Material-specific parameters

Model Equations to Describe Component Balances. The design of PVD reacting systems requires a set of model equations describing the component balances for the reacting species and an overall mass balance within the control volume of the surface reaction zone. Constitutive equations that describe the rate processes can then be used to obtain solutions to the model equations. Material-specific parameters may be estimated or obtained from the literature, collateral experiments, or numerical fits to experimental data. In any event, design-oriented solutions to the model equations can be obtained without recourse to equipment-specific fitting parameters. Thus translation of scale from laboratory apparatus to production-scale equipment is possible. 

For amorphous polymers which melt above their glass transition temperature Tg, the WLF equation (according to Williams, Landel, Ferry, Eq. 3.15) with two material-specific parameters q and c2 gives a better description for the shift factors aT than the Arrhenius function according to Eq. 3.14. 

The differing permeability of a given gas through various materials is expressed in terms of the gas and material specific parameter P. Its dimension results from Eq. (9-1) ... 

Such a curve of K, vs. d is naturally dependent on the material investigated and also on material specific parameters as molecular weight in PMMA this leads to a shift to lower K,-values or equivalently G -values with decreasing molecular weight It should be noted that slow crack propagation curves of quasi-brittle materials have been used by different authors [e.g. predict creep life curves ... 

The most advanced material model presently available for UHMWPE is the HM. This model focuses on creating a mathematical representation of the deformation resistance and flow characteristics for conventional and highly crosslinked UHMWPE at the molecular level. The physics of the deformation mechanisms establish the framework and equations necessary to model the behavior on the macroscale. As already mentioned, to use the constitutive model for a given material requires a calibration step where material-specific parameters are determined. A variety of numerical methods may be used to determine the material-specific parameters for a constitutive theory. In the previous section we employed a numerical optimization technique to identify the material parameters for the constitutive theory. 

Here Eg is bulk sample band gap, A and B are the material specific parameters. 

Here, Hhp = (Hq + kd ) and Hqc = (Cd ) represent dislocation-related dislocation hardening based on the H-P effect and bandgap-related hardening based on the quantum confinement effect, as indicated above, following Tse s [34] calculations. Ho is the single-crystal hardness and k is a material constant. C is a material-specific parameter equal to zero for metals and equal to 211Ny exp (1.191fi) for covalent materials, where Ne is the valence electron density and fj is the Philips ionicity of the chemical bond. 

The reference set of parameters was provided in Eikerling and Berg (2011). In the case of material-specific parameters, Nafion is the benchmark system. The pore walls should be considered as hydrophilic. Hence, 0 = 0 is a reasonable choice. For the mean value of the wall charge density, a value ao = —0.08 C m was taken at the fixed reference radius of 7 o = 1 nm. This value depends on the lEC and the structure of ionomer bundles. 

The particular utility of NMR microscopy lies in the contrasts that are available. Image contrast in NMRI depends on material-specific parameters (spin-density and nuclear spin relaxation times), operator-related parameters (pulse sequence, pulse delay and repetition times) and external parameters (temperature, viscosity, etc.). Common contrast mechanisms in solid-state NMR imaging are based on relaxation times (T, T2, T p. T ) and chemical shifts. Most studies develop contrast based either on spin density or T2 differences since these show up immediately without the need of modifying the imaging sequence. The unsurpassed soft-matter contrast of NMRI is hard to achieve with competitive methods like X-ray or computer tomography. 

Contrast in NMRI depends on both material-specific and operator-selected parameters. The material-specific parameters include the spin density and the relaxation times Tj and T2. The operator-selected parameters include the pulse sequence (inversion recovery, spin-echo, etc.) and the pulse delay and repetition times (timing parameters). For a given imaging system and pulse sequence, it is the delay and repetition times in conjunction with the intrinsic material parameters which dictate the appearance of the final image. If the correct pulse sequence is employed and the relaxation times of the two materials are known, it is possible to calculate the delay and/or repetition times that will produce the maximum diflerence in signal intensity between those materials. 

As a specific example, we introduce the Berthelot gas as the working substance the equation of state is given by (a and b are materials-specific parameters)... 

On the right-hand side of this equation we have a number of material specific parameters such as p, Ngt sind the function C(p, T). According to this relation, this particular combination of material properties yields a pure number, iV + 1. We have conjectured that this pure number is not material specific and is therefore universal. This hypothesis can be tested by comparing experimental data for polymer melts against Eq. (19)... 

Here, a and b are material-specific parameters that are adapted to measured data or can be calculated from the thermodynamic critical data of the gas ... 

TABLE 1. Material specific parameters of the CEF, ac u. OiJn and kcu —axe, for a bcc Ouo.Ao no.so alloy. The first set of parameters, indicated as LSMS, has been extracted from the qV data obtained by the exact LSMS calculations in Rcf.[8] for a 1024 atoms supcrccll that simulate a random alloy, The parameters in the second set have been calculated using the CPA+LF model of Ref.[7]. All the quantities are in atomic units. 

As discussed above, Eqs. (25-26) completely determine the distribution of charge excesses for a given alloy configuration. The three material specific parameters contained in the CEF can be extracted from order N as well as from CPA-I-LF calculations. In this section I shall compare the charge excesses obtained by the CEF with order N Locally Self-consistent Multiple Scattering (LSMS) theory calculations [8]. 

The Weibull parameter m and the characteristic stress Oq are material-specific parameters. 

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