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Student Support Forum: 'Smart curve fitting for some physical data' topicStudent Support Forum > General > "Smart curve fitting for some physical data"

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Seyyed Ali Hedayat Mofidi
05/14/12 11:24am

Hi everyone, I have some data for thermal expansion coefficient of silicon which I have to find a good curve fit for it.
Using Mathematica, I can find two equations for 2 different intervals of the data ( from 0-120K and 120K to 1600K). I have defined a 7th order polynomial which had a very good fit on the first interval and as of the second interval, there are some equations recommended in literature which I am using. I am trying to find a way to do this curve fit in a single equation which describes my data for all of the temperature range. Can anybody suggest a way that I can find such curve fit for my data? Does mathematica have a method to find a good equation as my model?
I have posted the data below:


T(K) Alpha (1E-6. K^-1)
4 0.005582094
6 -0.000852351
8 -0.002815759
10 -0.002122582
12 -0.00025849
14 0.001584079
16 0.002472693
18 0.001703956
20 -0.001225282
22 -0.006644603
24 -0.01473467
26 -0.025549902
28 -0.039039272
30 -0.055065273
32 -0.073421148
34 -0.093846448
36 -0.11604098
38 -0.139677243
40 -0.164411395
42 -0.18989285
44 -0.215772559
46 -0.241710057
48 -0.267379345
50 -0.292473688
52 -0.31670938
54 -0.339828582
56 -0.361601273
58 -0.38182641
60 -0.400332353
62 -0.41697664
64 -0.431645185
66 -0.444250953
68 -0.454732215
70 -0.463050423
72 -0.46918781
74 -0.473144759
76 -0.474937032
78 -0.474592926
80 -0.472150427
82 -0.467654439
84 -0.461154156
86 -0.452700651
88 -0.44234476
90 -0.430135324
92 -0.416117874
94 -0.400333813
96 -0.382820194
98 -0.36361014
100 -0.342734
102 -0.320221296
104 -0.296103549
106 -0.270418049
108 -0.243212638
110 -0.214551591
112 -0.184522649
114 -0.153245303
116 -0.120880372
118 -0.087640972
120 -0.053804933
122 -0.019728746
124 0.014136892
126 0.047229859
128 0.078857648
130 0.108176588
140 0.334015
160 0.739813
180 1.10164
200 1.42437
220 1.71232
240 1.96934
260 2.19885
280 2.4039
300 2.58719
320 2.75113
340 2.89787
360 3.0293
380 3.14711
400 3.25283
420 3.34777
440 3.43314
460 3.51
480 3.57928
500 3.64183
520 3.69838
540 3.74961
560 3.79611
580 3.83838
600 3.87691
620 3.91211
640 3.94435
660 3.97394
680 4.0012
700 4.02636
720 4.04968
740 4.07134
760 4.09154
780 4.11043
800 4.12817
820 4.14487
840 4.16065
860 4.17562
880 4.18986
900 4.20346
920 4.21648
940 4.22899
960 4.24105
980 4.2527
1000 4.264
1020 4.27497
1040 4.28566
1060 4.2961
1080 4.30632
1100 4.31633
1120 4.32617
1140 4.33585
1160 4.34538
1180 4.3548
1200 4.3641
1220 4.3733
1240 4.38242
1260 4.39145
1280 4.40042
1300 4.40933
1320 4.41818
1340 4.42698
1360 4.43574
1380 4.44445
1400 4.45314
1420 4.46179
1440 4.47042
1460 4.47902
1480 4.4876
1500 4.49617
1520 4.50471
1540 4.51324
1560 4.52176
1580 4.53026
1600 4.53876

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