| Summary: | The ability to control the temperature distribution <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>T</mi><mo stretchy="false">(</mo><mi>t</mi><mo>,</mo><mi>r</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> and the rate of temperature change <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">R</mi><mfenced separators="|"><mrow><mi>t</mi><mo>,</mo><mi>r</mi></mrow></mfenced></mrow></semantics></math></inline-formula> inside glasses is important for their microstructuring. The lattice temperature is considered at time <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>t</mi></mrow></semantics></math></inline-formula>, exceeding the electron–phonon thermalization time, and at a distance <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>r</mi></mrow></semantics></math></inline-formula> from the center of the model spherical heating zone. In order to describe thermal excitations, the heat capacity of glasses must be considered as a function of time due to its long-term relaxation. A method for the analytical calculation of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>T</mi><mo stretchy="false">(</mo><mi>t</mi><mo>,</mo><mi>r</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">R</mi><mo stretchy="false">(</mo><mi>t</mi><mo>,</mo><mi>r</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> for glasses with dynamic heat capacity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>c</mi></mrow><mrow><mi>d</mi><mi>y</mi><mi>n</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> is proposed. It is shown that during laser microstructuring, the local cooling rate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mi mathvariant="script">R</mi><mo stretchy="false">(</mo><mi>t</mi><mo>,</mo><mi>r</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> significantly depends on the time dispersion of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>c</mi></mrow><mrow><mi>d</mi><mi>y</mi><mi>n</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula>. It has been established that at the periphery of the model heating zone of the laser beam focus, the local cooling rate can reach more than 10<sup>11</sup> K/s. Strong cooling rate gradients were found at the periphery of the heating zone, affecting the microstructure of the material. This effect is significantly enhanced by the time dispersion of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>c</mi></mrow><mrow><mi>d</mi><mi>y</mi><mi>n</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula>. The effect associated with this time dispersion is significant, even well above the glass transition temperature <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>g</mi></mrow></msub></mrow></semantics></math></inline-formula>, since even short relaxation times of the dynamic heat capacity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>c</mi></mrow><mrow><mi>d</mi><mi>y</mi><mi>n</mi></mrow></msub><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> are significant.
|
|---|