Quantitative determination of mineral composition by powder X-ray diffraction

Claim 1

A method of quantitatively determining the mineral composition in a test sample containing a number (m) of minerals from a group (n) of known minerals, wherein n=13, where m≦n, by x-ray diffraction, comprising: determining from standard samples of the known minerals a set of (n) standard coefficients K j =(X j /X l )(I l /I j ) for each mineral (j=2 . . . n) in the group of known minerals (j=2 . . . n) relative to one mineral (l) in the group selected as a reference mineral, where X is the weight fraction of the mineral in a standard sample, and I is the x-ray integrated intensity peak of each mineral obtained from the standard sample; obtaining an x-ray diffraction pattern of the test sample; indentifying each of the (m) minerals in the test sample for the x-ray diffraction pattern; calculating the relative weight fractions X j /X l for each mineral (j=2 . . . m) compared to the reference mineral (l) from the ratio of the measured highest integrated intensity peak I j of each mineral in the test sample to the measured highest integrated intensity peak I l of the reference mineral in the test sample, and from the previously determined standard coefficients, X j /X l =K j (I j /I l ); and calculating the weight fraction of the reference mineral X l , and the weight fractions X j of each mineral (j=2 . . . m) from the condition that the sum of the weight fractions is 1, ΣX i =1 (i=1 . . . m).

Claim 2

A method of quantitatively determining the mineral composition in a test sample containing a number (m) of minerals from a group (n) of known minerals, wherein n=13, where m≦n, by x-ray diffraction, comprising: determining from standard samples of the known minerals a set of (n) standard coefficients K j =(X j /X l )(I l /I j ) for each mineral (j=2 . . . n) in the group of known minerals (j=2 . . . n) relative to one mineral (l) in the group selected as a reference mineral, where X is the weight fraction of the mineral in a standard sample, and I is the x-ray integrated intensity peak of each mineral obtained from the standard sample; obtaining an x-ray diffraction pattern of the test sample; indentifying each of the (m) minerals in the test sample for the x-ray diffraction pattern; calculating the relative weight fractions X j /X l for each mineral (j=2 . . . m) compared to the reference mineral (l) from the ratio of the measured highest integrated intensity peak I j of each mineral in the test sample to the measured highest integrated intensity peak I l of the reference mineral in the test sample, and from the previously determined standard coefficients, X j /X l =K j (I j /I l ); and calculating the weight fraction of the reference mineral X l , and the weight fractions X j of each mineral (j=2 . . . m) from the condition that the sum of the weight fractions is 1, ΣX i =1 (i=1 . . . m).

Claim 11

A method of quantitatively determining the mineral composition in a test sample containing a number (m) of minerals from a group (n) of known minerals, where m≦n, by x-ray diffraction, comprising: determining from standard samples of the known minerals a set of (n) standard coefficients K j =(X j /X l )(I l /I j ) for each mineral (j=2 . . . n) in the group of known minerals (j=2 . . . n) relative to one mineral (l) in the group selected as a reference mineral, where X is the weight fraction of the mineral in a standard sample, and I is the x-ray integrated intensity peak of each mineral obtained from the standard sample; obtaining an x-ray diffraction pattern of the test sample using a goniometer having a theta compensating slit to keep a constant area of the sample irradiated during a scan, wherein the scan covers the range 2°-45° 2θ and is performed in steps of 0.04° 2θ every 4 seconds; indentifying each of the (m) minerals in the test sample for the x-ray diffraction pattern; calculating the relative weight fractions X j /X l for each mineral (j=2 . . . m) compared to the reference mineral (l) from the ratio of the measured highest integrated intensity peak I j of each mineral in the test sample to the measured highest integrated intensity peak I l of the reference mineral in the test sample, and from the previously determined standard coefficients, X j /X l =K j (I j /I l ); and calculating the weight fraction of the reference mineral X l , and the weight fractions X j of each mineral (j=2 . . . m) from the condition that the sum of the weight fractions is 1, ΣX i =1 (i=1 . . . m).

Claim 12

A method of quantitatively determining the mineral composition in a test sample containing a number (m) of minerals from a group (n) of known minerals, where m≦n, by x-ray diffraction, comprising: determining from standard samples of the known minerals a set of (n) standard coefficients K j =(X j /X l )(I l /I j ) for each mineral (j=2 . . . n) in the group of known minerals (j=2 . . . n) relative to one mineral (l) in the group selected as a reference mineral, where X is the weight fraction of the mineral in a standard sample, and I is the x-ray integrated intensity peak of each mineral obtained from the standard sample; obtaining an x-ray diffraction pattern of the test sample using a goniometer having a theta compensating slit to keep a constant area of the sample irradiated during a scan, wherein the scan covers the range 2°-45° 2θ and is performed in steps of 0.04° 2θ every 4 seconds; indentifying each of the (m) minerals in the test sample for the x-ray diffraction pattern; calculating the relative weight fractions X j /X l for each mineral (j=2 . . . m) compared to the reference mineral (l) from the ratio of the measured highest integrated intensity peak I j of each mineral in the test sample to the measured highest integrated intensity peak I l of the reference mineral in the test sample, and from the previously determined standard coefficients, X j /X l =K j (I j /I l ); and calculating the weight fraction of the reference mineral X l , and the weight fractions X j of each mineral (j=2 . . . m) from the condition that the sum of the weight fractions is 1, ΣX i =1 (i=1 . . . m).