Structural phase diagram

This structural phase diagram is a result of extensive analyses of structural properties for more than 150 low-energy conformations with different values of interaction parameters [321]. 

Asymmetry parameter A at small effective string thickness [af = 0.5). The insets show corresponding conformations at q = 2.0,3.5, and 4.5, illustrating the transition from spherical to cylindrical low-energy structures. The conformational transition between Gi and B occurs near ef = 3.0. For larger values of cf, A starts to deviate significantly from zero and conformations become cylindrical. From [321]. 

Opening angle a of low-energy conformations for f = 3/2 as a function of erf (squares, iower scaie) and for 7f = 5/6 as a function of cf (circles, upper scale). The inset pictures show corresponding conformations at f = 3/2 and 7f = 1/2,4/5, illustrating the separation of the droplet from the string. From [321]. 

As expected, A increases for ef 3 and the structures become asymmetric. At this point, it is equally favorable for a monomer to stick to the string, or to form contacts to neighboring monomer layers. The conformations stretch along the string until they form a maximally compact monolayer tube surrounding the string for ef 4.5. 

Distance Ar of the center of mass of the polymer from the virtual surface of the cylinder with the radius that corresponds to the minimum position of the string potential 1.06af) for af = 1/Z. The intersection of the curve with the dotted line (Ar = 0) at er = 2.9, where the center of mass equals the radius of this cyiinder, defines the transition from Ge to C. Pictures show conformations at ef = 2,3, and 4. From [321]. 

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This text is written for a second-level materials science course. It assumes that the students have had a previous course covering crystal structures, phase diagrams, diffusion, Miller indices, polymers, ceramics, metals, and other basic topics. Many of those topics are discussed in further depth, and new topics and concepts are introduced. The coverage and order of chapters are admittedly somewhat arbitrary. However, each chapter is more or less self-contained so those using this text may omit certain topics or change the order of presentation. 

Abstract We review magnetic and structural phase diagrams of the La088MnOx,... 

Figure 2. Crystal structure phase diagram of the Lao ssMnOx (2.82

The alkylamine hydrate inclusion compounds form a large variety of structures. Phase diagram studies at the end of the last century [7651 (see Tkble 21.3), and an extensive series of phase diagram studies carried out between 1970 and 1981 [798], showed that aliphatic amines form a large variety of hydrates. Relatively few of these have been studied by X-ray crystal structure analysis and none by neutron diffraction [433, 799]. These hydrates differ from the gas hydrates and the alkyl ammonium salt hydrates in that there appear to be no definite structural types into which several hydrates can be classified. Hitherto, a different crystal structure has been observed for every alkylamine hydrate studied. In this respect, they resemble low hydrated crystals. 

Answers to such difficult questions can be found in applied thermodynamics - in terms of measured, macroscopic values of pressures, temperatures, compositions, volumes, enthalpies, etc. This chapter provides an overview of natural gas clathrate hydrates - structures, phase diagrams, and thermodynamic predictions/measurements that guide our understanding in dealing with such questions. The hydrate historical perspective provides an example of how knowledge advances in a technical field. At the conclusion of the chapter, future thermodynamic challenges are presented. 

Figure 12.21 Structural phase diagram of K2O-M0O3-P2O5 glasses. Structural units present in each region are determined by the units indicated on boundaries (After Selvaraj and Rao, 1985).

The present monograph was first written as a chapter for Volume 8 of the series Materials Sdence and Technology A Comprehensive Treatment , edited by Robert W. Cahn, Peter Haasen, and Edward J. Kramer (Volume Editor Dr. Karl Heinz Matucha). Its aim is to give an overview of intermetallics, which is both detailed and comprehensive and which includes the fundamentals as well as applications. The result is an extended, critical review of the whole field of intermetallics with an emphasis on those intermetallic phases which have already been applied as functional or structural materials or which are currently the subject of materials developments. A historical introduction and a discussion of the relationship between atomic bonding, crystal structure, phase stability and properties is followed by a discussion of the major classes of intermetallics. The titanium aluminides, nickel aluminides, iron aluminides, copper phases, A15 phases. Laves phases, beryllides, rare earth phases, and siliddes are reviewed. In particular, the crystal structures, phase diagrams, and physical properties as well as the mechanical and corrosion behavior are treated. The state of developments as well as prospects and problems are discussed in view of present and future applications. The publisher has decided to publish the review as a separate monograph in order to make it accessible to a wider audience. 

Transitions between the varions 2D phases can occur as a function of snrface temperatnre and coverage, giving rise to rather complex structural phase diagrams. For instance, the variation of the lattice misfit m with temperature (thermal expansion) or coverage (lateral compression) can indnee a change of the eqnilibrinm stractme among the various I, C, UC and HOC phases. As an example, the phase diagram... 

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Dri] Drits, M.E., Bochvar, N.R., Guzei, L.S., Lysova, E.V., Padezhnova, E.M., Rokhlin, L.L., Turkina, N.I., Cu-Fe-Ni in Binary and Multicomponent Copper-Base Systems , Nauka, Moscow, 113-115 (1979) (Crys. Structure, Phase Diagram, Phase Relations, Phys. Prop., Review, 11)... 

Zin] Zinovik, M.A., Homogeneity Region of Spinel Oxides , Russian J. Phys. Chem., 57(4), 546-548 (1983), translated from Zh. Fiz. Khim., 57(4), 904-907 (1983) (Ciys. Structure, Phase Diagram, Review, 5)... 

Akad. NaukSSSR, 70(4), 633-635 (1950) (Crys. Structure, Phase Diagram, Experimental, 5) [1951Sho] Shortsleeve, F.J., Nieholson, M.E., Transformations in Ferritic Chromium Steels Between 1100 and 1500°F (595 and 815°C) , Trans. Amer. Soc. Metals, 43, 142-160 (1951) (Crys. Straeture, Phase Relations, Experimental, Kinetics, 5)... 

Phase Equilibria in the Area of Crystallization of Alloys of die Mo-Mo2C-Cr7C3-Cr Partial System, Sov.Powder Metal. Met. Ceram., 26(5), 409-414 (1987), translated from Poroshk. Metall, (Kiev), (5), 70-76 (1987) (Crys. Structure, Phase Diagram, Experimental, 14)... 

Kuo3] Kuo, K., X-Ray Investigation of Carbides in Molybdenum Steels (in Swedish), Jernkon-torets Ann., 137(5), 141-148 (1953) (Experimental, Crys. Structure, Phase Diagram, 17) [1959Fuw] Fuwa, T., Chipman J., Activity of Carbon in Liquid-Iron Alloys , Trans. AIME, 215, 708... 

MSIT] C-Fe (Iron-Carbon) , Diagrams as Published, in MSIT Worhplace, Effenbeig, G. (Ed.), Materials Science International Services, GmbH, Stuttgart Document ID 30.13598.1.20 (2006) (Crys. Structure, Phase Diagram, Phase Relations, 2)... 

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