| Summary: | Both the chemical shift and quadrupole coupling tensors for <inline-formula> <math display="inline"> <semantics> <msup> <mrow></mrow> <mn>14</mn> </msup> </semantics> </math> </inline-formula>N and <inline-formula> <math display="inline"> <semantics> <msup> <mrow></mrow> <mn>27</mn> </msup> </semantics> </math> </inline-formula>Al in the wurtzite structure of aluminum nitride have been determined to high precision by single-crystal NMR spectroscopy. A homoepitaxially grown AlN single crystal with known morphology was used, which allowed for optical alignment of the crystal on the goniometer axis. From the analysis of the rotation patterns of <inline-formula> <math display="inline"> <semantics> <msup> <mrow></mrow> <mn>14</mn> </msup> </semantics> </math> </inline-formula>N (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>I</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics> </math> </inline-formula>) and <inline-formula> <math display="inline"> <semantics> <msup> <mrow></mrow> <mn>27</mn> </msup> </semantics> </math> </inline-formula>Al (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>I</mi> <mo>=</mo> <mn>5</mn> <mo>/</mo> <mn>2</mn> </mrow> </semantics> </math> </inline-formula>), the quadrupolar coupling constants were determined to <inline-formula> <math display="inline"> <semantics> <mrow> <mi>χ</mi> <mrow> <msup> <mo>(</mo> <mn>14</mn> </msup> <mi mathvariant="normal">N</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>8.19</mn> <mo>±</mo> <mn>0.02</mn> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> kHz, and <inline-formula> <math display="inline"> <semantics> <mrow> <mi>χ</mi> <mrow> <msup> <mo>(</mo> <mn>27</mn> </msup> <mi>Al</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>1.914</mn> <mo>±</mo> <mn>0.001</mn> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> MHz. The chemical shift parameters obtained from the data fit were <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>δ</mi> <mrow> <mi>i</mi> <mi>s</mi> <mi>o</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mrow> <mo>(</mo> <mn>292.6</mn> <mo>±</mo> <mn>0.6</mn> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> ppm and <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>δ</mi> <mo>Δ</mo> </msub> <mo>=</mo> <mo>−</mo> <mrow> <mo>(</mo> <mn>1.9</mn> <mo>±</mo> <mn>1.1</mn> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> ppm for <inline-formula> <math display="inline"> <semantics> <msup> <mrow></mrow> <mn>14</mn> </msup> </semantics> </math> </inline-formula>N, and (after correcting for the second-order quadrupolar shift) <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>δ</mi> <mrow> <mi>i</mi> <mi>s</mi> <mi>o</mi> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mn>113.6</mn> <mo>±</mo> <mn>0.3</mn> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> ppm and <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>δ</mi> <mo>Δ</mo> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mn>12.7</mn> <mo>±</mo> <mn>0.6</mn> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> ppm for <inline-formula> <math display="inline"> <semantics> <msup> <mrow></mrow> <mn>27</mn> </msup> </semantics> </math> </inline-formula>Al. DFT calculations of the NMR parameters for non-optimized crystal geometries of AlN generally did not match the experimental values, whereas optimized geometries came close for <inline-formula> <math display="inline"> <semantics> <msup> <mrow></mrow> <mn>27</mn> </msup> </semantics> </math> </inline-formula>Al with <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mover> <mi>χ</mi> <mo>¯</mo> </mover> <mi>calc</mi> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mn>1.791</mn> <mo>±</mo> <mn>0.003</mn> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> MHz, but not for <inline-formula> <math display="inline"> <semantics> <msup> <mrow></mrow> <mn>14</mn> </msup> </semantics> </math> </inline-formula>N with <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mover> <mi>χ</mi> <mo>¯</mo> </mover> <mi>calc</mi> </msub> <mo>=</mo> <mo>−</mo> <mrow> <mo>(</mo> <mn>19.5</mn> <mo>±</mo> <mn>3.3</mn> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> kHz.
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