Self‐consistent phonon calculation of the β phase and the α‐β transition in solid nitrogen

1974 ◽  
Vol 61 (4) ◽  
pp. 1411-1414 ◽  
Author(s):  
J. C. Raich ◽  
N. S. Gillis ◽  
T. R. Koehler
Keyword(s):  
Β Phase ◽  
Solid Nitrogen ◽  
Self Consistent ◽  
Phonon Calculation

Constitutive Analysis of the High-Temperature Deformation Behavior of Single Phase α-Ti and α+β Ti-6Al-4V Alloy

2007 ◽  
Vol 539-543 ◽  
pp. 3607-3612 ◽  
Author(s):  
Jeoung Han Kim ◽  
Jong Taek Yeom ◽  
Nho Kwang Park ◽  
Chong Soo Lee
Keyword(s):  
High Temperature ◽  
Flow Stress ◽  
Deformation Behavior ◽  
Single Phase ◽  
Volume Fraction ◽  
High Temperature Deformation ◽  
Temperature Deformation ◽  
Β Phase ◽  
Α Phase ◽  
Self Consistent

The high-temperature deformation behavior of the single-phase α (Ti-7.0Al-1.5V) and α + β (Ti-6Al-4V) alloy were determined and compared within the framework of self-consistent scheme at various temperature ranges. For this purpose, isothermal hot compression tests were conducted at temperatures between 650°C ~ 950°C to determine the effect of α/β phase volume fraction on average flow stress under hot-working condition. The flow behavior of α phase was estimated from the compression test results of single-phase α alloy whose chemical composition is close to that of α phase of Ti-6Al-4V alloy. On the other hand, the flow stress of β phase in Ti-6Al-4V was predicted by using self-consistent method. The flow stress of α phase was higher than that of β phase above 750°C, while the β phase revealed higher flow stress than α phase at 650°C. Also, at temperature above 750°C, the predicted strain rate of β phase was higher than that of α phase. It was found that the relative strength between α and β phase significantly varied with temperature.

scholarly journals Determining Ti-17 β-Phase Single-Crystal Elasticity Constants through X-Ray Diffraction and Inverse Scale Transition Model

2011 ◽  
Vol 681 ◽  
pp. 97-102 ◽  
Author(s):  
Sylvain Fréour ◽  
Emmanuel Lacoste ◽  
Manuel François ◽  
Ronald Guillén
Keyword(s):  
Mechanical Load ◽  
Cubic Phase ◽  
X Ray Diffraction ◽  
X Ray ◽  
Β Phase ◽  
Consistent Model ◽  
Self Consistent ◽  
Diffraction Lattice ◽  
Two Phases ◽  
Multi Phase

The scope of this work is the determination of single-crystals elastic constants (SEC) from X-ray diffraction lattice strains measurements performed on multi-phase polycrystals submitted to mechanical load through a bending device. An explicit three scales inverse self-consistent model is developed in order to express the SEC of a cubic phase, embedded in a multi-phase polycrystal, as a function of its X-ray Elasticity Constants. Finally, it is applied to a two-phases (α+β) titanium based alloy (Ti-17), in order to estimate Ti-17 β-phase unknown SEC. The purpose of the present work is to account the proper microstructure of the material. In particular, the morphologic texture of Ti-17 a-phase, i.e. the relative disorientation of the needle-shaped grains constituting this phase, is considered owing to the so-called Generalized Self-Consistent model.

Raman Study of Solid Nitrogen in the β Phase and Close to the Melting Line

2013 ◽  
Vol 32 (1) ◽  
pp. 25-31 ◽  
Author(s):  
E. Çetinbaş İşeri ◽  
H. Yurtseven
Keyword(s):  
Molecular Nitrogen ◽  
Melting Curve ◽  
Molecular Solids ◽  
Melting Line ◽  
Volume Data ◽  
Β Phase ◽  
Solid Nitrogen ◽  
Raman Study ◽  
Temperature And Pressure ◽  
Lattice Modes

AbstractThis study gives the Raman frequencies calculated as functions of temperature and pressure for the lattice modes in the solid β phase and close to the melting line (β-fluid transition). The experimental volume data from the literature is used to calculate the Raman frequencies for the molecular nitrogen system. Some observed Raman frequencies are also used as the initial data to perform our calculations given here.It is shown that our values predict the observed Raman frequencies of the lattice modes studied in the β phase and also on the solid β-fluid melting curve. This initiates the applicability of the method given here to calculate the frequency from the volume data in various phases of molecular solids such as solid nitrogen.

Self-consistent phonon calculation of structures and thermodynamic properties of small argon crystallites

1977 ◽  
Vol 15 (8) ◽  
pp. 4056-4064 ◽  
Author(s):  
R. D. Etters ◽  
Lynna Kanney ◽  
N. S. Gillis ◽  
Jaya Kaelberer
Keyword(s):  
Thermodynamic Properties ◽  
Self Consistent ◽  
Phonon Calculation

scholarly journals Characterizing and Modeling the Precursors to Coarse Grain Formation during Beta-Annealing of Ti-6Al-4V

2020 ◽  
Vol 321 ◽  
pp. 12007
Author(s):  
A.L. Pilchak ◽  
S. Srivatsa ◽  
N.C. Levkulich ◽  
V. Sinha ◽  
E.J. Payton ◽  
...  
Keyword(s):  
Finite Element ◽  
Strain Path ◽  
Element Model ◽  
Coarse Grain ◽  
Forging Process ◽  
Β Phase ◽  
Coarse Grains ◽  
Self Consistent ◽  
Grain Formation

Coarse prior β grains exceeding 3 mm in diameter have been sporadically observed following β annealing of α+β forged titanium alloys. Recent work has shown that the occurrence of coarse grains may be due in part to the stabilization of a {001}<110> texture during hot working that was further enhanced in intensity at the expense of other texture components during the early stages of β annealing. With the majority of the material comprised of low misorientation subgrains of a single texture component, the nuclei for coarse grains was the minority fraction of grains that were highly misoriented, and therefore had boundaries with higher energy and mobility, compared to the average grain. In this work, Ti-6Al-4V bar was side-pressed to various reductions in the α+β phase field to further investigate the role of texture and the effects of strain, strain-path, and deformation heating on the propensity to form abnormally large grains during β-annealing. The experiments were interpreted in the context of a continuum finite element model and viscoplastic self-consistent crystal plasticity simulations. Based on the results from experiment and modeling, we make recommendations with respect to the α+β forging process to avoid the occurrence of excessively coarse β grains.

Optical Birefringence in Solid Nitrogen

1973 ◽  
Vol 51 (14) ◽  
pp. 1590-1592 ◽  
Author(s):  
D. J. Gannon ◽  
J. A. Morrison
Keyword(s):  
Upper Bound ◽  
X Ray Diffraction ◽  
Optical Birefringence ◽  
Cubic Symmetry ◽  
X Ray ◽  
Β Phase ◽  
Quantitative Measurements ◽  
Α Phase ◽  
Solid Nitrogen ◽  
Solid Phases

Quantitative measurements have been made of optical birefringence in two solid phases (α and β) of nitrogen. For the β phase (T > 35.6 °K), the observed birefringence is consistent with the structure determined by X-ray diffraction (P63/mmc) and it fixes the c/a ratio of the lattice accurately. While the measurements do not distinguish between the two structures (Pa3 and P213) that have been proposed for the α phase (T < 35.6 °K), they place a strict upper bound on the possible distortion that might arise from displacement of the nitrogen molecules from sites of cubic symmetry.

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