Table 2 Calculated DFT elastic constants, bulk (B), shear (G) and Young’s moduli (E) in GPa, as well as Poisson’s ratio (ν).

From: Predicting elastic properties of hard-coating alloys using ab-initio and machine learning methods

Alloy	SB	c₁₁	c₁₂	c₁₃	c₃₃	c₄₄	B	G	E	ν
AlN	B1	432	167	–	–	307	256	219	511	0.167
HfN	B1	598	112	–	–	129	274	166	414	0.248
Hf_0.75Al_0.25N	B1	524	124	–	–	147	258	166	410	0.235
Hf_0.50Al_0.50N	B1	460	142	–	–	174	248	168	411	0.224
Hf_0.25Al_0.75N	B1	429	158	–	–	221	248	182	439	0.205
Hf_0.75Ti_0.25N	B1	581	113	–	–	134	269	168	417	0.242
Hf_0.50Ti_0.50N	B1	567	119	–	–	142	268	171	423	0.237
Hf_0.25Ti_0.75N	B1	577	122	–	–	153	274	180	443	0.231
Hf_0.75Zr_0.25N	B1	584	109	–	–	128	267	165	410	0.244
Hf_0.50Zr_0.50N	B1	569	108	–	–	128	262	162	403	0.244
Hf_0.25Zr_0.75N	B1	554	107	–	–	127	256	159	395	0.243
TiN	B1	584	136	–	–	166	285	187	460	0.231
Ti_0.75Al_0.25N	B1	535	139	–	–	181	271	187	456	0.22
Ti_0.50Al_0.50N	B1	492	155	–	–	214	268	194	469	0.208
Ti_0.25Al_0.75N	B1	443	161	–	–	250	255	199	474	0.19
ZrN	B1	544	110	–	–	125	255	156	389	0.246
Zr_0.75Al_0.25N	B1	477	124	–	–	139	242	153	379	0.239
Zr_0.50Al_0.50N	B1	427	141	–	–	166	236	156	384	0.229
Zr_0.25Al_0.75N	B1	411	157	–	–	215	242	174	421	0.21
Zr_0.75Ti_0.25N	B1	538	111	–	–	130	253	159	394	0.24
Zr_0.50Ti_0.50N	B1	540	116	–	–	138	257	164	406	0.237
Zr_0.25Ti_0.75N	B1	568	122	–	–	150	271	176	434	0.233
AlN	B3	285	152	–	–	178	196	120	299	0.246
HfN	B3	292	152	–	–	93	199	83	219	0.317
Hf_0.75Al_0.25N	B3	274	144	–	–	100	188	84	219	0.306
Hf_0.50Al_0.50N	B3	261	144	–	–	106	183	84	219	0.301
Hf_0.25Al_0.75N	B3	263	144	–	–	127	183	94	241	0.281
Hf_0.75Ti_0.25N	B3	287	150	–	–	93	196	82	216	0.316
Hf_0.50Ti_0.50N	B3	286	150	–	–	92	195	82	216	0.316
Hf_0.25Ti_0.75N	B3	289	152	–	–	92	198	82	216	0.318
Hf_0.75Zr_0.25N	B3	281	148	–	–	91	193	80	211	0.318
Hf_0.50Zr_0.50N	B3	272	147	–	–	90	189	78	206	0.319
Hf_0.25Zr_0.75N	B3	263	144	–	–	88	184	75	198	0.321
TiN	B3	293	155	–	–	91	201	81	214	0.322
Ti_0.75Al_0.25N	B3	282	154	–	–	103	197	85	223	0.311
Ti_0.50Al_0.50N	B3	274	154	–	–	116	194	89	232	0.301
Ti_0.25Al_0.75N	B3	271	153	–	–	138	192	98	251	0.282
ZrN	B3	258	144	–	–	87	182	73	193	0.323
Zr_0.75Al_0.25N	B3	247	140	–	–	92	176	74	195	0.316
Zr_0.50Al_0.50N	B3	240	142	–	–	98	175	74	195	0.315
Zr_0.25Al_0.75N	B3	253	146	–	–	123	182	88	227	0.292
Zr_0.75Ti_0.25N	B3	262	144	–	–	87	184	74	196	0.323
Zr_0.50Ti_0.50N	B3	269	148	–	–	88	188	76	201	0.322
Zr_0.25Ti_0.75N	B3	282	154	–	–	89	197	78	207	0.325
AlN	B4	376	129	98	352	112	194	121	301	0.242
HfN	B4	253	161	162	220	47	188	44	122	0.391
Hf_0.75Al_0.25N	B4 → B_k	296	204	113	359	107	201	79	210	0.326
Hf_0.50Al_0.50N	B4 → B_k	298	176	145	110	109	135	51	136	0.332
Hf_0.25Al_0.75N	B4	305	140	124	216	87	175	79	206	0.304
Hf_0.75Ti_0.25N	B4 → B_k	298	210	106	493	113	214	85	225	0.325
Hf_0.50Ti_0.50N	B4 → B_k	304	210	103	491	120	214	90	237	0.316
Hf_0.25Ti_0.75N	B4 → B_k	311	212	106	500	128	218	94	247	0.311
Hf_0.75Zr_0.25N	B4 → B_k	292	211	105	495	106	212	81	216	0.331
Hf_0.50Zr_0.50N	B4 → B_k	288	206	102	483	107	208	81	215	0.328
Hf_0.25Zr_0.75N	B4 → B_k	286	201	101	470	107	205	82	217	0.324
TiN	B4 → B_k	322	219	111	524	138	227	100	262	0.308
Ti_0.75Al_0.25N	B4 → B_k	311	212	120	438	138	218	93	244	0.313
Ti_0.50Al_0.50N	B4 → B_k	314	196	128	363	148	211	98	255	0.299
Ti_0.25Al_0.75N	B4	315	136	136	214	88	181	80	209	0.307
ZrN	B4 → B_k	284	195	101	458	106	202	82	217	0.321
Zr_0.75Al_0.25N	B4 → B_k	277	195	108	320	101	188	72	192	0.33
Zr_0.50Al_0.50N	B4 → B_k	287	177	125	202	110	176	74	195	0.316
Zr_0.25Al_0.75N	B4	302	147	122	190	89	169	76	198	0.304
Zr_0.75Ti_0.25N	B4 → B_k	288	200	101	453	110	203	83	219	0.32
Zr_0.50Ti_0.50N	B4 → B_k	297	205	102	461	116	207	87	229	0.316
Zr_0.25Ti_0.75N	B4 → B_k	307	210	105	485	125	215	92	242	0.313

The SB column refers to the Strukturbericht designation. Those B4 systems that relaxed into the Bk structure are marked by B4 → Bk in the SB column.

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Table 2 Calculated DFT elastic constants, bulk (B), shear (G) and Young’s moduli (E) in GPa, as well as Poisson’s ratio (ν).

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