# Is there a standard scholarly reference for lattice constants of crystals of the elements?

I need to discuss the lattice constants of bulk crystals of several metal and semiconductor elements. I can find plenty of tables and numbers that are probably "close enough" but for a paper I'd like to cite a standard source.

From https://periodictable.com/Properties/A/LatticeConstants.html I have the following numbers, but I don't want to use a "dot com" as a scholarly source, and I can not figure out how to use Wolfram Alpha (the source for this website) or understand where WA gets its numbers. They list several references here https://reference.wolfram.com/language/note/ElementDataSourceInformation.html , but it will be a challenge to track them all down one by one. I'm hoping someone will recognize one of them or simply be able to mention it.

I only need (at a minimum) three decimal places for the lattice constants in Angstroms (though four is better if they are known), but what I can't find is a citable, schollarly source that covers all of these and is likely to cover other common elemental crystals when I need them in the future.

element.   lattice constant
(a, b and c)
Angstroms

Au          4.0782
Ag          4.0853
Pb          4.9508
Ge          5.6575
Si          5.4309

• Wikipedia cites a lot of sources. Elements I'm pretty sure you will find in the CDC handbook. crystallography.net/cod it.iucr.org – Karl Aug 23 '20 at 14:21
• @Karl I'm having trouble understanding that link. I won't be purchasing an on-line copy, is this a book I can find in some library or is it strictly a paid access online database? I'd like to be able to cite something that one could actually check and confirm in a reasonably well-sized and libraried university. I can't even figure out which of the eight volumes (A through H) has an actual table of lattice constants with numbers in it. – uhoh Aug 23 '20 at 14:28
• @Karl I'm one of those people who won't cite something unless I've actually check it myself. – uhoh Aug 23 '20 at 14:30
• It's two links, and any uni library should give you access. The CRC (sorry, typo) handbook used to be printed, now it's online too, and your library should have access, too. hbcponline.com/faces/contents/… – Karl Aug 23 '20 at 14:31
• @Karl okay got it! Let me try a device that's connected to the library, this one isn't. :-) – uhoh Aug 23 '20 at 14:42

The CRC Handbook of Chemistry and Physics contains a dedicated compilation by H. W. King, titled «Crystal Structures and Lattice Parameters of Allotropes of the Elements». In case your research library is closed, you may access some of its editions freely or borrow them with the library card of archive.org.

In case of the 97th edition (by 2016), the section starts by page 12-16. (Elements liquid or gaseous at ambient conditions are included.)

source

• Thanks, this may be what I end up using. It's a real, recognized and trusted physical reference I can hold in my hand and read, and it lists its source from where these numbers come from, which I can also put my hands on and confirm. Thanks! – uhoh Aug 24 '20 at 16:03

The lattice constants of all five elements have been published in a single reference in 1925 (Ref.1):

The lattice constant $$a$$ has been determined within 0.1 percent (.03 percent for $$\ce{W}$$) for aluminum, iron, nickel, copper, molybdenum, palladium, silver, tungsten, platinum, gold, lead, and bismuth, by direct comparison with $$\ce{NaCl}$$, $$a(\ce{NaCl}) = \pu{2.814 \mathring A}$$. As pure samples as could be obtained were used, from 99.55 percent for $$\ce{Ni}$$ to 99.9995 percent for tungsten, and in many cases commercially pure samples were also measured for comparison. The results for the purest samples are summarized in Table XIII. The density from the x-ray data is in each case (except $$\ce{Al}$$ and $$\ce{Ag}$$) greater than the density of the bulk metal as given in the literature, the difference being rather large for $$\ce{Mo}$$ (10.21 vs 9.1), for $$\ce{Pd}$$ (12.25 vs 11.9) and $$\ce{W}$$ (19.32 vs 18.77). For pure $$\ce{W}$$ remarkably sharp lines were obtained. For $$\ce{Bi}$$ a piece of a single artificial crystal was used.

The relevant $$a$$ values are listed in a Wikipedia article as follows:

$$\begin{array}{c|ccc} \hline \text{Metal} & \text{Lattice constant}^a & \text{Crystal structure} & \text{Lattice constant given} \\ \hline \ce{Au} & \pu{4.065 \mathring A} & \text{FCC} & \pu{4.0782 \mathring A} \\ \ce{Ag} & \pu{4.079 \mathring A} & \text{FCC} & \pu{4.0853 \mathring A} \\ \ce{Pb} & \pu{4.920 \mathring A} & \text{FCC} & \pu{4.9508 \mathring A} \\ \ce{Ge} & \pu{5.658 \mathring A} & \text{Diamond (FCC)} & \pu{5.6575 \mathring A} \\ \ce{Si} & \pu{5.4310205 \mathring A} & \text{Diamond (FCC)} & \pu{5.4309 \mathring A} \\ \ce{Cu} & \pu{3.597 \mathring A} & \text{FCC} & \pu{3.6149 \mathring A} \\ \ce{Pt} & \pu{3.912 \mathring A} & \text{FCC} & \pu{3.9242 \mathring A} \\ \hline \end{array}\\ ^a \ \text{Values from: Phys. Rev. 1925, 25(6), 753-761 (Ref.1; as listed in Wikipedia)}$$

For comparison purposes, I have included $$\ce{Cu}$$ and $$\ce{Pt}$$ as well. Lattice Constants of Crystals of three elements of the 5 listed have also been discussed in a relatively new article (Ref.2).

References:

1. Wheeler P. Davey, “Precision Measurements of the Lattice Constants of Twelve Common Metals,” Phys. Rev. 1925, 25(6), 753-761 (https://doi.org/10.1103/PhysRev.25.753).
2. D. N. Batchelder, R. O. Simmons, “X‐Ray Lattice Constants of Crystals by a Rotating‐Camera Method: $$\ce{Al, Ar, Au, CaF2, Cu, Ge, Ne, Si,}$$Journal of Applied Physics 1965, 36(9), 2864-2868 (https://doi.org/10.1063/1.1714595).
• To resolve the discrepancy between Wolfram Alpha and (Davey 1925) that are tens to a a hundred times larger than three decimal places in Angstroms specified in the question, I'm going to need a more modern source which reasonably represents some generally agreed-upon values by the crystallographic community. I don't think it's reasonable to cite a single measurement in a single author paper from 1925 in a paper to be published in 2021. – uhoh Aug 23 '20 at 21:50
• -1 Checking both columns (1925 numbers and the ones from the question) against a CRC from 2012 (93rd Ed.) show that some of the numbers from 1925 are pretty poor; for the three metals mine are very close to CRC, the 1925 numbers differ by 0.3 to 0.6%! It is certainly up to you, but if you would consider deleting this answer I'd like to ask in a different SE site instead. Thanks! – uhoh Aug 24 '20 at 9:13
• @uhoh: You are completely wrong on this down voting. I have found a reliable literature satisfactory for your request "I only need (at a minimum) three decimal places for the lattice constants in Angstroms." What not reliable is your sited dot com page, which even not site any references for their claim. You didn't even appreciate my effort. Shame on you on that. – Mathew Mahindaratne Aug 24 '20 at 12:47
• I'm confident that my down vote accurately represents my view, which is that this answer is "not useful." When writing a paper no reasonable author chooses a 100 year old measurement to cite when much newer, more careful and more carefully reviewed data is available. Please recheck the complete text of my question post and my previous comment. – uhoh Aug 24 '20 at 13:03
• Measurement equipment gets better over time, we don't cite 100 year old measurements when far better values using better equipment is available. This is just common sense. They did great and pioneering research at GE Schenectady in the 1920's. We can honor that but that doesn't mean we should use those measurements and ignore a century of improvements! – uhoh Aug 24 '20 at 14:37