In the Search of Fundamental Inner Bond Strength of Solid Elements

Table 1

First 15 numbers of neighboring atoms and their relative distances for each atomic group in fcc, bcc, and hcp crystallography while the relations 𝑎=√2𝑑_𝑎,√3𝑎=2𝑑_𝑎, and 𝑎=𝑑_𝑎 (𝑎: lattice distance) are held in those crystal structure, respectively (knowing that: 𝑔_crystal(𝑖)=𝑑_𝑖/𝑑_𝑎).

𝑖	ccn(𝑖) in fcc	Distance in fcc as (𝑑𝑖/𝑑𝑎)^2	Distance in fcc as (𝑑𝑖/𝑎)^2	ccn(𝑖) in bcc	Distance in bcc as (𝑑𝑖/𝑑𝑎)^2	Distance in bcc as (𝑑𝑖/𝑎)^2	ccn(𝑖) in hcp	Distance in hcp as (𝑑𝑖/𝑑𝑎)^2	Distance in hcp as (𝑑𝑖/𝑎)^2
1	12	1	4/2	8	3/3	4/3	12	3/3	3/3
2	6	2	4/4	6	3/4	4/4	6	3/6	3/6
3	24	3	4/6	12	3/8	4/8	2	3/8	3/8
4	12	4	4/8	24	3/11	4/11	18	3/9	3/9
5	24	5	4/10	8	3/12	4/12	12	3/11	3/11
6	8	6	4/12	6	3/16	4/16	6	3/12	3/12
7	48	7	4/14	24	3/19	4/19	12	3/15	3/15
8	6	8	4/16	24	3/20	4/20	12	3/17	3/17
9	36	9	4/18	24	3/24	4/24	6	3/18	3/18
10	24	10	4/20	32	3/27	4/27	6	3/19	3/19
11	24	11	4/22	12	3/32	4/32	12	3/20	3/20
12	24	12	4/24	48	3/35	4/35	24	3/21	3/21
13	72	13	4/26	30	3/36	4/36	6	3/22	3/22
14	48	15	4/30	24	3/40	4/40	12	3/25	3/25
15	12	16	4/32	24	3/43	4/43	12	3/27	3/27