Structural homology of the strength for metallic glasses

doi:10.1016/j.jmst.2020.08.029

Abstract

Abstract:

The structure-property relationship, one of the central themes in materials science, is far from being well understood for metallic glasses (MGs) due to the great complexity of their amorphous structures. Based on the analysis of published experimental data for 165 MGs from more than 15 different alloy systems, the present study reveals a universal dependence of mechanical properties (Young’s moduli, shear moduli and yield strength) on simple structural parameters (the inter-atomic distance and/or valence electron density) originating from the interatomic potential and Fermi sphere-Brillouin zone interaction. This work establishes a structure-property relationship for metallic glasses and provides insights into the fundamentals of the mechanical properties of disordered systems.

Key words: Metallic glasses, Structure-property relationship, Mechanical properties, Inter-atomic distance, Valence electron density

Weiming Yang, Xinfa Sun, Haishun Liu, Changfeng Yu, Wenyu Li, Akihisa Inoue, Daniel Şopu, Jürgen Eckert, Chunguang Tang. Structural homology of the strength for metallic glasses[J]. J. Mater. Sci. Technol., 2021, 81: 123-130.

Figures/Tables 5

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Numbers	Compositions	σ_y (GPa)	E (GPa)	G (GPa)	ρ (e/Å³)	d (nm)	Refs.
1	Fe₆₀Co₂₀B₂₀		172.6	65.1	0.3506	0.1204	[38]
2	Fe₄₀Co₄₀B₂₀		174.2	65	0.3552	0.1202	[38]
3	Fe₇₁Nb₆B₂₃	4.85			0.3410	0.1209	[39]
4	Fe_56.05Co_13.45Nb_5.5B₂₅	4.5			0.3299	0.1200	[40]
5	Fe₆₅Mo₁₄C₁₅B₆	4.2	195	73		0.1208	[41]
6	Fe₆₆Mo₁₀P₁₂C₁₀B₂	2.55	176	66.1		0.1239	[42]
7	Fe₇₅Mo₅P₁₀C_7.5B_2.5	3.18				0.1241	[43]
8	Fe₆₃Cr₃Mo₁₂P₁₀C₇B₅	2.9	183	68.8		0.1244	[42]
9	Fe_75.924Si_9.5904B_8.3916P_5.994Cu_0.1	3.3			0.3044	0.1252	[44]
10	[(Fe_0.5Co_0.5)_0.75B_0.2Si_0.05]₉₆Nb₄	4.21	210	80.46	0.3375	0.1217	[45]
11	Fe₄₀Ni₄₀P₁₄B₆	2.23			0.3111	0.1243	[46,47]
12	Fe₆₆Nb₄B₃₀	4			0.3454	0.1182	[48,49]
13	(Fe_0.75B_0.2Si_0.05)₉₆Nb₄	3.16	180		0.3302	0.1220	[45]
14	Fe₆₁Zr₈Y₂Co₆Mo₇Al₁B₁₅		222			0.1269	[50]
15	Fe₆₈Cr₃Mo₁₀P₆C₁₀B₃	3.1	180	67.7		0.1234	[51]
16	((Co_0.6Fe_0.4)_0.75B_0.2Si_0.05)₉₆Nb₄	4.17	210			0.1187	[52]
17	((Co_0.7Fe_0.3)_0.75B_0.2Si_0.05)₉₆Nb₄	4.13	200			0.1187	[52]
18	((Co_0.8Fe_0.2)_0.75B_0.2Si_0.05)₉₆Nb₄	4.1	200			0.1186	[52]
19	((Co_0.9Fe_0.1)_0.75B_0.2Si0.05)₉₆Nb₄	3.98	190			0.1185	[52]
20	Co₅₀Cr₁₅Mo₁₄C₁₅B₆	4.42	210	78.7		0.11709	[53]
21	Co₅₀Cr₁₅Mo₁₄C₁₈B₃	4.5	209	77.4		0.11679	[53]
22	Ni₆₀Nb₁₅Zr₂₀Al₅	2.9			0.2724	0.1358	[54]
23	Ni₄₅Ti₂₀Zr₂₅Al₁₀	2.37	109.3	40.2	0.2322	0.1391	[55]
24	Ni₆₀Nb_12.5Zr₂₀Al₅Ti_2.5	2.885			0.2701	0.1357	[54]
25	Ni₆₀Nb₁₀Zr₂₀Al₅Ti₅	2.885			0.2677	0.1356	[54]
26	Ni₄₀Ti₁₇Zr₂₈Al₁₀Cu₅	2.3	127.6	47.3	0.2262	0.1398	[55]
27	Ni_62.5Zr₂₀Nb₁₅Pd_2.5	2.85			0.2794	0.1351	[56]
28	Ni₆₀Zr₂₀Nb₁₅Pd₅	2.81			0.2776	0.1355	[56]
29	Ni_52.5Zr₂₀Nb₁₅Pd_12.5	2.75			0.2723	0.1364	[56]
30	Ni₅₃Nb₂₀Ti₁₀Zr₈Co₆Cu₃				0.2812	0.1340	[57]
31	Ni₆₀Nb₃₇Sn₃	2.8	198.6	58.6		0.1339	[58]
32	Ni₆₀Nb₃₅Sn₅	2.5	183.2	54.1		0.1341	[58]
33	Ni₆₀Sn₆(Nb_0.8Ta_0.2)₃₄	3.5	161.3	59.41		0.1342	[59,60]
34	Ni₆₀Sn₆(Nb_0.6Ta_0.4)₃₄	3.58	163.7	60.1		0.1342	[59,60]
35	Ni₆₀Pd₂₀P₂₀	2.0			0.2856	0.1278	[61,62,63]
36	Ni₆₀Pd₂₀P₁₇B₃	2.022	106	38	0.2930	0.1268	[62,63]
37	Ni₅₀Nb₅₀	2.26	132	48.1	0.3112	0.1360	[50,64]
38	Mg₆₅Cu₂₅Y₁₀	0.68	50.1	18.9	0.1100	0.1540	[65]
39	Mg₆₅Cu₂₅Y₉Gd₁	1.06	49.2	19.5		0.1540	[65]
40	Mg_58.5Cu_30.5Y₁₁	1.22	53.9	20.4	0.1159	0.1524	[66]
41	Mg₅₈Cu₂₅Zn₇Y₁₀	1.09	55.2	21.3		0.1525	[66]
42	Mg₅₈Cu₂₇Zn₅Y₁₀	0.87	54.1	20.85		0.1523	[66]
43	Mg₇₅Cu_14.5Zn_3.5Y₇	0.875				0.1560	[66]
44	Mg₆₀Cu₂₅Zn₅Gd₁₀	1.169	54	20.64		0.1530	[66]
45	Mg₆₅Cu₂₅Tb₁₀	0.8	51.3	19.6		0.1537	[67]
46	Mg₆₅Cu₂₅Gd₁₀	0.85	50.6	19.3		0.1540	[68]
47	Mg₇₅Cu₁₅Gd₁₀	0.743	50			0.1572	[69]
48	Mg₇₅Cu₅Ni₁₀Gd₁₀	0.874	54			0.1568	[70]
49	Mg₆₁Cu₂₈Gd₁₁	1.075				0.1532	[71,72]
50	Mg₆₅Y₁₀Cu₁₅Ag₅Pd₅	0..77				0.1553	[73]
51	Mg₆₅Cu₂₀Y₁₅	0.82			0.1048	0.1566	[50]
52	Ca₄₈Mg₂₇Cu₂₅	0.411	29.8	12.1		0.1698	[74]
53	Ca₅₀Mg₂₀Cu₃₀		33.2	12.7		0.1689	[75]
54	Ca₆₅Mg₁₅Zn₂₀	0.364	26.4	10.1		0.1799	[75]
55	Ca₅₅Mg₁₈Zn₁₁Cu₁₆		31	11.9		0.1729	[75,76]
56	Ca₆₀Mg₁₅Cu₂₅	0.252				0.1742	[77,78]
57	Ca₆₅Ag₃₅		20			0.1785	[50]
58	Ca₅₇Mg₁₉Cu₂₄	0.545	38			0.1734	[50]
59	Ca₆₅Li_9.96Mg_8.54Zn_16.5	0.53	23.4	8.95		0.1791	[79]
60	Ti₄₅Zr₂₀Be₃₅	1.86	96.8	35.7	0.1942	0.1349	[80]
61	Ti₄₀Zr₂₅Be₃₅		99.6	37.2	0.1910	0.1376	[80]
62	Ti₃₀Zr₃₅Be₃₅		98.5	36.4	0.1848	0.1391	[80]
63	Ti₅₀Ni₄₂Cu₈	2.008			0.2558	0.1348	[81]
64	Ti_39.6Zr_9.9Cu_35.64Pd_13.86Nb₁				0.2174	0.1393	[82]
65	Ti₃₈Zr_9.5Cu_34.2Pd_13.3Nb₅				0.2202	0.1397	[82]
66	Ti₄₀Zr₂₅Ni₃Cu₁₂Be₂₀	1.8	96.2	35.5	0.1958	0.1397	[83]
67	Ti₅₀Cu₂₃Ni₂₀Sn₇	1.3	85.3			0.1378	[84]
68	Ti₄₅Zr₂₀Be₃₀Cr₅	1.72	105.6	39.2		0.1375	[85]
69	Zr₄₅Cu₄₅Al₁₀			35.4	0.1876	0.1513	[86]
70	Zr_47.5Cu_47.5Al₅	2.265	88.7	33	0.1875	0.1440	[87]
71	Zr₆₄Cu₂₆Al₁₀	2.045			0.1721	0.1500	[88]
72	Zr₆₅Cu₁₅Ni₁₀Al₁₀	1.45	82.96	30.27	0.1772	0.1499	[89,90]
73	Zr₆₂Cu_15.5Ni_12.5Al₁₀		79.65	28.89	0.1810	0.1488	[90]
74	Zr₅₃Cu₂₀Ni₁₂Al₁₀Ti₅		87.58	32.12	0.1857	0.1468	[50]
75	Zr₅₅Cu₂₀Ni₁₀Al₁₀Ti₅	1.63	85	31	0.1827	0.1476	[91]
76	Zr₅₇Cu₂₀Ni₈Al₁₀Ti₅	1.65	82	30.1	0.1798	0.1483	[92]
77	Zr₅₉Cu₂₀Ni₈Al₁₀Ti₃	1.45			0.1792	0.1486	[93]
78	Zr₅₉Ta₅Cu₁₈Ni₈Al₁₀	1.7	84.3	30.9		0.1491	[92]
79	Zr₅₇Nb₅Cu_15.4Ni_12.6Al₁₀	1.8	87.3	31.98	0.1872	0.1481	[94]
80	Zr₅₅Cu₃₅Al₁₀	1.74			0.1788	0.1471	[95]
81	Zr₄₁Ti₁₄Cu_12.5Ni₁₀Be_22.5	1.86	101.3	37.4	0.1943	0.1397	[83,96]
82	Zr_53.7Cu_28.5Ni_9.4Al_8.4	1.85	85		0.1865	0.1461	[19]
83	Zr_52.5Ti₅Cu_17.9Ni_14.6Al₁₀	1.86	88.6	32.3	0.1884	0.1466	[83,97]
84	Zr_64.13Cu_15.75Ni_10.12Al₁₀	1.721	78.41	28.46	0.1779	0.1496	[83,90]
85	Zr₆₂Cu₁₇Ni₁₃Al₈	1.46			0.1822	0.1485	[98]
86	Zr₄₆Cu_37.6Ag_8.4Al₈	1.716	92.4	33.8		0.1453	[99]
87	Zr_53.8Cu_31.6Ag₇Al_7.6	1.518	82	29.9		0.1475	[99]
88	Zr₄₈Cu₃₆Ag₈Al₈	1.85	115	44		0.1458	[100]
89	Zr_46.75Ti_8.25Cu_7.5Ni₁₀Be_27.5	1.83	83	37.2	0.1899	0.1398	[101,102]
90	Zr_52.25Ta₅Cu_28.5Ni_4.75Al_9.5	1.909	90			0.1470	[101]
91	Zr₆₁Cu_17.3Ni_12.8Al_7.9Sn₁	1.77	77.4	28.2		0.1485	[83]
92	Hf₅₀Ni₂₅Al₂₅	2.725	125.6	47		0.1463	[88]
93	Hf₅₃Ni₂₅Al₂₂		116.5	43.3		0.1467	[88]
94	Hf₅₅Ni₂₅Al₂₀	2.565	117.6	43.7		0.1471	[88]
95	Hf₅₈Ni₂₅Al₁₇		111.7	41.3		0.1475	[88]
96	Hf₆₀Ni₂₅Al₁₅		110.2	40.8		0.1479	[88]
97	Hf₆₂Ni₂₅Al₁₃	2.29	111.9	41.3		0.1457	[88]
98	Cu₆₈Zr₃₂		89.6	32	0.2060	0.1382	[103]
99	Cu₆₄Zr₃₆	1.944	92.0	34	0.2016	0.1395	[104]
100	Cu₅₀Zr₅₀	1.772	83.2	30	0.1878	0.1440	[87,104]
101	Cu₄₆Zr₅₄	1.5926	83.5	30	0.1843	0.1453	[104,105]
102	Cu₆₀Zr₃₀Ti₁₀		93	33.8	0.2039	0.1393	[106]
103	Cu₆₀Zr_32.5Ti_7.5		90	32.8	0.2022	0.1397	[89]
104	Cu₅₄Zr_42.5Al_3.5		81.3	29.2	0.1929	0.1422	[107]
105	Cu_53.2Zr_41.8Al₅		85.6	30.9	0.1928	0.1421	[107]
106	Cu_51.5Zr_40.5Al₈		87.4	31.6	0.1924	0.1422	[107]
107	Cu₅₀Zr₄₅Al₅	1.89	84	31	0.1897	0.1432	[89]
108	Cu_57.5Hf_27.5Ti₁₅	1.94	103	37.3		0.1383	[108]
109	Cu₄₇Zr₁₁Ti₃₄Ni₈	1.6			0.2214	0.1370	[89]
110	Cu₆₀Zr₂₀Hf₁₀Ti₁₀		101.1	36.93		0.1392	[55]
111	Cu₆₅Zr₃₅	2.019			0.2026	0.1392	[109,110]
112	Cu_61.4Zr_38.6	1.87			0.1988	0.1404	[109,110]
113	Cu₅₆Zr₄₄	1.82			0.1934	0.1421	[109,110,111]
114	Cu₄₀Zr₆₀	1.333			0.1794	0.1472	[112,113]
115	Cu_33.3Zr_66.7	1.17			0.1744	0.1493	[113]
116	Cu₄₈Zr₄₈Al₄	1.65	88.7	32.4	0.1875	0.1440	[87,114,115]
117	Cu_47.5Zr_47.5Al₅	1.742	87	33	0.1875	0.1440	[87,114,115]
118	Cu₄₇Zr₄₇Al₆	1.834	92.4	33.8	0.1874	0.1439	[87,114,116]
119	Cu₄₆Zr₄₆Al₈	1.926	93.7	34.3	0.1873	0.1439	[116,117]
120	Cu₄₇Ti₃₃Zr₁₁Ni₈Si₁	2.0	100	38.3	0.2181	0.1369	[118,119]
121	Cu₄₇Ti₃₃Zr₁₁Ni₈Fe₁	2.008	102	39	0.2226	0.1368	[119,120]
122	Cu₅₅Zr₃₀Ti₁₀Co₅	2.31	130		0.2075	0.1392	[50]
123	Cu₆₀Hf₃₀Ti₁₀	2.16	124			0.1390	[50]
124	Cu₆₀Hf₁₀Zr₂₀Ti₁₀	1.95	101	36.9		0.1392	[50]
125	Cu₆₀Zr₄₀	1.92	107		0.1974	0.1408	[121]
126	Pt_57.5Cu_14.7Ni_5.3P_22.5	1.4	94.8	33.3	0.2376	0.1346	[122]
127	Pt_74.7Cu_1.5Ag_0.3P₁₈B₄Si_1.5	1.20		32.4		0.1354	[122]
128	Pt₆₀Ni₁₅P₂₅		96	33.8	0.2428	0.1345	[50]
129	Pt₆₀Cu₁₆Co₂P₂₂	1.1	96		0.2359	0.1350	[50]
130	Ag₆₀Cu₄₀		39	12		0.1376	[123]
131	Pd_77.5Cu₆Si_16.5	1.4	89.7	31.8	0.2556	0.1360	[89]
132	Pd₄₀Cu₄₀P₂₀	1.7	93	33.2	0.2360	0.1320	[124]
133	Pd₇₉Cu₆Si₁₀P₅				0.2545	0.1358	[125]
134	Pd_42.5Cu₃₀Ni_7.5P₂₀		101.9	36.5	0.2428	0.1319	[126,127]
135	Pd₈₀Si₂₀	1.3	94.5	33.4	0.2535	0.1364	[89,124,128]
136	Pd₄₀Ni₄₀P₂₀	1.65	108	38.6	0.2702	0.1304	[89,124,128]
137	Pd₄₀Cu₃₀Ni₁₀P₂₀	1.72	92	34.5	0.2444	0.1316	[89,124,128]
138	Pd₈₀P₂₀			33.1	0.2440	0.1356	[89,124,128]
139	Pd₆₄Fe₁₆P₂₀			27.1	0.2516	0.1340	[89,124,128]
140	La₅₅Al₂₅Cu₁₀Ni₅Co₅	0.5	41.9	15.6	0.1124	0.1617	[68]
141	La₆₂Al₁₄(Cu_5/6Ag_1/6)₁₄(Ni_1/2Co_1/2))₁₀	0.65	35	13		0.1668	[83,129,130]
142	La₅₅Al₂₅Co₂₀	0.99	40.9	15.42	0.1185	0.1638	[131]
143	La₅₅Al₁₅Ni₁₀P₂₀	0.5	41		0.1106	0.1627	[50]
144	Ce₇₀Al₁₀Ni₁₀Cu₁₀	0.4	30.3	11.5		0.1669	[50]
145	Ce₆₀Al₁₀Ni₁₀Cu₂₀	0.40	30			0.1615	[132,133]
146	Er₅₀Y₆Al₂₄Co₂₀		71.1	26.98		0.1583	[50]
147	Er₅₅Al₂₅Co₂₀	1.117	70.72	27.08		0.1578	[83,112,131]
148	Al₈₉La₆Ni₅	1.033			0.1735	0.1447	[134,135]
149	Au₄₉Ag_5.5Pd_2.3Cu_26.9Si_16.3	1.12	74.4	26.5		0.1379	[83,136,137]
150	Y₅₅Al₂₅Co₂₀	1.203			0.1304	0.1600	[83,112,131]
151	Pr₅₅Al₂₅Co₂₀	1.007	45.9	17.35		0.1616	[83,112,131]
152	Nd₅₅Al₂₅Co₂₀	0.996				0.1611	[83,112,131]
153	Nd₆₀Al₁₀Fe₂₀Co₁₀	0.45	51	35.1		0.1615	[50]
154	Gd₅₅Al₂₅Co₂₀	0.734				0.1600	[83,112,131]
155	Gd₃₆Y₂₀Al₂₄Co₂₀		62.2	23.6		0.1603	[50]
156	Tb₅₅Al₂₅Co₂₀	0.834	59.53	22.85		0.1589	[83,112,131]
157	Dy₅₅Al₂₅Co₂₀	0.717	61.36	23.52		0.1583	[83,112,131]
158	Ho₅₅Al₂₅Co₂₀	0.869	66.64	25.42		0.1583	[83,112,131]
159	Ho₃₉Al₂₅Co₂₀Y₁₆		69.1	26.2		0.1588	[50]
160	Ta₄₂Ni₃₆Co₂₂	2.7	170			0.1345	[138]
161	Sr₆₀Li₅Mg₁₅Zn₂₀	0.3	19.7	7.71		0.1885	[139]
162	Zn₂₀Ca₂₀Sr₂₀Yb₂₀Li₁₁Mg₉	0.40	16.0	6.3		0.1803	[83]
163	Zn₄₀Mg₁₁Ca₃₁Yb₁₈	0.66	28.8			0.1692	[83]
164	Tm₃₉Al₂₅Co₂₀Y₁₆	1.98	75.0	29.4		0.1580	[140]
165	Lu₄₅Y₁₀Al₂₅Co₂₀	1.89	79.1	31.1		0.1568	[141]

Numbers	Compositions	σ_y (GPa)	E (GPa)	G (GPa)	ρ (e/Å³)	d (nm)	Refs.
1	Fe₆₀Co₂₀B₂₀		172.6	65.1	0.3506	0.1204	[38]
2	Fe₄₀Co₄₀B₂₀		174.2	65	0.3552	0.1202	[38]
3	Fe₇₁Nb₆B₂₃	4.85			0.3410	0.1209	[39]
4	Fe_56.05Co_13.45Nb_5.5B₂₅	4.5			0.3299	0.1200	[40]
5	Fe₆₅Mo₁₄C₁₅B₆	4.2	195	73		0.1208	[41]
6	Fe₆₆Mo₁₀P₁₂C₁₀B₂	2.55	176	66.1		0.1239	[42]
7	Fe₇₅Mo₅P₁₀C_7.5B_2.5	3.18				0.1241	[43]
8	Fe₆₃Cr₃Mo₁₂P₁₀C₇B₅	2.9	183	68.8		0.1244	[42]
9	Fe_75.924Si_9.5904B_8.3916P_5.994Cu_0.1	3.3			0.3044	0.1252	[44]
10	[(Fe_0.5Co_0.5)_0.75B_0.2Si_0.05]₉₆Nb₄	4.21	210	80.46	0.3375	0.1217	[45]
11	Fe₄₀Ni₄₀P₁₄B₆	2.23			0.3111	0.1243	[46,47]
12	Fe₆₆Nb₄B₃₀	4			0.3454	0.1182	[48,49]
13	(Fe_0.75B_0.2Si_0.05)₉₆Nb₄	3.16	180		0.3302	0.1220	[45]
14	Fe₆₁Zr₈Y₂Co₆Mo₇Al₁B₁₅		222			0.1269	[50]
15	Fe₆₈Cr₃Mo₁₀P₆C₁₀B₃	3.1	180	67.7		0.1234	[51]
16	((Co_0.6Fe_0.4)_0.75B_0.2Si_0.05)₉₆Nb₄	4.17	210			0.1187	[52]
17	((Co_0.7Fe_0.3)_0.75B_0.2Si_0.05)₉₆Nb₄	4.13	200			0.1187	[52]
18	((Co_0.8Fe_0.2)_0.75B_0.2Si_0.05)₉₆Nb₄	4.1	200			0.1186	[52]
19	((Co_0.9Fe_0.1)_0.75B_0.2Si0.05)₉₆Nb₄	3.98	190			0.1185	[52]
20	Co₅₀Cr₁₅Mo₁₄C₁₅B₆	4.42	210	78.7		0.11709	[53]
21	Co₅₀Cr₁₅Mo₁₄C₁₈B₃	4.5	209	77.4		0.11679	[53]
22	Ni₆₀Nb₁₅Zr₂₀Al₅	2.9			0.2724	0.1358	[54]
23	Ni₄₅Ti₂₀Zr₂₅Al₁₀	2.37	109.3	40.2	0.2322	0.1391	[55]
24	Ni₆₀Nb_12.5Zr₂₀Al₅Ti_2.5	2.885			0.2701	0.1357	[54]
25	Ni₆₀Nb₁₀Zr₂₀Al₅Ti₅	2.885			0.2677	0.1356	[54]
26	Ni₄₀Ti₁₇Zr₂₈Al₁₀Cu₅	2.3	127.6	47.3	0.2262	0.1398	[55]
27	Ni_62.5Zr₂₀Nb₁₅Pd_2.5	2.85			0.2794	0.1351	[56]
28	Ni₆₀Zr₂₀Nb₁₅Pd₅	2.81			0.2776	0.1355	[56]
29	Ni_52.5Zr₂₀Nb₁₅Pd_12.5	2.75			0.2723	0.1364	[56]
30	Ni₅₃Nb₂₀Ti₁₀Zr₈Co₆Cu₃				0.2812	0.1340	[57]
31	Ni₆₀Nb₃₇Sn₃	2.8	198.6	58.6		0.1339	[58]
32	Ni₆₀Nb₃₅Sn₅	2.5	183.2	54.1		0.1341	[58]
33	Ni₆₀Sn₆(Nb_0.8Ta_0.2)₃₄	3.5	161.3	59.41		0.1342	[59,60]
34	Ni₆₀Sn₆(Nb_0.6Ta_0.4)₃₄	3.58	163.7	60.1		0.1342	[59,60]
35	Ni₆₀Pd₂₀P₂₀	2.0			0.2856	0.1278	[61,62,63]
36	Ni₆₀Pd₂₀P₁₇B₃	2.022	106	38	0.2930	0.1268	[62,63]
37	Ni₅₀Nb₅₀	2.26	132	48.1	0.3112	0.1360	[50,64]
38	Mg₆₅Cu₂₅Y₁₀	0.68	50.1	18.9	0.1100	0.1540	[65]
39	Mg₆₅Cu₂₅Y₉Gd₁	1.06	49.2	19.5		0.1540	[65]
40	Mg_58.5Cu_30.5Y₁₁	1.22	53.9	20.4	0.1159	0.1524	[66]
41	Mg₅₈Cu₂₅Zn₇Y₁₀	1.09	55.2	21.3		0.1525	[66]
42	Mg₅₈Cu₂₇Zn₅Y₁₀	0.87	54.1	20.85		0.1523	[66]
43	Mg₇₅Cu_14.5Zn_3.5Y₇	0.875				0.1560	[66]
44	Mg₆₀Cu₂₅Zn₅Gd₁₀	1.169	54	20.64		0.1530	[66]
45	Mg₆₅Cu₂₅Tb₁₀	0.8	51.3	19.6		0.1537	[67]
46	Mg₆₅Cu₂₅Gd₁₀	0.85	50.6	19.3		0.1540	[68]
47	Mg₇₅Cu₁₅Gd₁₀	0.743	50			0.1572	[69]
48	Mg₇₅Cu₅Ni₁₀Gd₁₀	0.874	54			0.1568	[70]
49	Mg₆₁Cu₂₈Gd₁₁	1.075				0.1532	[71,72]
50	Mg₆₅Y₁₀Cu₁₅Ag₅Pd₅	0..77				0.1553	[73]
51	Mg₆₅Cu₂₀Y₁₅	0.82			0.1048	0.1566	[50]
52	Ca₄₈Mg₂₇Cu₂₅	0.411	29.8	12.1		0.1698	[74]
53	Ca₅₀Mg₂₀Cu₃₀		33.2	12.7		0.1689	[75]
54	Ca₆₅Mg₁₅Zn₂₀	0.364	26.4	10.1		0.1799	[75]
55	Ca₅₅Mg₁₈Zn₁₁Cu₁₆		31	11.9		0.1729	[75,76]
56	Ca₆₀Mg₁₅Cu₂₅	0.252				0.1742	[77,78]
57	Ca₆₅Ag₃₅		20			0.1785	[50]
58	Ca₅₇Mg₁₉Cu₂₄	0.545	38			0.1734	[50]
59	Ca₆₅Li_9.96Mg_8.54Zn_16.5	0.53	23.4	8.95		0.1791	[79]
60	Ti₄₅Zr₂₀Be₃₅	1.86	96.8	35.7	0.1942	0.1349	[80]
61	Ti₄₀Zr₂₅Be₃₅		99.6	37.2	0.1910	0.1376	[80]
62	Ti₃₀Zr₃₅Be₃₅		98.5	36.4	0.1848	0.1391	[80]
63	Ti₅₀Ni₄₂Cu₈	2.008			0.2558	0.1348	[81]
64	Ti_39.6Zr_9.9Cu_35.64Pd_13.86Nb₁				0.2174	0.1393	[82]
65	Ti₃₈Zr_9.5Cu_34.2Pd_13.3Nb₅				0.2202	0.1397	[82]
66	Ti₄₀Zr₂₅Ni₃Cu₁₂Be₂₀	1.8	96.2	35.5	0.1958	0.1397	[83]
67	Ti₅₀Cu₂₃Ni₂₀Sn₇	1.3	85.3			0.1378	[84]
68	Ti₄₅Zr₂₀Be₃₀Cr₅	1.72	105.6	39.2		0.1375	[85]
69	Zr₄₅Cu₄₅Al₁₀			35.4	0.1876	0.1513	[86]
70	Zr_47.5Cu_47.5Al₅	2.265	88.7	33	0.1875	0.1440	[87]
71	Zr₆₄Cu₂₆Al₁₀	2.045			0.1721	0.1500	[88]
72	Zr₆₅Cu₁₅Ni₁₀Al₁₀	1.45	82.96	30.27	0.1772	0.1499	[89,90]
73	Zr₆₂Cu_15.5Ni_12.5Al₁₀		79.65	28.89	0.1810	0.1488	[90]
74	Zr₅₃Cu₂₀Ni₁₂Al₁₀Ti₅		87.58	32.12	0.1857	0.1468	[50]
75	Zr₅₅Cu₂₀Ni₁₀Al₁₀Ti₅	1.63	85	31	0.1827	0.1476	[91]
76	Zr₅₇Cu₂₀Ni₈Al₁₀Ti₅	1.65	82	30.1	0.1798	0.1483	[92]
77	Zr₅₉Cu₂₀Ni₈Al₁₀Ti₃	1.45			0.1792	0.1486	[93]
78	Zr₅₉Ta₅Cu₁₈Ni₈Al₁₀	1.7	84.3	30.9		0.1491	[92]
79	Zr₅₇Nb₅Cu_15.4Ni_12.6Al₁₀	1.8	87.3	31.98	0.1872	0.1481	[94]
80	Zr₅₅Cu₃₅Al₁₀	1.74			0.1788	0.1471	[95]
81	Zr₄₁Ti₁₄Cu_12.5Ni₁₀Be_22.5	1.86	101.3	37.4	0.1943	0.1397	[83,96]
82	Zr_53.7Cu_28.5Ni_9.4Al_8.4	1.85	85		0.1865	0.1461	[19]
83	Zr_52.5Ti₅Cu_17.9Ni_14.6Al₁₀	1.86	88.6	32.3	0.1884	0.1466	[83,97]
84	Zr_64.13Cu_15.75Ni_10.12Al₁₀	1.721	78.41	28.46	0.1779	0.1496	[83,90]
85	Zr₆₂Cu₁₇Ni₁₃Al₈	1.46			0.1822	0.1485	[98]
86	Zr₄₆Cu_37.6Ag_8.4Al₈	1.716	92.4	33.8		0.1453	[99]
87	Zr_53.8Cu_31.6Ag₇Al_7.6	1.518	82	29.9		0.1475	[99]
88	Zr₄₈Cu₃₆Ag₈Al₈	1.85	115	44		0.1458	[100]
89	Zr_46.75Ti_8.25Cu_7.5Ni₁₀Be_27.5	1.83	83	37.2	0.1899	0.1398	[101,102]
90	Zr_52.25Ta₅Cu_28.5Ni_4.75Al_9.5	1.909	90			0.1470	[101]
91	Zr₆₁Cu_17.3Ni_12.8Al_7.9Sn₁	1.77	77.4	28.2		0.1485	[83]
92	Hf₅₀Ni₂₅Al₂₅	2.725	125.6	47		0.1463	[88]
93	Hf₅₃Ni₂₅Al₂₂		116.5	43.3		0.1467	[88]
94	Hf₅₅Ni₂₅Al₂₀	2.565	117.6	43.7		0.1471	[88]
95	Hf₅₈Ni₂₅Al₁₇		111.7	41.3		0.1475	[88]
96	Hf₆₀Ni₂₅Al₁₅		110.2	40.8		0.1479	[88]
97	Hf₆₂Ni₂₅Al₁₃	2.29	111.9	41.3		0.1457	[88]
98	Cu₆₈Zr₃₂		89.6	32	0.2060	0.1382	[103]
99	Cu₆₄Zr₃₆	1.944	92.0	34	0.2016	0.1395	[104]
100	Cu₅₀Zr₅₀	1.772	83.2	30	0.1878	0.1440	[87,104]
101	Cu₄₆Zr₅₄	1.5926	83.5	30	0.1843	0.1453	[104,105]
102	Cu₆₀Zr₃₀Ti₁₀		93	33.8	0.2039	0.1393	[106]
103	Cu₆₀Zr_32.5Ti_7.5		90	32.8	0.2022	0.1397	[89]
104	Cu₅₄Zr_42.5Al_3.5		81.3	29.2	0.1929	0.1422	[107]
105	Cu_53.2Zr_41.8Al₅		85.6	30.9	0.1928	0.1421	[107]
106	Cu_51.5Zr_40.5Al₈		87.4	31.6	0.1924	0.1422	[107]
107	Cu₅₀Zr₄₅Al₅	1.89	84	31	0.1897	0.1432	[89]
108	Cu_57.5Hf_27.5Ti₁₅	1.94	103	37.3		0.1383	[108]
109	Cu₄₇Zr₁₁Ti₃₄Ni₈	1.6			0.2214	0.1370	[89]
110	Cu₆₀Zr₂₀Hf₁₀Ti₁₀		101.1	36.93		0.1392	[55]
111	Cu₆₅Zr₃₅	2.019			0.2026	0.1392	[109,110]
112	Cu_61.4Zr_38.6	1.87			0.1988	0.1404	[109,110]
113	Cu₅₆Zr₄₄	1.82			0.1934	0.1421	[109,110,111]
114	Cu₄₀Zr₆₀	1.333			0.1794	0.1472	[112,113]
115	Cu_33.3Zr_66.7	1.17			0.1744	0.1493	[113]
116	Cu₄₈Zr₄₈Al₄	1.65	88.7	32.4	0.1875	0.1440	[87,114,115]
117	Cu_47.5Zr_47.5Al₅	1.742	87	33	0.1875	0.1440	[87,114,115]
118	Cu₄₇Zr₄₇Al₆	1.834	92.4	33.8	0.1874	0.1439	[87,114,116]
119	Cu₄₆Zr₄₆Al₈	1.926	93.7	34.3	0.1873	0.1439	[116,117]
120	Cu₄₇Ti₃₃Zr₁₁Ni₈Si₁	2.0	100	38.3	0.2181	0.1369	[118,119]
121	Cu₄₇Ti₃₃Zr₁₁Ni₈Fe₁	2.008	102	39	0.2226	0.1368	[119,120]
122	Cu₅₅Zr₃₀Ti₁₀Co₅	2.31	130		0.2075	0.1392	[50]
123	Cu₆₀Hf₃₀Ti₁₀	2.16	124			0.1390	[50]
124	Cu₆₀Hf₁₀Zr₂₀Ti₁₀	1.95	101	36.9		0.1392	[50]
125	Cu₆₀Zr₄₀	1.92	107		0.1974	0.1408	[121]
126	Pt_57.5Cu_14.7Ni_5.3P_22.5	1.4	94.8	33.3	0.2376	0.1346	[122]
127	Pt_74.7Cu_1.5Ag_0.3P₁₈B₄Si_1.5	1.20		32.4		0.1354	[122]
128	Pt₆₀Ni₁₅P₂₅		96	33.8	0.2428	0.1345	[50]
129	Pt₆₀Cu₁₆Co₂P₂₂	1.1	96		0.2359	0.1350	[50]
130	Ag₆₀Cu₄₀		39	12		0.1376	[123]
131	Pd_77.5Cu₆Si_16.5	1.4	89.7	31.8	0.2556	0.1360	[89]
132	Pd₄₀Cu₄₀P₂₀	1.7	93	33.2	0.2360	0.1320	[124]
133	Pd₇₉Cu₆Si₁₀P₅				0.2545	0.1358	[125]
134	Pd_42.5Cu₃₀Ni_7.5P₂₀		101.9	36.5	0.2428	0.1319	[126,127]
135	Pd₈₀Si₂₀	1.3	94.5	33.4	0.2535	0.1364	[89,124,128]
136	Pd₄₀Ni₄₀P₂₀	1.65	108	38.6	0.2702	0.1304	[89,124,128]
137	Pd₄₀Cu₃₀Ni₁₀P₂₀	1.72	92	34.5	0.2444	0.1316	[89,124,128]
138	Pd₈₀P₂₀			33.1	0.2440	0.1356	[89,124,128]
139	Pd₆₄Fe₁₆P₂₀			27.1	0.2516	0.1340	[89,124,128]
140	La₅₅Al₂₅Cu₁₀Ni₅Co₅	0.5	41.9	15.6	0.1124	0.1617	[68]
141	La₆₂Al₁₄(Cu_5/6Ag_1/6)₁₄(Ni_1/2Co_1/2))₁₀	0.65	35	13		0.1668	[83,129,130]
142	La₅₅Al₂₅Co₂₀	0.99	40.9	15.42	0.1185	0.1638	[131]
143	La₅₅Al₁₅Ni₁₀P₂₀	0.5	41		0.1106	0.1627	[50]
144	Ce₇₀Al₁₀Ni₁₀Cu₁₀	0.4	30.3	11.5		0.1669	[50]
145	Ce₆₀Al₁₀Ni₁₀Cu₂₀	0.40	30			0.1615	[132,133]
146	Er₅₀Y₆Al₂₄Co₂₀		71.1	26.98		0.1583	[50]
147	Er₅₅Al₂₅Co₂₀	1.117	70.72	27.08		0.1578	[83,112,131]
148	Al₈₉La₆Ni₅	1.033			0.1735	0.1447	[134,135]
149	Au₄₉Ag_5.5Pd_2.3Cu_26.9Si_16.3	1.12	74.4	26.5		0.1379	[83,136,137]
150	Y₅₅Al₂₅Co₂₀	1.203			0.1304	0.1600	[83,112,131]
151	Pr₅₅Al₂₅Co₂₀	1.007	45.9	17.35		0.1616	[83,112,131]
152	Nd₅₅Al₂₅Co₂₀	0.996				0.1611	[83,112,131]
153	Nd₆₀Al₁₀Fe₂₀Co₁₀	0.45	51	35.1		0.1615	[50]
154	Gd₅₅Al₂₅Co₂₀	0.734				0.1600	[83,112,131]
155	Gd₃₆Y₂₀Al₂₄Co₂₀		62.2	23.6		0.1603	[50]
156	Tb₅₅Al₂₅Co₂₀	0.834	59.53	22.85		0.1589	[83,112,131]
157	Dy₅₅Al₂₅Co₂₀	0.717	61.36	23.52		0.1583	[83,112,131]
158	Ho₅₅Al₂₅Co₂₀	0.869	66.64	25.42		0.1583	[83,112,131]
159	Ho₃₉Al₂₅Co₂₀Y₁₆		69.1	26.2		0.1588	[50]
160	Ta₄₂Ni₃₆Co₂₂	2.7	170			0.1345	[138]
161	Sr₆₀Li₅Mg₁₅Zn₂₀	0.3	19.7	7.71		0.1885	[139]
162	Zn₂₀Ca₂₀Sr₂₀Yb₂₀Li₁₁Mg₉	0.40	16.0	6.3		0.1803	[83]
163	Zn₄₀Mg₁₁Ca₃₁Yb₁₈	0.66	28.8			0.1692	[83]
164	Tm₃₉Al₂₅Co₂₀Y₁₆	1.98	75.0	29.4		0.1580	[140]
165	Lu₄₅Y₁₀Al₂₅Co₂₀	1.89	79.1	31.1		0.1568	[141]