Table 2.

Theoretical and measured values of the perimeter scaling factor ξ for small neighbourhood sizes, needed for calculating the effective J value in the CPM

	2D				3D
neigh.	neigh.	ξ , estimated	ξ , numer.	% error	neigh.	ξ , estimated	ξ , numer.	% error
number	radius	using Eq. 29	determined		radius	using Eq. 33	determined
1	1	0.67	1	50.00	1	0.79	1	27.32
2	$\sqrt{2}$	1.89	3	59.10	$\sqrt{2}$	3.14	5	59.15
3	2	5.33	5	-6.25	$\sqrt{3}$	7.07	9	27.32
4	$\sqrt{5}$	7.45	11	47.58	2	12.57	11	-12.46
5	$2\sqrt{2}$	15.08	15	-0.56	$\sqrt{5}$	19.64	23	17.14
6	3	18.00	18	0	$\sqrt{6}$	28.27	39	37.93
7	$\sqrt{10}$	21.08	26	23.33	$2\sqrt{2}$	50.27	47	-6.50
8	$\sqrt{13}$	31.25	36	15.21	3	63.62	70	10.03
12	$2\sqrt{5}$	59.63	68	14.04	$\sqrt{13}$	132.73	134	0.96
20	$2\sqrt{10}$	168.66	173	2.58	$\sqrt{22}$	380.13	410	7.86
100	$3\sqrt{29}$	2811.06	2850	1.39	$\sqrt{118}$	1.09·104	11127	1.75
1000	$\sqrt{3365}$	130133	130181	0.037	$3\sqrt{133}$	1.13·106	1127539	0.20