Compositions and properties of typical abrasives, carbides, and oxides
Compound	Main element	Crystal system	Mohs hardness	Vickers hardness (HV)	Remarks
Fe₃C (Cementite)	Fe	Orthorhombic	6—6.5	≈ 800—1000	Carbide found in carbon and tool steels. Easily polished with natural stones.
SiO₂ (Quartz)	Si	Hexagonal	7	≈ 1100	Main abrasive component of natural stones; relatively soft.
Cr₂O₃ (Chromium(III) oxide)	Cr	Hexagonal	8.5	≈ 1200	Main component of green buffing compound ("green rouge"). Used for leather strops.
Al₂O₃ (α-Alumina)	Al	Trigonal	9	≈ 1400—1800	Main component of WA (white alumina) whetstones; a reference standard for many sharpening stones.
Cr₃C₂/Cr₇C₃ (Chromium carbide)	Cr	Orthorhombic / Hexagonal	8—9	≈ 1200—2300	A relatively "sharpenable" carbide; can be abraded with natural stones given sufficient time.
Mo₂C (Molybdenum carbide)	Mo	Hexagonal	8—9	≈ 1500—1800	Present in small amounts in powder high-speed steels; hardness close to α-alumina.
TaC (Tantalum carbide)	Ta	Cubic	9—9.7	≈ 1900—2200	High melting point and high hardness; somewhat brittle.
NbC (Niobium carbide)	Nb	Cubic	9—9.5	≈ 2000—2600	Similar hardness to VC; found in CPM S110V and Magnacut powder steels.
WC (Tungsten carbide)	W	Hexagonal	9—9.5	≈ 2400—2900	Main component of cemented carbide tools.
SiC (Silicon carbide)	Si	Hexagonal / Cubic	≈ 9.5	≈ 2500—2800	Main component of GC (green carborundum) stones; harder than natural stones.
VC (Vanadium carbide)	V	Cubic	9.5—9.8	≈ 2800—3000	Abundant in 15V, 10V, 20CP, S110V, S90V and K390 steels; extremely hard.
cBN (Cubic boron nitride)	B, N	Cubic	≈ 9.8	≈ 4500—4800	Second only to diamond; suitable for grinding ferrous materials.
C (Diamond)	C	Cubic (sp³)	10	≈ 8000—10000	Highest hardness; reacts with iron at high temperatures.

Hard-to-Sharpen (HTS) Index for Blade Steels

Although the actual ease of sharpening also depends on heat treatment and microstructure, it is often practical to estimate the hardness to sharpen from the intrinsic hardness and the total fraction of carbide-forming elements in the alloy.

We propose the following empirical formula as a Hard-to-Sharpen (HTS) index — representing the hardness from the viewpoint of sharpening :

HTS index = (α k (Si + Cr + Mo) + W + V + Nb)^β · (1 + 0.087 W + 0.104 V + 0.065 Nb + δ Mo + γ k (0.015 Si + 0.038 Cr + 0.034 Mo))
α = 0.6 — Soft carbide contribution compensation
β = 1.2 — Carbide volume compensation factor
γ = 0.015 — Soft carbide compensation
δ = -0.2 — Mo degeneration compensation
k = max(0, C_rem / C_req,sec) — Correction factor for secondary carbide formation
C_rem = min(1, max(0, C - C_req,pri)) — Residual wt% C after primary carbide formation
C_req,pri = 0.065 W + 0.236 V + 0.129 Nb — wt% C required for primary carbide-forming metals
C_req,sec = 0.428 Si + 0.099 Cr + 0.063 Mo — wt% C required for secondary carbide-forming metals

Here, Si, Mo, W, V, Nb and Cr represent the weight percentages of each element. The max() and min() function return the larger or smaller of the given arguments, respectively.

Naturally, not all of the available carbon is strictly consumed by the primary carbide-forming elements. However, for simplicity — and to emphasize the practical influence of hard carbides on sharpening difficulty — this assumption is acceptable in the present formulation.

Note: Although Si is technically a metalloid, it is commonly treated as a carbide-forming element in metallurgical contexts.

Features of the HTS index

Main component: (αk (Si + Cr + Mo) + W + V + Nb)^β
- Proportional to the total amount of carbide-forming elements, with an exponent slightly above unity (β = 1.2) to reflect the empirical trend that sharpening difficulty increases more than linearly with carbide content.
Compensation term: (1 + 0.087 W + 0.104 V + 0.065 Nb + δ Mo + γ k (0.015 Si + 0.038 Cr + 0.034 Mo))
- W, V and Nb promote the formation of very hard carbides and therefore contribute positively.
- Mo tends to refine and homogenize carbides, increasing the smoothness of abrasion and making sharpening slightly easier, hence the negative correction (δ = -0.2).
- The k factor represents whether sufficient carbon remains available for the formation of secondary carbides.
- Overall, this term provides a simple, weighted adjustment based on the relative hardness contributions of each element.

Compositions and HTS indices of typical knife steels
Elements[%] Steels	HTS index	C	Si	Cr	Mo	W	V	Nb	Mn	Co	Type	Note
Maxamet	97.20	2.15	0.25	4.75	0	13	6	0	0.3	10	Tool
CPM REX T15	77.99	1.6	0.3	4	0	12	4.9	0	0.3	5	Tool
CPM 15V	60.90	3.4	0.9	5.25	1.3	0	14.5	0	0.5	0	Tool
CPM S125V	48.67	3.25	0.9	14	2.5	0.4	12	0	0.5	0	Stainless
CPM S110V	44.96	2.9	0.6	15.25	2.25	0.2	9.1	3	0.4	2.5	Stainless
Z-Max PM	41.56	2	0	4	5	10	5	0	0	9	Tool
M398	38.62	2.7	0.5	20	1	0.7	7.2	0	0.5	0	Stainless
CPM 10V	31.65	2.45	0.9	5.25	1.3	0	9.75	0	0.5	0	Tool
CPM S90V	30.00	2.3	0	14	1	0	9	0	0	0	Stainless
CPM REX 76	28.17	1.5	0.3	3.75	5.25	9.75	3.1	0	0.3	8.5	Tool
CTS 20CP	26.91	2.2	0.9	13	1.3	0	9.3	0	0.5	0	Stainless
K390	26.52	2.47	0.55	4.2	3.8	1	9	0	0.4	2	Tool
CPM S60V	26.05	2.15	0.4	17	0.4	0	5.5	0	0.4	0	Stainless
MagnaMax	21.62	2.04	0	10.65	2	0	8	0	0.5	0	Stainless	0.2%N
CPM 20CV	21.11	1.9	0.3	20	1	0.6	4	0	0.3	0	Stainless
M390	20.35	1.9	0.7	20	1	0.6	4	0	0.3	0	Stainless
ZDP-189	18.10	3	0.4	20	1.4	0.6	0	0	0.5	0	Stainless
CPM M4	15.26	1.4	0.55	4	5.25	5.5	4	0	0.3	0	Tool
CPM REX 45	14.97	1.3	0.5	4.05	5	6.25	3.05	0	0.3	8	Tool
Elmax	14.91	1.7	0.8	18	1	0	3	0	0.3	0	Stainless
HAP40	14.79	1.3	0	4	5	6	3	0	0	8	Tool
CTS XHP	12.57	1.6	0.4	16	0.8	0	0.45	0	0.5	0	Stainless	0.35%Ni
SPG STRIX ?4	12.38	1.6	0.19	15.86	2.73	1.08	1.99	0.33	0.14	0	Stainless	Japan Pat.7606235
CPM S45VN	11.99	1.48	0	16	2	0	3	0.5	0	0	Stainless
D-2	11.79	1.55	0.45	11.5	0.9	0	0.8	0	0.35	0	Tool
CPM S30V	11.55	1.45	0	14	2	0	4	0	0	0	Stainless
CPM S35VN	10.89	1.38	0	14	2	0	3	0.5	0	0	Stainless
CPM Cru-Wear	10.45	1.15	0	7.5	1.6	1	2.4	0	0	0	Tool
CPM MagnaCut	10.35	1.15	0	10.7	2	0	4	2	0	0	Stainless
CPM SPY27	8.92	1.25	0.5	14	2	0	2	1	0.5	1.5	Stainless
CPM 4V	7.64	1.35	0.8	5	2.95	0	3.85	0	0.4	0	Tool
Super Gold 2	7.64	1.4	0.45	15	2.8	0	2	0	0	0	Stainless
440C	7.47	1	0.3	17.5	0.5	0	0	0	0.5	0	Stainless
ATS-55	7.06	1	0.4	14	0.6	0	0	0	0.5	0.4	Stainless
VG10W	7.02	1	0.6	15	1	0.4	0.25	0	0.5	1.55	Stainless
AUS-10	6.92	1.025	1	13.75	0.205	0	0.185	0	0.5	0	Stainless	0.49%Ni
9Cr18Mo	6.89	1.025	0.8	17	0.55	0	0	0	0.8	0	Stainless
Cobalt Special	6.40	1.05	0.65	16	1.5	0.25	0.25	0	0.4	2.5	Stainless	0.25%Ni
VG10	6.38	1	0.6	15	1	0	0.25	0	0.5	1.55	Stainless
GIN-1	6.16	0.85	0.35	16	0.4	0	0	0	0.6	0	Stainless
8Cr13MoV	5.69	0.8	0.5	13	0.15	0	0.1	0	0.4	0	Stainless	0.2%Ni
CTS BD1N	5.68	0.9	1	16	0.5	0	0	0	1	0	Stainless
CPM 3V	5.17	0.8	0	7.5	1.3	0	2.75	0	0	0	Tool
AEB-L	4.81	0.67	0.4	13	0	0	0	0	0.6	0	Stainless
Blue Super Steel	4.73	1.45	0.15	0.4	0.4	2.25	0.4	0	0.25	0	Tool	Aogami Super
AUS-8	4.55	0.725	1	13.75	0.2	0	0.18	0	0.5	0	Stainless	0.49%Ni
Sandvik 12C27	4.23	0.6	0.4	13.5	0	0	0	0	0.4	0	Stainless
AUS-6	3.73	0.6	1	13.75	0	0	0.175	0	1	0	Stainless	0.49%Ni
420HC	3.15	0.46	0.3	13	0	0	0	0	0.4	0	Stainless
V-Toku2	2.49	1.05	0.45	0.35	0	1.25	0.2	0	0	0	Tool	0.25%Ni
RWL34	2.05	1.05	0.5	14	4	0	0.2	0	0.5	0	Stainless
154CM	1.96	1.05	0.3	14	4	0	0	0	0	0	Stainless
ATS-34	1.94	1.05	0.35	14	4	0	0	0	0.4	0	Stainless
LC200N	1.59	0.3	0.3	15	0.95	0	0	0	1	0	Stainless	0.5%Ni
Blue Steel 2	0.98	1.1	0.15	0.3	0.4	0.5	0	0	0.25	0	Tool	Aogami 2
420J2	0.69	0.15	1	13	0	0	0	0	1	0	Stainless
H-1	0.40	0.15	3.75	15	1	0	0	0	2	0	Stainless	7%Ni
SK5	0.18	0.85	0.25	0.15	0	0	0	0	0.3	0	Carbon
H-2	0.17	0.09	2.63	13.73	2.24	0	0	0	0.31	0	Stainless	8.25%Ni
1095	0.10	0.965	0.25	0	0	0	0	0	0.4	0	Carbon
White Steel 1	0.06	1.3	0.15	0	0	0	0	0	0.25	0	Carbon	Shirogami 1

Note: The values in the table are representative or estimated. Errors may exist. Please refer to manufacturer data for accurate specifications. Formulas and parameters are subject to change without notice.

Why Some Steels Are Harder to Sharpen

Toward a Hard-to-Sharpen Index

Comparison of Hardness among Abrasives, Carbides, and Oxides

Hard-to-Sharpen (HTS) Index for Blade Steels

Features of the HTS index

Conclusions or something like that