Accurate measurement of lattice constants and thermal expansion coefficients of halide perovskite alloy CH₃NH₃Pb(Br_1−xCl_x)₃

Abstract We accurately determined the lattice constants a and the thermal expansion coefficients α L of the mixed-halide perovskite CH 3 NH 3 Pb(Br 1− x Cl x ) 3 as functions of the Cl − -composition x . We used single-crystalline samples and performed X-ray photoelectron spectroscopy for the determination of x , and single-crystal X-ray diffraction for the determination of a . We found that mixed-halide single crystals were significantly Cl − -rich compared to the precursor solutions from which single crystals were grown. The obtained Cl − -composition-dependent lattice constant a ( x ) well follows the Vegard’s law: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>a</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:msub> <mml:mrow> <mml:mi>a</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>−</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>+</mml:mo> <mml:msub> <mml:mrow> <mml:mi>a</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mi>x</mml:mi> </mml:math> , where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>a</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>5.9366</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.0028</mml:mn> <mml:mspace width="0.25em"/> <mml:mi mathvariant="normal">Å</mml:mi> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>a</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>5.6866</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.0027</mml:mn> <mml:mspace width="0.25em"/> <mml:mi mathvariant="normal">Å</mml:mi> </mml:math> . In addition, from the temperature dependence of a ( x ), we determined the thermal expansion coefficients α L ( x ) of the mixed-halide perovskite CH 3 NH 3 Pb(Br 1− x Cl x ) 3 for the first time.