Interplanar Spacing of Crystal given Lattice Parameter Calculator

Calculate Interplanar Spacing









Formula

The formula to calculate Interplanar Spacing (d) is:

\[ d = \frac{a}{\sqrt{h^2 + k^2 + l^2}} \]

Where:

Definition

Interplanar Spacing is the distance between adjacent and parallel planes of the crystal.

Lattice Parameter is defined as the length between two points on the corners of a unit cell.

Miller Index h is the reciprocal of the x intercept of the atomic plane.

Miller Index k is the reciprocal of the y intercept of the atomic plane.

Miller Index l is the reciprocal of the z intercept of the atomic plane.

How to calculate Interplanar Spacing given Lattice Parameter and Miller Indices

Let's assume the following values:

Using the formula:

\[ d = \frac{a}{\sqrt{h^2 + k^2 + l^2}} \]

Evaluating:

\[ d = \frac{2.5E-10}{\sqrt{2^2 + 7^2 + 5^2}} \]

The Interplanar Spacing is 2.83069258536149E-11.

Interplanar Spacing Conversion Chart

Lattice Parameter (a) Miller Index h Miller Index k Miller Index l Interplanar Spacing (d)
2.0E-10 1 6 4 0.000000000027472
2.0E-10 1 6 5 0.000000000025400
2.0E-10 1 6 6 0.000000000023408
2.0E-10 1 7 4 0.000000000024618
2.0E-10 1 7 5 0.000000000023094
2.0E-10 1 7 6 0.000000000021567
2.0E-10 1 8 4 0.000000000022222
2.0E-10 1 8 5 0.000000000021082
2.0E-10 1 8 6 0.000000000019901
2.0E-10 2 6 4 0.000000000026726
2.0E-10 2 6 5 0.000000000024807
2.0E-10 2 6 6 0.000000000022942
2.0E-10 2 7 4 0.000000000024077
2.0E-10 2 7 5 0.000000000022646
2.0E-10 2 7 6 0.000000000021200
2.0E-10 2 8 4 0.000000000021822
2.0E-10 2 8 5 0.000000000020739
2.0E-10 2 8 6 0.000000000019612
2.0E-10 3 6 4 0.000000000025607
2.0E-10 3 6 5 0.000000000023905
2.0E-10 3 6 6 0.000000000022222
2.0E-10 3 7 4 0.000000000023250
2.0E-10 3 7 5 0.000000000021953
2.0E-10 3 7 6 0.000000000020628
2.0E-10 3 8 4 0.000000000021200
2.0E-10 3 8 5 0.000000000020203
2.0E-10 3 8 6 0.000000000019157
2.1E-10 1 6 4 0.000000000028846
2.1E-10 1 6 5 0.000000000026670
2.1E-10 1 6 6 0.000000000024579
2.1E-10 1 7 4 0.000000000025849
2.1E-10 1 7 5 0.000000000024249
2.1E-10 1 7 6 0.000000000022645
2.1E-10 1 8 4 0.000000000023333
2.1E-10 1 8 5 0.000000000022136
2.1E-10 1 8 6 0.000000000020896
2.1E-10 2 6 4 0.000000000028062
2.1E-10 2 6 5 0.000000000026047
2.1E-10 2 6 6 0.000000000024089
2.1E-10 2 7 4 0.000000000025281
2.1E-10 2 7 5 0.000000000023778
2.1E-10 2 7 6 0.000000000022260
2.1E-10 2 8 4 0.000000000022913
2.1E-10 2 8 5 0.000000000021776
2.1E-10 2 8 6 0.000000000020592
2.1E-10 3 6 4 0.000000000026888
2.1E-10 3 6 5 0.000000000025100
2.1E-10 3 6 6 0.000000000023333
2.1E-10 3 7 4 0.000000000024412
2.1E-10 3 7 5 0.000000000023050
2.1E-10 3 7 6 0.000000000021660
2.1E-10 3 8 4 0.000000000022260
2.1E-10 3 8 5 0.000000000021213
2.1E-10 3 8 6 0.000000000020114
2.2E-10 1 6 4 0.000000000030219
2.2E-10 1 6 5 0.000000000027940
2.2E-10 1 6 6 0.000000000025749
2.2E-10 1 7 4 0.000000000027080
2.2E-10 1 7 5 0.000000000025403
2.2E-10 1 7 6 0.000000000023723
2.2E-10 1 8 4 0.000000000024444
2.2E-10 1 8 5 0.000000000023190
2.2E-10 1 8 6 0.000000000021891
2.2E-10 2 6 4 0.000000000029399
2.2E-10 2 6 5 0.000000000027288
2.2E-10 2 6 6 0.000000000025236
2.2E-10 2 7 4 0.000000000026485
2.2E-10 2 7 5 0.000000000024910
2.2E-10 2 7 6 0.000000000023320
2.2E-10 2 8 4 0.000000000024004
2.2E-10 2 8 5 0.000000000022813
2.2E-10 2 8 6 0.000000000021573
2.2E-10 3 6 4 0.000000000028168
2.2E-10 3 6 5 0.000000000026295
2.2E-10 3 6 6 0.000000000024444
2.2E-10 3 7 4 0.000000000025574
2.2E-10 3 7 5 0.000000000024148
2.2E-10 3 7 6 0.000000000022691
2.2E-10 3 8 4 0.000000000023320
2.2E-10 3 8 5 0.000000000022223
2.2E-10 3 8 6 0.000000000021072
2.3E-10 1 6 4 0.000000000031593
2.3E-10 1 6 5 0.000000000029210
2.3E-10 1 6 6 0.000000000026919
2.3E-10 1 7 4 0.000000000028311
2.3E-10 1 7 5 0.000000000026558
2.3E-10 1 7 6 0.000000000024802
2.3E-10 1 8 4 0.000000000025556
2.3E-10 1 8 5 0.000000000024244
2.3E-10 1 8 6 0.000000000022886
2.3E-10 2 6 4 0.000000000030735
2.3E-10 2 6 5 0.000000000028528
2.3E-10 2 6 6 0.000000000026383
2.3E-10 2 7 4 0.000000000027689
2.3E-10 2 7 5 0.000000000026042
2.3E-10 2 7 6 0.000000000024380
2.3E-10 2 8 4 0.000000000025095
2.3E-10 2 8 5 0.000000000023850
2.3E-10 2 8 6 0.000000000022553
2.3E-10 3 6 4 0.000000000029448
2.3E-10 3 6 5 0.000000000027490
2.3E-10 3 6 6 0.000000000025556
2.3E-10 3 7 4 0.000000000026737
2.3E-10 3 7 5 0.000000000025246
2.3E-10 3 7 6 0.000000000023723
2.3E-10 3 8 4 0.000000000024380
2.3E-10 3 8 5 0.000000000023234
2.3E-10 3 8 6 0.000000000022030
2.4E-10 1 6 4 0.000000000032967
2.4E-10 1 6 5 0.000000000030480
2.4E-10 1 6 6 0.000000000028090
2.4E-10 1 7 4 0.000000000029542
2.4E-10 1 7 5 0.000000000027713
2.4E-10 1 7 6 0.000000000025880
2.4E-10 1 8 4 0.000000000026667
2.4E-10 1 8 5 0.000000000025298
2.4E-10 1 8 6 0.000000000023881
2.4E-10 2 6 4 0.000000000032071
2.4E-10 2 6 5 0.000000000029768
2.4E-10 2 6 6 0.000000000027530
2.4E-10 2 7 4 0.000000000028893
2.4E-10 2 7 5 0.000000000027175
2.4E-10 2 7 6 0.000000000025440
2.4E-10 2 8 4 0.000000000026186
2.4E-10 2 8 5 0.000000000024887
2.4E-10 2 8 6 0.000000000023534
2.4E-10 3 6 4 0.000000000030729
2.4E-10 3 6 5 0.000000000028685
2.4E-10 3 6 6 0.000000000026667
2.4E-10 3 7 4 0.000000000027899
2.4E-10 3 7 5 0.000000000026343
2.4E-10 3 7 6 0.000000000024754
2.4E-10 3 8 4 0.000000000025440
2.4E-10 3 8 5 0.000000000024244
2.4E-10 3 8 6 0.000000000022988
2.5E-10 1 6 4 0.000000000034340
2.5E-10 1 6 5 0.000000000031750
2.5E-10 1 6 6 0.000000000029260
2.5E-10 1 7 4 0.000000000030773
2.5E-10 1 7 5 0.000000000028868
2.5E-10 1 7 6 0.000000000026958
2.5E-10 1 8 4 0.000000000027778
2.5E-10 1 8 5 0.000000000026352
2.5E-10 1 8 6 0.000000000024876
2.5E-10 2 6 4 0.000000000033408
2.5E-10 2 6 5 0.000000000031009
2.5E-10 2 6 6 0.000000000028677
2.5E-10 2 7 4 0.000000000030096
2.5E-10 2 7 5 0.000000000028307
2.5E-10 2 7 6 0.000000000026500
2.5E-10 2 8 4 0.000000000027277
2.5E-10 2 8 5 0.000000000025924
2.5E-10 2 8 6 0.000000000024515
2.5E-10 3 6 4 0.000000000032009
2.5E-10 3 6 5 0.000000000029881
2.5E-10 3 6 6 0.000000000027778
2.5E-10 3 7 4 0.000000000029062
2.5E-10 3 7 5 0.000000000027441
2.5E-10 3 7 6 0.000000000025786
2.5E-10 3 8 4 0.000000000026500
2.5E-10 3 8 5 0.000000000025254
2.5E-10 3 8 6 0.000000000023946
2.6E-10 1 6 4 0.000000000035714
2.6E-10 1 6 5 0.000000000033020
2.6E-10 1 6 6 0.000000000030431
2.6E-10 1 7 4 0.000000000032004
2.6E-10 1 7 5 0.000000000030022
2.6E-10 1 7 6 0.000000000028037
2.6E-10 1 8 4 0.000000000028889
2.6E-10 1 8 5 0.000000000027406
2.6E-10 1 8 6 0.000000000025871
2.6E-10 2 6 4 0.000000000034744
2.6E-10 2 6 5 0.000000000032249
2.6E-10 2 6 6 0.000000000029824
2.6E-10 2 7 4 0.000000000031300
2.6E-10 2 7 5 0.000000000029439
2.6E-10 2 7 6 0.000000000027560
2.6E-10 2 8 4 0.000000000028368
2.6E-10 2 8 5 0.000000000026961
2.6E-10 2 8 6 0.000000000025495
2.6E-10 3 6 4 0.000000000033290
2.6E-10 3 6 5 0.000000000031076
2.6E-10 3 6 6 0.000000000028889
2.6E-10 3 7 4 0.000000000030224
2.6E-10 3 7 5 0.000000000028539
2.6E-10 3 7 6 0.000000000026817
2.6E-10 3 8 4 0.000000000027560
2.6E-10 3 8 5 0.000000000026264
2.6E-10 3 8 6 0.000000000024903
2.7E-10 1 6 4 0.000000000037087
2.7E-10 1 6 5 0.000000000034290
2.7E-10 1 6 6 0.000000000031601
2.7E-10 1 7 4 0.000000000033235
2.7E-10 1 7 5 0.000000000031177
2.7E-10 1 7 6 0.000000000029115
2.7E-10 1 8 4 0.000000000030000
2.7E-10 1 8 5 0.000000000028460
2.7E-10 1 8 6 0.000000000026866
2.7E-10 2 6 4 0.000000000036080
2.7E-10 2 6 5 0.000000000033489
2.7E-10 2 6 6 0.000000000030971
2.7E-10 2 7 4 0.000000000032504
2.7E-10 2 7 5 0.000000000030571
2.7E-10 2 7 6 0.000000000028620
2.7E-10 2 8 4 0.000000000029459
2.7E-10 2 8 5 0.000000000027998
2.7E-10 2 8 6 0.000000000026476
2.7E-10 3 6 4 0.000000000034570
2.7E-10 3 6 5 0.000000000032271
2.7E-10 3 6 6 0.000000000030000
2.7E-10 3 7 4 0.000000000031387
2.7E-10 3 7 5 0.000000000029636
2.7E-10 3 7 6 0.000000000027848
2.7E-10 3 8 4 0.000000000028620
2.7E-10 3 8 5 0.000000000027274
2.7E-10 3 8 6 0.000000000025861
2.8E-10 1 6 4 0.000000000038461
2.8E-10 1 6 5 0.000000000035560
2.8E-10 1 6 6 0.000000000032772
2.8E-10 1 7 4 0.000000000034466
2.8E-10 1 7 5 0.000000000032332
2.8E-10 1 7 6 0.000000000030193
2.8E-10 1 8 4 0.000000000031111
2.8E-10 1 8 5 0.000000000029515
2.8E-10 1 8 6 0.000000000027861
2.8E-10 2 6 4 0.000000000037417
2.8E-10 2 6 5 0.000000000034730
2.8E-10 2 6 6 0.000000000032118
2.8E-10 2 7 4 0.000000000033708
2.8E-10 2 7 5 0.000000000031704
2.8E-10 2 7 6 0.000000000029680
2.8E-10 2 8 4 0.000000000030551
2.8E-10 2 8 5 0.000000000029035
2.8E-10 2 8 6 0.000000000027456
2.8E-10 3 6 4 0.000000000035850
2.8E-10 3 6 5 0.000000000033466
2.8E-10 3 6 6 0.000000000031111
2.8E-10 3 7 4 0.000000000032549
2.8E-10 3 7 5 0.000000000030734
2.8E-10 3 7 6 0.000000000028880
2.8E-10 3 8 4 0.000000000029680
2.8E-10 3 8 5 0.000000000028284
2.8E-10 3 8 6 0.000000000026819
2.9E-10 1 6 4 0.000000000039835
2.9E-10 1 6 5 0.000000000036830
2.9E-10 1 6 6 0.000000000033942
2.9E-10 1 7 4 0.000000000035697
2.9E-10 1 7 5 0.000000000033486
2.9E-10 1 7 6 0.000000000031272
2.9E-10 1 8 4 0.000000000032222
2.9E-10 1 8 5 0.000000000030569
2.9E-10 1 8 6 0.000000000028856
2.9E-10 2 6 4 0.000000000038753
2.9E-10 2 6 5 0.000000000035970
2.9E-10 2 6 6 0.000000000033265
2.9E-10 2 7 4 0.000000000034912
2.9E-10 2 7 5 0.000000000032836
2.9E-10 2 7 6 0.000000000030740
2.9E-10 2 8 4 0.000000000031642
2.9E-10 2 8 5 0.000000000030072
2.9E-10 2 8 6 0.000000000028437
2.9E-10 3 6 4 0.000000000037131
2.9E-10 3 6 5 0.000000000034662
2.9E-10 3 6 6 0.000000000032222
2.9E-10 3 7 4 0.000000000033712
2.9E-10 3 7 5 0.000000000031832
2.9E-10 3 7 6 0.000000000029911
2.9E-10 3 8 4 0.000000000030740
2.9E-10 3 8 5 0.000000000029294
2.9E-10 3 8 6 0.000000000027777
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