Surface diffusion of tungsten adatoms on several smooth, low‐index planes of the tungsten lattice has for the first time been followed by direct observation of individual atoms in the field‐ion microscope. Contrary to expectation, the mobility at room temperature is found to increase in the order (211) > (321) ∼ (110) > (310) ∼ (111). Migrating atoms are reflected at the boundaries of the (110), (211), and (321) planes; on the latter two, motion along atomic rows is favored over diffusion across lattice steps. From quantitative determinations of the rate of change of the mean‐square displacement, diffusion coefficients are obtained as follows: (110), D=3×10−2exp(−22 000/RT)cm2/sec; (321), 1×10−3exp(−20 000/RT); (211), 2×10−7exp(−13 000/RT). Differences in diffusion on the (211) and (321), planes of very similar structure, suggest a weakening of interatomic forces at lattice edges.

1.
These have been reviewed by (a)
J. M.
Blakely
,
Progr. Mater. Sci.
10
,
395
(
1963
);
(b) N. A. Gjostein in Metal Surfaces: Structure, Energetics and Kinetics (American Society for Metals, Metals Park, Ohio, 1963), Chap. 4.
2.
E. W.
Müller
,
Z. Physik
126
,
642
(
1949
).
3.
A. J.
Melmed
and
R.
Gomer
,
J. Chem. Phys.
34
,
1802
(
1961
).
4.
History and technique of field‐ion microscopy are summarized by
E. W.
Müller
,
Science
149
,
591
(
1965
);
E. W.
Müller
,
Advan. Electron. Electron Phys.
13
,
83
(
1960
).
The possibility of diffusion studies in the ion microscope was already mentioned by
E. W.
Müller
,
Z. Elektrochem.
61
,
43
(
1957
).
5.
G.
Ehrlich
,
Advan. Catalysis
14
,
255
(
1963
).
6.
M.
v. Smoluchowski
,
Sitzber. Akad. Wiss. Wien Math. Naturw. Kl.
123
,
2381
(
1914
);
M.
v. Smoluchowski
,
Kolloid‐Z.
18
,
48
(
1916
).
7.
The basic relations of probability theory can be found in W. Feller, An Introduction to Probability Theory and its Applications (John Wiley & Sons, Inc., New York, 1957), 2nd ed., Vol. 1.
8.
This material is described by G. Ehrlich, J. Chem. Phys. (to be published).
9.
The error indicated for each point in this and subsequent figures is equal to the square root of the variance of s2, where s2 is itself the variance of the sample of n0 observations. This variance of the sample variance is related to the second and fourth moment of the distribution, σ2 and μ4, through
.
10.
M. Drechsler and H. Liepack, Colloq. Intern. Centre. Nat. Rech. Sci. (Nancy) (to be published).
11.
The high activation energy on the (110), compared with that on the (211) and (321), by itself indicates a deficiency in the traditional picture of pair interactions.
12.
M.
Drechsler
,
Z. Elektrochem.
58
,
327
(
1954
).
13.
R.
Smoluchowski
,
Phys. Rev.
60
,
661
(
1941
).
14.
W. K.
Burton
,
N.
Cabrera
, and
F. C.
Frank
,
Phil. Trans. Roy. Soc. (London)
243
,
299
(
1951
).
15.
R. L.
Parker
and
S. C.
Hardy
,
J. Chem. Phys.
37
,
1606
(
1962
).
16.
J. A.
Simmons
,
R. L.
Parker
, and
R. E.
Howard
,
J. Appl. Phys.
35
,
2271
(
1964
).
17.
We are indebted to J. J. Lander, Bell Telephone Laboratories, for discussions on this topic.
This content is only available via PDF.
You do not currently have access to this content.