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axial ratio


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parameter

crystal

William Hallowes Miller (1801—1880) mineralogist

 

'axial ratio' can also refer to...

 

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In the study of crystals, the position of a crystal face in space is given by the intercepts the face or plane makes on three (or four) imaginary lines, called ‘crystallographic axes’. The X-ray crystallographer can measure the ‘unit-cell’ dimensions in ångstrom units (Å), and the axial ratios express the relative, and not the absolute, lengths of the cell edges corresponding to the crystallographic axes. These ratios (or ‘parameters’) are often expressed reciprocally as ‘indices’, e.g. Miller indices.Note that if face DEF is selected as the parametral plane, then its indices would be 22, 11, 44 = 111.

Crystallographic Axes

a (x)

b (y)

c (z)

Intercepts of crystal

face DEF in

ångstroms, on a, b,

OD

OE

OF

and c axes,

20 Å

10 Å

40 Å

measured from

origin.

If b intercept is made

20

10

40

equal to 1 the axial

10

10

10

ratio is obtained for

2

:1

:4

the crystal.

Indices are obtained

by dividing the

1

1

1

intercepts of face

2

1

4

DEF into those of the

parametral plane,

which is a face of the

unit form with

intercepts (111).

Miller's indices of face

DEF are obtained by

removing fractions.

2

4

1

Subjects: Earth Sciences and Geography.


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