of magnitude in terms of either maximum area or total volume.

Fig. 7 displays a plot of total artifacts volume for the specimen set in parallel to B₀ against the case in perpendicular to B₀ for four BMGs and CP-Ti, which were imaged with both pulse sequences. It is indicated that the artifacts volume for the situation perpendicular to B₀ generally scale with the volume parallel to B₀. As a general trend, artifacts volume in the case perpendicular to B₀ is approximately three-folds larger than that parallel to B₀, irrespective of the imaging sequences. Such a relationship is meaningful to estimate the artifact severity when the orientation of cylinder-shape implants with respect to the B₀ situates between the two terminal conditions.

Fig 7.

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	Fig 7. Plot of total artifacts volume for the specimens imaged parallel to B0 against the case perpendicular to B0 for the investigated BMGs and CP-Ti. The images were acquired with FSE and GRE sequences at 3-T field strength. Dash lines represent the linear fitting of data.

As is well documented^{[11, 43, 45, 46, 47, 48, 49, 50]}, severity of susceptibility artifact is strongly dependent of imaging pulse sequence. The FSE sequence, especially when performed for a short echo time, is less sensitive to susceptibility effects than the GRE, because the GRE mode is absent from multiple refocusing 180° radiofrequency pulses which can reverse intravoxel dephasing, therefore its signal attenuation is more apparent ^{[45, 50, 51]}. In this work, it was confirmed again that the artifact in GRE images was more severe than that in FSE images, as shown in Fig. 5 and Fig. 6. Using all data of the artifacts volume for four BMGs in two-sequence images under a given specimen conditions, we suggested a correlation of artifact volume between two sequences, independent of the materials and orientation to B₀, as shown in Fig. 8. It is interesting to note that a good linear relationship between two situations was present. With linear fitting for these data, a master equation was attained as:

Fig 8.

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	Fig 8. Plot of total artifact volumes in GRE sequence against ones in FSE sequence for BMG materials, with all of measured data, independent of orientation relative to B0. Straight line represents a fitting

This indicates that, in an empirical sense, artifact volume of FSE images was approximately 20% less than that of GRE images. Such a simple correlation can be used as a helpful utility to estimate the artifact extent as long as any one sequenced image is available in the clinical diagnosis and material screening.

As noticed, among the six investigated metals, CoCrMo alloy exhibits the largest artifact extent, approximately 3-fold larger than that of CP-Ti as assessed by the total volume in 3D. On the contrary, Au-based BMG manifests the smallest artifact. Ti-based BMG is comparative to unalloyed crystalline CP-Ti. It is somewhat surprising to note that artifact extent of Zr-based BMG is approximately double larger than that of Au-based one, but is a half level of either CP-Ti or Ti-based BMG. While the Cu-based BMG situats between the Zr- and the Ti-based BMGs. For comparison, Fig. 9 shows a material ranking of artifact severity in terms of artifact volumes in 3D images under a given imaging conditions and orientation to B₀, together with CP-Ti as control material.

Fig 9.

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	Fig 9. Comparison of total artifact volumes in all imaging conditions of BMG materials with CP-Ti

The measured χ _v values of six investigated metals are listed in Table 2, as well as the value of agarose gel used as the phantom. As indicated, the χ _v of agarose gel in the current work is the nearly identical as the value provided by Imai et al.^[41], as well as to the value of human tissues [∼(-11.0 to -7.0 ppm)], whole blood (-7.9 ppm) and water at 37 ° C (-9.05 ppm), as summarized in Ref. ^[4]. Additionally, the χ _v value of CP-Ti was comparable to the previously presented value, χ _v = 182 ppm ^{[4, 52]}. The reason for minor difference between the data is probably caused by the differences in testing conditions or material purity. As noticed, the χ _v of Au-based BMG is more negative than that of the Au-xPt-Nb (5 ≤   x  ≤  40) crystalline alloys with the χ _v = -9 ppm ^[17]. The χ _v value of CoCrMo alloy is five-fold larger than that of CP-Ti. Additionally, the χ _v of Zr₆₁Ti₂Cu₂₅Al₁₂ BMG is comparative to that of Zr_52.5Ti₅Cu_17.9Ni_14.6Al₁₀ BMG (χ _v = 109 ppm), presented in Ref. ^[31]. It is surprising that the CuNiZrTi BMG exhibits the χ _v greater than that of the ZrTiCuAl even though the based metal Cu is diamagnetic. Obviously, ferromagnetic Ni element in the CuNiZrTi alloy plays a predominant role.

Table 2

Table 2

Table 2 Volume magnetic susceptibility of the investigated metals and gel used as phantom

Table 2 Volume magnetic susceptibility of the investigated metals and gel used as phantom

As is well-known, a difference in magnetic susceptibilities between adjacent objects, such as tissue and implanted metal, is a physical source to determine the severity of metal-induced artifacts in MRI. To reveal the correlation of artifact extent with the difference in magnetic susceptibilities given by Δ χ _v  =  χ _v -χ _v', where χ _v' is the value of agarose gel, Fig. 10 shows a plot of artifact volume in the MR images against Δ χ _v. Because the χ _v of the CoCrMo alloy is much greater than that of the others by several times, data in Fig. 10 only focused on the four BMGs, and then covered an interest range within 30-180 ppm for the Δ χ _v.

Fig 10.

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	Fig 10. Correlation of total artifacts volume in all imaging conditions with the difference in magnetic susceptibility between metals and agarose gel, Δ χ v, for four BMGs and CP-Ti

As shown in Fig. 10, under acquisition conditions parallel to B₀, the artifact extent was less sensitive to the increase in the χ _v values, even though the artifact in GRE image was somewhat severe with respect to that in the FSE case. In contrast, under perpendicular acquisition, artifact extent exhibits a stronger dependence on the Δ χ _v or material susceptibility. In other words, less artifact extent is consistent with lower susceptibility of the metal. As such, the Au- and Zr-based BMGs with a lower χ _v exhibits more MRI-compatible even superior to the CP-Ti, let alone the CoCrMo alloy with a higher χ _v. In this sense, it is conclusive that the element susceptibility is a predominant factor in designing the MRI-compatible alloys.

In addition, it was suggested that some physical properties such as elastic moduli of a BMG can be estimated by virtue of the approach that the averages of property can be weighted by volume fraction of constituent elements^[53], namely, a “ rule of mixture” based on its structure feature of a chemically-uniform single phase. Similarly, susceptibility of the investigated BMGs can also be estimated with Wiedemann's additivity law^[54]. This law is a consequence of the superposition principle for electrostatic and magnetic fields that specifies that the field at a given point in space is the linear vector sum of contributions from all sources. Wiedemann's law states that the overall magnetic susceptibility of a mixture is the weighted sum of the magnetic susceptibilities of the constituents, weighted according to their relative volumes of occupation of the mixture. Thus, in mathematical form it is written as:

where φ _i denotes the volume fraction of the mixture occupied by component i, whose volume magnetic susceptibility is χ _vi, c_i, M_i, ρ _i and c_j, M_j, ρ _j, represent the molar fraction, molecular weight and density of component i and j, respectively.

As such, for the Au- and Zr-based BMGs containing diamagnetic and paramagnetic components, the χ _v was calculated using Eq. (2), as listed in Table 2. As noted, the calculated χ _v of Au- and Zr-based BMGs is 87% and 13% lower than the experimental value of respective -38 ppm and 95 ppm, which, however, are substantially comparative to the value of host metal such as -34 ppm for Au and 109 ppm for Zr. It implies that the magnetic susceptibility of a BMG is basically dominated by its host metals if no incorporation of ferromagnetic elements. In other words, the magnetic susceptibility of either diamagnetic or paramagnetic BMG estimated with Wiedemann's additivity law manifests an underestimation with respect to the measured real value. On the contrary, in the cases of Cu- and Ti-based BMGs containing ferromagnetic Ni (χ _v  = 6 ×  10⁸  ppm) and Fe (χ _v  = 2 ×  10¹¹  ppm) elements, Wiedemann's law is no longer adequate since the calculated χ _v is dominated by the Ni and Fe because of their overwhelming susceptibility superiority.