Forward Simulation Analysis Research Articles

Diffusion coefficients and atomic mobilities in the BCC phase of the Al–Nb–V system

Diffusion coefficients in the BCC phase of the Al–Nb–V ternary system are studied for the first time, including an assessment of the atomic mobilities. Ternary interdiffusion coefficients are obtained from the intersecting diffusion paths of several sets of diffusion couples that are annealed at both 1100 °C and 1200 °C. Existing experimental data from the pertinent binary systems are also employed for the assessments of atomic mobilities using the 1-parameter Z-Z-Z binary diffusion coefficient model developed by Zhong et al [1]. Interdiffusion coefficients in the BCC region of the Al–V system are also extracted through a forward-simulation analysis and incorporated into the mobility modeling. A complete description of diffusion in the BCC phase of the Al–Nb–V system is presented following the Binary and Cross-Binary Parameters Only (BCBPO) model developed by Zhong and Zhao [2]. Our data will be valuable input to diffusion-related simulation of refractory high entropy alloys containing aluminum.

Experimental study of diffusion coefficients and assessment of atomic mobilities in FCC Al–Cu–V alloys

With the increasing demand for high-temperature aluminum (Al) alloys, there is a need for fundamental kinetic information to guide their design and development. This study investigates the diffusion behavior of the FCC Al–Cu–V system and assesses the atomic mobility parameters. Diffusion couples were assembled and annealed at 530, 555, and 580 °C for 1500 h to facilitate solute diffusion. The concentration profiles of Cu and V were measured using electron probe microanalysis (EPMA), and the diffusion coefficients were extracted using the Forward Simulation Analysis (FSA) method. The atomic mobility parameters for the Al–Cu–V system were assessed using the diffusion models in the DICTRA software program and verified by validation experiments involving annealing at temperatures of 535 and 565 °C for 1500 h. The activation energies for the diffusion of Cu and V were calculated and analyzed. The results reveal that adding Cu increased the diffusivity of V, while adding V decreased the diffusivity of Cu within the Al–Cu–V system. These findings of the kinetics of the FCC Al–Cu–V system would be beneficial for alloy design and processing optimization.

Interdiffusion behaviors and mechanical properties of Hf-X (X=Nb, Ta) binary systems

The diffusion behaviours and mechanical properties of the Hf-X (X = Nb, Ta) systems have been investigated using diffusion couples in the temperature range from 1150 °C to 1500 °C. The interdiffusion coefficients of Hf-X (X = Nb, Ta) systems were extracted using forward simulation analysis (FSA) based on the Sauer-Freise method. According to the results, the interdiffusion coefficients of the Hf-X (X = Nb, Ta) systems decreased as the Nb or Ta content increased. In the meantime, the diffusion activation energies of Hf-X (X = Nb, Ta) systems increased as the Nb or Ta content increased. Finally, the hardness and Young’s moduli of the Hf–Nb and Hf–Ta systems were determined by nanoindentation tests. The largest hardness values of the Hf–Nb and Hf–Ta were 5.2 GPa and 5.3 GPa, respectively. Young’s largest moduli of the Hf–Nb and Hf–Ta were 221 GPa and 238 GPa, respectively. The present results provide helpful diffusional data and mechanical properties for the materials design, research and development of hafnium-based alloys.

Interdiffusion behaviors and mechanical properties of Zn–Cr system

Diffusion couple technique has been utilized to study the interdiffusional behaviors of Zn–Cr system. Two intermetallic compounds (Zn13Cr, Zn17Cr) have been found in the diffusion zone between 598 K and 653 K. For the existence of Zn13Cr phase, the incremental diffusion couple has been used to confirm, and the results show that the Zn13Cr phase can be determined in the present work. However, the thickness of Zn13Cr is very thinner than that of Zn17Cr, which indicate the growth of Zn13Cr is very slow. The thickness of Zn17Cr satisfied the parabolic growth law. EPMA was used to obtain the composition profiles and the interdiffusion coefficients of Zn13Cr, Zn17Cr and Zn (hcp) have been extracted by forward simulation analysis embedded in ‘Pydiffusion’ code. The mechanical properties of Zn17Cr were also determined by nanoindentation technique, and the hardness and Young's modulus of Zn17Cr is 3.01 GPa and 165.78 GPa, respectively.

Experimental measurement of diffusion coefficients and assessment of diffusion mobilities in HCP Mg–Li–Al alloys

An atomic mobility database was established for the ternary HCP Mg–Li–Al system as a part of an ongoing effort to enable rapid development of novel lightweight Mg alloys. Three sets of three diffusion couples were assembled and annealed at temperatures ranging from 400 to 500 °C. Li concentration profiles were measured using a combination of Auger electron spectroscopy (AES) and inductively coupled plasma optical emission spectrometry (ICP-OES), while Al composition profiles were acquired using electron probe microanalysis (EPMA). The forward-simulation analysis (FSA) was employed to extract both interdiffusion and impurity diffusion coefficients from the collected experimental composition profiles. These measured diffusivity data were used to assess and iteratively optimize mobility parameters for the Mg–Li–Al system using the diffusion module within the Thermo-Calc Software package (DICTRA). The reliability of the assessed mobility parameters was further confirmed by two validation diffusion couples that were annealed at 425 and 475 °C for 96 and 48 h, respectively. It was observed that additions of Li increased the diffusivity of Al in HCP Mg, whereas additions of Al decreased the diffusivity of Li in HCP Mg.

Discrimination and application of the properties of the in-seam seismic wave in the collapse column of the working face

During in-seam wave seismic exploration of working face, the anomaly has serious diversification, and sometimes it is difficult to accurately determine the nature of the anomaly. Due to the large differences in the collapse column shape of the working face, especially when there are multiple sets of collapsed columns, it is difficult to effectively distinguish its nature. This has been an unresolved problem since the tunnel wave earthquake was introduced. Based on the analysis of the characteristics of the collapse column in the working face, the forward simulation analysis of the collapse column is carried out. Based on the field application case, the BPT algorithm and the SIRT algorithm in the calculation process of the energy attenuation coefficient tomography overlay inversion calculation are studied. Through analyzing the amplitude and frequency dispersion characteristics of the verification of the collapse column anomaly, a method for identifying the seismic properties of the working face collapse column groove wave is proposed, which effectively improves the accuracy of the in-seam wave seismic detection.

Diffusion Coefficients and Phase Equilibria of the Cu-Zn Binary System Studied Using Diffusion Couples

The diffusion behavior and phase equilibria in the Cu-Zn binary system were investigated using solid–solid and solid–liquid diffusion couples. Heat treatments at temperatures ranging from 100 to 750 °C were performed and the samples were examined using optical microscopy, energy dispersive x-ray spectroscopy, and electron probe microanalysis to identify the phases and to obtain composition profiles. Solubility limits of both solid solution and intermetallic phases were then evaluated, and a forward-simulation analysis (FSA) was applied to extract interdiffusion coefficients. The composition profiles from Hoxha et al. were also re-analyzed using FSA to obtain more reliable diffusion coefficient data without the assumption of constant diffusion coefficients for the intermetallic phases. A comprehensive assessment of the interdiffusion coefficients in three intermetallic phases of the Cu-Zn system was performed based on the results from the current study as well as those in the literature. Activation energies and Arrhenius pre-factors were evaluated for each phase as a function of composition. The fitted equations based on the comprehensive assessment have the capabilities of computing the interdiffusion coefficients of each of the phases at a given composition and temperature. Suggested modifications to the Cu-Zn binary phase diagram were presented based on the new experimental information gathered from the present study. A clear explanation is provided for the puzzling low Zn concentrations often observed in the Cu-rich fcc phase of Cu-Zn diffusion couples in comparison with the expected high solubility values based on the equilibrium Cu-Zn phase diagram.

First measurement of diffusion coefficients of lithium in magnesium

Diffusion coefficients of lithium in magnesium were measured for the first time using liquid-solid diffusion couples and a forward-simulation analysis. Since lithium is too light to be reliably measured using electron probe microanalysis (EPMA), the diffusion profiles of lithium were determined by the difference between 100 percent and the Mg composition measured using EPMA. Those profiles were then proportionally adjusted to match the solubility values evaluated from reliable Mg-Li phase diagram data. Such a combined method of lithium composition by difference and proportionating to match solubility data can substantially facilitate future measurements of lithium diffusion coefficients in other lithium-containing systems.

An integrated experimental and computational study of diffusion and atomic mobility of the aluminum–magnesium system

Diffusion between Al and Mg was investigated comprehensively using both high-throughput experiments and density functional theory (DFT) calculations. Experimental diffusion coefficients in fcc Al, hcp Mg, β–Mg17Al12, γ–Mg2Al3 andε−Mg23Al30 phases were collected by combining diffusion multiples with forward-simulation analysis together with a critical review of the experimental studies in the literature. The best settings to compute the dilute (impurity) diffusion coefficients of Al and Mg using DFT were tested by comparing the computed data using various DFT settings with the critically assessed experimental diffusion coefficients in stable phases (fcc Al and hcp Mg). The optimal DFT settings were employed to calculate the dilute diffusion coefficients of Al and Mg in metastable (hypothetical) phases (hcp Al and fcc Mg) where experimental measurements were impossible. The atomic mobilities of Al and Mg in the Al–Mg binary system across the entire composition range were then reliably optimized for both the fcc and hcp phases based on the comprehensive diffusion data obtained from both experimental measurements for the stable phases and DFT calculations for the metastable phases. This study demonstrates an efficient and reliable way to develop fundamental mobility databases using integrated experimental and computational methods.

Phase equilibria and diffusion coefficients in the Fe-Zn binary system

Phase diagram and diffusion coefficients of the Fe-Zn binary system are required to predict and control the microstructure of galvanized zinc coatings and thus were systematically investigated in the temperature range from 700 to 1100 °C using nine novel Fe/Zn liquid-solid diffusion couples (LSDCs). The equilibrium compositions of the α and Γ phases of the Fe-Zn system were determined and agree well with the recently established Fe-Zn phase diagram. The extracted interdiffusion coefficients in α-Fe at temperatures between 700 and 1100 °C and in Γ at 750 and 700 °C using the forward-simulation analysis (FSA) extend the experimental interdiffusivity measurements to the whole solubility range of these two phases. Three impurity diffusion coefficients of Zn in paramagnetic α-Fe were also determined by the FSA and show good agreement with the literature data. The temperature dependence of the Zn impurity diffusion coefficients in both the paramagnetic and ferromagnetic α-Fe phases across the Curie temperature TC was established by analyzing the reliable experimental results as well as by density functional theory (DFT) calculations. The newly measured phase equilibrium and diffusivity data provide reliable inputs for future thermodynamic and kinetic modeling of the Fe-Zn system.

Phase Equilibria and Diffusion in the Ni-Cr-Pt System at 1200 °C

Pt modified NiAl, which is often simply called Pt aluminide, is widely used in jet engines as a protective coating against oxidation and hot corrosion as well as a bond coat for thermal barrier coatings. Phase equilibria and diffusion coefficients in the Ni-Cr-Pt ternary system are thus valuable data for modeling the behavior of Pt aluminide coatings on Ni-based superalloys in which Cr is an essential alloying element. A Ni-Cr-Pt diffusion multiple was made and annealed at 1200 °C for 100 h to obtain the first reliable isothermal section phase diagram for this ternary system. Interdiffusion coefficients were extracted from the measured diffusion concentration profiles using a forward simulation analysis for all the single-phase regions of the Ni-Cr, Ni-Pt and Cr-Pt binary systems. The impurity diffusion coefficient data obtained from this study are combined with literature data to assess reliable Arrhenius equations for the impurity diffusion coefficients of Pt in Ni, Ni in Pt, and Cr in Ni. An Arrhenius equation for the impurity diffusion coefficient of Cr in Pt is recommended for the first time by combining a fitted prefactor from experimental data and an activation energy value from first principles calculations.

Measurements of diffusion coefficients of Ce, Gd and Mn in Mg

Easy-to-use liquid-solid diffusion couples (LSDCs) were employed to measure the diffusion coefficients of three key alloying elements Ce, Gd and Mn in Mg at elevated temperatures. Forward simulation analysis was then performed on the concentration profiles measured from LSDCs using EPMA to extract diffusion coefficients at multiple temperatures. The new experimental data were combined with limited experimental data in the literature to establish reliable diffusion coefficient datasets which are then compared with first principles calculation results. It is concluded that Ce diffuses faster than Gd in Mg while Mn is the slowest diffusing element among the three. The interdiffusion coefficients of Mg-Ce, Mg-Gd and Mg-Mn are also determined for the first time. The current study and our previous studies together have determined reliable impurity diffusion coefficients of 8 elements Al, Ca, Ce, Gd, Mn, Sn, Zn, and Y in Mg; and the results are summarized and compared.

Pydiffusion: A Python Library for Diffusion Simulation and Data Analysis

pydiffusion is a free and open-source Python library designed to solve diffusion problems for both single-phase and multi-phase binary systems. The key features of pydiffusion include fast simulation of multi-phase diffusion and extraction of diffusion coefficients from experimental concentration profiles using forward simulation analysis. pydiffusion also provides various mathematical models for diffusion profile smoothing, diffusion coefficient evaluation, and data optimization. In pydiffusion, diffusion profiles and various phases are easy to define or read from the experimental datasets. Visualization tools based on Matplotlib are also provided to help users present or refine their simulations and analysis. Funding statement: The development of pydiffusion is supported by the US National Science Foundation (NSF) under Grant number CMMI-1333999, and it is part of an NSF Designing Materials to Revolutionize and Engineer our Future (DMREF) project.

Measurement of Diffusion Coefficients in the bcc Phase of the Ti-Sn and Zr-Sn Binary Systems

Sn and Zr are two important alloying elements in low-modulus biomedical titanium alloys, yet experimental data on Sn diffusion in bcc Ti and bcc Zr are still very limited in the literature, and thus were systematically measured in the present study using solid–solid diffusion couples (SSDCs) and novel liquid–solid diffusion couples (LSDCs). Both interdiffusion and impurity diffusion coefficients in the bcc phase of the Ti-Sn and Zr-Sn systems were extracted with forward-simulation analysis (FSA), and show good agreement with existing literature. The interdiffusion coefficients in the Ti-Sn system at six temperatures, from 950 °C to 1200 °C, extend experimental measurements to a much wider composition range, and the interdiffusion coefficients in the Zr-Sn system at 1200 °C, 1150 °C, and 1100 °C are the first such data experimentally measured. The data obtained from this study, together with our previous data for the Ti-X (X = Cr, Hf, Mo, Nb, V, Zr) systems, provide reliable experimental inputs to improve the mobility databases for advanced Ti alloys development. In addition, the excellent agreement between the LSDCs and SSDCs results validates the reliability of this novel approach by combining LSDC experiments and FSA in evaluating diffusion coefficients at elevated temperatures.

Diffusion in the Ti-Al-V System

Diffusion in the Ti-Al-V system is studied and a CALculation of Phase Diagrams (CALPHAD) diffusion mobility description is developed. Diffusion couple experiments are performed to obtain diffusion paths in the hcp phase at 923 K, 1023 K and 1123 K. The diffusion coefficient of V in the hcp-Ti phase is found to decrease with increasing Al alloying. A forward-simulation analysis is used to evaluate the impurity diffusion coefficient for Al and V diffusion in the hcp Ti-V and the Ti-Al systems which are used as input in the mobility modeling. The composition dependency for the diffusion in the hcp phase in the ternary system is accounted for and a CALPHAD diffusion mobility description is obtained by directly optimizing the mobility parameters as a function of the experimental composition profiles from the diffusion couples. Both experimental data and previous diffusion mobility descriptions in the literature for the bcc Ti-Al-V phase are adopted. A complete description of diffusion in both the hcp and bcc phases for the Ti-Al-V system is presented with the aim to be used for design of Ti alloys and processes.

Experimental Determination of Impurity and Interdiffusion Coefficients in Seven Ti and Zr Binary Systems Using Diffusion Multiples

Diffusion coefficients of seven binary systems (Ti-Mo, Ti-Nb, Ti-Ta, Ti-Zr, Zr-Mo, Zr-Nb, and Zr-Ta) at 1200 °C, 1000 °C, and 800 °C were experimentally determined using three Ti-Mo-Nb-Ta-Zr diffusion multiples. Electron probe microanalysis (EPMA) was performed to collect concentration profiles at the binary diffusion regions. Forward simulation analysis (FSA) was then applied to extract both impurity and interdiffusion coefficients in Ti-rich and Zr-rich part of the bcc phase. Excellent agreements between our results and most of the literature data validate the high-throughput approach combining FSA with diffusion multiples to obtain a large amount of systematic diffusion data, which will help establish the diffusion (mobility) databases for the design and development of biomedical and structural Ti alloys.

First Reliable Diffusion Coefficients for Mg-Y and Additional Reliable Diffusion Coefficients for Mg-Sn and Mg-Zn

Forward-simulation analysis was performed on composition profiles collected from liquid-solid and solid-solid diffusion couples to obtain diffusion coefficients of Mg-Sn, Mg-Y, and Mg-Zn. Reliable impurity diffusion coefficient of Y in Mg is obtained for the first time, showing that Y diffusion in Mg is about the same as Sn below 390 °C. The first sets of interdiffusion coefficients of Mg-Sn and Mg-Y are also obtained together with wider temperature-range data for Mg-Zn.

Accurate and efficient measurement of impurity (dilute) diffusion coefficients without isotope tracer experiments

Most impurity diffusion coefficients were measured in the 1960s and 1970s using tracer experiments with only 14 sets of tracer measurements performed worldwide in the past 15years. It is thus impractical to rely on tracer experiments to obtain the missing thousands of impurity diffusion coefficients. A recently developed forward-simulation analysis can change the scenario by reliably extracting impurity diffusion coefficients from regular diffusion couple profiles. A comparison of 51 values obtained from the forward-simulation analysis with tracer experiment values in the literature shows an excellent agreement, thus validating the reliability of the forward-simulation analysis in obtaining accurate impurity diffusion coefficients.

First experimental measurement of calcium diffusion in magnesium using novel liquid-solid diffusion couples and forward-simulation analysis

A novel liquid-solid diffusion couple enables effective measurements of composition profiles at high temperatures. A forward-simulation analysis is then performed to extract both interdiffusion and impurity diffusion coefficients. The combined method enables measurement of the first ever set of impurity diffusion coefficients of Ca in Mg and reliable high-temperature diffusion data of Al in Mg. The results show that Ca diffuses faster than the Mg self-diffusion which is faster than the Al impurity diffusion in Mg; thus Ca may not be an ideal element for the enhancement of high-temperature creep strength of Mg alloys as has been often assumed.

Inverse Analysis of Pre- and Post-Impact Dynamics for Vehicle Accident Reconstruction

In the dynamic analysis of the vehicular accident reconstruction, the vehicle motion is typically analyzed in three phases. These are pre-impact motion, impact motion, and post-impact motion, which are usually analyzed in reverse order of occurrence. Tire-ground forces are important during the pre- and post-impact motions, and less important during the impact. We present a vehicular dynamic model for pre- and post-impact as a rigid body which moves under the influence of tire-ground forces. Using a forward simulation analysis, we show how the initial sliding conditions can be computed with several final data points for vehicle's position and orientation, referred to as the inverse analysis algorithm for the accident reconstruction.