# problem in calculating MSD of Cu adatom/adatoms moving randomly over the Ag (111) Surface

Respected Sir’s
I am working on the study of diffusion of Cu adatom/adatoms at Ag (111) surface, for this purpose i have to draw a graph of MSD Vs time, and it is supposed that MSD gradually increase with time and slop of MSD vs time graphs gives us diffusion coefficient of adatom/adatoms.

for this purpose i have defined the substrate and adatom regions as
region substrate block 0 80.0 0 80.0 0 40.0 units box
region adatom block 34 46.0 34 40.0 41.0 43.50 units box

fix 3 adatom deposit 2 2 60 29494 region adatom units box

Sample is equiliberated using nvt ensembles using commonds
fix 2 all nvt temp 500.0 500.0 1 drag 1
fix 4 all temp/rescale 1 500 500 5.05 1.0

To Calculate Mean Square Displacement MSD i use command

and to take the out put of MSD i use two ways
fix mymsd common ave/time 1 2000 2000 c_1[4] file tmp.avetime
and
c_1[4] directly .

Main Problem (In all the papers i have studied for simmilar system, it was mentioned that MSD gradually increase with the increase in the time (with slight fluctuation in its value), some says they take avearge over 2000 etc time steps to get a resonable value of MSD. As Cu adatom moves randomly over Ag(111) surface so im my problem the when adatom moves away from its starting position MSD starts increasing gradually but when the randomly moving adatom start moving toward the starting position the values the value of MSD start decreasing and even may be zero again when adatom passed through the starting position. I even try to calculate the avearge MSD but still my results are not resonable(gradually incresing) ) I have stuck to this problem from last few month but still find no solution to my problem. I need your help and suggestions, I will highly appriciate your help

the detail final input code is shown below
units metal
atom_style atomic
atom_modify map array
boundary p p p
atom_modify sort 0 0.0
lattice fcc 4.09
pair_style eam/alloy
pair_coeff * * AgCu.set.alloy Ag Cu Cu
region domain block -1 81 -1 81 -1 50 units box
region substrate1 block 0 80.0 0 80.0 0 40.0 units box
region adatom block 34 46.0 34 46.0 41.0 43.50 units box
region base block INF INF INF INF 0 3 units box
group substrate1 region substrate1
group base region base
group substrate subtract all base

set group substrate1 type 1

timestep 0.005
compute new all temp
velocity all create 500.0 482748 temp new

# base region is not integated kept fixed

fix 2 substrate nvt temp 500.0 500.0 1 drag 1
fix 4 substrate temp/rescale 1 500 500 5.05 1.0
fix 5 adatom nvt temp 500.0 500.0 1 drag 1
fix 6 adatom temp/rescale 1 500 500 5.05 1.0

#fix 3 adatom deposit 2 2 60 29494 region adatom units box
fix mymsd adatom ave/time 1 2000 2000 c_1[4] file tmp.avetime
dump 1 all atom 1000 diffusion.cuoverag.lammpstrj
thermo 10
thermo_modify temp new
variable t equal (0.005*step)
thermo_style custom step temp pe etotal c_1[4] c_2[1] c_2[2] c_2[3] v_t

run 600000
write_restart restart.final
###################################END###################
the out put of command fix mymsd adatom ave/time 1 2000 2000 c_1[4] file tmp.avetime is

# TimeStep c_1[4]

2000 3.52244
4000 9.63889
6000 19.9845
8000 18.3118
10000 18.5679
12000 23.1298
14000 20.9697
16000 15.535
18000 26.0443
20000 26.7434
22000 31.3512
24000 37.2784
26000 37.3587
28000 56.0674
30000 56.13
32000 69.2715
34000 97.3046
36000 109.482
38000 108.056
40000 77.8612
42000 56.6328
44000 156.059
46000 155.077
48000 157.952
50000 181.363
52000 101.212
54000 107.87
56000 112.121
58000 112.001
60000 117.818
62000 109.316
64000 106.493
66000 108.942
68000 109.197
70000 114.228
72000 112.576
74000 118.479
76000 125.604
78000 140.023
80000 140.436
82000 140.643
84000 140.556
86000 296.439
88000 302.496
90000 306.844
92000 271.263
94000 287.587
96000 287.621
98000 290.853
100000 248.167
102000 256.529
104000 244.386
106000 248.548
108000 304.022
110000 293.428
112000 262.881
114000 267.742
116000 264.54
118000 248.131
120000 248.669
122000 231.711
124000 267.378
126000 225.61
128000 231.325
130000 227.626
132000 227.762
134000 204.571
136000 274.742
138000 251.154
140000 249.727
142000 204.003
144000 251.416
146000 272.43
148000 274.485
150000 276.687
152000 274.107
154000 224.307
156000 216.05
158000 216.778
160000 185.676
162000 132.379
164000 160.481
166000 133.722
168000 114.894
170000 114.316
172000 115.164
174000 114.589
176000 100.423
178000 89.074
180000 74.766
182000 80.8786
184000 77.3656
186000 79.267
188000 91.4472
190000 91.2727
192000 88.528
194000 110.61
196000 97.2436
198000 94.1937
200000 90.3619
202000 44.9958
204000 42.6969
206000 46.4101
208000 43.7373
210000 46.1118
212000 44.1934
214000 42.791
216000 32.953
218000 30.1264
220000 46.038
222000 51.5328
224000 54.9239
226000 59.2962
228000 57.5418
230000 65.5686
232000 96.484
234000 97.5685
236000 100.535
238000 118.91
240000 116.51
242000 116.721
244000 115.035
246000 148.582
248000 155.377
250000 154.565
252000 158.012
254000 128.093
256000 119.22
258000 105.759
260000 79.4943
262000 98.7545
264000 100.529
266000 102.988
268000 111.895
270000 123.834
272000 130.656
274000 214.549
276000 179.328
278000 192.051
280000 203.145
282000 203.398
284000 220.656
286000 243.179
288000 228.664
290000 256.022
292000 322.108
294000 352.494
296000 352.271
298000 351.049
300000 278.003
302000 264.341
304000 309.822
306000 354.926
308000 374.212
310000 382.217
312000 386.043
314000 272.924
316000 271.69
318000 271.062
320000 297.181
322000 302.658
324000 366.693
326000 409.531
328000 304.829
330000 304.153
332000 304.223
334000 309.669
336000 276.321
338000 311.304
340000 314.137
342000 319.117
344000 317.797
346000 310.44
348000 254.912
350000 253.403
352000 257.857
354000 276.348
356000 309.101
358000 300.253
360000 252.742
362000 230.425
364000 196.629
366000 155.461
368000 125.539
370000 125.719
372000 124.603
374000 96.6058
376000 125.039
378000 119.618
380000 123.827
382000 123.233
384000 138.886
386000 99.7027
388000 83.6911
390000 80.9063
392000 64.8063
394000 75.1783
396000 63.8407
398000 27.0993
400000 27.8023
402000 40.0699
404000 40.9857
406000 52.8076
408000 61.9601
410000 74.8706
412000 92.0283
414000 92.9054
416000 93.5076
418000 91.8275
420000 78.5047
422000 82.5055
424000 80.708
426000 71.6554
428000 71.2699
430000 52.9439
432000 58.5756
434000 63.747
436000 112.464
438000 124.146
440000 100.619
442000 117.54
444000 151.972
446000 150.461
448000 159.247
450000 149.405
452000 154.937
454000 211.559
456000 237.726
458000 234.595
460000 270.272
462000 297.363
464000 318.189
466000 289.029
468000 356.018
470000 385.96
472000 480.097
474000 618.295
476000 487.906
478000 345.25
480000 236.987
482000 138.526
484000 154.885
486000 155.068
488000 153.039
490000 163.646
492000 163.64
494000 165.246
496000 166.789
498000 163.715
500000 173.413
502000 201.258
504000 255.518
506000 254.669
508000 235.308
510000 208.49
512000 206.422
514000 244.05
516000 171.351
518000 161.475
520000 162.837
522000 162.776
524000 165.732
526000 163.564
528000 168.901
530000 165.63
532000 163.475
534000 172.327
536000 163.531
538000 164.684
540000 163.741
542000 164.436
544000 191.744
546000 195.358
548000 231.913
550000 193.905
552000 191.495
554000 193.024
556000 191.605
558000 194.03
560000 244.799
562000 249.436
564000 255.093
566000 318.35
568000 339.796
570000 345.309
572000 347.423
574000 338.614
576000 385.899
578000 333.209
580000 386.566
582000 387.211
584000 401.122
586000 402.854
588000 397.33
590000 392.011
592000 368.899
594000 374.444
596000 374.525
598000 364.676
600000 448.099

thanks and regards
IMRAN
The Islamia University of bahawalpur (Pakistan)

If atoms aren’t diffusing, then the MSD will not increase.

Steve

Whatever the MSD does I would not trust the results at all. You are using fix temp/rescale combined with fix nvt. Why would you do that? Even if one has no idea about the physics behind both fixes the manual for fix temp/rescale explicitly states and I quote:
“Likewise, this fix should not normally be used on atoms that also have their temperature controlled by another fix - e.g. by fix nvt or fix langevin commands.”

You have much to worry about before the MSD issue…

Carlos