Abstract: A cutting element comprises a supporting substrate, and a cutting table attached to an end of the supporting substrate. The cutting table comprises inter-bonded diamond particles, and a thermally stable material within interstitial spaces between the inter-bonded diamond particles. The thermally stable material comprises a carbide precipitate having the general chemical formula, A3XZn-1, where A comprises one or more of Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Ac, Th, Pa, and U; X comprises one or more of Al, Ga, Sn, Be, Bi, Te, Sb, Se, As, Ge, Si, B, and P; Z comprises C; and n is greater than or equal to 0 and less than or equal to 0.75. A method of forming a cutting element, an earth-boring tool, a supporting substrate, and a method of forming a supporting substrate are also described.

Abstract: A cutting element comprises a supporting substrate, and a cutting table attached to an end of the supporting substrate. The cutting table comprises inter-bonded diamond particles, and a thermally stable material within interstitial spaces between the inter-bonded diamond particles. The thermally stable material comprises a carbide precipitate having the general chemical formula, A3XZn-1, where A comprises one or more of Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Ac, Th, Pa, and U; X comprises one or more of Al, Ga, Sn, Be, Bi, Te, Sb, Se, As, Ge, Si, B, and P; Z comprises C; and n is greater than or equal to 0 and less than or equal to 0.75. A method of forming a cutting element, an earth-boring tool, a supporting substrate, and a method of forming a supporting substrate are also described.

Abstract: A method of forming a supporting substrate for a cutting element comprises forming a precursor composition comprising discrete WC particles, a binding agent, and discrete particles comprising Co, one or more of Al, Be, Ga, Ge, Si, and Sn, and one or more of C and W. The precursor composition is subjected to a consolidation process to form a consolidated structure including WC particles dispersed in a homogenized binder comprising Co, W, C, and one or more of Al, Be, Ga, Ge, Si, and Sn. A method of forming a cutting element, a cutting element, a related structure, and an earth-boring tool are also described.

Abstract: A cutting element comprises a supporting substrate, and a cutting table attached to an end of the supporting substrate. The cutting table comprises inter-bonded diamond particles, and a thermally stable material within interstitial spaces between the inter-bonded diamond particles. The thermally stable material comprises a carbide precipitate having the general chemical formula, A3XZn-1, where A comprises one or more of Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Ac, Th, Pa, and U; X comprises one or more of Al, Ga, Sn, Be, Bi, Te, Sb, Se, As, Ge, Si, B, and P; Z comprises C; and n is greater than or equal to 0 and less than or equal to 0.75. A method of forming a cutting element, an earth-boring tool, a supporting substrate, and a method of forming a supporting substrate are also described.

Abstract: A cutting element comprises a supporting substrate, and a cutting table attached to an end of the supporting substrate. The cutting table comprises inter-bonded diamond particles, and a thermally stable material within interstitial spaces between the inter-bonded diamond particles. The thermally stable material comprises a carbide precipitate having the general chemical formula, A3XZn-1, where A comprises one or more of Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Ac, Th, Pa, and U; X comprises one or more of Al, Ga, Sn, Be, Bi, Te, Sb, Se, As, Ge, Si, B, and P; Z comprises C; and n is greater than or equal to 0 and less than or equal to 0.75. A method of forming a cutting element, an earth-boring tool, a supporting substrate, and a method of forming a supporting substrate are also described.

Abstract: A cutting element comprises a supporting substrate, and a cutting table attached to an end of the supporting substrate. The cutting table comprises inter-bonded diamond particles, and a thermally stable material within interstitial spaces between the inter-bonded diamond particles. The thermally stable material comprises a carbide precipitate having the general chemical formula, A3XZn-1, where A comprises one or more of Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Ac, Th, Pa, and U; X comprises one or more of Al, Ga, Sn, Be, Bi, Te, Sb, Se, As, Ge, Si, B, and P; Z comprises C; and n is greater than or equal to 0 and less than or equal to 0.75. A method of forming a cutting element, an earth-boring tool, a supporting substrate, and a method of forming a supporting substrate are also described.

Abstract: A method of forming a supporting substrate for a cutting element comprises forming a precursor composition comprising discrete WC particles, a binding agent, and discrete particles comprising Co, one or more of Al, Be, Ga, Ge, Si, and Sn, and one or more of C and W. The precursor composition is subjected to a consolidation process to form a consolidated structure including WC particles dispersed in a homogenized binder comprising Co, W, C, and one or more of Al, Be, Ga, Ge, Si, and Sn. A method of forming a cutting element, a cutting element, a related structure, and an earth-boring tool are also described.

Abstract: A method of forming a supporting substrate for a cutting element comprises forming a precursor composition comprising discrete WC particles, a binding agent, and discrete particles comprising Co, one or more of Al, Be, Ga, Ge, Si, and Sn, and one or more of C and W. The precursor composition is subjected to a consolidation process to form a consolidated structure including WC particles dispersed in a homogenized binder comprising Co, W, C, and one or more of Al, Be, Ga, Ge, Si, and Sn. A method of forming a cutting element, a cutting element, a related structure, and an earth-boring tool are also described.

Abstract: A method of forming a supporting substrate for a cutting element comprises forming a precursor composition comprising discrete WC particles, a binding agent, and discrete particles comprising Co, Al, and one or more of C and W. The precursor composition is subjected to a consolidation process to form a consolidated structure including WC particles dispersed in a homogenized binder comprising Co, Al, W, and C. A method of forming a cutting element, a cutting element, a related structure, and an earth-boring tool are also described.

Abstract: A polycrystalline diamond compact includes a polycrystalline diamond material having a plurality of grains of diamond bonded to one another by inter-granular bonds and an intermetallic gamma prime (??) or ?-carbide phase disposed within interstitial spaces between the inter-bonded diamond grains. The ordered intermetallic gamma prime (??) or ?-carbide phase includes a Group VIII metal, aluminum, and a stabilizer. An earth-boring tool includes a bit body and a polycrystalline diamond compact secured to the bit body. A method of forming polycrystalline diamond includes subjecting diamond particles in the presence of a metal material comprising a Group VIII metal and aluminum to a pressure of at least 4.5 GPa and a temperature of at least 1,000° C. to form inter-granular bonds between adjacent diamond particles, cooling the diamond particles and the metal material to a temperature below 500° C., and forming an intermetallic gamma prime (??) or ?-carbide phase adjacent the diamond particles.

Abstract: A method includes disposing a braze material adjacent a first body and a second body; heating the braze material and forming a transient liquid phase; and transforming the transient liquid phase to a solid phase and forming a bond between the first body and the second body. The braze material includes copper, silver, zinc, magnesium, and at least one material selected from the group consisting of nickel, tin, cobalt, iron, phosphorous, indium, lead, antimony, cadmium, and bismuth.

Abstract: A method of forming a supporting substrate for a cutting element comprises forming a precursor composition comprising discrete WC particles, a binding agent, and discrete particles comprising Co, Al, and one or more of C and W. The precursor composition is subjected to a consolidation process to form a consolidated structure including WC particles dispersed in a homogenized binder comprising Co, Al, W, and C. A method of forming a cutting element, a cutting element, a related structure, and an earth-boring tool are also described.

Abstract: A cutting element comprises a supporting substrate, and a cutting table attached to an end of the supporting substrate. The cutting table comprises inter-bonded diamond particles, and a thermally stable material within interstitial spaces between the inter-bonded diamond particles. The thermally stable material comprises a carbide precipitate having the general chemical formula, A3XZn-1, where A comprises one or more of Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Ac, Th, Pa, and U; X comprises one or more of Al, Ga, Sn, Be, Bi, Te, Sb, Se, As, Ge, Si, B, and P; Z comprises C; and n is greater than or equal to 0 and less than or equal to 0.75. A method of forming a cutting element, an earth-boring tool, a supporting substrate, and a method of forming a supporting substrate are also described.

Abstract: Magnetic sample holders for abrasive operations include an array of magnets embedded in a matrix material. Each magnet of the array is positioned between about 0 mm and about 4 mm from at least one adjacent magnet of the array. Exposed surfaces of the magnets of the array are coplanar with a planar working surface of the matrix material. Methods of forming a polycrystalline diamond compact element include magnetically securing an alloy sample to an array of magnets embedded in a matrix. Each of the magnets of the array is within about 4 mm of at least one adjacent magnet of the array. A portion of the alloy sample is abraded away, and the alloy sample is positioned proximate to diamond grains and a substrate. The alloy sample, diamond grains, and substrate are subjected to a high pressure/high temperature process to sinter the diamond grains.

Abstract: A polycrystalline diamond compact includes a polycrystalline diamond material having a plurality of grains of diamond bonded to one another by inter-granular bonds and an intermetallic gamma prime (??) or ?-carbide phase disposed within interstitial spaces between the inter-bonded diamond grains. The ordered intermetallic gamma prime (??) or ?-carbide phase includes a Group VIII metal, aluminum, and a stabilizer. An earth-boring tool includes a bit body and a polycrystalline diamond compact secured to the bit body. A method of forming polycrystalline diamond includes subjecting diamond particles in the presence of a metal material comprising a Group VIII metal and aluminum to a pressure of at least 4.5 GPa and a temperature of at least 1,000° C. to form inter-granular bonds between adjacent diamond particles, cooling the diamond particles and the metal material to a temperature below 500° C., and forming an intermetallic gamma prime (??) or ?-carbide phase adjacent the diamond particles.

Abstract: A method of modifying surfaces of diamond particles comprises forming spinodal alloy coatings over discrete diamond particles, thermally treating the spinodal alloy coatings to form modified coatings each independently exhibiting a reactive metal phase and a substantially non-reactive metal phase, and etching surfaces of the discrete diamond particles with at least one reactive metal of the reactive metal phase of the modified coatings. Diamond particles and earth-boring tools are also described.

Abstract: A polycrystalline diamond compact includes a polycrystalline diamond material having a plurality of grains of diamond bonded to one another by inter-granular bonds and an intermetallic gamma prime (??) or ?-carbide phase disposed within interstitial spaces between the inter-bonded diamond grains. The ordered intermetallic gamma prime (??) or ?-carbide phase includes a Group VIII metal, aluminum, and a stabilizer. An earth-boring tool includes a bit body and a polycrystalline diamond compact secured to the bit body. A method of forming polycrystalline diamond includes subjecting diamond particles in the presence of a metal material comprising a Group VIII metal and aluminum to a pressure of at least 4.5 GPa and a temperature of at least 1,000° C. to form inter-granular bonds between adjacent diamond particles, cooling the diamond particles and the metal material to a temperature below 500° C., and forming an intermetallic gamma prime (??) or ?-carbide phase adjacent the diamond particles.

Abstract: A method of modifying surfaces of diamond particles comprises forming spinodal alloy coatings over discrete diamond particles, thermally treating the spinodal alloy coatings to form modified coatings each independently exhibiting a reactive metal phase and a substantially non-reactive metal phase, and etching surfaces of the discrete diamond particles with at least one reactive metal of the reactive metal phase of the modified coatings. Diamond particles and earth-boring tools are also described.

Abstract: Cutting elements for earth-boring tools may include a superhard, polycrystalline material and a substrate adjacent to and secured to the superhard, polycrystalline material at an interface. The substrate may include a first region exhibiting a first coefficient of thermal expansion and a second region exhibiting a second, different coefficient of thermal expansion. The first region may be spaced from the superhard, polycrystalline material. The second region may extend from laterally adjacent to at least a portion of the first region to longitudinally between the first region and the superhard, polycrystalline material.

Abstract: A method of forming polycrystalline diamond includes providing an alloy over at least portions of a plurality of diamond particles, and subjecting the plurality of diamond particles to a high-temperature, high-pressure process to form a polycrystalline diamond material having inter-granular bonds between adjacent diamond particles. The alloy includes iridium and nickel, and a volume of the diamond particles is at least about 92% of a total volume of the alloy and the diamond particles. The polycrystalline diamond material includes at least about 92% diamond by volume. A polycrystalline diamond compact includes grains of diamond bonded to one another by inter-granular bonds and an alloy disposed within interstitial spaces between the grains of diamond. The grains of diamond occupy at least 94% by volume of the polycrystalline diamond compact. An earth-boring tool may include a bit body and such a polycrystalline diamond compact.