Michael, Luca, All,
At 11:32 AM 9/28/00 +0200, you wrote:
>Hi Jim,
>
>i) this is what the NIST web site shows under X-ray constants for the
>Silicon lattice parameter: "Concise form 543.102 088(16) x 10-12 m"
>ii) this is shown in your SRM 640c Certificate of Silicon Powder:
>"0.54311946 nm +-0.00000092 nm"
>
>I can see no overlap of the estimated standard deviations.
>Any comment?
The single crystal lattice parameter value listed on the web site under
X-ray constants is the result of a compilation of measurements from three
laboratories (PTB, NRLM, and IMGC) using combined X-ray and optical
interferometry. The value listed is for an "ideal" silicon of a specific
purity and under a vacuum. We (E. Kessler) measured the lattice parameter
of the silicon used for the SRM prior to comminution at 0.54310185(4) nm
using the NIST lattice parameter comparator. The discrepancy between these
two single crystal values is due to the pressure deference for which they
were determined. Discussion of the discrepancy between the values
determined for the powder and that of the single crystal should center on
two values determined for the SRM feedstock itself, before and after
comminution. The powder value is obtain from a NIST parallel beam
diffractometer constructed for first principle lattice parameter
measurements; see the SRM certificate on the web site (for a brief
description) or Deslattes, et al. Adv. X-ray Anal., 41, (1997) (for a more
complete one). We explain the discrepancy between the value obtained from
the powder and that of the single crystal in terms of the oxide layer on
the surface of the particles. This oxide layer is known to be in
compression. It exerts a hydrostatic tensile stress on the silicon
particles which expands the lattice. Hence the larger measured lattice
parameter for the silicon powder. Further evidence for this explanation
can be found in the slight degree of strain broadening observed in this
material (0.02 degrees for the 533 line), despite the annealing procedure
(van Berkum et al. (1995)). The hydrostatic stress level is inversely
proportional to the radius of curvature of the particles. Therefore, the
fact that the particle size distribution is not a delta function is
consistent with a distribution in the hydrostatic stress levels and
therefore the lattice parameter(s). The distribution in the lattice
parameter values is what we interpret as strain broadening.
Round robins test for consistency of measured values between
laboratories. They are not useful for determination of absolute values.
Regards,
Jim
James P. Cline [EMAIL PROTECTED]
Ceramics Division Voice (301) 975 5793
National Institute of Standards and Technology FAX (301) 975 5334
100 Bureau Dr. stop 8523
Gaithersburg, MD 20899-8523 USA
