Exploring the promising frontiers of barium hexaferrite and barium titanate composites for electromagnetic shielding applications

This study provides a comprehensive synthesis and meticulous examination of barium hexaferrite (BHF), barium titanate (BT), and their respective nanocomposites, unveiling their potential in specific applications, including electromagnetic interference shielding. The successful formation of BHF and BT was confirmed through Fourier-transform infrared (FTIR) spectroscopy and X-ray diffraction (XRD) analyses, revealing distinct absorption peaks indicative of the tetragonal configuration of BT and the BHF’s crystal structure. Scanning electron microscopy (SEM) depicted the unique morphologies and dispersions of particles in the synthesized nanocomposites, with BHF appearing larger (~ 82 nm) than BT (~ 50 nm). Vibrating sample magnetometry (VSM) findings exhibited an increased resistance to demagnetization with the addition of BT, despite a slight decline at 75% BT concentration due to the non-magnetic nature of BT dominating. Uniquely, the study presented an in-depth analysis of the composites’ conductivity, detailing their non-monotonic behavior across a frequency range. A detailed investigation into the complex permittivity and permeability revealed the composite’s enhanced ability to store and dissipate both electrical and magnetic energy, a function influenced by the concentrations of BT and BHF. A pivotal highlight of this research was the significant achievement of a reflection loss (RL) value of − 45 dB at 9.3 GHz for the composite with 75% BHF, suggesting the composite’s potential as an effective microwave absorber. This study represents a significant step toward designing and optimizing nanocomposites for specific applications in the realm of electromagnetic materials.


Introduction
In contemporary times, the realm of technological advancement is in a constant state of flux, propelled by swift innovation and the increasing assimilation of electronic and wireless communication systems into our daily routines.The extensive use of electronic devices has resulted in electromagnetic radiation.This inconspicuous ecological derivative possesses the capacity to interfere with the operational efficacy of our electronic infrastructure.Electromagnetic interference (EMI) presents considerable obstacles to the functionality and durability of electronic devices and the preservation of data and confidentiality.In light of this context, the scientific investigation of materials for applications related to electromagnetic interference and electromagnetic shielding is of paramount significance [1][2][3][4].
The process of electromagnetic shielding entails the utilization of materials that possess the ability to obstruct or reduce the intensity of electromagnetic fields.By manipulating materials' physical and chemical properties, scientists can create products that efficiently absorb, reflect, or scatter electromagnetic radiation.Various materials provide varying degrees of protection.Metals exhibit exceptional conductivity and shielding properties against electromagnetic radiation owing to the presence of their unbound electrons [5][6][7][8].Nevertheless, their practicality is sometimes limited by their weight, susceptibility to corrosion, and inadequate shielding against low-frequency magnetic fields.As a result, researchers have been investigating various substances, including conductive polymers, composites, and carbon-based materials, that provide advantages such as reduced weight, resistance to corrosion, and exceptional shielding efficacy over a broad range of frequencies [9][10][11].
Barium hexaferrite (BaFe 12 O 19 ) and barium titanate (BaTiO 3 ) are two intriguing materials that exhibit significant potential for shielding against electromagnetic interference (EMI).This is attributed to their distinctive magnetic and dielectric properties, respectively.Barium hexaferrite is a magnetic substance well known for its exceptional magnetic anisotropy, saturation magnetization, and chemical durability.The traits mentioned above render it a prime contender for mitigating and assimilating magnetic fields, thereby furnishing efficacious electromagnetic interference (EMI) shielding.Nonetheless, its insulating properties render it comparatively inefficient regarding electric field protection.Barium titanate is a dielectric material widely recognized for its high dielectric constant.It is a promising contender for electric field shielding.The material's ferroelectric characteristics and ability to adjust phase-transition temperature render it a viable option for applications necessitating EMI shielding properties contingent on frequency.Nevertheless, the efficacy of its magnetic field shielding is comparatively inadequate [12][13][14][15][16][17][18].
To address the constraints associated with the individual use of these materials, scholarly investigations have been focused on the amalgamation of composites that integrate the favorable characteristics of both materials [19].Incorporating barium hexaferrite particles within a barium titanate matrix enables the production of a composite material that provides electric and magnetic shielding capabilities.This composite material has the potential to utilize the superior magnetic permeability of barium hexaferrite to shield against magnetic fields, as well as the high dielectric constant of barium titanate to shield against electric fields [20,21].Additional enhancements have been achieved by incorporating supplementary materials into these composites, including carbon-based or conductive polymers, resulting in improved magnetic properties and electrical conductivity [21][22][23].The amalgamation of these strategies can yield a noteworthy enhancement in the shielding effectiveness (SE) of electromagnetic interference (EMI) over a wide range of frequencies.This presents a versatile, efficient, lightweight alternative for EMI shielding applications.Optimal impedance matching is crucial in achieving maximum absorption and minimizing the reflection of electromagnetic waves.This can be achieved by fine-tuning [24,25] barium hexaferrite particles' concentration, size, and distribution in the barium titanate matrix.
Investigating composites comprising barium hexaferrite and barium titanate represents a promising area of study within materials science.Utilizing these materials can offer effective shielding against electromagnetic interference (EMI) across multiple frequencies.This can enhance the safeguarding of vulnerable electronic devices, ensure the preservation of data integrity, promote human well-being, and contribute to maintaining national security.

Preparation of barium hexaferrite (BHF)
The present investigation employed an uncomplicated auto-combustion method [26,27] to synthesize nanoparticles of BaFe 12 O 19 (BHF).A precisely balanced mixture consisting of one mole of Ba(NO 3 ) 2 (barium nitrate), 12 moles of Fe(NO 3 ) 3 •9H 2 O (ferric nitrate), and 13 moles of C 6 H 8 O 7 (citric acid) was formulated.Following this, 250 ml of distilled water was introduced into the solution, and the amalgamation was subjected to agitation for 20 min utilizing a hot plate magnetic stirrer.The pH was modulated to a neutral value of 7 through the addition of NH 4 OH, which is an ammonia-based solution.Subsequently, the concoction underwent incessant agitation.The temperature was gradually elevated to 110 °C and sustained until the dissolvent dissipated, resulting in a remainder.Subsequently, the resultant substance underwent a sintering process at a temperature of 1100 °C for 4 h [28].

Preparation of barium titanite (BT)
The tartaric precursor method [29,30] was employed to synthesize nanoparticles of BaTiO 3 .The present study involves the precise weighing and mixing of a set of reagents, namely barium nitrate (Ba(NO 3 ) 2 ), titanium dioxide (TiO 2 ), and tartaric acid (C 4 H 6 O 6 ), in a predetermined ratio of 1:1:3 on a molar basis.Following the dissolution of the powders in distilled water and homogenization by stirring for 30 min at ambient conditions, the mixture underwent heating at 80 °C for 2 h to facilitate the evaporation of a significant portion of the water.At approximately 120 °C, the amalgamation transforms into a thick gel that undergoes spontaneous combustion, resulting in the formation of nanoparticles in the form of a fine powder.The powder underwent a 24-h pre-sintering process at 300 °C and a 4-h sintering process at 1100 °C.

Composites preparation
The study involved the preparation of three composite samples comprising (X) wt% BT/(100-X) wt% BHF, where X represents 25%, 50%, and 75%.The samples were created by Page 3 of 11 638 carefully mixing the desired weight ratios of BT and BHF.The powders were carefully weighed and well mixed utilizing an agate mortar.
Following the preparation of BT, BHF, and composite samples, 30 wt% of the target weight ratio of each sample in powdered form was combined with 70 wt% of high-purity paraffin (wax), where this ratio gave the best homogenous distribution in the paraffin matrix and subjected to heating at 50 °C with thorough agitation.Subsequently, the mixture was molded in a rectangular shape of dimensions 22.8 × 10.1 × 2 mm 3 to facilitate the quantification, computation, and assessment of the electromagnetic shielding characteristics of all specimens.It is worth mentioning that the prepared sample's thickness was 2 mm.A simulation was done by Matlab program for other thicknesses (1, 3, 4, and 5 mm) to obtain at which thickness we can get low reflection loss (RL) from the samples under investigation.This was accomplished by measuring the electrical and magnetic parameters necessary for the evaluation.

Characterizations
The composition of the prepared samples was analyzed through X-ray diffraction (XRD) using an Empyrean Panalytical diffractometer at room temperature.The diffraction was performed within the range of 20° ≤ 2θ ≤ 80°, with Cu-Kα radiation and a wavelength of 1.54 Å.The composition of the samples was evaluated through the utilization of Fourier-transform infrared spectroscopy (FTIR), which was carried out using a JASCO FT/IR4100 Series apparatus that measured within the range of 4000-300 cm −1 .The scanning electron microscope (SEM) model Zeiss EVO 10, Oberkochen, Germany, was used to analyze the synthesized samples' surface microstructure.The magnetic properties of the prepared samples were detected at room temperature using a Lake Shore 7410 vibrating sample magnetometer (VSM) with an applied magnetic field of up to ± 2T.
The study utilized a Rohde & Schwarz ZVA67 vector network analyzer (VNA) equipped with a waveguide WR-90 to investigate the electromagnetic shielding characteristics in the X-band frequency (f) range (8.2-12.4GHz) by analyzing the electrical and magnetic parameters.The Vector Network Analyzer (VNA) underwent a complete calibration process for all S-parameters, including S 11 , S 12 , S 22 , and S 21 .The real and imaginary components of permittivity (ɛ′ and ɛ″, respectively) and permeability (μ′ and μ″, respectively) were determined through the utilization of the Nicolson-Ross-Weir algorithm in conjunction with the transmission/reflection line method, utilizing the observed S-parameters.The equations utilized for the computation of the dielectric loss (tan δ E ), magnetic loss (tan δ M ), and conductivity (σ) are as follows [31,32]: The symbol ɛ o denotes the permittivity of free space, which has a value of 8.85 × 10 -12 F/m.
The RL measures the microwave absorption capacity of the material utilized for shielding against electromagnetic interference.The calculation of the RL (reflection loss) in decibels for all the prepared samples was performed using the following equation [2,31]: The parameter denoted by Z in represents the input impedance of a given material utilized for electromagnetic interference shielding.At the same time, Z o refers to the impedance of the surrounding free space.The calculation of the input impedance (Z in ) can be derived using the following equation [2,31]: The complex permeability, denoted as μ r , and the complex permittivity, denoted as ɛ r , of the absorber shield material are represented in the given equation.The thickness of the material is denoted by d, and the velocity of light in air is denoted by c.
638 Page 4 of 11 in the BT sample, which may be related to the orthorhombic (BaTi 4 O 9 ) phase with space group Pmmn [38,39] according to JCPDS card (PDF file) no.01-077-1345.From the main peaks of BHF and BT, the average crystallite size was calculated using Scherrer's formula [40,41], establishing a relationship between the crystallite size and the line broadening measured by the peak's full width at half-maximum (FWHM).The average crystallite size of the BHF and BT was determined to be 82 nm and 50 nm, respectively.The peaks observed in the XRD patterns of BHF and BT were also present in the prepared BHF/BT composites, indicating the presence of BT and BHF nanoparticles in the composite material.

Fourier-transform infrared (FTIR) spectroscopy discussion
The FTIR spectrum of all samples analyzed in this investigation is depicted in Fig. 2. The FTIR spectrum analysis of the BHF sample revealed several key transmittance bands.A band around 3444 cm −1 was associated with H-O vibrations of water molecules.Key transmittance bands of BHF were observed at around 595 cm −1 , attributed to the stretching vibration of metal ions at tetrahedral sites.Additional bending of metal ions at octahedral sites was observed at 432 and 333 cm −1 [42,43].The spectral band within the range of 1556 cm −1 is commonly associated with oxygen-metal bridging associations, and the transmission band attributed to metal-metal (M-M) interaction was observed at approximately 1417 cm −1 .A spectral band around 1639 cm −1 may indicate nitrate residue or the bending mode of water molecules, or alternatively, it may be due to the stretching vibrations of the N-H group of ammonia.The observed peaks around 2900 cm −1 can be attributed to the stretching vibration of C-H bonds, likely originating from citric acid.These observations confirmed the successful synthesis of BHF.
The FTIR findings, akin to those of XRD, corroborate the productive synthesis of BHF [42,43].The FTIR analysis reveals the emergence of the tetragonal configuration of BT by detecting distinct absorption peaks at 443 cm −1 and 592 cm −1 .The observed peaks are indicative of the stretching and bending vibrations exhibited by the oxygen and titanium atoms within the crystal lattice, thereby corroborating the perovskite-type configuration of the BT.Moreover, these peaks serve as evidence for the crystallization of the BT nanoparticles.Furthermore, the absorption band observed at 1018 cm −1 is attributed to the vibrational mode of C-O-Ti present in tetra butyl titanate.The spectral feature observed at 1647 cm −1 is ascribed to the stretching vibration of the C=O functional group.Additionally, the spectral peaks located at 1419 cm −1 and 858 cm −1 are assigned to the anti-symmetric stretching and bending vibrations of CO 3 moieties.The observed peaks can be attributed to tiny and certain quantities of carbonate, believed to have originated from the reaction between tartaric acid and barium titanate during preparation.Although the XRD analysis does not reveal the presence of these carbonates, they can be detected in the FTIR spectrum at sufficiently low concentrations.This has been reported in previous studies [21,[44][45][46][47][48][49][50].The FTIR spectrum analysis of the composite samples showed primary transmission bands consistent with their individual constituents, pure BHF and BT.This indicates that the characteristic chemical bonds and functional groups of both BHF and BT were preserved in the composite samples, confirming the successful preparation of the composites.

SEM discussion
The findings of an SEM investigation of the morphology and surface of BHF, BT, and BHF/BT composites with varying weight ratios are shown in Fig. 3. Based on the average crystal sizes calculated from the XRD; it is expected to find particles with two distinguishable sizes.BHF particles would appear larger (around 82 nm), while BT particles would be smaller (around 50 nm).The distribution of these nanoparticles could vary depending on how well the two powders have been mixed.The shape or morphology of the particles would depend on the synthesis method used to prepare the BHF and BT powders.BHF particles usually form hexagonal platelets or prisms.
In contrast, BT particles may appear as cuboids or spheres, depending on the synthesis conditions [51,52].BHF and BT nanoparticles tend to aggregate due to their high surface energy.Therefore, some clusters or aggregates of particles in the SEM images are observed.Depending on the weight ratios of the two powders, a more or less uniform surface is seen.If one type of nanoparticle is significantly more prevalent, it could create a 'background' on which the other type of nanoparticle is scattered.Areas of the image corresponding to elements with a higher atomic number will appear brighter (whiter) in SEM images.This is because elements with higher atomic numbers backscatter electrons more strongly.BHF and BT have different elemental compositions, but since both compounds contain barium and oxygen, the difference might not be substantial.However, iron in hexaferrite could make these particles appear slightly brighter [53].

VSM discussion
The magnetic characteristics of both the pure BHF and the composite materials were assessed through the utilization of a VSM technique, as illustrated in Fig. 4. Table 1 presents the magnetic parameters, namely the coercivity (H c ), remnant magnetization (M r ), saturation magnetization (M s ), and squareness ratios (S).By adding more BT to the (BHF) sample, coercivity (H c ) increases, indicating an increased resistance to demagnetization.However, it decreases slightly when BT is 75%, which could be due to the dominance of BT's non-magnetic nature influencing the overall magnetic behavior [54]-also, adding more BT, both M r and M s decrease, which could be expected as BT is not ferromagnetic, reducing the overall magnetic strength of the composite.The squareness ratio remains relatively constant across the samples.This might suggest that the ferromagnetic behavior of the material remains similar as the BT is added, even though the overall magnetization decreases.
As per previous studies, a high degree of anisotropic energy (H a ) is observed when the saturation magnetization is low [1,31,32,55].Augmented anisotropic energy leads to an amplified absorption of electromagnetic waves in highfrequency spectra [56].

Conductivity
Figure 5 shows the behavior of conductivity (σ) with changing frequency.All the results are non-monotonic and sometimes increase and decrease with no specific trend.The conductivity values change from 0.001 to 0.9 Ω −1 m −1 , the pure BHF has the lowest conductivity values, and the pure BT has the highest values.The non-monotonic behavior change in conductivity with frequency can be according to different factors (1) dielectric resonance: at certain frequencies, the materials may exhibit dielectric resonance, causing a rise and fall in conductivity, resembling a sine wave.This resonance is due to the polarization mechanisms in the materials; (2) magnetic resonance: in the case of bhf, a well-known magnetic material, magnetic resonance may occur at certain frequencies.This could lead to changes in the effective conductivity due to coupling between electric and magnetic Fig. 4 VSM loops of all samples that contain magnetic material properties; (3) interference patterns: the observed interference could be due to overlapping resonances or competing conduction mechanisms in the composite materials.The composites will have contributions from BT and BHF, which could interact in non-trivial ways, leading to the observed pattern; (4) relaxation processes: the non-monotonic behavior could indicate different relaxation processes occurring in the material.These processes might be due to intrinsic factors (e.g., defects, grain boundaries) or extrinsic factors (e.g., temperature, humidity).As frequency changes, different relaxation processes may dominate, leading to the observed pattern, and (5) composite material complexity: the weight ratio of BT to BHF in the composite also plays a role.Different weight ratios result in different microstructures, leading to varying electrical conduction pathways and, thus, different conductivities.
BT is a ferroelectric material with a high dielectric constant and good electric conductivity, especially when doped.Its high permittivity and good conductivity can be attributed to its crystal structure and defects, such as oxygen vacancies, which can act as charge carriers and thus contribute to electrical conduction [57].On the other hand, BHF is a ferrimagnetic material that is not as conductive [58] as BT.It is widely used in magnetic applications, but its electrical properties are not as prominent.The BHF crystal structure does not favor the formation of charge carriers to the same extent as BT.When you mix these two materials, the conductivity will fall between these two extremes, dependent on the weight ratio of BT to BHF.The composite's conductivity should theoretically increase as the weight percentage of BT increases due to its superior conductivity.However, the actual behavior can be much more complex, especially if there are interactions at the interface of these two materials in the composite or a percolation threshold.

Electromagnetic properties
As shown in Fig. 6, the complex permittivity and permeability, represented as ε = ε′ − jε′ and µ = µ′ − jµ′′, are the primary parameters that characterize a material's response to an applied electromagnetic field.They comprise real and imaginary parts, with the real part correlating with the material's ability to store electromagnetic energy and the imaginary part relating to the energy losses.Upon analysis, the real part of the permittivity exhibits an increase from 2.3 to 3.3.This change signifies an increased ability of the composite to store electrical energy in the presence of an electric field.The storage ability of a material is often linked Fig. 6 The relation between the real part of permittivity (ɛ′), the imaginary part of permittivity (ɛ″), the real part of permeability (μ′), the imaginary part of permeability (μ″), dielectric loss (tan δ E ), and magnetic loss (tan δ M ) versus frequency of all samples under investigation 638 Page 8 of 11 to its conductivity.In this case, including the BT component, which has a higher permittivity, enhances the overall conductivity and polarizability of the composite, thus driving up the real permittivity [31,32].
Conversely, the imaginary part of the permittivity, indicative of dielectric losses, increases from 0.1 to 0.9.This escalation suggests a rise in energy dissipation as heat during polarization and depolarization processes.This increased energy loss corresponds with the elevated conductive nature of BT in the composite [1,2,59].
Turning to the permeability behavior, the real partindicative of a material's magnetic storage capabilitychanges from 0.9 to 1.1.This slight increase suggests the composite's boosted capability to store magnetic energy by adding non-magnetic BT [1,32].Meanwhile, the imaginary part of the permeability, which points to magnetic losses, significantly increases from 0.2 to 1.This change is driven by the inherent property of BHF, which is prone to high magnetic losses, often triggered by domain wall displacement [57,60].When examining the observed electrical and magnetic losses, it is clear that the composite changes its loss tangents, with the electrical losses shifting from 0.05 to 0.4 and the magnetic losses moving from 0.2 to 1.In essence, these losses represent the inefficiencies in energy storage, where the stored energy is dissipated as heat.
For more specifications, the dielectric losses (electrical losses) represent the inefficiencies during the polarization process within the material.In contrast, the magnetic losses correspond to the inefficiencies during magnetization.The increase in these losses can be attributed to the high conductive nature of BT and the high magnetic losses of BHF, respectively [31,32,59].Throughout this analysis, it is evident that the behavior of the composite's electromagnetic properties is a function of its BT and BHF concentrations.The nuanced understanding of these dependencies allows us to manipulate the properties of such composites, enabling their customization for specific applications in a wide range of fields, from telecommunications to materials science.

EM shielding properties
In electromagnetic materials science, RL is a paramount metric for evaluating the effectiveness of microwave absorbers [55,61,62].This parameter provides insights into how much of the incident electromagnetic wave is reflected rather than absorbed by the material.An RL value of − 10 dB represents a scenario where 10% of the energy is reflected, and 90% is absorbed.In contrast, an RL of − 20 dB signifies a mere 1% reflection, with the material absorbing 99% of the incident energy [31,55].Hence, the material should ideally exhibit an RL value of ≤ − 10 dB to qualify as an efficient microwave absorber.
The RL values of the developed composites, calculated by Eqs.(4,5), reflect how the RL varies across different sample thicknesses, from 1 to 5 mm.As demonstrated in 7, the absorption peak escalated from − 3.5 dB to an impressive − 45 dB at 9.3 GHz for a 75% BHF composition.
This observed trend might be attributed to the high permittivity values associated with including BT in the composite.The heightened permittivity could lead to impedance mismatch, thereby increasing surface reflections [31].As a result, high permittivity, coupled with poor impedance matching, generally leads to increased reflection loss.
Contrarily, the composite comprising 25% BHF exhibited remarkable absorption results, which might be ascribed to a favorable interplay between the dielectric and magnetic losses within the composite [59].This outcome emphasizes the potential role of judicious compositional manipulation in achieving optimal microwave absorption characteristics.
Interestingly, Fig. 7 also reveals that the reflection loss curve for composites with lower BT concentration shifts towards lower thickness values with increasing frequency.This pattern implies that the composite exhibits a phenomenon of electromagnetic phase cancellation within the X-band frequency range.Furthermore, the observed inverse relationship between frequency and absorber thickness is consistent with the theory of electromagnetic phase cancellation, leading to high microwave absorption [63].In conclusion, the 25% BHF composite achieved notable RL values, reaching − 43 dB at 11.8 GHz and 9.3 GHz for 4 mm and 5 mm thicknesses, respectively.This performance underscores the composite's potential utility in applications necessitating high microwave absorption.
The understanding gained from this RL analysis significantly enriches our knowledge regarding the electromagnetic behavior of the BT/BHF composites.Future research efforts should focus on leveraging this understanding to optimize the composites further for specific applications in the field of electromagnetic materials science.

Conclusions
This investigation has exhaustively studied the magnetic, dielectric, and electromagnetic shielding properties of the nanocomposites made from barium hexaferrite (BHF) and barium titanate (BT), with an emphasis on understanding their interplay and possible tunability.The study has laid out clear evidence that the magnetic and dielectric characteristics of the composites can be significantly modulated by varying the concentrations of BHF and BT.A comprehensive exploration of magnetic hysteresis behavior revealed increased coercivity with the addition of non-magnetic BT.This is a noteworthy discovery as it provides a clear path for the modulation of magnetic properties by adjusting the composition of these two materials.Regarding conductivity, the research brought forth interesting insights into the influence of the composite's complexity and the overlap of resonances on the observed non-monotonic trends.The conductivity fluctuated between 0.001 and 0.9 Ω −1 m −1 , the pure BHF displaying the lowest conductivity values and the pure BT recording the highest values.These observations underscore the potential to tailor the composite's conductivity by manipulating the constituent materials' ratios.In analyzing the electromagnetic properties, the real parts of permittivity and permeability demonstrated an increased capacity for storing electrical and magnetic energy.
Moreover, the imaginary parts indicated increased energy dissipation, mainly as heat, during the polarization and depolarization processes.The evidence of these changes suggests a profound dependency of the composite's electromagnetic properties on the BT and BHF concentrations.Importantly, the composite with a higher BHF concentration (75%) manifested a remarkable RL value of − 45 dB at 9.3 GHz, signifying high microwave absorption.The ability to achieve such impressive R L values via compositional adjustments points to the potential application of these composites in electromagnetic interference shielding and microwave absorption.This study has elucidated the magnetic, dielectric, and electromagnetic absorption properties of BHF/BT nanocomposites, demonstrating how they can be tailored for specific uses.Future endeavors should leverage these findings to further optimize these composites, particularly in the field of electromagnetic materials science.The results open a promising pathway to material customization for various applications, from telecommunications to materials engineering.

Fig. 1 Fig. 2 FTIR
Fig. 1 XRD patterns of all samples under investigation

Table 1
The primary magnetic characteristics of the specimens were acquired through VSM measurements of their reaction to a magnetic field applied at ambient temperature Sample H c (T) M r (emu/g) M s (emu/g) S = M r /M s