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Phase Diagrams
Published in Yip-Wah Chung, Monica Kapoor, Introduction to Materials Science and Engineering, 2022
This is where phase diagrams can be helpful in deciphering the problem faced by our engineer in the above story. A phase is the part of the material with uniform structure and composition, which can be solid, liquid, or gas. A phase diagram is a graph showing what phases are present at a given temperature, pressure, and composition and their relative concentrations. For each phase, we can learn at what temperature it begins to solidify or melt. Since the presence and concentration of these phases control properties, phase diagrams are important in the design and processing of metallic alloys, ceramics, and polymers. In the preceding example, inspection of the tungsten-carbon phase diagram (Figure 5.1) shows that addition of 1.5 w/o carbon to tungsten reduces the melting point from 3415°C to about 2860°C. This is below the exhaust gas temperature of 3000°C; the nozzle failed simply because the temperature exceeds the melting point of the tungsten-carbon alloy!
Phase equilibria: non-reactive systems
Published in W. John Rankin, Chemical Thermodynamics, 2019
When the three phases (solid, liquid and gas) co-exist, P = 3 and F = 0, and neither temperature nor pressure can be varied independently. This condition can only be achieved at a unique temperature and pressure, and the equilibrium of the three phases is therefore represented by a point on the phase diagram, called the triple point. The triple point of water occurs at 273.16 K (0.01°C) and a pressure of 611.7 Pa. The system is said to be invariant. There is an upper limit to the vapour pressure curve in Figure 13.1, the critical point, the point at which the distinction between the vapour and liquid disappears and only one phase is present. At temperatures and pressures greater than those of the critical point, supercritical fluid fills the container (Section 3.4.1).
Phase and State Transitions and Transformations in Food Systems
Published in Dennis R. Heldman, Daryl B. Lund, Cristina M. Sabliov, Handbook of Food Engineering, 2018
Phase diagrams are important tools, or maps, which describe the equilibrium state of a material at any combination of pressure, temperature, and volume. A two-dimensional phase diagram may show regions of pressure and temperature at which various phases are thermodynamically stable. Phase boundaries in a phase diagram are lines, which describe the pressure–temperature combinations at which two phases may coexist at equilibrium.
Sequential adaptive design for jump regression estimation
Published in IISE Transactions, 2022
Chiwoo Park, Peihua Qiu, Jennifer Carpena-Núñez, Rahul Rao, Michael Susner, Benji Maruyama
The second motivating application is to optimize the design of experiments for effectively exploring a chemical phase diagram in chemistry. A phase diagram is a map that relates different experimental conditions to the physical states of materials. The physical state suddenly changes from one state to another around the experimental conditions where phase transitions occur, as illustrated in Figure 1(b). Typically, the elucidation of a phase diagram requires a large number of experiments to be performed to probe possible physical states that may exist in the experimental phase-space. Emerging trends in materials research are to use machine learning algorithms to achieve the data-driven optimization of experimental designs, namely, autonomous experimentation (Stach et al., 2021). In particular, we are interested in experiments to study the chemical conditions required for good carbon nanotube growth. The chemical conditions include the reaction temperature and a relative ratio of two chemical ingredients (i.e., a reducing agent and an oxidant). The total nanotube growth changes abruptly around the boundary condition in the relative ratio for a given temperature. Therefore, the total nanotube growth is a piecewise continuous function of the relative ratio and temperature. Optimizing the experimental design so as to relate the two conditions to the nanotube growth can be formulated as the problem of selecting the design points for estimating the piecewise continuous function.
Development of novel phase change materials based on methyl laurate and fatty acids for low-temperature applications
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2023
Zifeng Ma, Kai Yue, Zhihan Yao, Xinxin Zhang
The melting point and latent heat of the pure materials are presented in Table 1 and are used to calculate the specific compositions and eutectic points of the binary eutectic mixtures (Eq.. (1)) and plot the binary phase diagrams in MATLAB. Figure 3(a) shows that the liquidus temperature of the ML decreases, while that of LA increases with increasing molar ratio of LA. The two liquidus lines intersect at the point where the molar ratios of LA and ML are 14.05% and 85.95%, respectively. At this point (i.e., the ML-LA eutectic point), the two components simultaneously melt at the same temperature of 4.25°C. Moreover, the binary eutectic phase diagram demonstrates that the eutectic point has the lowest melting temperature in the mixture.
Configurational phase transition in AuxCu1−x nano-alloy: first principle and Monte-Carlo calculations
Published in Phase Transitions, 2018
Mujahid Eldaw Jahelnabi Mohammed, Mohammed Alshaikh Hamid Khalafalla, Mohamed Hassan Eisa, Rawia Abdelgani Elobaid Mohammed
Owing to their interesting chemical and physical properties, gold–copper (Au–Cu) nanoparticles have been regarded as valuable tools in a variety of disciplines [1–3] such as the communications [4], renewable energy [5], molecular sensing [6] and medical imaging [7,8]. For most of these applications, it is very instructive to thermodynamically characterize the active material. That is why thermodynamic phase diagrams are regarded as an important source of information in bulk material. Phase diagrams are maps (for solids, most often of temperature vs. composition) indicating which phases are present at equilibrium for the given conditions [9]. However, thermal stability in nanoparticles is often different from the corresponding bulk material [10]. Most often information about the thermodynamic properties of nanoparticles are obtained theoretically due to the relatively difficult experimental measurements of thermal stability of nanoparticles [11]. For instance, the Computer Calculation of Phase Diagrams (CALPHAD) method has widely been used for the prediction of phase structures of bulk alloys [12]. A modified version of CALPHAD method has also been used for the prediction of the phase diagram of nanoparticles [13], leading to the demonstration of the particle size dependence of the system’s energy [14]. Nevertheless, it has been shown that conventional CALPHAD was limited to particle sizes > 5 nm [15]. Interestingly, Monji and Jabbareh [11,16] have developed a new CALPHAD model for predicting the phase diagram of nanoparticles with radius < 5 nm. In comparison with the conventional models, the results showed better agreements with the experiments [17].