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Effects of dislocation arrangement and character on the work hardening of lath martensitic steels

段野下 宙志*; 長谷川 寛*; 樋口 翔*; 松田 広志*; Gong, W.; 川崎 卓郎; Harjo, S.; 梅澤 修*

Scripta Materialia, 236, p.115648_1 - 115648_5, 2023/11


Work-hardening behavior of a lath martensitic Fe-18Ni alloy during tensile deformation is discussed based on the Taylor's equation. The dislocation characteristics are monitored using in situ neutron diffraction. In the specimens of as-quenched (AQ) and tempered at 573 K (T573), the dislocations are extremely dense and randomly arranged. The dislocations in AQ and T573 form dislocation cells as deformation progresses. Consequently, a composite condition comprising cell walls and cell interiors is formed, and the coefficient $$alpha$$ in the Taylor's equation increases. Cells are already present in the specimen tempered at 773 K (T773), which has a low dislocation density and a large fraction of edge-type dislocations. As deformation continues, the dislocation density of T773 increases, its cell size decreases, and its composite condition become stronger. Simultaneously, the edge-type dislocation fraction decreases, keeping $$alpha$$ unchanged. Thus, both the dislocation arrangement and character affected $$alpha$$, thereby affecting the work-hardening behavior.


Oxygen interstitials make metastable $$beta$$ titanium alloys strong and ductile

Chong, Y.*; Gholizadeh, R.*; Guo, B.*; 都留 智仁; Zhao, G.*; 吉田 周平*; 光原 昌寿*; Godfrey, A.*; 辻 伸泰*

Acta Materialia, 257, p.119165_1 - 119165_14, 2023/09




Quantitatively evaluating respective contribution of austenite and deformation-induced martensite to flow stress, plastic strain, and strain hardening rate in tensile deformed TRIP steel

Mao, W.; Gao, S.*; Gong, W.; Bai, Y.*; Harjo, S.; Park, M.-H.*; 柴田 曉伸*; 辻 伸泰*

Acta Materialia, 256, p.119139_1 - 119139_16, 2023/09




Strengthening of $$alpha$$Mg and long-period stacking ordered phases in a Mg-Zn-Y alloy by hot-extrusion with low extrusion ratio

Harjo, S.; Gong, W.; 相澤 一也; 川崎 卓郎; 山崎 倫昭*

Acta Materialia, 255, p.119029_1 - 119029_12, 2023/08

 被引用回数:1 パーセンタイル:0.01(Materials Science, Multidisciplinary)

An as-cast sample and two hot-extruded samples with different extrusion ratios (R) of Mg$$_{97}$$Zn$$_{1}$$Y$$_{2}$$ alloy containing the HCP $$alpha$$ matrix ($$alpha$$Mg) and the long-period stacking ordered phase (LPSO) of about 25-vol%, were used in tensile deformation in situ neutron diffraction experiments, to elucidate the effects of uniquely different microstructural evolutions in $$alpha$$Mg and LPSO with varying the R value to the mechanical properties. $$alpha$$Mg behaved as the soft phase and LPSO as the hard phase, and hot-extrusion improved the strength of both. At the R value of 5.0, a bimodal microstructure was created in $$alpha$$Mg, increasing largely the yield strength of $$alpha$$Mg. With increasing the R value to 12.5, the bimodal microstructure of $$alpha$$Mg collapsed and the yield strength of $$alpha$$Mg decreased. However, the strength of LPSO increased monotonously with increasing the R value due to the developments of kink bands and texture.


Lattice parameters of austenite and martensite during transformation for Fe-18Ni alloy investigated through ${it in situ}$ neutron diffraction

Gong, W.; Harjo, S.; 友田 陽*; 諸岡 聡; 川崎 卓郎; 柴田 曉伸*; 辻 伸泰*

Acta Materialia, 250, p.118860_1 - 118860_16, 2023/05

 被引用回数:0 パーセンタイル:0.01(Materials Science, Multidisciplinary)

Martensitic transformation is accompanied by the generation of microscale and macroscale internal stresses during cooling below the martensitic transformation start temperature. These internal stresses have been determined through X-ray or neutron diffraction, but the reported results are not consistent, probably because the measured lattice parameter is influenced not only by the internal stress but also by several factors, including solute elements and crystal defects. Therefore, ${it in situ}$ neutron diffraction combined with dilatometry measurements during martensitic transformation and subsequent cyclic tempering were performed for an Fe-18Ni alloy. The phase strains calculated by lattice parameter variations show that a hydrostatic compressive strain in austenite and a tensile strain in martensite arose as the martensitic transformation progressed during continuous cooling or isothermal holding. However, the phase stresses of austenite and martensite estimated from these strains failed to hold stress balance law when dense crystal defects involved in the processes. After these crystal defects were removed by appropriate tempering, the stress balance law held well. Meanwhile, the phase stresses of austenite and martensite were changed to opposite, revealing their true identity. Various crystal defects in austenite and martensite, introduced by plastic accommodation, were suggested to affect their lattice parameters and then their phase stresses.


High-density nanoprecipitates and phase reversion via maraging enable ultrastrong yet strain-hardenable medium-entropy alloy

Kwon, H.*; Sathiyamoorthi, P.*; Gangaraju, M. K.*; Zargaran, A.*; Wang, J.*; Heo, Y.-U.*; Harjo, S.; Gong, W.; Lee, B.-J.*; Kim, H. S.*

Acta Materialia, 248, p.118810_1 - 118810_12, 2023/04

 被引用回数:0 パーセンタイル:0.01(Materials Science, Multidisciplinary)

Maraging steels, known for ultrahigh strength and good fracture toughness, derive their superior properties from lath martensite structure with high-density nanoprecipitates. In this work, we designed a novel Fe-based medium-entropy alloy with a chemical composition of Fe$$_{60}$$Co$$_{25}$$Ni$$_{10}$$Mo$$_5$$ in atomic% by utilizing the characteristics of the maraging steels. By a single-step aging of only 10 min at 650 $$^{circ}$$C, the alloy showed microstructures consisting of a very high number density of (Fe, Co, Ni)$$_7$$Mo$$_6$$-type nanoprecipitates in lath martensite structure and reverted FCC phase, which led to ultrahigh yield strength higher than 2 GPa. This work demonstrates a novel direction to produce strong and ductile materials by expanding the horizons of material design with the aid of high-entropy concept and overcoming the limits of conventional materials.


Competitive strengthening between dislocation slip and twinning in cast-wrought and additively manufactured CrCoNi medium entropy alloys

Woo, W.*; Kim, Y. S.*; Chae, H. B.*; Lee, S. Y.*; Jeong, J. S.*; Lee, C. M.*; Won, J. W.*; Na, Y. S.*; 川崎 卓郎; Harjo, S.; et al.

Acta Materialia, 246, p.118699_1 - 118699_13, 2023/03

 被引用回数:4 パーセンタイル:98.77(Materials Science, Multidisciplinary)

In situ neutron diffraction experiments have been performed under loading in cast-wrought (CW) and additively manufactured (AM) equiatomic CoCrNi medium-entropy alloys. The diffraction line profile analysis correlated the faulting-embedded crystal structure to the dislocation density, stacking/twin fault probability, and stacking fault energy as a function of strain. The results showed the initial dislocation density of 1.8$$times$$10$$^{13}$$ m$$^{-2}$$ in CW and 1.3$$times$$10$$^{14}$$ m$$^{-2}$$ in AM. It significantly increased up to 1.3$$times$$10$$^{15}$$ m-$$^{-2}$$ in CW and 1.7$$times$$10$$^{15}$$ m$$^{-2}$$ in AM near fracture. The dislocation density contributed to the flow stress of 470 MPa in CW and 600 MPa in AM, respectively. Meanwhile, the twin fault probability of CW (2.7%) was about two times higher than AM (1.3%) and the stacking fault probability showed the similar tendency. The twinning provided strengthening of 360 MPa in CW and 180 MPa in AM. Such a favorable strengthening via deformation twinning in CW and dislocation slip in AM was attributed to the stacking fault energy. It was estimated as 18.6 mJ/m$$^{2}$$ in CW and 37.5 mJ/m$$^{2}$$ in AM by the strain field of dislocations incorporated model. Dense dislocations, deformation twinning, and atomic-scale stacking structure were examined by using electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM).


Compressive deformation behavior of AZ31 alloy at 21K; An ${it In situ}$ neutron diffraction study

Gong, W.; 川崎 卓郎; Zheng, R.*; 眞山 剛*; Sun, B.*; 相澤 一也; Harjo, S.; 辻 伸泰*

Scripta Materialia, 225, p.115161_1 - 115161_5, 2023/03

 被引用回数:2 パーセンタイル:53.96(Nanoscience & Nanotechnology)

Deformation behavior during uniaxial compression at 21 K and 298 K in a commercial AZ31 magnesium alloy was studied by ${it in situ}$ neutron diffraction. Decreasing the deformation temperature resulted in a slight increase in yield stress (115 MPa $$rightarrow$$ 139 MPa), but a remarkable enhancement in both the fracture stress (365 MPa $$rightarrow$$ 551 MPa) and fracture strain (12.8% $$rightarrow$$ 16.5%). The low temperature sensitivity of the {10$$overline{1}$$2} extension twinning which governed the macroscopic yielding led to the slight increase in yield stress. At 21K, basal slip was suppressed, while the extension twinning was promoted resulted in higher twin volume fraction. In the late stage of deformation, the {10$$overline{1}$$1}-{10$$overline{1}$$2} double twinning was suppressed, which is considered to be the reason to delay the fracture at 21 K.


Tensile overload-induced texture effects on the fatigue resistance of a CoCrFeMnNi high-entropy alloy

Lam, T.-N.*; Chin, H.-H.*; Zhang, X.*; Feng, R.*; Wang, H.*; Chiang, C.-Y.*; Lee, S. Y.*; 川崎 卓郎; Harjo, S.; Liaw, P. K.*; et al.

Acta Materialia, 245, p.118585_1 - 118585_9, 2023/02

 被引用回数:2 パーセンタイル:32.61(Materials Science, Multidisciplinary)

The present study investigates the crystallographic-texture effects on the improved fatigue resistance in the CoCrFeMnNi high-entropy alloys (HEAs) with the full-size geometry of the ASTM Standards E647-99. We exploited X-ray nano-diffraction mapping to characterize the crystal-deformation levels ahead of the crack tip after stress unloading under both constant- and tensile overloaded-fatigue conditions. The crack-tip blunting-induced much higher deformation level was concentrated surrounding the crack-tip which delays the fatigue-crack growth immediately after a tensile overload. The predominant deformation texture orientation in the Paris regime was investigated, using electron backscatter diffraction and orientation distribution function analyses. The twinning formation-driven shear deformation gave rise to the development of the Goss-type texture within the plastic deformation regime under a tensile-overloaded-fatigue condition, which was attributed to enhance the crack deflection and thus the tensile induced crack-growth-retardation period in the CoCrFeMnNi HEA.


Evidence supporting reversible martensitic transformation under cyclic loading on Fe-Mn-Si-Al alloys using ${it in situ}$ neutron diffraction

澤口 孝宏*; 友田 陽*; 吉中 奎貴*; Harjo, S.

Acta Materialia, 242, p.118494_1 - 118494_14, 2023/01

 被引用回数:0 パーセンタイル:0(Materials Science, Multidisciplinary)

Fe-Mn-Si-based alloys, show superior resistance to plastic fatigue compared to the conventional steels, which is ascribed to the reversible back-and-forth movement of Shockley partial dislocations associated with a reversible martensitic transformation between the face-centered cubic $$gamma$$-austenite and hexagonal close-packed $$epsilon$$-martensite. The purpose of this study was to gather evidence of the reversible martensitic transformation using in situ neutron diffraction under cyclic loading. Three Fe-30Mn-Si-Al alloys with different Gibbs free energy differences at 298 K were studied to unravel the effect of phase stability on the degree of reversibility.


Unexpected dynamic transformation from $$alpha$$ phase to $$beta$$ phase in zirconium alloy revealed by in-situ neutron diffraction during high temperature deformation

Guo, B.*; Mao, W.; Chong, Y.*; 柴田 曉伸*; Harjo, S.; Gong, W.; Chen, H.*; Jonas, J. J.*; 辻 伸泰*

Acta Materialia, 242, p.118427_1 - 118427_11, 2023/01

 被引用回数:2 パーセンタイル:32.61(Materials Science, Multidisciplinary)

Dynamic transformation from alpha (HCP) to beta (BCC) phase in a zirconium alloy was revealed by the use of in-situ neutron diffraction during hot compression. The dynamic transformation was unexpectedly detected during isothermal compression at temperatures of 900$$^{circ}$$C and 950$$^{circ}$$C (alpha + beta two-phase region) and strain rates of 0.01 s$$^{-1}$$ and 0.001 s$$^{-1}$$, even though equilibrium two-phase states were achieved prior to the hot compression. Dynamic transformation was accompanied by diffusion of Sn from beta to alpha phase, which resulted in changes of lattice parameters and a characteristic microstructure of alpha grains. The details of dynamic transformation are discussed using the evolution of lattice constants.


Stress partitioning between bcc and cementite phases discussed from phase stress and dislocation density in martensite steels

土田 紀之*; 上路 林太郎*; Gong, W.; 川崎 卓郎; Harjo, S.

Scripta Materialia, 222, p.115002_1 - 115002_6, 2023/01

 被引用回数:4 パーセンタイル:68.37(Nanoscience & Nanotechnology)

The present study investigated the tensile deformation behavior of quenched and tempered martensite steels at various austenitization and tempering temperatures using in situ neutron diffraction experiments. Phase lattice strains in the bcc and cementite ($$theta$$) phases and dislocation structures in the bcc phase were analyzed. The phase lattice strain in bcc became almost stagnant after yielding as the tempering temperature increased. The phase lattice strain in $$theta$$ increased linearly with an increase in the flow stress, independent of the austenitization and tempering temperatures. The stress partitioning between bcc and $$theta$$ was confirmed after the yielding of bcc, which contributed to the work hardening. The phase stresses of bcc and $$theta$$ and their stress partitioning improve the mechanical properties of martensite steels, which can be summarized by the systematic changes in phase lattice strain and dislocation properties due to the austenitization and tempering temperatures.


Ultrahigh yield strength and large uniform elongation achieved in ultrafine-grained titanium containing nitrogen

Chong, Y.*; 都留 智仁; Guo, B.*; Gholizadeh, R.*; 井上 耕治*; 辻 伸泰*

Acta Materialia, 240, p.118356_1 - 118356_15, 2022/11

 被引用回数:5 パーセンタイル:68.37(Materials Science, Multidisciplinary)

本研究では、室温でのチタンの引張特性と変形挙動に及ぼす窒素含有量と結晶粒径の影響を体系的に調査した。巨大ひずみ加工と焼鈍により、超高降伏強度(1.04GPa)と大きな均一伸び(10%)の前例のない相乗効果を組み合わせた、完全再結晶微細構造を備えた超微細粒(UFG)Ti-0.3wt.%N合金が得られた。Ti-0.3wt.%N合金の硬化およびひずみ硬化メカニズムは、変形下部構造の観察と第一原理計算によって包括的に研究された。UFG Ti-0.3wt.%Nの優れた強度/延性バランスへの窒素の寄与は2倍であることが明らかになった。粒子内の窒素原子は、八面体から六面体のサイトへの窒素のシャッフルにより、角柱面上の$$<a>$$転位の運動を強く妨げ、純Tiの6倍の摩擦応力の増加を引き起こした。さらに、Ti-0.3wt.%N合金の柱面と錐面の間の積層欠陥エネルギー差が大幅に減少することで、$$<c+a>$$転位の活性化が容易になり、ひずみ硬化率の向上に寄与した。我々の実験的および理論的計算研究は、延性を大幅に犠牲にすることなく手頃な価格の高強度チタンの設計に関する知見を与える。


Rediscovery of Hall-Petch strengthening in bulk ultrafine grained pure Mg at cryogenic temperature; A Combined ${it in situ}$ neutron diffraction and electron microscopy study

Zheng, R.*; Gong, W.; Du, J.-P.*; Gao, S.*; Liu, M.*; Li, G.*; 川崎 卓郎; Harjo, S.; Ma, C.*; 尾方 成信*; et al.

Acta Materialia, 238, p.118243_1 - 118243_15, 2022/10

 被引用回数:9 パーセンタイル:90.29(Materials Science, Multidisciplinary)

Grain refinement can lead to the strengthening of metallic materials according to the Hall-Petch relationship. However, our recent results suggested that grain boundary sliding is the dominant deformation mode in bulk ultrafine grained (UFG) pure Mg at room temperature, leading to softening. Here, for the first time, we report that the Hall-Petch strengthening can be regained in bulk UFG pure Mg at cryogenic temperature. At 77K, the UFG pure Mg with a mean grain size of 0.6 $$mu$$m exhibited ultrahigh tensile yield strength and ultimate tensile strength of 309 MPa and 380 MPa, respectively. Combined ${it in situ}$ neutron diffraction and electron microscopy investigation indicated that residual dislocation structures and deformation twins hardly formed in the UFG specimen during tensile test at 298K. In contrast, fast accumulation of lattice defects and remarkable reorientation were evident at 77K, suggesting that the grain-boundary-mediated process was suppressed and the plastic deformation was dominated by dislocation slip and deformation twinning. In addition, all the pure Mg specimens exhibited pronounced strain hardening at 77 K, which was mainly attributed to the suppressed grain boundary sliding and dynamic recovery. The mean dislocation density and relative fractions of dislocations with various Burgers vectors of the UFG specimen deformed at 77K were determined quantitatively from neutron diffraction data.


Mechanical surface treatment studies by Bragg edge neutron imaging

Ramadhan, R. S.*; Glaser, D.*; 祖山 均*; Kockelmann, W.*; 篠原 武尚; Pirling, T.*; Fitzpatrick, M. E.*; Tremsin, A. S.*

Acta Materialia, 239, p.118259_1 - 118259_12, 2022/10

 被引用回数:2 パーセンタイル:32.61(Materials Science, Multidisciplinary)

Mechanical surface treatment technologies such as laser peening and cavitation peening require detailed characterization, including residual stress analysis, to optimize their processing parameters. Recent developments at neutron facilities allow non-destructive 2-dimensional residual strain mapping through Bragg edge imaging. The present work highlights the application of Bragg edge neutron imaging for the study of mechanical surface treatments, through determination of lattice spacing distributions by energy-resolved radiography. Through three different examples, the unique capabilities of the method are demonstrated, particularly for providing near surface residual strain maps within samples with complex geometries with relatively high spatial resolution. By providing a comparison with X-ray diffraction and neutron diffraction results, the present work emphasizes the potential of Bragg edge neutron imaging as a tool for surface treatment research.


Displacement of hydrogen position in di-hydride of V-Ti-Cr solid solution alloys

榊 浩司*; Kim, H.*; Majzoub, E. H.*; 町田 晃彦*; 綿貫 徹*; 池田 一貴*; 大友 季哉*; 水野 正隆*; 松村 大樹; 中村 優美子*

Acta Materialia, 234, p.118055_1 - 118055_10, 2022/08

 被引用回数:6 パーセンタイル:77.31(Materials Science, Multidisciplinary)

Local structure in the di-hydride phases of V-Ti-Cr solid solution alloys were investigated using synchrotron X-ray and neutron total scattering experiments. Both Rietveld refinement and pair distribution function (PDF) refinement of the X-ray scattering data indicated that the crystal structure of the metal lattice was a face centered cubic (FCC) structure and no difference between their local structure and average structure was observed. However, the CaF$$_{2}$$ structure model did not reproduce the first peak corresponding to the metal-hydrogen correlation in neutron PDF patterns. When special quasi-random structure (SQS) models are applied for the refinements, the whole neutron PDF patterns were reproduced. Distribution of interatomic distances between hydrogen and metal atoms in the relaxed SQS models showed that interatomic distance of hydrogen with Cr was shorter than that with V and that with Ti was longer than that with V, independently of the chemical compositions.


Regulation of strength and ductility of single-phase twinning-induced plasticity high-entropy alloys

Wei, D.*; Gong, W.; 川崎 卓郎; Harjo, S.; 加藤 秀実*

Scripta Materialia, 216, p.114738_1 - 114738_6, 2022/07

 被引用回数:15 パーセンタイル:98.07(Nanoscience & Nanotechnology)

Near-equiatomic single-phase twining-induced plasticity (TWIP) high-entropy alloys (HEAs) exhibit a good combination of strength and ductility, but their modest yield strength requires further improvement. Here, we propose a strategy for markedly enhancing their strength while retaining satisfactory ductility, taking advantage of the temperature dependence of the stacking fault energy. The room-temperature strength of a representative TWIP HEA was improved by the cryogenic pre-deformation-induced dislocations, martensite, nanotwins, and stacking faults. The tensile properties were further tuned by subsequent annealing to obtain partially recovered or recrystallized microstructures. The influence of regulated microstructures on the yield strength was clarified by neutron diffraction line profile analysis. This study presents possibilities for fabricating advanced HEAs by tuning the substructures.


Load redistribution in eutectic high entropy alloy AlCoCrFeNi$$_{2.1}$$ during high temperature deformation

Jaladurgam, N. R.*; Lozinko, A.*; Guo, S.*; Harjo, S.; Colliander, M. H.*

Materialia, 22, p.101392_1 - 101392_4, 2022/05

The load redistribution between and within phases in eutectic high entropy alloy AlCoCrFeNi$$_{2.1}$$ was measured using in-situ neutron diffraction during tensile deformation at 973 K. The load partitioning between phases is reversed compared to lower temperatures, with L1$$_{2}$$ becoming the stronger phase. The evolution of the orientation-specific stresses and strains in the L1$$_{2}$$ phase suggests that cube slip dominates the response. The low strength, internal load transfer and ideally plastic response of the B2 phase indicate a change in deformation mechanism compared to lower temperatures.


Achieving excellent mechanical properties in type 316 stainless steel by tailoring grain size in homogeneously recovered or recrystallized nanostructures

Liu, M.*; Gong, W.; Zheng, R.*; Li, J.*; Zhang, Z.*; Gao, S.*; Ma, C.*; 辻 伸泰*

Acta Materialia, 226, p.117629_1 - 117629_13, 2022/03

 被引用回数:28 パーセンタイル:99.47(Materials Science, Multidisciplinary)

One hopeful path to realize good comprehensive mechanical properties in metallic materials is to accomplish homogeneous nanocrystalline (NC) or ultrafine grained (UFG) structure with low dislocation density. In this work, high pressure torsion deformation followed by appropriate annealing was performed on 316 stainless steel (SS). For the first time, we successfully obtained NC/UFG 316 SS having uniform microstructures with various average grain sizes ranging from 46 nm to 2.54 $$mu$$m and low dislocation densities. Among the series, an un-precedentedly high yield strength (2.34 GPa) was achieved at the smallest grain size of 46 nm, in which dislocation scarcity induced hardening accounting for 57% of the strength. On the other hand, exceptional strength-ductility synergy with high yield strength (900 MPa) and large uniform elongation (27%) was obtained in the fully recrystallized specimen having the grain size of 0.38 $$mu$$m. The high yield stress and scarcity of dislocation sources in recrystallized UFGs activated stacking faults and deformation twins nucleating from grain boundaries during straining, and their interaction with dislocations allowed for sustainable strain hardening, which also agreed with the plaston concept recently proposed. The multiple deformation modes activated, together with the effective strengthening mechanisms, were responsible for the outstanding comprehensive mechanical performance of the material.


Modeling changes in the second harmonic generation of ultrasonic waves having wavelengths beyond the length scale of conventional molecular dynamics

森 承宇*; 松田 那由多*; 沖田 泰良*; 愛知 正温*; 板倉 充洋; 鈴木 克幸*

Materialia, 21, p.101371_1 - 101371_6, 2022/03

The nonlinear ultrasonic (NLU) technique is a nondestructive method for detecting nanostructure in crystalline materials. In this study, a method was developed to quantify the changes in NLU signals associated with nanostructure using molecular dynamics (MD). A nonreflective boundary, which reduces the computational cost to the first power of the wavelength, was used to achieve this. This method is distinct from previous studies using a conventional MD, for which the computational cost is proportional to the square of the wavelength. The nonreflective boundary eliminates the influence of reflected waves at the detection position by setting a buffer region at the end of the simulation cell opposite from the wave source, and periodically resetting the displacements and velocities of all atoms in this region. This method allows the introduction of elastic waves with wavelengths longer than the cell size, and only an extension of time is required, according to the extension of the wavelength, without increasing the cell size. Hence, it is possible to extend the NLU wavelength by approximately four orders of magnitude, which approaches the wavelengths used for inspections and, thus, to use MD to simulate the changes in the NLU signals induced by nanostructure. The NLU signal values obtained by the two methods were in good agreement for a perfect Fe crystal and a Fe crystal containing 1% monovacancies. No significant frequency dependence of the acoustic nonlinearity parameter was found at 0 K. This method will contribute to the development of an inspection technique based on scientific principles.

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