# Materials Algorithms ProjectProgram Library

## Program MAP_KINETICS_1DSPINODAL

### Provenance of Source Code

Professor Yoshiyuki Saito,
Waseda University,
Department of Materials Science and Engineering,
Tokyo,
Japan

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### Purpose

Simulation of one-dimensional spinodal decomposition in iron--chromium alloys. The program is based on the Cahn-Hilliard equation and is intended as an illustration for teaching purposes.

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### Specification

 Language: FORTRAN Product form: Source code

Complete program.

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### Description

Simulation of one-dimensional spinodal decomposition in iron--chromium alloys. The program is based on the Cahn-Hilliard equation and is intended as an illustration for teaching purposes.

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### References

1. M. Honjo and Y. Saito, 2000, ISIJ International, 40, 914-919.

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### Parameters

#### Input parameters

t - Real
Temperature / K, (750-850 K)

cwt - Real
Weight fraction of chromium (<0.49)

nzeitE - Integer
Heat treatment time / s (<720,000 s)

#### Output parameters

The output consists of a string of numbers, the first set of which identifies the initial distribution of chemical composition. The subsequent sets are all preceded by a value of time in seconds, followed by the string of numbers showing the new chemical composition at each location.

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### Error Indicators

Please use the program within the input ranges specified. This is to ensure stability of solutions. Every calculation will use the time values 900, 1800, 3600, 7200, 18000, 36000, 72000, 180000, 360000, 720000 seconds, up to the maximum value specified in the input.

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### Accuracy

No information supplied.

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None.

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### Example

#### 1. Program text

Complete program.

#### 2. Program data

```
Data are provided as dynamic inputs: temperature (in this example 850 K), composition (in this example 0.49) and maximum value of time (in this example 7200 s).
```

#### 3. Program results

Each string of numbers represents composition as a function of position, with equal distance intervals (0.25 nm) between each value.
```
Initial distribution of solute
0.511703   0.514240   0.528584   0.501890   0.493562   0.517719   0.494370
0.519690   0.505608   0.496655   0.502980   0.530341   0.504545   0.508784
0.507759   0.521648   0.490910   0.519797   0.497697   0.519352   0.523913
0.532150   0.524744   0.503600   0.511440   0.489043   0.506313   0.500277
0.524654   0.503148   0.502407   0.497484   0.488080   0.510785   0.518114
0.486905   0.494200   0.500652   0.530931   0.530165   0.493544   0.517725
0.493109   0.500440   0.509363   0.492298   0.508852   0.498533   0.527558
0.493694   0.486937   0.494563   0.511516   0.509340   0.517763   0.494244
0.491878   0.498637   0.525964   0.530292   0.531415   0.521756   0.497575
0.528942   0.515034   0.493747   0.532338   0.501198   0.514337   0.513181
0.521296   0.509273   0.527666   0.516331   0.498858   0.508111   0.494940
0.505895   0.520247   0.511672   0.487345   0.504944   0.513949   0.484415
0.522326   0.485877   0.508888   0.507580   0.503476   0.524213   0.486880
0.520792   0.485174   0.527708   0.509877   0.488342   0.512552   0.490057
0.522469   0.490516   0.486448
Time:     900
0.508888   0.516131   0.519140   0.517028   0.511128   0.504212   0.499187
0.497924   0.500739   0.506486   0.512981   0.517640   0.518302   0.514180
0.506644   0.499246   0.496364   0.500853   0.512031   0.525435   0.534977
0.536159   0.528193   0.514442   0.501051   0.493689   0.494394   0.500870
0.508258   0.512005   0.510061   0.503417   0.495241   0.489359   0.488742
0.494432   0.504992   0.516701   0.524943   0.526295   0.520189   0.509401
0.498945   0.493384   0.494240   0.499392   0.504794   0.507236   0.506207
0.503582   0.501628   0.501046   0.500680   0.499077   0.496462   0.495278
0.498613   0.507632   0.520059   0.531135   0.536420   0.534099   0.525553
0.514500   0.505231   0.500707   0.501673   0.506975   0.514381   0.521316
0.525442   0.525229   0.520526   0.512911   0.505303   0.500637   0.500271
0.503255   0.506969   0.508724   0.507284   0.503416   0.499252   0.496976
0.497638   0.500745   0.504722   0.507874   0.509290   0.509191   0.508605
0.508556   0.509276   0.509923   0.509065   0.505718   0.500296   0.494817
0.492029   0.493889   0.500298
Time:    1800
0.513830   0.527954   0.533885   0.529382   0.516142   0.499549   0.486789
0.483516   0.491265   0.506701   0.522788   0.532018   0.529851   0.516553
0.497700   0.482453   0.479071   0.490725   0.513609   0.538097   0.554003
0.555501   0.542002   0.518191   0.493812   0.479333   0.479862   0.492973
0.510247   0.521586   0.520553   0.507276   0.488308   0.473466   0.470647
0.482299   0.504419   0.527868   0.543160   0.545173   0.534068   0.514576
0.494644   0.481871   0.479755   0.486906   0.498684   0.509712   0.516197
0.516827   0.512158   0.503660   0.493315   0.483733   0.478158   0.479833
0.490620   0.509262   0.530717   0.548145   0.556143   0.552216   0.536925
0.514597   0.493178   0.480855   0.481872   0.495040   0.514455   0.532085
0.541586   0.540468   0.529983   0.514451   0.499961   0.491778   0.491872
0.498308   0.506521   0.511741   0.511342   0.505880   0.498473   0.492956
0.491832   0.495190   0.501066   0.506851   0.510843   0.512964   0.514265
0.515678   0.516929   0.516411   0.512188   0.503592   0.492408   0.482670
0.478905   0.483882   0.496983
Time:    3600
0.561508   0.601659   0.609607   0.584193   0.526884   0.459005   0.415685
0.413324   0.452836   0.520134   0.578987   0.602425   0.584352   0.527029
0.454296   0.406381   0.401816   0.443175   0.519055   0.589941   0.626815
0.629095   0.598088   0.534061   0.460391   0.416727   0.418643   0.462071
0.524994   0.568968   0.570669   0.528455   0.462472   0.411024   0.396778
0.425140   0.492417   0.568463   0.616618   0.629493   0.609169   0.553457
0.475184   0.413125   0.389991   0.406517   0.460144   0.532892   0.588195
0.606985   0.587544   0.531287   0.457254   0.401459   0.379906   0.393151
0.443962   0.523235   0.594014   0.632661   0.642755   0.627982   0.582359
0.505572   0.429483   0.389228   0.390872   0.433180   0.506976   0.577057
0.614456   0.618197   0.592457   0.540511   0.479406   0.437835   0.429814
0.452747   0.494247   0.533275   0.552028   0.545655   0.519496   0.486068
0.459941   0.449669   0.456426   0.477251   0.506398   0.536266   0.560272
0.574507   0.575907   0.560219   0.524461   0.475176   0.430369   0.405375
0.406712   0.438474   0.497882
Time:    7200
0.625737   0.673134   0.675723   0.637118   0.544494   0.428346   0.362300
0.360354   0.420518   0.529811   0.618735   0.647275   0.616347   0.524605
0.414443   0.353457   0.349699   0.403221   0.512735   0.616671   0.667518
0.677780   0.657474   0.598459   0.501253   0.418387   0.394641   0.428963
0.497795   0.548618   0.540578   0.476101   0.401245   0.361080   0.368338
0.432924   0.544439   0.635201   0.676178   0.681213   0.651916   0.570562
0.447735   0.360085   0.332061   0.354137   0.434199   0.555390   0.640054
0.664361   0.635005   0.543731   0.421142   0.344136   0.320836   0.339708
0.412577   0.537975   0.639881   0.685064   0.694794   0.678303   0.621055
0.506693   0.389715   0.332363   0.326423   0.368004   0.469931   0.592784
0.663683   0.684908   0.671531   0.614959   0.504717   0.396066   0.348020
0.359076   0.429655   0.542728   0.624732   0.642969   0.597634   0.492453
0.387894   0.338060   0.339244   0.394084   0.508051   0.619758   0.675962
0.690918   0.676191   0.618787   0.503283   0.385722   0.326214   0.311884
0.331194   0.397884   0.518783

```

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### Auxiliary Routines

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### Keywords

spinodal, iron, chromium, Cahn Hilliard

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