Journal articles: 'Phase planes'

1

Shimozaki, Toshitada, Takahisa Okino, C. G. Lee, and O. Taguchi. "A Limited Condition for Bifurcate or Trifurcate Kirkendall Planes in Multiple Phase Diffusion Couples." Defect and Diffusion Forum 297-301 (April 2010): 1487–92. http://dx.doi.org/10.4028/www.scientific.net/ddf.297-301.1487.

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In general, only one Kirkendall plane can be seen in a diffusion couple. However, bifurcate or trifurcate Kirkendall planes have been reported in Ti/TiAl3 or Co/CoSi2 multi-phase diffusion couples (M-couple) [1,2]. The authors [3] have previously shown a numerical technique to analyze the movement of multiple markers (M-M) embedded in a M-couple taking the molar volume change effect to the diffusion direction into account. Using this technique, one can visualize the places where vacancies (lattice planes) are annihilated or generated in the couple. Here, we try to demonstrate the bifurcate or trifurcate Kirkendall planes in the M-couple and clarify the limited conditions of bifurcate or trifurcate Kirkendall planes by using this numerical technique.

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2

Haq, Ayesha J., and P. R. Munroe. "Phase transformations in (111) Si after spherical indentation." Journal of Materials Research 24, no. 6 (June 2009): 1967–75. http://dx.doi.org/10.1557/jmr.2009.0249.

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Phase transformations in (111) Si after spherical indentation have been investigated by cross-sectional transmission electron microscopy. Even at an indentation load of 20 mN, a phase transformation zone including the high-pressure crystalline Si phases was observed within the residual imprints. The volume of the transformation zone, as well as that of the crystalline phases increased with the indentation load. Below the transformation zone, slip was found to occur on {311} planes rather than on {111} planes, usually observed on indentation of (100) Si. The distribution of defects was asymmetric, and for indentation loads up to 80 mN, their density was significantly lower than that reported for (100) Si. The experimental observations correlated well with modeling of the applied stress through ELASTICA.

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Kouh, Y. M., C. B. Carter, and H. Schmalzried. "The Spinel/Alumina Phase Boundary." Proceedings, annual meeting, Electron Microscopy Society of America 43 (August 1985): 216–17. http://dx.doi.org/10.1017/s042482010011800x.

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The formation of spinel during solid-state reactions between two oxides of the type A0 (e.g. Mg0) and B203 (e.g. A1203), has been extensively studied both from a theoretical viewpoint and an experimental one. The present paper will illustrate the structural aspects of the study of the spinel/sesquioxide interface. It has recently been shown by Carter and Schmalzried, that, when Co0 and A1203 react to form Co-Al spinel, the {111} oxygen planes in the spinel do not lie parallel to the (0001) oxygen planes in the parent alumina even though the oxygen ions are almost close-packed in both planes. The small rotation which is present implies that the mechanism whereby the alumina is transformed to spinel is not simply the glide of either isolated, or bundles of, Shockley partial-like transformation dislocations as had previously been assumed, but rather involves a new defect which causes a rotation of the oxygen sublattice.

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4

YEH, LI-MING. "HOMOGENIZATION OF TWO-PHASE FLOW IN FRACTURED MEDIA." Mathematical Models and Methods in Applied Sciences 16, no. 10 (October 2006): 1627–51. http://dx.doi.org/10.1142/s0218202506001650.

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In a fractured medium, there is an interconnected system of fracture planes dividing the porous rock into a collection of matrix blocks. The fracture planes, while very thin, form paths of high permeability. Most of the fluids reside in matrix blocks, where they move very slow. Let ε denote the size ratio of the matrix blocks to the whole medium and let the width of the fracture planes and the porous block diameter be in the same order. If permeability ratio of matrix blocks to fracture planes is of order ε2, microscopic models for two-phase, incompressible, immiscible flow in fractured media converge to a dual-porosity model as ε goes to 0. If the ratio is smaller than order ε2, the microscopic models approach a single-porosity model for fracture flow. If the ratio is greater than order ε2, then microscopic models tend to another type of single-porosity model. In this work, these results will be proved by a two-scale method.

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5

Leger, J. R., and G. J. Swanson. "Efficient array illuminator using binary-optics phase plates at fractional-Talbot planes." Optics Letters 15, no. 5 (March 1, 1990): 288. http://dx.doi.org/10.1364/ol.15.000288.

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6

Paidar, Václav, and Andriy Ostapovets. "Displacive Phase Transformations." Solid State Phenomena 150 (January 2009): 159–74. http://dx.doi.org/10.4028/www.scientific.net/ssp.150.159.

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Shear deformation and shuffling of atomic planes are elementary mechanisms of collective atomic motion that take place during displacive phase transformations. General displacements of atomic planes are examined, i.e. -surface type calculations extensively used for the stacking faults and crystal dislocations are applied to single plane shuffling and alternate shuffling of every other atomic plane producing in combination with homogeneous deformation the hcp structure (martensitic type) from the initial bcc structure (austenitic type). Similar approach considering shear type planar displacements leads to the Zener path between the bcc and fcc lattices. The effect of additional deformation required to obtain the close-packed atomic arrangements is examined as well. Finally, the influence of volume modification on phase transitions is investigated. The energies of various structural configurations are calculated using many-body potentials for the description of interatomic forces. Such atomic models are tested to check their suitability for investigation of the role of interfaces in the displacive structural transitions.

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Zhao, Xiaxia, Rong Mo, and Zhiyong Chang. "Enhanced geometric constraint-based phase unwrapping algorithm in binocular stereo vision fringe projection system." Insight - Non-Destructive Testing and Condition Monitoring 63, no. 9 (September 1, 2021): 540–46. http://dx.doi.org/10.1784/insi.2021.63.9.540.

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Phase unwrapping plays an important and central role in phase-based digital fringe projection profilometry. The unwrapping quality directly influences the three-dimensional measurement accuracy. Recently, an effective geometric constraint-based phase unwrapping algorithm has been proposed to obtain the continuous absolute phase map and the unwrapped phase accuracy was found to be high. However, in this technique the virtual depth plane at z = zmin is often created empirically, which increases the manual measurement error. For this reason, this paper proposes a method for accurately constructing the virtual plane and further applies it to phase unwrapping of objects with a larger depth range. In this method, a binocular stereo vision system is used as the measurement set-up for the virtual depth plane construction and a series of virtual depth planes at z = zimin (i ≥ 2) is automatically built using a computational framework. Then, the phase is unwrapped for each region according to the continuity of the unwrapped phase and a complete absolute phase map is obtained by merging the unwrapped phases in all regions for 3D reconstruction. In this process, the virtual depth planes are created automatically and quantitatively by the measurement system. No human intervention is required and it greatly reduces the manual measurement error. Experiments show that the artificial virtual planes can be built accurately and the phase is unwrapped correctly and readily.

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8

Iwai, Kazuhiko, Manabu Usui, and Shigeo Asai. "Alignment of Primary Phase of a Binary Alloy during Solidification." Advanced Materials Research 26-28 (October 2007): 563–65. http://dx.doi.org/10.4028/www.scientific.net/amr.26-28.563.

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A static magnetic field and an alternating current are imposed on a metallic alloy during solidification for a crystal alignment of the primary phase. A Sn-10%Pb is selected as a sample because its primary phase is expected to have an anisotropic nature in magnetic susceptibility. In the x-ray diffraction pattern of the sample solidified without the magnetic field, the first and second highest peaks are (101) and (211) planes. On the other hand, those solidified with the magnetic field are (200) and (220) planes which are magnetically preferred planes. That is, the primary phase crystals in the sample solidified with the magnetic field are aligned to the specific direction.

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9

Paidar, Václav. "Elemental Interfaces and Displacive Phase Transformations." Advances in Science and Technology 59 (September 2008): 63–68. http://dx.doi.org/10.4028/www.scientific.net/ast.59.63.

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Two basic processes, namely shear and shuffling of atomic planes can be considered as elementary mechanisms of displacive phase transformations. The atomistic models suitable to investigate the role of interfaces in the structural changes are tested. The many-body potentials are used for the description of interatomic forces. General displacements of atomic planes are examined, i.e. γ-surface type calculations extensively used for stacking fault and lattice dislocation analysis are applied to single plane shuffling and alternate shuffling of every other atomic plane producing in combination with homogeneous deformation the hcp structure. Similar approach considering shear type planar displacements leads to the Zener path between the bcc and fcc lattices. The effect of additional deformation required to obtain the close-packed atomic arrangements is analysed.

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10

Braga de Oliveira, Flávia, Gilberto Álvares da Silva, and Leonardo Martins Graça. "Defining the hematite topotaxial crystal growth in magnetite–hematite phase transformation." Journal of Applied Crystallography 53, no. 4 (June 18, 2020): 896–903. http://dx.doi.org/10.1107/s1600576720006305.

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Magnetite and hematite iron oxides are minerals of great economic and scientific importance. The oxidation of magnetite to hematite is characterized as a topotaxial reaction in which the crystallographic orientations of the hematite crystals are determined by the orientation of the magnetite crystals. Thus, the transformation between these minerals is described by specific orientation relationships, called topotaxial relationships. This study presents electron-backscatter diffraction analyses conducted on natural octahedral crystals of magnetite partially transformed into hematite. Inverse pole figure maps and pole figures were used to establish the topotaxial relationships between these phases. Transformation matrices were also applied to Euler angles to assess the diffraction patterns obtained and confirm the identified relationships. A new orientation condition resulting from the magnetite–hematite transformation was characterized, defined by the parallelism between the octahedral planes {111} of magnetite and rhombohedral planes \{10\bar {1}1\} of hematite. Moreover, there was a coincidence between one of the octahedral planes of magnetite and the basal {0001} plane of hematite, and between dodecahedral planes {110} of magnetite and prismatic planes \{11\bar {2}0\} of hematite. All these three orientation conditions are necessary and define a growth model for hematite crystals from a magnetite crystal. A new topotaxial relationship is also proposed: (111)Mag || (0001)Hem and (\bar {1}\bar {1}1)_{\rm Mag} || (10\bar {1}1)_{\rm Hem}.

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11

Murayama, M., L. Reich, and K. Hono. "Clustering and Segregation of Ag and Mg Atoms in the Nucleation and Growth Stage of Ω And T1 Precipitates In Al-Cu(-Li) Alloys." Microscopy and Microanalysis 4, S2 (July 1998): 116–17. http://dx.doi.org/10.1017/s1431927600020705.

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Trace additions of Ag and Mg in Al-Cu and Al-Li-Cu alloys change the precipitation processes drastically. In Al-Cu-Mg-Ag alloy, plate-like Ω phase precipitates on the {111} matrix planes. Similarly, additions of Ag and Mg to Al-Li-Cu alloy cause uniform dispersion of the T1 precipitate on the {111} matrix planes. Ω and T1 phases are structurally and morphologically similar, and a similar mechanism is expected to work in both alloy systems to enhance uniform dispersion of the plate-like precipitates on the {111} planes. A previous atom probe work [1] reported that Ag and Mg are segregated at the αΩ. interfaces in an Al-Cu-Mg-Ag alloy. In an Al-Li-Cu-Mg-Ag alloy, Ag and Mg atoms were found to be incorporated with the T, phase [2]; however, because of the thinness of the T1, plate, the exact location of these atoms with respect to the T1, phase could not be determined sucessfully by a conventional atom probe.

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12

Üner, Serkan, Erman Özsayin, Alkor Kutluay, and Kadir Dirik. "Polyphase tectonic evolution of the Aksu Basin, Isparta Angle (Southern Turkey)." Geologica Carpathica 66, no. 2 (April 1, 2015): 157–69. http://dx.doi.org/10.1515/geoca-2015-0017.

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Abstract The Aksu Basin, within the Isparta Angle, is located to the north of the intersection of the Aegean and Cyprus arcs and has been evolving since the Middle Miocene. Correlation of: (1) kinematic analysis of fault planes that cut the basin fill, (2) the reactivation/inversion of fault planes and (3) sedimentological data indicate that the Aksu Basin has evolved by four alternating compressional and extensional tectonic phases since its formation. The first phase was NW-SE oriented compression caused by the emplacement of the Lycian Nappe units which ended in Langhian. This compressional phase that induced the formation and the initial deformation of the basin was followed by a NW-SE extensional phase. This tectonic phase prevailed between the Langhian and Messinian and was terminated by a NE-SW compressional regime known as the Aksu Phase. The neotectonic period is characterized by NE-SW extension and began in the Late Pliocene. Correlation with the existing tectonic literature shows that the order of deformational phases proposed in this study might also be valid for the entire Isparta Angle area.

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13

Arrizón, Victor, and J. Ojeda-Castañeda. "Irradiance at Fresnel planes of a phase grating." Journal of the Optical Society of America A 9, no. 10 (October 1, 1992): 1801. http://dx.doi.org/10.1364/josaa.9.001801.

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14

Thompson, Scott M., and Hongbin Ma. "RECENT ADVANCES IN TWO-PHASE THERMAL GROUND PLANES." Annual Review of Heat Transfer 18 (2015): 101–53. http://dx.doi.org/10.1615/annualrevheattransfer.2015011163.

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15

Kath, William L. "Slowly Varying Phase Planes and Boundary-Layer Theory." Studies in Applied Mathematics 72, no. 3 (June 1985): 221–39. http://dx.doi.org/10.1002/sapm1985723221.

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16

Isernia, Tommaso, Giovanni Leone, and Rocco Pierri. "Unique phase reconstruction of near fields over planes." Optics Communications 130, no. 1-3 (September 1996): 131–42. http://dx.doi.org/10.1016/0030-4018(96)00301-x.

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17

Kumagai, Masaaki. "Development of a 3D Vision Range Sensor Using Equiphase Light Section Method." Journal of Robotics and Mechatronics 17, no. 2 (April 20, 2005): 110–15. http://dx.doi.org/10.20965/jrm.2005.p0110.

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Many autonomous and industrial robots require three-dimensional (3D) environmental sensors. Stereovision or laser range finders are often used to detect distance to obstacles or targets. We propose 3D measurement system using active stereovision based on light section and phase shift. A special light source consisting of a rotating cylinder and a lamp projects planes of lights whose intensities vary sinusoidally over time. Each plane phase differs from those of other planes, so we distinguish which plane sectioned the target from the phase. Images from the video camera are processed into phases of each pixel that indicate distance to measured targets. This needs only simple calculation for phase detection and simultaneously operates multiple systems. The basic principle and expansion for practical use are proposed and experimental results are detailed using a trial, verifying the proposal’s effectiveness.

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18

Fukuda, K. "Phenomenological analysis of α′L-to-β martensitic transformation in phosphorus-bearing dicalcium silicate." Journal of Materials Research 14, no. 2 (February 1999): 460–64. http://dx.doi.org/10.1557/jmr.1999.0066.

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Crystals of (Ca1.95□0.05) (Si0.9P0.1)O4, where □ denotes a vacancy, composed of both the α′L and β phases, were prepared and examined by the precession method. The β phase was exclusively twinned on (100)β, and the relative volumes of the twin-related variants were almost identical with each other. On the basis of the lattice correspondence between the two phases and their cell parameters, the phenomenological crystallographic theory was applied to determine the habit planes and the shape deformations upon α′L-to-β martensitic transformation. The habit planes, which define the coherent interphase boundaries between α′L and β, were nearly parallel to either (100)α′L or (010)α′L·. The alternate shape deformations that produce the former habit planes resulted in the actual (100) twin structure of the β phase. The total displacement was along [100]α′L with the magnitude of 0.008. Because the transformation involved a very small volumetric shrinkage of 0.6%, the strain accommodation would be almost completed. The coherency at the interface boundaries between the two phases and the effective strain accommodation probably caused the thermoelasticity of the Ca2SiO4 solid solutions.

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19

Vasil’ev, Mikhail G., Anton M. Vasil’ev, Alexander D. Izotov, Yuriy O. Kostin, and Alexey A. Shelyakin. "Growing epitaxial layers of InP/InGaAsP heterostructures on the profiled InP surfaces by liquid-phase epitaxy." Kondensirovannye sredy i mezhfaznye granitsy = Condensed Matter and Interphases 23, no. 2 (June 4, 2021): 204–11. http://dx.doi.org/10.17308/kcmf.2021.23/3430.

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The effect of various planes was studied when growing epitaxial layers by liquid-phase epitaxy (LPE) on the profiled InP substrates. The studies allowed obtaining buried heterostructures in the InP/InGaAsP system and creating highly efficient laser diodes and image sensors.It was found that protruding mesa strips or in-depth mesa strips in the form of channels formed by the {111}А, {111}B, {110}, {112}A, or {221}A family of planes can be obtained with the corresponding selection of an etching agent, strip orientation, and a method of obtaining a masking coating. It was noted that in the case of the polarity of axes being in the direction of <111>, the cut of mesa strips was conducted along the most densely packaged planes. This cut led to the difference in rates of both chemical etching and epitaxial burying of profiled surfaces.The cut was made along the planes at a low dissolution rate {111}A for a sphalerite lattice, to which the studied material, indium phosphide, belongs. Analysis of planes {110} and {Ī10} showed that the location of the most densely packaged planes {111}A and {111}B relative to them is different.

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20

Karnthaler, H. P., and T. Waitz. "In situ investigations of the fcc to hcp martensitic phase transformation in CoNi." Proceedings, annual meeting, Electron Microscopy Society of America 48, no. 4 (August 1990): 546–47. http://dx.doi.org/10.1017/s0424820100175867.

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CoNi alloys show like pure Co a martensitic phase transformation between the fcc high temperature phase and the hcp low temperature phase. In Co+32%Ni the mean transformation temperature is at room temperature RT. Since the hysteresis is rather large (± 150°C) both phases can be observed in a stable configuration at RT. The two close packed lattices can transform into each other by the movement of a Shockley partial dislocation on every other close packed plane. In the case of the fcc → hcp transition there are four {111} planes which can act as habit planes. Therefore, caused by topological reasons the growing lamellas will hinder each other during their expansion. This seems to be an important difference to the reversed transformation where only one habit plane exists.Single crystals of Co+32%Ni were grown under vacuum by a modified Bridgeman technique. The crystals were in the fcc phase at RT. Discs of 1mm diameter with 〈112〉 orientation were prepared by spark erosion.

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21

Cámara, F., J. C. Doukhan, and M. A. Carpenter. "Lattice defects in lawsonite: a TEM investigation." Mineralogical Magazine 65, no. 1 (February 2001): 33–39. http://dx.doi.org/10.1180/002646101550109.

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AbstractLattice defects in lawsonite have been studied by transmission electron microscopy. It is proposed that twinning and easy glide systems are 1/2[110] {110}; the easy glide planes are coincident with twin planes. This mineral displays high sensitivity to the electron beam, even at low temperatures. In situ precipitates appear as a consequence of beam irradiation. The precipitation takes places first on dislocations, then on twin boundaries and then in the matrix, causing ‘coffee-bean’ contrast features typical of precipitates. The studies were performed at low temperature (∼110 K) in order to investigate the low temperature displacive transitions from space group Cmcm to Pmcn and P21cn and elucidate their microscopic character. No characteristic microstructural texture, such as antiphase domains associated with the transition, were observed, however. This is probably due to the high mobility of protons under the electron beam. The development of regularly spaced dislocations along twin planes is hypothesized as the only evidence that a phase transition takes place at a nanoscale.

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22

Terai, Tomoyuki, Nobuki Tamai, Takashi Fukuda, and Tomoyuki Kakeshita. "Microstructures Formed by Charge Ordering Transition in Pr_0.55Ca_0.45MnO₃ and Nd_0.5Sr_0.5MnO₃." Materials Science Forum 512 (April 2006): 223–26. http://dx.doi.org/10.4028/www.scientific.net/msf.512.223.

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We have made crystallographic analysis for microstructures formed by charge ordering transitions in Pr0.55Ca0.45MnO3 and Nd0.5Sr0.5MnO3. From the results, it was found that all interfaces between crystallographic domains of Pr0.55Ca0.45MnO3 are {101}CO ( CO represents a charge ordered phase) twinning planes and that most of interfaces between crystallographic domains of Nd0.5Sr0.5MnO3 are {112}CO twinning planes. These twinning planes correspond to {110} planes in simple cubic perovskite structure.

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23

Bertazzo, S., and Celso A. Bertran. "Crystallites Size and Changes in Mineral Phase of Bone with Age and Type of Bone." Key Engineering Materials 309-311 (May 2006): 7–10. http://dx.doi.org/10.4028/www.scientific.net/kem.309-311.7.

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In this work, some modifications that occur in crystallites that compose the mineral phase of bone throughout the lives of animals were studied by X-ray diffractometry. The Debye-Scherrer equation was applied to the diffractograms, allowing the determination of the mean crystallite size and the changes in the mean crystallite size with relation to the diffraction planes 002 and 310. Likewise, the intensity of peaks in the diffractograms corresponding to the same diffraction planes was correlated with the number of crystallographic planes or of unit cells present in the crystallites.

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24

Wu, Dong, Xinbo Qi, Ze Cai, Dawei Wang, Yanlei Hu, Jiawen Li, and Jiaru Chu. "Direct Generation of Airy Beams at Designed Fourier Planes Using Integrated Airy Phase Plates." IEEE Photonics Technology Letters 33, no. 12 (June 15, 2021): 595–98. http://dx.doi.org/10.1109/lpt.2021.3078262.

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25

Zhang, J. X., and H. Q. Ye. "Deformation-induced α2 ↔ γ phase transformation in a Ti–48Al–2Cr alloy." Journal of Materials Research 15, no. 10 (October 2000): 2145–50. http://dx.doi.org/10.1557/jmr.2000.0309.

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The structure of γ–α2 interfaces in deformed Ti–48Al–2Cr alloy was analyzed by high-resolution transmission electron microscopy (HREM) and image simulations. Growth of γ–TiAl plate in α2–Ti3Al phase was found to be a result of a ledge mechanism consisting of Shockley partial dislocations on alternate (0001)α2 planes. The height of the ledges was always a multiple of two (0001)α2 planes. The γ → α2 phase transformation was also an interface-related process. Large ledges of six close packed planes (111)γ high were often observed at the γ–α2 interface. Every large ledge consisted of six Shockley partial dislocations that originated from the γ–a2 interfacial lattice misfit. The movement of these partial dislocations accomplished the transformation of γ → α2 phase. Comparing the experimental and simulated HREM image, it was found that atomic reordering appears during the deformation-induced γ↔α2 transformation.

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Li, Lei, Yudong Zhang, Claude Esling, Huixue Jiang, Zhihao Zhao, Yubo Zuo, and Jianzhong Cui. "Crystallographic features of the primary Al3Fe phase in as-cast Al–3.31wt% Fe alloy." Journal of Applied Crystallography 43, no. 5 (September 10, 2010): 1108–12. http://dx.doi.org/10.1107/s0021889810029493.

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The preferred crystallographic extension directions of the primary Al3Fe phase formed during the solidification of the Al–3.31wt% Fe alloy have been confirmed as 〈010〉 or 〈011〉. Two sorts of twins related to the extension directions were found and their complete twinning elements determined. The morphologies of the primary Al3Fe phase related to the crystallographic extension directions and twinning modes are analysed. The crystallographic surface planes binding the primary phase in the extension directions are identified. The formation of the twins is attributed to these surface planes.

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Soto, Marcos, and Eva Acosta. "Improved phase imaging from intensity measurements in multiple planes." Applied Optics 46, no. 33 (November 12, 2007): 7978. http://dx.doi.org/10.1364/ao.46.007978.

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28

Riera, José A. "Phase separation and pairing in coupled chains and planes." Physical Review B 49, no. 5 (February 1, 1994): 3629–32. http://dx.doi.org/10.1103/physrevb.49.3629.

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Hansen, Per Lyngs, Jesper Lemmich, John Hjort Ipsen, and Ole G. Mouritsen. "Two coupled Ising planes: Phase diagram and interplanar force." Journal of Statistical Physics 73, no. 3-4 (November 1993): 723–49. http://dx.doi.org/10.1007/bf01054347.

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30

Korovin, E. N., S. A. Filist, V. I. Serebrovskiy, and L. V. Shulga. "Contour Analysis of Phase Planes of Quasi-Periodic Biosignals." Biomedical Engineering 47, no. 4 (November 2013): 199–201. http://dx.doi.org/10.1007/s10527-013-9370-5.

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31

Winkler, H. P., D. Topa, and E. Keller. "Pb5In3Bi5S17[Pb4.94(3)In3.05(3)Bi4.99(3)S17] and its structural relationship with Pb4In3Bi7S18." Acta Crystallographica Section C Crystal Structure Communications 68, no. 7 (June 13, 2012): i45—i49. http://dx.doi.org/10.1107/s0108270112021865.

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The title phase (pentalead triindium pentabismuth heptadecasulfide) has been synthesized and structurally characterized. Its structure contains mixed Bi/In, In/Bi and Pb/In positions; all atoms lie on crystallographic mirror planes. The structural relationship between Pb5In3Bi5S17and a phase known by the formula Pb4In3Bi7S18is discussed. A comparatively large and complex structural `seed' is defined which is common to both phases. The structural changes within this seed when moving from one phase to the other are described by graphical means.

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Vilardy O., Juan M., Carlos J. Jimenez, and Cesar O. Torres M. "Optical Image Encryption System Using Several Tilted Planes." Photonics 6, no. 4 (November 7, 2019): 116. http://dx.doi.org/10.3390/photonics6040116.

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A well-known technique for optical image encryption is the double random phase encoding (DRPE) technique, which uses two random phase masks (RPMs), one RPM at the input plane of the encryption system and the other RPM at the Fourier plane of the optical system, in order to obtain the encrypted image. In this work, we propose to use tilted planes for the Fourier and the output planes of the optical DRPE encryption system with the purpose of adding two new security keys, which are the angles of the tilted planes. The optical diffraction on a tilted plane is computed using the angular spectrum of plane waves and the coordinate rotation in the Fourier domain. The tilted distributions at the intermediate and output planes of the optical DRPE encryption system are the second RPM and the encrypted image, respectively. The angles of the tilted planes allow improvement to the security of the encrypted image. We perform several numerical simulations with the purpose of demonstrating the validity and feasibility of the proposed image encryption system.

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ALBAYRAK, ERHAN, SEYMA AKKAYA, and SABAN YILMAZ. "THE CRYSTAL FIELD EFFECTS ON THE PHASE DIAGRAMS OF THE SPIN-2 BILAYER BETHE LATTICE." International Journal of Modern Physics B 22, no. 27 (October 30, 2008): 4877–98. http://dx.doi.org/10.1142/s0217979208049054.

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The bilayer spin-2 Ising model on the Bethe lattice is investigated by taking into account the intralayer coupling constants of the two layers J1 and J2, interlayer coupling constant between the layers J3 and crystal field interaction Δ by using the exact recursion equations in a pairwise approach. The ground state (GS) phase diagrams of the model are obtained on the (J2/|J1|, J3/q|J1|) planes for given Δ values and on the (Δ/qJ, J3/qJ) plane when J1 = J2 = J, and thus 33 distinct GS configurations are found. The temperature-dependent phase diagrams are obtained for J1 > 0, J2 > 0, and for J3 > 0 or J3 < 0 on the (kT/J1, J3/J1) planes for given Δ/qJ1 and J2/J1 and on the (Δ/J, kT/J) plane for given J3/J when J1 = J2 = J for the coordination number q = 3. It was found that the system exhibits both first- and second-order phase transitions and tricritical points. The paramagnetic phases are also classified by studying the thermal variations of the quadrupolar moments.

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34

Devan, Rupesh S., Jin-Han Lin, Wei-Der Ho, Sheng Yun Wu, Yung Liou, and Yuan-Ron Ma. "Investigation of high-temperature phase transformation in one-dimensional Ta2O5nanorods." Journal of Applied Crystallography 43, no. 5 (August 19, 2010): 1062–67. http://dx.doi.org/10.1107/s0021889810026646.

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The thermochromic phase transformations that occur in one-dimensional Ta2O5nanorods were analysed at elevated temperatures ranging from 300 to 750 K. X-ray photoemission spectroscopy data revealed not only the electronic structures and chemical properties of the one-dimensional Ta2O5nanorods, but also their stoichiometric Ta and O compositions. High-temperature X-ray diffraction data revealed complex and polymorphic thermochromic phase transformations of the α(1 0 11), α(200), α(2 0 10), β(3 11 1) and β(2 21 1) lattice planes in the one-dimensional Ta2O5nanorods, which incorporate β to α (β–α), β to β (β–β), α to α (α–α) and α to β (α–β) phase transitions. The thermochromic phase transformations between α- and β-phase crystals can be explained by a shift in 2θ and expansion of thedspacing of the lattice planes.

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35

CAMPOS-CANTÓN, E., J. S. GONZÁLEZ, and J. URÍAS. "POINCARÉ PLANES IN NONLINEAR ELECTRONICS." International Journal of Bifurcation and Chaos 17, no. 01 (January 2007): 199–208. http://dx.doi.org/10.1142/s0218127407017264.

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Details of electronic circuitry to define Poincaré planes in the phase space of nonlinear electronic systems are presented. It allows an experimental setup to capture data at every moment the system's orbit crosses the Poincaré plane. We illustrate how the circuit is used in an experimental setup that allows us (i) to reconstruct bifurcation cascades and to disclose induced first return chaotic maps in a harmonically forced nonlinear oscillator, and (ii) to study bistable switching in Chua's oscillator.

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36

Askarpour, V., H. Klefte, and M. J. Clouter. "Brillouin scattering near the α–β phase transitions of N2 and CO." Canadian Journal of Chemistry 66, no. 4 (April 1, 1988): 541–48. http://dx.doi.org/10.1139/v88-092.

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The technique of high resolution Brillouin spectroscopy has been used to determine the adiabatic elastic constants of single crystals of β-N2 and β-CO as a function of temperature, in an effort to study the α–β phase transition. For all elastic constants, there is an increase of approximately 1%/K on cooling and there is no evidence of further mode softening, even within 0.5 K of the phase transition. Three large single crystals of α-CO were grown. The orientations were determined, by Laue X-ray diffraction, and correlated to the orientations of the parent β-crystals. The β-phase hexagonal basal planes appear to transform to planes of the form {110} in the α-phase cubic structure.

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37

Cannelli, G., R. Cantelli, and F. Cordero. "ORDERING AND DIFFUSION OF OXYGEN AT LOW TEMPERATURE IN Y-Ba-Cu-O BY MEASUREMENTS OF ELASTIC ENERGY DISSIPATION AND MODULUS." International Journal of Modern Physics B 02, no. 05 (October 1988): 1157–70. http://dx.doi.org/10.1142/s0217979288001049.

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The anelastic relaxation spectrum between 300 and 50 K has been investigated in YBa 2 Cu 3 O 7−x in the super- and semiconducting state. In the superconductor a phase transformation has been detected at T t ≃ 240 K . The 2nd phase forming on cooling, likely has the same orthorombic symmetry (with higher distorsion) of that of the lattice and consists of a different oxygen vacancy ordering in the chains of the basal planes. The necessity of a phase diagram where the two orthorombic phases coexist in an extended region down to low temperature is pointed out. The 2nd phase is considered to contribute to the observed softening and hysteresis of frequency (elastic constants). The raise of elastic energy dissipation around T t with thermal cycling, which is not completely recoverable by the room temperature ageing, indicates the occurrence of progressive lattice damaging with cycling number, and is attributed to the non-elastic accommodation of the 2nd-phase misfitting domains. These lattice defects are identified with the additional twins, which have been reported to form and dissolve on cycling below 240 K. Other reproducible features observed in the superconducting state are dissipation maxima at 160 and 110 K, just above the critical temperature and a drastic decrease in dissipation below T c . When oxygen has been removed from the basal planes (6.2 ± 0.10 atoms per formula unit) all processes illustrated above practically disappear and a new intense thermally activated relaxation process manifests itself around 70 K (in the kHz range), attributed to the stress-induced hopping of oxygen in the basal planes. The derived diffusion coefficient is extremely high: D(T) = 4 × 104 exp (− 0.10 eV/kT ).

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38

Newhouse, Randal, and Gary S. Collins. "Diffusion in La_nCoIn_3n+2 Phases Studied by Perturbed Angular Correlation." Defect and Diffusion Forum 323-325 (April 2012): 453–58. http://dx.doi.org/10.4028/www.scientific.net/ddf.323-325.453.

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Jump frequencies of 111In/Cd tracer atoms were measured for a series of layered phases LanCoIn3n+2 using the technique of perturbed angular correlation of gamma rays (PAC). The frequencies were determined by analysis of nuclear quadrupole relaxation produced by fluctuating electric field gradients. Samples were synthesized having nominal values n= 1, 2, 3, 5 and , with n= corresponding to the L12 phase LaIn3. The phases form heuristically from LaIn3 by replacing every (n+1)th (100) mixed plane of La and In atoms with a plane of Co-atoms. For the n=1 phase, LaCoIn5, jump frequencies were too small to detect. Two signals were observed, one for indium atoms next to the Co-planes and the other for more distant indium atoms. No relaxation was observed for atoms next to the Co-planes, indicating that there is no diffusion across the Co-planes. With increasing n, jump rates for the other In-atoms increased toward values observed for LaIn3. Jump frequency activation enthalpies for n= 3 and 5 were observed to be the same as for n=, suggesting the same diffusion mechanism. However, the jump-frequency prefactors were found to be smaller for small n, which is attributed to reductions in the connectivity of the diffusion sublattice. We conclude that diffusion in the layered phases is remarkably similar to diffusion in LaIn3 once the reduced connectivity is taken into account.

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39

Deborah, J. Serrien, and Stephan P. Swinnen. "Isofrequency and Multifrequency: Coordination Patterns as a Function of the Planes of Motion." Quarterly Journal of Experimental Psychology Section A 50, no. 2 (May 1997): 386–404. http://dx.doi.org/10.1080/713755708.

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A series of studies examine the maintenance of the relative phase of simultaneous cyclic limb movements by the manipulation of the planes of motion during isofrequency and multifrequency conditions. To evaluate predictions from a dynamic pattern approach in which differences in the limbs’ uncoupled frequencies give way to competitive interactions when the limbs are moved simultaneously, Experiment 1 determined the preferred frequencies of single-limb movements during sagittal and transverse planes of motions. The results revealed that the plane in which the motion was produced significantly affected the cycle frequencies. In investigating isofrequency coordination, Experiment 2 showed that homologous limbs were more accurate in attaining the relative phasing when moving in one as compared to two separate planes, whereas no such effect was observed for non-homologous limbs. Furthermore, the planes of motion significantly influenced the variability of relative phasing such that two-plane motions were less stable than one-plane motions. Experiment 3 examined the effect of the planes of motion upon multifrequency coordination and demonstrated that the homologous and homolateral limbs were less successful in producing the relative phasing when the motions were produced in one as compared to two planes, whereas this effect was not observed for the heterolateral limbs. These findings indicate that frequency detuning resulting from the planes manipulation affects the quality of phase-locking during isofrequency and multifrequency conditions, even though it may be assumed that additional neural constraints are involved in the interlimb coordination process.

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40

Jiang, Janna, and Per Nylén. "Numerical Modelling of the Compression Behaviour of Single-Crystalline MAX-Phase Materials." Advanced Materials Research 89-91 (January 2010): 262–67. http://dx.doi.org/10.4028/www.scientific.net/amr.89-91.262.

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In this article a numerical model to describe the mechanical behaviour of nanophased singlecrystalline Ti3SiC2 is proposed. The approach is a two dimensional finite element periodic unit cell consisting of an elastic matrix interlayered with shear deformable slip planes which obey the Hill’s yield criterion. The periodic unit cell is used to predict compression material behaviour of Ti3SiC2 crystals with arbitrary slip plane orientations. Stress strain relationships are derived for Ti3SiC2, and the effect of slip plane volume fraction as well as orientation of the slip planes are investigated. The two main deformation mechanisms of the material namely; ordinary slip and so called kinking are considered in the study.

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41

Eibl, O., p. Pongratz, P. Skalicky, and J. H. Mazur. "TEM investigation of extended defects in hexagonal BaTiO3." Proceedings, annual meeting, Electron Microscopy Society of America 45 (August 1987): 174–75. http://dx.doi.org/10.1017/s0424820100125804.

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Barium titanate is known mostly for the ferroelectric, piezoelectric and dielectric properties of its tetragonal phase. Above 1330°c in strongly reducing atmosphere (pO2 = 10-20 bar) BaTi03 transforms from the cubic to the high temperature hexagonal polymorph preserved at room temperature as a metastable phase containing defects which are a subject of the present investigation. The hexagonal phase consists of close packed (Ba-03) planes and Ti planes stacked along the [001] direction resulting in a ABCACB stacking sequence. In this structure TiO6 octahedra are linked either by common corners or common faces. A high resolution image of the projected structure along [100] is shown in Fig. 1.Stacking faults are observed on (001) planes. The density of faults is l-2xl06 m-1 and the faults are extending over the whole grain size which is a few hundred microns. Partial dislocations usually 100 nm apart are found in the fault plane.

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42

Hall, Ernest L., and James D. Livingston. "Deformation modes in Laves phase intermetallics." Proceedings, annual meeting, Electron Microscopy Society of America 47 (August 6, 1989): 318–19. http://dx.doi.org/10.1017/s0424820100153567.

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There is at present a large amount of interest in the mechanical behavior of intermetallic alloys, and one of the largest classes of these alloys are the Laves phases. There are three basic types of Laves phases: cubic (C15), hexagonal (C14), and dihexagonal (C36), with stacking sequences on the close-packed planes of ABCABC..., ABAB..., and ABAC..., respectively, where each capital letter represents an interpenetrating four-atomic-layer unit. This structural complexity gives rise to a special mode of deformation for Laves phases, called synchroshear, which requires the cooperative movement of adjacent layers in different directions. Very little work has been done to date on the deformation modes in Laves phases because of the inherent brittleness of these materials at room temperature. However, through alloying it is possible to obtain mixtures of the various Laves phase types, and to affect such properties as stacking fault energy, and thus opportunities may exist for increasing ductility. In this study, the deformation microstructures of different Laves phase types were explored.

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43

Zhang, Xiao-Ling, Bao-Feng Zhang, and Yu-Chi Lin. "Accurate phase expansion on reference planes in grating projection profilometry." Measurement Science and Technology 22, no. 7 (May 26, 2011): 075301. http://dx.doi.org/10.1088/0957-0233/22/7/075301.

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44

Ortuo, M., and P. M. Echenique. "Phase shifts, image planes, and surface states at metal surfaces." Physical Review B 34, no. 8 (October 15, 1986): 5199–204. http://dx.doi.org/10.1103/physrevb.34.5199.

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45

Tippie, Abbie E., and James R. Fienup. "Phase-error correction for multiple planes using a sharpness metric." Optics Letters 34, no. 5 (February 27, 2009): 701. http://dx.doi.org/10.1364/ol.34.000701.

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46

Gladbach, Peter. "A Phase-field Model of Dislocations on Parallel Slip Planes." PAMM 15, no. 1 (October 2015): 545–46. http://dx.doi.org/10.1002/pamm.201510263.

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47

Achahbar, A., and J. Marro. "Phase transitions in a driven lattice gas in two planes." Journal of Statistical Physics 78, no. 5-6 (March 1995): 1493–520. http://dx.doi.org/10.1007/bf02180140.

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48

Liu, Yaping, Samuel M. Allen, and James D. Livingston. "Room temperature deformation and stress-induced phase transformation in Laves phase Fe2Zr." Proceedings, annual meeting, Electron Microscopy Society of America 50, no. 1 (August 1992): 180–81. http://dx.doi.org/10.1017/s0424820100121302.

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Laves phases have three structures: Cubic C15 (MgCu2), hexagonal C14 (MgZn2) and dihexagonal C36 (MgNi2). Their high-temperature deformability has been studied by many investigators. But the study of their room-temperature deformation is very limited. By such studies, it may be possible to enhance the room-temperature deformability of Laves phases.In the present study, arc-melted samples of Fe-10 at% Zr, containing α-Fe and Fe2Zr Laves phase, were annealed at 1190°C for 48 hr and then compressed at 0.001 inch/min to strains of 46∼48% at room temperature. The 0.2% offset yield stress is about 75 kg/mm2. Micrographs revealed dislocation structures in α-Fe and cracks in proeutectic Fe2Zr after deformation. X-ray diffraction patterns show that the crystal structure of Fe2Zr is mainly C36 before deformation. After compression, the C15 peaks, which overlap other peaks in the pattern, increase in intensity, as seen in Fig. 1. This demonstrates that a phase transformation occurred as a result of deformation. The detail and mechanism of the transformation were studied by TEM. A characteristic banded structure which was rarely found in undeformed sample was frequently observed in the compressed Fe2Zr particles, as shown in Fig. 2. Electron diffraction patterns and high-resolution TEM showed that these bands have a C15 structure with a {111} plane parallel to the basal plane of C36 structure in the adjacent parts of a particle. Fig. 3 is a high-resolution TEM picture showing the stacking sequence of the close-packed planes of the particle containing the C15 band in Fig. 2. It has a ABCABC stacking sequence in the central part (C15) and ABAC on the two sides (C36). Inside the C15 band there are many stacking faults on {111} planes. A twinned region (C15T) is also seen to the right of the C15 region.

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49

Huang, Jianyu, Yuntian T. Zhu, and Hirotaro Mori. "Structure and phase characteristics of amorphous boron–carbon–nitrogen under high pressure and high temperature." Journal of Materials Research 16, no. 4 (April 2001): 1178–84. http://dx.doi.org/10.1557/jmr.2001.0162.

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An amorphous boron–carbon–nitrogen (a-BCN) phase was synthesized by ball milling of a mixture of hexagonal BN (h-BN) and graphite with a nominal composition of (BN)0.5C0.5 in atomic ratio. Electron energy-loss spectroscopy studies indicated that the bonding of the a-BCN is in an sp2 configuration and the mixing between the BN and the C species was achieved at a nanometer scale, but the a-BCN phase was more likely a mechanical mixture rather than a chemical mixture. High-pressure and high-temperature (HPHT) treatment at 7.7 GPa and 2300 °C of the a-BCN phase resulted in complete segregation of the carbon and BN species, forming a nanocrystalline composite material comprising cubic BN (c-BN), amorphous carbon, and turbostratic graphite. The grain size of the c-BN phase was about 70 nm. No mutual solubilities between c-BN and carbon were found, and the two different species (C and BN) were well separated. An epitaxial relationship, i.e., the (0002) planes of graphite being parallel to the (111) planes of c-BN, was also found. The formation of ternary BCN phases was never found in the present experiment. Our experimental results also suggest the possibility of synthesizing c-BN grains encapsulated with graphite under controlled HPHT conditions.

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50

JUNG, J., H. YAN, H. DARHMAOUI, and M. ABDELHADI. "NANOSCOPIC PHASE SEPARATION AND THE UNIVERSAL TRANSPORT AND MAGNETIC PROPERTIES OF HIGH Tc SUPERCONDUCTORS." International Journal of Modern Physics B 13, no. 29n31 (December 20, 1999): 3528–31. http://dx.doi.org/10.1142/s0217979299003362.

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We have found the correlation between nanoscopic phase separation in the copper-oxygen planes of YBCO and TlBCCO and the transport and magnetic properties of these materials in the a-b planes such as: the temperature dependence of the critical current density Jc( T ), the temperature dependence of the superfluid density ns( T )∝1/λ2( T ) at low temperatures, the temperature dependence of the normalized logarithmic relaxation rate S(T), and the dependence of the effective energy barrier against vortex motion on the current density Ueff( J ). These properties are controlled by the ratio of the amount of an underdoped filamentary phase to that of an optimally doped one.

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Journal articles on the topic 'Phase planes'

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