Guangjun Wang | Mississippi State University (original) (raw)
Papers by Guangjun Wang
Journal of Applied Physics, 2002
Large magnetic entropy change |DeltaS| with a nearly temperature-independent magnitude over a wid... more Large magnetic entropy change |DeltaS| with a nearly temperature-independent magnitude over a wide temperature range (about 70 K span from ~140 K to 210 K) was observed in an Fe-based NaZn13-type compound LaFe11.375Al1.625. Such a behavior of magnetic entropy change is ascribed to two closely spaced magnetic transitions. One at 181 K (TN) with second-order nature is from the paramagnetic
Physical Review B, 2004
The magnetic properties of La(Fe1-xMnx)11.4Si1.6 (0<=x<=0.0... more The magnetic properties of La(Fe1-xMnx)11.4Si1.6 (0<=x<=0.08) compounds were investigated. A reentrant spin glass behavior for the sample with x=0.06 and a paramagnetic-to-spin glass transition for the sample with x=0.08 were observed. The spin-glass behavior for the sample with x=0.08 was systematically studied by the dc and ac measurements. DeltaTf(omega)/[Tf(omega)Delta log10 omega], a possible distinguishing criterion to assert the presence of
Physica B: Condensed Matter, 2006
Neutron diffraction was employed to investigate the crystallographic and magnetic structures of t... more Neutron diffraction was employed to investigate the crystallographic and magnetic structures of the cubic NaZn 13 -type intermetallic compound La(Fe 11.3 Co 0.6 Si 1.1 ). Rietveld analysis shows that Co atoms preferentially occupy the 96i site. The onset of the ferromagnetic ordering results in a large volume expansion. Even in the ferromagnetic state, the lattice expansion still correlates tightly with the magnetic moments r
Journal of Physics: Condensed Matter, 2003
Neutron diffraction was employed to investigate the crystallographic and magnetic structures of t... more Neutron diffraction was employed to investigate the crystallographic and magnetic structures of the cubic NaZn 13 -type intermetallic compound La(Fe 11.3 Co 0.6 Si 1.1 ). Rietveld analysis shows that Co atoms preferentially occupy the 96i site. The onset of the ferromagnetic ordering results in a large volume expansion. Even in the ferromagnetic state, the lattice expansion still correlates tightly with the magnetic moments r
Journal of Physics D: Applied Physics, 2003
The magnetic properties and magnetic entropy changes of La(Fe1-xMnx)11.7Si1.3 (x = 0-0.03) have b... more The magnetic properties and magnetic entropy changes of La(Fe1-xMnx)11.7Si1.3 (x = 0-0.03) have been studied. The Curie temperatures TC decrease monotonously with increasing Mn concentration from 188 to 127 K, and the saturation magnetization muS decreases from 23.9 muB/fu to 22.2 muB/fu respectively, as x increases from 0 to 0.03. The maximal magnetic entropy changes |DeltaS|, under a magnetic field
Journal of Magnetism and Magnetic Materials, 2006
Magnetic properties and hyperfine interactions of LaFe13−xSix intermetallic compounds with large ... more Magnetic properties and hyperfine interactions of LaFe13−xSix intermetallic compounds with large magnetic entropy changes were investigated by means of Mössbauer spectroscopy, band structure calculation and magnetization measurements. It was found that the 57Fe magnetic hyperfine field at FeI (8b) site is larger than that at the FeII (96i) site, whereas the magnetic moment of Fe atoms at the FeI site
![Research paper thumbnail of Effects of carbon on magnetic properties and magnetic entropy change of the LaFe[sub 11.5]Si[sub 1.5] compound](https://attachments.academia-assets.com/42005778/thumbnails/1.jpg)
](Journal of Applied Physics, 2003
Effects of the interstitial carbon atoms on the magnetic properties, especially on the magnetic e... more Effects of the interstitial carbon atoms on the magnetic properties, especially on the magnetic entropy change, of the LaFe11.5Si1.5 compound, have been studied. X-ray diffraction patterns reveal a monotonous increase of the lattice constant with the concentration of carbon, ...
Journal of Applied Physics, 2003
... Static properties of magnetic materials including order parameter, static susceptibility, hea... more ... Static properties of magnetic materials including order parameter, static susceptibility, heat capacities, critical exponents, etc. Body. Recently, much attention has been paid to materials with a large magnetocaloric effect (MCE) due to their potential for magnetic refrigeration. ...
![Research paper thumbnail of Direct observation of phase separation in La[sub 0.45]Sr[sub 0.55]MnO[sub 3−δ]](https://attachments.academia-assets.com/41293673/thumbnails/1.jpg)
](Journal of Applied Physics, 2002
We provide evidence of phase separation in La 0.45 Sr 0.55 MnO 3Ϫ␦ using electron spin resonance,... more We provide evidence of phase separation in La 0.45 Sr 0.55 MnO 3Ϫ␦ using electron spin resonance, magnetic force microscopy ͑MFM͒, x-ray diffraction, and magnetic and transport measurements. The results reveal that ferromagnetic and antiferromagnetic phase coexist at low temperature and that ferromagnetic and paramagnetic phases coexist in the temperature range between the Néel and the Curie temperature. Moreover, the size and shape of ferromagnetic phase ͑the minority phase͒ in the sample were observed directly by MFM. From these results, we infer an electroneutral type phase separation, possibly resulting from a nonuniform distribution of oxygen vacancies, as opposed to charge segregation.
![Research paper thumbnail of Pressure enhancement of the giant magnetocaloric effect in LaFe[sub 11.6]Si[sub 1.4]](https://attachments.academia-assets.com/42005776/thumbnails/1.jpg)
](Applied Physics Letters, 2006
Effects of temperature and pressure on magnetic, elastic, structural, and thermal properties of T... more Effects of temperature and pressure on magnetic, elastic, structural, and thermal properties of Tb5Si2Ge2 have been studied by means of macroscopic (thermal expansion and magnetization) and microscopic (neutron powder diffraction) techniques. We present evidence that the high-temperature second-order ferromagnetic transition can be coupled with the low-temperature first-order structural phase change into a single first-order magnetic-crystallographic transformation at and above a tricritical point in the vicinity of 8.6 kbar. This pressure-induced coupling has a remarkable effect on the magnetocaloric effect, transforming Tb5Si2Ge2 from an ordinary into a giant magnetocaloric effect material.
Applied Physics Letters, 2003
The local structure of the Fe-doped La 1Ϫx Ca x MnO 3 (xϭ0.00-1.00) compounds has been investigat... more The local structure of the Fe-doped La 1Ϫx Ca x MnO 3 (xϭ0.00-1.00) compounds has been investigated by means of Mössbauer spectroscopy. 57 Fe Mössbauer spectra provide direct evidence of Jahn-Teller distortion in these manganites. On the basis of the Mössbauer results, the Jahn-Teller coupling was estimated. It is noteworthy that the Ca-concentration dependence of the Jahn-Teller coupling strength is very consistent with the magnetic phase diagram. Our results reveal that Mössbauer spectroscopy cannot only detect the local structural distortion, but also provide a technique to investigate the Jahn-Teller coupling of Fe-doped La 1Ϫx Ca x MnO 3 colossal magnetoresistive perovskites.
Chinese Physics B, 2009
This paper investigates the structural and electronic properties of rhenium diboride by first-pri... more This paper investigates the structural and electronic properties of rhenium diboride by first-principles calculation based on density functional theory. The obtained results show that the calculated equilibrium structural parameters of ReB 2 are in excellent agreement with experimental values. The calculated bulk modulus is 361 GPa in comparison with that of the experiment. The compressibility of ReB 2 is lower than that of well-known OsB 2 . The anisotropy of the bulk modulus is confirmed by c/a ratio as a function of pressure curve and the bulk modulus along different axes along with the electron density distribution. The high bulk modulus is attributed to the strong covalent bond between Re-d and B-p orbitals and the wider pseudogap near the Fermi level, which could be deduced from both electron charge density distribution and density of states. The band structure and density of states of ReB 2 exhibit that this material presents metallic behavior. The good metallicity and ultra-incompressibility of ReB 2 might suggest its potential application as pressure-proof conductors.
Chinese Physics, 2004
Magnetism and magnetic entropy changes in LaFe11Al2Cx (x=0.0, 0.2 and 0.5) compounds have been in... more Magnetism and magnetic entropy changes in LaFe11Al2Cx (x=0.0, 0.2 and 0.5) compounds have been investigated. The Curie temperature TC is conveniently controlled from 200K to room temperature by varying the carbon concentration. Large magnetic entropy change is obtained over a wide temperature range due to the high magnetization and the drastic decrease in the magnetization around TC. The large magnetic
Chinese Physics, 2004
Effect of Co substitution on magnetic properties and magnetic entropy changes in LaFe11.83Si0.94A... more Effect of Co substitution on magnetic properties and magnetic entropy changes in LaFe11.83Si0.94Al0.23 compounds has been investigated by means of magnetization measurements. X-ray diffraction shows the prepared compounds to be single phase with the cubic NaZn13-type structure. Substitution of Co for Fe leads to an increase of Curie temperature of the material. The magnetic entropy changes in LaFe11.83Si0.94Al0.23 and LaFe11.03Co0.80Si0.94Al0.23
Chinese Physics, 2007
Magnetic properties and magnetic entropy changes in LaFe11.5Si1.5 have been investigated by parti... more Magnetic properties and magnetic entropy changes in LaFe11.5Si1.5 have been investigated by partially substituting Pr by La. It is found that La1-xPrxFe11.5Si1.5 compounds remain cubic NaZn13-type structures even when the Pr content is increased to 0.5, i.e. x = 0.5. Substitution of Pr for La leads to a reduction in both the crystal constant and the Curie temperature. A stepwise
Chinese Physics, 2002
... second-order magnetic transitions have been investigated in an attempt to achieve a large MCE... more ... second-order magnetic transitions have been investigated in an attempt to achieve a large MCE, of which Gd was considered historically to be the best room-temperature refrigerant for its idealCurie tem-perature T (293K) and its large magnetic entropy change (@AS@ ~9.8 J ...
Chinese Physics, 2003
... Wang Fang(Ћ Ђ), Chen Yuan-Fu(ЁЌЃ), Wang Guang-Jun(ЋЅЇ), Sun Ji-Rong(ЊІЈ), and Shen Bao-Gen(Љ ... more ... Wang Fang(Ћ Ђ), Chen Yuan-Fu(ЁЌЃ), Wang Guang-Jun(ЋЅЇ), Sun Ji-Rong(ЊІЈ), and Shen Bao-Gen(Љ Є) State Key Laboratory of Magnetism, Institute of Physics and Center of Condensed Matter Physics, Chinese Academy of Sciences, Beijing 100080, China ...
Chinese Physics, 2004
The structure and magnetic properties of La(Fe1-xMnx)11.4Al1.6 (0leqxleq0.25) compounds have been... more The structure and magnetic properties of La(Fe1-xMnx)11.4Al1.6 (0leqxleq0.25) compounds have been studied. The NaZn13-type structure is preserved and the lattice parameter increases linearly with increasing the Mn concentration. The magnetic ground state changes from the antiferromagnetic to the spin-glass or the cluster-glass state by the substitution of Mn for Fe. Furthermore, a field-induced transition from cluster glass to ferromagnet is
Journal of Long-Term Effects of Medical Implants, 2015
The atrioventricular valve leaflets (mitral and tricuspid) are different from the semilunar valve... more The atrioventricular valve leaflets (mitral and tricuspid) are different from the semilunar valve leaflets (aortic and pulmonary) in layered structure, ultrastructural constitution and organization, and leaflet thickness. These differences warrant a comparative look at the bending properties of the four types of leaflets. We found that the moment-curvature relationships in atrioventricular valves were stiffer than in semilunar valves, and the moment-curvature relationships of the left-side valve leaflets were stiffer than their morphological analog of the right side. These trends were supported by the moment-curvature curves and the flexural rigidity analysis (EI value decreased from mitral, tricuspid, aortic, to pulmonary leaflets). However, after taking away the geometric effect (moment of inertia I), the instantaneous effective bending modulus E showed a reversed trend. The overall trend of flexural rigidity (EI: mitral > tricuspid > aortic > pulmonary) might be correlated with the thickness variations among the four types of leaflets (thickness: mitral > tricuspid > aortic > pulmonary). The overall trend of the instantaneous effective bending modulus (E: mitral < tricuspid < aortic < pulmonary) might be correlated to the layered fibrous ultrastructures of the four types of leaflets, of which the fibers in mitral and tricuspid leaflets were less aligned, and the fibers in aortic and pulmonary leaflets were highly aligned. We also found that, for all types of leaflets, moment-curvature relationships are stiffer in against-curvature (AC) bending than in with-curvature bending (WC), which implies that leaflets tend to flex toward their natural curvature and comply with blood flow. Lastly, we observed that the leaflets were stiffer in circumferential bending compared with radial bending, likely reflecting the physiological motion of the leaflets, i.e., more bending moment and movement were experienced in radial direction than circumferential direction.
Journal of Applied Physics, 2002
Large magnetic entropy change |DeltaS| with a nearly temperature-independent magnitude over a wid... more Large magnetic entropy change |DeltaS| with a nearly temperature-independent magnitude over a wide temperature range (about 70 K span from ~140 K to 210 K) was observed in an Fe-based NaZn13-type compound LaFe11.375Al1.625. Such a behavior of magnetic entropy change is ascribed to two closely spaced magnetic transitions. One at 181 K (TN) with second-order nature is from the paramagnetic
Physical Review B, 2004
The magnetic properties of La(Fe1-xMnx)11.4Si1.6 (0&amp;amp;lt;=x&amp;amp;lt;=0.0... more The magnetic properties of La(Fe1-xMnx)11.4Si1.6 (0&amp;amp;lt;=x&amp;amp;lt;=0.08) compounds were investigated. A reentrant spin glass behavior for the sample with x=0.06 and a paramagnetic-to-spin glass transition for the sample with x=0.08 were observed. The spin-glass behavior for the sample with x=0.08 was systematically studied by the dc and ac measurements. DeltaTf(omega)/[Tf(omega)Delta log10 omega], a possible distinguishing criterion to assert the presence of
Physica B: Condensed Matter, 2006
Neutron diffraction was employed to investigate the crystallographic and magnetic structures of t... more Neutron diffraction was employed to investigate the crystallographic and magnetic structures of the cubic NaZn 13 -type intermetallic compound La(Fe 11.3 Co 0.6 Si 1.1 ). Rietveld analysis shows that Co atoms preferentially occupy the 96i site. The onset of the ferromagnetic ordering results in a large volume expansion. Even in the ferromagnetic state, the lattice expansion still correlates tightly with the magnetic moments r
Journal of Physics: Condensed Matter, 2003
Neutron diffraction was employed to investigate the crystallographic and magnetic structures of t... more Neutron diffraction was employed to investigate the crystallographic and magnetic structures of the cubic NaZn 13 -type intermetallic compound La(Fe 11.3 Co 0.6 Si 1.1 ). Rietveld analysis shows that Co atoms preferentially occupy the 96i site. The onset of the ferromagnetic ordering results in a large volume expansion. Even in the ferromagnetic state, the lattice expansion still correlates tightly with the magnetic moments r
Journal of Physics D: Applied Physics, 2003
The magnetic properties and magnetic entropy changes of La(Fe1-xMnx)11.7Si1.3 (x = 0-0.03) have b... more The magnetic properties and magnetic entropy changes of La(Fe1-xMnx)11.7Si1.3 (x = 0-0.03) have been studied. The Curie temperatures TC decrease monotonously with increasing Mn concentration from 188 to 127 K, and the saturation magnetization muS decreases from 23.9 muB/fu to 22.2 muB/fu respectively, as x increases from 0 to 0.03. The maximal magnetic entropy changes |DeltaS|, under a magnetic field
Journal of Magnetism and Magnetic Materials, 2006
Magnetic properties and hyperfine interactions of LaFe13−xSix intermetallic compounds with large ... more Magnetic properties and hyperfine interactions of LaFe13−xSix intermetallic compounds with large magnetic entropy changes were investigated by means of Mössbauer spectroscopy, band structure calculation and magnetization measurements. It was found that the 57Fe magnetic hyperfine field at FeI (8b) site is larger than that at the FeII (96i) site, whereas the magnetic moment of Fe atoms at the FeI site
Journal of Applied Physics, 2003
Effects of the interstitial carbon atoms on the magnetic properties, especially on the magnetic e... more Effects of the interstitial carbon atoms on the magnetic properties, especially on the magnetic entropy change, of the LaFe11.5Si1.5 compound, have been studied. X-ray diffraction patterns reveal a monotonous increase of the lattice constant with the concentration of carbon, ...
Journal of Applied Physics, 2003
... Static properties of magnetic materials including order parameter, static susceptibility, hea... more ... Static properties of magnetic materials including order parameter, static susceptibility, heat capacities, critical exponents, etc. Body. Recently, much attention has been paid to materials with a large magnetocaloric effect (MCE) due to their potential for magnetic refrigeration. ...
Journal of Applied Physics, 2002
We provide evidence of phase separation in La 0.45 Sr 0.55 MnO 3Ϫ␦ using electron spin resonance,... more We provide evidence of phase separation in La 0.45 Sr 0.55 MnO 3Ϫ␦ using electron spin resonance, magnetic force microscopy ͑MFM͒, x-ray diffraction, and magnetic and transport measurements. The results reveal that ferromagnetic and antiferromagnetic phase coexist at low temperature and that ferromagnetic and paramagnetic phases coexist in the temperature range between the Néel and the Curie temperature. Moreover, the size and shape of ferromagnetic phase ͑the minority phase͒ in the sample were observed directly by MFM. From these results, we infer an electroneutral type phase separation, possibly resulting from a nonuniform distribution of oxygen vacancies, as opposed to charge segregation.
Applied Physics Letters, 2006
Effects of temperature and pressure on magnetic, elastic, structural, and thermal properties of T... more Effects of temperature and pressure on magnetic, elastic, structural, and thermal properties of Tb5Si2Ge2 have been studied by means of macroscopic (thermal expansion and magnetization) and microscopic (neutron powder diffraction) techniques. We present evidence that the high-temperature second-order ferromagnetic transition can be coupled with the low-temperature first-order structural phase change into a single first-order magnetic-crystallographic transformation at and above a tricritical point in the vicinity of 8.6 kbar. This pressure-induced coupling has a remarkable effect on the magnetocaloric effect, transforming Tb5Si2Ge2 from an ordinary into a giant magnetocaloric effect material.
Applied Physics Letters, 2003
The local structure of the Fe-doped La 1Ϫx Ca x MnO 3 (xϭ0.00-1.00) compounds has been investigat... more The local structure of the Fe-doped La 1Ϫx Ca x MnO 3 (xϭ0.00-1.00) compounds has been investigated by means of Mössbauer spectroscopy. 57 Fe Mössbauer spectra provide direct evidence of Jahn-Teller distortion in these manganites. On the basis of the Mössbauer results, the Jahn-Teller coupling was estimated. It is noteworthy that the Ca-concentration dependence of the Jahn-Teller coupling strength is very consistent with the magnetic phase diagram. Our results reveal that Mössbauer spectroscopy cannot only detect the local structural distortion, but also provide a technique to investigate the Jahn-Teller coupling of Fe-doped La 1Ϫx Ca x MnO 3 colossal magnetoresistive perovskites.
Chinese Physics B, 2009
This paper investigates the structural and electronic properties of rhenium diboride by first-pri... more This paper investigates the structural and electronic properties of rhenium diboride by first-principles calculation based on density functional theory. The obtained results show that the calculated equilibrium structural parameters of ReB 2 are in excellent agreement with experimental values. The calculated bulk modulus is 361 GPa in comparison with that of the experiment. The compressibility of ReB 2 is lower than that of well-known OsB 2 . The anisotropy of the bulk modulus is confirmed by c/a ratio as a function of pressure curve and the bulk modulus along different axes along with the electron density distribution. The high bulk modulus is attributed to the strong covalent bond between Re-d and B-p orbitals and the wider pseudogap near the Fermi level, which could be deduced from both electron charge density distribution and density of states. The band structure and density of states of ReB 2 exhibit that this material presents metallic behavior. The good metallicity and ultra-incompressibility of ReB 2 might suggest its potential application as pressure-proof conductors.
Chinese Physics, 2004
Magnetism and magnetic entropy changes in LaFe11Al2Cx (x=0.0, 0.2 and 0.5) compounds have been in... more Magnetism and magnetic entropy changes in LaFe11Al2Cx (x=0.0, 0.2 and 0.5) compounds have been investigated. The Curie temperature TC is conveniently controlled from 200K to room temperature by varying the carbon concentration. Large magnetic entropy change is obtained over a wide temperature range due to the high magnetization and the drastic decrease in the magnetization around TC. The large magnetic
Chinese Physics, 2004
Effect of Co substitution on magnetic properties and magnetic entropy changes in LaFe11.83Si0.94A... more Effect of Co substitution on magnetic properties and magnetic entropy changes in LaFe11.83Si0.94Al0.23 compounds has been investigated by means of magnetization measurements. X-ray diffraction shows the prepared compounds to be single phase with the cubic NaZn13-type structure. Substitution of Co for Fe leads to an increase of Curie temperature of the material. The magnetic entropy changes in LaFe11.83Si0.94Al0.23 and LaFe11.03Co0.80Si0.94Al0.23
Chinese Physics, 2007
Magnetic properties and magnetic entropy changes in LaFe11.5Si1.5 have been investigated by parti... more Magnetic properties and magnetic entropy changes in LaFe11.5Si1.5 have been investigated by partially substituting Pr by La. It is found that La1-xPrxFe11.5Si1.5 compounds remain cubic NaZn13-type structures even when the Pr content is increased to 0.5, i.e. x = 0.5. Substitution of Pr for La leads to a reduction in both the crystal constant and the Curie temperature. A stepwise
Chinese Physics, 2002
... second-order magnetic transitions have been investigated in an attempt to achieve a large MCE... more ... second-order magnetic transitions have been investigated in an attempt to achieve a large MCE, of which Gd was considered historically to be the best room-temperature refrigerant for its idealCurie tem-perature T (293K) and its large magnetic entropy change (@AS@ ~9.8 J ...
Chinese Physics, 2003
... Wang Fang(Ћ Ђ), Chen Yuan-Fu(ЁЌЃ), Wang Guang-Jun(ЋЅЇ), Sun Ji-Rong(ЊІЈ), and Shen Bao-Gen(Љ ... more ... Wang Fang(Ћ Ђ), Chen Yuan-Fu(ЁЌЃ), Wang Guang-Jun(ЋЅЇ), Sun Ji-Rong(ЊІЈ), and Shen Bao-Gen(Љ Є) State Key Laboratory of Magnetism, Institute of Physics and Center of Condensed Matter Physics, Chinese Academy of Sciences, Beijing 100080, China ...
Chinese Physics, 2004
The structure and magnetic properties of La(Fe1-xMnx)11.4Al1.6 (0leqxleq0.25) compounds have been... more The structure and magnetic properties of La(Fe1-xMnx)11.4Al1.6 (0leqxleq0.25) compounds have been studied. The NaZn13-type structure is preserved and the lattice parameter increases linearly with increasing the Mn concentration. The magnetic ground state changes from the antiferromagnetic to the spin-glass or the cluster-glass state by the substitution of Mn for Fe. Furthermore, a field-induced transition from cluster glass to ferromagnet is
Journal of Long-Term Effects of Medical Implants, 2015
The atrioventricular valve leaflets (mitral and tricuspid) are different from the semilunar valve... more The atrioventricular valve leaflets (mitral and tricuspid) are different from the semilunar valve leaflets (aortic and pulmonary) in layered structure, ultrastructural constitution and organization, and leaflet thickness. These differences warrant a comparative look at the bending properties of the four types of leaflets. We found that the moment-curvature relationships in atrioventricular valves were stiffer than in semilunar valves, and the moment-curvature relationships of the left-side valve leaflets were stiffer than their morphological analog of the right side. These trends were supported by the moment-curvature curves and the flexural rigidity analysis (EI value decreased from mitral, tricuspid, aortic, to pulmonary leaflets). However, after taking away the geometric effect (moment of inertia I), the instantaneous effective bending modulus E showed a reversed trend. The overall trend of flexural rigidity (EI: mitral > tricuspid > aortic > pulmonary) might be correlated with the thickness variations among the four types of leaflets (thickness: mitral > tricuspid > aortic > pulmonary). The overall trend of the instantaneous effective bending modulus (E: mitral < tricuspid < aortic < pulmonary) might be correlated to the layered fibrous ultrastructures of the four types of leaflets, of which the fibers in mitral and tricuspid leaflets were less aligned, and the fibers in aortic and pulmonary leaflets were highly aligned. We also found that, for all types of leaflets, moment-curvature relationships are stiffer in against-curvature (AC) bending than in with-curvature bending (WC), which implies that leaflets tend to flex toward their natural curvature and comply with blood flow. Lastly, we observed that the leaflets were stiffer in circumferential bending compared with radial bending, likely reflecting the physiological motion of the leaflets, i.e., more bending moment and movement were experienced in radial direction than circumferential direction.