Stability of dendritic arrays

Warren, J A; Langer, J S

doi:10.1103/PhysRevA.42.3518

Title: Stability of dendritic arrays

Full Record
Other Related Research

Abstract

We propose an approximate method for studying steady-state properties and linear stability of the dendritic arrays that are formed in directional solidification of alloys. Our analysis is valid at high growth rates where the primary spacing between dendrites is larger than the velocity-dependent solutal diffusion length. We compute a neutral stability boundary and find that, in the situations where we expect our results to be valid, the experimental data of Somboonsuk, Mason, and Trivedi (Metall. Trans. A 15A, 967 (1984)) lie in the stable region, well away from the boundary.

Authors:

Warren, J A ^[1]; Langer, J S ^[2]

Department of Physics, University of California, Santa Barbara, CA (USA)
Institute for Theoretical Physics, University of California, Santa Barbara, CA (USA)

Publication Date:: Sat Sep 15 00:00:00 EDT 1990

OSTI Identifier:: 6487156

DOE Contract Number:: FG03-84ER45108

Resource Type:: Journal Article

Journal Name:: Physical Review, A (General Physics); (USA)

Additional Journal Information:: Journal Volume: 42:6; Journal ID: ISSN 0556-2791

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE; ALLOYS; CRYSTALLIZATION; STABILITY; DENDRITES; STEADY-STATE CONDITIONS; CRYSTALS; PHASE TRANSFORMATIONS; 360102* - Metals & Alloys- Structure & Phase Studies

Citation Formats


                    Warren, J A, and Langer, J S. Stability of dendritic arrays.  United States: N. p., 1990. 
        Web.  doi:10.1103/PhysRevA.42.3518.

Copy to clipboard


                    Warren, J A, & Langer, J S. Stability of dendritic arrays.  United States.  https://doi.org/10.1103/PhysRevA.42.3518

Copy to clipboard


                    Warren, J A, and Langer, J S. 1990.  
        "Stability of dendritic arrays".  United States.  https://doi.org/10.1103/PhysRevA.42.3518.

Copy to clipboard


                    
@article{osti_6487156,

  title        = {Stability of dendritic arrays},

  author       = {Warren, J A and Langer, J S},

  abstractNote = {We propose an approximate method for studying steady-state properties and linear stability of the dendritic arrays that are formed in directional solidification of alloys. Our analysis is valid at high growth rates where the primary spacing between dendrites is larger than the velocity-dependent solutal diffusion length. We compute a neutral stability boundary and find that, in the situations where we expect our results to be valid, the experimental data of Somboonsuk, Mason, and Trivedi (Metall. Trans. A 15A, 967 (1984)) lie in the stable region, well away from the boundary.},

  doi          = {10.1103/PhysRevA.42.3518},

  url          = {https://www.osti.gov/biblio/6487156},
  journal      = {Physical Review, A (General Physics); (USA)},

  issn         = {0556-2791},

  number       = ,

  volume       = 42:6,

  place        = {United States},

  year         = {Sat Sep 15 00:00:00 EDT 1990},

  month        = {Sat Sep 15 00:00:00 EDT 1990}

}

Copy to clipboard

Journal Article:

https://doi.org/10.1103/PhysRevA.42.3518

Other availability

Find in Google Scholar

Search WorldCat to find libraries that may hold this journal

Save / Share:

Export Metadata

Save to My Library

Similar records in OSTI.GOV collections:

Prediction of dendritic spacings in a directional-solidification experiment

Journal Article Warren, J; Langer, J - Physical Review E; (United States)

We present a theoretical analysis of the formation of a dendritic array in a directional-solidification experiment. Our calculation contains three sequential ingredients: acceleration of an initially flat interface and the concomitant buildup of a solutal boundary layer in front of it; onset of a morphological instability, triggered by thermal fluctuations, producing a relatively finely spaced array of dendritic tips; coarsening of this array and final selection of a steady-state primary spacing. For sufficiently large growth speeds, where the resulting dendrites interact with each other weakly, we find--with no adjustable parameters--good agreement with the experiments of Trivedi and Somboonsuk [Acta Metall.more »« less
https://doi.org/10.1103/PhysRevE.47.2702
Three-dimensional dendritic needle network model for alloy solidification

Journal Article Tourret, D.; Karma, A. - Acta Materialia

Here, we present a three-dimensional (3D) formulation of the multiscale Dendritic Needle Network (DNN) model for dendritic microstructure growth. This approach is aimed at simulating quantitatively the solidification dynamics of complex hierarchical networks in spatially extended dendritic arrays, hence bridging the scale gap between phase-field simulations at the scale of a few dendrites and coarse-grained simulations on the larger scale of entire polycrystalline structures. In the DNN model, the dendritic network is represented by a network of branches that interact through the solutal diffusion field. The tip velocity V(t) and tip radius ρ(t) of each needle is determined by combiningmore »« less
Cited by 41
https://doi.org/10.1016/j.actamat.2016.08.041

Full Text Available
Predictions of the Hunt-Lu array model compared with measurements for the growth undercooling of Al{sub 3}Fe dendrites in Al-Fe alloys

Journal Article Liang, D; Jones, H - Scripta Materialia

Earlier contributions by the authors reported the first measurements of growth temperature as a function of growth velocity V and alloy concentration C{sub 0} for a dendritic intermetallic phase (Al{sub 3}Fe, in Al-rich Al-Fe alloys). Comparison with predictions of the model of Kurz, Giovanola and Trivedi (KGT model) of dendrite growth of a needle gave predicted {Delta}T a factor between 1.1 and 2.5 above the measured values. A subsequent paper presented evidence that the Al{sub 3}Fe dendrite tips were indeed needle-like under the conditions studied, as distinct from the plate-like morphology that develops behind the dendrite tips. The KGT modelmore »« less
https://doi.org/10.1016/S1359-6462(97)80263-1
Phase-field modeling of microstructural pattern formation during directional solidification of peritectic alloys without morphological instability

Journal Article Shing Lo, Tak; Karma, Alain; Plapp, Mathis - Physical Review E

During the directional solidification of peritectic alloys, two stable solid phases (parent and peritectic) grow competitively into a metastable liquid phase of larger impurity content than either solid phase. When the parent or both solid phases are morphologically unstable, i.e., for a small temperature gradient/growth rate ratio (G/v{sub p}), one solid phase usually outgrows and covers the other phase, leading to a cellular-dendritic array structure closely analogous to the one formed during monophase solidification of a dilute binary alloy. In contrast, when G/v{sub p} is large enough for both phases to be morphologically stable, the formation of the microstructure becomesmore »« less
https://doi.org/10.1103/PhysRevE.63.031504
Direct Measurement of Dendritic Array Stability

Journal Article Losert, W; Cummins, H; Mesquita, O; ... - Physical Review Letters

Stability of a uniformly spaced dendritic array against a spatial period doubling instability was studied through UV thermal perturbations of every other dendrite tip. We observed that above a critical pulling speed the array is stable against these perturbations and we measured decreasing decay rates of the perturbed mode as we approached the critical speed. In the linear regime, our measurements are qualitatively consistent with the Warren-Langer linear stability analysis for a dendritic array [J.thinspA. Warren and J.thinspS. Langer, Phys.thinspthinspRev.thinspthinspA {bold 42}, 3518 (1990); Phys.thinspthinspRev.thinspthinspE {bold 47}, 2702 (1993)], while in the nonlinear regime fitting to a third order amplitudemore »« less
https://doi.org/10.1103/PhysRevLett.81.409

Similar Records