First Principles Study on the Precipitation and Properties of Carbides in the Surface Carburized Layer of Tantalum Alloys

doi:10.11900/0412.1961.2024.00096

Acta Metall Sin

2025, Vol. 61

Issue (5): 797-808 DOI: 10.11900/0412.1961.2024.00096

Research paper

Current Issue | Archive | Adv Search

First Principles Study on the Precipitation and Properties of Carbides in the Surface Carburized Layer of Tantalum Alloys

MENG Xianglong¹, LIU Ruiliang¹(

), Li D. Y.²(

)

1 Key Laboratory of Superlight Material and Surface Technology of Ministry of Education, College of Materials Science and Chemical Engineering, Harbin Engineering University, Harbin 150001, China
2 Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada T6G 1H9

Cite this article:

MENG Xianglong, LIU Ruiliang, Li D. Y.. First Principles Study on the Precipitation and Properties of Carbides in the Surface Carburized Layer of Tantalum Alloys. Acta Metall Sin, 2025, 61(5): 797-808.

Download:

HTML

PDF(1843KB)
Export: BibTeX | EndNote (RIS)

Abstract

Tantalum and its alloys have high melting points and good wear resistance, which are primarily used in fields such as the aerospace and nuclear energy industry. Surface modification techniques such as carburization can be used to obtain a modified layer containing tantalum carbide on the surface of tantalum and its alloys, thereby significantly improving their surface properties. However, the structure and properties of tantalum carbide precipitated on the surface of different tantalum alloys remain unclear. This study focuses on Ta-Mo and Ta-W alloys, and constructs fcc and hcp complex tantalum carbide (Ta, M)C (M = Mo, W) models with different alloying elements and their contents. The energy and mechanical properties of different complex tantalum carbide structures were calculated using the first principles method based on the density functional theory to explore the strengthening and toughening mechanisms of complex tantalum carbides. Calculation results indicate that when the content of Mo and W is less than 50%, fcc structured complex tantalum carbide can be easily formed, and the higher the concentration of Mo and W atoms, the lower the modulus and hardness of the complex tantalum carbide with an fcc structure, and the better the toughness. When the content of Mo and W exceeds 50%, tantalum carbides with an hcp structure are easy to form. As the concentration of Mo and W atoms increases, the modulus and hardness of complex tantalum carbides with an hcp structure increase, whereas the toughness decreases.

Key words: tantalum alloy complex tantalum carbide first-principles calculation crystal structure stability mechanical property

Received: 27 March 2024

ZTFLH:

TG146.4

Fund: National Natural Science Foundation of China(52371060);Natural Science Foundation of Heilongjiang Province(LH2023E060);Fundamental Research Funds for the Central Universities(3072023WD010)

Corresponding Authors: LIU Ruiliang, professor, Tel: (0451)82518731, E-mail: liuruiliang@hrbeu.edu.cn;
D. Y. Li, Tel: (0451)82518731, E-mail: dongyang.li@ualberta.ca

	Service

	E-mail this article
	Add to citation manager
	E-mail Alert
	RSS
	（）
	Articles by authors
	MENG Xianglong
	LIU Ruiliang
	Li D. Y.

URL:

https://www.ams.org.cn/EN/10.11900/0412.1961.2024.00096 OR https://www.ams.org.cn/EN/Y2025/V61/I5/797

Fig.1 Super structural models of the special quasi-random structure (SQS) of complex tantalum carbides
(a) fcc (b) hcp

Crystal structure	Carbide	Lattice constant nm	Angle (°)	Volume nm³	E_f eV·atom^-1	E_c eV·atom^-1
fcc	TaC, this work	$a ¯$ = 0.44781	α = β = γ = 90.00	0.71839	-0.5962	-8.5998
	TaC^[34]	a = 0.447			-0.59
	Ta_0.75Mo_0.25C	$a ¯$ = 0.44554	α = 90.04, β = γ = 90.00	0.70753	-0.4089	-8.1705
	Ta_0.5Mo_0.5C	$a ¯$ = 0.44320	α = β =89.78, γ = 90.22	0.69645	-0.2246	-7.7442
	Ta_0.25Mo_0.75C	$a ¯$ = 0.44061	α = 89.79, β = γ = 90.00	0.68428	-0.0432	-7.6155
	MoC	$a ¯$ = 0.43699	α = β = γ = 90.00	0.66756	0.1400	-6.8956
hcp	Ta₂C	a = b = 0.31249, c = 0.49593	α = β = 90.00, γ = 120.00	0.33551	-0.6163	-8.6566
	(P $3 ¯$ m1, this work)	a = b = 0.31249, c = 0.49593	α = β = 90.00, γ = 120.00
	Ta₂C (P $3 ¯$ m1)^[34]	a = b = 0.311, c = 0.495	γ = 120.00		-0.60
		a = b = 0.311, c = 0.495	γ = 120.00
	Ta_0.75Mo_0.25C	a = 0.45271, b = 0.45256, c = 0.43049	α = 90.05, β = 89.96, γ = 120.01	0.68590	-0.1681	-7.9208


	Ta_0.5Mo_0.5C	a = 0.44703, b = 0.44702, c = 0.42883	α = 90.07, β = 89.98, γ = 120.01	0.59361	-0.1616	-7.6633


	Ta_0.25Mo_0.75C	a = 0.44261, b = 0.44227, c = 0.42681	α = 89.99, β = 90.01, γ = 120.02	0.57870	-0.1610	-7.4476


	MoC	a = b = 0.43761, c = 0.42422	α = β = 90.00, γ = 120.00	0.56283	-0.1519	-7.1876
		a = b = 0.43761, c = 0.42422	α = β = 90.00, γ = 120.00

Table 1 Crystallographic parameters, formation energy (E_f), and cohesive energy (E_c) of complex tantalum carbide with Mo

Fig.2 E_c (a) and E_f (b) of complex tantalum carbide containing Mo with different structures

Crystal structure	Carbide	Lattice constant nm	Angle (°)	Volume nm³	E_f eV·atom^-1	E_c eV·atom^-1
fcc	TaC, this work	$a ¯$ =0.44781	α = β = γ = 90.00	0.71839	-0.5962	-8.5998
	TaC^[34]	a = 0.447			-0.59
	Ta_0.75W_0.25C	$a ¯$ = 0.44543	α = 90.00, β = 89.99, γ = 90.00	0.70699	-0.3759	-8.6364


	Ta_0.5W_0.5C	$a ¯$ = 0.44339	α = 89.79, β = 90.19, γ = 90.06	0.69731	-0.1566	-8.2123


	Ta_0.25W_0.75C	$a ¯$ = 0.44096	α = β = 90.00, γ = 90.06	0.68590	0.0565	-8.3138
			α = β = 90.00, γ = 90.06
	WC	$a ¯$ = 0.43821	α = β = γ = 90.00	0.67320	0.2909	-7.8169
hcp	Ta₂C	a = b = 0.31249, c = 0.49593	α = β = 90.00, γ = 120.00	0.33551	-0.6163	-8.6566
	(P $3 ¯$ m1, this work)	a = b = 0.31249, c = 0.49593	α = β = 90.00, γ = 120.00
	Ta₂C (P $3 ¯$ m1)^[34]	a = b = 0.311, c = 0.495	γ = 120		-0.60
		a = b = 0.311, c = 0.495
	Ta_0.75W_0.25C	a = 0.45263, b = 0.45262, c = 0.43127	α = 89.94, β =90.08, γ = 120.00	0.61212	-0.1640	-8.1946


	Ta_0.5W_0.5C	a = 0.44731, b = 0.44718, c = 0.43034	α = 89.93, β = 89.98, γ = 120.00	0.59638	-0.1561	-8.2137


	Ta_0.25W_0.75C	a = 0.44306, b = 0.44305, c = 0.42889	α = 90.00, β = 89.99, γ = 119.99	0.58335	-0.1573	-8.2381


	WC	a = b =0.43868, c = 0.42730	α = β = 90.00, γ = 120.00	0.56968	-0.1543	-8.2621
		a = b =0.43868, c = 0.42730	α = β = 90.00, γ = 120.00

Table 2 Lattice parameters, E_f, and E_c of complex tantalum carbide with W

Fig.3 Energy of complex tantalum carbides containing W with different structures
(a) E_c (b) E_f

Carbide (fcc)	C₁₁ ( $C ¯$ ₁₁) GPa	C₁₂ ( $C ¯$ ₁₂) GPa	C₄₄ ( $C ¯$ ₄₄) GPa	G GPa	B GPa	E GPa	H_V GPa	G / B	$ν$
TaC, this work	720	134	154	200	330	500	21.8	0.607	0.25
TaC^[34]	737	141	175	216.90	339.67		24.53
Ta_0.75Mo_0.25C	668	138	152	167	302	423	20.9	0.605	0.25
Ta_0.5Mo_0.5C	576	165	146	151	310	389	17.0	0.554	0.27
Ta_0.25Mo_0.75C	581	174	123	122	339	327	13.2	0.486	0.29
MoC	684	166	70	200	331	499	7.0	0.360	0.34
Ta_0.75W_0.25C	715	139	156	179	310	450	21.5	0.603	0.25
Ta_0.5W_0.5C	630	150	147	156	341	407	18.8	0.577	0.26
Ta_0.25W_0.75C	611	207	132	129	370	346	12.4	0.458	0.30
WC	769	170	67	200	330	500	7.0	0.348	0.34

Table 3 Elastic constants and mechanical properties of complex tantalum carbides with fcc structure

Carbide (hcp)	C₁₁	C₁₂	C₁₃	C₃₃	C₄₄
Ta₂C (P $3 ¯$ m1, this work)	480	143	138	498	120
Ta₂C (P $3 ¯$ m1)^[34]	479	164	149	504	133
Ta_0.75Mo_0.25C	511	194	138	764	120
Ta_0.5Mo_0.5C	532	203	151	783	157
Ta_0.25Mo_0.75C	568	206	159	811	203
MoC	618	213	159	854	263
Ta_0.75W_0.25C	537	197	138	787	130
Ta_0.5W_0.5C	581	209	154	823	181
Ta_0.25W_0.75C	621	224	164	878	235
WC	699	232	167	953	302

Table 4 Elastic constants of complex tantalum carbides with hcp structure

Carbide (hcp)	G GPa	B GPa	E GPa	H_v GPa	G / B GPa	$ν$
Ta₂C (P $3 ¯$ m1, this work)	149	255	374	16.9	0.583	0.26
Ta₂C (P $3 ¯$ m1)^[34]	148.08	264.66		15.87
Ta_0.75Mo_0.25C	160	300	407	15.6	0.532	0.27
Ta_0.5Mo_0.5C	180	315	454	18.8	0.573	0.26
Ta_0.25Mo_0.75C	209	330	517	23.6	0.632	0.24
MoC	246	348	597	30.3	0.706	0.21
Ta_0.75W_0.25C	171	310	433	17.2	0.552	0.27
Ta_0.5W_0.5C	203	333	507	22.1	0.609	0.25
Ta_0.25W_0.75C	234	356	576	26.8	0.658	0.23
WC	282	385	681	34.7	0.732	0.21

Table 5 Mechanical properties of complex tantalum carbides with hcp structure

Fig.4 Mechanical properties of complex tantalum carbide containing Mo with different structures
(a) modulus
(b) Vickers hardness
(c) G / Bvs Poisson's ratio

Fig.5 Mechanical properties of complex tantalum carbide containing W with different structures
(a) modulus
(b) Vickers hardness
(c) G / Bvs Poisson's ratio

Fig.6 Total and projected density of states (DOS) of the same component in multi-component carbides in different crystal structures (The dashed lines indicate the Fermi energy levels; TDOS—total density of states)
(a) Ta_0.5Mo_0.5C (fcc) (b) Ta_0.5Mo_0.5C (hcp) (c) Ta_0.5W_0.5C (fcc) (d) Ta_0.5W_0.5C (hcp)

Fig.7 f_m values of complex tantalum carbide containing Mo (a) and W (b) with different structures (f_m is an indicator of metal bonding strength)

Table 6 Average Bader charge of each atom in complex tantalum carbide with different structures

1	Taberna P L, Simon P, Fauvarque J F. Electrochemical characteristics and impedance spectroscopy studies of carbon-carbon supercapacitors [J]. J. Electrochem. Soc., 2003, 150: A292
2	Mani G, Porter D, Grove K, et al. A comprehensive review of biological and materials properties of tantalum and its alloys [J]. J. Biomed. Mater. Res., 2022, 110A: 1291
3	Massot L, Chamelot P, Taxil P. Preparation of tantalum carbide films by reaction of electrolytic carbon coating with the tantalum substrate [J]. J. Alloys Compd., 2006, 424: 199
4	Wang Z H. Advances on surface treatment process of tantalum [J]. Heat Treat. Met., 2024, 49: 259
	王哲昊. 金属钽表面处理工艺进展 [J]. 金属热处理, 2024, 49: 259
5	Carette L, Jacquet P, Cotton D, et al. (TaC/Ta₂C) bilayer formed on carburized and annealed tantalum; development of a numerical growth model [J]. Appl. Surf. Sci., 2019, 467-468: 84
6	Zhao Z Y, Cao L, Liang F, et al. A new strategy for preparing carbide coatings on easily oxidized tantalum by non-vacuum carburizing: Fe-coating-mediated carburization [J]. Vacuum, 2024, 221: 112951
7	Tang Q H, Zhuang X L, Fang J F, et al. Surface carburising of tantalum and its alloys [J]. Rare. Met., 1991, (2): 116
	唐全红, 庄祥麟, 方金法等. 钽及其合金的表面渗碳强化 [J]. 稀有金属, 1991, (2): 116
8	Zheng X. Surface treatment to improve the corrosion resistance of tantalum [J]. Rare. Met. Lett., 2002, (4): 21
	郑欣. 提高钽耐蚀性的表面处理法 [J]. 稀有金属快报, 2002, (4): 21
9	Zhou H L, Hu Y, Zhu K W, et al. Surface modification of tantalum sheets by methane plasma carburizing [J]. Chin. J. Vac. Sci. Technol., 2018, 38A: 48
	周寰林, 胡殷, 朱康伟等. 钽表面的甲烷等离子渗碳改性技术研究 [J]. 真空科学与技术学报, 2018, 38: 48
10	Zhou H L. Study of ionic carburisation modification of tantalum surfaces [D]. Mianyang: China Academy of Engineering Physics, 2017
	周寰林. 钽表面离子渗碳改性研究 [D]. 绵阳: 中国工程物理研究院, 2017
11	Li J, Yan X D, Yang Y, et al. Vacuum carburization process of Ta and Ta-W alloys [J]. Chin. J. Rare Met., 2018, 42: 925
	李佳, 闫晓东, 杨银等. Ta及Ta-W合金真空渗碳工艺研究 [J]. 稀有金属, 2018, 42: 925
12	Hui P F. Microstructure and properties of carbide coatings on metal (Ta, Mo, Ti6Al4V) surface prepared by interstitial carburization [D]. Xi'an: Xi'an University of Technology, 2019
	惠鹏飞. 间隙原子渗碳法制备金属(Ta、Mo、Ti6Al4V)表面碳化层的组织和性能研究 [D]. 西安: 西安理工大学, 2019
13	Zhang C, Yin H Q, Du Y, et al. Thermodynamic modeling of the Ta-Mo-C ternary system [J]. Calphad, 2017, 59: 99
14	Frisk K. A thermodynamic analysis of the Ta-W-C and the Ta-W-C-N systems [J]. Int. J. Mater. Res., 1999, 90: 704
15	Junquera J, Ghosez P. Critical thickness for ferroelectricity in perovskite ultrathin films [J]. Nature, 2003, 422: 506
16	Khazaei M, Arai M, Sasaki T, et al. Novel electronic and magnetic properties of two-dimensional transition metal carbides and nitrides [J]. Adv. Funct. Mater., 2013, 23: 2185
17	Sarker P, Harrington T, Toher C, et al. High-entropy high-hardness metal carbides discovered by entropy descriptors [J]. Nat. Commun., 2018, 9: 4980 doi: 10.1038/s41467-018-07160-7 pmid: 30478375
18	Liu R L, Li D Y. Electron work function as an indicator for tuning the bulk modulus of MC carbide by metal-substitution: A first-principles computational study [J]. Scr. Mater., 2021, 204: 114148
19	Kresse G, Furthmüller J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set [J]. Phys. Rev., 1996, 54B: 11169
20	Kresse G, Joubert D. From ultrasoft pseudopotentials to the projector augmented-wave method [J]. Phys. Rev., 1999, 59B: 1758
21	Perdew J P, Burke K, Ernzerhof M. Generalized gradient approximation made simple [J]. Phys. Rev. Lett., 1996, 77: 3865 doi: 10.1103/PhysRevLett.77.3865 pmid: 10062328
22	Monkhorst H J, Pack J D. Special points for Brillouin-zone integrations [J]. Phys. Rev., 1976, 13B: 5188
23	Liu Z T Y, Gall D, Khare S V. Electronic and bonding analysis of hardness in pyrite-type transition-metal pernitrides [J]. Phys. Rev., 2014, 90B: 134102
24	Yang Y, Wang W, Gan G Y, et al. Structural, mechanical and electronic properties of (TaNbHfTiZr)C high entropy carbide under pressure: Ab initio investigation [J]. Phys. Rev., 2018, 550B: 163
25	Tasnádi F, Odén M, Abrikosov I A. Ab initio elastic tensor of cubic Ti_0.5Al_0.5N alloys: Dependence of elastic constants on size and shape of the supercell model and their convergence [J]. Phys. Rev., 2012, 85B: 144112
26	Hossain M D, Borman T, Kumar A, et al. Carbon stoichiometry and mechanical properties of high entropy carbides [J]. Acta Mater., 2021, 215: 117051
27	Wu Z J, Zhao E J, Xiang H P, et al. Crystal structures and elastic properties of superhard IrN₂ and IrN₃ from first principles [J]. Phys. Rev., 2007, 76B: 054115
28	Shi Y J, Du Y L, Chen G. First-principles study on the elastic and electronic properties of hexagonal ε-Fe₃N [J]. Comput. Mater. Sci., 2013, 67: 341
29	Hill R. The elastic behaviour of a crystalline aggregate [J]. Proc. Phys. Soc., 1952, 65A: 349
30	Chen X Q, Niu H Y, Li D Z, et al. Modeling hardness of polycrystalline materials and bulk metallic glasses [J]. Intermetallics, 2011, 19: 1275
31	Van De Walle A, Asta M, Ceder G. The alloy theoretic automated toolkit: A user guide [J]. Calphad, 2002, 26: 539
32	Zunger A, Wei S H, Ferreira L G, et al. Special quasirandom structures [J]. Phys. Rev. Lett., 1990, 65: 353 pmid: 10042897
33	Mattheiss L F, Hamann D R. Bulk and surface electronic structure of hexagonal WC [J]. Phys. Rev., 1984, 30B: 1731
34	Yu X X, Weinberger C R, Thompson G B. Ab initio investigations of the phase stability in tantalum carbides [J]. Acta Mater., 2014, 80: 341
35	Liu R L, Zhang D, Tang Y Q, et al. (W_{1 -} _x, M_x ) C carbides with desired combinations of compatible density and properties—A first-principles study [J]. J. Am. Ceram. Soc., 2021, 104: 4239
36	Edström D, Sangiovanni D G, Hultman L, et al. Elastic properties and plastic deformation of TiC- and VC-based pseudobinary alloys [J]. Acta Mater., 2018, 144: 376
37	Zhao S J. Defect energetics and stacking fault formation in high-entropy carbide ceramics [J]. J. Eur. Ceram. Soc., 2022, 42: 5290
38	Shao L, Jiang H H, Xu C R, et al. The lattice distortion, mechanical and thermodynamic properties of A(Zr_0.2Sn_0.2Ti_0.2Hf_0.2Nb_0.2)O₃ (A = Sr, Ba) high-entropy perovskite with B-site disorder: First principles prediction [J]. Mater. Des., 2022, 224: 111308
39	Blakemore J S. Solid State Physics [M]. Cambridge: Cambridge University Press, 1985: 1

[1]	LEI Yunlong, YANG Kang, XIN Yue, JIANG Zitao, TONG Baohong, ZHANG Shihong. Microstructure Evolution of Mechanically-Alloying and Its Subsequently-Annealed AlCrCu_0.5Mo_0.5Ni High-Entropy Alloy[J]. 金属学报, 2025, 61(5): 731-743.
[2]	SUN Jun, LIU Gang, YANG Chong, ZHANG Peng, XUE Hang. Heat-Resistant Al Alloys: Microstructural Design and Preparation[J]. 金属学报, 2025, 61(4): 521-525.
[3]	CAI Zhengqing, YIN Dawei, YANG Liang, WANG Wenxiang, WANG Feilong, WEN Yongqing, MA Mingzhen. Effect of Ag Substitution of Cu on Properties of Zr-Ti-Cu-Al Amorphous Alloys[J]. 金属学报, 2025, 61(4): 572-582.
[4]	YANG Minghui, LI Xingwu, SUN Chonghao, RUAN Ying. Microstructure and Mechanical Properties of Monel K-500 Alloy in Synergetic Modulation of Directional Solidification and Thermal Processing[J]. 金属学报, 2025, 61(4): 561-571.
[5]	WANG Sheng, ZHU Yancheng, PAN Hucheng, LI Jingren, ZENG Zhihao, QIN Gaowu. Effect of Yb Content on Microstructure and Mechanical Property of Mg-Gd-Y-Zn-Zr Alloy[J]. 金属学报, 2025, 61(3): 499-508.
[6]	PANG Mengyao, WU Ruizhi, MA Xiaochun, JIN Siyuan, YU Zhe, Boris Krit. Effect of Hot Rolling Process on Mechanical Property and Corrosion Behavior of Rapidly Degrading Mg-Li Alloy[J]. 金属学报, 2025, 61(3): 509-520.
[7]	OUYANG Sihui, SHE Jia, CHEN Xianhua, PAN Fusheng. Preparation of Biodegradable Mg-Based Composites and Their Recent Advances in Orthopedic Applications[J]. 金属学报, 2025, 61(3): 455-474.
[8]	DAI Jincai, MIN Xiaohua, XIN Shewei, LIU Fengjin. Effect of Interstitial Element O on Cryogenic Mechanical Properties in β-Type Ti-15Mo Alloy[J]. 金属学报, 2025, 61(2): 243-252.
[9]	ZHAO Yanan, GUO Qianying, LIU Chenxi, MA Zongqing, LIU Yongchang. Effects of Subsequent Heat Treatment on Microstructure and High-Temperature Mechanical Properties of Laser 3D Printed GH4099 Alloy[J]. 金属学报, 2025, 61(1): 165-176.
[10]	ZHANG Shengyu, MA Qingshuang, YU Liming, ZHANG Jingwen, LI Huijun, GAO Qiuzhi. Effect of Pre-Aging on Microstructure and Properties of Cold-Rolled Alumina-Forming Austenitic Steel[J]. 金属学报, 2025, 61(1): 177-190.
[11]	ZHU Man, ZHANG Cheng, XU Junfeng, JIAN Zengyun, XI Zengzhe. Microstructure, Mechanical Properties, and High-Temperature Oxidation Behaviors of the CrNbTiVAl _x Refractory High-Entropy Alloys[J]. 金属学报, 2025, 61(1): 88-98.
[12]	WAN Jie, LI Haotian, LIU Shuji, LU Hongzhou, WANG Lisheng, ZHANG Zhendong, LIU Chunhai, JIA Jianlei, LIU Haifeng, CHEN Yuzeng. Homogenization of Nuclei in Al-Nb-B Inoculant and Its Effect on Microstructure and Mechanical Properties of Cast Al Alloy[J]. 金属学报, 2025, 61(1): 117-128.
[13]	ZHANG Qiankun, HU Xiaofeng, JIANG Haichang, RONG Lijian. Effect of Si on Microstructure and Mechanical Properties of a 9Cr Ferritic/Martensitic Steel[J]. 金属学报, 2024, 60(9): 1200-1212.
[14]	ZHOU Mu, WANG Qian, WANG Yanxu, ZHAI Zirong, HE Lunhua, LI Bing, MA Yingjie, LEI Jiafeng, YANG Rui. Effect of Prewelding Pretreatment on Welding Residual Stress of Titanium Alloy Thick Plate[J]. 金属学报, 2024, 60(8): 1064-1078.
[15]	CHEN Cheng, YANG Guangyu, JIN Menghui, WANG Qiang, TANG Xin, CHENG Huimin, JIE Wanqi. Effect of the Mold Positive and Negative Rotation on the Microstructure and Room-Temperature Mechanical Properties of K4169 Superalloy[J]. 金属学报, 2024, 60(7): 926-936.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Shared

Discussed