id	sid	tid	token	lemma	pos
asir-5424	1	1	applied	apply	VERB
asir-5424	1	2	science	science	NOUN
asir-5424	1	3	and	and	CCONJ
asir-5424	1	4	innovative	innovative	ADJ
asir-5424	1	5	research	research	NOUN
asir-5424	1	6	issn	issn	VERB
asir-5424	1	7	2474	2474	NUM
asir-5424	1	8	-	-	SYM
asir-5424	1	9	4972	4972	NUM
asir-5424	1	10	(	(	PUNCT
asir-5424	1	11	print	print	NOUN
asir-5424	1	12	)	)	PUNCT
asir-5424	1	13	issn	issn	VERB
asir-5424	1	14	2474	2474	NUM
asir-5424	1	15	-	-	SYM
asir-5424	1	16	4980	4980	NUM
asir-5424	1	17	(	(	PUNCT
asir-5424	1	18	online	online	ADJ
asir-5424	1	19	)	)	PUNCT
asir-5424	1	20	vol	vol	NOUN
asir-5424	1	21	.	.	PROPN
asir-5424	2	1	6	6	NUM
asir-5424	2	2	,	,	PUNCT
asir-5424	2	3	no	no	INTJ
asir-5424	2	4	.	.	NOUN
asir-5424	2	5	4	4	NUM
asir-5424	2	6	,	,	PUNCT
asir-5424	2	7	2022	2022	NUM
asir-5424	2	8	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	VERB
asir-5424	2	9	124	124	NUM
asir-5424	2	10	original	original	ADJ
asir-5424	2	11	paper	paper	NOUN
asir-5424	2	12	quantitative	quantitative	ADJ
asir-5424	2	13	interpretation	interpretation	NOUN
asir-5424	2	14	of	of	ADP
asir-5424	2	15	isotope	isotope	NOUN
asir-5424	2	16	correlation	correlation	NOUN
asir-5424	2	17	coefficient	coefficient	NOUN
asir-5424	2	18	ratios	ratio	NOUN
asir-5424	2	19	in	in	ADP
asir-5424	2	20	solid	solid	ADJ
asir-5424	2	21	diffusion	diffusion	NOUN
asir-5424	2	22	yuxi	yuxi	NOUN
asir-5424	2	23	jing1	jing1	PROPN
asir-5424	2	24	1	1	NUM
asir-5424	2	25	college	college	NOUN
asir-5424	2	26	of	of	ADP
asir-5424	2	27	materials	material	NOUN
asir-5424	2	28	and	and	CCONJ
asir-5424	2	29	chemical	chemical	PROPN
asir-5424	2	30	engineering	engineering	PROPN
asir-5424	2	31	,	,	PUNCT
asir-5424	2	32	chengdu	chengdu	PROPN
asir-5424	2	33	university	university	PROPN
asir-5424	2	34	of	of	ADP
asir-5424	2	35	technology	technology	PROPN
asir-5424	2	36	,	,	PUNCT
asir-5424	2	37	chengdu	chengdu	PROPN
asir-5424	2	38	610059	610059	NUM
asir-5424	2	39	,	,	PUNCT
asir-5424	2	40	china	china	PROPN
asir-5424	2	41	received	receive	VERB
asir-5424	2	42	:	:	PUNCT
asir-5424	2	43	november	november	PROPN
asir-5424	2	44	18	18	NUM
asir-5424	2	45	,	,	PUNCT
asir-5424	2	46	2022	2022	NUM
asir-5424	2	47	accepted	accept	VERB
asir-5424	2	48	:	:	PUNCT
asir-5424	2	49	november	november	PROPN
asir-5424	2	50	23	23	NUM
asir-5424	2	51	,	,	PUNCT
asir-5424	2	52	2022	2022	NUM
asir-5424	2	53	online	online	ADV
asir-5424	2	54	published	publish	VERB
asir-5424	2	55	:	:	PUNCT
asir-5424	2	56	november	november	PROPN
asir-5424	2	57	23	23	NUM
asir-5424	2	58	,	,	PUNCT
asir-5424	2	59	2022	2022	NUM
asir-5424	2	60	doi:10.22158	doi:10.22158	NOUN
asir-5424	2	61	/	/	SYM
asir-5424	2	62	asir.v6n4p124	asir.v6n4p124	PROPN
asir-5424	2	63	url	url	PROPN
asir-5424	2	64	:	:	PUNCT
asir-5424	2	65	http://doi.org/10.22158/asir.v6n4p124	http://doi.org/10.22158/asir.v6n4p124	X
asir-5424	2	66	abstract	abstract	NOUN
asir-5424	2	67	the	the	DET
asir-5424	2	68	correlation	correlation	NOUN
asir-5424	2	69	coefficient	coefficient	NOUN
asir-5424	2	70	f	f	PROPN
asir-5424	2	71	is	be	AUX
asir-5424	2	72	crucial	crucial	ADJ
asir-5424	2	73	in	in	ADP
asir-5424	2	74	the	the	DET
asir-5424	2	75	calculation	calculation	NOUN
asir-5424	2	76	of	of	ADP
asir-5424	2	77	the	the	DET
asir-5424	2	78	absolute	absolute	ADJ
asir-5424	2	79	diffusion	diffusion	NOUN
asir-5424	2	80	coefficient	coefficient	NOUN
asir-5424	2	81	d	d	NOUN
asir-5424	2	82	,	,	PUNCT
asir-5424	2	83	especially	especially	ADV
asir-5424	2	84	for	for	ADP
asir-5424	2	85	the	the	DET
asir-5424	2	86	vacancy	vacancy	NOUN
asir-5424	2	87	mechanism	mechanism	NOUN
asir-5424	2	88	.	.	PUNCT
asir-5424	3	1	the	the	DET
asir-5424	3	2	current	current	ADJ
asir-5424	3	3	study	study	NOUN
asir-5424	3	4	for	for	ADP
asir-5424	3	5	f	f	PROPN
asir-5424	3	6	is	be	AUX
asir-5424	3	7	complex	complex	ADJ
asir-5424	3	8	and	and	CCONJ
asir-5424	3	9	contains	contain	VERB
asir-5424	3	10	many	many	ADJ
asir-5424	3	11	approximations	approximation	NOUN
asir-5424	3	12	and	and	CCONJ
asir-5424	3	13	assumptions	assumption	NOUN
asir-5424	3	14	.	.	PUNCT
asir-5424	4	1	however	however	ADV
asir-5424	4	2	,	,	PUNCT
asir-5424	4	3	f	f	PROPN
asir-5424	4	4	can	can	AUX
asir-5424	4	5	be	be	AUX
asir-5424	4	6	ignored	ignore	VERB
asir-5424	4	7	when	when	SCONJ
asir-5424	4	8	considering	consider	VERB
asir-5424	4	9	the	the	DET
asir-5424	4	10	isotope	isotope	NOUN
asir-5424	4	11	effect	effect	NOUN
asir-5424	4	12	,	,	PUNCT
asir-5424	4	13	which	which	PRON
asir-5424	4	14	has	have	AUX
asir-5424	4	15	only	only	ADV
asir-5424	4	16	been	be	AUX
asir-5424	4	17	stated	state	VERB
asir-5424	4	18	qualitatively	qualitatively	ADV
asir-5424	4	19	by	by	ADP
asir-5424	4	20	previous	previous	ADJ
asir-5424	4	21	authors	author	NOUN
asir-5424	4	22	and	and	CCONJ
asir-5424	4	23	not	not	PART
asir-5424	4	24	explained	explain	VERB
asir-5424	4	25	from	from	ADP
asir-5424	4	26	a	a	DET
asir-5424	4	27	quantitative	quantitative	ADJ
asir-5424	4	28	perspective	perspective	NOUN
asir-5424	4	29	.	.	PUNCT
asir-5424	5	1	in	in	ADP
asir-5424	5	2	this	this	DET
asir-5424	5	3	paper	paper	NOUN
asir-5424	5	4	,	,	PUNCT
asir-5424	5	5	we	we	PRON
asir-5424	5	6	will	will	AUX
asir-5424	5	7	explain	explain	VERB
asir-5424	5	8	the	the	DET
asir-5424	5	9	reason	reason	NOUN
asir-5424	5	10	why	why	SCONJ
asir-5424	5	11	f	f	PROPN
asir-5424	5	12	can	can	AUX
asir-5424	5	13	be	be	AUX
asir-5424	5	14	neglected	neglect	VERB
asir-5424	5	15	in	in	ADP
asir-5424	5	16	the	the	DET
asir-5424	5	17	isotope	isotope	NOUN
asir-5424	5	18	diffusion	diffusion	NOUN
asir-5424	5	19	effect	effect	NOUN
asir-5424	5	20	by	by	ADP
asir-5424	5	21	finding	find	VERB
asir-5424	5	22	the	the	DET
asir-5424	5	23	most	most	ADV
asir-5424	5	24	essential	essential	ADJ
asir-5424	5	25	formula	formula	NOUN
asir-5424	5	26	and	and	CCONJ
asir-5424	5	27	source	source	NOUN
asir-5424	5	28	of	of	ADP
asir-5424	5	29	f	f	PROPN
asir-5424	5	30	,	,	PUNCT
asir-5424	5	31	as	as	ADP
asir-5424	5	32	a	a	DET
asir-5424	5	33	way	way	NOUN
asir-5424	5	34	to	to	PART
asir-5424	5	35	save	save	VERB
asir-5424	5	36	the	the	DET
asir-5424	5	37	most	most	ADV
asir-5424	5	38	troublesome	troublesome	ADJ
asir-5424	5	39	step	step	NOUN
asir-5424	5	40	in	in	ADP
asir-5424	5	41	the	the	DET
asir-5424	5	42	calculation	calculation	NOUN
asir-5424	5	43	of	of	ADP
asir-5424	5	44	the	the	DET
asir-5424	5	45	isotope	isotope	NOUN
asir-5424	5	46	diffusion	diffusion	NOUN
asir-5424	5	47	effect	effect	NOUN
asir-5424	5	48	.	.	PUNCT
asir-5424	6	1	keywords	keyword	VERB
asir-5424	6	2	correlation	correlation	NOUN
asir-5424	6	3	coefficient	coefficient	NOUN
asir-5424	6	4	,	,	PUNCT
asir-5424	6	5	solid	solid	ADJ
asir-5424	6	6	diffusion	diffusion	NOUN
asir-5424	6	7	,	,	PUNCT
asir-5424	6	8	isotope	isotope	NOUN
asir-5424	6	9	effect	effect	NOUN
asir-5424	6	10	1	1	NUM
asir-5424	6	11	.	.	X
asir-5424	7	1	introduction	introduction	NOUN
asir-5424	7	2	the	the	DET
asir-5424	7	3	correlation	correlation	NOUN
asir-5424	7	4	coefficient	coefficient	NOUN
asir-5424	7	5	f	f	PROPN
asir-5424	7	6	is	be	AUX
asir-5424	7	7	important	important	ADJ
asir-5424	7	8	in	in	ADP
asir-5424	7	9	the	the	DET
asir-5424	7	10	solid	solid	ADJ
asir-5424	7	11	state	state	NOUN
asir-5424	7	12	diffusion	diffusion	NOUN
asir-5424	7	13	of	of	ADP
asir-5424	7	14	crystalline	crystalline	NOUN
asir-5424	7	15	materials	material	NOUN
asir-5424	7	16	.	.	PUNCT
asir-5424	8	1	diffusion	diffusion	NOUN
asir-5424	8	2	is	be	AUX
asir-5424	8	3	mediated	mediate	VERB
asir-5424	8	4	by	by	ADP
asir-5424	8	5	diffusion	diffusion	NOUN
asir-5424	8	6	carriers	carrier	NOUN
asir-5424	8	7	,	,	PUNCT
asir-5424	8	8	such	such	ADJ
asir-5424	8	9	as	as	ADP
asir-5424	8	10	vacancies	vacancy	NOUN
asir-5424	8	11	,	,	PUNCT
asir-5424	8	12	vacancy	vacancy	NOUN
asir-5424	8	13	pairs	pair	NOUN
asir-5424	8	14	,	,	PUNCT
asir-5424	8	15	etc	etc	X
asir-5424	8	16	.	.	X
asir-5424	9	1	an	an	DET
asir-5424	9	2	equivalent	equivalent	ADJ
asir-5424	9	3	statement	statement	NOUN
asir-5424	9	4	is	be	AUX
asir-5424	9	5	that	that	SCONJ
asir-5424	9	6	at	at	ADV
asir-5424	9	7	least	least	ADV
asir-5424	9	8	three	three	NUM
asir-5424	9	9	identifiable	identifiable	ADJ
asir-5424	9	10	“	"	PUNCT
asir-5424	9	11	species	specie	NOUN
asir-5424	9	12	”	"	PUNCT
asir-5424	9	13	must	must	AUX
asir-5424	9	14	be	be	AUX
asir-5424	9	15	involved	involve	VERB
asir-5424	9	16	in	in	ADP
asir-5424	9	17	the	the	DET
asir-5424	9	18	diffusion	diffusion	NOUN
asir-5424	9	19	process	process	NOUN
asir-5424	9	20	.	.	PUNCT
asir-5424	10	1	for	for	ADP
asir-5424	10	2	example	example	NOUN
asir-5424	10	3	,	,	PUNCT
asir-5424	10	4	when	when	SCONJ
asir-5424	10	5	an	an	DET
asir-5424	10	6	impurity	impurity	NOUN
asir-5424	10	7	atom	atom	NOUN
asir-5424	10	8	diffusion	diffusion	NOUN
asir-5424	10	9	through	through	ADP
asir-5424	10	10	a	a	DET
asir-5424	10	11	vacancy	vacancy	NOUN
asir-5424	10	12	in	in	ADP
asir-5424	10	13	a	a	DET
asir-5424	10	14	crystal	crystal	NOUN
asir-5424	10	15	,	,	PUNCT
asir-5424	10	16	the	the	DET
asir-5424	10	17	three	three	NUM
asir-5424	10	18	“	"	PUNCT
asir-5424	10	19	species	specie	NOUN
asir-5424	10	20	”	"	PUNCT
asir-5424	10	21	involved	involve	VERB
asir-5424	10	22	are	be	AUX
asir-5424	10	23	the	the	DET
asir-5424	10	24	vacancy	vacancy	NOUN
asir-5424	10	25	,	,	PUNCT
asir-5424	10	26	the	the	DET
asir-5424	10	27	solvent	solvent	NOUN
asir-5424	10	28	atom	atom	NOUN
asir-5424	10	29	and	and	CCONJ
asir-5424	10	30	the	the	DET
asir-5424	10	31	impurity	impurity	NOUN
asir-5424	10	32	atom	atom	NOUN
asir-5424	10	33	.	.	PUNCT
asir-5424	11	1	there	there	PRON
asir-5424	11	2	is	be	VERB
asir-5424	11	3	no	no	DET
asir-5424	11	4	correlation	correlation	NOUN
asir-5424	11	5	between	between	ADP
asir-5424	11	6	two	two	NUM
asir-5424	11	7	successive	successive	ADJ
asir-5424	11	8	jumps	jump	NOUN
asir-5424	11	9	of	of	ADP
asir-5424	11	10	atoms	atom	NOUN
asir-5424	11	11	in	in	ADP
asir-5424	11	12	interstitial	interstitial	ADJ
asir-5424	11	13	diffusion	diffusion	NOUN
asir-5424	11	14	because	because	SCONJ
asir-5424	11	15	no	no	DET
asir-5424	11	16	diffusion	diffusion	NOUN
asir-5424	11	17	carriers	carrier	NOUN
asir-5424	11	18	are	be	AUX
asir-5424	11	19	involved	involve	VERB
asir-5424	11	20	,	,	PUNCT
asir-5424	11	21	but	but	CCONJ
asir-5424	11	22	there	there	PRON
asir-5424	11	23	is	be	VERB
asir-5424	11	24	a	a	DET
asir-5424	11	25	correlation	correlation	NOUN
asir-5424	11	26	between	between	ADP
asir-5424	11	27	two	two	NUM
asir-5424	11	28	successive	successive	ADJ
asir-5424	11	29	jumps	jump	NOUN
asir-5424	11	30	of	of	ADP
asir-5424	11	31	atoms	atom	NOUN
asir-5424	11	32	in	in	ADP
asir-5424	11	33	the	the	DET
asir-5424	11	34	vacancy	vacancy	NOUN
asir-5424	11	35	diffusion	diffusion	NOUN
asir-5424	11	36	mechanism	mechanism	NOUN
asir-5424	11	37	.	.	PUNCT
asir-5424	12	1	the	the	DET
asir-5424	12	2	correlation	correlation	NOUN
asir-5424	12	3	effect	effect	NOUN
asir-5424	12	4	refers	refer	VERB
asir-5424	12	5	to	to	ADP
asir-5424	12	6	the	the	DET
asir-5424	12	7	fact	fact	NOUN
asir-5424	12	8	that	that	SCONJ
asir-5424	12	9	the	the	DET
asir-5424	12	10	successive	successive	ADJ
asir-5424	12	11	jumps	jump	NOUN
asir-5424	12	12	of	of	ADP
asir-5424	12	13	particles	particle	NOUN
asir-5424	12	14	are	be	AUX
asir-5424	12	15	usually	usually	ADV
asir-5424	12	16	interdependent	interdependent	ADJ
asir-5424	12	17	for	for	ADP
asir-5424	12	18	the	the	DET
asir-5424	12	19	motion	motion	NOUN
asir-5424	12	20	caused	cause	VERB
asir-5424	12	21	by	by	ADP
asir-5424	12	22	defects	defect	NOUN
asir-5424	12	23	.	.	PUNCT
asir-5424	13	1	for	for	ADP
asir-5424	13	2	example	example	NOUN
asir-5424	13	3	,	,	PUNCT
asir-5424	13	4	for	for	ADP
asir-5424	13	5	the	the	DET
asir-5424	13	6	vacancy	vacancy	NOUN
asir-5424	13	7	mechanism	mechanism	NOUN
asir-5424	13	8	,	,	PUNCT
asir-5424	13	9	each	each	DET
asir-5424	13	10	particle	particle	NOUN
asir-5424	13	11	can	can	AUX
asir-5424	13	12	only	only	ADV
asir-5424	13	13	jump	jump	VERB
asir-5424	13	14	by	by	ADP
asir-5424	13	15	exchanging	exchange	VERB
asir-5424	13	16	positions	position	NOUN
asir-5424	13	17	with	with	ADP
asir-5424	13	18	its	its	PRON
asir-5424	13	19	neighboring	neighboring	NOUN
asir-5424	13	20	vacancies	vacancy	NOUN
asir-5424	13	21	.	.	PUNCT
asir-5424	14	1	after	after	ADP
asir-5424	14	2	each	each	DET
asir-5424	14	3	successful	successful	ADJ
asir-5424	14	4	exchange	exchange	NOUN
asir-5424	14	5	of	of	ADP
asir-5424	14	6	a	a	DET
asir-5424	14	7	particle	particle	NOUN
asir-5424	14	8	with	with	ADP
asir-5424	14	9	a	a	DET
asir-5424	14	10	vacancy	vacancy	NOUN
asir-5424	14	11	,	,	PUNCT
asir-5424	14	12	the	the	DET
asir-5424	14	13	vacancy	vacancy	NOUN
asir-5424	14	14	still	still	ADV
asir-5424	14	15	be	be	AUX
asir-5424	14	16	next	next	ADJ
asir-5424	14	17	to	to	ADP
asir-5424	14	18	the	the	DET
asir-5424	14	19	particle	particle	NOUN
asir-5424	14	20	,	,	PUNCT
asir-5424	14	21	thus	thus	ADV
asir-5424	14	22	increasing	increase	VERB
asir-5424	14	23	the	the	DET
asir-5424	14	24	probability	probability	NOUN
asir-5424	14	25	of	of	ADP
asir-5424	14	26	the	the	DET
asir-5424	14	27	particle	particle	NOUN
asir-5424	14	28	jumping	jump	VERB
asir-5424	14	29	in	in	ADP
asir-5424	14	30	the	the	DET
asir-5424	14	31	opposite	opposite	ADJ
asir-5424	14	32	direction	direction	NOUN
asir-5424	14	33	;	;	PUNCT
asir-5424	14	34	in	in	ADP
asir-5424	14	35	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-5424	14	36	applied	apply	VERB
asir-5424	14	37	science	science	NOUN
asir-5424	14	38	and	and	CCONJ
asir-5424	14	39	innovative	innovative	ADJ
asir-5424	14	40	research	research	NOUN
asir-5424	14	41	vol	vol	NOUN
asir-5424	14	42	.	.	PROPN
asir-5424	15	1	6	6	NUM
asir-5424	15	2	,	,	PUNCT
asir-5424	15	3	no	no	INTJ
asir-5424	15	4	.	.	NOUN
asir-5424	15	5	4	4	NUM
asir-5424	15	6	,	,	PUNCT
asir-5424	15	7	2022	2022	NUM
asir-5424	15	8	125	125	NUM
asir-5424	15	9	published	publish	VERB
asir-5424	15	10	by	by	ADP
asir-5424	15	11	scholink	scholink	PROPN
asir-5424	15	12	inc	inc	PROPN
asir-5424	15	13	.	.	PROPN
asir-5424	15	14	other	other	ADJ
asir-5424	15	15	words	word	NOUN
asir-5424	15	16	,	,	PUNCT
asir-5424	15	17	the	the	DET
asir-5424	15	18	probability	probability	NOUN
asir-5424	15	19	of	of	ADP
asir-5424	15	20	the	the	DET
asir-5424	15	21	particle	particle	NOUN
asir-5424	15	22	jumping	jump	VERB
asir-5424	15	23	back	back	ADV
asir-5424	15	24	to	to	ADP
asir-5424	15	25	the	the	DET
asir-5424	15	26	vacancy	vacancy	NOUN
asir-5424	15	27	again	again	ADV
asir-5424	15	28	is	be	AUX
asir-5424	15	29	maximized	maximize	VERB
asir-5424	15	30	.	.	PUNCT
asir-5424	16	1	if	if	SCONJ
asir-5424	16	2	there	there	PRON
asir-5424	16	3	is	be	VERB
asir-5424	16	4	no	no	DET
asir-5424	16	5	correlation	correlation	NOUN
asir-5424	16	6	effect	effect	NOUN
asir-5424	16	7	,	,	PUNCT
asir-5424	16	8	as	as	ADP
asir-5424	16	9	in	in	ADP
asir-5424	16	10	the	the	DET
asir-5424	16	11	case	case	NOUN
asir-5424	16	12	of	of	ADP
asir-5424	16	13	the	the	DET
asir-5424	16	14	interstitial	interstitial	ADJ
asir-5424	16	15	mechanism	mechanism	NOUN
asir-5424	16	16	,	,	PUNCT
asir-5424	16	17	and	and	CCONJ
asir-5424	16	18	the	the	DET
asir-5424	16	19	particle	particle	NOUN
asir-5424	16	20	makes	make	VERB
asir-5424	16	21	a	a	DET
asir-5424	16	22	random	random	ADJ
asir-5424	16	23	walk	walk	NOUN
asir-5424	16	24	involving	involve	VERB
asir-5424	16	25	a	a	DET
asir-5424	16	26	series	series	NOUN
asir-5424	16	27	of	of	ADP
asir-5424	16	28	independent	independent	ADJ
asir-5424	16	29	jumps	jump	NOUN
asir-5424	16	30	,	,	PUNCT
asir-5424	16	31	each	each	PRON
asir-5424	16	32	of	of	ADP
asir-5424	16	33	which	which	PRON
asir-5424	16	34	occurs	occur	VERB
asir-5424	16	35	independent	independent	ADJ
asir-5424	16	36	of	of	ADP
asir-5424	16	37	the	the	DET
asir-5424	16	38	previous	previous	ADJ
asir-5424	16	39	jump	jump	NOUN
asir-5424	16	40	,	,	PUNCT
asir-5424	16	41	then	then	ADV
asir-5424	16	42	the	the	DET
asir-5424	16	43	probability	probability	NOUN
asir-5424	16	44	of	of	ADP
asir-5424	16	45	the	the	DET
asir-5424	16	46	particle	particle	NOUN
asir-5424	16	47	jumping	jump	VERB
asir-5424	16	48	toward	toward	ADP
asir-5424	16	49	any	any	PRON
asir-5424	16	50	of	of	ADP
asir-5424	16	51	the	the	DET
asir-5424	16	52	interstitial	interstitial	ADJ
asir-5424	16	53	positions	position	NOUN
asir-5424	16	54	should	should	AUX
asir-5424	16	55	be	be	AUX
asir-5424	16	56	the	the	DET
asir-5424	16	57	same	same	ADJ
asir-5424	16	58	.	.	PUNCT
asir-5424	17	1	therefore	therefore	ADV
asir-5424	17	2	bardeen	bardeen	PROPN
asir-5424	17	3	and	and	CCONJ
asir-5424	17	4	herring	herring	PROPN
asir-5424	17	5	(	(	PUNCT
asir-5424	17	6	1952	1952	NUM
asir-5424	17	7	)	)	PUNCT
asir-5424	17	8	introduced	introduce	VERB
asir-5424	17	9	the	the	DET
asir-5424	17	10	correlation	correlation	NOUN
asir-5424	17	11	factor	factor	NOUN
asir-5424	17	12	into	into	ADP
asir-5424	17	13	the	the	DET
asir-5424	17	14	theory	theory	NOUN
asir-5424	17	15	of	of	ADP
asir-5424	17	16	solid	solid	ADJ
asir-5424	17	17	diffusion	diffusion	NOUN
asir-5424	17	18	.	.	PUNCT
asir-5424	18	1	the	the	DET
asir-5424	18	2	correlation	correlation	NOUN
asir-5424	18	3	factor	factor	NOUN
asir-5424	18	4	was	be	AUX
asir-5424	18	5	defined	define	VERB
asir-5424	18	6	as	as	ADP
asir-5424	18	7	the	the	DET
asir-5424	18	8	ratio	ratio	NOUN
asir-5424	18	9	between	between	ADP
asir-5424	18	10	the	the	DET
asir-5424	18	11	actual	actual	ADJ
asir-5424	18	12	impurity	impurity	NOUN
asir-5424	18	13	diffusion	diffusion	NOUN
asir-5424	18	14	coefficient	coefficient	NOUN
asir-5424	18	15	and	and	CCONJ
asir-5424	18	16	the	the	DET
asir-5424	18	17	diffusion	diffusion	NOUN
asir-5424	18	18	coefficient	coefficient	NOUN
asir-5424	18	19	resulting	result	VERB
asir-5424	18	20	from	from	ADP
asir-5424	18	21	uncorrelated	uncorrelated	ADJ
asir-5424	18	22	random	random	ADJ
asir-5424	18	23	walk	walk	NOUN
asir-5424	18	24	.	.	PUNCT
asir-5424	19	1	𝑓	𝑓	DET
asir-5424	19	2	≡	≡	PROPN
asir-5424	19	3	𝐷𝑎𝑐𝑡	𝐷𝑎𝑐𝑡	PROPN
asir-5424	19	4	𝐷𝑟𝑎𝑛𝑑𝑜𝑚	𝐷𝑟𝑎𝑛𝑑𝑜𝑚	PROPN
asir-5424	19	5	(	(	PUNCT
asir-5424	19	6	1	1	X
asir-5424	19	7	)	)	PUNCT
asir-5424	19	8	a	a	DET
asir-5424	19	9	very	very	ADV
asir-5424	19	10	simple	simple	ADJ
asir-5424	19	11	expression	expression	NOUN
asir-5424	19	12	for	for	ADP
asir-5424	19	13	the	the	DET
asir-5424	19	14	correlation	correlation	NOUN
asir-5424	19	15	factor	factor	NOUN
asir-5424	19	16	was	be	AUX
asir-5424	19	17	obtained	obtain	VERB
asir-5424	19	18	under	under	ADP
asir-5424	19	19	the	the	DET
asir-5424	19	20	assumption	assumption	NOUN
asir-5424	19	21	that	that	SCONJ
asir-5424	19	22	only	only	ADV
asir-5424	19	23	successive	successive	ADJ
asir-5424	19	24	jumps	jump	NOUN
asir-5424	19	25	of	of	ADP
asir-5424	19	26	impurity	impurity	NOUN
asir-5424	19	27	particles	particle	NOUN
asir-5424	19	28	are	be	AUX
asir-5424	19	29	correlated	correlate	VERB
asir-5424	19	30	and	and	CCONJ
asir-5424	19	31	based	base	VERB
asir-5424	19	32	on	on	ADP
asir-5424	19	33	the	the	DET
asir-5424	19	34	simplified	simplified	ADJ
asir-5424	19	35	assumption	assumption	NOUN
asir-5424	19	36	of	of	ADP
asir-5424	19	37	the	the	DET
asir-5424	19	38	particle	particle	NOUN
asir-5424	19	39	jumps	jump	VERB
asir-5424	19	40	types	type	NOUN
asir-5424	19	41	in	in	ADP
asir-5424	19	42	the	the	DET
asir-5424	19	43	lattice	lattice	NOUN
asir-5424	19	44	and	and	CCONJ
asir-5424	19	45	symmetry	symmetry	NOUN
asir-5424	19	46	of	of	ADP
asir-5424	19	47	lattice	lattice	NOUN
asir-5424	19	48	.	.	PUNCT
asir-5424	20	1	the	the	DET
asir-5424	20	2	expression	expression	NOUN
asir-5424	20	3	is	be	AUX
asir-5424	20	4	as	as	SCONJ
asir-5424	20	5	follows	follow	VERB
asir-5424	20	6	(	(	PUNCT
asir-5424	20	7	compaan	compaan	PROPN
asir-5424	20	8	&	&	CCONJ
asir-5424	20	9	haven	haven	PROPN
asir-5424	20	10	,	,	PUNCT
asir-5424	20	11	1956	1956	NUM
asir-5424	20	12	)	)	PUNCT
asir-5424	20	13	,	,	PUNCT
asir-5424	20	14	𝑓	𝑓	X
asir-5424	20	15	=	=	SYM
asir-5424	20	16	1	1	NUM
asir-5424	20	17	+	+	NOUN
asir-5424	20	18	<	<	X
asir-5424	20	19	𝑠𝜃	𝑠𝜃	X
asir-5424	20	20	>	>	X
asir-5424	20	21	1−	1−	NUM
asir-5424	20	22	<	<	X
asir-5424	20	23	𝑠𝜃	𝑠𝜃	PROPN
asir-5424	20	24	>	>	X
asir-5424	20	25	(	(	PUNCT
asir-5424	20	26	2	2	NUM
asir-5424	20	27	)	)	PUNCT
asir-5424	20	28	where	where	SCONJ
asir-5424	20	29	<	<	X
asir-5424	20	30	cos	cos	PART
asir-5424	20	31	θ	θ	PROPN
asir-5424	20	32	>	>	X
asir-5424	20	33	is	be	AUX
asir-5424	20	34	the	the	DET
asir-5424	20	35	average	average	ADJ
asir-5424	20	36	angle	angle	NOUN
asir-5424	20	37	between	between	ADP
asir-5424	20	38	two	two	NUM
asir-5424	20	39	consecutive	consecutive	ADJ
asir-5424	20	40	jumps	jump	NOUN
asir-5424	20	41	of	of	ADP
asir-5424	20	42	the	the	DET
asir-5424	20	43	impurity	impurity	NOUN
asir-5424	20	44	atom	atom	NOUN
asir-5424	20	45	.	.	PUNCT
asir-5424	21	1	equation	equation	NOUN
asir-5424	21	2	(	(	PUNCT
asir-5424	21	3	2	2	X
asir-5424	21	4	)	)	PUNCT
asir-5424	21	5	is	be	AUX
asir-5424	21	6	usually	usually	ADV
asir-5424	21	7	applied	apply	VERB
asir-5424	21	8	to	to	ADP
asir-5424	21	9	self	self	NOUN
asir-5424	21	10	-	-	PUNCT
asir-5424	21	11	diffusion	diffusion	NOUN
asir-5424	21	12	in	in	ADP
asir-5424	21	13	metals	metal	NOUN
asir-5424	21	14	and	and	CCONJ
asir-5424	21	15	is	be	AUX
asir-5424	21	16	satisfied	satisfied	ADJ
asir-5424	21	17	for	for	ADP
asir-5424	21	18	small	small	ADJ
asir-5424	21	19	vacancy	vacancy	NOUN
asir-5424	21	20	concentrations	concentration	NOUN
asir-5424	21	21	and	and	CCONJ
asir-5424	21	22	most	most	ADV
asir-5424	21	23	common	common	ADJ
asir-5424	21	24	lattice	lattice	NOUN
asir-5424	21	25	types	type	NOUN
asir-5424	21	26	.	.	PUNCT
asir-5424	22	1	although	although	SCONJ
asir-5424	22	2	we	we	PRON
asir-5424	22	3	know	know	VERB
asir-5424	22	4	that	that	SCONJ
asir-5424	22	5	the	the	DET
asir-5424	22	6	correlation	correlation	NOUN
asir-5424	22	7	coefficient	coefficient	NOUN
asir-5424	22	8	f	f	PROPN
asir-5424	22	9	is	be	AUX
asir-5424	22	10	crucial	crucial	ADJ
asir-5424	22	11	for	for	ADP
asir-5424	22	12	the	the	DET
asir-5424	22	13	study	study	NOUN
asir-5424	22	14	of	of	ADP
asir-5424	22	15	the	the	DET
asir-5424	22	16	diffusion	diffusion	NOUN
asir-5424	22	17	coefficient	coefficient	NOUN
asir-5424	22	18	d	d	PROPN
asir-5424	22	19	,	,	PUNCT
asir-5424	22	20	trying	try	VERB
asir-5424	22	21	to	to	PART
asir-5424	22	22	calculate	calculate	VERB
asir-5424	22	23	f	f	NOUN
asir-5424	22	24	exactly	exactly	ADV
asir-5424	22	25	is	be	AUX
asir-5424	22	26	complex	complex	ADJ
asir-5424	22	27	and	and	CCONJ
asir-5424	22	28	difficult	difficult	ADJ
asir-5424	22	29	because	because	SCONJ
asir-5424	22	30	it	it	PRON
asir-5424	22	31	is	be	AUX
asir-5424	22	32	closely	closely	ADV
asir-5424	22	33	related	relate	VERB
asir-5424	22	34	to	to	ADP
asir-5424	22	35	the	the	DET
asir-5424	22	36	lattice	lattice	NOUN
asir-5424	22	37	structure	structure	NOUN
asir-5424	22	38	,	,	PUNCT
asir-5424	22	39	with	with	SCONJ
asir-5424	22	40	different	different	ADJ
asir-5424	22	41	crystal	crystal	NOUN
asir-5424	22	42	types	type	NOUN
asir-5424	22	43	can	can	AUX
asir-5424	22	44	not	not	PART
asir-5424	22	45	be	be	AUX
asir-5424	22	46	described	describe	VERB
asir-5424	22	47	by	by	ADP
asir-5424	22	48	a	a	DET
asir-5424	22	49	general	general	ADJ
asir-5424	22	50	formula	formula	NOUN
asir-5424	22	51	.	.	PUNCT
asir-5424	23	1	therefore	therefore	ADV
asir-5424	23	2	,	,	PUNCT
asir-5424	23	3	previous	previous	ADJ
asir-5424	23	4	authors	author	NOUN
asir-5424	23	5	have	have	AUX
asir-5424	23	6	made	make	VERB
asir-5424	23	7	approximations	approximation	NOUN
asir-5424	23	8	and	and	CCONJ
asir-5424	23	9	assumptions	assumption	NOUN
asir-5424	23	10	based	base	VERB
asir-5424	23	11	on	on	ADP
asir-5424	23	12	equation	equation	NOUN
asir-5424	23	13	(	(	PUNCT
asir-5424	23	14	2	2	NUM
asir-5424	23	15	)	)	PUNCT
asir-5424	23	16	,	,	PUNCT
asir-5424	23	17	relying	rely	VERB
asir-5424	23	18	on	on	ADP
asir-5424	23	19	the	the	DET
asir-5424	23	20	jump	jump	NOUN
asir-5424	23	21	frequencies	frequency	NOUN
asir-5424	23	22	of	of	ADP
asir-5424	23	23	various	various	ADJ
asir-5424	23	24	types	type	NOUN
asir-5424	23	25	of	of	ADP
asir-5424	23	26	atoms	atom	NOUN
asir-5424	23	27	in	in	ADP
asir-5424	23	28	various	various	ADJ
asir-5424	23	29	crystal	crystal	NOUN
asir-5424	23	30	structures	structure	NOUN
asir-5424	23	31	involved	involve	VERB
asir-5424	23	32	in	in	ADP
asir-5424	23	33	the	the	DET
asir-5424	23	34	diffusion	diffusion	NOUN
asir-5424	23	35	process	process	NOUN
asir-5424	23	36	to	to	PART
asir-5424	23	37	calculate	calculate	VERB
asir-5424	23	38	it	it	PRON
asir-5424	23	39	,	,	PUNCT
asir-5424	23	40	such	such	ADJ
asir-5424	23	41	as	as	ADP
asir-5424	23	42	the	the	DET
asir-5424	23	43	five	five	NUM
asir-5424	23	44	-	-	PUNCT
asir-5424	23	45	frequency	frequency	NOUN
asir-5424	23	46	model	model	NOUN
asir-5424	23	47	(	(	PUNCT
asir-5424	23	48	manning	manning	NOUN
asir-5424	23	49	,	,	PUNCT
asir-5424	23	50	1959	1959	NUM
asir-5424	23	51	,	,	PUNCT
asir-5424	23	52	1962	1962	NUM
asir-5424	23	53	,	,	PUNCT
asir-5424	23	54	1964	1964	NUM
asir-5424	23	55	;	;	PUNCT
asir-5424	23	56	lidiard	lidiard	NOUN
asir-5424	23	57	,	,	PUNCT
asir-5424	23	58	1955	1955	NUM
asir-5424	23	59	)	)	PUNCT
asir-5424	23	60	,	,	PUNCT
asir-5424	23	61	the	the	DET
asir-5424	23	62	eight	eight	NUM
asir-5424	23	63	-	-	PUNCT
asir-5424	23	64	frequency	frequency	NOUN
asir-5424	23	65	model	model	NOUN
asir-5424	23	66	(	(	PUNCT
asir-5424	23	67	manning	manning	NOUN
asir-5424	23	68	,	,	PUNCT
asir-5424	23	69	1964	1964	NUM
asir-5424	23	70	)	)	PUNCT
asir-5424	23	71	,	,	PUNCT
asir-5424	23	72	and	and	CCONJ
asir-5424	23	73	the	the	DET
asir-5424	23	74	nine	nine	NUM
asir-5424	23	75	-	-	PUNCT
asir-5424	23	76	frequency	frequency	NOUN
asir-5424	23	77	model	model	NOUN
asir-5424	23	78	(	(	PUNCT
asir-5424	23	79	manning	manning	NOUN
asir-5424	23	80	,	,	PUNCT
asir-5424	23	81	1959	1959	NUM
asir-5424	23	82	)	)	PUNCT
asir-5424	23	83	.	.	PUNCT
asir-5424	24	1	in	in	ADP
asir-5424	24	2	order	order	NOUN
asir-5424	24	3	to	to	PART
asir-5424	24	4	study	study	VERB
asir-5424	24	5	the	the	DET
asir-5424	24	6	isotope	isotope	NOUN
asir-5424	24	7	diffusion	diffusion	NOUN
asir-5424	24	8	coefficient	coefficient	NOUN
asir-5424	24	9	ratio	ratio	NOUN
asir-5424	24	10	(	(	PUNCT
asir-5424	24	11	d*/d	d*/d	NOUN
asir-5424	24	12	)	)	PUNCT
asir-5424	24	13	,	,	PUNCT
asir-5424	24	14	we	we	PRON
asir-5424	24	15	had	have	VERB
asir-5424	24	16	to	to	PART
asir-5424	24	17	firstly	firstly	ADV
asir-5424	24	18	study	study	VERB
asir-5424	24	19	the	the	DET
asir-5424	24	20	isotope	isotope	NOUN
asir-5424	24	21	correlation	correlation	NOUN
asir-5424	24	22	coefficient	coefficient	NOUN
asir-5424	24	23	ratio	ratio	NOUN
asir-5424	24	24	(	(	PUNCT
asir-5424	24	25	f*/f	f*/f	NUM
asir-5424	24	26	)	)	PUNCT
asir-5424	24	27	.	.	PUNCT
asir-5424	25	1	the	the	DET
asir-5424	25	2	previous	previous	ADJ
asir-5424	25	3	works	work	NOUN
asir-5424	25	4	(	(	PUNCT
asir-5424	25	5	van	van	PROPN
asir-5424	25	6	orman	orman	PROPN
asir-5424	25	7	&	&	CCONJ
asir-5424	25	8	krawczynski	krawczynski	PROPN
asir-5424	25	9	,	,	PUNCT
asir-5424	25	10	2015	2015	NUM
asir-5424	25	11	)	)	PUNCT
asir-5424	25	12	can	can	AUX
asir-5424	25	13	only	only	ADV
asir-5424	25	14	qualitatively	qualitatively	ADV
asir-5424	25	15	assume	assume	VERB
asir-5424	25	16	that	that	SCONJ
asir-5424	25	17	the	the	DET
asir-5424	25	18	isotope	isotope	NOUN
asir-5424	25	19	correlation	correlation	NOUN
asir-5424	25	20	coefficient	coefficient	NOUN
asir-5424	25	21	ratio	ratio	NOUN
asir-5424	25	22	can	can	AUX
asir-5424	25	23	be	be	AUX
asir-5424	25	24	neglected	neglect	VERB
asir-5424	25	25	(	(	PUNCT
asir-5424	25	26	except	except	SCONJ
asir-5424	25	27	for	for	ADP
asir-5424	25	28	h	h	NOUN
asir-5424	25	29	,	,	PUNCT
asir-5424	25	30	he	he	PRON
asir-5424	25	31	,	,	PUNCT
asir-5424	25	32	where	where	SCONJ
asir-5424	25	33	quantum	quantum	NOUN
asir-5424	25	34	effects	effect	NOUN
asir-5424	25	35	exist	exist	VERB
asir-5424	25	36	)	)	PUNCT
asir-5424	25	37	,	,	PUNCT
asir-5424	25	38	but	but	CCONJ
asir-5424	25	39	there	there	PRON
asir-5424	25	40	is	be	VERB
asir-5424	25	41	no	no	DET
asir-5424	25	42	quantitative	quantitative	ADJ
asir-5424	25	43	explanation	explanation	NOUN
asir-5424	25	44	.	.	PUNCT
asir-5424	26	1	moreover	moreover	ADV
asir-5424	26	2	,	,	PUNCT
asir-5424	26	3	the	the	DET
asir-5424	26	4	previous	previous	ADJ
asir-5424	26	5	theoretical	theoretical	ADJ
asir-5424	26	6	studies	study	NOUN
asir-5424	26	7	of	of	ADP
asir-5424	26	8	correlation	correlation	NOUN
asir-5424	26	9	coefficients	coefficient	NOUN
asir-5424	26	10	have	have	VERB
asir-5424	26	11	too	too	ADV
asir-5424	26	12	many	many	ADJ
asir-5424	26	13	approximates	approximate	NOUN
asir-5424	26	14	and	and	CCONJ
asir-5424	26	15	assumptions	assumption	NOUN
asir-5424	26	16	to	to	PART
asir-5424	26	17	prove	prove	VERB
asir-5424	26	18	that	that	SCONJ
asir-5424	26	19	the	the	DET
asir-5424	26	20	ratio	ratio	NOUN
asir-5424	26	21	of	of	ADP
asir-5424	26	22	isotope	isotope	NOUN
asir-5424	26	23	correlation	correlation	NOUN
asir-5424	26	24	coefficients	coefficient	NOUN
asir-5424	26	25	f*/f	f*/f	NUM
asir-5424	26	26	can	can	AUX
asir-5424	26	27	be	be	AUX
asir-5424	26	28	neglected	neglect	VERB
asir-5424	26	29	,	,	PUNCT
asir-5424	26	30	so	so	CCONJ
asir-5424	26	31	this	this	DET
asir-5424	26	32	study	study	NOUN
asir-5424	26	33	will	will	AUX
asir-5424	26	34	search	search	VERB
asir-5424	26	35	for	for	ADP
asir-5424	26	36	the	the	DET
asir-5424	26	37	most	most	ADV
asir-5424	26	38	essential	essential	ADJ
asir-5424	26	39	relation	relation	NOUN
asir-5424	26	40	of	of	ADP
asir-5424	26	41	correlation	correlation	NOUN
asir-5424	26	42	coefficients	coefficient	NOUN
asir-5424	26	43	from	from	ADP
asir-5424	26	44	scratch	scratch	NOUN
asir-5424	26	45	to	to	PART
asir-5424	26	46	explain	explain	VERB
asir-5424	26	47	this	this	DET
asir-5424	26	48	phenomenon	phenomenon	NOUN
asir-5424	26	49	.	.	PUNCT
asir-5424	27	1	this	this	DET
asir-5424	27	2	work	work	NOUN
asir-5424	27	3	saves	save	VERB
asir-5424	27	4	a	a	DET
asir-5424	27	5	great	great	ADJ
asir-5424	27	6	deal	deal	NOUN
asir-5424	27	7	of	of	ADP
asir-5424	27	8	trouble	trouble	NOUN
asir-5424	27	9	in	in	ADP
asir-5424	27	10	studying	study	VERB
asir-5424	27	11	the	the	DET
asir-5424	27	12	isotope	isotope	NOUN
asir-5424	27	13	diffusion	diffusion	NOUN
asir-5424	27	14	effect	effect	NOUN
asir-5424	27	15	and	and	CCONJ
asir-5424	27	16	lays	lay	VERB
asir-5424	27	17	the	the	DET
asir-5424	27	18	foundation	foundation	NOUN
asir-5424	27	19	for	for	ADP
asir-5424	27	20	the	the	DET
asir-5424	27	21	subsequent	subsequent	ADJ
asir-5424	27	22	work	work	NOUN
asir-5424	27	23	.	.	PUNCT
asir-5424	28	1	2	2	X
asir-5424	28	2	.	.	X
asir-5424	28	3	quantitative	quantitative	ADJ
asir-5424	28	4	interpretation	interpretation	NOUN
asir-5424	28	5	in	in	ADP
asir-5424	28	6	crystals	crystal	NOUN
asir-5424	28	7	,	,	PUNCT
asir-5424	28	8	diffusion	diffusion	NOUN
asir-5424	28	9	is	be	AUX
asir-5424	28	10	the	the	DET
asir-5424	28	11	transformation	transformation	NOUN
asir-5424	28	12	process	process	NOUN
asir-5424	28	13	of	of	ADP
asir-5424	28	14	atoms	atom	NOUN
asir-5424	28	15	or	or	CCONJ
asir-5424	28	16	defects	defect	NOUN
asir-5424	28	17	(	(	PUNCT
asir-5424	28	18	interstitial	interstitial	ADJ
asir-5424	28	19	or	or	CCONJ
asir-5424	28	20	vacancy	vacancy	NOUN
asir-5424	28	21	)	)	PUNCT
asir-5424	28	22	by	by	ADP
asir-5424	28	23	thermal	thermal	ADJ
asir-5424	28	24	motion	motion	NOUN
asir-5424	28	25	from	from	ADP
asir-5424	28	26	one	one	NUM
asir-5424	28	27	equilibrium	equilibrium	NOUN
asir-5424	28	28	position	position	NOUN
asir-5424	28	29	to	to	ADP
asir-5424	28	30	another	another	DET
asir-5424	28	31	one	one	NOUN
asir-5424	28	32	,	,	PUNCT
asir-5424	28	33	atom	atom	NOUN
asir-5424	28	34	in	in	ADP
asir-5424	28	35	the	the	DET
asir-5424	28	36	micro	micro	ADJ
asir-5424	28	37	world	world	NOUN
asir-5424	28	38	can	can	AUX
asir-5424	28	39	achieve	achieve	VERB
asir-5424	28	40	macroscopic	macroscopic	ADJ
asir-5424	28	41	atomic	atomic	ADJ
asir-5424	28	42	migration	migration	NOUN
asir-5424	28	43	through	through	ADP
asir-5424	28	44	step	step	NOUN
asir-5424	28	45	by	by	ADP
asir-5424	28	46	step	step	NOUN
asir-5424	28	47	successive	successive	ADJ
asir-5424	28	48	jumps	jump	NOUN
asir-5424	28	49	in	in	ADP
asir-5424	28	50	the	the	DET
asir-5424	28	51	lattice	lattice	NOUN
asir-5424	28	52	(	(	PUNCT
asir-5424	28	53	figure	figure	NOUN
asir-5424	28	54	1	1	NUM
asir-5424	28	55	)	)	PUNCT
asir-5424	28	56	.	.	PUNCT
asir-5424	29	1	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	PROPN
asir-5424	29	2	applied	apply	VERB
asir-5424	29	3	science	science	NOUN
asir-5424	29	4	and	and	CCONJ
asir-5424	29	5	innovative	innovative	ADJ
asir-5424	29	6	research	research	NOUN
asir-5424	29	7	vol	vol	NOUN
asir-5424	29	8	.	.	PROPN
asir-5424	30	1	6	6	NUM
asir-5424	30	2	,	,	PUNCT
asir-5424	30	3	no	no	INTJ
asir-5424	30	4	.	.	NOUN
asir-5424	30	5	4	4	NUM
asir-5424	30	6	,	,	PUNCT
asir-5424	30	7	2022	2022	NUM
asir-5424	30	8	126	126	NUM
asir-5424	30	9	published	publish	VERB
asir-5424	30	10	by	by	ADP
asir-5424	30	11	scholink	scholink	PROPN
asir-5424	30	12	inc	inc	PROPN
asir-5424	30	13	.	.	PROPN
asir-5424	30	14	figure	figure	PROPN
asir-5424	30	15	1	1	NUM
asir-5424	30	16	.	.	PUNCT
asir-5424	30	17	schematic	schematic	ADJ
asir-5424	30	18	diagram	diagram	NOUN
asir-5424	30	19	of	of	ADP
asir-5424	30	20	the	the	DET
asir-5424	30	21	net	net	ADJ
asir-5424	30	22	displacement	displacement	NOUN
asir-5424	30	23	of	of	ADP
asir-5424	30	24	the	the	DET
asir-5424	30	25	diffusing	diffuse	VERB
asir-5424	30	26	particle	particle	NOUN
asir-5424	30	27	after	after	SCONJ
asir-5424	30	28	n	n	PRON
asir-5424	30	29	disorderly	disorderly	ADV
asir-5424	30	30	jumps	jump	VERB
asir-5424	30	31	in	in	ADP
asir-5424	30	32	time	time	NOUN
asir-5424	30	33	t	t	PROPN
asir-5424	30	34	based	base	VERB
asir-5424	30	35	on	on	ADP
asir-5424	30	36	the	the	DET
asir-5424	30	37	random	random	ADJ
asir-5424	30	38	walk	walk	NOUN
asir-5424	30	39	theory	theory	NOUN
asir-5424	30	40	and	and	CCONJ
asir-5424	30	41	the	the	DET
asir-5424	30	42	impurity	impurity	NOUN
asir-5424	30	43	atom	atom	NOUN
asir-5424	30	44	diffusion	diffusion	NOUN
asir-5424	30	45	with	with	ADP
asir-5424	30	46	single	single	ADJ
asir-5424	30	47	vacancy	vacancy	NOUN
asir-5424	30	48	mechanism	mechanism	NOUN
asir-5424	30	49	,	,	PUNCT
asir-5424	30	50	the	the	DET
asir-5424	30	51	microscopic	microscopic	ADJ
asir-5424	30	52	expression	expression	NOUN
asir-5424	30	53	of	of	ADP
asir-5424	30	54	d	d	PROPN
asir-5424	30	55	(	(	PUNCT
asir-5424	30	56	mehrer	mehrer	NOUN
asir-5424	30	57	,	,	PUNCT
asir-5424	30	58	2007	2007	NUM
asir-5424	30	59	)	)	PUNCT
asir-5424	30	60	is	be	AUX
asir-5424	30	61	:	:	PUNCT
asir-5424	30	62	=	=	SYM
asir-5424	30	63	𝑎2𝛤𝑓	𝑎2𝛤𝑓	X
asir-5424	30	64	(	(	PUNCT
asir-5424	30	65	3	3	X
asir-5424	30	66	)	)	PUNCT
asir-5424	30	67	𝑎	𝑎	NOUN
asir-5424	30	68	is	be	AUX
asir-5424	30	69	lattice	lattice	NOUN
asir-5424	30	70	parameters	parameter	NOUN
asir-5424	30	71	,	,	PUNCT
asir-5424	30	72	𝑓	𝑓	PRON
asir-5424	30	73	is	be	AUX
asir-5424	30	74	correlation	correlation	NOUN
asir-5424	30	75	coefficient	coefficient	NOUN
asir-5424	30	76	,	,	PUNCT
asir-5424	30	77	indicates	indicate	VERB
asir-5424	30	78	the	the	DET
asir-5424	30	79	degree	degree	NOUN
asir-5424	30	80	of	of	ADP
asir-5424	30	81	atomic	atomic	ADJ
asir-5424	30	82	diffusion	diffusion	NOUN
asir-5424	30	83	process	process	NOUN
asir-5424	30	84	deviation	deviation	NOUN
asir-5424	30	85	from	from	ADP
asir-5424	30	86	pure	pure	ADJ
asir-5424	30	87	random	random	ADJ
asir-5424	30	88	walk	walk	NOUN
asir-5424	30	89	.	.	PUNCT
asir-5424	31	1	in	in	ADP
asir-5424	31	2	interstitial	interstitial	ADJ
asir-5424	31	3	diffusion	diffusion	NOUN
asir-5424	31	4	mechanism	mechanism	NOUN
asir-5424	31	5	,	,	PUNCT
asir-5424	31	6	there	there	PRON
asir-5424	31	7	is	be	VERB
asir-5424	31	8	no	no	DET
asir-5424	31	9	correlation	correlation	NOUN
asir-5424	31	10	between	between	ADP
asir-5424	31	11	successive	successive	ADJ
asir-5424	31	12	jumps	jump	NOUN
asir-5424	31	13	,	,	PUNCT
asir-5424	31	14	f	f	PROPN
asir-5424	31	15	=	=	SYM
asir-5424	31	16	1	1	NUM
asir-5424	31	17	;	;	PUNCT
asir-5424	31	18	for	for	ADP
asir-5424	31	19	vacancy	vacancy	NOUN
asir-5424	31	20	diffusion	diffusion	NOUN
asir-5424	31	21	mechanism	mechanism	NOUN
asir-5424	31	22	,	,	PUNCT
asir-5424	31	23	there	there	PRON
asir-5424	31	24	is	be	VERB
asir-5424	31	25	usually	usually	ADV
asir-5424	31	26	a	a	DET
asir-5424	31	27	correlation	correlation	NOUN
asir-5424	31	28	between	between	ADP
asir-5424	31	29	them	they	PRON
asir-5424	31	30	,	,	PUNCT
asir-5424	31	31	f	f	PROPN
asir-5424	31	32	<	<	X
asir-5424	31	33	1	1	NUM
asir-5424	31	34	(	(	PUNCT
asir-5424	31	35	mehrer	mehrer	NOUN
asir-5424	31	36	,	,	PUNCT
asir-5424	31	37	2007	2007	NUM
asir-5424	31	38	)	)	PUNCT
asir-5424	31	39	.	.	PUNCT
asir-5424	32	1	this	this	DET
asir-5424	32	2	study	study	NOUN
asir-5424	32	3	only	only	ADV
asir-5424	32	4	focuses	focus	VERB
asir-5424	32	5	on	on	ADP
asir-5424	32	6	vacancy	vacancy	NOUN
asir-5424	32	7	diffusion	diffusion	NOUN
asir-5424	32	8	.	.	PUNCT
asir-5424	33	1	γ	γ	PROPN
asir-5424	33	2	is	be	AUX
asir-5424	33	3	the	the	DET
asir-5424	33	4	jump	jump	NOUN
asir-5424	33	5	rate	rate	NOUN
asir-5424	33	6	(	(	PUNCT
asir-5424	33	7	the	the	DET
asir-5424	33	8	impurity	impurity	NOUN
asir-5424	33	9	atom	atom	NOUN
asir-5424	33	10	jump	jump	NOUN
asir-5424	33	11	to	to	ADP
asir-5424	33	12	the	the	DET
asir-5424	33	13	adjacent	adjacent	ADJ
asir-5424	33	14	vacancy	vacancy	NOUN
asir-5424	33	15	)	)	PUNCT
asir-5424	33	16	,	,	PUNCT
asir-5424	33	17	represents	represent	VERB
asir-5424	33	18	the	the	DET
asir-5424	33	19	number	number	NOUN
asir-5424	33	20	of	of	ADP
asir-5424	33	21	atom	atom	NOUN
asir-5424	33	22	jumps	jump	NOUN
asir-5424	33	23	(	(	PUNCT
asir-5424	33	24	n	n	CCONJ
asir-5424	33	25	)	)	PUNCT
asir-5424	33	26	per	per	ADP
asir-5424	33	27	unit	unit	NOUN
asir-5424	33	28	time	time	NOUN
asir-5424	33	29	(	(	PUNCT
asir-5424	33	30	t	t	NOUN
asir-5424	33	31	)	)	PUNCT
asir-5424	33	32	.	.	PUNCT
asir-5424	34	1	for	for	ADP
asir-5424	34	2	different	different	ADJ
asir-5424	34	3	isotopes	isotope	NOUN
asir-5424	34	4	,	,	PUNCT
asir-5424	34	5	a	a	PRON
asir-5424	34	6	are	be	AUX
asir-5424	34	7	the	the	DET
asir-5424	34	8	same	same	ADJ
asir-5424	34	9	,	,	PUNCT
asir-5424	34	10	so	so	ADV
asir-5424	34	11	𝑓	𝑓	ADV
asir-5424	34	12	and	and	CCONJ
asir-5424	34	13	γ	γ	NOUN
asir-5424	34	14	are	be	AUX
asir-5424	34	15	the	the	DET
asir-5424	34	16	main	main	ADJ
asir-5424	34	17	influencing	influence	VERB
asir-5424	34	18	factors	factor	NOUN
asir-5424	34	19	of	of	ADP
asir-5424	34	20	isotope	isotope	NOUN
asir-5424	34	21	diffusion	diffusion	NOUN
asir-5424	34	22	coefficient	coefficient	NOUN
asir-5424	34	23	ratio	ratio	NOUN
asir-5424	34	24	.	.	PUNCT
asir-5424	35	1	the	the	DET
asir-5424	35	2	isotope	isotope	NOUN
asir-5424	35	3	diffusion	diffusion	NOUN
asir-5424	35	4	coefficient	coefficient	NOUN
asir-5424	35	5	ratio	ratio	NOUN
asir-5424	35	6	can	can	AUX
asir-5424	35	7	be	be	AUX
asir-5424	35	8	expressed	express	VERB
asir-5424	35	9	as	as	ADP
asir-5424	35	10	,	,	PUNCT
asir-5424	35	11	𝐷∗	𝐷∗	PROPN
asir-5424	35	12	𝐷	𝐷	PROPN
asir-5424	35	13	=	=	PUNCT
asir-5424	35	14	γ∗	γ∗	PROPN
asir-5424	35	15	γ	γ	PROPN
asir-5424	35	16	f∗	f∗	PROPN
asir-5424	35	17	f	f	X
asir-5424	35	18	(	(	PUNCT
asir-5424	35	19	4	4	X
asir-5424	35	20	)	)	PUNCT
asir-5424	35	21	previous	previous	ADJ
asir-5424	35	22	study	study	NOUN
asir-5424	35	23	(	(	PUNCT
asir-5424	35	24	van	van	PROPN
asir-5424	35	25	orman	orman	PROPN
asir-5424	35	26	&	&	CCONJ
asir-5424	35	27	krawczynski	krawczynski	PROPN
asir-5424	35	28	,	,	PUNCT
asir-5424	35	29	2015	2015	NUM
asir-5424	35	30	)	)	PUNCT
asir-5424	35	31	qualitatively	qualitatively	ADV
asir-5424	35	32	believed	believe	VERB
asir-5424	35	33	that	that	SCONJ
asir-5424	35	34	the	the	DET
asir-5424	35	35	effect	effect	NOUN
asir-5424	35	36	of	of	ADP
asir-5424	35	37	f	f	PROPN
asir-5424	35	38	for	for	ADP
asir-5424	35	39	two	two	NUM
asir-5424	35	40	isotopes	isotope	NOUN
asir-5424	35	41	on	on	ADP
asir-5424	35	42	isotope	isotope	NOUN
asir-5424	35	43	effect	effect	NOUN
asir-5424	35	44	was	be	AUX
asir-5424	35	45	negligible	negligible	ADJ
asir-5424	35	46	(	(	PUNCT
asir-5424	35	47	except	except	SCONJ
asir-5424	35	48	h	h	NOUN
asir-5424	35	49	,	,	PUNCT
asir-5424	35	50	he	he	PRON
asir-5424	35	51	)	)	PUNCT
asir-5424	35	52	.	.	PUNCT
asir-5424	36	1	however	however	ADV
asir-5424	36	2	,	,	PUNCT
asir-5424	36	3	there	there	PRON
asir-5424	36	4	is	be	VERB
asir-5424	36	5	no	no	DET
asir-5424	36	6	quantitative	quantitative	ADJ
asir-5424	36	7	explanation	explanation	NOUN
asir-5424	36	8	,	,	PUNCT
asir-5424	36	9	and	and	CCONJ
asir-5424	36	10	in	in	ADP
asir-5424	36	11	the	the	DET
asir-5424	36	12	following	following	NOUN
asir-5424	36	13	we	we	PRON
asir-5424	36	14	will	will	AUX
asir-5424	36	15	start	start	VERB
asir-5424	36	16	from	from	ADP
asir-5424	36	17	the	the	DET
asir-5424	36	18	initial	initial	ADJ
asir-5424	36	19	derivation	derivation	NOUN
asir-5424	36	20	of	of	ADP
asir-5424	36	21	the	the	DET
asir-5424	36	22	diffusion	diffusion	NOUN
asir-5424	36	23	coefficient	coefficient	NOUN
asir-5424	36	24	and	and	CCONJ
asir-5424	36	25	give	give	VERB
asir-5424	36	26	a	a	DET
asir-5424	36	27	specific	specific	ADJ
asir-5424	36	28	expression	expression	NOUN
asir-5424	36	29	for	for	ADP
asir-5424	36	30	f	f	PROPN
asir-5424	36	31	in	in	ADP
asir-5424	36	32	an	an	DET
asir-5424	36	33	attempt	attempt	NOUN
asir-5424	36	34	to	to	PART
asir-5424	36	35	give	give	VERB
asir-5424	36	36	quantitatively	quantitatively	ADV
asir-5424	36	37	its	its	PRON
asir-5424	36	38	effect	effect	NOUN
asir-5424	36	39	on	on	ADP
asir-5424	36	40	the	the	DET
asir-5424	36	41	isotope	isotope	NOUN
asir-5424	36	42	effect	effect	NOUN
asir-5424	36	43	.	.	PUNCT
asir-5424	37	1	einstein	einstein	PROPN
asir-5424	37	2	(	(	PUNCT
asir-5424	37	3	1906	1906	NUM
asir-5424	37	4	)	)	PUNCT
asir-5424	37	5	and	and	CCONJ
asir-5424	37	6	smoluchowski	smoluchowski	NOUN
asir-5424	37	7	(	(	PUNCT
asir-5424	37	8	1906	1906	NUM
asir-5424	37	9	)	)	PUNCT
asir-5424	37	10	almost	almost	ADV
asir-5424	37	11	simultaneously	simultaneously	ADV
asir-5424	37	12	proposed	propose	VERB
asir-5424	37	13	that	that	SCONJ
asir-5424	37	14	d	d	NOUN
asir-5424	37	15	is	be	AUX
asir-5424	37	16	directly	directly	ADV
asir-5424	37	17	proportional	proportional	ADJ
asir-5424	37	18	to	to	ADP
asir-5424	37	19	the	the	DET
asir-5424	37	20	mean	mean	ADJ
asir-5424	37	21	square	square	ADJ
asir-5424	37	22	displacement	displacement	NOUN
asir-5424	37	23	(	(	PUNCT
asir-5424	37	24	𝑹	𝑹	PROPN
asir-5424	37	25	2̅̅	2̅̅	NUM
asir-5424	37	26	̅̅	̅̅	NOUN
asir-5424	37	27	)	)	PUNCT
asir-5424	37	28	of	of	ADP
asir-5424	37	29	the	the	DET
asir-5424	37	30	number	number	NOUN
asir-5424	37	31	of	of	ADP
asir-5424	37	32	atom	atom	NOUN
asir-5424	37	33	jumps	jump	NOUN
asir-5424	37	34	(	(	PUNCT
asir-5424	37	35	n	n	CCONJ
asir-5424	37	36	)	)	PUNCT
asir-5424	37	37	in	in	ADP
asir-5424	37	38	a	a	DET
asir-5424	37	39	cubic	cubic	ADJ
asir-5424	37	40	lattice	lattice	NOUN
asir-5424	37	41	(	(	PUNCT
asir-5424	37	42	figure	figure	NOUN
asir-5424	37	43	1	1	NUM
asir-5424	37	44	)	)	PUNCT
asir-5424	37	45	,	,	PUNCT
asir-5424	37	46	and	and	CCONJ
asir-5424	37	47	inversely	inversely	ADV
asir-5424	37	48	proportional	proportional	ADJ
asir-5424	37	49	to	to	ADP
asir-5424	37	50	the	the	DET
asir-5424	37	51	diffusion	diffusion	NOUN
asir-5424	37	52	time	time	NOUN
asir-5424	37	53	(	(	PUNCT
asir-5424	37	54	t	t	NOUN
asir-5424	37	55	)	)	PUNCT
asir-5424	37	56	.	.	PUNCT
asir-5424	38	1	=	=	PUNCT
asir-5424	38	2	𝛼	𝛼	X
asir-5424	38	3	𝑹𝑛	𝑹𝑛	PROPN
asir-5424	38	4	2̅̅	2̅̅	NUM
asir-5424	38	5	̅̅	̅̅	NOUN
asir-5424	38	6	(	(	PUNCT
asir-5424	38	7	5	5	X
asir-5424	38	8	)	)	PUNCT
asir-5424	38	9	α	α	NOUN
asir-5424	38	10	is	be	AUX
asir-5424	38	11	geometric	geometric	ADJ
asir-5424	38	12	correction	correction	NOUN
asir-5424	38	13	factor	factor	NOUN
asir-5424	38	14	.	.	PUNCT
asir-5424	39	1	in	in	ADP
asir-5424	39	2	random	random	ADJ
asir-5424	39	3	walk	walk	NOUN
asir-5424	39	4	theory	theory	NOUN
asir-5424	39	5	(	(	PUNCT
asir-5424	39	6	mehrer	mehrer	NOUN
asir-5424	39	7	,	,	PUNCT
asir-5424	39	8	2007	2007	NUM
asir-5424	39	9	)	)	PUNCT
asir-5424	39	10	,	,	PUNCT
asir-5424	39	11	𝑹	𝑹	PROPN
asir-5424	39	12	2̅̅	2̅̅	NUM
asir-5424	39	13	̅̅	̅̅	NOUN
asir-5424	39	14	can	can	AUX
asir-5424	39	15	be	be	AUX
asir-5424	39	16	expressed	express	VERB
asir-5424	39	17	as	as	ADP
asir-5424	39	18	,	,	PUNCT
asir-5424	39	19	𝑹	𝑹	NOUN
asir-5424	39	20	2̅̅	2̅̅	NUM
asir-5424	39	21	̅̅	̅̅	NOUN
asir-5424	39	22	=	=	SYM
asir-5424	39	23	𝑛𝒓2	𝑛𝒓2	NOUN
asir-5424	39	24	1	1	NUM
asir-5424	39	25	+	+	CCONJ
asir-5424	39	26	2	2	NUM
asir-5424	39	27	∑	∑	DET
asir-5424	39	28	∑	∑	DET
asir-5424	39	29	𝑐𝑜𝑠𝜃𝑖,𝑖+𝑗	𝑐𝑜𝑠𝜃𝑖,𝑖+𝑗	NOUN
asir-5424	39	30	−𝑖	−𝑖	ADJ
asir-5424	39	31	𝑗=1	𝑗=1	PART
asir-5424	39	32	−1	−1	NOUN
asir-5424	39	33	𝑖=1	𝑖=1	PROPN
asir-5424	39	34	̅̅	̅̅	PROPN
asir-5424	39	35	̅̅	̅̅	PROPN
asir-5424	39	36	̅̅	̅̅	PROPN
asir-5424	39	37	̅̅	̅̅	PROPN
asir-5424	39	38	̅̅	̅̅	PROPN
asir-5424	39	39	̅̅	̅̅	PROPN
asir-5424	39	40	̅̅	̅̅	PROPN
asir-5424	39	41	̅̅	̅̅	PROPN
asir-5424	39	42	̅̅	̅̅	PROPN
asir-5424	39	43	̅̅	̅̅	PROPN
asir-5424	39	44	̅̅	̅̅	PROPN
asir-5424	39	45	̅̅	̅̅	PROPN
asir-5424	39	46	(	(	PUNCT
asir-5424	39	47	6	6	NUM
asir-5424	39	48	)	)	PUNCT
asir-5424	39	49	r	r	NOUN
asir-5424	39	50	is	be	AUX
asir-5424	39	51	the	the	DET
asir-5424	39	52	distance	distance	NOUN
asir-5424	39	53	of	of	ADP
asir-5424	39	54	each	each	DET
asir-5424	39	55	jump	jump	NOUN
asir-5424	39	56	,	,	PUNCT
asir-5424	39	57	and	and	CCONJ
asir-5424	39	58	𝜃𝑖,𝑖+𝑗	𝜃𝑖,𝑖+𝑗	NOUN
asir-5424	39	59	is	be	AUX
asir-5424	39	60	the	the	DET
asir-5424	39	61	angle	angle	NOUN
asir-5424	39	62	between	between	ADP
asir-5424	39	63	two	two	NUM
asir-5424	39	64	consecutive	consecutive	ADJ
asir-5424	39	65	jumps	jump	NOUN
asir-5424	39	66	(	(	PUNCT
asir-5424	39	67	fig.1	fig.1	PROPN
asir-5424	39	68	)	)	PUNCT
asir-5424	39	69	.	.	PUNCT
asir-5424	40	1	therefore	therefore	ADV
asir-5424	40	2	,	,	PUNCT
asir-5424	40	3	d	d	NOUN
asir-5424	40	4	can	can	AUX
asir-5424	40	5	be	be	AUX
asir-5424	40	6	expressed	express	VERB
asir-5424	40	7	as	as	ADP
asir-5424	40	8	,	,	PUNCT
asir-5424	40	9	=	=	SYM
asir-5424	40	10	𝛼𝒓2γ	𝛼𝒓2γ	NUM
asir-5424	40	11	1	1	NUM
asir-5424	40	12	+	+	CCONJ
asir-5424	40	13	2	2	NUM
asir-5424	40	14	∑	∑	DET
asir-5424	40	15	∑	∑	DET
asir-5424	40	16	𝑐𝑜𝑠𝜃𝑖,𝑖+𝑗	𝑐𝑜𝑠𝜃𝑖,𝑖+𝑗	NOUN
asir-5424	40	17	−𝑖	−𝑖	ADJ
asir-5424	40	18	𝑗=1	𝑗=1	PART
asir-5424	40	19	−1	−1	NOUN
asir-5424	40	20	𝑖=1	𝑖=1	PROPN
asir-5424	40	21	̅̅	̅̅	PROPN
asir-5424	40	22	̅̅	̅̅	PROPN
asir-5424	40	23	̅̅	̅̅	PROPN
asir-5424	40	24	̅̅	̅̅	PROPN
asir-5424	40	25	̅̅	̅̅	PROPN
asir-5424	40	26	̅̅	̅̅	PROPN
asir-5424	40	27	̅̅	̅̅	PROPN
asir-5424	40	28	̅̅	̅̅	PROPN
asir-5424	40	29	̅̅	̅̅	PROPN
asir-5424	40	30	̅̅	̅̅	PROPN
asir-5424	40	31	̅̅	̅̅	PROPN
asir-5424	40	32	̅̅	̅̅	PROPN
asir-5424	40	33	(	(	PUNCT
asir-5424	40	34	7	7	NUM
asir-5424	40	35	)	)	PUNCT
asir-5424	40	36	when	when	SCONJ
asir-5424	40	37	completely	completely	ADV
asir-5424	40	38	random	random	ADJ
asir-5424	40	39	,	,	PUNCT
asir-5424	40	40	∑	∑	ADP
asir-5424	40	41	∑	∑	ADP
asir-5424	40	42	𝑐𝑜𝑠𝜃𝑖,𝑖+𝑗	𝑐𝑜𝑠𝜃𝑖,𝑖+𝑗	DET
asir-5424	40	43	−𝑖	−𝑖	ADJ
asir-5424	40	44	𝑗=1	𝑗=1	PART
asir-5424	40	45	−1	−1	NOUN
asir-5424	40	46	𝑖=1	𝑖=1	PROPN
asir-5424	40	47	̅̅	̅̅	PROPN
asir-5424	40	48	̅̅	̅̅	PROPN
asir-5424	40	49	̅̅	̅̅	PROPN
asir-5424	40	50	̅̅	̅̅	PROPN
asir-5424	40	51	̅̅	̅̅	PROPN
asir-5424	40	52	̅̅	̅̅	PROPN
asir-5424	40	53	̅̅	̅̅	PROPN
asir-5424	40	54	̅̅	̅̅	PROPN
asir-5424	40	55	̅̅	̅̅	PROPN
asir-5424	40	56	̅̅	̅̅	PROPN
asir-5424	40	57	̅̅	̅̅	PROPN
asir-5424	40	58	̅̅	̅̅	PROPN
asir-5424	40	59	=	=	SYM
asir-5424	40	60	0	0	PROPN
asir-5424	40	61	,	,	PUNCT
asir-5424	40	62	each	each	DET
asir-5424	40	63	jump	jump	NOUN
asir-5424	40	64	of	of	ADP
asir-5424	40	65	an	an	DET
asir-5424	40	66	atom	atom	NOUN
asir-5424	40	67	in	in	ADP
asir-5424	40	68	a	a	DET
asir-5424	40	69	lattice	lattice	NOUN
asir-5424	40	70	is	be	AUX
asir-5424	40	71	independent	independent	ADJ
asir-5424	40	72	of	of	ADP
asir-5424	40	73	the	the	DET
asir-5424	40	74	previous	previous	ADJ
asir-5424	40	75	step	step	NOUN
asir-5424	40	76	,	,	PUNCT
asir-5424	40	77	and	and	CCONJ
asir-5424	41	1	=	=	PUNCT
asir-5424	41	2	𝑎2γ	𝑎2γ	NOUN
asir-5424	41	3	(	(	PUNCT
asir-5424	41	4	8)	8)	NUM
asir-5424	41	5	this	this	PRON
asir-5424	41	6	is	be	AUX
asir-5424	41	7	interstitial	interstitial	ADJ
asir-5424	41	8	diffusion	diffusion	NOUN
asir-5424	41	9	mechanism	mechanism	NOUN
asir-5424	41	10	.	.	PUNCT
asir-5424	42	1	however	however	ADV
asir-5424	42	2	,	,	PUNCT
asir-5424	42	3	successive	successive	ADJ
asir-5424	42	4	jumps	jump	NOUN
asir-5424	42	5	of	of	ADP
asir-5424	42	6	vacancy	vacancy	NOUN
asir-5424	42	7	mechanism	mechanism	NOUN
asir-5424	42	8	are	be	AUX
asir-5424	42	9	related	relate	VERB
asir-5424	42	10	,	,	PUNCT
asir-5424	42	11	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-5424	42	12	applied	apply	VERB
asir-5424	42	13	science	science	NOUN
asir-5424	42	14	and	and	CCONJ
asir-5424	42	15	innovative	innovative	ADJ
asir-5424	42	16	research	research	NOUN
asir-5424	42	17	vol	vol	NOUN
asir-5424	42	18	.	.	PROPN
asir-5424	43	1	6	6	NUM
asir-5424	43	2	,	,	PUNCT
asir-5424	43	3	no	no	INTJ
asir-5424	43	4	.	.	NOUN
asir-5424	43	5	4	4	NUM
asir-5424	43	6	,	,	PUNCT
asir-5424	43	7	2022	2022	NUM
asir-5424	43	8	127	127	NUM
asir-5424	43	9	published	publish	VERB
asir-5424	43	10	by	by	ADP
asir-5424	43	11	scholink	scholink	PROPN
asir-5424	43	12	inc	inc	PROPN
asir-5424	43	13	.	.	PROPN
asir-5424	43	14	means	mean	VERB
asir-5424	43	15	∑	∑	PROPN
asir-5424	43	16	∑	∑	PROPN
asir-5424	43	17	𝑐𝑜𝑠𝜃𝑖,𝑖+𝑗	𝑐𝑜𝑠𝜃𝑖,𝑖+𝑗	PRON
asir-5424	43	18	−𝑖	−𝑖	ADJ
asir-5424	43	19	𝑗=1	𝑗=1	PART
asir-5424	43	20	−1	−1	NOUN
asir-5424	43	21	𝑖=1	𝑖=1	PROPN
asir-5424	43	22	̅̅	̅̅	PROPN
asir-5424	43	23	̅̅	̅̅	PROPN
asir-5424	43	24	̅̅	̅̅	PROPN
asir-5424	43	25	̅̅	̅̅	PROPN
asir-5424	43	26	̅̅	̅̅	PROPN
asir-5424	43	27	̅̅	̅̅	PROPN
asir-5424	43	28	̅̅	̅̅	PROPN
asir-5424	43	29	̅̅	̅̅	PROPN
asir-5424	43	30	̅̅	̅̅	PROPN
asir-5424	43	31	̅̅	̅̅	PROPN
asir-5424	43	32	̅̅	̅̅	PROPN
asir-5424	43	33	̅̅	̅̅	PROPN
asir-5424	43	34	≠	≠	PROPN
asir-5424	43	35	0	0	NUM
asir-5424	43	36	,	,	PUNCT
asir-5424	43	37	f	f	PROPN
asir-5424	43	38	can	can	AUX
asir-5424	43	39	be	be	AUX
asir-5424	43	40	expressed	express	VERB
asir-5424	43	41	as	as	ADP
asir-5424	43	42	,	,	PUNCT
asir-5424	43	43	𝑓	𝑓	NOUN
asir-5424	43	44	=	=	SYM
asir-5424	43	45	1	1	NUM
asir-5424	43	46	+	+	NUM
asir-5424	43	47	2	2	NUM
asir-5424	43	48	∑	∑	DET
asir-5424	43	49	∑	∑	DET
asir-5424	43	50	𝑐𝑜𝑠𝜃𝑖,𝑖+𝑗	𝑐𝑜𝑠𝜃𝑖,𝑖+𝑗	NOUN
asir-5424	43	51	−𝑖	−𝑖	ADJ
asir-5424	43	52	𝑗=1	𝑗=1	PART
asir-5424	43	53	−1	−1	NOUN
asir-5424	43	54	𝑖=1	𝑖=1	PROPN
asir-5424	43	55	̅̅	̅̅	PROPN
asir-5424	43	56	̅̅	̅̅	PROPN
asir-5424	43	57	̅̅	̅̅	PROPN
asir-5424	43	58	̅̅	̅̅	PROPN
asir-5424	43	59	̅̅	̅̅	PROPN
asir-5424	43	60	̅̅	̅̅	PROPN
asir-5424	43	61	̅̅	̅̅	PROPN
asir-5424	43	62	̅̅	̅̅	PROPN
asir-5424	43	63	̅̅	̅̅	PROPN
asir-5424	43	64	̅̅	̅̅	PROPN
asir-5424	43	65	̅̅	̅̅	PROPN
asir-5424	43	66	̅̅	̅̅	PROPN
asir-5424	43	67	(	(	PUNCT
asir-5424	43	68	9	9	X
asir-5424	43	69	)	)	PUNCT
asir-5424	43	70	this	this	PRON
asir-5424	43	71	is	be	AUX
asir-5424	43	72	consistent	consistent	ADJ
asir-5424	43	73	with	with	ADP
asir-5424	43	74	the	the	DET
asir-5424	43	75	result	result	NOUN
asir-5424	43	76	of	of	ADP
asir-5424	43	77	bardeen	bardeen	PROPN
asir-5424	43	78	and	and	CCONJ
asir-5424	43	79	herring	herring	NOUN
asir-5424	43	80	(	(	PUNCT
asir-5424	43	81	1952	1952	NUM
asir-5424	43	82	)	)	PUNCT
asir-5424	43	83	.	.	PUNCT
asir-5424	44	1	for	for	ADP
asir-5424	44	2	the	the	DET
asir-5424	44	3	vacancy	vacancy	NOUN
asir-5424	44	4	mechanism	mechanism	NOUN
asir-5424	44	5	,	,	PUNCT
asir-5424	44	6	when	when	SCONJ
asir-5424	44	7	vacancy	vacancy	NOUN
asir-5424	44	8	and	and	CCONJ
asir-5424	44	9	vacancy	vacancy	NOUN
asir-5424	44	10	are	be	AUX
asir-5424	44	11	independent	independent	ADJ
asir-5424	44	12	,	,	PUNCT
asir-5424	44	13	after	after	SCONJ
asir-5424	44	14	the	the	DET
asir-5424	44	15	impurity	impurity	NOUN
asir-5424	44	16	atom	atom	NOUN
asir-5424	44	17	jumps	jump	VERB
asir-5424	44	18	into	into	ADP
asir-5424	44	19	the	the	DET
asir-5424	44	20	adjacent	adjacent	ADJ
asir-5424	44	21	vacancy	vacancy	NOUN
asir-5424	44	22	(	(	PUNCT
asir-5424	44	23	figure	figure	NOUN
asir-5424	44	24	2a	2a	NUM
asir-5424	44	25	)	)	PUNCT
asir-5424	44	26	,	,	PUNCT
asir-5424	44	27	the	the	DET
asir-5424	44	28	next	next	ADJ
asir-5424	44	29	jump	jump	NOUN
asir-5424	44	30	tends	tend	VERB
asir-5424	44	31	to	to	PART
asir-5424	44	32	return	return	VERB
asir-5424	44	33	to	to	ADP
asir-5424	44	34	the	the	DET
asir-5424	44	35	original	original	ADJ
asir-5424	44	36	position	position	NOUN
asir-5424	44	37	,	,	PUNCT
asir-5424	44	38	which	which	PRON
asir-5424	44	39	means	mean	VERB
asir-5424	44	40	that	that	SCONJ
asir-5424	44	41	the	the	DET
asir-5424	44	42	θ	θ	PROPN
asir-5424	44	43	is	be	AUX
asir-5424	44	44	zero	zero	NUM
asir-5424	44	45	.	.	PUNCT
asir-5424	45	1	therefore	therefore	ADV
asir-5424	45	2	,	,	PUNCT
asir-5424	45	3	if	if	SCONJ
asir-5424	45	4	the	the	DET
asir-5424	45	5	impurity	impurity	NOUN
asir-5424	45	6	atom	atom	NOUN
asir-5424	45	7	wants	want	VERB
asir-5424	45	8	to	to	PART
asir-5424	45	9	move	move	VERB
asir-5424	45	10	forward	forward	ADV
asir-5424	45	11	it	it	PRON
asir-5424	45	12	must	must	AUX
asir-5424	45	13	depend	depend	VERB
asir-5424	45	14	on	on	ADP
asir-5424	45	15	the	the	DET
asir-5424	45	16	solvent	solvent	NOUN
asir-5424	45	17	atoms	atom	NOUN
asir-5424	45	18	exchange	exchange	NOUN
asir-5424	45	19	with	with	ADP
asir-5424	45	20	the	the	DET
asir-5424	45	21	vacancy	vacancy	NOUN
asir-5424	45	22	continuously	continuously	ADV
asir-5424	45	23	and	and	CCONJ
asir-5424	45	24	bring	bring	VERB
asir-5424	45	25	the	the	DET
asir-5424	45	26	vacancy	vacancy	NOUN
asir-5424	45	27	adjacent	adjacent	ADJ
asir-5424	45	28	to	to	ADP
asir-5424	45	29	the	the	DET
asir-5424	45	30	impurity	impurity	NOUN
asir-5424	45	31	atom	atom	NOUN
asir-5424	45	32	.	.	PUNCT
asir-5424	46	1	there	there	PRON
asir-5424	46	2	are	be	VERB
asir-5424	46	3	many	many	ADJ
asir-5424	46	4	ways	way	NOUN
asir-5424	46	5	to	to	PART
asir-5424	46	6	bring	bring	VERB
asir-5424	46	7	the	the	DET
asir-5424	46	8	vacancy	vacancy	NOUN
asir-5424	46	9	back	back	ADV
asir-5424	46	10	near	near	ADP
asir-5424	46	11	the	the	DET
asir-5424	46	12	impurity	impurity	NOUN
asir-5424	46	13	atom	atom	NOUN
asir-5424	46	14	again	again	ADV
asir-5424	46	15	,	,	PUNCT
asir-5424	46	16	and	and	CCONJ
asir-5424	46	17	only	only	ADV
asir-5424	46	18	one	one	NUM
asir-5424	46	19	(	(	PUNCT
asir-5424	46	20	a	a	DET
asir-5424	46	21	~	~	NOUN
asir-5424	46	22	f	f	X
asir-5424	46	23	)	)	PUNCT
asir-5424	46	24	of	of	ADP
asir-5424	46	25	them	they	PRON
asir-5424	46	26	is	be	AUX
asir-5424	46	27	shown	show	VERB
asir-5424	46	28	in	in	ADP
asir-5424	46	29	figure	figure	NOUN
asir-5424	46	30	2b	2b	NOUN
asir-5424	46	31	.	.	PUNCT
asir-5424	47	1	when	when	SCONJ
asir-5424	47	2	a	a	DET
asir-5424	47	3	vacancy	vacancy	NOUN
asir-5424	47	4	is	be	AUX
asir-5424	47	5	next	next	ADJ
asir-5424	47	6	to	to	ADP
asir-5424	47	7	the	the	DET
asir-5424	47	8	impurity	impurity	NOUN
asir-5424	47	9	atom	atom	NOUN
asir-5424	47	10	again	again	ADV
asir-5424	47	11	,	,	PUNCT
asir-5424	47	12	impurity	impurity	NOUN
asir-5424	47	13	can	can	AUX
asir-5424	47	14	make	make	VERB
asir-5424	47	15	a	a	DET
asir-5424	47	16	second	second	ADJ
asir-5424	47	17	jump	jump	NOUN
asir-5424	47	18	to	to	PART
asir-5424	47	19	form	form	VERB
asir-5424	47	20	a	a	DET
asir-5424	47	21	group	group	NOUN
asir-5424	47	22	of	of	ADP
asir-5424	47	23	continuous	continuous	ADJ
asir-5424	47	24	jumps	jump	NOUN
asir-5424	47	25	(	(	PUNCT
asir-5424	47	26	figure	figure	NOUN
asir-5424	47	27	2c	2c	NUM
asir-5424	47	28	,	,	PUNCT
asir-5424	47	29	2d	2d	NUM
asir-5424	47	30	)	)	PUNCT
asir-5424	47	31	.	.	PUNCT
asir-5424	48	1	figure	figure	NOUN
asir-5424	48	2	2	2	NUM
asir-5424	48	3	.	.	PUNCT
asir-5424	48	4	schematic	schematic	ADJ
asir-5424	48	5	diagram	diagram	NOUN
asir-5424	48	6	of	of	ADP
asir-5424	48	7	two	two	NUM
asir-5424	48	8	successive	successive	ADJ
asir-5424	48	9	jumps	jump	NOUN
asir-5424	48	10	of	of	ADP
asir-5424	48	11	an	an	DET
asir-5424	48	12	impurity	impurity	NOUN
asir-5424	48	13	atom	atom	NOUN
asir-5424	48	14	in	in	ADP
asir-5424	48	15	a	a	DET
asir-5424	48	16	crystal	crystal	NOUN
asir-5424	48	17	.	.	PUNCT
asir-5424	49	1	black	black	ADJ
asir-5424	49	2	spheres	sphere	NOUN
asir-5424	49	3	represent	represent	VERB
asir-5424	49	4	solvent	solvent	ADJ
asir-5424	49	5	atoms	atom	NOUN
asir-5424	49	6	,	,	PUNCT
asir-5424	49	7	red	red	ADJ
asir-5424	49	8	spheres	sphere	NOUN
asir-5424	49	9	represent	represent	VERB
asir-5424	49	10	impurity	impurity	NOUN
asir-5424	49	11	atom	atom	NOUN
asir-5424	49	12	,	,	PUNCT
asir-5424	49	13	and	and	CCONJ
asir-5424	49	14	hollow	hollow	ADJ
asir-5424	49	15	spheres	sphere	NOUN
asir-5424	49	16	represent	represent	VERB
asir-5424	49	17	vacancy	vacancy	NOUN
asir-5424	49	18	.	.	PUNCT
asir-5424	50	1	(	(	PUNCT
asir-5424	50	2	a	a	X
asir-5424	50	3	)	)	PUNCT
asir-5424	50	4	first	first	ADJ
asir-5424	50	5	exchange	exchange	NOUN
asir-5424	50	6	of	of	ADP
asir-5424	50	7	impurity	impurity	NOUN
asir-5424	50	8	atom	atom	NOUN
asir-5424	50	9	with	with	ADP
asir-5424	50	10	vacancy	vacancy	NOUN
asir-5424	50	11	.	.	PUNCT
asir-5424	51	1	(	(	PUNCT
asir-5424	51	2	b	b	X
asir-5424	51	3	)	)	PUNCT
asir-5424	51	4	a	a	PROPN
asir-5424	51	5	-	-	PUNCT
asir-5424	51	6	f	f	PROPN
asir-5424	51	7	is	be	AUX
asir-5424	51	8	a	a	DET
asir-5424	51	9	possibility	possibility	NOUN
asir-5424	51	10	of	of	ADP
asir-5424	51	11	continuous	continuous	ADJ
asir-5424	51	12	exchange	exchange	NOUN
asir-5424	51	13	of	of	ADP
asir-5424	51	14	vacancy	vacancy	NOUN
asir-5424	51	15	with	with	ADP
asir-5424	51	16	solvent	solvent	ADJ
asir-5424	51	17	atoms	atom	NOUN
asir-5424	51	18	.	.	PUNCT
asir-5424	52	1	(	(	PUNCT
asir-5424	52	2	c	c	X
asir-5424	52	3	)	)	PUNCT
asir-5424	52	4	second	second	ADJ
asir-5424	52	5	exchange	exchange	NOUN
asir-5424	52	6	of	of	ADP
asir-5424	52	7	impurity	impurity	NOUN
asir-5424	52	8	atom	atom	NOUN
asir-5424	52	9	with	with	ADP
asir-5424	52	10	vacancy	vacancy	NOUN
asir-5424	52	11	.	.	PUNCT
asir-5424	53	1	(	(	PUNCT
asir-5424	53	2	d	d	X
asir-5424	53	3	)	)	PUNCT
asir-5424	53	4	the	the	DET
asir-5424	53	5	angle	angle	NOUN
asir-5424	53	6	θ	θ	PROPN
asir-5424	53	7	between	between	ADP
asir-5424	53	8	two	two	NUM
asir-5424	53	9	consecutive	consecutive	ADJ
asir-5424	53	10	exchanges	exchange	NOUN
asir-5424	53	11	therefore	therefore	ADV
asir-5424	53	12	,	,	PUNCT
asir-5424	53	13	the	the	DET
asir-5424	53	14	θ	θ	PROPN
asir-5424	53	15	is	be	AUX
asir-5424	53	16	affected	affect	VERB
asir-5424	53	17	by	by	ADP
asir-5424	53	18	the	the	DET
asir-5424	53	19	exchange	exchange	NOUN
asir-5424	53	20	mode	mode	NOUN
asir-5424	53	21	between	between	ADP
asir-5424	53	22	the	the	DET
asir-5424	53	23	solvent	solvent	ADJ
asir-5424	53	24	atom	atom	NOUN
asir-5424	53	25	and	and	CCONJ
asir-5424	53	26	the	the	DET
asir-5424	53	27	vacancy	vacancy	NOUN
asir-5424	53	28	,	,	PUNCT
asir-5424	53	29	which	which	PRON
asir-5424	53	30	related	relate	VERB
asir-5424	53	31	to	to	ADP
asir-5424	53	32	the	the	DET
asir-5424	53	33	binding	bind	VERB
asir-5424	53	34	energy	energy	NOUN
asir-5424	53	35	between	between	ADP
asir-5424	53	36	them	they	PRON
asir-5424	53	37	,	,	PUNCT
asir-5424	53	38	which	which	PRON
asir-5424	53	39	further	far	ADV
asir-5424	53	40	affects	affect	VERB
asir-5424	53	41	the	the	DET
asir-5424	53	42	jump	jump	NOUN
asir-5424	53	43	direction	direction	NOUN
asir-5424	53	44	of	of	ADP
asir-5424	53	45	the	the	DET
asir-5424	53	46	vacancy	vacancy	NOUN
asir-5424	53	47	.	.	PUNCT
asir-5424	54	1	however	however	ADV
asir-5424	54	2	,	,	PUNCT
asir-5424	54	3	all	all	DET
asir-5424	54	4	the	the	DET
asir-5424	54	5	above	above	ADJ
asir-5424	54	6	are	be	AUX
asir-5424	54	7	independent	independent	ADJ
asir-5424	54	8	of	of	ADP
asir-5424	54	9	the	the	DET
asir-5424	54	10	mass	mass	NOUN
asir-5424	54	11	of	of	ADP
asir-5424	54	12	solute	solute	NOUN
asir-5424	54	13	.	.	PUNCT
asir-5424	55	1	so	so	ADV
asir-5424	55	2	we	we	PRON
asir-5424	55	3	can	can	AUX
asir-5424	55	4	avoid	avoid	VERB
asir-5424	55	5	the	the	DET
asir-5424	55	6	difficulty	difficulty	NOUN
asir-5424	55	7	of	of	ADP
asir-5424	55	8	calculating	calculate	VERB
asir-5424	55	9	the	the	DET
asir-5424	55	10	absolute	absolute	ADJ
asir-5424	55	11	value	value	NOUN
asir-5424	55	12	of	of	ADP
asir-5424	55	13	f	f	PROPN
asir-5424	55	14	in	in	ADP
asir-5424	55	15	study	study	NOUN
asir-5424	55	16	of	of	ADP
asir-5424	55	17	the	the	DET
asir-5424	55	18	isotope	isotope	NOUN
asir-5424	55	19	effect	effect	NOUN
asir-5424	55	20	.	.	PUNCT
asir-5424	56	1	the	the	DET
asir-5424	56	2	form	form	NOUN
asir-5424	56	3	of	of	ADP
asir-5424	56	4	solvent	solvent	ADJ
asir-5424	56	5	-	-	PUNCT
asir-5424	56	6	vacancy	vacancy	NOUN
asir-5424	56	7	exchange	exchange	NOUN
asir-5424	56	8	remains	remain	VERB
asir-5424	56	9	unchanged	unchanged	ADJ
asir-5424	56	10	before	before	ADV
asir-5424	56	11	and	and	CCONJ
asir-5424	56	12	after	after	ADP
asir-5424	56	13	impurity	impurity	NOUN
asir-5424	56	14	isotopes	isotope	NOUN
asir-5424	56	15	substitution	substitution	NOUN
asir-5424	56	16	.	.	PUNCT
asir-5424	57	1	neglecting	neglect	VERB
asir-5424	57	2	the	the	DET
asir-5424	57	3	nuclear	nuclear	ADJ
asir-5424	57	4	volume	volume	NOUN
asir-5424	57	5	effect	effect	NOUN
asir-5424	57	6	of	of	ADP
asir-5424	57	7	isotopes	isotope	NOUN
asir-5424	57	8	and	and	CCONJ
asir-5424	57	9	combining	combine	VERB
asir-5424	57	10	with	with	ADP
asir-5424	57	11	the	the	DET
asir-5424	57	12	geometric	geometric	ADJ
asir-5424	57	13	characteristics	characteristic	NOUN
asir-5424	57	14	of	of	ADP
asir-5424	57	15	solids	solid	NOUN
asir-5424	57	16	,	,	PUNCT
asir-5424	57	17	isotopic	isotopic	ADJ
asir-5424	57	18	atoms	atom	NOUN
asir-5424	57	19	will	will	AUX
asir-5424	57	20	jump	jump	VERB
asir-5424	57	21	into	into	ADP
asir-5424	57	22	the	the	DET
asir-5424	57	23	same	same	ADJ
asir-5424	57	24	geometric	geometric	ADJ
asir-5424	57	25	center	center	NOUN
asir-5424	57	26	of	of	ADP
asir-5424	57	27	mass	mass	NOUN
asir-5424	57	28	in	in	ADP
asir-5424	57	29	the	the	DET
asir-5424	57	30	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-5424	57	31	applied	apply	VERB
asir-5424	57	32	science	science	NOUN
asir-5424	57	33	and	and	CCONJ
asir-5424	57	34	innovative	innovative	ADJ
asir-5424	57	35	research	research	NOUN
asir-5424	57	36	vol	vol	NOUN
asir-5424	57	37	.	.	PROPN
asir-5424	58	1	6	6	NUM
asir-5424	58	2	,	,	PUNCT
asir-5424	58	3	no	no	INTJ
asir-5424	58	4	.	.	NOUN
asir-5424	58	5	4	4	NUM
asir-5424	58	6	,	,	PUNCT
asir-5424	58	7	2022	2022	NUM
asir-5424	58	8	128	128	NUM
asir-5424	58	9	published	publish	VERB
asir-5424	58	10	by	by	ADP
asir-5424	58	11	scholink	scholink	PROPN
asir-5424	58	12	inc	inc	PROPN
asir-5424	58	13	.	.	PROPN
asir-5424	58	14	vacancy	vacancy	PROPN
asir-5424	58	15	.	.	PUNCT
asir-5424	59	1	therefore	therefore	ADV
asir-5424	59	2	,	,	PUNCT
asir-5424	59	3	the	the	DET
asir-5424	59	4	θ	θ	PROPN
asir-5424	59	5	(	(	PUNCT
asir-5424	59	6	figure	figure	NOUN
asir-5424	59	7	2d	2d	NOUN
asir-5424	59	8	)	)	PUNCT
asir-5424	59	9	for	for	ADP
asir-5424	59	10	isotopes	isotope	NOUN
asir-5424	59	11	are	be	AUX
asir-5424	59	12	the	the	DET
asir-5424	59	13	same	same	ADJ
asir-5424	59	14	,	,	PUNCT
asir-5424	59	15	the	the	DET
asir-5424	59	16	ratio	ratio	NOUN
asir-5424	59	17	𝑓∗/𝑓	𝑓∗/𝑓	NOUN
asir-5424	59	18	is	be	AUX
asir-5424	59	19	1	1	NUM
asir-5424	59	20	according	accord	VERB
asir-5424	59	21	to	to	ADP
asir-5424	59	22	eq.(9	eq.(9	NOUN
asir-5424	59	23	)	)	PUNCT
asir-5424	59	24	.	.	PUNCT
asir-5424	60	1	it	it	PRON
asir-5424	60	2	shows	show	VERB
asir-5424	60	3	that	that	SCONJ
asir-5424	60	4	the	the	DET
asir-5424	60	5	effect	effect	NOUN
asir-5424	60	6	of	of	ADP
asir-5424	60	7	f	f	PROPN
asir-5424	60	8	can	can	AUX
asir-5424	60	9	not	not	PART
asir-5424	60	10	be	be	AUX
asir-5424	60	11	ignored	ignore	VERB
asir-5424	60	12	when	when	SCONJ
asir-5424	60	13	studying	study	VERB
asir-5424	60	14	the	the	DET
asir-5424	60	15	d	d	PROPN
asir-5424	60	16	of	of	ADP
asir-5424	60	17	vacancy	vacancy	NOUN
asir-5424	60	18	diffusion	diffusion	NOUN
asir-5424	60	19	,	,	PUNCT
asir-5424	60	20	however	however	ADV
asir-5424	60	21	,	,	PUNCT
asir-5424	60	22	the	the	DET
asir-5424	60	23	effect	effect	NOUN
asir-5424	60	24	of	of	ADP
asir-5424	60	25	𝑓∗/𝑓	𝑓∗/𝑓	NOUN
asir-5424	60	26	is	be	AUX
asir-5424	60	27	ignored	ignore	VERB
asir-5424	60	28	when	when	SCONJ
asir-5424	60	29	studying	study	VERB
asir-5424	60	30	the	the	DET
asir-5424	60	31	isotope	isotope	NOUN
asir-5424	60	32	effect	effect	NOUN
asir-5424	60	33	.	.	PUNCT
asir-5424	61	1	thus	thus	ADV
asir-5424	61	2	,	,	PUNCT
asir-5424	61	3	equation	equation	NOUN
asir-5424	61	4	(	(	PUNCT
asir-5424	61	5	10	10	NUM
asir-5424	61	6	)	)	PUNCT
asir-5424	61	7	can	can	AUX
asir-5424	61	8	be	be	AUX
asir-5424	61	9	used	use	VERB
asir-5424	61	10	to	to	PART
asir-5424	61	11	study	study	VERB
asir-5424	61	12	isotope	isotope	NOUN
asir-5424	61	13	effects	effect	NOUN
asir-5424	61	14	regardless	regardless	ADV
asir-5424	61	15	of	of	ADP
asir-5424	61	16	whether	whether	SCONJ
asir-5424	61	17	it	it	PRON
asir-5424	61	18	is	be	AUX
asir-5424	61	19	vacancy	vacancy	NOUN
asir-5424	61	20	diffusion	diffusion	NOUN
asir-5424	61	21	or	or	CCONJ
asir-5424	61	22	interstitial	interstitial	ADJ
asir-5424	61	23	diffusion	diffusion	NOUN
asir-5424	61	24	.	.	PUNCT
asir-5424	62	1	𝐷∗	𝐷∗	PROPN
asir-5424	62	2	𝐷	𝐷	PROPN
asir-5424	62	3	=	=	PROPN
asir-5424	62	4	γ∗	γ∗	PROPN
asir-5424	62	5	γ	γ	X
asir-5424	62	6	(	(	PUNCT
asir-5424	62	7	10	10	NUM
asir-5424	62	8	)	)	PUNCT
asir-5424	62	9	this	this	PRON
asir-5424	62	10	also	also	ADV
asir-5424	62	11	suggests	suggest	VERB
asir-5424	62	12	that	that	SCONJ
asir-5424	62	13	diffusive	diffusive	ADJ
asir-5424	62	14	isotope	isotope	NOUN
asir-5424	62	15	effects	effect	NOUN
asir-5424	62	16	essentially	essentially	ADV
asir-5424	62	17	do	do	AUX
asir-5424	62	18	not	not	PART
asir-5424	62	19	change	change	VERB
asir-5424	62	20	the	the	DET
asir-5424	62	21	direction	direction	NOUN
asir-5424	62	22	of	of	ADP
asir-5424	62	23	isotope	isotope	NOUN
asir-5424	62	24	diffusion	diffusion	NOUN
asir-5424	62	25	,	,	PUNCT
asir-5424	62	26	but	but	CCONJ
asir-5424	62	27	rather	rather	ADV
asir-5424	62	28	greatly	greatly	ADV
asir-5424	62	29	affect	affect	VERB
asir-5424	62	30	the	the	DET
asir-5424	62	31	diffusion	diffusion	NOUN
asir-5424	62	32	rate	rate	NOUN
asir-5424	62	33	,	,	PUNCT
asir-5424	62	34	leading	lead	VERB
asir-5424	62	35	to	to	ADP
asir-5424	62	36	isotope	isotope	NOUN
asir-5424	62	37	fractionation	fractionation	NOUN
asir-5424	62	38	.	.	PUNCT
asir-5424	63	1	3	3	X
asir-5424	63	2	.	.	X
asir-5424	63	3	conclusion	conclusion	NOUN
asir-5424	63	4	this	this	DET
asir-5424	63	5	paper	paper	NOUN
asir-5424	63	6	explains	explain	VERB
asir-5424	63	7	that	that	SCONJ
asir-5424	63	8	the	the	DET
asir-5424	63	9	correlation	correlation	NOUN
asir-5424	63	10	coefficient	coefficient	NOUN
asir-5424	63	11	ratio	ratio	NOUN
asir-5424	63	12	𝑓∗/𝑓	𝑓∗/𝑓	NOUN
asir-5424	63	13	can	can	AUX
asir-5424	63	14	be	be	AUX
asir-5424	63	15	neglected	neglect	VERB
asir-5424	63	16	when	when	SCONJ
asir-5424	63	17	studying	study	VERB
asir-5424	63	18	the	the	DET
asir-5424	63	19	isotope	isotope	NOUN
asir-5424	63	20	diffusion	diffusion	NOUN
asir-5424	63	21	effect	effect	NOUN
asir-5424	63	22	,	,	PUNCT
asir-5424	63	23	either	either	CCONJ
asir-5424	63	24	in	in	ADP
asir-5424	63	25	the	the	DET
asir-5424	63	26	interstitial	interstitial	ADJ
asir-5424	63	27	mechanism	mechanism	NOUN
asir-5424	63	28	or	or	CCONJ
asir-5424	63	29	vacancy	vacancy	NOUN
asir-5424	63	30	mechanism	mechanism	NOUN
asir-5424	63	31	,	,	PUNCT
asir-5424	63	32	allowing	allow	VERB
asir-5424	63	33	us	we	PRON
asir-5424	63	34	to	to	PART
asir-5424	63	35	study	study	VERB
asir-5424	63	36	the	the	DET
asir-5424	63	37	isotope	isotope	NOUN
asir-5424	63	38	diffusion	diffusion	NOUN
asir-5424	63	39	effect	effect	NOUN
asir-5424	63	40	more	more	ADV
asir-5424	63	41	conveniently	conveniently	ADV
asir-5424	63	42	in	in	ADP
asir-5424	63	43	the	the	DET
asir-5424	63	44	next	next	ADJ
asir-5424	63	45	step	step	NOUN
asir-5424	63	46	.	.	PUNCT
asir-5424	64	1	references	reference	NOUN
asir-5424	64	2	bardeen	bardeen	PROPN
asir-5424	64	3	,	,	PUNCT
asir-5424	64	4	j.	j.	PROPN
asir-5424	64	5	,	,	PUNCT
asir-5424	64	6	&	&	CCONJ
asir-5424	64	7	herring	herring	PROPN
asir-5424	64	8	,	,	PUNCT
asir-5424	64	9	c.	c.	PROPN
asir-5424	64	10	(	(	PUNCT
asir-5424	64	11	1952	1952	NUM
asir-5424	64	12	)	)	PUNCT
asir-5424	64	13	.	.	PUNCT
asir-5424	65	1	in	in	ADP
asir-5424	65	2	imperfections	imperfection	NOUN
asir-5424	65	3	in	in	ADP
asir-5424	65	4	nearly	nearly	ADV
asir-5424	65	5	perfect	perfect	ADJ
asir-5424	65	6	solids	solid	NOUN
asir-5424	65	7	(	(	PUNCT
asir-5424	65	8	p.	p.	NOUN
asir-5424	65	9	262	262	NUM
asir-5424	65	10	)	)	PUNCT
asir-5424	65	11	.	.	PUNCT
asir-5424	66	1	wiley	wiley	PROPN
asir-5424	66	2	,	,	PUNCT
asir-5424	66	3	new	new	PROPN
asir-5424	66	4	york	york	PROPN
asir-5424	66	5	.	.	PUNCT
asir-5424	67	1	compaan	compaan	PROPN
asir-5424	67	2	,	,	PUNCT
asir-5424	67	3	k.	k.	PROPN
asir-5424	67	4	,	,	PUNCT
asir-5424	67	5	&	&	CCONJ
asir-5424	67	6	haven	haven	PROPN
asir-5424	67	7	,	,	PUNCT
asir-5424	67	8	y.	y.	PROPN
asir-5424	67	9	(	(	PUNCT
asir-5424	67	10	1956	1956	NUM
asir-5424	67	11	)	)	PUNCT
asir-5424	67	12	.	.	PUNCT
asir-5424	68	1	correlation	correlation	NOUN
asir-5424	68	2	factors	factor	NOUN
asir-5424	68	3	for	for	ADP
asir-5424	68	4	diffusion	diffusion	NOUN
asir-5424	68	5	in	in	ADP
asir-5424	68	6	solids	solid	NOUN
asir-5424	68	7	.	.	PUNCT
asir-5424	69	1	transactions	transaction	NOUN
asir-5424	69	2	of	of	ADP
asir-5424	69	3	the	the	DET
asir-5424	69	4	faraday	faraday	PROPN
asir-5424	69	5	society	society	PROPN
asir-5424	69	6	.	.	PUNCT
asir-5424	70	1	https://doi.org/10.1039/tf9565200786	https://doi.org/10.1039/tf9565200786	X
asir-5424	70	2	einstein	einstein	PROPN
asir-5424	70	3	,	,	PUNCT
asir-5424	70	4	a.	a.	NOUN
asir-5424	70	5	(	(	PUNCT
asir-5424	70	6	1906	1906	NUM
asir-5424	70	7	)	)	PUNCT
asir-5424	70	8	.	.	PUNCT
asir-5424	71	1	annalen	annalen	PROPN
asir-5424	71	2	der	der	PROPN
asir-5424	71	3	physik	physik	PROPN
asir-5424	71	4	,	,	PUNCT
asir-5424	71	5	19	19	NUM
asir-5424	71	6	,	,	PUNCT
asir-5424	71	7	371	371	NUM
asir-5424	71	8	.	.	PUNCT
asir-5424	72	1	https://doi.org/10.1002/andp.19063240208	https://doi.org/10.1002/andp.19063240208	NOUN
asir-5424	72	2	lidiard	lidiard	NOUN
asir-5424	72	3	,	,	PUNCT
asir-5424	72	4	a.	a.	PROPN
asir-5424	72	5	b.	b.	PROPN
asir-5424	72	6	(	(	PUNCT
asir-5424	72	7	1955	1955	NUM
asir-5424	72	8	)	)	PUNCT
asir-5424	72	9	.	.	PUNCT
asir-5424	73	1	cxxxiii	cxxxiii	PROPN
asir-5424	73	2	.	.	PUNCT
asir-5424	74	1	impurity	impurity	NOUN
asir-5424	74	2	diffusion	diffusion	NOUN
asir-5424	74	3	in	in	ADP
asir-5424	74	4	crystals	crystal	NOUN
asir-5424	74	5	(	(	PUNCT
asir-5424	74	6	mainly	mainly	ADV
asir-5424	74	7	ionic	ionic	ADJ
asir-5424	74	8	crystals	crystal	NOUN
asir-5424	74	9	with	with	ADP
asir-5424	74	10	the	the	DET
asir-5424	74	11	sodium	sodium	NOUN
asir-5424	74	12	chloride	chloride	NOUN
asir-5424	74	13	structure	structure	NOUN
asir-5424	74	14	)	)	PUNCT
asir-5424	74	15	.	.	PUNCT
asir-5424	75	1	the	the	DET
asir-5424	75	2	london	london	PROPN
asir-5424	75	3	,	,	PUNCT
asir-5424	75	4	edinburgh	edinburgh	PROPN
asir-5424	75	5	,	,	PUNCT
asir-5424	75	6	and	and	CCONJ
asir-5424	75	7	dublin	dublin	PROPN
asir-5424	75	8	philosophical	philosophical	PROPN
asir-5424	75	9	magazine	magazine	NOUN
asir-5424	75	10	and	and	CCONJ
asir-5424	75	11	journal	journal	NOUN
asir-5424	75	12	of	of	ADP
asir-5424	75	13	science	science	NOUN
asir-5424	75	14	,	,	PUNCT
asir-5424	75	15	46(382	46(382	PROPN
asir-5424	75	16	)	)	PUNCT
asir-5424	75	17	,	,	PUNCT
asir-5424	75	18	1218	1218	NUM
asir-5424	75	19	-	-	SYM
asir-5424	75	20	1237	1237	NUM
asir-5424	75	21	.	.	PUNCT
asir-5424	76	1	https://doi.org/10.1080/14786441108520633	https://doi.org/10.1080/14786441108520633	NOUN
asir-5424	76	2	manning	manning	NOUN
asir-5424	76	3	,	,	PUNCT
asir-5424	76	4	j.	j.	PROPN
asir-5424	76	5	r.	r.	PROPN
asir-5424	76	6	(	(	PUNCT
asir-5424	76	7	1959	1959	NUM
asir-5424	76	8	)	)	PUNCT
asir-5424	76	9	.	.	PUNCT
asir-5424	77	1	correlation	correlation	NOUN
asir-5424	77	2	effects	effect	NOUN
asir-5424	77	3	in	in	ADP
asir-5424	77	4	impurity	impurity	NOUN
asir-5424	77	5	diffusion	diffusion	NOUN
asir-5424	77	6	.	.	PUNCT
asir-5424	78	1	physical	physical	PROPN
asir-5424	78	2	review	review	PROPN
asir-5424	78	3	,	,	PUNCT
asir-5424	78	4	4	4	NUM
asir-5424	78	5	,	,	PUNCT
asir-5424	78	6	819	819	NUM
asir-5424	78	7	-	-	SYM
asir-5424	78	8	827	827	NUM
asir-5424	78	9	.	.	PUNCT
asir-5424	79	1	https://doi.org/10.1103/physrev.116.819	https://doi.org/10.1103/physrev.116.819	PROPN
asir-5424	79	2	manning	manning	PROPN
asir-5424	79	3	,	,	PUNCT
asir-5424	79	4	j.	j.	PROPN
asir-5424	79	5	r.	r.	PROPN
asir-5424	79	6	(	(	PUNCT
asir-5424	79	7	1962	1962	NUM
asir-5424	79	8	)	)	PUNCT
asir-5424	79	9	.	.	PUNCT
asir-5424	80	1	correlation	correlation	NOUN
asir-5424	80	2	factors	factor	NOUN
asir-5424	80	3	for	for	ADP
asir-5424	80	4	impurity	impurity	NOUN
asir-5424	80	5	diffusion	diffusion	NOUN
asir-5424	80	6	-	-	PUNCT
asir-5424	80	7	fcc	fcc	PROPN
asir-5424	80	8	lattice	lattice	PROPN
asir-5424	80	9	.	.	PUNCT
asir-5424	81	1	physical	physical	PROPN
asir-5424	81	2	review	review	PROPN
asir-5424	81	3	,	,	PUNCT
asir-5424	81	4	5	5	NUM
asir-5424	81	5	,	,	PUNCT
asir-5424	81	6	2169	2169	NUM
asir-5424	81	7	-	-	SYM
asir-5424	81	8	2174	2174	NUM
asir-5424	81	9	.	.	PUNCT
asir-5424	82	1	https://doi.org/10.1103/physrev.128.2169	https://doi.org/10.1103/physrev.128.2169	PROPN
asir-5424	82	2	manning	manning	PROPN
asir-5424	82	3	,	,	PUNCT
asir-5424	82	4	j.	j.	PROPN
asir-5424	82	5	r.	r.	PROPN
asir-5424	82	6	(	(	PUNCT
asir-5424	82	7	1964	1964	NUM
asir-5424	82	8	)	)	PUNCT
asir-5424	82	9	.	.	PUNCT
asir-5424	83	1	correlation	correlation	NOUN
asir-5424	83	2	factors	factor	NOUN
asir-5424	83	3	for	for	ADP
asir-5424	83	4	impurity	impurity	NOUN
asir-5424	83	5	diffusion	diffusion	NOUN
asir-5424	83	6	.	.	PUNCT
asir-5424	84	1	bcc	bcc	PROPN
asir-5424	84	2	,	,	PUNCT
asir-5424	84	3	diamond	diamond	NOUN
asir-5424	84	4	,	,	PUNCT
asir-5424	84	5	and	and	CCONJ
asir-5424	84	6	fcc	fcc	PROPN
asir-5424	84	7	structures	structure	NOUN
asir-5424	84	8	.	.	PUNCT
asir-5424	85	1	physical	physical	ADJ
asir-5424	85	2	review	review	PROPN
asir-5424	85	3	,	,	PUNCT
asir-5424	85	4	6a	6a	NOUN
asir-5424	85	5	,	,	PUNCT
asir-5424	85	6	1758	1758	NUM
asir-5424	85	7	-	-	SYM
asir-5424	85	8	1766	1766	NUM
asir-5424	85	9	.	.	PUNCT
asir-5424	86	1	https://doi.org/10.1103/physrev.136.a1758	https://doi.org/10.1103/physrev.136.a1758	NOUN
asir-5424	86	2	mehrer	mehrer	PROPN
asir-5424	86	3	,	,	PUNCT
asir-5424	86	4	h.	h.	PROPN
asir-5424	86	5	(	(	PUNCT
asir-5424	86	6	2007	2007	NUM
asir-5424	86	7	)	)	PUNCT
asir-5424	86	8	.	.	PUNCT
asir-5424	87	1	diffusion	diffusion	NOUN
asir-5424	87	2	in	in	ADP
asir-5424	87	3	solids	solid	NOUN
asir-5424	87	4	:	:	PUNCT
asir-5424	87	5	fundamentals	fundamental	NOUN
asir-5424	87	6	,	,	PUNCT
asir-5424	87	7	methods	method	NOUN
asir-5424	87	8	,	,	PUNCT
asir-5424	87	9	methods	method	NOUN
asir-5424	87	10	,	,	PUNCT
asir-5424	87	11	materials	material	NOUN
asir-5424	87	12	,	,	PUNCT
asir-5424	87	13	diffusion	diffusion	NOUN
asir-5424	87	14	-	-	PUNCT
asir-5424	87	15	controlled	control	VERB
asir-5424	87	16	process	process	NOUN
asir-5424	87	17	.	.	PUNCT
asir-5424	88	1	spring	spring	NOUN
asir-5424	88	2	berlin	berlin	PROPN
asir-5424	88	3	heidelberg	heidelberg	PROPN
asir-5424	88	4	,	,	PUNCT
asir-5424	88	5	new	new	PROPN
asir-5424	88	6	york	york	PROPN
asir-5424	88	7	.	.	PUNCT
asir-5424	89	1	https://doi.org/10.1007/978-3-540-71488-0	https://doi.org/10.1007/978-3-540-71488-0	PROPN
asir-5424	89	2	van	van	PROPN
asir-5424	89	3	orman	orman	PROPN
asir-5424	89	4	,	,	PUNCT
asir-5424	89	5	j.	j.	PROPN
asir-5424	89	6	a.	a.	PROPN
asir-5424	89	7	,	,	PUNCT
asir-5424	89	8	&	&	CCONJ
asir-5424	89	9	krawczynski	krawczynski	PROPN
asir-5424	89	10	,	,	PUNCT
asir-5424	89	11	m.	m.	NOUN
asir-5424	89	12	j.	j.	PROPN
asir-5424	89	13	(	(	PUNCT
asir-5424	89	14	2015	2015	NUM
asir-5424	89	15	)	)	PUNCT
asir-5424	89	16	.	.	PUNCT
asir-5424	90	1	theoretical	theoretical	ADJ
asir-5424	90	2	constraints	constraint	NOUN
asir-5424	90	3	on	on	ADP
asir-5424	90	4	the	the	DET
asir-5424	90	5	isotope	isotope	NOUN
asir-5424	90	6	effect	effect	NOUN
asir-5424	90	7	for	for	ADP
asir-5424	90	8	diffusion	diffusion	NOUN
asir-5424	90	9	in	in	ADP
asir-5424	90	10	minerals	mineral	NOUN
asir-5424	90	11	.	.	PUNCT
asir-5424	91	1	geochimica	geochimica	PROPN
asir-5424	91	2	et	et	PROPN
asir-5424	91	3	cosmochimica	cosmochimica	PROPN
asir-5424	91	4	acta	acta	PROPN
asir-5424	91	5	,	,	PUNCT
asir-5424	91	6	164	164	NUM
asir-5424	91	7	,	,	PUNCT
asir-5424	91	8	365	365	NUM
asir-5424	91	9	-	-	SYM
asir-5424	91	10	381	381	NUM
asir-5424	91	11	.	.	PUNCT
asir-5424	92	1	https://doi.org/10.1016/j.gca.2015.04.051	https://doi.org/10.1016/j.gca.2015.04.051	PROPN
asir-5424	92	2	van	van	PROPN
asir-5424	92	3	smoluchowski	smoluchowski	NOUN
asir-5424	92	4	,	,	PUNCT
asir-5424	92	5	m.	m.	NOUN
asir-5424	92	6	(	(	PUNCT
asir-5424	92	7	1906	1906	NUM
asir-5424	92	8	)	)	PUNCT
asir-5424	92	9	.	.	PUNCT
asir-5424	93	1	annalen	annalen	PROPN
asir-5424	93	2	der	der	PROPN
asir-5424	93	3	physik	physik	PROPN
asir-5424	93	4	,	,	PUNCT
asir-5424	93	5	21	21	NUM
asir-5424	93	6	,	,	PUNCT
asir-5424	93	7	756	756	NUM
asir-5424	93	8	.	.	PUNCT
asir-5424	93	9	https://doi.org/10.1002/andp.19063261405	https://doi.org/10.1002/andp.19063261405	PROPN